Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2925,2,Mod(2224,2925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2925.2224");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2925.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: | \(23.3562425912\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2224.3 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2925.2224 |
Dual form | 2925.2.c.o.2224.2 |
$q$-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 \(\left(\mathbb{Z}/2925\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(2251\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56155i | 1.10418i | 0.833783 | + | 0.552092i | \(0.186170\pi\) | ||||
−0.833783 | + | 0.552092i | \(0.813830\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.438447 | −0.219224 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.56155i | − 1.72410i | −0.506819 | − | 0.862052i | \(-0.669179\pi\) | ||||
0.506819 | − | 0.862052i | \(-0.330821\pi\) | |||||||
\(8\) | 2.43845i | 0.862121i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 7.12311 | 1.90373 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 2.56155i | 0.621268i | 0.950530 | + | 0.310634i | \(0.100541\pi\) | ||||
−0.950530 | + | 0.310634i | \(0.899459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12311 | −0.716490 | −0.358245 | − | 0.933628i | \(-0.616625\pi\) | ||||
−0.358245 | + | 0.933628i | \(0.616625\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 4.00000i | − 0.852803i | ||||||||
\(23\) | 6.56155i | 1.36818i | 0.729398 | + | 0.684089i | \(0.239800\pi\) | ||||
−0.729398 | + | 0.684089i | \(0.760200\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.56155 | −0.306246 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | 1.12311 | 0.208555 | 0.104278 | − | 0.994548i | \(-0.466747\pi\) | ||||
0.104278 | + | 0.994548i | \(0.466747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | − 2.43845i | − 0.431061i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.68466i | 0.276956i | 0.990366 | + | 0.138478i | \(0.0442210\pi\) | ||||
−0.990366 | + | 0.138478i | \(0.955779\pi\) | |||||||
\(38\) | − 4.87689i | − 0.791137i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.561553 | 0.0876998 | 0.0438499 | − | 0.999038i | \(-0.486038\pi\) | ||||
0.0438499 | + | 0.999038i | \(0.486038\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.12311i | 0.781266i | 0.920546 | + | 0.390633i | \(0.127744\pi\) | ||||
−0.920546 | + | 0.390633i | \(0.872256\pi\) | |||||||
\(44\) | 1.12311 | 0.169315 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.2462 | −1.51072 | ||||||||
\(47\) | − 2.87689i | − 0.419638i | −0.977740 | − | 0.209819i | \(-0.932712\pi\) | ||||
0.977740 | − | 0.209819i | \(-0.0672875\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.8078 | −1.97254 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 0.438447i | − 0.0608017i | ||||||||
\(53\) | 7.68466i | 1.05557i | 0.849378 | + | 0.527785i | \(0.176977\pi\) | ||||
−0.849378 | + | 0.527785i | \(0.823023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.1231 | 1.48639 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.75379i | 0.230284i | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.68466 | 0.727846 | 0.363923 | − | 0.931429i | \(-0.381437\pi\) | ||||
0.363923 | + | 0.931429i | \(0.381437\pi\) | |||||||
\(62\) | 9.36932i | 1.18990i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.56155 | −0.695194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.3693i | 1.63332i | 0.577118 | + | 0.816661i | \(0.304177\pi\) | ||||
−0.577118 | + | 0.816661i | \(0.695823\pi\) | |||||||
\(68\) | − 1.12311i | − 0.136197i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.5616 | −1.72814 | −0.864069 | − | 0.503373i | \(-0.832092\pi\) | ||||
−0.864069 | + | 0.503373i | \(0.832092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | −2.63068 | −0.305811 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.36932 | 0.157071 | ||||||||
\(77\) | 11.6847i | 1.33159i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.68466 | 0.864592 | 0.432296 | − | 0.901732i | \(-0.357704\pi\) | ||||
0.432296 | + | 0.901732i | \(0.357704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.876894i | 0.0968368i | ||||||||
\(83\) | 16.4924i | 1.81028i | 0.425115 | + | 0.905139i | \(0.360234\pi\) | ||||
−0.425115 | + | 0.905139i | \(0.639766\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 6.24621i | − 0.665848i | ||||||||
\(89\) | −1.68466 | −0.178573 | −0.0892867 | − | 0.996006i | \(-0.528459\pi\) | ||||
−0.0892867 | + | 0.996006i | \(0.528459\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.56155 | 0.478181 | ||||||||
\(92\) | − 2.87689i | − 0.299937i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.49242 | 0.463358 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 11.9309i | − 1.21140i | −0.795695 | − | 0.605698i | \(-0.792894\pi\) | ||||
0.795695 | − | 0.605698i | \(-0.207106\pi\) | |||||||
\(98\) | − 21.5616i | − 2.17805i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.24621 | 0.621521 | 0.310761 | − | 0.950488i | \(-0.399416\pi\) | ||||
0.310761 | + | 0.950488i | \(0.399416\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.87689i | 0.677601i | 0.940858 | + | 0.338800i | \(0.110021\pi\) | ||||
−0.940858 | + | 0.338800i | \(0.889979\pi\) | |||||||
\(104\) | −2.43845 | −0.239109 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 17.9309i | 1.73344i | 0.498793 | + | 0.866721i | \(0.333777\pi\) | ||||
−0.498793 | + | 0.866721i | \(0.666223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 21.3693i | 2.01921i | ||||||||
\(113\) | − 13.1231i | − 1.23452i | −0.786760 | − | 0.617259i | \(-0.788243\pi\) | ||||
0.786760 | − | 0.617259i | \(-0.211757\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.492423 | −0.0457203 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.7386i | 1.72503i | ||||||||
\(119\) | 11.6847 | 1.07113 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 8.87689i | 0.803676i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.63068 | −0.236242 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2462i | 1.61909i | 0.587058 | + | 0.809545i | \(0.300286\pi\) | ||||
−0.587058 | + | 0.809545i | \(0.699714\pi\) | |||||||
\(128\) | − 13.5616i | − 1.19868i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.2462i | 1.23530i | ||||||||
\(134\) | −20.8769 | −1.80349 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.24621 | −0.535608 | ||||||||
\(137\) | 7.12311i | 0.608568i | 0.952581 | + | 0.304284i | \(0.0984172\pi\) | ||||
−0.952581 | + | 0.304284i | \(0.901583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.6847 | −1.33036 | −0.665178 | − | 0.746685i | \(-0.731644\pi\) | ||||
−0.665178 | + | 0.746685i | \(0.731644\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 22.7386i | − 1.90818i | ||||||||
\(143\) | − 2.56155i | − 0.214208i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.36932 | −0.775410 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 0.738634i | − 0.0607153i | ||||||||
\(149\) | 2.80776 | 0.230021 | 0.115010 | − | 0.993364i | \(-0.463310\pi\) | ||||
0.115010 | + | 0.993364i | \(0.463310\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3693 | −1.08798 | −0.543990 | − | 0.839092i | \(-0.683087\pi\) | ||||
−0.543990 | + | 0.839092i | \(0.683087\pi\) | |||||||
\(152\) | − 7.61553i | − 0.617701i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −18.2462 | −1.47032 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 21.3693i | − 1.70546i | −0.522354 | − | 0.852729i | \(-0.674946\pi\) | ||||
0.522354 | − | 0.852729i | \(-0.325054\pi\) | |||||||
\(158\) | 12.0000i | 0.954669i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 29.9309 | 2.35888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.0540i | 1.64907i | 0.565808 | + | 0.824537i | \(0.308564\pi\) | ||||
−0.565808 | + | 0.824537i | \(0.691436\pi\) | |||||||
\(164\) | −0.246211 | −0.0192259 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.7538 | −1.99888 | ||||||||
\(167\) | − 13.1231i | − 1.01550i | −0.861506 | − | 0.507748i | \(-0.830478\pi\) | ||||
0.861506 | − | 0.507748i | \(-0.169522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 2.24621i | − 0.171272i | ||||||||
\(173\) | 21.1231i | 1.60596i | 0.596006 | + | 0.802980i | \(0.296753\pi\) | ||||
−0.596006 | + | 0.802980i | \(0.703247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0000 | 0.904534 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 2.63068i | − 0.197178i | ||||||||
\(179\) | −13.1231 | −0.980867 | −0.490433 | − | 0.871479i | \(-0.663162\pi\) | ||||
−0.490433 | + | 0.871479i | \(0.663162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.6847 | 1.90913 | 0.954563 | − | 0.298010i | \(-0.0963228\pi\) | ||||
0.954563 | + | 0.298010i | \(0.0963228\pi\) | |||||||
\(182\) | 7.12311i | 0.528000i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.0000 | −1.17954 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.56155i | − 0.479828i | ||||||||
\(188\) | 1.26137i | 0.0919946i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6155 | 1.56404 | 0.782022 | − | 0.623250i | \(-0.214188\pi\) | ||||
0.782022 | + | 0.623250i | \(0.214188\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 15.4384i | − 1.11128i | −0.831422 | − | 0.555642i | \(-0.812473\pi\) | ||||
0.831422 | − | 0.555642i | \(-0.187527\pi\) | |||||||
\(194\) | 18.6307 | 1.33761 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.05398 | 0.432427 | ||||||||
\(197\) | − 21.3693i | − 1.52250i | −0.648458 | − | 0.761250i | \(-0.724586\pi\) | ||||
0.648458 | − | 0.761250i | \(-0.275414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.75379i | 0.686274i | ||||||||
\(203\) | − 5.12311i | − 0.359572i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.7386 | −0.748196 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 4.68466i | − 0.324823i | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.2462 | −0.705378 | −0.352689 | − | 0.935741i | \(-0.614733\pi\) | ||||
−0.352689 | + | 0.935741i | \(0.614733\pi\) | |||||||
\(212\) | − 3.36932i | − 0.231406i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −28.0000 | −1.91404 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 27.3693i | − 1.85795i | ||||||||
\(218\) | 3.12311i | 0.211523i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.56155 | −0.172309 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 9.36932i | − 0.627416i | −0.949520 | − | 0.313708i | \(-0.898429\pi\) | ||||
0.949520 | − | 0.313708i | \(-0.101571\pi\) | |||||||
\(224\) | −11.1231 | −0.743194 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.4924 | 1.36314 | ||||||||
\(227\) | − 22.2462i | − 1.47653i | −0.674509 | − | 0.738266i | \(-0.735645\pi\) | ||||
0.674509 | − | 0.738266i | \(-0.264355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.87689 | −0.586602 | −0.293301 | − | 0.956020i | \(-0.594754\pi\) | ||||
−0.293301 | + | 0.956020i | \(0.594754\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.73863i | 0.179800i | ||||||||
\(233\) | − 7.19224i | − 0.471179i | −0.971853 | − | 0.235590i | \(-0.924298\pi\) | ||||
0.971853 | − | 0.235590i | \(-0.0757021\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.26137 | −0.342486 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.2462i | 1.18273i | ||||||||
\(239\) | −5.93087 | −0.383636 | −0.191818 | − | 0.981431i | \(-0.561438\pi\) | ||||
−0.191818 | + | 0.981431i | \(0.561438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.7386 | −1.59356 | −0.796778 | − | 0.604272i | \(-0.793464\pi\) | ||||
−0.796778 | + | 0.604272i | \(0.793464\pi\) | |||||||
\(242\) | − 6.93087i | − 0.445533i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.49242 | −0.159561 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3.12311i | − 0.198718i | ||||||||
\(248\) | 14.6307i | 0.929049i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.75379 | −0.615654 | −0.307827 | − | 0.951442i | \(-0.599602\pi\) | ||||
−0.307827 | + | 0.951442i | \(0.599602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 16.8078i | − 1.05670i | ||||||||
\(254\) | −28.4924 | −1.78777 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | 21.1231i | 1.31762i | 0.752308 | + | 0.658812i | \(0.228941\pi\) | ||||
−0.752308 | + | 0.658812i | \(0.771059\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.68466 | 0.477501 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.2462i | 0.878459i | 0.898375 | + | 0.439230i | \(0.144749\pi\) | ||||
−0.898375 | + | 0.439230i | \(0.855251\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −22.2462 | −1.36400 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 5.86174i | − 0.358063i | ||||||||
\(269\) | −9.12311 | −0.556246 | −0.278123 | − | 0.960546i | \(-0.589712\pi\) | ||||
−0.278123 | + | 0.960546i | \(0.589712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.36932 | 0.326163 | 0.163081 | − | 0.986613i | \(-0.447857\pi\) | ||||
0.163081 | + | 0.986613i | \(0.447857\pi\) | |||||||
\(272\) | − 12.0000i | − 0.727607i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.1231 | −0.671971 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.24621i | 0.255130i | 0.991830 | + | 0.127565i | \(0.0407162\pi\) | ||||
−0.991830 | + | 0.127565i | \(0.959284\pi\) | |||||||
\(278\) | − 24.4924i | − 1.46896i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2462 | 0.730548 | 0.365274 | − | 0.930900i | \(-0.380975\pi\) | ||||
0.365274 | + | 0.930900i | \(0.380975\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000i | 0.237775i | 0.992908 | + | 0.118888i | \(0.0379328\pi\) | ||||
−0.992908 | + | 0.118888i | \(0.962067\pi\) | |||||||
\(284\) | 6.38447 | 0.378849 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | − 2.56155i | − 0.151204i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4384 | 0.614026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 2.63068i | − 0.153949i | ||||||||
\(293\) | − 3.75379i | − 0.219299i | −0.993970 | − | 0.109649i | \(-0.965027\pi\) | ||||
0.993970 | − | 0.109649i | \(-0.0349728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.10795 | −0.238770 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.38447i | 0.253986i | ||||||||
\(299\) | −6.56155 | −0.379464 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.3693 | 1.34699 | ||||||||
\(302\) | − 20.8769i | − 1.20133i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.6307 | 0.839127 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.43845i | 0.196243i | 0.995174 | + | 0.0981213i | \(0.0312833\pi\) | ||||
−0.995174 | + | 0.0981213i | \(0.968717\pi\) | |||||||
\(308\) | − 5.12311i | − 0.291916i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.3693 | −1.55197 | −0.775986 | − | 0.630750i | \(-0.782747\pi\) | ||||
−0.775986 | + | 0.630750i | \(0.782747\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 20.8769i | − 1.18003i | −0.807392 | − | 0.590016i | \(-0.799121\pi\) | ||||
0.807392 | − | 0.590016i | \(-0.200879\pi\) | |||||||
\(314\) | 33.3693 | 1.88314 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.36932 | −0.189539 | ||||||||
\(317\) | − 34.4924i | − 1.93729i | −0.248454 | − | 0.968644i | \(-0.579922\pi\) | ||||
0.248454 | − | 0.968644i | \(-0.420078\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.87689 | −0.161075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 46.7386i | 2.60464i | ||||||||
\(323\) | − 8.00000i | − 0.445132i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −32.8769 | −1.82088 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.36932i | 0.0756079i | ||||||||
\(329\) | −13.1231 | −0.723500 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.8769 | 1.14750 | 0.573749 | − | 0.819031i | \(-0.305489\pi\) | ||||
0.573749 | + | 0.819031i | \(0.305489\pi\) | |||||||
\(332\) | − 7.23106i | − 0.396856i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.4924 | 1.12130 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.49242i | 0.135771i | 0.997693 | + | 0.0678855i | \(0.0216252\pi\) | ||||
−0.997693 | + | 0.0678855i | \(0.978375\pi\) | |||||||
\(338\) | − 1.56155i | − 0.0849373i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.3693 | −0.832295 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 31.0540i | 1.67676i | ||||||||
\(344\) | −12.4924 | −0.673546 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −32.9848 | −1.77328 | ||||||||
\(347\) | − 11.0540i | − 0.593408i | −0.954969 | − | 0.296704i | \(-0.904112\pi\) | ||||
0.954969 | − | 0.296704i | \(-0.0958876\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.36932 | −0.0732979 | −0.0366489 | − | 0.999328i | \(-0.511668\pi\) | ||||
−0.0366489 | + | 0.999328i | \(0.511668\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.24621i | 0.332924i | ||||||||
\(353\) | 10.4924i | 0.558455i | 0.960225 | + | 0.279228i | \(0.0900784\pi\) | ||||
−0.960225 | + | 0.279228i | \(0.909922\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.738634 | 0.0391475 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 20.4924i | − 1.08306i | ||||||||
\(359\) | 2.24621 | 0.118550 | 0.0592752 | − | 0.998242i | \(-0.481121\pi\) | ||||
0.0592752 | + | 0.998242i | \(0.481121\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.24621 | −0.486643 | ||||||||
\(362\) | 40.1080i | 2.10803i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 18.2462i | − 0.952444i | −0.879325 | − | 0.476222i | \(-0.842006\pi\) | ||||
0.879325 | − | 0.476222i | \(-0.157994\pi\) | |||||||
\(368\) | − 30.7386i | − 1.60236i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.0540 | 1.81991 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.24621i | 0.219860i | 0.993939 | + | 0.109930i | \(0.0350627\pi\) | ||||
−0.993939 | + | 0.109930i | \(0.964937\pi\) | |||||||
\(374\) | 10.2462 | 0.529819 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.01515 | 0.361779 | ||||||||
\(377\) | 1.12311i | 0.0578429i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.49242 | −0.128027 | −0.0640136 | − | 0.997949i | \(-0.520390\pi\) | ||||
−0.0640136 | + | 0.997949i | \(0.520390\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 33.7538i | 1.72699i | ||||||||
\(383\) | 36.4924i | 1.86468i | 0.361588 | + | 0.932338i | \(0.382235\pi\) | ||||
−0.361588 | + | 0.932338i | \(0.617765\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.1080 | 1.22706 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.23106i | 0.265567i | ||||||||
\(389\) | −19.8617 | −1.00703 | −0.503515 | − | 0.863986i | \(-0.667960\pi\) | ||||
−0.503515 | + | 0.863986i | \(0.667960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.8078 | −0.850005 | ||||||||
\(392\) | − 33.6695i | − 1.70057i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 33.3693 | 1.68112 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8.56155i | − 0.429692i | −0.976648 | − | 0.214846i | \(-0.931075\pi\) | ||||
0.976648 | − | 0.214846i | \(-0.0689250\pi\) | |||||||
\(398\) | 12.4924i | 0.626189i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2462 | −1.01105 | −0.505524 | − | 0.862813i | \(-0.668701\pi\) | ||||
−0.505524 | + | 0.862813i | \(0.668701\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000i | 0.298881i | ||||||||
\(404\) | −2.73863 | −0.136252 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.00000 | 0.397033 | ||||||||
\(407\) | − 4.31534i | − 0.213904i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1231 | 0.747789 | 0.373895 | − | 0.927471i | \(-0.378022\pi\) | ||||
0.373895 | + | 0.927471i | \(0.378022\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 3.01515i | − 0.148546i | ||||||||
\(413\) | − 54.7386i | − 2.69351i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.43845 | 0.119555 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.4924i | 0.611024i | ||||||||
\(419\) | −33.6155 | −1.64223 | −0.821113 | − | 0.570766i | \(-0.806646\pi\) | ||||
−0.821113 | + | 0.570766i | \(0.806646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.6307 | 0.713056 | 0.356528 | − | 0.934285i | \(-0.383960\pi\) | ||||
0.356528 | + | 0.934285i | \(0.383960\pi\) | |||||||
\(422\) | − 16.0000i | − 0.778868i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.7386 | −0.910029 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 25.9309i | − 1.25488i | ||||||||
\(428\) | − 7.86174i | − 0.380012i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.4924 | 1.75778 | 0.878889 | − | 0.477026i | \(-0.158285\pi\) | ||||
0.878889 | + | 0.477026i | \(0.158285\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 31.6155i | − 1.51935i | −0.650306 | − | 0.759673i | \(-0.725359\pi\) | ||||
0.650306 | − | 0.759673i | \(-0.274641\pi\) | |||||||
\(434\) | 42.7386 | 2.05152 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.876894 | −0.0419956 | ||||||||
\(437\) | − 20.4924i | − 0.980286i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0540 | 0.718487 | 0.359244 | − | 0.933244i | \(-0.383035\pi\) | ||||
0.359244 | + | 0.933244i | \(0.383035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 4.00000i | − 0.190261i | ||||||||
\(443\) | 12.8078i | 0.608515i | 0.952590 | + | 0.304258i | \(0.0984084\pi\) | ||||
−0.952590 | + | 0.304258i | \(0.901592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.6307 | 0.692783 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 25.3693i | 1.19859i | ||||||||
\(449\) | 10.1771 | 0.480286 | 0.240143 | − | 0.970738i | \(-0.422806\pi\) | ||||
0.240143 | + | 0.970738i | \(0.422806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.43845 | −0.0677338 | ||||||||
\(452\) | 5.75379i | 0.270635i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 34.7386 | 1.63036 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 25.6847i | − 1.20148i | −0.799445 | − | 0.600739i | \(-0.794873\pi\) | ||||
0.799445 | − | 0.600739i | \(-0.205127\pi\) | |||||||
\(458\) | − 13.8617i | − 0.647717i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.0540 | 1.35318 | 0.676589 | − | 0.736361i | \(-0.263457\pi\) | ||||
0.676589 | + | 0.736361i | \(0.263457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0691303i | 0.00321276i | 0.999999 | + | 0.00160638i | \(0.000511327\pi\) | ||||
−0.999999 | + | 0.00160638i | \(0.999489\pi\) | |||||||
\(464\) | −5.26137 | −0.244253 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.2311 | 0.520269 | ||||||||
\(467\) | 21.9309i | 1.01484i | 0.861699 | + | 0.507420i | \(0.169401\pi\) | ||||
−0.861699 | + | 0.507420i | \(0.830599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 60.9848 | 2.81602 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 29.2614i | 1.34686i | ||||||||
\(473\) | − 13.1231i | − 0.603401i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.12311 | −0.234817 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 9.26137i | − 0.423605i | ||||||||
\(479\) | −11.0540 | −0.505069 | −0.252535 | − | 0.967588i | \(-0.581264\pi\) | ||||
−0.252535 | + | 0.967588i | \(0.581264\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.68466 | −0.0768138 | ||||||||
\(482\) | − 38.6307i | − 1.75958i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.94602 | 0.0884557 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.05398i | 0.229017i | 0.993422 | + | 0.114509i | \(0.0365294\pi\) | ||||
−0.993422 | + | 0.114509i | \(0.963471\pi\) | |||||||
\(488\) | 13.8617i | 0.627491i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.6155 | −0.614460 | −0.307230 | − | 0.951635i | \(-0.599402\pi\) | ||||
−0.307230 | + | 0.951635i | \(0.599402\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.87689i | 0.129569i | ||||||||
\(494\) | 4.87689 | 0.219422 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.1080 | −1.26208 | ||||||||
\(497\) | 66.4233i | 2.97949i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.9848 | 1.38707 | 0.693536 | − | 0.720422i | \(-0.256052\pi\) | ||||
0.693536 | + | 0.720422i | \(0.256052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 15.2311i | − 0.679795i | ||||||||
\(503\) | 30.2462i | 1.34861i | 0.738452 | + | 0.674306i | \(0.235557\pi\) | ||||
−0.738452 | + | 0.674306i | \(0.764443\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 26.2462 | 1.16679 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 8.00000i | − 0.354943i | ||||||||
\(509\) | −19.4384 | −0.861594 | −0.430797 | − | 0.902449i | \(-0.641768\pi\) | ||||
−0.430797 | + | 0.902449i | \(0.641768\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.3693 | 1.21075 | ||||||||
\(512\) | − 11.4233i | − 0.504843i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −32.9848 | −1.45490 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.36932i | 0.324102i | ||||||||
\(518\) | 12.0000i | 0.527250i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.8617 | −1.39589 | −0.697944 | − | 0.716152i | \(-0.745902\pi\) | ||||
−0.697944 | + | 0.716152i | \(0.745902\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 18.7386i | − 0.819383i | −0.912224 | − | 0.409692i | \(-0.865636\pi\) | ||||
0.912224 | − | 0.409692i | \(-0.134364\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.2462 | −0.969981 | ||||||||
\(527\) | 15.3693i | 0.669498i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0540 | −0.871912 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 6.24621i | − 0.270808i | ||||||||
\(533\) | 0.561553i | 0.0243236i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −32.6004 | −1.40812 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 14.2462i | − 0.614198i | ||||||||
\(539\) | 35.3693 | 1.52346 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.1231 | 1.16611 | 0.583057 | − | 0.812431i | \(-0.301857\pi\) | ||||
0.583057 | + | 0.812431i | \(0.301857\pi\) | |||||||
\(542\) | 8.38447i | 0.360144i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.24621 | 0.267804 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.3693i | 0.828172i | 0.910238 | + | 0.414086i | \(0.135899\pi\) | ||||
−0.910238 | + | 0.414086i | \(0.864101\pi\) | |||||||
\(548\) | − 3.12311i | − 0.133412i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.50758 | −0.149428 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 35.0540i | − 1.49065i | ||||||||
\(554\) | −6.63068 | −0.281711 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.87689 | 0.291645 | ||||||||
\(557\) | 26.4924i | 1.12252i | 0.827640 | + | 0.561260i | \(0.189683\pi\) | ||||
−0.827640 | + | 0.561260i | \(0.810317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.12311 | −0.216684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.1231i | 0.806660i | ||||||||
\(563\) | − 31.6847i | − 1.33535i | −0.744453 | − | 0.667675i | \(-0.767290\pi\) | ||||
0.744453 | − | 0.667675i | \(-0.232710\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.24621 | −0.262548 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 35.5076i | − 1.48986i | ||||||||
\(569\) | −41.1231 | −1.72397 | −0.861985 | − | 0.506934i | \(-0.830779\pi\) | ||||
−0.861985 | + | 0.506934i | \(0.830779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0540 | 0.629989 | 0.314995 | − | 0.949093i | \(-0.397997\pi\) | ||||
0.314995 | + | 0.949093i | \(0.397997\pi\) | |||||||
\(572\) | 1.12311i | 0.0469594i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.5616i | 1.18903i | 0.804083 | + | 0.594517i | \(0.202657\pi\) | ||||
−0.804083 | + | 0.594517i | \(0.797343\pi\) | |||||||
\(578\) | 16.3002i | 0.677998i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 75.2311 | 3.12111 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 19.6847i | − 0.815255i | ||||||||
\(584\) | −14.6307 | −0.605422 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.86174 | 0.242146 | ||||||||
\(587\) | − 0.492423i | − 0.0203245i | −0.999948 | − | 0.0101622i | \(-0.996765\pi\) | ||||
0.999948 | − | 0.0101622i | \(-0.00323479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.7386 | −0.772112 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 7.89205i | − 0.324361i | ||||||||
\(593\) | 7.75379i | 0.318410i | 0.987246 | + | 0.159205i | \(0.0508931\pi\) | ||||
−0.987246 | + | 0.159205i | \(0.949107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.23106 | −0.0504260 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 10.2462i | − 0.418999i | ||||||||
\(599\) | 15.3693 | 0.627973 | 0.313987 | − | 0.949427i | \(-0.398335\pi\) | ||||
0.313987 | + | 0.949427i | \(0.398335\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.5464 | 1.69471 | 0.847356 | − | 0.531025i | \(-0.178193\pi\) | ||||
0.847356 | + | 0.531025i | \(0.178193\pi\) | |||||||
\(602\) | 36.4924i | 1.48732i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.86174 | 0.238511 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.0000i | − 0.974130i | −0.873366 | − | 0.487065i | \(-0.838067\pi\) | ||||
0.873366 | − | 0.487065i | \(-0.161933\pi\) | |||||||
\(608\) | 7.61553i | 0.308850i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.87689 | 0.116387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 37.5464i | − 1.51648i | −0.651973 | − | 0.758242i | \(-0.726058\pi\) | ||||
0.651973 | − | 0.758242i | \(-0.273942\pi\) | |||||||
\(614\) | −5.36932 | −0.216688 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28.4924 | −1.14799 | ||||||||
\(617\) | 48.7386i | 1.96214i | 0.193645 | + | 0.981072i | \(0.437969\pi\) | ||||
−0.193645 | + | 0.981072i | \(0.562031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.3693 | 1.34123 | 0.670613 | − | 0.741807i | \(-0.266031\pi\) | ||||
0.670613 | + | 0.741807i | \(0.266031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 42.7386i | − 1.71366i | ||||||||
\(623\) | 7.68466i | 0.307879i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32.6004 | 1.30297 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.36932i | 0.373876i | ||||||||
\(629\) | −4.31534 | −0.172064 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7386 | 0.666354 | 0.333177 | − | 0.942864i | \(-0.391879\pi\) | ||||
0.333177 | + | 0.942864i | \(0.391879\pi\) | |||||||
\(632\) | 18.7386i | 0.745383i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 53.8617 | 2.13912 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 13.8078i | − 0.547084i | ||||||||
\(638\) | − 4.49242i | − 0.177857i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.9848 | −1.30282 | −0.651412 | − | 0.758725i | \(-0.725823\pi\) | ||||
−0.651412 | + | 0.758725i | \(0.725823\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.68466i | − 0.0664364i | −0.999448 | − | 0.0332182i | \(-0.989424\pi\) | ||||
0.999448 | − | 0.0332182i | \(-0.0105756\pi\) | |||||||
\(644\) | −13.1231 | −0.517123 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.4924 | 0.491508 | ||||||||
\(647\) | − 11.1922i | − 0.440012i | −0.975498 | − | 0.220006i | \(-0.929392\pi\) | ||||
0.975498 | − | 0.220006i | \(-0.0706077\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.7386 | −1.20660 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 9.23106i | − 0.361516i | ||||||||
\(653\) | − 8.63068i | − 0.337745i | −0.985638 | − | 0.168872i | \(-0.945987\pi\) | ||||
0.985638 | − | 0.168872i | \(-0.0540126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.63068 | −0.102711 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 20.4924i | − 0.798878i | ||||||||
\(659\) | 9.12311 | 0.355386 | 0.177693 | − | 0.984086i | \(-0.443137\pi\) | ||||
0.177693 | + | 0.984086i | \(0.443137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.4924 | −1.03044 | −0.515218 | − | 0.857059i | \(-0.672289\pi\) | ||||
−0.515218 | + | 0.857059i | \(0.672289\pi\) | |||||||
\(662\) | 32.6004i | 1.26705i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −40.2159 | −1.56068 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.36932i | 0.285341i | ||||||||
\(668\) | 5.75379i | 0.222621i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.5616 | −0.562143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.7386i | 1.26198i | 0.775790 | + | 0.630991i | \(0.217351\pi\) | ||||
−0.775790 | + | 0.630991i | \(0.782649\pi\) | |||||||
\(674\) | −3.89205 | −0.149916 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.438447 | 0.0168634 | ||||||||
\(677\) | 18.5616i | 0.713378i | 0.934223 | + | 0.356689i | \(0.116094\pi\) | ||||
−0.934223 | + | 0.356689i | \(0.883906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −54.4233 | −2.08857 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 24.0000i | − 0.919007i | ||||||||
\(683\) | − 0.492423i | − 0.0188420i | −0.999956 | − | 0.00942101i | \(-0.997001\pi\) | ||||
0.999956 | − | 0.00942101i | \(-0.00299885\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −48.4924 | −1.85145 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 24.0000i | − 0.914991i | ||||||||
\(689\) | −7.68466 | −0.292762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.6155 | 0.746210 | 0.373105 | − | 0.927789i | \(-0.378293\pi\) | ||||
0.373105 | + | 0.927789i | \(0.378293\pi\) | |||||||
\(692\) | − 9.26137i | − 0.352064i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.2614 | 0.655233 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.43845i | 0.0544851i | ||||||||
\(698\) | − 2.13826i | − 0.0809344i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.9848 | −0.641509 | −0.320754 | − | 0.947162i | \(-0.603936\pi\) | ||||
−0.320754 | + | 0.947162i | \(0.603936\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.26137i | − 0.198436i | ||||||||
\(704\) | 14.2462 | 0.536924 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.3845 | −0.616638 | ||||||||
\(707\) | − 28.4924i | − 1.07157i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.876894 | −0.0329325 | −0.0164662 | − | 0.999864i | \(-0.505242\pi\) | ||||
−0.0164662 | + | 0.999864i | \(0.505242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 4.10795i | − 0.153952i | ||||||||
\(713\) | 39.3693i | 1.47439i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.75379 | 0.215029 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.50758i | 0.130902i | ||||||||
\(719\) | 36.0000 | 1.34257 | 0.671287 | − | 0.741198i | \(-0.265742\pi\) | ||||
0.671287 | + | 0.741198i | \(0.265742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.3693 | 1.16825 | ||||||||
\(722\) | − 14.4384i | − 0.537343i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.2614 | −0.418525 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.1231i | 0.783413i | 0.920090 | + | 0.391706i | \(0.128115\pi\) | ||||
−0.920090 | + | 0.391706i | \(0.871885\pi\) | |||||||
\(728\) | 11.1231i | 0.412250i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.1231 | −0.485376 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5616i | 0.759458i | 0.925098 | + | 0.379729i | \(0.123983\pi\) | ||||
−0.925098 | + | 0.379729i | \(0.876017\pi\) | |||||||
\(734\) | 28.4924 | 1.05167 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | 0.589768 | ||||||||
\(737\) | − 34.2462i | − 1.26148i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.738634 | 0.0271711 | 0.0135855 | − | 0.999908i | \(-0.495675\pi\) | ||||
0.0135855 | + | 0.999908i | \(0.495675\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 54.7386i | 2.00952i | ||||||||
\(743\) | − 30.7386i | − 1.12769i | −0.825880 | − | 0.563846i | \(-0.809321\pi\) | ||||
0.825880 | − | 0.563846i | \(-0.190679\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.63068 | −0.242767 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.87689i | 0.105190i | ||||||||
\(749\) | 81.7926 | 2.98864 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.0540 | −0.841252 | −0.420626 | − | 0.907234i | \(-0.638189\pi\) | ||||
−0.420626 | + | 0.907234i | \(0.638189\pi\) | |||||||
\(752\) | 13.4773i | 0.491465i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.75379 | −0.0638692 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.4924i | 0.672119i | 0.941841 | + | 0.336059i | \(0.109094\pi\) | ||||
−0.941841 | + | 0.336059i | \(0.890906\pi\) | |||||||
\(758\) | − 3.89205i | − 0.141366i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.2311 | 1.34962 | 0.674812 | − | 0.737989i | \(-0.264225\pi\) | ||||
0.674812 | + | 0.737989i | \(0.264225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9.12311i | − 0.330279i | ||||||||
\(764\) | −9.47727 | −0.342876 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −56.9848 | −2.05895 | ||||||||
\(767\) | 12.0000i | 0.433295i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0000 | 1.08183 | 0.540914 | − | 0.841078i | \(-0.318079\pi\) | ||||
0.540914 | + | 0.841078i | \(0.318079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.76894i | 0.243620i | ||||||||
\(773\) | − 0.876894i | − 0.0315397i | −0.999876 | − | 0.0157698i | \(-0.994980\pi\) | ||||
0.999876 | − | 0.0157698i | \(-0.00501991\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29.0928 | 1.04437 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 31.0152i | − 1.11195i | ||||||||
\(779\) | −1.75379 | −0.0628360 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.3002 | 1.33471 | ||||||||
\(782\) | − 26.2462i | − 0.938563i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 64.6847 | 2.31017 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 13.3693i | − 0.476565i | −0.971196 | − | 0.238282i | \(-0.923416\pi\) | ||||
0.971196 | − | 0.238282i | \(-0.0765844\pi\) | |||||||
\(788\) | 9.36932i | 0.333768i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59.8617 | −2.12844 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.68466i | 0.201868i | ||||||||
\(794\) | 13.3693 | 0.474459 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.50758 | −0.124323 | ||||||||
\(797\) | 7.68466i | 0.272205i | 0.990695 | + | 0.136102i | \(0.0434576\pi\) | ||||
−0.990695 | + | 0.136102i | \(0.956542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.36932 | 0.260708 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 31.6155i | − 1.11638i | ||||||||
\(803\) | − 15.3693i | − 0.542371i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.36932 | −0.330020 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.2311i | 0.535827i | ||||||||
\(809\) | 40.4924 | 1.42364 | 0.711819 | − | 0.702363i | \(-0.247872\pi\) | ||||
0.711819 | + | 0.702363i | \(0.247872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.2462 | −0.430023 | −0.215011 | − | 0.976612i | \(-0.568979\pi\) | ||||
−0.215011 | + | 0.976612i | \(0.568979\pi\) | |||||||
\(812\) | 2.24621i | 0.0788266i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.73863 | 0.236189 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 16.0000i | − 0.559769i | ||||||||
\(818\) | 23.6155i | 0.825698i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.5464 | 0.751974 | 0.375987 | − | 0.926625i | \(-0.377304\pi\) | ||||
0.375987 | + | 0.926625i | \(0.377304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.2462i | 1.61204i | 0.591887 | + | 0.806021i | \(0.298383\pi\) | ||||
−0.591887 | + | 0.806021i | \(0.701617\pi\) | |||||||
\(824\) | −16.7689 | −0.584174 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 85.4773 | 2.97413 | ||||||||
\(827\) | 1.12311i | 0.0390542i | 0.999809 | + | 0.0195271i | \(0.00621607\pi\) | ||||
−0.999809 | + | 0.0195271i | \(0.993784\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.7386 | 1.69276 | 0.846381 | − | 0.532577i | \(-0.178776\pi\) | ||||
0.846381 | + | 0.532577i | \(0.178776\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 5.56155i | − 0.192812i | ||||||||
\(833\) | − 35.3693i | − 1.22547i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.50758 | −0.121312 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 52.4924i | − 1.81332i | ||||||||
\(839\) | 41.7926 | 1.44284 | 0.721421 | − | 0.692497i | \(-0.243490\pi\) | ||||
0.721421 | + | 0.692497i | \(0.243490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7386 | −0.956505 | ||||||||
\(842\) | 22.8466i | 0.787345i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.49242 | 0.154636 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.2462i | 0.695668i | ||||||||
\(848\) | − 36.0000i | − 1.23625i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0540 | −0.378925 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.4233i | 0.699280i | 0.936884 | + | 0.349640i | \(0.113696\pi\) | ||||
−0.936884 | + | 0.349640i | \(0.886304\pi\) | |||||||
\(854\) | 40.4924 | 1.38562 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −43.7235 | −1.49444 | ||||||||
\(857\) | − 6.56155i | − 0.224138i | −0.993700 | − | 0.112069i | \(-0.964252\pi\) | ||||
0.993700 | − | 0.112069i | \(-0.0357478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.8078 | 0.573474 | 0.286737 | − | 0.958009i | \(-0.407429\pi\) | ||||
0.286737 | + | 0.958009i | \(0.407429\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 56.9848i | 1.94091i | ||||||||
\(863\) | 15.3693i | 0.523178i | 0.965179 | + | 0.261589i | \(0.0842464\pi\) | ||||
−0.965179 | + | 0.261589i | \(0.915754\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 49.3693 | 1.67764 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.0000i | 0.407307i | ||||||||
\(869\) | −19.6847 | −0.667756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.3693 | −0.453002 | ||||||||
\(872\) | 4.87689i | 0.165152i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.0000 | 1.08242 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 18.9848i | − 0.641073i | −0.947236 | − | 0.320536i | \(-0.896137\pi\) | ||||
0.947236 | − | 0.320536i | \(-0.103863\pi\) | |||||||
\(878\) | 23.5076i | 0.793342i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.36932 | −0.113515 | −0.0567576 | − | 0.998388i | \(-0.518076\pi\) | ||||
−0.0567576 | + | 0.998388i | \(0.518076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 18.1080i | − 0.609381i | −0.952451 | − | 0.304691i | \(-0.901447\pi\) | ||||
0.952451 | − | 0.304691i | \(-0.0985530\pi\) | |||||||
\(884\) | 1.12311 | 0.0377741 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.0000 | −0.671913 | ||||||||
\(887\) | − 1.43845i | − 0.0482983i | −0.999708 | − | 0.0241492i | \(-0.992312\pi\) | ||||
0.999708 | − | 0.0241492i | \(-0.00768767\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 83.2311 | 2.79148 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.10795i | 0.137544i | ||||||||
\(893\) | 8.98485i | 0.300666i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −61.8617 | −2.06666 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.8920i | 0.530325i | ||||||||
\(899\) | 6.73863 | 0.224746 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.6847 | −0.655791 | ||||||||
\(902\) | − 2.24621i | − 0.0747907i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.0000 | 1.06430 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 27.3693i | − 0.908783i | −0.890802 | − | 0.454392i | \(-0.849857\pi\) | ||||
0.890802 | − | 0.454392i | \(-0.150143\pi\) | |||||||
\(908\) | 9.75379i | 0.323691i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 42.2462i | − 1.39815i | ||||||||
\(914\) | 40.1080 | 1.32665 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.89205 | 0.128597 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.0540 | −1.28827 | −0.644136 | − | 0.764911i | \(-0.722783\pi\) | ||||
−0.644136 | + | 0.764911i | \(0.722783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 45.3693i | 1.49416i | ||||||||
\(923\) | − 14.5616i | − 0.479299i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.107951 | −0.00354748 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 2.73863i | − 0.0899001i | ||||||||
\(929\) | −38.6695 | −1.26871 | −0.634353 | − | 0.773044i | \(-0.718733\pi\) | ||||
−0.634353 | + | 0.773044i | \(0.718733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43.1231 | 1.41330 | ||||||||
\(932\) | 3.15342i | 0.103294i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.2462 | −1.12057 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.63068i | − 0.0859407i | −0.999076 | − | 0.0429703i | \(-0.986318\pi\) | ||||
0.999076 | − | 0.0429703i | \(-0.0136821\pi\) | |||||||
\(938\) | 95.2311i | 3.10940i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.1922 | 0.690847 | 0.345424 | − | 0.938447i | \(-0.387735\pi\) | ||||
0.345424 | + | 0.938447i | \(0.387735\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.68466i | 0.119989i | ||||||||
\(944\) | −56.2159 | −1.82967 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.4924 | 0.666266 | ||||||||
\(947\) | 46.6004i | 1.51431i | 0.653236 | + | 0.757154i | \(0.273411\pi\) | ||||
−0.653236 | + | 0.757154i | \(0.726589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | −0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 28.4924i | 0.923445i | ||||||||
\(953\) | 25.4384i | 0.824032i | 0.911177 | + | 0.412016i | \(0.135175\pi\) | ||||
−0.911177 | + | 0.412016i | \(0.864825\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.60037 | 0.0841021 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 17.2614i | − 0.557689i | ||||||||
\(959\) | 32.4924 | 1.04924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | − 2.63068i | − 0.0848166i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.8466 | 0.349345 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3693i | 0.558560i | 0.960210 | + | 0.279280i | \(0.0900957\pi\) | ||||
−0.960210 | + | 0.279280i | \(0.909904\pi\) | |||||||
\(968\) | − 10.8229i | − 0.347862i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.49242 | −0.272535 | −0.136267 | − | 0.990672i | \(-0.543511\pi\) | ||||
−0.136267 | + | 0.990672i | \(0.543511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 71.5464i | 2.29367i | ||||||||
\(974\) | −7.89205 | −0.252878 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.6307 | −0.852427 | ||||||||
\(977\) | − 55.4773i | − 1.77488i | −0.460928 | − | 0.887438i | \(-0.652483\pi\) | ||||
0.460928 | − | 0.887438i | \(-0.347517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.31534 | 0.137919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 21.2614i | − 0.678477i | ||||||||
\(983\) | − 6.73863i | − 0.214929i | −0.994209 | − | 0.107465i | \(-0.965727\pi\) | ||||
0.994209 | − | 0.107465i | \(-0.0342732\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.49242 | −0.143068 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.36932i | 0.0435638i | ||||||||
\(989\) | −33.6155 | −1.06891 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.0540 | −0.859398 | −0.429699 | − | 0.902972i | \(-0.641380\pi\) | ||||
−0.429699 | + | 0.902972i | \(0.641380\pi\) | |||||||
\(992\) | − 14.6307i | − 0.464525i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −103.723 | −3.28991 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7538i | 0.372246i | 0.982526 | + | 0.186123i | \(0.0595923\pi\) | ||||
−0.982526 | + | 0.186123i | \(0.940408\pi\) | |||||||
\(998\) | 48.3845i | 1.53158i | ||||||||
\(999\) | 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 | 2925.2.c.o.2224.3 | 4 | ||
3.2 | odd | 2 | 2925.2.c.p.2224.2 | 4 | |||
5.2 | odd | 4 | 2925.2.a.bc.1.1 | 2 | |||
5.3 | odd | 4 | 585.2.a.j.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 2925.2.c.o.2224.2 | 4 | ||
15.2 | even | 4 | 2925.2.a.x.1.2 | 2 | |||
15.8 | even | 4 | 585.2.a.l.1.1 | yes | 2 | ||
15.14 | odd | 2 | 2925.2.c.p.2224.3 | 4 | |||
20.3 | even | 4 | 9360.2.a.cl.1.2 | 2 | |||
60.23 | odd | 4 | 9360.2.a.cw.1.2 | 2 | |||
65.38 | odd | 4 | 7605.2.a.bi.1.1 | 2 | |||
195.38 | even | 4 | 7605.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.a.j.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
585.2.a.l.1.1 | yes | 2 | 15.8 | even | 4 | ||
2925.2.a.x.1.2 | 2 | 15.2 | even | 4 | |||
2925.2.a.bc.1.1 | 2 | 5.2 | odd | 4 | |||
2925.2.c.o.2224.2 | 4 | 5.4 | even | 2 | inner | ||
2925.2.c.o.2224.3 | 4 | 1.1 | even | 1 | trivial | ||
2925.2.c.p.2224.2 | 4 | 3.2 | odd | 2 | |||
2925.2.c.p.2224.3 | 4 | 15.14 | odd | 2 | |||
7605.2.a.bd.1.2 | 2 | 195.38 | even | 4 | |||
7605.2.a.bi.1.1 | 2 | 65.38 | odd | 4 | |||
9360.2.a.cl.1.2 | 2 | 20.3 | even | 4 | |||
9360.2.a.cw.1.2 | 2 | 60.23 | odd | 4 |