Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,4,Mod(1,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, 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("2160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.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: | \(127.444125612\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1772.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.654334\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1 |
$q$-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 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.8065 | 0.637492 | 0.318746 | − | 0.947840i | \(-0.396738\pi\) | ||||
0.318746 | + | 0.947840i | \(0.396738\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 56.2376 | 1.54148 | 0.770740 | − | 0.637150i | \(-0.219887\pi\) | ||||
0.770740 | + | 0.637150i | \(0.219887\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.5961 | 0.738094 | 0.369047 | − | 0.929411i | \(-0.379684\pi\) | ||||
0.369047 | + | 0.929411i | \(0.379684\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 39.2675 | 0.560221 | 0.280111 | − | 0.959968i | \(-0.409629\pi\) | ||||
0.280111 | + | 0.959968i | \(0.409629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 146.561 | 1.76965 | 0.884825 | − | 0.465924i | \(-0.154278\pi\) | ||||
0.884825 | + | 0.465924i | \(0.154278\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.5777 | 0.213752 | 0.106876 | − | 0.994272i | \(-0.465915\pi\) | ||||
0.106876 | + | 0.994272i | \(0.465915\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 161.003 | 1.03095 | 0.515473 | − | 0.856906i | \(-0.327616\pi\) | ||||
0.515473 | + | 0.856906i | \(0.327616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.5465 | 0.171184 | 0.0855921 | − | 0.996330i | \(-0.472722\pi\) | ||||
0.0855921 | + | 0.996330i | \(0.472722\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 59.0326 | 0.285095 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −217.688 | −0.967233 | −0.483617 | − | 0.875280i | \(-0.660677\pi\) | ||||
−0.483617 | + | 0.875280i | \(0.660677\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 142.290 | 0.541999 | 0.270999 | − | 0.962580i | \(-0.412646\pi\) | ||||
0.270999 | + | 0.962580i | \(0.412646\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 468.030 | 1.65986 | 0.829929 | − | 0.557869i | \(-0.188381\pi\) | ||||
0.829929 | + | 0.557869i | \(0.188381\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −394.318 | −1.22377 | −0.611886 | − | 0.790946i | \(-0.709589\pi\) | ||||
−0.611886 | + | 0.790946i | \(0.709589\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −203.606 | −0.593604 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −134.780 | −0.349311 | −0.174655 | − | 0.984630i | \(-0.555881\pi\) | ||||
−0.174655 | + | 0.984630i | \(0.555881\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 281.188 | 0.689371 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 131.195 | 0.289495 | 0.144747 | − | 0.989469i | \(-0.453763\pi\) | ||||
0.144747 | + | 0.989469i | \(0.453763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 259.801 | 0.545313 | 0.272657 | − | 0.962111i | \(-0.412098\pi\) | ||||
0.272657 | + | 0.962111i | \(0.412098\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 172.980 | 0.330086 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −445.244 | −0.811869 | −0.405935 | − | 0.913902i | \(-0.633054\pi\) | ||||
−0.405935 | + | 0.913902i | \(0.633054\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −560.841 | −0.937459 | −0.468729 | − | 0.883342i | \(-0.655288\pi\) | ||||
−0.468729 | + | 0.883342i | \(0.655288\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −88.6681 | −0.142162 | −0.0710809 | − | 0.997471i | \(-0.522645\pi\) | ||||
−0.0710809 | + | 0.997471i | \(0.522645\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 663.970 | 0.982681 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −450.342 | −0.641360 | −0.320680 | − | 0.947188i | \(-0.603911\pi\) | ||||
−0.320680 | + | 0.947188i | \(0.603911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −284.295 | −0.375969 | −0.187985 | − | 0.982172i | \(-0.560196\pi\) | ||||
−0.187985 | + | 0.982172i | \(0.560196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 196.337 | 0.250539 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 625.305 | 0.744744 | 0.372372 | − | 0.928083i | \(-0.378545\pi\) | ||||
0.372372 | + | 0.928083i | \(0.378545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 408.459 | 0.470529 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 732.804 | 0.791411 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −193.261 | −0.202296 | −0.101148 | − | 0.994871i | \(-0.532252\pi\) | ||||
−0.101148 | + | 0.994871i | \(0.532252\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1374.86 | 1.35449 | 0.677245 | − | 0.735758i | \(-0.263174\pi\) | ||||
0.677245 | + | 0.735758i | \(0.263174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2029.60 | −1.94158 | −0.970789 | − | 0.239935i | \(-0.922874\pi\) | ||||
−0.970789 | + | 0.239935i | \(0.922874\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 823.062 | 0.743630 | 0.371815 | − | 0.928307i | \(-0.378736\pi\) | ||||
0.371815 | + | 0.928307i | \(0.378736\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −829.868 | −0.729238 | −0.364619 | − | 0.931157i | \(-0.618801\pi\) | ||||
−0.364619 | + | 0.931157i | \(0.618801\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1503.37 | −1.25155 | −0.625773 | − | 0.780005i | \(-0.715216\pi\) | ||||
−0.625773 | + | 0.780005i | \(0.715216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 117.889 | 0.0955928 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 463.612 | 0.357137 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1831.67 | 1.37616 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 576.348 | 0.402698 | 0.201349 | − | 0.979520i | \(-0.435468\pi\) | ||||
0.201349 | + | 0.979520i | \(0.435468\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2390.04 | −1.59403 | −0.797017 | − | 0.603957i | \(-0.793590\pi\) | ||||
−0.797017 | + | 0.603957i | \(0.793590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1730.37 | 1.12814 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1002.46 | 0.625152 | 0.312576 | − | 0.949893i | \(-0.398808\pi\) | ||||
0.312576 | + | 0.949893i | \(0.398808\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −131.817 | −0.0804356 | −0.0402178 | − | 0.999191i | \(-0.512805\pi\) | ||||
−0.0402178 | + | 0.999191i | \(0.512805\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1945.60 | 1.13776 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 805.013 | 0.461053 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1019.49 | 0.560533 | 0.280267 | − | 0.959922i | \(-0.409577\pi\) | ||||
0.280267 | + | 0.959922i | \(0.409577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2822.38 | −1.52107 | −0.760537 | − | 0.649295i | \(-0.775064\pi\) | ||||
−0.760537 | + | 0.649295i | \(0.775064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 147.733 | 0.0765559 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 476.499 | 0.242222 | 0.121111 | − | 0.992639i | \(-0.461354\pi\) | ||||
0.121111 | + | 0.992639i | \(0.461354\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 278.371 | 0.136265 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2242.26 | 1.07747 | 0.538734 | − | 0.842476i | \(-0.318903\pi\) | ||||
0.538734 | + | 0.842476i | \(0.318903\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −95.0390 | −0.0440380 | −0.0220190 | − | 0.999758i | \(-0.507009\pi\) | ||||
−0.0220190 | + | 0.999758i | \(0.507009\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1000.11 | −0.455217 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2133.76 | −0.937727 | −0.468864 | − | 0.883271i | \(-0.655336\pi\) | ||||
−0.468864 | + | 0.883271i | \(0.655336\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 295.163 | 0.127498 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1704.68 | 0.711808 | 0.355904 | − | 0.934523i | \(-0.384173\pi\) | ||||
0.355904 | + | 0.934523i | \(0.384173\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1360.98 | −0.558902 | −0.279451 | − | 0.960160i | \(-0.590152\pi\) | ||||
−0.279451 | + | 0.960160i | \(0.590152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1088.44 | −0.432560 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2208.31 | 0.863570 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1096.84 | 0.415522 | 0.207761 | − | 0.978180i | \(-0.433382\pi\) | ||||
0.207761 | + | 0.978180i | \(0.433382\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2867.27 | −1.06938 | −0.534691 | − | 0.845048i | \(-0.679572\pi\) | ||||
−0.534691 | + | 0.845048i | \(0.679572\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 724.139 | 0.261892 | 0.130946 | − | 0.991389i | \(-0.458199\pi\) | ||||
0.130946 | + | 0.991389i | \(0.458199\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1693.65 | 0.603315 | 0.301658 | − | 0.953416i | \(-0.402460\pi\) | ||||
0.301658 | + | 0.953416i | \(0.402460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1900.88 | 0.657220 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 711.449 | 0.242389 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8242.22 | 2.72788 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −947.452 | −0.309124 | −0.154562 | − | 0.987983i | \(-0.549397\pi\) | ||||
−0.154562 | + | 0.987983i | \(0.549397\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2340.15 | 0.742311 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 348.841 | 0.109129 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1358.50 | 0.413496 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −111.866 | −0.0335923 | −0.0167961 | − | 0.999859i | \(-0.505347\pi\) | ||||
−0.0167961 | + | 0.999859i | \(0.505347\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1200.70 | −0.351072 | −0.175536 | − | 0.984473i | \(-0.556166\pi\) | ||||
−0.175536 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 822.380 | 0.237312 | 0.118656 | − | 0.992935i | \(-0.462141\pi\) | ||||
0.118656 | + | 0.992935i | \(0.462141\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5329.21 | −1.49840 | −0.749202 | − | 0.662341i | \(-0.769563\pi\) | ||||
−0.749202 | + | 0.662341i | \(0.769563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1971.59 | −0.547287 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7085.61 | 1.91770 | 0.958850 | − | 0.283914i | \(-0.0916331\pi\) | ||||
0.958850 | + | 0.283914i | \(0.0916331\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6560.09 | −1.75341 | −0.876707 | − | 0.481025i | \(-0.840265\pi\) | ||||
−0.876707 | + | 0.481025i | \(0.840265\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1018.03 | −0.265468 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5070.42 | 1.30617 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −714.222 | −0.179607 | −0.0898033 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898033 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1325.95 | 0.329494 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4396.59 | 1.06713 | 0.533563 | − | 0.845760i | \(-0.320853\pi\) | ||||
0.533563 | + | 0.845760i | \(0.320853\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2570.13 | −0.616604 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7550.31 | 1.77024 | 0.885118 | − | 0.465367i | \(-0.154078\pi\) | ||||
0.885118 | + | 0.465367i | \(0.154078\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −673.900 | −0.156216 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5536.86 | −1.25497 | −0.627487 | − | 0.778627i | \(-0.715917\pi\) | ||||
−0.627487 | + | 0.778627i | \(0.715917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3058.25 | −0.685518 | −0.342759 | − | 0.939423i | \(-0.611361\pi\) | ||||
−0.342759 | + | 0.939423i | \(0.611361\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1405.94 | 0.308296 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4070.19 | −0.882865 | −0.441433 | − | 0.897294i | \(-0.645530\pi\) | ||||
−0.441433 | + | 0.897294i | \(0.645530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7446.19 | 1.58079 | 0.790396 | − | 0.612597i | \(-0.209875\pi\) | ||||
0.790396 | + | 0.612597i | \(0.209875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 774.651 | 0.162715 | 0.0813573 | − | 0.996685i | \(-0.474075\pi\) | ||||
0.0813573 | + | 0.996685i | \(0.474075\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1679.95 | 0.345520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3371.06 | −0.686152 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6749.23 | 1.34571 | 0.672857 | − | 0.739772i | \(-0.265067\pi\) | ||||
0.672857 | + | 0.739772i | \(0.265067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 655.977 | 0.129466 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 815.696 | 0.157769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5525.80 | 1.05815 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1299.01 | 0.243872 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2204.39 | 0.409808 | 0.204904 | − | 0.978782i | \(-0.434312\pi\) | ||||
0.204904 | + | 0.978782i | \(0.434312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6032.98 | 1.10000 | 0.549998 | − | 0.835166i | \(-0.314628\pi\) | ||||
0.549998 | + | 0.835166i | \(0.314628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5772.96 | −1.04251 | −0.521257 | − | 0.853400i | \(-0.674537\pi\) | ||||
−0.521257 | + | 0.853400i | \(0.674537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3302.07 | −0.585057 | −0.292528 | − | 0.956257i | \(-0.594497\pi\) | ||||
−0.292528 | + | 0.956257i | \(0.594497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9054.41 | 1.58918 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5755.07 | 0.991395 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 864.901 | 0.147619 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4655.53 | −0.780144 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8053.15 | −1.33728 | −0.668642 | − | 0.743584i | \(-0.733124\pi\) | ||||
−0.668642 | + | 0.743584i | \(0.733124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2226.22 | −0.363079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3460.33 | 0.559335 | 0.279668 | − | 0.960097i | \(-0.409776\pi\) | ||||
0.279668 | + | 0.960097i | \(0.409776\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1661.62 | 0.263877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6453.51 | −1.01591 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9328.27 | 1.44314 | 0.721568 | − | 0.692344i | \(-0.243422\pi\) | ||||
0.721568 | + | 0.692344i | \(0.243422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8899.42 | 1.36497 | 0.682486 | − | 0.730899i | \(-0.260899\pi\) | ||||
0.682486 | + | 0.730899i | \(0.260899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3722.45 | 0.561264 | 0.280632 | − | 0.959816i | \(-0.409456\pi\) | ||||
0.280632 | + | 0.959816i | \(0.409456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2804.21 | −0.419244 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11029.3 | −1.62145 | −0.810727 | − | 0.585425i | \(-0.800928\pi\) | ||||
−0.810727 | + | 0.585425i | \(0.800928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14621.1 | 2.13166 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −443.340 | −0.0635767 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4853.11 | 0.690274 | 0.345137 | − | 0.938552i | \(-0.387833\pi\) | ||||
0.345137 | + | 0.938552i | \(0.387833\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1591.28 | −0.222683 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12373.8 | −1.71767 | −0.858834 | − | 0.512254i | \(-0.828811\pi\) | ||||
−0.858834 | + | 0.512254i | \(0.828811\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5570.06 | 0.760935 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11150.6 | −1.51127 | −0.755634 | − | 0.654994i | \(-0.772671\pi\) | ||||
−0.755634 | + | 0.654994i | \(0.772671\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2199.59 | −0.293457 | −0.146728 | − | 0.989177i | \(-0.546874\pi\) | ||||
−0.146728 | + | 0.989177i | \(0.546874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3319.85 | 0.439468 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9218.92 | 1.20159 | 0.600794 | − | 0.799404i | \(-0.294851\pi\) | ||||
0.600794 | + | 0.799404i | \(0.294851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 925.838 | 0.119748 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2251.71 | −0.286825 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1119.36 | 0.141509 | 0.0707544 | − | 0.997494i | \(-0.477459\pi\) | ||||
0.0707544 | + | 0.997494i | \(0.477459\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12296.9 | 1.53137 | 0.765683 | − | 0.643218i | \(-0.222401\pi\) | ||||
0.765683 | + | 0.643218i | \(0.222401\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1022.19 | 0.126350 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12242.2 | −1.49097 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2500.22 | 0.302269 | 0.151134 | − | 0.988513i | \(-0.451707\pi\) | ||||
0.151134 | + | 0.988513i | \(0.451707\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1548.96 | 0.184551 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1421.48 | −0.168139 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8332.97 | 0.971581 | 0.485790 | − | 0.874075i | \(-0.338532\pi\) | ||||
0.485790 | + | 0.874075i | \(0.338532\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11374.2 | 1.31673 | 0.658367 | − | 0.752697i | \(-0.271248\pi\) | ||||
0.658367 | + | 0.752697i | \(0.271248\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 981.687 | 0.112044 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3067.35 | 0.347633 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10030.2 | 1.12097 | 0.560484 | − | 0.828165i | \(-0.310615\pi\) | ||||
0.560484 | + | 0.828165i | \(0.310615\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7609.38 | 0.844535 | 0.422267 | − | 0.906471i | \(-0.361234\pi\) | ||||
0.422267 | + | 0.906471i | \(0.361234\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3455.57 | 0.378266 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12370.5 | 1.34490 | 0.672450 | − | 0.740143i | \(-0.265242\pi\) | ||||
0.672450 | + | 0.740143i | \(0.265242\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12084.4 | 1.29605 | 0.648023 | − | 0.761621i | \(-0.275596\pi\) | ||||
0.648023 | + | 0.761621i | \(0.275596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3126.53 | 0.333060 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −625.550 | −0.0657495 | −0.0328747 | − | 0.999459i | \(-0.510466\pi\) | ||||
−0.0328747 | + | 0.999459i | \(0.510466\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8002.04 | 0.835480 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2042.29 | 0.210427 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1811.22 | 0.185395 | 0.0926974 | − | 0.995694i | \(-0.470451\pi\) | ||||
0.0926974 | + | 0.995694i | \(0.470451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11625.0 | −1.17447 | −0.587233 | − | 0.809418i | \(-0.699783\pi\) | ||||
−0.587233 | + | 0.809418i | \(0.699783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7291.88 | −0.731928 | −0.365964 | − | 0.930629i | \(-0.619261\pi\) | ||||
−0.365964 | + | 0.930629i | \(0.619261\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11637.6 | 1.15316 | 0.576579 | − | 0.817042i | \(-0.304387\pi\) | ||||
0.576579 | + | 0.817042i | \(0.304387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5256.78 | −0.517560 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26320.9 | 2.55864 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3664.02 | 0.353930 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12041.4 | −1.14862 | −0.574309 | − | 0.818639i | \(-0.694729\pi\) | ||||
−0.574309 | + | 0.818639i | \(0.694729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7531.14 | −0.713909 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −966.307 | −0.0904695 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7037.81 | −0.654853 | −0.327427 | − | 0.944877i | \(-0.606181\pi\) | ||||
−0.327427 | + | 0.944877i | \(0.606181\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6603.07 | −0.606909 | −0.303454 | − | 0.952846i | \(-0.598140\pi\) | ||||
−0.303454 | + | 0.952846i | \(0.598140\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6322.17 | 0.577558 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6621.58 | −0.597623 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.7047 | 0.00329284 | 0.00164642 | − | 0.999999i | \(-0.499476\pi\) | ||||
0.00164642 | + | 0.999999i | \(0.499476\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21242.5 | −1.88302 | −0.941508 | − | 0.336990i | \(-0.890591\pi\) | ||||
−0.941508 | + | 0.336990i | \(0.890591\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6874.29 | 0.605746 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11280.4 | −0.982309 | −0.491155 | − | 0.871072i | \(-0.663425\pi\) | ||||
−0.491155 | + | 0.871072i | \(0.663425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1046.86 | −0.0906270 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10148.0 | −0.868300 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22175.5 | −1.88642 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10239.3 | −0.861023 | −0.430511 | − | 0.902585i | \(-0.641667\pi\) | ||||
−0.430511 | + | 0.902585i | \(0.641667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2822.00 | 0.235942 | 0.117971 | − | 0.993017i | \(-0.462361\pi\) | ||||
0.117971 | + | 0.993017i | \(0.462361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1160.22 | 0.0959010 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11611.1 | −0.954310 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4922.67 | 0.400046 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4115.31 | 0.332561 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11450.3 | −0.915028 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9409.63 | −0.747785 | −0.373892 | − | 0.927472i | \(-0.621977\pi\) | ||||
−0.373892 | + | 0.927472i | \(0.621977\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4149.34 | −0.326125 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3836.43 | 0.299879 | 0.149940 | − | 0.988695i | \(-0.452092\pi\) | ||||
0.149940 | + | 0.988695i | \(0.452092\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23596.7 | 1.82441 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5316.97 | −0.408862 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6145.92 | 0.467524 | 0.233762 | − | 0.972294i | \(-0.424896\pi\) | ||||
0.233762 | + | 0.972294i | \(0.424896\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16192.0 | 1.22513 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13247.9 | −0.991707 | −0.495854 | − | 0.868406i | \(-0.665145\pi\) | ||||
−0.495854 | + | 0.868406i | \(0.665145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7516.83 | −0.559709 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6544.89 | 0.482208 | 0.241104 | − | 0.970499i | \(-0.422491\pi\) | ||||
0.241104 | + | 0.970499i | \(0.422491\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20362.1 | −1.49234 | −0.746170 | − | 0.665755i | \(-0.768110\pi\) | ||||
−0.746170 | + | 0.665755i | \(0.768110\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 589.443 | 0.0427504 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26247.4 | −1.89375 | −0.946876 | − | 0.321600i | \(-0.895779\pi\) | ||||
−0.946876 | + | 0.321600i | \(0.895779\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3356.54 | −0.239677 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7579.71 | −0.538455 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14098.2 | 0.991301 | 0.495650 | − | 0.868522i | \(-0.334930\pi\) | ||||
0.495650 | + | 0.868522i | \(0.334930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4330.36 | 0.302936 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3476.71 | 0.240761 | 0.120380 | − | 0.992728i | \(-0.461589\pi\) | ||||
0.120380 | + | 0.992728i | \(0.461589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2318.06 | 0.159716 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16179.0 | 1.10360 | 0.551798 | − | 0.833978i | \(-0.313942\pi\) | ||||
0.551798 | + | 0.833978i | \(0.313942\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8112.16 | 0.550586 | 0.275293 | − | 0.961360i | \(-0.411225\pi\) | ||||
0.275293 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9158.34 | 0.615437 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21139.2 | −1.41353 | −0.706765 | − | 0.707449i | \(-0.749846\pi\) | ||||
−0.706765 | + | 0.707449i | \(0.749846\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13641.9 | −0.903258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11440.3 | −0.753785 | −0.376892 | − | 0.926257i | \(-0.623007\pi\) | ||||
−0.376892 | + | 0.926257i | \(0.623007\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21566.2 | 1.40717 | 0.703584 | − | 0.710612i | \(-0.251582\pi\) | ||||
0.703584 | + | 0.710612i | \(0.251582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15198.3 | 0.986866 | 0.493433 | − | 0.869784i | \(-0.335742\pi\) | ||||
0.493433 | + | 0.869784i | \(0.335742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7382.68 | 0.474769 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8548.05 | −0.541865 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4929.66 | 0.311009 | 0.155504 | − | 0.987835i | \(-0.450300\pi\) | ||||
0.155504 | + | 0.987835i | \(0.450300\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2881.74 | 0.180092 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7043.97 | −0.438135 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7535.73 | −0.464342 | −0.232171 | − | 0.972675i | \(-0.574583\pi\) | ||||
−0.232171 | + | 0.972675i | \(0.574583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15997.2 | 0.981135 | 0.490568 | − | 0.871403i | \(-0.336789\pi\) | ||||
0.490568 | + | 0.871403i | \(0.336789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6020.46 | −0.365825 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7378.12 | 0.446250 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10948.7 | 0.656133 | 0.328067 | − | 0.944655i | \(-0.393603\pi\) | ||||
0.328067 | + | 0.944655i | \(0.393603\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11950.2 | −0.712874 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12338.3 | 0.729334 | 0.364667 | − | 0.931138i | \(-0.381183\pi\) | ||||
0.364667 | + | 0.931138i | \(0.381183\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20016.8 | 1.17786 | 0.588928 | − | 0.808186i | \(-0.299550\pi\) | ||||
0.588928 | + | 0.808186i | \(0.299550\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8651.86 | 0.504518 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3796.08 | 0.220367 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14610.6 | 0.840589 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8419.22 | −0.482225 | −0.241112 | − | 0.970497i | \(-0.577512\pi\) | ||||
−0.241112 | + | 0.970497i | \(0.577512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25707.1 | −1.45938 | −0.729692 | − | 0.683776i | \(-0.760337\pi\) | ||||
−0.729692 | + | 0.683776i | \(0.760337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2281.74 | −0.128962 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19624.3 | −1.09942 | −0.549708 | − | 0.835357i | \(-0.685261\pi\) | ||||
−0.549708 | + | 0.835357i | \(0.685261\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5012.30 | 0.279577 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4662.86 | −0.257824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7273.23 | −0.400415 | −0.200207 | − | 0.979754i | \(-0.564162\pi\) | ||||
−0.200207 | + | 0.979754i | \(0.564162\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −659.084 | −0.0359719 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5587.37 | 0.303639 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17644.3 | −0.950664 | −0.475332 | − | 0.879807i | \(-0.657672\pi\) | ||||
−0.475332 | + | 0.879807i | \(0.657672\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31904.5 | −1.71166 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16232.3 | 0.863476 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24304.4 | 1.28741 | 0.643703 | − | 0.765276i | \(-0.277397\pi\) | ||||
0.643703 | + | 0.765276i | \(0.277397\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 696.639 | 0.0365909 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9728.00 | 0.508820 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15170.2 | −0.786863 | −0.393431 | − | 0.919354i | \(-0.628712\pi\) | ||||
−0.393431 | + | 0.919354i | \(0.628712\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23962.5 | −1.23774 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4025.07 | 0.206189 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17487.0 | 0.892102 | 0.446051 | − | 0.895008i | \(-0.352830\pi\) | ||||
0.446051 | + | 0.895008i | \(0.352830\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18378.4 | 0.929888 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18698.0 | 0.942194 | 0.471097 | − | 0.882082i | \(-0.343858\pi\) | ||||
0.471097 | + | 0.882082i | \(0.343858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25039.5 | −1.25148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35250.3 | 1.75467 | 0.877336 | − | 0.479876i | \(-0.159318\pi\) | ||||
0.877336 | + | 0.479876i | \(0.159318\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11133.6 | −0.549731 | −0.274866 | − | 0.961483i | \(-0.588633\pi\) | ||||
−0.274866 | + | 0.961483i | \(0.588633\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5097.43 | 0.250678 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9717.49 | 0.474058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17197.6 | −0.835619 | −0.417809 | − | 0.908535i | \(-0.637202\pi\) | ||||
−0.417809 | + | 0.908535i | \(0.637202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14111.9 | −0.680245 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 804.647 | 0.0386333 | 0.0193166 | − | 0.999813i | \(-0.493851\pi\) | ||||
0.0193166 | + | 0.999813i | \(0.493851\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26208.9 | 1.24845 | 0.624225 | − | 0.781245i | \(-0.285415\pi\) | ||||
0.624225 | + | 0.781245i | \(0.285415\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9797.85 | −0.464883 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4538.85 | 0.213674 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36544.2 | 1.71367 | 0.856837 | − | 0.515587i | \(-0.172426\pi\) | ||||
0.856837 | + | 0.515587i | \(0.172426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42387.4 | −1.97228 | −0.986139 | − | 0.165923i | \(-0.946940\pi\) | ||||
−0.986139 | + | 0.165923i | \(0.946940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 738.663 | 0.0342368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20854.1 | 0.959148 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31540.4 | −1.44507 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2382.50 | 0.108325 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26849.4 | −1.21611 | −0.608054 | − | 0.793896i | \(-0.708050\pi\) | ||||
−0.608054 | + | 0.793896i | \(0.708050\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17749.5 | −0.797851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8988.09 | 0.402492 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31307.0 | −1.39141 | −0.695704 | − | 0.718328i | \(-0.744908\pi\) | ||||
−0.695704 | + | 0.718328i | \(0.744908\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15483.9 | −0.685583 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4986.48 | −0.219140 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1391.85 | 0.0609396 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10011.9 | −0.435106 | −0.217553 | − | 0.976049i | \(-0.569807\pi\) | ||||
−0.217553 | + | 0.976049i | \(0.569807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4603.68 | −0.199331 | −0.0996653 | − | 0.995021i | \(-0.531777\pi\) | ||||
−0.0996653 | + | 0.995021i | \(0.531777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11211.3 | 0.481858 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 68594.8 | 2.93737 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35429.0 | −1.50607 | −0.753033 | − | 0.657983i | \(-0.771410\pi\) | ||||
−0.753033 | + | 0.657983i | \(0.771410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28297.6 | 1.19853 | 0.599265 | − | 0.800550i | \(-0.295459\pi\) | ||||
0.599265 | + | 0.800550i | \(0.295459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41059.9 | −1.72647 | −0.863236 | − | 0.504800i | \(-0.831566\pi\) | ||||
−0.863236 | + | 0.504800i | \(0.831566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9030.68 | 0.378345 | 0.189173 | − | 0.981944i | \(-0.439419\pi\) | ||||
0.189173 | + | 0.981944i | \(0.439419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7995.10 | −0.332550 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −475.195 | −0.0196944 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5227.81 | −0.215118 | −0.107559 | − | 0.994199i | \(-0.534303\pi\) | ||||
−0.107559 | + | 0.994199i | \(0.534303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1532.87 | 0.0628508 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5000.56 | −0.203579 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21625.6 | 0.877290 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5132.58 | −0.206748 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30002.9 | −1.20432 | −0.602158 | − | 0.798377i | \(-0.705692\pi\) | ||||
−0.602158 | + | 0.798377i | \(0.705692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15671.7 | 0.624662 | 0.312331 | − | 0.949973i | \(-0.398890\pi\) | ||||
0.312331 | + | 0.949973i | \(0.398890\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31306.8 | 1.24351 | 0.621755 | − | 0.783212i | \(-0.286420\pi\) | ||||
0.621755 | + | 0.783212i | \(0.286420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13212.3 | −0.521150 | −0.260575 | − | 0.965454i | \(-0.583912\pi\) | ||||
−0.260575 | + | 0.965454i | \(0.583912\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10668.8 | −0.419364 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25326.2 | −0.988643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15403.7 | −0.599236 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1475.81 | 0.0570190 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15440.6 | 0.594519 | 0.297260 | − | 0.954797i | \(-0.403927\pi\) | ||||
0.297260 | + | 0.954797i | \(0.403927\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27563.1 | −1.05406 | −0.527029 | − | 0.849847i | \(-0.676694\pi\) | ||||
−0.527029 | + | 0.849847i | \(0.676694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19897.7 | −0.758337 | −0.379169 | − | 0.925328i | \(-0.623790\pi\) | ||||
−0.379169 | + | 0.925328i | \(0.623790\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40061.6 | −1.51650 | −0.758251 | − | 0.651963i | \(-0.773946\pi\) | ||||
−0.758251 | + | 0.651963i | \(0.773946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6804.66 | 0.256716 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −57791.6 | −2.16565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8523.39 | 0.318330 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4757.07 | 0.176482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5292.47 | −0.195691 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6804.92 | −0.249948 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27839.6 | −1.01918 | −0.509591 | − | 0.860417i | \(-0.670203\pi\) | ||||
−0.509591 | + | 0.860417i | \(0.670203\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22251.0 | −0.809232 | −0.404616 | − | 0.914487i | \(-0.632595\pi\) | ||||
−0.404616 | + | 0.914487i | \(0.632595\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15988.1 | −0.579549 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28218.0 | −1.01618 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29480.5 | −1.05819 | −0.529093 | − | 0.848564i | \(-0.677468\pi\) | ||||
−0.529093 | + | 0.848564i | \(0.677468\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19402.9 | −0.691933 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5442.19 | −0.193447 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42351.8 | 1.49571 | 0.747857 | − | 0.663860i | \(-0.231083\pi\) | ||||
0.747857 | + | 0.663860i | \(0.231083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29840.7 | −1.05047 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11041.5 | 0.386200 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35930.6 | −1.25272 | −0.626362 | − | 0.779532i | \(-0.715457\pi\) | ||||
−0.626362 | + | 0.779532i | \(0.715457\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21564.0 | −0.747041 | −0.373521 | − | 0.927622i | \(-0.621849\pi\) | ||||
−0.373521 | + | 0.927622i | \(0.621849\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3354.87 | 0.115853 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16632.4 | 0.570729 | 0.285364 | − | 0.958419i | \(-0.407885\pi\) | ||||
0.285364 | + | 0.958419i | \(0.407885\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3067.57 | −0.104929 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39557.8 | 1.34460 | 0.672299 | − | 0.740279i | \(-0.265307\pi\) | ||||
0.672299 | + | 0.740279i | \(0.265307\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5484.21 | 0.185827 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11835.5 | 0.398529 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28918.0 | −0.970696 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14336.3 | −0.478242 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10666.2 | 0.354707 | 0.177354 | − | 0.984147i | \(-0.443246\pi\) | ||||
0.177354 | + | 0.984147i | \(0.443246\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31821.8 | −1.05171 | −0.525855 | − | 0.850574i | \(-0.676254\pi\) | ||||
−0.525855 | + | 0.850574i | \(0.676254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1556.30 | −0.0512771 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11126.5 | 0.364347 | 0.182173 | − | 0.983266i | \(-0.441687\pi\) | ||||
0.182173 | + | 0.983266i | \(0.441687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35165.7 | 1.14801 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 991.225 | 0.0321619 | 0.0160810 | − | 0.999871i | \(-0.494881\pi\) | ||||
0.0160810 | + | 0.999871i | \(0.494881\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3620.69 | 0.117122 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11035.1 | 0.354798 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48714.9 | 1.56153 | 0.780767 | − | 0.624822i | \(-0.214829\pi\) | ||||
0.780767 | + | 0.624822i | \(0.214829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8468.25 | 0.269811 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42207.2 | −1.34074 | −0.670369 | − | 0.742028i | \(-0.733864\pi\) | ||||
−0.670369 | + | 0.742028i | \(0.733864\pi\) | |||||||
\(998\) | 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 | 2160.4.a.bq.1.2 | 3 | ||
3.2 | odd | 2 | 2160.4.a.bi.1.2 | 3 | |||
4.3 | odd | 2 | 135.4.a.h.1.3 | yes | 3 | ||
12.11 | even | 2 | 135.4.a.e.1.1 | ✓ | 3 | ||
20.3 | even | 4 | 675.4.b.n.649.1 | 6 | |||
20.7 | even | 4 | 675.4.b.n.649.6 | 6 | |||
20.19 | odd | 2 | 675.4.a.p.1.1 | 3 | |||
36.7 | odd | 6 | 405.4.e.q.271.1 | 6 | |||
36.11 | even | 6 | 405.4.e.v.271.3 | 6 | |||
36.23 | even | 6 | 405.4.e.v.136.3 | 6 | |||
36.31 | odd | 6 | 405.4.e.q.136.1 | 6 | |||
60.23 | odd | 4 | 675.4.b.m.649.6 | 6 | |||
60.47 | odd | 4 | 675.4.b.m.649.1 | 6 | |||
60.59 | even | 2 | 675.4.a.s.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.e.1.1 | ✓ | 3 | 12.11 | even | 2 | ||
135.4.a.h.1.3 | yes | 3 | 4.3 | odd | 2 | ||
405.4.e.q.136.1 | 6 | 36.31 | odd | 6 | |||
405.4.e.q.271.1 | 6 | 36.7 | odd | 6 | |||
405.4.e.v.136.3 | 6 | 36.23 | even | 6 | |||
405.4.e.v.271.3 | 6 | 36.11 | even | 6 | |||
675.4.a.p.1.1 | 3 | 20.19 | odd | 2 | |||
675.4.a.s.1.3 | 3 | 60.59 | even | 2 | |||
675.4.b.m.649.1 | 6 | 60.47 | odd | 4 | |||
675.4.b.m.649.6 | 6 | 60.23 | odd | 4 | |||
675.4.b.n.649.1 | 6 | 20.3 | even | 4 | |||
675.4.b.n.649.6 | 6 | 20.7 | even | 4 | |||
2160.4.a.bi.1.2 | 3 | 3.2 | odd | 2 | |||
2160.4.a.bq.1.2 | 3 | 1.1 | even | 1 | trivial |