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: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2555057.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 21x^{2} - 4x + 36 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.68488\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.68488 | −1.30280 | −0.651400 | − | 0.758734i | \(-0.725818\pi\) | ||||
−0.651400 | + | 0.758734i | \(0.725818\pi\) | |||||||
\(3\) | 9.05894 | 1.74339 | 0.871697 | − | 0.490046i | \(-0.163020\pi\) | ||||
0.871697 | + | 0.490046i | \(0.163020\pi\) | |||||||
\(4\) | 5.57832 | 0.697290 | ||||||||
\(5\) | −7.08909 | −0.634067 | −0.317034 | − | 0.948414i | \(-0.602687\pi\) | ||||
−0.317034 | + | 0.948414i | \(0.602687\pi\) | |||||||
\(6\) | −33.3811 | −2.27129 | ||||||||
\(7\) | −28.1854 | −1.52187 | −0.760935 | − | 0.648828i | \(-0.775259\pi\) | ||||
−0.760935 | + | 0.648828i | \(0.775259\pi\) | |||||||
\(8\) | 8.92359 | 0.394371 | ||||||||
\(9\) | 55.0643 | 2.03942 | ||||||||
\(10\) | 26.1224 | 0.826064 | ||||||||
\(11\) | 15.3047 | 0.419503 | 0.209751 | − | 0.977755i | \(-0.432735\pi\) | ||||
0.209751 | + | 0.977755i | \(0.432735\pi\) | |||||||
\(12\) | 50.5336 | 1.21565 | ||||||||
\(13\) | 2.51532 | 0.0536634 | 0.0268317 | − | 0.999640i | \(-0.491458\pi\) | ||||
0.0268317 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(14\) | 103.860 | 1.98269 | ||||||||
\(15\) | −64.2196 | −1.10543 | ||||||||
\(16\) | −77.5089 | −1.21108 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −202.905 | −2.65696 | ||||||||
\(19\) | 14.3453 | 0.173212 | 0.0866062 | − | 0.996243i | \(-0.472398\pi\) | ||||
0.0866062 | + | 0.996243i | \(0.472398\pi\) | |||||||
\(20\) | −39.5452 | −0.442129 | ||||||||
\(21\) | −255.330 | −2.65322 | ||||||||
\(22\) | −56.3958 | −0.546529 | ||||||||
\(23\) | −180.191 | −1.63359 | −0.816793 | − | 0.576931i | \(-0.804250\pi\) | ||||
−0.816793 | + | 0.576931i | \(0.804250\pi\) | |||||||
\(24\) | 80.8383 | 0.687544 | ||||||||
\(25\) | −74.7448 | −0.597958 | ||||||||
\(26\) | −9.26864 | −0.0699127 | ||||||||
\(27\) | 254.233 | 1.81212 | ||||||||
\(28\) | −157.227 | −1.06118 | ||||||||
\(29\) | −41.2425 | −0.264088 | −0.132044 | − | 0.991244i | \(-0.542154\pi\) | ||||
−0.132044 | + | 0.991244i | \(0.542154\pi\) | |||||||
\(30\) | 236.641 | 1.44015 | ||||||||
\(31\) | −155.242 | −0.899426 | −0.449713 | − | 0.893173i | \(-0.648474\pi\) | ||||
−0.449713 | + | 0.893173i | \(0.648474\pi\) | |||||||
\(32\) | 214.222 | 1.18342 | ||||||||
\(33\) | 138.644 | 0.731358 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 199.809 | 0.964968 | ||||||||
\(36\) | 307.167 | 1.42207 | ||||||||
\(37\) | 225.676 | 1.00273 | 0.501363 | − | 0.865237i | \(-0.332832\pi\) | ||||
0.501363 | + | 0.865237i | \(0.332832\pi\) | |||||||
\(38\) | −52.8606 | −0.225661 | ||||||||
\(39\) | 22.7861 | 0.0935564 | ||||||||
\(40\) | −63.2602 | −0.250058 | ||||||||
\(41\) | −234.306 | −0.892497 | −0.446249 | − | 0.894909i | \(-0.647240\pi\) | ||||
−0.446249 | + | 0.894909i | \(0.647240\pi\) | |||||||
\(42\) | 940.860 | 3.45661 | ||||||||
\(43\) | −321.875 | −1.14152 | −0.570761 | − | 0.821117i | \(-0.693352\pi\) | ||||
−0.570761 | + | 0.821117i | \(0.693352\pi\) | |||||||
\(44\) | 85.3743 | 0.292515 | ||||||||
\(45\) | −390.356 | −1.29313 | ||||||||
\(46\) | 663.983 | 2.12824 | ||||||||
\(47\) | −326.183 | −1.01231 | −0.506156 | − | 0.862442i | \(-0.668934\pi\) | ||||
−0.506156 | + | 0.862442i | \(0.668934\pi\) | |||||||
\(48\) | −702.148 | −2.11138 | ||||||||
\(49\) | 451.418 | 1.31609 | ||||||||
\(50\) | 275.425 | 0.779021 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 14.0313 | 0.0374189 | ||||||||
\(53\) | −57.1579 | −0.148137 | −0.0740683 | − | 0.997253i | \(-0.523598\pi\) | ||||
−0.0740683 | + | 0.997253i | \(0.523598\pi\) | |||||||
\(54\) | −936.818 | −2.36083 | ||||||||
\(55\) | −108.496 | −0.265993 | ||||||||
\(56\) | −251.515 | −0.600181 | ||||||||
\(57\) | 129.953 | 0.301977 | ||||||||
\(58\) | 151.974 | 0.344054 | ||||||||
\(59\) | −241.623 | −0.533164 | −0.266582 | − | 0.963812i | \(-0.585894\pi\) | ||||
−0.266582 | + | 0.963812i | \(0.585894\pi\) | |||||||
\(60\) | −358.238 | −0.770805 | ||||||||
\(61\) | −460.925 | −0.967465 | −0.483732 | − | 0.875216i | \(-0.660719\pi\) | ||||
−0.483732 | + | 0.875216i | \(0.660719\pi\) | |||||||
\(62\) | 572.046 | 1.17177 | ||||||||
\(63\) | −1552.01 | −3.10373 | ||||||||
\(64\) | −169.311 | −0.330685 | ||||||||
\(65\) | −17.8313 | −0.0340262 | ||||||||
\(66\) | −510.886 | −0.952814 | ||||||||
\(67\) | 392.696 | 0.716052 | 0.358026 | − | 0.933712i | \(-0.383450\pi\) | ||||
0.358026 | + | 0.933712i | \(0.383450\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1632.34 | −2.84798 | ||||||||
\(70\) | −736.272 | −1.25716 | ||||||||
\(71\) | −615.558 | −1.02892 | −0.514460 | − | 0.857515i | \(-0.672007\pi\) | ||||
−0.514460 | + | 0.857515i | \(0.672007\pi\) | |||||||
\(72\) | 491.372 | 0.804288 | ||||||||
\(73\) | 697.452 | 1.11823 | 0.559114 | − | 0.829091i | \(-0.311142\pi\) | ||||
0.559114 | + | 0.829091i | \(0.311142\pi\) | |||||||
\(74\) | −831.587 | −1.30635 | ||||||||
\(75\) | −677.109 | −1.04248 | ||||||||
\(76\) | 80.0226 | 0.120779 | ||||||||
\(77\) | −431.369 | −0.638429 | ||||||||
\(78\) | −83.9641 | −0.121885 | ||||||||
\(79\) | −991.317 | −1.41180 | −0.705898 | − | 0.708313i | \(-0.749456\pi\) | ||||
−0.705898 | + | 0.708313i | \(0.749456\pi\) | |||||||
\(80\) | 549.468 | 0.767904 | ||||||||
\(81\) | 816.345 | 1.11981 | ||||||||
\(82\) | 863.387 | 1.16275 | ||||||||
\(83\) | −98.9057 | −0.130799 | −0.0653995 | − | 0.997859i | \(-0.520832\pi\) | ||||
−0.0653995 | + | 0.997859i | \(0.520832\pi\) | |||||||
\(84\) | −1424.31 | −1.85006 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1186.07 | 1.48717 | ||||||||
\(87\) | −373.613 | −0.460409 | ||||||||
\(88\) | 136.573 | 0.165440 | ||||||||
\(89\) | 698.470 | 0.831884 | 0.415942 | − | 0.909391i | \(-0.363452\pi\) | ||||
0.415942 | + | 0.909391i | \(0.363452\pi\) | |||||||
\(90\) | 1438.41 | 1.68469 | ||||||||
\(91\) | −70.8954 | −0.0816687 | ||||||||
\(92\) | −1005.16 | −1.13908 | ||||||||
\(93\) | −1406.32 | −1.56805 | ||||||||
\(94\) | 1201.94 | 1.31884 | ||||||||
\(95\) | −101.695 | −0.109828 | ||||||||
\(96\) | 1940.62 | 2.06317 | ||||||||
\(97\) | 1428.66 | 1.49545 | 0.747725 | − | 0.664009i | \(-0.231146\pi\) | ||||
0.747725 | + | 0.664009i | \(0.231146\pi\) | |||||||
\(98\) | −1663.42 | −1.71460 | ||||||||
\(99\) | 842.741 | 0.855542 | ||||||||
\(100\) | −416.950 | −0.416950 | ||||||||
\(101\) | 408.671 | 0.402617 | 0.201308 | − | 0.979528i | \(-0.435481\pi\) | ||||
0.201308 | + | 0.979528i | \(0.435481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1649.55 | 1.57801 | 0.789007 | − | 0.614384i | \(-0.210596\pi\) | ||||
0.789007 | + | 0.614384i | \(0.210596\pi\) | |||||||
\(104\) | 22.4457 | 0.0211633 | ||||||||
\(105\) | 1810.06 | 1.68232 | ||||||||
\(106\) | 210.620 | 0.192993 | ||||||||
\(107\) | −2055.01 | −1.85668 | −0.928340 | − | 0.371731i | \(-0.878764\pi\) | ||||
−0.928340 | + | 0.371731i | \(0.878764\pi\) | |||||||
\(108\) | 1418.19 | 1.26357 | ||||||||
\(109\) | 445.064 | 0.391095 | 0.195548 | − | 0.980694i | \(-0.437352\pi\) | ||||
0.195548 | + | 0.980694i | \(0.437352\pi\) | |||||||
\(110\) | 399.795 | 0.346536 | ||||||||
\(111\) | 2044.38 | 1.74814 | ||||||||
\(112\) | 2184.62 | 1.84310 | ||||||||
\(113\) | −1226.02 | −1.02066 | −0.510330 | − | 0.859979i | \(-0.670477\pi\) | ||||
−0.510330 | + | 0.859979i | \(0.670477\pi\) | |||||||
\(114\) | −478.861 | −0.393416 | ||||||||
\(115\) | 1277.39 | 1.03580 | ||||||||
\(116\) | −230.064 | −0.184146 | ||||||||
\(117\) | 138.504 | 0.109442 | ||||||||
\(118\) | 890.352 | 0.694607 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −573.070 | −0.435949 | ||||||||
\(121\) | −1096.77 | −0.824017 | ||||||||
\(122\) | 1698.45 | 1.26041 | ||||||||
\(123\) | −2122.56 | −1.55597 | ||||||||
\(124\) | −865.987 | −0.627161 | ||||||||
\(125\) | 1416.01 | 1.01321 | ||||||||
\(126\) | 5718.97 | 4.04354 | ||||||||
\(127\) | −591.124 | −0.413022 | −0.206511 | − | 0.978444i | \(-0.566211\pi\) | ||||
−0.206511 | + | 0.978444i | \(0.566211\pi\) | |||||||
\(128\) | −1089.89 | −0.752604 | ||||||||
\(129\) | −2915.84 | −1.99012 | ||||||||
\(130\) | 65.7063 | 0.0443294 | ||||||||
\(131\) | −2025.27 | −1.35075 | −0.675375 | − | 0.737474i | \(-0.736018\pi\) | ||||
−0.675375 | + | 0.737474i | \(0.736018\pi\) | |||||||
\(132\) | 773.401 | 0.509969 | ||||||||
\(133\) | −404.328 | −0.263607 | ||||||||
\(134\) | −1447.04 | −0.932873 | ||||||||
\(135\) | −1802.28 | −1.14901 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 623.919 | 0.389087 | 0.194544 | − | 0.980894i | \(-0.437677\pi\) | ||||
0.194544 | + | 0.980894i | \(0.437677\pi\) | |||||||
\(138\) | 6014.98 | 3.71036 | ||||||||
\(139\) | 1033.14 | 0.630429 | 0.315214 | − | 0.949020i | \(-0.397924\pi\) | ||||
0.315214 | + | 0.949020i | \(0.397924\pi\) | |||||||
\(140\) | 1114.60 | 0.672863 | ||||||||
\(141\) | −2954.87 | −1.76486 | ||||||||
\(142\) | 2268.25 | 1.34048 | ||||||||
\(143\) | 38.4961 | 0.0225119 | ||||||||
\(144\) | −4267.98 | −2.46989 | ||||||||
\(145\) | 292.372 | 0.167449 | ||||||||
\(146\) | −2570.02 | −1.45683 | ||||||||
\(147\) | 4089.37 | 2.29446 | ||||||||
\(148\) | 1258.89 | 0.699190 | ||||||||
\(149\) | −284.476 | −0.156411 | −0.0782054 | − | 0.996937i | \(-0.524919\pi\) | ||||
−0.0782054 | + | 0.996937i | \(0.524919\pi\) | |||||||
\(150\) | 2495.06 | 1.35814 | ||||||||
\(151\) | 3153.25 | 1.69939 | 0.849696 | − | 0.527273i | \(-0.176786\pi\) | ||||
0.849696 | + | 0.527273i | \(0.176786\pi\) | |||||||
\(152\) | 128.012 | 0.0683099 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1589.54 | 0.831745 | ||||||||
\(155\) | 1100.52 | 0.570297 | ||||||||
\(156\) | 127.108 | 0.0652359 | ||||||||
\(157\) | −482.335 | −0.245188 | −0.122594 | − | 0.992457i | \(-0.539121\pi\) | ||||
−0.122594 | + | 0.992457i | \(0.539121\pi\) | |||||||
\(158\) | 3652.88 | 1.83929 | ||||||||
\(159\) | −517.790 | −0.258261 | ||||||||
\(160\) | −1518.64 | −0.750369 | ||||||||
\(161\) | 5078.77 | 2.48611 | ||||||||
\(162\) | −3008.13 | −1.45890 | ||||||||
\(163\) | 3717.39 | 1.78631 | 0.893155 | − | 0.449749i | \(-0.148487\pi\) | ||||
0.893155 | + | 0.449749i | \(0.148487\pi\) | |||||||
\(164\) | −1307.03 | −0.622329 | ||||||||
\(165\) | −982.860 | −0.463731 | ||||||||
\(166\) | 364.455 | 0.170405 | ||||||||
\(167\) | −2128.93 | −0.986475 | −0.493237 | − | 0.869895i | \(-0.664187\pi\) | ||||
−0.493237 | + | 0.869895i | \(0.664187\pi\) | |||||||
\(168\) | −2278.46 | −1.04635 | ||||||||
\(169\) | −2190.67 | −0.997120 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 789.914 | 0.353253 | ||||||||
\(172\) | −1795.52 | −0.795971 | ||||||||
\(173\) | 1197.86 | 0.526426 | 0.263213 | − | 0.964738i | \(-0.415218\pi\) | ||||
0.263213 | + | 0.964738i | \(0.415218\pi\) | |||||||
\(174\) | 1376.72 | 0.599821 | ||||||||
\(175\) | 2106.71 | 0.910015 | ||||||||
\(176\) | −1186.25 | −0.508050 | ||||||||
\(177\) | −2188.85 | −0.929515 | ||||||||
\(178\) | −2573.78 | −1.08378 | ||||||||
\(179\) | 4095.63 | 1.71018 | 0.855089 | − | 0.518482i | \(-0.173503\pi\) | ||||
0.855089 | + | 0.518482i | \(0.173503\pi\) | |||||||
\(180\) | −2177.53 | −0.901687 | ||||||||
\(181\) | −1297.08 | −0.532660 | −0.266330 | − | 0.963882i | \(-0.585811\pi\) | ||||
−0.266330 | + | 0.963882i | \(0.585811\pi\) | |||||||
\(182\) | 261.241 | 0.106398 | ||||||||
\(183\) | −4175.49 | −1.68667 | ||||||||
\(184\) | −1607.95 | −0.644239 | ||||||||
\(185\) | −1599.83 | −0.635795 | ||||||||
\(186\) | 5182.13 | 2.04286 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1819.55 | −0.705876 | ||||||||
\(189\) | −7165.67 | −2.75781 | ||||||||
\(190\) | 374.734 | 0.143084 | ||||||||
\(191\) | 4381.72 | 1.65995 | 0.829974 | − | 0.557803i | \(-0.188355\pi\) | ||||
0.829974 | + | 0.557803i | \(0.188355\pi\) | |||||||
\(192\) | −1533.77 | −0.576514 | ||||||||
\(193\) | 1022.20 | 0.381240 | 0.190620 | − | 0.981664i | \(-0.438950\pi\) | ||||
0.190620 | + | 0.981664i | \(0.438950\pi\) | |||||||
\(194\) | −5264.44 | −1.94827 | ||||||||
\(195\) | −161.533 | −0.0593211 | ||||||||
\(196\) | 2518.15 | 0.917695 | ||||||||
\(197\) | −2202.50 | −0.796555 | −0.398278 | − | 0.917265i | \(-0.630392\pi\) | ||||
−0.398278 | + | 0.917265i | \(0.630392\pi\) | |||||||
\(198\) | −3105.40 | −1.11460 | ||||||||
\(199\) | −76.0165 | −0.0270787 | −0.0135394 | − | 0.999908i | \(-0.504310\pi\) | ||||
−0.0135394 | + | 0.999908i | \(0.504310\pi\) | |||||||
\(200\) | −666.992 | −0.235817 | ||||||||
\(201\) | 3557.41 | 1.24836 | ||||||||
\(202\) | −1505.90 | −0.524529 | ||||||||
\(203\) | 1162.44 | 0.401907 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1661.01 | 0.565904 | ||||||||
\(206\) | −6078.40 | −2.05584 | ||||||||
\(207\) | −9922.12 | −3.33157 | ||||||||
\(208\) | −194.960 | −0.0649905 | ||||||||
\(209\) | 219.550 | 0.0726631 | ||||||||
\(210\) | −6669.84 | −2.19173 | ||||||||
\(211\) | 1972.63 | 0.643609 | 0.321804 | − | 0.946806i | \(-0.395711\pi\) | ||||
0.321804 | + | 0.946806i | \(0.395711\pi\) | |||||||
\(212\) | −318.845 | −0.103294 | ||||||||
\(213\) | −5576.30 | −1.79381 | ||||||||
\(214\) | 7572.44 | 2.41889 | ||||||||
\(215\) | 2281.80 | 0.723801 | ||||||||
\(216\) | 2268.67 | 0.714647 | ||||||||
\(217\) | 4375.55 | 1.36881 | ||||||||
\(218\) | −1640.01 | −0.509520 | ||||||||
\(219\) | 6318.17 | 1.94951 | ||||||||
\(220\) | −605.226 | −0.185474 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7533.29 | −2.27748 | ||||||||
\(223\) | 1177.47 | 0.353584 | 0.176792 | − | 0.984248i | \(-0.443428\pi\) | ||||
0.176792 | + | 0.984248i | \(0.443428\pi\) | |||||||
\(224\) | −6037.94 | −1.80101 | ||||||||
\(225\) | −4115.77 | −1.21949 | ||||||||
\(226\) | 4517.75 | 1.32972 | ||||||||
\(227\) | 2845.44 | 0.831976 | 0.415988 | − | 0.909370i | \(-0.363436\pi\) | ||||
0.415988 | + | 0.909370i | \(0.363436\pi\) | |||||||
\(228\) | 724.920 | 0.210566 | ||||||||
\(229\) | 3605.93 | 1.04055 | 0.520277 | − | 0.853998i | \(-0.325829\pi\) | ||||
0.520277 | + | 0.853998i | \(0.325829\pi\) | |||||||
\(230\) | −4707.03 | −1.34945 | ||||||||
\(231\) | −3907.74 | −1.11303 | ||||||||
\(232\) | −368.032 | −0.104149 | ||||||||
\(233\) | −835.204 | −0.234833 | −0.117416 | − | 0.993083i | \(-0.537461\pi\) | ||||
−0.117416 | + | 0.993083i | \(0.537461\pi\) | |||||||
\(234\) | −510.372 | −0.142581 | ||||||||
\(235\) | 2312.34 | 0.641875 | ||||||||
\(236\) | −1347.85 | −0.371770 | ||||||||
\(237\) | −8980.28 | −2.46132 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4057.52 | −1.09816 | −0.549078 | − | 0.835771i | \(-0.685021\pi\) | ||||
−0.549078 | + | 0.835771i | \(0.685021\pi\) | |||||||
\(240\) | 4977.59 | 1.33876 | ||||||||
\(241\) | −2130.64 | −0.569487 | −0.284743 | − | 0.958604i | \(-0.591908\pi\) | ||||
−0.284743 | + | 0.958604i | \(0.591908\pi\) | |||||||
\(242\) | 4041.45 | 1.07353 | ||||||||
\(243\) | 530.923 | 0.140159 | ||||||||
\(244\) | −2571.19 | −0.674604 | ||||||||
\(245\) | −3200.14 | −0.834489 | ||||||||
\(246\) | 7821.37 | 2.02712 | ||||||||
\(247\) | 36.0830 | 0.00929516 | ||||||||
\(248\) | −1385.31 | −0.354708 | ||||||||
\(249\) | −895.981 | −0.228034 | ||||||||
\(250\) | −5217.82 | −1.32002 | ||||||||
\(251\) | 2164.17 | 0.544227 | 0.272113 | − | 0.962265i | \(-0.412277\pi\) | ||||
0.272113 | + | 0.962265i | \(0.412277\pi\) | |||||||
\(252\) | −8657.62 | −2.16420 | ||||||||
\(253\) | −2757.77 | −0.685294 | ||||||||
\(254\) | 2178.22 | 0.538085 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5370.59 | 1.31118 | ||||||||
\(257\) | 6991.31 | 1.69691 | 0.848456 | − | 0.529267i | \(-0.177533\pi\) | ||||
0.848456 | + | 0.529267i | \(0.177533\pi\) | |||||||
\(258\) | 10744.5 | 2.59273 | ||||||||
\(259\) | −6360.76 | −1.52602 | ||||||||
\(260\) | −99.4688 | −0.0237261 | ||||||||
\(261\) | −2270.99 | −0.538586 | ||||||||
\(262\) | 7462.85 | 1.75976 | ||||||||
\(263\) | −2985.57 | −0.699993 | −0.349996 | − | 0.936751i | \(-0.613817\pi\) | ||||
−0.349996 | + | 0.936751i | \(0.613817\pi\) | |||||||
\(264\) | 1237.20 | 0.288426 | ||||||||
\(265\) | 405.198 | 0.0939287 | ||||||||
\(266\) | 1489.90 | 0.343427 | ||||||||
\(267\) | 6327.40 | 1.45030 | ||||||||
\(268\) | 2190.58 | 0.499296 | ||||||||
\(269\) | −4063.25 | −0.920969 | −0.460484 | − | 0.887668i | \(-0.652324\pi\) | ||||
−0.460484 | + | 0.887668i | \(0.652324\pi\) | |||||||
\(270\) | 6641.19 | 1.49693 | ||||||||
\(271\) | 6295.85 | 1.41124 | 0.705619 | − | 0.708591i | \(-0.250669\pi\) | ||||
0.705619 | + | 0.708591i | \(0.250669\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −642.237 | −0.142381 | ||||||||
\(274\) | −2299.06 | −0.506903 | ||||||||
\(275\) | −1143.94 | −0.250845 | ||||||||
\(276\) | −9105.72 | −1.98587 | ||||||||
\(277\) | −4710.13 | −1.02168 | −0.510838 | − | 0.859677i | \(-0.670665\pi\) | ||||
−0.510838 | + | 0.859677i | \(0.670665\pi\) | |||||||
\(278\) | −3806.99 | −0.821323 | ||||||||
\(279\) | −8548.28 | −1.83431 | ||||||||
\(280\) | 1783.01 | 0.380555 | ||||||||
\(281\) | −2458.26 | −0.521878 | −0.260939 | − | 0.965355i | \(-0.584032\pi\) | ||||
−0.260939 | + | 0.965355i | \(0.584032\pi\) | |||||||
\(282\) | 10888.3 | 2.29926 | ||||||||
\(283\) | −9204.70 | −1.93344 | −0.966718 | − | 0.255843i | \(-0.917647\pi\) | ||||
−0.966718 | + | 0.255843i | \(0.917647\pi\) | |||||||
\(284\) | −3433.78 | −0.717455 | ||||||||
\(285\) | −921.249 | −0.191474 | ||||||||
\(286\) | −141.854 | −0.0293286 | ||||||||
\(287\) | 6604.00 | 1.35826 | ||||||||
\(288\) | 11796.0 | 2.41349 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1077.35 | −0.218153 | ||||||||
\(291\) | 12942.2 | 2.60716 | ||||||||
\(292\) | 3890.61 | 0.779729 | ||||||||
\(293\) | 423.010 | 0.0843431 | 0.0421716 | − | 0.999110i | \(-0.486572\pi\) | ||||
0.0421716 | + | 0.999110i | \(0.486572\pi\) | |||||||
\(294\) | −15068.8 | −2.98922 | ||||||||
\(295\) | 1712.89 | 0.338062 | ||||||||
\(296\) | 2013.84 | 0.395446 | ||||||||
\(297\) | 3890.95 | 0.760189 | ||||||||
\(298\) | 1048.26 | 0.203772 | ||||||||
\(299\) | −453.239 | −0.0876638 | ||||||||
\(300\) | −3777.13 | −0.726909 | ||||||||
\(301\) | 9072.17 | 1.73725 | ||||||||
\(302\) | −11619.4 | −2.21397 | ||||||||
\(303\) | 3702.12 | 0.701919 | ||||||||
\(304\) | −1111.89 | −0.209773 | ||||||||
\(305\) | 3267.54 | 0.613438 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 632.590 | 0.117602 | 0.0588010 | − | 0.998270i | \(-0.481272\pi\) | ||||
0.0588010 | + | 0.998270i | \(0.481272\pi\) | |||||||
\(308\) | −2406.31 | −0.445170 | ||||||||
\(309\) | 14943.2 | 2.75110 | ||||||||
\(310\) | −4055.29 | −0.742983 | ||||||||
\(311\) | 5293.07 | 0.965089 | 0.482544 | − | 0.875872i | \(-0.339713\pi\) | ||||
0.482544 | + | 0.875872i | \(0.339713\pi\) | |||||||
\(312\) | 203.334 | 0.0368959 | ||||||||
\(313\) | 3817.93 | 0.689464 | 0.344732 | − | 0.938701i | \(-0.387970\pi\) | ||||
0.344732 | + | 0.938701i | \(0.387970\pi\) | |||||||
\(314\) | 1777.35 | 0.319431 | ||||||||
\(315\) | 11002.4 | 1.96798 | ||||||||
\(316\) | −5529.88 | −0.984431 | ||||||||
\(317\) | 1389.54 | 0.246197 | 0.123098 | − | 0.992394i | \(-0.460717\pi\) | ||||
0.123098 | + | 0.992394i | \(0.460717\pi\) | |||||||
\(318\) | 1907.99 | 0.336462 | ||||||||
\(319\) | −631.203 | −0.110786 | ||||||||
\(320\) | 1200.26 | 0.209677 | ||||||||
\(321\) | −18616.2 | −3.23692 | ||||||||
\(322\) | −18714.6 | −3.23890 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4553.83 | 0.780836 | ||||||||
\(325\) | −188.007 | −0.0320885 | ||||||||
\(326\) | −13698.1 | −2.32721 | ||||||||
\(327\) | 4031.81 | 0.681833 | ||||||||
\(328\) | −2090.85 | −0.351975 | ||||||||
\(329\) | 9193.61 | 1.54061 | ||||||||
\(330\) | 3621.72 | 0.604149 | ||||||||
\(331\) | −5736.36 | −0.952565 | −0.476282 | − | 0.879292i | \(-0.658016\pi\) | ||||
−0.476282 | + | 0.879292i | \(0.658016\pi\) | |||||||
\(332\) | −551.728 | −0.0912048 | ||||||||
\(333\) | 12426.7 | 2.04498 | ||||||||
\(334\) | 7844.83 | 1.28518 | ||||||||
\(335\) | −2783.86 | −0.454025 | ||||||||
\(336\) | 19790.3 | 3.21325 | ||||||||
\(337\) | 3997.46 | 0.646159 | 0.323080 | − | 0.946372i | \(-0.395282\pi\) | ||||
0.323080 | + | 0.946372i | \(0.395282\pi\) | |||||||
\(338\) | 8072.36 | 1.29905 | ||||||||
\(339\) | −11106.5 | −1.77941 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2375.92 | −0.377312 | ||||||||
\(342\) | −2910.74 | −0.460218 | ||||||||
\(343\) | −3055.81 | −0.481045 | ||||||||
\(344\) | −2872.28 | −0.450183 | ||||||||
\(345\) | 11571.8 | 1.80581 | ||||||||
\(346\) | −4413.97 | −0.685828 | ||||||||
\(347\) | 2485.37 | 0.384500 | 0.192250 | − | 0.981346i | \(-0.438422\pi\) | ||||
0.192250 | + | 0.981346i | \(0.438422\pi\) | |||||||
\(348\) | −2084.14 | −0.321038 | ||||||||
\(349\) | −9518.10 | −1.45986 | −0.729932 | − | 0.683520i | \(-0.760448\pi\) | ||||
−0.729932 | + | 0.683520i | \(0.760448\pi\) | |||||||
\(350\) | −7762.98 | −1.18557 | ||||||||
\(351\) | 639.478 | 0.0972444 | ||||||||
\(352\) | 3278.60 | 0.496448 | ||||||||
\(353\) | 174.509 | 0.0263121 | 0.0131561 | − | 0.999913i | \(-0.495812\pi\) | ||||
0.0131561 | + | 0.999913i | \(0.495812\pi\) | |||||||
\(354\) | 8065.65 | 1.21097 | ||||||||
\(355\) | 4363.74 | 0.652404 | ||||||||
\(356\) | 3896.29 | 0.580065 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15091.9 | −2.22802 | ||||||||
\(359\) | −8112.87 | −1.19270 | −0.596352 | − | 0.802723i | \(-0.703384\pi\) | ||||
−0.596352 | + | 0.802723i | \(0.703384\pi\) | |||||||
\(360\) | −3483.38 | −0.509973 | ||||||||
\(361\) | −6653.21 | −0.969997 | ||||||||
\(362\) | 4779.59 | 0.693949 | ||||||||
\(363\) | −9935.55 | −1.43659 | ||||||||
\(364\) | −395.477 | −0.0569468 | ||||||||
\(365\) | −4944.30 | −0.709031 | ||||||||
\(366\) | 15386.2 | 2.19740 | ||||||||
\(367\) | −41.1424 | −0.00585181 | −0.00292591 | − | 0.999996i | \(-0.500931\pi\) | ||||
−0.00292591 | + | 0.999996i | \(0.500931\pi\) | |||||||
\(368\) | 13966.4 | 1.97840 | ||||||||
\(369\) | −12901.9 | −1.82018 | ||||||||
\(370\) | 5895.19 | 0.828315 | ||||||||
\(371\) | 1611.02 | 0.225445 | ||||||||
\(372\) | −7844.93 | −1.09339 | ||||||||
\(373\) | 1275.50 | 0.177059 | 0.0885296 | − | 0.996074i | \(-0.471783\pi\) | ||||
0.0885296 | + | 0.996074i | \(0.471783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12827.5 | 1.76643 | ||||||||
\(376\) | −2910.73 | −0.399227 | ||||||||
\(377\) | −103.738 | −0.0141718 | ||||||||
\(378\) | 26404.6 | 3.59288 | ||||||||
\(379\) | −4101.12 | −0.555832 | −0.277916 | − | 0.960605i | \(-0.589644\pi\) | ||||
−0.277916 | + | 0.960605i | \(0.589644\pi\) | |||||||
\(380\) | −567.287 | −0.0765822 | ||||||||
\(381\) | −5354.95 | −0.720059 | ||||||||
\(382\) | −16146.1 | −2.16258 | ||||||||
\(383\) | −10390.1 | −1.38619 | −0.693094 | − | 0.720848i | \(-0.743753\pi\) | ||||
−0.693094 | + | 0.720848i | \(0.743753\pi\) | |||||||
\(384\) | −9873.22 | −1.31209 | ||||||||
\(385\) | 3058.01 | 0.404807 | ||||||||
\(386\) | −3766.67 | −0.496679 | ||||||||
\(387\) | −17723.8 | −2.32804 | ||||||||
\(388\) | 7969.53 | 1.04276 | ||||||||
\(389\) | 6213.37 | 0.809846 | 0.404923 | − | 0.914351i | \(-0.367298\pi\) | ||||
0.404923 | + | 0.914351i | \(0.367298\pi\) | |||||||
\(390\) | 595.229 | 0.0772835 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 4028.27 | 0.519027 | ||||||||
\(393\) | −18346.8 | −2.35489 | ||||||||
\(394\) | 8115.93 | 1.03775 | ||||||||
\(395\) | 7027.54 | 0.895174 | ||||||||
\(396\) | 4701.08 | 0.596561 | ||||||||
\(397\) | −171.318 | −0.0216580 | −0.0108290 | − | 0.999941i | \(-0.503447\pi\) | ||||
−0.0108290 | + | 0.999941i | \(0.503447\pi\) | |||||||
\(398\) | 280.111 | 0.0352782 | ||||||||
\(399\) | −3662.78 | −0.459570 | ||||||||
\(400\) | 5793.39 | 0.724174 | ||||||||
\(401\) | −9328.60 | −1.16172 | −0.580858 | − | 0.814005i | \(-0.697283\pi\) | ||||
−0.580858 | + | 0.814005i | \(0.697283\pi\) | |||||||
\(402\) | −13108.6 | −1.62636 | ||||||||
\(403\) | −390.482 | −0.0482663 | ||||||||
\(404\) | 2279.70 | 0.280741 | ||||||||
\(405\) | −5787.14 | −0.710038 | ||||||||
\(406\) | −4283.44 | −0.523605 | ||||||||
\(407\) | 3453.89 | 0.420646 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6370.74 | −0.770202 | −0.385101 | − | 0.922874i | \(-0.625833\pi\) | ||||
−0.385101 | + | 0.922874i | \(0.625833\pi\) | |||||||
\(410\) | −6120.63 | −0.737260 | ||||||||
\(411\) | 5652.04 | 0.678332 | ||||||||
\(412\) | 9201.74 | 1.10033 | ||||||||
\(413\) | 6810.26 | 0.811406 | ||||||||
\(414\) | 36561.8 | 4.34037 | ||||||||
\(415\) | 701.152 | 0.0829354 | ||||||||
\(416\) | 538.837 | 0.0635064 | ||||||||
\(417\) | 9359.13 | 1.09909 | ||||||||
\(418\) | −809.014 | −0.0946655 | ||||||||
\(419\) | −8067.75 | −0.940657 | −0.470329 | − | 0.882491i | \(-0.655865\pi\) | ||||
−0.470329 | + | 0.882491i | \(0.655865\pi\) | |||||||
\(420\) | 10097.1 | 1.17306 | ||||||||
\(421\) | −6254.81 | −0.724088 | −0.362044 | − | 0.932161i | \(-0.617921\pi\) | ||||
−0.362044 | + | 0.932161i | \(0.617921\pi\) | |||||||
\(422\) | −7268.90 | −0.838494 | ||||||||
\(423\) | −17961.1 | −2.06453 | ||||||||
\(424\) | −510.054 | −0.0584208 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 20548.0 | 2.33698 | ||||||||
\(427\) | 12991.4 | 1.47236 | ||||||||
\(428\) | −11463.5 | −1.29464 | ||||||||
\(429\) | 348.734 | 0.0392472 | ||||||||
\(430\) | −8408.14 | −0.942969 | ||||||||
\(431\) | −5910.99 | −0.660609 | −0.330305 | − | 0.943874i | \(-0.607151\pi\) | ||||
−0.330305 | + | 0.943874i | \(0.607151\pi\) | |||||||
\(432\) | −19705.3 | −2.19461 | ||||||||
\(433\) | 11833.5 | 1.31335 | 0.656677 | − | 0.754172i | \(-0.271962\pi\) | ||||
0.656677 | + | 0.754172i | \(0.271962\pi\) | |||||||
\(434\) | −16123.4 | −1.78329 | ||||||||
\(435\) | 2648.58 | 0.291930 | ||||||||
\(436\) | 2482.71 | 0.272707 | ||||||||
\(437\) | −2584.90 | −0.282957 | ||||||||
\(438\) | −23281.7 | −2.53982 | ||||||||
\(439\) | −7520.94 | −0.817665 | −0.408833 | − | 0.912609i | \(-0.634064\pi\) | ||||
−0.408833 | + | 0.912609i | \(0.634064\pi\) | |||||||
\(440\) | −968.176 | −0.104900 | ||||||||
\(441\) | 24857.0 | 2.68406 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8478.34 | 0.909296 | 0.454648 | − | 0.890671i | \(-0.349765\pi\) | ||||
0.454648 | + | 0.890671i | \(0.349765\pi\) | |||||||
\(444\) | 11404.2 | 1.21896 | ||||||||
\(445\) | −4951.52 | −0.527471 | ||||||||
\(446\) | −4338.83 | −0.460649 | ||||||||
\(447\) | −2577.05 | −0.272685 | ||||||||
\(448\) | 4772.09 | 0.503259 | ||||||||
\(449\) | 1078.67 | 0.113375 | 0.0566877 | − | 0.998392i | \(-0.481946\pi\) | ||||
0.0566877 | + | 0.998392i | \(0.481946\pi\) | |||||||
\(450\) | 15166.1 | 1.58875 | ||||||||
\(451\) | −3585.97 | −0.374405 | ||||||||
\(452\) | −6839.15 | −0.711696 | ||||||||
\(453\) | 28565.1 | 2.96271 | ||||||||
\(454\) | −10485.1 | −1.08390 | ||||||||
\(455\) | 502.584 | 0.0517835 | ||||||||
\(456\) | 1159.65 | 0.119091 | ||||||||
\(457\) | 5664.74 | 0.579837 | 0.289918 | − | 0.957051i | \(-0.406372\pi\) | ||||
0.289918 | + | 0.957051i | \(0.406372\pi\) | |||||||
\(458\) | −13287.4 | −1.35563 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7125.70 | 0.722256 | ||||||||
\(461\) | 710.717 | 0.0718034 | 0.0359017 | − | 0.999355i | \(-0.488570\pi\) | ||||
0.0359017 | + | 0.999355i | \(0.488570\pi\) | |||||||
\(462\) | 14399.5 | 1.45006 | ||||||||
\(463\) | 8328.23 | 0.835952 | 0.417976 | − | 0.908458i | \(-0.362740\pi\) | ||||
0.417976 | + | 0.908458i | \(0.362740\pi\) | |||||||
\(464\) | 3196.66 | 0.319831 | ||||||||
\(465\) | 9969.56 | 0.994252 | ||||||||
\(466\) | 3077.62 | 0.305940 | ||||||||
\(467\) | −14132.8 | −1.40040 | −0.700201 | − | 0.713946i | \(-0.746906\pi\) | ||||
−0.700201 | + | 0.713946i | \(0.746906\pi\) | |||||||
\(468\) | 772.622 | 0.0763130 | ||||||||
\(469\) | −11068.3 | −1.08974 | ||||||||
\(470\) | −8520.69 | −0.836235 | ||||||||
\(471\) | −4369.44 | −0.427459 | ||||||||
\(472\) | −2156.15 | −0.210264 | ||||||||
\(473\) | −4926.18 | −0.478871 | ||||||||
\(474\) | 33091.2 | 3.20660 | ||||||||
\(475\) | −1072.24 | −0.103574 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3147.36 | −0.302113 | ||||||||
\(478\) | 14951.5 | 1.43068 | ||||||||
\(479\) | −6522.89 | −0.622210 | −0.311105 | − | 0.950376i | \(-0.600699\pi\) | ||||
−0.311105 | + | 0.950376i | \(0.600699\pi\) | |||||||
\(480\) | −13757.3 | −1.30819 | ||||||||
\(481\) | 567.646 | 0.0538096 | ||||||||
\(482\) | 7851.13 | 0.741928 | ||||||||
\(483\) | 46008.3 | 4.33426 | ||||||||
\(484\) | −6118.12 | −0.574579 | ||||||||
\(485\) | −10127.9 | −0.948216 | ||||||||
\(486\) | −1956.39 | −0.182600 | ||||||||
\(487\) | 2178.49 | 0.202704 | 0.101352 | − | 0.994851i | \(-0.467683\pi\) | ||||
0.101352 | + | 0.994851i | \(0.467683\pi\) | |||||||
\(488\) | −4113.11 | −0.381540 | ||||||||
\(489\) | 33675.6 | 3.11424 | ||||||||
\(490\) | 11792.1 | 1.08717 | ||||||||
\(491\) | −12618.8 | −1.15983 | −0.579915 | − | 0.814677i | \(-0.696914\pi\) | ||||
−0.579915 | + | 0.814677i | \(0.696914\pi\) | |||||||
\(492\) | −11840.3 | −1.08496 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −132.961 | −0.0121097 | ||||||||
\(495\) | −5974.27 | −0.542472 | ||||||||
\(496\) | 12032.6 | 1.08927 | ||||||||
\(497\) | 17349.8 | 1.56588 | ||||||||
\(498\) | 3301.58 | 0.297083 | ||||||||
\(499\) | −13762.8 | −1.23469 | −0.617343 | − | 0.786694i | \(-0.711791\pi\) | ||||
−0.617343 | + | 0.786694i | \(0.711791\pi\) | |||||||
\(500\) | 7898.95 | 0.706504 | ||||||||
\(501\) | −19285.8 | −1.71981 | ||||||||
\(502\) | −7974.69 | −0.709019 | ||||||||
\(503\) | −491.671 | −0.0435836 | −0.0217918 | − | 0.999763i | \(-0.506937\pi\) | ||||
−0.0217918 | + | 0.999763i | \(0.506937\pi\) | |||||||
\(504\) | −13849.5 | −1.22402 | ||||||||
\(505\) | −2897.11 | −0.255286 | ||||||||
\(506\) | 10162.0 | 0.892802 | ||||||||
\(507\) | −19845.2 | −1.73837 | ||||||||
\(508\) | −3297.48 | −0.287996 | ||||||||
\(509\) | 576.514 | 0.0502034 | 0.0251017 | − | 0.999685i | \(-0.492009\pi\) | ||||
0.0251017 | + | 0.999685i | \(0.492009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19658.0 | −1.70180 | ||||||||
\(512\) | −11070.9 | −0.955600 | ||||||||
\(513\) | 3647.05 | 0.313881 | ||||||||
\(514\) | −25762.1 | −2.21074 | ||||||||
\(515\) | −11693.8 | −1.00057 | ||||||||
\(516\) | −16265.5 | −1.38769 | ||||||||
\(517\) | −4992.12 | −0.424668 | ||||||||
\(518\) | 23438.6 | 1.98810 | ||||||||
\(519\) | 10851.4 | 0.917768 | ||||||||
\(520\) | −159.120 | −0.0134189 | ||||||||
\(521\) | −6102.95 | −0.513196 | −0.256598 | − | 0.966518i | \(-0.582602\pi\) | ||||
−0.256598 | + | 0.966518i | \(0.582602\pi\) | |||||||
\(522\) | 8368.33 | 0.701670 | ||||||||
\(523\) | 13593.3 | 1.13651 | 0.568255 | − | 0.822853i | \(-0.307619\pi\) | ||||
0.568255 | + | 0.822853i | \(0.307619\pi\) | |||||||
\(524\) | −11297.6 | −0.941864 | ||||||||
\(525\) | 19084.6 | 1.58651 | ||||||||
\(526\) | 11001.5 | 0.911951 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −10746.1 | −0.885731 | ||||||||
\(529\) | 20301.9 | 1.66860 | ||||||||
\(530\) | −1493.10 | −0.122370 | ||||||||
\(531\) | −13304.8 | −1.08735 | ||||||||
\(532\) | −2255.47 | −0.183810 | ||||||||
\(533\) | −589.354 | −0.0478944 | ||||||||
\(534\) | −23315.7 | −1.88945 | ||||||||
\(535\) | 14568.1 | 1.17726 | ||||||||
\(536\) | 3504.26 | 0.282390 | ||||||||
\(537\) | 37102.1 | 2.98151 | ||||||||
\(538\) | 14972.6 | 1.19984 | ||||||||
\(539\) | 6908.80 | 0.552103 | ||||||||
\(540\) | −10053.7 | −0.801190 | ||||||||
\(541\) | 20360.3 | 1.61803 | 0.809017 | − | 0.587786i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587786i | \(0.200000\pi\) | |||||||
\(542\) | −23199.4 | −1.83856 | ||||||||
\(543\) | −11750.2 | −0.928635 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3155.10 | −0.247981 | ||||||||
\(546\) | 2366.56 | 0.185494 | ||||||||
\(547\) | 253.860 | 0.0198433 | 0.00992164 | − | 0.999951i | \(-0.496842\pi\) | ||||
0.00992164 | + | 0.999951i | \(0.496842\pi\) | |||||||
\(548\) | 3480.42 | 0.271307 | ||||||||
\(549\) | −25380.5 | −1.97307 | ||||||||
\(550\) | 4215.29 | 0.326801 | ||||||||
\(551\) | −591.636 | −0.0457433 | ||||||||
\(552\) | −14566.4 | −1.12316 | ||||||||
\(553\) | 27940.7 | 2.14857 | ||||||||
\(554\) | 17356.2 | 1.33104 | ||||||||
\(555\) | −14492.8 | −1.10844 | ||||||||
\(556\) | 5763.17 | 0.439592 | ||||||||
\(557\) | 1519.94 | 0.115623 | 0.0578116 | − | 0.998328i | \(-0.481588\pi\) | ||||
0.0578116 | + | 0.998328i | \(0.481588\pi\) | |||||||
\(558\) | 31499.4 | 2.38974 | ||||||||
\(559\) | −809.617 | −0.0612579 | ||||||||
\(560\) | −15487.0 | −1.16865 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9058.40 | 0.679903 | ||||||||
\(563\) | −25112.9 | −1.87990 | −0.939948 | − | 0.341317i | \(-0.889127\pi\) | ||||
−0.939948 | + | 0.341317i | \(0.889127\pi\) | |||||||
\(564\) | −16483.2 | −1.23062 | ||||||||
\(565\) | 8691.39 | 0.647168 | ||||||||
\(566\) | 33918.2 | 2.51888 | ||||||||
\(567\) | −23009.0 | −1.70421 | ||||||||
\(568\) | −5492.99 | −0.405776 | ||||||||
\(569\) | 3649.16 | 0.268859 | 0.134430 | − | 0.990923i | \(-0.457080\pi\) | ||||
0.134430 | + | 0.990923i | \(0.457080\pi\) | |||||||
\(570\) | 3394.69 | 0.249452 | ||||||||
\(571\) | −4111.91 | −0.301362 | −0.150681 | − | 0.988582i | \(-0.548147\pi\) | ||||
−0.150681 | + | 0.988582i | \(0.548147\pi\) | |||||||
\(572\) | 214.744 | 0.0156974 | ||||||||
\(573\) | 39693.7 | 2.89394 | ||||||||
\(574\) | −24334.9 | −1.76955 | ||||||||
\(575\) | 13468.4 | 0.976817 | ||||||||
\(576\) | −9322.98 | −0.674405 | ||||||||
\(577\) | 25307.1 | 1.82591 | 0.912954 | − | 0.408062i | \(-0.133795\pi\) | ||||
0.912954 | + | 0.408062i | \(0.133795\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9260.01 | 0.664651 | ||||||||
\(580\) | 1630.94 | 0.116761 | ||||||||
\(581\) | 2787.70 | 0.199059 | ||||||||
\(582\) | −47690.3 | −3.39661 | ||||||||
\(583\) | −874.783 | −0.0621438 | ||||||||
\(584\) | 6223.78 | 0.440996 | ||||||||
\(585\) | −981.870 | −0.0693938 | ||||||||
\(586\) | −1558.74 | −0.109882 | ||||||||
\(587\) | 6734.14 | 0.473506 | 0.236753 | − | 0.971570i | \(-0.423917\pi\) | ||||
0.236753 | + | 0.971570i | \(0.423917\pi\) | |||||||
\(588\) | 22811.8 | 1.59990 | ||||||||
\(589\) | −2226.99 | −0.155792 | ||||||||
\(590\) | −6311.79 | −0.440427 | ||||||||
\(591\) | −19952.3 | −1.38871 | ||||||||
\(592\) | −17491.9 | −1.21438 | ||||||||
\(593\) | 885.596 | 0.0613273 | 0.0306636 | − | 0.999530i | \(-0.490238\pi\) | ||||
0.0306636 | + | 0.999530i | \(0.490238\pi\) | |||||||
\(594\) | −14337.7 | −0.990374 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1586.90 | −0.109064 | ||||||||
\(597\) | −688.629 | −0.0472089 | ||||||||
\(598\) | 1670.13 | 0.114208 | ||||||||
\(599\) | 7411.88 | 0.505578 | 0.252789 | − | 0.967521i | \(-0.418652\pi\) | ||||
0.252789 | + | 0.967521i | \(0.418652\pi\) | |||||||
\(600\) | −6042.24 | −0.411123 | ||||||||
\(601\) | −19232.0 | −1.30531 | −0.652653 | − | 0.757657i | \(-0.726344\pi\) | ||||
−0.652653 | + | 0.757657i | \(0.726344\pi\) | |||||||
\(602\) | −33429.8 | −2.26329 | ||||||||
\(603\) | 21623.6 | 1.46033 | ||||||||
\(604\) | 17589.9 | 1.18497 | ||||||||
\(605\) | 7775.08 | 0.522483 | ||||||||
\(606\) | −13641.9 | −0.914461 | ||||||||
\(607\) | 3485.07 | 0.233039 | 0.116519 | − | 0.993188i | \(-0.462826\pi\) | ||||
0.116519 | + | 0.993188i | \(0.462826\pi\) | |||||||
\(608\) | 3073.08 | 0.204983 | ||||||||
\(609\) | 10530.5 | 0.700682 | ||||||||
\(610\) | −12040.5 | −0.799188 | ||||||||
\(611\) | −820.455 | −0.0543241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27347.9 | −1.80191 | −0.900954 | − | 0.433915i | \(-0.857132\pi\) | ||||
−0.900954 | + | 0.433915i | \(0.857132\pi\) | |||||||
\(614\) | −2331.02 | −0.153212 | ||||||||
\(615\) | 15047.0 | 0.986592 | ||||||||
\(616\) | −3849.36 | −0.251778 | ||||||||
\(617\) | −12625.9 | −0.823822 | −0.411911 | − | 0.911224i | \(-0.635139\pi\) | ||||
−0.411911 | + | 0.911224i | \(0.635139\pi\) | |||||||
\(618\) | −55063.9 | −3.58413 | ||||||||
\(619\) | −16469.8 | −1.06943 | −0.534714 | − | 0.845033i | \(-0.679581\pi\) | ||||
−0.534714 | + | 0.845033i | \(0.679581\pi\) | |||||||
\(620\) | 6139.06 | 0.397662 | ||||||||
\(621\) | −45810.6 | −2.96025 | ||||||||
\(622\) | −19504.3 | −1.25732 | ||||||||
\(623\) | −19686.7 | −1.26602 | ||||||||
\(624\) | −1766.13 | −0.113304 | ||||||||
\(625\) | −695.113 | −0.0444872 | ||||||||
\(626\) | −14068.6 | −0.898235 | ||||||||
\(627\) | 1988.89 | 0.126680 | ||||||||
\(628\) | −2690.62 | −0.170967 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −40542.3 | −2.56388 | ||||||||
\(631\) | 6691.13 | 0.422139 | 0.211069 | − | 0.977471i | \(-0.432305\pi\) | ||||
0.211069 | + | 0.977471i | \(0.432305\pi\) | |||||||
\(632\) | −8846.11 | −0.556771 | ||||||||
\(633\) | 17869.9 | 1.12206 | ||||||||
\(634\) | −5120.28 | −0.320745 | ||||||||
\(635\) | 4190.53 | 0.261884 | ||||||||
\(636\) | −2888.40 | −0.180082 | ||||||||
\(637\) | 1135.46 | 0.0706258 | ||||||||
\(638\) | 2325.91 | 0.144332 | ||||||||
\(639\) | −33895.3 | −2.09840 | ||||||||
\(640\) | 7726.31 | 0.477202 | ||||||||
\(641\) | −14335.5 | −0.883335 | −0.441668 | − | 0.897179i | \(-0.645613\pi\) | ||||
−0.441668 | + | 0.897179i | \(0.645613\pi\) | |||||||
\(642\) | 68598.3 | 4.21707 | ||||||||
\(643\) | −30421.9 | −1.86582 | −0.932910 | − | 0.360109i | \(-0.882740\pi\) | ||||
−0.932910 | + | 0.360109i | \(0.882740\pi\) | |||||||
\(644\) | 28331.0 | 1.73354 | ||||||||
\(645\) | 20670.7 | 1.26187 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9221.00 | −0.560301 | −0.280151 | − | 0.959956i | \(-0.590384\pi\) | ||||
−0.280151 | + | 0.959956i | \(0.590384\pi\) | |||||||
\(648\) | 7284.73 | 0.441622 | ||||||||
\(649\) | −3697.96 | −0.223664 | ||||||||
\(650\) | 692.783 | 0.0418049 | ||||||||
\(651\) | 39637.8 | 2.38637 | ||||||||
\(652\) | 20736.8 | 1.24558 | ||||||||
\(653\) | 24958.5 | 1.49572 | 0.747858 | − | 0.663859i | \(-0.231082\pi\) | ||||
0.747858 | + | 0.663859i | \(0.231082\pi\) | |||||||
\(654\) | −14856.7 | −0.888293 | ||||||||
\(655\) | 14357.3 | 0.856467 | ||||||||
\(656\) | 18160.8 | 1.08088 | ||||||||
\(657\) | 38404.7 | 2.28054 | ||||||||
\(658\) | −33877.3 | −2.00711 | ||||||||
\(659\) | −3367.32 | −0.199047 | −0.0995236 | − | 0.995035i | \(-0.531732\pi\) | ||||
−0.0995236 | + | 0.995035i | \(0.531732\pi\) | |||||||
\(660\) | −5482.71 | −0.323355 | ||||||||
\(661\) | −6389.67 | −0.375990 | −0.187995 | − | 0.982170i | \(-0.560199\pi\) | ||||
−0.187995 | + | 0.982170i | \(0.560199\pi\) | |||||||
\(662\) | 21137.8 | 1.24100 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −882.595 | −0.0515833 | ||||||||
\(665\) | 2866.32 | 0.167144 | ||||||||
\(666\) | −45790.8 | −2.66420 | ||||||||
\(667\) | 7431.55 | 0.431410 | ||||||||
\(668\) | −11875.8 | −0.687859 | ||||||||
\(669\) | 10666.6 | 0.616436 | ||||||||
\(670\) | 10258.2 | 0.591504 | ||||||||
\(671\) | −7054.30 | −0.405854 | ||||||||
\(672\) | −54697.3 | −3.13987 | ||||||||
\(673\) | 27441.4 | 1.57175 | 0.785877 | − | 0.618383i | \(-0.212212\pi\) | ||||
0.785877 | + | 0.618383i | \(0.212212\pi\) | |||||||
\(674\) | −14730.2 | −0.841817 | ||||||||
\(675\) | −19002.6 | −1.08357 | ||||||||
\(676\) | −12220.3 | −0.695282 | ||||||||
\(677\) | 16931.5 | 0.961194 | 0.480597 | − | 0.876941i | \(-0.340420\pi\) | ||||
0.480597 | + | 0.876941i | \(0.340420\pi\) | |||||||
\(678\) | 40926.0 | 2.31822 | ||||||||
\(679\) | −40267.4 | −2.27588 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25776.7 | 1.45046 | ||||||||
\(682\) | 8754.98 | 0.491562 | ||||||||
\(683\) | −69.2829 | −0.00388146 | −0.00194073 | − | 0.999998i | \(-0.500618\pi\) | ||||
−0.00194073 | + | 0.999998i | \(0.500618\pi\) | |||||||
\(684\) | 4406.39 | 0.246320 | ||||||||
\(685\) | −4423.01 | −0.246708 | ||||||||
\(686\) | 11260.3 | 0.626705 | ||||||||
\(687\) | 32665.9 | 1.81409 | ||||||||
\(688\) | 24948.1 | 1.38247 | ||||||||
\(689\) | −143.770 | −0.00794952 | ||||||||
\(690\) | −42640.7 | −2.35262 | ||||||||
\(691\) | 1509.96 | 0.0831282 | 0.0415641 | − | 0.999136i | \(-0.486766\pi\) | ||||
0.0415641 | + | 0.999136i | \(0.486766\pi\) | |||||||
\(692\) | 6682.05 | 0.367072 | ||||||||
\(693\) | −23753.0 | −1.30202 | ||||||||
\(694\) | −9158.27 | −0.500927 | ||||||||
\(695\) | −7324.01 | −0.399734 | ||||||||
\(696\) | −3333.98 | −0.181572 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 35073.0 | 1.90191 | ||||||||
\(699\) | −7566.06 | −0.409406 | ||||||||
\(700\) | 11751.9 | 0.634544 | ||||||||
\(701\) | −16452.5 | −0.886449 | −0.443224 | − | 0.896411i | \(-0.646165\pi\) | ||||
−0.443224 | + | 0.896411i | \(0.646165\pi\) | |||||||
\(702\) | −2356.40 | −0.126690 | ||||||||
\(703\) | 3237.38 | 0.173684 | ||||||||
\(704\) | −2591.24 | −0.138723 | ||||||||
\(705\) | 20947.4 | 1.11904 | ||||||||
\(706\) | −643.045 | −0.0342795 | ||||||||
\(707\) | −11518.6 | −0.612730 | ||||||||
\(708\) | −12210.1 | −0.648141 | ||||||||
\(709\) | 4602.45 | 0.243792 | 0.121896 | − | 0.992543i | \(-0.461103\pi\) | ||||
0.121896 | + | 0.992543i | \(0.461103\pi\) | |||||||
\(710\) | −16079.9 | −0.849953 | ||||||||
\(711\) | −54586.2 | −2.87925 | ||||||||
\(712\) | 6232.87 | 0.328071 | ||||||||
\(713\) | 27973.2 | 1.46929 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −272.903 | −0.0142741 | ||||||||
\(716\) | 22846.7 | 1.19249 | ||||||||
\(717\) | −36756.8 | −1.91452 | ||||||||
\(718\) | 29894.9 | 1.55386 | ||||||||
\(719\) | 23515.7 | 1.21973 | 0.609865 | − | 0.792505i | \(-0.291224\pi\) | ||||
0.609865 | + | 0.792505i | \(0.291224\pi\) | |||||||
\(720\) | 30256.1 | 1.56608 | ||||||||
\(721\) | −46493.4 | −2.40153 | ||||||||
\(722\) | 24516.3 | 1.26371 | ||||||||
\(723\) | −19301.3 | −0.992839 | ||||||||
\(724\) | −7235.54 | −0.371418 | ||||||||
\(725\) | 3082.66 | 0.157914 | ||||||||
\(726\) | 36611.3 | 1.87159 | ||||||||
\(727\) | −8389.04 | −0.427968 | −0.213984 | − | 0.976837i | \(-0.568644\pi\) | ||||
−0.213984 | + | 0.976837i | \(0.568644\pi\) | |||||||
\(728\) | −632.641 | −0.0322078 | ||||||||
\(729\) | −17231.7 | −0.875462 | ||||||||
\(730\) | 18219.1 | 0.923727 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −23292.2 | −1.17610 | ||||||||
\(733\) | −7677.37 | −0.386863 | −0.193431 | − | 0.981114i | \(-0.561962\pi\) | ||||
−0.193431 | + | 0.981114i | \(0.561962\pi\) | |||||||
\(734\) | 151.605 | 0.00762374 | ||||||||
\(735\) | −28989.9 | −1.45484 | ||||||||
\(736\) | −38601.0 | −1.93322 | ||||||||
\(737\) | 6010.08 | 0.300386 | ||||||||
\(738\) | 47541.9 | 2.37133 | ||||||||
\(739\) | 26617.3 | 1.32494 | 0.662472 | − | 0.749087i | \(-0.269507\pi\) | ||||
0.662472 | + | 0.749087i | \(0.269507\pi\) | |||||||
\(740\) | −8924.39 | −0.443334 | ||||||||
\(741\) | 326.873 | 0.0162051 | ||||||||
\(742\) | −5936.41 | −0.293710 | ||||||||
\(743\) | 20951.6 | 1.03451 | 0.517253 | − | 0.855832i | \(-0.326954\pi\) | ||||
0.517253 | + | 0.855832i | \(0.326954\pi\) | |||||||
\(744\) | −12549.5 | −0.618395 | ||||||||
\(745\) | 2016.68 | 0.0991750 | ||||||||
\(746\) | −4700.07 | −0.230673 | ||||||||
\(747\) | −5446.18 | −0.266754 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 57921.2 | 2.82563 | ||||||||
\(750\) | −47267.9 | −2.30131 | ||||||||
\(751\) | 8252.35 | 0.400975 | 0.200488 | − | 0.979696i | \(-0.435747\pi\) | ||||
0.200488 | + | 0.979696i | \(0.435747\pi\) | |||||||
\(752\) | 25282.1 | 1.22599 | ||||||||
\(753\) | 19605.0 | 0.948801 | ||||||||
\(754\) | 382.262 | 0.0184631 | ||||||||
\(755\) | −22353.7 | −1.07753 | ||||||||
\(756\) | −39972.4 | −1.92299 | ||||||||
\(757\) | −21203.1 | −1.01802 | −0.509010 | − | 0.860760i | \(-0.669988\pi\) | ||||
−0.509010 | + | 0.860760i | \(0.669988\pi\) | |||||||
\(758\) | 15112.1 | 0.724139 | ||||||||
\(759\) | −24982.4 | −1.19474 | ||||||||
\(760\) | −907.485 | −0.0433131 | ||||||||
\(761\) | 29378.2 | 1.39942 | 0.699711 | − | 0.714426i | \(-0.253312\pi\) | ||||
0.699711 | + | 0.714426i | \(0.253312\pi\) | |||||||
\(762\) | 19732.3 | 0.938094 | ||||||||
\(763\) | −12544.3 | −0.595196 | ||||||||
\(764\) | 24442.6 | 1.15746 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38286.3 | 1.80593 | ||||||||
\(767\) | −607.760 | −0.0286114 | ||||||||
\(768\) | 48651.8 | 2.28590 | ||||||||
\(769\) | −16559.6 | −0.776532 | −0.388266 | − | 0.921547i | \(-0.626926\pi\) | ||||
−0.388266 | + | 0.921547i | \(0.626926\pi\) | |||||||
\(770\) | −11268.4 | −0.527383 | ||||||||
\(771\) | 63333.9 | 2.95838 | ||||||||
\(772\) | 5702.13 | 0.265835 | ||||||||
\(773\) | −39537.3 | −1.83966 | −0.919830 | − | 0.392317i | \(-0.871673\pi\) | ||||
−0.919830 | + | 0.392317i | \(0.871673\pi\) | |||||||
\(774\) | 65310.1 | 3.03297 | ||||||||
\(775\) | 11603.5 | 0.537820 | ||||||||
\(776\) | 12748.8 | 0.589762 | ||||||||
\(777\) | −57621.7 | −2.66045 | ||||||||
\(778\) | −22895.5 | −1.05507 | ||||||||
\(779\) | −3361.18 | −0.154592 | ||||||||
\(780\) | −901.082 | −0.0413640 | ||||||||
\(781\) | −9420.91 | −0.431634 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10485.2 | −0.478558 | ||||||||
\(784\) | −34988.9 | −1.59388 | ||||||||
\(785\) | 3419.32 | 0.155466 | ||||||||
\(786\) | 67605.5 | 3.06795 | ||||||||
\(787\) | 17801.2 | 0.806280 | 0.403140 | − | 0.915138i | \(-0.367919\pi\) | ||||
0.403140 | + | 0.915138i | \(0.367919\pi\) | |||||||
\(788\) | −12286.2 | −0.555430 | ||||||||
\(789\) | −27046.1 | −1.22036 | ||||||||
\(790\) | −25895.6 | −1.16623 | ||||||||
\(791\) | 34556.0 | 1.55331 | ||||||||
\(792\) | 7520.28 | 0.337401 | ||||||||
\(793\) | −1159.37 | −0.0519175 | ||||||||
\(794\) | 631.287 | 0.0282161 | ||||||||
\(795\) | 3670.66 | 0.163755 | ||||||||
\(796\) | −424.044 | −0.0188817 | ||||||||
\(797\) | 34006.4 | 1.51138 | 0.755688 | − | 0.654932i | \(-0.227303\pi\) | ||||
0.755688 | + | 0.654932i | \(0.227303\pi\) | |||||||
\(798\) | 13496.9 | 0.598728 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −16012.0 | −0.707636 | ||||||||
\(801\) | 38460.8 | 1.69656 | ||||||||
\(802\) | 34374.7 | 1.51348 | ||||||||
\(803\) | 10674.3 | 0.469099 | ||||||||
\(804\) | 19844.4 | 0.870469 | ||||||||
\(805\) | −36003.8 | −1.57636 | ||||||||
\(806\) | 1438.88 | 0.0628813 | ||||||||
\(807\) | −36808.7 | −1.60561 | ||||||||
\(808\) | 3646.81 | 0.158780 | ||||||||
\(809\) | −7943.98 | −0.345235 | −0.172618 | − | 0.984989i | \(-0.555223\pi\) | ||||
−0.172618 | + | 0.984989i | \(0.555223\pi\) | |||||||
\(810\) | 21324.9 | 0.925038 | ||||||||
\(811\) | 29182.7 | 1.26355 | 0.631777 | − | 0.775150i | \(-0.282326\pi\) | ||||
0.631777 | + | 0.775150i | \(0.282326\pi\) | |||||||
\(812\) | 6484.45 | 0.280246 | ||||||||
\(813\) | 57033.7 | 2.46034 | ||||||||
\(814\) | −12727.2 | −0.548018 | ||||||||
\(815\) | −26352.9 | −1.13264 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4617.38 | −0.197726 | ||||||||
\(818\) | 23475.4 | 1.00342 | ||||||||
\(819\) | −3903.81 | −0.166557 | ||||||||
\(820\) | 9265.66 | 0.394599 | ||||||||
\(821\) | −29589.4 | −1.25783 | −0.628913 | − | 0.777475i | \(-0.716500\pi\) | ||||
−0.628913 | + | 0.777475i | \(0.716500\pi\) | |||||||
\(822\) | −20827.1 | −0.883732 | ||||||||
\(823\) | 11121.5 | 0.471046 | 0.235523 | − | 0.971869i | \(-0.424320\pi\) | ||||
0.235523 | + | 0.971869i | \(0.424320\pi\) | |||||||
\(824\) | 14720.0 | 0.622323 | ||||||||
\(825\) | −10362.9 | −0.437322 | ||||||||
\(826\) | −25095.0 | −1.05710 | ||||||||
\(827\) | 12401.7 | 0.521461 | 0.260730 | − | 0.965412i | \(-0.416037\pi\) | ||||
0.260730 | + | 0.965412i | \(0.416037\pi\) | |||||||
\(828\) | −55348.7 | −2.32307 | ||||||||
\(829\) | −6224.06 | −0.260761 | −0.130380 | − | 0.991464i | \(-0.541620\pi\) | ||||
−0.130380 | + | 0.991464i | \(0.541620\pi\) | |||||||
\(830\) | −2583.66 | −0.108048 | ||||||||
\(831\) | −42668.8 | −1.78118 | ||||||||
\(832\) | −425.870 | −0.0177457 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −34487.3 | −1.43189 | ||||||||
\(835\) | 15092.1 | 0.625491 | ||||||||
\(836\) | 1224.72 | 0.0506672 | ||||||||
\(837\) | −39467.6 | −1.62987 | ||||||||
\(838\) | 29728.7 | 1.22549 | ||||||||
\(839\) | −36811.6 | −1.51475 | −0.757377 | − | 0.652978i | \(-0.773519\pi\) | ||||
−0.757377 | + | 0.652978i | \(0.773519\pi\) | |||||||
\(840\) | 16152.2 | 0.663458 | ||||||||
\(841\) | −22688.1 | −0.930258 | ||||||||
\(842\) | 23048.2 | 0.943342 | ||||||||
\(843\) | −22269.3 | −0.909839 | ||||||||
\(844\) | 11004.0 | 0.448782 | ||||||||
\(845\) | 15529.9 | 0.632241 | ||||||||
\(846\) | 66184.3 | 2.68967 | ||||||||
\(847\) | 30912.8 | 1.25405 | ||||||||
\(848\) | 4430.25 | 0.179405 | ||||||||
\(849\) | −83384.8 | −3.37074 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40664.8 | −1.63804 | ||||||||
\(852\) | −31106.4 | −1.25081 | ||||||||
\(853\) | −3319.10 | −0.133228 | −0.0666141 | − | 0.997779i | \(-0.521220\pi\) | ||||
−0.0666141 | + | 0.997779i | \(0.521220\pi\) | |||||||
\(854\) | −47871.6 | −1.91819 | ||||||||
\(855\) | −5599.77 | −0.223986 | ||||||||
\(856\) | −18338.0 | −0.732221 | ||||||||
\(857\) | 8084.66 | 0.322248 | 0.161124 | − | 0.986934i | \(-0.448488\pi\) | ||||
0.161124 | + | 0.986934i | \(0.448488\pi\) | |||||||
\(858\) | −1285.04 | −0.0511313 | ||||||||
\(859\) | −23619.8 | −0.938181 | −0.469091 | − | 0.883150i | \(-0.655418\pi\) | ||||
−0.469091 | + | 0.883150i | \(0.655418\pi\) | |||||||
\(860\) | 12728.6 | 0.504699 | ||||||||
\(861\) | 59825.3 | 2.36799 | ||||||||
\(862\) | 21781.3 | 0.860642 | ||||||||
\(863\) | −34938.3 | −1.37812 | −0.689058 | − | 0.724706i | \(-0.741975\pi\) | ||||
−0.689058 | + | 0.724706i | \(0.741975\pi\) | |||||||
\(864\) | 54462.4 | 2.14450 | ||||||||
\(865\) | −8491.75 | −0.333790 | ||||||||
\(866\) | −43605.0 | −1.71104 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24408.2 | 0.954457 | ||||||||
\(869\) | −15171.8 | −0.592252 | ||||||||
\(870\) | −9759.69 | −0.380327 | ||||||||
\(871\) | 987.756 | 0.0384258 | ||||||||
\(872\) | 3971.57 | 0.154237 | ||||||||
\(873\) | 78668.3 | 3.04985 | ||||||||
\(874\) | 9525.02 | 0.368637 | ||||||||
\(875\) | −39910.8 | −1.54198 | ||||||||
\(876\) | 35244.8 | 1.35937 | ||||||||
\(877\) | −20700.0 | −0.797022 | −0.398511 | − | 0.917164i | \(-0.630473\pi\) | ||||
−0.398511 | + | 0.917164i | \(0.630473\pi\) | |||||||
\(878\) | 27713.8 | 1.06525 | ||||||||
\(879\) | 3832.02 | 0.147043 | ||||||||
\(880\) | 8409.42 | 0.322138 | ||||||||
\(881\) | 5183.11 | 0.198211 | 0.0991053 | − | 0.995077i | \(-0.468402\pi\) | ||||
0.0991053 | + | 0.995077i | \(0.468402\pi\) | |||||||
\(882\) | −91595.2 | −3.49679 | ||||||||
\(883\) | 7357.34 | 0.280401 | 0.140201 | − | 0.990123i | \(-0.455225\pi\) | ||||
0.140201 | + | 0.990123i | \(0.455225\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15517.0 | 0.589375 | ||||||||
\(886\) | −31241.6 | −1.18463 | ||||||||
\(887\) | 35702.2 | 1.35148 | 0.675740 | − | 0.737140i | \(-0.263824\pi\) | ||||
0.675740 | + | 0.737140i | \(0.263824\pi\) | |||||||
\(888\) | 18243.2 | 0.689417 | ||||||||
\(889\) | 16661.1 | 0.628565 | ||||||||
\(890\) | 18245.7 | 0.687189 | ||||||||
\(891\) | 12493.9 | 0.469765 | ||||||||
\(892\) | 6568.30 | 0.246550 | ||||||||
\(893\) | −4679.19 | −0.175345 | ||||||||
\(894\) | 9496.12 | 0.355255 | ||||||||
\(895\) | −29034.3 | −1.08437 | ||||||||
\(896\) | 30718.9 | 1.14537 | ||||||||
\(897\) | −4105.86 | −0.152832 | ||||||||
\(898\) | −3974.77 | −0.147706 | ||||||||
\(899\) | 6402.56 | 0.237528 | ||||||||
\(900\) | −22959.1 | −0.850337 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 13213.9 | 0.487775 | ||||||||
\(903\) | 82184.2 | 3.02870 | ||||||||
\(904\) | −10940.5 | −0.402519 | ||||||||
\(905\) | 9195.14 | 0.337742 | ||||||||
\(906\) | −105259. | −3.85982 | ||||||||
\(907\) | 5660.56 | 0.207228 | 0.103614 | − | 0.994618i | \(-0.466959\pi\) | ||||
0.103614 | + | 0.994618i | \(0.466959\pi\) | |||||||
\(908\) | 15872.8 | 0.580128 | ||||||||
\(909\) | 22503.2 | 0.821105 | ||||||||
\(910\) | −1851.96 | −0.0674636 | ||||||||
\(911\) | 11754.9 | 0.427506 | 0.213753 | − | 0.976888i | \(-0.431431\pi\) | ||||
0.213753 | + | 0.976888i | \(0.431431\pi\) | |||||||
\(912\) | −10072.5 | −0.365718 | ||||||||
\(913\) | −1513.72 | −0.0548705 | ||||||||
\(914\) | −20873.9 | −0.755412 | ||||||||
\(915\) | 29600.4 | 1.06946 | ||||||||
\(916\) | 20115.0 | 0.725567 | ||||||||
\(917\) | 57083.0 | 2.05567 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4513.88 | 0.162023 | 0.0810116 | − | 0.996713i | \(-0.474185\pi\) | ||||
0.0810116 | + | 0.996713i | \(0.474185\pi\) | |||||||
\(920\) | 11398.9 | 0.408491 | ||||||||
\(921\) | 5730.59 | 0.205027 | ||||||||
\(922\) | −2618.90 | −0.0935455 | ||||||||
\(923\) | −1548.32 | −0.0552153 | ||||||||
\(924\) | −21798.6 | −0.776106 | ||||||||
\(925\) | −16868.1 | −0.599588 | ||||||||
\(926\) | −30688.5 | −1.08908 | ||||||||
\(927\) | 90831.6 | 3.21823 | ||||||||
\(928\) | −8835.06 | −0.312527 | ||||||||
\(929\) | 15124.4 | 0.534138 | 0.267069 | − | 0.963677i | \(-0.413945\pi\) | ||||
0.267069 | + | 0.963677i | \(0.413945\pi\) | |||||||
\(930\) | −36736.6 | −1.29531 | ||||||||
\(931\) | 6475.72 | 0.227963 | ||||||||
\(932\) | −4659.03 | −0.163746 | ||||||||
\(933\) | 47949.6 | 1.68253 | ||||||||
\(934\) | 52077.6 | 1.82444 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1235.96 | 0.0431608 | ||||||||
\(937\) | −19918.8 | −0.694470 | −0.347235 | − | 0.937778i | \(-0.612879\pi\) | ||||
−0.347235 | + | 0.937778i | \(0.612879\pi\) | |||||||
\(938\) | 40785.4 | 1.41971 | ||||||||
\(939\) | 34586.4 | 1.20201 | ||||||||
\(940\) | 12899.0 | 0.447573 | ||||||||
\(941\) | −2072.11 | −0.0717843 | −0.0358921 | − | 0.999356i | \(-0.511427\pi\) | ||||
−0.0358921 | + | 0.999356i | \(0.511427\pi\) | |||||||
\(942\) | 16100.9 | 0.556894 | ||||||||
\(943\) | 42219.8 | 1.45797 | ||||||||
\(944\) | 18728.0 | 0.645703 | ||||||||
\(945\) | 50798.1 | 1.74864 | ||||||||
\(946\) | 18152.4 | 0.623874 | ||||||||
\(947\) | 5522.83 | 0.189512 | 0.0947560 | − | 0.995501i | \(-0.469793\pi\) | ||||
0.0947560 | + | 0.995501i | \(0.469793\pi\) | |||||||
\(948\) | −50094.9 | −1.71625 | ||||||||
\(949\) | 1754.31 | 0.0600079 | ||||||||
\(950\) | 3951.06 | 0.134936 | ||||||||
\(951\) | 12587.8 | 0.429217 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39192.3 | −1.33218 | −0.666089 | − | 0.745873i | \(-0.732033\pi\) | ||||
−0.666089 | + | 0.745873i | \(0.732033\pi\) | |||||||
\(954\) | 11597.6 | 0.393593 | ||||||||
\(955\) | −31062.4 | −1.05252 | ||||||||
\(956\) | −22634.1 | −0.765733 | ||||||||
\(957\) | −5718.03 | −0.193143 | ||||||||
\(958\) | 24036.1 | 0.810616 | ||||||||
\(959\) | −17585.4 | −0.592140 | ||||||||
\(960\) | 10873.1 | 0.365549 | ||||||||
\(961\) | −5691.04 | −0.191032 | ||||||||
\(962\) | −2091.71 | −0.0701033 | ||||||||
\(963\) | −113158. | −3.78655 | ||||||||
\(964\) | −11885.4 | −0.397097 | ||||||||
\(965\) | −7246.44 | −0.241732 | ||||||||
\(966\) | −169535. | −5.64668 | ||||||||
\(967\) | 53414.4 | 1.77631 | 0.888155 | − | 0.459543i | \(-0.151987\pi\) | ||||
0.888155 | + | 0.459543i | \(0.151987\pi\) | |||||||
\(968\) | −9787.11 | −0.324968 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 37320.1 | 1.23534 | ||||||||
\(971\) | −39644.8 | −1.31026 | −0.655130 | − | 0.755516i | \(-0.727386\pi\) | ||||
−0.655130 | + | 0.755516i | \(0.727386\pi\) | |||||||
\(972\) | 2961.66 | 0.0977317 | ||||||||
\(973\) | −29119.4 | −0.959431 | ||||||||
\(974\) | −8027.47 | −0.264083 | ||||||||
\(975\) | −1703.14 | −0.0559428 | ||||||||
\(976\) | 35725.8 | 1.17167 | ||||||||
\(977\) | 40232.8 | 1.31746 | 0.658732 | − | 0.752378i | \(-0.271093\pi\) | ||||
0.658732 | + | 0.752378i | \(0.271093\pi\) | |||||||
\(978\) | −124090. | −4.05723 | ||||||||
\(979\) | 10689.9 | 0.348978 | ||||||||
\(980\) | −17851.4 | −0.581880 | ||||||||
\(981\) | 24507.2 | 0.797608 | ||||||||
\(982\) | 46498.6 | 1.51103 | ||||||||
\(983\) | 40449.2 | 1.31244 | 0.656220 | − | 0.754569i | \(-0.272154\pi\) | ||||
0.656220 | + | 0.754569i | \(0.272154\pi\) | |||||||
\(984\) | −18940.9 | −0.613631 | ||||||||
\(985\) | 15613.7 | 0.505070 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 83284.3 | 2.68589 | ||||||||
\(988\) | 201.282 | 0.00648142 | ||||||||
\(989\) | 57999.0 | 1.86477 | ||||||||
\(990\) | 22014.5 | 0.706733 | ||||||||
\(991\) | −41635.0 | −1.33459 | −0.667296 | − | 0.744793i | \(-0.732548\pi\) | ||||
−0.667296 | + | 0.744793i | \(0.732548\pi\) | |||||||
\(992\) | −33256.2 | −1.06440 | ||||||||
\(993\) | −51965.4 | −1.66070 | ||||||||
\(994\) | −63931.7 | −2.04003 | ||||||||
\(995\) | 538.888 | 0.0171697 | ||||||||
\(996\) | −4998.07 | −0.159006 | ||||||||
\(997\) | −33986.6 | −1.07960 | −0.539802 | − | 0.841792i | \(-0.681501\pi\) | ||||
−0.539802 | + | 0.841792i | \(0.681501\pi\) | |||||||
\(998\) | 50714.3 | 1.60855 | ||||||||
\(999\) | 57374.2 | 1.81706 |
(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.d.1.1 | yes | 4 | |
17.4 | even | 4 | 289.4.b.d.288.7 | 8 | |||
17.13 | even | 4 | 289.4.b.d.288.8 | 8 | |||
17.16 | even | 2 | 289.4.a.c.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.c.1.1 | ✓ | 4 | 17.16 | even | 2 | ||
289.4.a.d.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
289.4.b.d.288.7 | 8 | 17.4 | even | 4 | |||
289.4.b.d.288.8 | 8 | 17.13 | even | 4 |