Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,4,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(32.2740447731\) |
Analytic rank: | \(0\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.13291 | −1.46120 | −0.730602 | − | 0.682803i | \(-0.760761\pi\) | ||||
−0.730602 | + | 0.682803i | \(0.760761\pi\) | |||||||
\(3\) | 8.01594 | 1.54267 | 0.771334 | − | 0.636430i | \(-0.219590\pi\) | ||||
0.771334 | + | 0.636430i | \(0.219590\pi\) | |||||||
\(4\) | 9.08096 | 1.13512 | ||||||||
\(5\) | −4.43214 | −0.396423 | −0.198211 | − | 0.980159i | \(-0.563513\pi\) | ||||
−0.198211 | + | 0.980159i | \(0.563513\pi\) | |||||||
\(6\) | −33.1292 | −2.25416 | ||||||||
\(7\) | 17.8969 | 0.966343 | 0.483171 | − | 0.875526i | \(-0.339485\pi\) | ||||
0.483171 | + | 0.875526i | \(0.339485\pi\) | |||||||
\(8\) | −4.46750 | −0.197437 | ||||||||
\(9\) | 37.2553 | 1.37983 | ||||||||
\(10\) | 18.3177 | 0.579255 | ||||||||
\(11\) | 54.6583 | 1.49819 | 0.749095 | − | 0.662463i | \(-0.230489\pi\) | ||||
0.749095 | + | 0.662463i | \(0.230489\pi\) | |||||||
\(12\) | 72.7924 | 1.75111 | ||||||||
\(13\) | 85.9516 | 1.83374 | 0.916872 | − | 0.399181i | \(-0.130706\pi\) | ||||
0.916872 | + | 0.399181i | \(0.130706\pi\) | |||||||
\(14\) | −73.9664 | −1.41202 | ||||||||
\(15\) | −35.5278 | −0.611549 | ||||||||
\(16\) | −54.1839 | −0.846623 | ||||||||
\(17\) | 34.7132 | 0.495247 | 0.247623 | − | 0.968856i | \(-0.420350\pi\) | ||||
0.247623 | + | 0.968856i | \(0.420350\pi\) | |||||||
\(18\) | −153.973 | −2.01621 | ||||||||
\(19\) | 7.75375 | 0.0936227 | 0.0468114 | − | 0.998904i | \(-0.485094\pi\) | ||||
0.0468114 | + | 0.998904i | \(0.485094\pi\) | |||||||
\(20\) | −40.2481 | −0.449987 | ||||||||
\(21\) | 143.461 | 1.49075 | ||||||||
\(22\) | −225.898 | −2.18916 | ||||||||
\(23\) | −13.5082 | −0.122463 | −0.0612315 | − | 0.998124i | \(-0.519503\pi\) | ||||
−0.0612315 | + | 0.998124i | \(0.519503\pi\) | |||||||
\(24\) | −35.8112 | −0.304581 | ||||||||
\(25\) | −105.356 | −0.842849 | ||||||||
\(26\) | −355.230 | −2.67948 | ||||||||
\(27\) | 82.2062 | 0.585948 | ||||||||
\(28\) | 162.521 | 1.09691 | ||||||||
\(29\) | 22.5537 | 0.144418 | 0.0722088 | − | 0.997390i | \(-0.476995\pi\) | ||||
0.0722088 | + | 0.997390i | \(0.476995\pi\) | |||||||
\(30\) | 146.833 | 0.893599 | ||||||||
\(31\) | −192.016 | −1.11248 | −0.556242 | − | 0.831020i | \(-0.687757\pi\) | ||||
−0.556242 | + | 0.831020i | \(0.687757\pi\) | |||||||
\(32\) | 259.677 | 1.43453 | ||||||||
\(33\) | 438.137 | 2.31121 | ||||||||
\(34\) | −143.467 | −0.723657 | ||||||||
\(35\) | −79.3217 | −0.383080 | ||||||||
\(36\) | 338.314 | 1.56627 | ||||||||
\(37\) | 145.256 | 0.645404 | 0.322702 | − | 0.946501i | \(-0.395409\pi\) | ||||
0.322702 | + | 0.946501i | \(0.395409\pi\) | |||||||
\(38\) | −32.0455 | −0.136802 | ||||||||
\(39\) | 688.983 | 2.82886 | ||||||||
\(40\) | 19.8006 | 0.0782687 | ||||||||
\(41\) | 455.088 | 1.73348 | 0.866742 | − | 0.498756i | \(-0.166210\pi\) | ||||
0.866742 | + | 0.498756i | \(0.166210\pi\) | |||||||
\(42\) | −592.910 | −2.17829 | ||||||||
\(43\) | −287.889 | −1.02099 | −0.510497 | − | 0.859880i | \(-0.670539\pi\) | ||||
−0.510497 | + | 0.859880i | \(0.670539\pi\) | |||||||
\(44\) | 496.349 | 1.70062 | ||||||||
\(45\) | −165.121 | −0.546995 | ||||||||
\(46\) | 55.8281 | 0.178943 | ||||||||
\(47\) | −339.202 | −1.05272 | −0.526359 | − | 0.850263i | \(-0.676443\pi\) | ||||
−0.526359 | + | 0.850263i | \(0.676443\pi\) | |||||||
\(48\) | −434.335 | −1.30606 | ||||||||
\(49\) | −22.7004 | −0.0661820 | ||||||||
\(50\) | 435.427 | 1.23157 | ||||||||
\(51\) | 278.259 | 0.764002 | ||||||||
\(52\) | 780.522 | 2.08152 | ||||||||
\(53\) | 163.091 | 0.422686 | 0.211343 | − | 0.977412i | \(-0.432216\pi\) | ||||
0.211343 | + | 0.977412i | \(0.432216\pi\) | |||||||
\(54\) | −339.751 | −0.856189 | ||||||||
\(55\) | −242.253 | −0.593917 | ||||||||
\(56\) | −79.9545 | −0.190792 | ||||||||
\(57\) | 62.1536 | 0.144429 | ||||||||
\(58\) | −93.2122 | −0.211024 | ||||||||
\(59\) | 63.0464 | 0.139118 | 0.0695588 | − | 0.997578i | \(-0.477841\pi\) | ||||
0.0695588 | + | 0.997578i | \(0.477841\pi\) | |||||||
\(60\) | −322.626 | −0.694182 | ||||||||
\(61\) | −257.410 | −0.540295 | −0.270147 | − | 0.962819i | \(-0.587072\pi\) | ||||
−0.270147 | + | 0.962819i | \(0.587072\pi\) | |||||||
\(62\) | 793.584 | 1.62557 | ||||||||
\(63\) | 666.756 | 1.33339 | ||||||||
\(64\) | −639.752 | −1.24952 | ||||||||
\(65\) | −380.950 | −0.726938 | ||||||||
\(66\) | −1810.78 | −3.37715 | ||||||||
\(67\) | −488.364 | −0.890495 | −0.445247 | − | 0.895408i | \(-0.646884\pi\) | ||||
−0.445247 | + | 0.895408i | \(0.646884\pi\) | |||||||
\(68\) | 315.229 | 0.562164 | ||||||||
\(69\) | −108.281 | −0.188920 | ||||||||
\(70\) | 327.830 | 0.559759 | ||||||||
\(71\) | −298.165 | −0.498389 | −0.249195 | − | 0.968453i | \(-0.580166\pi\) | ||||
−0.249195 | + | 0.968453i | \(0.580166\pi\) | |||||||
\(72\) | −166.438 | −0.272430 | ||||||||
\(73\) | 512.834 | 0.822229 | 0.411114 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411114 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(74\) | −600.330 | −0.943067 | ||||||||
\(75\) | −844.528 | −1.30024 | ||||||||
\(76\) | 70.4114 | 0.106273 | ||||||||
\(77\) | 978.214 | 1.44776 | ||||||||
\(78\) | −2847.50 | −4.13354 | ||||||||
\(79\) | −371.381 | −0.528907 | −0.264454 | − | 0.964398i | \(-0.585192\pi\) | ||||
−0.264454 | + | 0.964398i | \(0.585192\pi\) | |||||||
\(80\) | 240.151 | 0.335621 | ||||||||
\(81\) | −346.934 | −0.475904 | ||||||||
\(82\) | −1880.84 | −2.53298 | ||||||||
\(83\) | −444.044 | −0.587231 | −0.293615 | − | 0.955924i | \(-0.594858\pi\) | ||||
−0.293615 | + | 0.955924i | \(0.594858\pi\) | |||||||
\(84\) | 1302.76 | 1.69218 | ||||||||
\(85\) | −153.854 | −0.196327 | ||||||||
\(86\) | 1189.82 | 1.49188 | ||||||||
\(87\) | 180.789 | 0.222788 | ||||||||
\(88\) | −244.186 | −0.295799 | ||||||||
\(89\) | 261.381 | 0.311307 | 0.155653 | − | 0.987812i | \(-0.450252\pi\) | ||||
0.155653 | + | 0.987812i | \(0.450252\pi\) | |||||||
\(90\) | 682.430 | 0.799272 | ||||||||
\(91\) | 1538.27 | 1.77203 | ||||||||
\(92\) | −122.667 | −0.139010 | ||||||||
\(93\) | −1539.19 | −1.71620 | ||||||||
\(94\) | 1401.89 | 1.53824 | ||||||||
\(95\) | −34.3657 | −0.0371142 | ||||||||
\(96\) | 2081.56 | 2.21300 | ||||||||
\(97\) | 267.187 | 0.279678 | 0.139839 | − | 0.990174i | \(-0.455341\pi\) | ||||
0.139839 | + | 0.990174i | \(0.455341\pi\) | |||||||
\(98\) | 93.8188 | 0.0967054 | ||||||||
\(99\) | 2036.31 | 2.06724 | ||||||||
\(100\) | −956.734 | −0.956734 | ||||||||
\(101\) | 1716.53 | 1.69110 | 0.845552 | − | 0.533893i | \(-0.179271\pi\) | ||||
0.845552 | + | 0.533893i | \(0.179271\pi\) | |||||||
\(102\) | −1150.02 | −1.11636 | ||||||||
\(103\) | −156.424 | −0.149640 | −0.0748200 | − | 0.997197i | \(-0.523838\pi\) | ||||
−0.0748200 | + | 0.997197i | \(0.523838\pi\) | |||||||
\(104\) | −383.989 | −0.362050 | ||||||||
\(105\) | −635.838 | −0.590966 | ||||||||
\(106\) | −674.043 | −0.617630 | ||||||||
\(107\) | 540.532 | 0.488366 | 0.244183 | − | 0.969729i | \(-0.421480\pi\) | ||||
0.244183 | + | 0.969729i | \(0.421480\pi\) | |||||||
\(108\) | 746.511 | 0.665121 | ||||||||
\(109\) | 1635.85 | 1.43749 | 0.718745 | − | 0.695274i | \(-0.244717\pi\) | ||||
0.718745 | + | 0.695274i | \(0.244717\pi\) | |||||||
\(110\) | 1001.21 | 0.867834 | ||||||||
\(111\) | 1164.36 | 0.995645 | ||||||||
\(112\) | −969.724 | −0.818128 | ||||||||
\(113\) | 1058.53 | 0.881222 | 0.440611 | − | 0.897698i | \(-0.354762\pi\) | ||||
0.440611 | + | 0.897698i | \(0.354762\pi\) | |||||||
\(114\) | −256.875 | −0.211040 | ||||||||
\(115\) | 59.8701 | 0.0485471 | ||||||||
\(116\) | 204.809 | 0.163931 | ||||||||
\(117\) | 3202.15 | 2.53025 | ||||||||
\(118\) | −260.565 | −0.203279 | ||||||||
\(119\) | 621.260 | 0.478578 | ||||||||
\(120\) | 158.720 | 0.120743 | ||||||||
\(121\) | 1656.52 | 1.24457 | ||||||||
\(122\) | 1063.85 | 0.789481 | ||||||||
\(123\) | 3647.96 | 2.67419 | ||||||||
\(124\) | −1743.69 | −1.26280 | ||||||||
\(125\) | 1020.97 | 0.730548 | ||||||||
\(126\) | −2755.64 | −1.94835 | ||||||||
\(127\) | −1020.54 | −0.713059 | −0.356530 | − | 0.934284i | \(-0.616040\pi\) | ||||
−0.356530 | + | 0.934284i | \(0.616040\pi\) | |||||||
\(128\) | 566.620 | 0.391270 | ||||||||
\(129\) | −2307.71 | −1.57506 | ||||||||
\(130\) | 1574.43 | 1.06221 | ||||||||
\(131\) | −2641.60 | −1.76181 | −0.880907 | − | 0.473289i | \(-0.843067\pi\) | ||||
−0.880907 | + | 0.473289i | \(0.843067\pi\) | |||||||
\(132\) | 3978.71 | 2.62350 | ||||||||
\(133\) | 138.768 | 0.0904716 | ||||||||
\(134\) | 2018.36 | 1.30120 | ||||||||
\(135\) | −364.349 | −0.232283 | ||||||||
\(136\) | −155.081 | −0.0977803 | ||||||||
\(137\) | −2542.74 | −1.58570 | −0.792849 | − | 0.609418i | \(-0.791403\pi\) | ||||
−0.792849 | + | 0.609418i | \(0.791403\pi\) | |||||||
\(138\) | 447.515 | 0.276050 | ||||||||
\(139\) | 968.563 | 0.591025 | 0.295512 | − | 0.955339i | \(-0.404510\pi\) | ||||
0.295512 | + | 0.955339i | \(0.404510\pi\) | |||||||
\(140\) | −720.317 | −0.434842 | ||||||||
\(141\) | −2719.02 | −1.62399 | ||||||||
\(142\) | 1232.29 | 0.728249 | ||||||||
\(143\) | 4697.96 | 2.74730 | ||||||||
\(144\) | −2018.64 | −1.16819 | ||||||||
\(145\) | −99.9610 | −0.0572504 | ||||||||
\(146\) | −2119.50 | −1.20144 | ||||||||
\(147\) | −181.965 | −0.102097 | ||||||||
\(148\) | 1319.06 | 0.732611 | ||||||||
\(149\) | 1314.64 | 0.722818 | 0.361409 | − | 0.932407i | \(-0.382296\pi\) | ||||
0.361409 | + | 0.932407i | \(0.382296\pi\) | |||||||
\(150\) | 3490.36 | 1.89991 | ||||||||
\(151\) | 302.259 | 0.162897 | 0.0814486 | − | 0.996678i | \(-0.474045\pi\) | ||||
0.0814486 | + | 0.996678i | \(0.474045\pi\) | |||||||
\(152\) | −34.6399 | −0.0184846 | ||||||||
\(153\) | 1293.25 | 0.683355 | ||||||||
\(154\) | −4042.87 | −2.11548 | ||||||||
\(155\) | 851.041 | 0.441015 | ||||||||
\(156\) | 6256.62 | 3.21109 | ||||||||
\(157\) | −3444.31 | −1.75087 | −0.875434 | − | 0.483338i | \(-0.839424\pi\) | ||||
−0.875434 | + | 0.483338i | \(0.839424\pi\) | |||||||
\(158\) | 1534.89 | 0.772842 | ||||||||
\(159\) | 1307.33 | 0.652064 | ||||||||
\(160\) | −1150.93 | −0.568679 | ||||||||
\(161\) | −241.755 | −0.118341 | ||||||||
\(162\) | 1433.85 | 0.695393 | ||||||||
\(163\) | −3457.41 | −1.66138 | −0.830691 | − | 0.556733i | \(-0.812055\pi\) | ||||
−0.830691 | + | 0.556733i | \(0.812055\pi\) | |||||||
\(164\) | 4132.64 | 1.96771 | ||||||||
\(165\) | −1941.89 | −0.916217 | ||||||||
\(166\) | 1835.19 | 0.858064 | ||||||||
\(167\) | 3672.32 | 1.70163 | 0.850817 | − | 0.525462i | \(-0.176107\pi\) | ||||
0.850817 | + | 0.525462i | \(0.176107\pi\) | |||||||
\(168\) | −640.910 | −0.294329 | ||||||||
\(169\) | 5190.67 | 2.36262 | ||||||||
\(170\) | 635.865 | 0.286874 | ||||||||
\(171\) | 288.868 | 0.129183 | ||||||||
\(172\) | −2614.31 | −1.15895 | ||||||||
\(173\) | 1001.42 | 0.440094 | 0.220047 | − | 0.975489i | \(-0.429379\pi\) | ||||
0.220047 | + | 0.975489i | \(0.429379\pi\) | |||||||
\(174\) | −747.184 | −0.325539 | ||||||||
\(175\) | −1885.55 | −0.814481 | ||||||||
\(176\) | −2961.60 | −1.26840 | ||||||||
\(177\) | 505.376 | 0.214612 | ||||||||
\(178\) | −1080.26 | −0.454883 | ||||||||
\(179\) | 2549.94 | 1.06476 | 0.532378 | − | 0.846507i | \(-0.321298\pi\) | ||||
0.532378 | + | 0.846507i | \(0.321298\pi\) | |||||||
\(180\) | −1499.46 | −0.620905 | ||||||||
\(181\) | 820.681 | 0.337020 | 0.168510 | − | 0.985700i | \(-0.446104\pi\) | ||||
0.168510 | + | 0.985700i | \(0.446104\pi\) | |||||||
\(182\) | −6357.52 | −2.58929 | ||||||||
\(183\) | −2063.38 | −0.833496 | ||||||||
\(184\) | 60.3477 | 0.0241788 | ||||||||
\(185\) | −643.796 | −0.255853 | ||||||||
\(186\) | 6361.32 | 2.50771 | ||||||||
\(187\) | 1897.36 | 0.741973 | ||||||||
\(188\) | −3080.28 | −1.19496 | ||||||||
\(189\) | 1471.24 | 0.566226 | ||||||||
\(190\) | 142.030 | 0.0542314 | ||||||||
\(191\) | −4354.94 | −1.64980 | −0.824902 | − | 0.565276i | \(-0.808770\pi\) | ||||
−0.824902 | + | 0.565276i | \(0.808770\pi\) | |||||||
\(192\) | −5128.21 | −1.92759 | ||||||||
\(193\) | −1466.15 | −0.546816 | −0.273408 | − | 0.961898i | \(-0.588151\pi\) | ||||
−0.273408 | + | 0.961898i | \(0.588151\pi\) | |||||||
\(194\) | −1104.26 | −0.408667 | ||||||||
\(195\) | −3053.67 | −1.12142 | ||||||||
\(196\) | −206.142 | −0.0751245 | ||||||||
\(197\) | 712.470 | 0.257672 | 0.128836 | − | 0.991666i | \(-0.458876\pi\) | ||||
0.128836 | + | 0.991666i | \(0.458876\pi\) | |||||||
\(198\) | −8415.90 | −3.02066 | ||||||||
\(199\) | 860.619 | 0.306571 | 0.153286 | − | 0.988182i | \(-0.451015\pi\) | ||||
0.153286 | + | 0.988182i | \(0.451015\pi\) | |||||||
\(200\) | 470.678 | 0.166410 | ||||||||
\(201\) | −3914.70 | −1.37374 | ||||||||
\(202\) | −7094.28 | −2.47105 | ||||||||
\(203\) | 403.641 | 0.139557 | ||||||||
\(204\) | 2526.86 | 0.867233 | ||||||||
\(205\) | −2017.02 | −0.687193 | ||||||||
\(206\) | 646.487 | 0.218655 | ||||||||
\(207\) | −503.251 | −0.168978 | ||||||||
\(208\) | −4657.19 | −1.55249 | ||||||||
\(209\) | 423.806 | 0.140265 | ||||||||
\(210\) | 2627.86 | 0.863523 | ||||||||
\(211\) | 2090.15 | 0.681952 | 0.340976 | − | 0.940072i | \(-0.389242\pi\) | ||||
0.340976 | + | 0.940072i | \(0.389242\pi\) | |||||||
\(212\) | 1481.03 | 0.479799 | ||||||||
\(213\) | −2390.07 | −0.768849 | ||||||||
\(214\) | −2233.97 | −0.713603 | ||||||||
\(215\) | 1275.97 | 0.404745 | ||||||||
\(216\) | −367.256 | −0.115688 | ||||||||
\(217\) | −3436.49 | −1.07504 | ||||||||
\(218\) | −6760.84 | −2.10047 | ||||||||
\(219\) | 4110.85 | 1.26843 | ||||||||
\(220\) | −2199.89 | −0.674166 | ||||||||
\(221\) | 2983.66 | 0.908156 | ||||||||
\(222\) | −4812.21 | −1.45484 | ||||||||
\(223\) | −63.0624 | −0.0189371 | −0.00946854 | − | 0.999955i | \(-0.503014\pi\) | ||||
−0.00946854 | + | 0.999955i | \(0.503014\pi\) | |||||||
\(224\) | 4647.42 | 1.38624 | ||||||||
\(225\) | −3925.08 | −1.16299 | ||||||||
\(226\) | −4374.81 | −1.28765 | ||||||||
\(227\) | 2042.66 | 0.597252 | 0.298626 | − | 0.954370i | \(-0.403472\pi\) | ||||
0.298626 | + | 0.954370i | \(0.403472\pi\) | |||||||
\(228\) | 564.414 | 0.163944 | ||||||||
\(229\) | 1044.91 | 0.301526 | 0.150763 | − | 0.988570i | \(-0.451827\pi\) | ||||
0.150763 | + | 0.988570i | \(0.451827\pi\) | |||||||
\(230\) | −247.438 | −0.0709373 | ||||||||
\(231\) | 7841.31 | 2.23342 | ||||||||
\(232\) | −100.758 | −0.0285134 | ||||||||
\(233\) | 3215.45 | 0.904083 | 0.452041 | − | 0.891997i | \(-0.350696\pi\) | ||||
0.452041 | + | 0.891997i | \(0.350696\pi\) | |||||||
\(234\) | −13234.2 | −3.69721 | ||||||||
\(235\) | 1503.39 | 0.417321 | ||||||||
\(236\) | 572.522 | 0.157915 | ||||||||
\(237\) | −2976.97 | −0.815928 | ||||||||
\(238\) | −2567.61 | −0.699301 | ||||||||
\(239\) | 1090.37 | 0.295105 | 0.147553 | − | 0.989054i | \(-0.452860\pi\) | ||||
0.147553 | + | 0.989054i | \(0.452860\pi\) | |||||||
\(240\) | 1925.03 | 0.517752 | ||||||||
\(241\) | 575.585 | 0.153845 | 0.0769225 | − | 0.997037i | \(-0.475491\pi\) | ||||
0.0769225 | + | 0.997037i | \(0.475491\pi\) | |||||||
\(242\) | −6846.27 | −1.81857 | ||||||||
\(243\) | −5000.57 | −1.32011 | ||||||||
\(244\) | −2337.53 | −0.613299 | ||||||||
\(245\) | 100.612 | 0.0262361 | ||||||||
\(246\) | −15076.7 | −3.90754 | ||||||||
\(247\) | 666.447 | 0.171680 | ||||||||
\(248\) | 857.830 | 0.219646 | ||||||||
\(249\) | −3559.43 | −0.905903 | ||||||||
\(250\) | −4219.58 | −1.06748 | ||||||||
\(251\) | −6966.67 | −1.75192 | −0.875960 | − | 0.482383i | \(-0.839771\pi\) | ||||
−0.875960 | + | 0.482383i | \(0.839771\pi\) | |||||||
\(252\) | 6054.78 | 1.51355 | ||||||||
\(253\) | −738.333 | −0.183473 | ||||||||
\(254\) | 4217.81 | 1.04193 | ||||||||
\(255\) | −1233.28 | −0.302868 | ||||||||
\(256\) | 2776.22 | 0.677789 | ||||||||
\(257\) | −3245.89 | −0.787834 | −0.393917 | − | 0.919146i | \(-0.628880\pi\) | ||||
−0.393917 | + | 0.919146i | \(0.628880\pi\) | |||||||
\(258\) | 9537.54 | 2.30148 | ||||||||
\(259\) | 2599.64 | 0.623681 | ||||||||
\(260\) | −3459.39 | −0.825162 | ||||||||
\(261\) | 840.244 | 0.199271 | ||||||||
\(262\) | 10917.5 | 2.57437 | ||||||||
\(263\) | 7790.93 | 1.82665 | 0.913326 | − | 0.407229i | \(-0.133505\pi\) | ||||
0.913326 | + | 0.407229i | \(0.133505\pi\) | |||||||
\(264\) | −1957.38 | −0.456319 | ||||||||
\(265\) | −722.845 | −0.167562 | ||||||||
\(266\) | −573.516 | −0.132198 | ||||||||
\(267\) | 2095.21 | 0.480243 | ||||||||
\(268\) | −4434.81 | −1.01082 | ||||||||
\(269\) | −6258.67 | −1.41858 | −0.709289 | − | 0.704918i | \(-0.750984\pi\) | ||||
−0.709289 | + | 0.704918i | \(0.750984\pi\) | |||||||
\(270\) | 1505.82 | 0.339413 | ||||||||
\(271\) | −4577.50 | −1.02606 | −0.513032 | − | 0.858369i | \(-0.671478\pi\) | ||||
−0.513032 | + | 0.858369i | \(0.671478\pi\) | |||||||
\(272\) | −1880.90 | −0.419287 | ||||||||
\(273\) | 12330.7 | 2.73365 | ||||||||
\(274\) | 10508.9 | 2.31703 | ||||||||
\(275\) | −5758.58 | −1.26275 | ||||||||
\(276\) | −983.292 | −0.214447 | ||||||||
\(277\) | 1188.20 | 0.257733 | 0.128866 | − | 0.991662i | \(-0.458866\pi\) | ||||
0.128866 | + | 0.991662i | \(0.458866\pi\) | |||||||
\(278\) | −4002.99 | −0.863608 | ||||||||
\(279\) | −7153.61 | −1.53504 | ||||||||
\(280\) | 354.370 | 0.0756344 | ||||||||
\(281\) | 5759.46 | 1.22271 | 0.611354 | − | 0.791358i | \(-0.290625\pi\) | ||||
0.611354 | + | 0.791358i | \(0.290625\pi\) | |||||||
\(282\) | 11237.5 | 2.37299 | ||||||||
\(283\) | −3166.41 | −0.665102 | −0.332551 | − | 0.943085i | \(-0.607909\pi\) | ||||
−0.332551 | + | 0.943085i | \(0.607909\pi\) | |||||||
\(284\) | −2707.62 | −0.565731 | ||||||||
\(285\) | −275.474 | −0.0572549 | ||||||||
\(286\) | −19416.3 | −4.01436 | ||||||||
\(287\) | 8144.68 | 1.67514 | ||||||||
\(288\) | 9674.36 | 1.97940 | ||||||||
\(289\) | −3707.99 | −0.754731 | ||||||||
\(290\) | 413.130 | 0.0836546 | ||||||||
\(291\) | 2141.76 | 0.431451 | ||||||||
\(292\) | 4657.03 | 0.933328 | ||||||||
\(293\) | −8113.37 | −1.61771 | −0.808853 | − | 0.588011i | \(-0.799911\pi\) | ||||
−0.808853 | + | 0.588011i | \(0.799911\pi\) | |||||||
\(294\) | 752.046 | 0.149184 | ||||||||
\(295\) | −279.431 | −0.0551494 | ||||||||
\(296\) | −648.931 | −0.127427 | ||||||||
\(297\) | 4493.25 | 0.877860 | ||||||||
\(298\) | −5433.31 | −1.05619 | ||||||||
\(299\) | −1161.05 | −0.224566 | ||||||||
\(300\) | −7669.13 | −1.47592 | ||||||||
\(301\) | −5152.33 | −0.986630 | ||||||||
\(302\) | −1249.21 | −0.238026 | ||||||||
\(303\) | 13759.6 | 2.60881 | ||||||||
\(304\) | −420.128 | −0.0792631 | ||||||||
\(305\) | 1140.88 | 0.214185 | ||||||||
\(306\) | −5344.90 | −0.998522 | ||||||||
\(307\) | 257.041 | 0.0477853 | 0.0238926 | − | 0.999715i | \(-0.492394\pi\) | ||||
0.0238926 | + | 0.999715i | \(0.492394\pi\) | |||||||
\(308\) | 8883.12 | 1.64339 | ||||||||
\(309\) | −1253.89 | −0.230845 | ||||||||
\(310\) | −3517.28 | −0.644413 | ||||||||
\(311\) | 1137.07 | 0.207322 | 0.103661 | − | 0.994613i | \(-0.466944\pi\) | ||||
0.103661 | + | 0.994613i | \(0.466944\pi\) | |||||||
\(312\) | −3078.03 | −0.558523 | ||||||||
\(313\) | 6607.47 | 1.19321 | 0.596607 | − | 0.802533i | \(-0.296515\pi\) | ||||
0.596607 | + | 0.802533i | \(0.296515\pi\) | |||||||
\(314\) | 14235.0 | 2.55838 | ||||||||
\(315\) | −2955.16 | −0.528585 | ||||||||
\(316\) | −3372.50 | −0.600373 | ||||||||
\(317\) | 2277.77 | 0.403571 | 0.201786 | − | 0.979430i | \(-0.435326\pi\) | ||||
0.201786 | + | 0.979430i | \(0.435326\pi\) | |||||||
\(318\) | −5403.09 | −0.952799 | ||||||||
\(319\) | 1232.74 | 0.216365 | ||||||||
\(320\) | 2835.47 | 0.495336 | ||||||||
\(321\) | 4332.87 | 0.753387 | ||||||||
\(322\) | 999.150 | 0.172921 | ||||||||
\(323\) | 269.158 | 0.0463663 | ||||||||
\(324\) | −3150.49 | −0.540208 | ||||||||
\(325\) | −9055.52 | −1.54557 | ||||||||
\(326\) | 14289.2 | 2.42762 | ||||||||
\(327\) | 13112.9 | 2.21757 | ||||||||
\(328\) | −2033.11 | −0.342255 | ||||||||
\(329\) | −6070.67 | −1.01729 | ||||||||
\(330\) | 8025.65 | 1.33878 | ||||||||
\(331\) | −5412.68 | −0.898814 | −0.449407 | − | 0.893327i | \(-0.648365\pi\) | ||||
−0.449407 | + | 0.893327i | \(0.648365\pi\) | |||||||
\(332\) | −4032.34 | −0.666577 | ||||||||
\(333\) | 5411.56 | 0.890546 | ||||||||
\(334\) | −15177.4 | −2.48644 | ||||||||
\(335\) | 2164.50 | 0.353013 | ||||||||
\(336\) | −7773.25 | −1.26210 | ||||||||
\(337\) | −4295.39 | −0.694316 | −0.347158 | − | 0.937807i | \(-0.612853\pi\) | ||||
−0.347158 | + | 0.937807i | \(0.612853\pi\) | |||||||
\(338\) | −21452.6 | −3.45227 | ||||||||
\(339\) | 8485.11 | 1.35943 | ||||||||
\(340\) | −1397.14 | −0.222855 | ||||||||
\(341\) | −10495.2 | −1.66671 | ||||||||
\(342\) | −1193.87 | −0.188763 | ||||||||
\(343\) | −6544.91 | −1.03030 | ||||||||
\(344\) | 1286.15 | 0.201582 | ||||||||
\(345\) | 479.916 | 0.0748921 | ||||||||
\(346\) | −4138.76 | −0.643067 | ||||||||
\(347\) | 2284.59 | 0.353439 | 0.176719 | − | 0.984261i | \(-0.443452\pi\) | ||||
0.176719 | + | 0.984261i | \(0.443452\pi\) | |||||||
\(348\) | 1641.74 | 0.252891 | ||||||||
\(349\) | −6204.33 | −0.951605 | −0.475802 | − | 0.879552i | \(-0.657842\pi\) | ||||
−0.475802 | + | 0.879552i | \(0.657842\pi\) | |||||||
\(350\) | 7792.81 | 1.19012 | ||||||||
\(351\) | 7065.75 | 1.07448 | ||||||||
\(352\) | 14193.5 | 2.14919 | ||||||||
\(353\) | −6615.29 | −0.997440 | −0.498720 | − | 0.866763i | \(-0.666196\pi\) | ||||
−0.498720 | + | 0.866763i | \(0.666196\pi\) | |||||||
\(354\) | −2088.68 | −0.313593 | ||||||||
\(355\) | 1321.51 | 0.197573 | ||||||||
\(356\) | 2373.59 | 0.353370 | ||||||||
\(357\) | 4979.98 | 0.738287 | ||||||||
\(358\) | −10538.7 | −1.55583 | ||||||||
\(359\) | 3926.62 | 0.577267 | 0.288634 | − | 0.957440i | \(-0.406799\pi\) | ||||
0.288634 | + | 0.957440i | \(0.406799\pi\) | |||||||
\(360\) | 737.678 | 0.107997 | ||||||||
\(361\) | −6798.88 | −0.991235 | ||||||||
\(362\) | −3391.80 | −0.492456 | ||||||||
\(363\) | 13278.6 | 1.91996 | ||||||||
\(364\) | 13968.9 | 2.01146 | ||||||||
\(365\) | −2272.95 | −0.325950 | ||||||||
\(366\) | 8527.78 | 1.21791 | ||||||||
\(367\) | 3312.85 | 0.471197 | 0.235598 | − | 0.971851i | \(-0.424295\pi\) | ||||
0.235598 | + | 0.971851i | \(0.424295\pi\) | |||||||
\(368\) | 731.925 | 0.103680 | ||||||||
\(369\) | 16954.5 | 2.39191 | ||||||||
\(370\) | 2660.75 | 0.373854 | ||||||||
\(371\) | 2918.83 | 0.408459 | ||||||||
\(372\) | −13977.3 | −1.94809 | ||||||||
\(373\) | −8350.37 | −1.15916 | −0.579579 | − | 0.814916i | \(-0.696783\pi\) | ||||
−0.579579 | + | 0.814916i | \(0.696783\pi\) | |||||||
\(374\) | −7841.64 | −1.08418 | ||||||||
\(375\) | 8184.05 | 1.12699 | ||||||||
\(376\) | 1515.39 | 0.207846 | ||||||||
\(377\) | 1938.52 | 0.264825 | ||||||||
\(378\) | −6080.49 | −0.827372 | ||||||||
\(379\) | 3866.52 | 0.524036 | 0.262018 | − | 0.965063i | \(-0.415612\pi\) | ||||
0.262018 | + | 0.965063i | \(0.415612\pi\) | |||||||
\(380\) | −312.074 | −0.0421290 | ||||||||
\(381\) | −8180.61 | −1.10001 | ||||||||
\(382\) | 17998.6 | 2.41070 | ||||||||
\(383\) | 460.086 | 0.0613820 | 0.0306910 | − | 0.999529i | \(-0.490229\pi\) | ||||
0.0306910 | + | 0.999529i | \(0.490229\pi\) | |||||||
\(384\) | 4541.99 | 0.603600 | ||||||||
\(385\) | −4335.59 | −0.573927 | ||||||||
\(386\) | 6059.46 | 0.799011 | ||||||||
\(387\) | −10725.4 | −1.40879 | ||||||||
\(388\) | 2426.32 | 0.317468 | ||||||||
\(389\) | 13981.6 | 1.82235 | 0.911175 | − | 0.412019i | \(-0.135176\pi\) | ||||
0.911175 | + | 0.412019i | \(0.135176\pi\) | |||||||
\(390\) | 12620.5 | 1.63863 | ||||||||
\(391\) | −468.912 | −0.0606494 | ||||||||
\(392\) | 101.414 | 0.0130668 | ||||||||
\(393\) | −21174.9 | −2.71790 | ||||||||
\(394\) | −2944.58 | −0.376512 | ||||||||
\(395\) | 1646.01 | 0.209671 | ||||||||
\(396\) | 18491.7 | 2.34657 | ||||||||
\(397\) | −7238.31 | −0.915064 | −0.457532 | − | 0.889193i | \(-0.651266\pi\) | ||||
−0.457532 | + | 0.889193i | \(0.651266\pi\) | |||||||
\(398\) | −3556.86 | −0.447963 | ||||||||
\(399\) | 1112.36 | 0.139568 | ||||||||
\(400\) | 5708.60 | 0.713575 | ||||||||
\(401\) | 4187.60 | 0.521493 | 0.260747 | − | 0.965407i | \(-0.416031\pi\) | ||||
0.260747 | + | 0.965407i | \(0.416031\pi\) | |||||||
\(402\) | 16179.1 | 2.00731 | ||||||||
\(403\) | −16504.0 | −2.04001 | ||||||||
\(404\) | 15587.8 | 1.91961 | ||||||||
\(405\) | 1537.66 | 0.188659 | ||||||||
\(406\) | −1668.21 | −0.203921 | ||||||||
\(407\) | 7939.44 | 0.966937 | ||||||||
\(408\) | −1243.12 | −0.150843 | ||||||||
\(409\) | 9828.49 | 1.18823 | 0.594117 | − | 0.804379i | \(-0.297502\pi\) | ||||
0.594117 | + | 0.804379i | \(0.297502\pi\) | |||||||
\(410\) | 8336.15 | 1.00413 | ||||||||
\(411\) | −20382.4 | −2.44621 | ||||||||
\(412\) | −1420.48 | −0.169859 | ||||||||
\(413\) | 1128.34 | 0.134435 | ||||||||
\(414\) | 2079.89 | 0.246911 | ||||||||
\(415\) | 1968.07 | 0.232792 | ||||||||
\(416\) | 22319.7 | 2.63056 | ||||||||
\(417\) | 7763.95 | 0.911755 | ||||||||
\(418\) | −1751.55 | −0.204955 | ||||||||
\(419\) | −1703.49 | −0.198618 | −0.0993092 | − | 0.995057i | \(-0.531663\pi\) | ||||
−0.0993092 | + | 0.995057i | \(0.531663\pi\) | |||||||
\(420\) | −5774.02 | −0.670817 | ||||||||
\(421\) | −1139.44 | −0.131907 | −0.0659536 | − | 0.997823i | \(-0.521009\pi\) | ||||
−0.0659536 | + | 0.997823i | \(0.521009\pi\) | |||||||
\(422\) | −8638.41 | −0.996472 | ||||||||
\(423\) | −12637.1 | −1.45257 | ||||||||
\(424\) | −728.611 | −0.0834540 | ||||||||
\(425\) | −3657.25 | −0.417418 | ||||||||
\(426\) | 9877.95 | 1.12345 | ||||||||
\(427\) | −4606.84 | −0.522110 | ||||||||
\(428\) | 4908.54 | 0.554354 | ||||||||
\(429\) | 37658.6 | 4.23817 | ||||||||
\(430\) | −5273.46 | −0.591416 | ||||||||
\(431\) | −8359.34 | −0.934235 | −0.467118 | − | 0.884195i | \(-0.654708\pi\) | ||||
−0.467118 | + | 0.884195i | \(0.654708\pi\) | |||||||
\(432\) | −4454.25 | −0.496077 | ||||||||
\(433\) | −4342.97 | −0.482009 | −0.241004 | − | 0.970524i | \(-0.577477\pi\) | ||||
−0.241004 | + | 0.970524i | \(0.577477\pi\) | |||||||
\(434\) | 14202.7 | 1.57086 | ||||||||
\(435\) | −801.282 | −0.0883184 | ||||||||
\(436\) | 14855.1 | 1.63172 | ||||||||
\(437\) | −104.739 | −0.0114653 | ||||||||
\(438\) | −16989.8 | −1.85343 | ||||||||
\(439\) | 14668.0 | 1.59469 | 0.797343 | − | 0.603527i | \(-0.206238\pi\) | ||||
0.797343 | + | 0.603527i | \(0.206238\pi\) | |||||||
\(440\) | 1082.27 | 0.117261 | ||||||||
\(441\) | −845.712 | −0.0913197 | ||||||||
\(442\) | −12331.2 | −1.32700 | ||||||||
\(443\) | −15972.8 | −1.71308 | −0.856538 | − | 0.516084i | \(-0.827389\pi\) | ||||
−0.856538 | + | 0.516084i | \(0.827389\pi\) | |||||||
\(444\) | 10573.5 | 1.13018 | ||||||||
\(445\) | −1158.48 | −0.123409 | ||||||||
\(446\) | 260.631 | 0.0276710 | ||||||||
\(447\) | 10538.1 | 1.11507 | ||||||||
\(448\) | −11449.6 | −1.20746 | ||||||||
\(449\) | 10764.5 | 1.13142 | 0.565711 | − | 0.824604i | \(-0.308602\pi\) | ||||
0.565711 | + | 0.824604i | \(0.308602\pi\) | |||||||
\(450\) | 16222.0 | 1.69936 | ||||||||
\(451\) | 24874.3 | 2.59709 | ||||||||
\(452\) | 9612.46 | 1.00029 | ||||||||
\(453\) | 2422.89 | 0.251296 | ||||||||
\(454\) | −8442.14 | −0.872707 | ||||||||
\(455\) | −6817.82 | −0.702471 | ||||||||
\(456\) | −277.671 | −0.0285157 | ||||||||
\(457\) | 3048.91 | 0.312083 | 0.156042 | − | 0.987750i | \(-0.450127\pi\) | ||||
0.156042 | + | 0.987750i | \(0.450127\pi\) | |||||||
\(458\) | −4318.52 | −0.440592 | ||||||||
\(459\) | 2853.64 | 0.290189 | ||||||||
\(460\) | 543.678 | 0.0551068 | ||||||||
\(461\) | −10219.5 | −1.03247 | −0.516237 | − | 0.856446i | \(-0.672667\pi\) | ||||
−0.516237 | + | 0.856446i | \(0.672667\pi\) | |||||||
\(462\) | −32407.4 | −3.26349 | ||||||||
\(463\) | −10323.3 | −1.03621 | −0.518103 | − | 0.855318i | \(-0.673362\pi\) | ||||
−0.518103 | + | 0.855318i | \(0.673362\pi\) | |||||||
\(464\) | −1222.04 | −0.122267 | ||||||||
\(465\) | 6821.90 | 0.680339 | ||||||||
\(466\) | −13289.2 | −1.32105 | ||||||||
\(467\) | 3566.38 | 0.353388 | 0.176694 | − | 0.984266i | \(-0.443460\pi\) | ||||
0.176694 | + | 0.984266i | \(0.443460\pi\) | |||||||
\(468\) | 29078.6 | 2.87214 | ||||||||
\(469\) | −8740.21 | −0.860523 | ||||||||
\(470\) | −6213.39 | −0.609792 | ||||||||
\(471\) | −27609.4 | −2.70101 | ||||||||
\(472\) | −281.660 | −0.0274670 | ||||||||
\(473\) | −15735.5 | −1.52964 | ||||||||
\(474\) | 12303.6 | 1.19224 | ||||||||
\(475\) | −816.905 | −0.0789098 | ||||||||
\(476\) | 5641.63 | 0.543243 | ||||||||
\(477\) | 6076.03 | 0.583233 | ||||||||
\(478\) | −4506.40 | −0.431209 | ||||||||
\(479\) | −15365.2 | −1.46567 | −0.732834 | − | 0.680407i | \(-0.761803\pi\) | ||||
−0.732834 | + | 0.680407i | \(0.761803\pi\) | |||||||
\(480\) | −9225.76 | −0.877284 | ||||||||
\(481\) | 12485.0 | 1.18351 | ||||||||
\(482\) | −2378.84 | −0.224799 | ||||||||
\(483\) | −1937.89 | −0.182561 | ||||||||
\(484\) | 15042.8 | 1.41274 | ||||||||
\(485\) | −1184.21 | −0.110871 | ||||||||
\(486\) | 20666.9 | 1.92895 | ||||||||
\(487\) | 12202.4 | 1.13540 | 0.567702 | − | 0.823234i | \(-0.307833\pi\) | ||||
0.567702 | + | 0.823234i | \(0.307833\pi\) | |||||||
\(488\) | 1149.98 | 0.106674 | ||||||||
\(489\) | −27714.4 | −2.56296 | ||||||||
\(490\) | −415.818 | −0.0383363 | ||||||||
\(491\) | −7775.84 | −0.714702 | −0.357351 | − | 0.933970i | \(-0.616320\pi\) | ||||
−0.357351 | + | 0.933970i | \(0.616320\pi\) | |||||||
\(492\) | 33127.0 | 3.03553 | ||||||||
\(493\) | 782.910 | 0.0715223 | ||||||||
\(494\) | −2754.36 | −0.250860 | ||||||||
\(495\) | −9025.22 | −0.819502 | ||||||||
\(496\) | 10404.2 | 0.941855 | ||||||||
\(497\) | −5336.23 | −0.481615 | ||||||||
\(498\) | 14710.8 | 1.32371 | ||||||||
\(499\) | −10285.6 | −0.922738 | −0.461369 | − | 0.887208i | \(-0.652642\pi\) | ||||
−0.461369 | + | 0.887208i | \(0.652642\pi\) | |||||||
\(500\) | 9271.40 | 0.829259 | ||||||||
\(501\) | 29437.1 | 2.62506 | ||||||||
\(502\) | 28792.6 | 2.55992 | ||||||||
\(503\) | −16257.7 | −1.44114 | −0.720572 | − | 0.693380i | \(-0.756121\pi\) | ||||
−0.720572 | + | 0.693380i | \(0.756121\pi\) | |||||||
\(504\) | −2978.73 | −0.263260 | ||||||||
\(505\) | −7607.93 | −0.670393 | ||||||||
\(506\) | 3051.46 | 0.268091 | ||||||||
\(507\) | 41608.1 | 3.64474 | ||||||||
\(508\) | −9267.51 | −0.809408 | ||||||||
\(509\) | 17537.6 | 1.52720 | 0.763598 | − | 0.645692i | \(-0.223431\pi\) | ||||
0.763598 | + | 0.645692i | \(0.223431\pi\) | |||||||
\(510\) | 5097.06 | 0.442552 | ||||||||
\(511\) | 9178.15 | 0.794555 | ||||||||
\(512\) | −16006.8 | −1.38166 | ||||||||
\(513\) | 637.406 | 0.0548580 | ||||||||
\(514\) | 13415.0 | 1.15119 | ||||||||
\(515\) | 693.294 | 0.0593207 | ||||||||
\(516\) | −20956.2 | −1.78788 | ||||||||
\(517\) | −18540.2 | −1.57717 | ||||||||
\(518\) | −10744.1 | −0.911326 | ||||||||
\(519\) | 8027.29 | 0.678919 | ||||||||
\(520\) | 1701.89 | 0.143525 | ||||||||
\(521\) | 982.730 | 0.0826376 | 0.0413188 | − | 0.999146i | \(-0.486844\pi\) | ||||
0.0413188 | + | 0.999146i | \(0.486844\pi\) | |||||||
\(522\) | −3472.65 | −0.291176 | ||||||||
\(523\) | 6047.59 | 0.505626 | 0.252813 | − | 0.967515i | \(-0.418644\pi\) | ||||
0.252813 | + | 0.967515i | \(0.418644\pi\) | |||||||
\(524\) | −23988.3 | −1.99987 | ||||||||
\(525\) | −15114.5 | −1.25647 | ||||||||
\(526\) | −32199.2 | −2.66911 | ||||||||
\(527\) | −6665.48 | −0.550955 | ||||||||
\(528\) | −23740.0 | −1.95672 | ||||||||
\(529\) | −11984.5 | −0.985003 | ||||||||
\(530\) | 2987.45 | 0.244843 | ||||||||
\(531\) | 2348.81 | 0.191958 | ||||||||
\(532\) | 1260.15 | 0.102696 | ||||||||
\(533\) | 39115.6 | 3.17877 | ||||||||
\(534\) | −8659.33 | −0.701734 | ||||||||
\(535\) | −2395.71 | −0.193599 | ||||||||
\(536\) | 2181.77 | 0.175817 | ||||||||
\(537\) | 20440.2 | 1.64257 | ||||||||
\(538\) | 25866.5 | 2.07283 | ||||||||
\(539\) | −1240.77 | −0.0991531 | ||||||||
\(540\) | −3308.64 | −0.263669 | ||||||||
\(541\) | −21044.1 | −1.67238 | −0.836191 | − | 0.548439i | \(-0.815222\pi\) | ||||
−0.836191 | + | 0.548439i | \(0.815222\pi\) | |||||||
\(542\) | 18918.4 | 1.49929 | ||||||||
\(543\) | 6578.53 | 0.519911 | ||||||||
\(544\) | 9014.23 | 0.710445 | ||||||||
\(545\) | −7250.34 | −0.569854 | ||||||||
\(546\) | −50961.6 | −3.99442 | ||||||||
\(547\) | −547.000 | −0.0427569 | ||||||||
\(548\) | −23090.5 | −1.79996 | ||||||||
\(549\) | −9589.89 | −0.745513 | ||||||||
\(550\) | 23799.7 | 1.84513 | ||||||||
\(551\) | 174.875 | 0.0135208 | ||||||||
\(552\) | 483.744 | 0.0372998 | ||||||||
\(553\) | −6646.58 | −0.511105 | ||||||||
\(554\) | −4910.73 | −0.376601 | ||||||||
\(555\) | −5160.63 | −0.394696 | ||||||||
\(556\) | 8795.48 | 0.670884 | ||||||||
\(557\) | −21175.6 | −1.61084 | −0.805420 | − | 0.592704i | \(-0.798060\pi\) | ||||
−0.805420 | + | 0.592704i | \(0.798060\pi\) | |||||||
\(558\) | 29565.2 | 2.24300 | ||||||||
\(559\) | −24744.5 | −1.87224 | ||||||||
\(560\) | 4297.96 | 0.324325 | ||||||||
\(561\) | 15209.2 | 1.14462 | ||||||||
\(562\) | −23803.3 | −1.78663 | ||||||||
\(563\) | 13176.6 | 0.986371 | 0.493186 | − | 0.869924i | \(-0.335832\pi\) | ||||
0.493186 | + | 0.869924i | \(0.335832\pi\) | |||||||
\(564\) | −24691.3 | −1.84343 | ||||||||
\(565\) | −4691.55 | −0.349337 | ||||||||
\(566\) | 13086.5 | 0.971850 | ||||||||
\(567\) | −6209.05 | −0.459886 | ||||||||
\(568\) | 1332.05 | 0.0984007 | ||||||||
\(569\) | −2414.54 | −0.177896 | −0.0889478 | − | 0.996036i | \(-0.528350\pi\) | ||||
−0.0889478 | + | 0.996036i | \(0.528350\pi\) | |||||||
\(570\) | 1138.51 | 0.0836611 | ||||||||
\(571\) | 585.979 | 0.0429465 | 0.0214733 | − | 0.999769i | \(-0.493164\pi\) | ||||
0.0214733 | + | 0.999769i | \(0.493164\pi\) | |||||||
\(572\) | 42662.0 | 3.11851 | ||||||||
\(573\) | −34909.0 | −2.54510 | ||||||||
\(574\) | −33661.2 | −2.44772 | ||||||||
\(575\) | 1423.17 | 0.103218 | ||||||||
\(576\) | −23834.2 | −1.72411 | ||||||||
\(577\) | 27231.6 | 1.96476 | 0.982381 | − | 0.186891i | \(-0.0598412\pi\) | ||||
0.982381 | + | 0.186891i | \(0.0598412\pi\) | |||||||
\(578\) | 15324.8 | 1.10282 | ||||||||
\(579\) | −11752.5 | −0.843557 | ||||||||
\(580\) | −907.742 | −0.0649861 | ||||||||
\(581\) | −7947.02 | −0.567466 | ||||||||
\(582\) | −8851.70 | −0.630438 | ||||||||
\(583\) | 8914.30 | 0.633263 | ||||||||
\(584\) | −2291.09 | −0.162339 | ||||||||
\(585\) | −14192.4 | −1.00305 | ||||||||
\(586\) | 33531.8 | 2.36380 | ||||||||
\(587\) | −13881.2 | −0.976042 | −0.488021 | − | 0.872832i | \(-0.662281\pi\) | ||||
−0.488021 | + | 0.872832i | \(0.662281\pi\) | |||||||
\(588\) | −1652.42 | −0.115892 | ||||||||
\(589\) | −1488.84 | −0.104154 | ||||||||
\(590\) | 1154.86 | 0.0805846 | ||||||||
\(591\) | 5711.12 | 0.397503 | ||||||||
\(592\) | −7870.54 | −0.546414 | ||||||||
\(593\) | −13743.6 | −0.951740 | −0.475870 | − | 0.879516i | \(-0.657867\pi\) | ||||
−0.475870 | + | 0.879516i | \(0.657867\pi\) | |||||||
\(594\) | −18570.2 | −1.28273 | ||||||||
\(595\) | −2753.51 | −0.189719 | ||||||||
\(596\) | 11938.2 | 0.820485 | ||||||||
\(597\) | 6898.67 | 0.472938 | ||||||||
\(598\) | 4798.51 | 0.328136 | ||||||||
\(599\) | 23063.7 | 1.57322 | 0.786610 | − | 0.617450i | \(-0.211834\pi\) | ||||
0.786610 | + | 0.617450i | \(0.211834\pi\) | |||||||
\(600\) | 3772.93 | 0.256715 | ||||||||
\(601\) | −21928.1 | −1.48830 | −0.744148 | − | 0.668015i | \(-0.767144\pi\) | ||||
−0.744148 | + | 0.668015i | \(0.767144\pi\) | |||||||
\(602\) | 21294.1 | 1.44167 | ||||||||
\(603\) | −18194.2 | −1.22873 | ||||||||
\(604\) | 2744.80 | 0.184908 | ||||||||
\(605\) | −7341.96 | −0.493377 | ||||||||
\(606\) | −56867.4 | −3.81201 | ||||||||
\(607\) | 18710.7 | 1.25114 | 0.625571 | − | 0.780167i | \(-0.284866\pi\) | ||||
0.625571 | + | 0.780167i | \(0.284866\pi\) | |||||||
\(608\) | 2013.47 | 0.134304 | ||||||||
\(609\) | 3235.56 | 0.215290 | ||||||||
\(610\) | −4715.15 | −0.312968 | ||||||||
\(611\) | −29155.0 | −1.93041 | ||||||||
\(612\) | 11744.0 | 0.775690 | ||||||||
\(613\) | 19774.9 | 1.30294 | 0.651468 | − | 0.758676i | \(-0.274153\pi\) | ||||
0.651468 | + | 0.758676i | \(0.274153\pi\) | |||||||
\(614\) | −1062.33 | −0.0698241 | ||||||||
\(615\) | −16168.3 | −1.06011 | ||||||||
\(616\) | −4370.17 | −0.285843 | ||||||||
\(617\) | −9684.87 | −0.631926 | −0.315963 | − | 0.948772i | \(-0.602328\pi\) | ||||
−0.315963 | + | 0.948772i | \(0.602328\pi\) | |||||||
\(618\) | 5182.20 | 0.337312 | ||||||||
\(619\) | −16148.3 | −1.04855 | −0.524277 | − | 0.851548i | \(-0.675664\pi\) | ||||
−0.524277 | + | 0.851548i | \(0.675664\pi\) | |||||||
\(620\) | 7728.27 | 0.500604 | ||||||||
\(621\) | −1110.45 | −0.0717569 | ||||||||
\(622\) | −4699.39 | −0.302939 | ||||||||
\(623\) | 4677.91 | 0.300829 | ||||||||
\(624\) | −37331.8 | −2.39498 | ||||||||
\(625\) | 8644.42 | 0.553243 | ||||||||
\(626\) | −27308.1 | −1.74353 | ||||||||
\(627\) | 3397.21 | 0.216382 | ||||||||
\(628\) | −31277.7 | −1.98744 | ||||||||
\(629\) | 5042.31 | 0.319634 | ||||||||
\(630\) | 12213.4 | 0.772371 | ||||||||
\(631\) | −13912.3 | −0.877720 | −0.438860 | − | 0.898556i | \(-0.644618\pi\) | ||||
−0.438860 | + | 0.898556i | \(0.644618\pi\) | |||||||
\(632\) | 1659.15 | 0.104426 | ||||||||
\(633\) | 16754.5 | 1.05203 | ||||||||
\(634\) | −9413.81 | −0.589701 | ||||||||
\(635\) | 4523.19 | 0.282673 | ||||||||
\(636\) | 11871.8 | 0.740171 | ||||||||
\(637\) | −1951.14 | −0.121361 | ||||||||
\(638\) | −5094.82 | −0.316153 | ||||||||
\(639\) | −11108.2 | −0.687691 | ||||||||
\(640\) | −2511.34 | −0.155108 | ||||||||
\(641\) | 21571.1 | 1.32918 | 0.664591 | − | 0.747207i | \(-0.268606\pi\) | ||||
0.664591 | + | 0.747207i | \(0.268606\pi\) | |||||||
\(642\) | −17907.4 | −1.10085 | ||||||||
\(643\) | −14895.6 | −0.913567 | −0.456783 | − | 0.889578i | \(-0.650999\pi\) | ||||
−0.456783 | + | 0.889578i | \(0.650999\pi\) | |||||||
\(644\) | −2195.36 | −0.134331 | ||||||||
\(645\) | 10228.1 | 0.624388 | ||||||||
\(646\) | −1112.40 | −0.0677507 | ||||||||
\(647\) | 31426.1 | 1.90956 | 0.954782 | − | 0.297307i | \(-0.0960884\pi\) | ||||
0.954782 | + | 0.297307i | \(0.0960884\pi\) | |||||||
\(648\) | 1549.93 | 0.0939613 | ||||||||
\(649\) | 3446.01 | 0.208425 | ||||||||
\(650\) | 37425.7 | 2.25839 | ||||||||
\(651\) | −27546.7 | −1.65843 | ||||||||
\(652\) | −31396.6 | −1.88587 | ||||||||
\(653\) | 16387.0 | 0.982041 | 0.491020 | − | 0.871148i | \(-0.336624\pi\) | ||||
0.491020 | + | 0.871148i | \(0.336624\pi\) | |||||||
\(654\) | −54194.5 | −3.24032 | ||||||||
\(655\) | 11708.0 | 0.698424 | ||||||||
\(656\) | −24658.5 | −1.46761 | ||||||||
\(657\) | 19105.8 | 1.13453 | ||||||||
\(658\) | 25089.5 | 1.48646 | ||||||||
\(659\) | 23831.3 | 1.40870 | 0.704350 | − | 0.709852i | \(-0.251238\pi\) | ||||
0.704350 | + | 0.709852i | \(0.251238\pi\) | |||||||
\(660\) | −17634.2 | −1.04002 | ||||||||
\(661\) | 31788.5 | 1.87054 | 0.935271 | − | 0.353932i | \(-0.115156\pi\) | ||||
0.935271 | + | 0.353932i | \(0.115156\pi\) | |||||||
\(662\) | 22370.1 | 1.31335 | ||||||||
\(663\) | 23916.8 | 1.40098 | ||||||||
\(664\) | 1983.77 | 0.115941 | ||||||||
\(665\) | −615.040 | −0.0358650 | ||||||||
\(666\) | −22365.5 | −1.30127 | ||||||||
\(667\) | −304.659 | −0.0176858 | ||||||||
\(668\) | 33348.2 | 1.93156 | ||||||||
\(669\) | −505.504 | −0.0292136 | ||||||||
\(670\) | −8945.68 | −0.515824 | ||||||||
\(671\) | −14069.6 | −0.809464 | ||||||||
\(672\) | 37253.5 | 2.13852 | ||||||||
\(673\) | −19746.6 | −1.13102 | −0.565510 | − | 0.824742i | \(-0.691321\pi\) | ||||
−0.565510 | + | 0.824742i | \(0.691321\pi\) | |||||||
\(674\) | 17752.4 | 1.01454 | ||||||||
\(675\) | −8660.92 | −0.493865 | ||||||||
\(676\) | 47136.3 | 2.68185 | ||||||||
\(677\) | −21362.6 | −1.21275 | −0.606376 | − | 0.795178i | \(-0.707377\pi\) | ||||
−0.606376 | + | 0.795178i | \(0.707377\pi\) | |||||||
\(678\) | −35068.2 | −1.98641 | ||||||||
\(679\) | 4781.83 | 0.270265 | ||||||||
\(680\) | 687.343 | 0.0387623 | ||||||||
\(681\) | 16373.9 | 0.921362 | ||||||||
\(682\) | 43375.9 | 2.43541 | ||||||||
\(683\) | 814.972 | 0.0456575 | 0.0228287 | − | 0.999739i | \(-0.492733\pi\) | ||||
0.0228287 | + | 0.999739i | \(0.492733\pi\) | |||||||
\(684\) | 2623.20 | 0.146638 | ||||||||
\(685\) | 11269.8 | 0.628607 | ||||||||
\(686\) | 27049.5 | 1.50548 | ||||||||
\(687\) | 8375.93 | 0.465155 | ||||||||
\(688\) | 15599.0 | 0.864397 | ||||||||
\(689\) | 14018.0 | 0.775097 | ||||||||
\(690\) | −1983.45 | −0.109433 | ||||||||
\(691\) | 25662.9 | 1.41282 | 0.706412 | − | 0.707801i | \(-0.250313\pi\) | ||||
0.706412 | + | 0.707801i | \(0.250313\pi\) | |||||||
\(692\) | 9093.81 | 0.499559 | ||||||||
\(693\) | 36443.7 | 1.99766 | ||||||||
\(694\) | −9442.01 | −0.516446 | ||||||||
\(695\) | −4292.81 | −0.234296 | ||||||||
\(696\) | −807.674 | −0.0439868 | ||||||||
\(697\) | 15797.6 | 0.858503 | ||||||||
\(698\) | 25641.9 | 1.39049 | ||||||||
\(699\) | 25774.9 | 1.39470 | ||||||||
\(700\) | −17122.6 | −0.924533 | ||||||||
\(701\) | 25978.0 | 1.39968 | 0.699840 | − | 0.714300i | \(-0.253255\pi\) | ||||
0.699840 | + | 0.714300i | \(0.253255\pi\) | |||||||
\(702\) | −29202.1 | −1.57003 | ||||||||
\(703\) | 1126.28 | 0.0604245 | ||||||||
\(704\) | −34967.7 | −1.87201 | ||||||||
\(705\) | 12051.1 | 0.643789 | ||||||||
\(706\) | 27340.4 | 1.45746 | ||||||||
\(707\) | 30720.7 | 1.63419 | ||||||||
\(708\) | 4589.30 | 0.243611 | ||||||||
\(709\) | −15753.7 | −0.834474 | −0.417237 | − | 0.908798i | \(-0.637002\pi\) | ||||
−0.417237 | + | 0.908798i | \(0.637002\pi\) | |||||||
\(710\) | −5461.68 | −0.288694 | ||||||||
\(711\) | −13835.9 | −0.729800 | ||||||||
\(712\) | −1167.72 | −0.0614636 | ||||||||
\(713\) | 2593.78 | 0.136238 | ||||||||
\(714\) | −20581.8 | −1.07879 | ||||||||
\(715\) | −20822.0 | −1.08909 | ||||||||
\(716\) | 23155.9 | 1.20863 | ||||||||
\(717\) | 8740.34 | 0.455250 | ||||||||
\(718\) | −16228.4 | −0.843506 | ||||||||
\(719\) | −17232.3 | −0.893820 | −0.446910 | − | 0.894579i | \(-0.647476\pi\) | ||||
−0.446910 | + | 0.894579i | \(0.647476\pi\) | |||||||
\(720\) | 8946.89 | 0.463099 | ||||||||
\(721\) | −2799.51 | −0.144603 | ||||||||
\(722\) | 28099.2 | 1.44840 | ||||||||
\(723\) | 4613.85 | 0.237332 | ||||||||
\(724\) | 7452.56 | 0.382559 | ||||||||
\(725\) | −2376.16 | −0.121722 | ||||||||
\(726\) | −54879.3 | −2.80546 | ||||||||
\(727\) | 4356.85 | 0.222265 | 0.111132 | − | 0.993806i | \(-0.464552\pi\) | ||||
0.111132 | + | 0.993806i | \(0.464552\pi\) | |||||||
\(728\) | −6872.21 | −0.349864 | ||||||||
\(729\) | −30717.1 | −1.56059 | ||||||||
\(730\) | 9393.92 | 0.476280 | ||||||||
\(731\) | −9993.57 | −0.505644 | ||||||||
\(732\) | −18737.5 | −0.946117 | ||||||||
\(733\) | 21830.1 | 1.10002 | 0.550008 | − | 0.835159i | \(-0.314625\pi\) | ||||
0.550008 | + | 0.835159i | \(0.314625\pi\) | |||||||
\(734\) | −13691.7 | −0.688515 | ||||||||
\(735\) | 806.496 | 0.0404735 | ||||||||
\(736\) | −3507.76 | −0.175676 | ||||||||
\(737\) | −26693.1 | −1.33413 | ||||||||
\(738\) | −70071.3 | −3.49507 | ||||||||
\(739\) | −18445.7 | −0.918184 | −0.459092 | − | 0.888389i | \(-0.651825\pi\) | ||||
−0.459092 | + | 0.888389i | \(0.651825\pi\) | |||||||
\(740\) | −5846.28 | −0.290424 | ||||||||
\(741\) | 5342.20 | 0.264846 | ||||||||
\(742\) | −12063.3 | −0.596842 | ||||||||
\(743\) | 10726.7 | 0.529641 | 0.264821 | − | 0.964298i | \(-0.414687\pi\) | ||||
0.264821 | + | 0.964298i | \(0.414687\pi\) | |||||||
\(744\) | 6876.31 | 0.338841 | ||||||||
\(745\) | −5826.69 | −0.286542 | ||||||||
\(746\) | 34511.4 | 1.69377 | ||||||||
\(747\) | −16543.0 | −0.810277 | ||||||||
\(748\) | 17229.9 | 0.842229 | ||||||||
\(749\) | 9673.85 | 0.471929 | ||||||||
\(750\) | −33823.9 | −1.64677 | ||||||||
\(751\) | −2105.22 | −0.102291 | −0.0511455 | − | 0.998691i | \(-0.516287\pi\) | ||||
−0.0511455 | + | 0.998691i | \(0.516287\pi\) | |||||||
\(752\) | 18379.3 | 0.891255 | ||||||||
\(753\) | −55844.4 | −2.70263 | ||||||||
\(754\) | −8011.74 | −0.386963 | ||||||||
\(755\) | −1339.65 | −0.0645762 | ||||||||
\(756\) | 13360.2 | 0.642734 | ||||||||
\(757\) | 35718.3 | 1.71493 | 0.857467 | − | 0.514539i | \(-0.172037\pi\) | ||||
0.857467 | + | 0.514539i | \(0.172037\pi\) | |||||||
\(758\) | −15980.0 | −0.765725 | ||||||||
\(759\) | −5918.43 | −0.283038 | ||||||||
\(760\) | 153.529 | 0.00732773 | ||||||||
\(761\) | −21571.1 | −1.02753 | −0.513766 | − | 0.857930i | \(-0.671750\pi\) | ||||
−0.513766 | + | 0.857930i | \(0.671750\pi\) | |||||||
\(762\) | 33809.7 | 1.60735 | ||||||||
\(763\) | 29276.7 | 1.38911 | ||||||||
\(764\) | −39547.0 | −1.87273 | ||||||||
\(765\) | −5731.88 | −0.270898 | ||||||||
\(766\) | −1901.49 | −0.0896916 | ||||||||
\(767\) | 5418.94 | 0.255106 | ||||||||
\(768\) | 22254.1 | 1.04560 | ||||||||
\(769\) | −32715.7 | −1.53415 | −0.767074 | − | 0.641558i | \(-0.778288\pi\) | ||||
−0.767074 | + | 0.641558i | \(0.778288\pi\) | |||||||
\(770\) | 17918.6 | 0.838625 | ||||||||
\(771\) | −26018.9 | −1.21537 | ||||||||
\(772\) | −13314.0 | −0.620702 | ||||||||
\(773\) | 14274.8 | 0.664201 | 0.332100 | − | 0.943244i | \(-0.392243\pi\) | ||||
0.332100 | + | 0.943244i | \(0.392243\pi\) | |||||||
\(774\) | 44327.2 | 2.05854 | ||||||||
\(775\) | 20230.0 | 0.937657 | ||||||||
\(776\) | −1193.66 | −0.0552189 | ||||||||
\(777\) | 20838.5 | 0.962134 | ||||||||
\(778\) | −57784.6 | −2.66283 | ||||||||
\(779\) | 3528.64 | 0.162294 | ||||||||
\(780\) | −27730.2 | −1.27295 | ||||||||
\(781\) | −16297.2 | −0.746681 | ||||||||
\(782\) | 1937.97 | 0.0886212 | ||||||||
\(783\) | 1854.05 | 0.0846211 | ||||||||
\(784\) | 1230.00 | 0.0560312 | ||||||||
\(785\) | 15265.7 | 0.694084 | ||||||||
\(786\) | 87514.1 | 3.97140 | ||||||||
\(787\) | −154.800 | −0.00701147 | −0.00350574 | − | 0.999994i | \(-0.501116\pi\) | ||||
−0.00350574 | + | 0.999994i | \(0.501116\pi\) | |||||||
\(788\) | 6469.91 | 0.292489 | ||||||||
\(789\) | 62451.7 | 2.81792 | ||||||||
\(790\) | −6802.83 | −0.306372 | ||||||||
\(791\) | 18944.4 | 0.851562 | ||||||||
\(792\) | −9097.22 | −0.408151 | ||||||||
\(793\) | −22124.8 | −0.990762 | ||||||||
\(794\) | 29915.3 | 1.33710 | ||||||||
\(795\) | −5794.28 | −0.258493 | ||||||||
\(796\) | 7815.25 | 0.347995 | ||||||||
\(797\) | 1210.82 | 0.0538136 | 0.0269068 | − | 0.999638i | \(-0.491434\pi\) | ||||
0.0269068 | + | 0.999638i | \(0.491434\pi\) | |||||||
\(798\) | −4597.27 | −0.203937 | ||||||||
\(799\) | −11774.8 | −0.521355 | ||||||||
\(800\) | −27358.6 | −1.20909 | ||||||||
\(801\) | 9737.83 | 0.429550 | ||||||||
\(802\) | −17307.0 | −0.762008 | ||||||||
\(803\) | 28030.6 | 1.23185 | ||||||||
\(804\) | −35549.2 | −1.55936 | ||||||||
\(805\) | 1071.49 | 0.0469131 | ||||||||
\(806\) | 68209.8 | 2.98088 | ||||||||
\(807\) | −50169.1 | −2.18840 | ||||||||
\(808\) | −7668.62 | −0.333887 | ||||||||
\(809\) | −24108.3 | −1.04772 | −0.523859 | − | 0.851805i | \(-0.675508\pi\) | ||||
−0.523859 | + | 0.851805i | \(0.675508\pi\) | |||||||
\(810\) | −6355.02 | −0.275670 | ||||||||
\(811\) | −28376.6 | −1.22865 | −0.614326 | − | 0.789052i | \(-0.710572\pi\) | ||||
−0.614326 | + | 0.789052i | \(0.710572\pi\) | |||||||
\(812\) | 3665.44 | 0.158414 | ||||||||
\(813\) | −36693.0 | −1.58288 | ||||||||
\(814\) | −32813.0 | −1.41289 | ||||||||
\(815\) | 15323.7 | 0.658610 | ||||||||
\(816\) | −15077.2 | −0.646822 | ||||||||
\(817\) | −2232.22 | −0.0955882 | ||||||||
\(818\) | −40620.3 | −1.73625 | ||||||||
\(819\) | 57308.7 | 2.44509 | ||||||||
\(820\) | −18316.4 | −0.780046 | ||||||||
\(821\) | 32553.3 | 1.38382 | 0.691911 | − | 0.721983i | \(-0.256769\pi\) | ||||
0.691911 | + | 0.721983i | \(0.256769\pi\) | |||||||
\(822\) | 84238.8 | 3.57441 | ||||||||
\(823\) | 42105.4 | 1.78335 | 0.891677 | − | 0.452672i | \(-0.149529\pi\) | ||||
0.891677 | + | 0.452672i | \(0.149529\pi\) | |||||||
\(824\) | 698.824 | 0.0295445 | ||||||||
\(825\) | −46160.5 | −1.94800 | ||||||||
\(826\) | −4663.31 | −0.196438 | ||||||||
\(827\) | −16938.3 | −0.712215 | −0.356107 | − | 0.934445i | \(-0.615896\pi\) | ||||
−0.356107 | + | 0.934445i | \(0.615896\pi\) | |||||||
\(828\) | −4570.00 | −0.191810 | ||||||||
\(829\) | −27507.1 | −1.15243 | −0.576214 | − | 0.817299i | \(-0.695470\pi\) | ||||
−0.576214 | + | 0.817299i | \(0.695470\pi\) | |||||||
\(830\) | −8133.84 | −0.340156 | ||||||||
\(831\) | 9524.54 | 0.397597 | ||||||||
\(832\) | −54987.7 | −2.29129 | ||||||||
\(833\) | −788.005 | −0.0327764 | ||||||||
\(834\) | −32087.7 | −1.33226 | ||||||||
\(835\) | −16276.3 | −0.674567 | ||||||||
\(836\) | 3848.57 | 0.159217 | ||||||||
\(837\) | −15784.9 | −0.651858 | ||||||||
\(838\) | 7040.39 | 0.290222 | ||||||||
\(839\) | −15189.7 | −0.625036 | −0.312518 | − | 0.949912i | \(-0.601173\pi\) | ||||
−0.312518 | + | 0.949912i | \(0.601173\pi\) | |||||||
\(840\) | 2840.61 | 0.116679 | ||||||||
\(841\) | −23880.3 | −0.979144 | ||||||||
\(842\) | 4709.20 | 0.192743 | ||||||||
\(843\) | 46167.5 | 1.88623 | ||||||||
\(844\) | 18980.6 | 0.774097 | ||||||||
\(845\) | −23005.8 | −0.936596 | ||||||||
\(846\) | 52228.0 | 2.12250 | ||||||||
\(847\) | 29646.7 | 1.20268 | ||||||||
\(848\) | −8836.93 | −0.357855 | ||||||||
\(849\) | −25381.8 | −1.02603 | ||||||||
\(850\) | 15115.1 | 0.609933 | ||||||||
\(851\) | −1962.14 | −0.0790381 | ||||||||
\(852\) | −21704.1 | −0.872736 | ||||||||
\(853\) | 40128.8 | 1.61077 | 0.805384 | − | 0.592753i | \(-0.201959\pi\) | ||||
0.805384 | + | 0.592753i | \(0.201959\pi\) | |||||||
\(854\) | 19039.7 | 0.762909 | ||||||||
\(855\) | −1280.31 | −0.0512112 | ||||||||
\(856\) | −2414.82 | −0.0964217 | ||||||||
\(857\) | 22634.7 | 0.902201 | 0.451101 | − | 0.892473i | \(-0.351032\pi\) | ||||
0.451101 | + | 0.892473i | \(0.351032\pi\) | |||||||
\(858\) | −155640. | −6.19283 | ||||||||
\(859\) | 31716.0 | 1.25976 | 0.629880 | − | 0.776692i | \(-0.283104\pi\) | ||||
0.629880 | + | 0.776692i | \(0.283104\pi\) | |||||||
\(860\) | 11587.0 | 0.459434 | ||||||||
\(861\) | 65287.3 | 2.58419 | ||||||||
\(862\) | 34548.4 | 1.36511 | ||||||||
\(863\) | 23915.4 | 0.943324 | 0.471662 | − | 0.881780i | \(-0.343654\pi\) | ||||
0.471662 | + | 0.881780i | \(0.343654\pi\) | |||||||
\(864\) | 21347.1 | 0.840558 | ||||||||
\(865\) | −4438.42 | −0.174463 | ||||||||
\(866\) | 17949.1 | 0.704314 | ||||||||
\(867\) | −29723.0 | −1.16430 | ||||||||
\(868\) | −31206.6 | −1.22030 | ||||||||
\(869\) | −20299.1 | −0.792403 | ||||||||
\(870\) | 3311.63 | 0.129051 | ||||||||
\(871\) | −41975.6 | −1.63294 | ||||||||
\(872\) | −7308.18 | −0.283814 | ||||||||
\(873\) | 9954.16 | 0.385907 | ||||||||
\(874\) | 432.877 | 0.0167532 | ||||||||
\(875\) | 18272.2 | 0.705959 | ||||||||
\(876\) | 37330.4 | 1.43982 | ||||||||
\(877\) | 26014.0 | 1.00163 | 0.500816 | − | 0.865554i | \(-0.333033\pi\) | ||||
0.500816 | + | 0.865554i | \(0.333033\pi\) | |||||||
\(878\) | −60621.7 | −2.33016 | ||||||||
\(879\) | −65036.3 | −2.49558 | ||||||||
\(880\) | 13126.2 | 0.502824 | ||||||||
\(881\) | 25233.4 | 0.964965 | 0.482483 | − | 0.875905i | \(-0.339735\pi\) | ||||
0.482483 | + | 0.875905i | \(0.339735\pi\) | |||||||
\(882\) | 3495.25 | 0.133437 | ||||||||
\(883\) | −18268.5 | −0.696244 | −0.348122 | − | 0.937449i | \(-0.613180\pi\) | ||||
−0.348122 | + | 0.937449i | \(0.613180\pi\) | |||||||
\(884\) | 27094.5 | 1.03087 | ||||||||
\(885\) | −2239.90 | −0.0850773 | ||||||||
\(886\) | 66014.3 | 2.50315 | ||||||||
\(887\) | −5992.15 | −0.226828 | −0.113414 | − | 0.993548i | \(-0.536179\pi\) | ||||
−0.113414 | + | 0.993548i | \(0.536179\pi\) | |||||||
\(888\) | −5201.80 | −0.196578 | ||||||||
\(889\) | −18264.6 | −0.689060 | ||||||||
\(890\) | 4787.88 | 0.180326 | ||||||||
\(891\) | −18962.8 | −0.712995 | ||||||||
\(892\) | −572.667 | −0.0214959 | ||||||||
\(893\) | −2630.09 | −0.0985582 | ||||||||
\(894\) | −43553.1 | −1.62934 | ||||||||
\(895\) | −11301.7 | −0.422094 | ||||||||
\(896\) | 10140.7 | 0.378101 | ||||||||
\(897\) | −9306.89 | −0.346431 | ||||||||
\(898\) | −44488.7 | −1.65324 | ||||||||
\(899\) | −4330.65 | −0.160662 | ||||||||
\(900\) | −35643.5 | −1.32013 | ||||||||
\(901\) | 5661.43 | 0.209334 | ||||||||
\(902\) | −102803. | −3.79488 | ||||||||
\(903\) | −41300.8 | −1.52204 | ||||||||
\(904\) | −4728.98 | −0.173986 | ||||||||
\(905\) | −3637.37 | −0.133603 | ||||||||
\(906\) | −10013.6 | −0.367196 | ||||||||
\(907\) | 10017.5 | 0.366730 | 0.183365 | − | 0.983045i | \(-0.441301\pi\) | ||||
0.183365 | + | 0.983045i | \(0.441301\pi\) | |||||||
\(908\) | 18549.3 | 0.677952 | ||||||||
\(909\) | 63950.1 | 2.33343 | ||||||||
\(910\) | 28177.5 | 1.02645 | ||||||||
\(911\) | −28206.8 | −1.02583 | −0.512915 | − | 0.858439i | \(-0.671434\pi\) | ||||
−0.512915 | + | 0.858439i | \(0.671434\pi\) | |||||||
\(912\) | −3367.72 | −0.122277 | ||||||||
\(913\) | −24270.7 | −0.879783 | ||||||||
\(914\) | −12600.9 | −0.456018 | ||||||||
\(915\) | 9145.21 | 0.330417 | ||||||||
\(916\) | 9488.78 | 0.342269 | ||||||||
\(917\) | −47276.5 | −1.70252 | ||||||||
\(918\) | −11793.8 | −0.424025 | ||||||||
\(919\) | 15141.5 | 0.543496 | 0.271748 | − | 0.962368i | \(-0.412398\pi\) | ||||
0.271748 | + | 0.962368i | \(0.412398\pi\) | |||||||
\(920\) | −267.470 | −0.00958502 | ||||||||
\(921\) | 2060.42 | 0.0737169 | ||||||||
\(922\) | 42236.3 | 1.50865 | ||||||||
\(923\) | −25627.7 | −0.913918 | ||||||||
\(924\) | 71206.6 | 2.53520 | ||||||||
\(925\) | −15303.6 | −0.543978 | ||||||||
\(926\) | 42665.2 | 1.51411 | ||||||||
\(927\) | −5827.63 | −0.206477 | ||||||||
\(928\) | 5856.67 | 0.207171 | ||||||||
\(929\) | −28368.3 | −1.00187 | −0.500933 | − | 0.865486i | \(-0.667010\pi\) | ||||
−0.500933 | + | 0.865486i | \(0.667010\pi\) | |||||||
\(930\) | −28194.3 | −0.994115 | ||||||||
\(931\) | −176.013 | −0.00619614 | ||||||||
\(932\) | 29199.4 | 1.02624 | ||||||||
\(933\) | 9114.65 | 0.319829 | ||||||||
\(934\) | −14739.5 | −0.516372 | ||||||||
\(935\) | −8409.39 | −0.294135 | ||||||||
\(936\) | −14305.6 | −0.499566 | ||||||||
\(937\) | 11298.3 | 0.393917 | 0.196958 | − | 0.980412i | \(-0.436894\pi\) | ||||
0.196958 | + | 0.980412i | \(0.436894\pi\) | |||||||
\(938\) | 36122.5 | 1.25740 | ||||||||
\(939\) | 52965.1 | 1.84074 | ||||||||
\(940\) | 13652.2 | 0.473710 | ||||||||
\(941\) | −49135.8 | −1.70221 | −0.851106 | − | 0.524993i | \(-0.824068\pi\) | ||||
−0.851106 | + | 0.524993i | \(0.824068\pi\) | |||||||
\(942\) | 114107. | 3.94673 | ||||||||
\(943\) | −6147.41 | −0.212288 | ||||||||
\(944\) | −3416.10 | −0.117780 | ||||||||
\(945\) | −6520.73 | −0.224465 | ||||||||
\(946\) | 65033.6 | 2.23512 | ||||||||
\(947\) | −40776.4 | −1.39921 | −0.699607 | − | 0.714528i | \(-0.746642\pi\) | ||||
−0.699607 | + | 0.714528i | \(0.746642\pi\) | |||||||
\(948\) | −27033.7 | −0.926176 | ||||||||
\(949\) | 44078.9 | 1.50776 | ||||||||
\(950\) | 3376.19 | 0.115303 | ||||||||
\(951\) | 18258.4 | 0.622577 | ||||||||
\(952\) | −2775.48 | −0.0944892 | ||||||||
\(953\) | 57911.4 | 1.96845 | 0.984225 | − | 0.176922i | \(-0.0566140\pi\) | ||||
0.984225 | + | 0.176922i | \(0.0566140\pi\) | |||||||
\(954\) | −25111.7 | −0.852223 | ||||||||
\(955\) | 19301.7 | 0.654020 | ||||||||
\(956\) | 9901.60 | 0.334980 | ||||||||
\(957\) | 9881.60 | 0.333779 | ||||||||
\(958\) | 63503.1 | 2.14164 | ||||||||
\(959\) | −45507.1 | −1.53233 | ||||||||
\(960\) | 22729.0 | 0.764140 | ||||||||
\(961\) | 7079.02 | 0.237623 | ||||||||
\(962\) | −51599.3 | −1.72934 | ||||||||
\(963\) | 20137.7 | 0.673861 | ||||||||
\(964\) | 5226.86 | 0.174633 | ||||||||
\(965\) | 6498.17 | 0.216771 | ||||||||
\(966\) | 8009.13 | 0.266759 | ||||||||
\(967\) | −10786.0 | −0.358691 | −0.179346 | − | 0.983786i | \(-0.557398\pi\) | ||||
−0.179346 | + | 0.983786i | \(0.557398\pi\) | |||||||
\(968\) | −7400.52 | −0.245725 | ||||||||
\(969\) | 2157.55 | 0.0715279 | ||||||||
\(970\) | 4894.25 | 0.162005 | ||||||||
\(971\) | −31577.6 | −1.04364 | −0.521820 | − | 0.853056i | \(-0.674747\pi\) | ||||
−0.521820 | + | 0.853056i | \(0.674747\pi\) | |||||||
\(972\) | −45410.0 | −1.49848 | ||||||||
\(973\) | 17334.3 | 0.571132 | ||||||||
\(974\) | −50431.3 | −1.65906 | ||||||||
\(975\) | −72588.5 | −2.38430 | ||||||||
\(976\) | 13947.5 | 0.457426 | ||||||||
\(977\) | 10340.3 | 0.338603 | 0.169301 | − | 0.985564i | \(-0.445849\pi\) | ||||
0.169301 | + | 0.985564i | \(0.445849\pi\) | |||||||
\(978\) | 114541. | 3.74501 | ||||||||
\(979\) | 14286.6 | 0.466397 | ||||||||
\(980\) | 913.649 | 0.0297811 | ||||||||
\(981\) | 60944.3 | 1.98349 | ||||||||
\(982\) | 32136.9 | 1.04433 | ||||||||
\(983\) | 22041.8 | 0.715184 | 0.357592 | − | 0.933878i | \(-0.383598\pi\) | ||||
0.357592 | + | 0.933878i | \(0.383598\pi\) | |||||||
\(984\) | −16297.3 | −0.527986 | ||||||||
\(985\) | −3157.77 | −0.102147 | ||||||||
\(986\) | −3235.70 | −0.104509 | ||||||||
\(987\) | −48662.2 | −1.56933 | ||||||||
\(988\) | 6051.97 | 0.194877 | ||||||||
\(989\) | 3888.86 | 0.125034 | ||||||||
\(990\) | 37300.5 | 1.19746 | ||||||||
\(991\) | −24259.6 | −0.777632 | −0.388816 | − | 0.921315i | \(-0.627116\pi\) | ||||
−0.388816 | + | 0.921315i | \(0.627116\pi\) | |||||||
\(992\) | −49862.1 | −1.59589 | ||||||||
\(993\) | −43387.7 | −1.38657 | ||||||||
\(994\) | 22054.2 | 0.703738 | ||||||||
\(995\) | −3814.39 | −0.121532 | ||||||||
\(996\) | −32323.0 | −1.02831 | ||||||||
\(997\) | 17540.2 | 0.557175 | 0.278587 | − | 0.960411i | \(-0.410134\pi\) | ||||
0.278587 | + | 0.960411i | \(0.410134\pi\) | |||||||
\(998\) | 42509.4 | 1.34831 | ||||||||
\(999\) | 11940.9 | 0.378173 |
(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 | 547.4.a.b.1.11 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.4.a.b.1.11 | ✓ | 71 | 1.1 | even | 1 | trivial |