Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{137}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 34 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.35235\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.7047 | −1.49411 | −0.747057 | − | 0.664760i | \(-0.768534\pi\) | ||||
−0.747057 | + | 0.664760i | \(0.768534\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.7047 | 0.622339 | 0.311169 | − | 0.950354i | \(-0.399279\pi\) | ||||
0.311169 | + | 0.950354i | \(0.399279\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.4094 | 0.243415 | 0.121708 | − | 0.992566i | \(-0.461163\pi\) | ||||
0.121708 | + | 0.992566i | \(0.461163\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −50.1141 | −0.862627 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.29530 | 0.0470134 | 0.0235067 | − | 0.999724i | \(-0.492517\pi\) | ||||
0.0235067 | + | 0.999724i | \(0.492517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 62.8188 | 0.758506 | 0.379253 | − | 0.925293i | \(-0.376181\pi\) | ||||
0.379253 | + | 0.925293i | \(0.376181\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −76.1141 | −0.690039 | −0.345019 | − | 0.938596i | \(-0.612128\pi\) | ||||
−0.345019 | + | 0.938596i | \(0.612128\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 154.047 | 1.23238 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 216.094 | 1.38371 | 0.691856 | − | 0.722036i | \(-0.256793\pi\) | ||||
0.691856 | + | 0.722036i | \(0.256793\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −149.638 | −0.866958 | −0.433479 | − | 0.901164i | \(-0.642714\pi\) | ||||
−0.433479 | + | 0.901164i | \(0.642714\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 68.1141 | 0.359307 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 116.933 | 0.564722 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −187.866 | −0.834728 | −0.417364 | − | 0.908739i | \(-0.637046\pi\) | ||||
−0.417364 | + | 0.908739i | \(0.637046\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 34.2282 | 0.140536 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −23.2953 | −0.0887345 | −0.0443673 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443673 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −214.094 | −0.759280 | −0.379640 | − | 0.925134i | \(-0.623952\pi\) | ||||
−0.379640 | + | 0.925134i | \(0.623952\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −150.342 | −0.498038 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 187.960 | 0.583335 | 0.291668 | − | 0.956520i | \(-0.405790\pi\) | ||||
0.291668 | + | 0.956520i | \(0.405790\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.88590 | 0.0271432 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 122.685 | 0.317963 | 0.158981 | − | 0.987282i | \(-0.449179\pi\) | ||||
0.158981 | + | 0.987282i | \(0.449179\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −379.275 | −0.929845 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 188.456 | 0.437924 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 225.409 | 0.497387 | 0.248693 | − | 0.968582i | \(-0.419999\pi\) | ||||
0.248693 | + | 0.968582i | \(0.419999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 546.188 | 1.14643 | 0.573215 | − | 0.819405i | \(-0.305696\pi\) | ||||
0.573215 | + | 0.819405i | \(0.305696\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −190.591 | −0.363690 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −353.141 | −0.643926 | −0.321963 | − | 0.946752i | \(-0.604343\pi\) | ||||
−0.321963 | + | 0.946752i | \(0.604343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −228.342 | −0.398394 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −465.523 | −0.778133 | −0.389067 | − | 0.921210i | \(-0.627202\pi\) | ||||
−0.389067 | + | 0.921210i | \(0.627202\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 430.416 | 0.690088 | 0.345044 | − | 0.938587i | \(-0.387864\pi\) | ||||
0.345044 | + | 0.938587i | \(0.387864\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 462.141 | 0.711513 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −158.933 | −0.235222 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −532.497 | −0.758361 | −0.379181 | − | 0.925323i | \(-0.623794\pi\) | ||||
−0.379181 | + | 0.925323i | \(0.623794\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 185.181 | 0.244895 | 0.122447 | − | 0.992475i | \(-0.460926\pi\) | ||||
0.122447 | + | 0.992475i | \(0.460926\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −55.0470 | −0.0702434 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 648.282 | 0.798886 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1597.31 | −1.90241 | −0.951205 | − | 0.308561i | \(-0.900153\pi\) | ||||
−0.951205 | + | 0.308561i | \(0.900153\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −79.8658 | −0.0920023 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −448.913 | −0.500539 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1049.37 | −1.13329 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1605.69 | −1.68076 | −0.840378 | − | 0.542001i | \(-0.817667\pi\) | ||||
−0.840378 | + | 0.542001i | \(0.817667\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 204.342 | 0.207446 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1359.94 | −1.33979 | −0.669896 | − | 0.742455i | \(-0.733661\pi\) | ||||
−0.669896 | + | 0.742455i | \(0.733661\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1821.56 | −1.74256 | −0.871278 | − | 0.490789i | \(-0.836709\pi\) | ||||
−0.871278 | + | 0.490789i | \(0.836709\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 350.799 | 0.326042 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1440.53 | 1.30151 | 0.650754 | − | 0.759289i | \(-0.274453\pi\) | ||||
0.650754 | + | 0.759289i | \(0.274453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −884.014 | −0.776818 | −0.388409 | − | 0.921487i | \(-0.626975\pi\) | ||||
−0.388409 | + | 0.921487i | \(0.626975\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −563.597 | −0.481931 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1493.46 | −1.24330 | −0.621651 | − | 0.783294i | \(-0.713538\pi\) | ||||
−0.621651 | + | 0.783294i | \(0.713538\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1271.46 | 1.03100 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 102.685 | 0.0811384 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −23.0671 | −0.0177694 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −815.497 | −0.612695 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −69.8859 | −0.0512309 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −485.221 | −0.347196 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1421.41 | −0.993147 | −0.496574 | − | 0.867995i | \(-0.665409\pi\) | ||||
−0.496574 | + | 0.867995i | \(0.665409\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −642.282 | −0.438370 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 755.087 | 0.503605 | 0.251803 | − | 0.967779i | \(-0.418977\pi\) | ||||
0.251803 | + | 0.967779i | \(0.418977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −439.732 | −0.286688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −451.027 | −0.287542 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1618.98 | 1.00963 | 0.504813 | − | 0.863229i | \(-0.331561\pi\) | ||||
0.504813 | + | 0.863229i | \(0.331561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1458.93 | −0.890248 | −0.445124 | − | 0.895469i | \(-0.646840\pi\) | ||||
−0.445124 | + | 0.895469i | \(0.646840\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 563.879 | 0.336789 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 259.047 | 0.151487 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3609.79 | −2.06742 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3270.07 | −1.79795 | −0.898974 | − | 0.438001i | \(-0.855687\pi\) | ||||
−0.898974 | + | 0.438001i | \(0.855687\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1198.01 | −0.645649 | −0.322824 | − | 0.946459i | \(-0.604632\pi\) | ||||
−0.322824 | + | 0.946459i | \(0.604632\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.6577 | 0.0156711 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2499.65 | 1.29533 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1255.75 | 0.638340 | 0.319170 | − | 0.947697i | \(-0.396596\pi\) | ||||
0.319170 | + | 0.947697i | \(0.396596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 368.054 | 0.183576 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 532.799 | 0.260810 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1208.23 | 0.580587 | 0.290294 | − | 0.956938i | \(-0.406247\pi\) | ||||
0.290294 | + | 0.956938i | \(0.406247\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1137.83 | −0.536846 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2785.14 | 1.29054 | 0.645271 | − | 0.763953i | \(-0.276744\pi\) | ||||
0.645271 | + | 0.763953i | \(0.276744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2066.83 | −0.940749 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 565.369 | 0.252835 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −875.832 | −0.384903 | −0.192452 | − | 0.981306i | \(-0.561644\pi\) | ||||
−0.192452 | + | 0.981306i | \(0.561644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1078.33 | −0.465794 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 676.228 | 0.287166 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1148.72 | −0.479661 | −0.239830 | − | 0.970815i | \(-0.577092\pi\) | ||||
−0.239830 | + | 0.970815i | \(0.577092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1738.15 | −0.713787 | −0.356894 | − | 0.934145i | \(-0.616164\pi\) | ||||
−0.356894 | + | 0.934145i | \(0.616164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1638.56 | 0.661891 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3138.24 | 1.24718 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 74.8188 | 0.0292582 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3779.34 | 1.43174 | 0.715872 | − | 0.698231i | \(-0.246029\pi\) | ||||
0.715872 | + | 0.698231i | \(0.246029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3966.15 | −1.47922 | −0.739610 | − | 0.673035i | \(-0.764990\pi\) | ||||
−0.739610 | + | 0.673035i | \(0.764990\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −571.772 | −0.209977 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2593.05 | −0.937802 | −0.468901 | − | 0.883251i | \(-0.655350\pi\) | ||||
−0.468901 | + | 0.883251i | \(0.655350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4407.76 | 1.57014 | 0.785070 | − | 0.619407i | \(-0.212627\pi\) | ||||
0.785070 | + | 0.619407i | \(0.212627\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1059.42 | −0.371771 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1512.66 | −0.522994 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 389.141 | 0.132579 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −685.027 | −0.230013 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1426.28 | 0.472048 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3745.13 | −1.22192 | −0.610960 | − | 0.791661i | \(-0.709217\pi\) | ||||
−0.610960 | + | 0.791661i | \(0.709217\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1396.57 | −0.449256 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3576.38 | 1.13445 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1047.46 | 0.327679 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1291.25 | 0.398422 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 37.5974 | 0.0114438 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1199.17 | 0.360100 | 0.180050 | − | 0.983657i | \(-0.442374\pi\) | ||||
0.180050 | + | 0.983657i | \(0.442374\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1386.42 | 0.410792 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4378.08 | 1.28010 | 0.640052 | − | 0.768332i | \(-0.278913\pi\) | ||||
0.640052 | + | 0.768332i | \(0.278913\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5518.82 | 1.59255 | 0.796275 | − | 0.604935i | \(-0.206801\pi\) | ||||
0.796275 | + | 0.604935i | \(0.206801\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −476.799 | −0.135805 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2511.79 | 0.706234 | 0.353117 | − | 0.935579i | \(-0.385122\pi\) | ||||
0.353117 | + | 0.935579i | \(0.385122\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3139.81 | −0.871569 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1597.49 | −0.437840 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7146.56 | −1.93419 | −0.967097 | − | 0.254408i | \(-0.918120\pi\) | ||||
−0.967097 | + | 0.254408i | \(0.918120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −332.563 | −0.0888892 | −0.0444446 | − | 0.999012i | \(-0.514152\pi\) | ||||
−0.0444446 | + | 0.999012i | \(0.514152\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −818.530 | −0.213445 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 716.725 | 0.184632 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 555.544 | 0.141390 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4833.25 | −1.21543 | −0.607713 | − | 0.794157i | \(-0.707913\pi\) | ||||
−0.607713 | + | 0.794157i | \(0.707913\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1728.15 | −0.429438 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −165.141 | −0.0405550 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1372.18 | −0.333052 | −0.166526 | − | 0.986037i | \(-0.553255\pi\) | ||||
−0.166526 | + | 0.986037i | \(0.553255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1315.06 | 0.315498 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1944.85 | 0.461237 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1170.60 | 0.274457 | 0.137228 | − | 0.990539i | \(-0.456181\pi\) | ||||
0.137228 | + | 0.990539i | \(0.456181\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2049.41 | −0.475073 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4791.93 | −1.09836 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4260.36 | −0.965645 | −0.482822 | − | 0.875718i | \(-0.660388\pi\) | ||||
−0.482822 | + | 0.875718i | \(0.660388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2574.85 | 0.577161 | 0.288581 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288581 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −239.597 | −0.0531176 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3497.59 | 0.766955 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6453.13 | 1.39975 | 0.699875 | − | 0.714265i | \(-0.253239\pi\) | ||||
0.699875 | + | 0.714265i | \(0.253239\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1346.74 | −0.288986 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 349.664 | 0.0742321 | 0.0371160 | − | 0.999311i | \(-0.488183\pi\) | ||||
0.0371160 | + | 0.999311i | \(0.488183\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −699.865 | −0.147006 | −0.0735029 | − | 0.997295i | \(-0.523418\pi\) | ||||
−0.0735029 | + | 0.997295i | \(0.523418\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3148.11 | −0.654308 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 163.067 | 0.0335385 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4902.14 | −0.997790 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4817.07 | −0.970385 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −162.087 | −0.0323182 | −0.0161591 | − | 0.999869i | \(-0.505144\pi\) | ||||
−0.0161591 | + | 0.999869i | \(0.505144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3765.40 | −0.743152 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 613.027 | 0.119769 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −868.416 | −0.167966 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1498.66 | 0.286981 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4079.82 | −0.773530 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9123.91 | −1.71290 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2185.16 | 0.406233 | 0.203116 | − | 0.979155i | \(-0.434893\pi\) | ||||
0.203116 | + | 0.979155i | \(0.434893\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5464.67 | −1.00607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4763.42 | 0.868517 | 0.434259 | − | 0.900788i | \(-0.357010\pi\) | ||||
0.434259 | + | 0.900788i | \(0.357010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1080.84 | −0.195185 | −0.0975926 | − | 0.995226i | \(-0.531114\pi\) | ||||
−0.0975926 | + | 0.995226i | \(0.531114\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1052.40 | 0.188241 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5832.91 | 1.03347 | 0.516734 | − | 0.856146i | \(-0.327148\pi\) | ||||
0.516734 | + | 0.856146i | \(0.327148\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4906.35 | 0.861137 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4321.59 | 0.751426 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 207.007 | 0.0356600 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1757.58 | 0.299979 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2652.04 | −0.448496 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1315.72 | −0.220480 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3483.11 | −0.578397 | −0.289198 | − | 0.957269i | \(-0.593389\pi\) | ||||
−0.289198 | + | 0.957269i | \(0.593389\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1690.79 | −0.278243 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5899.11 | 0.962099 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6625.03 | −1.07089 | −0.535443 | − | 0.844571i | \(-0.679855\pi\) | ||||
−0.535443 | + | 0.844571i | \(0.679855\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4480.39 | −0.717821 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3397.48 | −0.539542 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3814.39 | 0.595246 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5567.83 | −0.861374 | −0.430687 | − | 0.902501i | \(-0.641729\pi\) | ||||
−0.430687 | + | 0.902501i | \(0.641729\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4552.55 | −0.698259 | −0.349130 | − | 0.937074i | \(-0.613523\pi\) | ||||
−0.349130 | + | 0.937074i | \(0.613523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 308.054 | 0.0468453 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4627.15 | −0.697672 | −0.348836 | − | 0.937184i | \(-0.613423\pi\) | ||||
−0.348836 | + | 0.937184i | \(0.613423\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7776.43 | 1.16262 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −69.2013 | −0.0102592 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8347.95 | 1.22726 | 0.613632 | − | 0.789592i | \(-0.289708\pi\) | ||||
0.613632 | + | 0.789592i | \(0.289708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2912.80 | −0.424668 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2446.49 | −0.353739 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7189.97 | −1.03107 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11015.9 | 1.56683 | 0.783417 | − | 0.621497i | \(-0.213475\pi\) | ||||
0.783417 | + | 0.621497i | \(0.213475\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −209.658 | −0.0295782 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −858.792 | −0.120179 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3459.93 | 0.480291 | 0.240145 | − | 0.970737i | \(-0.422805\pi\) | ||||
0.240145 | + | 0.970737i | \(0.422805\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1455.66 | −0.200454 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2465.50 | 0.336817 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13137.3 | −1.78053 | −0.890264 | − | 0.455445i | \(-0.849480\pi\) | ||||
−0.890264 | + | 0.455445i | \(0.849480\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4264.23 | −0.573394 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11542.6 | 1.53995 | 0.769973 | − | 0.638076i | \(-0.220269\pi\) | ||||
0.769973 | + | 0.638076i | \(0.220269\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2654.93 | 0.351448 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1926.85 | −0.253093 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13580.9 | 1.77012 | 0.885061 | − | 0.465475i | \(-0.154116\pi\) | ||||
0.885061 | + | 0.465475i | \(0.154116\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −250.819 | −0.0324411 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2265.26 | 0.290757 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8895.20 | 1.13308 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15560.6 | −1.96717 | −0.983584 | − | 0.180450i | \(-0.942245\pi\) | ||||
−0.983584 | + | 0.180450i | \(0.942245\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1319.19 | −0.165520 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 320.322 | 0.0398906 | 0.0199453 | − | 0.999801i | \(-0.493651\pi\) | ||||
0.0199453 | + | 0.999801i | \(0.493651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1707.28 | −0.211031 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1353.08 | −0.166013 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4265.44 | −0.519484 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2303.79 | −0.278521 | −0.139260 | − | 0.990256i | \(-0.544472\pi\) | ||||
−0.139260 | + | 0.990256i | \(0.544472\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4856.94 | 0.582908 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1577.87 | −0.187994 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3093.40 | −0.365901 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4376.78 | −0.513985 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9770.19 | −1.13915 | −0.569576 | − | 0.821938i | \(-0.692893\pi\) | ||||
−0.569576 | + | 0.821938i | \(0.692893\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 918.792 | 0.106364 | 0.0531819 | − | 0.998585i | \(-0.483064\pi\) | ||||
0.0531819 | + | 0.998585i | \(0.483064\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1691.64 | 0.194445 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 507.631 | 0.0579382 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3823.32 | −0.433310 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 777.141 | 0.0874609 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12570.7 | −1.40489 | −0.702446 | − | 0.711737i | \(-0.747909\pi\) | ||||
−0.702446 | + | 0.711737i | \(0.747909\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8107.80 | 0.899852 | 0.449926 | − | 0.893066i | \(-0.351450\pi\) | ||||
0.449926 | + | 0.893066i | \(0.351450\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10829.4 | −1.19363 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4781.40 | −0.523399 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12395.2 | −1.34758 | −0.673792 | − | 0.738921i | \(-0.735336\pi\) | ||||
−0.673792 | + | 0.738921i | \(0.735336\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 934.503 | 0.100225 | 0.0501124 | − | 0.998744i | \(-0.484042\pi\) | ||||
0.0501124 | + | 0.998744i | \(0.484042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26682.6 | 2.84242 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9810.20 | −1.03805 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13725.7 | 1.44266 | 0.721331 | − | 0.692591i | \(-0.243531\pi\) | ||||
0.721331 | + | 0.692591i | \(0.243531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −528.913 | −0.0552229 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3594.04 | −0.372765 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1334.13 | 0.137462 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15676.9 | −1.60467 | −0.802337 | − | 0.596872i | \(-0.796410\pi\) | ||||
−0.802337 | + | 0.596872i | \(0.796410\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 88.9731 | 0.00904773 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19210.4 | −1.94082 | −0.970410 | − | 0.241463i | \(-0.922373\pi\) | ||||
−0.970410 | + | 0.241463i | \(0.922373\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2935.18 | 0.294621 | 0.147310 | − | 0.989090i | \(-0.452938\pi\) | ||||
0.147310 | + | 0.989090i | \(0.452938\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7498.95 | 0.747862 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10685.1 | −1.05878 | −0.529389 | − | 0.848379i | \(-0.677579\pi\) | ||||
−0.529389 | + | 0.848379i | \(0.677579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2471.99 | 0.243381 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3767.24 | 0.368546 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4860.94 | −0.472529 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9677.05 | 0.934765 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1104.16 | 0.105988 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6984.90 | −0.666280 | −0.333140 | − | 0.942877i | \(-0.608108\pi\) | ||||
−0.333140 | + | 0.942877i | \(0.608108\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2143.44 | −0.203186 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1598.40 | 0.150579 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26822.6 | 2.51124 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1157.50 | −0.107703 | −0.0538516 | − | 0.998549i | \(-0.517150\pi\) | ||||
−0.0538516 | + | 0.998549i | \(0.517150\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3624.68 | 0.335202 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19036.2 | 1.74968 | 0.874839 | − | 0.484414i | \(-0.160967\pi\) | ||||
0.874839 | + | 0.484414i | \(0.160967\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 712.095 | 0.0650530 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3413.48 | −0.309948 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3258.66 | 0.294107 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13623.3 | 1.22217 | 0.611085 | − | 0.791565i | \(-0.290733\pi\) | ||||
0.611085 | + | 0.791565i | \(0.290733\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8355.42 | 0.745095 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3211.73 | 0.284700 | 0.142350 | − | 0.989816i | \(-0.454534\pi\) | ||||
0.142350 | + | 0.989816i | \(0.454534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22717.4 | 2.00180 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6200.48 | −0.543142 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5483.82 | −0.477536 | −0.238768 | − | 0.971077i | \(-0.576744\pi\) | ||||
−0.238768 | + | 0.971077i | \(0.576744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3012.91 | −0.260829 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1696.11 | 0.145975 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30428.6 | 2.60358 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4267.57 | 0.363032 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2627.50 | −0.222224 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16008.9 | 1.34618 | 0.673091 | − | 0.739560i | \(-0.264966\pi\) | ||||
0.673091 | + | 0.739560i | \(0.264966\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12791.7 | 1.06948 | 0.534742 | − | 0.845016i | \(-0.320409\pi\) | ||||
0.534742 | + | 0.845016i | \(0.320409\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3234.99 | −0.268926 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −493.101 | −0.0407586 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6373.64 | −0.523847 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2028.68 | 0.165796 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −265.785 | −0.0215993 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24063.6 | −1.94460 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3446.15 | −0.276932 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1112.53 | 0.0889055 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7091.14 | −0.563534 | −0.281767 | − | 0.959483i | \(-0.590921\pi\) | ||||
−0.281767 | + | 0.959483i | \(0.590921\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5214.44 | −0.412105 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14767.2 | 1.16065 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4704.93 | −0.367766 | −0.183883 | − | 0.982948i | \(-0.558867\pi\) | ||||
−0.183883 | + | 0.982948i | \(0.558867\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4915.69 | 0.382143 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13574.8 | 1.04955 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3727.48 | 0.286634 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9414.73 | 0.720059 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3295.22 | −0.250670 | −0.125335 | − | 0.992114i | \(-0.540001\pi\) | ||||
−0.125335 | + | 0.992114i | \(0.540001\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2442.68 | −0.184820 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 224.456 | 0.0168923 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6620.17 | 0.495572 | 0.247786 | − | 0.968815i | \(-0.420297\pi\) | ||||
0.247786 | + | 0.968815i | \(0.420297\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24947.9 | 1.85764 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16960.6 | 1.24961 | 0.624804 | − | 0.780781i | \(-0.285179\pi\) | ||||
0.624804 | + | 0.780781i | \(0.285179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15713.6 | −1.15165 | −0.575826 | − | 0.817572i | \(-0.695320\pi\) | ||||
−0.575826 | + | 0.817572i | \(0.695320\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11338.0 | 0.826618 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11725.1 | −0.850387 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26793.7 | 1.93317 | 0.966583 | − | 0.256354i | \(-0.0825214\pi\) | ||||
0.966583 | + | 0.256354i | \(0.0825214\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11898.4 | −0.854028 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1296.27 | −0.0925616 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2785.52 | 0.197880 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1715.32 | −0.121230 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25425.5 | 1.78777 | 0.893885 | − | 0.448296i | \(-0.147969\pi\) | ||||
0.893885 | + | 0.448296i | \(0.147969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9400.05 | −0.657593 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7779.14 | −0.541440 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10089.0 | −0.698660 | −0.349330 | − | 0.937000i | \(-0.613591\pi\) | ||||
−0.349330 | + | 0.937000i | \(0.613591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 385.329 | 0.0265495 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13223.3 | 0.906520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17402.3 | 1.18704 | 0.593520 | − | 0.804819i | \(-0.297738\pi\) | ||||
0.593520 | + | 0.804819i | \(0.297738\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2731.58 | 0.185397 | 0.0926985 | − | 0.995694i | \(-0.470451\pi\) | ||||
0.0926985 | + | 0.995694i | \(0.470451\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3178.27 | −0.214642 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13622.6 | 0.915436 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5374.07 | 0.359352 | 0.179676 | − | 0.983726i | \(-0.442495\pi\) | ||||
0.179676 | + | 0.983726i | \(0.442495\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4537.97 | −0.301951 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2144.51 | 0.141993 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24411.6 | 1.60844 | 0.804222 | − | 0.594330i | \(-0.202583\pi\) | ||||
0.804222 | + | 0.594330i | \(0.202583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1167.42 | 0.0765448 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8070.23 | 0.526572 | 0.263286 | − | 0.964718i | \(-0.415194\pi\) | ||||
0.263286 | + | 0.964718i | \(0.415194\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22451.4 | −1.45783 | −0.728915 | − | 0.684604i | \(-0.759975\pi\) | ||||
−0.728915 | + | 0.684604i | \(0.759975\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2055.08 | −0.132798 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11181.2 | 0.719043 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11150.4 | −0.713625 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4278.85 | 0.272537 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −619.074 | −0.0392434 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23936.0 | −1.51011 | −0.755054 | − | 0.655662i | \(-0.772390\pi\) | ||||
−0.755054 | + | 0.655662i | \(0.772390\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11235.4 | −0.705476 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23744.2 | 1.48387 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 559.061 | 0.0347736 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4189.71 | −0.259378 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10470.3 | −0.645164 | −0.322582 | − | 0.946542i | \(-0.604551\pi\) | ||||
−0.322582 | + | 0.946542i | \(0.604551\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7322.20 | 0.449081 | 0.224541 | − | 0.974465i | \(-0.427912\pi\) | ||||
0.224541 | + | 0.974465i | \(0.427912\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10729.1 | 0.654975 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10714.9 | −0.651074 | −0.325537 | − | 0.945529i | \(-0.605545\pi\) | ||||
−0.325537 | + | 0.945529i | \(0.605545\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5117.85 | 0.309543 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3142.39 | 0.189186 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −265.840 | −0.0159313 | −0.00796565 | − | 0.999968i | \(-0.502536\pi\) | ||||
−0.00796565 | + | 0.999968i | \(0.502536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12613.5 | −0.752443 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3873.75 | 0.230029 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1989.35 | −0.117593 | −0.0587967 | − | 0.998270i | \(-0.518726\pi\) | ||||
−0.0587967 | + | 0.998270i | \(0.518726\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5879.26 | 0.345956 | 0.172978 | − | 0.984926i | \(-0.444661\pi\) | ||||
0.172978 | + | 0.984926i | \(0.444661\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 112.792 | 0.00660707 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7345.58 | 0.428345 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16447.8 | −0.954815 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3597.50 | 0.207904 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12401.0 | 0.713467 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16670.1 | −0.954805 | −0.477403 | − | 0.878685i | \(-0.658422\pi\) | ||||
−0.477403 | + | 0.878685i | \(0.658422\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4159.27 | 0.237171 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13648.0 | 0.774795 | 0.387398 | − | 0.921913i | \(-0.373374\pi\) | ||||
0.387398 | + | 0.921913i | \(0.373374\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11239.8 | 0.635266 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13134.2 | 0.739068 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 811.575 | 0.0454671 | 0.0227336 | − | 0.999742i | \(-0.492763\pi\) | ||||
0.0227336 | + | 0.999742i | \(0.492763\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27044.6 | −1.50850 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16556.5 | 0.919459 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1399.76 | 0.0773970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4615.20 | −0.254082 | −0.127041 | − | 0.991897i | \(-0.540548\pi\) | ||||
−0.127041 | + | 0.991897i | \(0.540548\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1430.40 | −0.0784073 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24370.9 | 1.33013 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −76.7650 | −0.00417171 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7535.36 | 0.407744 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6054.51 | 0.326214 | 0.163107 | − | 0.986608i | \(-0.447848\pi\) | ||||
0.163107 | + | 0.986608i | \(0.447848\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11801.5 | −0.633147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9419.44 | −0.503201 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9519.58 | 0.506394 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19774.2 | −1.04744 | −0.523721 | − | 0.851890i | \(-0.675457\pi\) | ||||
−0.523721 | + | 0.851890i | \(0.675457\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4792.47 | −0.252787 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11389.5 | 0.598235 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4327.30 | −0.226338 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21439.7 | −1.11671 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26139.8 | 1.35584 | 0.677920 | − | 0.735135i | \(-0.262881\pi\) | ||||
0.677920 | + | 0.735135i | \(0.262881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12750.9 | 0.658625 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −997.690 | −0.0513202 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33288.6 | 1.70525 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19081.7 | −0.973454 | −0.486727 | − | 0.873554i | \(-0.661809\pi\) | ||||
−0.486727 | + | 0.873554i | \(0.661809\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −705.504 | −0.0356963 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34359.5 | 1.73138 | 0.865688 | − | 0.500584i | \(-0.166881\pi\) | ||||
0.865688 | + | 0.500584i | \(0.166881\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2455.59 | −0.123232 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8017.96 | −0.400740 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4097.73 | 0.203975 | 0.101988 | − | 0.994786i | \(-0.467480\pi\) | ||||
0.101988 | + | 0.994786i | \(0.467480\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2150.17 | 0.106597 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5253.98 | −0.259421 | −0.129711 | − | 0.991552i | \(-0.541405\pi\) | ||||
−0.129711 | + | 0.991552i | \(0.541405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54625.5 | 2.68634 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1666.63 | 0.0816316 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10083.7 | −0.491924 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 128.052 | 0.00622195 | 0.00311098 | − | 0.999995i | \(-0.499010\pi\) | ||||
0.00311098 | + | 0.999995i | \(0.499010\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14499.7 | −0.701727 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20012.5 | 0.964673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16625.5 | −0.798235 | −0.399117 | − | 0.916900i | \(-0.630683\pi\) | ||||
−0.399117 | + | 0.916900i | \(0.630683\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5184.44 | −0.247936 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29091.6 | −1.38577 | −0.692885 | − | 0.721048i | \(-0.743661\pi\) | ||||
−0.692885 | + | 0.721048i | \(0.743661\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6188.10 | 0.293610 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −495.423 | −0.0234145 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2571.79 | 0.121071 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2004.69 | −0.0940063 | −0.0470032 | − | 0.998895i | \(-0.514967\pi\) | ||||
−0.0470032 | + | 0.998895i | \(0.514967\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4116.54 | −0.192288 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10983.8 | −0.511071 | −0.255536 | − | 0.966800i | \(-0.582252\pi\) | ||||
−0.255536 | + | 0.966800i | \(0.582252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23051.2 | −1.06842 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3945.18 | 0.182153 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1463.38 | −0.0673057 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10569.6 | −0.484262 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5834.54 | 0.266295 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20976.8 | −0.953753 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21513.7 | −0.974436 | −0.487218 | − | 0.873280i | \(-0.661988\pi\) | ||||
−0.487218 | + | 0.873280i | \(0.661988\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3511.79 | 0.158458 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10454.2 | 0.469924 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6231.68 | 0.279058 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6148.23 | −0.274283 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5231.43 | −0.232505 | −0.116253 | − | 0.993220i | \(-0.537088\pi\) | ||||
−0.116253 | + | 0.993220i | \(0.537088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 619.384 | 0.0274246 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14375.8 | −0.634136 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9772.47 | 0.429468 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8900.24 | −0.389680 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12781.1 | −0.557515 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18118.0 | −0.787384 | −0.393692 | − | 0.919242i | \(-0.628802\pi\) | ||||
−0.393692 | + | 0.919242i | \(0.628802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34536.2 | 1.49535 | 0.747676 | − | 0.664064i | \(-0.231170\pi\) | ||||
0.747676 | + | 0.664064i | \(0.231170\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7724.54 | 0.333224 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20183.1 | −0.867464 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13449.1 | −0.575919 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −718.792 | −0.0306674 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10122.4 | 0.430297 | 0.215148 | − | 0.976581i | \(-0.430976\pi\) | ||||
0.215148 | + | 0.976581i | \(0.430976\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1623.67 | 0.0687696 | 0.0343848 | − | 0.999409i | \(-0.489053\pi\) | ||||
0.0343848 | + | 0.999409i | \(0.489053\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10492.8 | 0.442802 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23112.3 | −0.971819 | −0.485910 | − | 0.874009i | \(-0.661512\pi\) | ||||
−0.485910 | + | 0.874009i | \(0.661512\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23292.5 | −0.975851 | −0.487925 | − | 0.872885i | \(-0.662246\pi\) | ||||
−0.487925 | + | 0.872885i | \(0.662246\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19359.4 | 0.808146 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 161.470 | 0.00671620 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −46524.9 | −1.92822 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4040.22 | −0.166846 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21603.7 | 0.888968 | 0.444484 | − | 0.895787i | \(-0.353387\pi\) | ||||
0.444484 | + | 0.895787i | \(0.353387\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22307.6 | 0.914659 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1048.99 | 0.0428579 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34525.7 | 1.40559 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5708.48 | 0.231577 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2099.60 | −0.0848739 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14299.2 | 0.575995 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38664.5 | −1.55199 | −0.775995 | − | 0.630739i | \(-0.782752\pi\) | ||||
−0.775995 | + | 0.630739i | \(0.782752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9444.32 | −0.377765 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9703.63 | 0.386779 | 0.193390 | − | 0.981122i | \(-0.438052\pi\) | ||||
0.193390 | + | 0.981122i | \(0.438052\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21634.2 | 0.859312 | 0.429656 | − | 0.902993i | \(-0.358635\pi\) | ||||
0.429656 | + | 0.902993i | \(0.358635\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 489.201 | 0.0193635 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27307.4 | −1.07712 | −0.538561 | − | 0.842587i | \(-0.681032\pi\) | ||||
−0.538561 | + | 0.842587i | \(0.681032\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14630.5 | 0.575089 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14706.4 | −0.576074 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12090.2 | −0.471958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4029.13 | −0.156741 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14451.2 | −0.560252 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3396.55 | 0.131228 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32605.7 | −1.25544 | −0.627718 | − | 0.778441i | \(-0.716011\pi\) | ||||
−0.627718 | + | 0.778441i | \(0.716011\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −486.261 | −0.0186589 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19306.3 | −0.738303 | −0.369151 | − | 0.929369i | \(-0.620352\pi\) | ||||
−0.369151 | + | 0.929369i | \(0.620352\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14203.0 | −0.541299 | −0.270650 | − | 0.962678i | \(-0.587239\pi\) | ||||
−0.270650 | + | 0.962678i | \(0.587239\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11296.2 | −0.429059 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1468.77 | −0.0555991 | −0.0277996 | − | 0.999614i | \(-0.508850\pi\) | ||||
−0.0277996 | + | 0.999614i | \(0.508850\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9949.87 | 0.375374 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1839.08 | 0.0691487 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11807.4 | 0.442463 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19189.0 | 0.716667 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2605.25 | −0.0969752 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32335.8 | −1.19962 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 404.283 | 0.0149485 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4495.97 | 0.165688 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29035.2 | 1.06648 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4131.84 | −0.151263 | −0.0756314 | − | 0.997136i | \(-0.524097\pi\) | ||||
−0.0756314 | + | 0.997136i | \(0.524097\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12239.5 | −0.446598 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45434.5 | 1.65237 | 0.826187 | − | 0.563395i | \(-0.190505\pi\) | ||||
0.826187 | + | 0.563395i | \(0.190505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4204.48 | 0.152408 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27371.7 | −0.988941 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5285.61 | −0.190345 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14032.4 | 0.503685 | 0.251842 | − | 0.967768i | \(-0.418964\pi\) | ||||
0.251842 | + | 0.967768i | \(0.418964\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6555.47 | 0.234538 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5311.34 | −0.189410 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28940.2 | −1.02870 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16394.0 | −0.580852 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48732.4 | −1.72105 | −0.860527 | − | 0.509405i | \(-0.829866\pi\) | ||||
−0.860527 | + | 0.509405i | \(0.829866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3078.12 | 0.108358 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14290.3 | 0.501439 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1249.83 | −0.0437152 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12813.8 | 0.446755 | 0.223378 | − | 0.974732i | \(-0.428292\pi\) | ||||
0.223378 | + | 0.974732i | \(0.428292\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3242.53 | −0.112690 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28586.5 | −0.990323 | −0.495162 | − | 0.868801i | \(-0.664891\pi\) | ||||
−0.495162 | + | 0.868801i | \(0.664891\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1773.10 | 0.0612302 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3157.19 | 0.108681 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32669.6 | 1.12103 | 0.560517 | − | 0.828143i | \(-0.310603\pi\) | ||||
0.560517 | + | 0.828143i | \(0.310603\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4910.79 | 0.167978 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17498.7 | 0.596672 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3583.93 | −0.121821 | −0.0609103 | − | 0.998143i | \(-0.519400\pi\) | ||||
−0.0609103 | + | 0.998143i | \(0.519400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63132.7 | −2.13919 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14719.0 | 0.497178 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11332.9 | −0.381603 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7399.59 | −0.248383 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12964.8 | 0.433836 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 66253.3 | 2.21012 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6332.28 | −0.210582 | −0.105291 | − | 0.994441i | \(-0.533577\pi\) | ||||
−0.105291 | + | 0.994441i | \(0.533577\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 621.020 | 0.0205883 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21547.7 | −0.712152 | −0.356076 | − | 0.934457i | \(-0.615886\pi\) | ||||
−0.356076 | + | 0.934457i | \(0.615886\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10212.5 | 0.336482 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5272.75 | 0.173193 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15024.3 | −0.491987 | −0.245994 | − | 0.969271i | \(-0.579114\pi\) | ||||
−0.245994 | + | 0.969271i | \(0.579114\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36266.4 | −1.18394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7956.12 | −0.258939 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22229.5 | 0.721271 | 0.360636 | − | 0.932707i | \(-0.382560\pi\) | ||||
0.360636 | + | 0.932707i | \(0.382560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43316.1 | 1.40118 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3947.16 | −0.127294 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16295.6 | 0.523932 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37009.0 | 1.18631 | 0.593154 | − | 0.805089i | \(-0.297883\pi\) | ||||
0.593154 | + | 0.805089i | \(0.297883\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10449.3 | −0.333937 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −73630.3 | −2.34597 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15364.0 | 0.488048 | 0.244024 | − | 0.969769i | \(-0.421532\pi\) | ||||
0.244024 | + | 0.969769i | \(0.421532\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5072.38 | −0.160644 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1344.4.a.bm.1.1 | 2 | ||
4.3 | odd | 2 | 1344.4.a.be.1.1 | 2 | |||
8.3 | odd | 2 | 672.4.a.m.1.2 | yes | 2 | ||
8.5 | even | 2 | 672.4.a.h.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 2016.4.a.i.1.1 | 2 | |||
24.11 | even | 2 | 2016.4.a.j.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.h.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
672.4.a.m.1.2 | yes | 2 | 8.3 | odd | 2 | ||
1344.4.a.be.1.1 | 2 | 4.3 | odd | 2 | |||
1344.4.a.bm.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2016.4.a.i.1.1 | 2 | 24.5 | odd | 2 | |||
2016.4.a.j.1.1 | 2 | 24.11 | even | 2 |