Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,4,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(107.088466660\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70156 | −0.955146 | −0.477573 | − | 0.878592i | \(-0.658483\pi\) | ||||
−0.477573 | + | 0.878592i | \(0.658483\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −0.701562 | −0.0876953 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −8.10469 | −0.551454 | ||||||||
\(7\) | 10.1047 | 0.545602 | 0.272801 | − | 0.962071i | \(-0.412050\pi\) | ||||
0.272801 | + | 0.962071i | \(0.412050\pi\) | |||||||
\(8\) | 23.5078 | 1.03891 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −13.5078 | −0.427154 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.10469 | −0.0506309 | ||||||||
\(13\) | 26.7016 | 0.569668 | 0.284834 | − | 0.958577i | \(-0.408062\pi\) | ||||
0.284834 | + | 0.958577i | \(0.408062\pi\) | |||||||
\(14\) | −27.2984 | −0.521130 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −57.8953 | −0.904614 | ||||||||
\(17\) | −36.1938 | −0.516369 | −0.258185 | − | 0.966096i | \(-0.583124\pi\) | ||||
−0.258185 | + | 0.966096i | \(0.583124\pi\) | |||||||
\(18\) | −24.3141 | −0.318382 | ||||||||
\(19\) | −66.3141 | −0.800710 | −0.400355 | − | 0.916360i | \(-0.631113\pi\) | ||||
−0.400355 | + | 0.916360i | \(0.631113\pi\) | |||||||
\(20\) | −3.50781 | −0.0392185 | ||||||||
\(21\) | 30.3141 | 0.315003 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 70.7484 | 0.641394 | 0.320697 | − | 0.947182i | \(-0.396083\pi\) | ||||
0.320697 | + | 0.947182i | \(0.396083\pi\) | |||||||
\(24\) | 70.5234 | 0.599814 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −72.1359 | −0.544116 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −7.08907 | −0.0478467 | ||||||||
\(29\) | −41.0891 | −0.263105 | −0.131553 | − | 0.991309i | \(-0.541996\pi\) | ||||
−0.131553 | + | 0.991309i | \(0.541996\pi\) | |||||||
\(30\) | −40.5234 | −0.246618 | ||||||||
\(31\) | −24.2672 | −0.140597 | −0.0702987 | − | 0.997526i | \(-0.522395\pi\) | ||||
−0.0702987 | + | 0.997526i | \(0.522395\pi\) | |||||||
\(32\) | −31.6547 | −0.174869 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 97.7797 | 0.493208 | ||||||||
\(35\) | 50.5234 | 0.244001 | ||||||||
\(36\) | −6.31406 | −0.0292318 | ||||||||
\(37\) | −367.423 | −1.63254 | −0.816271 | − | 0.577669i | \(-0.803962\pi\) | ||||
−0.816271 | + | 0.577669i | \(0.803962\pi\) | |||||||
\(38\) | 179.152 | 0.764795 | ||||||||
\(39\) | 80.1047 | 0.328898 | ||||||||
\(40\) | 117.539 | 0.464614 | ||||||||
\(41\) | −10.2094 | −0.0388887 | −0.0194443 | − | 0.999811i | \(-0.506190\pi\) | ||||
−0.0194443 | + | 0.999811i | \(0.506190\pi\) | |||||||
\(42\) | −81.8953 | −0.300874 | ||||||||
\(43\) | −79.8844 | −0.283308 | −0.141654 | − | 0.989916i | \(-0.545242\pi\) | ||||
−0.141654 | + | 0.989916i | \(0.545242\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −191.131 | −0.612625 | ||||||||
\(47\) | −99.3985 | −0.308484 | −0.154242 | − | 0.988033i | \(-0.549294\pi\) | ||||
−0.154242 | + | 0.988033i | \(0.549294\pi\) | |||||||
\(48\) | −173.686 | −0.522279 | ||||||||
\(49\) | −240.895 | −0.702319 | ||||||||
\(50\) | −67.5391 | −0.191029 | ||||||||
\(51\) | −108.581 | −0.298126 | ||||||||
\(52\) | −18.7328 | −0.0499572 | ||||||||
\(53\) | −460.298 | −1.19296 | −0.596480 | − | 0.802628i | \(-0.703434\pi\) | ||||
−0.596480 | + | 0.802628i | \(0.703434\pi\) | |||||||
\(54\) | −72.9422 | −0.183818 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 237.539 | 0.566830 | ||||||||
\(57\) | −198.942 | −0.462290 | ||||||||
\(58\) | 111.005 | 0.251304 | ||||||||
\(59\) | −753.475 | −1.66261 | −0.831306 | − | 0.555815i | \(-0.812406\pi\) | ||||
−0.831306 | + | 0.555815i | \(0.812406\pi\) | |||||||
\(60\) | −10.5234 | −0.0226428 | ||||||||
\(61\) | 424.183 | 0.890345 | 0.445172 | − | 0.895445i | \(-0.353142\pi\) | ||||
0.445172 | + | 0.895445i | \(0.353142\pi\) | |||||||
\(62\) | 65.5593 | 0.134291 | ||||||||
\(63\) | 90.9422 | 0.181867 | ||||||||
\(64\) | 548.680 | 1.07164 | ||||||||
\(65\) | 133.508 | 0.254763 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1049.23 | −1.91320 | −0.956600 | − | 0.291405i | \(-0.905877\pi\) | ||||
−0.956600 | + | 0.291405i | \(0.905877\pi\) | |||||||
\(68\) | 25.3922 | 0.0452831 | ||||||||
\(69\) | 212.245 | 0.370309 | ||||||||
\(70\) | −136.492 | −0.233056 | ||||||||
\(71\) | 263.695 | 0.440773 | 0.220386 | − | 0.975413i | \(-0.429268\pi\) | ||||
0.220386 | + | 0.975413i | \(0.429268\pi\) | |||||||
\(72\) | 211.570 | 0.346303 | ||||||||
\(73\) | 117.550 | 0.188468 | 0.0942342 | − | 0.995550i | \(-0.469960\pi\) | ||||
0.0942342 | + | 0.995550i | \(0.469960\pi\) | |||||||
\(74\) | 992.617 | 1.55932 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 46.5234 | 0.0702185 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −216.408 | −0.314146 | ||||||||
\(79\) | 707.408 | 1.00746 | 0.503732 | − | 0.863860i | \(-0.331960\pi\) | ||||
0.503732 | + | 0.863860i | \(0.331960\pi\) | |||||||
\(80\) | −289.477 | −0.404556 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 27.5813 | 0.0371444 | ||||||||
\(83\) | 535.758 | 0.708519 | 0.354259 | − | 0.935147i | \(-0.384733\pi\) | ||||
0.354259 | + | 0.935147i | \(0.384733\pi\) | |||||||
\(84\) | −21.2672 | −0.0276243 | ||||||||
\(85\) | −180.969 | −0.230927 | ||||||||
\(86\) | 215.813 | 0.270601 | ||||||||
\(87\) | −123.267 | −0.151904 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −823.287 | −0.980543 | −0.490271 | − | 0.871570i | \(-0.663102\pi\) | ||||
−0.490271 | + | 0.871570i | \(0.663102\pi\) | |||||||
\(90\) | −121.570 | −0.142385 | ||||||||
\(91\) | 269.811 | 0.310812 | ||||||||
\(92\) | −49.6344 | −0.0562472 | ||||||||
\(93\) | −72.8016 | −0.0811739 | ||||||||
\(94\) | 268.531 | 0.294648 | ||||||||
\(95\) | −331.570 | −0.358088 | ||||||||
\(96\) | −94.9641 | −0.100961 | ||||||||
\(97\) | 128.481 | 0.134488 | 0.0672438 | − | 0.997737i | \(-0.478579\pi\) | ||||
0.0672438 | + | 0.997737i | \(0.478579\pi\) | |||||||
\(98\) | 650.794 | 0.670817 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −17.5391 | −0.0175391 | ||||||||
\(101\) | 225.748 | 0.222404 | 0.111202 | − | 0.993798i | \(-0.464530\pi\) | ||||
0.111202 | + | 0.993798i | \(0.464530\pi\) | |||||||
\(102\) | 293.339 | 0.284754 | ||||||||
\(103\) | −979.798 | −0.937305 | −0.468652 | − | 0.883383i | \(-0.655260\pi\) | ||||
−0.468652 | + | 0.883383i | \(0.655260\pi\) | |||||||
\(104\) | 627.695 | 0.591833 | ||||||||
\(105\) | 151.570 | 0.140874 | ||||||||
\(106\) | 1243.52 | 1.13945 | ||||||||
\(107\) | −185.961 | −0.168014 | −0.0840071 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840071 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(108\) | −18.9422 | −0.0168770 | ||||||||
\(109\) | 5.66566 | 0.00497864 | 0.00248932 | − | 0.999997i | \(-0.499208\pi\) | ||||
0.00248932 | + | 0.999997i | \(0.499208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1102.27 | −0.942548 | ||||||||
\(112\) | −585.014 | −0.493559 | ||||||||
\(113\) | 415.311 | 0.345745 | 0.172872 | − | 0.984944i | \(-0.444695\pi\) | ||||
0.172872 | + | 0.984944i | \(0.444695\pi\) | |||||||
\(114\) | 537.455 | 0.441555 | ||||||||
\(115\) | 353.742 | 0.286840 | ||||||||
\(116\) | 28.8265 | 0.0230731 | ||||||||
\(117\) | 240.314 | 0.189889 | ||||||||
\(118\) | 2035.56 | 1.58804 | ||||||||
\(119\) | −365.727 | −0.281732 | ||||||||
\(120\) | 352.617 | 0.268245 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1145.96 | −0.850410 | ||||||||
\(123\) | −30.6281 | −0.0224524 | ||||||||
\(124\) | 17.0249 | 0.0123297 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −245.686 | −0.173710 | ||||||||
\(127\) | 113.159 | 0.0790650 | 0.0395325 | − | 0.999218i | \(-0.487413\pi\) | ||||
0.0395325 | + | 0.999218i | \(0.487413\pi\) | |||||||
\(128\) | −1229.05 | −0.848704 | ||||||||
\(129\) | −239.653 | −0.163568 | ||||||||
\(130\) | −360.680 | −0.243336 | ||||||||
\(131\) | 943.106 | 0.629004 | 0.314502 | − | 0.949257i | \(-0.398162\pi\) | ||||
0.314502 | + | 0.949257i | \(0.398162\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −670.083 | −0.436869 | ||||||||
\(134\) | 2834.57 | 1.82739 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | −850.836 | −0.536460 | ||||||||
\(137\) | 2767.42 | 1.72582 | 0.862909 | − | 0.505359i | \(-0.168640\pi\) | ||||
0.862909 | + | 0.505359i | \(0.168640\pi\) | |||||||
\(138\) | −573.394 | −0.353699 | ||||||||
\(139\) | −363.369 | −0.221731 | −0.110865 | − | 0.993835i | \(-0.535362\pi\) | ||||
−0.110865 | + | 0.993835i | \(0.535362\pi\) | |||||||
\(140\) | −35.4453 | −0.0213977 | ||||||||
\(141\) | −298.195 | −0.178103 | ||||||||
\(142\) | −712.389 | −0.421003 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −521.058 | −0.301538 | ||||||||
\(145\) | −205.445 | −0.117664 | ||||||||
\(146\) | −317.569 | −0.180015 | ||||||||
\(147\) | −722.686 | −0.405484 | ||||||||
\(148\) | 257.770 | 0.143166 | ||||||||
\(149\) | −161.100 | −0.0885760 | −0.0442880 | − | 0.999019i | \(-0.514102\pi\) | ||||
−0.0442880 | + | 0.999019i | \(0.514102\pi\) | |||||||
\(150\) | −202.617 | −0.110291 | ||||||||
\(151\) | 176.217 | 0.0949693 | 0.0474846 | − | 0.998872i | \(-0.484879\pi\) | ||||
0.0474846 | + | 0.998872i | \(0.484879\pi\) | |||||||
\(152\) | −1558.90 | −0.831864 | ||||||||
\(153\) | −325.744 | −0.172123 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −121.336 | −0.0628770 | ||||||||
\(156\) | −56.1984 | −0.0288428 | ||||||||
\(157\) | −137.895 | −0.0700971 | −0.0350485 | − | 0.999386i | \(-0.511159\pi\) | ||||
−0.0350485 | + | 0.999386i | \(0.511159\pi\) | |||||||
\(158\) | −1911.11 | −0.962275 | ||||||||
\(159\) | −1380.90 | −0.688755 | ||||||||
\(160\) | −158.273 | −0.0782039 | ||||||||
\(161\) | 714.891 | 0.349946 | ||||||||
\(162\) | −218.827 | −0.106127 | ||||||||
\(163\) | −952.656 | −0.457778 | −0.228889 | − | 0.973453i | \(-0.573509\pi\) | ||||
−0.228889 | + | 0.973453i | \(0.573509\pi\) | |||||||
\(164\) | 7.16251 | 0.00341035 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1447.38 | −0.676739 | ||||||||
\(167\) | −2100.45 | −0.973282 | −0.486641 | − | 0.873602i | \(-0.661778\pi\) | ||||
−0.486641 | + | 0.873602i | \(0.661778\pi\) | |||||||
\(168\) | 712.617 | 0.327260 | ||||||||
\(169\) | −1484.03 | −0.675479 | ||||||||
\(170\) | 488.898 | 0.220569 | ||||||||
\(171\) | −596.827 | −0.266903 | ||||||||
\(172\) | 56.0438 | 0.0248448 | ||||||||
\(173\) | −1040.22 | −0.457147 | −0.228573 | − | 0.973527i | \(-0.573406\pi\) | ||||
−0.228573 | + | 0.973527i | \(0.573406\pi\) | |||||||
\(174\) | 333.014 | 0.145090 | ||||||||
\(175\) | 252.617 | 0.109120 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2260.42 | −0.959909 | ||||||||
\(178\) | 2224.16 | 0.936562 | ||||||||
\(179\) | 1570.93 | 0.655959 | 0.327980 | − | 0.944685i | \(-0.393632\pi\) | ||||
0.327980 | + | 0.944685i | \(0.393632\pi\) | |||||||
\(180\) | −31.5703 | −0.0130728 | ||||||||
\(181\) | 2883.25 | 1.18403 | 0.592017 | − | 0.805925i | \(-0.298332\pi\) | ||||
0.592017 | + | 0.805925i | \(0.298332\pi\) | |||||||
\(182\) | −728.911 | −0.296871 | ||||||||
\(183\) | 1272.55 | 0.514041 | ||||||||
\(184\) | 1663.14 | 0.666350 | ||||||||
\(185\) | −1837.12 | −0.730095 | ||||||||
\(186\) | 196.678 | 0.0775330 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 69.7342 | 0.0270526 | ||||||||
\(189\) | 272.827 | 0.105001 | ||||||||
\(190\) | 895.758 | 0.342027 | ||||||||
\(191\) | −4176.94 | −1.58237 | −0.791186 | − | 0.611575i | \(-0.790536\pi\) | ||||
−0.791186 | + | 0.611575i | \(0.790536\pi\) | |||||||
\(192\) | 1646.04 | 0.618712 | ||||||||
\(193\) | −1346.96 | −0.502363 | −0.251181 | − | 0.967940i | \(-0.580819\pi\) | ||||
−0.251181 | + | 0.967940i | \(0.580819\pi\) | |||||||
\(194\) | −347.100 | −0.128455 | ||||||||
\(195\) | 400.523 | 0.147088 | ||||||||
\(196\) | 169.003 | 0.0615900 | ||||||||
\(197\) | −3488.00 | −1.26147 | −0.630736 | − | 0.775998i | \(-0.717247\pi\) | ||||
−0.630736 | + | 0.775998i | \(0.717247\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1969.15 | −0.701454 | −0.350727 | − | 0.936478i | \(-0.614066\pi\) | ||||
−0.350727 | + | 0.936478i | \(0.614066\pi\) | |||||||
\(200\) | 587.695 | 0.207782 | ||||||||
\(201\) | −3147.70 | −1.10459 | ||||||||
\(202\) | −609.873 | −0.212428 | ||||||||
\(203\) | −415.192 | −0.143551 | ||||||||
\(204\) | 76.1765 | 0.0261442 | ||||||||
\(205\) | −51.0469 | −0.0173915 | ||||||||
\(206\) | 2646.99 | 0.895263 | ||||||||
\(207\) | 636.736 | 0.213798 | ||||||||
\(208\) | −1545.90 | −0.515330 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −409.477 | −0.134555 | ||||||||
\(211\) | 3829.56 | 1.24947 | 0.624734 | − | 0.780837i | \(-0.285207\pi\) | ||||
0.624734 | + | 0.780837i | \(0.285207\pi\) | |||||||
\(212\) | 322.928 | 0.104617 | ||||||||
\(213\) | 791.086 | 0.254480 | ||||||||
\(214\) | 502.385 | 0.160478 | ||||||||
\(215\) | −399.422 | −0.126699 | ||||||||
\(216\) | 634.711 | 0.199938 | ||||||||
\(217\) | −245.212 | −0.0767101 | ||||||||
\(218\) | −15.3061 | −0.00475533 | ||||||||
\(219\) | 352.650 | 0.108812 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −966.430 | −0.294159 | ||||||||
\(222\) | 2977.85 | 0.900272 | ||||||||
\(223\) | 3783.58 | 1.13618 | 0.568088 | − | 0.822968i | \(-0.307683\pi\) | ||||
0.568088 | + | 0.822968i | \(0.307683\pi\) | |||||||
\(224\) | −319.861 | −0.0954089 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −1121.99 | −0.330237 | ||||||||
\(227\) | −3305.66 | −0.966539 | −0.483270 | − | 0.875472i | \(-0.660551\pi\) | ||||
−0.483270 | + | 0.875472i | \(0.660551\pi\) | |||||||
\(228\) | 139.570 | 0.0405407 | ||||||||
\(229\) | 1881.69 | 0.542994 | 0.271497 | − | 0.962439i | \(-0.412481\pi\) | ||||
0.271497 | + | 0.962439i | \(0.412481\pi\) | |||||||
\(230\) | −955.656 | −0.273974 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −965.914 | −0.273342 | ||||||||
\(233\) | 6167.54 | 1.73412 | 0.867058 | − | 0.498207i | \(-0.166008\pi\) | ||||
0.867058 | + | 0.498207i | \(0.166008\pi\) | |||||||
\(234\) | −649.223 | −0.181372 | ||||||||
\(235\) | −496.992 | −0.137958 | ||||||||
\(236\) | 528.609 | 0.145803 | ||||||||
\(237\) | 2122.22 | 0.581659 | ||||||||
\(238\) | 988.033 | 0.269095 | ||||||||
\(239\) | −2574.48 | −0.696776 | −0.348388 | − | 0.937350i | \(-0.613271\pi\) | ||||
−0.348388 | + | 0.937350i | \(0.613271\pi\) | |||||||
\(240\) | −868.430 | −0.233570 | ||||||||
\(241\) | 1125.12 | 0.300728 | 0.150364 | − | 0.988631i | \(-0.451955\pi\) | ||||
0.150364 | + | 0.988631i | \(0.451955\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −297.591 | −0.0780790 | ||||||||
\(245\) | −1204.48 | −0.314086 | ||||||||
\(246\) | 82.7438 | 0.0214453 | ||||||||
\(247\) | −1770.69 | −0.456139 | ||||||||
\(248\) | −570.469 | −0.146068 | ||||||||
\(249\) | 1607.27 | 0.409063 | ||||||||
\(250\) | −337.695 | −0.0854309 | ||||||||
\(251\) | 558.309 | 0.140399 | 0.0701995 | − | 0.997533i | \(-0.477636\pi\) | ||||
0.0701995 | + | 0.997533i | \(0.477636\pi\) | |||||||
\(252\) | −63.8016 | −0.0159489 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −305.707 | −0.0755187 | ||||||||
\(255\) | −542.906 | −0.133326 | ||||||||
\(256\) | −1069.07 | −0.261003 | ||||||||
\(257\) | −166.553 | −0.0404252 | −0.0202126 | − | 0.999796i | \(-0.506434\pi\) | ||||
−0.0202126 | + | 0.999796i | \(0.506434\pi\) | |||||||
\(258\) | 647.438 | 0.156231 | ||||||||
\(259\) | −3712.70 | −0.890718 | ||||||||
\(260\) | −93.6640 | −0.0223415 | ||||||||
\(261\) | −369.802 | −0.0877017 | ||||||||
\(262\) | −2547.86 | −0.600791 | ||||||||
\(263\) | −5678.97 | −1.33148 | −0.665742 | − | 0.746182i | \(-0.731885\pi\) | ||||
−0.665742 | + | 0.746182i | \(0.731885\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2301.49 | −0.533508 | ||||||||
\(266\) | 1810.27 | 0.417274 | ||||||||
\(267\) | −2469.86 | −0.566117 | ||||||||
\(268\) | 736.103 | 0.167779 | ||||||||
\(269\) | 2056.03 | 0.466015 | 0.233008 | − | 0.972475i | \(-0.425143\pi\) | ||||
0.233008 | + | 0.972475i | \(0.425143\pi\) | |||||||
\(270\) | −364.711 | −0.0822059 | ||||||||
\(271\) | 6349.58 | 1.42328 | 0.711641 | − | 0.702544i | \(-0.247952\pi\) | ||||
0.711641 | + | 0.702544i | \(0.247952\pi\) | |||||||
\(272\) | 2095.45 | 0.467115 | ||||||||
\(273\) | 809.433 | 0.179447 | ||||||||
\(274\) | −7476.37 | −1.64841 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −148.903 | −0.0324744 | ||||||||
\(277\) | −5318.77 | −1.15370 | −0.576848 | − | 0.816851i | \(-0.695718\pi\) | ||||
−0.576848 | + | 0.816851i | \(0.695718\pi\) | |||||||
\(278\) | 981.664 | 0.211785 | ||||||||
\(279\) | −218.405 | −0.0468658 | ||||||||
\(280\) | 1187.70 | 0.253494 | ||||||||
\(281\) | −8731.32 | −1.85362 | −0.926810 | − | 0.375532i | \(-0.877460\pi\) | ||||
−0.926810 | + | 0.375532i | \(0.877460\pi\) | |||||||
\(282\) | 805.593 | 0.170115 | ||||||||
\(283\) | 8899.43 | 1.86931 | 0.934657 | − | 0.355550i | \(-0.115706\pi\) | ||||
0.934657 | + | 0.355550i | \(0.115706\pi\) | |||||||
\(284\) | −184.999 | −0.0386537 | ||||||||
\(285\) | −994.711 | −0.206742 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −103.163 | −0.0212177 | ||||||||
\(288\) | −284.892 | −0.0582897 | ||||||||
\(289\) | −3603.01 | −0.733363 | ||||||||
\(290\) | 555.023 | 0.112387 | ||||||||
\(291\) | 385.444 | 0.0776464 | ||||||||
\(292\) | −82.4686 | −0.0165278 | ||||||||
\(293\) | −8071.93 | −1.60944 | −0.804722 | − | 0.593652i | \(-0.797686\pi\) | ||||
−0.804722 | + | 0.593652i | \(0.797686\pi\) | |||||||
\(294\) | 1952.38 | 0.387296 | ||||||||
\(295\) | −3767.37 | −0.743542 | ||||||||
\(296\) | −8637.32 | −1.69606 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 435.222 | 0.0846031 | ||||||||
\(299\) | 1889.09 | 0.365382 | ||||||||
\(300\) | −52.6172 | −0.0101262 | ||||||||
\(301\) | −807.206 | −0.154573 | ||||||||
\(302\) | −476.062 | −0.0907096 | ||||||||
\(303\) | 677.245 | 0.128405 | ||||||||
\(304\) | 3839.27 | 0.724334 | ||||||||
\(305\) | 2120.91 | 0.398174 | ||||||||
\(306\) | 880.017 | 0.164403 | ||||||||
\(307\) | −2698.56 | −0.501677 | −0.250839 | − | 0.968029i | \(-0.580706\pi\) | ||||
−0.250839 | + | 0.968029i | \(0.580706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2939.39 | −0.541153 | ||||||||
\(310\) | 327.797 | 0.0600568 | ||||||||
\(311\) | −2955.76 | −0.538926 | −0.269463 | − | 0.963011i | \(-0.586846\pi\) | ||||
−0.269463 | + | 0.963011i | \(0.586846\pi\) | |||||||
\(312\) | 1883.09 | 0.341695 | ||||||||
\(313\) | −2124.40 | −0.383636 | −0.191818 | − | 0.981431i | \(-0.561438\pi\) | ||||
−0.191818 | + | 0.981431i | \(0.561438\pi\) | |||||||
\(314\) | 372.533 | 0.0669530 | ||||||||
\(315\) | 454.711 | 0.0813335 | ||||||||
\(316\) | −496.291 | −0.0883498 | ||||||||
\(317\) | −2404.95 | −0.426105 | −0.213053 | − | 0.977041i | \(-0.568341\pi\) | ||||
−0.213053 | + | 0.977041i | \(0.568341\pi\) | |||||||
\(318\) | 3730.57 | 0.657862 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2743.40 | 0.479252 | ||||||||
\(321\) | −557.882 | −0.0970030 | ||||||||
\(322\) | −1931.32 | −0.334250 | ||||||||
\(323\) | 2400.15 | 0.413462 | ||||||||
\(324\) | −56.8265 | −0.00974392 | ||||||||
\(325\) | 667.539 | 0.113934 | ||||||||
\(326\) | 2573.66 | 0.437245 | ||||||||
\(327\) | 16.9970 | 0.00287442 | ||||||||
\(328\) | −240.000 | −0.0404018 | ||||||||
\(329\) | −1004.39 | −0.168310 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6375.50 | −1.05870 | −0.529349 | − | 0.848404i | \(-0.677564\pi\) | ||||
−0.529349 | + | 0.848404i | \(0.677564\pi\) | |||||||
\(332\) | −375.867 | −0.0621337 | ||||||||
\(333\) | −3306.81 | −0.544181 | ||||||||
\(334\) | 5674.51 | 0.929627 | ||||||||
\(335\) | −5246.17 | −0.855609 | ||||||||
\(336\) | −1755.04 | −0.284957 | ||||||||
\(337\) | 8482.64 | 1.37115 | 0.685577 | − | 0.728000i | \(-0.259550\pi\) | ||||
0.685577 | + | 0.728000i | \(0.259550\pi\) | |||||||
\(338\) | 4009.19 | 0.645181 | ||||||||
\(339\) | 1245.93 | 0.199616 | ||||||||
\(340\) | 126.961 | 0.0202512 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1612.36 | 0.254932 | ||||||||
\(343\) | −5900.08 | −0.928788 | ||||||||
\(344\) | −1877.91 | −0.294331 | ||||||||
\(345\) | 1061.23 | 0.165607 | ||||||||
\(346\) | 2810.22 | 0.436642 | ||||||||
\(347\) | −1062.72 | −0.164409 | −0.0822044 | − | 0.996615i | \(-0.526196\pi\) | ||||
−0.0822044 | + | 0.996615i | \(0.526196\pi\) | |||||||
\(348\) | 86.4796 | 0.0133212 | ||||||||
\(349\) | 5284.62 | 0.810542 | 0.405271 | − | 0.914197i | \(-0.367177\pi\) | ||||
0.405271 | + | 0.914197i | \(0.367177\pi\) | |||||||
\(350\) | −682.461 | −0.104226 | ||||||||
\(351\) | 720.942 | 0.109633 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12074.0 | −1.82049 | −0.910244 | − | 0.414072i | \(-0.864106\pi\) | ||||
−0.910244 | + | 0.414072i | \(0.864106\pi\) | |||||||
\(354\) | 6106.68 | 0.916854 | ||||||||
\(355\) | 1318.48 | 0.197120 | ||||||||
\(356\) | 577.587 | 0.0859889 | ||||||||
\(357\) | −1097.18 | −0.162658 | ||||||||
\(358\) | −4243.96 | −0.626537 | ||||||||
\(359\) | −6002.96 | −0.882519 | −0.441259 | − | 0.897380i | \(-0.645468\pi\) | ||||
−0.441259 | + | 0.897380i | \(0.645468\pi\) | |||||||
\(360\) | 1057.85 | 0.154871 | ||||||||
\(361\) | −2461.45 | −0.358864 | ||||||||
\(362\) | −7789.28 | −1.13093 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −189.289 | −0.0272567 | ||||||||
\(365\) | 587.750 | 0.0842856 | ||||||||
\(366\) | −3437.87 | −0.490984 | ||||||||
\(367\) | 2684.43 | 0.381815 | 0.190908 | − | 0.981608i | \(-0.438857\pi\) | ||||
0.190908 | + | 0.981608i | \(0.438857\pi\) | |||||||
\(368\) | −4096.00 | −0.580214 | ||||||||
\(369\) | −91.8844 | −0.0129629 | ||||||||
\(370\) | 4963.09 | 0.697347 | ||||||||
\(371\) | −4651.17 | −0.650881 | ||||||||
\(372\) | 51.0748 | 0.00711857 | ||||||||
\(373\) | 9694.41 | 1.34573 | 0.672866 | − | 0.739765i | \(-0.265063\pi\) | ||||
0.672866 | + | 0.739765i | \(0.265063\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | −2336.64 | −0.320487 | ||||||||
\(377\) | −1097.14 | −0.149882 | ||||||||
\(378\) | −737.058 | −0.100291 | ||||||||
\(379\) | 8409.86 | 1.13980 | 0.569902 | − | 0.821713i | \(-0.306981\pi\) | ||||
0.569902 | + | 0.821713i | \(0.306981\pi\) | |||||||
\(380\) | 232.617 | 0.0314027 | ||||||||
\(381\) | 339.478 | 0.0456482 | ||||||||
\(382\) | 11284.3 | 1.51140 | ||||||||
\(383\) | −13673.0 | −1.82417 | −0.912085 | − | 0.410001i | \(-0.865528\pi\) | ||||
−0.912085 | + | 0.410001i | \(0.865528\pi\) | |||||||
\(384\) | −3687.16 | −0.489999 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3638.89 | 0.479830 | ||||||||
\(387\) | −718.959 | −0.0944360 | ||||||||
\(388\) | −90.1376 | −0.0117939 | ||||||||
\(389\) | −6628.44 | −0.863946 | −0.431973 | − | 0.901886i | \(-0.642182\pi\) | ||||
−0.431973 | + | 0.901886i | \(0.642182\pi\) | |||||||
\(390\) | −1082.04 | −0.140490 | ||||||||
\(391\) | −2560.65 | −0.331196 | ||||||||
\(392\) | −5662.92 | −0.729645 | ||||||||
\(393\) | 2829.32 | 0.363156 | ||||||||
\(394\) | 9423.06 | 1.20489 | ||||||||
\(395\) | 3537.04 | 0.450551 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1787.98 | 0.226036 | 0.113018 | − | 0.993593i | \(-0.463948\pi\) | ||||
0.113018 | + | 0.993593i | \(0.463948\pi\) | |||||||
\(398\) | 5319.78 | 0.669992 | ||||||||
\(399\) | −2010.25 | −0.252226 | ||||||||
\(400\) | −1447.38 | −0.180923 | ||||||||
\(401\) | −5846.25 | −0.728049 | −0.364025 | − | 0.931389i | \(-0.618598\pi\) | ||||
−0.364025 | + | 0.931389i | \(0.618598\pi\) | |||||||
\(402\) | 8503.72 | 1.05504 | ||||||||
\(403\) | −647.972 | −0.0800938 | ||||||||
\(404\) | −158.377 | −0.0195038 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 1121.67 | 0.137112 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −2552.51 | −0.309725 | ||||||||
\(409\) | −12683.5 | −1.53339 | −0.766695 | − | 0.642011i | \(-0.778100\pi\) | ||||
−0.766695 | + | 0.642011i | \(0.778100\pi\) | |||||||
\(410\) | 137.906 | 0.0166115 | ||||||||
\(411\) | 8302.27 | 0.996401 | ||||||||
\(412\) | 687.389 | 0.0821972 | ||||||||
\(413\) | −7613.63 | −0.907124 | ||||||||
\(414\) | −1720.18 | −0.204208 | ||||||||
\(415\) | 2678.79 | 0.316859 | ||||||||
\(416\) | −845.230 | −0.0996173 | ||||||||
\(417\) | −1090.11 | −0.128016 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6841.28 | 0.797657 | 0.398829 | − | 0.917025i | \(-0.369417\pi\) | ||||
0.398829 | + | 0.917025i | \(0.369417\pi\) | |||||||
\(420\) | −106.336 | −0.0123540 | ||||||||
\(421\) | −1807.76 | −0.209275 | −0.104637 | − | 0.994510i | \(-0.533368\pi\) | ||||
−0.104637 | + | 0.994510i | \(0.533368\pi\) | |||||||
\(422\) | −10345.8 | −1.19343 | ||||||||
\(423\) | −894.586 | −0.102828 | ||||||||
\(424\) | −10820.6 | −1.23938 | ||||||||
\(425\) | −904.844 | −0.103274 | ||||||||
\(426\) | −2137.17 | −0.243066 | ||||||||
\(427\) | 4286.23 | 0.485774 | ||||||||
\(428\) | 130.463 | 0.0147340 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1079.06 | 0.121016 | ||||||||
\(431\) | −1777.64 | −0.198667 | −0.0993337 | − | 0.995054i | \(-0.531671\pi\) | ||||
−0.0993337 | + | 0.995054i | \(0.531671\pi\) | |||||||
\(432\) | −1563.17 | −0.174093 | ||||||||
\(433\) | 12979.4 | 1.44053 | 0.720264 | − | 0.693700i | \(-0.244021\pi\) | ||||
0.720264 | + | 0.693700i | \(0.244021\pi\) | |||||||
\(434\) | 662.457 | 0.0732694 | ||||||||
\(435\) | −616.336 | −0.0679334 | ||||||||
\(436\) | −3.97481 | −0.000436603 0 | ||||||||
\(437\) | −4691.62 | −0.513571 | ||||||||
\(438\) | −952.706 | −0.103932 | ||||||||
\(439\) | 4471.38 | 0.486121 | 0.243061 | − | 0.970011i | \(-0.421849\pi\) | ||||
0.243061 | + | 0.970011i | \(0.421849\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2168.06 | −0.234106 | ||||||||
\(442\) | 2610.87 | 0.280965 | ||||||||
\(443\) | 5115.99 | 0.548686 | 0.274343 | − | 0.961632i | \(-0.411540\pi\) | ||||
0.274343 | + | 0.961632i | \(0.411540\pi\) | |||||||
\(444\) | 773.311 | 0.0826570 | ||||||||
\(445\) | −4116.44 | −0.438512 | ||||||||
\(446\) | −10221.6 | −1.08522 | ||||||||
\(447\) | −483.300 | −0.0511394 | ||||||||
\(448\) | 5544.24 | 0.584689 | ||||||||
\(449\) | −5834.81 | −0.613278 | −0.306639 | − | 0.951826i | \(-0.599204\pi\) | ||||
−0.306639 | + | 0.951826i | \(0.599204\pi\) | |||||||
\(450\) | −607.851 | −0.0636764 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −291.366 | −0.0303202 | ||||||||
\(453\) | 528.652 | 0.0548305 | ||||||||
\(454\) | 8930.45 | 0.923186 | ||||||||
\(455\) | 1349.05 | 0.138999 | ||||||||
\(456\) | −4676.70 | −0.480277 | ||||||||
\(457\) | −15429.8 | −1.57938 | −0.789691 | − | 0.613504i | \(-0.789759\pi\) | ||||
−0.789691 | + | 0.613504i | \(0.789759\pi\) | |||||||
\(458\) | −5083.51 | −0.518639 | ||||||||
\(459\) | −977.231 | −0.0993753 | ||||||||
\(460\) | −248.172 | −0.0251545 | ||||||||
\(461\) | 1187.92 | 0.120015 | 0.0600074 | − | 0.998198i | \(-0.480888\pi\) | ||||
0.0600074 | + | 0.998198i | \(0.480888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3781.30 | 0.379550 | 0.189775 | − | 0.981828i | \(-0.439224\pi\) | ||||
0.189775 | + | 0.981828i | \(0.439224\pi\) | |||||||
\(464\) | 2378.86 | 0.238009 | ||||||||
\(465\) | −364.008 | −0.0363021 | ||||||||
\(466\) | −16662.0 | −1.65634 | ||||||||
\(467\) | 590.287 | 0.0584908 | 0.0292454 | − | 0.999572i | \(-0.490690\pi\) | ||||
0.0292454 | + | 0.999572i | \(0.490690\pi\) | |||||||
\(468\) | −168.595 | −0.0166524 | ||||||||
\(469\) | −10602.2 | −1.04385 | ||||||||
\(470\) | 1342.66 | 0.131770 | ||||||||
\(471\) | −413.686 | −0.0404706 | ||||||||
\(472\) | −17712.5 | −1.72730 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5733.32 | −0.555570 | ||||||||
\(475\) | −1657.85 | −0.160142 | ||||||||
\(476\) | 256.580 | 0.0247066 | ||||||||
\(477\) | −4142.69 | −0.397653 | ||||||||
\(478\) | 6955.12 | 0.665523 | ||||||||
\(479\) | −17061.5 | −1.62747 | −0.813735 | − | 0.581236i | \(-0.802569\pi\) | ||||
−0.813735 | + | 0.581236i | \(0.802569\pi\) | |||||||
\(480\) | −474.820 | −0.0451510 | ||||||||
\(481\) | −9810.78 | −0.930006 | ||||||||
\(482\) | −3039.59 | −0.287239 | ||||||||
\(483\) | 2144.67 | 0.202041 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 642.406 | 0.0601447 | ||||||||
\(486\) | −656.480 | −0.0612727 | ||||||||
\(487\) | −12480.6 | −1.16129 | −0.580646 | − | 0.814156i | \(-0.697200\pi\) | ||||
−0.580646 | + | 0.814156i | \(0.697200\pi\) | |||||||
\(488\) | 9971.61 | 0.924987 | ||||||||
\(489\) | −2857.97 | −0.264298 | ||||||||
\(490\) | 3253.97 | 0.299999 | ||||||||
\(491\) | −12257.3 | −1.12661 | −0.563303 | − | 0.826250i | \(-0.690470\pi\) | ||||
−0.563303 | + | 0.826250i | \(0.690470\pi\) | |||||||
\(492\) | 21.4875 | 0.00196897 | ||||||||
\(493\) | 1487.17 | 0.135859 | ||||||||
\(494\) | 4783.63 | 0.435679 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1404.96 | 0.127186 | ||||||||
\(497\) | 2664.56 | 0.240486 | ||||||||
\(498\) | −4342.15 | −0.390716 | ||||||||
\(499\) | 2873.79 | 0.257813 | 0.128907 | − | 0.991657i | \(-0.458853\pi\) | ||||
0.128907 | + | 0.991657i | \(0.458853\pi\) | |||||||
\(500\) | −87.6953 | −0.00784370 | ||||||||
\(501\) | −6301.36 | −0.561925 | ||||||||
\(502\) | −1508.31 | −0.134102 | ||||||||
\(503\) | 1150.72 | 0.102004 | 0.0510020 | − | 0.998699i | \(-0.483759\pi\) | ||||
0.0510020 | + | 0.998699i | \(0.483759\pi\) | |||||||
\(504\) | 2137.85 | 0.188943 | ||||||||
\(505\) | 1128.74 | 0.0994621 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4452.08 | −0.389988 | ||||||||
\(508\) | −79.3882 | −0.00693363 | ||||||||
\(509\) | 1002.22 | 0.0872745 | 0.0436372 | − | 0.999047i | \(-0.486105\pi\) | ||||
0.0436372 | + | 0.999047i | \(0.486105\pi\) | |||||||
\(510\) | 1466.70 | 0.127346 | ||||||||
\(511\) | 1187.81 | 0.102829 | ||||||||
\(512\) | 12720.6 | 1.09800 | ||||||||
\(513\) | −1790.48 | −0.154097 | ||||||||
\(514\) | 449.953 | 0.0386120 | ||||||||
\(515\) | −4898.99 | −0.419175 | ||||||||
\(516\) | 168.132 | 0.0143441 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 10030.1 | 0.850766 | ||||||||
\(519\) | −3120.66 | −0.263934 | ||||||||
\(520\) | 3138.48 | 0.264676 | ||||||||
\(521\) | −14545.1 | −1.22310 | −0.611549 | − | 0.791207i | \(-0.709453\pi\) | ||||
−0.611549 | + | 0.791207i | \(0.709453\pi\) | |||||||
\(522\) | 999.042 | 0.0837680 | ||||||||
\(523\) | 8685.21 | 0.726152 | 0.363076 | − | 0.931759i | \(-0.381726\pi\) | ||||
0.363076 | + | 0.931759i | \(0.381726\pi\) | |||||||
\(524\) | −661.647 | −0.0551607 | ||||||||
\(525\) | 757.851 | 0.0630007 | ||||||||
\(526\) | 15342.1 | 1.27176 | ||||||||
\(527\) | 878.321 | 0.0726001 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7161.66 | −0.588613 | ||||||||
\(530\) | 6217.62 | 0.509578 | ||||||||
\(531\) | −6781.27 | −0.554204 | ||||||||
\(532\) | 470.105 | 0.0383113 | ||||||||
\(533\) | −272.606 | −0.0221536 | ||||||||
\(534\) | 6672.49 | 0.540724 | ||||||||
\(535\) | −929.804 | −0.0751382 | ||||||||
\(536\) | −24665.2 | −1.98764 | ||||||||
\(537\) | 4712.78 | 0.378718 | ||||||||
\(538\) | −5554.48 | −0.445113 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −94.7109 | −0.00754761 | ||||||||
\(541\) | −21517.2 | −1.70998 | −0.854988 | − | 0.518648i | \(-0.826436\pi\) | ||||
−0.854988 | + | 0.518648i | \(0.826436\pi\) | |||||||
\(542\) | −17153.8 | −1.35944 | ||||||||
\(543\) | 8649.75 | 0.683603 | ||||||||
\(544\) | 1145.70 | 0.0902970 | ||||||||
\(545\) | 28.3283 | 0.00222651 | ||||||||
\(546\) | −2186.73 | −0.171398 | ||||||||
\(547\) | 12053.4 | 0.942170 | 0.471085 | − | 0.882088i | \(-0.343862\pi\) | ||||
0.471085 | + | 0.882088i | \(0.343862\pi\) | |||||||
\(548\) | −1941.52 | −0.151346 | ||||||||
\(549\) | 3817.65 | 0.296782 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2724.78 | 0.210671 | ||||||||
\(552\) | 4989.42 | 0.384717 | ||||||||
\(553\) | 7148.13 | 0.549674 | ||||||||
\(554\) | 14369.0 | 1.10195 | ||||||||
\(555\) | −5511.35 | −0.421520 | ||||||||
\(556\) | 254.926 | 0.0194447 | ||||||||
\(557\) | −4454.51 | −0.338857 | −0.169429 | − | 0.985542i | \(-0.554192\pi\) | ||||
−0.169429 | + | 0.985542i | \(0.554192\pi\) | |||||||
\(558\) | 590.034 | 0.0447637 | ||||||||
\(559\) | −2133.04 | −0.161392 | ||||||||
\(560\) | −2925.07 | −0.220726 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23588.2 | 1.77048 | ||||||||
\(563\) | −13628.5 | −1.02020 | −0.510102 | − | 0.860114i | \(-0.670392\pi\) | ||||
−0.510102 | + | 0.860114i | \(0.670392\pi\) | |||||||
\(564\) | 209.203 | 0.0156188 | ||||||||
\(565\) | 2076.55 | 0.154622 | ||||||||
\(566\) | −24042.4 | −1.78547 | ||||||||
\(567\) | 818.480 | 0.0606224 | ||||||||
\(568\) | 6198.90 | 0.457923 | ||||||||
\(569\) | 2064.07 | 0.152075 | 0.0760373 | − | 0.997105i | \(-0.475773\pi\) | ||||
0.0760373 | + | 0.997105i | \(0.475773\pi\) | |||||||
\(570\) | 2687.27 | 0.197469 | ||||||||
\(571\) | −666.014 | −0.0488123 | −0.0244061 | − | 0.999702i | \(-0.507769\pi\) | ||||
−0.0244061 | + | 0.999702i | \(0.507769\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12530.8 | −0.913583 | ||||||||
\(574\) | 278.700 | 0.0202660 | ||||||||
\(575\) | 1768.71 | 0.128279 | ||||||||
\(576\) | 4938.12 | 0.357213 | ||||||||
\(577\) | 2115.23 | 0.152614 | 0.0763068 | − | 0.997084i | \(-0.475687\pi\) | ||||
0.0763068 | + | 0.997084i | \(0.475687\pi\) | |||||||
\(578\) | 9733.76 | 0.700469 | ||||||||
\(579\) | −4040.87 | −0.290039 | ||||||||
\(580\) | 144.133 | 0.0103186 | ||||||||
\(581\) | 5413.66 | 0.386569 | ||||||||
\(582\) | −1041.30 | −0.0741637 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2763.34 | 0.195801 | ||||||||
\(585\) | 1201.57 | 0.0849211 | ||||||||
\(586\) | 21806.8 | 1.53725 | ||||||||
\(587\) | −16525.0 | −1.16194 | −0.580969 | − | 0.813926i | \(-0.697326\pi\) | ||||
−0.580969 | + | 0.813926i | \(0.697326\pi\) | |||||||
\(588\) | 507.009 | 0.0355590 | ||||||||
\(589\) | 1609.26 | 0.112578 | ||||||||
\(590\) | 10177.8 | 0.710192 | ||||||||
\(591\) | −10464.0 | −0.728311 | ||||||||
\(592\) | 21272.1 | 1.47682 | ||||||||
\(593\) | 26736.2 | 1.85147 | 0.925736 | − | 0.378171i | \(-0.123447\pi\) | ||||
0.925736 | + | 0.378171i | \(0.123447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1828.63 | −0.125994 | ||||||||
\(596\) | 113.022 | 0.00776770 | ||||||||
\(597\) | −5907.45 | −0.404985 | ||||||||
\(598\) | −5103.50 | −0.348993 | ||||||||
\(599\) | 15220.7 | 1.03823 | 0.519117 | − | 0.854703i | \(-0.326261\pi\) | ||||
0.519117 | + | 0.854703i | \(0.326261\pi\) | |||||||
\(600\) | 1763.09 | 0.119963 | ||||||||
\(601\) | 24398.7 | 1.65598 | 0.827989 | − | 0.560744i | \(-0.189485\pi\) | ||||
0.827989 | + | 0.560744i | \(0.189485\pi\) | |||||||
\(602\) | 2180.72 | 0.147640 | ||||||||
\(603\) | −9443.11 | −0.637733 | ||||||||
\(604\) | −123.627 | −0.00832836 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1829.62 | −0.122646 | ||||||||
\(607\) | −23619.4 | −1.57938 | −0.789688 | − | 0.613509i | \(-0.789758\pi\) | ||||
−0.789688 | + | 0.613509i | \(0.789758\pi\) | |||||||
\(608\) | 2099.15 | 0.140019 | ||||||||
\(609\) | −1245.58 | −0.0828790 | ||||||||
\(610\) | −5729.78 | −0.380315 | ||||||||
\(611\) | −2654.09 | −0.175733 | ||||||||
\(612\) | 228.529 | 0.0150944 | ||||||||
\(613\) | 23250.9 | 1.53197 | 0.765984 | − | 0.642859i | \(-0.222252\pi\) | ||||
0.765984 | + | 0.642859i | \(0.222252\pi\) | |||||||
\(614\) | 7290.33 | 0.479175 | ||||||||
\(615\) | −153.141 | −0.0100410 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15687.9 | 1.02362 | 0.511809 | − | 0.859099i | \(-0.328976\pi\) | ||||
0.511809 | + | 0.859099i | \(0.328976\pi\) | |||||||
\(618\) | 7940.96 | 0.516881 | ||||||||
\(619\) | 15447.8 | 1.00307 | 0.501534 | − | 0.865138i | \(-0.332769\pi\) | ||||
0.501534 | + | 0.865138i | \(0.332769\pi\) | |||||||
\(620\) | 85.1247 | 0.00551402 | ||||||||
\(621\) | 1910.21 | 0.123436 | ||||||||
\(622\) | 7985.18 | 0.514753 | ||||||||
\(623\) | −8319.06 | −0.534986 | ||||||||
\(624\) | −4637.69 | −0.297526 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 5739.19 | 0.366428 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 96.7421 | 0.00614718 | ||||||||
\(629\) | 13298.4 | 0.842994 | ||||||||
\(630\) | −1228.43 | −0.0776854 | ||||||||
\(631\) | −26681.2 | −1.68330 | −0.841648 | − | 0.540026i | \(-0.818414\pi\) | ||||
−0.841648 | + | 0.540026i | \(0.818414\pi\) | |||||||
\(632\) | 16629.6 | 1.04666 | ||||||||
\(633\) | 11488.7 | 0.721381 | ||||||||
\(634\) | 6497.12 | 0.406993 | ||||||||
\(635\) | 565.796 | 0.0353590 | ||||||||
\(636\) | 968.784 | 0.0604006 | ||||||||
\(637\) | −6432.28 | −0.400088 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2373.26 | 0.146924 | ||||||||
\(640\) | −6145.27 | −0.379552 | ||||||||
\(641\) | −15244.1 | −0.939321 | −0.469661 | − | 0.882847i | \(-0.655624\pi\) | ||||
−0.469661 | + | 0.882847i | \(0.655624\pi\) | |||||||
\(642\) | 1507.15 | 0.0926521 | ||||||||
\(643\) | −24128.9 | −1.47986 | −0.739929 | − | 0.672684i | \(-0.765141\pi\) | ||||
−0.739929 | + | 0.672684i | \(0.765141\pi\) | |||||||
\(644\) | −501.540 | −0.0306886 | ||||||||
\(645\) | −1198.27 | −0.0731498 | ||||||||
\(646\) | −6484.17 | −0.394917 | ||||||||
\(647\) | 5415.41 | 0.329060 | 0.164530 | − | 0.986372i | \(-0.447389\pi\) | ||||
0.164530 | + | 0.986372i | \(0.447389\pi\) | |||||||
\(648\) | 1904.13 | 0.115434 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1803.40 | −0.108823 | ||||||||
\(651\) | −735.637 | −0.0442886 | ||||||||
\(652\) | 668.347 | 0.0401449 | ||||||||
\(653\) | 11335.3 | 0.679303 | 0.339651 | − | 0.940551i | \(-0.389691\pi\) | ||||
0.339651 | + | 0.940551i | \(0.389691\pi\) | |||||||
\(654\) | −45.9184 | −0.00274549 | ||||||||
\(655\) | 4715.53 | 0.281299 | ||||||||
\(656\) | 591.075 | 0.0351793 | ||||||||
\(657\) | 1057.95 | 0.0628228 | ||||||||
\(658\) | 2713.42 | 0.160760 | ||||||||
\(659\) | 25441.6 | 1.50389 | 0.751945 | − | 0.659226i | \(-0.229116\pi\) | ||||
0.751945 | + | 0.659226i | \(0.229116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 312.429 | 0.0183844 | 0.00919219 | − | 0.999958i | \(-0.497074\pi\) | ||||
0.00919219 | + | 0.999958i | \(0.497074\pi\) | |||||||
\(662\) | 17223.8 | 1.01121 | ||||||||
\(663\) | −2899.29 | −0.169833 | ||||||||
\(664\) | 12594.5 | 0.736086 | ||||||||
\(665\) | −3350.41 | −0.195374 | ||||||||
\(666\) | 8933.55 | 0.519772 | ||||||||
\(667\) | −2906.99 | −0.168754 | ||||||||
\(668\) | 1473.60 | 0.0853522 | ||||||||
\(669\) | 11350.7 | 0.655972 | ||||||||
\(670\) | 14172.9 | 0.817232 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −959.582 | −0.0550844 | ||||||||
\(673\) | 13815.1 | 0.791280 | 0.395640 | − | 0.918406i | \(-0.370523\pi\) | ||||
0.395640 | + | 0.918406i | \(0.370523\pi\) | |||||||
\(674\) | −22916.4 | −1.30965 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 1041.14 | 0.0592363 | ||||||||
\(677\) | 23931.4 | 1.35858 | 0.679290 | − | 0.733870i | \(-0.262288\pi\) | ||||
0.679290 | + | 0.733870i | \(0.262288\pi\) | |||||||
\(678\) | −3365.96 | −0.190662 | ||||||||
\(679\) | 1298.26 | 0.0733766 | ||||||||
\(680\) | −4254.18 | −0.239912 | ||||||||
\(681\) | −9916.98 | −0.558032 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6301.98 | −0.353058 | −0.176529 | − | 0.984295i | \(-0.556487\pi\) | ||||
−0.176529 | + | 0.984295i | \(0.556487\pi\) | |||||||
\(684\) | 418.711 | 0.0234062 | ||||||||
\(685\) | 13837.1 | 0.771809 | ||||||||
\(686\) | 15939.4 | 0.887129 | ||||||||
\(687\) | 5645.08 | 0.313498 | ||||||||
\(688\) | 4624.93 | 0.256285 | ||||||||
\(689\) | −12290.7 | −0.679591 | ||||||||
\(690\) | −2866.97 | −0.158179 | ||||||||
\(691\) | 8554.84 | 0.470972 | 0.235486 | − | 0.971878i | \(-0.424332\pi\) | ||||
0.235486 | + | 0.971878i | \(0.424332\pi\) | |||||||
\(692\) | 729.778 | 0.0400896 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2871.01 | 0.157034 | ||||||||
\(695\) | −1816.84 | −0.0991609 | ||||||||
\(696\) | −2897.74 | −0.157814 | ||||||||
\(697\) | 369.515 | 0.0200809 | ||||||||
\(698\) | −14276.7 | −0.774187 | ||||||||
\(699\) | 18502.6 | 1.00119 | ||||||||
\(700\) | −177.227 | −0.00956934 | ||||||||
\(701\) | −29410.3 | −1.58461 | −0.792306 | − | 0.610124i | \(-0.791120\pi\) | ||||
−0.792306 | + | 0.610124i | \(0.791120\pi\) | |||||||
\(702\) | −1947.67 | −0.104715 | ||||||||
\(703\) | 24365.3 | 1.30719 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1490.98 | −0.0796503 | ||||||||
\(706\) | 32618.6 | 1.73883 | ||||||||
\(707\) | 2281.12 | 0.121344 | ||||||||
\(708\) | 1585.83 | 0.0841795 | ||||||||
\(709\) | 15207.4 | 0.805537 | 0.402768 | − | 0.915302i | \(-0.368048\pi\) | ||||
0.402768 | + | 0.915302i | \(0.368048\pi\) | |||||||
\(710\) | −3561.95 | −0.188278 | ||||||||
\(711\) | 6366.67 | 0.335821 | ||||||||
\(712\) | −19353.7 | −1.01869 | ||||||||
\(713\) | −1716.87 | −0.0901783 | ||||||||
\(714\) | 2964.10 | 0.155362 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1102.10 | −0.0575245 | ||||||||
\(717\) | −7723.45 | −0.402284 | ||||||||
\(718\) | 16217.4 | 0.842935 | ||||||||
\(719\) | −13773.8 | −0.714431 | −0.357215 | − | 0.934022i | \(-0.616274\pi\) | ||||
−0.357215 | + | 0.934022i | \(0.616274\pi\) | |||||||
\(720\) | −2605.29 | −0.134852 | ||||||||
\(721\) | −9900.55 | −0.511395 | ||||||||
\(722\) | 6649.75 | 0.342767 | ||||||||
\(723\) | 3375.37 | 0.173625 | ||||||||
\(724\) | −2022.78 | −0.103834 | ||||||||
\(725\) | −1027.23 | −0.0526210 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33429.1 | 1.70539 | 0.852694 | − | 0.522410i | \(-0.174967\pi\) | ||||
0.852694 | + | 0.522410i | \(0.174967\pi\) | |||||||
\(728\) | 6342.66 | 0.322905 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −1587.84 | −0.0805051 | ||||||||
\(731\) | 2891.31 | 0.146292 | ||||||||
\(732\) | −892.772 | −0.0450790 | ||||||||
\(733\) | 7774.73 | 0.391768 | 0.195884 | − | 0.980627i | \(-0.437242\pi\) | ||||
0.195884 | + | 0.980627i | \(0.437242\pi\) | |||||||
\(734\) | −7252.16 | −0.364690 | ||||||||
\(735\) | −3613.43 | −0.181338 | ||||||||
\(736\) | −2239.52 | −0.112160 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 248.231 | 0.0123815 | ||||||||
\(739\) | −37474.1 | −1.86537 | −0.932684 | − | 0.360693i | \(-0.882540\pi\) | ||||
−0.932684 | + | 0.360693i | \(0.882540\pi\) | |||||||
\(740\) | 1288.85 | 0.0640259 | ||||||||
\(741\) | −5312.07 | −0.263352 | ||||||||
\(742\) | 12565.4 | 0.621687 | ||||||||
\(743\) | 30510.7 | 1.50650 | 0.753250 | − | 0.657735i | \(-0.228485\pi\) | ||||
0.753250 | + | 0.657735i | \(0.228485\pi\) | |||||||
\(744\) | −1711.41 | −0.0843322 | ||||||||
\(745\) | −805.500 | −0.0396124 | ||||||||
\(746\) | −26190.1 | −1.28537 | ||||||||
\(747\) | 4821.82 | 0.236173 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1879.08 | −0.0916688 | ||||||||
\(750\) | −1013.09 | −0.0493236 | ||||||||
\(751\) | 34091.1 | 1.65646 | 0.828229 | − | 0.560389i | \(-0.189348\pi\) | ||||
0.828229 | + | 0.560389i | \(0.189348\pi\) | |||||||
\(752\) | 5754.71 | 0.279059 | ||||||||
\(753\) | 1674.93 | 0.0810594 | ||||||||
\(754\) | 2964.00 | 0.143160 | ||||||||
\(755\) | 881.087 | 0.0424716 | ||||||||
\(756\) | −191.405 | −0.00920810 | ||||||||
\(757\) | 901.287 | 0.0432733 | 0.0216366 | − | 0.999766i | \(-0.493112\pi\) | ||||
0.0216366 | + | 0.999766i | \(0.493112\pi\) | |||||||
\(758\) | −22719.8 | −1.08868 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7794.49 | −0.372021 | ||||||||
\(761\) | −5030.20 | −0.239612 | −0.119806 | − | 0.992797i | \(-0.538227\pi\) | ||||
−0.119806 | + | 0.992797i | \(0.538227\pi\) | |||||||
\(762\) | −917.120 | −0.0436007 | ||||||||
\(763\) | 57.2497 | 0.00271635 | ||||||||
\(764\) | 2930.39 | 0.138767 | ||||||||
\(765\) | −1628.72 | −0.0769758 | ||||||||
\(766\) | 36938.4 | 1.74235 | ||||||||
\(767\) | −20119.0 | −0.947136 | ||||||||
\(768\) | −3207.21 | −0.150690 | ||||||||
\(769\) | 13447.0 | 0.630574 | 0.315287 | − | 0.948996i | \(-0.397899\pi\) | ||||
0.315287 | + | 0.948996i | \(0.397899\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −499.658 | −0.0233395 | ||||||||
\(772\) | 944.974 | 0.0440548 | ||||||||
\(773\) | 35885.7 | 1.66975 | 0.834876 | − | 0.550438i | \(-0.185539\pi\) | ||||
0.834876 | + | 0.550438i | \(0.185539\pi\) | |||||||
\(774\) | 1942.31 | 0.0902003 | ||||||||
\(775\) | −606.680 | −0.0281195 | ||||||||
\(776\) | 3020.31 | 0.139720 | ||||||||
\(777\) | −11138.1 | −0.514256 | ||||||||
\(778\) | 17907.1 | 0.825195 | ||||||||
\(779\) | 677.025 | 0.0311386 | ||||||||
\(780\) | −280.992 | −0.0128989 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6917.76 | 0.316341 | ||||||||
\(783\) | −1109.40 | −0.0506346 | ||||||||
\(784\) | 13946.7 | 0.635328 | ||||||||
\(785\) | −689.477 | −0.0313484 | ||||||||
\(786\) | −7643.58 | −0.346867 | ||||||||
\(787\) | 29894.2 | 1.35402 | 0.677010 | − | 0.735974i | \(-0.263275\pi\) | ||||
0.677010 | + | 0.735974i | \(0.263275\pi\) | |||||||
\(788\) | 2447.05 | 0.110625 | ||||||||
\(789\) | −17036.9 | −0.768732 | ||||||||
\(790\) | −9555.53 | −0.430342 | ||||||||
\(791\) | 4196.59 | 0.188639 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11326.3 | 0.507201 | ||||||||
\(794\) | −4830.34 | −0.215897 | ||||||||
\(795\) | −6904.48 | −0.308021 | ||||||||
\(796\) | 1381.48 | 0.0615142 | ||||||||
\(797\) | 14033.8 | 0.623716 | 0.311858 | − | 0.950129i | \(-0.399049\pi\) | ||||
0.311858 | + | 0.950129i | \(0.399049\pi\) | |||||||
\(798\) | 5430.81 | 0.240913 | ||||||||
\(799\) | 3597.60 | 0.159292 | ||||||||
\(800\) | −791.367 | −0.0349738 | ||||||||
\(801\) | −7409.59 | −0.326848 | ||||||||
\(802\) | 15794.0 | 0.695394 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2208.31 | 0.0968670 | ||||||||
\(805\) | 3574.45 | 0.156501 | ||||||||
\(806\) | 1750.54 | 0.0765013 | ||||||||
\(807\) | 6168.08 | 0.269054 | ||||||||
\(808\) | 5306.85 | 0.231057 | ||||||||
\(809\) | 45008.7 | 1.95602 | 0.978011 | − | 0.208552i | \(-0.0668751\pi\) | ||||
0.978011 | + | 0.208552i | \(0.0668751\pi\) | |||||||
\(810\) | −1094.13 | −0.0474616 | ||||||||
\(811\) | −26921.1 | −1.16563 | −0.582816 | − | 0.812604i | \(-0.698049\pi\) | ||||
−0.582816 | + | 0.812604i | \(0.698049\pi\) | |||||||
\(812\) | 291.283 | 0.0125887 | ||||||||
\(813\) | 19048.7 | 0.821732 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4763.28 | −0.204724 | ||||||||
\(816\) | 6286.35 | 0.269689 | ||||||||
\(817\) | 5297.46 | 0.226848 | ||||||||
\(818\) | 34265.2 | 1.46461 | ||||||||
\(819\) | 2428.30 | 0.103604 | ||||||||
\(820\) | 35.8125 | 0.00152516 | ||||||||
\(821\) | 11197.0 | 0.475976 | 0.237988 | − | 0.971268i | \(-0.423512\pi\) | ||||
0.237988 | + | 0.971268i | \(0.423512\pi\) | |||||||
\(822\) | −22429.1 | −0.951709 | ||||||||
\(823\) | 1247.54 | 0.0528392 | 0.0264196 | − | 0.999651i | \(-0.491589\pi\) | ||||
0.0264196 | + | 0.999651i | \(0.491589\pi\) | |||||||
\(824\) | −23032.9 | −0.973774 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20568.7 | 0.866436 | ||||||||
\(827\) | −11594.1 | −0.487504 | −0.243752 | − | 0.969838i | \(-0.578378\pi\) | ||||
−0.243752 | + | 0.969838i | \(0.578378\pi\) | |||||||
\(828\) | −446.710 | −0.0187491 | ||||||||
\(829\) | 1658.14 | 0.0694689 | 0.0347344 | − | 0.999397i | \(-0.488941\pi\) | ||||
0.0347344 | + | 0.999397i | \(0.488941\pi\) | |||||||
\(830\) | −7236.91 | −0.302647 | ||||||||
\(831\) | −15956.3 | −0.666087 | ||||||||
\(832\) | 14650.6 | 0.610479 | ||||||||
\(833\) | 8718.91 | 0.362656 | ||||||||
\(834\) | 2944.99 | 0.122274 | ||||||||
\(835\) | −10502.3 | −0.435265 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −655.214 | −0.0270580 | ||||||||
\(838\) | −18482.1 | −0.761880 | ||||||||
\(839\) | −15906.9 | −0.654549 | −0.327275 | − | 0.944929i | \(-0.606130\pi\) | ||||
−0.327275 | + | 0.944929i | \(0.606130\pi\) | |||||||
\(840\) | 3563.09 | 0.146355 | ||||||||
\(841\) | −22700.7 | −0.930776 | ||||||||
\(842\) | 4883.77 | 0.199888 | ||||||||
\(843\) | −26194.0 | −1.07019 | ||||||||
\(844\) | −2686.68 | −0.109573 | ||||||||
\(845\) | −7420.13 | −0.302083 | ||||||||
\(846\) | 2416.78 | 0.0982159 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 26649.1 | 1.07917 | ||||||||
\(849\) | 26698.3 | 1.07925 | ||||||||
\(850\) | 2444.49 | 0.0986416 | ||||||||
\(851\) | −25994.6 | −1.04710 | ||||||||
\(852\) | −554.996 | −0.0223167 | ||||||||
\(853\) | 9055.06 | 0.363469 | 0.181735 | − | 0.983348i | \(-0.441829\pi\) | ||||
0.181735 | + | 0.983348i | \(0.441829\pi\) | |||||||
\(854\) | −11579.5 | −0.463985 | ||||||||
\(855\) | −2984.13 | −0.119363 | ||||||||
\(856\) | −4371.53 | −0.174551 | ||||||||
\(857\) | 8173.52 | 0.325790 | 0.162895 | − | 0.986643i | \(-0.447917\pi\) | ||||
0.162895 | + | 0.986643i | \(0.447917\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41286.0 | 1.63988 | 0.819941 | − | 0.572447i | \(-0.194006\pi\) | ||||
0.819941 | + | 0.572447i | \(0.194006\pi\) | |||||||
\(860\) | 280.219 | 0.0111109 | ||||||||
\(861\) | −309.488 | −0.0122501 | ||||||||
\(862\) | 4802.39 | 0.189757 | ||||||||
\(863\) | 18537.1 | 0.731182 | 0.365591 | − | 0.930776i | \(-0.380867\pi\) | ||||
0.365591 | + | 0.930776i | \(0.380867\pi\) | |||||||
\(864\) | −854.677 | −0.0336536 | ||||||||
\(865\) | −5201.09 | −0.204442 | ||||||||
\(866\) | −35064.6 | −1.37591 | ||||||||
\(867\) | −10809.0 | −0.423407 | ||||||||
\(868\) | 172.032 | 0.00672712 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1665.07 | 0.0648864 | ||||||||
\(871\) | −28016.2 | −1.08989 | ||||||||
\(872\) | 133.187 | 0.00517235 | ||||||||
\(873\) | 1156.33 | 0.0448292 | ||||||||
\(874\) | 12674.7 | 0.490535 | ||||||||
\(875\) | 1263.09 | 0.0488001 | ||||||||
\(876\) | −247.406 | −0.00954232 | ||||||||
\(877\) | 22220.2 | 0.855558 | 0.427779 | − | 0.903883i | \(-0.359296\pi\) | ||||
0.427779 | + | 0.903883i | \(0.359296\pi\) | |||||||
\(878\) | −12079.7 | −0.464317 | ||||||||
\(879\) | −24215.8 | −0.929213 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50496.5 | −1.93107 | −0.965534 | − | 0.260275i | \(-0.916187\pi\) | ||||
−0.965534 | + | 0.260275i | \(0.916187\pi\) | |||||||
\(882\) | 5857.14 | 0.223606 | ||||||||
\(883\) | 22313.1 | 0.850391 | 0.425196 | − | 0.905102i | \(-0.360205\pi\) | ||||
0.425196 | + | 0.905102i | \(0.360205\pi\) | |||||||
\(884\) | 678.010 | 0.0257963 | ||||||||
\(885\) | −11302.1 | −0.429284 | ||||||||
\(886\) | −13821.2 | −0.524076 | ||||||||
\(887\) | −41393.3 | −1.56691 | −0.783456 | − | 0.621447i | \(-0.786545\pi\) | ||||
−0.783456 | + | 0.621447i | \(0.786545\pi\) | |||||||
\(888\) | −25912.0 | −0.979221 | ||||||||
\(889\) | 1143.44 | 0.0431380 | ||||||||
\(890\) | 11120.8 | 0.418843 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2654.42 | −0.0996373 | ||||||||
\(893\) | 6591.52 | 0.247006 | ||||||||
\(894\) | 1305.67 | 0.0488456 | ||||||||
\(895\) | 7854.64 | 0.293354 | ||||||||
\(896\) | −12419.2 | −0.463054 | ||||||||
\(897\) | 5667.28 | 0.210953 | ||||||||
\(898\) | 15763.1 | 0.585770 | ||||||||
\(899\) | 997.116 | 0.0369919 | ||||||||
\(900\) | −157.851 | −0.00584635 | ||||||||
\(901\) | 16659.9 | 0.616007 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2421.62 | −0.0892430 | ||||||||
\(904\) | 9763.05 | 0.359197 | ||||||||
\(905\) | 14416.2 | 0.529516 | ||||||||
\(906\) | −1428.19 | −0.0523712 | ||||||||
\(907\) | 47821.8 | 1.75071 | 0.875356 | − | 0.483479i | \(-0.160627\pi\) | ||||
0.875356 | + | 0.483479i | \(0.160627\pi\) | |||||||
\(908\) | 2319.13 | 0.0847609 | ||||||||
\(909\) | 2031.74 | 0.0741347 | ||||||||
\(910\) | −3644.55 | −0.132765 | ||||||||
\(911\) | 32560.8 | 1.18418 | 0.592091 | − | 0.805871i | \(-0.298303\pi\) | ||||
0.592091 | + | 0.805871i | \(0.298303\pi\) | |||||||
\(912\) | 11517.8 | 0.418194 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 41684.7 | 1.50854 | ||||||||
\(915\) | 6362.74 | 0.229886 | ||||||||
\(916\) | −1320.12 | −0.0476180 | ||||||||
\(917\) | 9529.79 | 0.343186 | ||||||||
\(918\) | 2640.05 | 0.0949179 | ||||||||
\(919\) | 13638.7 | 0.489554 | 0.244777 | − | 0.969579i | \(-0.421285\pi\) | ||||
0.244777 | + | 0.969579i | \(0.421285\pi\) | |||||||
\(920\) | 8315.70 | 0.298001 | ||||||||
\(921\) | −8095.68 | −0.289643 | ||||||||
\(922\) | −3209.23 | −0.114632 | ||||||||
\(923\) | 7041.08 | 0.251094 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9185.59 | −0.326508 | ||||||||
\(926\) | −10215.4 | −0.362526 | ||||||||
\(927\) | −8818.18 | −0.312435 | ||||||||
\(928\) | 1300.66 | 0.0460090 | ||||||||
\(929\) | −17716.2 | −0.625672 | −0.312836 | − | 0.949807i | \(-0.601279\pi\) | ||||
−0.312836 | + | 0.949807i | \(0.601279\pi\) | |||||||
\(930\) | 983.390 | 0.0346738 | ||||||||
\(931\) | 15974.7 | 0.562354 | ||||||||
\(932\) | −4326.91 | −0.152074 | ||||||||
\(933\) | −8867.29 | −0.311149 | ||||||||
\(934\) | −1594.70 | −0.0558673 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5649.26 | 0.197278 | ||||||||
\(937\) | −46320.5 | −1.61497 | −0.807483 | − | 0.589890i | \(-0.799171\pi\) | ||||
−0.807483 | + | 0.589890i | \(0.799171\pi\) | |||||||
\(938\) | 28642.5 | 0.997025 | ||||||||
\(939\) | −6373.19 | −0.221492 | ||||||||
\(940\) | 348.671 | 0.0120983 | ||||||||
\(941\) | −7828.97 | −0.271219 | −0.135609 | − | 0.990762i | \(-0.543299\pi\) | ||||
−0.135609 | + | 0.990762i | \(0.543299\pi\) | |||||||
\(942\) | 1117.60 | 0.0386553 | ||||||||
\(943\) | −722.297 | −0.0249430 | ||||||||
\(944\) | 43622.7 | 1.50402 | ||||||||
\(945\) | 1364.13 | 0.0469579 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23815.7 | −0.817219 | −0.408610 | − | 0.912709i | \(-0.633986\pi\) | ||||
−0.408610 | + | 0.912709i | \(0.633986\pi\) | |||||||
\(948\) | −1488.87 | −0.0510088 | ||||||||
\(949\) | 3138.77 | 0.107364 | ||||||||
\(950\) | 4478.79 | 0.152959 | ||||||||
\(951\) | −7214.85 | −0.246012 | ||||||||
\(952\) | −8597.43 | −0.292694 | ||||||||
\(953\) | 2187.90 | 0.0743685 | 0.0371842 | − | 0.999308i | \(-0.488161\pi\) | ||||
0.0371842 | + | 0.999308i | \(0.488161\pi\) | |||||||
\(954\) | 11191.7 | 0.379817 | ||||||||
\(955\) | −20884.7 | −0.707658 | ||||||||
\(956\) | 1806.16 | 0.0611039 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 46092.6 | 1.55447 | ||||||||
\(959\) | 27964.0 | 0.941609 | ||||||||
\(960\) | 8230.19 | 0.276696 | ||||||||
\(961\) | −29202.1 | −0.980232 | ||||||||
\(962\) | 26504.4 | 0.888292 | ||||||||
\(963\) | −1673.65 | −0.0560047 | ||||||||
\(964\) | −789.343 | −0.0263724 | ||||||||
\(965\) | −6734.78 | −0.224664 | ||||||||
\(966\) | −5793.96 | −0.192979 | ||||||||
\(967\) | −14139.2 | −0.470201 | −0.235101 | − | 0.971971i | \(-0.575542\pi\) | ||||
−0.235101 | + | 0.971971i | \(0.575542\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7200.46 | 0.238712 | ||||||||
\(970\) | −1735.50 | −0.0574470 | ||||||||
\(971\) | −6358.97 | −0.210164 | −0.105082 | − | 0.994464i | \(-0.533510\pi\) | ||||
−0.105082 | + | 0.994464i | \(0.533510\pi\) | |||||||
\(972\) | −170.480 | −0.00562565 | ||||||||
\(973\) | −3671.73 | −0.120977 | ||||||||
\(974\) | 33717.1 | 1.10920 | ||||||||
\(975\) | 2002.62 | 0.0657796 | ||||||||
\(976\) | −24558.2 | −0.805419 | ||||||||
\(977\) | 46153.9 | 1.51136 | 0.755678 | − | 0.654944i | \(-0.227308\pi\) | ||||
0.755678 | + | 0.654944i | \(0.227308\pi\) | |||||||
\(978\) | 7720.98 | 0.252443 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 845.015 | 0.0275439 | ||||||||
\(981\) | 50.9909 | 0.00165955 | ||||||||
\(982\) | 33113.8 | 1.07607 | ||||||||
\(983\) | 20863.0 | 0.676935 | 0.338467 | − | 0.940978i | \(-0.390091\pi\) | ||||
0.338467 | + | 0.940978i | \(0.390091\pi\) | |||||||
\(984\) | −720.000 | −0.0233260 | ||||||||
\(985\) | −17440.0 | −0.564147 | ||||||||
\(986\) | −4017.68 | −0.129766 | ||||||||
\(987\) | −3013.17 | −0.0971735 | ||||||||
\(988\) | 1242.25 | 0.0400012 | ||||||||
\(989\) | −5651.69 | −0.181712 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21394.4 | 0.685788 | 0.342894 | − | 0.939374i | \(-0.388593\pi\) | ||||
0.342894 | + | 0.939374i | \(0.388593\pi\) | |||||||
\(992\) | 768.171 | 0.0245861 | ||||||||
\(993\) | −19126.5 | −0.611240 | ||||||||
\(994\) | −7198.47 | −0.229700 | ||||||||
\(995\) | −9845.76 | −0.313700 | ||||||||
\(996\) | −1127.60 | −0.0358729 | ||||||||
\(997\) | −46133.4 | −1.46546 | −0.732728 | − | 0.680521i | \(-0.761753\pi\) | ||||
−0.732728 | + | 0.680521i | \(0.761753\pi\) | |||||||
\(998\) | −7763.73 | −0.246249 | ||||||||
\(999\) | −9920.43 | −0.314183 |
(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 | 1815.4.a.o.1.1 | yes | 2 | |
11.10 | odd | 2 | 1815.4.a.i.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.4.a.i.1.2 | ✓ | 2 | 11.10 | odd | 2 | ||
1815.4.a.o.1.1 | yes | 2 | 1.1 | even | 1 | trivial |