Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,4,Mod(1,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, 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("960.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.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: | \(56.6418336055\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{201}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 480) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.58872\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.1 |
$q$-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 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.3549 | 1.42303 | 0.711515 | − | 0.702671i | \(-0.248009\pi\) | ||||
0.711515 | + | 0.702671i | \(0.248009\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.0000 | 0.548202 | 0.274101 | − | 0.961701i | \(-0.411620\pi\) | ||||
0.274101 | + | 0.961701i | \(0.411620\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.3549 | 0.860956 | 0.430478 | − | 0.902601i | \(-0.358345\pi\) | ||||
0.430478 | + | 0.902601i | \(0.358345\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 101.065 | 1.44187 | 0.720935 | − | 0.693003i | \(-0.243713\pi\) | ||||
0.720935 | + | 0.693003i | \(0.243713\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.6451 | 0.357950 | 0.178975 | − | 0.983854i | \(-0.442722\pi\) | ||||
0.178975 | + | 0.983854i | \(0.442722\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 79.0647 | 0.821587 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −22.3549 | −0.202666 | −0.101333 | − | 0.994853i | \(-0.532311\pi\) | ||||
−0.101333 | + | 0.994853i | \(0.532311\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −187.420 | −1.20010 | −0.600051 | − | 0.799962i | \(-0.704853\pi\) | ||||
−0.600051 | + | 0.799962i | \(0.704853\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −293.194 | −1.69868 | −0.849342 | − | 0.527843i | \(-0.823001\pi\) | ||||
−0.849342 | + | 0.527843i | \(0.823001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 60.0000 | 0.316505 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 131.774 | 0.636399 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.77447 | 0.00788435 | 0.00394217 | − | 0.999992i | \(-0.498745\pi\) | ||||
0.00394217 | + | 0.999992i | \(0.498745\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 121.065 | 0.497073 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 229.290 | 0.873393 | 0.436697 | − | 0.899609i | \(-0.356148\pi\) | ||||
0.436697 | + | 0.899609i | \(0.356148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 146.580 | 0.519844 | 0.259922 | − | 0.965630i | \(-0.416303\pi\) | ||||
0.259922 | + | 0.965630i | \(0.416303\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 538.614 | 1.67159 | 0.835796 | − | 0.549039i | \(-0.185006\pi\) | ||||
0.835796 | + | 0.549039i | \(0.185006\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 351.580 | 1.02502 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 303.194 | 0.832464 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −432.129 | −1.11995 | −0.559977 | − | 0.828508i | \(-0.689190\pi\) | ||||
−0.559977 | + | 0.828508i | \(0.689190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 100.000 | 0.245164 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 88.9353 | 0.206663 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −502.839 | −1.10956 | −0.554780 | − | 0.831997i | \(-0.687198\pi\) | ||||
−0.554780 | + | 0.831997i | \(0.687198\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −937.808 | −1.96843 | −0.984213 | − | 0.176989i | \(-0.943364\pi\) | ||||
−0.984213 | + | 0.176989i | \(0.943364\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 237.194 | 0.474344 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 201.774 | 0.385031 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −483.098 | −0.880893 | −0.440446 | − | 0.897779i | \(-0.645180\pi\) | ||||
−0.440446 | + | 0.897779i | \(0.645180\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −67.0647 | −0.117009 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 397.161 | 0.663864 | 0.331932 | − | 0.943303i | \(-0.392300\pi\) | ||||
0.331932 | + | 0.943303i | \(0.392300\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −56.3881 | −0.0904072 | −0.0452036 | − | 0.998978i | \(-0.514394\pi\) | ||||
−0.0452036 | + | 0.998978i | \(0.514394\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 527.098 | 0.780109 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 327.516 | 0.466435 | 0.233218 | − | 0.972425i | \(-0.425075\pi\) | ||||
0.233218 | + | 0.972425i | \(0.425075\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 473.678 | 0.626421 | 0.313211 | − | 0.949684i | \(-0.398595\pi\) | ||||
0.313211 | + | 0.949684i | \(0.398595\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 505.323 | 0.644824 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −562.259 | −0.692879 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −436.647 | −0.520050 | −0.260025 | − | 0.965602i | \(-0.583731\pi\) | ||||
−0.260025 | + | 0.965602i | \(0.583731\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1063.55 | 1.22517 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −879.582 | −0.980736 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 148.226 | 0.160080 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1429.87 | 1.49672 | 0.748359 | − | 0.663294i | \(-0.230842\pi\) | ||||
0.748359 | + | 0.663294i | \(0.230842\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 180.000 | 0.182734 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −152.063 | −0.149810 | −0.0749051 | − | 0.997191i | \(-0.523865\pi\) | ||||
−0.0749051 | + | 0.997191i | \(0.523865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −160.484 | −0.153524 | −0.0767621 | − | 0.997049i | \(-0.524458\pi\) | ||||
−0.0767621 | + | 0.997049i | \(0.524458\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 395.323 | 0.367425 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1186.65 | 1.07213 | 0.536063 | − | 0.844178i | \(-0.319911\pi\) | ||||
0.536063 | + | 0.844178i | \(0.319911\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1477.10 | −1.29798 | −0.648992 | − | 0.760795i | \(-0.724809\pi\) | ||||
−0.648992 | + | 0.760795i | \(0.724809\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.32341 | 0.00455203 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1385.32 | 1.15328 | 0.576638 | − | 0.817000i | \(-0.304364\pi\) | ||||
0.576638 | + | 0.817000i | \(0.304364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −111.774 | −0.0906350 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 363.194 | 0.286985 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2663.55 | 2.05182 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 687.871 | 0.504254 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −903.582 | −0.631338 | −0.315669 | − | 0.948869i | \(-0.602229\pi\) | ||||
−0.315669 | + | 0.948869i | \(0.602229\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 439.741 | 0.300132 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1100.58 | −0.734034 | −0.367017 | − | 0.930214i | \(-0.619621\pi\) | ||||
−0.367017 | + | 0.930214i | \(0.619621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 781.294 | 0.509374 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1839.65 | −1.14724 | −0.573619 | − | 0.819123i | \(-0.694461\pi\) | ||||
−0.573619 | + | 0.819123i | \(0.694461\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1858.87 | 1.13430 | 0.567149 | − | 0.823615i | \(-0.308046\pi\) | ||||
0.567149 | + | 0.823615i | \(0.308046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1615.84 | 0.965095 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 807.098 | 0.471978 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −937.098 | −0.536702 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1054.74 | 0.591793 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2831.29 | −1.55670 | −0.778351 | − | 0.627829i | \(-0.783944\pi\) | ||||
−0.778351 | + | 0.627829i | \(0.783944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2503.71 | 1.34933 | 0.674667 | − | 0.738122i | \(-0.264287\pi\) | ||||
0.674667 | + | 0.738122i | \(0.264287\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 909.582 | 0.480623 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1465.97 | −0.759675 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2152.42 | 1.09415 | 0.547076 | − | 0.837083i | \(-0.315741\pi\) | ||||
0.547076 | + | 0.837083i | \(0.315741\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1296.39 | −0.646605 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −589.161 | −0.288400 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2710.84 | 1.30263 | 0.651317 | − | 0.758806i | \(-0.274217\pi\) | ||||
0.651317 | + | 0.758806i | \(0.274217\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 300.000 | 0.141545 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2175.71 | 1.00815 | 0.504076 | − | 0.863659i | \(-0.331833\pi\) | ||||
0.504076 | + | 0.863659i | \(0.331833\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −568.483 | −0.258754 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 266.806 | 0.119317 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1010.13 | 0.443922 | 0.221961 | − | 0.975056i | \(-0.428754\pi\) | ||||
0.221961 | + | 0.975056i | \(0.428754\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 658.872 | 0.284606 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1508.52 | −0.640605 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2266.26 | 0.946304 | 0.473152 | − | 0.880981i | \(-0.343116\pi\) | ||||
0.473152 | + | 0.880981i | \(0.343116\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4722.01 | −1.93914 | −0.969569 | − | 0.244818i | \(-0.921272\pi\) | ||||
−0.969569 | + | 0.244818i | \(0.921272\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2813.42 | −1.13647 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.87234 | 0.00352599 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2021.29 | 0.790437 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 711.582 | 0.273862 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 333.028 | 0.126163 | 0.0630813 | − | 0.998008i | \(-0.479907\pi\) | ||||
0.0630813 | + | 0.998008i | \(0.479907\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4503.23 | −1.67953 | −0.839767 | − | 0.542948i | \(-0.817308\pi\) | ||||
−0.839767 | + | 0.542948i | \(0.817308\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 605.323 | 0.222298 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3325.03 | 1.20253 | 0.601266 | − | 0.799049i | \(-0.294663\pi\) | ||||
0.601266 | + | 0.799049i | \(0.294663\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3235.32 | 1.15249 | 0.576246 | − | 0.817276i | \(-0.304517\pi\) | ||||
0.576246 | + | 0.817276i | \(0.304517\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1449.29 | −0.508584 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4939.42 | −1.70778 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1146.45 | 0.390593 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −201.194 | −0.0675553 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 592.902 | 0.196229 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3181.71 | 1.03810 | 0.519048 | − | 0.854745i | \(-0.326287\pi\) | ||||
0.519048 | + | 0.854745i | \(0.326287\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1191.48 | 0.383282 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 732.902 | 0.232481 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7727.10 | −2.41728 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −169.164 | −0.0521966 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4078.45 | 1.24139 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1848.03 | −0.554948 | −0.277474 | − | 0.960733i | \(-0.589497\pi\) | ||||
−0.277474 | + | 0.960733i | \(0.589497\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −592.643 | −0.173282 | −0.0866412 | − | 0.996240i | \(-0.527613\pi\) | ||||
−0.0866412 | + | 0.996240i | \(0.527613\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −402.060 | −0.116021 | −0.0580106 | − | 0.998316i | \(-0.518476\pi\) | ||||
−0.0580106 | + | 0.998316i | \(0.518476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1581.29 | 0.450396 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5961.52 | 1.67619 | 0.838095 | − | 0.545524i | \(-0.183669\pi\) | ||||
0.838095 | + | 0.545524i | \(0.183669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2693.07 | 0.747559 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 982.547 | 0.269297 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2389.23 | 0.646637 | 0.323319 | − | 0.946290i | \(-0.395201\pi\) | ||||
0.323319 | + | 0.946290i | \(0.395201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 608.329 | 0.162597 | 0.0812985 | − | 0.996690i | \(-0.474093\pi\) | ||||
0.0812985 | + | 0.996690i | \(0.474093\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1757.90 | 0.458401 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1196.33 | 0.308180 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1421.03 | 0.361664 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6852.07 | −1.72310 | −0.861551 | − | 0.507671i | \(-0.830507\pi\) | ||||
−0.861551 | + | 0.507671i | \(0.830507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −447.098 | −0.111102 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1515.97 | 0.372289 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4000.23 | −0.970924 | −0.485462 | − | 0.874258i | \(-0.661349\pi\) | ||||
−0.485462 | + | 0.874258i | \(0.661349\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 46.7659 | 0.0112197 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1686.78 | −0.400034 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3588.03 | 0.841246 | 0.420623 | − | 0.907236i | \(-0.361812\pi\) | ||||
0.420623 | + | 0.907236i | \(0.361812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2160.65 | −0.500858 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1309.94 | −0.300251 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3399.69 | 0.770567 | 0.385283 | − | 0.922798i | \(-0.374104\pi\) | ||||
0.385283 | + | 0.922798i | \(0.374104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7754.49 | −1.73820 | −0.869099 | − | 0.494638i | \(-0.835300\pi\) | ||||
−0.869099 | + | 0.494638i | \(0.835300\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3190.65 | 0.707351 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 500.000 | 0.109640 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2247.07 | −0.487414 | −0.243707 | − | 0.969849i | \(-0.578364\pi\) | ||||
−0.243707 | + | 0.969849i | \(0.578364\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2638.75 | −0.566228 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −719.101 | −0.152662 | −0.0763309 | − | 0.997083i | \(-0.524321\pi\) | ||||
−0.0763309 | + | 0.997083i | \(0.524321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5225.16 | −1.09754 | −0.548770 | − | 0.835974i | \(-0.684904\pi\) | ||||
−0.548770 | + | 0.835974i | \(0.684904\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 444.677 | 0.0924223 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6042.92 | 1.24286 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5301.07 | 1.07899 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4289.62 | 0.864131 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6408.79 | 1.27783 | 0.638917 | − | 0.769276i | \(-0.279383\pi\) | ||||
0.638917 | + | 0.769276i | \(0.279383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2514.20 | −0.496211 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 540.000 | 0.105502 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −902.129 | −0.174487 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3863.11 | 0.739754 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −456.189 | −0.0864930 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4689.04 | −0.880307 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4354.91 | −0.809603 | −0.404801 | − | 0.914405i | \(-0.632659\pi\) | ||||
−0.404801 | + | 0.914405i | \(0.632659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −481.453 | −0.0886372 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7515.82 | −1.37036 | −0.685182 | − | 0.728372i | \(-0.740277\pi\) | ||||
−0.685182 | + | 0.728372i | \(0.740277\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8534.34 | 1.54118 | 0.770590 | − | 0.637331i | \(-0.219962\pi\) | ||||
0.770590 | + | 0.637331i | \(0.219962\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1185.97 | 0.212133 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2260.90 | 0.400583 | 0.200291 | − | 0.979736i | \(-0.435811\pi\) | ||||
0.200291 | + | 0.979736i | \(0.435811\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3748.39 | −0.657899 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3559.94 | 0.618992 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2996.07 | 0.516118 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1008.87 | 0.172191 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4431.29 | −0.749392 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14195.1 | 2.37873 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1258.62 | 0.209003 | 0.104502 | − | 0.994525i | \(-0.466675\pi\) | ||||
0.104502 | + | 0.994525i | \(0.466675\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.9702 | 0.00262812 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2415.49 | −0.393947 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10796.0 | −1.74509 | −0.872546 | − | 0.488532i | \(-0.837533\pi\) | ||||
−0.872546 | + | 0.488532i | \(0.837533\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4155.97 | 0.665845 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5863.88 | −0.931223 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 226.136 | 0.0355983 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −335.323 | −0.0523281 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 585.877 | 0.0906385 | 0.0453192 | − | 0.998973i | \(-0.485569\pi\) | ||||
0.0453192 | + | 0.998973i | \(0.485569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12103.1 | −1.85634 | −0.928172 | − | 0.372151i | \(-0.878620\pi\) | ||||
−0.928172 | + | 0.372151i | \(0.878620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1089.58 | 0.165691 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1689.38 | 0.254721 | 0.127360 | − | 0.991857i | \(-0.459350\pi\) | ||||
0.127360 | + | 0.991857i | \(0.459350\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1985.80 | 0.296889 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7990.65 | 1.18462 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5792.40 | 0.851563 | 0.425781 | − | 0.904826i | \(-0.359999\pi\) | ||||
0.425781 | + | 0.904826i | \(0.359999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5980.17 | −0.871872 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2793.00 | −0.403842 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −281.940 | −0.0404313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9651.40 | −1.37275 | −0.686375 | − | 0.727248i | \(-0.740799\pi\) | ||||
−0.686375 | + | 0.727248i | \(0.740799\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2063.61 | 0.291131 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11388.7 | −1.59373 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9720.23 | −1.34931 | −0.674657 | − | 0.738131i | \(-0.735709\pi\) | ||||
−0.674657 | + | 0.738131i | \(0.735709\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7563.30 | −1.03324 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2315.32 | 0.313800 | 0.156900 | − | 0.987614i | \(-0.449850\pi\) | ||||
0.156900 | + | 0.987614i | \(0.449850\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2710.75 | −0.364503 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8955.71 | −1.19482 | −0.597409 | − | 0.801936i | \(-0.703803\pi\) | ||||
−0.597409 | + | 0.801936i | \(0.703803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2635.49 | 0.348875 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1319.22 | 0.173281 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4201.48 | −0.547619 | −0.273809 | − | 0.961784i | \(-0.588284\pi\) | ||||
−0.273809 | + | 0.961784i | \(0.588284\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2259.29 | −0.292218 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3301.75 | −0.423795 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1637.58 | 0.208596 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1318.23 | −0.166649 | −0.0833247 | − | 0.996522i | \(-0.526554\pi\) | ||||
−0.0833247 | + | 0.996522i | \(0.526554\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2343.88 | 0.294087 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4319.04 | 0.537862 | 0.268931 | − | 0.963159i | \(-0.413330\pi\) | ||||
0.268931 | + | 0.963159i | \(0.413330\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11831.8 | −1.46249 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.4894 | 0.00432222 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2075.17 | −0.250882 | −0.125441 | − | 0.992101i | \(-0.540035\pi\) | ||||
−0.125441 | + | 0.992101i | \(0.540035\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5518.94 | −0.662358 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13252.3 | −1.57894 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2368.39 | 0.280144 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5576.62 | 0.654888 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13509.1 | 1.57509 | 0.787545 | − | 0.616257i | \(-0.211352\pi\) | ||||
0.787545 | + | 0.616257i | \(0.211352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8258.06 | −0.955993 | −0.477997 | − | 0.878362i | \(-0.658637\pi\) | ||||
−0.477997 | + | 0.878362i | \(0.658637\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4847.52 | 0.557198 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2526.62 | 0.288374 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24715.8 | −2.80113 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2421.29 | 0.272497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2975.11 | 0.332497 | 0.166248 | − | 0.986084i | \(-0.446835\pi\) | ||||
0.166248 | + | 0.986084i | \(0.446835\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1357.81 | 0.150698 | 0.0753488 | − | 0.997157i | \(-0.475993\pi\) | ||||
0.0753488 | + | 0.997157i | \(0.475993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2811.29 | −0.309865 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −662.713 | −0.0725443 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6925.51 | 0.752931 | 0.376465 | − | 0.926431i | \(-0.377139\pi\) | ||||
0.376465 | + | 0.926431i | \(0.377139\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3164.22 | 0.341672 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9300.77 | −0.997501 | −0.498750 | − | 0.866746i | \(-0.666208\pi\) | ||||
−0.498750 | + | 0.866746i | \(0.666208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2183.23 | −0.232574 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8493.88 | −0.898762 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14928.1 | 1.56904 | 0.784521 | − | 0.620103i | \(-0.212909\pi\) | ||||
0.784521 | + | 0.620103i | \(0.212909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4585.80 | 0.478796 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7511.14 | 0.779038 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5317.74 | 0.547911 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16323.7 | −1.67088 | −0.835438 | − | 0.549585i | \(-0.814786\pi\) | ||||
−0.835438 | + | 0.549585i | \(0.814786\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2728.75 | 0.277488 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8960.71 | −0.905297 | −0.452649 | − | 0.891689i | \(-0.649521\pi\) | ||||
−0.452649 | + | 0.891689i | \(0.649521\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12194.3 | −1.22401 | −0.612006 | − | 0.790853i | \(-0.709637\pi\) | ||||
−0.612006 | + | 0.790853i | \(0.709637\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4397.91 | −0.438598 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11673.9 | 1.15675 | 0.578376 | − | 0.815770i | \(-0.303687\pi\) | ||||
0.578376 | + | 0.815770i | \(0.303687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12732.0 | −1.25354 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6457.26 | 0.631709 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2931.61 | 0.284980 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 741.128 | 0.0715900 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3889.16 | −0.373318 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10062.2 | −0.959821 | −0.479910 | − | 0.877318i | \(-0.659331\pi\) | ||||
−0.479910 | + | 0.877318i | \(0.659331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 71.6085 | 0.00678808 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1767.48 | −0.166508 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7149.37 | 0.669353 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9345.25 | 0.869556 | 0.434778 | − | 0.900538i | \(-0.356827\pi\) | ||||
0.434778 | + | 0.900538i | \(0.356827\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8132.52 | 0.752076 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15282.5 | −1.40466 | −0.702330 | − | 0.711852i | \(-0.747857\pi\) | ||||
−0.702330 | + | 0.711852i | \(0.747857\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18941.5 | −1.73039 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 900.000 | 0.0817212 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10467.1 | 0.944698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7171.02 | 0.643324 | 0.321662 | − | 0.946854i | \(-0.395758\pi\) | ||||
0.321662 | + | 0.946854i | \(0.395758\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6527.12 | 0.582057 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14066.2 | −1.24688 | −0.623439 | − | 0.781872i | \(-0.714265\pi\) | ||||
−0.623439 | + | 0.781872i | \(0.714265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −760.315 | −0.0669972 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1705.45 | −0.149392 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 968.322 | 0.0843224 | 0.0421612 | − | 0.999111i | \(-0.486576\pi\) | ||||
0.0421612 | + | 0.999111i | \(0.486576\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1486.10 | −0.128652 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 800.418 | 0.0688875 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −802.421 | −0.0686581 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10772.3 | 0.916371 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3030.38 | 0.256298 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8255.03 | 0.694164 | 0.347082 | − | 0.937835i | \(-0.387173\pi\) | ||||
0.347082 | + | 0.937835i | \(0.387173\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8777.73 | −0.733888 | −0.366944 | − | 0.930243i | \(-0.619596\pi\) | ||||
−0.366944 | + | 0.930243i | \(0.619596\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1976.62 | 0.164317 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29631.6 | −2.44928 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11667.3 | −0.958926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4525.55 | −0.369854 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9252.98 | 0.751953 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5933.23 | 0.479469 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6798.79 | 0.546349 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7031.61 | 0.561916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10814.3 | 0.859412 | 0.429706 | − | 0.902969i | \(-0.358617\pi\) | ||||
0.429706 | + | 0.902969i | \(0.358617\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14166.0 | −1.11956 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7385.49 | −0.580476 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9580.54 | 0.748875 | 0.374437 | − | 0.927252i | \(-0.377836\pi\) | ||||
0.374437 | + | 0.927252i | \(0.377836\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8440.27 | −0.656142 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5556.07 | −0.429577 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8631.64 | 0.663752 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.6170 | 0.00203573 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17896.0 | 1.36136 | 0.680679 | − | 0.732582i | \(-0.261685\pi\) | ||||
0.680679 | + | 0.732582i | \(0.261685\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5915.24 | 0.447563 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6063.88 | 0.456359 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20954.2 | −1.56858 | −0.784292 | − | 0.620392i | \(-0.786974\pi\) | ||||
−0.784292 | + | 0.620392i | \(0.786974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6926.62 | 0.515761 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2134.75 | 0.158115 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6614.54 | −0.487339 | −0.243670 | − | 0.969858i | \(-0.578351\pi\) | ||||
−0.243670 | + | 0.969858i | \(0.578351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7293.53 | −0.534544 | −0.267272 | − | 0.963621i | \(-0.586122\pi\) | ||||
−0.267272 | + | 0.963621i | \(0.586122\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 999.084 | 0.0728400 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −558.872 | −0.0405332 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14724.7 | 1.06239 | 0.531195 | − | 0.847250i | \(-0.321743\pi\) | ||||
0.531195 | + | 0.847250i | \(0.321743\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13509.7 | −0.969679 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12483.7 | 0.891416 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8642.59 | −0.613961 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1815.97 | 0.128344 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3976.96 | 0.279637 | 0.139818 | − | 0.990177i | \(-0.455348\pi\) | ||||
0.139818 | + | 0.990177i | \(0.455348\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8691.77 | −0.608044 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9975.09 | 0.694282 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21972.5 | −1.52159 | −0.760795 | − | 0.648993i | \(-0.775191\pi\) | ||||
−0.760795 | + | 0.648993i | \(0.775191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13317.7 | 0.917604 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9705.97 | 0.665392 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13515.5 | 0.921916 | 0.460958 | − | 0.887422i | \(-0.347506\pi\) | ||||
0.460958 | + | 0.887422i | \(0.347506\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13789.2 | −0.935899 | −0.467949 | − | 0.883755i | \(-0.655007\pi\) | ||||
−0.467949 | + | 0.883755i | \(0.655007\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4347.88 | −0.293631 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4655.00 | −0.312814 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29097.6 | 1.94569 | 0.972845 | − | 0.231459i | \(-0.0743498\pi\) | ||||
0.972845 | + | 0.231459i | \(0.0743498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14818.3 | −0.985988 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21735.7 | 1.43917 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6066.37 | −0.399703 | −0.199852 | − | 0.979826i | \(-0.564046\pi\) | ||||
−0.199852 | + | 0.979826i | \(0.564046\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3439.35 | 0.225509 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17963.1 | −1.17207 | −0.586037 | − | 0.810285i | \(-0.699313\pi\) | ||||
−0.586037 | + | 0.810285i | \(0.699313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11980.6 | −0.777935 | −0.388968 | − | 0.921251i | \(-0.627168\pi\) | ||||
−0.388968 | + | 0.921251i | \(0.627168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −603.582 | −0.0390031 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11507.8 | −0.740047 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1778.71 | 0.113293 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 179.336 | 0.0113682 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25246.2 | −1.59276 | −0.796382 | − | 0.604794i | \(-0.793256\pi\) | ||||
−0.796382 | + | 0.604794i | \(0.793256\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9545.13 | 0.599344 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4517.91 | −0.282343 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14188.0 | 0.882494 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3574.45 | 0.221288 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3234.97 | 0.199335 | 0.0996674 | − | 0.995021i | \(-0.468222\pi\) | ||||
0.0996674 | + | 0.995021i | \(0.468222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6664.27 | 0.408730 | 0.204365 | − | 0.978895i | \(-0.434487\pi\) | ||||
0.204365 | + | 0.978895i | \(0.434487\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2198.71 | 0.134223 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5008.94 | −0.304361 | −0.152181 | − | 0.988353i | \(-0.548630\pi\) | ||||
−0.152181 | + | 0.988353i | \(0.548630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10056.8 | −0.608264 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23181.3 | −1.39562 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4808.71 | 0.288176 | 0.144088 | − | 0.989565i | \(-0.453975\pi\) | ||||
0.144088 | + | 0.989565i | \(0.453975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5502.92 | −0.328270 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −507.493 | −0.0301357 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23465.7 | 1.38709 | 0.693546 | − | 0.720413i | \(-0.256048\pi\) | ||||
0.693546 | + | 0.720413i | \(0.256048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5006.86 | −0.294621 | −0.147310 | − | 0.989090i | \(-0.547062\pi\) | ||||
−0.147310 | + | 0.989090i | \(0.547062\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12235.4 | 0.716715 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3906.47 | 0.227799 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4189.74 | 0.243220 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5544.10 | −0.320400 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18756.2 | −1.07910 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28544.8 | −1.63495 | −0.817475 | − | 0.575964i | \(-0.804627\pi\) | ||||
−0.817475 | + | 0.575964i | \(0.804627\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −275.964 | −0.0156664 | −0.00783321 | − | 0.999969i | \(-0.502493\pi\) | ||||
−0.00783321 | + | 0.999969i | \(0.502493\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37684.2 | 2.12988 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1777.93 | −0.100045 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32423.7 | 1.81649 | 0.908243 | − | 0.418444i | \(-0.137424\pi\) | ||||
0.908243 | + | 0.418444i | \(0.137424\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9198.23 | −0.513060 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1206.18 | −0.0669848 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17438.5 | −0.964231 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23410.8 | 1.28884 | 0.644419 | − | 0.764672i | \(-0.277099\pi\) | ||||
0.644419 | + | 0.764672i | \(0.277099\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4743.88 | 0.260036 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9294.36 | 0.507274 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23173.1 | 1.25932 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17884.6 | 0.967749 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3314.51 | 0.178584 | 0.0892920 | − | 0.996005i | \(-0.471540\pi\) | ||||
0.0892920 | + | 0.996005i | \(0.471540\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.6043 | 0.00282220 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8079.20 | 0.431603 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4007.60 | −0.213185 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3593.16 | 0.190330 | 0.0951651 | − | 0.995462i | \(-0.469662\pi\) | ||||
0.0951651 | + | 0.995462i | \(0.469662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2947.64 | 0.155478 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6554.32 | 0.344265 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4035.49 | 0.211075 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7167.68 | 0.373336 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9962.26 | 0.516731 | 0.258365 | − | 0.966047i | \(-0.416816\pi\) | ||||
0.258365 | + | 0.966047i | \(0.416816\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4229.55 | −0.218469 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1824.99 | 0.0938754 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4685.49 | −0.240020 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35638.3 | 1.81809 | 0.909045 | − | 0.416698i | \(-0.136813\pi\) | ||||
0.909045 | + | 0.416698i | \(0.136813\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14814.1 | 0.749548 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22413.2 | 1.12940 | 0.564700 | − | 0.825296i | \(-0.308992\pi\) | ||||
0.564700 | + | 0.825296i | \(0.308992\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5273.71 | 0.264658 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9661.96 | −0.482907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1068.64 | −0.0531941 | −0.0265971 | − | 0.999646i | \(-0.508467\pi\) | ||||
−0.0265971 | + | 0.999646i | \(0.508467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3588.98 | 0.177928 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9514.38 | −0.469783 | −0.234891 | − | 0.972022i | \(-0.575473\pi\) | ||||
−0.234891 | + | 0.972022i | \(0.575473\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14156.5 | −0.696178 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4263.10 | 0.208807 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31274.0 | 1.52567 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32245.8 | −1.56680 | −0.783398 | − | 0.621520i | \(-0.786515\pi\) | ||||
−0.783398 | + | 0.621520i | \(0.786515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20556.2 | −0.994833 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12518.6 | 0.603440 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13864.8 | 0.665688 | 0.332844 | − | 0.942982i | \(-0.391992\pi\) | ||||
0.332844 | + | 0.942982i | \(0.391992\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1341.29 | −0.0641448 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7817.11 | 0.372365 | 0.186183 | − | 0.982515i | \(-0.440388\pi\) | ||||
0.186183 | + | 0.982515i | \(0.440388\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38928.8 | −1.84707 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4547.91 | 0.214941 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20292.0 | −0.955283 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10091.0 | 0.473202 | 0.236601 | − | 0.971607i | \(-0.423967\pi\) | ||||
0.236601 | + | 0.971607i | \(0.423967\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12000.7 | −0.560563 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11257.8 | −0.523825 | −0.261912 | − | 0.965092i | \(-0.584353\pi\) | ||||
−0.261912 | + | 0.965092i | \(0.584353\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7329.85 | −0.339737 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 140.298 | 0.00647768 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6797.33 | 0.312631 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7943.22 | 0.363932 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5060.33 | −0.230960 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10762.1 | 0.489320 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37864.2 | −1.71501 | −0.857505 | − | 0.514475i | \(-0.827987\pi\) | ||||
−0.857505 | + | 0.514475i | \(0.827987\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10764.1 | 0.485693 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36510.1 | 1.64115 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37845.1 | −1.69473 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6481.94 | −0.289171 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33482.9 | −1.48811 | −0.744056 | − | 0.668117i | \(-0.767100\pi\) | ||||
−0.744056 | + | 0.668117i | \(0.767100\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54434.8 | 2.41022 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3929.82 | −0.173350 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1127.76 | −0.0495615 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2945.80 | −0.128976 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10199.1 | 0.444887 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40425.0 | 1.75682 | 0.878410 | − | 0.477909i | \(-0.158605\pi\) | ||||
0.878410 | + | 0.477909i | \(0.158605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2720.26 | 0.117782 | 0.0588910 | − | 0.998264i | \(-0.481244\pi\) | ||||
0.0588910 | + | 0.998264i | \(0.481244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23263.5 | −1.00355 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13554.2 | 0.582556 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4345.39 | 0.186078 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9571.94 | 0.408389 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38982.6 | 1.65713 | 0.828563 | − | 0.559896i | \(-0.189159\pi\) | ||||
0.828563 | + | 0.559896i | \(0.189159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15194.2 | 0.643545 | 0.321772 | − | 0.946817i | \(-0.395721\pi\) | ||||
0.321772 | + | 0.946817i | \(0.395721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1500.00 | 0.0633010 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5073.07 | −0.213311 | −0.106655 | − | 0.994296i | \(-0.534014\pi\) | ||||
−0.106655 | + | 0.994296i | \(0.534014\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29064.4 | 1.21767 | 0.608834 | − | 0.793298i | \(-0.291638\pi\) | ||||
0.608834 | + | 0.793298i | \(0.291638\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6741.22 | −0.281409 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35532.4 | 1.47794 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10878.5 | 0.450859 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7916.24 | −0.326912 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30858.6 | 1.26979 | 0.634897 | − | 0.772597i | \(-0.281042\pi\) | ||||
0.634897 | + | 0.772597i | \(0.281042\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10737.1 | 0.440243 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2157.30 | −0.0881394 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2842.41 | −0.115718 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24536.4 | −0.995373 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15675.5 | −0.633665 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.6681 | −0.00159789 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15449.4 | −0.620138 | −0.310069 | − | 0.950714i | \(-0.600352\pi\) | ||||
−0.310069 | + | 0.950714i | \(0.600352\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1334.03 | 0.0533601 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30036.3 | 1.19722 | 0.598612 | − | 0.801039i | \(-0.295719\pi\) | ||||
0.598612 | + | 0.801039i | \(0.295719\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23949.6 | 0.951278 | 0.475639 | − | 0.879640i | \(-0.342217\pi\) | ||||
0.475639 | + | 0.879640i | \(0.342217\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18128.8 | 0.717568 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13084.4 | −0.516105 | −0.258052 | − | 0.966131i | \(-0.583081\pi\) | ||||
−0.258052 | + | 0.966131i | \(0.583081\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5050.63 | 0.198528 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15903.2 | 0.622954 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6550.31 | 0.255701 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19495.4 | −0.758410 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12868.9 | 0.498906 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3294.36 | 0.127280 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33296.4 | −1.28203 | −0.641015 | − | 0.767528i | \(-0.721486\pi\) | ||||
−0.641015 | + | 0.767528i | \(0.721486\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19226.4 | 0.737758 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27460.6 | −1.05014 | −0.525068 | − | 0.851060i | \(-0.675960\pi\) | ||||
−0.525068 | + | 0.851060i | \(0.675960\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29831.5 | 1.13693 | 0.568466 | − | 0.822707i | \(-0.307537\pi\) | ||||
0.568466 | + | 0.822707i | \(0.307537\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7542.59 | −0.286487 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3402.93 | 0.128815 | 0.0644077 | − | 0.997924i | \(-0.479484\pi\) | ||||
0.0644077 | + | 0.997924i | \(0.479484\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23813.8 | −0.898413 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1620.00 | 0.0609114 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15967.3 | 0.598347 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11331.3 | 0.423200 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2706.39 | −0.100740 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 54950.3 | 2.03859 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43673.0 | −1.61483 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11589.3 | 0.427097 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23610.0 | −0.867209 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10442.8 | −0.382300 | −0.191150 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191150 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1368.57 | −0.0499367 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43858.4 | 1.59505 | 0.797527 | − | 0.603283i | \(-0.206141\pi\) | ||||
0.797527 | + | 0.603283i | \(0.206141\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9473.57 | 0.343406 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14067.1 | −0.508245 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29005.8 | −1.04455 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19120.3 | −0.686313 | −0.343156 | − | 0.939278i | \(-0.611496\pi\) | ||||
−0.343156 | + | 0.939278i | \(0.611496\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13064.7 | −0.467424 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16027.4 | 0.571558 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.3617 | 0.00157687 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1444.36 | −0.0511747 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39572.8 | −1.39757 | −0.698784 | − | 0.715333i | \(-0.746275\pi\) | ||||
−0.698784 | + | 0.715333i | \(0.746275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10422.6 | 0.366905 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22547.5 | −0.791180 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10106.5 | 0.353494 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16251.0 | 0.566593 | 0.283296 | − | 0.959032i | \(-0.408572\pi\) | ||||
0.283296 | + | 0.959032i | \(0.408572\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25603.0 | 0.889801 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13456.6 | −0.466176 | −0.233088 | − | 0.972456i | \(-0.574883\pi\) | ||||
−0.233088 | + | 0.972456i | \(0.574883\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5125.76 | −0.177007 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3557.91 | 0.122475 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25628.9 | 0.879437 | 0.439718 | − | 0.898136i | \(-0.355078\pi\) | ||||
0.439718 | + | 0.898136i | \(0.355078\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2275.54 | −0.0778367 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6782.70 | 0.231277 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15570.2 | −0.529244 | −0.264622 | − | 0.964352i | \(-0.585247\pi\) | ||||
−0.264622 | + | 0.964352i | \(0.585247\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1665.14 | 0.0564217 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11245.2 | −0.379838 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −48483.7 | −1.63255 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56171.7 | 1.88553 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10679.8 | 0.357375 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22516.2 | −0.751110 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20978.9 | 0.697659 | 0.348830 | − | 0.937186i | \(-0.386579\pi\) | ||||
0.348830 | + | 0.937186i | \(0.386579\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8988.22 | 0.297981 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53556.2 | −1.77003 | −0.885016 | − | 0.465561i | \(-0.845852\pi\) | ||||
−0.885016 | + | 0.465561i | \(0.845852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48990.4 | 1.61414 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3026.62 | 0.0994147 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10356.5 | −0.339135 | −0.169568 | − | 0.985519i | \(-0.554237\pi\) | ||||
−0.169568 | + | 0.985519i | \(0.554237\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8732.94 | −0.285093 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13293.9 | −0.432662 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41887.6 | −1.35911 | −0.679556 | − | 0.733624i | \(-0.737828\pi\) | ||||
−0.679556 | + | 0.733624i | \(0.737828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16625.2 | 0.537788 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42585.3 | 1.37336 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3276.79 | −0.105355 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31978.8 | −1.02507 | −0.512533 | − | 0.858668i | \(-0.671293\pi\) | ||||
−0.512533 | + | 0.858668i | \(0.671293\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3775.86 | 0.120668 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16176.6 | 0.515410 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −56184.5 | −1.78474 | −0.892368 | − | 0.451309i | \(-0.850957\pi\) | ||||
−0.892368 | + | 0.451309i | \(0.850957\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 47.9107 | 0.00151734 |
(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 | 960.4.a.bp.1.2 | 2 | ||
4.3 | odd | 2 | 960.4.a.bl.1.1 | 2 | |||
8.3 | odd | 2 | 480.4.a.p.1.1 | yes | 2 | ||
8.5 | even | 2 | 480.4.a.n.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 1440.4.a.ba.1.2 | 2 | |||
24.11 | even | 2 | 1440.4.a.bf.1.1 | 2 | |||
40.19 | odd | 2 | 2400.4.a.z.1.2 | 2 | |||
40.29 | even | 2 | 2400.4.a.ba.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.4.a.n.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
480.4.a.p.1.1 | yes | 2 | 8.3 | odd | 2 | ||
960.4.a.bl.1.1 | 2 | 4.3 | odd | 2 | |||
960.4.a.bp.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1440.4.a.ba.1.2 | 2 | 24.5 | odd | 2 | |||
1440.4.a.bf.1.1 | 2 | 24.11 | even | 2 | |||
2400.4.a.z.1.2 | 2 | 40.19 | odd | 2 | |||
2400.4.a.ba.1.1 | 2 | 40.29 | even | 2 |