Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.410040 | 0.144971 | 0.0724855 | − | 0.997369i | \(-0.476907\pi\) | ||||
0.0724855 | + | 0.997369i | \(0.476907\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.83187 | −0.978983 | ||||||||
\(5\) | 19.1512 | 1.71294 | 0.856469 | − | 0.516198i | \(-0.172653\pi\) | ||||
0.856469 | + | 0.516198i | \(0.172653\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.0347 | −0.595818 | −0.297909 | − | 0.954594i | \(-0.596289\pi\) | ||||
−0.297909 | + | 0.954594i | \(0.596289\pi\) | |||||||
\(8\) | −6.49170 | −0.286895 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.85278 | 0.248327 | ||||||||
\(11\) | −19.6472 | −0.538531 | −0.269266 | − | 0.963066i | \(-0.586781\pi\) | ||||
−0.269266 | + | 0.963066i | \(0.586781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.5272 | −0.416606 | −0.208303 | − | 0.978064i | \(-0.566794\pi\) | ||||
−0.208303 | + | 0.978064i | \(0.566794\pi\) | |||||||
\(14\) | −4.52467 | −0.0863764 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 59.9931 | 0.937392 | ||||||||
\(17\) | −102.431 | −1.46136 | −0.730680 | − | 0.682720i | \(-0.760797\pi\) | ||||
−0.730680 | + | 0.682720i | \(0.760797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.5918 | 0.188264 | 0.0941319 | − | 0.995560i | \(-0.469992\pi\) | ||||
0.0941319 | + | 0.995560i | \(0.469992\pi\) | |||||||
\(20\) | −149.990 | −1.67694 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.05612 | −0.0780714 | ||||||||
\(23\) | 153.505 | 1.39165 | 0.695824 | − | 0.718212i | \(-0.255039\pi\) | ||||
0.695824 | + | 0.718212i | \(0.255039\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 241.770 | 1.93416 | ||||||||
\(26\) | −8.00694 | −0.0603958 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 86.4224 | 0.583296 | ||||||||
\(29\) | −5.88022 | −0.0376528 | −0.0188264 | − | 0.999823i | \(-0.505993\pi\) | ||||
−0.0188264 | + | 0.999823i | \(0.505993\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 209.861 | 1.21588 | 0.607938 | − | 0.793985i | \(-0.291997\pi\) | ||||
0.607938 | + | 0.793985i | \(0.291997\pi\) | |||||||
\(32\) | 76.5332 | 0.422790 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −42.0008 | −0.211855 | ||||||||
\(35\) | −211.328 | −1.02060 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 289.738 | 1.28737 | 0.643684 | − | 0.765291i | \(-0.277405\pi\) | ||||
0.643684 | + | 0.765291i | \(0.277405\pi\) | |||||||
\(38\) | 6.39328 | 0.0272928 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −124.324 | −0.491434 | ||||||||
\(41\) | 189.759 | 0.722815 | 0.361407 | − | 0.932408i | \(-0.382296\pi\) | ||||
0.361407 | + | 0.932408i | \(0.382296\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −380.254 | −1.34856 | −0.674281 | − | 0.738475i | \(-0.735546\pi\) | ||||
−0.674281 | + | 0.738475i | \(0.735546\pi\) | |||||||
\(44\) | 153.874 | 0.527213 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 62.9430 | 0.201749 | ||||||||
\(47\) | 61.6120 | 0.191213 | 0.0956067 | − | 0.995419i | \(-0.469521\pi\) | ||||
0.0956067 | + | 0.995419i | \(0.469521\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −221.235 | −0.645000 | ||||||||
\(50\) | 99.1354 | 0.280397 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 152.934 | 0.407850 | ||||||||
\(53\) | −499.156 | −1.29367 | −0.646834 | − | 0.762631i | \(-0.723907\pi\) | ||||
−0.646834 | + | 0.762631i | \(0.723907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −376.267 | −0.922471 | ||||||||
\(56\) | 71.6341 | 0.170938 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.41113 | −0.00545856 | ||||||||
\(59\) | −806.008 | −1.77853 | −0.889265 | − | 0.457392i | \(-0.848784\pi\) | ||||
−0.889265 | + | 0.457392i | \(0.848784\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 231.215 | 0.485313 | 0.242657 | − | 0.970112i | \(-0.421981\pi\) | ||||
0.242657 | + | 0.970112i | \(0.421981\pi\) | |||||||
\(62\) | 86.0514 | 0.176267 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −448.563 | −0.876099 | ||||||||
\(65\) | −373.970 | −0.713620 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1037.28 | −1.89139 | −0.945697 | − | 0.325050i | \(-0.894619\pi\) | ||||
−0.945697 | + | 0.325050i | \(0.894619\pi\) | |||||||
\(68\) | 802.225 | 1.43065 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −86.6531 | −0.147958 | ||||||||
\(71\) | −253.204 | −0.423236 | −0.211618 | − | 0.977352i | \(-0.567873\pi\) | ||||
−0.211618 | + | 0.977352i | \(0.567873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −597.809 | −0.958469 | −0.479234 | − | 0.877687i | \(-0.659086\pi\) | ||||
−0.479234 | + | 0.877687i | \(0.659086\pi\) | |||||||
\(74\) | 118.804 | 0.186631 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −122.113 | −0.184307 | ||||||||
\(77\) | 216.801 | 0.320867 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 590.837 | 0.841447 | 0.420724 | − | 0.907189i | \(-0.361776\pi\) | ||||
0.420724 | + | 0.907189i | \(0.361776\pi\) | |||||||
\(80\) | 1148.94 | 1.60569 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 77.8089 | 0.104787 | ||||||||
\(83\) | 856.619 | 1.13284 | 0.566422 | − | 0.824115i | \(-0.308327\pi\) | ||||
0.566422 | + | 0.824115i | \(0.308327\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1961.68 | −2.50322 | ||||||||
\(86\) | −155.919 | −0.195502 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 127.543 | 0.154502 | ||||||||
\(89\) | 425.114 | 0.506314 | 0.253157 | − | 0.967425i | \(-0.418531\pi\) | ||||
0.253157 | + | 0.967425i | \(0.418531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 215.477 | 0.248221 | ||||||||
\(92\) | −1202.23 | −1.36240 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 25.2634 | 0.0277204 | ||||||||
\(95\) | 298.603 | 0.322484 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1191.43 | 1.24713 | 0.623566 | − | 0.781771i | \(-0.285683\pi\) | ||||
0.623566 | + | 0.781771i | \(0.285683\pi\) | |||||||
\(98\) | −90.7153 | −0.0935064 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1893.51 | −1.89351 | ||||||||
\(101\) | −278.923 | −0.274791 | −0.137395 | − | 0.990516i | \(-0.543873\pi\) | ||||
−0.137395 | + | 0.990516i | \(0.543873\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 30.6207 | 0.0292927 | 0.0146463 | − | 0.999893i | \(-0.495338\pi\) | ||||
0.0146463 | + | 0.999893i | \(0.495338\pi\) | |||||||
\(104\) | 126.765 | 0.119522 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −204.674 | −0.187544 | ||||||||
\(107\) | 13.2134 | 0.0119382 | 0.00596910 | − | 0.999982i | \(-0.498100\pi\) | ||||
0.00596910 | + | 0.999982i | \(0.498100\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 300.208 | 0.263804 | 0.131902 | − | 0.991263i | \(-0.457892\pi\) | ||||
0.131902 | + | 0.991263i | \(0.457892\pi\) | |||||||
\(110\) | −154.285 | −0.133732 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −662.006 | −0.558515 | ||||||||
\(113\) | −1058.39 | −0.881108 | −0.440554 | − | 0.897726i | \(-0.645218\pi\) | ||||
−0.440554 | + | 0.897726i | \(0.645218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2939.80 | 2.38381 | ||||||||
\(116\) | 46.0531 | 0.0368614 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −330.496 | −0.257835 | ||||||||
\(119\) | 1130.30 | 0.870706 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −944.989 | −0.709984 | ||||||||
\(122\) | 94.8076 | 0.0703564 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1643.60 | −1.19032 | ||||||||
\(125\) | 2236.29 | 1.60016 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2694.61 | 1.88274 | 0.941369 | − | 0.337378i | \(-0.109540\pi\) | ||||
0.941369 | + | 0.337378i | \(0.109540\pi\) | |||||||
\(128\) | −796.194 | −0.549799 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −153.343 | −0.103454 | ||||||||
\(131\) | 502.907 | 0.335414 | 0.167707 | − | 0.985837i | \(-0.446364\pi\) | ||||
0.167707 | + | 0.985837i | \(0.446364\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −172.051 | −0.112171 | ||||||||
\(134\) | −425.325 | −0.274197 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 664.951 | 0.419258 | ||||||||
\(137\) | −1986.88 | −1.23905 | −0.619527 | − | 0.784976i | \(-0.712675\pi\) | ||||
−0.619527 | + | 0.784976i | \(0.712675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 554.567 | 0.338401 | 0.169201 | − | 0.985582i | \(-0.445881\pi\) | ||||
0.169201 | + | 0.985582i | \(0.445881\pi\) | |||||||
\(140\) | 1655.10 | 0.999151 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −103.824 | −0.0613570 | ||||||||
\(143\) | 383.654 | 0.224355 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −112.614 | −0.0644969 | ||||||||
\(146\) | −245.126 | −0.138950 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2269.19 | −1.26031 | ||||||||
\(149\) | −1389.90 | −0.764196 | −0.382098 | − | 0.924122i | \(-0.624798\pi\) | ||||
−0.382098 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3690.17 | −1.98876 | −0.994378 | − | 0.105892i | \(-0.966230\pi\) | ||||
−0.994378 | + | 0.105892i | \(0.966230\pi\) | |||||||
\(152\) | −101.218 | −0.0540120 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 88.8970 | 0.0465164 | ||||||||
\(155\) | 4019.10 | 2.08272 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1878.88 | −0.955101 | −0.477550 | − | 0.878604i | \(-0.658475\pi\) | ||||
−0.477550 | + | 0.878604i | \(0.658475\pi\) | |||||||
\(158\) | 242.267 | 0.121985 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1465.71 | 0.724214 | ||||||||
\(161\) | −1693.88 | −0.829170 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2899.69 | −1.39338 | −0.696691 | − | 0.717372i | \(-0.745345\pi\) | ||||
−0.696691 | + | 0.717372i | \(0.745345\pi\) | |||||||
\(164\) | −1486.17 | −0.707624 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 351.248 | 0.164230 | ||||||||
\(167\) | 687.351 | 0.318496 | 0.159248 | − | 0.987239i | \(-0.449093\pi\) | ||||
0.159248 | + | 0.987239i | \(0.449093\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1815.69 | −0.826440 | ||||||||
\(170\) | −804.367 | −0.362895 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2978.10 | 1.32022 | ||||||||
\(173\) | 255.193 | 0.112150 | 0.0560751 | − | 0.998427i | \(-0.482141\pi\) | ||||
0.0560751 | + | 0.998427i | \(0.482141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2667.86 | −1.15241 | ||||||||
\(176\) | −1178.69 | −0.504815 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 174.314 | 0.0734009 | ||||||||
\(179\) | −4686.20 | −1.95678 | −0.978388 | − | 0.206777i | \(-0.933703\pi\) | ||||
−0.978388 | + | 0.206777i | \(0.933703\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1470.17 | −0.603741 | −0.301870 | − | 0.953349i | \(-0.597611\pi\) | ||||
−0.301870 | + | 0.953349i | \(0.597611\pi\) | |||||||
\(182\) | 88.3542 | 0.0359849 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −996.506 | −0.399257 | ||||||||
\(185\) | 5548.84 | 2.20518 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2012.48 | 0.786988 | ||||||||
\(188\) | −482.537 | −0.187195 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 122.439 | 0.0467509 | ||||||||
\(191\) | −1676.69 | −0.635187 | −0.317594 | − | 0.948227i | \(-0.602875\pi\) | ||||
−0.317594 | + | 0.948227i | \(0.602875\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3509.26 | −1.30882 | −0.654410 | − | 0.756140i | \(-0.727083\pi\) | ||||
−0.654410 | + | 0.756140i | \(0.727083\pi\) | |||||||
\(194\) | 488.536 | 0.180798 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1732.68 | 0.631445 | ||||||||
\(197\) | 899.057 | 0.325153 | 0.162577 | − | 0.986696i | \(-0.448020\pi\) | ||||
0.162577 | + | 0.986696i | \(0.448020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2940.66 | 1.04753 | 0.523763 | − | 0.851864i | \(-0.324528\pi\) | ||||
0.523763 | + | 0.851864i | \(0.324528\pi\) | |||||||
\(200\) | −1569.50 | −0.554901 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −114.370 | −0.0398367 | ||||||||
\(203\) | 64.8866 | 0.0224342 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3634.12 | 1.23814 | ||||||||
\(206\) | 12.5557 | 0.00424659 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1171.50 | −0.390523 | ||||||||
\(209\) | −306.335 | −0.101386 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 399.675 | 0.130402 | 0.0652008 | − | 0.997872i | \(-0.479231\pi\) | ||||
0.0652008 | + | 0.997872i | \(0.479231\pi\) | |||||||
\(212\) | 3909.32 | 1.26648 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.41802 | 0.00173069 | ||||||||
\(215\) | −7282.33 | −2.31000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2315.75 | −0.724441 | ||||||||
\(218\) | 123.097 | 0.0382440 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2946.88 | 0.903083 | ||||||||
\(221\) | 2000.19 | 0.608811 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4539.97 | −1.36331 | −0.681657 | − | 0.731672i | \(-0.738740\pi\) | ||||
−0.681657 | + | 0.731672i | \(0.738740\pi\) | |||||||
\(224\) | −844.522 | −0.251906 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −433.983 | −0.127735 | ||||||||
\(227\) | 3502.99 | 1.02424 | 0.512118 | − | 0.858915i | \(-0.328861\pi\) | ||||
0.512118 | + | 0.858915i | \(0.328861\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5815.73 | −1.67823 | −0.839114 | − | 0.543956i | \(-0.816926\pi\) | ||||
−0.839114 | + | 0.543956i | \(0.816926\pi\) | |||||||
\(230\) | 1205.44 | 0.345583 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 38.1727 | 0.0108024 | ||||||||
\(233\) | 4023.74 | 1.13135 | 0.565673 | − | 0.824630i | \(-0.308616\pi\) | ||||
0.565673 | + | 0.824630i | \(0.308616\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1179.95 | 0.327537 | ||||||||
\(236\) | 6312.55 | 1.74115 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 463.466 | 0.126227 | ||||||||
\(239\) | −239.000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2859.61 | 0.764330 | 0.382165 | − | 0.924094i | \(-0.375179\pi\) | ||||
0.382165 | + | 0.924094i | \(0.375179\pi\) | |||||||
\(242\) | −387.484 | −0.102927 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1810.85 | −0.475113 | ||||||||
\(245\) | −4236.93 | −1.10485 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −304.465 | −0.0784318 | ||||||||
\(248\) | −1362.35 | −0.348829 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 916.968 | 0.231977 | ||||||||
\(251\) | 454.207 | 0.114220 | 0.0571101 | − | 0.998368i | \(-0.481811\pi\) | ||||
0.0571101 | + | 0.998368i | \(0.481811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3015.93 | −0.749446 | ||||||||
\(254\) | 1104.90 | 0.272943 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3262.03 | 0.796395 | ||||||||
\(257\) | 1391.28 | 0.337687 | 0.168843 | − | 0.985643i | \(-0.445997\pi\) | ||||
0.168843 | + | 0.985643i | \(0.445997\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3197.18 | −0.767038 | ||||||||
\(260\) | 2928.88 | 0.698622 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 206.212 | 0.0486253 | ||||||||
\(263\) | −5779.48 | −1.35505 | −0.677525 | − | 0.735500i | \(-0.736947\pi\) | ||||
−0.677525 | + | 0.735500i | \(0.736947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9559.46 | −2.21597 | ||||||||
\(266\) | −70.5480 | −0.0162616 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8123.80 | 1.85164 | ||||||||
\(269\) | 1726.44 | 0.391311 | 0.195656 | − | 0.980673i | \(-0.437317\pi\) | ||||
0.195656 | + | 0.980673i | \(0.437317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1584.05 | 0.355072 | 0.177536 | − | 0.984114i | \(-0.443187\pi\) | ||||
0.177536 | + | 0.984114i | \(0.443187\pi\) | |||||||
\(272\) | −6145.14 | −1.36987 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −814.699 | −0.179627 | ||||||||
\(275\) | −4750.09 | −1.04160 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1591.17 | −0.345140 | −0.172570 | − | 0.984997i | \(-0.555207\pi\) | ||||
−0.172570 | + | 0.984997i | \(0.555207\pi\) | |||||||
\(278\) | 227.395 | 0.0490584 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1371.88 | 0.292806 | ||||||||
\(281\) | 113.733 | 0.0241451 | 0.0120725 | − | 0.999927i | \(-0.496157\pi\) | ||||
0.0120725 | + | 0.999927i | \(0.496157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1352.24 | 0.284036 | 0.142018 | − | 0.989864i | \(-0.454641\pi\) | ||||
0.142018 | + | 0.989864i | \(0.454641\pi\) | |||||||
\(284\) | 1983.06 | 0.414341 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 157.314 | 0.0325250 | ||||||||
\(287\) | −2093.94 | −0.430666 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5579.08 | 1.13558 | ||||||||
\(290\) | −46.1761 | −0.00935018 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4681.96 | 0.938325 | ||||||||
\(293\) | −6661.54 | −1.32823 | −0.664115 | − | 0.747630i | \(-0.731192\pi\) | ||||
−0.664115 | + | 0.747630i | \(0.731192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15436.0 | −3.04651 | ||||||||
\(296\) | −1880.89 | −0.369340 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −569.916 | −0.110786 | ||||||||
\(299\) | −2997.51 | −0.579768 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4195.99 | 0.803498 | ||||||||
\(302\) | −1513.12 | −0.288312 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 935.403 | 0.176477 | ||||||||
\(305\) | 4428.06 | 0.831312 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6091.74 | −1.13249 | −0.566245 | − | 0.824237i | \(-0.691604\pi\) | ||||
−0.566245 | + | 0.824237i | \(0.691604\pi\) | |||||||
\(308\) | −1697.95 | −0.314123 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1647.99 | 0.301934 | ||||||||
\(311\) | −964.699 | −0.175894 | −0.0879471 | − | 0.996125i | \(-0.528031\pi\) | ||||
−0.0879471 | + | 0.996125i | \(0.528031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1734.62 | 0.313247 | 0.156623 | − | 0.987658i | \(-0.449939\pi\) | ||||
0.156623 | + | 0.987658i | \(0.449939\pi\) | |||||||
\(314\) | −770.416 | −0.138462 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4627.35 | −0.823763 | ||||||||
\(317\) | −1182.23 | −0.209466 | −0.104733 | − | 0.994500i | \(-0.533399\pi\) | ||||
−0.104733 | + | 0.994500i | \(0.533399\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 115.530 | 0.0202772 | ||||||||
\(320\) | −8590.54 | −1.50070 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −694.558 | −0.120206 | ||||||||
\(323\) | −1597.09 | −0.275121 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4721.09 | −0.805781 | ||||||||
\(326\) | −1188.99 | −0.202000 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1231.86 | −0.207372 | ||||||||
\(329\) | −679.871 | −0.113928 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5918.46 | −0.982804 | −0.491402 | − | 0.870933i | \(-0.663515\pi\) | ||||
−0.491402 | + | 0.870933i | \(0.663515\pi\) | |||||||
\(332\) | −6708.92 | −1.10904 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 281.841 | 0.0461727 | ||||||||
\(335\) | −19865.1 | −3.23984 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4897.54 | −0.791650 | −0.395825 | − | 0.918326i | \(-0.629541\pi\) | ||||
−0.395825 | + | 0.918326i | \(0.629541\pi\) | |||||||
\(338\) | −744.505 | −0.119810 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15363.6 | 2.45061 | ||||||||
\(341\) | −4123.17 | −0.654786 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6226.17 | 0.980122 | ||||||||
\(344\) | 2468.49 | 0.386896 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 104.640 | 0.0162585 | ||||||||
\(347\) | 9378.30 | 1.45087 | 0.725437 | − | 0.688288i | \(-0.241637\pi\) | ||||
0.725437 | + | 0.688288i | \(0.241637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 671.157 | 0.102941 | 0.0514703 | − | 0.998675i | \(-0.483609\pi\) | ||||
0.0514703 | + | 0.998675i | \(0.483609\pi\) | |||||||
\(350\) | −1093.93 | −0.167066 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1503.66 | −0.227686 | ||||||||
\(353\) | −173.097 | −0.0260992 | −0.0130496 | − | 0.999915i | \(-0.504154\pi\) | ||||
−0.0130496 | + | 0.999915i | \(0.504154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4849.17 | −0.724978 | ||||||||
\(356\) | −3329.43 | −0.495673 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1921.53 | −0.283676 | ||||||||
\(359\) | −7107.06 | −1.04484 | −0.522418 | − | 0.852689i | \(-0.674970\pi\) | ||||
−0.522418 | + | 0.852689i | \(0.674970\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6615.89 | −0.964557 | ||||||||
\(362\) | −602.830 | −0.0875250 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1687.59 | −0.243004 | ||||||||
\(365\) | −11448.8 | −1.64180 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9164.35 | 1.30347 | 0.651737 | − | 0.758445i | \(-0.274041\pi\) | ||||
0.651737 | + | 0.758445i | \(0.274041\pi\) | |||||||
\(368\) | 9209.21 | 1.30452 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2275.25 | 0.319688 | ||||||||
\(371\) | 5508.04 | 0.770791 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4223.88 | 0.586338 | 0.293169 | − | 0.956061i | \(-0.405290\pi\) | ||||
0.293169 | + | 0.956061i | \(0.405290\pi\) | |||||||
\(374\) | 825.196 | 0.114091 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −399.967 | −0.0548583 | ||||||||
\(377\) | 114.824 | 0.0156863 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1150.78 | −0.155967 | −0.0779834 | − | 0.996955i | \(-0.524848\pi\) | ||||
−0.0779834 | + | 0.996955i | \(0.524848\pi\) | |||||||
\(380\) | −2338.62 | −0.315707 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −687.509 | −0.0920838 | ||||||||
\(383\) | −9157.79 | −1.22178 | −0.610889 | − | 0.791716i | \(-0.709188\pi\) | ||||
−0.610889 | + | 0.791716i | \(0.709188\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4152.00 | 0.549625 | ||||||||
\(386\) | −1438.94 | −0.189741 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9331.15 | −1.22092 | ||||||||
\(389\) | 2370.80 | 0.309008 | 0.154504 | − | 0.987992i | \(-0.450622\pi\) | ||||
0.154504 | + | 0.987992i | \(0.450622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15723.6 | −2.03370 | ||||||||
\(392\) | 1436.19 | 0.185048 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 368.649 | 0.0471378 | ||||||||
\(395\) | 11315.3 | 1.44135 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4487.57 | 0.567316 | 0.283658 | − | 0.958926i | \(-0.408452\pi\) | ||||
0.283658 | + | 0.958926i | \(0.408452\pi\) | |||||||
\(398\) | 1205.79 | 0.151861 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14504.5 | 1.81306 | ||||||||
\(401\) | −13496.7 | −1.68079 | −0.840393 | − | 0.541977i | \(-0.817676\pi\) | ||||
−0.840393 | + | 0.541977i | \(0.817676\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4098.00 | −0.506540 | ||||||||
\(404\) | 2184.49 | 0.269016 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26.6061 | 0.00325231 | ||||||||
\(407\) | −5692.53 | −0.693288 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5635.52 | −0.681317 | −0.340658 | − | 0.940187i | \(-0.610650\pi\) | ||||
−0.340658 | + | 0.940187i | \(0.610650\pi\) | |||||||
\(410\) | 1490.14 | 0.179494 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −239.817 | −0.0286770 | ||||||||
\(413\) | 8894.06 | 1.05968 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16405.3 | 1.94049 | ||||||||
\(416\) | −1494.48 | −0.176137 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −125.610 | −0.0146980 | ||||||||
\(419\) | 15387.8 | 1.79414 | 0.897068 | − | 0.441892i | \(-0.145693\pi\) | ||||
0.897068 | + | 0.441892i | \(0.145693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7068.70 | −0.818308 | −0.409154 | − | 0.912465i | \(-0.634176\pi\) | ||||
−0.409154 | + | 0.912465i | \(0.634176\pi\) | |||||||
\(422\) | 163.883 | 0.0189045 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3240.37 | 0.371147 | ||||||||
\(425\) | −24764.7 | −2.82650 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2551.40 | −0.289158 | ||||||||
\(428\) | −103.486 | −0.0116873 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2986.05 | −0.334884 | ||||||||
\(431\) | 12414.8 | 1.38747 | 0.693736 | − | 0.720230i | \(-0.255964\pi\) | ||||
0.693736 | + | 0.720230i | \(0.255964\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9540.57 | −1.05887 | −0.529435 | − | 0.848351i | \(-0.677596\pi\) | ||||
−0.529435 | + | 0.848351i | \(0.677596\pi\) | |||||||
\(434\) | −949.552 | −0.105023 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2351.19 | −0.258260 | ||||||||
\(437\) | 2393.42 | 0.261997 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12109.2 | −1.31650 | −0.658248 | − | 0.752801i | \(-0.728702\pi\) | ||||
−0.658248 | + | 0.752801i | \(0.728702\pi\) | |||||||
\(440\) | 2442.62 | 0.264653 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 820.158 | 0.0882600 | ||||||||
\(443\) | 10745.2 | 1.15241 | 0.576205 | − | 0.817305i | \(-0.304533\pi\) | ||||
0.576205 | + | 0.817305i | \(0.304533\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8141.45 | 0.867285 | ||||||||
\(446\) | −1861.57 | −0.197641 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4949.76 | 0.521996 | ||||||||
\(449\) | −12251.4 | −1.28771 | −0.643854 | − | 0.765149i | \(-0.722665\pi\) | ||||
−0.643854 | + | 0.765149i | \(0.722665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3728.23 | −0.389258 | ||||||||
\(452\) | 8289.19 | 0.862590 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1436.37 | 0.148485 | ||||||||
\(455\) | 4126.65 | 0.425188 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9561.13 | 0.978667 | 0.489334 | − | 0.872097i | \(-0.337240\pi\) | ||||
0.489334 | + | 0.872097i | \(0.337240\pi\) | |||||||
\(458\) | −2384.68 | −0.243294 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −23024.1 | −2.33371 | ||||||||
\(461\) | −9185.83 | −0.928041 | −0.464021 | − | 0.885824i | \(-0.653594\pi\) | ||||
−0.464021 | + | 0.885824i | \(0.653594\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3944.19 | −0.395900 | −0.197950 | − | 0.980212i | \(-0.563428\pi\) | ||||
−0.197950 | + | 0.980212i | \(0.563428\pi\) | |||||||
\(464\) | −352.773 | −0.0352954 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1649.89 | 0.164013 | ||||||||
\(467\) | 12677.7 | 1.25622 | 0.628111 | − | 0.778124i | \(-0.283828\pi\) | ||||
0.628111 | + | 0.778124i | \(0.283828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11446.0 | 1.12693 | ||||||||
\(470\) | 483.825 | 0.0474834 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5232.36 | 0.510252 | ||||||||
\(473\) | 7470.91 | 0.726242 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3769.64 | 0.364132 | ||||||||
\(476\) | −8852.32 | −0.852406 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −97.9996 | −0.00937740 | ||||||||
\(479\) | −5220.89 | −0.498013 | −0.249007 | − | 0.968502i | \(-0.580104\pi\) | ||||
−0.249007 | + | 0.968502i | \(0.580104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5657.77 | −0.536325 | ||||||||
\(482\) | 1172.55 | 0.110806 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7401.03 | 0.695063 | ||||||||
\(485\) | 22817.4 | 2.13626 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12640.9 | −1.17621 | −0.588106 | − | 0.808784i | \(-0.700126\pi\) | ||||
−0.588106 | + | 0.808784i | \(0.700126\pi\) | |||||||
\(488\) | −1500.98 | −0.139234 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1737.31 | −0.160171 | ||||||||
\(491\) | 1322.37 | 0.121543 | 0.0607715 | − | 0.998152i | \(-0.480644\pi\) | ||||
0.0607715 | + | 0.998152i | \(0.480644\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 602.316 | 0.0550243 | ||||||||
\(494\) | −124.843 | −0.0113703 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12590.2 | 1.13975 | ||||||||
\(497\) | 2794.03 | 0.252172 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1861.29 | 0.166980 | 0.0834900 | − | 0.996509i | \(-0.473393\pi\) | ||||
0.0834900 | + | 0.996509i | \(0.473393\pi\) | |||||||
\(500\) | −17514.3 | −1.56653 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 186.243 | 0.0165586 | ||||||||
\(503\) | −10146.4 | −0.899412 | −0.449706 | − | 0.893177i | \(-0.648471\pi\) | ||||
−0.449706 | + | 0.893177i | \(0.648471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5341.72 | −0.470700 | ||||||||
\(506\) | −1236.65 | −0.108648 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21103.8 | −1.84317 | ||||||||
\(509\) | 10573.5 | 0.920750 | 0.460375 | − | 0.887724i | \(-0.347715\pi\) | ||||
0.460375 | + | 0.887724i | \(0.347715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6596.65 | 0.571073 | ||||||||
\(512\) | 7707.12 | 0.665253 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 570.480 | 0.0489548 | ||||||||
\(515\) | 586.424 | 0.0501766 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1210.50 | −0.102974 | ||||||||
\(518\) | −1310.97 | −0.111198 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2427.70 | 0.204734 | ||||||||
\(521\) | 569.399 | 0.0478806 | 0.0239403 | − | 0.999713i | \(-0.492379\pi\) | ||||
0.0239403 | + | 0.999713i | \(0.492379\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15735.2 | 1.31559 | 0.657793 | − | 0.753199i | \(-0.271490\pi\) | ||||
0.657793 | + | 0.753199i | \(0.271490\pi\) | |||||||
\(524\) | −3938.70 | −0.328365 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2369.82 | −0.196443 | ||||||||
\(527\) | −21496.2 | −1.77683 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11396.6 | 0.936685 | ||||||||
\(530\) | −3919.76 | −0.321252 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1347.48 | 0.109814 | ||||||||
\(533\) | −3705.47 | −0.301129 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 253.053 | 0.0204494 | ||||||||
\(536\) | 6733.68 | 0.542632 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 707.908 | 0.0567288 | ||||||||
\(539\) | 4346.64 | 0.347353 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17202.3 | −1.36707 | −0.683533 | − | 0.729919i | \(-0.739558\pi\) | ||||
−0.683533 | + | 0.729919i | \(0.739558\pi\) | |||||||
\(542\) | 649.526 | 0.0514751 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7839.36 | −0.617849 | ||||||||
\(545\) | 5749.35 | 0.451881 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24396.8 | −1.90700 | −0.953501 | − | 0.301390i | \(-0.902549\pi\) | ||||
−0.953501 | + | 0.301390i | \(0.902549\pi\) | |||||||
\(548\) | 15561.0 | 1.21301 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1947.73 | −0.151003 | ||||||||
\(551\) | −91.6835 | −0.00708865 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6519.71 | −0.501350 | ||||||||
\(554\) | −652.442 | −0.0500354 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4343.30 | −0.331289 | ||||||||
\(557\) | 17490.8 | 1.33054 | 0.665268 | − | 0.746604i | \(-0.268317\pi\) | ||||
0.665268 | + | 0.746604i | \(0.268317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7425.29 | 0.561818 | ||||||||
\(560\) | −12678.2 | −0.956702 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 46.6352 | 0.00350034 | ||||||||
\(563\) | 5212.73 | 0.390213 | 0.195107 | − | 0.980782i | \(-0.437495\pi\) | ||||
0.195107 | + | 0.980782i | \(0.437495\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20269.5 | −1.50928 | ||||||||
\(566\) | 554.472 | 0.0411770 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1643.72 | 0.121425 | ||||||||
\(569\) | 7606.26 | 0.560406 | 0.280203 | − | 0.959941i | \(-0.409598\pi\) | ||||
0.280203 | + | 0.959941i | \(0.409598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16718.9 | −1.22533 | −0.612665 | − | 0.790343i | \(-0.709902\pi\) | ||||
−0.612665 | + | 0.790343i | \(0.709902\pi\) | |||||||
\(572\) | −3004.73 | −0.219640 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −858.599 | −0.0624342 | ||||||||
\(575\) | 37112.8 | 2.69167 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12336.2 | −0.890059 | −0.445029 | − | 0.895516i | \(-0.646807\pi\) | ||||
−0.445029 | + | 0.895516i | \(0.646807\pi\) | |||||||
\(578\) | 2287.65 | 0.164626 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 881.974 | 0.0631414 | ||||||||
\(581\) | −9452.54 | −0.674970 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9807.00 | 0.696680 | ||||||||
\(584\) | 3880.80 | 0.274980 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2731.50 | −0.192555 | ||||||||
\(587\) | 7213.07 | 0.507181 | 0.253590 | − | 0.967312i | \(-0.418388\pi\) | ||||
0.253590 | + | 0.967312i | \(0.418388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3272.12 | 0.228905 | ||||||||
\(590\) | −6329.40 | −0.441656 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17382.3 | 1.20677 | ||||||||
\(593\) | −16759.1 | −1.16057 | −0.580283 | − | 0.814415i | \(-0.697058\pi\) | ||||
−0.580283 | + | 0.814415i | \(0.697058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21646.6 | 1.49147 | ||||||||
\(596\) | 10885.5 | 0.748136 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1229.10 | −0.0840497 | ||||||||
\(599\) | 18652.0 | 1.27229 | 0.636143 | − | 0.771571i | \(-0.280529\pi\) | ||||
0.636143 | + | 0.771571i | \(0.280529\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11696.1 | 0.793833 | 0.396916 | − | 0.917855i | \(-0.370080\pi\) | ||||
0.396916 | + | 0.917855i | \(0.370080\pi\) | |||||||
\(602\) | 1720.52 | 0.116484 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 28900.9 | 1.94696 | ||||||||
\(605\) | −18097.7 | −1.21616 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7834.42 | 0.523871 | 0.261935 | − | 0.965085i | \(-0.415639\pi\) | ||||
0.261935 | + | 0.965085i | \(0.415639\pi\) | |||||||
\(608\) | 1193.29 | 0.0795961 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1815.68 | 0.120516 | ||||||||
\(611\) | −1203.11 | −0.0796606 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21976.9 | 1.44802 | 0.724012 | − | 0.689787i | \(-0.242296\pi\) | ||||
0.724012 | + | 0.689787i | \(0.242296\pi\) | |||||||
\(614\) | −2497.86 | −0.164178 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1407.41 | −0.0920552 | ||||||||
\(617\) | 24333.9 | 1.58776 | 0.793879 | − | 0.608076i | \(-0.208058\pi\) | ||||
0.793879 | + | 0.608076i | \(0.208058\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21713.5 | 1.40992 | 0.704960 | − | 0.709247i | \(-0.250965\pi\) | ||||
0.704960 | + | 0.709247i | \(0.250965\pi\) | |||||||
\(620\) | −31477.0 | −2.03895 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −395.565 | −0.0254996 | ||||||||
\(623\) | −4691.01 | −0.301671 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12606.4 | 0.806812 | ||||||||
\(626\) | 711.262 | 0.0454117 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14715.1 | 0.935028 | ||||||||
\(629\) | −29678.1 | −1.88131 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17221.7 | −1.08651 | −0.543253 | − | 0.839569i | \(-0.682808\pi\) | ||||
−0.543253 | + | 0.839569i | \(0.682808\pi\) | |||||||
\(632\) | −3835.54 | −0.241407 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −484.762 | −0.0303665 | ||||||||
\(635\) | 51605.1 | 3.22502 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4320.10 | 0.268711 | ||||||||
\(638\) | 47.3718 | 0.00293960 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15248.1 | −0.941772 | ||||||||
\(641\) | 10816.8 | 0.666516 | 0.333258 | − | 0.942836i | \(-0.391852\pi\) | ||||
0.333258 | + | 0.942836i | \(0.391852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 205.221 | 0.0125865 | 0.00629326 | − | 0.999980i | \(-0.497997\pi\) | ||||
0.00629326 | + | 0.999980i | \(0.497997\pi\) | |||||||
\(644\) | 13266.2 | 0.811743 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −654.869 | −0.0398847 | ||||||||
\(647\) | −12818.8 | −0.778916 | −0.389458 | − | 0.921044i | \(-0.627338\pi\) | ||||
−0.389458 | + | 0.921044i | \(0.627338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15835.8 | 0.957794 | ||||||||
\(650\) | −1935.84 | −0.116815 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22710.0 | 1.36410 | ||||||||
\(653\) | −18071.7 | −1.08300 | −0.541501 | − | 0.840700i | \(-0.682144\pi\) | ||||
−0.541501 | + | 0.840700i | \(0.682144\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9631.30 | 0.574543 | ||||||||
\(656\) | 11384.2 | 0.677561 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −278.774 | −0.0165163 | ||||||||
\(659\) | 25375.3 | 1.49997 | 0.749985 | − | 0.661455i | \(-0.230061\pi\) | ||||
0.749985 | + | 0.661455i | \(0.230061\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24947.5 | −1.46800 | −0.733998 | − | 0.679152i | \(-0.762348\pi\) | ||||
−0.733998 | + | 0.679152i | \(0.762348\pi\) | |||||||
\(662\) | −2426.81 | −0.142478 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5560.91 | −0.325008 | ||||||||
\(665\) | −3295.00 | −0.192142 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −902.641 | −0.0523994 | ||||||||
\(668\) | −5383.24 | −0.311802 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8145.49 | −0.469683 | ||||||||
\(671\) | −4542.73 | −0.261356 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10576.2 | −0.605768 | −0.302884 | − | 0.953027i | \(-0.597950\pi\) | ||||
−0.302884 | + | 0.953027i | \(0.597950\pi\) | |||||||
\(674\) | −2008.19 | −0.114766 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14220.2 | 0.809071 | ||||||||
\(677\) | 27468.3 | 1.55937 | 0.779684 | − | 0.626174i | \(-0.215380\pi\) | ||||
0.779684 | + | 0.626174i | \(0.215380\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13147.1 | −0.743064 | ||||||||
\(680\) | 12734.6 | 0.718163 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1690.67 | −0.0949251 | ||||||||
\(683\) | 28341.1 | 1.58776 | 0.793881 | − | 0.608074i | \(-0.208057\pi\) | ||||
0.793881 | + | 0.608074i | \(0.208057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38051.1 | −2.12242 | ||||||||
\(686\) | 2552.98 | 0.142089 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −22812.6 | −1.26413 | ||||||||
\(689\) | 9747.12 | 0.538949 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7519.91 | −0.413995 | −0.206998 | − | 0.978341i | \(-0.566369\pi\) | ||||
−0.206998 | + | 0.978341i | \(0.566369\pi\) | |||||||
\(692\) | −1998.64 | −0.109793 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3845.48 | 0.210335 | ||||||||
\(695\) | 10620.6 | 0.579660 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19437.2 | −1.05629 | ||||||||
\(698\) | 275.202 | 0.0149234 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20894.3 | 1.12819 | ||||||||
\(701\) | −11013.6 | −0.593406 | −0.296703 | − | 0.954970i | \(-0.595887\pi\) | ||||
−0.296703 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4517.55 | 0.242365 | ||||||||
\(704\) | 8812.99 | 0.471807 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −70.9766 | −0.00378363 | ||||||||
\(707\) | 3077.84 | 0.163726 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15265.0 | −0.808587 | −0.404293 | − | 0.914629i | \(-0.632482\pi\) | ||||
−0.404293 | + | 0.914629i | \(0.632482\pi\) | |||||||
\(710\) | −1988.35 | −0.105101 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2759.71 | −0.145259 | ||||||||
\(713\) | 32214.6 | 1.69207 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7347.45 | 0.384306 | ||||||||
\(716\) | 36701.7 | 1.91565 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2914.18 | −0.151471 | ||||||||
\(719\) | 10445.5 | 0.541797 | 0.270898 | − | 0.962608i | \(-0.412679\pi\) | ||||
0.270898 | + | 0.962608i | \(0.412679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −337.890 | −0.0174531 | ||||||||
\(722\) | −2712.78 | −0.139833 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11514.2 | 0.591052 | ||||||||
\(725\) | −1421.66 | −0.0728264 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11779.3 | 0.600923 | 0.300462 | − | 0.953794i | \(-0.402859\pi\) | ||||
0.300462 | + | 0.953794i | \(0.402859\pi\) | |||||||
\(728\) | −1398.81 | −0.0712135 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4694.46 | −0.238013 | ||||||||
\(731\) | 38949.7 | 1.97074 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4037.13 | −0.203431 | −0.101715 | − | 0.994814i | \(-0.532433\pi\) | ||||
−0.101715 | + | 0.994814i | \(0.532433\pi\) | |||||||
\(734\) | 3757.75 | 0.188966 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11748.2 | 0.588375 | ||||||||
\(737\) | 20379.5 | 1.01857 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32609.4 | −1.62322 | −0.811609 | − | 0.584201i | \(-0.801408\pi\) | ||||
−0.811609 | + | 0.584201i | \(0.801408\pi\) | |||||||
\(740\) | −43457.8 | −2.15884 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2258.52 | 0.111742 | ||||||||
\(743\) | 10619.4 | 0.524343 | 0.262171 | − | 0.965021i | \(-0.415561\pi\) | ||||
0.262171 | + | 0.965021i | \(0.415561\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26618.4 | −1.30902 | ||||||||
\(746\) | 1731.96 | 0.0850021 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15761.4 | −0.770448 | ||||||||
\(749\) | −145.806 | −0.00711300 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8276.31 | −0.402139 | −0.201070 | − | 0.979577i | \(-0.564442\pi\) | ||||
−0.201070 | + | 0.979577i | \(0.564442\pi\) | |||||||
\(752\) | 3696.29 | 0.179242 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 47.0826 | 0.00227407 | ||||||||
\(755\) | −70671.4 | −3.40662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 237.768 | 0.0114159 | 0.00570794 | − | 0.999984i | \(-0.498183\pi\) | ||||
0.00570794 | + | 0.999984i | \(0.498183\pi\) | |||||||
\(758\) | −471.864 | −0.0226107 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1938.44 | −0.0925193 | ||||||||
\(761\) | −41263.6 | −1.96558 | −0.982789 | − | 0.184730i | \(-0.940859\pi\) | ||||
−0.982789 | + | 0.184730i | \(0.940859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3312.71 | −0.157180 | ||||||||
\(764\) | 13131.6 | 0.621838 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3755.06 | −0.177123 | ||||||||
\(767\) | 15739.1 | 0.740945 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14056.7 | 0.659165 | 0.329582 | − | 0.944127i | \(-0.393092\pi\) | ||||
0.329582 | + | 0.944127i | \(0.393092\pi\) | |||||||
\(770\) | 1702.49 | 0.0796797 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 27484.1 | 1.28131 | ||||||||
\(773\) | 12138.6 | 0.564806 | 0.282403 | − | 0.959296i | \(-0.408868\pi\) | ||||
0.282403 | + | 0.959296i | \(0.408868\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 50738.0 | 2.35170 | ||||||||
\(776\) | −7734.43 | −0.357796 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 972.122 | 0.0447972 | ||||||||
\(779\) | 2958.70 | 0.136080 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4974.74 | 0.227926 | ||||||||
\(782\) | −6447.31 | −0.294828 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13272.6 | −0.604618 | ||||||||
\(785\) | −35982.9 | −1.63603 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34214.6 | 1.54971 | 0.774854 | − | 0.632140i | \(-0.217823\pi\) | ||||
0.774854 | + | 0.632140i | \(0.217823\pi\) | |||||||
\(788\) | −7041.29 | −0.318319 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4639.71 | 0.208954 | ||||||||
\(791\) | 11679.1 | 0.524980 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4514.99 | −0.202184 | ||||||||
\(794\) | 1840.08 | 0.0822444 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23030.8 | −1.02551 | ||||||||
\(797\) | −20283.0 | −0.901458 | −0.450729 | − | 0.892661i | \(-0.648836\pi\) | ||||
−0.450729 | + | 0.892661i | \(0.648836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6310.97 | −0.279432 | ||||||||
\(800\) | 18503.4 | 0.817743 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5534.21 | −0.243665 | ||||||||
\(803\) | 11745.2 | 0.516165 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32439.9 | −1.42032 | ||||||||
\(806\) | −1680.34 | −0.0734337 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1810.69 | 0.0788363 | ||||||||
\(809\) | −22553.6 | −0.980153 | −0.490076 | − | 0.871680i | \(-0.663031\pi\) | ||||
−0.490076 | + | 0.871680i | \(0.663031\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13204.3 | 0.571722 | 0.285861 | − | 0.958271i | \(-0.407720\pi\) | ||||
0.285861 | + | 0.958271i | \(0.407720\pi\) | |||||||
\(812\) | −508.183 | −0.0219627 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2334.17 | −0.100507 | ||||||||
\(815\) | −55532.6 | −2.38678 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5928.86 | −0.253885 | ||||||||
\(818\) | −2310.79 | −0.0987713 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −28462.0 | −1.21212 | ||||||||
\(821\) | −27494.5 | −1.16877 | −0.584387 | − | 0.811475i | \(-0.698665\pi\) | ||||
−0.584387 | + | 0.811475i | \(0.698665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33702.9 | −1.42747 | −0.713737 | − | 0.700414i | \(-0.752999\pi\) | ||||
−0.713737 | + | 0.700414i | \(0.752999\pi\) | |||||||
\(824\) | −198.780 | −0.00840393 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3646.92 | 0.153623 | ||||||||
\(827\) | −42658.3 | −1.79368 | −0.896842 | − | 0.442352i | \(-0.854144\pi\) | ||||
−0.896842 | + | 0.442352i | \(0.854144\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17343.7 | 0.726625 | 0.363312 | − | 0.931667i | \(-0.381646\pi\) | ||||
0.363312 | + | 0.931667i | \(0.381646\pi\) | |||||||
\(830\) | 6726.84 | 0.281316 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8759.18 | 0.364988 | ||||||||
\(833\) | 22661.3 | 0.942578 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13163.6 | 0.545564 | ||||||||
\(836\) | 2399.18 | 0.0992552 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6309.61 | 0.260098 | ||||||||
\(839\) | −26880.4 | −1.10610 | −0.553048 | − | 0.833149i | \(-0.686535\pi\) | ||||
−0.553048 | + | 0.833149i | \(0.686535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24354.4 | −0.998582 | ||||||||
\(842\) | −2898.45 | −0.118631 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3130.20 | −0.127661 | ||||||||
\(845\) | −34772.7 | −1.41564 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10427.7 | 0.423022 | ||||||||
\(848\) | −29945.9 | −1.21267 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10154.5 | −0.409761 | ||||||||
\(851\) | 44476.1 | 1.79156 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20392.0 | −0.818535 | −0.409267 | − | 0.912415i | \(-0.634216\pi\) | ||||
−0.409267 | + | 0.912415i | \(0.634216\pi\) | |||||||
\(854\) | −1046.17 | −0.0419196 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −85.7774 | −0.00342501 | ||||||||
\(857\) | −32975.6 | −1.31438 | −0.657190 | − | 0.753725i | \(-0.728255\pi\) | ||||
−0.657190 | + | 0.753725i | \(0.728255\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3473.29 | 0.137960 | 0.0689798 | − | 0.997618i | \(-0.478026\pi\) | ||||
0.0689798 | + | 0.997618i | \(0.478026\pi\) | |||||||
\(860\) | 57034.2 | 2.26146 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5090.57 | 0.201143 | ||||||||
\(863\) | 21960.8 | 0.866226 | 0.433113 | − | 0.901340i | \(-0.357415\pi\) | ||||
0.433113 | + | 0.901340i | \(0.357415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4887.27 | 0.192106 | ||||||||
\(866\) | −3912.02 | −0.153505 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18136.7 | 0.709215 | ||||||||
\(869\) | −11608.3 | −0.453145 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20255.1 | 0.787965 | ||||||||
\(872\) | −1948.86 | −0.0756843 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 981.398 | 0.0379820 | ||||||||
\(875\) | −24676.8 | −0.953403 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45991.0 | 1.77082 | 0.885408 | − | 0.464815i | \(-0.153879\pi\) | ||||
0.885408 | + | 0.464815i | \(0.153879\pi\) | |||||||
\(878\) | −4965.27 | −0.190854 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −22573.4 | −0.864716 | ||||||||
\(881\) | 21002.8 | 0.803181 | 0.401591 | − | 0.915819i | \(-0.368458\pi\) | ||||
0.401591 | + | 0.915819i | \(0.368458\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6205.12 | −0.236488 | −0.118244 | − | 0.992985i | \(-0.537727\pi\) | ||||
−0.118244 | + | 0.992985i | \(0.537727\pi\) | |||||||
\(884\) | −15665.2 | −0.596016 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4405.95 | 0.167066 | ||||||||
\(887\) | 21820.0 | 0.825980 | 0.412990 | − | 0.910735i | \(-0.364484\pi\) | ||||
0.412990 | + | 0.910735i | \(0.364484\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29734.2 | −1.12177 | ||||||||
\(890\) | 3338.32 | 0.125731 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 35556.5 | 1.33466 | ||||||||
\(893\) | 960.644 | 0.0359986 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −89746.5 | −3.35184 | ||||||||
\(896\) | 8785.77 | 0.327580 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5023.58 | −0.186680 | ||||||||
\(899\) | −1234.03 | −0.0457811 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51129.0 | 1.89051 | ||||||||
\(902\) | −1528.72 | −0.0564312 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6870.77 | 0.252786 | ||||||||
\(905\) | −28155.6 | −1.03417 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6136.19 | 0.224640 | 0.112320 | − | 0.993672i | \(-0.464172\pi\) | ||||
0.112320 | + | 0.993672i | \(0.464172\pi\) | |||||||
\(908\) | −27435.0 | −1.00271 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1692.09 | 0.0616399 | ||||||||
\(911\) | −33424.3 | −1.21558 | −0.607791 | − | 0.794097i | \(-0.707944\pi\) | ||||
−0.607791 | + | 0.794097i | \(0.707944\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16830.1 | −0.610072 | ||||||||
\(914\) | 3920.45 | 0.141878 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 45548.0 | 1.64296 | ||||||||
\(917\) | −5549.44 | −0.199846 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31125.9 | 1.11724 | 0.558622 | − | 0.829422i | \(-0.311330\pi\) | ||||
0.558622 | + | 0.829422i | \(0.311330\pi\) | |||||||
\(920\) | −19084.3 | −0.683904 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3766.56 | −0.134539 | ||||||||
\(923\) | 4944.37 | 0.176323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 70049.9 | 2.48998 | ||||||||
\(926\) | −1617.27 | −0.0573941 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −450.032 | −0.0159192 | ||||||||
\(929\) | −49957.1 | −1.76431 | −0.882153 | − | 0.470963i | \(-0.843906\pi\) | ||||
−0.882153 | + | 0.470963i | \(0.843906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3449.46 | −0.121430 | ||||||||
\(932\) | −31513.4 | −1.10757 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5198.38 | 0.182116 | ||||||||
\(935\) | 38541.4 | 1.34806 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46502.5 | 1.62131 | 0.810656 | − | 0.585522i | \(-0.199110\pi\) | ||||
0.810656 | + | 0.585522i | \(0.199110\pi\) | |||||||
\(938\) | 4693.33 | 0.163372 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9241.18 | −0.320653 | ||||||||
\(941\) | −6850.70 | −0.237329 | −0.118664 | − | 0.992934i | \(-0.537861\pi\) | ||||
−0.118664 | + | 0.992934i | \(0.537861\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29128.9 | 1.00590 | ||||||||
\(944\) | −48354.9 | −1.66718 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3063.37 | 0.105284 | ||||||||
\(947\) | 17782.3 | 0.610187 | 0.305093 | − | 0.952322i | \(-0.401312\pi\) | ||||
0.305093 | + | 0.952322i | \(0.401312\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11673.5 | 0.399303 | ||||||||
\(950\) | 1545.70 | 0.0527887 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7337.54 | −0.249801 | ||||||||
\(953\) | 43227.9 | 1.46935 | 0.734675 | − | 0.678420i | \(-0.237335\pi\) | ||||
0.734675 | + | 0.678420i | \(0.237335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32110.6 | −1.08804 | ||||||||
\(956\) | 1871.82 | 0.0633252 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2140.77 | −0.0721976 | ||||||||
\(959\) | 21924.6 | 0.738251 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14250.6 | 0.478352 | ||||||||
\(962\) | −2319.91 | −0.0777516 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22396.1 | −0.748267 | ||||||||
\(965\) | −67206.7 | −2.24193 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15458.1 | 0.514062 | 0.257031 | − | 0.966403i | \(-0.417256\pi\) | ||||
0.257031 | + | 0.966403i | \(0.417256\pi\) | |||||||
\(968\) | 6134.59 | 0.203691 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9356.06 | 0.309696 | ||||||||
\(971\) | 37978.0 | 1.25517 | 0.627586 | − | 0.778548i | \(-0.284043\pi\) | ||||
0.627586 | + | 0.778548i | \(0.284043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6119.49 | −0.201626 | ||||||||
\(974\) | −5183.29 | −0.170517 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13871.3 | 0.454929 | ||||||||
\(977\) | 8636.65 | 0.282816 | 0.141408 | − | 0.989951i | \(-0.454837\pi\) | ||||
0.141408 | + | 0.989951i | \(0.454837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8352.28 | −0.272666 | ||||||||
\(980\) | 33183.0 | 1.08163 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 542.223 | 0.0176202 | ||||||||
\(983\) | 25884.9 | 0.839877 | 0.419939 | − | 0.907552i | \(-0.362052\pi\) | ||||
0.419939 | + | 0.907552i | \(0.362052\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17218.0 | 0.556967 | ||||||||
\(986\) | 246.974 | 0.00797693 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2384.53 | 0.0767834 | ||||||||
\(989\) | −58370.7 | −1.87672 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18732.3 | −0.600457 | −0.300228 | − | 0.953867i | \(-0.597063\pi\) | ||||
−0.300228 | + | 0.953867i | \(0.597063\pi\) | |||||||
\(992\) | 16061.3 | 0.514060 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1145.67 | 0.0365577 | ||||||||
\(995\) | 56317.3 | 1.79435 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47122.4 | −1.49687 | −0.748436 | − | 0.663207i | \(-0.769195\pi\) | ||||
−0.748436 | + | 0.663207i | \(0.769195\pi\) | |||||||
\(998\) | 763.206 | 0.0242073 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2151.4.a.b.1.14 | 28 | ||
3.2 | odd | 2 | 717.4.a.b.1.15 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.4.a.b.1.15 | ✓ | 28 | 3.2 | odd | 2 | ||
2151.4.a.b.1.14 | 28 | 1.1 | even | 1 | trivial |