Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
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([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.10 | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.f.288.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.26162 | −0.446051 | −0.223026 | − | 0.974813i | \(-0.571593\pi\) | ||||
−0.223026 | + | 0.974813i | \(0.571593\pi\) | |||||||
\(3\) | − 6.09538i | − 1.17306i | −0.809929 | − | 0.586528i | \(-0.800494\pi\) | ||||
0.809929 | − | 0.586528i | \(-0.199506\pi\) | |||||||
\(4\) | −6.40830 | −0.801038 | ||||||||
\(5\) | 13.2627i | 1.18625i | 0.805111 | + | 0.593124i | \(0.202106\pi\) | ||||
−0.805111 | + | 0.593124i | \(0.797894\pi\) | |||||||
\(6\) | 7.69007i | 0.523243i | ||||||||
\(7\) | 27.2593i | 1.47186i | 0.677055 | + | 0.735932i | \(0.263256\pi\) | ||||
−0.677055 | + | 0.735932i | \(0.736744\pi\) | |||||||
\(8\) | 18.1779 | 0.803356 | ||||||||
\(9\) | −10.1536 | −0.376059 | ||||||||
\(10\) | − 16.7325i | − 0.529128i | ||||||||
\(11\) | − 45.5149i | − 1.24757i | −0.781596 | − | 0.623785i | \(-0.785594\pi\) | ||||
0.781596 | − | 0.623785i | \(-0.214406\pi\) | |||||||
\(12\) | 39.0610i | 0.939662i | ||||||||
\(13\) | −52.5379 | −1.12088 | −0.560438 | − | 0.828196i | \(-0.689367\pi\) | ||||
−0.560438 | + | 0.828196i | \(0.689367\pi\) | |||||||
\(14\) | − 34.3910i | − 0.656527i | ||||||||
\(15\) | 80.8409 | 1.39153 | ||||||||
\(16\) | 28.3328 | 0.442700 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 12.8100 | 0.167742 | ||||||||
\(19\) | −3.08418 | −0.0372400 | −0.0186200 | − | 0.999827i | \(-0.505927\pi\) | ||||
−0.0186200 | + | 0.999827i | \(0.505927\pi\) | |||||||
\(20\) | − 84.9911i | − 0.950230i | ||||||||
\(21\) | 166.156 | 1.72658 | ||||||||
\(22\) | 57.4227i | 0.556480i | ||||||||
\(23\) | − 112.369i | − 1.01872i | −0.860554 | − | 0.509359i | \(-0.829882\pi\) | ||||
0.860554 | − | 0.509359i | \(-0.170118\pi\) | |||||||
\(24\) | − 110.801i | − 0.942381i | ||||||||
\(25\) | −50.8981 | −0.407185 | ||||||||
\(26\) | 66.2831 | 0.499968 | ||||||||
\(27\) | − 102.685i | − 0.731917i | ||||||||
\(28\) | − 174.686i | − 1.17902i | ||||||||
\(29\) | − 18.6294i | − 0.119290i | −0.998220 | − | 0.0596448i | \(-0.981003\pi\) | ||||
0.998220 | − | 0.0596448i | \(-0.0189968\pi\) | |||||||
\(30\) | −101.991 | −0.620696 | ||||||||
\(31\) | 238.763i | 1.38333i | 0.722219 | + | 0.691664i | \(0.243122\pi\) | ||||
−0.722219 | + | 0.691664i | \(0.756878\pi\) | |||||||
\(32\) | −181.168 | −1.00082 | ||||||||
\(33\) | −277.430 | −1.46347 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −361.531 | −1.74600 | ||||||||
\(36\) | 65.0674 | 0.301238 | ||||||||
\(37\) | − 162.717i | − 0.722986i | −0.932375 | − | 0.361493i | \(-0.882267\pi\) | ||||
0.932375 | − | 0.361493i | \(-0.117733\pi\) | |||||||
\(38\) | 3.89108 | 0.0166110 | ||||||||
\(39\) | 320.238i | 1.31485i | ||||||||
\(40\) | 241.087i | 0.952979i | ||||||||
\(41\) | − 383.816i | − 1.46200i | −0.682378 | − | 0.730999i | \(-0.739054\pi\) | ||||
0.682378 | − | 0.730999i | \(-0.260946\pi\) | |||||||
\(42\) | −209.626 | −0.770143 | ||||||||
\(43\) | −468.761 | −1.66245 | −0.831226 | − | 0.555935i | \(-0.812360\pi\) | ||||
−0.831226 | + | 0.555935i | \(0.812360\pi\) | |||||||
\(44\) | 291.673i | 0.999350i | ||||||||
\(45\) | − 134.664i | − 0.446100i | ||||||||
\(46\) | 141.767i | 0.454401i | ||||||||
\(47\) | −199.727 | −0.619856 | −0.309928 | − | 0.950760i | \(-0.600305\pi\) | ||||
−0.309928 | + | 0.950760i | \(0.600305\pi\) | |||||||
\(48\) | − 172.699i | − 0.519312i | ||||||||
\(49\) | −400.071 | −1.16639 | ||||||||
\(50\) | 64.2142 | 0.181625 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 336.679 | 0.897864 | ||||||||
\(53\) | 105.679 | 0.273889 | 0.136944 | − | 0.990579i | \(-0.456272\pi\) | ||||
0.136944 | + | 0.990579i | \(0.456272\pi\) | |||||||
\(54\) | 129.550i | 0.326473i | ||||||||
\(55\) | 603.649 | 1.47993 | ||||||||
\(56\) | 495.516i | 1.18243i | ||||||||
\(57\) | 18.7993i | 0.0436846i | ||||||||
\(58\) | 23.5033i | 0.0532093i | ||||||||
\(59\) | −207.142 | −0.457078 | −0.228539 | − | 0.973535i | \(-0.573395\pi\) | ||||
−0.228539 | + | 0.973535i | \(0.573395\pi\) | |||||||
\(60\) | −518.053 | −1.11467 | ||||||||
\(61\) | − 586.101i | − 1.23021i | −0.788447 | − | 0.615103i | \(-0.789114\pi\) | ||||
0.788447 | − | 0.615103i | \(-0.210886\pi\) | |||||||
\(62\) | − 301.230i | − 0.617036i | ||||||||
\(63\) | − 276.780i | − 0.553508i | ||||||||
\(64\) | 1.90375 | 0.00371826 | ||||||||
\(65\) | − 696.792i | − 1.32964i | ||||||||
\(66\) | 350.013 | 0.652782 | ||||||||
\(67\) | 401.953 | 0.732931 | 0.366466 | − | 0.930432i | \(-0.380568\pi\) | ||||
0.366466 | + | 0.930432i | \(0.380568\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −684.930 | −1.19501 | ||||||||
\(70\) | 456.116 | 0.778805 | ||||||||
\(71\) | − 481.559i | − 0.804937i | −0.915434 | − | 0.402468i | \(-0.868152\pi\) | ||||
0.915434 | − | 0.402468i | \(-0.131848\pi\) | |||||||
\(72\) | −184.571 | −0.302109 | ||||||||
\(73\) | − 725.281i | − 1.16285i | −0.813602 | − | 0.581423i | \(-0.802496\pi\) | ||||
0.813602 | − | 0.581423i | \(-0.197504\pi\) | |||||||
\(74\) | 205.287i | 0.322489i | ||||||||
\(75\) | 310.243i | 0.477650i | ||||||||
\(76\) | 19.7644 | 0.0298307 | ||||||||
\(77\) | 1240.71 | 1.83625 | ||||||||
\(78\) | − 404.020i | − 0.586491i | ||||||||
\(79\) | 382.621i | 0.544914i | 0.962168 | + | 0.272457i | \(0.0878363\pi\) | ||||
−0.962168 | + | 0.272457i | \(0.912164\pi\) | |||||||
\(80\) | 375.768i | 0.525152i | ||||||||
\(81\) | −900.052 | −1.23464 | ||||||||
\(82\) | 484.231i | 0.652127i | ||||||||
\(83\) | 182.391 | 0.241204 | 0.120602 | − | 0.992701i | \(-0.461517\pi\) | ||||
0.120602 | + | 0.992701i | \(0.461517\pi\) | |||||||
\(84\) | −1064.78 | −1.38306 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 591.401 | 0.741539 | ||||||||
\(87\) | −113.553 | −0.139933 | ||||||||
\(88\) | − 827.364i | − 1.00224i | ||||||||
\(89\) | −623.009 | −0.742010 | −0.371005 | − | 0.928631i | \(-0.620987\pi\) | ||||
−0.371005 | + | 0.928631i | \(0.620987\pi\) | |||||||
\(90\) | 169.895i | 0.198983i | ||||||||
\(91\) | − 1432.15i | − 1.64978i | ||||||||
\(92\) | 720.094i | 0.816032i | ||||||||
\(93\) | 1455.35 | 1.62272 | ||||||||
\(94\) | 251.981 | 0.276488 | ||||||||
\(95\) | − 40.9045i | − 0.0441759i | ||||||||
\(96\) | 1104.29i | 1.17402i | ||||||||
\(97\) | − 369.544i | − 0.386820i | −0.981118 | − | 0.193410i | \(-0.938045\pi\) | ||||
0.981118 | − | 0.193410i | \(-0.0619547\pi\) | |||||||
\(98\) | 504.739 | 0.520268 | ||||||||
\(99\) | 462.140i | 0.469160i | ||||||||
\(100\) | 326.170 | 0.326170 | ||||||||
\(101\) | 810.381 | 0.798375 | 0.399188 | − | 0.916869i | \(-0.369292\pi\) | ||||
0.399188 | + | 0.916869i | \(0.369292\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 772.683 | 0.739172 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(104\) | −955.026 | −0.900462 | ||||||||
\(105\) | 2203.67i | 2.04815i | ||||||||
\(106\) | −133.327 | −0.122169 | ||||||||
\(107\) | − 996.966i | − 0.900751i | −0.892839 | − | 0.450375i | \(-0.851290\pi\) | ||||
0.892839 | − | 0.450375i | \(-0.148710\pi\) | |||||||
\(108\) | 658.038i | 0.586293i | ||||||||
\(109\) | − 700.996i | − 0.615993i | −0.951388 | − | 0.307996i | \(-0.900342\pi\) | ||||
0.951388 | − | 0.307996i | \(-0.0996585\pi\) | |||||||
\(110\) | −761.578 | −0.660123 | ||||||||
\(111\) | −991.820 | −0.848102 | ||||||||
\(112\) | 772.333i | 0.651595i | ||||||||
\(113\) | − 1459.26i | − 1.21483i | −0.794384 | − | 0.607415i | \(-0.792206\pi\) | ||||
0.794384 | − | 0.607415i | \(-0.207794\pi\) | |||||||
\(114\) | − 23.7176i | − 0.0194856i | ||||||||
\(115\) | 1490.31 | 1.20845 | ||||||||
\(116\) | 119.383i | 0.0955554i | ||||||||
\(117\) | 533.449 | 0.421516 | ||||||||
\(118\) | 261.335 | 0.203880 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1469.51 | 1.11790 | ||||||||
\(121\) | −740.607 | −0.556429 | ||||||||
\(122\) | 739.439i | 0.548735i | ||||||||
\(123\) | −2339.50 | −1.71501 | ||||||||
\(124\) | − 1530.07i | − 1.10810i | ||||||||
\(125\) | 982.788i | 0.703226i | ||||||||
\(126\) | 349.193i | 0.246893i | ||||||||
\(127\) | −426.418 | −0.297941 | −0.148970 | − | 0.988842i | \(-0.547596\pi\) | ||||
−0.148970 | + | 0.988842i | \(0.547596\pi\) | |||||||
\(128\) | 1446.94 | 0.999164 | ||||||||
\(129\) | 2857.28i | 1.95015i | ||||||||
\(130\) | 879.089i | 0.593086i | ||||||||
\(131\) | − 19.9037i | − 0.0132747i | −0.999978 | − | 0.00663737i | \(-0.997887\pi\) | ||||
0.999978 | − | 0.00663737i | \(-0.00211276\pi\) | |||||||
\(132\) | 1777.86 | 1.17229 | ||||||||
\(133\) | − 84.0728i | − 0.0548123i | ||||||||
\(134\) | −507.114 | −0.326925 | ||||||||
\(135\) | 1361.88 | 0.868235 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1824.89 | −1.13804 | −0.569019 | − | 0.822324i | \(-0.692677\pi\) | ||||
−0.569019 | + | 0.822324i | \(0.692677\pi\) | |||||||
\(138\) | 864.125 | 0.533037 | ||||||||
\(139\) | 1803.87i | 1.10074i | 0.834922 | + | 0.550368i | \(0.185512\pi\) | ||||
−0.834922 | + | 0.550368i | \(0.814488\pi\) | |||||||
\(140\) | 2316.80 | 1.39861 | ||||||||
\(141\) | 1217.41i | 0.727126i | ||||||||
\(142\) | 607.546i | 0.359043i | ||||||||
\(143\) | 2391.26i | 1.39837i | ||||||||
\(144\) | −287.680 | −0.166482 | ||||||||
\(145\) | 247.076 | 0.141507 | ||||||||
\(146\) | 915.032i | 0.518689i | ||||||||
\(147\) | 2438.58i | 1.36824i | ||||||||
\(148\) | 1042.74i | 0.579139i | ||||||||
\(149\) | 2742.46 | 1.50786 | 0.753929 | − | 0.656955i | \(-0.228156\pi\) | ||||
0.753929 | + | 0.656955i | \(0.228156\pi\) | |||||||
\(150\) | − 391.410i | − 0.213057i | ||||||||
\(151\) | −2085.22 | −1.12379 | −0.561896 | − | 0.827208i | \(-0.689928\pi\) | ||||
−0.561896 | + | 0.827208i | \(0.689928\pi\) | |||||||
\(152\) | −56.0639 | −0.0299170 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1565.30 | −0.819063 | ||||||||
\(155\) | −3166.64 | −1.64097 | ||||||||
\(156\) | − 2052.18i | − 1.05324i | ||||||||
\(157\) | −2703.53 | −1.37430 | −0.687149 | − | 0.726516i | \(-0.741138\pi\) | ||||
−0.687149 | + | 0.726516i | \(0.741138\pi\) | |||||||
\(158\) | − 482.724i | − 0.243060i | ||||||||
\(159\) | − 644.152i | − 0.321287i | ||||||||
\(160\) | − 2402.77i | − 1.18722i | ||||||||
\(161\) | 3063.10 | 1.49942 | ||||||||
\(162\) | 1135.53 | 0.550712 | ||||||||
\(163\) | − 2923.57i | − 1.40486i | −0.711755 | − | 0.702428i | \(-0.752099\pi\) | ||||
0.711755 | − | 0.702428i | \(-0.247901\pi\) | |||||||
\(164\) | 2459.61i | 1.17112i | ||||||||
\(165\) | − 3679.46i | − 1.73604i | ||||||||
\(166\) | −230.108 | −0.107590 | ||||||||
\(167\) | 2419.31i | 1.12103i | 0.828145 | + | 0.560514i | \(0.189397\pi\) | ||||
−0.828145 | + | 0.560514i | \(0.810603\pi\) | |||||||
\(168\) | 3020.36 | 1.38706 | ||||||||
\(169\) | 563.229 | 0.256363 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31.3156 | 0.0140045 | ||||||||
\(172\) | 3003.97 | 1.33169 | ||||||||
\(173\) | 393.655i | 0.173000i | 0.996252 | + | 0.0865000i | \(0.0275683\pi\) | ||||
−0.996252 | + | 0.0865000i | \(0.972432\pi\) | |||||||
\(174\) | 143.262 | 0.0624174 | ||||||||
\(175\) | − 1387.45i | − 0.599321i | ||||||||
\(176\) | − 1289.57i | − 0.552299i | ||||||||
\(177\) | 1262.61i | 0.536178i | ||||||||
\(178\) | 786.004 | 0.330975 | ||||||||
\(179\) | −1918.60 | −0.801133 | −0.400567 | − | 0.916268i | \(-0.631187\pi\) | ||||
−0.400567 | + | 0.916268i | \(0.631187\pi\) | |||||||
\(180\) | 862.966i | 0.357343i | ||||||||
\(181\) | − 1677.03i | − 0.688688i | −0.938844 | − | 0.344344i | \(-0.888101\pi\) | ||||
0.938844 | − | 0.344344i | \(-0.111899\pi\) | |||||||
\(182\) | 1806.83i | 0.735886i | ||||||||
\(183\) | −3572.51 | −1.44310 | ||||||||
\(184\) | − 2042.63i | − 0.818393i | ||||||||
\(185\) | 2158.06 | 0.857640 | ||||||||
\(186\) | −1836.11 | −0.723817 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1279.91 | 0.496529 | ||||||||
\(189\) | 2799.13 | 1.07728 | ||||||||
\(190\) | 51.6061i | 0.0197047i | ||||||||
\(191\) | 2347.19 | 0.889196 | 0.444598 | − | 0.895730i | \(-0.353347\pi\) | ||||
0.444598 | + | 0.895730i | \(0.353347\pi\) | |||||||
\(192\) | − 11.6041i | − 0.00436173i | ||||||||
\(193\) | 650.982i | 0.242791i | 0.992604 | + | 0.121396i | \(0.0387369\pi\) | ||||
−0.992604 | + | 0.121396i | \(0.961263\pi\) | |||||||
\(194\) | 466.226i | 0.172542i | ||||||||
\(195\) | −4247.21 | −1.55974 | ||||||||
\(196\) | 2563.77 | 0.934320 | ||||||||
\(197\) | − 2681.01i | − 0.969614i | −0.874621 | − | 0.484807i | \(-0.838890\pi\) | ||||
0.874621 | − | 0.484807i | \(-0.161110\pi\) | |||||||
\(198\) | − 583.047i | − 0.209269i | ||||||||
\(199\) | 1784.74i | 0.635762i | 0.948131 | + | 0.317881i | \(0.102971\pi\) | ||||
−0.948131 | + | 0.317881i | \(0.897029\pi\) | |||||||
\(200\) | −925.218 | −0.327114 | ||||||||
\(201\) | − 2450.06i | − 0.859769i | ||||||||
\(202\) | −1022.40 | −0.356116 | ||||||||
\(203\) | 507.825 | 0.175578 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5090.42 | 1.73429 | ||||||||
\(206\) | −974.835 | −0.329709 | ||||||||
\(207\) | 1140.95i | 0.383099i | ||||||||
\(208\) | −1488.55 | −0.496212 | ||||||||
\(209\) | 140.376i | 0.0464595i | ||||||||
\(210\) | − 2780.20i | − 0.913581i | ||||||||
\(211\) | 68.5651i | 0.0223707i | 0.999937 | + | 0.0111853i | \(0.00356048\pi\) | ||||
−0.999937 | + | 0.0111853i | \(0.996440\pi\) | |||||||
\(212\) | −677.222 | −0.219395 | ||||||||
\(213\) | −2935.28 | −0.944235 | ||||||||
\(214\) | 1257.80i | 0.401781i | ||||||||
\(215\) | − 6217.02i | − 1.97208i | ||||||||
\(216\) | − 1866.60i | − 0.587990i | ||||||||
\(217\) | −6508.53 | −2.03607 | ||||||||
\(218\) | 884.393i | 0.274765i | ||||||||
\(219\) | −4420.86 | −1.36408 | ||||||||
\(220\) | −3868.36 | −1.18548 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1251.30 | 0.378297 | ||||||||
\(223\) | −4734.22 | −1.42164 | −0.710822 | − | 0.703372i | \(-0.751677\pi\) | ||||
−0.710822 | + | 0.703372i | \(0.751677\pi\) | |||||||
\(224\) | − 4938.52i | − 1.47308i | ||||||||
\(225\) | 516.799 | 0.153126 | ||||||||
\(226\) | 1841.04i | 0.541877i | ||||||||
\(227\) | 1722.86i | 0.503745i | 0.967760 | + | 0.251873i | \(0.0810464\pi\) | ||||
−0.967760 | + | 0.251873i | \(0.918954\pi\) | |||||||
\(228\) | − 120.471i | − 0.0349930i | ||||||||
\(229\) | 313.375 | 0.0904297 | 0.0452149 | − | 0.998977i | \(-0.485603\pi\) | ||||
0.0452149 | + | 0.998977i | \(0.485603\pi\) | |||||||
\(230\) | −1880.21 | −0.539032 | ||||||||
\(231\) | − 7562.57i | − 2.15403i | ||||||||
\(232\) | − 338.643i | − 0.0958319i | ||||||||
\(233\) | 2101.61i | 0.590905i | 0.955357 | + | 0.295453i | \(0.0954705\pi\) | ||||
−0.955357 | + | 0.295453i | \(0.904530\pi\) | |||||||
\(234\) | −673.012 | −0.188018 | ||||||||
\(235\) | − 2648.92i | − 0.735303i | ||||||||
\(236\) | 1327.43 | 0.366137 | ||||||||
\(237\) | 2332.22 | 0.639215 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5525.44 | −1.49544 | −0.747721 | − | 0.664013i | \(-0.768852\pi\) | ||||
−0.747721 | + | 0.664013i | \(0.768852\pi\) | |||||||
\(240\) | 2290.45 | 0.616033 | ||||||||
\(241\) | − 2005.92i | − 0.536153i | −0.963398 | − | 0.268076i | \(-0.913612\pi\) | ||||
0.963398 | − | 0.268076i | \(-0.0863880\pi\) | |||||||
\(242\) | 934.367 | 0.248196 | ||||||||
\(243\) | 2713.65i | 0.716383i | ||||||||
\(244\) | 3755.91i | 0.985442i | ||||||||
\(245\) | − 5306.00i | − 1.38362i | ||||||||
\(246\) | 2951.57 | 0.764981 | ||||||||
\(247\) | 162.037 | 0.0417414 | ||||||||
\(248\) | 4340.21i | 1.11130i | ||||||||
\(249\) | − 1111.74i | − 0.282946i | ||||||||
\(250\) | − 1239.91i | − 0.313675i | ||||||||
\(251\) | 4427.81 | 1.11347 | 0.556735 | − | 0.830690i | \(-0.312054\pi\) | ||||
0.556735 | + | 0.830690i | \(0.312054\pi\) | |||||||
\(252\) | 1773.69i | 0.443381i | ||||||||
\(253\) | −5114.46 | −1.27092 | ||||||||
\(254\) | 537.979 | 0.132897 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1840.73 | −0.449397 | ||||||||
\(257\) | 6198.01 | 1.50436 | 0.752182 | − | 0.658956i | \(-0.229002\pi\) | ||||
0.752182 | + | 0.658956i | \(0.229002\pi\) | |||||||
\(258\) | − 3604.81i | − 0.869867i | ||||||||
\(259\) | 4435.55 | 1.06414 | ||||||||
\(260\) | 4465.26i | 1.06509i | ||||||||
\(261\) | 189.156i | 0.0448599i | ||||||||
\(262\) | 25.1109i | 0.00592122i | ||||||||
\(263\) | −477.072 | −0.111854 | −0.0559269 | − | 0.998435i | \(-0.517811\pi\) | ||||
−0.0559269 | + | 0.998435i | \(0.517811\pi\) | |||||||
\(264\) | −5043.09 | −1.17569 | ||||||||
\(265\) | 1401.58i | 0.324900i | ||||||||
\(266\) | 106.068i | 0.0244491i | ||||||||
\(267\) | 3797.48i | 0.870419i | ||||||||
\(268\) | −2575.84 | −0.587106 | ||||||||
\(269\) | 7583.93i | 1.71896i | 0.511168 | + | 0.859481i | \(0.329213\pi\) | ||||
−0.511168 | + | 0.859481i | \(0.670787\pi\) | |||||||
\(270\) | −1718.18 | −0.387278 | ||||||||
\(271\) | −5431.92 | −1.21759 | −0.608793 | − | 0.793329i | \(-0.708346\pi\) | ||||
−0.608793 | + | 0.793329i | \(0.708346\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8729.47 | −1.93528 | ||||||||
\(274\) | 2302.33 | 0.507624 | ||||||||
\(275\) | 2316.62i | 0.507991i | ||||||||
\(276\) | 4389.24 | 0.957251 | ||||||||
\(277\) | 4091.98i | 0.887594i | 0.896127 | + | 0.443797i | \(0.146369\pi\) | ||||
−0.896127 | + | 0.443797i | \(0.853631\pi\) | |||||||
\(278\) | − 2275.81i | − 0.490985i | ||||||||
\(279\) | − 2424.31i | − 0.520213i | ||||||||
\(280\) | −6571.86 | −1.40266 | ||||||||
\(281\) | 3410.26 | 0.723983 | 0.361991 | − | 0.932181i | \(-0.382097\pi\) | ||||
0.361991 | + | 0.932181i | \(0.382097\pi\) | |||||||
\(282\) | − 1535.92i | − 0.324336i | ||||||||
\(283\) | 4322.86i | 0.908011i | 0.890999 | + | 0.454006i | \(0.150005\pi\) | ||||
−0.890999 | + | 0.454006i | \(0.849995\pi\) | |||||||
\(284\) | 3085.97i | 0.644785i | ||||||||
\(285\) | −249.328 | −0.0518208 | ||||||||
\(286\) | − 3016.87i | − 0.623745i | ||||||||
\(287\) | 10462.6 | 2.15186 | ||||||||
\(288\) | 1839.51 | 0.376369 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −311.716 | −0.0631194 | ||||||||
\(291\) | −2252.51 | −0.453761 | ||||||||
\(292\) | 4647.82i | 0.931484i | ||||||||
\(293\) | 3073.56 | 0.612831 | 0.306416 | − | 0.951898i | \(-0.400870\pi\) | ||||
0.306416 | + | 0.951898i | \(0.400870\pi\) | |||||||
\(294\) | − 3076.57i | − 0.610304i | ||||||||
\(295\) | − 2747.26i | − 0.542208i | ||||||||
\(296\) | − 2957.84i | − 0.580815i | ||||||||
\(297\) | −4673.70 | −0.913117 | ||||||||
\(298\) | −3459.95 | −0.672583 | ||||||||
\(299\) | 5903.62i | 1.14186i | ||||||||
\(300\) | − 1988.13i | − 0.382616i | ||||||||
\(301\) | − 12778.1i | − 2.44690i | ||||||||
\(302\) | 2630.76 | 0.501269 | ||||||||
\(303\) | − 4939.57i | − 0.936538i | ||||||||
\(304\) | −87.3836 | −0.0164862 | ||||||||
\(305\) | 7773.26 | 1.45933 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3954.45 | −0.735154 | −0.367577 | − | 0.929993i | \(-0.619813\pi\) | ||||
−0.367577 | + | 0.929993i | \(0.619813\pi\) | |||||||
\(308\) | −7950.82 | −1.47091 | ||||||||
\(309\) | − 4709.79i | − 0.867089i | ||||||||
\(310\) | 3995.11 | 0.731957 | ||||||||
\(311\) | 8984.40i | 1.63813i | 0.573701 | + | 0.819065i | \(0.305507\pi\) | ||||
−0.573701 | + | 0.819065i | \(0.694493\pi\) | |||||||
\(312\) | 5821.24i | 1.05629i | ||||||||
\(313\) | − 1737.01i | − 0.313680i | −0.987624 | − | 0.156840i | \(-0.949869\pi\) | ||||
0.987624 | − | 0.156840i | \(-0.0501306\pi\) | |||||||
\(314\) | 3410.83 | 0.613008 | ||||||||
\(315\) | 3670.84 | 0.656598 | ||||||||
\(316\) | − 2451.95i | − 0.436497i | ||||||||
\(317\) | − 8232.55i | − 1.45863i | −0.684177 | − | 0.729316i | \(-0.739838\pi\) | ||||
0.684177 | − | 0.729316i | \(-0.260162\pi\) | |||||||
\(318\) | 812.678i | 0.143310i | ||||||||
\(319\) | −847.916 | −0.148822 | ||||||||
\(320\) | 25.2488i | 0.00441078i | ||||||||
\(321\) | −6076.88 | −1.05663 | ||||||||
\(322\) | −3864.48 | −0.668817 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5767.81 | 0.988993 | ||||||||
\(325\) | 2674.08 | 0.456403 | ||||||||
\(326\) | 3688.44i | 0.626638i | ||||||||
\(327\) | −4272.83 | −0.722594 | ||||||||
\(328\) | − 6976.95i | − 1.17451i | ||||||||
\(329\) | − 5444.44i | − 0.912345i | ||||||||
\(330\) | 4642.10i | 0.774361i | ||||||||
\(331\) | 4153.12 | 0.689655 | 0.344828 | − | 0.938666i | \(-0.387937\pi\) | ||||
0.344828 | + | 0.938666i | \(0.387937\pi\) | |||||||
\(332\) | −1168.81 | −0.193214 | ||||||||
\(333\) | 1652.16i | 0.271885i | ||||||||
\(334\) | − 3052.26i | − 0.500037i | ||||||||
\(335\) | 5330.97i | 0.869439i | ||||||||
\(336\) | 4707.66 | 0.764357 | ||||||||
\(337\) | 6569.49i | 1.06191i | 0.847401 | + | 0.530954i | \(0.178166\pi\) | ||||
−0.847401 | + | 0.530954i | \(0.821834\pi\) | |||||||
\(338\) | −710.584 | −0.114351 | ||||||||
\(339\) | −8894.75 | −1.42506 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10867.3 | 1.72580 | ||||||||
\(342\) | −39.5085 | −0.00624671 | ||||||||
\(343\) | − 1555.70i | − 0.244898i | ||||||||
\(344\) | −8521.08 | −1.33554 | ||||||||
\(345\) | − 9084.00i | − 1.41758i | ||||||||
\(346\) | − 496.644i | − 0.0771669i | ||||||||
\(347\) | 2038.58i | 0.315380i | 0.987489 | + | 0.157690i | \(0.0504047\pi\) | ||||
−0.987489 | + | 0.157690i | \(0.949595\pi\) | |||||||
\(348\) | 727.684 | 0.112092 | ||||||||
\(349\) | 1791.21 | 0.274731 | 0.137365 | − | 0.990520i | \(-0.456137\pi\) | ||||
0.137365 | + | 0.990520i | \(0.456137\pi\) | |||||||
\(350\) | 1750.44i | 0.267328i | ||||||||
\(351\) | 5394.86i | 0.820388i | ||||||||
\(352\) | 8245.86i | 1.24860i | ||||||||
\(353\) | −5928.71 | −0.893919 | −0.446959 | − | 0.894554i | \(-0.647493\pi\) | ||||
−0.446959 | + | 0.894554i | \(0.647493\pi\) | |||||||
\(354\) | − 1592.94i | − 0.239163i | ||||||||
\(355\) | 6386.75 | 0.954854 | ||||||||
\(356\) | 3992.43 | 0.594378 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2420.55 | 0.357347 | ||||||||
\(359\) | −413.998 | −0.0608634 | −0.0304317 | − | 0.999537i | \(-0.509688\pi\) | ||||
−0.0304317 | + | 0.999537i | \(0.509688\pi\) | |||||||
\(360\) | − 2447.90i | − 0.358377i | ||||||||
\(361\) | −6849.49 | −0.998613 | ||||||||
\(362\) | 2115.78i | 0.307190i | ||||||||
\(363\) | 4514.28i | 0.652722i | ||||||||
\(364\) | 9177.63i | 1.32154i | ||||||||
\(365\) | 9619.15 | 1.37942 | ||||||||
\(366\) | 4507.16 | 0.643697 | ||||||||
\(367\) | − 6979.15i | − 0.992667i | −0.868132 | − | 0.496334i | \(-0.834679\pi\) | ||||
0.868132 | − | 0.496334i | \(-0.165321\pi\) | |||||||
\(368\) | − 3183.73i | − 0.450987i | ||||||||
\(369\) | 3897.11i | 0.549798i | ||||||||
\(370\) | −2722.66 | −0.382552 | ||||||||
\(371\) | 2880.73i | 0.403127i | ||||||||
\(372\) | −9326.34 | −1.29986 | ||||||||
\(373\) | 6855.64 | 0.951667 | 0.475833 | − | 0.879535i | \(-0.342147\pi\) | ||||
0.475833 | + | 0.879535i | \(0.342147\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5990.46 | 0.824923 | ||||||||
\(376\) | −3630.62 | −0.497965 | ||||||||
\(377\) | 978.750i | 0.133709i | ||||||||
\(378\) | −3531.45 | −0.480524 | ||||||||
\(379\) | − 8206.78i | − 1.11228i | −0.831089 | − | 0.556140i | \(-0.812282\pi\) | ||||
0.831089 | − | 0.556140i | \(-0.187718\pi\) | |||||||
\(380\) | 262.128i | 0.0353866i | ||||||||
\(381\) | 2599.18i | 0.349501i | ||||||||
\(382\) | −2961.27 | −0.396627 | ||||||||
\(383\) | 889.401 | 0.118659 | 0.0593293 | − | 0.998238i | \(-0.481104\pi\) | ||||
0.0593293 | + | 0.998238i | \(0.481104\pi\) | |||||||
\(384\) | − 8819.67i | − 1.17208i | ||||||||
\(385\) | 16455.1i | 2.17825i | ||||||||
\(386\) | − 821.294i | − 0.108297i | ||||||||
\(387\) | 4759.62 | 0.625180 | ||||||||
\(388\) | 2368.15i | 0.309857i | ||||||||
\(389\) | 12992.8 | 1.69347 | 0.846736 | − | 0.532013i | \(-0.178564\pi\) | ||||
0.846736 | + | 0.532013i | \(0.178564\pi\) | |||||||
\(390\) | 5358.38 | 0.695723 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −7272.43 | −0.937023 | ||||||||
\(393\) | −121.320 | −0.0155720 | ||||||||
\(394\) | 3382.42i | 0.432498i | ||||||||
\(395\) | −5074.57 | −0.646403 | ||||||||
\(396\) | − 2961.54i | − 0.375815i | ||||||||
\(397\) | − 4325.29i | − 0.546801i | −0.961900 | − | 0.273400i | \(-0.911852\pi\) | ||||
0.961900 | − | 0.273400i | \(-0.0881484\pi\) | |||||||
\(398\) | − 2251.67i | − 0.283583i | ||||||||
\(399\) | −512.455 | −0.0642979 | ||||||||
\(400\) | −1442.09 | −0.180261 | ||||||||
\(401\) | 11849.1i | 1.47560i | 0.675022 | + | 0.737798i | \(0.264134\pi\) | ||||
−0.675022 | + | 0.737798i | \(0.735866\pi\) | |||||||
\(402\) | 3091.05i | 0.383501i | ||||||||
\(403\) | − 12544.1i | − 1.55054i | ||||||||
\(404\) | −5193.17 | −0.639529 | ||||||||
\(405\) | − 11937.1i | − 1.46459i | ||||||||
\(406\) | −640.685 | −0.0783168 | ||||||||
\(407\) | −7406.04 | −0.901975 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7677.24 | 0.928154 | 0.464077 | − | 0.885795i | \(-0.346386\pi\) | ||||
0.464077 | + | 0.885795i | \(0.346386\pi\) | |||||||
\(410\) | −6422.19 | −0.773584 | ||||||||
\(411\) | 11123.4i | 1.33498i | ||||||||
\(412\) | −4951.59 | −0.592105 | ||||||||
\(413\) | − 5646.55i | − 0.672757i | ||||||||
\(414\) | − 1439.45i | − 0.170882i | ||||||||
\(415\) | 2418.98i | 0.286128i | ||||||||
\(416\) | 9518.20 | 1.12180 | ||||||||
\(417\) | 10995.3 | 1.29122 | ||||||||
\(418\) | − 177.102i | − 0.0207233i | ||||||||
\(419\) | 3235.83i | 0.377280i | 0.982046 | + | 0.188640i | \(0.0604080\pi\) | ||||
−0.982046 | + | 0.188640i | \(0.939592\pi\) | |||||||
\(420\) | − 14121.8i | − 1.64065i | ||||||||
\(421\) | 14496.6 | 1.67820 | 0.839100 | − | 0.543977i | \(-0.183082\pi\) | ||||
0.839100 | + | 0.543977i | \(0.183082\pi\) | |||||||
\(422\) | − 86.5033i | − 0.00997848i | ||||||||
\(423\) | 2027.95 | 0.233103 | ||||||||
\(424\) | 1921.02 | 0.220030 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3703.22 | 0.421178 | ||||||||
\(427\) | 15976.7 | 1.81070 | ||||||||
\(428\) | 6388.86i | 0.721536i | ||||||||
\(429\) | 14575.6 | 1.64037 | ||||||||
\(430\) | 7843.54i | 0.879649i | ||||||||
\(431\) | − 7136.25i | − 0.797543i | −0.917050 | − | 0.398771i | \(-0.869437\pi\) | ||||
0.917050 | − | 0.398771i | \(-0.130563\pi\) | |||||||
\(432\) | − 2909.36i | − 0.324020i | ||||||||
\(433\) | −11434.3 | −1.26904 | −0.634521 | − | 0.772905i | \(-0.718803\pi\) | ||||
−0.634521 | + | 0.772905i | \(0.718803\pi\) | |||||||
\(434\) | 8211.32 | 0.908193 | ||||||||
\(435\) | − 1506.02i | − 0.165996i | ||||||||
\(436\) | 4492.20i | 0.493434i | ||||||||
\(437\) | 346.566i | 0.0379371i | ||||||||
\(438\) | 5577.46 | 0.608451 | ||||||||
\(439\) | − 13308.0i | − 1.44682i | −0.690417 | − | 0.723412i | \(-0.742573\pi\) | ||||
0.690417 | − | 0.723412i | \(-0.257427\pi\) | |||||||
\(440\) | 10973.0 | 1.18891 | ||||||||
\(441\) | 4062.16 | 0.438630 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10897.9 | −1.16880 | −0.584398 | − | 0.811467i | \(-0.698669\pi\) | ||||
−0.584398 | + | 0.811467i | \(0.698669\pi\) | |||||||
\(444\) | 6355.88 | 0.679362 | ||||||||
\(445\) | − 8262.76i | − 0.880208i | ||||||||
\(446\) | 5972.80 | 0.634126 | ||||||||
\(447\) | − 16716.3i | − 1.76880i | ||||||||
\(448\) | 51.8949i | 0.00547278i | ||||||||
\(449\) | 16756.4i | 1.76121i | 0.473855 | + | 0.880603i | \(0.342862\pi\) | ||||
−0.473855 | + | 0.880603i | \(0.657138\pi\) | |||||||
\(450\) | −652.006 | −0.0683019 | ||||||||
\(451\) | −17469.3 | −1.82394 | ||||||||
\(452\) | 9351.40i | 0.973126i | ||||||||
\(453\) | 12710.2i | 1.31827i | ||||||||
\(454\) | − 2173.60i | − 0.224696i | ||||||||
\(455\) | 18994.1 | 1.95705 | ||||||||
\(456\) | 341.730i | 0.0350943i | ||||||||
\(457\) | −13561.8 | −1.38817 | −0.694087 | − | 0.719891i | \(-0.744192\pi\) | ||||
−0.694087 | + | 0.719891i | \(0.744192\pi\) | |||||||
\(458\) | −395.361 | −0.0403363 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9550.36 | −0.968017 | ||||||||
\(461\) | −15516.4 | −1.56762 | −0.783810 | − | 0.621000i | \(-0.786727\pi\) | ||||
−0.783810 | + | 0.621000i | \(0.786727\pi\) | |||||||
\(462\) | 9541.11i | 0.960807i | ||||||||
\(463\) | −15186.4 | −1.52435 | −0.762174 | − | 0.647372i | \(-0.775868\pi\) | ||||
−0.762174 | + | 0.647372i | \(0.775868\pi\) | |||||||
\(464\) | − 527.824i | − 0.0528095i | ||||||||
\(465\) | 19301.8i | 1.92495i | ||||||||
\(466\) | − 2651.44i | − 0.263574i | ||||||||
\(467\) | −10544.3 | −1.04482 | −0.522412 | − | 0.852693i | \(-0.674968\pi\) | ||||
−0.522412 | + | 0.852693i | \(0.674968\pi\) | |||||||
\(468\) | −3418.50 | −0.337650 | ||||||||
\(469\) | 10957.0i | 1.07878i | ||||||||
\(470\) | 3341.94i | 0.327983i | ||||||||
\(471\) | 16479.0i | 1.61213i | ||||||||
\(472\) | −3765.40 | −0.367196 | ||||||||
\(473\) | 21335.6i | 2.07402i | ||||||||
\(474\) | −2942.38 | −0.285123 | ||||||||
\(475\) | 156.979 | 0.0151636 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1073.02 | −0.102998 | ||||||||
\(478\) | 6971.02 | 0.667044 | ||||||||
\(479\) | − 5762.22i | − 0.549650i | −0.961494 | − | 0.274825i | \(-0.911380\pi\) | ||||
0.961494 | − | 0.274825i | \(-0.0886200\pi\) | |||||||
\(480\) | −14645.8 | −1.39268 | ||||||||
\(481\) | 8548.79i | 0.810377i | ||||||||
\(482\) | 2530.72i | 0.239152i | ||||||||
\(483\) | − 18670.7i | − 1.75890i | ||||||||
\(484\) | 4746.03 | 0.445721 | ||||||||
\(485\) | 4901.14 | 0.458864 | ||||||||
\(486\) | − 3423.61i | − 0.319544i | ||||||||
\(487\) | − 5369.36i | − 0.499608i | −0.968296 | − | 0.249804i | \(-0.919634\pi\) | ||||
0.968296 | − | 0.249804i | \(-0.0803661\pi\) | |||||||
\(488\) | − 10654.1i | − 0.988293i | ||||||||
\(489\) | −17820.2 | −1.64797 | ||||||||
\(490\) | 6694.18i | 0.617167i | ||||||||
\(491\) | −17878.0 | −1.64322 | −0.821611 | − | 0.570049i | \(-0.806924\pi\) | ||||
−0.821611 | + | 0.570049i | \(0.806924\pi\) | |||||||
\(492\) | 14992.2 | 1.37378 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −204.429 | −0.0186188 | ||||||||
\(495\) | −6129.21 | −0.556540 | ||||||||
\(496\) | 6764.84i | 0.612400i | ||||||||
\(497\) | 13127.0 | 1.18476 | ||||||||
\(498\) | 1402.60i | 0.126209i | ||||||||
\(499\) | 3507.03i | 0.314622i | 0.987549 | + | 0.157311i | \(0.0502825\pi\) | ||||
−0.987549 | + | 0.157311i | \(0.949718\pi\) | |||||||
\(500\) | − 6298.01i | − 0.563311i | ||||||||
\(501\) | 14746.6 | 1.31503 | ||||||||
\(502\) | −5586.23 | −0.496665 | ||||||||
\(503\) | − 1207.56i | − 0.107043i | −0.998567 | − | 0.0535214i | \(-0.982955\pi\) | ||||
0.998567 | − | 0.0535214i | \(-0.0170445\pi\) | |||||||
\(504\) | − 5031.27i | − 0.444664i | ||||||||
\(505\) | 10747.8i | 0.947071i | ||||||||
\(506\) | 6452.52 | 0.566897 | ||||||||
\(507\) | − 3433.09i | − 0.300728i | ||||||||
\(508\) | 2732.62 | 0.238662 | ||||||||
\(509\) | −14092.1 | −1.22716 | −0.613578 | − | 0.789634i | \(-0.710270\pi\) | ||||
−0.613578 | + | 0.789634i | \(0.710270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19770.7 | 1.71155 | ||||||||
\(512\) | −9253.25 | −0.798710 | ||||||||
\(513\) | 316.700i | 0.0272566i | ||||||||
\(514\) | −7819.56 | −0.671023 | ||||||||
\(515\) | 10247.8i | 0.876841i | ||||||||
\(516\) | − 18310.3i | − 1.56214i | ||||||||
\(517\) | 9090.58i | 0.773314i | ||||||||
\(518\) | −5595.99 | −0.474660 | ||||||||
\(519\) | 2399.47 | 0.202939 | ||||||||
\(520\) | − 12666.2i | − 1.06817i | ||||||||
\(521\) | − 10080.1i | − 0.847635i | −0.905748 | − | 0.423818i | \(-0.860690\pi\) | ||||
0.905748 | − | 0.423818i | \(-0.139310\pi\) | |||||||
\(522\) | − 238.643i | − 0.0200098i | ||||||||
\(523\) | 12330.2 | 1.03090 | 0.515452 | − | 0.856919i | \(-0.327624\pi\) | ||||
0.515452 | + | 0.856919i | \(0.327624\pi\) | |||||||
\(524\) | 127.549i | 0.0106336i | ||||||||
\(525\) | −8457.01 | −0.703036 | ||||||||
\(526\) | 601.886 | 0.0498925 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −7860.38 | −0.647877 | ||||||||
\(529\) | −459.760 | −0.0377875 | ||||||||
\(530\) | − 1768.27i | − 0.144922i | ||||||||
\(531\) | 2103.24 | 0.171888 | ||||||||
\(532\) | 538.764i | 0.0439067i | ||||||||
\(533\) | 20164.9i | 1.63872i | ||||||||
\(534\) | − 4790.99i | − 0.388252i | ||||||||
\(535\) | 13222.4 | 1.06851 | ||||||||
\(536\) | 7306.65 | 0.588805 | ||||||||
\(537\) | 11694.6i | 0.939774i | ||||||||
\(538\) | − 9568.07i | − 0.766745i | ||||||||
\(539\) | 18209.2i | 1.45515i | ||||||||
\(540\) | −8727.33 | −0.695490 | ||||||||
\(541\) | − 7122.72i | − 0.566044i | −0.959113 | − | 0.283022i | \(-0.908663\pi\) | ||||
0.959113 | − | 0.283022i | \(-0.0913369\pi\) | |||||||
\(542\) | 6853.04 | 0.543106 | ||||||||
\(543\) | −10222.1 | −0.807869 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9297.07 | 0.730720 | ||||||||
\(546\) | 11013.3 | 0.863235 | ||||||||
\(547\) | − 14919.7i | − 1.16622i | −0.812394 | − | 0.583109i | \(-0.801836\pi\) | ||||
0.812394 | − | 0.583109i | \(-0.198164\pi\) | |||||||
\(548\) | 11694.5 | 0.911612 | ||||||||
\(549\) | 5951.04i | 0.462630i | ||||||||
\(550\) | − 2922.70i | − 0.226590i | ||||||||
\(551\) | 57.4566i | 0.00444234i | ||||||||
\(552\) | −12450.6 | −0.960021 | ||||||||
\(553\) | −10430.0 | −0.802040 | ||||||||
\(554\) | − 5162.55i | − 0.395913i | ||||||||
\(555\) | − 13154.2i | − 1.00606i | ||||||||
\(556\) | − 11559.7i | − 0.881731i | ||||||||
\(557\) | −18935.0 | −1.44039 | −0.720197 | − | 0.693769i | \(-0.755949\pi\) | ||||
−0.720197 | + | 0.693769i | \(0.755949\pi\) | |||||||
\(558\) | 3058.57i | 0.232042i | ||||||||
\(559\) | 24627.7 | 1.86340 | ||||||||
\(560\) | −10243.2 | −0.772953 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4302.47 | −0.322934 | ||||||||
\(563\) | −8150.42 | −0.610123 | −0.305062 | − | 0.952333i | \(-0.598677\pi\) | ||||
−0.305062 | + | 0.952333i | \(0.598677\pi\) | |||||||
\(564\) | − 7801.56i | − 0.582456i | ||||||||
\(565\) | 19353.7 | 1.44109 | ||||||||
\(566\) | − 5453.82i | − 0.405020i | ||||||||
\(567\) | − 24534.8i | − 1.81722i | ||||||||
\(568\) | − 8753.71i | − 0.646650i | ||||||||
\(569\) | −18218.2 | −1.34226 | −0.671131 | − | 0.741338i | \(-0.734191\pi\) | ||||
−0.671131 | + | 0.741338i | \(0.734191\pi\) | |||||||
\(570\) | 314.558 | 0.0231147 | ||||||||
\(571\) | 2443.35i | 0.179073i | 0.995984 | + | 0.0895367i | \(0.0285386\pi\) | ||||
−0.995984 | + | 0.0895367i | \(0.971461\pi\) | |||||||
\(572\) | − 15323.9i | − 1.12015i | ||||||||
\(573\) | − 14307.0i | − 1.04308i | ||||||||
\(574\) | −13199.8 | −0.959842 | ||||||||
\(575\) | 5719.36i | 0.414806i | ||||||||
\(576\) | −19.3299 | −0.00139829 | ||||||||
\(577\) | −852.752 | −0.0615261 | −0.0307630 | − | 0.999527i | \(-0.509794\pi\) | ||||
−0.0307630 | + | 0.999527i | \(0.509794\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3967.98 | 0.284807 | ||||||||
\(580\) | −1583.34 | −0.113352 | ||||||||
\(581\) | 4971.84i | 0.355020i | ||||||||
\(582\) | 2841.82 | 0.202401 | ||||||||
\(583\) | − 4809.96i | − 0.341695i | ||||||||
\(584\) | − 13184.1i | − 0.934179i | ||||||||
\(585\) | 7074.95i | 0.500022i | ||||||||
\(586\) | −3877.68 | −0.273354 | ||||||||
\(587\) | −900.272 | −0.0633019 | −0.0316509 | − | 0.999499i | \(-0.510076\pi\) | ||||
−0.0316509 | + | 0.999499i | \(0.510076\pi\) | |||||||
\(588\) | − 15627.2i | − 1.09601i | ||||||||
\(589\) | − 736.390i | − 0.0515152i | ||||||||
\(590\) | 3466.00i | 0.241853i | ||||||||
\(591\) | −16341.7 | −1.13741 | ||||||||
\(592\) | − 4610.22i | − 0.320066i | ||||||||
\(593\) | 25007.2 | 1.73174 | 0.865870 | − | 0.500268i | \(-0.166765\pi\) | ||||
0.865870 | + | 0.500268i | \(0.166765\pi\) | |||||||
\(594\) | 5896.46 | 0.407297 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17574.5 | −1.20785 | ||||||||
\(597\) | 10878.6 | 0.745784 | ||||||||
\(598\) | − 7448.15i | − 0.509327i | ||||||||
\(599\) | −3448.82 | −0.235251 | −0.117625 | − | 0.993058i | \(-0.537528\pi\) | ||||
−0.117625 | + | 0.993058i | \(0.537528\pi\) | |||||||
\(600\) | 5639.55i | 0.383723i | ||||||||
\(601\) | 942.873i | 0.0639943i | 0.999488 | + | 0.0319972i | \(0.0101868\pi\) | ||||
−0.999488 | + | 0.0319972i | \(0.989813\pi\) | |||||||
\(602\) | 16121.2i | 1.09145i | ||||||||
\(603\) | −4081.27 | −0.275626 | ||||||||
\(604\) | 13362.7 | 0.900201 | ||||||||
\(605\) | − 9822.41i | − 0.660063i | ||||||||
\(606\) | 6231.89i | 0.417744i | ||||||||
\(607\) | 10173.9i | 0.680306i | 0.940370 | + | 0.340153i | \(0.110479\pi\) | ||||
−0.940370 | + | 0.340153i | \(0.889521\pi\) | |||||||
\(608\) | 558.756 | 0.0372707 | ||||||||
\(609\) | − 3095.39i | − 0.205963i | ||||||||
\(610\) | −9806.93 | −0.650936 | ||||||||
\(611\) | 10493.3 | 0.694782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17327.0 | −1.14165 | −0.570824 | − | 0.821073i | \(-0.693376\pi\) | ||||
−0.570824 | + | 0.821073i | \(0.693376\pi\) | |||||||
\(614\) | 4989.03 | 0.327916 | ||||||||
\(615\) | − 31028.0i | − 2.03442i | ||||||||
\(616\) | 22553.4 | 1.47516 | ||||||||
\(617\) | 19782.8i | 1.29080i | 0.763844 | + | 0.645401i | \(0.223310\pi\) | ||||
−0.763844 | + | 0.645401i | \(0.776690\pi\) | |||||||
\(618\) | 5941.98i | 0.386766i | ||||||||
\(619\) | − 15033.2i | − 0.976147i | −0.872802 | − | 0.488074i | \(-0.837700\pi\) | ||||
0.872802 | − | 0.488074i | \(-0.162300\pi\) | |||||||
\(620\) | 20292.8 | 1.31448 | ||||||||
\(621\) | −11538.6 | −0.745618 | ||||||||
\(622\) | − 11334.9i | − 0.730690i | ||||||||
\(623\) | − 16982.8i | − 1.09214i | ||||||||
\(624\) | 9073.25i | 0.582084i | ||||||||
\(625\) | −19396.6 | −1.24139 | ||||||||
\(626\) | 2191.46i | 0.139917i | ||||||||
\(627\) | 855.647 | 0.0544996 | ||||||||
\(628\) | 17325.0 | 1.10087 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −4631.22 | −0.292877 | ||||||||
\(631\) | 24060.5 | 1.51796 | 0.758979 | − | 0.651115i | \(-0.225698\pi\) | ||||
0.758979 | + | 0.651115i | \(0.225698\pi\) | |||||||
\(632\) | 6955.23i | 0.437760i | ||||||||
\(633\) | 417.930 | 0.0262421 | ||||||||
\(634\) | 10386.4i | 0.650625i | ||||||||
\(635\) | − 5655.44i | − 0.353432i | ||||||||
\(636\) | 4127.92i | 0.257363i | ||||||||
\(637\) | 21018.9 | 1.30737 | ||||||||
\(638\) | 1069.75 | 0.0663822 | ||||||||
\(639\) | 4889.55i | 0.302704i | ||||||||
\(640\) | 19190.3i | 1.18526i | ||||||||
\(641\) | − 4886.07i | − 0.301074i | −0.988604 | − | 0.150537i | \(-0.951900\pi\) | ||||
0.988604 | − | 0.150537i | \(-0.0481002\pi\) | |||||||
\(642\) | 7666.74 | 0.471312 | ||||||||
\(643\) | − 24508.4i | − 1.50314i | −0.659655 | − | 0.751568i | \(-0.729298\pi\) | ||||
0.659655 | − | 0.751568i | \(-0.270702\pi\) | |||||||
\(644\) | −19629.3 | −1.20109 | ||||||||
\(645\) | −37895.1 | −2.31336 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2932.50 | 0.178189 | 0.0890947 | − | 0.996023i | \(-0.471603\pi\) | ||||
0.0890947 | + | 0.996023i | \(0.471603\pi\) | |||||||
\(648\) | −16361.0 | −0.991854 | ||||||||
\(649\) | 9428.06i | 0.570237i | ||||||||
\(650\) | −3373.68 | −0.203579 | ||||||||
\(651\) | 39671.9i | 2.38843i | ||||||||
\(652\) | 18735.1i | 1.12534i | ||||||||
\(653\) | − 19977.8i | − 1.19723i | −0.801035 | − | 0.598617i | \(-0.795717\pi\) | ||||
0.801035 | − | 0.598617i | \(-0.204283\pi\) | |||||||
\(654\) | 5390.71 | 0.322314 | ||||||||
\(655\) | 263.975 | 0.0157471 | ||||||||
\(656\) | − 10874.6i | − 0.647227i | ||||||||
\(657\) | 7364.21i | 0.437299i | ||||||||
\(658\) | 6868.83i | 0.406953i | ||||||||
\(659\) | 28222.7 | 1.66829 | 0.834143 | − | 0.551548i | \(-0.185963\pi\) | ||||
0.834143 | + | 0.551548i | \(0.185963\pi\) | |||||||
\(660\) | 23579.1i | 1.39063i | ||||||||
\(661\) | −20712.8 | −1.21881 | −0.609405 | − | 0.792859i | \(-0.708592\pi\) | ||||
−0.609405 | + | 0.792859i | \(0.708592\pi\) | |||||||
\(662\) | −5239.67 | −0.307622 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3315.47 | 0.193773 | ||||||||
\(665\) | 1115.03 | 0.0650210 | ||||||||
\(666\) | − 2084.41i | − 0.121275i | ||||||||
\(667\) | −2093.37 | −0.121522 | ||||||||
\(668\) | − 15503.7i | − 0.897987i | ||||||||
\(669\) | 28856.8i | 1.66767i | ||||||||
\(670\) | − 6725.68i | − 0.387814i | ||||||||
\(671\) | −26676.3 | −1.53477 | ||||||||
\(672\) | −30102.2 | −1.72800 | ||||||||
\(673\) | − 395.468i | − 0.0226511i | −0.999936 | − | 0.0113255i | \(-0.996395\pi\) | ||||
0.999936 | − | 0.0113255i | \(-0.00360511\pi\) | |||||||
\(674\) | − 8288.23i | − 0.473666i | ||||||||
\(675\) | 5226.48i | 0.298025i | ||||||||
\(676\) | −3609.34 | −0.205356 | ||||||||
\(677\) | − 2297.47i | − 0.130427i | −0.997871 | − | 0.0652135i | \(-0.979227\pi\) | ||||
0.997871 | − | 0.0652135i | \(-0.0207729\pi\) | |||||||
\(678\) | 11221.8 | 0.635652 | ||||||||
\(679\) | 10073.5 | 0.569347 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10501.5 | 0.590921 | ||||||||
\(682\) | −13710.4 | −0.769794 | ||||||||
\(683\) | − 28611.7i | − 1.60292i | −0.598048 | − | 0.801461i | \(-0.704057\pi\) | ||||
0.598048 | − | 0.801461i | \(-0.295943\pi\) | |||||||
\(684\) | −200.680 | −0.0112181 | ||||||||
\(685\) | − 24202.9i | − 1.35000i | ||||||||
\(686\) | 1962.71i | 0.109237i | ||||||||
\(687\) | − 1910.14i | − 0.106079i | ||||||||
\(688\) | −13281.3 | −0.735968 | ||||||||
\(689\) | −5552.14 | −0.306995 | ||||||||
\(690\) | 11460.6i | 0.632315i | ||||||||
\(691\) | − 4902.87i | − 0.269919i | −0.990851 | − | 0.134959i | \(-0.956910\pi\) | ||||
0.990851 | − | 0.134959i | \(-0.0430904\pi\) | |||||||
\(692\) | − 2522.66i | − 0.138580i | ||||||||
\(693\) | −12597.6 | −0.690540 | ||||||||
\(694\) | − 2571.93i | − 0.140676i | ||||||||
\(695\) | −23924.1 | −1.30575 | ||||||||
\(696\) | −2064.16 | −0.112416 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2259.83 | −0.122544 | ||||||||
\(699\) | 12810.1 | 0.693165 | ||||||||
\(700\) | 8891.18i | 0.480079i | ||||||||
\(701\) | 1714.99 | 0.0924027 | 0.0462014 | − | 0.998932i | \(-0.485288\pi\) | ||||
0.0462014 | + | 0.998932i | \(0.485288\pi\) | |||||||
\(702\) | − 6806.28i | − 0.365935i | ||||||||
\(703\) | 501.849i | 0.0269240i | ||||||||
\(704\) | − 86.6490i | − 0.00463879i | ||||||||
\(705\) | −16146.1 | −0.862552 | ||||||||
\(706\) | 7479.80 | 0.398734 | ||||||||
\(707\) | 22090.4i | 1.17510i | ||||||||
\(708\) | − 8091.18i | − 0.429499i | ||||||||
\(709\) | − 13939.8i | − 0.738393i | −0.929351 | − | 0.369196i | \(-0.879633\pi\) | ||||
0.929351 | − | 0.369196i | \(-0.120367\pi\) | |||||||
\(710\) | −8057.67 | −0.425914 | ||||||||
\(711\) | − 3884.98i | − 0.204920i | ||||||||
\(712\) | −11325.0 | −0.596098 | ||||||||
\(713\) | 26829.6 | 1.40922 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31714.4 | −1.65881 | ||||||||
\(716\) | 12295.0 | 0.641738 | ||||||||
\(717\) | 33679.6i | 1.75424i | ||||||||
\(718\) | 522.310 | 0.0271482 | ||||||||
\(719\) | − 1779.18i | − 0.0922839i | −0.998935 | − | 0.0461419i | \(-0.985307\pi\) | ||||
0.998935 | − | 0.0461419i | \(-0.0146926\pi\) | |||||||
\(720\) | − 3815.40i | − 0.197488i | ||||||||
\(721\) | 21062.8i | 1.08796i | ||||||||
\(722\) | 8641.48 | 0.445433 | ||||||||
\(723\) | −12226.9 | −0.628937 | ||||||||
\(724\) | 10746.9i | 0.551665i | ||||||||
\(725\) | 948.201i | 0.0485729i | ||||||||
\(726\) | − 5695.32i | − 0.291148i | ||||||||
\(727\) | 9141.02 | 0.466330 | 0.233165 | − | 0.972437i | \(-0.425092\pi\) | ||||
0.233165 | + | 0.972437i | \(0.425092\pi\) | |||||||
\(728\) | − 26033.4i | − 1.32536i | ||||||||
\(729\) | −7760.65 | −0.394282 | ||||||||
\(730\) | −12135.8 | −0.615294 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 22893.7 | 1.15598 | ||||||||
\(733\) | −12176.0 | −0.613547 | −0.306773 | − | 0.951783i | \(-0.599249\pi\) | ||||
−0.306773 | + | 0.951783i | \(0.599249\pi\) | |||||||
\(734\) | 8805.07i | 0.442781i | ||||||||
\(735\) | −32342.1 | −1.62307 | ||||||||
\(736\) | 20357.7i | 1.01956i | ||||||||
\(737\) | − 18294.9i | − 0.914383i | ||||||||
\(738\) | − 4916.69i | − 0.245238i | ||||||||
\(739\) | −25025.4 | −1.24570 | −0.622852 | − | 0.782339i | \(-0.714026\pi\) | ||||
−0.622852 | + | 0.782339i | \(0.714026\pi\) | |||||||
\(740\) | −13829.5 | −0.687003 | ||||||||
\(741\) | − 987.673i | − 0.0489650i | ||||||||
\(742\) | − 3634.40i | − 0.179816i | ||||||||
\(743\) | − 10781.3i | − 0.532339i | −0.963926 | − | 0.266170i | \(-0.914242\pi\) | ||||
0.963926 | − | 0.266170i | \(-0.0857581\pi\) | |||||||
\(744\) | 26455.2 | 1.30362 | ||||||||
\(745\) | 36372.3i | 1.78869i | ||||||||
\(746\) | −8649.24 | −0.424492 | ||||||||
\(747\) | −1851.92 | −0.0907072 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27176.6 | 1.32578 | ||||||||
\(750\) | −7557.71 | −0.367958 | ||||||||
\(751\) | 33910.7i | 1.64769i | 0.566812 | + | 0.823847i | \(0.308177\pi\) | ||||
−0.566812 | + | 0.823847i | \(0.691823\pi\) | |||||||
\(752\) | −5658.84 | −0.274410 | ||||||||
\(753\) | − 26989.2i | − 1.30616i | ||||||||
\(754\) | − 1234.81i | − 0.0596410i | ||||||||
\(755\) | − 27655.5i | − 1.33310i | ||||||||
\(756\) | −17937.7 | −0.862945 | ||||||||
\(757\) | 31545.0 | 1.51456 | 0.757281 | − | 0.653090i | \(-0.226528\pi\) | ||||
0.757281 | + | 0.653090i | \(0.226528\pi\) | |||||||
\(758\) | 10353.9i | 0.496134i | ||||||||
\(759\) | 31174.5i | 1.49086i | ||||||||
\(760\) | − 743.556i | − 0.0354890i | ||||||||
\(761\) | 9150.51 | 0.435881 | 0.217941 | − | 0.975962i | \(-0.430066\pi\) | ||||
0.217941 | + | 0.975962i | \(0.430066\pi\) | |||||||
\(762\) | − 3279.19i | − 0.155895i | ||||||||
\(763\) | 19108.7 | 0.906658 | ||||||||
\(764\) | −15041.5 | −0.712280 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1122.09 | −0.0529279 | ||||||||
\(767\) | 10882.8 | 0.512328 | ||||||||
\(768\) | 11219.9i | 0.527168i | ||||||||
\(769\) | 33797.5 | 1.58488 | 0.792438 | − | 0.609952i | \(-0.208811\pi\) | ||||
0.792438 | + | 0.609952i | \(0.208811\pi\) | |||||||
\(770\) | − 20760.1i | − 0.971612i | ||||||||
\(771\) | − 37779.2i | − 1.76470i | ||||||||
\(772\) | − 4171.69i | − 0.194485i | ||||||||
\(773\) | 33969.4 | 1.58059 | 0.790295 | − | 0.612727i | \(-0.209927\pi\) | ||||
0.790295 | + | 0.612727i | \(0.209927\pi\) | |||||||
\(774\) | −6004.85 | −0.278863 | ||||||||
\(775\) | − 12152.6i | − 0.563270i | ||||||||
\(776\) | − 6717.52i | − 0.310754i | ||||||||
\(777\) | − 27036.3i | − 1.24829i | ||||||||
\(778\) | −16392.0 | −0.755376 | ||||||||
\(779\) | 1183.76i | 0.0544449i | ||||||||
\(780\) | 27217.4 | 1.24941 | ||||||||
\(781\) | −21918.1 | −1.00421 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1912.96 | −0.0873100 | ||||||||
\(784\) | −11335.1 | −0.516359 | ||||||||
\(785\) | − 35856.0i | − 1.63026i | ||||||||
\(786\) | 153.061 | 0.00694592 | ||||||||
\(787\) | − 10962.7i | − 0.496543i | −0.968691 | − | 0.248271i | \(-0.920138\pi\) | ||||
0.968691 | − | 0.248271i | \(-0.0798624\pi\) | |||||||
\(788\) | 17180.7i | 0.776698i | ||||||||
\(789\) | 2907.93i | 0.131211i | ||||||||
\(790\) | 6402.20 | 0.288329 | ||||||||
\(791\) | 39778.5 | 1.78807 | ||||||||
\(792\) | 8400.72i | 0.376902i | ||||||||
\(793\) | 30792.5i | 1.37891i | ||||||||
\(794\) | 5456.89i | 0.243901i | ||||||||
\(795\) | 8543.17 | 0.381126 | ||||||||
\(796\) | − 11437.1i | − 0.509270i | ||||||||
\(797\) | 8041.29 | 0.357386 | 0.178693 | − | 0.983905i | \(-0.442813\pi\) | ||||
0.178693 | + | 0.983905i | \(0.442813\pi\) | |||||||
\(798\) | 646.526 | 0.0286802 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 9221.12 | 0.407520 | ||||||||
\(801\) | 6325.79 | 0.279040 | ||||||||
\(802\) | − 14949.1i | − 0.658192i | ||||||||
\(803\) | −33011.1 | −1.45073 | ||||||||
\(804\) | 15700.7i | 0.688708i | ||||||||
\(805\) | 40624.8i | 1.77868i | ||||||||
\(806\) | 15826.0i | 0.691620i | ||||||||
\(807\) | 46226.9 | 2.01644 | ||||||||
\(808\) | 14731.0 | 0.641379 | ||||||||
\(809\) | − 36568.0i | − 1.58920i | −0.607134 | − | 0.794599i | \(-0.707681\pi\) | ||||
0.607134 | − | 0.794599i | \(-0.292319\pi\) | |||||||
\(810\) | 15060.1i | 0.653282i | ||||||||
\(811\) | 37315.7i | 1.61570i | 0.589390 | + | 0.807849i | \(0.299368\pi\) | ||||
−0.589390 | + | 0.807849i | \(0.700632\pi\) | |||||||
\(812\) | −3254.30 | −0.140645 | ||||||||
\(813\) | 33109.6i | 1.42830i | ||||||||
\(814\) | 9343.64 | 0.402327 | ||||||||
\(815\) | 38774.3 | 1.66651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1445.75 | 0.0619097 | ||||||||
\(818\) | −9685.79 | −0.414005 | ||||||||
\(819\) | 14541.4i | 0.620414i | ||||||||
\(820\) | −32620.9 | −1.38924 | ||||||||
\(821\) | − 27365.1i | − 1.16328i | −0.813448 | − | 0.581638i | \(-0.802412\pi\) | ||||
0.813448 | − | 0.581638i | \(-0.197588\pi\) | |||||||
\(822\) | − 14033.6i | − 0.595471i | ||||||||
\(823\) | 21138.4i | 0.895308i | 0.894207 | + | 0.447654i | \(0.147740\pi\) | ||||
−0.894207 | + | 0.447654i | \(0.852260\pi\) | |||||||
\(824\) | 14045.7 | 0.593818 | ||||||||
\(825\) | 14120.7 | 0.595902 | ||||||||
\(826\) | 7123.83i | 0.300084i | ||||||||
\(827\) | 43453.3i | 1.82711i | 0.406717 | + | 0.913554i | \(0.366673\pi\) | ||||
−0.406717 | + | 0.913554i | \(0.633327\pi\) | |||||||
\(828\) | − 7311.55i | − 0.306877i | ||||||||
\(829\) | 36460.2 | 1.52752 | 0.763760 | − | 0.645501i | \(-0.223351\pi\) | ||||
0.763760 | + | 0.645501i | \(0.223351\pi\) | |||||||
\(830\) | − 3051.85i | − 0.127628i | ||||||||
\(831\) | 24942.2 | 1.04120 | ||||||||
\(832\) | −100.019 | −0.00416771 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −13871.9 | −0.575952 | ||||||||
\(835\) | −32086.5 | −1.32982 | ||||||||
\(836\) | − 899.575i | − 0.0372158i | ||||||||
\(837\) | 24517.4 | 1.01248 | ||||||||
\(838\) | − 4082.39i | − 0.168286i | ||||||||
\(839\) | − 20236.0i | − 0.832687i | −0.909207 | − | 0.416344i | \(-0.863311\pi\) | ||||
0.909207 | − | 0.416344i | \(-0.136689\pi\) | |||||||
\(840\) | 40058.0i | 1.64539i | ||||||||
\(841\) | 24041.9 | 0.985770 | ||||||||
\(842\) | −18289.3 | −0.748564 | ||||||||
\(843\) | − 20786.8i | − 0.849272i | ||||||||
\(844\) | − 439.386i | − 0.0179198i | ||||||||
\(845\) | 7469.92i | 0.304110i | ||||||||
\(846\) | −2558.51 | −0.103976 | ||||||||
\(847\) | − 20188.4i | − 0.818988i | ||||||||
\(848\) | 2994.18 | 0.121251 | ||||||||
\(849\) | 26349.4 | 1.06515 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18284.3 | −0.736519 | ||||||||
\(852\) | 18810.2 | 0.756368 | ||||||||
\(853\) | − 6934.19i | − 0.278338i | −0.990269 | − | 0.139169i | \(-0.955557\pi\) | ||||
0.990269 | − | 0.139169i | \(-0.0444431\pi\) | |||||||
\(854\) | −20156.6 | −0.807664 | ||||||||
\(855\) | 415.328i | 0.0166128i | ||||||||
\(856\) | − 18122.7i | − 0.723623i | ||||||||
\(857\) | 19207.8i | 0.765607i | 0.923830 | + | 0.382803i | \(0.125041\pi\) | ||||
−0.923830 | + | 0.382803i | \(0.874959\pi\) | |||||||
\(858\) | −18388.9 | −0.731688 | ||||||||
\(859\) | 9954.55 | 0.395395 | 0.197698 | − | 0.980263i | \(-0.436654\pi\) | ||||
0.197698 | + | 0.980263i | \(0.436654\pi\) | |||||||
\(860\) | 39840.6i | 1.57971i | ||||||||
\(861\) | − 63773.2i | − 2.52426i | ||||||||
\(862\) | 9003.26i | 0.355745i | ||||||||
\(863\) | −33698.0 | −1.32919 | −0.664596 | − | 0.747203i | \(-0.731396\pi\) | ||||
−0.664596 | + | 0.747203i | \(0.731396\pi\) | |||||||
\(864\) | 18603.3i | 0.732519i | ||||||||
\(865\) | −5220.91 | −0.205221 | ||||||||
\(866\) | 14425.7 | 0.566058 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 41708.6 | 1.63097 | ||||||||
\(869\) | 17415.0 | 0.679818 | ||||||||
\(870\) | 1900.03i | 0.0740425i | ||||||||
\(871\) | −21117.8 | −0.821525 | ||||||||
\(872\) | − 12742.6i | − 0.494861i | ||||||||
\(873\) | 3752.20i | 0.145467i | ||||||||
\(874\) | − 437.236i | − 0.0169219i | ||||||||
\(875\) | −26790.1 | −1.03505 | ||||||||
\(876\) | 28330.2 | 1.09268 | ||||||||
\(877\) | 4469.65i | 0.172097i | 0.996291 | + | 0.0860487i | \(0.0274241\pi\) | ||||
−0.996291 | + | 0.0860487i | \(0.972576\pi\) | |||||||
\(878\) | 16789.7i | 0.645358i | ||||||||
\(879\) | − 18734.5i | − 0.718885i | ||||||||
\(880\) | 17103.1 | 0.655164 | ||||||||
\(881\) | − 2081.32i | − 0.0795930i | −0.999208 | − | 0.0397965i | \(-0.987329\pi\) | ||||
0.999208 | − | 0.0397965i | \(-0.0126710\pi\) | |||||||
\(882\) | −5124.91 | −0.195652 | ||||||||
\(883\) | 10124.4 | 0.385857 | 0.192929 | − | 0.981213i | \(-0.438201\pi\) | ||||
0.192929 | + | 0.981213i | \(0.438201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16745.6 | −0.636040 | ||||||||
\(886\) | 13749.1 | 0.521343 | ||||||||
\(887\) | 42725.3i | 1.61733i | 0.588268 | + | 0.808666i | \(0.299810\pi\) | ||||
−0.588268 | + | 0.808666i | \(0.700190\pi\) | |||||||
\(888\) | −18029.2 | −0.681328 | ||||||||
\(889\) | − 11623.9i | − 0.438529i | ||||||||
\(890\) | 10424.5i | 0.392618i | ||||||||
\(891\) | 40965.8i | 1.54030i | ||||||||
\(892\) | 30338.3 | 1.13879 | ||||||||
\(893\) | 615.996 | 0.0230835 | ||||||||
\(894\) | 21089.7i | 0.788977i | ||||||||
\(895\) | − 25445.7i | − 0.950343i | ||||||||
\(896\) | 39442.7i | 1.47063i | ||||||||
\(897\) | 35984.8 | 1.33946 | ||||||||
\(898\) | − 21140.2i | − 0.785588i | ||||||||
\(899\) | 4448.02 | 0.165017 | ||||||||
\(900\) | −3311.80 | −0.122659 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 22039.7 | 0.813573 | ||||||||
\(903\) | −77887.4 | −2.87036 | ||||||||
\(904\) | − 26526.3i | − 0.975941i | ||||||||
\(905\) | 22241.8 | 0.816954 | ||||||||
\(906\) | − 16035.5i | − 0.588017i | ||||||||
\(907\) | − 21767.6i | − 0.796893i | −0.917192 | − | 0.398446i | \(-0.869550\pi\) | ||||
0.917192 | − | 0.398446i | \(-0.130450\pi\) | |||||||
\(908\) | − 11040.6i | − 0.403519i | ||||||||
\(909\) | −8228.28 | −0.300236 | ||||||||
\(910\) | −23963.4 | −0.872943 | ||||||||
\(911\) | − 21654.2i | − 0.787524i | −0.919212 | − | 0.393762i | \(-0.871173\pi\) | ||||
0.919212 | − | 0.393762i | \(-0.128827\pi\) | |||||||
\(912\) | 532.636i | 0.0193392i | ||||||||
\(913\) | − 8301.49i | − 0.300919i | ||||||||
\(914\) | 17109.9 | 0.619197 | ||||||||
\(915\) | − 47380.9i | − 1.71187i | ||||||||
\(916\) | −2008.20 | −0.0724376 | ||||||||
\(917\) | 542.560 | 0.0195386 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21445.1 | 0.769760 | 0.384880 | − | 0.922967i | \(-0.374243\pi\) | ||||
0.384880 | + | 0.922967i | \(0.374243\pi\) | |||||||
\(920\) | 27090.6 | 0.970818 | ||||||||
\(921\) | 24103.8i | 0.862376i | ||||||||
\(922\) | 19575.9 | 0.699239 | ||||||||
\(923\) | 25300.1i | 0.902234i | ||||||||
\(924\) | 48463.2i | 1.72546i | ||||||||
\(925\) | 8281.97i | 0.294389i | ||||||||
\(926\) | 19159.6 | 0.679938 | ||||||||
\(927\) | −7845.51 | −0.277972 | ||||||||
\(928\) | 3375.06i | 0.119388i | ||||||||
\(929\) | 24271.4i | 0.857177i | 0.903500 | + | 0.428589i | \(0.140989\pi\) | ||||
−0.903500 | + | 0.428589i | \(0.859011\pi\) | |||||||
\(930\) | − 24351.7i | − 0.858626i | ||||||||
\(931\) | 1233.89 | 0.0434363 | ||||||||
\(932\) | − 13467.7i | − 0.473338i | ||||||||
\(933\) | 54763.3 | 1.92162 | ||||||||
\(934\) | 13303.0 | 0.466046 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9696.96 | 0.338627 | ||||||||
\(937\) | −38491.5 | −1.34201 | −0.671005 | − | 0.741453i | \(-0.734137\pi\) | ||||
−0.671005 | + | 0.741453i | \(0.734137\pi\) | |||||||
\(938\) | − 13823.6i | − 0.481190i | ||||||||
\(939\) | −10587.7 | −0.367964 | ||||||||
\(940\) | 16975.1i | 0.589006i | ||||||||
\(941\) | 31323.4i | 1.08514i | 0.840012 | + | 0.542568i | \(0.182548\pi\) | ||||
−0.840012 | + | 0.542568i | \(0.817452\pi\) | |||||||
\(942\) | − 20790.3i | − 0.719092i | ||||||||
\(943\) | −43128.9 | −1.48937 | ||||||||
\(944\) | −5868.92 | −0.202349 | ||||||||
\(945\) | 37123.9i | 1.27793i | ||||||||
\(946\) | − 26917.5i | − 0.925121i | ||||||||
\(947\) | − 32096.4i | − 1.10136i | −0.834715 | − | 0.550682i | \(-0.814368\pi\) | ||||
0.834715 | − | 0.550682i | \(-0.185632\pi\) | |||||||
\(948\) | −14945.6 | −0.512035 | ||||||||
\(949\) | 38104.7i | 1.30341i | ||||||||
\(950\) | −198.049 | −0.00676373 | ||||||||
\(951\) | −50180.5 | −1.71106 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10493.3 | 0.356675 | 0.178338 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178338 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(954\) | 1353.75 | 0.0459426 | ||||||||
\(955\) | 31129.9i | 1.05481i | ||||||||
\(956\) | 35408.7 | 1.19791 | ||||||||
\(957\) | 5168.37i | 0.174576i | ||||||||
\(958\) | 7269.75i | 0.245172i | ||||||||
\(959\) | − 49745.4i | − 1.67504i | ||||||||
\(960\) | 153.901 | 0.00517409 | ||||||||
\(961\) | −27217.0 | −0.913597 | ||||||||
\(962\) | − 10785.4i | − 0.361470i | ||||||||
\(963\) | 10122.8i | 0.338736i | ||||||||
\(964\) | 12854.6i | 0.429479i | ||||||||
\(965\) | −8633.74 | −0.288010 | ||||||||
\(966\) | 23555.4i | 0.784559i | ||||||||
\(967\) | −31468.2 | −1.04648 | −0.523242 | − | 0.852184i | \(-0.675278\pi\) | ||||
−0.523242 | + | 0.852184i | \(0.675278\pi\) | |||||||
\(968\) | −13462.6 | −0.447010 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6183.39 | −0.204677 | ||||||||
\(971\) | 46923.8 | 1.55083 | 0.775415 | − | 0.631452i | \(-0.217541\pi\) | ||||
0.775415 | + | 0.631452i | \(0.217541\pi\) | |||||||
\(972\) | − 17389.9i | − 0.573850i | ||||||||
\(973\) | −49172.3 | −1.62013 | ||||||||
\(974\) | 6774.11i | 0.222851i | ||||||||
\(975\) | − 16299.5i | − 0.535387i | ||||||||
\(976\) | − 16605.9i | − 0.544612i | ||||||||
\(977\) | −8666.25 | −0.283785 | −0.141893 | − | 0.989882i | \(-0.545319\pi\) | ||||
−0.141893 | + | 0.989882i | \(0.545319\pi\) | |||||||
\(978\) | 22482.4 | 0.735081 | ||||||||
\(979\) | 28356.2i | 0.925709i | ||||||||
\(980\) | 34002.5i | 1.10834i | ||||||||
\(981\) | 7117.63i | 0.231650i | ||||||||
\(982\) | 22555.3 | 0.732961 | ||||||||
\(983\) | 35155.3i | 1.14067i | 0.821412 | + | 0.570336i | \(0.193187\pi\) | ||||
−0.821412 | + | 0.570336i | \(0.806813\pi\) | |||||||
\(984\) | −42527.1 | −1.37776 | ||||||||
\(985\) | 35557.3 | 1.15020 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33185.9 | −1.07023 | ||||||||
\(988\) | −1038.38 | −0.0334365 | ||||||||
\(989\) | 52674.2i | 1.69357i | ||||||||
\(990\) | 7732.75 | 0.248246 | ||||||||
\(991\) | − 11236.2i | − 0.360170i | −0.983651 | − | 0.180085i | \(-0.942363\pi\) | ||||
0.983651 | − | 0.180085i | \(-0.0576374\pi\) | |||||||
\(992\) | − 43256.3i | − 1.38447i | ||||||||
\(993\) | − 25314.8i | − 0.809004i | ||||||||
\(994\) | −16561.3 | −0.528463 | ||||||||
\(995\) | −23670.4 | −0.754172 | ||||||||
\(996\) | 7124.36i | 0.226651i | ||||||||
\(997\) | − 18825.0i | − 0.597987i | −0.954255 | − | 0.298994i | \(-0.903349\pi\) | ||||
0.954255 | − | 0.298994i | \(-0.0966509\pi\) | |||||||
\(998\) | − 4424.56i | − 0.140338i | ||||||||
\(999\) | −16708.6 | −0.529166 |
(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.b.f.288.10 | 24 | ||
17.4 | even | 4 | 289.4.a.i.1.8 | yes | 12 | ||
17.13 | even | 4 | 289.4.a.h.1.8 | ✓ | 12 | ||
17.16 | even | 2 | inner | 289.4.b.f.288.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.8 | ✓ | 12 | 17.13 | even | 4 | ||
289.4.a.i.1.8 | yes | 12 | 17.4 | even | 4 | ||
289.4.b.f.288.9 | 24 | 17.16 | even | 2 | inner | ||
289.4.b.f.288.10 | 24 | 1.1 | even | 1 | trivial |