Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(2015,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.2015");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2015.13 | ||
Character | \(\chi\) | \(=\) | 2394.2015 |
Dual form | 2394.2.f.b.2015.14 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.335231 | 0.149920 | 0.0749599 | − | 0.997187i | \(-0.476117\pi\) | ||||
0.0749599 | + | 0.997187i | \(0.476117\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.35234 | + | 1.21100i | −0.889100 | + | 0.457714i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 0.335231i | − | 0.106009i | ||||||
\(11\) | 0.185254i | 0.0558561i | 0.999610 | + | 0.0279280i | \(0.00889092\pi\) | ||||
−0.999610 | + | 0.0279280i | \(0.991109\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.757021i | 0.209960i | 0.994474 | + | 0.104980i | \(0.0334778\pi\) | ||||
−0.994474 | + | 0.104980i | \(0.966522\pi\) | |||||||
\(14\) | 1.21100 | + | 2.35234i | 0.323652 | + | 0.628688i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.456509 | −0.110720 | −0.0553598 | − | 0.998466i | \(-0.517631\pi\) | ||||
−0.0553598 | + | 0.998466i | \(0.517631\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −0.335231 | −0.0749599 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.185254 | 0.0394962 | ||||||||
\(23\) | 1.64986i | 0.344020i | 0.985095 | + | 0.172010i | \(0.0550261\pi\) | ||||
−0.985095 | + | 0.172010i | \(0.944974\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88762 | −0.977524 | ||||||||
\(26\) | 0.757021 | 0.148464 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.35234 | − | 1.21100i | 0.444550 | − | 0.228857i | ||||
\(29\) | − | 3.90862i | − | 0.725813i | −0.931826 | − | 0.362907i | \(-0.881784\pi\) | ||
0.931826 | − | 0.362907i | \(-0.118216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.21951i | − | 1.65587i | −0.560823 | − | 0.827936i | \(-0.689515\pi\) | ||
0.560823 | − | 0.827936i | \(-0.310485\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.456509i | 0.0782906i | ||||||||
\(35\) | −0.788575 | + | 0.405963i | −0.133294 | + | 0.0686203i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.23896 | 0.861280 | 0.430640 | − | 0.902524i | \(-0.358288\pi\) | ||||
0.430640 | + | 0.902524i | \(0.358288\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.335231i | 0.0530046i | ||||||||
\(41\) | 11.9325 | 1.86354 | 0.931771 | − | 0.363047i | \(-0.118264\pi\) | ||||
0.931771 | + | 0.363047i | \(0.118264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.93699 | 0.905382 | 0.452691 | − | 0.891668i | \(-0.350464\pi\) | ||||
0.452691 | + | 0.891668i | \(0.350464\pi\) | |||||||
\(44\) | − | 0.185254i | − | 0.0279280i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.64986 | 0.243259 | ||||||||
\(47\) | 2.36902 | 0.345557 | 0.172778 | − | 0.984961i | \(-0.444726\pi\) | ||||
0.172778 | + | 0.984961i | \(0.444726\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.06698 | − | 5.69734i | 0.580997 | − | 0.813906i | ||||
\(50\) | 4.88762i | 0.691214i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 0.757021i | − | 0.104980i | ||||||
\(53\) | 4.49358i | 0.617241i | 0.951185 | + | 0.308620i | \(0.0998672\pi\) | ||||
−0.951185 | + | 0.308620i | \(0.900133\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0621027i | 0.00837392i | ||||||||
\(56\) | −1.21100 | − | 2.35234i | −0.161826 | − | 0.314344i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.90862 | −0.513227 | ||||||||
\(59\) | −6.16386 | −0.802466 | −0.401233 | − | 0.915976i | \(-0.631418\pi\) | ||||
−0.401233 | + | 0.915976i | \(0.631418\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.83232i | − | 0.618715i | −0.950946 | − | 0.309357i | \(-0.899886\pi\) | ||
0.950946 | − | 0.309357i | \(-0.100114\pi\) | |||||||
\(62\) | −9.21951 | −1.17088 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.253777i | 0.0314771i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6219 | 1.41985 | 0.709923 | − | 0.704279i | \(-0.248730\pi\) | ||||
0.709923 | + | 0.704279i | \(0.248730\pi\) | |||||||
\(68\) | 0.456509 | 0.0553598 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.405963 | + | 0.788575i | 0.0485219 | + | 0.0942528i | ||||
\(71\) | − | 5.10688i | − | 0.606076i | −0.952979 | − | 0.303038i | \(-0.901999\pi\) | ||
0.952979 | − | 0.303038i | \(-0.0980008\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.0776i | − | 1.41358i | −0.707424 | − | 0.706789i | \(-0.750143\pi\) | ||
0.707424 | − | 0.706789i | \(-0.249857\pi\) | |||||||
\(74\) | − | 5.23896i | − | 0.609017i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000i | 0.114708i | ||||||||
\(77\) | −0.224341 | − | 0.435779i | −0.0255661 | − | 0.0496616i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.519106 | 0.0584040 | 0.0292020 | − | 0.999574i | \(-0.490703\pi\) | ||||
0.0292020 | + | 0.999574i | \(0.490703\pi\) | |||||||
\(80\) | 0.335231 | 0.0374799 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 11.9325i | − | 1.31772i | ||||||
\(83\) | −8.81830 | −0.967934 | −0.483967 | − | 0.875086i | \(-0.660805\pi\) | ||||
−0.483967 | + | 0.875086i | \(0.660805\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.153036 | −0.0165991 | ||||||||
\(86\) | − | 5.93699i | − | 0.640202i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.185254 | −0.0197481 | ||||||||
\(89\) | 3.20306 | 0.339523 | 0.169762 | − | 0.985485i | \(-0.445700\pi\) | ||||
0.169762 | + | 0.985485i | \(0.445700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.916750 | − | 1.78077i | −0.0961015 | − | 0.186675i | ||||
\(92\) | − | 1.64986i | − | 0.172010i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 2.36902i | − | 0.244345i | ||||||
\(95\) | − | 0.335231i | − | 0.0343939i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 16.2754i | − | 1.65252i | −0.563291 | − | 0.826258i | \(-0.690465\pi\) | ||
0.563291 | − | 0.826258i | \(-0.309535\pi\) | |||||||
\(98\) | −5.69734 | − | 4.06698i | −0.575518 | − | 0.410827i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.88762 | 0.488762 | ||||||||
\(101\) | −6.98657 | −0.695190 | −0.347595 | − | 0.937645i | \(-0.613002\pi\) | ||||
−0.347595 | + | 0.937645i | \(0.613002\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.05580i | − | 0.892294i | −0.894960 | − | 0.446147i | \(-0.852796\pi\) | ||
0.894960 | − | 0.446147i | \(-0.147204\pi\) | |||||||
\(104\) | −0.757021 | −0.0742320 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.49358 | 0.436455 | ||||||||
\(107\) | − | 9.44558i | − | 0.913139i | −0.889688 | − | 0.456569i | \(-0.849078\pi\) | ||
0.889688 | − | 0.456569i | \(-0.150922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7360 | 1.21988 | 0.609942 | − | 0.792446i | \(-0.291193\pi\) | ||||
0.609942 | + | 0.792446i | \(0.291193\pi\) | |||||||
\(110\) | 0.0621027 | 0.00592126 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.35234 | + | 1.21100i | −0.222275 | + | 0.114428i | ||||
\(113\) | 16.9974i | 1.59898i | 0.600677 | + | 0.799492i | \(0.294898\pi\) | ||||
−0.600677 | + | 0.799492i | \(0.705102\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.553084i | 0.0515754i | ||||||||
\(116\) | 3.90862i | 0.362907i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.16386i | 0.567429i | ||||||||
\(119\) | 1.07386 | − | 0.552831i | 0.0984408 | − | 0.0506779i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9657 | 0.996880 | ||||||||
\(122\) | −4.83232 | −0.437497 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.21951i | 0.827936i | ||||||||
\(125\) | −3.31463 | −0.296470 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.39380 | −0.389887 | −0.194943 | − | 0.980815i | \(-0.562452\pi\) | ||||
−0.194943 | + | 0.980815i | \(0.562452\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.253777 | 0.0222577 | ||||||||
\(131\) | 9.40934 | 0.822098 | 0.411049 | − | 0.911613i | \(-0.365163\pi\) | ||||
0.411049 | + | 0.911613i | \(0.365163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.21100 | + | 2.35234i | 0.105007 | + | 0.203973i | ||||
\(134\) | − | 11.6219i | − | 1.00398i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 0.456509i | − | 0.0391453i | ||||||
\(137\) | 2.27085i | 0.194012i | 0.995284 | + | 0.0970058i | \(0.0309265\pi\) | ||||
−0.995284 | + | 0.0970058i | \(0.969073\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.39303i | − | 0.372612i | −0.982492 | − | 0.186306i | \(-0.940348\pi\) | ||
0.982492 | − | 0.186306i | \(-0.0596516\pi\) | |||||||
\(140\) | 0.788575 | − | 0.405963i | 0.0666468 | − | 0.0343101i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.10688 | −0.428560 | ||||||||
\(143\) | −0.140241 | −0.0117275 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.31029i | − | 0.108814i | ||||||
\(146\) | −12.0776 | −0.999551 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.23896 | −0.430640 | ||||||||
\(149\) | 2.44847i | 0.200587i | 0.994958 | + | 0.100293i | \(0.0319781\pi\) | ||||
−0.994958 | + | 0.100293i | \(0.968022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.09905 | −0.333576 | −0.166788 | − | 0.985993i | \(-0.553340\pi\) | ||||
−0.166788 | + | 0.985993i | \(0.553340\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.435779 | + | 0.224341i | −0.0351161 | + | 0.0180779i | ||||
\(155\) | − | 3.09066i | − | 0.248248i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.6622i | − | 0.930745i | −0.885115 | − | 0.465372i | \(-0.845920\pi\) | ||
0.885115 | − | 0.465372i | \(-0.154080\pi\) | |||||||
\(158\) | − | 0.519106i | − | 0.0412978i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 0.335231i | − | 0.0265023i | ||||||
\(161\) | −1.99798 | − | 3.88103i | −0.157463 | − | 0.305868i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.5586 | −1.37530 | −0.687649 | − | 0.726044i | \(-0.741357\pi\) | ||||
−0.687649 | + | 0.726044i | \(0.741357\pi\) | |||||||
\(164\) | −11.9325 | −0.931771 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.81830i | 0.684433i | ||||||||
\(167\) | −11.9515 | −0.924831 | −0.462416 | − | 0.886663i | \(-0.653017\pi\) | ||||
−0.462416 | + | 0.886663i | \(0.653017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4269 | 0.955917 | ||||||||
\(170\) | 0.153036i | 0.0117373i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.93699 | −0.452691 | ||||||||
\(173\) | 19.0517 | 1.44847 | 0.724235 | − | 0.689553i | \(-0.242193\pi\) | ||||
0.724235 | + | 0.689553i | \(0.242193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.4973 | − | 5.91889i | 0.869116 | − | 0.447426i | ||||
\(176\) | 0.185254i | 0.0139640i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 3.20306i | − | 0.240079i | ||||||
\(179\) | − | 12.9510i | − | 0.968003i | −0.875067 | − | 0.484002i | \(-0.839183\pi\) | ||
0.875067 | − | 0.484002i | \(-0.160817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.64615i | − | 0.419675i | −0.977736 | − | 0.209837i | \(-0.932707\pi\) | ||
0.977736 | − | 0.209837i | \(-0.0672934\pi\) | |||||||
\(182\) | −1.78077 | + | 0.916750i | −0.131999 | + | 0.0679540i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.64986 | −0.121629 | ||||||||
\(185\) | 1.75626 | 0.129123 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.0845699i | − | 0.00618436i | ||||||
\(188\) | −2.36902 | −0.172778 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.335231 | −0.0243202 | ||||||||
\(191\) | 11.0980i | 0.803026i | 0.915853 | + | 0.401513i | \(0.131516\pi\) | ||||
−0.915853 | + | 0.401513i | \(0.868484\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.02100 | −0.361419 | −0.180710 | − | 0.983536i | \(-0.557839\pi\) | ||||
−0.180710 | + | 0.983536i | \(0.557839\pi\) | |||||||
\(194\) | −16.2754 | −1.16851 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.06698 | + | 5.69734i | −0.290498 | + | 0.406953i | ||||
\(197\) | 15.4710i | 1.10226i | 0.834419 | + | 0.551130i | \(0.185803\pi\) | ||||
−0.834419 | + | 0.551130i | \(0.814197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.21243i | − | 0.369499i | −0.982786 | − | 0.184750i | \(-0.940853\pi\) | ||
0.982786 | − | 0.184750i | \(-0.0591474\pi\) | |||||||
\(200\) | − | 4.88762i | − | 0.345607i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.98657i | 0.491573i | ||||||||
\(203\) | 4.73333 | + | 9.19440i | 0.332215 | + | 0.645320i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00014 | 0.279382 | ||||||||
\(206\) | −9.05580 | −0.630947 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.757021i | 0.0524900i | ||||||||
\(209\) | 0.185254 | 0.0128143 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1551 | −0.767950 | −0.383975 | − | 0.923343i | \(-0.625445\pi\) | ||||
−0.383975 | + | 0.923343i | \(0.625445\pi\) | |||||||
\(212\) | − | 4.49358i | − | 0.308620i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.44558 | −0.645687 | ||||||||
\(215\) | 1.99026 | 0.135735 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.1648 | + | 21.6874i | 0.757915 | + | 1.47224i | ||||
\(218\) | − | 12.7360i | − | 0.862588i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 0.0621027i | − | 0.00418696i | ||||||
\(221\) | − | 0.345587i | − | 0.0232467i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.3838i | 1.83376i | 0.399166 | + | 0.916878i | \(0.369300\pi\) | ||||
−0.399166 | + | 0.916878i | \(0.630700\pi\) | |||||||
\(224\) | 1.21100 | + | 2.35234i | 0.0809131 | + | 0.157172i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.9974 | 1.13065 | ||||||||
\(227\) | −14.1354 | −0.938202 | −0.469101 | − | 0.883145i | \(-0.655422\pi\) | ||||
−0.469101 | + | 0.883145i | \(0.655422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 20.5265i | − | 1.35643i | −0.734863 | − | 0.678216i | \(-0.762753\pi\) | ||
0.734863 | − | 0.678216i | \(-0.237247\pi\) | |||||||
\(230\) | 0.553084 | 0.0364693 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.90862 | 0.256614 | ||||||||
\(233\) | 2.91114i | 0.190715i | 0.995443 | + | 0.0953577i | \(0.0303995\pi\) | ||||
−0.995443 | + | 0.0953577i | \(0.969601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.794167 | 0.0518058 | ||||||||
\(236\) | 6.16386 | 0.401233 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.552831 | − | 1.07386i | −0.0358347 | − | 0.0696082i | ||||
\(239\) | − | 16.1133i | − | 1.04229i | −0.853470 | − | 0.521143i | \(-0.825506\pi\) | ||
0.853470 | − | 0.521143i | \(-0.174494\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.6759i | − | 1.33185i | −0.746019 | − | 0.665924i | \(-0.768037\pi\) | ||
0.746019 | − | 0.665924i | \(-0.231963\pi\) | |||||||
\(242\) | − | 10.9657i | − | 0.704901i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.83232i | 0.309357i | ||||||||
\(245\) | 1.36337 | − | 1.90992i | 0.0871028 | − | 0.122021i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.757021 | 0.0481681 | ||||||||
\(248\) | 9.21951 | 0.585439 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.31463i | 0.209636i | ||||||||
\(251\) | −10.2039 | −0.644065 | −0.322032 | − | 0.946729i | \(-0.604366\pi\) | ||||
−0.322032 | + | 0.946729i | \(0.604366\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.305643 | −0.0192156 | ||||||||
\(254\) | 4.39380i | 0.275691i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.7388 | 1.85506 | 0.927528 | − | 0.373755i | \(-0.121930\pi\) | ||||
0.927528 | + | 0.373755i | \(0.121930\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.3238 | + | 6.34436i | −0.765764 | + | 0.394219i | ||||
\(260\) | − | 0.253777i | − | 0.0157386i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 9.40934i | − | 0.581311i | ||||||
\(263\) | − | 8.14216i | − | 0.502067i | −0.967978 | − | 0.251034i | \(-0.919230\pi\) | ||
0.967978 | − | 0.251034i | \(-0.0807705\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.50639i | 0.0925365i | ||||||||
\(266\) | 2.35234 | − | 1.21100i | 0.144231 | − | 0.0742509i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.6219 | −0.709923 | ||||||||
\(269\) | −25.9102 | −1.57977 | −0.789885 | − | 0.613255i | \(-0.789860\pi\) | ||||
−0.789885 | + | 0.613255i | \(0.789860\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.2972i | 0.929237i | 0.885511 | + | 0.464619i | \(0.153809\pi\) | ||||
−0.885511 | + | 0.464619i | \(0.846191\pi\) | |||||||
\(272\) | −0.456509 | −0.0276799 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.27085 | 0.137187 | ||||||||
\(275\) | − | 0.905449i | − | 0.0546006i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.68378 | −0.401589 | −0.200795 | − | 0.979633i | \(-0.564352\pi\) | ||||
−0.200795 | + | 0.979633i | \(0.564352\pi\) | |||||||
\(278\) | −4.39303 | −0.263477 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.405963 | − | 0.788575i | −0.0242609 | − | 0.0471264i | ||||
\(281\) | − | 10.3331i | − | 0.616419i | −0.951319 | − | 0.308209i | \(-0.900270\pi\) | ||
0.951319 | − | 0.308209i | \(-0.0997297\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.39813i | − | 0.201998i | −0.994887 | − | 0.100999i | \(-0.967796\pi\) | ||
0.994887 | − | 0.100999i | \(-0.0322039\pi\) | |||||||
\(284\) | 5.10688i | 0.303038i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.140241i | 0.00829262i | ||||||||
\(287\) | −28.0692 | + | 14.4502i | −1.65687 | + | 0.852968i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7916 | −0.987741 | ||||||||
\(290\) | −1.31029 | −0.0769429 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.0776i | 0.706789i | ||||||||
\(293\) | 32.4348 | 1.89486 | 0.947431 | − | 0.319961i | \(-0.103670\pi\) | ||||
0.947431 | + | 0.319961i | \(0.103670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.06632 | −0.120306 | ||||||||
\(296\) | 5.23896i | 0.304508i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.44847 | 0.141836 | ||||||||
\(299\) | −1.24898 | −0.0722304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.9658 | + | 7.18967i | −0.804975 | + | 0.414406i | ||||
\(302\) | 4.09905i | 0.235874i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 1.00000i | − | 0.0573539i | ||||||
\(305\) | − | 1.61994i | − | 0.0927575i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.6149i | − | 0.777044i | −0.921440 | − | 0.388522i | \(-0.872986\pi\) | ||
0.921440 | − | 0.388522i | \(-0.127014\pi\) | |||||||
\(308\) | 0.224341 | + | 0.435779i | 0.0127830 | + | 0.0248308i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.09066 | −0.175538 | ||||||||
\(311\) | 10.5231 | 0.596710 | 0.298355 | − | 0.954455i | \(-0.403562\pi\) | ||||
0.298355 | + | 0.954455i | \(0.403562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.6817i | 1.22552i | 0.790269 | + | 0.612760i | \(0.209941\pi\) | ||||
−0.790269 | + | 0.612760i | \(0.790059\pi\) | |||||||
\(314\) | −11.6622 | −0.658136 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.519106 | −0.0292020 | ||||||||
\(317\) | − | 16.2235i | − | 0.911203i | −0.890184 | − | 0.455602i | \(-0.849424\pi\) | ||
0.890184 | − | 0.455602i | \(-0.150576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.724087 | 0.0405411 | ||||||||
\(320\) | −0.335231 | −0.0187400 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.88103 | + | 1.99798i | −0.216281 | + | 0.111343i | ||||
\(323\) | 0.456509i | 0.0254008i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.70003i | − | 0.205241i | ||||||
\(326\) | 17.5586i | 0.972482i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.9325i | 0.658861i | ||||||||
\(329\) | −5.57273 | + | 2.86887i | −0.307234 | + | 0.158166i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2594 | 0.618872 | 0.309436 | − | 0.950920i | \(-0.399860\pi\) | ||||
0.309436 | + | 0.950920i | \(0.399860\pi\) | |||||||
\(332\) | 8.81830 | 0.483967 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.9515i | 0.653954i | ||||||||
\(335\) | 3.89603 | 0.212863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7008 | 1.56343 | 0.781717 | − | 0.623633i | \(-0.214344\pi\) | ||||
0.781717 | + | 0.623633i | \(0.214344\pi\) | |||||||
\(338\) | − | 12.4269i | − | 0.675935i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.153036 | 0.00829953 | ||||||||
\(341\) | 1.70795 | 0.0924905 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.66744 | + | 18.3272i | −0.144028 | + | 0.989574i | ||||
\(344\) | 5.93699i | 0.320101i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 19.0517i | − | 1.02422i | ||||||
\(347\) | 29.7352i | 1.59627i | 0.602480 | + | 0.798134i | \(0.294179\pi\) | ||||
−0.602480 | + | 0.798134i | \(0.705821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.2667i | 0.924263i | 0.886811 | + | 0.462131i | \(0.152915\pi\) | ||||
−0.886811 | + | 0.462131i | \(0.847085\pi\) | |||||||
\(350\) | −5.91889 | − | 11.4973i | −0.316378 | − | 0.614558i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.185254 | 0.00987405 | ||||||||
\(353\) | 12.1035 | 0.644204 | 0.322102 | − | 0.946705i | \(-0.395611\pi\) | ||||
0.322102 | + | 0.946705i | \(0.395611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.71198i | − | 0.0908627i | ||||||
\(356\) | −3.20306 | −0.169762 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.9510 | −0.684482 | ||||||||
\(359\) | − | 23.3990i | − | 1.23495i | −0.786591 | − | 0.617475i | \(-0.788156\pi\) | ||
0.786591 | − | 0.617475i | \(-0.211844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −5.64615 | −0.296755 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.916750 | + | 1.78077i | 0.0480507 | + | 0.0933376i | ||||
\(365\) | − | 4.04879i | − | 0.211923i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12.4496i | − | 0.649865i | −0.945737 | − | 0.324933i | \(-0.894658\pi\) | ||
0.945737 | − | 0.324933i | \(-0.105342\pi\) | |||||||
\(368\) | 1.64986i | 0.0860050i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 1.75626i | − | 0.0913036i | ||||||
\(371\) | −5.44171 | − | 10.5704i | −0.282519 | − | 0.548788i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.78536 | 0.144220 | 0.0721102 | − | 0.997397i | \(-0.477027\pi\) | ||||
0.0721102 | + | 0.997397i | \(0.477027\pi\) | |||||||
\(374\) | −0.0845699 | −0.00437301 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.36902i | 0.122173i | ||||||||
\(377\) | 2.95891 | 0.152392 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.35912 | 0.326646 | 0.163323 | − | 0.986573i | \(-0.447779\pi\) | ||||
0.163323 | + | 0.986573i | \(0.447779\pi\) | |||||||
\(380\) | 0.335231i | 0.0171970i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.0980 | 0.567825 | ||||||||
\(383\) | 17.0337 | 0.870381 | 0.435190 | − | 0.900338i | \(-0.356681\pi\) | ||||
0.435190 | + | 0.900338i | \(0.356681\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0752061 | − | 0.146086i | −0.00383286 | − | 0.00744525i | ||||
\(386\) | 5.02100i | 0.255562i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.2754i | 0.826258i | ||||||||
\(389\) | 4.80916i | 0.243834i | 0.992540 | + | 0.121917i | \(0.0389042\pi\) | ||||
−0.992540 | + | 0.121917i | \(0.961096\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.753176i | − | 0.0380898i | ||||||
\(392\) | 5.69734 | + | 4.06698i | 0.287759 | + | 0.205413i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.4710 | 0.779416 | ||||||||
\(395\) | 0.174020 | 0.00875590 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.28472i | 0.114667i | 0.998355 | + | 0.0573334i | \(0.0182598\pi\) | ||||
−0.998355 | + | 0.0573334i | \(0.981740\pi\) | |||||||
\(398\) | −5.21243 | −0.261275 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.88762 | −0.244381 | ||||||||
\(401\) | 24.2802i | 1.21249i | 0.795277 | + | 0.606247i | \(0.207326\pi\) | ||||
−0.795277 | + | 0.606247i | \(0.792674\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.97936 | 0.347667 | ||||||||
\(404\) | 6.98657 | 0.347595 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.19440 | − | 4.73333i | 0.456310 | − | 0.234911i | ||||
\(407\) | 0.970536i | 0.0481077i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.01833i | 0.297587i | 0.988868 | + | 0.148794i | \(0.0475390\pi\) | ||||
−0.988868 | + | 0.148794i | \(0.952461\pi\) | |||||||
\(410\) | − | 4.00014i | − | 0.197553i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.05580i | 0.446147i | ||||||||
\(413\) | 14.4995 | − | 7.46441i | 0.713473 | − | 0.367300i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.95617 | −0.145112 | ||||||||
\(416\) | 0.757021 | 0.0371160 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 0.185254i | − | 0.00906105i | ||||||
\(419\) | 8.32697 | 0.406799 | 0.203400 | − | 0.979096i | \(-0.434801\pi\) | ||||
0.203400 | + | 0.979096i | \(0.434801\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.5208 | −1.24381 | −0.621905 | − | 0.783093i | \(-0.713641\pi\) | ||||
−0.621905 | + | 0.783093i | \(0.713641\pi\) | |||||||
\(422\) | 11.1551i | 0.543023i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.49358 | −0.218227 | ||||||||
\(425\) | 2.23124 | 0.108231 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.85192 | + | 11.3672i | 0.283194 | + | 0.550099i | ||||
\(428\) | 9.44558i | 0.456569i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 1.99026i | − | 0.0959788i | ||||||
\(431\) | − | 0.484959i | − | 0.0233596i | −0.999932 | − | 0.0116798i | \(-0.996282\pi\) | ||
0.999932 | − | 0.0116798i | \(-0.00371789\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.0041i | − | 0.624937i | −0.949928 | − | 0.312469i | \(-0.898844\pi\) | ||
0.949928 | − | 0.312469i | \(-0.101156\pi\) | |||||||
\(434\) | 21.6874 | − | 11.1648i | 1.04103 | − | 0.535927i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.7360 | −0.609942 | ||||||||
\(437\) | 1.64986 | 0.0789236 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.0339i | 0.956164i | 0.878315 | + | 0.478082i | \(0.158668\pi\) | ||||
−0.878315 | + | 0.478082i | \(0.841332\pi\) | |||||||
\(440\) | −0.0621027 | −0.00296063 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.345587 | −0.0164379 | ||||||||
\(443\) | 13.3813i | 0.635765i | 0.948130 | + | 0.317883i | \(0.102972\pi\) | ||||
−0.948130 | + | 0.317883i | \(0.897028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.07376 | 0.0509012 | ||||||||
\(446\) | 27.3838 | 1.29666 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.35234 | − | 1.21100i | 0.111137 | − | 0.0572142i | ||||
\(449\) | 21.4895i | 1.01415i | 0.861901 | + | 0.507076i | \(0.169274\pi\) | ||||
−0.861901 | + | 0.507076i | \(0.830726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.21054i | 0.104090i | ||||||||
\(452\) | − | 16.9974i | − | 0.799492i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.1354i | 0.663409i | ||||||||
\(455\) | −0.307323 | − | 0.596968i | −0.0144075 | − | 0.0279863i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.4559 | −1.28433 | −0.642167 | − | 0.766565i | \(-0.721964\pi\) | ||||
−0.642167 | + | 0.766565i | \(0.721964\pi\) | |||||||
\(458\) | −20.5265 | −0.959142 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 0.553084i | − | 0.0257877i | ||||||
\(461\) | −18.3684 | −0.855502 | −0.427751 | − | 0.903897i | \(-0.640694\pi\) | ||||
−0.427751 | + | 0.903897i | \(0.640694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.44046 | −0.299314 | −0.149657 | − | 0.988738i | \(-0.547817\pi\) | ||||
−0.149657 | + | 0.988738i | \(0.547817\pi\) | |||||||
\(464\) | − | 3.90862i | − | 0.181453i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.91114 | 0.134856 | ||||||||
\(467\) | 25.6442 | 1.18667 | 0.593336 | − | 0.804955i | \(-0.297811\pi\) | ||||
0.593336 | + | 0.804955i | \(0.297811\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.3387 | + | 14.0741i | −1.26238 | + | 0.649883i | ||||
\(470\) | − | 0.794167i | − | 0.0366322i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 6.16386i | − | 0.283715i | ||||||
\(473\) | 1.09985i | 0.0505711i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.88762i | 0.224259i | ||||||||
\(476\) | −1.07386 | + | 0.552831i | −0.0492204 | + | 0.0253389i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.1133 | −0.737007 | ||||||||
\(479\) | −11.5000 | −0.525448 | −0.262724 | − | 0.964871i | \(-0.584621\pi\) | ||||
−0.262724 | + | 0.964871i | \(0.584621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.96600i | 0.180834i | ||||||||
\(482\) | −20.6759 | −0.941759 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9657 | −0.498440 | ||||||||
\(485\) | − | 5.45601i | − | 0.247745i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.9663 | −0.904761 | −0.452380 | − | 0.891825i | \(-0.649425\pi\) | ||||
−0.452380 | + | 0.891825i | \(0.649425\pi\) | |||||||
\(488\) | 4.83232 | 0.218749 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.90992 | − | 1.36337i | −0.0862816 | − | 0.0615910i | ||||
\(491\) | 21.9310i | 0.989730i | 0.868970 | + | 0.494865i | \(0.164783\pi\) | ||||
−0.868970 | + | 0.494865i | \(0.835217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.78432i | 0.0803618i | ||||||||
\(494\) | − | 0.757021i | − | 0.0340600i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 9.21951i | − | 0.413968i | ||||||
\(497\) | 6.18442 | + | 12.0131i | 0.277409 | + | 0.538862i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.0948850 | −0.00424764 | −0.00212382 | − | 0.999998i | \(-0.500676\pi\) | ||||
−0.00212382 | + | 0.999998i | \(0.500676\pi\) | |||||||
\(500\) | 3.31463 | 0.148235 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.2039i | 0.455422i | ||||||||
\(503\) | 0.568508 | 0.0253485 | 0.0126743 | − | 0.999920i | \(-0.495966\pi\) | ||||
0.0126743 | + | 0.999920i | \(0.495966\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.34211 | −0.104223 | ||||||||
\(506\) | 0.305643i | 0.0135875i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.39380 | 0.194943 | ||||||||
\(509\) | 29.9561 | 1.32778 | 0.663889 | − | 0.747831i | \(-0.268905\pi\) | ||||
0.663889 | + | 0.747831i | \(0.268905\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6259 | + | 28.4106i | 0.647014 | + | 1.25681i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 29.7388i | − | 1.31172i | ||||||
\(515\) | − | 3.03578i | − | 0.133772i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.438869i | 0.0193014i | ||||||||
\(518\) | 6.34436 | + | 12.3238i | 0.278755 | + | 0.541477i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.253777 | −0.0111288 | ||||||||
\(521\) | −20.4964 | −0.897962 | −0.448981 | − | 0.893541i | \(-0.648213\pi\) | ||||
−0.448981 | + | 0.893541i | \(0.648213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.0668i | 1.18355i | 0.806103 | + | 0.591775i | \(0.201572\pi\) | ||||
−0.806103 | + | 0.591775i | \(0.798428\pi\) | |||||||
\(524\) | −9.40934 | −0.411049 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.14216 | −0.355015 | ||||||||
\(527\) | 4.20879i | 0.183338i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.2780 | 0.881650 | ||||||||
\(530\) | 1.50639 | 0.0654332 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.21100 | − | 2.35234i | −0.0525033 | − | 0.101987i | ||||
\(533\) | 9.03314i | 0.391269i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.16645i | − | 0.136898i | ||||||
\(536\) | 11.6219i | 0.501991i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.9102i | 1.11707i | ||||||||
\(539\) | 1.05545 | + | 0.753422i | 0.0454616 | + | 0.0324522i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.4399 | 1.30871 | 0.654357 | − | 0.756186i | \(-0.272939\pi\) | ||||
0.654357 | + | 0.756186i | \(0.272939\pi\) | |||||||
\(542\) | 15.2972 | 0.657070 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.456509i | 0.0195727i | ||||||||
\(545\) | 4.26948 | 0.182885 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.8784 | −0.935451 | −0.467725 | − | 0.883874i | \(-0.654926\pi\) | ||||
−0.467725 | + | 0.883874i | \(0.654926\pi\) | |||||||
\(548\) | − | 2.27085i | − | 0.0970058i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.905449 | −0.0386085 | ||||||||
\(551\) | −3.90862 | −0.166513 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.22111 | + | 0.628635i | −0.0519269 | + | 0.0267323i | ||||
\(554\) | 6.68378i | 0.283967i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.39303i | 0.186306i | ||||||||
\(557\) | − | 16.7695i | − | 0.710548i | −0.934762 | − | 0.355274i | \(-0.884388\pi\) | ||
0.934762 | − | 0.355274i | \(-0.115612\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.49442i | 0.190094i | ||||||||
\(560\) | −0.788575 | + | 0.405963i | −0.0333234 | + | 0.0171551i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.3331 | −0.435874 | ||||||||
\(563\) | 13.5027 | 0.569072 | 0.284536 | − | 0.958665i | \(-0.408160\pi\) | ||||
0.284536 | + | 0.958665i | \(0.408160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.69806i | 0.239719i | ||||||||
\(566\) | −3.39813 | −0.142834 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.10688 | 0.214280 | ||||||||
\(569\) | 36.4004i | 1.52599i | 0.646407 | + | 0.762993i | \(0.276271\pi\) | ||||
−0.646407 | + | 0.762993i | \(0.723729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5493 | −0.818115 | −0.409057 | − | 0.912509i | \(-0.634142\pi\) | ||||
−0.409057 | + | 0.912509i | \(0.634142\pi\) | |||||||
\(572\) | 0.140241 | 0.00586377 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.4502 | + | 28.0692i | 0.603140 | + | 1.17159i | ||||
\(575\) | − | 8.06390i | − | 0.336288i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.3784i | − | 0.806732i | −0.915039 | − | 0.403366i | \(-0.867840\pi\) | ||
0.915039 | − | 0.403366i | \(-0.132160\pi\) | |||||||
\(578\) | 16.7916i | 0.698438i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.31029i | 0.0544069i | ||||||||
\(581\) | 20.7436 | − | 10.6789i | 0.860590 | − | 0.443037i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.832452 | −0.0344766 | ||||||||
\(584\) | 12.0776 | 0.499775 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 32.4348i | − | 1.33987i | ||||||
\(587\) | 41.2573 | 1.70287 | 0.851435 | − | 0.524461i | \(-0.175733\pi\) | ||||
0.851435 | + | 0.524461i | \(0.175733\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.21951 | −0.379883 | ||||||||
\(590\) | 2.06632i | 0.0850689i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.23896 | 0.215320 | ||||||||
\(593\) | 41.8374 | 1.71806 | 0.859028 | − | 0.511928i | \(-0.171068\pi\) | ||||
0.859028 | + | 0.511928i | \(0.171068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.359992 | − | 0.185326i | 0.0147582 | − | 0.00759762i | ||||
\(596\) | − | 2.44847i | − | 0.100293i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.24898i | 0.0510746i | ||||||||
\(599\) | − | 46.3554i | − | 1.89403i | −0.321191 | − | 0.947014i | \(-0.604083\pi\) | ||
0.321191 | − | 0.947014i | \(-0.395917\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.1173i | − | 1.02456i | −0.858819 | − | 0.512279i | \(-0.828802\pi\) | ||
0.858819 | − | 0.512279i | \(-0.171198\pi\) | |||||||
\(602\) | 7.18967 | + | 13.9658i | 0.293029 | + | 0.569203i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.09905 | 0.166788 | ||||||||
\(605\) | 3.67603 | 0.149452 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.00166i | − | 0.324777i | −0.986727 | − | 0.162389i | \(-0.948080\pi\) | ||
0.986727 | − | 0.162389i | \(-0.0519198\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.61994 | −0.0655895 | ||||||||
\(611\) | 1.79340i | 0.0725530i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.0962021 | 0.00388557 | 0.00194278 | − | 0.999998i | \(-0.499382\pi\) | ||||
0.00194278 | + | 0.999998i | \(0.499382\pi\) | |||||||
\(614\) | −13.6149 | −0.549453 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.435779 | − | 0.224341i | 0.0175580 | − | 0.00903897i | ||||
\(617\) | − | 22.6139i | − | 0.910403i | −0.890389 | − | 0.455201i | \(-0.849567\pi\) | ||
0.890389 | − | 0.455201i | \(-0.150433\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.8822i | − | 1.16087i | −0.814305 | − | 0.580437i | \(-0.802882\pi\) | ||
0.814305 | − | 0.580437i | \(-0.197118\pi\) | |||||||
\(620\) | 3.09066i | 0.124124i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 10.5231i | − | 0.421938i | ||||||
\(623\) | −7.53467 | + | 3.87889i | −0.301870 | + | 0.155404i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3269 | 0.933077 | ||||||||
\(626\) | 21.6817 | 0.866574 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.6622i | 0.465372i | ||||||||
\(629\) | −2.39163 | −0.0953606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.36072 | −0.253216 | −0.126608 | − | 0.991953i | \(-0.540409\pi\) | ||||
−0.126608 | + | 0.991953i | \(0.540409\pi\) | |||||||
\(632\) | 0.519106i | 0.0206489i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.2235 | −0.644318 | ||||||||
\(635\) | −1.47294 | −0.0584517 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.31301 | + | 3.07879i | 0.170888 | + | 0.121986i | ||||
\(638\) | − | 0.724087i | − | 0.0286669i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.335231i | 0.0132512i | ||||||||
\(641\) | 29.7991i | 1.17699i | 0.808499 | + | 0.588497i | \(0.200280\pi\) | ||||
−0.808499 | + | 0.588497i | \(0.799720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.46000i | − | 0.215321i | −0.994188 | − | 0.107661i | \(-0.965664\pi\) | ||
0.994188 | − | 0.107661i | \(-0.0343360\pi\) | |||||||
\(644\) | 1.99798 | + | 3.88103i | 0.0787313 | + | 0.152934i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.456509 | 0.0179611 | ||||||||
\(647\) | −47.9433 | −1.88485 | −0.942424 | − | 0.334421i | \(-0.891459\pi\) | ||||
−0.942424 | + | 0.334421i | \(0.891459\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.14188i | − | 0.0448226i | ||||||
\(650\) | −3.70003 | −0.145127 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.5586 | 0.687649 | ||||||||
\(653\) | 25.1366i | 0.983670i | 0.870689 | + | 0.491835i | \(0.163674\pi\) | ||||
−0.870689 | + | 0.491835i | \(0.836326\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.15430 | 0.123249 | ||||||||
\(656\) | 11.9325 | 0.465885 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.86887 | + | 5.57273i | 0.111840 | + | 0.217247i | ||||
\(659\) | 16.2227i | 0.631946i | 0.948768 | + | 0.315973i | \(0.102331\pi\) | ||||
−0.948768 | + | 0.315973i | \(0.897669\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.874259i | 0.0340047i | 0.999855 | + | 0.0170024i | \(0.00541228\pi\) | ||||
−0.999855 | + | 0.0170024i | \(0.994588\pi\) | |||||||
\(662\) | − | 11.2594i | − | 0.437608i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 8.81830i | − | 0.342217i | ||||||
\(665\) | 0.405963 | + | 0.788575i | 0.0157426 | + | 0.0305796i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.44869 | 0.249694 | ||||||||
\(668\) | 11.9515 | 0.462416 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 3.89603i | − | 0.150517i | ||||||
\(671\) | 0.895204 | 0.0345590 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.09769 | 0.312143 | 0.156072 | − | 0.987746i | \(-0.450117\pi\) | ||||
0.156072 | + | 0.987746i | \(0.450117\pi\) | |||||||
\(674\) | − | 28.7008i | − | 1.10551i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.4269 | −0.477958 | ||||||||
\(677\) | 6.73366 | 0.258796 | 0.129398 | − | 0.991593i | \(-0.458696\pi\) | ||||
0.129398 | + | 0.991593i | \(0.458696\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.7095 | + | 38.2852i | 0.756379 | + | 1.46925i | ||||
\(680\) | − | 0.153036i | − | 0.00586865i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 1.70795i | − | 0.0654007i | ||||||
\(683\) | 39.6495i | 1.51715i | 0.651588 | + | 0.758573i | \(0.274103\pi\) | ||||
−0.651588 | + | 0.758573i | \(0.725897\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.761257i | 0.0290861i | ||||||||
\(686\) | 18.3272 | + | 2.66744i | 0.699734 | + | 0.101843i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.93699 | 0.226345 | ||||||||
\(689\) | −3.40173 | −0.129596 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.10834i | 0.0421632i | 0.999778 | + | 0.0210816i | \(0.00671098\pi\) | ||||
−0.999778 | + | 0.0210816i | \(0.993289\pi\) | |||||||
\(692\) | −19.0517 | −0.724235 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 29.7352 | 1.12873 | ||||||||
\(695\) | − | 1.47268i | − | 0.0558619i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.44729 | −0.206331 | ||||||||
\(698\) | 17.2667 | 0.653552 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.4973 | + | 5.91889i | −0.434558 | + | 0.223713i | ||||
\(701\) | − | 45.6448i | − | 1.72398i | −0.506924 | − | 0.861991i | \(-0.669218\pi\) | ||
0.506924 | − | 0.861991i | \(-0.330782\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.23896i | − | 0.197591i | ||||||
\(704\) | − | 0.185254i | − | 0.00698201i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 12.1035i | − | 0.455521i | ||||||
\(707\) | 16.4348 | − | 8.46071i | 0.618093 | − | 0.318198i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.6506 | −0.700439 | −0.350220 | − | 0.936668i | \(-0.613893\pi\) | ||||
−0.350220 | + | 0.936668i | \(0.613893\pi\) | |||||||
\(710\) | −1.71198 | −0.0642496 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.20306i | 0.120040i | ||||||||
\(713\) | 15.2109 | 0.569653 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0470130 | −0.00175819 | ||||||||
\(716\) | 12.9510i | 0.484002i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −23.3990 | −0.873242 | ||||||||
\(719\) | −18.6947 | −0.697195 | −0.348598 | − | 0.937272i | \(-0.613342\pi\) | ||||
−0.348598 | + | 0.937272i | \(0.613342\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.9665 | + | 21.3023i | 0.408415 | + | 0.793338i | ||||
\(722\) | 1.00000i | 0.0372161i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.64615i | 0.209837i | ||||||||
\(725\) | 19.1039i | 0.709500i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.5941i | − | 0.949232i | −0.880193 | − | 0.474616i | \(-0.842587\pi\) | ||
0.880193 | − | 0.474616i | \(-0.157413\pi\) | |||||||
\(728\) | 1.78077 | − | 0.916750i | 0.0659997 | − | 0.0339770i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.04879 | −0.149852 | ||||||||
\(731\) | −2.71029 | −0.100244 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 25.5018i | − | 0.941930i | −0.882152 | − | 0.470965i | \(-0.843906\pi\) | ||
0.882152 | − | 0.470965i | \(-0.156094\pi\) | |||||||
\(734\) | −12.4496 | −0.459524 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.64986 | 0.0608147 | ||||||||
\(737\) | 2.15301i | 0.0793070i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.0480 | 0.406408 | 0.203204 | − | 0.979136i | \(-0.434865\pi\) | ||||
0.203204 | + | 0.979136i | \(0.434865\pi\) | |||||||
\(740\) | −1.75626 | −0.0645614 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.5704 | + | 5.44171i | −0.388052 | + | 0.199771i | ||||
\(743\) | 33.6803i | 1.23561i | 0.786331 | + | 0.617805i | \(0.211978\pi\) | ||||
−0.786331 | + | 0.617805i | \(0.788022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.820803i | 0.0300719i | ||||||||
\(746\) | − | 2.78536i | − | 0.101979i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.0845699i | 0.00309218i | ||||||||
\(749\) | 11.4386 | + | 22.2192i | 0.417956 | + | 0.811871i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.4142 | 0.927376 | 0.463688 | − | 0.885999i | \(-0.346526\pi\) | ||||
0.463688 | + | 0.885999i | \(0.346526\pi\) | |||||||
\(752\) | 2.36902 | 0.0863892 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 2.95891i | − | 0.107757i | ||||||
\(755\) | −1.37413 | −0.0500096 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.8036 | 0.392663 | 0.196332 | − | 0.980538i | \(-0.437097\pi\) | ||||
0.196332 | + | 0.980538i | \(0.437097\pi\) | |||||||
\(758\) | − | 6.35912i | − | 0.230974i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.335231 | 0.0121601 | ||||||||
\(761\) | 19.3196 | 0.700335 | 0.350168 | − | 0.936687i | \(-0.386125\pi\) | ||||
0.350168 | + | 0.936687i | \(0.386125\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.9593 | + | 15.4232i | −1.08460 | + | 0.558357i | ||||
\(764\) | − | 11.0980i | − | 0.401513i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 17.0337i | − | 0.615452i | ||||||
\(767\) | − | 4.66617i | − | 0.168486i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 16.1081i | − | 0.580872i | −0.956894 | − | 0.290436i | \(-0.906200\pi\) | ||
0.956894 | − | 0.290436i | \(-0.0938003\pi\) | |||||||
\(770\) | −0.146086 | + | 0.0752061i | −0.00526459 | + | 0.00271024i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.02100 | 0.180710 | ||||||||
\(773\) | 13.2644 | 0.477086 | 0.238543 | − | 0.971132i | \(-0.423330\pi\) | ||||
0.238543 | + | 0.971132i | \(0.423330\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.0614i | 1.61865i | ||||||||
\(776\) | 16.2754 | 0.584253 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.80916 | 0.172417 | ||||||||
\(779\) | − | 11.9325i | − | 0.427526i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.946068 | 0.0338530 | ||||||||
\(782\) | −0.753176 | −0.0269335 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.06698 | − | 5.69734i | 0.145249 | − | 0.203477i | ||||
\(785\) | − | 3.90953i | − | 0.139537i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.18595i | − | 0.113567i | −0.998387 | − | 0.0567834i | \(-0.981916\pi\) | ||
0.998387 | − | 0.0567834i | \(-0.0180844\pi\) | |||||||
\(788\) | − | 15.4710i | − | 0.551130i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 0.174020i | − | 0.00619136i | ||||||
\(791\) | −20.5838 | − | 39.9837i | −0.731876 | − | 1.42166i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.65817 | 0.129905 | ||||||||
\(794\) | 2.28472 | 0.0810817 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.21243i | 0.184750i | ||||||||
\(797\) | −41.1036 | −1.45596 | −0.727982 | − | 0.685596i | \(-0.759542\pi\) | ||||
−0.727982 | + | 0.685596i | \(0.759542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.08148 | −0.0382599 | ||||||||
\(800\) | 4.88762i | 0.172803i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.2802 | 0.857362 | ||||||||
\(803\) | 2.23742 | 0.0789569 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.669783 | − | 1.30104i | −0.0236067 | − | 0.0458556i | ||||
\(806\) | − | 6.97936i | − | 0.245837i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 6.98657i | − | 0.245787i | ||||||
\(809\) | − | 14.2230i | − | 0.500053i | −0.968239 | − | 0.250027i | \(-0.919561\pi\) | ||
0.968239 | − | 0.250027i | \(-0.0804394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.82019i | − | 0.169260i | −0.996412 | − | 0.0846299i | \(-0.973029\pi\) | ||
0.996412 | − | 0.0846299i | \(-0.0269708\pi\) | |||||||
\(812\) | −4.73333 | − | 9.19440i | −0.166107 | − | 0.322660i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.970536 | 0.0340173 | ||||||||
\(815\) | −5.88619 | −0.206184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5.93699i | − | 0.207709i | ||||||
\(818\) | 6.01833 | 0.210426 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.00014 | −0.139691 | ||||||||
\(821\) | − | 45.9816i | − | 1.60477i | −0.596807 | − | 0.802385i | \(-0.703564\pi\) | ||
0.596807 | − | 0.802385i | \(-0.296436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.6266 | −1.31158 | −0.655791 | − | 0.754943i | \(-0.727665\pi\) | ||||
−0.655791 | + | 0.754943i | \(0.727665\pi\) | |||||||
\(824\) | 9.05580 | 0.315474 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.46441 | − | 14.4995i | −0.259720 | − | 0.504501i | ||||
\(827\) | − | 21.9153i | − | 0.762069i | −0.924561 | − | 0.381035i | \(-0.875568\pi\) | ||
0.924561 | − | 0.381035i | \(-0.124432\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.98931i | 0.208017i | 0.994576 | + | 0.104009i | \(0.0331670\pi\) | ||||
−0.994576 | + | 0.104009i | \(0.966833\pi\) | |||||||
\(830\) | 2.95617i | 0.102610i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.757021i | − | 0.0262450i | ||||||
\(833\) | −1.85661 | + | 2.60089i | −0.0643277 | + | 0.0901154i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00649 | −0.138650 | ||||||||
\(836\) | −0.185254 | −0.00640713 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 8.32697i | − | 0.287650i | ||||||
\(839\) | −42.0006 | −1.45002 | −0.725011 | − | 0.688737i | \(-0.758165\pi\) | ||||
−0.725011 | + | 0.688737i | \(0.758165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.7227 | 0.473195 | ||||||||
\(842\) | 25.5208i | 0.879506i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.1551 | 0.383975 | ||||||||
\(845\) | 4.16588 | 0.143311 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.7950 | + | 13.2794i | −0.886326 | + | 0.456286i | ||||
\(848\) | 4.49358i | 0.154310i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 2.23124i | − | 0.0765310i | ||||||
\(851\) | 8.64356i | 0.296297i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.4255i | 0.493919i | 0.969026 | + | 0.246960i | \(0.0794315\pi\) | ||||
−0.969026 | + | 0.246960i | \(0.920569\pi\) | |||||||
\(854\) | 11.3672 | − | 5.85192i | 0.388979 | − | 0.200249i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.44558 | 0.322843 | ||||||||
\(857\) | −9.25307 | −0.316079 | −0.158039 | − | 0.987433i | \(-0.550517\pi\) | ||||
−0.158039 | + | 0.987433i | \(0.550517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.7183i | 1.28693i | 0.765474 | + | 0.643466i | \(0.222504\pi\) | ||||
−0.765474 | + | 0.643466i | \(0.777496\pi\) | |||||||
\(860\) | −1.99026 | −0.0678673 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.484959 | −0.0165178 | ||||||||
\(863\) | 14.3315i | 0.487851i | 0.969794 | + | 0.243926i | \(0.0784353\pi\) | ||||
−0.969794 | + | 0.243926i | \(0.921565\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.38670 | 0.217154 | ||||||||
\(866\) | −13.0041 | −0.441897 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.1648 | − | 21.6874i | −0.378958 | − | 0.736118i | ||||
\(869\) | 0.0961662i | 0.00326222i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.79806i | 0.298111i | ||||||||
\(872\) | 12.7360i | 0.431294i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.64986i | − | 0.0558074i | ||||||
\(875\) | 7.79713 | − | 4.01401i | 0.263591 | − | 0.135698i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.3302 | −1.05795 | −0.528973 | − | 0.848639i | \(-0.677423\pi\) | ||||
−0.528973 | + | 0.848639i | \(0.677423\pi\) | |||||||
\(878\) | 20.0339 | 0.676110 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.0621027i | 0.00209348i | ||||||||
\(881\) | 21.4228 | 0.721753 | 0.360876 | − | 0.932614i | \(-0.382478\pi\) | ||||
0.360876 | + | 0.932614i | \(0.382478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.1919 | 1.11700 | 0.558498 | − | 0.829506i | \(-0.311378\pi\) | ||||
0.558498 | + | 0.829506i | \(0.311378\pi\) | |||||||
\(884\) | 0.345587i | 0.0116233i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.3813 | 0.449554 | ||||||||
\(887\) | −19.8206 | −0.665512 | −0.332756 | − | 0.943013i | \(-0.607979\pi\) | ||||
−0.332756 | + | 0.943013i | \(0.607979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3357 | − | 5.32087i | 0.346648 | − | 0.178456i | ||||
\(890\) | − | 1.07376i | − | 0.0359926i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 27.3838i | − | 0.916878i | ||||||
\(893\) | − | 2.36902i | − | 0.0792761i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 4.34157i | − | 0.145123i | ||||||
\(896\) | −1.21100 | − | 2.35234i | −0.0404565 | − | 0.0785861i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.4895 | 0.717114 | ||||||||
\(899\) | −36.0356 | −1.20185 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.05136i | − | 0.0683407i | ||||||
\(902\) | 2.21054 | 0.0736028 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.9974 | −0.565326 | ||||||||
\(905\) | − | 1.89276i | − | 0.0629175i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.5431 | 1.57864 | 0.789322 | − | 0.613980i | \(-0.210432\pi\) | ||||
0.789322 | + | 0.613980i | \(0.210432\pi\) | |||||||
\(908\) | 14.1354 | 0.469101 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.596968 | + | 0.307323i | −0.0197893 | + | 0.0101876i | ||||
\(911\) | 9.15848i | 0.303434i | 0.988424 | + | 0.151717i | \(0.0484802\pi\) | ||||
−0.988424 | + | 0.151717i | \(0.951520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.63362i | − | 0.0540650i | ||||||
\(914\) | 27.4559i | 0.908161i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.5265i | 0.678216i | ||||||||
\(917\) | −22.1339 | + | 11.3947i | −0.730927 | + | 0.376285i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.1704 | −1.35809 | −0.679043 | − | 0.734099i | \(-0.737605\pi\) | ||||
−0.679043 | + | 0.734099i | \(0.737605\pi\) | |||||||
\(920\) | −0.553084 | −0.0182346 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.3684i | 0.604931i | ||||||||
\(923\) | 3.86602 | 0.127252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.6061 | −0.841922 | ||||||||
\(926\) | 6.44046i | 0.211647i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.90862 | −0.128307 | ||||||||
\(929\) | 5.86170 | 0.192316 | 0.0961581 | − | 0.995366i | \(-0.469345\pi\) | ||||
0.0961581 | + | 0.995366i | \(0.469345\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.69734 | − | 4.06698i | −0.186723 | − | 0.133290i | ||||
\(932\) | − | 2.91114i | − | 0.0953577i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 25.6442i | − | 0.839103i | ||||||
\(935\) | − | 0.0283504i | − | 0.000927158i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 21.9623i | − | 0.717478i | −0.933438 | − | 0.358739i | \(-0.883207\pi\) | ||
0.933438 | − | 0.358739i | \(-0.116793\pi\) | |||||||
\(938\) | 14.0741 | + | 27.3387i | 0.459537 | + | 0.892641i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.794167 | −0.0259029 | ||||||||
\(941\) | −17.1006 | −0.557462 | −0.278731 | − | 0.960369i | \(-0.589914\pi\) | ||||
−0.278731 | + | 0.960369i | \(0.589914\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.6870i | 0.641095i | ||||||||
\(944\) | −6.16386 | −0.200617 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.09985 | 0.0357591 | ||||||||
\(947\) | − | 55.3886i | − | 1.79989i | −0.436006 | − | 0.899944i | \(-0.643608\pi\) | ||
0.436006 | − | 0.899944i | \(-0.356392\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.14301 | 0.296795 | ||||||||
\(950\) | 4.88762 | 0.158575 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.552831 | + | 1.07386i | 0.0179173 | + | 0.0348041i | ||||
\(953\) | 5.72474i | 0.185442i | 0.995692 | + | 0.0927212i | \(0.0295565\pi\) | ||||
−0.995692 | + | 0.0927212i | \(0.970443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.72040i | 0.120389i | ||||||||
\(956\) | 16.1133i | 0.521143i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.5000i | 0.371548i | ||||||||
\(959\) | −2.74999 | − | 5.34180i | −0.0888017 | − | 0.172496i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −53.9993 | −1.74191 | ||||||||
\(962\) | 3.96600 | 0.127869 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.6759i | 0.665924i | ||||||||
\(965\) | −1.68319 | −0.0541839 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.602657 | 0.0193801 | 0.00969007 | − | 0.999953i | \(-0.496916\pi\) | ||||
0.00969007 | + | 0.999953i | \(0.496916\pi\) | |||||||
\(968\) | 10.9657i | 0.352450i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.45601 | −0.175182 | ||||||||
\(971\) | −33.1846 | −1.06494 | −0.532472 | − | 0.846448i | \(-0.678737\pi\) | ||||
−0.532472 | + | 0.846448i | \(0.678737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.31995 | + | 10.3339i | 0.170550 | + | 0.331289i | ||||
\(974\) | 19.9663i | 0.639763i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 4.83232i | − | 0.154679i | ||||||
\(977\) | − | 10.6340i | − | 0.340211i | −0.985426 | − | 0.170105i | \(-0.945589\pi\) | ||
0.985426 | − | 0.170105i | \(-0.0544108\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.593378i | 0.0189644i | ||||||||
\(980\) | −1.36337 | + | 1.90992i | −0.0435514 | + | 0.0610103i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.9310 | 0.699845 | ||||||||
\(983\) | −45.3442 | −1.44626 | −0.723128 | − | 0.690714i | \(-0.757296\pi\) | ||||
−0.723128 | + | 0.690714i | \(0.757296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.18634i | 0.165250i | ||||||||
\(986\) | 1.78432 | 0.0568244 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.757021 | −0.0240840 | ||||||||
\(989\) | 9.79520i | 0.311469i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.9935 | −1.20690 | −0.603451 | − | 0.797400i | \(-0.706208\pi\) | ||||
−0.603451 | + | 0.797400i | \(0.706208\pi\) | |||||||
\(992\) | −9.21951 | −0.292720 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0131 | − | 6.18442i | 0.381033 | − | 0.196158i | ||||
\(995\) | − | 1.74737i | − | 0.0553952i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.7690i | 0.562748i | 0.959598 | + | 0.281374i | \(0.0907902\pi\) | ||||
−0.959598 | + | 0.281374i | \(0.909210\pi\) | |||||||
\(998\) | 0.0948850i | 0.00300353i | ||||||||
\(999\) | 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 | 2394.2.f.b.2015.13 | yes | 24 | |
3.2 | odd | 2 | 2394.2.f.a.2015.14 | yes | 24 | ||
7.6 | odd | 2 | 2394.2.f.a.2015.13 | ✓ | 24 | ||
21.20 | even | 2 | inner | 2394.2.f.b.2015.14 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.f.a.2015.13 | ✓ | 24 | 7.6 | odd | 2 | ||
2394.2.f.a.2015.14 | yes | 24 | 3.2 | odd | 2 | ||
2394.2.f.b.2015.13 | yes | 24 | 1.1 | even | 1 | trivial | |
2394.2.f.b.2015.14 | yes | 24 | 21.20 | even | 2 | inner |