Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1151,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.cg (of order \(6\), degree \(2\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.3 | ||
Character | \(\chi\) | \(=\) | 2736.1151 |
Dual form | 2736.2.cg.b.2591.3 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.15944 | − | 1.24676i | −0.965733 | − | 0.557566i | −0.0678003 | − | 0.997699i | \(-0.521598\pi\) |
−0.897933 | + | 0.440133i | \(0.854931\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.872468i | 0.329762i | 0.986313 | + | 0.164881i | \(0.0527240\pi\) | ||||
−0.986313 | + | 0.164881i | \(0.947276\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.41030 | −0.726733 | −0.363367 | − | 0.931646i | \(-0.618373\pi\) | ||||
−0.363367 | + | 0.931646i | \(0.618373\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.98130 | − | 3.43171i | −0.549514 | − | 0.951786i | −0.998308 | − | 0.0581510i | \(-0.981480\pi\) |
0.448794 | − | 0.893635i | \(-0.351854\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.303025 | + | 0.174952i | 0.0734945 | + | 0.0424321i | 0.536297 | − | 0.844029i | \(-0.319823\pi\) |
−0.462802 | + | 0.886461i | \(0.653156\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.35622 | − | 4.14254i | 0.311138 | − | 0.950365i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.88372 | + | 6.72680i | 0.809812 | + | 1.40264i | 0.912994 | + | 0.407973i | \(0.133764\pi\) |
−0.103182 | + | 0.994663i | \(0.532902\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.608801 | + | 1.05447i | 0.121760 | + | 0.210895i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.96395 | + | 4.59799i | −1.47887 | + | 0.853825i | −0.999714 | − | 0.0239054i | \(-0.992390\pi\) |
−0.479154 | + | 0.877731i | \(0.659057\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.43850i | − | 0.437967i | −0.975729 | − | 0.218983i | \(-0.929726\pi\) | ||
0.975729 | − | 0.218983i | \(-0.0702741\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.08776 | − | 1.88405i | 0.183864 | − | 0.318462i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.18021 | 1.01602 | 0.508010 | − | 0.861351i | \(-0.330381\pi\) | ||||
0.508010 | + | 0.861351i | \(0.330381\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.31650 | − | 0.760080i | −0.205602 | − | 0.118705i | 0.393664 | − | 0.919255i | \(-0.371207\pi\) |
−0.599266 | + | 0.800550i | \(0.704541\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.24748 | − | 3.02963i | −0.800233 | − | 0.462015i | 0.0433195 | − | 0.999061i | \(-0.486207\pi\) |
−0.843553 | + | 0.537046i | \(0.819540\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.05152 | + | 7.01744i | 0.590975 | + | 1.02360i | 0.994101 | + | 0.108455i | \(0.0345903\pi\) |
−0.403126 | + | 0.915145i | \(0.632076\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.23880 | 0.891257 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.41943 | + | 1.97421i | −0.469695 | + | 0.271179i | −0.716112 | − | 0.697985i | \(-0.754080\pi\) |
0.246417 | + | 0.969164i | \(0.420747\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.20491 | + | 3.00506i | 0.701830 | + | 0.405202i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.55163 | + | 2.68750i | −0.202005 | + | 0.349883i | −0.949174 | − | 0.314751i | \(-0.898079\pi\) |
0.747170 | + | 0.664634i | \(0.231412\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.53184 | + | 11.3135i | 0.836316 | + | 1.44854i | 0.892954 | + | 0.450147i | \(0.148628\pi\) |
−0.0566386 | + | 0.998395i | \(0.518038\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.88080i | 1.22556i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.04454 | + | 2.91247i | −0.616289 | + | 0.355815i | −0.775423 | − | 0.631442i | \(-0.782463\pi\) |
0.159134 | + | 0.987257i | \(0.449130\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.65667 | − | 8.06559i | 0.552645 | − | 0.957209i | −0.445437 | − | 0.895313i | \(-0.646952\pi\) |
0.998083 | − | 0.0618964i | \(-0.0197148\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.01576 | + | 1.75935i | −0.118886 | + | 0.205916i | −0.919326 | − | 0.393496i | \(-0.871266\pi\) |
0.800441 | + | 0.599412i | \(0.204599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.10291i | − | 0.239649i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8347 | + | 6.25541i | 1.21900 | + | 0.703788i | 0.964703 | − | 0.263339i | \(-0.0848237\pi\) |
0.254294 | + | 0.967127i | \(0.418157\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.29106 | 0.690533 | 0.345267 | − | 0.938505i | \(-0.387788\pi\) | ||||
0.345267 | + | 0.938505i | \(0.387788\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.436244 | − | 0.755598i | −0.0473174 | − | 0.0819561i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0641 | + | 8.11993i | −1.49080 | + | 0.860711i | −0.999945 | − | 0.0105322i | \(-0.996647\pi\) |
−0.490851 | + | 0.871243i | \(0.663314\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.99406 | − | 1.72862i | 0.313863 | − | 0.181209i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.09342 | + | 7.25472i | −0.830368 | + | 0.744318i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.90950 | + | 15.4317i | −0.904622 | + | 1.56685i | −0.0831993 | + | 0.996533i | \(0.526514\pi\) |
−0.821423 | + | 0.570319i | \(0.806820\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.725701 | + | 0.418984i | −0.0722099 | + | 0.0416904i | −0.535670 | − | 0.844427i | \(-0.679941\pi\) |
0.463460 | + | 0.886118i | \(0.346608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.56741i | 0.548573i | 0.961648 | + | 0.274287i | \(0.0884417\pi\) | ||||
−0.961648 | + | 0.274287i | \(0.911558\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.97716 | −0.287813 | −0.143907 | − | 0.989591i | \(-0.545967\pi\) | ||||
−0.143907 | + | 0.989591i | \(0.545967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.33514 | + | 12.7048i | −0.702579 | + | 1.21690i | 0.264979 | + | 0.964254i | \(0.414635\pi\) |
−0.967558 | + | 0.252649i | \(0.918698\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.07542i | 0.101167i | 0.998720 | + | 0.0505835i | \(0.0161081\pi\) | ||||
−0.998720 | + | 0.0505835i | \(0.983892\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 19.3682i | − | 1.80610i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.152640 | + | 0.264380i | −0.0139925 | + | 0.0242357i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.19045 | −0.471859 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.43145i | 0.843575i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.85067 | − | 5.10994i | 0.785370 | − | 0.453434i | −0.0529600 | − | 0.998597i | \(-0.516866\pi\) |
0.838330 | + | 0.545163i | \(0.183532\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.78592 | − | 6.55741i | 0.330777 | − | 0.572923i | −0.651887 | − | 0.758316i | \(-0.726022\pi\) |
0.982665 | + | 0.185393i | \(0.0593557\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.61424 | + | 1.18326i | 0.313394 | + | 0.102602i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.81417 | − | 1.04741i | 0.154995 | − | 0.0894862i | −0.420497 | − | 0.907294i | \(-0.638144\pi\) |
0.575491 | + | 0.817808i | \(0.304811\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.2674 | − | 9.96934i | 1.46460 | − | 0.845588i | 0.465383 | − | 0.885109i | \(-0.345917\pi\) |
0.999219 | + | 0.0395212i | \(0.0125833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.77553 | + | 8.27147i | 0.399350 | + | 0.691695i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.9303 | 1.90426 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.14614 | − | 3.54847i | −0.503511 | − | 0.290702i | 0.226651 | − | 0.973976i | \(-0.427222\pi\) |
−0.730162 | + | 0.683274i | \(0.760556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.25075i | 0.427300i | 0.976910 | + | 0.213650i | \(0.0685352\pi\) | ||||
−0.976910 | + | 0.213650i | \(0.931465\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.04021 | + | 5.26580i | −0.244196 | + | 0.422959i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.877101 | + | 1.51918i | −0.0700003 | + | 0.121244i | −0.898901 | − | 0.438151i | \(-0.855633\pi\) |
0.828901 | + | 0.559396i | \(0.188967\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.86892 | + | 3.38842i | −0.462536 | + | 0.267045i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6318i | 1.22438i | 0.790712 | + | 0.612188i | \(0.209710\pi\) | ||||
−0.790712 | + | 0.612188i | \(0.790290\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.96384 | + | 3.40147i | 0.151967 | + | 0.263214i | 0.931950 | − | 0.362586i | \(-0.118106\pi\) |
−0.779984 | + | 0.625800i | \(0.784773\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.35111 | + | 2.34019i | −0.103932 | + | 0.180015i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.93385 | + | 4.00326i | 0.527171 | + | 0.304362i | 0.739864 | − | 0.672757i | \(-0.234890\pi\) |
−0.212693 | + | 0.977119i | \(0.568223\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.919995 | + | 0.531160i | −0.0695451 | + | 0.0401519i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.8431 | 1.55789 | 0.778945 | − | 0.627092i | \(-0.215755\pi\) | ||||
0.778945 | + | 0.627092i | \(0.215755\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.38314 | + | 4.12772i | 0.177137 | + | 0.306811i | 0.940899 | − | 0.338688i | \(-0.109983\pi\) |
−0.763762 | + | 0.645499i | \(0.776650\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.3458 | − | 7.70521i | −0.981204 | − | 0.566498i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.730383 | − | 0.421687i | −0.0534109 | − | 0.0308368i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9420 | 0.864094 | 0.432047 | − | 0.901851i | \(-0.357791\pi\) | ||||
0.432047 | + | 0.901851i | \(0.357791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.108240 | − | 0.187477i | 0.00779129 | − | 0.0134949i | −0.862103 | − | 0.506732i | \(-0.830853\pi\) |
0.869895 | + | 0.493237i | \(0.164187\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.3961i | 1.73815i | 0.494681 | + | 0.869075i | \(0.335285\pi\) | ||||
−0.494681 | + | 0.869075i | \(0.664715\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.63892 | + | 1.52358i | −0.187068 | + | 0.108004i | −0.590609 | − | 0.806958i | \(-0.701113\pi\) |
0.403541 | + | 0.914962i | \(0.367779\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.01160 | − | 6.94830i | −0.281559 | − | 0.487675i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.89527 | + | 3.28270i | 0.132371 | + | 0.229274i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.26890 | + | 9.98478i | −0.226115 | + | 0.690662i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3816 | − | 9.45790i | −1.12775 | − | 0.651109i | −0.184385 | − | 0.982854i | \(-0.559029\pi\) |
−0.943369 | + | 0.331745i | \(0.892363\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.55443 | + | 13.0847i | 0.515208 | + | 0.892366i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.12751 | 0.144425 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.38653i | − | 0.0932680i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.5577 | + | 8.98227i | 1.04182 | + | 0.601497i | 0.920349 | − | 0.391097i | \(-0.127904\pi\) |
0.121474 | + | 0.992595i | \(0.461238\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.86062 | −0.322611 | −0.161305 | − | 0.986905i | \(-0.551570\pi\) | ||||
−0.161305 | + | 0.986905i | \(0.551570\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8282 | 0.913791 | 0.456896 | − | 0.889520i | \(-0.348961\pi\) | ||||
0.456896 | + | 0.889520i | \(0.348961\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.77985 | + | 1.60495i | 0.182114 | + | 0.105144i | 0.588286 | − | 0.808653i | \(-0.299803\pi\) |
−0.406172 | + | 0.913797i | \(0.633136\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 20.2050i | − | 1.31803i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.5476 | −1.58785 | −0.793926 | − | 0.608014i | \(-0.791967\pi\) | ||||
−0.793926 | + | 0.608014i | \(0.791967\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0130168 | + | 0.0225458i | 0.000838488 | + | 0.00145230i | 0.866444 | − | 0.499274i | \(-0.166400\pi\) |
−0.865606 | + | 0.500726i | \(0.833066\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.4723 | − | 7.77826i | −0.860716 | − | 0.496935i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.9031 | + | 3.55347i | −1.07552 | + | 0.226102i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.69579 | + | 9.86539i | 0.359515 | + | 0.622698i | 0.987880 | − | 0.155221i | \(-0.0496089\pi\) |
−0.628365 | + | 0.777919i | \(0.716276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.36094 | − | 16.2136i | −0.588517 | − | 1.01934i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.41804 | + | 1.39606i | −0.150833 | + | 0.0870837i | −0.573517 | − | 0.819194i | \(-0.694421\pi\) |
0.422684 | + | 0.906277i | \(0.361088\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.39203i | 0.335045i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.5051 | + | 23.3915i | −0.832759 | + | 1.44238i | 0.0630823 | + | 0.998008i | \(0.479907\pi\) |
−0.895842 | + | 0.444373i | \(0.853426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.84544 | 0.604800 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.17984 | − | 2.99058i | −0.315820 | − | 0.182339i | 0.333708 | − | 0.942677i | \(-0.391700\pi\) |
−0.649528 | + | 0.760338i | \(0.725034\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.27136 | − | 3.62077i | −0.380958 | − | 0.219946i | 0.297277 | − | 0.954791i | \(-0.403922\pi\) |
−0.678235 | + | 0.734845i | \(0.737255\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.46739 | − | 2.54160i | −0.0884872 | − | 0.153264i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.27144 | −0.136478 | −0.0682388 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682388 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3360 | − | 5.96752i | 0.616597 | − | 0.355992i | −0.158946 | − | 0.987287i | \(-0.550810\pi\) |
0.775543 | + | 0.631295i | \(0.217476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.08849 | − | 1.20579i | −0.124148 | − | 0.0716769i | 0.436640 | − | 0.899636i | \(-0.356168\pi\) |
−0.560788 | + | 0.827959i | \(0.689502\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.663145 | − | 1.14860i | 0.0391442 | − | 0.0677998i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.43878 | − | 14.6164i | −0.496399 | − | 0.859788i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 21.5726i | − | 1.26028i | −0.776480 | − | 0.630142i | \(-0.782997\pi\) | ||
0.776480 | − | 0.630142i | \(-0.217003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.70131 | − | 3.86900i | 0.390165 | − | 0.225262i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.3896 | − | 26.6557i | 0.890006 | − | 1.54154i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.64326 | − | 4.57826i | 0.152355 | − | 0.263887i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 32.5744i | − | 1.86521i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.3229 | − | 14.0428i | −1.38818 | − | 0.801466i | −0.395069 | − | 0.918651i | \(-0.629279\pi\) |
−0.993110 | + | 0.117186i | \(0.962613\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.3069 | −0.981382 | −0.490691 | − | 0.871334i | \(-0.663256\pi\) | ||||
−0.490691 | + | 0.871334i | \(0.663256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.82124 | + | 4.88653i | 0.159466 | + | 0.276203i | 0.934676 | − | 0.355500i | \(-0.115689\pi\) |
−0.775210 | + | 0.631703i | \(0.782356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.65525 | + | 4.99711i | −0.486127 | + | 0.280666i | −0.722966 | − | 0.690883i | \(-0.757222\pi\) |
0.236839 | + | 0.971549i | \(0.423889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.1955 | − | 11.0825i | 1.07474 | − | 0.620503i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.13571 | − | 1.01802i | 0.0631929 | − | 0.0566443i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41244 | − | 4.17846i | 0.133818 | − | 0.231779i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.12250 | + | 3.53483i | −0.337544 | + | 0.194881i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.8452i | 1.64044i | 0.572047 | + | 0.820221i | \(0.306149\pi\) | ||||
−0.572047 | + | 0.820221i | \(0.693851\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.5246 | 0.793561 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.01263 | − | 15.6103i | 0.490949 | − | 0.850349i | −0.508997 | − | 0.860769i | \(-0.669983\pi\) |
0.999946 | + | 0.0104196i | \(0.00331673\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.87751i | 0.318285i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5504i | 0.623665i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.35411 | − | 11.0056i | 0.341106 | − | 0.590813i | −0.643532 | − | 0.765419i | \(-0.722532\pi\) |
0.984638 | + | 0.174606i | \(0.0558651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0832 | −0.646799 | −0.323399 | − | 0.946263i | \(-0.604826\pi\) | ||||
−0.323399 | + | 0.946263i | \(0.604826\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.13272i | 0.113513i | 0.998388 | + | 0.0567566i | \(0.0180759\pi\) | ||||
−0.998388 | + | 0.0567566i | \(0.981924\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.1116 | + | 11.6115i | −1.06742 | + | 0.616273i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.1267 | + | 26.2002i | −0.798355 | + | 1.38279i | 0.122332 | + | 0.992489i | \(0.460963\pi\) |
−0.920687 | + | 0.390302i | \(0.872371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3213 | − | 11.2364i | −0.806386 | − | 0.591390i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.38696 | − | 2.53281i | 0.229624 | − | 0.132573i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.9344 | − | 18.4373i | 1.66696 | − | 0.962421i | 0.697700 | − | 0.716390i | \(-0.254207\pi\) |
0.969262 | − | 0.246031i | \(-0.0791264\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.72244 | − | 2.98335i | −0.0894245 | − | 0.154888i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.0837 | −1.03990 | −0.519948 | − | 0.854198i | \(-0.674049\pi\) | ||||
−0.519948 | + | 0.854198i | \(0.674049\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.5580 | + | 18.2200i | 1.62532 | + | 0.938378i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.8800i | 0.764332i | 0.924094 | + | 0.382166i | \(0.124822\pi\) | ||||
−0.924094 | + | 0.382166i | \(0.875178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.105222 | − | 0.182250i | 0.00537660 | − | 0.00931254i | −0.863325 | − | 0.504649i | \(-0.831622\pi\) |
0.868701 | + | 0.495337i | \(0.164955\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.62182 | + | 4.54112i | −0.133620 | + | 0.231437i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.88933 | − | 2.24551i | 0.197197 | − | 0.113852i | −0.398150 | − | 0.917320i | \(-0.630348\pi\) |
0.595347 | + | 0.803468i | \(0.297014\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.71786i | 0.137448i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.5979 | − | 27.0164i | −0.784817 | − | 1.35934i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0390 | − | 22.5842i | 0.654407 | − | 1.13347i | −0.327635 | − | 0.944805i | \(-0.606251\pi\) |
0.982042 | − | 0.188662i | \(-0.0604152\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.2353 | − | 10.5282i | −0.910629 | − | 0.525752i | −0.0299955 | − | 0.999550i | \(-0.509549\pi\) |
−0.880633 | + | 0.473798i | \(0.842883\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.36822 | + | 4.83140i | −0.416851 | + | 0.240669i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.8962 | −0.738375 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.13874 | + | 10.6326i | 0.303541 | + | 0.525749i | 0.976935 | − | 0.213535i | \(-0.0684977\pi\) |
−0.673394 | + | 0.739283i | \(0.735164\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.34476 | − | 1.35375i | −0.115378 | − | 0.0666135i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.5852 | − | 7.84342i | −0.666871 | − | 0.385018i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.9467 | 1.26758 | 0.633791 | − | 0.773505i | \(-0.281498\pi\) | ||||
0.633791 | + | 0.773505i | \(0.281498\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.8963 | + | 27.5332i | −0.774737 | + | 1.34188i | 0.160205 | + | 0.987084i | \(0.448784\pi\) |
−0.934942 | + | 0.354800i | \(0.884549\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.426043i | 0.0206661i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.87065 | + | 5.69882i | −0.477674 | + | 0.275785i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.1686 | − | 22.8087i | −0.634308 | − | 1.09865i | −0.986661 | − | 0.162787i | \(-0.947952\pi\) |
0.352353 | − | 0.935867i | \(-0.385382\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.38362 | + | 2.39650i | 0.0664925 | + | 0.115168i | 0.897355 | − | 0.441309i | \(-0.145486\pi\) |
−0.830863 | + | 0.556478i | \(0.812152\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.1333 | − | 6.96546i | 1.58498 | − | 0.333203i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.903581 | + | 0.521683i | 0.0431256 | + | 0.0248986i | 0.521408 | − | 0.853308i | \(-0.325407\pi\) |
−0.478282 | + | 0.878206i | \(0.658740\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.5933 | − | 35.6686i | −0.978416 | − | 1.69467i | −0.668169 | − | 0.744010i | \(-0.732921\pi\) |
−0.310247 | − | 0.950656i | \(-0.600412\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 40.4943 | 1.91961 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.61751i | 0.359492i | 0.983713 | + | 0.179746i | \(0.0575277\pi\) | ||||
−0.983713 | + | 0.179746i | \(0.942472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.17315 | + | 1.83202i | 0.149418 | + | 0.0862665i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.62068 | −0.404144 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.2754 | −1.27589 | −0.637945 | − | 0.770082i | \(-0.720215\pi\) | ||||
−0.637945 | + | 0.770082i | \(0.720215\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.16049 | + | 5.28881i | 0.426647 | + | 0.246324i | 0.697917 | − | 0.716179i | \(-0.254110\pi\) |
−0.271270 | + | 0.962503i | \(0.587444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 33.5895i | − | 1.56104i | −0.625134 | − | 0.780518i | \(-0.714956\pi\) | ||
0.625134 | − | 0.780518i | \(-0.285044\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.7016 | 0.587758 | 0.293879 | − | 0.955843i | \(-0.405054\pi\) | ||||
0.293879 | + | 0.955843i | \(0.405054\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.54104 | − | 4.40121i | −0.117334 | − | 0.203229i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.6480 | + | 7.30233i | 0.581556 | + | 0.335762i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.19387 | − | 1.09189i | 0.238311 | − | 0.0500991i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.5935 | + | 18.3485i | 0.484029 | + | 0.838363i | 0.999832 | − | 0.0183448i | \(-0.00583965\pi\) |
−0.515803 | + | 0.856707i | \(0.672506\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.2448 | − | 21.2087i | −0.558317 | − | 0.967034i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 38.4791 | − | 22.2159i | 1.74725 | − | 1.00877i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.5829i | 1.47647i | 0.674541 | + | 0.738237i | \(0.264341\pi\) | ||||
−0.674541 | + | 0.738237i | \(0.735659\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.36736 | + | 5.83244i | −0.151967 | + | 0.263214i | −0.931950 | − | 0.362586i | \(-0.881894\pi\) |
0.779984 | + | 0.625800i | \(0.215227\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.21771 | −0.144918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.03697 | + | 4.06280i | 0.315651 | + | 0.182241i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.1798 | − | 8.18673i | −0.634777 | − | 0.366489i | 0.147823 | − | 0.989014i | \(-0.452773\pi\) |
−0.782600 | + | 0.622525i | \(0.786107\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.2751 | − | 21.2611i | −0.547320 | − | 0.947986i | −0.998457 | − | 0.0555311i | \(-0.982315\pi\) |
0.451137 | − | 0.892455i | \(-0.351019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.08948 | 0.0929807 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.111741 | − | 0.0645136i | 0.00495282 | − | 0.00285951i | −0.497522 | − | 0.867452i | \(-0.665756\pi\) |
0.502474 | + | 0.864592i | \(0.332423\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.53498 | − | 0.886218i | −0.0679033 | − | 0.0392040i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.94120 | − | 12.0225i | 0.305866 | − | 0.529775i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.76539 | − | 16.9142i | −0.429482 | − | 0.743884i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.37366i | 0.103992i | 0.998647 | + | 0.0519960i | \(0.0165583\pi\) | ||||
−0.998647 | + | 0.0519960i | \(0.983442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9732 | − | 8.64479i | 0.654733 | − | 0.378010i | −0.135534 | − | 0.990773i | \(-0.543275\pi\) |
0.790267 | + | 0.612762i | \(0.209942\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.426619 | − | 0.738927i | 0.0185838 | − | 0.0321881i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.6666 | + | 32.3315i | −0.811591 | + | 1.40572i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.02379i | 0.260919i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.42902 | + | 3.71180i | 0.277951 | + | 0.160475i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.0374 | −0.647706 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.88044 | − | 3.25701i | −0.0808463 | − | 0.140030i | 0.822767 | − | 0.568378i | \(-0.192429\pi\) |
−0.903614 | + | 0.428348i | \(0.859096\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.6797 | − | 18.2903i | 1.35701 | − | 0.783469i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2655 | + | 8.23618i | −0.609948 | + | 0.352154i | −0.772945 | − | 0.634473i | \(-0.781217\pi\) |
0.162997 | + | 0.986627i | \(0.447884\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.24650 | + | 39.2269i | 0.351313 | + | 1.67112i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.45765 | + | 9.45292i | −0.232083 | + | 0.401979i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.8362 | − | 14.3392i | 1.05234 | − | 0.607570i | 0.129038 | − | 0.991640i | \(-0.458811\pi\) |
0.923304 | + | 0.384069i | \(0.125478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0105i | 1.01553i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.9715 | 1.26315 | 0.631574 | − | 0.775316i | \(-0.282409\pi\) | ||||
0.631574 | + | 0.775316i | \(0.282409\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.34079 | − | 2.32231i | 0.0564073 | − | 0.0977002i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 41.8354i | − | 1.75383i | −0.480645 | − | 0.876915i | \(-0.659597\pi\) | ||
0.480645 | − | 0.876915i | \(-0.340403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8770i | 0.538886i | 0.963016 | + | 0.269443i | \(0.0868396\pi\) | ||||
−0.963016 | + | 0.269443i | \(0.913160\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.72883 | + | 8.19057i | −0.197206 | + | 0.341570i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.3277 | −0.638101 | −0.319050 | − | 0.947738i | \(-0.603364\pi\) | ||||
−0.319050 | + | 0.947738i | \(0.603364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.48875i | 0.227712i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.24187 | − | 4.75844i | 0.341343 | − | 0.197075i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.4588 | − | 28.5074i | 0.679326 | − | 1.17663i | −0.295858 | − | 0.955232i | \(-0.595606\pi\) |
0.975184 | − | 0.221395i | \(-0.0710611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.1016 | − | 3.30714i | −0.416228 | − | 0.136268i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.43447 | − | 3.71494i | 0.264232 | − | 0.152554i | −0.362032 | − | 0.932166i | \(-0.617917\pi\) |
0.626264 | + | 0.779611i | \(0.284583\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.659235 | − | 0.380609i | 0.0270260 | − | 0.0156035i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.4459 | + | 25.0210i | 0.590242 | + | 1.02233i | 0.994200 | + | 0.107551i | \(0.0343009\pi\) |
−0.403958 | + | 0.914778i | \(0.632366\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.79064 | −0.236205 | −0.118103 | − | 0.993001i | \(-0.537681\pi\) | ||||
−0.118103 | + | 0.993001i | \(0.537681\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.2085 | + | 6.47122i | 0.455690 | + | 0.263093i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.2721i | 0.538698i | 0.963043 | + | 0.269349i | \(0.0868084\pi\) | ||||
−0.963043 | + | 0.269349i | \(0.913192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0546 | − | 27.8073i | 0.649499 | − | 1.12496i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.8422 | + | 20.5113i | −0.478302 | + | 0.828443i | −0.999691 | − | 0.0248760i | \(-0.992081\pi\) |
0.521388 | + | 0.853319i | \(0.325414\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.2958 | − | 9.40837i | 0.656044 | − | 0.378767i | −0.134724 | − | 0.990883i | \(-0.543015\pi\) |
0.790768 | + | 0.612116i | \(0.209682\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.7559i | 1.67831i | 0.543892 | + | 0.839155i | \(0.316950\pi\) | ||||
−0.543892 | + | 0.839155i | \(0.683050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.08439 | − | 12.2705i | −0.283830 | − | 0.491608i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8027 | − | 25.6391i | 0.592109 | − | 1.02556i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.87276 | + | 1.08124i | 0.0746718 | + | 0.0431118i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.42656 | − | 1.40098i | 0.0965999 | − | 0.0557720i | −0.450922 | − | 0.892563i | \(-0.648905\pi\) |
0.547522 | + | 0.836791i | \(0.315571\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.4834 | −1.01128 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.3609 | − | 21.4098i | −0.489758 | − | 0.848286i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.697803 | + | 0.402877i | 0.0275615 | + | 0.0159127i | 0.513717 | − | 0.857959i | \(-0.328268\pi\) |
−0.486156 | + | 0.873872i | \(0.661601\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.1911 | + | 16.2761i | 1.11175 | + | 0.641869i | 0.939282 | − | 0.343147i | \(-0.111493\pi\) |
0.172467 | + | 0.985015i | \(0.444826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.3718 | −0.761582 | −0.380791 | − | 0.924661i | \(-0.624348\pi\) | ||||
−0.380791 | + | 0.924661i | \(0.624348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.73989 | − | 6.47768i | 0.146804 | − | 0.254271i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 24.9996i | − | 0.978310i | −0.872197 | − | 0.489155i | \(-0.837305\pi\) | ||
0.872197 | − | 0.489155i | \(-0.162695\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.3510 | + | 9.44024i | −0.638885 | + | 0.368861i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.1955 | − | 26.3194i | −0.591932 | − | 1.02526i | −0.993972 | − | 0.109635i | \(-0.965032\pi\) |
0.402040 | − | 0.915622i | \(-0.368301\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.1929 | − | 43.6354i | −0.979890 | − | 1.69722i | −0.662749 | − | 0.748842i | \(-0.730610\pi\) |
−0.317141 | − | 0.948378i | \(-0.602723\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.32951 | − | 7.06126i | −0.245448 | − | 0.273824i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −61.8596 | − | 35.7146i | −2.39521 | − | 1.38288i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.7437 | − | 27.2689i | −0.607779 | − | 1.05270i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.3999 | 0.593621 | 0.296811 | − | 0.954936i | \(-0.404077\pi\) | ||||
0.296811 | + | 0.954936i | \(0.404077\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 24.1461i | − | 0.928011i | −0.885832 | − | 0.464006i | \(-0.846412\pi\) | ||
0.885832 | − | 0.464006i | \(-0.153588\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.4637 | − | 7.77326i | −0.516688 | − | 0.298310i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.74618 | −0.258136 | −0.129068 | − | 0.991636i | \(-0.541198\pi\) | ||||
−0.129068 | + | 0.991636i | \(0.541198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.22346 | −0.199578 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.5499 | + | 7.82301i | 0.516209 | + | 0.298033i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 16.8381i | − | 0.640553i | −0.947324 | − | 0.320276i | \(-0.896224\pi\) | ||
0.947324 | − | 0.320276i | \(-0.103776\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −49.7173 | −1.88589 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.265955 | − | 0.460647i | −0.0100738 | − | 0.0174482i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.6147 | − | 15.3660i | −1.00522 | − | 0.580365i | −0.0954327 | − | 0.995436i | \(-0.530423\pi\) |
−0.909789 | + | 0.415071i | \(0.863757\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.38172 | − | 25.6018i | 0.316123 | − | 0.965589i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.365550 | − | 0.633151i | −0.0137479 | − | 0.0238121i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.147095 | − | 0.254777i | −0.00552428 | − | 0.00956834i | 0.863250 | − | 0.504777i | \(-0.168425\pi\) |
−0.868774 | + | 0.495208i | \(0.835092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.4033 | − | 9.47044i | 0.614308 | − | 0.354671i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 23.8157i | − | 0.890657i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.4185 | + | 44.0261i | −0.947948 | + | 1.64189i | −0.198211 | + | 0.980159i | \(0.563513\pi\) |
−0.749738 | + | 0.661735i | \(0.769820\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.85739 | −0.180899 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.69692 | − | 5.59852i | −0.360135 | − | 0.207924i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.2657 | + | 14.5871i | 0.937052 | + | 0.541007i | 0.889035 | − | 0.457839i | \(-0.151376\pi\) |
0.0480173 | + | 0.998847i | \(0.484710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.06008 | − | 1.83611i | −0.0392085 | − | 0.0679111i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.798680 | 0.0294999 | 0.0147500 | − | 0.999891i | \(-0.495305\pi\) | ||||
0.0147500 | + | 0.999891i | \(0.495305\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.1589 | − | 7.01993i | 0.447878 | − | 0.258582i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.3843 | − | 7.72742i | −0.492349 | − | 0.284258i | 0.233199 | − | 0.972429i | \(-0.425081\pi\) |
−0.725549 | + | 0.688171i | \(0.758414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.37017 | − | 14.4976i | 0.307072 | − | 0.531864i | −0.670649 | − | 0.741775i | \(-0.733984\pi\) |
0.977720 | + | 0.209911i | \(0.0673175\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.84816 | + | 15.3255i | 0.324172 | + | 0.561482i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.59748i | − | 0.0949099i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.27226 | − | 2.46659i | 0.155897 | − | 0.0900071i | −0.420022 | − | 0.907514i | \(-0.637978\pi\) |
0.575919 | + | 0.817507i | \(0.304644\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.54640 | − | 11.3387i | 0.238248 | − | 0.412657i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.3296 | − | 42.1402i | 0.884276 | − | 1.53161i | 0.0377340 | − | 0.999288i | \(-0.487986\pi\) |
0.846542 | − | 0.532323i | \(-0.178681\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.7399i | 1.47682i | 0.674351 | + | 0.738411i | \(0.264424\pi\) | ||||
−0.674351 | + | 0.738411i | \(0.735576\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.0846 | − | 6.39968i | −0.401288 | − | 0.231684i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.2970 | 0.444018 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.00912 | − | 15.6043i | −0.324877 | − | 0.562704i | 0.656610 | − | 0.754230i | \(-0.271990\pi\) |
−0.981487 | + | 0.191526i | \(0.938656\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.4933 | + | 23.3788i | −1.45644 | + | 0.840878i | −0.998834 | − | 0.0482746i | \(-0.984628\pi\) |
−0.457610 | + | 0.889153i | \(0.651294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.57133 | − | 1.48456i | 0.0923650 | − | 0.0533269i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.93412 | + | 4.42281i | −0.176783 | + | 0.158464i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.2240 | + | 19.4405i | −0.401626 | + | 0.695636i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.78810 | − | 2.18706i | 0.135203 | − | 0.0780596i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.9843i | 0.641070i | 0.947237 | + | 0.320535i | \(0.103863\pi\) | ||||
−0.947237 | + | 0.320535i | \(0.896137\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.938269 | −0.0333610 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.8831 | − | 44.8308i | 0.919135 | − | 1.59199i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.4462i | 1.68063i | 0.542099 | + | 0.840315i | \(0.317630\pi\) | ||||
−0.542099 | + | 0.840315i | \(0.682370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.83529i | 0.100305i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.44829 | − | 4.24056i | 0.0863982 | − | 0.149646i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.8982 | 0.595582 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.25995i | 0.0794558i | 0.999211 | + | 0.0397279i | \(0.0126491\pi\) | ||||
−0.999211 | + | 0.0397279i | \(0.987351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.1260 | − | 8.15565i | 0.496031 | − | 0.286383i | −0.231042 | − | 0.972944i | \(-0.574214\pi\) |
0.727073 | + | 0.686560i | \(0.240880\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.4890 | − | 33.7560i | 0.682671 | − | 1.18242i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.6671 | + | 17.6291i | −0.688066 | + | 0.616763i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.5399 | − | 10.1267i | 0.612148 | − | 0.353424i | −0.161658 | − | 0.986847i | \(-0.551684\pi\) |
0.773806 | + | 0.633423i | \(0.218351\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.6500 | + | 13.6544i | −0.824389 | + | 0.475961i | −0.851928 | − | 0.523660i | \(-0.824566\pi\) |
0.0275388 | + | 0.999621i | \(0.491233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.8405 | + | 32.6326i | 0.655147 | + | 1.13475i | 0.981857 | + | 0.189623i | \(0.0607266\pi\) |
−0.326710 | + | 0.945125i | \(0.605940\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.47580 | −0.0512568 | −0.0256284 | − | 0.999672i | \(-0.508159\pi\) | ||||
−0.0256284 | + | 0.999672i | \(0.508159\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.89051 | + | 1.09149i | 0.0655025 | + | 0.0378179i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 9.79373i | − | 0.338926i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.93971 | − | 10.2879i | 0.205062 | − | 0.355177i | −0.745091 | − | 0.666963i | \(-0.767594\pi\) |
0.950152 | + | 0.311786i | \(0.100927\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.7830 | − | 48.1216i | 0.958035 | − | 1.65937i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.83530 | − | 3.36901i | 0.200740 | − | 0.115898i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.52850i | − | 0.155601i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0022 | + | 41.5730i | 0.822785 | + | 1.42511i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.0432 | + | 45.1081i | −0.891701 | + | 1.54447i | −0.0538658 | + | 0.998548i | \(0.517154\pi\) |
−0.837835 | + | 0.545923i | \(0.816179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.2925 | − | 12.8706i | −0.761499 | − | 0.439652i | 0.0683348 | − | 0.997662i | \(-0.478231\pi\) |
−0.829834 | + | 0.558011i | \(0.811565\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.9616 | + | 20.1851i | −1.19287 | + | 0.688706i | −0.958957 | − | 0.283551i | \(-0.908488\pi\) |
−0.233916 | + | 0.972257i | \(0.575154\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.58624 | 0.292279 | 0.146139 | − | 0.989264i | \(-0.453315\pi\) | ||||
0.146139 | + | 0.989264i | \(0.453315\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.98218 | − | 17.2896i | −0.339404 | − | 0.587865i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.1149 | − | 15.0774i | −0.885886 | − | 0.511466i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.9895 | + | 11.5410i | 0.677319 | + | 0.391051i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.22865 | −0.278179 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.1777 | − | 26.2885i | 0.512514 | − | 0.887700i | −0.487381 | − | 0.873189i | \(-0.662048\pi\) |
0.999895 | − | 0.0145104i | \(-0.00461895\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.7828i | − | 0.801264i | −0.916239 | − | 0.400632i | \(-0.868791\pi\) | ||
0.916239 | − | 0.400632i | \(-0.131209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.2046 | + | 9.93310i | −0.578982 | + | 0.334275i | −0.760729 | − | 0.649070i | \(-0.775158\pi\) |
0.181747 | + | 0.983345i | \(0.441825\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.1517 | − | 40.0999i | −0.777358 | − | 1.34642i | −0.933459 | − | 0.358683i | \(-0.883226\pi\) |
0.156101 | − | 0.987741i | \(-0.450107\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.45826 | + | 7.72193i | 0.149525 | + | 0.258985i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.5648 | − | 7.26641i | 1.15667 | − | 0.243161i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45.0096 | − | 25.9863i | −1.50451 | − | 0.868627i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.2122 | + | 19.4201i | 0.373947 | + | 0.647696i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.38157 | −0.0460267 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 11.8848i | − | 0.395063i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.3210 | + | 15.7738i | 0.907178 | + | 0.523759i | 0.879522 | − | 0.475858i | \(-0.157862\pi\) |
0.0276559 | + | 0.999618i | \(0.491196\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.7826 | 0.920480 | 0.460240 | − | 0.887795i | \(-0.347763\pi\) | ||||
0.460240 | + | 0.887795i | \(0.347763\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.1633 | −0.501834 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.72113 | + | 3.30310i | 0.188928 | + | 0.109078i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.8311i | 1.34690i | 0.739235 | + | 0.673448i | \(0.235187\pi\) | ||||
−0.739235 | + | 0.673448i | \(0.764813\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.9051 | −1.21475 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.76252 | + | 6.51687i | 0.123711 | + | 0.214273i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.27054 | + | 2.46560i | 0.140112 | + | 0.0808936i | 0.568417 | − | 0.822740i | \(-0.307556\pi\) |
−0.428305 | + | 0.903634i | \(0.640889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.46119 | − | 25.8445i | 0.277304 | − | 0.847019i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.05148 | + | 1.82122i | 0.0343871 | + | 0.0595602i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.91420 | + | 5.04754i | 0.0952028 | + | 0.164896i | 0.909693 | − | 0.415281i | \(-0.136317\pi\) |
−0.814490 | + | 0.580177i | \(0.802983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.9364 | − | 6.89149i | 0.389116 | − | 0.224656i | −0.292661 | − | 0.956216i | \(-0.594541\pi\) |
0.681777 | + | 0.731560i | \(0.261207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 11.8078i | − | 0.384513i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.20691 | + | 5.55454i | −0.104211 | + | 0.180498i | −0.913415 | − | 0.407028i | \(-0.866565\pi\) |
0.809205 | + | 0.587527i | \(0.199898\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.05011 | 0.261318 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.4432 | − | 23.3499i | −1.31008 | − | 0.756377i | −0.327974 | − | 0.944687i | \(-0.606366\pi\) |
−0.982110 | + | 0.188310i | \(0.939699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.7881 | − | 14.8888i | −0.834484 | − | 0.481790i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.913832 | + | 1.58280i | 0.0295092 | + | 0.0511114i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0537 | 0.808185 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.467477 | + | 0.269898i | −0.0150486 | + | 0.00868832i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.6384 | + | 11.3382i | 0.631528 | + | 0.364613i | 0.781343 | − | 0.624101i | \(-0.214535\pi\) |
−0.149816 | + | 0.988714i | \(0.547868\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.1706 | − | 19.3480i | 0.358481 | − | 0.620908i | −0.629226 | − | 0.777222i | \(-0.716628\pi\) |
0.987707 | + | 0.156315i | \(0.0499613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.69793 | + | 15.0653i | 0.278843 | + | 0.482970i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.3329i | 1.73826i | 0.494581 | + | 0.869131i | \(0.335321\pi\) | ||||
−0.494581 | + | 0.869131i | \(0.664679\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.8988 | − | 19.5715i | 1.08341 | − | 0.625508i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.6715 | + | 32.3399i | −0.595528 | + | 1.03148i | 0.397945 | + | 0.917409i | \(0.369724\pi\) |
−0.993472 | + | 0.114075i | \(0.963610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.4160 | − | 52.6820i | 0.969133 | − | 1.67859i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 47.0650i | − | 1.49658i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.22238 | + | 3.59249i | 0.197660 | + | 0.114119i | 0.595564 | − | 0.803308i | \(-0.296929\pi\) |
−0.397903 | + | 0.917427i | \(0.630262\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.59815 | 0.240877 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.8737 | + | 53.4748i | 0.977779 | + | 1.69356i | 0.670441 | + | 0.741963i | \(0.266105\pi\) |
0.307339 | + | 0.951600i | \(0.400562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2736.2.cg.b.1151.3 | yes | 24 | |
3.2 | odd | 2 | inner | 2736.2.cg.b.1151.10 | yes | 24 | |
4.3 | odd | 2 | 2736.2.cg.a.1151.3 | ✓ | 24 | ||
12.11 | even | 2 | 2736.2.cg.a.1151.10 | yes | 24 | ||
19.7 | even | 3 | 2736.2.cg.a.2591.10 | yes | 24 | ||
57.26 | odd | 6 | 2736.2.cg.a.2591.3 | yes | 24 | ||
76.7 | odd | 6 | inner | 2736.2.cg.b.2591.10 | yes | 24 | |
228.83 | even | 6 | inner | 2736.2.cg.b.2591.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.cg.a.1151.3 | ✓ | 24 | 4.3 | odd | 2 | ||
2736.2.cg.a.1151.10 | yes | 24 | 12.11 | even | 2 | ||
2736.2.cg.a.2591.3 | yes | 24 | 57.26 | odd | 6 | ||
2736.2.cg.a.2591.10 | yes | 24 | 19.7 | even | 3 | ||
2736.2.cg.b.1151.3 | yes | 24 | 1.1 | even | 1 | trivial | |
2736.2.cg.b.1151.10 | yes | 24 | 3.2 | odd | 2 | inner | |
2736.2.cg.b.2591.3 | yes | 24 | 228.83 | even | 6 | inner | |
2736.2.cg.b.2591.10 | yes | 24 | 76.7 | odd | 6 | inner |