Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2500,2,Mod(1249,2500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2500.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2500 = 2^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2500.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.9626005053\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.4 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2500.1249 |
Dual form | 2500.2.c.a.1249.1 |
$q$-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 \(\left(\mathbb{Z}/2500\mathbb{Z}\right)^\times\).
\(n\) | \(1251\) | \(1877\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.61803i | 0.934172i | 0.884212 | + | 0.467086i | \(0.154696\pi\) | ||||
−0.884212 | + | 0.467086i | \(0.845304\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.61803i | 0.611559i | 0.952102 | + | 0.305780i | \(0.0989171\pi\) | ||||
−0.952102 | + | 0.305780i | \(0.901083\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.381966 | 0.127322 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.61803 | 1.09088 | 0.545439 | − | 0.838150i | \(-0.316363\pi\) | ||||
0.545439 | + | 0.838150i | \(0.316363\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.00000i | − 0.832050i | −0.909353 | − | 0.416025i | \(-0.863423\pi\) | ||||
0.909353 | − | 0.416025i | \(-0.136577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.47214i | 1.32719i | 0.748093 | + | 0.663594i | \(0.230970\pi\) | ||||
−0.748093 | + | 0.663594i | \(0.769030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.61803 | 0.600618 | 0.300309 | − | 0.953842i | \(-0.402910\pi\) | ||||
0.300309 | + | 0.953842i | \(0.402910\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.61803 | −0.571302 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 0.381966i | − 0.0796454i | −0.999207 | − | 0.0398227i | \(-0.987321\pi\) | ||||
0.999207 | − | 0.0398227i | \(-0.0126793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47214i | 1.05311i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.70820 | 1.05999 | 0.529993 | − | 0.848002i | \(-0.322194\pi\) | ||||
0.529993 | + | 0.848002i | \(0.322194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.47214 | −1.52164 | −0.760820 | − | 0.648963i | \(-0.775203\pi\) | ||||
−0.760820 | + | 0.648963i | \(0.775203\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.85410i | 1.01907i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.47214i | − 0.242018i | −0.992651 | − | 0.121009i | \(-0.961387\pi\) | ||||
0.992651 | − | 0.121009i | \(-0.0386129\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.85410 | 0.777278 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4721 | 1.63547 | 0.817736 | − | 0.575593i | \(-0.195229\pi\) | ||||
0.817736 | + | 0.575593i | \(0.195229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 10.0000i | − 1.52499i | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||||
0.646997 | − | 0.762493i | \(-0.276025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 4.32624i | − 0.631047i | −0.948918 | − | 0.315523i | \(-0.897820\pi\) | ||||
0.948918 | − | 0.315523i | \(-0.102180\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.38197 | 0.625995 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.85410 | −1.23982 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.47214i | 1.16374i | 0.813283 | + | 0.581869i | \(0.197678\pi\) | ||||
−0.813283 | + | 0.581869i | \(0.802322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.23607i | 0.561081i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.76393 | 0.750400 | 0.375200 | − | 0.926944i | \(-0.377574\pi\) | ||||
0.375200 | + | 0.926944i | \(0.377574\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3262 | 1.57821 | 0.789107 | − | 0.614256i | \(-0.210544\pi\) | ||||
0.789107 | + | 0.614256i | \(0.210544\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.618034i | 0.0778650i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.18034i | 1.12156i | 0.827966 | + | 0.560779i | \(0.189498\pi\) | ||||
−0.827966 | + | 0.560779i | \(0.810502\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.618034 | 0.0744025 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.09017 | −0.604092 | −0.302046 | − | 0.953293i | \(-0.597670\pi\) | ||||
−0.302046 | + | 0.953293i | \(0.597670\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 4.38197i | − 0.512870i | −0.966561 | − | 0.256435i | \(-0.917452\pi\) | ||||
0.966561 | − | 0.256435i | \(-0.0825480\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.85410i | 0.667137i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0000 | −1.46261 | −0.731307 | − | 0.682048i | \(-0.761089\pi\) | ||||
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.94427i | 0.542704i | 0.962480 | + | 0.271352i | \(0.0874708\pi\) | ||||
−0.962480 | + | 0.271352i | \(0.912529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.23607i | 0.990210i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.38197 | −0.570487 | −0.285244 | − | 0.958455i | \(-0.592075\pi\) | ||||
−0.285244 | + | 0.958455i | \(0.592075\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.85410 | 0.508848 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 13.7082i | − 1.42147i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.8541i | 1.91434i | 0.289520 | + | 0.957172i | \(0.406504\pi\) | ||||
−0.289520 | + | 0.957172i | \(0.593496\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.38197 | 0.138893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7082 | −1.06551 | −0.532753 | − | 0.846271i | \(-0.678843\pi\) | ||||
−0.532753 | + | 0.846271i | \(0.678843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0344i | 1.57992i | 0.613158 | + | 0.789960i | \(0.289899\pi\) | ||||
−0.613158 | + | 0.789960i | \(0.710101\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.5623i | 1.31112i | 0.755144 | + | 0.655559i | \(0.227567\pi\) | ||||
−0.755144 | + | 0.655559i | \(0.772433\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.56231 | −0.436990 | −0.218495 | − | 0.975838i | \(-0.570115\pi\) | ||||
−0.218495 | + | 0.975838i | \(0.570115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.38197 | 0.226086 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 18.2361i | − 1.71550i | −0.514063 | − | 0.857752i | \(-0.671860\pi\) | ||||
0.514063 | − | 0.857752i | \(-0.328140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.14590i | − 0.105938i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.85410 | −0.811654 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.09017 | 0.190015 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.9443i | 1.52781i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.09017i | 0.0967369i | 0.998830 | + | 0.0483685i | \(0.0154022\pi\) | ||||
−0.998830 | + | 0.0483685i | \(0.984598\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.1803 | 1.42460 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.18034 | 0.539979 | 0.269989 | − | 0.962863i | \(-0.412980\pi\) | ||||
0.269989 | + | 0.962863i | \(0.412980\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.23607i | 0.367314i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.76393i | 0.834189i | 0.908863 | + | 0.417095i | \(0.136952\pi\) | ||||
−0.908863 | + | 0.417095i | \(0.863048\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.708204 | 0.0600691 | 0.0300345 | − | 0.999549i | \(-0.490438\pi\) | ||||
0.0300345 | + | 0.999549i | \(0.490438\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.00000 | 0.589506 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 10.8541i | − 0.907666i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.09017i | 0.584787i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.0344 | −1.31359 | −0.656796 | − | 0.754068i | \(-0.728089\pi\) | ||||
−0.656796 | + | 0.754068i | \(0.728089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.1803 | −1.72363 | −0.861816 | − | 0.507221i | \(-0.830673\pi\) | ||||
−0.861816 | + | 0.507221i | \(0.830673\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.09017i | 0.168980i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 7.47214i | − 0.596341i | −0.954513 | − | 0.298171i | \(-0.903624\pi\) | ||||
0.954513 | − | 0.298171i | \(-0.0963765\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.7082 | −1.08713 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.618034 | 0.0487079 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.61803i | 0.283386i | 0.989911 | + | 0.141693i | \(0.0452546\pi\) | ||||
−0.989911 | + | 0.141693i | \(0.954745\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.29180i | − 0.0999622i | −0.998750 | − | 0.0499811i | \(-0.984084\pi\) | ||||
0.998750 | − | 0.0499811i | \(-0.0159161\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 23.2361i | − 1.76661i | −0.468803 | − | 0.883303i | \(-0.655315\pi\) | ||||
0.468803 | − | 0.883303i | \(-0.344685\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.32624i | 0.701003i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.4721 | −1.30593 | −0.652964 | − | 0.757389i | \(-0.726475\pi\) | ||||
−0.652964 | + | 0.757389i | \(0.726475\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8541 | 1.17843 | 0.589213 | − | 0.807978i | \(-0.299438\pi\) | ||||
0.589213 | + | 0.807978i | \(0.299438\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.9443i | 1.47432i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.7984i | 1.44780i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.85410 | −0.644041 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.1246 | 1.31145 | 0.655725 | − | 0.754999i | \(-0.272363\pi\) | ||||
0.655725 | + | 0.754999i | \(0.272363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000i | 0.431889i | 0.976406 | + | 0.215945i | \(0.0692831\pi\) | ||||
−0.976406 | + | 0.215945i | \(0.930717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.52786i | 0.536338i | 0.963372 | + | 0.268169i | \(0.0864186\pi\) | ||||
−0.963372 | + | 0.268169i | \(0.913581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.14590 | 0.435671 | 0.217836 | − | 0.975985i | \(-0.430100\pi\) | ||||
0.217836 | + | 0.975985i | \(0.430100\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.8541 | −1.04773 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.23607i | 0.648245i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 0.145898i | − 0.0101406i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.47214 | 0.655201 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | −0.0688428 | −0.0344214 | − | 0.999407i | \(-0.510959\pi\) | ||||
−0.0344214 | + | 0.999407i | \(0.510959\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 8.23607i | − 0.564326i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 13.7082i | − 0.930574i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.09017 | 0.479109 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.4164 | 1.10429 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.56231i | − 0.171585i | −0.996313 | − | 0.0857923i | \(-0.972658\pi\) | ||||
0.996313 | − | 0.0857923i | \(-0.0273422\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 24.6525i | − 1.63624i | −0.575046 | − | 0.818121i | \(-0.695016\pi\) | ||||
0.575046 | − | 0.818121i | \(-0.304984\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.76393 | 0.248728 | 0.124364 | − | 0.992237i | \(-0.460311\pi\) | ||||
0.124364 | + | 0.992237i | \(0.460311\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.47214 | −0.623221 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 14.6180i | − 0.957659i | −0.877908 | − | 0.478830i | \(-0.841061\pi\) | ||||
0.877908 | − | 0.478830i | \(-0.158939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 21.0344i | − 1.36633i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3820 | 0.668761 | 0.334381 | − | 0.942438i | \(-0.391473\pi\) | ||||
0.334381 | + | 0.942438i | \(0.391473\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.94427i | 0.253025i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 7.85410i | − 0.499745i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.00000 | −0.506979 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.00000 | 0.315597 | 0.157799 | − | 0.987471i | \(-0.449560\pi\) | ||||
0.157799 | + | 0.987471i | \(0.449560\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.38197i | − 0.0868835i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 0.180340i | − 0.0112493i | −0.999984 | − | 0.00562465i | \(-0.998210\pi\) | ||||
0.999984 | − | 0.00562465i | \(-0.00179039\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.38197 | 0.148008 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.18034 | 0.134960 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.1459i | 0.995599i | 0.867292 | + | 0.497799i | \(0.165858\pi\) | ||||
−0.867292 | + | 0.497799i | \(0.834142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 8.70820i | − 0.532933i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.6525 | −1.74697 | −0.873486 | − | 0.486849i | \(-0.838146\pi\) | ||||
−0.873486 | + | 0.486849i | \(0.838146\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.18034 | −0.0717005 | −0.0358503 | − | 0.999357i | \(-0.511414\pi\) | ||||
−0.0358503 | + | 0.999357i | \(0.511414\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.85410i | 0.475352i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.7082i | 1.24424i | 0.782924 | + | 0.622118i | \(0.213727\pi\) | ||||
−0.782924 | + | 0.622118i | \(0.786273\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.23607 | −0.193738 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.47214 | −0.207130 | −0.103565 | − | 0.994623i | \(-0.533025\pi\) | ||||
−0.103565 | + | 0.994623i | \(0.533025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.76393i | − 0.223743i | −0.993723 | − | 0.111871i | \(-0.964316\pi\) | ||||
0.993723 | − | 0.111871i | \(-0.0356844\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.9443i | 1.00019i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.9443 | −0.761428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −30.5066 | −1.78833 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 14.2705i | − 0.833692i | −0.908977 | − | 0.416846i | \(-0.863135\pi\) | ||||
0.908977 | − | 0.416846i | \(-0.136865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.7984i | 1.14882i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.14590 | −0.0662690 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.1803 | 0.932619 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 17.3262i | − 0.995366i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0344i | 0.572696i | 0.958126 | + | 0.286348i | \(0.0924413\pi\) | ||||
−0.958126 | + | 0.286348i | \(0.907559\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.9443 | −1.47592 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.50658 | −0.255545 | −0.127772 | − | 0.991804i | \(-0.540783\pi\) | ||||
−0.127772 | + | 0.991804i | \(0.540783\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 6.14590i | − 0.347387i | −0.984800 | − | 0.173693i | \(-0.944430\pi\) | ||||
0.984800 | − | 0.173693i | \(-0.0555702\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.6180i | 1.66351i | 0.555139 | + | 0.831757i | \(0.312665\pi\) | ||||
−0.555139 | + | 0.831757i | \(0.687335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.6525 | 1.15632 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.9443 | −1.22481 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.3262i | 0.797133i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 7.38197i | − 0.408224i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.00000 | 0.385922 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.00000 | 0.164895 | 0.0824475 | − | 0.996595i | \(-0.473726\pi\) | ||||
0.0824475 | + | 0.996595i | \(0.473726\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 0.562306i | − 0.0308142i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 30.9443i | − 1.68564i | −0.538194 | − | 0.842821i | \(-0.680893\pi\) | ||||
0.538194 | − | 0.842821i | \(-0.319107\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.5066 | 1.60258 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.6525 | −1.65992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4164i | 0.994393i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 29.4721i | − 1.58215i | −0.611721 | − | 0.791074i | \(-0.709522\pi\) | ||||
0.611721 | − | 0.791074i | \(-0.290478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.5967 | 1.31663 | 0.658317 | − | 0.752741i | \(-0.271269\pi\) | ||||
0.658317 | + | 0.752741i | \(0.271269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.4164 | 0.876243 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 21.5967i | − 1.14948i | −0.818336 | − | 0.574739i | \(-0.805103\pi\) | ||||
0.818336 | − | 0.574739i | \(-0.194897\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 14.3262i | − 0.758225i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.3607 | 1.76071 | 0.880355 | − | 0.474316i | \(-0.157305\pi\) | ||||
0.880355 | + | 0.474316i | \(0.157305\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1459 | −0.639258 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.38197i | 0.177507i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 12.4721i | − 0.651040i | −0.945535 | − | 0.325520i | \(-0.894461\pi\) | ||||
0.945535 | − | 0.325520i | \(-0.105539\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.7082 | −0.711694 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.09017i | 0.470671i | 0.971914 | + | 0.235336i | \(0.0756189\pi\) | ||||
−0.971914 | + | 0.235336i | \(0.924381\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 17.1246i | − 0.881962i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.18034 | −0.420196 | −0.210098 | − | 0.977680i | \(-0.567378\pi\) | ||||
−0.210098 | + | 0.977680i | \(0.567378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.76393 | −0.0903690 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 21.0344i | − 1.07481i | −0.843324 | − | 0.537405i | \(-0.819405\pi\) | ||||
0.843324 | − | 0.537405i | \(-0.180595\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3.81966i | − 0.194164i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.0344 | −0.559468 | −0.279734 | − | 0.960077i | \(-0.590246\pi\) | ||||
−0.279734 | + | 0.960077i | \(0.590246\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.09017 | 0.105704 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.0000i | 0.504433i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 26.4721i | − 1.32860i | −0.747467 | − | 0.664299i | \(-0.768730\pi\) | ||||
0.747467 | − | 0.664299i | \(-0.231270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.85410 | −0.343134 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.3820 | 1.56714 | 0.783570 | − | 0.621303i | \(-0.213396\pi\) | ||||
0.783570 | + | 0.621303i | \(0.213396\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.4164i | 1.26608i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 5.32624i | − 0.264012i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.5967 | 1.16678 | 0.583392 | − | 0.812191i | \(-0.301725\pi\) | ||||
0.583392 | + | 0.812191i | \(0.301725\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.7984 | −0.779276 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.32624i | 0.458914i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.14590i | 0.0561149i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0557 | 0.491254 | 0.245627 | − | 0.969364i | \(-0.421006\pi\) | ||||
0.245627 | + | 0.969364i | \(0.421006\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.6525 | 1.05528 | 0.527639 | − | 0.849469i | \(-0.323078\pi\) | ||||
0.527639 | + | 0.849469i | \(0.323078\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 1.65248i | − 0.0803461i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.9443i | 0.965171i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.5623 | 0.847916 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.583592 | −0.0281106 | −0.0140553 | − | 0.999901i | \(-0.504474\pi\) | ||||
−0.0140553 | + | 0.999901i | \(0.504474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 11.2148i | − 0.538948i | −0.963008 | − | 0.269474i | \(-0.913150\pi\) | ||||
0.963008 | − | 0.269474i | \(-0.0868498\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.00000i | − 0.0478365i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2016 | 0.582352 | 0.291176 | − | 0.956670i | \(-0.405954\pi\) | ||||
0.291176 | + | 0.956670i | \(0.405954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.67376 | 0.0797030 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.6525i | 1.26630i | 0.774030 | + | 0.633149i | \(0.218238\pi\) | ||||
−0.774030 | + | 0.633149i | \(0.781762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 25.9443i | − 1.22712i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.6525 | 1.39939 | 0.699693 | − | 0.714443i | \(-0.253320\pi\) | ||||
0.699693 | + | 0.714443i | \(0.253320\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.8885 | 1.78410 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 34.2705i | − 1.61017i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 19.9443i | − 0.932954i | −0.884533 | − | 0.466477i | \(-0.845523\pi\) | ||||
0.884533 | − | 0.466477i | \(-0.154477\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.9443 | −1.39768 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8541 | 0.505526 | 0.252763 | − | 0.967528i | \(-0.418661\pi\) | ||||
0.252763 | + | 0.967528i | \(0.418661\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.5623i | 1.69919i | 0.527432 | + | 0.849597i | \(0.323155\pi\) | ||||
−0.527432 | + | 0.849597i | \(0.676845\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.4377i | 0.575548i | 0.957698 | + | 0.287774i | \(0.0929152\pi\) | ||||
−0.957698 | + | 0.287774i | \(0.907085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.8541 | −0.685899 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0902 | 0.557086 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 36.1803i | − 1.66357i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.23607i | 0.148169i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.12461 | −0.0513848 | −0.0256924 | − | 0.999670i | \(-0.508179\pi\) | ||||
−0.0256924 | + | 0.999670i | \(0.508179\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.41641 | −0.201371 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000i | 0.0455016i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 42.7082i | − 1.93529i | −0.252309 | − | 0.967647i | \(-0.581190\pi\) | ||||
0.252309 | − | 0.967647i | \(-0.418810\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.85410 | −0.264732 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.58359 | −0.297113 | −0.148557 | − | 0.988904i | \(-0.547463\pi\) | ||||
−0.148557 | + | 0.988904i | \(0.547463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.2361i | 1.40680i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 8.23607i | − 0.369438i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.7639 | −1.06382 | −0.531910 | − | 0.846801i | \(-0.678525\pi\) | ||||
−0.531910 | + | 0.846801i | \(0.678525\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.09017 | 0.0933819 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 40.4853i | − 1.80515i | −0.430533 | − | 0.902575i | \(-0.641674\pi\) | ||||
0.430533 | − | 0.902575i | \(-0.358326\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.47214i | 0.287438i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.2705 | 1.25307 | 0.626534 | − | 0.779394i | \(-0.284473\pi\) | ||||
0.626534 | + | 0.779394i | \(0.284473\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.09017 | 0.313651 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.3262i | 0.632519i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 15.6525i | − 0.688395i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 37.5967 | 1.65031 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.94427 | −0.435666 | −0.217833 | − | 0.975986i | \(-0.569899\pi\) | ||||
−0.217833 | + | 0.975986i | \(0.569899\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.18034i | − 0.0953396i | −0.998863 | − | 0.0476698i | \(-0.984820\pi\) | ||||
0.998863 | − | 0.0476698i | \(-0.0151795\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 46.3607i | − 2.01950i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8541 | 0.993657 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.20163 | 0.0955424 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 31.4164i | − 1.36080i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 28.2705i | − 1.21996i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.8541 | 0.682885 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0689 | −1.29276 | −0.646381 | − | 0.763015i | \(-0.723718\pi\) | ||||
−0.646381 | + | 0.763015i | \(0.723718\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.6525i | 1.10085i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.36068i | 0.0581785i | 0.999577 | + | 0.0290892i | \(0.00926070\pi\) | ||||
−0.999577 | + | 0.0290892i | \(0.990739\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.70820 | 0.200941 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.9443 | 0.636647 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 21.0344i | − 0.894475i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 35.4508i | − 1.50210i | −0.660245 | − | 0.751050i | \(-0.729548\pi\) | ||||
0.660245 | − | 0.751050i | \(-0.270452\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.0000 | −1.26886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.0344 | −1.35250 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 46.0132i | − 1.93922i | −0.244649 | − | 0.969612i | \(-0.578673\pi\) | ||||
0.244649 | − | 0.969612i | \(-0.421327\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 12.4721i | − 0.523780i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.7639 | −0.744703 | −0.372351 | − | 0.928092i | \(-0.621448\pi\) | ||||
−0.372351 | + | 0.928092i | \(0.621448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.94427 | −0.248760 | −0.124380 | − | 0.992235i | \(-0.539694\pi\) | ||||
−0.124380 | + | 0.992235i | \(0.539694\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.3262i | 1.22512i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 18.1246i | − 0.754537i | −0.926104 | − | 0.377269i | \(-0.876863\pi\) | ||||
0.926104 | − | 0.377269i | \(-0.123137\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.70820 | −0.403459 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.00000 | −0.331896 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.6525i | 1.26950i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.7984i | 1.27118i | 0.772025 | + | 0.635592i | \(0.219244\pi\) | ||||
−0.772025 | + | 0.635592i | \(0.780756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.1803 | −0.913925 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.1803 | −0.501032 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 23.8328i | − 0.978696i | −0.872088 | − | 0.489348i | \(-0.837235\pi\) | ||||
0.872088 | − | 0.489348i | \(-0.162765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.94427i | 0.406992i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.1803 | −1.88688 | −0.943439 | − | 0.331547i | \(-0.892430\pi\) | ||||
−0.943439 | + | 0.331547i | \(0.892430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.5967 | 1.20728 | 0.603638 | − | 0.797258i | \(-0.293717\pi\) | ||||
0.603638 | + | 0.797258i | \(0.293717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.50658i | 0.142799i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.4721i | 1.07447i | 0.843432 | + | 0.537235i | \(0.180531\pi\) | ||||
−0.843432 | + | 0.537235i | \(0.819469\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.9443 | −0.605572 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.9787 | −0.525063 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2361i | 0.776937i | 0.921462 | + | 0.388469i | \(0.126996\pi\) | ||||
−0.921462 | + | 0.388469i | \(0.873004\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 30.6312i | − 1.23317i | −0.787290 | − | 0.616583i | \(-0.788517\pi\) | ||||
0.787290 | − | 0.616583i | \(-0.211483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.1246 | −0.406943 | −0.203471 | − | 0.979081i | \(-0.565222\pi\) | ||||
−0.203471 | + | 0.979081i | \(0.565222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.09017 | 0.0838756 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 8.70820i | − 0.348887i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.3262i | 0.612071i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.05573 | 0.321203 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1803 | 0.922795 | 0.461397 | − | 0.887194i | \(-0.347348\pi\) | ||||
0.461397 | + | 0.887194i | \(0.347348\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 1.61803i | − 0.0643111i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 13.1459i | − 0.520859i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.94427 | −0.0769142 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.6525 | −1.13170 | −0.565852 | − | 0.824507i | \(-0.691453\pi\) | ||||
−0.565852 | + | 0.824507i | \(0.691453\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.3050i | 1.58947i | 0.606955 | + | 0.794736i | \(0.292391\pi\) | ||||
−0.606955 | + | 0.794736i | \(0.707609\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 43.8328i | − 1.72325i | −0.507549 | − | 0.861623i | \(-0.669448\pi\) | ||||
0.507549 | − | 0.861623i | \(-0.330552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.8541 | 0.818595 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.1803 | 0.869316 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 0.0344419i | − 0.00134781i | −1.00000 | 0.000673907i | \(-0.999785\pi\) | |||||
1.00000 | 0.000673907i | \(-0.000214511\pi\) | ||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 1.67376i | − 0.0652997i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.2705 | 0.906490 | 0.453245 | − | 0.891386i | \(-0.350266\pi\) | ||||
0.453245 | + | 0.891386i | \(0.350266\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.8197 | −0.615313 | −0.307657 | − | 0.951497i | \(-0.599545\pi\) | ||||
−0.307657 | + | 0.951497i | \(0.599545\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.5623i | 1.03159i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.18034i | − 0.0844231i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.14590 | 0.160290 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.5967 | 1.72164 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5279i | 0.560008i | 0.959999 | + | 0.280004i | \(0.0903358\pi\) | ||||
−0.959999 | + | 0.280004i | \(0.909664\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.72949i | 0.297068i | 0.988907 | + | 0.148534i | \(0.0474555\pi\) | ||||
−0.988907 | + | 0.148534i | \(0.952544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.5066 | −1.17074 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 39.8885 | 1.52853 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 46.7984i | − 1.79069i | −0.445373 | − | 0.895345i | \(-0.646929\pi\) | ||||
0.445373 | − | 0.895345i | \(-0.353071\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.09017i | 0.232354i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.4164 | 0.968288 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.0557 | −0.686872 | −0.343436 | − | 0.939176i | \(-0.611591\pi\) | ||||
−0.343436 | + | 0.939176i | \(0.611591\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.23607i | 0.0849412i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 57.3050i | 2.17058i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.6525 | 0.894619 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.3607 | −1.03340 | −0.516699 | − | 0.856167i | \(-0.672839\pi\) | ||||
−0.516699 | + | 0.856167i | \(0.672839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 3.85410i | − 0.145360i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 17.3262i | − 0.651620i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.7639 | −0.516915 | −0.258458 | − | 0.966023i | \(-0.583214\pi\) | ||||
−0.258458 | + | 0.966023i | \(0.583214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.96556 | −0.186223 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.23607i | 0.121192i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.47214i | 0.241706i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.6180 | −0.918098 | −0.459049 | − | 0.888411i | \(-0.651810\pi\) | ||||
−0.459049 | + | 0.888411i | \(0.651810\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.9443 | −0.966215 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.7984i | 0.624738i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 18.6738i | − 0.692571i | −0.938129 | − | 0.346286i | \(-0.887443\pi\) | ||||
0.938129 | − | 0.346286i | \(-0.112557\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.5066 | −1.09284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.7214 | 2.02394 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 47.2492i | − 1.74519i | −0.488445 | − | 0.872595i | \(-0.662436\pi\) | ||||
0.488445 | − | 0.872595i | \(-0.337564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.2148i | 1.22348i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.7639 | −1.02131 | −0.510656 | − | 0.859785i | \(-0.670598\pi\) | ||||
−0.510656 | + | 0.859785i | \(0.670598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.7082 | 0.466848 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.6738i | 0.575015i | 0.957778 | + | 0.287507i | \(0.0928266\pi\) | ||||
−0.957778 | + | 0.287507i | \(0.907173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.88854i | 0.0690982i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.9443 | −0.801826 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.0344 | −1.13246 | −0.566231 | − | 0.824246i | \(-0.691599\pi\) | ||||
−0.566231 | + | 0.824246i | \(0.691599\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.09017i | 0.294822i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.47214i | 0.0535057i | 0.999642 | + | 0.0267528i | \(0.00851671\pi\) | ||||
−0.999642 | + | 0.0267528i | \(0.991483\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.23607 | 0.0811641 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.9787 | −0.869228 | −0.434614 | − | 0.900617i | \(-0.643115\pi\) | ||||
−0.434614 | + | 0.900617i | \(0.643115\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.38197i | − 0.267245i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 17.2918i | − 0.624371i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.81966 | 0.245923 | 0.122962 | − | 0.992411i | \(-0.460761\pi\) | ||||
0.122962 | + | 0.992411i | \(0.460761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.291796 | 0.0105088 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 21.5836i | − 0.776308i | −0.921595 | − | 0.388154i | \(-0.873113\pi\) | ||||
0.921595 | − | 0.388154i | \(-0.126887\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.85410i | 0.138265i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.4164 | 0.982295 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.4164 | −0.658991 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 31.2361i | 1.11629i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.1246i | 0.859950i | 0.902841 | + | 0.429975i | \(0.141478\pi\) | ||||
−0.902841 | + | 0.429975i | \(0.858522\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.1246 | −0.930061 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.5066 | 1.04913 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 36.9787i | − 1.31315i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.43769i | 0.192613i | 0.995352 | + | 0.0963065i | \(0.0307029\pi\) | ||||
−0.995352 | + | 0.0963065i | \(0.969297\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.6738 | 0.837517 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.05573 | −0.0726356 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 15.8541i | − 0.559479i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 46.3607i | − 1.63197i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.1591 | 1.34160 | 0.670800 | − | 0.741638i | \(-0.265951\pi\) | ||||
0.670800 | + | 0.741638i | \(0.265951\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.8885 | −0.663266 | −0.331633 | − | 0.943408i | \(-0.607600\pi\) | ||||
−0.331633 | + | 0.943408i | \(0.607600\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.90983i | − 0.0669807i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 26.1803i | − 0.915934i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.85410 | 0.0647876 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.4721 | 0.365480 | 0.182740 | − | 0.983161i | \(-0.441503\pi\) | ||||
0.182740 | + | 0.983161i | \(0.441503\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 10.4164i | − 0.363093i | −0.983382 | − | 0.181547i | \(-0.941890\pi\) | ||||
0.983382 | − | 0.181547i | \(-0.0581103\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 24.0689i | − 0.836957i | −0.908227 | − | 0.418479i | \(-0.862564\pi\) | ||||
0.908227 | − | 0.418479i | \(-0.137436\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.1246 | −1.63671 | −0.818353 | − | 0.574716i | \(-0.805112\pi\) | ||||
−0.818353 | + | 0.574716i | \(0.805112\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.5066 | −1.16233 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.9787i | 0.830813i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 46.3607i | − 1.60246i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.09017 | 0.210256 | 0.105128 | − | 0.994459i | \(-0.466475\pi\) | ||||
0.105128 | + | 0.994459i | \(0.466475\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.58359 | 0.123572 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 5.61803i | − 0.193495i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.38197i | 0.116206i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.09017 | 0.209014 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.562306 | −0.0192756 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 16.9098i | − 0.578982i | −0.957181 | − | 0.289491i | \(-0.906514\pi\) | ||||
0.957181 | − | 0.289491i | \(-0.0934860\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.7082i | 0.809857i | 0.914348 | + | 0.404928i | \(0.132704\pi\) | ||||
−0.914348 | + | 0.404928i | \(0.867296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.7214 | −1.90119 | −0.950594 | − | 0.310436i | \(-0.899525\pi\) | ||||
−0.950594 | + | 0.310436i | \(0.899525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.4164 | −0.934349 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.29180i | 0.316296i | 0.987415 | + | 0.158148i | \(0.0505524\pi\) | ||||
−0.987415 | + | 0.158148i | \(0.949448\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 20.9443i | − 0.711305i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47.0344 | −1.59553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.5410 | 0.933192 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.20163i | 0.243738i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.74265i | 0.261451i | 0.991419 | + | 0.130725i | \(0.0417306\pi\) | ||||
−0.991419 | + | 0.130725i | \(0.958269\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.0902 | 0.778812 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.25735 | −0.143434 | −0.0717170 | − | 0.997425i | \(-0.522848\pi\) | ||||
−0.0717170 | + | 0.997425i | \(0.522848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.6525i | 1.33441i | 0.744873 | + | 0.667206i | \(0.232510\pi\) | ||||
−0.744873 | + | 0.667206i | \(0.767490\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.7639i | 0.831491i | 0.909481 | + | 0.415746i | \(0.136479\pi\) | ||||
−0.909481 | + | 0.415746i | \(0.863521\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.76393 | −0.0591604 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.8885 | −0.934301 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 11.3262i | − 0.379018i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1.85410i | − 0.0619067i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −48.3607 | −1.61292 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.3607 | −1.54450 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26.1803i | 0.871227i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.56231i | 0.118284i | 0.998250 | + | 0.0591422i | \(0.0188365\pi\) | ||||
−0.998250 | + | 0.0591422i | \(0.981163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.09017 | −0.135662 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.1803 | 1.43063 | 0.715314 | − | 0.698803i | \(-0.246284\pi\) | ||||
0.715314 | + | 0.698803i | \(0.246284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.8885i | 0.592024i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.0000i | 0.330229i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0132 | 1.12199 | 0.560995 | − | 0.827819i | \(-0.310419\pi\) | ||||
0.560995 | + | 0.827819i | \(0.310419\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.2361 | −0.534997 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.2705i | 0.502635i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.12461i | 0.201159i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.0132 | 1.31279 | 0.656395 | − | 0.754418i | \(-0.272081\pi\) | ||||
0.656395 | + | 0.754418i | \(0.272081\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4721 | 0.375984 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 7.29180i | − 0.238723i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 12.5967i | − 0.411518i | −0.978603 | − | 0.205759i | \(-0.934034\pi\) | ||||
0.978603 | − | 0.205759i | \(-0.0659663\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.94427 | 0.324519 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.65248 | 0.249464 | 0.124732 | − | 0.992190i | \(-0.460193\pi\) | ||||
0.124732 | + | 0.992190i | \(0.460193\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 4.00000i | − 0.130258i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.7082i | 0.607935i | 0.952682 | + | 0.303967i | \(0.0983114\pi\) | ||||
−0.952682 | + | 0.303967i | \(0.901689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.1459 | −0.426734 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.9230 | −1.55401 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 8.56231i | − 0.277360i | −0.990337 | − | 0.138680i | \(-0.955714\pi\) | ||||
0.990337 | − | 0.138680i | \(-0.0442860\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.4164i | 1.08020i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.7984 | −0.510156 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.7771 | 1.31539 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.18034i | 0.166934i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.3607i | 0.622597i | 0.950312 | + | 0.311299i | \(0.100764\pi\) | ||||
−0.950312 | + | 0.311299i | \(0.899236\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.1803 | −0.744660 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.4508 | −0.463750 | −0.231875 | − | 0.972746i | \(-0.574486\pi\) | ||||
−0.231875 | + | 0.972746i | \(0.574486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.14590i | 0.0367358i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 39.1803i | − 1.25349i | −0.779224 | − | 0.626745i | \(-0.784387\pi\) | ||||
0.779224 | − | 0.626745i | \(-0.215613\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.4721 | −0.622332 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.74265 | −0.0556384 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.88854i | 0.315396i | 0.987487 | + | 0.157698i | \(0.0504072\pi\) | ||||
−0.987487 | + | 0.157698i | \(0.949593\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.3262i | 0.360518i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.81966 | −0.121458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.1246 | 1.62403 | 0.812013 | − | 0.583639i | \(-0.198372\pi\) | ||||
0.812013 | + | 0.583639i | \(0.198372\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.85410i | 0.154040i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 8.03444i | − 0.254453i | −0.991874 | − | 0.127227i | \(-0.959392\pi\) | ||||
0.991874 | − | 0.127227i | \(-0.0406076\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.05573 | 0.254872 |
(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 | 2500.2.c.a.1249.4 | 4 | ||
5.2 | odd | 4 | 2500.2.a.b.1.2 | yes | 2 | ||
5.3 | odd | 4 | 2500.2.a.a.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 2500.2.c.a.1249.1 | 4 | ||
20.3 | even | 4 | 10000.2.a.j.1.2 | 2 | |||
20.7 | even | 4 | 10000.2.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2500.2.a.a.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
2500.2.a.b.1.2 | yes | 2 | 5.2 | odd | 4 | ||
2500.2.c.a.1249.1 | 4 | 5.4 | even | 2 | inner | ||
2500.2.c.a.1249.4 | 4 | 1.1 | even | 1 | trivial | ||
10000.2.a.e.1.1 | 2 | 20.7 | even | 4 | |||
10000.2.a.j.1.2 | 2 | 20.3 | even | 4 |