Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, 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("289.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 54x^{6} - 20x^{5} + 677x^{4} + 380x^{3} - 2216x^{2} - 1000x + 476 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.53205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.11783 | 0.748767 | 0.374384 | − | 0.927274i | \(-0.377854\pi\) | ||||
0.374384 | + | 0.927274i | \(0.377854\pi\) | |||||||
\(3\) | −8.38287 | −1.61328 | −0.806642 | − | 0.591040i | \(-0.798717\pi\) | ||||
−0.806642 | + | 0.591040i | \(0.798717\pi\) | |||||||
\(4\) | −3.51478 | −0.439347 | ||||||||
\(5\) | −14.3637 | −1.28473 | −0.642366 | − | 0.766398i | \(-0.722047\pi\) | ||||
−0.642366 | + | 0.766398i | \(0.722047\pi\) | |||||||
\(6\) | −17.7535 | −1.20797 | ||||||||
\(7\) | −4.54811 | −0.245575 | −0.122787 | − | 0.992433i | \(-0.539183\pi\) | ||||
−0.122787 | + | 0.992433i | \(0.539183\pi\) | |||||||
\(8\) | −24.3864 | −1.07774 | ||||||||
\(9\) | 43.2725 | 1.60269 | ||||||||
\(10\) | −30.4200 | −0.961965 | ||||||||
\(11\) | −48.0908 | −1.31817 | −0.659087 | − | 0.752067i | \(-0.729057\pi\) | ||||
−0.659087 | + | 0.752067i | \(0.729057\pi\) | |||||||
\(12\) | 29.4639 | 0.708792 | ||||||||
\(13\) | −49.5377 | −1.05687 | −0.528434 | − | 0.848974i | \(-0.677221\pi\) | ||||
−0.528434 | + | 0.848974i | \(0.677221\pi\) | |||||||
\(14\) | −9.63214 | −0.183878 | ||||||||
\(15\) | 120.409 | 2.07264 | ||||||||
\(16\) | −23.5281 | −0.367627 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 91.6440 | 1.20004 | ||||||||
\(19\) | 31.1112 | 0.375653 | 0.187826 | − | 0.982202i | \(-0.439856\pi\) | ||||
0.187826 | + | 0.982202i | \(0.439856\pi\) | |||||||
\(20\) | 50.4854 | 0.564443 | ||||||||
\(21\) | 38.1262 | 0.396182 | ||||||||
\(22\) | −101.848 | −0.987006 | ||||||||
\(23\) | −41.8837 | −0.379711 | −0.189856 | − | 0.981812i | \(-0.560802\pi\) | ||||
−0.189856 | + | 0.981812i | \(0.560802\pi\) | |||||||
\(24\) | 204.428 | 1.73870 | ||||||||
\(25\) | 81.3170 | 0.650536 | ||||||||
\(26\) | −104.913 | −0.791349 | ||||||||
\(27\) | −136.410 | −0.972303 | ||||||||
\(28\) | 15.9856 | 0.107893 | ||||||||
\(29\) | 121.361 | 0.777109 | 0.388555 | − | 0.921426i | \(-0.372975\pi\) | ||||
0.388555 | + | 0.921426i | \(0.372975\pi\) | |||||||
\(30\) | 255.007 | 1.55192 | ||||||||
\(31\) | 167.926 | 0.972918 | 0.486459 | − | 0.873703i | \(-0.338288\pi\) | ||||
0.486459 | + | 0.873703i | \(0.338288\pi\) | |||||||
\(32\) | 145.263 | 0.802470 | ||||||||
\(33\) | 403.139 | 2.12659 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 65.3279 | 0.315498 | ||||||||
\(36\) | −152.093 | −0.704136 | ||||||||
\(37\) | −356.317 | −1.58319 | −0.791596 | − | 0.611044i | \(-0.790750\pi\) | ||||
−0.791596 | + | 0.611044i | \(0.790750\pi\) | |||||||
\(38\) | 65.8884 | 0.281277 | ||||||||
\(39\) | 415.268 | 1.70503 | ||||||||
\(40\) | 350.280 | 1.38460 | ||||||||
\(41\) | 63.3621 | 0.241354 | 0.120677 | − | 0.992692i | \(-0.461494\pi\) | ||||
0.120677 | + | 0.992692i | \(0.461494\pi\) | |||||||
\(42\) | 80.7450 | 0.296648 | ||||||||
\(43\) | −87.7863 | −0.311332 | −0.155666 | − | 0.987810i | \(-0.549752\pi\) | ||||
−0.155666 | + | 0.987810i | \(0.549752\pi\) | |||||||
\(44\) | 169.028 | 0.579136 | ||||||||
\(45\) | −621.555 | −2.05902 | ||||||||
\(46\) | −88.7028 | −0.284316 | ||||||||
\(47\) | −281.901 | −0.874884 | −0.437442 | − | 0.899247i | \(-0.644115\pi\) | ||||
−0.437442 | + | 0.899247i | \(0.644115\pi\) | |||||||
\(48\) | 197.233 | 0.593086 | ||||||||
\(49\) | −322.315 | −0.939693 | ||||||||
\(50\) | 172.216 | 0.487100 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 174.114 | 0.464332 | ||||||||
\(53\) | −5.63254 | −0.0145979 | −0.00729895 | − | 0.999973i | \(-0.502323\pi\) | ||||
−0.00729895 | + | 0.999973i | \(0.502323\pi\) | |||||||
\(54\) | −288.894 | −0.728029 | ||||||||
\(55\) | 690.763 | 1.69350 | ||||||||
\(56\) | 110.912 | 0.264665 | ||||||||
\(57\) | −260.801 | −0.606035 | ||||||||
\(58\) | 257.022 | 0.581874 | ||||||||
\(59\) | −134.352 | −0.296460 | −0.148230 | − | 0.988953i | \(-0.547358\pi\) | ||||
−0.148230 | + | 0.988953i | \(0.547358\pi\) | |||||||
\(60\) | −423.212 | −0.910608 | ||||||||
\(61\) | −598.035 | −1.25525 | −0.627627 | − | 0.778514i | \(-0.715974\pi\) | ||||
−0.627627 | + | 0.778514i | \(0.715974\pi\) | |||||||
\(62\) | 355.640 | 0.728490 | ||||||||
\(63\) | −196.808 | −0.393579 | ||||||||
\(64\) | 495.867 | 0.968490 | ||||||||
\(65\) | 711.547 | 1.35779 | ||||||||
\(66\) | 853.781 | 1.59232 | ||||||||
\(67\) | −951.761 | −1.73546 | −0.867732 | − | 0.497032i | \(-0.834423\pi\) | ||||
−0.867732 | + | 0.497032i | \(0.834423\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 351.106 | 0.612582 | ||||||||
\(70\) | 138.354 | 0.236235 | ||||||||
\(71\) | 332.263 | 0.555385 | 0.277693 | − | 0.960670i | \(-0.410430\pi\) | ||||
0.277693 | + | 0.960670i | \(0.410430\pi\) | |||||||
\(72\) | −1055.26 | −1.72727 | ||||||||
\(73\) | −26.5290 | −0.0425340 | −0.0212670 | − | 0.999774i | \(-0.506770\pi\) | ||||
−0.0212670 | + | 0.999774i | \(0.506770\pi\) | |||||||
\(74\) | −754.620 | −1.18544 | ||||||||
\(75\) | −681.670 | −1.04950 | ||||||||
\(76\) | −109.349 | −0.165042 | ||||||||
\(77\) | 218.722 | 0.323710 | ||||||||
\(78\) | 879.470 | 1.27667 | ||||||||
\(79\) | 33.1438 | 0.0472021 | 0.0236010 | − | 0.999721i | \(-0.492487\pi\) | ||||
0.0236010 | + | 0.999721i | \(0.492487\pi\) | |||||||
\(80\) | 337.952 | 0.472302 | ||||||||
\(81\) | −24.8476 | −0.0340845 | ||||||||
\(82\) | 134.190 | 0.180718 | ||||||||
\(83\) | 283.887 | 0.375430 | 0.187715 | − | 0.982224i | \(-0.439892\pi\) | ||||
0.187715 | + | 0.982224i | \(0.439892\pi\) | |||||||
\(84\) | −134.005 | −0.174062 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −185.917 | −0.233115 | ||||||||
\(87\) | −1017.35 | −1.25370 | ||||||||
\(88\) | 1172.76 | 1.42064 | ||||||||
\(89\) | 191.442 | 0.228009 | 0.114005 | − | 0.993480i | \(-0.463632\pi\) | ||||
0.114005 | + | 0.993480i | \(0.463632\pi\) | |||||||
\(90\) | −1316.35 | −1.54173 | ||||||||
\(91\) | 225.303 | 0.259540 | ||||||||
\(92\) | 147.212 | 0.166825 | ||||||||
\(93\) | −1407.70 | −1.56959 | ||||||||
\(94\) | −597.020 | −0.655085 | ||||||||
\(95\) | −446.874 | −0.482613 | ||||||||
\(96\) | −1217.72 | −1.29461 | ||||||||
\(97\) | −287.119 | −0.300541 | −0.150271 | − | 0.988645i | \(-0.548015\pi\) | ||||
−0.150271 | + | 0.988645i | \(0.548015\pi\) | |||||||
\(98\) | −682.609 | −0.703612 | ||||||||
\(99\) | −2081.01 | −2.11262 | ||||||||
\(100\) | −285.811 | −0.285811 | ||||||||
\(101\) | 154.062 | 0.151780 | 0.0758899 | − | 0.997116i | \(-0.475820\pi\) | ||||
0.0758899 | + | 0.997116i | \(0.475820\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 765.082 | 0.731900 | 0.365950 | − | 0.930634i | \(-0.380744\pi\) | ||||
0.365950 | + | 0.930634i | \(0.380744\pi\) | |||||||
\(104\) | 1208.05 | 1.13903 | ||||||||
\(105\) | −547.635 | −0.508988 | ||||||||
\(106\) | −11.9288 | −0.0109304 | ||||||||
\(107\) | 395.483 | 0.357315 | 0.178658 | − | 0.983911i | \(-0.442825\pi\) | ||||
0.178658 | + | 0.983911i | \(0.442825\pi\) | |||||||
\(108\) | 479.452 | 0.427179 | ||||||||
\(109\) | −877.900 | −0.771446 | −0.385723 | − | 0.922615i | \(-0.626048\pi\) | ||||
−0.385723 | + | 0.922615i | \(0.626048\pi\) | |||||||
\(110\) | 1462.92 | 1.26804 | ||||||||
\(111\) | 2986.96 | 2.55414 | ||||||||
\(112\) | 107.008 | 0.0902799 | ||||||||
\(113\) | 2046.06 | 1.70334 | 0.851669 | − | 0.524079i | \(-0.175590\pi\) | ||||
0.851669 | + | 0.524079i | \(0.175590\pi\) | |||||||
\(114\) | −552.334 | −0.453779 | ||||||||
\(115\) | 601.607 | 0.487827 | ||||||||
\(116\) | −426.557 | −0.341421 | ||||||||
\(117\) | −2143.62 | −1.69383 | ||||||||
\(118\) | −284.535 | −0.221980 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2936.35 | −2.23376 | ||||||||
\(121\) | 981.722 | 0.737582 | ||||||||
\(122\) | −1266.54 | −0.939894 | ||||||||
\(123\) | −531.156 | −0.389372 | ||||||||
\(124\) | −590.224 | −0.427449 | ||||||||
\(125\) | 627.452 | 0.448968 | ||||||||
\(126\) | −416.807 | −0.294699 | ||||||||
\(127\) | 2106.13 | 1.47156 | 0.735782 | − | 0.677218i | \(-0.236815\pi\) | ||||
0.735782 | + | 0.677218i | \(0.236815\pi\) | |||||||
\(128\) | −111.936 | −0.0772959 | ||||||||
\(129\) | 735.901 | 0.502267 | ||||||||
\(130\) | 1506.94 | 1.01667 | ||||||||
\(131\) | 1390.56 | 0.927434 | 0.463717 | − | 0.885983i | \(-0.346515\pi\) | ||||
0.463717 | + | 0.885983i | \(0.346515\pi\) | |||||||
\(132\) | −1416.94 | −0.934311 | ||||||||
\(133\) | −141.497 | −0.0922509 | ||||||||
\(134\) | −2015.67 | −1.29946 | ||||||||
\(135\) | 1959.36 | 1.24915 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2309.58 | −1.44030 | −0.720149 | − | 0.693820i | \(-0.755926\pi\) | ||||
−0.720149 | + | 0.693820i | \(0.755926\pi\) | |||||||
\(138\) | 743.584 | 0.458682 | ||||||||
\(139\) | 2477.09 | 1.51154 | 0.755769 | − | 0.654838i | \(-0.227263\pi\) | ||||
0.755769 | + | 0.654838i | \(0.227263\pi\) | |||||||
\(140\) | −229.613 | −0.138613 | ||||||||
\(141\) | 2363.14 | 1.41144 | ||||||||
\(142\) | 703.678 | 0.415855 | ||||||||
\(143\) | 2382.31 | 1.39314 | ||||||||
\(144\) | −1018.12 | −0.589190 | ||||||||
\(145\) | −1743.20 | −0.998377 | ||||||||
\(146\) | −56.1840 | −0.0318481 | ||||||||
\(147\) | 2701.92 | 1.51599 | ||||||||
\(148\) | 1252.37 | 0.695571 | ||||||||
\(149\) | −1521.60 | −0.836607 | −0.418304 | − | 0.908307i | \(-0.637375\pi\) | ||||
−0.418304 | + | 0.908307i | \(0.637375\pi\) | |||||||
\(150\) | −1443.66 | −0.785831 | ||||||||
\(151\) | −397.910 | −0.214447 | −0.107223 | − | 0.994235i | \(-0.534196\pi\) | ||||
−0.107223 | + | 0.994235i | \(0.534196\pi\) | |||||||
\(152\) | −758.691 | −0.404855 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 463.217 | 0.242384 | ||||||||
\(155\) | −2412.05 | −1.24994 | ||||||||
\(156\) | −1459.58 | −0.749100 | ||||||||
\(157\) | 1068.19 | 0.543001 | 0.271501 | − | 0.962438i | \(-0.412480\pi\) | ||||
0.271501 | + | 0.962438i | \(0.412480\pi\) | |||||||
\(158\) | 70.1930 | 0.0353434 | ||||||||
\(159\) | 47.2168 | 0.0235505 | ||||||||
\(160\) | −2086.51 | −1.03096 | ||||||||
\(161\) | 190.492 | 0.0932476 | ||||||||
\(162\) | −52.6231 | −0.0255214 | ||||||||
\(163\) | 845.422 | 0.406249 | 0.203124 | − | 0.979153i | \(-0.434890\pi\) | ||||
0.203124 | + | 0.979153i | \(0.434890\pi\) | |||||||
\(164\) | −222.704 | −0.106038 | ||||||||
\(165\) | −5790.58 | −2.73210 | ||||||||
\(166\) | 601.226 | 0.281109 | ||||||||
\(167\) | −2613.54 | −1.21103 | −0.605515 | − | 0.795834i | \(-0.707033\pi\) | ||||
−0.605515 | + | 0.795834i | \(0.707033\pi\) | |||||||
\(168\) | −929.761 | −0.426980 | ||||||||
\(169\) | 256.987 | 0.116972 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1346.26 | 0.602054 | ||||||||
\(172\) | 308.549 | 0.136783 | ||||||||
\(173\) | 3084.82 | 1.35569 | 0.677846 | − | 0.735204i | \(-0.262913\pi\) | ||||
0.677846 | + | 0.735204i | \(0.262913\pi\) | |||||||
\(174\) | −2154.59 | −0.938728 | ||||||||
\(175\) | −369.839 | −0.159755 | ||||||||
\(176\) | 1131.48 | 0.484596 | ||||||||
\(177\) | 1126.26 | 0.478274 | ||||||||
\(178\) | 405.443 | 0.170726 | ||||||||
\(179\) | 918.935 | 0.383712 | 0.191856 | − | 0.981423i | \(-0.438549\pi\) | ||||
0.191856 | + | 0.981423i | \(0.438549\pi\) | |||||||
\(180\) | 2184.63 | 0.904625 | ||||||||
\(181\) | −2158.66 | −0.886475 | −0.443238 | − | 0.896404i | \(-0.646170\pi\) | ||||
−0.443238 | + | 0.896404i | \(0.646170\pi\) | |||||||
\(182\) | 477.155 | 0.194335 | ||||||||
\(183\) | 5013.25 | 2.02508 | ||||||||
\(184\) | 1021.39 | 0.409229 | ||||||||
\(185\) | 5118.04 | 2.03398 | ||||||||
\(186\) | −2981.29 | −1.17526 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 990.821 | 0.384378 | ||||||||
\(189\) | 620.409 | 0.238773 | ||||||||
\(190\) | −946.404 | −0.361365 | ||||||||
\(191\) | −1349.67 | −0.511302 | −0.255651 | − | 0.966769i | \(-0.582290\pi\) | ||||
−0.255651 | + | 0.966769i | \(0.582290\pi\) | |||||||
\(192\) | −4156.79 | −1.56245 | ||||||||
\(193\) | −3509.11 | −1.30876 | −0.654382 | − | 0.756164i | \(-0.727071\pi\) | ||||
−0.654382 | + | 0.756164i | \(0.727071\pi\) | |||||||
\(194\) | −608.070 | −0.225036 | ||||||||
\(195\) | −5964.81 | −2.19051 | ||||||||
\(196\) | 1132.86 | 0.412852 | ||||||||
\(197\) | −3548.60 | −1.28339 | −0.641694 | − | 0.766961i | \(-0.721768\pi\) | ||||
−0.641694 | + | 0.766961i | \(0.721768\pi\) | |||||||
\(198\) | −4407.23 | −1.58186 | ||||||||
\(199\) | 3071.91 | 1.09428 | 0.547141 | − | 0.837041i | \(-0.315716\pi\) | ||||
0.547141 | + | 0.837041i | \(0.315716\pi\) | |||||||
\(200\) | −1983.03 | −0.701106 | ||||||||
\(201\) | 7978.49 | 2.79980 | ||||||||
\(202\) | 326.278 | 0.113648 | ||||||||
\(203\) | −551.963 | −0.190838 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −910.116 | −0.310075 | ||||||||
\(206\) | 1620.32 | 0.548023 | ||||||||
\(207\) | −1812.41 | −0.608558 | ||||||||
\(208\) | 1165.53 | 0.388533 | ||||||||
\(209\) | −1496.16 | −0.495176 | ||||||||
\(210\) | −1159.80 | −0.381113 | ||||||||
\(211\) | −6021.99 | −1.96479 | −0.982395 | − | 0.186817i | \(-0.940183\pi\) | ||||
−0.982395 | + | 0.186817i | \(0.940183\pi\) | |||||||
\(212\) | 19.7971 | 0.00641354 | ||||||||
\(213\) | −2785.32 | −0.895995 | ||||||||
\(214\) | 837.567 | 0.267546 | ||||||||
\(215\) | 1260.94 | 0.399978 | ||||||||
\(216\) | 3326.56 | 1.04789 | ||||||||
\(217\) | −763.748 | −0.238924 | ||||||||
\(218\) | −1859.25 | −0.577634 | ||||||||
\(219\) | 222.389 | 0.0686194 | ||||||||
\(220\) | −2427.88 | −0.744035 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6325.88 | 1.91246 | ||||||||
\(223\) | −3581.06 | −1.07536 | −0.537680 | − | 0.843149i | \(-0.680699\pi\) | ||||
−0.537680 | + | 0.843149i | \(0.680699\pi\) | |||||||
\(224\) | −660.670 | −0.197066 | ||||||||
\(225\) | 3518.79 | 1.04260 | ||||||||
\(226\) | 4333.22 | 1.27540 | ||||||||
\(227\) | −4244.38 | −1.24101 | −0.620506 | − | 0.784202i | \(-0.713073\pi\) | ||||
−0.620506 | + | 0.784202i | \(0.713073\pi\) | |||||||
\(228\) | 916.659 | 0.266260 | ||||||||
\(229\) | 5146.73 | 1.48518 | 0.742589 | − | 0.669748i | \(-0.233598\pi\) | ||||
0.742589 | + | 0.669748i | \(0.233598\pi\) | |||||||
\(230\) | 1274.10 | 0.365269 | ||||||||
\(231\) | −1833.52 | −0.522237 | ||||||||
\(232\) | −2959.56 | −0.837519 | ||||||||
\(233\) | −2847.35 | −0.800584 | −0.400292 | − | 0.916388i | \(-0.631091\pi\) | ||||
−0.400292 | + | 0.916388i | \(0.631091\pi\) | |||||||
\(234\) | −4539.84 | −1.26828 | ||||||||
\(235\) | 4049.16 | 1.12399 | ||||||||
\(236\) | 472.218 | 0.130249 | ||||||||
\(237\) | −277.840 | −0.0761504 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3984.47 | 1.07839 | 0.539193 | − | 0.842182i | \(-0.318729\pi\) | ||||
0.539193 | + | 0.842182i | \(0.318729\pi\) | |||||||
\(240\) | −2833.00 | −0.761957 | ||||||||
\(241\) | −1794.52 | −0.479648 | −0.239824 | − | 0.970816i | \(-0.577090\pi\) | ||||
−0.239824 | + | 0.970816i | \(0.577090\pi\) | |||||||
\(242\) | 2079.12 | 0.552278 | ||||||||
\(243\) | 3891.37 | 1.02729 | ||||||||
\(244\) | 2101.96 | 0.551493 | ||||||||
\(245\) | 4629.64 | 1.20725 | ||||||||
\(246\) | −1124.90 | −0.291549 | ||||||||
\(247\) | −1541.18 | −0.397016 | ||||||||
\(248\) | −4095.12 | −1.04855 | ||||||||
\(249\) | −2379.79 | −0.605675 | ||||||||
\(250\) | 1328.84 | 0.336173 | ||||||||
\(251\) | 4658.75 | 1.17154 | 0.585772 | − | 0.810476i | \(-0.300791\pi\) | ||||
0.585772 | + | 0.810476i | \(0.300791\pi\) | |||||||
\(252\) | 691.737 | 0.172918 | ||||||||
\(253\) | 2014.22 | 0.500526 | ||||||||
\(254\) | 4460.43 | 1.10186 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4204.00 | −1.02637 | ||||||||
\(257\) | 6235.43 | 1.51345 | 0.756723 | − | 0.653736i | \(-0.226799\pi\) | ||||
0.756723 | + | 0.653736i | \(0.226799\pi\) | |||||||
\(258\) | 1558.52 | 0.376081 | ||||||||
\(259\) | 1620.57 | 0.388792 | ||||||||
\(260\) | −2500.93 | −0.596543 | ||||||||
\(261\) | 5251.59 | 1.24546 | ||||||||
\(262\) | 2944.98 | 0.694432 | ||||||||
\(263\) | 149.037 | 0.0349430 | 0.0174715 | − | 0.999847i | \(-0.494438\pi\) | ||||
0.0174715 | + | 0.999847i | \(0.494438\pi\) | |||||||
\(264\) | −9831.10 | −2.29190 | ||||||||
\(265\) | 80.9043 | 0.0187544 | ||||||||
\(266\) | −299.668 | −0.0690745 | ||||||||
\(267\) | −1604.83 | −0.367844 | ||||||||
\(268\) | 3345.23 | 0.762472 | ||||||||
\(269\) | −3110.04 | −0.704915 | −0.352458 | − | 0.935828i | \(-0.614654\pi\) | ||||
−0.352458 | + | 0.935828i | \(0.614654\pi\) | |||||||
\(270\) | 4149.60 | 0.935322 | ||||||||
\(271\) | 4725.42 | 1.05922 | 0.529610 | − | 0.848241i | \(-0.322338\pi\) | ||||
0.529610 | + | 0.848241i | \(0.322338\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1888.69 | −0.418713 | ||||||||
\(274\) | −4891.31 | −1.07845 | ||||||||
\(275\) | −3910.60 | −0.857519 | ||||||||
\(276\) | −1234.06 | −0.269136 | ||||||||
\(277\) | 900.145 | 0.195251 | 0.0976254 | − | 0.995223i | \(-0.468875\pi\) | ||||
0.0976254 | + | 0.995223i | \(0.468875\pi\) | |||||||
\(278\) | 5246.06 | 1.13179 | ||||||||
\(279\) | 7266.60 | 1.55928 | ||||||||
\(280\) | −1593.11 | −0.340024 | ||||||||
\(281\) | 9165.72 | 1.94584 | 0.972920 | − | 0.231143i | \(-0.0742465\pi\) | ||||
0.972920 | + | 0.231143i | \(0.0742465\pi\) | |||||||
\(282\) | 5004.75 | 1.05684 | ||||||||
\(283\) | 3541.31 | 0.743847 | 0.371924 | − | 0.928263i | \(-0.378698\pi\) | ||||
0.371924 | + | 0.928263i | \(0.378698\pi\) | |||||||
\(284\) | −1167.83 | −0.244007 | ||||||||
\(285\) | 3746.08 | 0.778592 | ||||||||
\(286\) | 5045.33 | 1.04314 | ||||||||
\(287\) | −288.178 | −0.0592704 | ||||||||
\(288\) | 6285.87 | 1.28611 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −3691.80 | −0.747552 | ||||||||
\(291\) | 2406.88 | 0.484859 | ||||||||
\(292\) | 93.2435 | 0.0186872 | ||||||||
\(293\) | −1268.29 | −0.252882 | −0.126441 | − | 0.991974i | \(-0.540355\pi\) | ||||
−0.126441 | + | 0.991974i | \(0.540355\pi\) | |||||||
\(294\) | 5722.22 | 1.13513 | ||||||||
\(295\) | 1929.80 | 0.380872 | ||||||||
\(296\) | 8689.28 | 1.70626 | ||||||||
\(297\) | 6560.08 | 1.28166 | ||||||||
\(298\) | −3222.50 | −0.626424 | ||||||||
\(299\) | 2074.83 | 0.401305 | ||||||||
\(300\) | 2395.92 | 0.461095 | ||||||||
\(301\) | 399.262 | 0.0764554 | ||||||||
\(302\) | −842.708 | −0.160571 | ||||||||
\(303\) | −1291.48 | −0.244864 | ||||||||
\(304\) | −731.988 | −0.138100 | ||||||||
\(305\) | 8590.02 | 1.61267 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9924.22 | 1.84497 | 0.922484 | − | 0.386034i | \(-0.126155\pi\) | ||||
0.922484 | + | 0.386034i | \(0.126155\pi\) | |||||||
\(308\) | −768.760 | −0.142221 | ||||||||
\(309\) | −6413.58 | −1.18076 | ||||||||
\(310\) | −5108.32 | −0.935914 | ||||||||
\(311\) | −1458.67 | −0.265959 | −0.132980 | − | 0.991119i | \(-0.542454\pi\) | ||||
−0.132980 | + | 0.991119i | \(0.542454\pi\) | |||||||
\(312\) | −10126.9 | −1.83757 | ||||||||
\(313\) | −797.861 | −0.144082 | −0.0720412 | − | 0.997402i | \(-0.522951\pi\) | ||||
−0.0720412 | + | 0.997402i | \(0.522951\pi\) | |||||||
\(314\) | 2262.26 | 0.406582 | ||||||||
\(315\) | 2826.90 | 0.505644 | ||||||||
\(316\) | −116.493 | −0.0207381 | ||||||||
\(317\) | −3852.53 | −0.682586 | −0.341293 | − | 0.939957i | \(-0.610865\pi\) | ||||
−0.341293 | + | 0.939957i | \(0.610865\pi\) | |||||||
\(318\) | 99.9974 | 0.0176339 | ||||||||
\(319\) | −5836.34 | −1.02436 | ||||||||
\(320\) | −7122.50 | −1.24425 | ||||||||
\(321\) | −3315.28 | −0.576451 | ||||||||
\(322\) | 403.430 | 0.0698208 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 87.3338 | 0.0149749 | ||||||||
\(325\) | −4028.26 | −0.687531 | ||||||||
\(326\) | 1790.46 | 0.304186 | ||||||||
\(327\) | 7359.32 | 1.24456 | ||||||||
\(328\) | −1545.17 | −0.260115 | ||||||||
\(329\) | 1282.12 | 0.214850 | ||||||||
\(330\) | −12263.5 | −2.04570 | ||||||||
\(331\) | −8470.40 | −1.40657 | −0.703286 | − | 0.710907i | \(-0.748285\pi\) | ||||
−0.703286 | + | 0.710907i | \(0.748285\pi\) | |||||||
\(332\) | −997.800 | −0.164944 | ||||||||
\(333\) | −15418.7 | −2.53736 | ||||||||
\(334\) | −5535.05 | −0.906780 | ||||||||
\(335\) | 13670.8 | 2.22961 | ||||||||
\(336\) | −897.038 | −0.145647 | ||||||||
\(337\) | −1922.89 | −0.310821 | −0.155411 | − | 0.987850i | \(-0.549670\pi\) | ||||
−0.155411 | + | 0.987850i | \(0.549670\pi\) | |||||||
\(338\) | 544.256 | 0.0875848 | ||||||||
\(339\) | −17151.9 | −2.74797 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8075.71 | −1.28248 | ||||||||
\(342\) | 2851.16 | 0.450798 | ||||||||
\(343\) | 3025.92 | 0.476340 | ||||||||
\(344\) | 2140.79 | 0.335534 | ||||||||
\(345\) | −5043.19 | −0.787004 | ||||||||
\(346\) | 6533.15 | 1.01510 | ||||||||
\(347\) | −2564.08 | −0.396677 | −0.198339 | − | 0.980134i | \(-0.563555\pi\) | ||||
−0.198339 | + | 0.980134i | \(0.563555\pi\) | |||||||
\(348\) | 3575.77 | 0.550809 | ||||||||
\(349\) | −283.156 | −0.0434298 | −0.0217149 | − | 0.999764i | \(-0.506913\pi\) | ||||
−0.0217149 | + | 0.999764i | \(0.506913\pi\) | |||||||
\(350\) | −783.257 | −0.119620 | ||||||||
\(351\) | 6757.46 | 1.02760 | ||||||||
\(352\) | −6985.79 | −1.05779 | ||||||||
\(353\) | −10695.1 | −1.61259 | −0.806295 | − | 0.591514i | \(-0.798530\pi\) | ||||
−0.806295 | + | 0.591514i | \(0.798530\pi\) | |||||||
\(354\) | 2385.22 | 0.358116 | ||||||||
\(355\) | −4772.54 | −0.713521 | ||||||||
\(356\) | −672.877 | −0.100175 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1946.15 | 0.287311 | ||||||||
\(359\) | 8702.38 | 1.27937 | 0.639685 | − | 0.768637i | \(-0.279065\pi\) | ||||
0.639685 | + | 0.768637i | \(0.279065\pi\) | |||||||
\(360\) | 15157.5 | 2.21908 | ||||||||
\(361\) | −5891.09 | −0.858885 | ||||||||
\(362\) | −4571.69 | −0.663764 | ||||||||
\(363\) | −8229.65 | −1.18993 | ||||||||
\(364\) | −791.890 | −0.114028 | ||||||||
\(365\) | 381.055 | 0.0546448 | ||||||||
\(366\) | 10617.2 | 1.51632 | ||||||||
\(367\) | 11921.7 | 1.69566 | 0.847831 | − | 0.530266i | \(-0.177908\pi\) | ||||
0.847831 | + | 0.530266i | \(0.177908\pi\) | |||||||
\(368\) | 985.445 | 0.139592 | ||||||||
\(369\) | 2741.84 | 0.386814 | ||||||||
\(370\) | 10839.2 | 1.52298 | ||||||||
\(371\) | 25.6174 | 0.00358488 | ||||||||
\(372\) | 4947.77 | 0.689597 | ||||||||
\(373\) | −11054.6 | −1.53454 | −0.767270 | − | 0.641324i | \(-0.778385\pi\) | ||||
−0.767270 | + | 0.641324i | \(0.778385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5259.85 | −0.724313 | ||||||||
\(376\) | 6874.56 | 0.942894 | ||||||||
\(377\) | −6011.95 | −0.821302 | ||||||||
\(378\) | 1313.92 | 0.178786 | ||||||||
\(379\) | −11548.5 | −1.56519 | −0.782596 | − | 0.622529i | \(-0.786105\pi\) | ||||
−0.782596 | + | 0.622529i | \(0.786105\pi\) | |||||||
\(380\) | 1570.66 | 0.212035 | ||||||||
\(381\) | −17655.4 | −2.37405 | ||||||||
\(382\) | −2858.38 | −0.382847 | ||||||||
\(383\) | 10238.7 | 1.36599 | 0.682995 | − | 0.730423i | \(-0.260677\pi\) | ||||
0.682995 | + | 0.730423i | \(0.260677\pi\) | |||||||
\(384\) | 938.349 | 0.124700 | ||||||||
\(385\) | −3141.67 | −0.415881 | ||||||||
\(386\) | −7431.72 | −0.979960 | ||||||||
\(387\) | −3798.73 | −0.498968 | ||||||||
\(388\) | 1009.16 | 0.132042 | ||||||||
\(389\) | 4378.48 | 0.570688 | 0.285344 | − | 0.958425i | \(-0.407892\pi\) | ||||
0.285344 | + | 0.958425i | \(0.407892\pi\) | |||||||
\(390\) | −12632.5 | −1.64018 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 7860.09 | 1.01274 | ||||||||
\(393\) | −11656.9 | −1.49621 | ||||||||
\(394\) | −7515.35 | −0.960959 | ||||||||
\(395\) | −476.068 | −0.0606420 | ||||||||
\(396\) | 7314.28 | 0.928173 | ||||||||
\(397\) | −10055.9 | −1.27126 | −0.635629 | − | 0.771995i | \(-0.719259\pi\) | ||||
−0.635629 | + | 0.771995i | \(0.719259\pi\) | |||||||
\(398\) | 6505.80 | 0.819363 | ||||||||
\(399\) | 1186.15 | 0.148827 | ||||||||
\(400\) | −1913.23 | −0.239154 | ||||||||
\(401\) | 8216.40 | 1.02321 | 0.511605 | − | 0.859221i | \(-0.329051\pi\) | ||||
0.511605 | + | 0.859221i | \(0.329051\pi\) | |||||||
\(402\) | 16897.1 | 2.09640 | ||||||||
\(403\) | −8318.69 | −1.02825 | ||||||||
\(404\) | −541.495 | −0.0666841 | ||||||||
\(405\) | 356.904 | 0.0437894 | ||||||||
\(406\) | −1168.97 | −0.142894 | ||||||||
\(407\) | 17135.6 | 2.08692 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5402.57 | −0.653154 | −0.326577 | − | 0.945171i | \(-0.605895\pi\) | ||||
−0.326577 | + | 0.945171i | \(0.605895\pi\) | |||||||
\(410\) | −1927.48 | −0.232174 | ||||||||
\(411\) | 19360.9 | 2.32361 | ||||||||
\(412\) | −2689.09 | −0.321558 | ||||||||
\(413\) | 611.048 | 0.0728031 | ||||||||
\(414\) | −3838.39 | −0.455668 | ||||||||
\(415\) | −4077.68 | −0.482326 | ||||||||
\(416\) | −7195.98 | −0.848105 | ||||||||
\(417\) | −20765.1 | −2.43854 | ||||||||
\(418\) | −3168.63 | −0.370772 | ||||||||
\(419\) | −6305.19 | −0.735152 | −0.367576 | − | 0.929993i | \(-0.619812\pi\) | ||||
−0.367576 | + | 0.929993i | \(0.619812\pi\) | |||||||
\(420\) | 1924.82 | 0.223622 | ||||||||
\(421\) | 6492.45 | 0.751598 | 0.375799 | − | 0.926701i | \(-0.377368\pi\) | ||||
0.375799 | + | 0.926701i | \(0.377368\pi\) | |||||||
\(422\) | −12753.6 | −1.47117 | ||||||||
\(423\) | −12198.6 | −1.40216 | ||||||||
\(424\) | 137.357 | 0.0157327 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5898.84 | −0.670892 | ||||||||
\(427\) | 2719.93 | 0.308259 | ||||||||
\(428\) | −1390.03 | −0.156986 | ||||||||
\(429\) | −19970.6 | −2.24753 | ||||||||
\(430\) | 2670.46 | 0.299491 | ||||||||
\(431\) | 13477.5 | 1.50624 | 0.753118 | − | 0.657886i | \(-0.228549\pi\) | ||||
0.753118 | + | 0.657886i | \(0.228549\pi\) | |||||||
\(432\) | 3209.48 | 0.357445 | ||||||||
\(433\) | −13237.8 | −1.46921 | −0.734605 | − | 0.678495i | \(-0.762633\pi\) | ||||
−0.734605 | + | 0.678495i | \(0.762633\pi\) | |||||||
\(434\) | −1617.49 | −0.178899 | ||||||||
\(435\) | 14613.0 | 1.61067 | ||||||||
\(436\) | 3085.63 | 0.338933 | ||||||||
\(437\) | −1303.05 | −0.142640 | ||||||||
\(438\) | 470.983 | 0.0513800 | ||||||||
\(439\) | −10249.1 | −1.11426 | −0.557130 | − | 0.830425i | \(-0.688098\pi\) | ||||
−0.557130 | + | 0.830425i | \(0.688098\pi\) | |||||||
\(440\) | −16845.2 | −1.82515 | ||||||||
\(441\) | −13947.4 | −1.50603 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8163.30 | −0.875508 | −0.437754 | − | 0.899095i | \(-0.644226\pi\) | ||||
−0.437754 | + | 0.899095i | \(0.644226\pi\) | |||||||
\(444\) | −10498.5 | −1.12215 | ||||||||
\(445\) | −2749.82 | −0.292931 | ||||||||
\(446\) | −7584.09 | −0.805195 | ||||||||
\(447\) | 12755.4 | 1.34969 | ||||||||
\(448\) | −2255.26 | −0.237837 | ||||||||
\(449\) | 4382.67 | 0.460648 | 0.230324 | − | 0.973114i | \(-0.426021\pi\) | ||||
0.230324 | + | 0.973114i | \(0.426021\pi\) | |||||||
\(450\) | 7452.21 | 0.780668 | ||||||||
\(451\) | −3047.13 | −0.318146 | ||||||||
\(452\) | −7191.45 | −0.748357 | ||||||||
\(453\) | 3335.63 | 0.345964 | ||||||||
\(454\) | −8988.90 | −0.929229 | ||||||||
\(455\) | −3236.19 | −0.333440 | ||||||||
\(456\) | 6360.01 | 0.653146 | ||||||||
\(457\) | −10463.4 | −1.07102 | −0.535509 | − | 0.844530i | \(-0.679880\pi\) | ||||
−0.535509 | + | 0.844530i | \(0.679880\pi\) | |||||||
\(458\) | 10899.9 | 1.11205 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2114.52 | −0.214326 | ||||||||
\(461\) | −7540.64 | −0.761828 | −0.380914 | − | 0.924610i | \(-0.624391\pi\) | ||||
−0.380914 | + | 0.924610i | \(0.624391\pi\) | |||||||
\(462\) | −3883.09 | −0.391034 | ||||||||
\(463\) | 12962.0 | 1.30107 | 0.650536 | − | 0.759475i | \(-0.274544\pi\) | ||||
0.650536 | + | 0.759475i | \(0.274544\pi\) | |||||||
\(464\) | −2855.39 | −0.285686 | ||||||||
\(465\) | 20219.9 | 2.01651 | ||||||||
\(466\) | −6030.21 | −0.599451 | ||||||||
\(467\) | 12536.8 | 1.24226 | 0.621130 | − | 0.783707i | \(-0.286674\pi\) | ||||
0.621130 | + | 0.783707i | \(0.286674\pi\) | |||||||
\(468\) | 7534.36 | 0.744179 | ||||||||
\(469\) | 4328.71 | 0.426186 | ||||||||
\(470\) | 8575.45 | 0.841608 | ||||||||
\(471\) | −8954.53 | −0.876015 | ||||||||
\(472\) | 3276.36 | 0.319506 | ||||||||
\(473\) | 4221.71 | 0.410390 | ||||||||
\(474\) | −588.419 | −0.0570189 | ||||||||
\(475\) | 2529.87 | 0.244376 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −243.734 | −0.0233958 | ||||||||
\(478\) | 8438.46 | 0.807460 | ||||||||
\(479\) | 1048.55 | 0.100020 | 0.0500099 | − | 0.998749i | \(-0.484075\pi\) | ||||
0.0500099 | + | 0.998749i | \(0.484075\pi\) | |||||||
\(480\) | 17491.0 | 1.66323 | ||||||||
\(481\) | 17651.1 | 1.67323 | ||||||||
\(482\) | −3800.50 | −0.359145 | ||||||||
\(483\) | −1596.87 | −0.150435 | ||||||||
\(484\) | −3450.54 | −0.324055 | ||||||||
\(485\) | 4124.10 | 0.386115 | ||||||||
\(486\) | 8241.28 | 0.769202 | ||||||||
\(487\) | 903.684 | 0.0840859 | 0.0420429 | − | 0.999116i | \(-0.486613\pi\) | ||||
0.0420429 | + | 0.999116i | \(0.486613\pi\) | |||||||
\(488\) | 14583.9 | 1.35283 | ||||||||
\(489\) | −7087.06 | −0.655394 | ||||||||
\(490\) | 9804.82 | 0.903952 | ||||||||
\(491\) | 14922.5 | 1.37158 | 0.685789 | − | 0.727800i | \(-0.259457\pi\) | ||||
0.685789 | + | 0.727800i | \(0.259457\pi\) | |||||||
\(492\) | 1866.90 | 0.171069 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −3263.96 | −0.297273 | ||||||||
\(495\) | 29891.1 | 2.71415 | ||||||||
\(496\) | −3950.99 | −0.357671 | ||||||||
\(497\) | −1511.17 | −0.136389 | ||||||||
\(498\) | −5040.00 | −0.453509 | ||||||||
\(499\) | −2628.41 | −0.235799 | −0.117900 | − | 0.993026i | \(-0.537616\pi\) | ||||
−0.117900 | + | 0.993026i | \(0.537616\pi\) | |||||||
\(500\) | −2205.35 | −0.197253 | ||||||||
\(501\) | 21909.0 | 1.95373 | ||||||||
\(502\) | 9866.45 | 0.877214 | ||||||||
\(503\) | −6500.03 | −0.576187 | −0.288093 | − | 0.957602i | \(-0.593021\pi\) | ||||
−0.288093 | + | 0.957602i | \(0.593021\pi\) | |||||||
\(504\) | 4799.44 | 0.424175 | ||||||||
\(505\) | −2212.91 | −0.194996 | ||||||||
\(506\) | 4265.79 | 0.374777 | ||||||||
\(507\) | −2154.29 | −0.188709 | ||||||||
\(508\) | −7402.58 | −0.646528 | ||||||||
\(509\) | −1931.57 | −0.168203 | −0.0841013 | − | 0.996457i | \(-0.526802\pi\) | ||||
−0.0841013 | + | 0.996457i | \(0.526802\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 120.657 | 0.0104453 | ||||||||
\(512\) | −8007.88 | −0.691214 | ||||||||
\(513\) | −4243.89 | −0.365249 | ||||||||
\(514\) | 13205.6 | 1.13322 | ||||||||
\(515\) | −10989.4 | −0.940296 | ||||||||
\(516\) | −2586.53 | −0.220670 | ||||||||
\(517\) | 13556.9 | 1.15325 | ||||||||
\(518\) | 3432.10 | 0.291115 | ||||||||
\(519\) | −25859.7 | −2.18712 | ||||||||
\(520\) | −17352.1 | −1.46334 | ||||||||
\(521\) | 5287.08 | 0.444589 | 0.222295 | − | 0.974980i | \(-0.428645\pi\) | ||||
0.222295 | + | 0.974980i | \(0.428645\pi\) | |||||||
\(522\) | 11122.0 | 0.932561 | ||||||||
\(523\) | −8406.61 | −0.702859 | −0.351430 | − | 0.936214i | \(-0.614304\pi\) | ||||
−0.351430 | + | 0.936214i | \(0.614304\pi\) | |||||||
\(524\) | −4887.51 | −0.407466 | ||||||||
\(525\) | 3100.31 | 0.257731 | ||||||||
\(526\) | 315.635 | 0.0261642 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −9485.09 | −0.781791 | ||||||||
\(529\) | −10412.8 | −0.855819 | ||||||||
\(530\) | 171.342 | 0.0140427 | ||||||||
\(531\) | −5813.75 | −0.475132 | ||||||||
\(532\) | 497.332 | 0.0405302 | ||||||||
\(533\) | −3138.81 | −0.255079 | ||||||||
\(534\) | −3398.77 | −0.275429 | ||||||||
\(535\) | −5680.61 | −0.459054 | ||||||||
\(536\) | 23210.0 | 1.87037 | ||||||||
\(537\) | −7703.31 | −0.619036 | ||||||||
\(538\) | −6586.54 | −0.527818 | ||||||||
\(539\) | 15500.4 | 1.23868 | ||||||||
\(540\) | −6886.72 | −0.548810 | ||||||||
\(541\) | −11319.4 | −0.899553 | −0.449776 | − | 0.893141i | \(-0.648496\pi\) | ||||
−0.449776 | + | 0.893141i | \(0.648496\pi\) | |||||||
\(542\) | 10007.6 | 0.793110 | ||||||||
\(543\) | 18095.8 | 1.43014 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12609.9 | 0.991101 | ||||||||
\(546\) | −3999.93 | −0.313518 | ||||||||
\(547\) | 1201.61 | 0.0939251 | 0.0469626 | − | 0.998897i | \(-0.485046\pi\) | ||||
0.0469626 | + | 0.998897i | \(0.485046\pi\) | |||||||
\(548\) | 8117.66 | 0.632791 | ||||||||
\(549\) | −25878.5 | −2.01178 | ||||||||
\(550\) | −8281.99 | −0.642082 | ||||||||
\(551\) | 3775.69 | 0.291923 | ||||||||
\(552\) | −8562.21 | −0.660202 | ||||||||
\(553\) | −150.742 | −0.0115916 | ||||||||
\(554\) | 1906.36 | 0.146197 | ||||||||
\(555\) | −42903.9 | −3.28138 | ||||||||
\(556\) | −8706.41 | −0.664090 | ||||||||
\(557\) | 5277.38 | 0.401454 | 0.200727 | − | 0.979647i | \(-0.435670\pi\) | ||||
0.200727 | + | 0.979647i | \(0.435670\pi\) | |||||||
\(558\) | 15389.4 | 1.16754 | ||||||||
\(559\) | 4348.73 | 0.329037 | ||||||||
\(560\) | −1537.04 | −0.115985 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19411.5 | 1.45698 | ||||||||
\(563\) | 2341.00 | 0.175243 | 0.0876213 | − | 0.996154i | \(-0.472073\pi\) | ||||
0.0876213 | + | 0.996154i | \(0.472073\pi\) | |||||||
\(564\) | −8305.92 | −0.620111 | ||||||||
\(565\) | −29389.1 | −2.18833 | ||||||||
\(566\) | 7499.90 | 0.556969 | ||||||||
\(567\) | 113.010 | 0.00837030 | ||||||||
\(568\) | −8102.70 | −0.598559 | ||||||||
\(569\) | −3732.25 | −0.274981 | −0.137490 | − | 0.990503i | \(-0.543904\pi\) | ||||
−0.137490 | + | 0.990503i | \(0.543904\pi\) | |||||||
\(570\) | 7933.58 | 0.582985 | ||||||||
\(571\) | 4505.21 | 0.330187 | 0.165094 | − | 0.986278i | \(-0.447207\pi\) | ||||
0.165094 | + | 0.986278i | \(0.447207\pi\) | |||||||
\(572\) | −8373.28 | −0.612071 | ||||||||
\(573\) | 11314.1 | 0.824876 | ||||||||
\(574\) | −610.313 | −0.0443797 | ||||||||
\(575\) | −3405.86 | −0.247016 | ||||||||
\(576\) | 21457.4 | 1.55218 | ||||||||
\(577\) | −15292.7 | −1.10337 | −0.551685 | − | 0.834053i | \(-0.686015\pi\) | ||||
−0.551685 | + | 0.834053i | \(0.686015\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29416.4 | 2.11141 | ||||||||
\(580\) | 6126.95 | 0.438634 | ||||||||
\(581\) | −1291.15 | −0.0921961 | ||||||||
\(582\) | 5097.37 | 0.363046 | ||||||||
\(583\) | 270.873 | 0.0192426 | ||||||||
\(584\) | 646.946 | 0.0458405 | ||||||||
\(585\) | 30790.4 | 2.17612 | ||||||||
\(586\) | −2686.03 | −0.189350 | ||||||||
\(587\) | −11208.5 | −0.788116 | −0.394058 | − | 0.919086i | \(-0.628929\pi\) | ||||
−0.394058 | + | 0.919086i | \(0.628929\pi\) | |||||||
\(588\) | −9496.66 | −0.666047 | ||||||||
\(589\) | 5224.40 | 0.365480 | ||||||||
\(590\) | 4086.99 | 0.285184 | ||||||||
\(591\) | 29747.5 | 2.07047 | ||||||||
\(592\) | 8383.46 | 0.582024 | ||||||||
\(593\) | 10220.6 | 0.707774 | 0.353887 | − | 0.935288i | \(-0.384860\pi\) | ||||
0.353887 | + | 0.935288i | \(0.384860\pi\) | |||||||
\(594\) | 13893.2 | 0.959669 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5348.09 | 0.367561 | ||||||||
\(597\) | −25751.4 | −1.76539 | ||||||||
\(598\) | 4394.14 | 0.300484 | ||||||||
\(599\) | −9068.76 | −0.618597 | −0.309298 | − | 0.950965i | \(-0.600094\pi\) | ||||
−0.309298 | + | 0.950965i | \(0.600094\pi\) | |||||||
\(600\) | 16623.5 | 1.13108 | ||||||||
\(601\) | 14293.5 | 0.970122 | 0.485061 | − | 0.874480i | \(-0.338797\pi\) | ||||
0.485061 | + | 0.874480i | \(0.338797\pi\) | |||||||
\(602\) | 845.570 | 0.0572473 | ||||||||
\(603\) | −41185.1 | −2.78140 | ||||||||
\(604\) | 1398.57 | 0.0942167 | ||||||||
\(605\) | −14101.2 | −0.947595 | ||||||||
\(606\) | −2735.15 | −0.183346 | ||||||||
\(607\) | −13055.6 | −0.873000 | −0.436500 | − | 0.899704i | \(-0.643782\pi\) | ||||
−0.436500 | + | 0.899704i | \(0.643782\pi\) | |||||||
\(608\) | 4519.30 | 0.301450 | ||||||||
\(609\) | 4627.03 | 0.307877 | ||||||||
\(610\) | 18192.2 | 1.20751 | ||||||||
\(611\) | 13964.8 | 0.924638 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15590.7 | −1.02725 | −0.513623 | − | 0.858016i | \(-0.671697\pi\) | ||||
−0.513623 | + | 0.858016i | \(0.671697\pi\) | |||||||
\(614\) | 21017.9 | 1.38145 | ||||||||
\(615\) | 7629.39 | 0.500238 | ||||||||
\(616\) | −5333.84 | −0.348874 | ||||||||
\(617\) | −25884.6 | −1.68894 | −0.844469 | − | 0.535605i | \(-0.820084\pi\) | ||||
−0.844469 | + | 0.535605i | \(0.820084\pi\) | |||||||
\(618\) | −13582.9 | −0.884117 | ||||||||
\(619\) | 448.382 | 0.0291147 | 0.0145574 | − | 0.999894i | \(-0.495366\pi\) | ||||
0.0145574 | + | 0.999894i | \(0.495366\pi\) | |||||||
\(620\) | 8477.82 | 0.549157 | ||||||||
\(621\) | 5713.38 | 0.369195 | ||||||||
\(622\) | −3089.21 | −0.199142 | ||||||||
\(623\) | −870.700 | −0.0559933 | ||||||||
\(624\) | −9770.48 | −0.626814 | ||||||||
\(625\) | −19177.2 | −1.22734 | ||||||||
\(626\) | −1689.74 | −0.107884 | ||||||||
\(627\) | 12542.1 | 0.798859 | ||||||||
\(628\) | −3754.47 | −0.238566 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 5986.91 | 0.378610 | ||||||||
\(631\) | −6811.18 | −0.429713 | −0.214856 | − | 0.976646i | \(-0.568928\pi\) | ||||
−0.214856 | + | 0.976646i | \(0.568928\pi\) | |||||||
\(632\) | −808.257 | −0.0508714 | ||||||||
\(633\) | 50481.5 | 3.16976 | ||||||||
\(634\) | −8159.03 | −0.511098 | ||||||||
\(635\) | −30251.9 | −1.89057 | ||||||||
\(636\) | −165.957 | −0.0103469 | ||||||||
\(637\) | 15966.7 | 0.993132 | ||||||||
\(638\) | −12360.4 | −0.767011 | ||||||||
\(639\) | 14377.9 | 0.890108 | ||||||||
\(640\) | 1607.83 | 0.0993045 | ||||||||
\(641\) | 14093.7 | 0.868434 | 0.434217 | − | 0.900808i | \(-0.357025\pi\) | ||||
0.434217 | + | 0.900808i | \(0.357025\pi\) | |||||||
\(642\) | −7021.21 | −0.431628 | ||||||||
\(643\) | 8650.68 | 0.530559 | 0.265280 | − | 0.964172i | \(-0.414536\pi\) | ||||
0.265280 | + | 0.964172i | \(0.414536\pi\) | |||||||
\(644\) | −669.537 | −0.0409681 | ||||||||
\(645\) | −10570.3 | −0.645279 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10310.7 | −0.626515 | −0.313258 | − | 0.949668i | \(-0.601420\pi\) | ||||
−0.313258 | + | 0.949668i | \(0.601420\pi\) | |||||||
\(648\) | 605.943 | 0.0367341 | ||||||||
\(649\) | 6461.09 | 0.390786 | ||||||||
\(650\) | −8531.18 | −0.514801 | ||||||||
\(651\) | 6402.40 | 0.385453 | ||||||||
\(652\) | −2971.47 | −0.178484 | ||||||||
\(653\) | 8590.34 | 0.514803 | 0.257401 | − | 0.966305i | \(-0.417134\pi\) | ||||
0.257401 | + | 0.966305i | \(0.417134\pi\) | |||||||
\(654\) | 15585.8 | 0.931887 | ||||||||
\(655\) | −19973.6 | −1.19150 | ||||||||
\(656\) | −1490.79 | −0.0887280 | ||||||||
\(657\) | −1147.98 | −0.0681686 | ||||||||
\(658\) | 2715.32 | 0.160872 | ||||||||
\(659\) | 4635.27 | 0.273998 | 0.136999 | − | 0.990571i | \(-0.456254\pi\) | ||||
0.136999 | + | 0.990571i | \(0.456254\pi\) | |||||||
\(660\) | 20352.6 | 1.20034 | ||||||||
\(661\) | 27861.5 | 1.63946 | 0.819732 | − | 0.572747i | \(-0.194122\pi\) | ||||
0.819732 | + | 0.572747i | \(0.194122\pi\) | |||||||
\(662\) | −17938.9 | −1.05320 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6922.98 | −0.404614 | ||||||||
\(665\) | 2032.43 | 0.118518 | ||||||||
\(666\) | −32654.3 | −1.89989 | ||||||||
\(667\) | −5083.05 | −0.295077 | ||||||||
\(668\) | 9186.02 | 0.532063 | ||||||||
\(669\) | 30019.6 | 1.73486 | ||||||||
\(670\) | 28952.6 | 1.66946 | ||||||||
\(671\) | 28760.0 | 1.65464 | ||||||||
\(672\) | 5538.31 | 0.317924 | ||||||||
\(673\) | 8480.12 | 0.485713 | 0.242856 | − | 0.970062i | \(-0.421916\pi\) | ||||
0.242856 | + | 0.970062i | \(0.421916\pi\) | |||||||
\(674\) | −4072.37 | −0.232733 | ||||||||
\(675\) | −11092.5 | −0.632518 | ||||||||
\(676\) | −903.253 | −0.0513913 | ||||||||
\(677\) | 11284.7 | 0.640627 | 0.320314 | − | 0.947312i | \(-0.396212\pi\) | ||||
0.320314 | + | 0.947312i | \(0.396212\pi\) | |||||||
\(678\) | −36324.8 | −2.05759 | ||||||||
\(679\) | 1305.85 | 0.0738054 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 35580.1 | 2.00210 | ||||||||
\(682\) | −17103.0 | −0.960276 | ||||||||
\(683\) | 2315.69 | 0.129733 | 0.0648665 | − | 0.997894i | \(-0.479338\pi\) | ||||
0.0648665 | + | 0.997894i | \(0.479338\pi\) | |||||||
\(684\) | −4731.81 | −0.264511 | ||||||||
\(685\) | 33174.2 | 1.85040 | ||||||||
\(686\) | 6408.41 | 0.356668 | ||||||||
\(687\) | −43144.4 | −2.39601 | ||||||||
\(688\) | 2065.45 | 0.114454 | ||||||||
\(689\) | 279.023 | 0.0154281 | ||||||||
\(690\) | −10680.6 | −0.589283 | ||||||||
\(691\) | 8175.26 | 0.450074 | 0.225037 | − | 0.974350i | \(-0.427750\pi\) | ||||
0.225037 | + | 0.974350i | \(0.427750\pi\) | |||||||
\(692\) | −10842.5 | −0.595620 | ||||||||
\(693\) | 9464.66 | 0.518806 | ||||||||
\(694\) | −5430.30 | −0.297019 | ||||||||
\(695\) | −35580.2 | −1.94192 | ||||||||
\(696\) | 24809.6 | 1.35116 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −599.677 | −0.0325188 | ||||||||
\(699\) | 23868.9 | 1.29157 | ||||||||
\(700\) | 1299.90 | 0.0701880 | ||||||||
\(701\) | 22583.3 | 1.21677 | 0.608387 | − | 0.793640i | \(-0.291817\pi\) | ||||
0.608387 | + | 0.793640i | \(0.291817\pi\) | |||||||
\(702\) | 14311.2 | 0.769431 | ||||||||
\(703\) | −11085.5 | −0.594731 | ||||||||
\(704\) | −23846.6 | −1.27664 | ||||||||
\(705\) | −33943.6 | −1.81332 | ||||||||
\(706\) | −22650.5 | −1.20745 | ||||||||
\(707\) | −700.692 | −0.0372733 | ||||||||
\(708\) | −3958.54 | −0.210129 | ||||||||
\(709\) | 23125.7 | 1.22497 | 0.612484 | − | 0.790483i | \(-0.290170\pi\) | ||||
0.612484 | + | 0.790483i | \(0.290170\pi\) | |||||||
\(710\) | −10107.4 | −0.534262 | ||||||||
\(711\) | 1434.21 | 0.0756501 | ||||||||
\(712\) | −4668.58 | −0.245734 | ||||||||
\(713\) | −7033.38 | −0.369428 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34218.8 | −1.78981 | ||||||||
\(716\) | −3229.85 | −0.168583 | ||||||||
\(717\) | −33401.3 | −1.73974 | ||||||||
\(718\) | 18430.2 | 0.957951 | ||||||||
\(719\) | 34843.0 | 1.80727 | 0.903634 | − | 0.428305i | \(-0.140889\pi\) | ||||
0.903634 | + | 0.428305i | \(0.140889\pi\) | |||||||
\(720\) | 14624.0 | 0.756951 | ||||||||
\(721\) | −3479.68 | −0.179736 | ||||||||
\(722\) | −12476.4 | −0.643105 | ||||||||
\(723\) | 15043.2 | 0.773809 | ||||||||
\(724\) | 7587.22 | 0.389471 | ||||||||
\(725\) | 9868.70 | 0.505537 | ||||||||
\(726\) | −17429.0 | −0.890981 | ||||||||
\(727\) | −11782.3 | −0.601077 | −0.300538 | − | 0.953770i | \(-0.597166\pi\) | ||||
−0.300538 | + | 0.953770i | \(0.597166\pi\) | |||||||
\(728\) | −5494.33 | −0.279716 | ||||||||
\(729\) | −31950.0 | −1.62323 | ||||||||
\(730\) | 807.012 | 0.0409162 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −17620.5 | −0.889715 | ||||||||
\(733\) | −20099.0 | −1.01279 | −0.506394 | − | 0.862302i | \(-0.669022\pi\) | ||||
−0.506394 | + | 0.862302i | \(0.669022\pi\) | |||||||
\(734\) | 25248.2 | 1.26966 | ||||||||
\(735\) | −38809.7 | −1.94764 | ||||||||
\(736\) | −6084.14 | −0.304707 | ||||||||
\(737\) | 45770.9 | 2.28764 | ||||||||
\(738\) | 5806.75 | 0.289634 | ||||||||
\(739\) | 12538.4 | 0.624132 | 0.312066 | − | 0.950060i | \(-0.398979\pi\) | ||||
0.312066 | + | 0.950060i | \(0.398979\pi\) | |||||||
\(740\) | −17988.8 | −0.893623 | ||||||||
\(741\) | 12919.5 | 0.640500 | ||||||||
\(742\) | 54.2534 | 0.00268424 | ||||||||
\(743\) | −3294.68 | −0.162679 | −0.0813393 | − | 0.996686i | \(-0.525920\pi\) | ||||
−0.0813393 | + | 0.996686i | \(0.525920\pi\) | |||||||
\(744\) | 34328.8 | 1.69161 | ||||||||
\(745\) | 21855.9 | 1.07482 | ||||||||
\(746\) | −23411.7 | −1.14901 | ||||||||
\(747\) | 12284.5 | 0.601696 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1798.70 | −0.0877477 | ||||||||
\(750\) | −11139.5 | −0.542342 | ||||||||
\(751\) | −7252.15 | −0.352376 | −0.176188 | − | 0.984357i | \(-0.556377\pi\) | ||||
−0.176188 | + | 0.984357i | \(0.556377\pi\) | |||||||
\(752\) | 6632.61 | 0.321631 | ||||||||
\(753\) | −39053.7 | −1.89003 | ||||||||
\(754\) | −12732.3 | −0.614965 | ||||||||
\(755\) | 5715.48 | 0.275507 | ||||||||
\(756\) | −2180.60 | −0.104904 | ||||||||
\(757\) | 26725.2 | 1.28315 | 0.641574 | − | 0.767061i | \(-0.278282\pi\) | ||||
0.641574 | + | 0.767061i | \(0.278282\pi\) | |||||||
\(758\) | −24457.9 | −1.17197 | ||||||||
\(759\) | −16885.0 | −0.807490 | ||||||||
\(760\) | 10897.6 | 0.520130 | ||||||||
\(761\) | −1638.39 | −0.0780443 | −0.0390222 | − | 0.999238i | \(-0.512424\pi\) | ||||
−0.0390222 | + | 0.999238i | \(0.512424\pi\) | |||||||
\(762\) | −37391.2 | −1.77761 | ||||||||
\(763\) | 3992.79 | 0.189448 | ||||||||
\(764\) | 4743.79 | 0.224639 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21683.9 | 1.02281 | ||||||||
\(767\) | 6655.50 | 0.313319 | ||||||||
\(768\) | 35241.6 | 1.65582 | ||||||||
\(769\) | −9542.58 | −0.447483 | −0.223741 | − | 0.974649i | \(-0.571827\pi\) | ||||
−0.223741 | + | 0.974649i | \(0.571827\pi\) | |||||||
\(770\) | −6653.53 | −0.311398 | ||||||||
\(771\) | −52270.8 | −2.44162 | ||||||||
\(772\) | 12333.8 | 0.575002 | ||||||||
\(773\) | 10640.1 | 0.495080 | 0.247540 | − | 0.968878i | \(-0.420378\pi\) | ||||
0.247540 | + | 0.968878i | \(0.420378\pi\) | |||||||
\(774\) | −8045.09 | −0.373611 | ||||||||
\(775\) | 13655.3 | 0.632918 | ||||||||
\(776\) | 7001.80 | 0.323904 | ||||||||
\(777\) | −13585.0 | −0.627233 | ||||||||
\(778\) | 9272.90 | 0.427313 | ||||||||
\(779\) | 1971.27 | 0.0906652 | ||||||||
\(780\) | 20965.0 | 0.962393 | ||||||||
\(781\) | −15978.8 | −0.732095 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16554.9 | −0.755586 | ||||||||
\(784\) | 7583.45 | 0.345456 | ||||||||
\(785\) | −15343.3 | −0.697611 | ||||||||
\(786\) | −24687.4 | −1.12032 | ||||||||
\(787\) | 4358.23 | 0.197400 | 0.0987002 | − | 0.995117i | \(-0.468532\pi\) | ||||
0.0987002 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(788\) | 12472.5 | 0.563853 | ||||||||
\(789\) | −1249.36 | −0.0563730 | ||||||||
\(790\) | −1008.23 | −0.0454068 | ||||||||
\(791\) | −9305.71 | −0.418297 | ||||||||
\(792\) | 50748.3 | 2.27685 | ||||||||
\(793\) | 29625.3 | 1.32664 | ||||||||
\(794\) | −21296.7 | −0.951876 | ||||||||
\(795\) | −678.210 | −0.0302561 | ||||||||
\(796\) | −10797.1 | −0.480770 | ||||||||
\(797\) | 19901.9 | 0.884517 | 0.442259 | − | 0.896888i | \(-0.354177\pi\) | ||||
0.442259 | + | 0.896888i | \(0.354177\pi\) | |||||||
\(798\) | 2512.08 | 0.111437 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 11812.3 | 0.522035 | ||||||||
\(801\) | 8284.18 | 0.365427 | ||||||||
\(802\) | 17401.0 | 0.766147 | ||||||||
\(803\) | 1275.80 | 0.0560672 | ||||||||
\(804\) | −28042.6 | −1.23008 | ||||||||
\(805\) | −2736.18 | −0.119798 | ||||||||
\(806\) | −17617.6 | −0.769918 | ||||||||
\(807\) | 26071.0 | 1.13723 | ||||||||
\(808\) | −3757.02 | −0.163579 | ||||||||
\(809\) | 28136.7 | 1.22279 | 0.611394 | − | 0.791326i | \(-0.290609\pi\) | ||||
0.611394 | + | 0.791326i | \(0.290609\pi\) | |||||||
\(810\) | 755.864 | 0.0327881 | ||||||||
\(811\) | 213.599 | 0.00924845 | 0.00462422 | − | 0.999989i | \(-0.498528\pi\) | ||||
0.00462422 | + | 0.999989i | \(0.498528\pi\) | |||||||
\(812\) | 1940.03 | 0.0838444 | ||||||||
\(813\) | −39612.6 | −1.70882 | ||||||||
\(814\) | 36290.3 | 1.56262 | ||||||||
\(815\) | −12143.4 | −0.521921 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2731.14 | −0.116953 | ||||||||
\(818\) | −11441.8 | −0.489061 | ||||||||
\(819\) | 9749.43 | 0.415962 | ||||||||
\(820\) | 3198.86 | 0.136230 | ||||||||
\(821\) | −10422.0 | −0.443033 | −0.221517 | − | 0.975157i | \(-0.571101\pi\) | ||||
−0.221517 | + | 0.975157i | \(0.571101\pi\) | |||||||
\(822\) | 41003.2 | 1.73984 | ||||||||
\(823\) | −25083.0 | −1.06238 | −0.531189 | − | 0.847253i | \(-0.678255\pi\) | ||||
−0.531189 | + | 0.847253i | \(0.678255\pi\) | |||||||
\(824\) | −18657.6 | −0.788796 | ||||||||
\(825\) | 32782.0 | 1.38342 | ||||||||
\(826\) | 1294.10 | 0.0545126 | ||||||||
\(827\) | 27880.2 | 1.17230 | 0.586148 | − | 0.810204i | \(-0.300644\pi\) | ||||
0.586148 | + | 0.810204i | \(0.300644\pi\) | |||||||
\(828\) | 6370.24 | 0.267368 | ||||||||
\(829\) | −28128.7 | −1.17847 | −0.589235 | − | 0.807962i | \(-0.700571\pi\) | ||||
−0.589235 | + | 0.807962i | \(0.700571\pi\) | |||||||
\(830\) | −8635.85 | −0.361150 | ||||||||
\(831\) | −7545.80 | −0.314995 | ||||||||
\(832\) | −24564.1 | −1.02357 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −43977.0 | −1.82590 | ||||||||
\(835\) | 37540.2 | 1.55585 | ||||||||
\(836\) | 5258.68 | 0.217554 | ||||||||
\(837\) | −22906.9 | −0.945971 | ||||||||
\(838\) | −13353.4 | −0.550458 | ||||||||
\(839\) | −39229.0 | −1.61422 | −0.807112 | − | 0.590398i | \(-0.798971\pi\) | ||||
−0.807112 | + | 0.590398i | \(0.798971\pi\) | |||||||
\(840\) | 13354.8 | 0.548555 | ||||||||
\(841\) | −9660.52 | −0.396101 | ||||||||
\(842\) | 13749.9 | 0.562772 | ||||||||
\(843\) | −76835.0 | −3.13919 | ||||||||
\(844\) | 21165.9 | 0.863225 | ||||||||
\(845\) | −3691.30 | −0.150278 | ||||||||
\(846\) | −25834.6 | −1.04989 | ||||||||
\(847\) | −4464.98 | −0.181132 | ||||||||
\(848\) | 132.523 | 0.00536657 | ||||||||
\(849\) | −29686.3 | −1.20004 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14923.9 | 0.601156 | ||||||||
\(852\) | 9789.78 | 0.393653 | ||||||||
\(853\) | 38686.5 | 1.55287 | 0.776436 | − | 0.630196i | \(-0.217026\pi\) | ||||
0.776436 | + | 0.630196i | \(0.217026\pi\) | |||||||
\(854\) | 5760.36 | 0.230814 | ||||||||
\(855\) | −19337.3 | −0.773477 | ||||||||
\(856\) | −9644.39 | −0.385092 | ||||||||
\(857\) | −9417.90 | −0.375390 | −0.187695 | − | 0.982227i | \(-0.560102\pi\) | ||||
−0.187695 | + | 0.982227i | \(0.560102\pi\) | |||||||
\(858\) | −42294.4 | −1.68287 | ||||||||
\(859\) | 43890.4 | 1.74333 | 0.871666 | − | 0.490101i | \(-0.163040\pi\) | ||||
0.871666 | + | 0.490101i | \(0.163040\pi\) | |||||||
\(860\) | −4431.92 | −0.175729 | ||||||||
\(861\) | 2415.76 | 0.0956199 | ||||||||
\(862\) | 28543.1 | 1.12782 | ||||||||
\(863\) | 6822.88 | 0.269123 | 0.134562 | − | 0.990905i | \(-0.457037\pi\) | ||||
0.134562 | + | 0.990905i | \(0.457037\pi\) | |||||||
\(864\) | −19815.3 | −0.780244 | ||||||||
\(865\) | −44309.6 | −1.74170 | ||||||||
\(866\) | −28035.5 | −1.10010 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2684.40 | 0.104971 | ||||||||
\(869\) | −1593.91 | −0.0622206 | ||||||||
\(870\) | 30947.9 | 1.20601 | ||||||||
\(871\) | 47148.1 | 1.83416 | ||||||||
\(872\) | 21408.8 | 0.831415 | ||||||||
\(873\) | −12424.4 | −0.481673 | ||||||||
\(874\) | −2759.65 | −0.106804 | ||||||||
\(875\) | −2853.72 | −0.110255 | ||||||||
\(876\) | −781.648 | −0.0301478 | ||||||||
\(877\) | −34548.2 | −1.33023 | −0.665114 | − | 0.746742i | \(-0.731617\pi\) | ||||
−0.665114 | + | 0.746742i | \(0.731617\pi\) | |||||||
\(878\) | −21705.8 | −0.834322 | ||||||||
\(879\) | 10631.9 | 0.407970 | ||||||||
\(880\) | −16252.4 | −0.622576 | ||||||||
\(881\) | 30611.4 | 1.17063 | 0.585315 | − | 0.810806i | \(-0.300971\pi\) | ||||
0.585315 | + | 0.810806i | \(0.300971\pi\) | |||||||
\(882\) | −29538.2 | −1.12767 | ||||||||
\(883\) | 42598.5 | 1.62350 | 0.811751 | − | 0.584003i | \(-0.198514\pi\) | ||||
0.811751 | + | 0.584003i | \(0.198514\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16177.2 | −0.614454 | ||||||||
\(886\) | −17288.5 | −0.655552 | ||||||||
\(887\) | 19049.1 | 0.721091 | 0.360545 | − | 0.932742i | \(-0.382591\pi\) | ||||
0.360545 | + | 0.932742i | \(0.382591\pi\) | |||||||
\(888\) | −72841.1 | −2.75269 | ||||||||
\(889\) | −9578.91 | −0.361379 | ||||||||
\(890\) | −5823.67 | −0.219337 | ||||||||
\(891\) | 1194.94 | 0.0449293 | ||||||||
\(892\) | 12586.6 | 0.472457 | ||||||||
\(893\) | −8770.30 | −0.328653 | ||||||||
\(894\) | 27013.8 | 1.01060 | ||||||||
\(895\) | −13199.3 | −0.492967 | ||||||||
\(896\) | 509.099 | 0.0189819 | ||||||||
\(897\) | −17393.0 | −0.647419 | ||||||||
\(898\) | 9281.77 | 0.344918 | ||||||||
\(899\) | 20379.7 | 0.756064 | ||||||||
\(900\) | −12367.8 | −0.458065 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −6453.32 | −0.238217 | ||||||||
\(903\) | −3346.96 | −0.123344 | ||||||||
\(904\) | −49896.1 | −1.83575 | ||||||||
\(905\) | 31006.4 | 1.13888 | ||||||||
\(906\) | 7064.31 | 0.259047 | ||||||||
\(907\) | 8388.99 | 0.307113 | 0.153557 | − | 0.988140i | \(-0.450927\pi\) | ||||
0.153557 | + | 0.988140i | \(0.450927\pi\) | |||||||
\(908\) | 14918.1 | 0.545235 | ||||||||
\(909\) | 6666.66 | 0.243255 | ||||||||
\(910\) | −6853.72 | −0.249669 | ||||||||
\(911\) | 10467.7 | 0.380694 | 0.190347 | − | 0.981717i | \(-0.439039\pi\) | ||||
0.190347 | + | 0.981717i | \(0.439039\pi\) | |||||||
\(912\) | 6136.16 | 0.222795 | ||||||||
\(913\) | −13652.3 | −0.494882 | ||||||||
\(914\) | −22159.6 | −0.801943 | ||||||||
\(915\) | −72009.0 | −2.60169 | ||||||||
\(916\) | −18089.6 | −0.652509 | ||||||||
\(917\) | −6324.42 | −0.227754 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16180.4 | −0.580787 | −0.290394 | − | 0.956907i | \(-0.593786\pi\) | ||||
−0.290394 | + | 0.956907i | \(0.593786\pi\) | |||||||
\(920\) | −14671.0 | −0.525749 | ||||||||
\(921\) | −83193.5 | −2.97646 | ||||||||
\(922\) | −15969.8 | −0.570432 | ||||||||
\(923\) | −16459.6 | −0.586970 | ||||||||
\(924\) | 6444.41 | 0.229443 | ||||||||
\(925\) | −28974.6 | −1.02992 | ||||||||
\(926\) | 27451.4 | 0.974201 | ||||||||
\(927\) | 33107.0 | 1.17301 | ||||||||
\(928\) | 17629.2 | 0.623606 | ||||||||
\(929\) | 14214.9 | 0.502020 | 0.251010 | − | 0.967985i | \(-0.419237\pi\) | ||||
0.251010 | + | 0.967985i | \(0.419237\pi\) | |||||||
\(930\) | 42822.4 | 1.50989 | ||||||||
\(931\) | −10027.6 | −0.352998 | ||||||||
\(932\) | 10007.8 | 0.351734 | ||||||||
\(933\) | 12227.8 | 0.429068 | ||||||||
\(934\) | 26550.9 | 0.930164 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 52275.2 | 1.82550 | ||||||||
\(937\) | 49244.5 | 1.71691 | 0.858456 | − | 0.512887i | \(-0.171424\pi\) | ||||
0.858456 | + | 0.512887i | \(0.171424\pi\) | |||||||
\(938\) | 9167.50 | 0.319115 | ||||||||
\(939\) | 6688.37 | 0.232446 | ||||||||
\(940\) | −14231.9 | −0.493823 | ||||||||
\(941\) | −15645.1 | −0.541993 | −0.270997 | − | 0.962580i | \(-0.587353\pi\) | ||||
−0.270997 | + | 0.962580i | \(0.587353\pi\) | |||||||
\(942\) | −18964.2 | −0.655932 | ||||||||
\(943\) | −2653.84 | −0.0916447 | ||||||||
\(944\) | 3161.05 | 0.108987 | ||||||||
\(945\) | −8911.40 | −0.306760 | ||||||||
\(946\) | 8940.88 | 0.307287 | ||||||||
\(947\) | −33064.5 | −1.13459 | −0.567293 | − | 0.823516i | \(-0.692009\pi\) | ||||
−0.567293 | + | 0.823516i | \(0.692009\pi\) | |||||||
\(948\) | 976.546 | 0.0334565 | ||||||||
\(949\) | 1314.19 | 0.0449529 | ||||||||
\(950\) | 5357.85 | 0.182981 | ||||||||
\(951\) | 32295.3 | 1.10121 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47771.2 | −1.62378 | −0.811890 | − | 0.583811i | \(-0.801561\pi\) | ||||
−0.811890 | + | 0.583811i | \(0.801561\pi\) | |||||||
\(954\) | −516.188 | −0.0175180 | ||||||||
\(955\) | 19386.3 | 0.656886 | ||||||||
\(956\) | −14004.5 | −0.473786 | ||||||||
\(957\) | 48925.3 | 1.65259 | ||||||||
\(958\) | 2220.65 | 0.0748915 | ||||||||
\(959\) | 10504.2 | 0.353701 | ||||||||
\(960\) | 59707.0 | 2.00733 | ||||||||
\(961\) | −1591.73 | −0.0534300 | ||||||||
\(962\) | 37382.2 | 1.25286 | ||||||||
\(963\) | 17113.5 | 0.572664 | ||||||||
\(964\) | 6307.34 | 0.210732 | ||||||||
\(965\) | 50404.0 | 1.68141 | ||||||||
\(966\) | −3381.90 | −0.112641 | ||||||||
\(967\) | −29494.2 | −0.980837 | −0.490418 | − | 0.871487i | \(-0.663156\pi\) | ||||
−0.490418 | + | 0.871487i | \(0.663156\pi\) | |||||||
\(968\) | −23940.7 | −0.794919 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8734.16 | 0.289110 | ||||||||
\(971\) | 32058.3 | 1.05953 | 0.529763 | − | 0.848146i | \(-0.322281\pi\) | ||||
0.529763 | + | 0.848146i | \(0.322281\pi\) | |||||||
\(972\) | −13677.3 | −0.451338 | ||||||||
\(973\) | −11266.1 | −0.371196 | ||||||||
\(974\) | 1913.85 | 0.0629608 | ||||||||
\(975\) | 33768.4 | 1.10918 | ||||||||
\(976\) | 14070.6 | 0.461465 | ||||||||
\(977\) | −47602.0 | −1.55878 | −0.779388 | − | 0.626542i | \(-0.784470\pi\) | ||||
−0.779388 | + | 0.626542i | \(0.784470\pi\) | |||||||
\(978\) | −15009.2 | −0.490738 | ||||||||
\(979\) | −9206.60 | −0.300556 | ||||||||
\(980\) | −16272.2 | −0.530404 | ||||||||
\(981\) | −37989.0 | −1.23639 | ||||||||
\(982\) | 31603.5 | 1.02699 | ||||||||
\(983\) | 28860.0 | 0.936410 | 0.468205 | − | 0.883620i | \(-0.344901\pi\) | ||||
0.468205 | + | 0.883620i | \(0.344901\pi\) | |||||||
\(984\) | 12953.0 | 0.419640 | ||||||||
\(985\) | 50971.2 | 1.64881 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10747.8 | −0.346613 | ||||||||
\(988\) | 5416.91 | 0.174428 | ||||||||
\(989\) | 3676.82 | 0.118216 | ||||||||
\(990\) | 63304.3 | 2.03227 | ||||||||
\(991\) | 4704.04 | 0.150786 | 0.0753930 | − | 0.997154i | \(-0.475979\pi\) | ||||
0.0753930 | + | 0.997154i | \(0.475979\pi\) | |||||||
\(992\) | 24393.4 | 0.780737 | ||||||||
\(993\) | 71006.3 | 2.26920 | ||||||||
\(994\) | −3200.41 | −0.102123 | ||||||||
\(995\) | −44124.1 | −1.40586 | ||||||||
\(996\) | 8364.43 | 0.266102 | ||||||||
\(997\) | −32982.5 | −1.04771 | −0.523854 | − | 0.851808i | \(-0.675506\pi\) | ||||
−0.523854 | + | 0.851808i | \(0.675506\pi\) | |||||||
\(998\) | −5566.54 | −0.176559 | ||||||||
\(999\) | 48605.3 | 1.53934 |
(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 | 289.4.a.f.1.5 | 8 | ||
17.2 | even | 8 | 17.4.c.a.4.3 | ✓ | 8 | ||
17.4 | even | 4 | 289.4.b.c.288.4 | 8 | |||
17.9 | even | 8 | 17.4.c.a.13.2 | yes | 8 | ||
17.13 | even | 4 | 289.4.b.c.288.3 | 8 | |||
17.16 | even | 2 | inner | 289.4.a.f.1.6 | 8 | ||
51.2 | odd | 8 | 153.4.f.a.55.2 | 8 | |||
51.26 | odd | 8 | 153.4.f.a.64.3 | 8 | |||
68.19 | odd | 8 | 272.4.o.e.225.4 | 8 | |||
68.43 | odd | 8 | 272.4.o.e.81.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.c.a.4.3 | ✓ | 8 | 17.2 | even | 8 | ||
17.4.c.a.13.2 | yes | 8 | 17.9 | even | 8 | ||
153.4.f.a.55.2 | 8 | 51.2 | odd | 8 | |||
153.4.f.a.64.3 | 8 | 51.26 | odd | 8 | |||
272.4.o.e.81.4 | 8 | 68.43 | odd | 8 | |||
272.4.o.e.225.4 | 8 | 68.19 | odd | 8 | |||
289.4.a.f.1.5 | 8 | 1.1 | even | 1 | trivial | ||
289.4.a.f.1.6 | 8 | 17.16 | even | 2 | inner | ||
289.4.b.c.288.3 | 8 | 17.13 | even | 4 | |||
289.4.b.c.288.4 | 8 | 17.4 | even | 4 |