Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 32x^{2} - 35x + 120 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 175) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.50478\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.504784 | −0.178468 | −0.0892340 | − | 0.996011i | \(-0.528442\pi\) | ||||
−0.0892340 | + | 0.996011i | \(0.528442\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.74519 | −0.968149 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 7.94792 | 0.351252 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −54.8800 | −1.50427 | −0.752134 | − | 0.659010i | \(-0.770975\pi\) | ||||
−0.752134 | + | 0.659010i | \(0.770975\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.0073 | −0.341510 | −0.170755 | − | 0.985313i | \(-0.554621\pi\) | ||||
−0.170755 | + | 0.985313i | \(0.554621\pi\) | |||||||
\(14\) | 3.53349 | 0.0674546 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 57.9496 | 0.905462 | ||||||||
\(17\) | −0.422056 | −0.00602139 | −0.00301069 | − | 0.999995i | \(-0.500958\pi\) | ||||
−0.00301069 | + | 0.999995i | \(0.500958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 127.501 | 1.53952 | 0.769758 | − | 0.638336i | \(-0.220377\pi\) | ||||
0.769758 | + | 0.638336i | \(0.220377\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 27.7025 | 0.268464 | ||||||||
\(23\) | 51.1101 | 0.463357 | 0.231678 | − | 0.972792i | \(-0.425578\pi\) | ||||
0.231678 | + | 0.972792i | \(0.425578\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.08024 | 0.0609487 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 54.2164 | 0.365926 | ||||||||
\(29\) | −41.4750 | −0.265576 | −0.132788 | − | 0.991144i | \(-0.542393\pi\) | ||||
−0.132788 | + | 0.991144i | \(0.542393\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 192.354 | 1.11445 | 0.557224 | − | 0.830362i | \(-0.311866\pi\) | ||||
0.557224 | + | 0.830362i | \(0.311866\pi\) | |||||||
\(32\) | −92.8353 | −0.512848 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.213047 | 0.00107462 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 189.232 | 0.840801 | 0.420400 | − | 0.907339i | \(-0.361890\pi\) | ||||
0.420400 | + | 0.907339i | \(0.361890\pi\) | |||||||
\(38\) | −64.3605 | −0.274754 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 76.3187 | 0.290707 | 0.145353 | − | 0.989380i | \(-0.453568\pi\) | ||||
0.145353 | + | 0.989380i | \(0.453568\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −294.499 | −1.04443 | −0.522216 | − | 0.852813i | \(-0.674895\pi\) | ||||
−0.522216 | + | 0.852813i | \(0.674895\pi\) | |||||||
\(44\) | 425.056 | 1.45636 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −25.7996 | −0.0826943 | ||||||||
\(47\) | 540.297 | 1.67682 | 0.838408 | − | 0.545043i | \(-0.183487\pi\) | ||||
0.838408 | + | 0.545043i | \(0.183487\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 123.980 | 0.330633 | ||||||||
\(53\) | −661.316 | −1.71394 | −0.856969 | − | 0.515368i | \(-0.827655\pi\) | ||||
−0.856969 | + | 0.515368i | \(0.827655\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −55.6354 | −0.132761 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 20.9359 | 0.0473969 | ||||||||
\(59\) | −410.312 | −0.905390 | −0.452695 | − | 0.891665i | \(-0.649537\pi\) | ||||
−0.452695 | + | 0.891665i | \(0.649537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 46.0495 | 0.0966563 | 0.0483281 | − | 0.998832i | \(-0.484611\pi\) | ||||
0.0483281 | + | 0.998832i | \(0.484611\pi\) | |||||||
\(62\) | −97.0974 | −0.198893 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −416.735 | −0.813935 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4074 | −0.0189771 | −0.00948854 | − | 0.999955i | \(-0.503020\pi\) | ||||
−0.00948854 | + | 0.999955i | \(0.503020\pi\) | |||||||
\(68\) | 3.26890 | 0.00582960 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 491.117 | 0.820913 | 0.410456 | − | 0.911880i | \(-0.365369\pi\) | ||||
0.410456 | + | 0.911880i | \(0.365369\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 814.540 | 1.30595 | 0.652977 | − | 0.757378i | \(-0.273520\pi\) | ||||
0.652977 | + | 0.757378i | \(0.273520\pi\) | |||||||
\(74\) | −95.5215 | −0.150056 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −987.522 | −1.49048 | ||||||||
\(77\) | 384.160 | 0.568560 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −858.725 | −1.22296 | −0.611482 | − | 0.791258i | \(-0.709426\pi\) | ||||
−0.611482 | + | 0.791258i | \(0.709426\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −38.5244 | −0.0518818 | ||||||||
\(83\) | −1055.80 | −1.39626 | −0.698129 | − | 0.715972i | \(-0.745984\pi\) | ||||
−0.698129 | + | 0.715972i | \(0.745984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 148.658 | 0.186398 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −436.182 | −0.528376 | ||||||||
\(89\) | −341.567 | −0.406809 | −0.203405 | − | 0.979095i | \(-0.565201\pi\) | ||||
−0.203405 | + | 0.979095i | \(0.565201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 112.051 | 0.129079 | ||||||||
\(92\) | −395.858 | −0.448598 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −272.733 | −0.299258 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1417.21 | 1.48346 | 0.741731 | − | 0.670697i | \(-0.234005\pi\) | ||||
0.741731 | + | 0.670697i | \(0.234005\pi\) | |||||||
\(98\) | −24.7344 | −0.0254954 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 121.051 | 0.119258 | 0.0596289 | − | 0.998221i | \(-0.481008\pi\) | ||||
0.0596289 | + | 0.998221i | \(0.481008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 655.594 | 0.627161 | 0.313581 | − | 0.949562i | \(-0.398471\pi\) | ||||
0.313581 | + | 0.949562i | \(0.398471\pi\) | |||||||
\(104\) | −127.225 | −0.119956 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 333.821 | 0.305883 | ||||||||
\(107\) | 2069.81 | 1.87006 | 0.935031 | − | 0.354567i | \(-0.115372\pi\) | ||||
0.935031 | + | 0.354567i | \(0.115372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 904.218 | 0.794573 | 0.397286 | − | 0.917695i | \(-0.369952\pi\) | ||||
0.397286 | + | 0.917695i | \(0.369952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −405.647 | −0.342232 | ||||||||
\(113\) | −843.350 | −0.702086 | −0.351043 | − | 0.936359i | \(-0.614173\pi\) | ||||
−0.351043 | + | 0.936359i | \(0.614173\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 321.232 | 0.257117 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 207.119 | 0.161583 | ||||||||
\(119\) | 2.95439 | 0.00227587 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1680.81 | 1.26282 | ||||||||
\(122\) | −23.2450 | −0.0172501 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1489.82 | −1.07895 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2030.50 | −1.41872 | −0.709362 | − | 0.704845i | \(-0.751017\pi\) | ||||
−0.709362 | + | 0.704845i | \(0.751017\pi\) | |||||||
\(128\) | 953.043 | 0.658109 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2872.47 | −1.91579 | −0.957897 | − | 0.287113i | \(-0.907305\pi\) | ||||
−0.957897 | + | 0.287113i | \(0.907305\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −892.509 | −0.581882 | ||||||||
\(134\) | 5.25348 | 0.00338680 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.35446 | −0.00211502 | ||||||||
\(137\) | −1621.62 | −1.01127 | −0.505636 | − | 0.862747i | \(-0.668742\pi\) | ||||
−0.505636 | + | 0.862747i | \(0.668742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2617.72 | 1.59735 | 0.798677 | − | 0.601760i | \(-0.205534\pi\) | ||||
0.798677 | + | 0.601760i | \(0.205534\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −247.908 | −0.146507 | ||||||||
\(143\) | 878.482 | 0.513723 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −411.166 | −0.233071 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1465.64 | −0.814021 | ||||||||
\(149\) | −2252.63 | −1.23854 | −0.619270 | − | 0.785178i | \(-0.712571\pi\) | ||||
−0.619270 | + | 0.785178i | \(0.712571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1849.61 | −0.996813 | −0.498407 | − | 0.866943i | \(-0.666081\pi\) | ||||
−0.498407 | + | 0.866943i | \(0.666081\pi\) | |||||||
\(152\) | 1013.37 | 0.540757 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −193.918 | −0.101470 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3337.59 | 1.69661 | 0.848307 | − | 0.529505i | \(-0.177622\pi\) | ||||
0.848307 | + | 0.529505i | \(0.177622\pi\) | |||||||
\(158\) | 433.471 | 0.218260 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −357.771 | −0.175132 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 471.099 | 0.226376 | 0.113188 | − | 0.993574i | \(-0.463894\pi\) | ||||
0.113188 | + | 0.993574i | \(0.463894\pi\) | |||||||
\(164\) | −591.103 | −0.281447 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 532.952 | 0.249187 | ||||||||
\(167\) | −3676.72 | −1.70367 | −0.851836 | − | 0.523809i | \(-0.824511\pi\) | ||||
−0.851836 | + | 0.523809i | \(0.824511\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1940.77 | −0.883371 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2280.95 | 1.01117 | ||||||||
\(173\) | 1009.11 | 0.443475 | 0.221737 | − | 0.975106i | \(-0.428827\pi\) | ||||
0.221737 | + | 0.975106i | \(0.428827\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3180.27 | −1.36206 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 172.417 | 0.0726024 | ||||||||
\(179\) | −3201.27 | −1.33673 | −0.668364 | − | 0.743835i | \(-0.733005\pi\) | ||||
−0.668364 | + | 0.743835i | \(0.733005\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1970.14 | −0.809056 | −0.404528 | − | 0.914526i | \(-0.632564\pi\) | ||||
−0.404528 | + | 0.914526i | \(0.632564\pi\) | |||||||
\(182\) | −56.5617 | −0.0230364 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 406.219 | 0.162755 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.1624 | 0.00905778 | ||||||||
\(188\) | −4184.70 | −1.62341 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3953.39 | −1.49768 | −0.748842 | − | 0.662749i | \(-0.769390\pi\) | ||||
−0.748842 | + | 0.662749i | \(0.769390\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2425.45 | −0.904598 | −0.452299 | − | 0.891866i | \(-0.649396\pi\) | ||||
−0.452299 | + | 0.891866i | \(0.649396\pi\) | |||||||
\(194\) | −715.385 | −0.264751 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −379.514 | −0.138307 | ||||||||
\(197\) | 3126.50 | 1.13073 | 0.565366 | − | 0.824840i | \(-0.308735\pi\) | ||||
0.565366 | + | 0.824840i | \(0.308735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3566.13 | −1.27033 | −0.635166 | − | 0.772376i | \(-0.719068\pi\) | ||||
−0.635166 | + | 0.772376i | \(0.719068\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −61.1046 | −0.0212837 | ||||||||
\(203\) | 290.325 | 0.100378 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −330.933 | −0.111928 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −927.618 | −0.309225 | ||||||||
\(209\) | −6997.27 | −2.31584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3699.18 | −1.20693 | −0.603465 | − | 0.797389i | \(-0.706214\pi\) | ||||
−0.603465 | + | 0.797389i | \(0.706214\pi\) | |||||||
\(212\) | 5122.02 | 1.65935 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1044.81 | −0.333746 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1346.48 | −0.421222 | ||||||||
\(218\) | −456.435 | −0.141806 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.75599 | 0.00205637 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 102.041 | 0.0306419 | 0.0153210 | − | 0.999883i | \(-0.495123\pi\) | ||||
0.0153210 | + | 0.999883i | \(0.495123\pi\) | |||||||
\(224\) | 649.847 | 0.193838 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 425.709 | 0.125300 | ||||||||
\(227\) | 5739.91 | 1.67829 | 0.839144 | − | 0.543909i | \(-0.183057\pi\) | ||||
0.839144 | + | 0.543909i | \(0.183057\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −843.125 | −0.243298 | −0.121649 | − | 0.992573i | \(-0.538818\pi\) | ||||
−0.121649 | + | 0.992573i | \(0.538818\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −329.640 | −0.0932841 | ||||||||
\(233\) | −2017.65 | −0.567300 | −0.283650 | − | 0.958928i | \(-0.591545\pi\) | ||||
−0.283650 | + | 0.958928i | \(0.591545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3177.94 | 0.876553 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.49133 | −0.000406170 0 | ||||||||
\(239\) | −243.685 | −0.0659526 | −0.0329763 | − | 0.999456i | \(-0.510499\pi\) | ||||
−0.0329763 | + | 0.999456i | \(0.510499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3060.58 | −0.818048 | −0.409024 | − | 0.912524i | \(-0.634131\pi\) | ||||
−0.409024 | + | 0.912524i | \(0.634131\pi\) | |||||||
\(242\) | −848.448 | −0.225373 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −356.662 | −0.0935777 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2040.95 | −0.525760 | ||||||||
\(248\) | 1528.82 | 0.391452 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6594.14 | 1.65824 | 0.829120 | − | 0.559070i | \(-0.188842\pi\) | ||||
0.829120 | + | 0.559070i | \(0.188842\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2804.92 | −0.697012 | ||||||||
\(254\) | 1024.96 | 0.253197 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2852.80 | 0.696484 | ||||||||
\(257\) | 512.646 | 0.124428 | 0.0622139 | − | 0.998063i | \(-0.480184\pi\) | ||||
0.0622139 | + | 0.998063i | \(0.480184\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1324.63 | −0.317793 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1449.98 | 0.341908 | ||||||||
\(263\) | −3560.04 | −0.834681 | −0.417341 | − | 0.908750i | \(-0.637038\pi\) | ||||
−0.417341 | + | 0.908750i | \(0.637038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 450.524 | 0.103847 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 80.6072 | 0.0183726 | ||||||||
\(269\) | 549.744 | 0.124604 | 0.0623020 | − | 0.998057i | \(-0.480156\pi\) | ||||
0.0623020 | + | 0.998057i | \(0.480156\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3944.91 | −0.884267 | −0.442134 | − | 0.896949i | \(-0.645778\pi\) | ||||
−0.442134 | + | 0.896949i | \(0.645778\pi\) | |||||||
\(272\) | −24.4580 | −0.00545214 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 818.567 | 0.180480 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1254.67 | 0.272150 | 0.136075 | − | 0.990699i | \(-0.456551\pi\) | ||||
0.136075 | + | 0.990699i | \(0.456551\pi\) | |||||||
\(278\) | −1321.38 | −0.285077 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 681.496 | 0.144679 | 0.0723393 | − | 0.997380i | \(-0.476954\pi\) | ||||
0.0723393 | + | 0.997380i | \(0.476954\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5946.88 | 1.24914 | 0.624568 | − | 0.780970i | \(-0.285275\pi\) | ||||
0.624568 | + | 0.780970i | \(0.285275\pi\) | |||||||
\(284\) | −3803.79 | −0.794766 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −443.444 | −0.0916831 | ||||||||
\(287\) | −534.231 | −0.109877 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4912.82 | −0.999964 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6308.77 | −1.26436 | ||||||||
\(293\) | 2171.03 | 0.432877 | 0.216438 | − | 0.976296i | \(-0.430556\pi\) | ||||
0.216438 | + | 0.976296i | \(0.430556\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1504.00 | 0.295333 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1137.09 | 0.221040 | ||||||||
\(299\) | −818.137 | −0.158241 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2061.49 | 0.394759 | ||||||||
\(302\) | 933.651 | 0.177899 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7388.64 | 1.39397 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3644.59 | 0.677549 | 0.338775 | − | 0.940868i | \(-0.389988\pi\) | ||||
0.338775 | + | 0.940868i | \(0.389988\pi\) | |||||||
\(308\) | −2975.39 | −0.550451 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2584.19 | −0.471177 | −0.235589 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235589 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6693.63 | −1.20878 | −0.604388 | − | 0.796690i | \(-0.706582\pi\) | ||||
−0.604388 | + | 0.796690i | \(0.706582\pi\) | |||||||
\(314\) | −1684.76 | −0.302791 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6650.99 | 1.18401 | ||||||||
\(317\) | −3843.36 | −0.680962 | −0.340481 | − | 0.940251i | \(-0.610590\pi\) | ||||
−0.340481 | + | 0.940251i | \(0.610590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2276.15 | 0.399498 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 180.597 | 0.0312555 | ||||||||
\(323\) | −53.8126 | −0.00927002 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −237.803 | −0.0404009 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 606.575 | 0.102111 | ||||||||
\(329\) | −3782.08 | −0.633777 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −821.922 | −0.136486 | −0.0682431 | − | 0.997669i | \(-0.521739\pi\) | ||||
−0.0682431 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(332\) | 8177.39 | 1.35179 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1855.95 | 0.304051 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1032.55 | −0.166904 | −0.0834520 | − | 0.996512i | \(-0.526595\pi\) | ||||
−0.0834520 | + | 0.996512i | \(0.526595\pi\) | |||||||
\(338\) | 979.667 | 0.157653 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10556.4 | −1.67643 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −2340.65 | −0.366859 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −509.382 | −0.0791461 | ||||||||
\(347\) | −2587.70 | −0.400332 | −0.200166 | − | 0.979762i | \(-0.564148\pi\) | ||||
−0.200166 | + | 0.979762i | \(0.564148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8454.24 | −1.29669 | −0.648345 | − | 0.761346i | \(-0.724539\pi\) | ||||
−0.648345 | + | 0.761346i | \(0.724539\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5094.80 | 0.771460 | ||||||||
\(353\) | −4129.63 | −0.622658 | −0.311329 | − | 0.950302i | \(-0.600774\pi\) | ||||
−0.311329 | + | 0.950302i | \(0.600774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2645.50 | 0.393852 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1615.95 | 0.238563 | ||||||||
\(359\) | 4536.69 | 0.666957 | 0.333478 | − | 0.942758i | \(-0.391778\pi\) | ||||
0.333478 | + | 0.942758i | \(0.391778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9397.56 | 1.37011 | ||||||||
\(362\) | 994.492 | 0.144390 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −867.859 | −0.124968 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1643.00 | −0.233689 | −0.116844 | − | 0.993150i | \(-0.537278\pi\) | ||||
−0.116844 | + | 0.993150i | \(0.537278\pi\) | |||||||
\(368\) | 2961.81 | 0.419552 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4629.21 | 0.647808 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9019.53 | −1.25205 | −0.626024 | − | 0.779804i | \(-0.715319\pi\) | ||||
−0.626024 | + | 0.779804i | \(0.715319\pi\) | |||||||
\(374\) | −11.6920 | −0.00161652 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4294.23 | 0.588984 | ||||||||
\(377\) | 663.904 | 0.0906971 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2463.63 | −0.333900 | −0.166950 | − | 0.985965i | \(-0.553392\pi\) | ||||
−0.166950 | + | 0.985965i | \(0.553392\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1995.61 | 0.267289 | ||||||||
\(383\) | −11007.2 | −1.46852 | −0.734261 | − | 0.678867i | \(-0.762471\pi\) | ||||
−0.734261 | + | 0.678867i | \(0.762471\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1224.33 | 0.161442 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10976.6 | −1.43621 | ||||||||
\(389\) | −6162.79 | −0.803254 | −0.401627 | − | 0.915803i | \(-0.631555\pi\) | ||||
−0.401627 | + | 0.915803i | \(0.631555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.5713 | −0.00279005 | ||||||||
\(392\) | 389.448 | 0.0501788 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1578.21 | −0.201799 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15137.9 | 1.91373 | 0.956864 | − | 0.290537i | \(-0.0938338\pi\) | ||||
0.956864 | + | 0.290537i | \(0.0938338\pi\) | |||||||
\(398\) | 1800.12 | 0.226714 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3302.29 | −0.411243 | −0.205622 | − | 0.978632i | \(-0.565922\pi\) | ||||
−0.205622 | + | 0.978632i | \(0.565922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3079.08 | −0.380596 | ||||||||
\(404\) | −937.564 | −0.115459 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −146.551 | −0.0179143 | ||||||||
\(407\) | −10385.1 | −1.26479 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4576.40 | 0.553273 | 0.276636 | − | 0.960975i | \(-0.410780\pi\) | ||||
0.276636 | + | 0.960975i | \(0.410780\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5077.70 | −0.607186 | ||||||||
\(413\) | 2872.18 | 0.342205 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1486.05 | 0.175143 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3532.11 | 0.413304 | ||||||||
\(419\) | 6778.05 | 0.790285 | 0.395142 | − | 0.918620i | \(-0.370695\pi\) | ||||
0.395142 | + | 0.918620i | \(0.370695\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3952.68 | −0.457582 | −0.228791 | − | 0.973476i | \(-0.573477\pi\) | ||||
−0.228791 | + | 0.973476i | \(0.573477\pi\) | |||||||
\(422\) | 1867.29 | 0.215398 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5256.08 | −0.602024 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −322.346 | −0.0365326 | ||||||||
\(428\) | −16031.1 | −1.81050 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3435.10 | 0.383905 | 0.191952 | − | 0.981404i | \(-0.438518\pi\) | ||||
0.191952 | + | 0.981404i | \(0.438518\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5457.82 | 0.605742 | 0.302871 | − | 0.953032i | \(-0.402055\pi\) | ||||
0.302871 | + | 0.953032i | \(0.402055\pi\) | |||||||
\(434\) | 679.682 | 0.0751746 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7003.35 | −0.769265 | ||||||||
\(437\) | 6516.61 | 0.713344 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4188.10 | 0.455323 | 0.227662 | − | 0.973740i | \(-0.426892\pi\) | ||||
0.227662 | + | 0.973740i | \(0.426892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.41031 | −0.000366996 0 | ||||||||
\(443\) | 2097.50 | 0.224955 | 0.112478 | − | 0.993654i | \(-0.464121\pi\) | ||||
0.112478 | + | 0.993654i | \(0.464121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −51.5085 | −0.00546860 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2917.14 | 0.307639 | ||||||||
\(449\) | −11318.2 | −1.18962 | −0.594809 | − | 0.803867i | \(-0.702772\pi\) | ||||
−0.594809 | + | 0.803867i | \(0.702772\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4188.37 | −0.437301 | ||||||||
\(452\) | 6531.91 | 0.679724 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2897.41 | −0.299521 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11696.4 | 1.19723 | 0.598617 | − | 0.801036i | \(-0.295717\pi\) | ||||
0.598617 | + | 0.801036i | \(0.295717\pi\) | |||||||
\(458\) | 425.596 | 0.0434209 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10685.0 | −1.07951 | −0.539753 | − | 0.841823i | \(-0.681482\pi\) | ||||
−0.539753 | + | 0.841823i | \(0.681482\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10407.2 | 1.04463 | 0.522315 | − | 0.852752i | \(-0.325068\pi\) | ||||
0.522315 | + | 0.852752i | \(0.325068\pi\) | |||||||
\(464\) | −2403.46 | −0.240469 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1018.48 | 0.101245 | ||||||||
\(467\) | −2978.24 | −0.295111 | −0.147555 | − | 0.989054i | \(-0.547140\pi\) | ||||
−0.147555 | + | 0.989054i | \(0.547140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 72.8517 | 0.00717266 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3261.12 | −0.318020 | ||||||||
\(473\) | 16162.1 | 1.57111 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −22.8823 | −0.00220338 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 123.008 | 0.0117704 | ||||||||
\(479\) | 14214.3 | 1.35588 | 0.677940 | − | 0.735117i | \(-0.262873\pi\) | ||||
0.677940 | + | 0.735117i | \(0.262873\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3029.11 | −0.287142 | ||||||||
\(482\) | 1544.93 | 0.145995 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13018.2 | −1.22260 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18097.0 | −1.68389 | −0.841946 | − | 0.539562i | \(-0.818590\pi\) | ||||
−0.841946 | + | 0.539562i | \(0.818590\pi\) | |||||||
\(488\) | 365.998 | 0.0339507 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13750.8 | 1.26388 | 0.631940 | − | 0.775017i | \(-0.282259\pi\) | ||||
0.631940 | + | 0.775017i | \(0.282259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.5048 | 0.00159914 | ||||||||
\(494\) | 1030.24 | 0.0938314 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11146.9 | 1.00909 | ||||||||
\(497\) | −3437.82 | −0.310276 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15684.2 | 1.40706 | 0.703528 | − | 0.710667i | \(-0.251607\pi\) | ||||
0.703528 | + | 0.710667i | \(0.251607\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3328.61 | −0.295943 | ||||||||
\(503\) | 977.937 | 0.0866880 | 0.0433440 | − | 0.999060i | \(-0.486199\pi\) | ||||
0.0433440 | + | 0.999060i | \(0.486199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1415.88 | 0.124394 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15726.6 | 1.37354 | ||||||||
\(509\) | 19664.6 | 1.71242 | 0.856208 | − | 0.516632i | \(-0.172814\pi\) | ||||
0.856208 | + | 0.516632i | \(0.172814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5701.78 | −0.493604 | ||||||||
\(512\) | −9064.39 | −0.782409 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −258.775 | −0.0222064 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29651.5 | −2.52238 | ||||||||
\(518\) | 668.650 | 0.0567158 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12522.8 | −1.05304 | −0.526519 | − | 0.850163i | \(-0.676503\pi\) | ||||
−0.526519 | + | 0.850163i | \(0.676503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1104.42 | −0.0923382 | −0.0461691 | − | 0.998934i | \(-0.514701\pi\) | ||||
−0.0461691 | + | 0.998934i | \(0.514701\pi\) | |||||||
\(524\) | 22247.8 | 1.85477 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1797.05 | 0.148964 | ||||||||
\(527\) | −81.1843 | −0.00671052 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9554.75 | −0.785301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6912.65 | 0.563349 | ||||||||
\(533\) | −1221.66 | −0.0992794 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −82.7170 | −0.00666573 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −277.502 | −0.0222378 | ||||||||
\(539\) | −2689.12 | −0.214895 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2126.45 | −0.168989 | −0.0844945 | − | 0.996424i | \(-0.526928\pi\) | ||||
−0.0844945 | + | 0.996424i | \(0.526928\pi\) | |||||||
\(542\) | 1991.33 | 0.157813 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 39.1817 | 0.00308805 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2137.04 | 0.167044 | 0.0835220 | − | 0.996506i | \(-0.473383\pi\) | ||||
0.0835220 | + | 0.996506i | \(0.473383\pi\) | |||||||
\(548\) | 12559.8 | 0.979063 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5288.11 | −0.408859 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6011.08 | 0.462237 | ||||||||
\(554\) | −633.335 | −0.0485701 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20274.8 | −1.54648 | ||||||||
\(557\) | −19435.1 | −1.47844 | −0.739219 | − | 0.673465i | \(-0.764805\pi\) | ||||
−0.739219 | + | 0.673465i | \(0.764805\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4714.14 | 0.356685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −344.008 | −0.0258205 | ||||||||
\(563\) | 1467.52 | 0.109855 | 0.0549276 | − | 0.998490i | \(-0.482507\pi\) | ||||
0.0549276 | + | 0.998490i | \(0.482507\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3001.89 | −0.222931 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3903.35 | 0.288347 | ||||||||
\(569\) | −15080.3 | −1.11107 | −0.555536 | − | 0.831493i | \(-0.687487\pi\) | ||||
−0.555536 | + | 0.831493i | \(0.687487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15800.8 | 1.15804 | 0.579022 | − | 0.815312i | \(-0.303435\pi\) | ||||
0.579022 | + | 0.815312i | \(0.303435\pi\) | |||||||
\(572\) | −6804.02 | −0.497361 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 269.671 | 0.0196095 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6165.64 | −0.444851 | −0.222425 | − | 0.974950i | \(-0.571397\pi\) | ||||
−0.222425 | + | 0.974950i | \(0.571397\pi\) | |||||||
\(578\) | 2479.91 | 0.178461 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7390.62 | 0.527736 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36293.0 | 2.57822 | ||||||||
\(584\) | 6473.89 | 0.458719 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1095.90 | −0.0772547 | ||||||||
\(587\) | 23104.0 | 1.62454 | 0.812268 | − | 0.583285i | \(-0.198233\pi\) | ||||
0.812268 | + | 0.583285i | \(0.198233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24525.4 | 1.71571 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10965.9 | 0.761313 | ||||||||
\(593\) | 6544.43 | 0.453200 | 0.226600 | − | 0.973988i | \(-0.427239\pi\) | ||||
0.226600 | + | 0.973988i | \(0.427239\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17447.0 | 1.19909 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 412.982 | 0.0282410 | ||||||||
\(599\) | −3215.71 | −0.219349 | −0.109675 | − | 0.993968i | \(-0.534981\pi\) | ||||
−0.109675 | + | 0.993968i | \(0.534981\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −234.653 | −0.0159263 | −0.00796313 | − | 0.999968i | \(-0.502535\pi\) | ||||
−0.00796313 | + | 0.999968i | \(0.502535\pi\) | |||||||
\(602\) | −1040.61 | −0.0704517 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14325.6 | 0.965064 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14528.7 | 0.971501 | 0.485750 | − | 0.874098i | \(-0.338546\pi\) | ||||
0.485750 | + | 0.874098i | \(0.338546\pi\) | |||||||
\(608\) | −11836.6 | −0.789537 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8648.71 | −0.572650 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11332.7 | −0.746696 | −0.373348 | − | 0.927691i | \(-0.621790\pi\) | ||||
−0.373348 | + | 0.927691i | \(0.621790\pi\) | |||||||
\(614\) | −1839.73 | −0.120921 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3053.27 | 0.199708 | ||||||||
\(617\) | −17400.2 | −1.13534 | −0.567672 | − | 0.823255i | \(-0.692156\pi\) | ||||
−0.567672 | + | 0.823255i | \(0.692156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11987.8 | −0.778402 | −0.389201 | − | 0.921153i | \(-0.627249\pi\) | ||||
−0.389201 | + | 0.921153i | \(0.627249\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1304.46 | 0.0840900 | ||||||||
\(623\) | 2390.97 | 0.153759 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3378.84 | 0.215728 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −25850.3 | −1.64258 | ||||||||
\(629\) | −79.8667 | −0.00506279 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3800.38 | −0.239764 | −0.119882 | − | 0.992788i | \(-0.538252\pi\) | ||||
−0.119882 | + | 0.992788i | \(0.538252\pi\) | |||||||
\(632\) | −6825.08 | −0.429568 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1940.07 | 0.121530 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −784.359 | −0.0487872 | ||||||||
\(638\) | −1148.96 | −0.0712976 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12294.2 | −0.757552 | −0.378776 | − | 0.925488i | \(-0.623655\pi\) | ||||
−0.378776 | + | 0.925488i | \(0.623655\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14615.4 | −0.896382 | −0.448191 | − | 0.893938i | \(-0.647932\pi\) | ||||
−0.448191 | + | 0.893938i | \(0.647932\pi\) | |||||||
\(644\) | 2771.01 | 0.169554 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.1637 | 0.00165440 | ||||||||
\(647\) | −16047.0 | −0.975071 | −0.487536 | − | 0.873103i | \(-0.662104\pi\) | ||||
−0.487536 | + | 0.873103i | \(0.662104\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22517.9 | 1.36195 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3648.75 | −0.219166 | ||||||||
\(653\) | 623.425 | 0.0373607 | 0.0186803 | − | 0.999826i | \(-0.494054\pi\) | ||||
0.0186803 | + | 0.999826i | \(0.494054\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4422.63 | 0.263224 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1909.13 | 0.113109 | ||||||||
\(659\) | −963.459 | −0.0569515 | −0.0284758 | − | 0.999594i | \(-0.509065\pi\) | ||||
−0.0284758 | + | 0.999594i | \(0.509065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24183.6 | 1.42304 | 0.711522 | − | 0.702664i | \(-0.248006\pi\) | ||||
0.711522 | + | 0.702664i | \(0.248006\pi\) | |||||||
\(662\) | 414.893 | 0.0243584 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8391.43 | −0.490438 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2119.79 | −0.123057 | ||||||||
\(668\) | 28476.9 | 1.64941 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2527.20 | −0.145397 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14167.0 | −0.811437 | −0.405718 | − | 0.913998i | \(-0.632979\pi\) | ||||
−0.405718 | + | 0.913998i | \(0.632979\pi\) | |||||||
\(674\) | 521.215 | 0.0297870 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15031.6 | 0.855235 | ||||||||
\(677\) | −19397.1 | −1.10117 | −0.550584 | − | 0.834780i | \(-0.685595\pi\) | ||||
−0.550584 | + | 0.834780i | \(0.685595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9920.47 | −0.560696 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5328.71 | 0.299189 | ||||||||
\(683\) | 20984.8 | 1.17564 | 0.587820 | − | 0.808992i | \(-0.299986\pi\) | ||||
0.587820 | + | 0.808992i | \(0.299986\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 173.141 | 0.00963636 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17066.1 | −0.945694 | ||||||||
\(689\) | 10585.9 | 0.585328 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18079.2 | −0.995320 | −0.497660 | − | 0.867372i | \(-0.665807\pi\) | ||||
−0.497660 | + | 0.867372i | \(0.665807\pi\) | |||||||
\(692\) | −7815.75 | −0.429350 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1306.23 | 0.0714465 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.2107 | −0.00175046 | ||||||||
\(698\) | 4267.56 | 0.231418 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18660.6 | −1.00542 | −0.502711 | − | 0.864455i | \(-0.667664\pi\) | ||||
−0.502711 | + | 0.864455i | \(0.667664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24127.4 | 1.29443 | ||||||||
\(704\) | 22870.4 | 1.22438 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2084.57 | 0.111125 | ||||||||
\(707\) | −847.358 | −0.0450752 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24545.4 | −1.30017 | −0.650085 | − | 0.759862i | \(-0.725267\pi\) | ||||
−0.650085 | + | 0.759862i | \(0.725267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2714.74 | −0.142892 | ||||||||
\(713\) | 9831.26 | 0.516387 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24794.5 | 1.29415 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2290.05 | −0.119030 | ||||||||
\(719\) | 7300.32 | 0.378659 | 0.189330 | − | 0.981914i | \(-0.439369\pi\) | ||||
0.189330 | + | 0.981914i | \(0.439369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4589.16 | −0.237045 | ||||||||
\(722\) | −4743.74 | −0.244520 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15259.1 | 0.783286 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15466.0 | −0.788998 | −0.394499 | − | 0.918896i | \(-0.629082\pi\) | ||||
−0.394499 | + | 0.918896i | \(0.629082\pi\) | |||||||
\(728\) | 890.574 | 0.0453391 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 124.295 | 0.00628893 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13830.5 | 0.696917 | 0.348459 | − | 0.937324i | \(-0.386705\pi\) | ||||
0.348459 | + | 0.937324i | \(0.386705\pi\) | |||||||
\(734\) | 829.358 | 0.0417060 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4744.83 | −0.237631 | ||||||||
\(737\) | 571.157 | 0.0285466 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11714.5 | 0.583118 | 0.291559 | − | 0.956553i | \(-0.405826\pi\) | ||||
0.291559 | + | 0.956553i | \(0.405826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2336.75 | −0.115613 | ||||||||
\(743\) | 28963.4 | 1.43010 | 0.715050 | − | 0.699074i | \(-0.246404\pi\) | ||||
0.715050 | + | 0.699074i | \(0.246404\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4552.91 | 0.223450 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −179.397 | −0.00876928 | ||||||||
\(749\) | −14488.7 | −0.706817 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6331.99 | 0.307667 | 0.153833 | − | 0.988097i | \(-0.450838\pi\) | ||||
0.153833 | + | 0.988097i | \(0.450838\pi\) | |||||||
\(752\) | 31310.0 | 1.51829 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −335.128 | −0.0161865 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6256.80 | 0.300406 | 0.150203 | − | 0.988655i | \(-0.452007\pi\) | ||||
0.150203 | + | 0.988655i | \(0.452007\pi\) | |||||||
\(758\) | 1243.60 | 0.0595905 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13953.7 | −0.664679 | −0.332340 | − | 0.943160i | \(-0.607838\pi\) | ||||
−0.332340 | + | 0.943160i | \(0.607838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6329.53 | −0.300320 | ||||||||
\(764\) | 30619.8 | 1.44998 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5556.28 | 0.262084 | ||||||||
\(767\) | 6568.00 | 0.309200 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34278.1 | 1.60741 | 0.803707 | − | 0.595025i | \(-0.202858\pi\) | ||||
0.803707 | + | 0.595025i | \(0.202858\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18785.5 | 0.875786 | ||||||||
\(773\) | 8769.31 | 0.408034 | 0.204017 | − | 0.978967i | \(-0.434600\pi\) | ||||
0.204017 | + | 0.978967i | \(0.434600\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11263.9 | 0.521069 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3110.88 | 0.143355 | ||||||||
\(779\) | 9730.73 | 0.447547 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26952.5 | −1.23487 | ||||||||
\(782\) | 10.8889 | 0.000497934 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2839.53 | 0.129352 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3546.15 | 0.160618 | 0.0803092 | − | 0.996770i | \(-0.474409\pi\) | ||||
0.0803092 | + | 0.996770i | \(0.474409\pi\) | |||||||
\(788\) | −24215.4 | −1.09472 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5903.45 | 0.265363 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −737.130 | −0.0330091 | ||||||||
\(794\) | −7641.37 | −0.341539 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27620.3 | 1.22987 | ||||||||
\(797\) | −18169.4 | −0.807520 | −0.403760 | − | 0.914865i | \(-0.632297\pi\) | ||||
−0.403760 | + | 0.914865i | \(0.632297\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −228.035 | −0.0100968 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1666.94 | 0.0733938 | ||||||||
\(803\) | −44702.0 | −1.96451 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1554.27 | 0.0679241 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 962.104 | 0.0418895 | ||||||||
\(809\) | −11853.0 | −0.515115 | −0.257557 | − | 0.966263i | \(-0.582918\pi\) | ||||
−0.257557 | + | 0.966263i | \(0.582918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11921.1 | −0.516161 | −0.258080 | − | 0.966123i | \(-0.583090\pi\) | ||||
−0.258080 | + | 0.966123i | \(0.583090\pi\) | |||||||
\(812\) | −2248.62 | −0.0971813 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5242.22 | 0.225724 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37548.9 | −1.60792 | ||||||||
\(818\) | −2310.09 | −0.0987415 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42094.1 | 1.78940 | 0.894698 | − | 0.446671i | \(-0.147390\pi\) | ||||
0.894698 | + | 0.446671i | \(0.147390\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1622.17 | −0.0687064 | −0.0343532 | − | 0.999410i | \(-0.510937\pi\) | ||||
−0.0343532 | + | 0.999410i | \(0.510937\pi\) | |||||||
\(824\) | 5210.61 | 0.220291 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1449.83 | −0.0610727 | ||||||||
\(827\) | 28171.7 | 1.18455 | 0.592277 | − | 0.805735i | \(-0.298229\pi\) | ||||
0.592277 | + | 0.805735i | \(0.298229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9244.23 | −0.387293 | −0.193646 | − | 0.981071i | \(-0.562031\pi\) | ||||
−0.193646 | + | 0.981071i | \(0.562031\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6670.81 | 0.277967 | ||||||||
\(833\) | −20.6807 | −0.000860198 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 54195.2 | 2.24208 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3421.45 | −0.141041 | ||||||||
\(839\) | 43012.5 | 1.76991 | 0.884956 | − | 0.465674i | \(-0.154188\pi\) | ||||
0.884956 | + | 0.465674i | \(0.154188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22668.8 | −0.929469 | ||||||||
\(842\) | 1995.25 | 0.0816637 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28650.9 | 1.16849 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11765.7 | −0.477302 | ||||||||
\(848\) | −38323.0 | −1.55191 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9671.70 | 0.389591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19756.9 | 0.793041 | 0.396521 | − | 0.918026i | \(-0.370217\pi\) | ||||
0.396521 | + | 0.918026i | \(0.370217\pi\) | |||||||
\(854\) | 162.715 | 0.00651991 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16450.7 | 0.656862 | ||||||||
\(857\) | 325.658 | 0.0129805 | 0.00649024 | − | 0.999979i | \(-0.497934\pi\) | ||||
0.00649024 | + | 0.999979i | \(0.497934\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3275.22 | 0.130092 | 0.0650461 | − | 0.997882i | \(-0.479281\pi\) | ||||
0.0650461 | + | 0.997882i | \(0.479281\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1733.98 | −0.0685147 | ||||||||
\(863\) | 44585.0 | 1.75862 | 0.879311 | − | 0.476247i | \(-0.158003\pi\) | ||||
0.879311 | + | 0.476247i | \(0.158003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2755.02 | −0.108106 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10428.8 | 0.407805 | ||||||||
\(869\) | 47126.9 | 1.83967 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 166.594 | 0.00648087 | ||||||||
\(872\) | 7186.65 | 0.279095 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3289.48 | −0.127309 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16433.8 | −0.632761 | −0.316380 | − | 0.948632i | \(-0.602468\pi\) | ||||
−0.316380 | + | 0.948632i | \(0.602468\pi\) | |||||||
\(878\) | −2114.08 | −0.0812607 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39080.2 | 1.49449 | 0.747245 | − | 0.664549i | \(-0.231376\pi\) | ||||
0.747245 | + | 0.664549i | \(0.231376\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48548.2 | −1.85026 | −0.925129 | − | 0.379652i | \(-0.876044\pi\) | ||||
−0.925129 | + | 0.379652i | \(0.876044\pi\) | |||||||
\(884\) | −52.3264 | −0.00199087 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1058.78 | −0.0401473 | ||||||||
\(887\) | −13447.1 | −0.509029 | −0.254514 | − | 0.967069i | \(-0.581916\pi\) | ||||
−0.254514 | + | 0.967069i | \(0.581916\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14213.5 | 0.536227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −790.325 | −0.0296660 | ||||||||
\(893\) | 68888.5 | 2.58148 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6671.30 | −0.248742 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5713.24 | 0.212309 | ||||||||
\(899\) | −7977.90 | −0.295971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 279.112 | 0.0103203 | ||||||||
\(902\) | 2114.22 | 0.0780442 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6702.87 | −0.246609 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15750.3 | −0.576604 | −0.288302 | − | 0.957539i | \(-0.593091\pi\) | ||||
−0.288302 | + | 0.957539i | \(0.593091\pi\) | |||||||
\(908\) | −44456.7 | −1.62483 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31449.7 | −1.14377 | −0.571886 | − | 0.820333i | \(-0.693788\pi\) | ||||
−0.571886 | + | 0.820333i | \(0.693788\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57942.4 | 2.10034 | ||||||||
\(914\) | −5904.16 | −0.213668 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6530.17 | 0.235549 | ||||||||
\(917\) | 20107.3 | 0.724102 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30355.6 | −1.08960 | −0.544798 | − | 0.838567i | \(-0.683394\pi\) | ||||
−0.544798 | + | 0.838567i | \(0.683394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5393.64 | 0.192657 | ||||||||
\(923\) | −7861.46 | −0.280350 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5253.39 | −0.186433 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3850.34 | 0.136200 | ||||||||
\(929\) | 28533.8 | 1.00771 | 0.503856 | − | 0.863788i | \(-0.331914\pi\) | ||||
0.503856 | + | 0.863788i | \(0.331914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6247.56 | 0.219931 | ||||||||
\(932\) | 15627.1 | 0.549231 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1503.37 | 0.0526678 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19269.1 | 0.671817 | 0.335908 | − | 0.941895i | \(-0.390957\pi\) | ||||
0.335908 | + | 0.941895i | \(0.390957\pi\) | |||||||
\(938\) | −36.7743 | −0.00128009 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2097.84 | 0.0726756 | 0.0363378 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363378 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3900.66 | 0.134701 | ||||||||
\(944\) | −23777.4 | −0.819797 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8158.36 | −0.280392 | ||||||||
\(947\) | 5072.14 | 0.174047 | 0.0870235 | − | 0.996206i | \(-0.472264\pi\) | ||||
0.0870235 | + | 0.996206i | \(0.472264\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13038.6 | −0.445997 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 23.4813 | 0.000799403 0 | ||||||||
\(953\) | −23464.1 | −0.797564 | −0.398782 | − | 0.917046i | \(-0.630567\pi\) | ||||
−0.398782 | + | 0.917046i | \(0.630567\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1887.39 | 0.0638519 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7175.13 | −0.241981 | ||||||||
\(959\) | 11351.3 | 0.382225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7209.24 | 0.241994 | ||||||||
\(962\) | 1529.04 | 0.0512457 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23704.8 | 0.791992 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6994.27 | 0.232596 | 0.116298 | − | 0.993214i | \(-0.462897\pi\) | ||||
0.116298 | + | 0.993214i | \(0.462897\pi\) | |||||||
\(968\) | 13359.0 | 0.443568 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37752.5 | −1.24772 | −0.623860 | − | 0.781536i | \(-0.714436\pi\) | ||||
−0.623860 | + | 0.781536i | \(0.714436\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18324.0 | −0.603743 | ||||||||
\(974\) | 9135.09 | 0.300521 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2668.55 | 0.0875186 | ||||||||
\(977\) | −6380.21 | −0.208926 | −0.104463 | − | 0.994529i | \(-0.533312\pi\) | ||||
−0.104463 | + | 0.994529i | \(0.533312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18745.2 | 0.611950 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6941.18 | −0.225562 | ||||||||
\(983\) | 17330.0 | 0.562299 | 0.281150 | − | 0.959664i | \(-0.409284\pi\) | ||||
0.281150 | + | 0.959664i | \(0.409284\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.83612 | −0.000285395 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15807.6 | 0.509014 | ||||||||
\(989\) | −15051.9 | −0.483945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32191.8 | 1.03189 | 0.515947 | − | 0.856621i | \(-0.327440\pi\) | ||||
0.515947 | + | 0.856621i | \(0.327440\pi\) | |||||||
\(992\) | −17857.3 | −0.571542 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1735.35 | 0.0553743 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2678.20 | 0.0850748 | 0.0425374 | − | 0.999095i | \(-0.486456\pi\) | ||||
0.0425374 | + | 0.999095i | \(0.486456\pi\) | |||||||
\(998\) | −7917.13 | −0.251114 | ||||||||
\(999\) | 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 | 1575.4.a.bl.1.2 | 4 | ||
3.2 | odd | 2 | 175.4.a.g.1.3 | ✓ | 4 | ||
5.4 | even | 2 | 1575.4.a.bg.1.3 | 4 | |||
15.2 | even | 4 | 175.4.b.f.99.5 | 8 | |||
15.8 | even | 4 | 175.4.b.f.99.4 | 8 | |||
15.14 | odd | 2 | 175.4.a.h.1.2 | yes | 4 | ||
21.20 | even | 2 | 1225.4.a.z.1.3 | 4 | |||
105.104 | even | 2 | 1225.4.a.bd.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.4.a.g.1.3 | ✓ | 4 | 3.2 | odd | 2 | ||
175.4.a.h.1.2 | yes | 4 | 15.14 | odd | 2 | ||
175.4.b.f.99.4 | 8 | 15.8 | even | 4 | |||
175.4.b.f.99.5 | 8 | 15.2 | even | 4 | |||
1225.4.a.z.1.3 | 4 | 21.20 | even | 2 | |||
1225.4.a.bd.1.2 | 4 | 105.104 | even | 2 | |||
1575.4.a.bg.1.3 | 4 | 5.4 | even | 2 | |||
1575.4.a.bl.1.2 | 4 | 1.1 | even | 1 | trivial |