Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(783,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.783");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.f (of order \(2\), degree \(1\), 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: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 783.18 | ||
Character | \(\chi\) | \(=\) | 784.783 |
Dual form | 784.4.f.j.783.17 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.30860 | 0.829190 | 0.414595 | − | 0.910006i | \(-0.363923\pi\) | ||||
0.414595 | + | 0.910006i | \(0.363923\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 7.29492i | − 0.652477i | −0.945287 | − | 0.326239i | \(-0.894219\pi\) | ||||
0.945287 | − | 0.326239i | \(-0.105781\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.43597 | −0.312443 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 21.8273i | − 0.598289i | −0.954208 | − | 0.299145i | \(-0.903299\pi\) | ||||
0.954208 | − | 0.299145i | \(-0.0967013\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 30.5508i | − 0.651789i | −0.945406 | − | 0.325895i | \(-0.894334\pi\) | ||||
0.945406 | − | 0.325895i | \(-0.105666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 31.4309i | − 0.541028i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 55.0978i | 0.786070i | 0.919524 | + | 0.393035i | \(0.128575\pi\) | ||||
−0.919524 | + | 0.393035i | \(0.871425\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 58.7072 | 0.708861 | 0.354431 | − | 0.935082i | \(-0.384675\pi\) | ||||
0.354431 | + | 0.935082i | \(0.384675\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 79.6503i | − 0.722097i | −0.932547 | − | 0.361049i | \(-0.882419\pi\) | ||||
0.932547 | − | 0.361049i | \(-0.117581\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71.7842 | 0.574274 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −152.679 | −1.08827 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −116.193 | −0.744018 | −0.372009 | − | 0.928229i | \(-0.621331\pi\) | ||||
−0.372009 | + | 0.928229i | \(0.621331\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −110.020 | −0.637426 | −0.318713 | − | 0.947851i | \(-0.603251\pi\) | ||||
−0.318713 | + | 0.947851i | \(0.603251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 94.0451i | − 0.496096i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −376.127 | −1.67121 | −0.835607 | − | 0.549328i | \(-0.814884\pi\) | ||||
−0.835607 | + | 0.549328i | \(0.814884\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 131.631i | − 0.540457i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 232.841i | − 0.886918i | −0.896295 | − | 0.443459i | \(-0.853751\pi\) | ||||
0.896295 | − | 0.443459i | \(-0.146249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 260.884i | − 0.925219i | −0.886562 | − | 0.462610i | \(-0.846913\pi\) | ||||
0.886562 | − | 0.462610i | \(-0.153087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 61.5397i | 0.203862i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 36.5870 | 0.113548 | 0.0567741 | − | 0.998387i | \(-0.481919\pi\) | ||||
0.0567741 | + | 0.998387i | \(0.481919\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 237.394i | 0.651801i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 59.1734 | 0.153360 | 0.0766801 | − | 0.997056i | \(-0.475568\pi\) | ||||
0.0766801 | + | 0.997056i | \(0.475568\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −159.228 | −0.390370 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 252.946 | 0.587781 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −707.304 | −1.56073 | −0.780366 | − | 0.625323i | \(-0.784967\pi\) | ||||
−0.780366 | + | 0.625323i | \(0.784967\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 323.781i | − 0.679605i | −0.940497 | − | 0.339802i | \(-0.889640\pi\) | ||||
0.940497 | − | 0.339802i | \(-0.110360\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −222.865 | −0.425278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 239.434i | 0.436589i | 0.975883 | + | 0.218295i | \(0.0700494\pi\) | ||||
−0.975883 | + | 0.218295i | \(0.929951\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 343.181i | − 0.598756i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 887.119i | − 1.48284i | −0.671042 | − | 0.741420i | \(-0.734153\pi\) | ||||
0.671042 | − | 0.741420i | \(-0.265847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 550.887i | − 0.883238i | −0.897203 | − | 0.441619i | \(-0.854404\pi\) | ||||
0.897203 | − | 0.441619i | \(-0.145596\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 309.289 | 0.476182 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1248.76i | 1.77843i | 0.457489 | + | 0.889215i | \(0.348749\pi\) | ||||
−0.457489 | + | 0.889215i | \(0.651251\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −430.063 | −0.589936 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1393.89 | −1.84336 | −0.921681 | − | 0.387949i | \(-0.873184\pi\) | ||||
−0.921681 | + | 0.387949i | \(0.873184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 401.934 | 0.512893 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −500.630 | −0.616933 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 982.787i | 1.17051i | 0.810850 | + | 0.585254i | \(0.199005\pi\) | ||||
−0.810850 | + | 0.585254i | \(0.800995\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −474.033 | −0.528548 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 428.264i | − 0.462516i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 441.547i | − 0.462188i | −0.972931 | − | 0.231094i | \(-0.925769\pi\) | ||||
0.972931 | − | 0.231094i | \(-0.0742305\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 184.135i | 0.186932i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1110.09i | − 1.09364i | −0.837249 | − | 0.546822i | \(-0.815837\pi\) | ||||
0.837249 | − | 0.546822i | \(-0.184163\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −898.555 | −0.859585 | −0.429792 | − | 0.902928i | \(-0.641413\pi\) | ||||
−0.429792 | + | 0.902928i | \(0.641413\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1198.80i | 1.08310i | 0.840667 | + | 0.541552i | \(0.182163\pi\) | ||||
−0.840667 | + | 0.541552i | \(0.817837\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1304.01 | 1.14588 | 0.572942 | − | 0.819596i | \(-0.305802\pi\) | ||||
0.572942 | + | 0.819596i | \(0.305802\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1620.58 | −1.38575 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1948.52 | 1.62213 | 0.811067 | − | 0.584953i | \(-0.198887\pi\) | ||||
0.811067 | + | 0.584953i | \(0.198887\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −581.042 | −0.471152 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 257.726i | 0.203647i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 854.569 | 0.642050 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1003.22i | − 0.735424i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1435.52i | − 1.02718i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2444.26i | − 1.70782i | −0.520419 | − | 0.853911i | \(-0.674224\pi\) | ||||
0.520419 | − | 0.853911i | \(-0.325776\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 1124.04i | − 0.767183i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 552.936 | 0.368780 | 0.184390 | − | 0.982853i | \(-0.440969\pi\) | ||||
0.184390 | + | 0.982853i | \(0.440969\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1113.78i | 0.710068i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 76.1775 | 0.0475057 | 0.0237529 | − | 0.999718i | \(-0.492439\pi\) | ||||
0.0237529 | + | 0.999718i | \(0.492439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2410.83 | −1.47111 | −0.735555 | − | 0.677465i | \(-0.763078\pi\) | ||||
−0.735555 | + | 0.677465i | \(0.763078\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 157.639 | 0.0941531 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −666.841 | −0.389959 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 847.619i | 0.485455i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 745.876 | 0.410098 | 0.205049 | − | 0.978752i | \(-0.434265\pi\) | ||||
0.205049 | + | 0.978752i | \(0.434265\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 2658.43i | − 1.43271i | −0.697735 | − | 0.716356i | \(-0.745809\pi\) | ||||
0.697735 | − | 0.716356i | \(-0.254191\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 464.804i | − 0.245602i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 802.588i | 0.415906i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 761.304i | − 0.386998i | −0.981100 | − | 0.193499i | \(-0.938016\pi\) | ||||
0.981100 | − | 0.193499i | \(-0.0619836\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 254.955 | 0.127165 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1239.24i | 0.595489i | 0.954646 | + | 0.297745i | \(0.0962344\pi\) | ||||
−0.954646 | + | 0.297745i | \(0.903766\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −686.051 | −0.323691 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1306.07 | −0.605192 | −0.302596 | − | 0.953119i | \(-0.597853\pi\) | ||||
−0.302596 | + | 0.953119i | \(0.597853\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1263.65 | 0.575170 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −495.253 | −0.221479 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1471.23i | − 0.646564i | −0.946303 | − | 0.323282i | \(-0.895214\pi\) | ||||
0.946303 | − | 0.323282i | \(-0.104786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3047.49 | −1.29414 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3129.95i | 1.30695i | 0.756949 | + | 0.653474i | \(0.226689\pi\) | ||||
−0.756949 | + | 0.653474i | \(0.773311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1037.83i | − 0.426196i | −0.977031 | − | 0.213098i | \(-0.931645\pi\) | ||||
0.977031 | − | 0.213098i | \(-0.0683554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 1395.04i | − 0.563522i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2743.82i | 1.09043i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1202.64 | 0.470297 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 229.006i | 0.0867553i | 0.999059 | + | 0.0433777i | \(0.0138119\pi\) | ||||
−0.999059 | + | 0.0433777i | \(0.986188\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 723.322 | 0.269771 | 0.134886 | − | 0.990861i | \(-0.456933\pi\) | ||||
0.134886 | + | 0.990861i | \(0.456933\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −960.238 | −0.352636 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2377.97 | −0.860018 | −0.430009 | − | 0.902825i | \(-0.641490\pi\) | ||||
−0.430009 | + | 0.902825i | \(0.641490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1011.77 | −0.360414 | −0.180207 | − | 0.983629i | \(-0.557677\pi\) | ||||
−0.180207 | + | 0.983629i | \(0.557677\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1031.62i | 0.362016i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1698.56 | −0.578694 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 671.928i | 0.225615i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 1281.42i | − 0.424104i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1861.01i | − 0.607189i | −0.952801 | − | 0.303595i | \(-0.901813\pi\) | ||||
0.952801 | − | 0.303595i | \(-0.0981869\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3822.24i | − 1.22956i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1903.13 | −0.603684 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2373.55i | − 0.732373i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1683.28 | 0.512352 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6228.99 | 1.87051 | 0.935256 | − | 0.353972i | \(-0.115169\pi\) | ||||
0.935256 | + | 0.353972i | \(0.115169\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −605.570 | −0.179428 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2708.74 | −0.792007 | −0.396004 | − | 0.918249i | \(-0.629603\pi\) | ||||
−0.396004 | + | 0.918249i | \(0.629603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2794.23i | − 0.806321i | −0.915129 | − | 0.403161i | \(-0.867912\pi\) | ||||
0.915129 | − | 0.403161i | \(-0.132088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2110.75 | −0.593476 | −0.296738 | − | 0.954959i | \(-0.595899\pi\) | ||||
−0.296738 | + | 0.954959i | \(0.595899\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 266.899i | − 0.0740876i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5380.39i | 1.47466i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 106.409i | 0.0287993i | 0.999896 | + | 0.0143997i | \(0.00458372\pi\) | ||||
−0.999896 | + | 0.0143997i | \(0.995416\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7211.58i | 1.92755i | 0.266723 | + | 0.963773i | \(0.414059\pi\) | ||||
−0.266723 | + | 0.963773i | \(0.585941\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2269.37 | 0.599097 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1793.55i | − 0.462028i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6005.70 | −1.52850 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 925.020 | 0.232616 | 0.116308 | − | 0.993213i | \(-0.462894\pi\) | ||||
0.116308 | + | 0.993213i | \(0.462894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1738.55 | −0.432023 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1731.77 | 0.425286 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 2766.80i | − 0.671549i | −0.941942 | − | 0.335775i | \(-0.891002\pi\) | ||||
0.941942 | − | 0.335775i | \(-0.108998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 980.202 | 0.232464 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2199.92i | 0.515791i | 0.966173 | + | 0.257895i | \(0.0830290\pi\) | ||||
−0.966173 | + | 0.257895i | \(0.916971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 431.665i | − 0.100064i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4234.43i | 0.970573i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1265.42i | − 0.286819i | −0.989663 | − | 0.143409i | \(-0.954193\pi\) | ||||
0.989663 | − | 0.143409i | \(-0.0458065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −486.107 | −0.108963 | −0.0544814 | − | 0.998515i | \(-0.517351\pi\) | ||||
−0.0544814 | + | 0.998515i | \(0.517351\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1566.86i | − 0.343582i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3926.80 | 0.851764 | 0.425882 | − | 0.904779i | \(-0.359964\pi\) | ||||
0.425882 | + | 0.904779i | \(0.359964\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 928.128 | 0.199160 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3224.97 | −0.684646 | −0.342323 | − | 0.939582i | \(-0.611214\pi\) | ||||
−0.342323 | + | 0.939582i | \(0.611214\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2706.20 | 0.568434 | 0.284217 | − | 0.958760i | \(-0.408266\pi\) | ||||
0.284217 | + | 0.958760i | \(0.408266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1845.22i | − 0.383514i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1877.23 | 0.382094 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1902.45i | − 0.383242i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2199.96i | − 0.438645i | −0.975652 | − | 0.219323i | \(-0.929615\pi\) | ||||
0.975652 | − | 0.219323i | \(-0.0703847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5159.72i | 1.01834i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3332.58i | 0.651097i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2433.38 | −0.470655 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 4782.93i | − 0.906839i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2361.95 | −0.443427 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8312.27 | 1.54530 | 0.772649 | − | 0.634833i | \(-0.218931\pi\) | ||||
0.772649 | + | 0.634833i | \(0.218931\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3871.51 | −0.712759 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7991.41 | 1.45708 | 0.728539 | − | 0.685004i | \(-0.240200\pi\) | ||||
0.728539 | + | 0.685004i | \(0.240200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6852.64i | 1.23749i | 0.785592 | + | 0.618744i | \(0.212358\pi\) | ||||
−0.785592 | + | 0.618744i | \(0.787642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10508.0 | 1.86180 | 0.930898 | − | 0.365280i | \(-0.119027\pi\) | ||||
0.930898 | + | 0.365280i | \(0.119027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2536.18i | 0.445138i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5165.13i | 0.898099i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3234.64i | 0.557214i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2193.06i | − 0.374305i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5618.45 | 0.950157 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4480.16i | − 0.743963i | −0.928240 | − | 0.371981i | \(-0.878679\pi\) | ||||
0.928240 | − | 0.371981i | \(-0.121321\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3173.00 | 0.522160 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1746.65 | 0.284865 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7920.93 | 1.28036 | 0.640179 | − | 0.768226i | \(-0.278860\pi\) | ||||
0.640179 | + | 0.768226i | \(0.278860\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8395.39 | 1.34506 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2401.45i | 0.381365i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2503.48 | −0.390675 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1483.19i | 0.229457i | 0.993397 | + | 0.114729i | \(0.0365999\pi\) | ||||
−0.993397 | + | 0.114729i | \(0.963400\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8732.67i | 1.33940i | 0.742634 | + | 0.669698i | \(0.233576\pi\) | ||||
−0.742634 | + | 0.669698i | \(0.766424\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4664.48i | 0.709320i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7881.53i | 1.18836i | 0.804331 | + | 0.594181i | \(0.202524\pi\) | ||||
−0.804331 | + | 0.594181i | \(0.797476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6471.46 | −0.967519 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 7699.83i | − 1.13198i | −0.824412 | − | 0.565991i | \(-0.808494\pi\) | ||||
0.824412 | − | 0.565991i | \(-0.191506\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3412.46 | −0.497516 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3681.99 | 0.532382 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4018.67 | −0.576293 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1261.06 | 0.179365 | 0.0896825 | − | 0.995970i | \(-0.471415\pi\) | ||||
0.0896825 | + | 0.995970i | \(0.471415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1964.24i | 0.277112i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10012.5 | 1.38989 | 0.694944 | − | 0.719064i | \(-0.255429\pi\) | ||||
0.694944 | + | 0.719064i | \(0.255429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 6185.10i | − 0.851726i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3549.79i | 0.484943i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2464.21i | 0.333979i | 0.985959 | + | 0.166990i | \(0.0534046\pi\) | ||||
−0.985959 | + | 0.166990i | \(0.946595\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 10531.4i | − 1.41611i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7470.63 | −0.996688 | −0.498344 | − | 0.866979i | \(-0.666058\pi\) | ||||
−0.498344 | + | 0.866979i | \(0.666058\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2200.81i | 0.289079i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2044.68 | 0.266503 | 0.133251 | − | 0.991082i | \(-0.457458\pi\) | ||||
0.133251 | + | 0.991082i | \(0.457458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4388.56 | 0.567619 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2382.38 | 0.305789 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9109.57 | 1.16039 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2251.63i | − 0.284649i | −0.989820 | − | 0.142325i | \(-0.954542\pi\) | ||||
0.989820 | − | 0.142325i | \(-0.0454577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10049.5 | 1.25149 | 0.625745 | − | 0.780028i | \(-0.284795\pi\) | ||||
0.625745 | + | 0.780028i | \(0.284795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3361.20i | 0.415468i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3137.27i | 0.384919i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8209.84i | 0.999869i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7448.43i | 0.900492i | 0.892905 | + | 0.450246i | \(0.148664\pi\) | ||||
−0.892905 | + | 0.450246i | \(0.851336\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 328.218 | 0.0393913 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10168.3i | 1.20275i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10387.3 | −1.21983 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10836.7 | 1.26350 | 0.631751 | − | 0.775171i | \(-0.282337\pi\) | ||||
0.631751 | + | 0.775171i | \(0.282337\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13758.0 | −1.59270 | −0.796348 | − | 0.604839i | \(-0.793237\pi\) | ||||
−0.796348 | + | 0.604839i | \(0.793237\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −308.647 | −0.0354774 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3955.15i | 0.451419i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2873.15 | −0.323350 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16039.8i | 1.79260i | 0.443448 | + | 0.896300i | \(0.353755\pi\) | ||||
−0.443448 | + | 0.896300i | \(0.646245\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 61.8807i | 0.00686789i | 0.999994 | + | 0.00343395i | \(0.00109306\pi\) | ||||
−0.999994 | + | 0.00343395i | \(0.998907\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3652.05i | 0.402534i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4676.05i | − 0.511867i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9208.19 | 1.00110 | 0.500550 | − | 0.865708i | \(-0.333131\pi\) | ||||
0.500550 | + | 0.865708i | \(0.333131\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 11063.1i | − 1.18651i | −0.805014 | − | 0.593256i | \(-0.797842\pi\) | ||||
0.805014 | − | 0.593256i | \(-0.202158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7169.35 | 0.763729 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3213.68 | 0.340049 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12834.1 | 1.34895 | 0.674473 | − | 0.738299i | \(-0.264371\pi\) | ||||
0.674473 | + | 0.738299i | \(0.264371\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5082.29 | −0.530634 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 11454.1i | − 1.18799i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3870.88 | −0.396220 | −0.198110 | − | 0.980180i | \(-0.563480\pi\) | ||||
−0.198110 | + | 0.980180i | \(0.563480\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 8412.30i | − 0.855453i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 3071.29i | − 0.310291i | −0.987892 | − | 0.155146i | \(-0.950415\pi\) | ||||
0.987892 | − | 0.155146i | \(-0.0495846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10063.3i | 1.01011i | 0.863088 | + | 0.505054i | \(0.168527\pi\) | ||||
−0.863088 | + | 0.505054i | \(0.831473\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3458.03i | 0.344865i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7436.68 | −0.736892 | −0.368446 | − | 0.929649i | \(-0.620110\pi\) | ||||
−0.368446 | + | 0.929649i | \(0.620110\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 3280.15i | − 0.320895i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5694.39 | −0.553549 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4214.25 | 0.407080 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −499.185 | −0.0479164 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11401.1 | −1.08753 | −0.543767 | − | 0.839236i | \(-0.683003\pi\) | ||||
−0.543767 | + | 0.839236i | \(0.683003\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11491.0i | 1.08928i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3221.05 | −0.301567 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1925.77i | 0.179189i | 0.995978 | + | 0.0895945i | \(0.0285571\pi\) | ||||
−0.995978 | + | 0.0895945i | \(0.971443\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5339.39i | 0.493774i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 20769.7i | − 1.90901i | −0.298192 | − | 0.954506i | \(-0.596383\pi\) | ||||
0.298192 | − | 0.954506i | \(-0.403617\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6401.99i | − 0.584850i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1343.25 | 0.121969 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4017.64i | 0.360429i | 0.983627 | + | 0.180215i | \(0.0576792\pi\) | ||||
−0.983627 | + | 0.180215i | \(0.942321\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5627.35 | −0.501819 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12683.3 | −1.12429 | −0.562147 | − | 0.827037i | \(-0.690025\pi\) | ||||
−0.562147 | + | 0.827037i | \(0.690025\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8098.01 | −0.713578 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5444.56 | 0.476926 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 16422.8i | − 1.43011i | −0.699068 | − | 0.715055i | \(-0.746402\pi\) | ||||
0.699068 | − | 0.715055i | \(-0.253598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8963.39 | −0.771429 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6554.88i | 0.560859i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 798.596i | − 0.0679347i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 6338.94i | − 0.536124i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12611.5i | 1.06050i | 0.847843 | + | 0.530248i | \(0.177901\pi\) | ||||
−0.847843 | + | 0.530248i | \(0.822099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8227.18 | 0.687858 | 0.343929 | − | 0.938996i | \(-0.388242\pi\) | ||||
0.343929 | + | 0.938996i | \(0.388242\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 6061.88i | − 0.501062i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5822.83 | 0.478575 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5966.80 | 0.487640 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7113.47 | −0.578084 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8745.12 | 0.706700 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13485.7i | 1.08371i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14128.7 | −1.12281 | −0.561404 | − | 0.827542i | \(-0.689739\pi\) | ||||
−0.561404 | + | 0.827542i | \(0.689739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 4471.60i | − 0.353398i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 9512.64i | − 0.747664i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 5978.72i | − 0.467334i | −0.972317 | − | 0.233667i | \(-0.924927\pi\) | ||||
0.972317 | − | 0.233667i | \(-0.0750725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2731.41i | 0.212338i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6821.38 | −0.527406 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11822.0i | 0.904173i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17085.3 | 1.29969 | 0.649844 | − | 0.760068i | \(-0.274834\pi\) | ||||
0.649844 | + | 0.760068i | \(0.274834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7970.21 | −0.603048 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5181.68 | 0.389966 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18164.9 | −1.35979 | −0.679893 | − | 0.733312i | \(-0.737974\pi\) | ||||
−0.679893 | + | 0.733312i | \(0.737974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 14214.3i | − 1.05841i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2716.25 | −0.200125 | −0.100063 | − | 0.994981i | \(-0.531904\pi\) | ||||
−0.100063 | + | 0.994981i | \(0.531904\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 16040.2i | − 1.17559i | −0.809009 | − | 0.587796i | \(-0.799996\pi\) | ||||
0.809009 | − | 0.587796i | \(-0.200004\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 986.694i | 0.0719367i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 5717.63i | − 0.414681i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8635.18i | 0.623028i | 0.950242 | + | 0.311514i | \(0.100836\pi\) | ||||
−0.950242 | + | 0.311514i | \(0.899164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3116.51 | 0.223692 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1291.60i | − 0.0917538i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1880.09 | 0.132875 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27896.0 | −1.96148 | −0.980742 | − | 0.195307i | \(-0.937430\pi\) | ||||
−0.980742 | + | 0.195307i | \(0.937430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6458.98 | −0.451847 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10245.7 | −0.713119 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 11146.7i | − 0.771903i | −0.922519 | − | 0.385952i | \(-0.873873\pi\) | ||||
0.922519 | − | 0.385952i | \(-0.126127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4359.31 | −0.298852 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 2535.71i | − 0.172966i | −0.996253 | − | 0.0864829i | \(-0.972437\pi\) | ||||
0.996253 | − | 0.0864829i | \(-0.0275628\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 24136.0i | − 1.63815i | −0.573689 | − | 0.819073i | \(-0.694488\pi\) | ||||
0.573689 | − | 0.819073i | \(-0.305512\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2019.86i | − 0.136409i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 6234.01i | − 0.418923i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26255.6 | 1.75565 | 0.877825 | − | 0.478981i | \(-0.158994\pi\) | ||||
0.877825 | + | 0.478981i | \(0.158994\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1117.76i | − 0.0740095i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3121.21 | 0.205651 | 0.102826 | − | 0.994699i | \(-0.467212\pi\) | ||||
0.102826 | + | 0.994699i | \(0.467212\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7318.39 | −0.479847 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24316.0 | 1.58659 | 0.793295 | − | 0.608837i | \(-0.208364\pi\) | ||||
0.793295 | + | 0.608837i | \(0.208364\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6864.03 | −0.445701 | −0.222850 | − | 0.974853i | \(-0.571536\pi\) | ||||
−0.222850 | + | 0.974853i | \(0.571536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12161.0i | 0.785834i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1499.00 | −0.0959362 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 5521.13i | − 0.351663i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 20723.8i | − 1.31369i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 5366.60i | − 0.338575i | −0.985567 | − | 0.169288i | \(-0.945853\pi\) | ||||
0.985567 | − | 0.169288i | \(-0.0541467\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 8018.33i | − 0.503475i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17830.7 | −1.11431 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7483.71i | 0.463304i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30589.1 | −1.88486 | −0.942431 | − | 0.334399i | \(-0.891467\pi\) | ||||
−0.942431 | + | 0.334399i | \(0.891467\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15703.2 | −0.963098 | −0.481549 | − | 0.876419i | \(-0.659926\pi\) | ||||
−0.481549 | + | 0.876419i | \(0.659926\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8199.81 | −0.500569 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 620.287 | 0.0376909 | 0.0188454 | − | 0.999822i | \(-0.494001\pi\) | ||||
0.0188454 | + | 0.999822i | \(0.494001\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15438.5i | 0.933769i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2820.96 | 0.169055 | 0.0845275 | − | 0.996421i | \(-0.473062\pi\) | ||||
0.0845275 | + | 0.996421i | \(0.473062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 4033.62i | − 0.240621i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4647.27i | 0.275962i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 12783.8i | − 0.755668i | −0.925873 | − | 0.377834i | \(-0.876669\pi\) | ||||
0.925873 | − | 0.377834i | \(-0.123331\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 26233.0i | − 1.54364i | −0.635841 | − | 0.771820i | \(-0.719347\pi\) | ||||
0.635841 | − | 0.771820i | \(-0.280653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7252.59 | 0.424837 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9254.82i | 0.537254i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26838.2 | 1.55101 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7067.27 | −0.406600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11105.6 | 0.636091 | 0.318046 | − | 0.948075i | \(-0.396973\pi\) | ||||
0.318046 | + | 0.948075i | \(0.396973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10960.0 | −0.624962 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 18882.3i | − 1.07195i | −0.844235 | − | 0.535973i | \(-0.819945\pi\) | ||||
0.844235 | − | 0.535973i | \(-0.180055\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11670.9 | −0.656725 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5600.98i | − 0.313785i | −0.987616 | − | 0.156893i | \(-0.949852\pi\) | ||||
0.987616 | − | 0.156893i | \(-0.0501477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 555.709i | − 0.0309964i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 12039.2i | − 0.668594i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1807.79i | − 0.0999586i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7871.27 | 0.433339 | 0.216670 | − | 0.976245i | \(-0.430481\pi\) | ||||
0.216670 | + | 0.976245i | \(0.430481\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17586.8i | 0.959865i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12829.0 | 0.697180 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9094.39 | −0.492105 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 366.142 | 0.0197275 | 0.00986377 | − | 0.999951i | \(-0.496860\pi\) | ||||
0.00986377 | + | 0.999951i | \(0.496860\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22081.4 | −1.18466 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 1149.96i | − 0.0614327i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6287.99 | 0.333076 | 0.166538 | − | 0.986035i | \(-0.446741\pi\) | ||||
0.166538 | + | 0.986035i | \(0.446741\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 10534.5i | − 0.555659i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8763.15i | 0.460284i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4864.55i | 0.254439i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 458.475i | 0.0238801i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37302.8 | −1.93485 | −0.967427 | − | 0.253149i | \(-0.918534\pi\) | ||||
−0.967427 | + | 0.253149i | \(0.918534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31071.8i | 1.59830i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8340.83 | −0.427270 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21013.4 | −1.07200 | −0.536000 | − | 0.844218i | \(-0.680065\pi\) | ||||
−0.536000 | + | 0.844218i | \(0.680065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21389.5 | 1.08670 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14374.1 | 0.727287 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28825.5i | 1.45252i | 0.687423 | + | 0.726258i | \(0.258742\pi\) | ||||
−0.687423 | + | 0.726258i | \(0.741258\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5226.19 | 0.261207 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15856.8i | 0.789312i | 0.918829 | + | 0.394656i | \(0.129136\pi\) | ||||
−0.918829 | + | 0.394656i | \(0.870864\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 7727.70i | − 0.383109i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 17589.1i | − 0.868481i | −0.900797 | − | 0.434241i | \(-0.857017\pi\) | ||||
0.900797 | − | 0.434241i | \(-0.142983\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 5441.11i | − 0.267579i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11758.8 | 0.575946 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37263.1i | 1.81059i | 0.424786 | + | 0.905294i | \(0.360349\pi\) | ||||
−0.424786 | + | 0.905294i | \(0.639651\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3985.54 | 0.192883 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19393.0 | −0.934812 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28065.2 | 1.34748 | 0.673742 | − | 0.738967i | \(-0.264686\pi\) | ||||
0.673742 | + | 0.738967i | \(0.264686\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7490.72 | −0.358229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13162.9i | 0.627013i | 0.949586 | + | 0.313506i | \(0.101504\pi\) | ||||
−0.949586 | + | 0.313506i | \(0.898496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3390.71 | −0.160250 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21608.7i | 1.01727i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 86.1491i | − 0.00403981i | −0.999998 | − | 0.00201991i | \(-0.999357\pi\) | ||||
0.999998 | − | 0.00201991i | \(-0.000642957\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 11921.0i | − 0.556842i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 21795.5i | − 1.01414i | −0.861905 | − | 0.507070i | \(-0.830728\pi\) | ||||
0.861905 | − | 0.507070i | \(-0.169272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7897.71 | −0.366057 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 13669.4i | − 0.628702i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19363.4 | −0.887167 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17740.3 | 0.809689 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5553.65 | −0.252507 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15336.7 | −0.694655 | −0.347328 | − | 0.937744i | \(-0.612911\pi\) | ||||
−0.347328 | + | 0.937744i | \(0.612911\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9478.58i | 0.427689i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9891.76 | −0.442959 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1859.87i | − 0.0829721i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6023.38i | − 0.267703i | −0.991001 | − | 0.133851i | \(-0.957266\pi\) | ||||
0.991001 | − | 0.133851i | \(-0.0427345\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2015.87i | 0.0892568i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 8290.76i | − 0.365717i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12024.4 | −0.528432 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 5452.20i | − 0.237827i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10694.5 | −0.464770 | −0.232385 | − | 0.972624i | \(-0.574653\pi\) | ||||
−0.232385 | + | 0.972624i | \(0.574653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11140.5 | 0.482362 | 0.241181 | − | 0.970480i | \(-0.422465\pi\) | ||||
0.241181 | + | 0.970480i | \(0.422465\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2094.44 | −0.0903508 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9040.15 | 0.388543 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 15315.8i | − 0.655852i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20793.3 | 0.883912 | 0.441956 | − | 0.897037i | \(-0.354285\pi\) | ||||
0.441956 | + | 0.897037i | \(0.354285\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 34204.9i | − 1.44874i | −0.689414 | − | 0.724368i | \(-0.742132\pi\) | ||||
0.689414 | − | 0.724368i | \(-0.257868\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 6750.95i | − 0.284895i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13200.0i | 0.555028i | 0.960722 | + | 0.277514i | \(0.0895104\pi\) | ||||
−0.960722 | + | 0.277514i | \(0.910490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 21786.2i | − 0.912745i | −0.889789 | − | 0.456373i | \(-0.849148\pi\) | ||||
0.889789 | − | 0.456373i | \(-0.150852\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16919.0 | 0.706275 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9527.70i | 0.394874i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16797.8 | 0.693689 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34045.3 | −1.40092 | −0.700462 | − | 0.713690i | \(-0.747022\pi\) | ||||
−0.700462 | + | 0.713690i | \(0.747022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10888.2 | −0.446437 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13895.1 | −0.567702 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 9218.22i | − 0.375286i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11659.9 | 0.471340 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29958.7i | 1.20678i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24531.8i | 0.984703i | 0.870397 | + | 0.492351i | \(0.163863\pi\) | ||||
−0.870397 | + | 0.492351i | \(0.836137\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3612.83i | 0.144510i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 704.704i | 0.0280890i | 0.999901 | + | 0.0140445i | \(0.00447064\pi\) | ||||
−0.999901 | + | 0.0140445i | \(0.995529\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44971.5 | 1.78627 | 0.893137 | − | 0.449785i | \(-0.148499\pi\) | ||||
0.893137 | + | 0.449785i | \(0.148499\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 10675.4i | − 0.421084i | −0.977585 | − | 0.210542i | \(-0.932477\pi\) | ||||
0.977585 | − | 0.210542i | \(-0.0675229\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10732.5 | −0.421868 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8088.23 | 0.316829 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27257.0 | 1.06402 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7314.89 | 0.284564 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3724.88i | 0.144408i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21401.4 | −0.824030 | −0.412015 | − | 0.911177i | \(-0.635175\pi\) | ||||
−0.412015 | + | 0.911177i | \(0.635175\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 9478.75i | − 0.363720i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 45960.0i | − 1.75758i | −0.477205 | − | 0.878792i | \(-0.658350\pi\) | ||||
0.477205 | − | 0.878792i | \(-0.341650\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22863.2i | 0.871357i | 0.900102 | + | 0.435679i | \(0.143492\pi\) | ||||
−0.900102 | + | 0.435679i | \(0.856508\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22231.2i | 0.844399i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28962.2 | −1.09634 | −0.548170 | − | 0.836367i | \(-0.684675\pi\) | ||||
−0.548170 | + | 0.836367i | \(0.684675\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9387.12i | 0.352952i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2147.92 | 0.0804899 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22832.7 | 0.852754 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10484.5 | −0.390263 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12783.6 | 0.474257 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3260.33i | 0.120552i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7570.90 | −0.278083 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 12131.8i | − 0.444133i | −0.975032 | − | 0.222067i | \(-0.928720\pi\) | ||||
0.975032 | − | 0.222067i | \(-0.0712802\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9364.69i | 0.341702i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 37975.1i | − 1.38109i | −0.723291 | − | 0.690543i | \(-0.757371\pi\) | ||||
0.723291 | − | 0.690543i | \(-0.242629\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30424.8i | 1.10286i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10176.7 | −0.367685 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 8404.14i | − 0.301662i | −0.988560 | − | 0.150831i | \(-0.951805\pi\) | ||||
0.988560 | − | 0.150831i | \(-0.0481949\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35814.3 | 1.28135 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27102.2 | −0.966499 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27000.0 | −0.959734 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7580.18 | 0.268572 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 34512.7i | − 1.21886i | −0.792838 | − | 0.609432i | \(-0.791397\pi\) | ||||
0.792838 | − | 0.609432i | \(-0.208603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34431.8 | 1.20820 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 8773.14i | − 0.306858i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41349.8i | 1.44166i | 0.693110 | + | 0.720832i | \(0.256240\pi\) | ||||
−0.693110 | + | 0.720832i | \(0.743760\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29525.3i | 1.02611i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19799.0i | 0.685898i | 0.939354 | + | 0.342949i | \(0.111426\pi\) | ||||
−0.939354 | + | 0.342949i | \(0.888574\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18545.9 | −0.640441 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 54100.3i | − 1.85641i | −0.372066 | − | 0.928206i | \(-0.621351\pi\) | ||||
0.372066 | − | 0.928206i | \(-0.378649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16830.0 | −0.575685 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45274.8 | 1.54378 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36760.6 | −1.24952 | −0.624761 | − | 0.780816i | \(-0.714803\pi\) | ||||
−0.624761 | + | 0.780816i | \(0.714803\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1670.58 | 0.0566059 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10927.4i | 0.369104i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17686.5 | −0.593688 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 10113.0i | − 0.338409i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 5276.58i | − 0.176020i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 3530.73i | − 0.117415i | −0.998275 | − | 0.0587077i | \(-0.981302\pi\) | ||||
0.998275 | − | 0.0587077i | \(-0.0186980\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13936.8i | 0.462037i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20605.2 | −0.681000 | −0.340500 | − | 0.940245i | \(-0.610596\pi\) | ||||
−0.340500 | + | 0.940245i | \(0.610596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 9449.03i | − 0.310370i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6352.62 | −0.208023 | −0.104011 | − | 0.994576i | \(-0.533168\pi\) | ||||
−0.104011 | + | 0.994576i | \(0.533168\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21451.6 | 0.700302 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11000.6 | −0.358024 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5353.15 | 0.173692 | 0.0868459 | − | 0.996222i | \(-0.472321\pi\) | ||||
0.0868459 | + | 0.996222i | \(0.472321\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17347.1i | 0.561142i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20779.5 | −0.668098 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 6358.28i | − 0.203812i | −0.994794 | − | 0.101906i | \(-0.967506\pi\) | ||||
0.994794 | − | 0.101906i | \(-0.0324941\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 19303.2i | − 0.616887i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7380.77i | 0.235162i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27647.2i | 0.878232i | 0.898430 | + | 0.439116i | \(0.144708\pi\) | ||||
−0.898430 | + | 0.439116i | \(0.855292\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 57426.9 | 1.81872 |
(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 | 784.4.f.j.783.18 | yes | 24 | |
4.3 | odd | 2 | inner | 784.4.f.j.783.8 | yes | 24 | |
7.6 | odd | 2 | inner | 784.4.f.j.783.7 | ✓ | 24 | |
28.27 | even | 2 | inner | 784.4.f.j.783.17 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.4.f.j.783.7 | ✓ | 24 | 7.6 | odd | 2 | inner | |
784.4.f.j.783.8 | yes | 24 | 4.3 | odd | 2 | inner | |
784.4.f.j.783.17 | yes | 24 | 28.27 | even | 2 | inner | |
784.4.f.j.783.18 | yes | 24 | 1.1 | even | 1 | trivial |