Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3312,2,Mod(2575,3312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("3312.2575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3312.i (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.4464531494\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2575.1 | ||
Root | \(0.500000 - 2.19293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3312.2575 |
Dual form | 3312.2.i.f.2575.5 |
$q$-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 \(\left(\mathbb{Z}/3312\mathbb{Z}\right)^\times\).
\(n\) | \(415\) | \(2305\) | \(2485\) | \(2945\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.00000i | − | 0.894427i | −0.894427 | − | 0.447214i | \(-0.852416\pi\) | ||
0.894427 | − | 0.447214i | \(-0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.38587 | −1.27974 | −0.639869 | − | 0.768484i | \(-0.721011\pi\) | ||||
−0.639869 | + | 0.768484i | \(0.721011\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.73205 | 1.42677 | 0.713384 | − | 0.700774i | \(-0.247162\pi\) | ||||
0.713384 | + | 0.700774i | \(0.247162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46410 | −0.960769 | −0.480384 | − | 0.877058i | \(-0.659503\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.732051i | 0.177548i | 0.996052 | + | 0.0887742i | \(0.0282950\pi\) | ||||
−0.996052 | + | 0.0887742i | \(0.971705\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.47863 | −0.568636 | −0.284318 | − | 0.958730i | \(-0.591767\pi\) | ||||
−0.284318 | + | 0.958730i | \(0.591767\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.26795 | − | 4.62518i | 0.264386 | − | 0.964417i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.29311 | −0.797210 | −0.398605 | − | 0.917123i | \(-0.630506\pi\) | ||||
−0.398605 | + | 0.917123i | \(0.630506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000i | 1.07763i | 0.842424 | + | 0.538816i | \(0.181128\pi\) | ||||
−0.842424 | + | 0.538816i | \(0.818872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.77174i | 1.14463i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.1576i | − | 1.66990i | −0.550326 | − | 0.834950i | \(-0.685497\pi\) | ||
0.550326 | − | 0.834950i | \(-0.314503\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.7290 | −1.83176 | −0.915880 | − | 0.401451i | \(-0.868506\pi\) | ||||
−0.915880 | + | 0.401451i | \(0.868506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.47863 | 0.377987 | 0.188994 | − | 0.981978i | \(-0.439477\pi\) | ||||
0.188994 | + | 0.981978i | \(0.439477\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.29311i | 0.626214i | 0.949718 | + | 0.313107i | \(0.101370\pi\) | ||||
−0.949718 | + | 0.313107i | \(0.898630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.46410 | 0.637729 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.535898i | − | 0.0736113i | −0.999322 | − | 0.0368057i | \(-0.988282\pi\) | ||
0.999322 | − | 0.0368057i | \(-0.0117182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.46410i | − | 1.27614i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7290i | 1.52698i | 0.645817 | + | 0.763492i | \(0.276517\pi\) | ||||
−0.645817 | + | 0.763492i | \(0.723483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.57139i | − | 0.201195i | −0.994927 | − | 0.100598i | \(-0.967924\pi\) | ||
0.994927 | − | 0.100598i | \(-0.0320755\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.92820i | 0.859338i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.25036 | 1.13011 | 0.565056 | − | 0.825053i | \(-0.308855\pi\) | ||||
0.565056 | + | 0.825053i | \(0.308855\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.81448i | − | 0.215339i | −0.994187 | − | 0.107670i | \(-0.965661\pi\) | ||
0.994187 | − | 0.107670i | \(-0.0343389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3923 | −1.45041 | −0.725205 | − | 0.688533i | \(-0.758255\pi\) | ||||
−0.725205 | + | 0.688533i | \(0.758255\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.0221 | −1.82589 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.34312 | −0.938675 | −0.469337 | − | 0.883019i | \(-0.655507\pi\) | ||||
−0.469337 | + | 0.883019i | \(0.655507\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.19615 | −0.241059 | −0.120530 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120530 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.46410 | 0.158804 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.1244i | 1.39118i | 0.718439 | + | 0.695589i | \(0.244857\pi\) | ||||
−0.718439 | + | 0.695589i | \(0.755143\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.7290 | 1.22953 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.95725i | 0.508604i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7290i | 1.19090i | 0.803393 | + | 0.595449i | \(0.203026\pi\) | ||||
−0.803393 | + | 0.595449i | \(0.796974\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.7290 | −1.16708 | −0.583539 | − | 0.812085i | \(-0.698333\pi\) | ||||
−0.583539 | + | 0.812085i | \(0.698333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.38587 | 0.333619 | 0.166810 | − | 0.985989i | \(-0.446653\pi\) | ||||
0.166810 | + | 0.985989i | \(0.446653\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.12436 | −0.882085 | −0.441042 | − | 0.897486i | \(-0.645391\pi\) | ||||
−0.441042 | + | 0.897486i | \(0.645391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.57139i | 0.150512i | 0.997164 | + | 0.0752558i | \(0.0239773\pi\) | ||||
−0.997164 | + | 0.0752558i | \(0.976023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.1244i | 1.23464i | 0.786714 | + | 0.617318i | \(0.211781\pi\) | ||||
−0.786714 | + | 0.617318i | \(0.788219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.25036 | − | 2.53590i | −0.862601 | − | 0.236474i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.47863i | − | 0.227215i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.0000i | − | 1.07331i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.53590i | 0.757438i | 0.925512 | + | 0.378719i | \(0.123635\pi\) | ||||
−0.925512 | + | 0.378719i | \(0.876365\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.5007i | 1.61642i | 0.588897 | + | 0.808208i | \(0.299562\pi\) | ||||
−0.588897 | + | 0.808208i | \(0.700438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.39230 | 0.727705 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18.1962i | − | 1.55460i | −0.629129 | − | 0.777301i | \(-0.716588\pi\) | ||
0.629129 | − | 0.777301i | \(-0.283412\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.53590i | − | 0.724005i | −0.932177 | − | 0.362003i | \(-0.882093\pi\) | ||
0.932177 | − | 0.362003i | \(-0.117907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.3923 | −1.37079 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.58622i | 0.713047i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3205i | 1.09126i | 0.838027 | + | 0.545629i | \(0.183709\pi\) | ||||
−0.838027 | + | 0.545629i | \(0.816291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9282i | 1.05208i | 0.850459 | + | 0.526041i | \(0.176324\pi\) | ||||
−0.850459 | + | 0.526041i | \(0.823676\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0000 | 0.963863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.8866i | 1.74674i | 0.487057 | + | 0.873370i | \(0.338070\pi\) | ||||
−0.487057 | + | 0.873370i | \(0.661930\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.29311 | + | 15.6603i | −0.338344 | + | 1.23420i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.46410i | 0.271329i | 0.990755 | + | 0.135665i | \(0.0433170\pi\) | ||||
−0.990755 | + | 0.135665i | \(0.956683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.81448i | 0.140409i | 0.997533 | + | 0.0702044i | \(0.0223651\pi\) | ||||
−0.997533 | + | 0.0702044i | \(0.977635\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.29311 | −0.326399 | −0.163199 | − | 0.986593i | \(-0.552181\pi\) | ||||
−0.163199 | + | 0.986593i | \(0.552181\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.38587 | −0.255948 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.7290i | 0.876666i | 0.898813 | + | 0.438333i | \(0.144431\pi\) | ||||
−0.898813 | + | 0.438333i | \(0.855569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.3004i | − | 0.988609i | −0.869289 | − | 0.494305i | \(-0.835423\pi\) | ||
0.869289 | − | 0.494305i | \(-0.164577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.3152 | −1.49360 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.46410i | 0.253320i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8564 | 1.00261 | 0.501307 | − | 0.865269i | \(-0.332853\pi\) | ||||
0.501307 | + | 0.865269i | \(0.332853\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.46410 | −0.681241 | −0.340620 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340620 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.7290 | −0.835656 | −0.417828 | − | 0.908526i | \(-0.637209\pi\) | ||||
−0.417828 | + | 0.908526i | \(0.637209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.9721 | −0.848679 | −0.424339 | − | 0.905503i | \(-0.639494\pi\) | ||||
−0.424339 | + | 0.905503i | \(0.639494\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.5359 | 1.02022 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.4580i | 1.63838i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.7290 | −0.811311 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 18.9282i | − | 1.30307i | −0.758618 | − | 0.651536i | \(-0.774125\pi\) | ||
0.758618 | − | 0.651536i | \(-0.225875\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.95725i | − | 0.338082i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 20.3152i | − | 1.37909i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.53590i | − | 0.170583i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.9282i | − | 1.66932i | −0.550769 | − | 0.834658i | \(-0.685665\pi\) | ||
0.550769 | − | 0.834658i | \(-0.314335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.6603 | 1.57039 | 0.785193 | − | 0.619251i | \(-0.212564\pi\) | ||||
0.785193 | + | 0.619251i | \(0.212564\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1576i | 0.671233i | 0.941999 | + | 0.335617i | \(0.108945\pi\) | ||||
−0.941999 | + | 0.335617i | \(0.891055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.58622 | 0.560103 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.25036i | 0.598356i | 0.954197 | + | 0.299178i | \(0.0967125\pi\) | ||||
−0.954197 | + | 0.299178i | \(0.903288\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.58622i | − | 0.553087i | −0.961001 | − | 0.276543i | \(-0.910811\pi\) | ||
0.961001 | − | 0.276543i | \(-0.0891890\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 8.92820i | − | 0.570402i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.58622 | 0.546328 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.0526 | −1.01323 | −0.506614 | − | 0.862173i | \(-0.669103\pi\) | ||||
−0.506614 | + | 0.862173i | \(0.669103\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | − | 21.8866i | 0.377217 | − | 1.37600i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.3152 | −1.26723 | −0.633614 | − | 0.773649i | \(-0.718429\pi\) | ||||
−0.633614 | + | 0.773649i | \(0.718429\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 34.3923i | 2.13703i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.60770 | −0.469111 | −0.234555 | − | 0.972103i | \(-0.575363\pi\) | ||||
−0.234555 | + | 0.972103i | \(0.575363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.07180 | −0.0658400 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.7290 | −0.715129 | −0.357565 | − | 0.933888i | \(-0.616393\pi\) | ||||
−0.357565 | + | 0.933888i | \(0.616393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.60770i | 0.0976605i | 0.998807 | + | 0.0488303i | \(0.0155493\pi\) | ||||
−0.998807 | + | 0.0488303i | \(0.984451\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.73205 | 0.285353 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7846 | −1.12866 | −0.564329 | − | 0.825550i | \(-0.690865\pi\) | ||||
−0.564329 | + | 0.825550i | \(0.690865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.5885i | − | 1.34751i | −0.738953 | − | 0.673757i | \(-0.764679\pi\) | ||
0.738953 | − | 0.673757i | \(-0.235321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.25036 | 0.549877 | 0.274939 | − | 0.961462i | \(-0.411343\pi\) | ||||
0.274939 | + | 0.961462i | \(0.411343\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39.7128 | 2.34417 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4641 | 0.968477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.92820i | 0.287909i | 0.989584 | + | 0.143954i | \(0.0459818\pi\) | ||||
−0.989584 | + | 0.143954i | \(0.954018\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.4580 | 1.36578 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.39230 | + | 16.0221i | −0.254014 | + | 0.926582i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.39230 | −0.483724 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.14277 | −0.179955 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.53590i | 0.487169i | 0.969880 | + | 0.243585i | \(0.0783234\pi\) | ||||
−0.969880 | + | 0.243585i | \(0.921677\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.3152i | − | 1.15197i | −0.817460 | − | 0.575985i | \(-0.804619\pi\) | ||
0.817460 | − | 0.575985i | \(-0.195381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.4580i | − | 1.32592i | −0.748653 | − | 0.662962i | \(-0.769299\pi\) | ||
0.748653 | − | 0.662962i | \(-0.230701\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.1649 | 1.07641 | 0.538203 | − | 0.842815i | \(-0.319103\pi\) | ||||
0.538203 | + | 0.842815i | \(0.319103\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.3152 | −1.13743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.81448i | − | 0.100960i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.46410 | −0.192154 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 14.5359i | − | 0.801390i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 13.8564i | − | 0.761617i | −0.924654 | − | 0.380808i | \(-0.875646\pi\) | ||
0.924654 | − | 0.380808i | \(-0.124354\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 18.5007i | − | 1.01080i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 35.1870i | − | 1.91676i | −0.285502 | − | 0.958378i | \(-0.592160\pi\) | ||
0.285502 | − | 0.958378i | \(-0.407840\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.3923i | 1.53753i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.58622 | 0.463612 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.9014i | 1.55151i | 0.631034 | + | 0.775755i | \(0.282631\pi\) | ||||
−0.631034 | + | 0.775755i | \(0.717369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3923 | 0.556287 | 0.278144 | − | 0.960539i | \(-0.410281\pi\) | ||||
0.278144 | + | 0.960539i | \(0.410281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.0442 | 1.70554 | 0.852770 | − | 0.522286i | \(-0.174921\pi\) | ||||
0.852770 | + | 0.522286i | \(0.174921\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.62896 | −0.192605 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.3923 | −1.49849 | −0.749244 | − | 0.662294i | \(-0.769583\pi\) | ||||
−0.749244 | + | 0.662294i | \(0.769583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8564 | −0.676653 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.7846i | 1.29729i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.0721 | −1.04776 | −0.523878 | − | 0.851793i | \(-0.675515\pi\) | ||||
−0.523878 | + | 0.851793i | \(0.675515\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.81448i | 0.0942032i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.3004i | 0.688667i | 0.938847 | + | 0.344334i | \(0.111895\pi\) | ||||
−0.938847 | + | 0.344334i | \(0.888105\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.8718 | 0.765935 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.9794 | −1.07764 | −0.538819 | − | 0.842422i | \(-0.681129\pi\) | ||||
−0.538819 | + | 0.842422i | \(0.681129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.3205 | −1.19162 | −0.595811 | − | 0.803125i | \(-0.703169\pi\) | ||||
−0.595811 | + | 0.803125i | \(0.703169\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.0442i | 1.63312i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.4641i | 1.59529i | 0.603125 | + | 0.797647i | \(0.293922\pi\) | ||||
−0.603125 | + | 0.797647i | \(0.706078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.38587 | + | 0.928203i | 0.171231 | + | 0.0469413i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.6862i | 0.839576i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0000 | 0.702640 | 0.351320 | − | 0.936255i | \(-0.385733\pi\) | ||||
0.351320 | + | 0.936255i | \(0.385733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 25.1244i | − | 1.25465i | −0.778757 | − | 0.627325i | \(-0.784150\pi\) | ||
0.778757 | − | 0.627325i | \(-0.215850\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.7846i | − | 1.03536i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 48.0663i | − | 2.38256i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.3923 | −0.810547 | −0.405274 | − | 0.914195i | \(-0.632824\pi\) | ||||
−0.405274 | + | 0.914195i | \(0.632824\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 39.7128i | − | 1.95414i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.39230i | 0.215610i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.4449 | −1.58504 | −0.792518 | − | 0.609849i | \(-0.791230\pi\) | ||||
−0.792518 | + | 0.609849i | \(0.791230\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 30.4728i | − | 1.48515i | −0.669761 | − | 0.742577i | \(-0.733603\pi\) | ||
0.669761 | − | 0.742577i | \(-0.266397\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.732051i | 0.0355097i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.32051i | 0.257477i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.07180 | −0.244300 | −0.122150 | − | 0.992512i | \(-0.538979\pi\) | ||||
−0.122150 | + | 0.992512i | \(0.538979\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.14277i | 0.151032i | 0.997145 | + | 0.0755160i | \(0.0240604\pi\) | ||||
−0.997145 | + | 0.0755160i | \(0.975940\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.14277 | + | 11.4641i | −0.150339 | + | 0.548402i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.32051i | 0.253934i | 0.991907 | + | 0.126967i | \(0.0405242\pi\) | ||||
−0.991907 | + | 0.126967i | \(0.959476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 3.62896i | − | 0.172417i | −0.996277 | − | 0.0862086i | \(-0.972525\pi\) | ||
0.996277 | − | 0.0862086i | \(-0.0274752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.2487 | 1.24431 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.14277 | −0.148317 | −0.0741583 | − | 0.997246i | \(-0.523627\pi\) | ||||
−0.0741583 | + | 0.997246i | \(0.523627\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −55.5022 | −2.61350 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 23.4580i | − | 1.09973i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.14277i | − | 0.147013i | −0.997295 | − | 0.0735064i | \(-0.976581\pi\) | ||
0.997295 | − | 0.0735064i | \(-0.0234189\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.9014 | 1.34607 | 0.673037 | − | 0.739609i | \(-0.264990\pi\) | ||||
0.673037 | + | 0.739609i | \(0.264990\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4641i | 1.27637i | 0.769885 | + | 0.638183i | \(0.220313\pi\) | ||||
−0.769885 | + | 0.638183i | \(0.779687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.0526 | 0.742824 | 0.371412 | − | 0.928468i | \(-0.378874\pi\) | ||||
0.371412 | + | 0.928468i | \(0.378874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.3205 | −1.44625 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7290 | 0.539300 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.47863 | −0.113727 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.4641 | −0.980720 | −0.490360 | − | 0.871520i | \(-0.663135\pi\) | ||||
−0.490360 | + | 0.871520i | \(0.663135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.1870i | 1.60439i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.4580 | 1.06517 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.3923i | − | 1.01469i | −0.861742 | − | 0.507346i | \(-0.830627\pi\) | ||
0.861742 | − | 0.507346i | \(-0.169373\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.1870i | 1.58797i | 0.607940 | + | 0.793983i | \(0.291996\pi\) | ||||
−0.607940 | + | 0.793983i | \(0.708004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.14277i | − | 0.141543i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.14359i | 0.275578i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.5359i | 0.919313i | 0.888097 | + | 0.459657i | \(0.152027\pi\) | ||||
−0.888097 | + | 0.459657i | \(0.847973\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.0718 | −0.761194 | −0.380597 | − | 0.924741i | \(-0.624281\pi\) | ||||
−0.380597 | + | 0.924741i | \(0.624281\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.4580i | 1.04387i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.7511 | −1.23005 | −0.615023 | − | 0.788509i | \(-0.710853\pi\) | ||||
−0.615023 | + | 0.788509i | \(0.710853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 41.9587 | 1.85614 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 6.77174i | − | 0.298398i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.3152i | 0.893462i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.41154i | 0.412327i | 0.978518 | + | 0.206164i | \(0.0660979\pi\) | ||||
−0.978518 | + | 0.206164i | \(0.933902\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.3931 | 0.541914 | 0.270957 | − | 0.962591i | \(-0.412660\pi\) | ||||
0.270957 | + | 0.962591i | \(0.412660\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.39230 | −0.191332 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7846 | − | 11.7290i | −0.860200 | − | 0.509956i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.6304 | 1.75990 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.2487i | 0.788961i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.1244 | 0.909890 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.53590 | −0.366987 | −0.183493 | − | 0.983021i | \(-0.558741\pi\) | ||||
−0.183493 | + | 0.983021i | \(0.558741\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.14277 | 0.134622 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.7846i | − | 0.888686i | −0.895857 | − | 0.444343i | \(-0.853437\pi\) | ||
0.895857 | − | 0.444343i | \(-0.146563\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.6410 | 0.453323 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.2487 | 1.20126 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.14359i | 0.345055i | 0.985005 | + | 0.172528i | \(0.0551934\pi\) | ||||
−0.985005 | + | 0.172528i | \(0.944807\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.58622 | −0.363158 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.0526 | 0.676535 | 0.338267 | − | 0.941050i | \(-0.390159\pi\) | ||||
0.338267 | + | 0.941050i | \(0.390159\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.2487 | 1.10429 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 14.5885i | − | 0.611580i | −0.952099 | − | 0.305790i | \(-0.901079\pi\) | ||
0.952099 | − | 0.305790i | \(-0.0989205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.3801 | 1.31321 | 0.656607 | − | 0.754233i | \(-0.271991\pi\) | ||||
0.656607 | + | 0.754233i | \(0.271991\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.26795 | − | 4.62518i | 0.0528771 | − | 0.192883i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.7846 | 1.61462 | 0.807312 | − | 0.590125i | \(-0.200921\pi\) | ||||
0.807312 | + | 0.590125i | \(0.200921\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.43588 | 0.308492 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.53590i | − | 0.105026i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.5007i | 0.763607i | 0.924244 | + | 0.381803i | \(0.124697\pi\) | ||||
−0.924244 | + | 0.381803i | \(0.875303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 14.8718i | − | 0.612780i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.3152 | 0.834246 | 0.417123 | − | 0.908850i | \(-0.363038\pi\) | ||||
0.417123 | + | 0.908850i | \(0.363038\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.95725 | −0.203228 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 31.3801i | − | 1.28215i | −0.767476 | − | 0.641077i | \(-0.778488\pi\) | ||
0.767476 | − | 0.641077i | \(-0.221512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.9282 | 0.527352 | 0.263676 | − | 0.964611i | \(-0.415065\pi\) | ||||
0.263676 | + | 0.964611i | \(0.415065\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 22.7846i | − | 0.926326i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 45.7128i | − | 1.85543i | −0.373294 | − | 0.927713i | \(-0.621772\pi\) | ||
0.373294 | − | 0.927713i | \(-0.378228\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 14.8718i | − | 0.601647i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 21.8866i | − | 0.883991i | −0.897017 | − | 0.441996i | \(-0.854271\pi\) | ||
0.897017 | − | 0.441996i | \(-0.145729\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.7321i | − | 0.512573i | −0.966601 | − | 0.256287i | \(-0.917501\pi\) | ||
0.966601 | − | 0.256287i | \(-0.0824991\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.664146 | −0.0266943 | −0.0133471 | − | 0.999911i | \(-0.504249\pi\) | ||||
−0.0133471 | + | 0.999911i | \(0.504249\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 44.4373i | − | 1.78034i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.43588 | 0.296488 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.5156 | 1.01576 | 0.507879 | − | 0.861428i | \(-0.330430\pi\) | ||||
0.507879 | + | 0.861428i | \(0.330430\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.0718 | 0.677474 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.4641 | −0.612710 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.94744i | 0.155915i | 0.996957 | + | 0.0779573i | \(0.0248398\pi\) | ||||
−0.996957 | + | 0.0779573i | \(0.975160\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.0648 | 0.436355 | 0.218177 | − | 0.975909i | \(-0.429989\pi\) | ||||
0.218177 | + | 0.975909i | \(0.429989\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 26.6008i | − | 1.04578i | −0.852399 | − | 0.522892i | \(-0.824853\pi\) | ||
0.852399 | − | 0.522892i | \(-0.175147\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.5022i | 2.17865i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.9014 | 1.13100 | 0.565500 | − | 0.824748i | \(-0.308683\pi\) | ||||
0.565500 | + | 0.824748i | \(0.308683\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.0015 | 1.44577 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.4449 | −1.73133 | −0.865663 | − | 0.500627i | \(-0.833103\pi\) | ||||
−0.865663 | + | 0.500627i | \(0.833103\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57139i | 0.0611199i | 0.999533 | + | 0.0305599i | \(0.00972904\pi\) | ||||
−0.999533 | + | 0.0305599i | \(0.990271\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 16.7846i | − | 0.650879i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.44344 | + | 19.8564i | −0.210771 | + | 0.768843i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.43588i | − | 0.287059i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7846 | −0.569905 | −0.284952 | − | 0.958542i | \(-0.591978\pi\) | ||||
−0.284952 | + | 0.958542i | \(0.591978\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 28.2487i | − | 1.08569i | −0.839834 | − | 0.542843i | \(-0.817348\pi\) | ||
0.839834 | − | 0.542843i | \(-0.182652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 39.7128i | − | 1.52404i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.62896i | 0.138858i | 0.997587 | + | 0.0694292i | \(0.0221178\pi\) | ||||
−0.997587 | + | 0.0694292i | \(0.977882\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.3923 | −1.39048 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.85641i | 0.0707235i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.92820i | 0.263561i | 0.991279 | + | 0.131781i | \(0.0420694\pi\) | ||||
−0.991279 | + | 0.131781i | \(0.957931\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.0718 | −0.647570 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.58622i | − | 0.325226i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.8564i | − | 1.05212i | −0.850447 | − | 0.526061i | \(-0.823668\pi\) | ||
0.850447 | − | 0.526061i | \(-0.176332\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.1769i | 0.949565i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 39.7128 | 1.49355 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.8866i | 0.821968i | 0.911642 | + | 0.410984i | \(0.134815\pi\) | ||||
−0.911642 | + | 0.410984i | \(0.865185\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.7511 | + | 7.60770i | 1.03929 | + | 0.284910i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.7846i | 1.22607i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.14277i | 0.117206i | 0.998281 | + | 0.0586028i | \(0.0186646\pi\) | ||||
−0.998281 | + | 0.0586028i | \(0.981335\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.4641 | −0.426945 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.29311 | −0.159442 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.7156 | 1.54715 | 0.773573 | − | 0.633707i | \(-0.218467\pi\) | ||||
0.773573 | + | 0.633707i | \(0.218467\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.81448i | 0.0671110i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.3300i | − | 1.00946i | −0.863278 | − | 0.504729i | \(-0.831592\pi\) | ||
0.863278 | − | 0.504729i | \(-0.168408\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.7732 | 1.61241 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24.0000i | − | 0.882854i | −0.897297 | − | 0.441427i | \(-0.854472\pi\) | ||
0.897297 | − | 0.441427i | \(-0.145528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.1051 | 1.17782 | 0.588911 | − | 0.808198i | \(-0.299557\pi\) | ||||
0.588911 | + | 0.808198i | \(0.299557\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.6410 | 0.976051 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.8939 | 1.12884 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.1591 | −1.72086 | −0.860429 | − | 0.509570i | \(-0.829804\pi\) | ||||
−0.860429 | + | 0.509570i | \(0.829804\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.8564 | 0.941011 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.1576i | 0.369184i | 0.982815 | + | 0.184592i | \(0.0590964\pi\) | ||||
−0.982815 | + | 0.184592i | \(0.940904\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.58622 | −0.311250 | −0.155625 | − | 0.987816i | \(-0.549739\pi\) | ||||
−0.155625 | + | 0.987816i | \(0.549739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 5.32051i | − | 0.192615i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 40.6304i | − | 1.46708i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 14.8718i | − | 0.536290i | −0.963379 | − | 0.268145i | \(-0.913589\pi\) | ||
0.963379 | − | 0.268145i | \(-0.0864106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 25.7128i | − | 0.924826i | −0.886665 | − | 0.462413i | \(-0.846984\pi\) | ||
0.886665 | − | 0.462413i | \(-0.153016\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000i | 0.215526i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.0718 | 1.04161 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 8.58622i | − | 0.307239i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43.7732 | 1.56233 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.9794 | −0.747833 | −0.373917 | − | 0.927462i | \(-0.621985\pi\) | ||||
−0.373917 | + | 0.927462i | \(0.621985\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 44.4373i | − | 1.58001i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.44344i | 0.193302i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.39230i | 0.226427i | 0.993571 | + | 0.113214i | \(0.0361144\pi\) | ||||
−0.993571 | + | 0.113214i | \(0.963886\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.14277 | −0.111183 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −58.6410 | −2.06940 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31.3205 | + | 8.58622i | 1.10390 | + | 0.302624i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.58622 | 0.301875 | 0.150938 | − | 0.988543i | \(-0.451771\pi\) | ||||
0.150938 | + | 0.988543i | \(0.451771\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.7128i | 0.551751i | 0.961193 | + | 0.275876i | \(0.0889678\pi\) | ||||
−0.961193 | + | 0.275876i | \(0.911032\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.92820 | 0.242684 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.14359 | −0.214937 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.3594 | 1.82736 | 0.913678 | − | 0.406439i | \(-0.133230\pi\) | ||||
0.913678 | + | 0.406439i | \(0.133230\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 21.7128i | − | 0.756861i | −0.925630 | − | 0.378431i | \(-0.876464\pi\) | ||
0.925630 | − | 0.378431i | \(-0.123536\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.58846 | 0.229103 | 0.114552 | − | 0.993417i | \(-0.463457\pi\) | ||||
0.114552 | + | 0.993417i | \(0.463457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5359 | 0.713241 | 0.356621 | − | 0.934249i | \(-0.383929\pi\) | ||||
0.356621 | + | 0.934249i | \(0.383929\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.26795i | 0.113228i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.62896 | 0.125585 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.5692 | 1.02084 | 0.510421 | − | 0.859924i | \(-0.329489\pi\) | ||||
0.510421 | + | 0.859924i | \(0.329489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5692 | −0.364456 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.00000i | 0.0688021i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.5728 | −1.32538 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46.9808 | − | 12.8793i | −1.61048 | − | 0.441498i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0000 | 0.342393 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.0442 | 1.09461 | 0.547304 | − | 0.836934i | \(-0.315654\pi\) | ||||
0.547304 | + | 0.836934i | \(0.315654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.0000i | − | 0.409435i | −0.978821 | − | 0.204717i | \(-0.934372\pi\) | ||
0.978821 | − | 0.204717i | \(-0.0656275\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 3.14277i | − | 0.106981i | −0.998568 | − | 0.0534906i | \(-0.982965\pi\) | ||
0.998568 | − | 0.0534906i | \(-0.0170347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.58622i | 0.291940i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.4801 | −1.33927 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.0442 | −1.08578 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40.6304i | 1.37356i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.7846 | −0.769382 | −0.384691 | − | 0.923045i | \(-0.625692\pi\) | ||||
−0.384691 | + | 0.923045i | \(0.625692\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.7321i | 0.428954i | 0.976729 | + | 0.214477i | \(0.0688046\pi\) | ||||
−0.976729 | + | 0.214477i | \(0.931195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.6410i | − | 0.358099i | −0.983840 | − | 0.179049i | \(-0.942698\pi\) | ||
0.983840 | − | 0.179049i | \(-0.0573022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.29311i | − | 0.144148i | −0.997399 | − | 0.0720742i | \(-0.977038\pi\) | ||
0.997399 | − | 0.0720742i | \(-0.0229619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 28.9014i | − | 0.969323i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 10.6410i | − | 0.356088i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.4580 | 0.784114 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 25.7587i | − | 0.859099i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.392305 | 0.0130696 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.6008 | −0.884239 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.6953 | −1.71651 | −0.858256 | − | 0.513221i | \(-0.828452\pi\) | ||||
−0.858256 | + | 0.513221i | \(0.828452\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.3205 | −1.17022 | −0.585110 | − | 0.810954i | \(-0.698949\pi\) | ||||
−0.585110 | + | 0.810954i | \(0.698949\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.3923 | −0.343935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 62.6410i | − | 2.06859i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0721 | 0.662118 | 0.331059 | − | 0.943610i | \(-0.392594\pi\) | ||||
0.331059 | + | 0.943610i | \(0.392594\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.28555i | 0.206891i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 10.1576i | − | 0.333980i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.6008 | −0.872742 | −0.436371 | − | 0.899767i | \(-0.643737\pi\) | ||||
−0.436371 | + | 0.899767i | \(0.643737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.0648 | −0.362636 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.92820 | 0.226576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.58622i | − | 0.280499i | −0.990116 | − | 0.140250i | \(-0.955209\pi\) | ||
0.990116 | − | 0.140250i | \(-0.0447905\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.4641i | 1.02570i | 0.858478 | + | 0.512850i | \(0.171410\pi\) | ||||
−0.858478 | + | 0.512850i | \(0.828590\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.8718 | + | 54.2487i | −0.484291 | + | 1.76658i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 43.7732i | − | 1.42244i | −0.702971 | − | 0.711219i | \(-0.748144\pi\) | ||
0.702971 | − | 0.711219i | \(-0.251856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.9282 | 1.39351 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.6603i | 1.28472i | 0.766402 | + | 0.642361i | \(0.222045\pi\) | ||||
−0.766402 | + | 0.642361i | \(0.777955\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 27.7128i | − | 0.896766i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 61.6098i | 1.98948i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.9282i | 0.609320i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.8564i | 1.41033i | 0.709045 | + | 0.705163i | \(0.249126\pi\) | ||||
−0.709045 | + | 0.705163i | \(0.750874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.3397 | 0.781100 | 0.390550 | − | 0.920582i | \(-0.372285\pi\) | ||||
0.390550 | + | 0.920582i | \(0.372285\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.9014i | 0.926537i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 22.1962i | − | 0.710118i | −0.934844 | − | 0.355059i | \(-0.884461\pi\) | ||
0.934844 | − | 0.355059i | \(-0.115539\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 62.1051i | 1.98489i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.5359 | −1.61184 | −0.805922 | − | 0.592021i | \(-0.798330\pi\) | ||||
−0.805922 | + | 0.592021i | \(0.798330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.4580i | 0.747433i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.14277 | − | 11.4641i | 0.0999344 | − | 0.364537i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.7846i | 0.850841i | 0.904996 | + | 0.425421i | \(0.139874\pi\) | ||||
−0.904996 | + | 0.425421i | \(0.860126\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.9442i | 0.759081i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.0333 | −1.04618 | −0.523088 | − | 0.852279i | \(-0.675220\pi\) | ||||
−0.523088 | + | 0.852279i | \(0.675220\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3312.2.i.f.2575.1 | yes | 8 | |
3.2 | odd | 2 | 3312.2.i.b.2575.5 | yes | 8 | ||
4.3 | odd | 2 | 3312.2.i.b.2575.4 | yes | 8 | ||
12.11 | even | 2 | inner | 3312.2.i.f.2575.8 | yes | 8 | |
23.22 | odd | 2 | 3312.2.i.b.2575.8 | yes | 8 | ||
69.68 | even | 2 | inner | 3312.2.i.f.2575.4 | yes | 8 | |
92.91 | even | 2 | inner | 3312.2.i.f.2575.5 | yes | 8 | |
276.275 | odd | 2 | 3312.2.i.b.2575.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3312.2.i.b.2575.1 | ✓ | 8 | 276.275 | odd | 2 | ||
3312.2.i.b.2575.4 | yes | 8 | 4.3 | odd | 2 | ||
3312.2.i.b.2575.5 | yes | 8 | 3.2 | odd | 2 | ||
3312.2.i.b.2575.8 | yes | 8 | 23.22 | odd | 2 | ||
3312.2.i.f.2575.1 | yes | 8 | 1.1 | even | 1 | trivial | |
3312.2.i.f.2575.4 | yes | 8 | 69.68 | even | 2 | inner | |
3312.2.i.f.2575.5 | yes | 8 | 92.91 | even | 2 | inner | |
3312.2.i.f.2575.8 | yes | 8 | 12.11 | even | 2 | inner |