Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(0\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.13470 | −1.10828 | −0.554142 | − | 0.832422i | \(-0.686954\pi\) | ||||
−0.554142 | + | 0.832422i | \(0.686954\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.82636 | 0.228295 | ||||||||
\(5\) | −4.91209 | −0.439351 | −0.219675 | − | 0.975573i | \(-0.570500\pi\) | ||||
−0.219675 | + | 0.975573i | \(0.570500\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 36.3874 | 1.96474 | 0.982368 | − | 0.186956i | \(-0.0598621\pi\) | ||||
0.982368 | + | 0.186956i | \(0.0598621\pi\) | |||||||
\(8\) | 19.3525 | 0.855269 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 15.3979 | 0.486926 | ||||||||
\(11\) | 0.654849 | 0.0179495 | 0.00897475 | − | 0.999960i | \(-0.497143\pi\) | ||||
0.00897475 | + | 0.999960i | \(0.497143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.3822 | −0.904207 | −0.452104 | − | 0.891965i | \(-0.649326\pi\) | ||||
−0.452104 | + | 0.891965i | \(0.649326\pi\) | |||||||
\(14\) | −114.064 | −2.17749 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −75.2753 | −1.17618 | ||||||||
\(17\) | −41.8110 | −0.596509 | −0.298255 | − | 0.954486i | \(-0.596404\pi\) | ||||
−0.298255 | + | 0.954486i | \(0.596404\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −79.2470 | −0.956869 | −0.478434 | − | 0.878123i | \(-0.658796\pi\) | ||||
−0.478434 | + | 0.878123i | \(0.658796\pi\) | |||||||
\(20\) | −8.97125 | −0.100302 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.05276 | −0.0198932 | ||||||||
\(23\) | 103.434 | 0.937715 | 0.468857 | − | 0.883274i | \(-0.344666\pi\) | ||||
0.468857 | + | 0.883274i | \(0.344666\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −100.871 | −0.806971 | ||||||||
\(26\) | 132.855 | 1.00212 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 66.4566 | 0.448540 | ||||||||
\(29\) | 150.719 | 0.965100 | 0.482550 | − | 0.875868i | \(-0.339711\pi\) | ||||
0.482550 | + | 0.875868i | \(0.339711\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −43.3756 | −0.251306 | −0.125653 | − | 0.992074i | \(-0.540103\pi\) | ||||
−0.125653 | + | 0.992074i | \(0.540103\pi\) | |||||||
\(32\) | 81.1455 | 0.448270 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 131.065 | 0.661102 | ||||||||
\(35\) | −178.738 | −0.863209 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −328.704 | −1.46050 | −0.730252 | − | 0.683178i | \(-0.760597\pi\) | ||||
−0.730252 | + | 0.683178i | \(0.760597\pi\) | |||||||
\(38\) | 248.416 | 1.06048 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −95.0614 | −0.375763 | ||||||||
\(41\) | 227.006 | 0.864693 | 0.432346 | − | 0.901708i | \(-0.357686\pi\) | ||||
0.432346 | + | 0.901708i | \(0.357686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −88.1867 | −0.312752 | −0.156376 | − | 0.987698i | \(-0.549981\pi\) | ||||
−0.156376 | + | 0.987698i | \(0.549981\pi\) | |||||||
\(44\) | 1.19599 | 0.00409778 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −324.234 | −1.03925 | ||||||||
\(47\) | 161.362 | 0.500787 | 0.250394 | − | 0.968144i | \(-0.419440\pi\) | ||||
0.250394 | + | 0.968144i | \(0.419440\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 981.045 | 2.86019 | ||||||||
\(50\) | 316.202 | 0.894354 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −77.4051 | −0.206426 | ||||||||
\(53\) | 206.317 | 0.534714 | 0.267357 | − | 0.963598i | \(-0.413850\pi\) | ||||
0.267357 | + | 0.963598i | \(0.413850\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.21668 | −0.00788613 | ||||||||
\(56\) | 704.189 | 1.68038 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −472.461 | −1.06961 | ||||||||
\(59\) | −427.414 | −0.943128 | −0.471564 | − | 0.881832i | \(-0.656310\pi\) | ||||
−0.471564 | + | 0.881832i | \(0.656310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38.0290 | −0.0798215 | −0.0399108 | − | 0.999203i | \(-0.512707\pi\) | ||||
−0.0399108 | + | 0.999203i | \(0.512707\pi\) | |||||||
\(62\) | 135.970 | 0.278519 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 347.835 | 0.679366 | ||||||||
\(65\) | 208.185 | 0.397264 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 594.441 | 1.08392 | 0.541959 | − | 0.840405i | \(-0.317683\pi\) | ||||
0.541959 | + | 0.840405i | \(0.317683\pi\) | |||||||
\(68\) | −76.3620 | −0.136180 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 560.292 | 0.956681 | ||||||||
\(71\) | 905.766 | 1.51401 | 0.757004 | − | 0.653410i | \(-0.226662\pi\) | ||||
0.757004 | + | 0.653410i | \(0.226662\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 155.597 | 0.249469 | 0.124735 | − | 0.992190i | \(-0.460192\pi\) | ||||
0.124735 | + | 0.992190i | \(0.460192\pi\) | |||||||
\(74\) | 1030.39 | 1.61865 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −144.734 | −0.218448 | ||||||||
\(77\) | 23.8283 | 0.0352660 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 63.7719 | 0.0908216 | 0.0454108 | − | 0.998968i | \(-0.485540\pi\) | ||||
0.0454108 | + | 0.998968i | \(0.485540\pi\) | |||||||
\(80\) | 369.759 | 0.516754 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −711.597 | −0.958326 | ||||||||
\(83\) | −834.746 | −1.10392 | −0.551960 | − | 0.833871i | \(-0.686120\pi\) | ||||
−0.551960 | + | 0.833871i | \(0.686120\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 205.379 | 0.262077 | ||||||||
\(86\) | 276.439 | 0.346619 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.6730 | 0.0153516 | ||||||||
\(89\) | −601.888 | −0.716855 | −0.358427 | − | 0.933558i | \(-0.616687\pi\) | ||||
−0.358427 | + | 0.933558i | \(0.616687\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1542.18 | −1.77653 | ||||||||
\(92\) | 188.907 | 0.214076 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −505.820 | −0.555015 | ||||||||
\(95\) | 389.268 | 0.420401 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −495.710 | −0.518883 | −0.259442 | − | 0.965759i | \(-0.583539\pi\) | ||||
−0.259442 | + | 0.965759i | \(0.583539\pi\) | |||||||
\(98\) | −3075.29 | −3.16991 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −184.228 | −0.184228 | ||||||||
\(101\) | −149.594 | −0.147378 | −0.0736891 | − | 0.997281i | \(-0.523477\pi\) | ||||
−0.0736891 | + | 0.997281i | \(0.523477\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 564.393 | 0.539915 | 0.269958 | − | 0.962872i | \(-0.412990\pi\) | ||||
0.269958 | + | 0.962872i | \(0.412990\pi\) | |||||||
\(104\) | −820.202 | −0.773340 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −646.742 | −0.592615 | ||||||||
\(107\) | 2111.34 | 1.90758 | 0.953788 | − | 0.300480i | \(-0.0971468\pi\) | ||||
0.953788 | + | 0.300480i | \(0.0971468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 240.393 | 0.211243 | 0.105621 | − | 0.994406i | \(-0.466317\pi\) | ||||
0.105621 | + | 0.994406i | \(0.466317\pi\) | |||||||
\(110\) | 10.0833 | 0.00874008 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2739.07 | −2.31088 | ||||||||
\(113\) | −548.514 | −0.456636 | −0.228318 | − | 0.973587i | \(-0.573323\pi\) | ||||
−0.228318 | + | 0.973587i | \(0.573323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −508.076 | −0.411986 | ||||||||
\(116\) | 275.268 | 0.220328 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1339.82 | 1.04525 | ||||||||
\(119\) | −1521.39 | −1.17198 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.57 | −0.999678 | ||||||||
\(122\) | 119.210 | 0.0884650 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −79.2195 | −0.0573719 | ||||||||
\(125\) | 1109.50 | 0.793894 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2477.98 | −1.73138 | −0.865690 | − | 0.500581i | \(-0.833120\pi\) | ||||
−0.865690 | + | 0.500581i | \(0.833120\pi\) | |||||||
\(128\) | −1739.52 | −1.20120 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −652.598 | −0.440282 | ||||||||
\(131\) | −240.252 | −0.160236 | −0.0801180 | − | 0.996785i | \(-0.525530\pi\) | ||||
−0.0801180 | + | 0.996785i | \(0.525530\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2883.59 | −1.87999 | ||||||||
\(134\) | −1863.39 | −1.20129 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −809.148 | −0.510176 | ||||||||
\(137\) | −143.473 | −0.0894728 | −0.0447364 | − | 0.998999i | \(-0.514245\pi\) | ||||
−0.0447364 | + | 0.998999i | \(0.514245\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −340.457 | −0.207750 | −0.103875 | − | 0.994590i | \(-0.533124\pi\) | ||||
−0.103875 | + | 0.994590i | \(0.533124\pi\) | |||||||
\(140\) | −326.441 | −0.197066 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2839.31 | −1.67795 | ||||||||
\(143\) | −27.7539 | −0.0162301 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −740.348 | −0.424017 | ||||||||
\(146\) | −487.750 | −0.276483 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −600.333 | −0.333426 | ||||||||
\(149\) | 1418.37 | 0.779847 | 0.389923 | − | 0.920847i | \(-0.372501\pi\) | ||||
0.389923 | + | 0.920847i | \(0.372501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 335.359 | 0.180736 | 0.0903679 | − | 0.995908i | \(-0.471196\pi\) | ||||
0.0903679 | + | 0.995908i | \(0.471196\pi\) | |||||||
\(152\) | −1533.63 | −0.818380 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −74.6946 | −0.0390848 | ||||||||
\(155\) | 213.065 | 0.110411 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2823.71 | 1.43539 | 0.717697 | − | 0.696355i | \(-0.245196\pi\) | ||||
0.717697 | + | 0.696355i | \(0.245196\pi\) | |||||||
\(158\) | −199.906 | −0.100656 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −398.594 | −0.196948 | ||||||||
\(161\) | 3763.69 | 1.84236 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1947.03 | 0.935603 | 0.467802 | − | 0.883833i | \(-0.345046\pi\) | ||||
0.467802 | + | 0.883833i | \(0.345046\pi\) | |||||||
\(164\) | 414.595 | 0.197405 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2616.68 | 1.22346 | ||||||||
\(167\) | 2376.81 | 1.10134 | 0.550669 | − | 0.834724i | \(-0.314373\pi\) | ||||
0.550669 | + | 0.834724i | \(0.314373\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −400.753 | −0.182409 | ||||||||
\(170\) | −643.803 | −0.290456 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −161.061 | −0.0713999 | ||||||||
\(173\) | −820.399 | −0.360542 | −0.180271 | − | 0.983617i | \(-0.557697\pi\) | ||||
−0.180271 | + | 0.983617i | \(0.557697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3670.45 | −1.58549 | ||||||||
\(176\) | −49.2940 | −0.0211118 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1886.74 | 0.794479 | ||||||||
\(179\) | 2688.77 | 1.12273 | 0.561364 | − | 0.827569i | \(-0.310277\pi\) | ||||
0.561364 | + | 0.827569i | \(0.310277\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2543.72 | 1.04460 | 0.522301 | − | 0.852761i | \(-0.325074\pi\) | ||||
0.522301 | + | 0.852761i | \(0.325074\pi\) | |||||||
\(182\) | 4834.27 | 1.96890 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2001.70 | 0.801998 | ||||||||
\(185\) | 1614.62 | 0.641673 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.3799 | −0.0107070 | ||||||||
\(188\) | 294.704 | 0.114327 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1220.24 | −0.465924 | ||||||||
\(191\) | −2251.64 | −0.852999 | −0.426499 | − | 0.904488i | \(-0.640253\pi\) | ||||
−0.426499 | + | 0.904488i | \(0.640253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 889.559 | 0.331771 | 0.165886 | − | 0.986145i | \(-0.446952\pi\) | ||||
0.165886 | + | 0.986145i | \(0.446952\pi\) | |||||||
\(194\) | 1553.90 | 0.575071 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1791.74 | 0.652968 | ||||||||
\(197\) | −3780.75 | −1.36735 | −0.683673 | − | 0.729788i | \(-0.739619\pi\) | ||||
−0.683673 | + | 0.729788i | \(0.739619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −118.565 | −0.0422355 | −0.0211178 | − | 0.999777i | \(-0.506722\pi\) | ||||
−0.0211178 | + | 0.999777i | \(0.506722\pi\) | |||||||
\(200\) | −1952.12 | −0.690177 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 468.934 | 0.163337 | ||||||||
\(203\) | 5484.29 | 1.89617 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1115.07 | −0.379903 | ||||||||
\(206\) | −1769.20 | −0.598380 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3190.33 | 1.06351 | ||||||||
\(209\) | −51.8948 | −0.0171753 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −919.251 | −0.299924 | −0.149962 | − | 0.988692i | \(-0.547915\pi\) | ||||
−0.149962 | + | 0.988692i | \(0.547915\pi\) | |||||||
\(212\) | 376.809 | 0.122073 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6618.41 | −2.11414 | ||||||||
\(215\) | 433.181 | 0.137408 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1578.33 | −0.493750 | ||||||||
\(218\) | −753.561 | −0.234117 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.87482 | −0.00180037 | ||||||||
\(221\) | 1772.04 | 0.539368 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1530.63 | 0.459635 | 0.229817 | − | 0.973234i | \(-0.426187\pi\) | ||||
0.229817 | + | 0.973234i | \(0.426187\pi\) | |||||||
\(224\) | 2952.68 | 0.880732 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1719.43 | 0.506082 | ||||||||
\(227\) | 3079.49 | 0.900411 | 0.450205 | − | 0.892925i | \(-0.351351\pi\) | ||||
0.450205 | + | 0.892925i | \(0.351351\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1241.32 | 0.358205 | 0.179103 | − | 0.983830i | \(-0.442681\pi\) | ||||
0.179103 | + | 0.983830i | \(0.442681\pi\) | |||||||
\(230\) | 1592.67 | 0.456597 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2916.80 | 0.825420 | ||||||||
\(233\) | −421.662 | −0.118558 | −0.0592789 | − | 0.998241i | \(-0.518880\pi\) | ||||
−0.0592789 | + | 0.998241i | \(0.518880\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −792.623 | −0.220021 | ||||||||
\(236\) | −780.612 | −0.215312 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4769.12 | 1.29889 | ||||||||
\(239\) | −239.000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −990.944 | −0.264864 | −0.132432 | − | 0.991192i | \(-0.542279\pi\) | ||||
−0.132432 | + | 0.991192i | \(0.542279\pi\) | |||||||
\(242\) | 4170.95 | 1.10793 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −69.4547 | −0.0182229 | ||||||||
\(245\) | −4818.98 | −1.25663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3358.66 | 0.865208 | ||||||||
\(248\) | −839.427 | −0.214934 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3477.95 | −0.879861 | ||||||||
\(251\) | 745.327 | 0.187429 | 0.0937144 | − | 0.995599i | \(-0.470126\pi\) | ||||
0.0937144 | + | 0.995599i | \(0.470126\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 67.7336 | 0.0168315 | ||||||||
\(254\) | 7767.73 | 1.91886 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2670.21 | 0.651906 | ||||||||
\(257\) | 1146.21 | 0.278205 | 0.139102 | − | 0.990278i | \(-0.455578\pi\) | ||||
0.139102 | + | 0.990278i | \(0.455578\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11960.7 | −2.86951 | ||||||||
\(260\) | 380.221 | 0.0906935 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 753.119 | 0.177587 | ||||||||
\(263\) | 6051.57 | 1.41884 | 0.709421 | − | 0.704785i | \(-0.248956\pi\) | ||||
0.709421 | + | 0.704785i | \(0.248956\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1013.45 | −0.234927 | ||||||||
\(266\) | 9039.21 | 2.08357 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1085.66 | 0.247453 | ||||||||
\(269\) | 4009.38 | 0.908758 | 0.454379 | − | 0.890808i | \(-0.349861\pi\) | ||||
0.454379 | + | 0.890808i | \(0.349861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6262.91 | 1.40386 | 0.701928 | − | 0.712248i | \(-0.252323\pi\) | ||||
0.701928 | + | 0.712248i | \(0.252323\pi\) | |||||||
\(272\) | 3147.33 | 0.701600 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 449.747 | 0.0991613 | ||||||||
\(275\) | −66.0556 | −0.0144847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6892.58 | −1.49507 | −0.747536 | − | 0.664222i | \(-0.768763\pi\) | ||||
−0.747536 | + | 0.664222i | \(0.768763\pi\) | |||||||
\(278\) | 1067.23 | 0.230246 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3459.04 | −0.738275 | ||||||||
\(281\) | 1312.21 | 0.278577 | 0.139288 | − | 0.990252i | \(-0.455518\pi\) | ||||
0.139288 | + | 0.990252i | \(0.455518\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5425.57 | 1.13963 | 0.569817 | − | 0.821771i | \(-0.307014\pi\) | ||||
0.569817 | + | 0.821771i | \(0.307014\pi\) | |||||||
\(284\) | 1654.26 | 0.345641 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 87.0003 | 0.0179875 | ||||||||
\(287\) | 8260.17 | 1.69889 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3164.84 | −0.644177 | ||||||||
\(290\) | 2320.77 | 0.469932 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 284.176 | 0.0569526 | ||||||||
\(293\) | −7531.35 | −1.50166 | −0.750830 | − | 0.660496i | \(-0.770346\pi\) | ||||
−0.750830 | + | 0.660496i | \(0.770346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2099.50 | 0.414364 | ||||||||
\(296\) | −6361.26 | −1.24912 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4446.16 | −0.864292 | ||||||||
\(299\) | −4383.75 | −0.847888 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3208.89 | −0.614476 | ||||||||
\(302\) | −1051.25 | −0.200307 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5965.34 | 1.12545 | ||||||||
\(305\) | 186.802 | 0.0350697 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 591.840 | 0.110026 | 0.0550132 | − | 0.998486i | \(-0.482480\pi\) | ||||
0.0550132 | + | 0.998486i | \(0.482480\pi\) | |||||||
\(308\) | 43.5191 | 0.00805107 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −667.895 | −0.122367 | ||||||||
\(311\) | 9484.96 | 1.72940 | 0.864699 | − | 0.502290i | \(-0.167509\pi\) | ||||
0.864699 | + | 0.502290i | \(0.167509\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4919.24 | −0.888344 | −0.444172 | − | 0.895942i | \(-0.646502\pi\) | ||||
−0.444172 | + | 0.895942i | \(0.646502\pi\) | |||||||
\(314\) | −8851.51 | −1.59083 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 116.471 | 0.0207341 | ||||||||
\(317\) | −496.312 | −0.0879358 | −0.0439679 | − | 0.999033i | \(-0.514000\pi\) | ||||
−0.0439679 | + | 0.999033i | \(0.514000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 98.6986 | 0.0173231 | ||||||||
\(320\) | −1708.60 | −0.298480 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11798.1 | −2.04186 | ||||||||
\(323\) | 3313.39 | 0.570781 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4275.15 | 0.729669 | ||||||||
\(326\) | −6103.37 | −1.03691 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4393.14 | 0.739545 | ||||||||
\(329\) | 5871.53 | 0.983915 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2231.61 | −0.370575 | −0.185287 | − | 0.982684i | \(-0.559322\pi\) | ||||
−0.185287 | + | 0.982684i | \(0.559322\pi\) | |||||||
\(332\) | −1524.55 | −0.252019 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7450.61 | −1.22060 | ||||||||
\(335\) | −2919.95 | −0.476220 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3569.71 | −0.577016 | −0.288508 | − | 0.957478i | \(-0.593159\pi\) | ||||
−0.288508 | + | 0.957478i | \(0.593159\pi\) | |||||||
\(338\) | 1256.24 | 0.202161 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 375.097 | 0.0598308 | ||||||||
\(341\) | −28.4045 | −0.00451082 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 23216.8 | 3.65478 | ||||||||
\(344\) | −1706.64 | −0.267487 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2571.71 | 0.399583 | ||||||||
\(347\) | −5048.57 | −0.781042 | −0.390521 | − | 0.920594i | \(-0.627705\pi\) | ||||
−0.390521 | + | 0.920594i | \(0.627705\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1860.49 | 0.285358 | 0.142679 | − | 0.989769i | \(-0.454428\pi\) | ||||
0.142679 | + | 0.989769i | \(0.454428\pi\) | |||||||
\(350\) | 11505.8 | 1.75717 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 53.1381 | 0.00804622 | ||||||||
\(353\) | 11335.4 | 1.70912 | 0.854562 | − | 0.519349i | \(-0.173825\pi\) | ||||
0.854562 | + | 0.519349i | \(0.173825\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4449.20 | −0.665181 | ||||||||
\(356\) | −1099.27 | −0.163654 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8428.50 | −1.24430 | ||||||||
\(359\) | 3148.65 | 0.462895 | 0.231447 | − | 0.972847i | \(-0.425654\pi\) | ||||
0.231447 | + | 0.972847i | \(0.425654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −578.917 | −0.0844025 | ||||||||
\(362\) | −7973.80 | −1.15772 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2816.57 | −0.405573 | ||||||||
\(365\) | −764.307 | −0.109604 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6448.54 | 0.917197 | 0.458598 | − | 0.888644i | \(-0.348352\pi\) | ||||
0.458598 | + | 0.888644i | \(0.348352\pi\) | |||||||
\(368\) | −7786.01 | −1.10292 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5061.37 | −0.711157 | ||||||||
\(371\) | 7507.35 | 1.05057 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1545.86 | −0.214588 | −0.107294 | − | 0.994227i | \(-0.534219\pi\) | ||||
−0.107294 | + | 0.994227i | \(0.534219\pi\) | |||||||
\(374\) | 85.8279 | 0.0118665 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3122.75 | 0.428308 | ||||||||
\(377\) | −6387.82 | −0.872651 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6544.96 | −0.887050 | −0.443525 | − | 0.896262i | \(-0.646272\pi\) | ||||
−0.443525 | + | 0.896262i | \(0.646272\pi\) | |||||||
\(380\) | 710.945 | 0.0959755 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7058.21 | 0.945366 | ||||||||
\(383\) | 14067.3 | 1.87677 | 0.938386 | − | 0.345590i | \(-0.112321\pi\) | ||||
0.938386 | + | 0.345590i | \(0.112321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −117.047 | −0.0154942 | ||||||||
\(386\) | −2788.50 | −0.367697 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −905.345 | −0.118459 | ||||||||
\(389\) | 7313.15 | 0.953191 | 0.476595 | − | 0.879123i | \(-0.341871\pi\) | ||||
0.476595 | + | 0.879123i | \(0.341871\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4324.67 | −0.559355 | ||||||||
\(392\) | 18985.7 | 2.44623 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11851.5 | 1.51541 | ||||||||
\(395\) | −313.254 | −0.0399025 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3707.91 | 0.468752 | 0.234376 | − | 0.972146i | \(-0.424695\pi\) | ||||
0.234376 | + | 0.972146i | \(0.424695\pi\) | |||||||
\(398\) | 371.667 | 0.0468090 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7593.12 | 0.949140 | ||||||||
\(401\) | 6435.24 | 0.801398 | 0.400699 | − | 0.916210i | \(-0.368767\pi\) | ||||
0.400699 | + | 0.916210i | \(0.368767\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1838.35 | 0.227233 | ||||||||
\(404\) | −273.213 | −0.0336457 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17191.6 | −2.10149 | ||||||||
\(407\) | −215.252 | −0.0262153 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9429.39 | −1.13998 | −0.569992 | − | 0.821650i | \(-0.693054\pi\) | ||||
−0.569992 | + | 0.821650i | \(0.693054\pi\) | |||||||
\(410\) | 3495.43 | 0.421041 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1030.78 | 0.123260 | ||||||||
\(413\) | −15552.5 | −1.85300 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4100.35 | 0.485008 | ||||||||
\(416\) | −3439.12 | −0.405329 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 162.675 | 0.0190351 | ||||||||
\(419\) | −8421.77 | −0.981934 | −0.490967 | − | 0.871178i | \(-0.663356\pi\) | ||||
−0.490967 | + | 0.871178i | \(0.663356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8329.85 | −0.964304 | −0.482152 | − | 0.876088i | \(-0.660145\pi\) | ||||
−0.482152 | + | 0.876088i | \(0.660145\pi\) | |||||||
\(422\) | 2881.58 | 0.332401 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3992.75 | 0.457324 | ||||||||
\(425\) | 4217.53 | 0.481365 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1383.78 | −0.156828 | ||||||||
\(428\) | 3856.06 | 0.435490 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1357.89 | −0.152287 | ||||||||
\(431\) | −5846.23 | −0.653372 | −0.326686 | − | 0.945133i | \(-0.605932\pi\) | ||||
−0.326686 | + | 0.945133i | \(0.605932\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11619.0 | 1.28954 | 0.644772 | − | 0.764375i | \(-0.276952\pi\) | ||||
0.644772 | + | 0.764375i | \(0.276952\pi\) | |||||||
\(434\) | 4947.58 | 0.547216 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 439.044 | 0.0482257 | ||||||||
\(437\) | −8196.82 | −0.897270 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10508.6 | 1.14248 | 0.571240 | − | 0.820783i | \(-0.306463\pi\) | ||||
0.571240 | + | 0.820783i | \(0.306463\pi\) | |||||||
\(440\) | −62.2509 | −0.00674476 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5554.82 | −0.597773 | ||||||||
\(443\) | 11819.1 | 1.26759 | 0.633793 | − | 0.773503i | \(-0.281497\pi\) | ||||
0.633793 | + | 0.773503i | \(0.281497\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2956.53 | 0.314951 | ||||||||
\(446\) | −4798.07 | −0.509406 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12656.8 | 1.33478 | ||||||||
\(449\) | −9424.13 | −0.990539 | −0.495269 | − | 0.868739i | \(-0.664931\pi\) | ||||
−0.495269 | + | 0.868739i | \(0.664931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 148.655 | 0.0155208 | ||||||||
\(452\) | −1001.78 | −0.104248 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9653.30 | −0.997912 | ||||||||
\(455\) | 7575.32 | 0.780520 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8426.48 | 0.862526 | 0.431263 | − | 0.902226i | \(-0.358068\pi\) | ||||
0.431263 | + | 0.902226i | \(0.358068\pi\) | |||||||
\(458\) | −3891.18 | −0.396993 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −927.931 | −0.0940543 | ||||||||
\(461\) | −11913.7 | −1.20363 | −0.601817 | − | 0.798634i | \(-0.705557\pi\) | ||||
−0.601817 | + | 0.798634i | \(0.705557\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10300.0 | 1.03386 | 0.516932 | − | 0.856026i | \(-0.327074\pi\) | ||||
0.516932 | + | 0.856026i | \(0.327074\pi\) | |||||||
\(464\) | −11345.5 | −1.13513 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1321.78 | 0.131396 | ||||||||
\(467\) | −1463.70 | −0.145036 | −0.0725179 | − | 0.997367i | \(-0.523103\pi\) | ||||
−0.0725179 | + | 0.997367i | \(0.523103\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21630.2 | 2.12961 | ||||||||
\(470\) | 2484.64 | 0.243846 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8271.54 | −0.806628 | ||||||||
\(473\) | −57.7490 | −0.00561375 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7993.75 | 0.772165 | ||||||||
\(476\) | −2778.62 | −0.267558 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 749.194 | 0.0716890 | ||||||||
\(479\) | 400.076 | 0.0381627 | 0.0190813 | − | 0.999818i | \(-0.493926\pi\) | ||||
0.0190813 | + | 0.999818i | \(0.493926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13931.2 | 1.32060 | ||||||||
\(482\) | 3106.32 | 0.293545 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2430.10 | −0.228222 | ||||||||
\(485\) | 2434.97 | 0.227972 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14121.7 | 1.31400 | 0.656999 | − | 0.753891i | \(-0.271825\pi\) | ||||
0.656999 | + | 0.753891i | \(0.271825\pi\) | |||||||
\(488\) | −735.957 | −0.0682689 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15106.1 | 1.39270 | ||||||||
\(491\) | −11270.3 | −1.03589 | −0.517945 | − | 0.855414i | \(-0.673303\pi\) | ||||
−0.517945 | + | 0.855414i | \(0.673303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6301.73 | −0.575691 | ||||||||
\(494\) | −10528.4 | −0.958896 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3265.11 | 0.295580 | ||||||||
\(497\) | 32958.5 | 2.97463 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11360.2 | 1.01915 | 0.509573 | − | 0.860428i | \(-0.329803\pi\) | ||||
0.509573 | + | 0.860428i | \(0.329803\pi\) | |||||||
\(500\) | 2026.35 | 0.181242 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2336.38 | −0.207724 | ||||||||
\(503\) | 16393.5 | 1.45318 | 0.726589 | − | 0.687073i | \(-0.241105\pi\) | ||||
0.726589 | + | 0.687073i | \(0.241105\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 734.821 | 0.0647507 | ||||||||
\(506\) | −212.325 | −0.0186541 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4525.69 | −0.395265 | ||||||||
\(509\) | −9306.18 | −0.810391 | −0.405196 | − | 0.914230i | \(-0.632797\pi\) | ||||
−0.405196 | + | 0.914230i | \(0.632797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5661.77 | 0.490141 | ||||||||
\(512\) | 5545.88 | 0.478703 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3593.03 | −0.308330 | ||||||||
\(515\) | −2772.35 | −0.237212 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 105.668 | 0.00898888 | ||||||||
\(518\) | 37493.2 | 3.18023 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4028.91 | 0.339768 | ||||||||
\(521\) | −19266.7 | −1.62014 | −0.810068 | − | 0.586337i | \(-0.800570\pi\) | ||||
−0.810068 | + | 0.586337i | \(0.800570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11768.3 | −0.983920 | −0.491960 | − | 0.870618i | \(-0.663719\pi\) | ||||
−0.491960 | + | 0.870618i | \(0.663719\pi\) | |||||||
\(524\) | −438.787 | −0.0365811 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18969.9 | −1.57248 | ||||||||
\(527\) | 1813.58 | 0.149906 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1468.45 | −0.120691 | ||||||||
\(530\) | 3176.86 | 0.260366 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5266.48 | −0.429194 | ||||||||
\(533\) | −9621.01 | −0.781861 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10371.1 | −0.838095 | ||||||||
\(536\) | 11503.9 | 0.927041 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12568.2 | −1.00716 | ||||||||
\(539\) | 642.437 | 0.0513390 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17595.6 | 1.39833 | 0.699164 | − | 0.714962i | \(-0.253556\pi\) | ||||
0.699164 | + | 0.714962i | \(0.253556\pi\) | |||||||
\(542\) | −19632.4 | −1.55587 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3392.77 | −0.267397 | ||||||||
\(545\) | −1180.83 | −0.0928097 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15293.3 | 1.19542 | 0.597710 | − | 0.801713i | \(-0.296077\pi\) | ||||
0.597710 | + | 0.801713i | \(0.296077\pi\) | |||||||
\(548\) | −262.034 | −0.0204262 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 207.065 | 0.0160532 | ||||||||
\(551\) | −11944.1 | −0.923474 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2320.50 | 0.178440 | ||||||||
\(554\) | 21606.2 | 1.65696 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −621.798 | −0.0474283 | ||||||||
\(557\) | 7410.55 | 0.563725 | 0.281863 | − | 0.959455i | \(-0.409048\pi\) | ||||
0.281863 | + | 0.959455i | \(0.409048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3737.54 | 0.282793 | ||||||||
\(560\) | 13454.6 | 1.01529 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4113.40 | −0.308743 | ||||||||
\(563\) | 12331.7 | 0.923128 | 0.461564 | − | 0.887107i | \(-0.347288\pi\) | ||||
0.461564 | + | 0.887107i | \(0.347288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2694.35 | 0.200623 | ||||||||
\(566\) | −17007.6 | −1.26304 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17528.9 | 1.29488 | ||||||||
\(569\) | −5561.27 | −0.409738 | −0.204869 | − | 0.978789i | \(-0.565677\pi\) | ||||
−0.204869 | + | 0.978789i | \(0.565677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24919.9 | −1.82638 | −0.913192 | − | 0.407529i | \(-0.866390\pi\) | ||||
−0.913192 | + | 0.407529i | \(0.866390\pi\) | |||||||
\(572\) | −50.6887 | −0.00370525 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −25893.2 | −1.88286 | ||||||||
\(575\) | −10433.5 | −0.756708 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1269.21 | 0.0915733 | 0.0457866 | − | 0.998951i | \(-0.485421\pi\) | ||||
0.0457866 | + | 0.998951i | \(0.485421\pi\) | |||||||
\(578\) | 9920.84 | 0.713931 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1352.14 | −0.0968011 | ||||||||
\(581\) | −30374.3 | −2.16891 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 135.107 | 0.00959784 | ||||||||
\(584\) | 3011.19 | 0.213363 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23608.5 | 1.66427 | ||||||||
\(587\) | −3024.29 | −0.212651 | −0.106325 | − | 0.994331i | \(-0.533908\pi\) | ||||
−0.106325 | + | 0.994331i | \(0.533908\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3437.38 | 0.240467 | ||||||||
\(590\) | −6581.30 | −0.459234 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24743.3 | 1.71781 | ||||||||
\(593\) | −7958.20 | −0.551103 | −0.275552 | − | 0.961286i | \(-0.588860\pi\) | ||||
−0.275552 | + | 0.961286i | \(0.588860\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7473.23 | 0.514912 | ||||||||
\(596\) | 2590.45 | 0.178035 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13741.7 | 0.939702 | ||||||||
\(599\) | 15551.4 | 1.06079 | 0.530395 | − | 0.847751i | \(-0.322044\pi\) | ||||
0.530395 | + | 0.847751i | \(0.322044\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12402.8 | 0.841798 | 0.420899 | − | 0.907108i | \(-0.361715\pi\) | ||||
0.420899 | + | 0.907108i | \(0.361715\pi\) | |||||||
\(602\) | 10058.9 | 0.681015 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 612.486 | 0.0412611 | ||||||||
\(605\) | 6535.89 | 0.439209 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7545.59 | −0.504557 | −0.252278 | − | 0.967655i | \(-0.581180\pi\) | ||||
−0.252278 | + | 0.967655i | \(0.581180\pi\) | |||||||
\(608\) | −6430.53 | −0.428935 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −585.568 | −0.0388672 | ||||||||
\(611\) | −6838.85 | −0.452815 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3744.35 | 0.246710 | 0.123355 | − | 0.992363i | \(-0.460635\pi\) | ||||
0.123355 | + | 0.992363i | \(0.460635\pi\) | |||||||
\(614\) | −1855.24 | −0.121940 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 461.138 | 0.0301619 | ||||||||
\(617\) | 19319.9 | 1.26060 | 0.630300 | − | 0.776352i | \(-0.282932\pi\) | ||||
0.630300 | + | 0.776352i | \(0.282932\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4231.21 | −0.274744 | −0.137372 | − | 0.990520i | \(-0.543866\pi\) | ||||
−0.137372 | + | 0.990520i | \(0.543866\pi\) | |||||||
\(620\) | 389.133 | 0.0252064 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −29732.5 | −1.91667 | ||||||||
\(623\) | −21901.2 | −1.40843 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7158.95 | 0.458173 | ||||||||
\(626\) | 15420.3 | 0.984538 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5157.12 | 0.327694 | ||||||||
\(629\) | 13743.4 | 0.871204 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19238.3 | 1.21373 | 0.606866 | − | 0.794804i | \(-0.292426\pi\) | ||||
0.606866 | + | 0.794804i | \(0.292426\pi\) | |||||||
\(632\) | 1234.15 | 0.0776769 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1555.79 | 0.0974579 | ||||||||
\(635\) | 12172.1 | 0.760683 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41578.8 | −2.58620 | ||||||||
\(638\) | −309.391 | −0.0191989 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8544.70 | 0.527748 | ||||||||
\(641\) | 2485.24 | 0.153138 | 0.0765688 | − | 0.997064i | \(-0.475604\pi\) | ||||
0.0765688 | + | 0.997064i | \(0.475604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26682.8 | 1.63649 | 0.818247 | − | 0.574867i | \(-0.194946\pi\) | ||||
0.818247 | + | 0.574867i | \(0.194946\pi\) | |||||||
\(644\) | 6873.86 | 0.420602 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10386.5 | −0.632588 | ||||||||
\(647\) | 27899.1 | 1.69525 | 0.847624 | − | 0.530598i | \(-0.178033\pi\) | ||||
0.847624 | + | 0.530598i | \(0.178033\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −279.892 | −0.0169287 | ||||||||
\(650\) | −13401.3 | −0.808681 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3555.98 | 0.213594 | ||||||||
\(653\) | −2943.64 | −0.176406 | −0.0882032 | − | 0.996103i | \(-0.528112\pi\) | ||||
−0.0882032 | + | 0.996103i | \(0.528112\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1180.14 | 0.0703998 | ||||||||
\(656\) | −17088.0 | −1.01703 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18405.5 | −1.09046 | ||||||||
\(659\) | 23688.2 | 1.40025 | 0.700124 | − | 0.714021i | \(-0.253128\pi\) | ||||
0.700124 | + | 0.714021i | \(0.253128\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23515.5 | 1.38373 | 0.691867 | − | 0.722025i | \(-0.256788\pi\) | ||||
0.691867 | + | 0.722025i | \(0.256788\pi\) | |||||||
\(662\) | 6995.43 | 0.410702 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16154.4 | −0.944148 | ||||||||
\(665\) | 14164.5 | 0.825977 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15589.5 | 0.904989 | ||||||||
\(668\) | 4340.92 | 0.251430 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9153.17 | 0.527788 | ||||||||
\(671\) | −24.9033 | −0.00143276 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6923.43 | 0.396551 | 0.198275 | − | 0.980146i | \(-0.436466\pi\) | ||||
0.198275 | + | 0.980146i | \(0.436466\pi\) | |||||||
\(674\) | 11190.0 | 0.639498 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −731.920 | −0.0416431 | ||||||||
\(677\) | −22544.6 | −1.27985 | −0.639925 | − | 0.768437i | \(-0.721035\pi\) | ||||
−0.639925 | + | 0.768437i | \(0.721035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18037.6 | −1.01947 | ||||||||
\(680\) | 3974.61 | 0.224146 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 89.0396 | 0.00499927 | ||||||||
\(683\) | 18136.0 | 1.01604 | 0.508020 | − | 0.861345i | \(-0.330377\pi\) | ||||
0.508020 | + | 0.861345i | \(0.330377\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 704.755 | 0.0393099 | ||||||||
\(686\) | −72777.8 | −4.05054 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6638.28 | 0.367852 | ||||||||
\(689\) | −8744.16 | −0.483492 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16072.8 | −0.884858 | −0.442429 | − | 0.896803i | \(-0.645883\pi\) | ||||
−0.442429 | + | 0.896803i | \(0.645883\pi\) | |||||||
\(692\) | −1498.34 | −0.0823100 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15825.8 | 0.865617 | ||||||||
\(695\) | 1672.36 | 0.0912750 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9491.35 | −0.515797 | ||||||||
\(698\) | −5832.10 | −0.316258 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6703.57 | −0.361959 | ||||||||
\(701\) | 10999.4 | 0.592640 | 0.296320 | − | 0.955089i | \(-0.404240\pi\) | ||||
0.296320 | + | 0.955089i | \(0.404240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26048.8 | 1.39751 | ||||||||
\(704\) | 227.780 | 0.0121943 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35533.0 | −1.89420 | ||||||||
\(707\) | −5443.36 | −0.289559 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9279.33 | 0.491527 | 0.245763 | − | 0.969330i | \(-0.420961\pi\) | ||||
0.245763 | + | 0.969330i | \(0.420961\pi\) | |||||||
\(710\) | 13946.9 | 0.737210 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11648.1 | −0.613103 | ||||||||
\(713\) | −4486.50 | −0.235653 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 136.330 | 0.00713070 | ||||||||
\(716\) | 4910.67 | 0.256313 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9870.07 | −0.513019 | ||||||||
\(719\) | −4475.10 | −0.232119 | −0.116059 | − | 0.993242i | \(-0.537026\pi\) | ||||
−0.116059 | + | 0.993242i | \(0.537026\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20536.8 | 1.06079 | ||||||||
\(722\) | 1814.73 | 0.0935421 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4645.75 | 0.238478 | ||||||||
\(725\) | −15203.3 | −0.778808 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24722.2 | 1.26120 | 0.630601 | − | 0.776107i | \(-0.282808\pi\) | ||||
0.630601 | + | 0.776107i | \(0.282808\pi\) | |||||||
\(728\) | −29845.0 | −1.51941 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2395.87 | 0.121473 | ||||||||
\(731\) | 3687.18 | 0.186560 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2743.32 | 0.138236 | 0.0691180 | − | 0.997608i | \(-0.477982\pi\) | ||||
0.0691180 | + | 0.997608i | \(0.477982\pi\) | |||||||
\(734\) | −20214.3 | −1.01652 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8393.19 | 0.420349 | ||||||||
\(737\) | 389.269 | 0.0194558 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19302.2 | 0.960814 | 0.480407 | − | 0.877046i | \(-0.340489\pi\) | ||||
0.480407 | + | 0.877046i | \(0.340489\pi\) | |||||||
\(740\) | 2948.89 | 0.146491 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23533.3 | −1.16433 | ||||||||
\(743\) | −33863.2 | −1.67203 | −0.836017 | − | 0.548704i | \(-0.815121\pi\) | ||||
−0.836017 | + | 0.548704i | \(0.815121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6967.15 | −0.342626 | ||||||||
\(746\) | 4845.80 | 0.237825 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −50.0056 | −0.00244437 | ||||||||
\(749\) | 76826.1 | 3.74789 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30272.2 | −1.47090 | −0.735451 | − | 0.677578i | \(-0.763029\pi\) | ||||
−0.735451 | + | 0.677578i | \(0.763029\pi\) | |||||||
\(752\) | −12146.5 | −0.589014 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20023.9 | 0.967145 | ||||||||
\(755\) | −1647.31 | −0.0794064 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2202.96 | −0.105770 | −0.0528849 | − | 0.998601i | \(-0.516842\pi\) | ||||
−0.0528849 | + | 0.998601i | \(0.516842\pi\) | |||||||
\(758\) | 20516.5 | 0.983104 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7533.32 | 0.359556 | ||||||||
\(761\) | −4867.98 | −0.231885 | −0.115942 | − | 0.993256i | \(-0.536989\pi\) | ||||
−0.115942 | + | 0.993256i | \(0.536989\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8747.28 | 0.415037 | ||||||||
\(764\) | −4112.30 | −0.194736 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −44096.7 | −2.08000 | ||||||||
\(767\) | 18114.7 | 0.852784 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1744.23 | −0.0817928 | −0.0408964 | − | 0.999163i | \(-0.513021\pi\) | ||||
−0.0408964 | + | 0.999163i | \(0.513021\pi\) | |||||||
\(770\) | 366.907 | 0.0171719 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1624.66 | 0.0757418 | ||||||||
\(773\) | −31838.9 | −1.48145 | −0.740727 | − | 0.671806i | \(-0.765519\pi\) | ||||
−0.740727 | + | 0.671806i | \(0.765519\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4375.35 | 0.202797 | ||||||||
\(776\) | −9593.23 | −0.443785 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22924.5 | −1.05641 | ||||||||
\(779\) | −17989.5 | −0.827397 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 593.140 | 0.0271757 | ||||||||
\(782\) | 13556.6 | 0.619925 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −73848.5 | −3.36409 | ||||||||
\(785\) | −13870.3 | −0.630642 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6132.91 | −0.277782 | −0.138891 | − | 0.990308i | \(-0.544354\pi\) | ||||
−0.138891 | + | 0.990308i | \(0.544354\pi\) | |||||||
\(788\) | −6905.02 | −0.312159 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 981.957 | 0.0442234 | ||||||||
\(791\) | −19959.0 | −0.897169 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1611.75 | 0.0721752 | ||||||||
\(794\) | −11623.2 | −0.519510 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −216.543 | −0.00964217 | ||||||||
\(797\) | −40316.5 | −1.79182 | −0.895911 | − | 0.444233i | \(-0.853476\pi\) | ||||
−0.895911 | + | 0.444233i | \(0.853476\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6746.68 | −0.298724 | ||||||||
\(800\) | −8185.26 | −0.361741 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20172.6 | −0.888178 | ||||||||
\(803\) | 101.893 | 0.00447785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18487.6 | −0.809443 | ||||||||
\(806\) | −5762.68 | −0.251838 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2895.03 | −0.126048 | ||||||||
\(809\) | 1070.47 | 0.0465211 | 0.0232605 | − | 0.999729i | \(-0.492595\pi\) | ||||
0.0232605 | + | 0.999729i | \(0.492595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31220.1 | 1.35177 | 0.675885 | − | 0.737007i | \(-0.263761\pi\) | ||||
0.675885 | + | 0.737007i | \(0.263761\pi\) | |||||||
\(812\) | 10016.3 | 0.432886 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 674.750 | 0.0290540 | ||||||||
\(815\) | −9564.00 | −0.411058 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6988.53 | 0.299263 | ||||||||
\(818\) | 29558.4 | 1.26343 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2036.53 | −0.0867301 | ||||||||
\(821\) | −42159.9 | −1.79219 | −0.896096 | − | 0.443860i | \(-0.853609\pi\) | ||||
−0.896096 | + | 0.443860i | \(0.853609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1888.54 | 0.0799884 | 0.0399942 | − | 0.999200i | \(-0.487266\pi\) | ||||
0.0399942 | + | 0.999200i | \(0.487266\pi\) | |||||||
\(824\) | 10922.4 | 0.461773 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 48752.5 | 2.05365 | ||||||||
\(827\) | −8491.02 | −0.357027 | −0.178514 | − | 0.983937i | \(-0.557129\pi\) | ||||
−0.178514 | + | 0.983937i | \(0.557129\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30959.9 | 1.29708 | 0.648541 | − | 0.761180i | \(-0.275380\pi\) | ||||
0.648541 | + | 0.761180i | \(0.275380\pi\) | |||||||
\(830\) | −12853.4 | −0.537527 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14742.0 | −0.614288 | ||||||||
\(833\) | −41018.5 | −1.70613 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11675.1 | −0.483874 | ||||||||
\(836\) | −94.7787 | −0.00392104 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26399.7 | 1.08826 | ||||||||
\(839\) | 40700.5 | 1.67478 | 0.837389 | − | 0.546608i | \(-0.184081\pi\) | ||||
0.837389 | + | 0.546608i | \(0.184081\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1672.64 | −0.0685818 | ||||||||
\(842\) | 26111.6 | 1.06872 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1678.88 | −0.0684711 | ||||||||
\(845\) | 1968.54 | 0.0801416 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −48416.1 | −1.96410 | ||||||||
\(848\) | −15530.6 | −0.628918 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13220.7 | −0.533490 | ||||||||
\(851\) | −33999.1 | −1.36954 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38855.2 | 1.55964 | 0.779822 | − | 0.626001i | \(-0.215309\pi\) | ||||
0.779822 | + | 0.626001i | \(0.215309\pi\) | |||||||
\(854\) | 4337.73 | 0.173810 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 40859.7 | 1.63149 | ||||||||
\(857\) | 44433.6 | 1.77109 | 0.885544 | − | 0.464555i | \(-0.153786\pi\) | ||||
0.885544 | + | 0.464555i | \(0.153786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7511.88 | −0.298372 | −0.149186 | − | 0.988809i | \(-0.547665\pi\) | ||||
−0.149186 | + | 0.988809i | \(0.547665\pi\) | |||||||
\(860\) | 791.146 | 0.0313696 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18326.2 | 0.724122 | ||||||||
\(863\) | 8869.88 | 0.349866 | 0.174933 | − | 0.984580i | \(-0.444029\pi\) | ||||
0.174933 | + | 0.984580i | \(0.444029\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4029.87 | 0.158404 | ||||||||
\(866\) | −36422.0 | −1.42918 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2882.59 | −0.112721 | ||||||||
\(869\) | 41.7610 | 0.00163020 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25193.7 | −0.980086 | ||||||||
\(872\) | 4652.21 | 0.180669 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25694.6 | 0.994430 | ||||||||
\(875\) | 40371.9 | 1.55979 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42946.9 | −1.65361 | −0.826804 | − | 0.562491i | \(-0.809843\pi\) | ||||
−0.826804 | + | 0.562491i | \(0.809843\pi\) | |||||||
\(878\) | −32941.4 | −1.26619 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 242.137 | 0.00927548 | ||||||||
\(881\) | −10522.8 | −0.402409 | −0.201205 | − | 0.979549i | \(-0.564486\pi\) | ||||
−0.201205 | + | 0.979549i | \(0.564486\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33736.0 | −1.28574 | −0.642870 | − | 0.765975i | \(-0.722256\pi\) | ||||
−0.642870 | + | 0.765975i | \(0.722256\pi\) | |||||||
\(884\) | 3236.38 | 0.123135 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −37049.3 | −1.40485 | ||||||||
\(887\) | 13266.6 | 0.502196 | 0.251098 | − | 0.967962i | \(-0.419208\pi\) | ||||
0.251098 | + | 0.967962i | \(0.419208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −90167.3 | −3.40170 | ||||||||
\(890\) | −9267.85 | −0.349055 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2795.48 | 0.104932 | ||||||||
\(893\) | −12787.4 | −0.479187 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13207.5 | −0.493271 | ||||||||
\(896\) | −63296.8 | −2.36004 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29541.8 | 1.09780 | ||||||||
\(899\) | −6537.54 | −0.242535 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8626.32 | −0.318961 | ||||||||
\(902\) | −465.989 | −0.0172015 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10615.1 | −0.390546 | ||||||||
\(905\) | −12495.0 | −0.458947 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39503.9 | −1.44620 | −0.723100 | − | 0.690743i | \(-0.757284\pi\) | ||||
−0.723100 | + | 0.690743i | \(0.757284\pi\) | |||||||
\(908\) | 5624.27 | 0.205559 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −23746.4 | −0.865038 | ||||||||
\(911\) | 45573.3 | 1.65742 | 0.828711 | − | 0.559676i | \(-0.189075\pi\) | ||||
0.828711 | + | 0.559676i | \(0.189075\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −546.633 | −0.0198148 | ||||||||
\(914\) | −26414.5 | −0.955924 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2267.10 | 0.0817765 | ||||||||
\(917\) | −8742.16 | −0.314822 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43624.1 | −1.56586 | −0.782930 | − | 0.622110i | \(-0.786276\pi\) | ||||
−0.782930 | + | 0.622110i | \(0.786276\pi\) | |||||||
\(920\) | −9832.56 | −0.352358 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 37345.9 | 1.33397 | ||||||||
\(923\) | −38388.3 | −1.36898 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33156.8 | 1.17858 | ||||||||
\(926\) | −32287.3 | −1.14582 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12230.2 | 0.432625 | ||||||||
\(929\) | −40824.6 | −1.44178 | −0.720889 | − | 0.693050i | \(-0.756266\pi\) | ||||
−0.720889 | + | 0.693050i | \(0.756266\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −77744.9 | −2.73683 | ||||||||
\(932\) | −770.107 | −0.0270662 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4588.25 | 0.160741 | ||||||||
\(935\) | 134.493 | 0.00470415 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2247.16 | 0.0783474 | 0.0391737 | − | 0.999232i | \(-0.487527\pi\) | ||||
0.0391737 | + | 0.999232i | \(0.487527\pi\) | |||||||
\(938\) | −67804.2 | −2.36022 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1447.62 | −0.0502298 | ||||||||
\(941\) | 52797.3 | 1.82906 | 0.914528 | − | 0.404522i | \(-0.132562\pi\) | ||||
0.914528 | + | 0.404522i | \(0.132562\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23480.1 | 0.810835 | ||||||||
\(944\) | 32173.7 | 1.10929 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 181.026 | 0.00622163 | ||||||||
\(947\) | 8350.80 | 0.286552 | 0.143276 | − | 0.989683i | \(-0.454236\pi\) | ||||
0.143276 | + | 0.989683i | \(0.454236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6594.53 | −0.225572 | ||||||||
\(950\) | −25058.0 | −0.855779 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29442.8 | −1.00236 | ||||||||
\(953\) | −18670.3 | −0.634616 | −0.317308 | − | 0.948323i | \(-0.602779\pi\) | ||||
−0.317308 | + | 0.948323i | \(0.602779\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11060.2 | 0.374766 | ||||||||
\(956\) | −436.500 | −0.0147672 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1254.12 | −0.0422951 | ||||||||
\(959\) | −5220.63 | −0.175790 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27909.6 | −0.936845 | ||||||||
\(962\) | −43670.1 | −1.46360 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1809.82 | −0.0604673 | ||||||||
\(965\) | −4369.60 | −0.145764 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34012.8 | 1.13110 | 0.565551 | − | 0.824713i | \(-0.308663\pi\) | ||||
0.565551 | + | 0.824713i | \(0.308663\pi\) | |||||||
\(968\) | −25749.9 | −0.854993 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7632.91 | −0.252658 | ||||||||
\(971\) | 45188.5 | 1.49348 | 0.746739 | − | 0.665117i | \(-0.231619\pi\) | ||||
0.746739 | + | 0.665117i | \(0.231619\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12388.4 | −0.408174 | ||||||||
\(974\) | −44267.5 | −1.45628 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2862.64 | 0.0938842 | ||||||||
\(977\) | −21244.1 | −0.695658 | −0.347829 | − | 0.937558i | \(-0.613081\pi\) | ||||
−0.347829 | + | 0.937558i | \(0.613081\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −394.146 | −0.0128672 | ||||||||
\(980\) | −8801.20 | −0.286882 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 35329.1 | 1.14806 | ||||||||
\(983\) | 35357.8 | 1.14724 | 0.573621 | − | 0.819121i | \(-0.305538\pi\) | ||||
0.573621 | + | 0.819121i | \(0.305538\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18571.4 | 0.600745 | ||||||||
\(986\) | 19754.0 | 0.638030 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6134.12 | 0.197523 | ||||||||
\(989\) | −9121.49 | −0.293273 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21457.7 | 0.687815 | 0.343908 | − | 0.939003i | \(-0.388249\pi\) | ||||
0.343908 | + | 0.939003i | \(0.388249\pi\) | |||||||
\(992\) | −3519.73 | −0.112653 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −103315. | −3.29674 | ||||||||
\(995\) | 582.404 | 0.0185562 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26463.2 | −0.840621 | −0.420310 | − | 0.907380i | \(-0.638079\pi\) | ||||
−0.420310 | + | 0.907380i | \(0.638079\pi\) | |||||||
\(998\) | −35610.9 | −1.12950 | ||||||||
\(999\) | 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 | 2151.4.a.h.1.13 | yes | 59 | |
3.2 | odd | 2 | 2151.4.a.g.1.47 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.47 | ✓ | 59 | 3.2 | odd | 2 | ||
2151.4.a.h.1.13 | yes | 59 | 1.1 | even | 1 | trivial |