Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.b (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: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 890.69 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.16 |
$q$-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 \(\left(\mathbb{Z}/1143\mathbb{Z}\right)^\times\).
\(n\) | \(128\) | \(892\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.71611i | 1.35806i | 0.734112 | + | 0.679028i | \(0.237598\pi\) | ||||
−0.734112 | + | 0.679028i | \(0.762402\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.37726 | −0.844316 | ||||||||
\(5\) | 6.95811i | 1.39162i | 0.718224 | + | 0.695811i | \(0.244955\pi\) | ||||
−0.718224 | + | 0.695811i | \(0.755045\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.31599 | 0.616570 | 0.308285 | − | 0.951294i | \(-0.400245\pi\) | ||||
0.308285 | + | 0.951294i | \(0.400245\pi\) | |||||||
\(8\) | 1.69142i | 0.211428i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −18.8990 | −1.88990 | ||||||||
\(11\) | − 10.6740i | − 0.970364i | −0.874413 | − | 0.485182i | \(-0.838753\pi\) | ||||
0.874413 | − | 0.485182i | \(-0.161247\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.5086 | 0.962199 | 0.481099 | − | 0.876666i | \(-0.340238\pi\) | ||||
0.481099 | + | 0.876666i | \(0.340238\pi\) | |||||||
\(14\) | 11.7227i | 0.837337i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −18.1031 | −1.13145 | ||||||||
\(17\) | 32.6178i | 1.91869i | 0.282232 | + | 0.959346i | \(0.408925\pi\) | ||||
−0.282232 | + | 0.959346i | \(0.591075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −15.7237 | −0.827566 | −0.413783 | − | 0.910376i | \(-0.635793\pi\) | ||||
−0.413783 | + | 0.910376i | \(0.635793\pi\) | |||||||
\(20\) | − 23.4994i | − 1.17497i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 28.9918 | 1.31781 | ||||||||
\(23\) | − 11.1858i | − 0.486341i | −0.969984 | − | 0.243170i | \(-0.921813\pi\) | ||||
0.969984 | − | 0.243170i | \(-0.0781874\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.4154 | −0.936615 | ||||||||
\(26\) | 33.9747i | 1.30672i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −14.5762 | −0.520580 | ||||||||
\(29\) | 42.0647i | 1.45051i | 0.688482 | + | 0.725254i | \(0.258278\pi\) | ||||
−0.688482 | + | 0.725254i | \(0.741722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −12.3795 | −0.399339 | −0.199669 | − | 0.979863i | \(-0.563987\pi\) | ||||
−0.199669 | + | 0.979863i | \(0.563987\pi\) | |||||||
\(32\) | − 42.4045i | − 1.32514i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −88.5935 | −2.60569 | ||||||||
\(35\) | 30.0312i | 0.858033i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.23275 | −0.195480 | −0.0977399 | − | 0.995212i | \(-0.531161\pi\) | ||||
−0.0977399 | + | 0.995212i | \(0.531161\pi\) | |||||||
\(38\) | − 42.7075i | − 1.12388i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.7691 | −0.294228 | ||||||||
\(41\) | − 3.87379i | − 0.0944826i | −0.998884 | − | 0.0472413i | \(-0.984957\pi\) | ||||
0.998884 | − | 0.0472413i | \(-0.0150430\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16.1935 | −0.376593 | −0.188297 | − | 0.982112i | \(-0.560297\pi\) | ||||
−0.188297 | + | 0.982112i | \(0.560297\pi\) | |||||||
\(44\) | 36.0489i | 0.819293i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 30.3820 | 0.660478 | ||||||||
\(47\) | 2.07073i | 0.0440580i | 0.999757 | + | 0.0220290i | \(0.00701262\pi\) | ||||
−0.999757 | + | 0.0220290i | \(0.992987\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −30.3722 | −0.619841 | ||||||||
\(50\) | − 63.5987i | − 1.27197i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −42.2448 | −0.812400 | ||||||||
\(53\) | 3.76342i | 0.0710079i | 0.999370 | + | 0.0355039i | \(0.0113036\pi\) | ||||
−0.999370 | + | 0.0355039i | \(0.988696\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 74.2709 | 1.35038 | ||||||||
\(56\) | 7.30016i | 0.130360i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −114.252 | −1.96987 | ||||||||
\(59\) | 64.3455i | 1.09060i | 0.838240 | + | 0.545301i | \(0.183585\pi\) | ||||
−0.838240 | + | 0.545301i | \(0.816415\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −52.2457 | −0.856486 | −0.428243 | − | 0.903664i | \(-0.640867\pi\) | ||||
−0.428243 | + | 0.903664i | \(0.640867\pi\) | |||||||
\(62\) | − 33.6241i | − 0.542325i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 42.7627 | 0.668167 | ||||||||
\(65\) | 87.0362i | 1.33902i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 112.184 | 1.67438 | 0.837192 | − | 0.546909i | \(-0.184196\pi\) | ||||
0.837192 | + | 0.546909i | \(0.184196\pi\) | |||||||
\(68\) | − 110.159i | − 1.61998i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −81.5680 | −1.16526 | ||||||||
\(71\) | 56.2639i | 0.792449i | 0.918154 | + | 0.396224i | \(0.129680\pi\) | ||||
−0.918154 | + | 0.396224i | \(0.870320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25.1935 | −0.345117 | −0.172558 | − | 0.984999i | \(-0.555203\pi\) | ||||
−0.172558 | + | 0.984999i | \(0.555203\pi\) | |||||||
\(74\) | − 19.6450i | − 0.265472i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 53.1032 | 0.698727 | ||||||||
\(77\) | − 46.0689i | − 0.598297i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.5144 | 0.740688 | 0.370344 | − | 0.928895i | \(-0.379240\pi\) | ||||
0.370344 | + | 0.928895i | \(0.379240\pi\) | |||||||
\(80\) | − 125.964i | − 1.57455i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.5216 | 0.128313 | ||||||||
\(83\) | − 90.6579i | − 1.09226i | −0.837699 | − | 0.546132i | \(-0.816100\pi\) | ||||
0.837699 | − | 0.546132i | \(-0.183900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −226.958 | −2.67010 | ||||||||
\(86\) | − 43.9834i | − 0.511435i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 18.0542 | 0.205162 | ||||||||
\(89\) | − 76.9304i | − 0.864387i | −0.901781 | − | 0.432193i | \(-0.857740\pi\) | ||||
0.901781 | − | 0.432193i | \(-0.142260\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 53.9869 | 0.593263 | ||||||||
\(92\) | 37.7775i | 0.410625i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.62433 | −0.0598333 | ||||||||
\(95\) | − 109.408i | − 1.15166i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −41.6816 | −0.429707 | −0.214854 | − | 0.976646i | \(-0.568927\pi\) | ||||
−0.214854 | + | 0.976646i | \(0.568927\pi\) | |||||||
\(98\) | − 82.4944i | − 0.841779i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 79.0798 | 0.790798 | ||||||||
\(101\) | − 18.4549i | − 0.182722i | −0.995818 | − | 0.0913608i | \(-0.970878\pi\) | ||||
0.995818 | − | 0.0913608i | \(-0.0291216\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.37878 | 0.0425124 | 0.0212562 | − | 0.999774i | \(-0.493233\pi\) | ||||
0.0212562 | + | 0.999774i | \(0.493233\pi\) | |||||||
\(104\) | 21.1573i | 0.203436i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.2219 | −0.0964326 | ||||||||
\(107\) | − 120.961i | − 1.13048i | −0.824927 | − | 0.565240i | \(-0.808784\pi\) | ||||
0.824927 | − | 0.565240i | \(-0.191216\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 22.7798 | 0.208989 | 0.104494 | − | 0.994525i | \(-0.466678\pi\) | ||||
0.104494 | + | 0.994525i | \(0.466678\pi\) | |||||||
\(110\) | 201.728i | 1.83389i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −78.1330 | −0.697616 | ||||||||
\(113\) | 22.4867i | 0.198997i | 0.995038 | + | 0.0994985i | \(0.0317239\pi\) | ||||
−0.995038 | + | 0.0994985i | \(0.968276\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 77.8323 | 0.676803 | ||||||||
\(116\) | − 142.064i | − 1.22469i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −174.770 | −1.48110 | ||||||||
\(119\) | 140.778i | 1.18301i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.06569 | 0.0583942 | ||||||||
\(122\) | − 141.905i | − 1.16316i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 41.8088 | 0.337168 | ||||||||
\(125\) | 11.0261i | 0.0882086i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2694 | −0.0887357 | ||||||||
\(128\) | − 53.4696i | − 0.417731i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −236.400 | −1.81846 | ||||||||
\(131\) | − 91.7796i | − 0.700608i | −0.936636 | − | 0.350304i | \(-0.886078\pi\) | ||||
0.936636 | − | 0.350304i | \(-0.113922\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −67.8636 | −0.510252 | ||||||||
\(134\) | 304.703i | 2.27391i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −55.1704 | −0.405665 | ||||||||
\(137\) | − 89.3843i | − 0.652440i | −0.945294 | − | 0.326220i | \(-0.894225\pi\) | ||||
0.945294 | − | 0.326220i | \(-0.105775\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −149.686 | −1.07687 | −0.538437 | − | 0.842666i | \(-0.680985\pi\) | ||||
−0.538437 | + | 0.842666i | \(0.680985\pi\) | |||||||
\(140\) | − 101.423i | − 0.724451i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −152.819 | −1.07619 | ||||||||
\(143\) | − 133.517i | − 0.933683i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −292.691 | −2.01856 | ||||||||
\(146\) | − 68.4284i | − 0.468688i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 24.4269 | 0.165047 | ||||||||
\(149\) | 124.068i | 0.832674i | 0.909210 | + | 0.416337i | \(0.136686\pi\) | ||||
−0.909210 | + | 0.416337i | \(0.863314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 216.165 | 1.43156 | 0.715779 | − | 0.698327i | \(-0.246072\pi\) | ||||
0.715779 | + | 0.698327i | \(0.246072\pi\) | |||||||
\(152\) | − 26.5955i | − 0.174970i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 125.128 | 0.812521 | ||||||||
\(155\) | − 86.1380i | − 0.555729i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −229.144 | −1.45952 | −0.729758 | − | 0.683706i | \(-0.760367\pi\) | ||||
−0.729758 | + | 0.683706i | \(0.760367\pi\) | |||||||
\(158\) | 158.932i | 1.00590i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 295.055 | 1.84410 | ||||||||
\(161\) | − 48.2780i | − 0.299863i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −123.348 | −0.756736 | −0.378368 | − | 0.925655i | \(-0.623515\pi\) | ||||
−0.378368 | + | 0.925655i | \(0.623515\pi\) | |||||||
\(164\) | 13.0828i | 0.0797732i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 246.237 | 1.48336 | ||||||||
\(167\) | − 63.7232i | − 0.381576i | −0.981631 | − | 0.190788i | \(-0.938896\pi\) | ||||
0.981631 | − | 0.190788i | \(-0.0611043\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5353 | −0.0741735 | ||||||||
\(170\) | − 616.444i | − 3.62614i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 54.6898 | 0.317964 | ||||||||
\(173\) | − 35.2926i | − 0.204004i | −0.994784 | − | 0.102002i | \(-0.967475\pi\) | ||||
0.994784 | − | 0.102002i | \(-0.0325248\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −101.060 | −0.577489 | ||||||||
\(176\) | 193.233i | 1.09791i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 208.952 | 1.17389 | ||||||||
\(179\) | − 241.836i | − 1.35104i | −0.737342 | − | 0.675519i | \(-0.763920\pi\) | ||||
0.737342 | − | 0.675519i | \(-0.236080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 288.741 | 1.59526 | 0.797628 | − | 0.603150i | \(-0.206088\pi\) | ||||
0.797628 | + | 0.603150i | \(0.206088\pi\) | |||||||
\(182\) | 146.635i | 0.805684i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.9200 | 0.102826 | ||||||||
\(185\) | − 50.3263i | − 0.272034i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 348.162 | 1.86183 | ||||||||
\(188\) | − 6.99339i | − 0.0371989i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 297.163 | 1.56402 | ||||||||
\(191\) | 91.5192i | 0.479158i | 0.970877 | + | 0.239579i | \(0.0770095\pi\) | ||||
−0.970877 | + | 0.239579i | \(0.922991\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 226.506 | 1.17361 | 0.586803 | − | 0.809730i | \(-0.300386\pi\) | ||||
0.586803 | + | 0.809730i | \(0.300386\pi\) | |||||||
\(194\) | − 113.212i | − 0.583566i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 102.575 | 0.523342 | ||||||||
\(197\) | 272.020i | 1.38081i | 0.723423 | + | 0.690405i | \(0.242568\pi\) | ||||
−0.723423 | + | 0.690405i | \(0.757432\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −152.048 | −0.764059 | −0.382029 | − | 0.924150i | \(-0.624775\pi\) | ||||
−0.382029 | + | 0.924150i | \(0.624775\pi\) | |||||||
\(200\) | − 39.6053i | − 0.198026i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 50.1255 | 0.248146 | ||||||||
\(203\) | 181.551i | 0.894340i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.9543 | 0.131484 | ||||||||
\(206\) | 11.8933i | 0.0577343i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −226.445 | −1.08868 | ||||||||
\(209\) | 167.835i | 0.803040i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 210.301 | 0.996685 | 0.498342 | − | 0.866980i | \(-0.333942\pi\) | ||||
0.498342 | + | 0.866980i | \(0.333942\pi\) | |||||||
\(212\) | − 12.7100i | − 0.0599531i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 328.544 | 1.53525 | ||||||||
\(215\) | − 112.676i | − 0.524076i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −53.4298 | −0.246220 | ||||||||
\(218\) | 61.8725i | 0.283819i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −250.832 | −1.14015 | ||||||||
\(221\) | 408.002i | 1.84616i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 198.451 | 0.889913 | 0.444956 | − | 0.895552i | \(-0.353219\pi\) | ||||
0.444956 | + | 0.895552i | \(0.353219\pi\) | |||||||
\(224\) | − 183.017i | − 0.817042i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −61.0763 | −0.270249 | ||||||||
\(227\) | 161.325i | 0.710685i | 0.934736 | + | 0.355342i | \(0.115636\pi\) | ||||
−0.934736 | + | 0.355342i | \(0.884364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 394.501 | 1.72271 | 0.861356 | − | 0.508002i | \(-0.169616\pi\) | ||||
0.861356 | + | 0.508002i | \(0.169616\pi\) | |||||||
\(230\) | 211.401i | 0.919136i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −71.1492 | −0.306678 | ||||||||
\(233\) | 385.938i | 1.65639i | 0.560442 | + | 0.828194i | \(0.310631\pi\) | ||||
−0.560442 | + | 0.828194i | \(0.689369\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.4084 | −0.0613122 | ||||||||
\(236\) | − 217.312i | − 0.920812i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −382.369 | −1.60659 | ||||||||
\(239\) | 393.051i | 1.64456i | 0.569081 | + | 0.822281i | \(0.307299\pi\) | ||||
−0.569081 | + | 0.822281i | \(0.692701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 80.5872 | 0.334387 | 0.167193 | − | 0.985924i | \(-0.446530\pi\) | ||||
0.167193 | + | 0.985924i | \(0.446530\pi\) | |||||||
\(242\) | 19.1912i | 0.0793025i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 176.447 | 0.723145 | ||||||||
\(245\) | − 211.333i | − 0.862585i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −196.682 | −0.796283 | ||||||||
\(248\) | − 20.9390i | − 0.0844314i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −29.9481 | −0.119792 | ||||||||
\(251\) | 156.298i | 0.622699i | 0.950295 | + | 0.311350i | \(0.100781\pi\) | ||||
−0.950295 | + | 0.311350i | \(0.899219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −119.398 | −0.471927 | ||||||||
\(254\) | − 30.6090i | − 0.120508i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 316.280 | 1.23547 | ||||||||
\(257\) | − 334.933i | − 1.30324i | −0.758546 | − | 0.651620i | \(-0.774090\pi\) | ||||
0.758546 | − | 0.651620i | \(-0.225910\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.2165 | −0.120527 | ||||||||
\(260\) | − 293.944i | − 1.13055i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 249.284 | 0.951465 | ||||||||
\(263\) | 403.738i | 1.53513i | 0.640973 | + | 0.767563i | \(0.278531\pi\) | ||||
−0.640973 | + | 0.767563i | \(0.721469\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.1863 | −0.0988162 | ||||||||
\(266\) | − 184.325i | − 0.692951i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −378.874 | −1.41371 | ||||||||
\(269\) | 96.1414i | 0.357403i | 0.983903 | + | 0.178701i | \(0.0571896\pi\) | ||||
−0.983903 | + | 0.178701i | \(0.942810\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 189.580 | 0.699556 | 0.349778 | − | 0.936833i | \(-0.386257\pi\) | ||||
0.349778 | + | 0.936833i | \(0.386257\pi\) | |||||||
\(272\) | − 590.484i | − 2.17090i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 242.778 | 0.886050 | ||||||||
\(275\) | 249.936i | 0.908857i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 171.642 | 0.619646 | 0.309823 | − | 0.950794i | \(-0.399730\pi\) | ||||
0.309823 | + | 0.950794i | \(0.399730\pi\) | |||||||
\(278\) | − 406.563i | − 1.46246i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −50.7954 | −0.181412 | ||||||||
\(281\) | 45.9693i | 0.163592i | 0.996649 | + | 0.0817959i | \(0.0260656\pi\) | ||||
−0.996649 | + | 0.0817959i | \(0.973934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −130.208 | −0.460098 | −0.230049 | − | 0.973179i | \(-0.573889\pi\) | ||||
−0.230049 | + | 0.973179i | \(0.573889\pi\) | |||||||
\(284\) | − 190.018i | − 0.669077i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 362.646 | 1.26799 | ||||||||
\(287\) | − 16.7192i | − 0.0582552i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −774.919 | −2.68138 | ||||||||
\(290\) | − 794.982i | − 2.74132i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 85.0851 | 0.291387 | ||||||||
\(293\) | 500.515i | 1.70824i | 0.520075 | + | 0.854121i | \(0.325904\pi\) | ||||
−0.520075 | + | 0.854121i | \(0.674096\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −447.723 | −1.51771 | ||||||||
\(296\) | − 12.2336i | − 0.0413299i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −336.984 | −1.13082 | ||||||||
\(299\) | − 139.919i | − 0.467956i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −69.8911 | −0.232196 | ||||||||
\(302\) | 587.129i | 1.94414i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 284.649 | 0.936347 | ||||||||
\(305\) | − 363.531i | − 1.19191i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 65.9196 | 0.214722 | 0.107361 | − | 0.994220i | \(-0.465760\pi\) | ||||
0.107361 | + | 0.994220i | \(0.465760\pi\) | |||||||
\(308\) | 155.587i | 0.505152i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 233.961 | 0.754711 | ||||||||
\(311\) | − 309.588i | − 0.995459i | −0.867332 | − | 0.497730i | \(-0.834167\pi\) | ||||
0.867332 | − | 0.497730i | \(-0.165833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 147.814 | 0.472248 | 0.236124 | − | 0.971723i | \(-0.424123\pi\) | ||||
0.236124 | + | 0.971723i | \(0.424123\pi\) | |||||||
\(314\) | − 622.381i | − 1.98210i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −197.618 | −0.625375 | ||||||||
\(317\) | − 148.170i | − 0.467413i | −0.972307 | − | 0.233706i | \(-0.924915\pi\) | ||||
0.972307 | − | 0.233706i | \(-0.0750854\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 448.999 | 1.40752 | ||||||||
\(320\) | 297.548i | 0.929837i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 131.128 | 0.407231 | ||||||||
\(323\) | − 512.874i | − 1.58784i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −292.893 | −0.901209 | ||||||||
\(326\) | − 335.027i | − 1.02769i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.55221 | 0.0199763 | ||||||||
\(329\) | 8.93724i | 0.0271649i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −286.761 | −0.866348 | −0.433174 | − | 0.901310i | \(-0.642606\pi\) | ||||
−0.433174 | + | 0.901310i | \(0.642606\pi\) | |||||||
\(332\) | 306.176i | 0.922216i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 173.079 | 0.518201 | ||||||||
\(335\) | 780.587i | 2.33011i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −480.605 | −1.42613 | −0.713063 | − | 0.701100i | \(-0.752693\pi\) | ||||
−0.713063 | + | 0.701100i | \(0.752693\pi\) | |||||||
\(338\) | − 34.0473i | − 0.100732i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 766.498 | 2.25440 | ||||||||
\(341\) | 132.139i | 0.387504i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −342.570 | −0.998746 | ||||||||
\(344\) | − 27.3901i | − 0.0796223i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 95.8588 | 0.277049 | ||||||||
\(347\) | 421.056i | 1.21342i | 0.794924 | + | 0.606709i | \(0.207511\pi\) | ||||
−0.794924 | + | 0.606709i | \(0.792489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −192.726 | −0.552224 | −0.276112 | − | 0.961125i | \(-0.589046\pi\) | ||||
−0.276112 | + | 0.961125i | \(0.589046\pi\) | |||||||
\(350\) | − 274.492i | − 0.784262i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −452.625 | −1.28587 | ||||||||
\(353\) | 687.481i | 1.94754i | 0.227541 | + | 0.973769i | \(0.426931\pi\) | ||||
−0.227541 | + | 0.973769i | \(0.573069\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −391.490 | −1.10279 | ||||||||
\(356\) | 259.814i | 0.729815i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 656.853 | 1.83479 | ||||||||
\(359\) | 620.707i | 1.72899i | 0.502643 | + | 0.864494i | \(0.332361\pi\) | ||||
−0.502643 | + | 0.864494i | \(0.667639\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −113.764 | −0.315135 | ||||||||
\(362\) | 784.254i | 2.16645i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −182.328 | −0.500901 | ||||||||
\(365\) | − 175.299i | − 0.480272i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 189.875 | 0.517371 | 0.258686 | − | 0.965962i | \(-0.416711\pi\) | ||||
0.258686 | + | 0.965962i | \(0.416711\pi\) | |||||||
\(368\) | 202.499i | 0.550268i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 136.692 | 0.369438 | ||||||||
\(371\) | 16.2429i | 0.0437813i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 439.303 | 1.17776 | 0.588878 | − | 0.808222i | \(-0.299570\pi\) | ||||
0.588878 | + | 0.808222i | \(0.299570\pi\) | |||||||
\(374\) | 945.647i | 2.52847i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.50247 | −0.00931509 | ||||||||
\(377\) | 526.170i | 1.39568i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −514.039 | −1.35630 | −0.678152 | − | 0.734922i | \(-0.737219\pi\) | ||||
−0.678152 | + | 0.734922i | \(0.737219\pi\) | |||||||
\(380\) | 369.498i | 0.972364i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −248.576 | −0.650724 | ||||||||
\(383\) | − 400.504i | − 1.04570i | −0.852424 | − | 0.522851i | \(-0.824868\pi\) | ||||
0.852424 | − | 0.522851i | \(-0.175132\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 320.553 | 0.832604 | ||||||||
\(386\) | 615.215i | 1.59382i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 140.770 | 0.362808 | ||||||||
\(389\) | 714.324i | 1.83631i | 0.396222 | + | 0.918155i | \(0.370321\pi\) | ||||
−0.396222 | + | 0.918155i | \(0.629679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 364.857 | 0.933138 | ||||||||
\(392\) | − 51.3723i | − 0.131052i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −738.836 | −1.87522 | ||||||||
\(395\) | 407.150i | 1.03076i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 45.5606 | 0.114762 | 0.0573811 | − | 0.998352i | \(-0.481725\pi\) | ||||
0.0573811 | + | 0.998352i | \(0.481725\pi\) | |||||||
\(398\) | − 412.979i | − 1.03763i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 423.892 | 1.05973 | ||||||||
\(401\) | − 378.312i | − 0.943423i | −0.881753 | − | 0.471711i | \(-0.843636\pi\) | ||||
0.881753 | − | 0.471711i | \(-0.156364\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −154.850 | −0.384243 | ||||||||
\(404\) | 62.3270i | 0.154275i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −493.113 | −1.21456 | ||||||||
\(407\) | 77.2024i | 0.189686i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −226.210 | −0.553080 | −0.276540 | − | 0.961002i | \(-0.589188\pi\) | ||||
−0.276540 | + | 0.961002i | \(0.589188\pi\) | |||||||
\(410\) | 73.2108i | 0.178563i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.7883 | −0.0358939 | ||||||||
\(413\) | 277.715i | 0.672432i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 630.808 | 1.52002 | ||||||||
\(416\) | − 530.420i | − 1.27505i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −455.860 | −1.09057 | ||||||||
\(419\) | − 36.9462i | − 0.0881771i | −0.999028 | − | 0.0440885i | \(-0.985962\pi\) | ||||
0.999028 | − | 0.0440885i | \(-0.0140384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 162.731 | 0.386535 | 0.193268 | − | 0.981146i | \(-0.438091\pi\) | ||||
0.193268 | + | 0.981146i | \(0.438091\pi\) | |||||||
\(422\) | 571.200i | 1.35355i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.36553 | −0.0150130 | ||||||||
\(425\) | − 763.757i | − 1.79708i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −225.492 | −0.528084 | ||||||||
\(428\) | 408.518i | 0.954482i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 306.042 | 0.711725 | ||||||||
\(431\) | − 680.810i | − 1.57960i | −0.613361 | − | 0.789802i | \(-0.710183\pi\) | ||||
0.613361 | − | 0.789802i | \(-0.289817\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −43.8082 | −0.101174 | −0.0505869 | − | 0.998720i | \(-0.516109\pi\) | ||||
−0.0505869 | + | 0.998720i | \(0.516109\pi\) | |||||||
\(434\) | − 145.121i | − 0.334381i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −76.9334 | −0.176453 | ||||||||
\(437\) | 175.883i | 0.402479i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −208.320 | −0.474532 | −0.237266 | − | 0.971445i | \(-0.576251\pi\) | ||||
−0.237266 | + | 0.971445i | \(0.576251\pi\) | |||||||
\(440\) | 125.624i | 0.285508i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1108.18 | −2.50719 | ||||||||
\(443\) | 63.6117i | 0.143593i | 0.997419 | + | 0.0717965i | \(0.0228732\pi\) | ||||
−0.997419 | + | 0.0717965i | \(0.977127\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 535.291 | 1.20290 | ||||||||
\(446\) | 539.014i | 1.20855i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 184.563 | 0.411972 | ||||||||
\(449\) | 803.599i | 1.78975i | 0.446314 | + | 0.894876i | \(0.352736\pi\) | ||||
−0.446314 | + | 0.894876i | \(0.647264\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.3488 | −0.0916825 | ||||||||
\(452\) | − 75.9434i | − 0.168016i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −438.178 | −0.965150 | ||||||||
\(455\) | 375.647i | 0.825598i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 576.381 | 1.26123 | 0.630613 | − | 0.776097i | \(-0.282803\pi\) | ||||
0.630613 | + | 0.776097i | \(0.282803\pi\) | |||||||
\(458\) | 1071.51i | 2.33954i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −262.860 | −0.571435 | ||||||||
\(461\) | 309.110i | 0.670521i | 0.942126 | + | 0.335260i | \(0.108824\pi\) | ||||
−0.942126 | + | 0.335260i | \(0.891176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 699.328 | 1.51043 | 0.755214 | − | 0.655479i | \(-0.227533\pi\) | ||||
0.755214 | + | 0.655479i | \(0.227533\pi\) | |||||||
\(464\) | − 761.504i | − 1.64117i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1048.25 | −2.24947 | ||||||||
\(467\) | − 785.231i | − 1.68144i | −0.541472 | − | 0.840719i | \(-0.682133\pi\) | ||||
0.541472 | − | 0.840719i | \(-0.317867\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 484.184 | 1.03237 | ||||||||
\(470\) | − 39.1347i | − 0.0832653i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −108.835 | −0.230584 | ||||||||
\(473\) | 172.850i | 0.365433i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 368.177 | 0.775110 | ||||||||
\(476\) | − 475.444i | − 0.998833i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1067.57 | −2.23341 | ||||||||
\(479\) | 404.198i | 0.843836i | 0.906634 | + | 0.421918i | \(0.138643\pi\) | ||||
−0.906634 | + | 0.421918i | \(0.861357\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −90.4715 | −0.188090 | ||||||||
\(482\) | 218.884i | 0.454116i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −23.8627 | −0.0493031 | ||||||||
\(485\) | − 290.025i | − 0.597990i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −301.492 | −0.619081 | −0.309541 | − | 0.950886i | \(-0.600175\pi\) | ||||
−0.309541 | + | 0.950886i | \(0.600175\pi\) | |||||||
\(488\) | − 88.3695i | − 0.181085i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 574.005 | 1.17144 | ||||||||
\(491\) | 825.810i | 1.68189i | 0.541118 | + | 0.840947i | \(0.318001\pi\) | ||||
−0.541118 | + | 0.840947i | \(0.681999\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1372.06 | −2.78308 | ||||||||
\(494\) | − 534.210i | − 1.08140i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 224.108 | 0.451831 | ||||||||
\(497\) | 242.834i | 0.488600i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 814.889 | 1.63304 | 0.816522 | − | 0.577315i | \(-0.195899\pi\) | ||||
0.816522 | + | 0.577315i | \(0.195899\pi\) | |||||||
\(500\) | − 37.2380i | − 0.0744760i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −424.522 | −0.845661 | ||||||||
\(503\) | − 727.680i | − 1.44668i | −0.690493 | − | 0.723340i | \(-0.742606\pi\) | ||||
0.690493 | − | 0.723340i | \(-0.257394\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 128.411 | 0.254280 | ||||||||
\(506\) | − 324.297i | − 0.640904i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 38.0598 | 0.0749209 | ||||||||
\(509\) | 81.3689i | 0.159860i | 0.996800 | + | 0.0799302i | \(0.0254697\pi\) | ||||
−0.996800 | + | 0.0799302i | \(0.974530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −108.735 | −0.212789 | ||||||||
\(512\) | 645.174i | 1.26011i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 909.714 | 1.76987 | ||||||||
\(515\) | 30.4681i | 0.0591613i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.1029 | 0.0427523 | ||||||||
\(518\) | − 84.7875i | − 0.163682i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −147.215 | −0.283106 | ||||||||
\(521\) | − 980.158i | − 1.88130i | −0.339376 | − | 0.940651i | \(-0.610216\pi\) | ||||
0.339376 | − | 0.940651i | \(-0.389784\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.12508 | 0.0136235 | 0.00681174 | − | 0.999977i | \(-0.497832\pi\) | ||||
0.00681174 | + | 0.999977i | \(0.497832\pi\) | |||||||
\(524\) | 309.964i | 0.591534i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1096.60 | −2.08479 | ||||||||
\(527\) | − 403.792i | − 0.766209i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 403.877 | 0.763473 | ||||||||
\(530\) | − 71.1249i | − 0.134198i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 229.193 | 0.430814 | ||||||||
\(533\) | − 48.4556i | − 0.0909111i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 841.663 | 1.57320 | ||||||||
\(536\) | 189.750i | 0.354011i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −261.131 | −0.485373 | ||||||||
\(539\) | 324.193i | 0.601472i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 880.813 | 1.62812 | 0.814060 | − | 0.580780i | \(-0.197252\pi\) | ||||
0.814060 | + | 0.580780i | \(0.197252\pi\) | |||||||
\(542\) | 514.919i | 0.950036i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1383.14 | 2.54254 | ||||||||
\(545\) | 158.504i | 0.290834i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1050.90 | 1.92121 | 0.960607 | − | 0.277910i | \(-0.0896417\pi\) | ||||
0.960607 | + | 0.277910i | \(0.0896417\pi\) | |||||||
\(548\) | 301.874i | 0.550865i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −678.853 | −1.23428 | ||||||||
\(551\) | − 661.415i | − 1.20039i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 252.548 | 0.456686 | ||||||||
\(554\) | 466.199i | 0.841514i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 505.527 | 0.909222 | ||||||||
\(557\) | − 1054.84i | − 1.89379i | −0.321544 | − | 0.946895i | \(-0.604202\pi\) | ||||
0.321544 | − | 0.946895i | \(-0.395798\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −202.558 | −0.362358 | ||||||||
\(560\) | − 543.658i | − 0.970819i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −124.858 | −0.222167 | ||||||||
\(563\) | 125.889i | 0.223603i | 0.993731 | + | 0.111802i | \(0.0356621\pi\) | ||||
−0.993731 | + | 0.111802i | \(0.964338\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −156.465 | −0.276929 | ||||||||
\(566\) | − 353.659i | − 0.624839i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −95.1660 | −0.167546 | ||||||||
\(569\) | 68.3275i | 0.120083i | 0.998196 | + | 0.0600417i | \(0.0191234\pi\) | ||||
−0.998196 | + | 0.0600417i | \(0.980877\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −517.216 | −0.905807 | −0.452904 | − | 0.891559i | \(-0.649612\pi\) | ||||
−0.452904 | + | 0.891559i | \(0.649612\pi\) | |||||||
\(572\) | 450.921i | 0.788323i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 45.4113 | 0.0791138 | ||||||||
\(575\) | 261.920i | 0.455514i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 724.772 | 1.25610 | 0.628052 | − | 0.778171i | \(-0.283852\pi\) | ||||
0.628052 | + | 0.778171i | \(0.283852\pi\) | |||||||
\(578\) | − 2104.77i | − 3.64147i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 988.495 | 1.70430 | ||||||||
\(581\) | − 391.279i | − 0.673458i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.1707 | 0.0689035 | ||||||||
\(584\) | − 42.6129i | − 0.0729673i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1359.45 | −2.31989 | ||||||||
\(587\) | − 96.7186i | − 0.164768i | −0.996601 | − | 0.0823838i | \(-0.973747\pi\) | ||||
0.996601 | − | 0.0823838i | \(-0.0262533\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 194.652 | 0.330479 | ||||||||
\(590\) | − 1216.07i | − 2.06113i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 130.936 | 0.221175 | ||||||||
\(593\) | − 644.219i | − 1.08637i | −0.839612 | − | 0.543186i | \(-0.817218\pi\) | ||||
0.839612 | − | 0.543186i | \(-0.182782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −979.550 | −1.64630 | ||||||||
\(596\) | − 419.012i | − 0.703040i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 380.036 | 0.635511 | ||||||||
\(599\) | 756.993i | 1.26376i | 0.775066 | + | 0.631881i | \(0.217717\pi\) | ||||
−0.775066 | + | 0.631881i | \(0.782283\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −898.672 | −1.49529 | −0.747647 | − | 0.664096i | \(-0.768817\pi\) | ||||
−0.747647 | + | 0.664096i | \(0.768817\pi\) | |||||||
\(602\) | − 189.832i | − 0.315335i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −730.047 | −1.20869 | ||||||||
\(605\) | 49.1639i | 0.0812627i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1046.26 | 1.72366 | 0.861832 | − | 0.507193i | \(-0.169317\pi\) | ||||
0.861832 | + | 0.507193i | \(0.169317\pi\) | |||||||
\(608\) | 666.757i | 1.09664i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 987.392 | 1.61867 | ||||||||
\(611\) | 25.9019i | 0.0423926i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −328.003 | −0.535078 | −0.267539 | − | 0.963547i | \(-0.586210\pi\) | ||||
−0.267539 | + | 0.963547i | \(0.586210\pi\) | |||||||
\(614\) | 179.045i | 0.291604i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 77.9220 | 0.126497 | ||||||||
\(617\) | 638.293i | 1.03451i | 0.855831 | + | 0.517255i | \(0.173046\pi\) | ||||
−0.855831 | + | 0.517255i | \(0.826954\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 713.100 | 1.15202 | 0.576010 | − | 0.817443i | \(-0.304609\pi\) | ||||
0.576010 | + | 0.817443i | \(0.304609\pi\) | |||||||
\(620\) | 290.911i | 0.469211i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 840.875 | 1.35189 | ||||||||
\(623\) | − 332.031i | − 0.532955i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −662.105 | −1.05937 | ||||||||
\(626\) | 401.478i | 0.641339i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 773.879 | 1.23229 | ||||||||
\(629\) | − 235.916i | − 0.375066i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 376.709 | 0.597003 | 0.298502 | − | 0.954409i | \(-0.403513\pi\) | ||||
0.298502 | + | 0.954409i | \(0.403513\pi\) | |||||||
\(632\) | 98.9725i | 0.156602i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 402.446 | 0.634772 | ||||||||
\(635\) | − 78.4140i | − 0.123487i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −379.914 | −0.596411 | ||||||||
\(638\) | 1219.53i | 1.91149i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 372.048 | 0.581324 | ||||||||
\(641\) | − 7.88021i | − 0.0122936i | −0.999981 | − | 0.00614681i | \(-0.998043\pi\) | ||||
0.999981 | − | 0.00614681i | \(-0.00195660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 115.955 | 0.180335 | 0.0901674 | − | 0.995927i | \(-0.471260\pi\) | ||||
0.0901674 | + | 0.995927i | \(0.471260\pi\) | |||||||
\(644\) | 163.047i | 0.253179i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1393.02 | 2.15638 | ||||||||
\(647\) | − 509.586i | − 0.787613i | −0.919193 | − | 0.393806i | \(-0.871158\pi\) | ||||
0.919193 | − | 0.393806i | \(-0.128842\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 686.824 | 1.05828 | ||||||||
\(650\) | − 795.530i | − 1.22389i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 416.579 | 0.638924 | ||||||||
\(653\) | 430.316i | 0.658983i | 0.944159 | + | 0.329491i | \(0.106877\pi\) | ||||
−0.944159 | + | 0.329491i | \(0.893123\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 638.613 | 0.974982 | ||||||||
\(656\) | 70.1277i | 0.106902i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.2745 | −0.0368914 | ||||||||
\(659\) | 497.970i | 0.755646i | 0.925878 | + | 0.377823i | \(0.123327\pi\) | ||||
−0.925878 | + | 0.377823i | \(0.876673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −55.0164 | −0.0832321 | −0.0416161 | − | 0.999134i | \(-0.513251\pi\) | ||||
−0.0416161 | + | 0.999134i | \(0.513251\pi\) | |||||||
\(662\) | − 778.875i | − 1.17655i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 153.341 | 0.230935 | ||||||||
\(665\) | − 472.202i | − 0.710079i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 470.529 | 0.705441 | ||||||||
\(668\) | 215.210i | 0.322171i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2120.16 | −3.16442 | ||||||||
\(671\) | 557.670i | 0.831103i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 819.232 | 1.21728 | 0.608642 | − | 0.793445i | \(-0.291715\pi\) | ||||
0.608642 | + | 0.793445i | \(0.291715\pi\) | |||||||
\(674\) | − 1305.38i | − 1.93676i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 42.3351 | 0.0626258 | ||||||||
\(677\) | 876.071i | 1.29405i | 0.762469 | + | 0.647025i | \(0.223987\pi\) | ||||
−0.762469 | + | 0.647025i | \(0.776013\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −179.897 | −0.264945 | ||||||||
\(680\) | − 383.882i | − 0.564533i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −358.904 | −0.526252 | ||||||||
\(683\) | − 1239.06i | − 1.81414i | −0.420978 | − | 0.907071i | \(-0.638313\pi\) | ||||
0.420978 | − | 0.907071i | \(-0.361687\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 621.946 | 0.907950 | ||||||||
\(686\) | − 930.458i | − 1.35635i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 293.154 | 0.426095 | ||||||||
\(689\) | 47.0750i | 0.0683237i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −737.495 | −1.06729 | −0.533643 | − | 0.845710i | \(-0.679178\pi\) | ||||
−0.533643 | + | 0.845710i | \(0.679178\pi\) | |||||||
\(692\) | 119.193i | 0.172244i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1143.63 | −1.64789 | ||||||||
\(695\) | − 1041.53i | − 1.49860i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 126.354 | 0.181283 | ||||||||
\(698\) | − 523.466i | − 0.749951i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 341.308 | 0.487583 | ||||||||
\(701\) | − 86.5794i | − 0.123508i | −0.998091 | − | 0.0617542i | \(-0.980330\pi\) | ||||
0.998091 | − | 0.0617542i | \(-0.0196695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 113.726 | 0.161772 | ||||||||
\(704\) | − 456.449i | − 0.648365i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1867.27 | −2.64486 | ||||||||
\(707\) | − 79.6511i | − 0.112661i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −879.191 | −1.24004 | −0.620022 | − | 0.784585i | \(-0.712876\pi\) | ||||
−0.620022 | + | 0.784585i | \(0.712876\pi\) | |||||||
\(710\) | − 1063.33i | − 1.49765i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 130.122 | 0.182755 | ||||||||
\(713\) | 138.475i | 0.194215i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 929.024 | 1.29933 | ||||||||
\(716\) | 816.743i | 1.14070i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1685.91 | −2.34806 | ||||||||
\(719\) | − 553.678i | − 0.770066i | −0.922903 | − | 0.385033i | \(-0.874190\pi\) | ||||
0.922903 | − | 0.385033i | \(-0.125810\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.8988 | 0.0262119 | ||||||||
\(722\) | − 308.995i | − 0.427971i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −975.155 | −1.34690 | ||||||||
\(725\) | − 984.961i | − 1.35857i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.52118 | 0.0117210 | 0.00586051 | − | 0.999983i | \(-0.498135\pi\) | ||||
0.00586051 | + | 0.999983i | \(0.498135\pi\) | |||||||
\(728\) | 91.3147i | 0.125432i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 476.133 | 0.652237 | ||||||||
\(731\) | − 528.196i | − 0.722567i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1240.93 | −1.69294 | −0.846472 | − | 0.532433i | \(-0.821278\pi\) | ||||
−0.846472 | + | 0.532433i | \(0.821278\pi\) | |||||||
\(734\) | 515.722i | 0.702619i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −474.329 | −0.644469 | ||||||||
\(737\) | − 1197.45i | − 1.62476i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −236.646 | −0.320225 | −0.160113 | − | 0.987099i | \(-0.551186\pi\) | ||||
−0.160113 | + | 0.987099i | \(0.551186\pi\) | |||||||
\(740\) | 169.965i | 0.229683i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −44.1175 | −0.0594575 | ||||||||
\(743\) | 962.986i | 1.29608i | 0.761607 | + | 0.648039i | \(0.224411\pi\) | ||||
−0.761607 | + | 0.648039i | \(0.775589\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −863.282 | −1.15877 | ||||||||
\(746\) | 1193.20i | 1.59946i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1175.84 | −1.57197 | ||||||||
\(749\) | − 522.068i | − 0.697020i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 192.651 | 0.256526 | 0.128263 | − | 0.991740i | \(-0.459060\pi\) | ||||
0.128263 | + | 0.991740i | \(0.459060\pi\) | |||||||
\(752\) | − 37.4867i | − 0.0498493i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1429.14 | −1.89541 | ||||||||
\(755\) | 1504.10i | 1.99219i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −473.144 | −0.625026 | −0.312513 | − | 0.949914i | \(-0.601171\pi\) | ||||
−0.312513 | + | 0.949914i | \(0.601171\pi\) | |||||||
\(758\) | − 1396.19i | − 1.84194i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 185.055 | 0.243493 | ||||||||
\(761\) | 306.374i | 0.402593i | 0.979530 | + | 0.201297i | \(0.0645155\pi\) | ||||
−0.979530 | + | 0.201297i | \(0.935484\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 98.3174 | 0.128856 | ||||||||
\(764\) | − 309.085i | − 0.404561i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1087.81 | 1.42012 | ||||||||
\(767\) | 804.871i | 1.04938i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1329.71 | 1.72914 | 0.864572 | − | 0.502508i | \(-0.167589\pi\) | ||||
0.864572 | + | 0.502508i | \(0.167589\pi\) | |||||||
\(770\) | 870.657i | 1.13072i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −764.970 | −0.990894 | ||||||||
\(773\) | − 1473.99i | − 1.90685i | −0.301634 | − | 0.953424i | \(-0.597532\pi\) | ||||
0.301634 | − | 0.953424i | \(-0.402468\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 289.871 | 0.374027 | ||||||||
\(776\) | − 70.5012i | − 0.0908520i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1940.18 | −2.49381 | ||||||||
\(779\) | 60.9105i | 0.0781906i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 600.561 | 0.768964 | ||||||||
\(782\) | 990.992i | 1.26725i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 549.833 | 0.701317 | ||||||||
\(785\) | − 1594.41i | − 2.03110i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 542.649 | 0.689516 | 0.344758 | − | 0.938692i | \(-0.387961\pi\) | ||||
0.344758 | + | 0.938692i | \(0.387961\pi\) | |||||||
\(788\) | − 918.682i | − 1.16584i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1105.86 | −1.39983 | ||||||||
\(791\) | 97.0523i | 0.122696i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −653.519 | −0.824110 | ||||||||
\(794\) | 123.748i | 0.155853i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 513.505 | 0.645107 | ||||||||
\(797\) | − 1010.34i | − 1.26768i | −0.773462 | − | 0.633842i | \(-0.781477\pi\) | ||||
0.773462 | − | 0.633842i | \(-0.218523\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −67.5425 | −0.0845338 | ||||||||
\(800\) | 992.916i | 1.24115i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1027.54 | 1.28122 | ||||||||
\(803\) | 268.916i | 0.334889i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 335.924 | 0.417296 | ||||||||
\(806\) | − 420.590i | − 0.521824i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 31.2150 | 0.0386324 | ||||||||
\(809\) | 476.543i | 0.589051i | 0.955644 | + | 0.294526i | \(0.0951616\pi\) | ||||
−0.955644 | + | 0.294526i | \(0.904838\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1459.91 | −1.80014 | −0.900069 | − | 0.435748i | \(-0.856484\pi\) | ||||
−0.900069 | + | 0.435748i | \(0.856484\pi\) | |||||||
\(812\) | − 613.145i | − 0.755105i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −209.690 | −0.257605 | ||||||||
\(815\) | − 858.269i | − 1.05309i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 254.623 | 0.311656 | ||||||||
\(818\) | − 614.411i | − 0.751113i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −91.0316 | −0.111014 | ||||||||
\(821\) | − 990.138i | − 1.20602i | −0.797735 | − | 0.603008i | \(-0.793969\pi\) | ||||
0.797735 | − | 0.603008i | \(-0.206031\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −108.153 | −0.131413 | −0.0657065 | − | 0.997839i | \(-0.520930\pi\) | ||||
−0.0657065 | + | 0.997839i | \(0.520930\pi\) | |||||||
\(824\) | 7.40637i | 0.00898831i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −754.304 | −0.913201 | ||||||||
\(827\) | 755.525i | 0.913573i | 0.889576 | + | 0.456787i | \(0.151000\pi\) | ||||
−0.889576 | + | 0.456787i | \(0.849000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 603.366 | 0.727824 | 0.363912 | − | 0.931433i | \(-0.381441\pi\) | ||||
0.363912 | + | 0.931433i | \(0.381441\pi\) | |||||||
\(830\) | 1713.35i | 2.06427i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 534.901 | 0.642910 | ||||||||
\(833\) | − 990.674i | − 1.18928i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 443.393 | 0.531010 | ||||||||
\(836\) | − 566.824i | − 0.678019i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 100.350 | 0.119749 | ||||||||
\(839\) | 81.2325i | 0.0968206i | 0.998828 | + | 0.0484103i | \(0.0154155\pi\) | ||||
−0.998828 | + | 0.0484103i | \(0.984585\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −928.440 | −1.10397 | ||||||||
\(842\) | 441.996i | 0.524936i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −710.240 | −0.841517 | ||||||||
\(845\) | − 87.2222i | − 0.103222i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.4955 | 0.0360041 | ||||||||
\(848\) | − 68.1297i | − 0.0803416i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2074.45 | 2.44053 | ||||||||
\(851\) | 80.9044i | 0.0950698i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 532.064 | 0.623756 | 0.311878 | − | 0.950122i | \(-0.399042\pi\) | ||||
0.311878 | + | 0.950122i | \(0.399042\pi\) | |||||||
\(854\) | − 612.461i | − 0.717167i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 204.597 | 0.239015 | ||||||||
\(857\) | 98.9583i | 0.115471i | 0.998332 | + | 0.0577353i | \(0.0183879\pi\) | ||||
−0.998332 | + | 0.0577353i | \(0.981612\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −124.582 | −0.145032 | −0.0725158 | − | 0.997367i | \(-0.523103\pi\) | ||||
−0.0725158 | + | 0.997367i | \(0.523103\pi\) | |||||||
\(860\) | 380.538i | 0.442486i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1849.16 | 2.14519 | ||||||||
\(863\) | 1163.67i | 1.34840i | 0.738547 | + | 0.674202i | \(0.235512\pi\) | ||||
−0.738547 | + | 0.674202i | \(0.764488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 245.570 | 0.283896 | ||||||||
\(866\) | − 118.988i | − 0.137400i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 180.447 | 0.207888 | ||||||||
\(869\) | − 624.583i | − 0.718737i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1403.26 | 1.61109 | ||||||||
\(872\) | 38.5303i | 0.0441861i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −477.719 | −0.546589 | ||||||||
\(875\) | 47.5885i | 0.0543868i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 93.2868 | 0.106370 | 0.0531852 | − | 0.998585i | \(-0.483063\pi\) | ||||
0.0531852 | + | 0.998585i | \(0.483063\pi\) | |||||||
\(878\) | − 565.819i | − 0.644441i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1344.54 | −1.52788 | ||||||||
\(881\) | − 674.774i | − 0.765918i | −0.923765 | − | 0.382959i | \(-0.874905\pi\) | ||||
0.923765 | − | 0.382959i | \(-0.125095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −595.635 | −0.674558 | −0.337279 | − | 0.941405i | \(-0.609507\pi\) | ||||
−0.337279 | + | 0.941405i | \(0.609507\pi\) | |||||||
\(884\) | − 1377.93i | − 1.55875i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −172.776 | −0.195007 | ||||||||
\(887\) | − 432.077i | − 0.487121i | −0.969886 | − | 0.243561i | \(-0.921684\pi\) | ||||
0.969886 | − | 0.243561i | \(-0.0783155\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.6387 | −0.0547118 | ||||||||
\(890\) | 1453.91i | 1.63361i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −670.220 | −0.751368 | ||||||||
\(893\) | − 32.5596i | − 0.0364609i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1682.72 | 1.88014 | ||||||||
\(896\) | − 230.774i | − 0.257561i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2182.66 | −2.43058 | ||||||||
\(899\) | − 520.740i | − 0.579244i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −122.754 | −0.136242 | ||||||||
\(902\) | − 112.308i | − 0.124510i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −38.0345 | −0.0420735 | ||||||||
\(905\) | 2009.10i | 2.21999i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1369.79 | 1.51025 | 0.755123 | − | 0.655583i | \(-0.227577\pi\) | ||||
0.755123 | + | 0.655583i | \(0.227577\pi\) | |||||||
\(908\) | − 544.839i | − 0.600043i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1020.30 | −1.12121 | ||||||||
\(911\) | 759.290i | 0.833469i | 0.909028 | + | 0.416734i | \(0.136825\pi\) | ||||
−0.909028 | + | 0.416734i | \(0.863175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −967.683 | −1.05989 | ||||||||
\(914\) | 1565.51i | 1.71282i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1332.33 | −1.45451 | ||||||||
\(917\) | − 396.120i | − 0.431974i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 560.626 | 0.610039 | 0.305019 | − | 0.952346i | \(-0.401337\pi\) | ||||
0.305019 | + | 0.952346i | \(0.401337\pi\) | |||||||
\(920\) | 131.647i | 0.143095i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −839.578 | −0.910605 | ||||||||
\(923\) | 703.781i | 0.762493i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 169.358 | 0.183089 | ||||||||
\(926\) | 1899.45i | 2.05125i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1783.73 | 1.92213 | ||||||||
\(929\) | − 91.4794i | − 0.0984708i | −0.998787 | − | 0.0492354i | \(-0.984322\pi\) | ||||
0.998787 | − | 0.0492354i | \(-0.0156785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 477.565 | 0.512959 | ||||||||
\(932\) | − 1303.42i | − 1.39851i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2132.78 | 2.28349 | ||||||||
\(935\) | 2422.55i | 2.59097i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −858.127 | −0.915824 | −0.457912 | − | 0.888998i | \(-0.651402\pi\) | ||||
−0.457912 | + | 0.888998i | \(0.651402\pi\) | |||||||
\(938\) | 1315.10i | 1.40202i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 48.6608 | 0.0517668 | ||||||||
\(941\) | − 475.385i | − 0.505191i | −0.967572 | − | 0.252596i | \(-0.918716\pi\) | ||||
0.967572 | − | 0.252596i | \(-0.0812842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.3315 | −0.0459507 | ||||||||
\(944\) | − 1164.86i | − 1.23396i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −469.479 | −0.496278 | ||||||||
\(947\) | 955.194i | 1.00865i | 0.863513 | + | 0.504326i | \(0.168259\pi\) | ||||
−0.863513 | + | 0.504326i | \(0.831741\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −315.135 | −0.332071 | ||||||||
\(950\) | 1000.01i | 1.05264i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −238.115 | −0.250121 | ||||||||
\(953\) | − 1128.75i | − 1.18441i | −0.805786 | − | 0.592206i | \(-0.798257\pi\) | ||||
0.805786 | − | 0.592206i | \(-0.201743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −636.801 | −0.666808 | ||||||||
\(956\) | − 1327.44i | − 1.38853i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1097.85 | −1.14598 | ||||||||
\(959\) | − 385.782i | − 0.402275i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −807.748 | −0.840528 | ||||||||
\(962\) | − 245.731i | − 0.255437i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −272.164 | −0.282328 | ||||||||
\(965\) | 1576.05i | 1.63322i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −873.591 | −0.903404 | −0.451702 | − | 0.892169i | \(-0.649183\pi\) | ||||
−0.451702 | + | 0.892169i | \(0.649183\pi\) | |||||||
\(968\) | 11.9511i | 0.0123462i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 787.741 | 0.812104 | ||||||||
\(971\) | − 1506.38i | − 1.55137i | −0.631120 | − | 0.775685i | \(-0.717404\pi\) | ||||
0.631120 | − | 0.775685i | \(-0.282596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −646.041 | −0.663969 | ||||||||
\(974\) | − 818.887i | − 0.840747i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 945.811 | 0.969068 | ||||||||
\(977\) | 648.296i | 0.663558i | 0.943357 | + | 0.331779i | \(0.107649\pi\) | ||||
−0.943357 | + | 0.331779i | \(0.892351\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −821.155 | −0.838769 | ||||||||
\(980\) | 713.729i | 0.728294i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2242.99 | −2.28411 | ||||||||
\(983\) | 1659.56i | 1.68826i | 0.536140 | + | 0.844129i | \(0.319882\pi\) | ||||
−0.536140 | + | 0.844129i | \(0.680118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1892.74 | −1.92157 | ||||||||
\(986\) | − 3726.66i | − 3.77958i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 664.246 | 0.672314 | ||||||||
\(989\) | 181.138i | 0.183153i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 106.575 | 0.107542 | 0.0537712 | − | 0.998553i | \(-0.482876\pi\) | ||||
0.0537712 | + | 0.998553i | \(0.482876\pi\) | |||||||
\(992\) | 524.946i | 0.529180i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −659.565 | −0.663546 | ||||||||
\(995\) | − 1057.97i | − 1.06328i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 888.924 | 0.891598 | 0.445799 | − | 0.895133i | \(-0.352920\pi\) | ||||
0.445799 | + | 0.895133i | \(0.352920\pi\) | |||||||
\(998\) | 2213.33i | 2.21776i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1143.3.b.a.890.69 | yes | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.16 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.16 | ✓ | 84 | 3.2 | odd | 2 | inner | |
1143.3.b.a.890.69 | yes | 84 | 1.1 | even | 1 | trivial |