Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} + 28 x^{13} + 373 x^{12} - 920 x^{11} + 1088 x^{10} - 168 x^{9} + 16460 x^{8} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.1 | ||
Root | \(1.49885 + 1.49885i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.b.1471.9 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.84428 | −1.83097 | −0.915484 | − | 0.402355i | \(-0.868192\pi\) | ||||
−0.915484 | + | 0.402355i | \(0.868192\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.09487 | −0.933138 | −0.466569 | − | 0.884485i | \(-0.654510\pi\) | ||||
−0.466569 | + | 0.884485i | \(0.654510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.53183 | −1.25690 | −0.628452 | − | 0.777848i | \(-0.716311\pi\) | ||||
−0.628452 | + | 0.777848i | \(0.716311\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.04944i | − | 0.254526i | −0.991869 | − | 0.127263i | \(-0.959381\pi\) | ||
0.991869 | − | 0.127263i | \(-0.0406192\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.05893 | −0.701766 | −0.350883 | − | 0.936419i | \(-0.614119\pi\) | ||||
−0.350883 | + | 0.936419i | \(0.614119\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.84428i | 1.05711i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.79485 | + | 0.0971617i | −0.999795 | + | 0.0202596i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.44565 | −0.454146 | −0.227073 | − | 0.973878i | \(-0.572916\pi\) | ||||
−0.227073 | + | 0.973878i | \(0.572916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.08441i | 0.553977i | 0.960873 | + | 0.276988i | \(0.0893363\pi\) | ||||
−0.960873 | + | 0.276988i | \(0.910664\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.09487i | 0.538748i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.84428i | 0.818833i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.78545i | − | 0.622325i | −0.950357 | − | 0.311162i | \(-0.899282\pi\) | ||
0.950357 | − | 0.311162i | \(-0.100718\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.53183i | 0.725674i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.04608 | 0.631891 | 0.315946 | − | 0.948777i | \(-0.397678\pi\) | ||||
0.315946 | + | 0.948777i | \(0.397678\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.53119 | −0.386002 | −0.193001 | − | 0.981199i | \(-0.561822\pi\) | ||||
−0.193001 | + | 0.981199i | \(0.561822\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.83718i | − | 0.559711i | −0.960042 | − | 0.279855i | \(-0.909713\pi\) | ||
0.960042 | − | 0.279855i | \(-0.0902865\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.4671 | 2.35244 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.04944 | −0.146950 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.14281i | − | 1.11850i | −0.828999 | − | 0.559251i | \(-0.811089\pi\) | ||
0.828999 | − | 0.559251i | \(-0.188911\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.09487i | 0.417312i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.05893i | 0.405165i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.64825i | 0.605151i | 0.953125 | + | 0.302575i | \(0.0978464\pi\) | ||||
−0.953125 | + | 0.302575i | \(0.902154\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3650i | 1.45514i | 0.686033 | + | 0.727570i | \(0.259351\pi\) | ||||
−0.686033 | + | 0.727570i | \(0.740649\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.84428 | 0.610322 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.53183i | 0.562105i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.77906 | −0.461686 | −0.230843 | − | 0.972991i | \(-0.574148\pi\) | ||||
−0.230843 | + | 0.972991i | \(0.574148\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0971617 | + | 4.79485i | 0.0116969 | + | 0.577232i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.2737i | − | 1.57530i | −0.616122 | − | 0.787651i | \(-0.711297\pi\) | ||
0.616122 | − | 0.787651i | \(-0.288703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.53642 | 0.296865 | 0.148433 | − | 0.988923i | \(-0.452577\pi\) | ||||
0.148433 | + | 0.988923i | \(0.452577\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.9924 | 1.70855 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.04304 | −0.117351 | −0.0586754 | − | 0.998277i | \(-0.518688\pi\) | ||||
−0.0586754 | + | 0.998277i | \(0.518688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.24974 | 0.466470 | 0.233235 | − | 0.972420i | \(-0.425069\pi\) | ||||
0.233235 | + | 0.972420i | \(0.425069\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.04944 | −0.113827 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.44565i | 0.262202i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.89654i | − | 0.413033i | −0.978443 | − | 0.206516i | \(-0.933787\pi\) | ||
0.978443 | − | 0.206516i | \(-0.0662127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.9535 | 2.30135 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.08441 | 0.319839 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.05893i | 0.313839i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.72909i | 0.581701i | 0.956768 | + | 0.290851i | \(0.0939383\pi\) | ||||
−0.956768 | + | 0.290851i | \(0.906062\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.09487 | 0.311046 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.97419 | 0.395447 | 0.197724 | − | 0.980258i | \(-0.436645\pi\) | ||||
0.197724 | + | 0.980258i | \(0.436645\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.3249 | −1.31294 | −0.656471 | − | 0.754351i | \(-0.727952\pi\) | ||||
−0.656471 | + | 0.754351i | \(0.727952\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.84428 | 0.472754 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.4779 | 1.10961 | 0.554806 | − | 0.831980i | \(-0.312793\pi\) | ||||
0.554806 | + | 0.831980i | \(0.312793\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.3604i | − | 1.27970i | −0.768501 | − | 0.639848i | \(-0.778997\pi\) | ||
0.768501 | − | 0.639848i | \(-0.221003\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.78545 | −0.359299 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.7468i | − | 1.19912i | −0.800331 | − | 0.599559i | \(-0.795343\pi\) | ||
0.800331 | − | 0.599559i | \(-0.204657\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0971617 | + | 4.79485i | 0.00906038 | + | 0.447122i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.53183 | 0.418968 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.08377i | 0.466028i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.42178 | −0.129253 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.04608i | − | 0.364823i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.34087i | 0.118983i | 0.998229 | + | 0.0594913i | \(0.0189479\pi\) | ||||
−0.998229 | + | 0.0594913i | \(0.981052\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.53119i | 0.222859i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.8225i | 1.12030i | 0.828390 | + | 0.560152i | \(0.189257\pi\) | ||||
−0.828390 | + | 0.560152i | \(0.810743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.8183 | 1.28491 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.67251i | − | 0.313763i | −0.987617 | − | 0.156882i | \(-0.949856\pi\) | ||
0.987617 | − | 0.156882i | \(-0.0501441\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.5659i | 0.981009i | 0.871439 | + | 0.490504i | \(0.163187\pi\) | ||||
−0.871439 | + | 0.490504i | \(0.836813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.83718 | −0.323149 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.0254 | 1.17287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.44565i | 0.203100i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 16.4671i | − | 1.35818i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.2359i | − | 1.00240i | −0.865330 | − | 0.501202i | \(-0.832891\pi\) | ||
0.865330 | − | 0.501202i | \(-0.167109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.3471i | − | 0.923415i | −0.887032 | − | 0.461708i | \(-0.847237\pi\) | ||
0.887032 | − | 0.461708i | \(-0.152763\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.04944i | 0.0848419i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.08441 | 0.247746 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3681i | 0.827461i | 0.910399 | + | 0.413730i | \(0.135774\pi\) | ||||
−0.910399 | + | 0.413730i | \(0.864226\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.14281 | −0.645767 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.2276 | − | 0.470679i | 1.83059 | − | 0.0370947i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.7920i | − | 0.923623i | −0.886978 | − | 0.461811i | \(-0.847200\pi\) | ||
0.886978 | − | 0.461811i | \(-0.152800\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.09487 | 0.240935 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3234i | 1.18576i | 0.805290 | + | 0.592881i | \(0.202010\pi\) | ||||
−0.805290 | + | 0.592881i | \(0.797990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.53751 | 0.579808 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.05893 | 0.233922 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.12803 | 0.237820 | 0.118910 | − | 0.992905i | \(-0.462060\pi\) | ||||
0.118910 | + | 0.992905i | \(0.462060\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.84428 | 0.366193 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.64825 | 0.349384 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.9800i | 1.94184i | 0.239404 | + | 0.970920i | \(0.423048\pi\) | ||||
−0.239404 | + | 0.970920i | \(0.576952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3758i | 1.14288i | 0.820645 | + | 0.571439i | \(0.193615\pi\) | ||||
−0.820645 | + | 0.571439i | \(0.806385\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.3650 | 0.840126 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.78545 | −0.278312 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.24787i | 0.237508i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 4.84428i | − | 0.352370i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.659707 | −0.0477347 | −0.0238674 | − | 0.999715i | \(-0.507598\pi\) | ||||
−0.0238674 | + | 0.999715i | \(0.507598\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2828 | 0.956120 | 0.478060 | − | 0.878327i | \(-0.341340\pi\) | ||||
0.478060 | + | 0.878327i | \(0.341340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.53183 | 0.324531 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.33165 | −0.0948761 | −0.0474380 | − | 0.998874i | \(-0.515106\pi\) | ||||
−0.0474380 | + | 0.998874i | \(0.515106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.42710 | 0.242941 | 0.121470 | − | 0.992595i | \(-0.461239\pi\) | ||||
0.121470 | + | 0.992595i | \(0.461239\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.77906i | 0.266554i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.8474 | 0.831527 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.04608i | − | 0.282590i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.79485 | − | 0.0971617i | 0.333265 | − | 0.00675321i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.46698 | 0.654845 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 22.7762i | − | 1.56798i | −0.620774 | − | 0.783989i | \(-0.713182\pi\) | ||
0.620774 | − | 0.783989i | \(-0.286818\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.2737 | −0.909501 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.53119i | 0.172626i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.9418i | − | 1.01431i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 2.53642i | − | 0.171395i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.75587i | 0.319914i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 12.5342i | − | 0.839353i | −0.907674 | − | 0.419677i | \(-0.862144\pi\) | ||
0.907674 | − | 0.419677i | \(-0.137856\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.4186 | −1.62072 | −0.810359 | − | 0.585933i | \(-0.800728\pi\) | ||||
−0.810359 | + | 0.585933i | \(0.800728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.3713i | 1.67658i | 0.545225 | + | 0.838290i | \(0.316444\pi\) | ||||
−0.545225 | + | 0.838290i | \(0.683556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 14.9924i | − | 0.986429i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.675614 | 0.0442609 | 0.0221305 | − | 0.999755i | \(-0.492955\pi\) | ||||
0.0221305 | + | 0.999755i | \(0.492955\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.83718 | −0.250310 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.04304i | 0.0677526i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.80756i | 0.634398i | 0.948359 | + | 0.317199i | \(0.102742\pi\) | ||||
−0.948359 | + | 0.317199i | \(0.897258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.2922i | − | 0.662978i | −0.943459 | − | 0.331489i | \(-0.892449\pi\) | ||
0.943459 | − | 0.331489i | \(-0.107551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 16.4671i | − | 1.05204i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8625 | 0.882053 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.24974i | − | 0.269316i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.41799 | 0.531339 | 0.265669 | − | 0.964064i | \(-0.414407\pi\) | ||||
0.265669 | + | 0.964064i | \(0.414407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.8394 | − | 0.300703i | 0.932947 | − | 0.0189050i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.04944i | 0.0657182i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.93222 | 0.307663 | 0.153832 | − | 0.988097i | \(-0.450839\pi\) | ||||
0.153832 | + | 0.988097i | \(0.450839\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.3378i | 1.13946i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.44565 | 0.151382 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.3726 | −0.762924 | −0.381462 | − | 0.924384i | \(-0.624579\pi\) | ||||
−0.381462 | + | 0.924384i | \(0.624579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.14281 | −0.500209 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.89654 | −0.238465 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.2075 | −1.78081 | −0.890406 | − | 0.455166i | \(-0.849580\pi\) | ||||
−0.890406 | + | 0.455166i | \(0.849580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.1560i | − | 0.981409i | −0.871326 | − | 0.490704i | \(-0.836740\pi\) | ||
0.871326 | − | 0.490704i | \(-0.163260\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 21.9535i | − | 1.32869i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.09487 | 0.186628 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.8559 | −1.49345 | −0.746723 | − | 0.665135i | \(-0.768374\pi\) | ||||
−0.746723 | + | 0.665135i | \(0.768374\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.08441i | − | 0.184659i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.4409i | 1.10009i | 0.835134 | + | 0.550046i | \(0.185390\pi\) | ||||
−0.835134 | + | 0.550046i | \(0.814610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.823367 | −0.0489441 | −0.0244720 | − | 0.999701i | \(-0.507790\pi\) | ||||
−0.0244720 | + | 0.999701i | \(0.507790\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.05893 | 0.181195 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.6004 | −1.15697 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8987 | 0.935217 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.72909 | 0.335845 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.91225i | 0.403818i | 0.979404 | + | 0.201909i | \(0.0647145\pi\) | ||||
−0.979404 | + | 0.201909i | \(0.935285\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.64825 | 0.270632 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.09487i | − | 0.179583i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.7294 | − | 0.440321i | 1.25665 | − | 0.0254644i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2618 | 0.706758 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.97419i | − | 0.228312i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.3650 | 0.650759 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 30.2075i | − | 1.72403i | −0.506879 | − | 0.862017i | \(-0.669201\pi\) | ||
0.506879 | − | 0.862017i | \(-0.330799\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.3249i | 0.758028i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.6281i | − | 0.942896i | −0.881894 | − | 0.471448i | \(-0.843732\pi\) | ||
0.881894 | − | 0.471448i | \(-0.156268\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 31.9251i | − | 1.80451i | −0.431202 | − | 0.902255i | \(-0.641910\pi\) | ||
0.431202 | − | 0.902255i | \(-0.358090\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 4.84428i | − | 0.272944i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.2873 | 1.19561 | 0.597806 | − | 0.801641i | \(-0.296039\pi\) | ||||
0.597806 | + | 0.801641i | \(0.296039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.56898 | 0.423781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 11.4779i | − | 0.640635i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.21015i | 0.178617i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.53183 | 0.251381 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.3604 | −0.738833 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.5884i | 1.02481i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0651i | 1.04791i | 0.851745 | + | 0.523956i | \(0.175544\pi\) | ||||
−0.851745 | + | 0.523956i | \(0.824456\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.78545i | 0.207442i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.77906i | 0.206472i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.3374i | 0.998901i | 0.866342 | + | 0.499451i | \(0.166465\pi\) | ||||
−0.866342 | + | 0.499451i | \(0.833535\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.7468 | −0.692311 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 9.54585i | − | 0.516937i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −45.8612 | −2.47627 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.79485 | − | 0.0971617i | 0.258146 | − | 0.00523101i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.6634i | 0.733489i | 0.930322 | + | 0.366744i | \(0.119528\pi\) | ||||
−0.930322 | + | 0.366744i | \(0.880472\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.1112 | 1.66534 | 0.832671 | − | 0.553768i | \(-0.186810\pi\) | ||||
0.832671 | + | 0.553768i | \(0.186810\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.53183i | − | 0.241891i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.5128 | 1.67726 | 0.838630 | − | 0.544702i | \(-0.183357\pi\) | ||||
0.838630 | + | 0.544702i | \(0.183357\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.2737 | −0.704496 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.08377 | 0.269061 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.1464 | −1.80218 | −0.901088 | − | 0.433636i | \(-0.857230\pi\) | ||||
−0.901088 | + | 0.433636i | \(0.857230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.64296 | −0.507524 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.42178i | 0.0746242i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.53642i | − | 0.132762i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.17921 | −0.479151 | −0.239576 | − | 0.970878i | \(-0.577008\pi\) | ||||
−0.239576 | + | 0.970878i | \(0.577008\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.04608 | −0.210630 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 39.4461i | 2.04794i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.7943i | 0.817795i | 0.912580 | + | 0.408898i | \(0.134087\pi\) | ||||
−0.912580 | + | 0.408898i | \(0.865913\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.0833 | 0.570819 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0170 | 0.565905 | 0.282952 | − | 0.959134i | \(-0.408686\pi\) | ||||
0.282952 | + | 0.959134i | \(0.408686\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.34087 | 0.0686947 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.892024 | −0.0455803 | −0.0227901 | − | 0.999740i | \(-0.507255\pi\) | ||||
−0.0227901 | + | 0.999740i | \(0.507255\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 14.9924i | − | 0.764085i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.53119 | 0.128667 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.970666i | 0.0492147i | 0.999697 | + | 0.0246074i | \(0.00783356\pi\) | ||||
−0.999697 | + | 0.0246074i | \(0.992166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.101965 | + | 5.03189i | 0.00515659 | + | 0.254473i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.8225 | 0.646808 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.04304i | 0.0524809i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.57904 | −0.480758 | −0.240379 | − | 0.970679i | \(-0.577272\pi\) | ||||
−0.240379 | + | 0.970679i | \(0.577272\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 14.8183i | − | 0.741844i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.6070i | 1.02906i | 0.857471 | + | 0.514532i | \(0.172034\pi\) | ||||
−0.857471 | + | 0.514532i | \(0.827966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 13.9780i | − | 0.696296i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.7155i | 0.580715i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.4878 | 0.765822 | 0.382911 | − | 0.923785i | \(-0.374922\pi\) | ||||
0.382911 | + | 0.923785i | \(0.374922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.67251 | −0.181151 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 22.5174i | − | 1.10801i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.24974i | − | 0.208612i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.5659 | 0.566386 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.3366 | −1.72631 | −0.863154 | − | 0.504941i | \(-0.831514\pi\) | ||||
−0.863154 | + | 0.504941i | \(0.831514\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 9.54836i | − | 0.465359i | −0.972554 | − | 0.232679i | \(-0.925251\pi\) | ||
0.972554 | − | 0.232679i | \(-0.0747492\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.83718i | 0.186570i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.04944i | 0.0509051i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 55.0553i | − | 2.66431i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 14.0254i | − | 0.677154i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.9390 | 1.20127 | 0.600634 | − | 0.799524i | \(-0.294915\pi\) | ||||
0.600634 | + | 0.799524i | \(0.294915\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 38.3664i | − | 1.84377i | −0.387464 | − | 0.921885i | \(-0.626649\pi\) | ||
0.387464 | − | 0.921885i | \(-0.373351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.44565 | 0.117260 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.6671 | − | 0.297211i | 0.701622 | − | 0.0142175i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.96764i | − | 0.141638i | −0.997489 | − | 0.0708189i | \(-0.977439\pi\) | ||
0.997489 | − | 0.0708189i | \(-0.0225612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.4671 | −0.784147 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.100101i | 0.00475595i | 0.999997 | + | 0.00237797i | \(0.000756933\pi\) | ||||
−0.999997 | + | 0.00237797i | \(0.999243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.89654 | −0.184714 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.2359 | −0.578739 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.2186 | −1.52049 | −0.760245 | − | 0.649637i | \(-0.774921\pi\) | ||||
−0.760245 | + | 0.649637i | \(0.774921\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.5221 | −0.589642 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.3471 | −0.533134 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 21.9535i | − | 1.02920i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.8778i | 0.836288i | 0.908381 | + | 0.418144i | \(0.137319\pi\) | ||||
−0.908381 | + | 0.418144i | \(0.862681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.04944 | 0.0489835 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.34372 | 0.248882 | 0.124441 | − | 0.992227i | \(-0.460286\pi\) | ||||
0.124441 | + | 0.992227i | \(0.460286\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.9996i | − | 1.20830i | −0.796870 | − | 0.604151i | \(-0.793512\pi\) | ||
0.796870 | − | 0.604151i | \(-0.206488\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 3.08441i | − | 0.143036i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.57869 | 0.165602 | 0.0828010 | − | 0.996566i | \(-0.473613\pi\) | ||||
0.0828010 | + | 0.996566i | \(0.473613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.3068 | 0.845331 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.3681 | 0.477735 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.83370 | 0.360194 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.05893 | 0.140353 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.14281i | 0.372834i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.8270 | 1.36283 | 0.681416 | − | 0.731896i | \(-0.261365\pi\) | ||||
0.681416 | + | 0.731896i | \(0.261365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.1550i | 0.782203i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.470679 | − | 23.2276i | −0.0214166 | − | 1.05689i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.72909 | 0.260145 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.6321i | 1.65996i | 0.557793 | + | 0.829980i | \(0.311648\pi\) | ||||
−0.557793 | + | 0.829980i | \(0.688352\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.7920 | −0.533254 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.1982i | 1.27257i | 0.771455 | + | 0.636284i | \(0.219529\pi\) | ||||
−0.771455 | + | 0.636284i | \(0.780471\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.56656i | 0.115592i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 3.09487i | − | 0.139104i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 64.3017i | 2.88432i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 25.4668i | − | 1.14005i | −0.821627 | − | 0.570025i | \(-0.806934\pi\) | ||
0.821627 | − | 0.570025i | \(-0.193066\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.3234 | 0.684600 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.4532 | 0.956552 | 0.478276 | − | 0.878210i | \(-0.341262\pi\) | ||||
0.478276 | + | 0.878210i | \(0.341262\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.97419i | − | 0.176849i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 7.53751i | − | 0.334752i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.58966 | 0.425054 | 0.212527 | − | 0.977155i | \(-0.431831\pi\) | ||||
0.212527 | + | 0.977155i | \(0.431831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.2871 | −0.543550 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.05893i | − | 0.135055i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.3249i | 0.587166i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.8756i | 0.522287i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 3.12803i | − | 0.137305i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0956i | 0.573727i | 0.957971 | + | 0.286863i | \(0.0926126\pi\) | ||||
−0.957971 | + | 0.286863i | \(0.907387\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.40732 | −0.280173 | −0.140086 | − | 0.990139i | \(-0.544738\pi\) | ||||
−0.140086 | + | 0.990139i | \(0.544738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 4.84428i | − | 0.211422i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.23689 | 0.141001 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9811 | − | 0.931751i | 0.999179 | − | 0.0405109i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4.64825i | − | 0.201717i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.3361 | −0.794227 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 11.4779i | − | 0.496233i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.9800 | 1.12112 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −50.9635 | −2.19515 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.4405 | −1.30874 | −0.654370 | − | 0.756174i | \(-0.727066\pi\) | ||||
−0.654370 | + | 0.756174i | \(0.727066\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.3758 | 0.659841 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.3604 | −0.572298 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.9045i | 1.23587i | 0.786230 | + | 0.617934i | \(0.212030\pi\) | ||||
−0.786230 | + | 0.617934i | \(0.787970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 11.3650i | − | 0.485047i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.48108 | 0.318705 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.05277 | 0.214866 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.78545i | 0.160684i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.2748i | 0.647212i | 0.946192 | + | 0.323606i | \(0.104895\pi\) | ||||
−0.946192 | + | 0.323606i | \(0.895105\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.4709 | 0.485168 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.24787 | 0.137125 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.19626 | −0.0925612 | −0.0462806 | − | 0.998928i | \(-0.514737\pi\) | ||||
−0.0462806 | + | 0.998928i | \(0.514737\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.7468 | −0.536262 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.84428 | −0.203441 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.6847i | 1.16060i | 0.814401 | + | 0.580302i | \(0.197066\pi\) | ||||
−0.814401 | + | 0.580302i | \(0.802934\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.6755 | 1.20003 | 0.600016 | − | 0.799988i | \(-0.295161\pi\) | ||||
0.600016 | + | 0.799988i | \(0.295161\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.659707i | 0.0275597i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.79485 | − | 0.0971617i | 0.199959 | − | 0.00405192i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.26705 | −0.0943785 | −0.0471892 | − | 0.998886i | \(-0.515026\pi\) | ||||
−0.0471892 | + | 0.998886i | \(0.515026\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 13.2828i | − | 0.552016i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.5869 | −0.854090 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.2009i | 1.04372i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 4.53183i | − | 0.187368i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.1170i | 0.417574i | 0.977961 | + | 0.208787i | \(0.0669515\pi\) | ||||
−0.977961 | + | 0.208787i | \(0.933048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.43499i | − | 0.388762i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.33165i | 0.0547767i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.3649 | 1.32907 | 0.664533 | − | 0.747259i | \(-0.268630\pi\) | ||||
0.664533 | + | 0.747259i | \(0.268630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.08377 | 0.208414 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 3.42710i | − | 0.140262i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 3.27236i | − | 0.133705i | −0.997763 | − | 0.0668526i | \(-0.978704\pi\) | ||
0.997763 | − | 0.0668526i | \(-0.0212957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.2903 | 1.43952 | 0.719761 | − | 0.694222i | \(-0.244251\pi\) | ||||
0.719761 | + | 0.694222i | \(0.244251\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.77906 | 0.153895 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.42178i | 0.0578036i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5.72385i | − | 0.232324i | −0.993230 | − | 0.116162i | \(-0.962941\pi\) | ||
0.993230 | − | 0.116162i | \(-0.0370591\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 11.8474i | − | 0.480082i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.3895i | 0.703503i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 11.1031i | − | 0.448449i | −0.974538 | − | 0.224224i | \(-0.928015\pi\) | ||
0.974538 | − | 0.224224i | \(-0.0719848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.04608 | −0.163154 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.915087i | 0.0368400i | 0.999830 | + | 0.0184200i | \(0.00586360\pi\) | ||||
−0.999830 | + | 0.0184200i | \(0.994136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.2320 | 1.29552 | 0.647758 | − | 0.761847i | \(-0.275707\pi\) | ||||
0.647758 | + | 0.761847i | \(0.275707\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0971617 | − | 4.79485i | −0.00389896 | − | 0.192411i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.8760i | 0.756249i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 9.46698i | − | 0.378075i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.97259 | −0.158398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.724543 | −0.0288436 | −0.0144218 | − | 0.999896i | \(-0.504591\pi\) | ||||
−0.0144218 | + | 0.999896i | \(0.504591\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.7762 | −0.905273 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.34087 | 0.0532107 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −74.6261 | −2.95679 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.2737i | 0.525100i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 9.49638i | − | 0.375084i | −0.982257 | − | 0.187542i | \(-0.939948\pi\) | ||
0.982257 | − | 0.187542i | \(-0.0600521\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.33887 | 0.289417 | 0.144708 | − | 0.989474i | \(-0.453776\pi\) | ||||
0.144708 | + | 0.989474i | \(0.453776\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.53119 | 0.0996654 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.89013i | 0.349507i | 0.984612 | + | 0.174753i | \(0.0559128\pi\) | ||||
−0.984612 | + | 0.174753i | \(0.944087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.3857i | − | 0.564689i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.9418 | −0.585614 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.3035 | −1.65546 | −0.827732 | − | 0.561124i | \(-0.810369\pi\) | ||||
−0.827732 | + | 0.561124i | \(0.810369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.8225 | 0.501015 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.53642 | −0.0989550 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.34063 | 0.0911781 | 0.0455891 | − | 0.998960i | \(-0.485484\pi\) | ||||
0.0455891 | + | 0.998960i | \(0.485484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.00716i | 0.233652i | 0.993152 | + | 0.116826i | \(0.0372719\pi\) | ||||
−0.993152 | + | 0.116826i | \(0.962728\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.75587 | 0.184703 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 14.8183i | − | 0.574630i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7265 | − | 0.237624i | 0.454053 | − | 0.00920083i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.5342 | −0.484601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 35.1732i | − | 1.35785i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.2984 | −1.51484 | −0.757420 | − | 0.652928i | \(-0.773540\pi\) | ||||
−0.757420 | + | 0.652928i | \(0.773540\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 10.1936i | − | 0.391772i | −0.980627 | − | 0.195886i | \(-0.937242\pi\) | ||
0.980627 | − | 0.195886i | \(-0.0627583\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 27.7533i | − | 1.06508i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.4186i | 0.935722i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.94854i | 0.189350i | 0.995508 | + | 0.0946752i | \(0.0301813\pi\) | ||||
−0.995508 | + | 0.0946752i | \(0.969819\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.67251 | −0.140319 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.3713 | 0.967974 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.9019i | 1.40585i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0509i | 1.14319i | 0.820536 | + | 0.571595i | \(0.193675\pi\) | ||||
−0.820536 | + | 0.571595i | \(0.806325\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.9924 | −0.569515 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.5659 | 0.438720 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4.24610i | − | 0.160833i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 0.675614i | − | 0.0255541i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.9951i | 0.717434i | 0.933446 | + | 0.358717i | \(0.116786\pi\) | ||||
−0.933446 | + | 0.358717i | \(0.883214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.5794i | 0.436727i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.83718i | 0.144517i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.2521 | −0.724051 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3208i | 0.387605i | 0.981041 | + | 0.193802i | \(0.0620820\pi\) | ||||
−0.981041 | + | 0.193802i | \(0.937918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.04304 | 0.0391170 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.299687 | − | 14.7893i | −0.0112234 | − | 0.553863i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 14.0254i | − | 0.524521i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.80756 | 0.366270 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 28.4693i | − | 1.06172i | −0.847458 | − | 0.530862i | \(-0.821868\pi\) | ||
0.847458 | − | 0.530862i | \(-0.178132\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 64.5497 | 2.40395 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.2922 | −0.382770 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.44565 | 0.0908293 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.62136 | 0.134309 | 0.0671543 | − | 0.997743i | \(-0.478608\pi\) | ||||
0.0671543 | + | 0.997743i | \(0.478608\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.65632i | 0.0982475i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.39563i | − | 0.125420i | −0.998032 | − | 0.0627102i | \(-0.980026\pi\) | ||
0.998032 | − | 0.0627102i | \(-0.0199744\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.4671 | −0.607397 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.6957 | 0.430817 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 45.6318i | − | 1.67859i | −0.543675 | − | 0.839296i | \(-0.682968\pi\) | ||
0.543675 | − | 0.839296i | \(-0.317032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 13.8625i | − | 0.509253i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.29853 | 0.304444 | 0.152222 | − | 0.988346i | \(-0.451357\pi\) | ||||
0.152222 | + | 0.988346i | \(0.451357\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.2359 | −0.448289 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.24974 | −0.155490 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −55.6023 | −2.03166 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.1817 | 1.42976 | 0.714880 | − | 0.699247i | \(-0.246481\pi\) | ||||
0.714880 | + | 0.699247i | \(0.246481\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 8.41799i | − | 0.306769i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.3471 | −0.412964 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.3641i | − | 1.35802i | −0.734128 | − | 0.679011i | \(-0.762409\pi\) | ||
0.734128 | − | 0.679011i | \(-0.237591\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.300703 | − | 14.8394i | −0.0109148 | − | 0.538637i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.2385 | 0.479896 | 0.239948 | − | 0.970786i | \(-0.422870\pi\) | ||||
0.239948 | + | 0.970786i | \(0.422870\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 64.7217i | 2.34308i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.04944 | 0.0379424 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 21.0651i | − | 0.760616i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.6263i | 1.21260i | 0.795237 | + | 0.606298i | \(0.207346\pi\) | ||||
−0.795237 | + | 0.606298i | \(0.792654\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 4.93222i | − | 0.177630i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 17.5764i | − | 0.632177i | −0.948730 | − | 0.316089i | \(-0.897630\pi\) | ||
0.948730 | − | 0.316089i | \(-0.102370\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.08441i | − | 0.110795i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.3378 | 0.657865 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.3767 | −0.443440 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.0804i | 1.46997i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.44565i | − | 0.0874005i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.3681 | 0.370052 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.3182 | −1.22331 | −0.611656 | − | 0.791124i | \(-0.709496\pi\) | ||||
−0.611656 | + | 0.791124i | \(0.709496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.3726i | 0.440475i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.7491i | 2.19555i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 51.5043i | − | 1.82897i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.14281i | 0.288796i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.808358i | 0.0286335i | 0.999898 | + | 0.0143168i | \(0.00455732\pi\) | ||||
−0.999898 | + | 0.0143168i | \(0.995443\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.02688 | −0.142461 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.89654i | 0.137678i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.84988 | −0.277016 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.470679 | − | 23.2276i | −0.0165892 | − | 0.818665i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.2075i | 1.02815i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.4177 | 0.366268 | 0.183134 | − | 0.983088i | \(-0.441376\pi\) | ||||
0.183134 | + | 0.983088i | \(0.441376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.0907i | 0.740593i | 0.928914 | + | 0.370297i | \(0.120744\pi\) | ||||
−0.928914 | + | 0.370297i | \(0.879256\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.1560 | −0.566617 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.7920 | −0.413057 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.74272 | 0.270883 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.9535 | −0.767117 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.8269 | −0.412761 | −0.206380 | − | 0.978472i | \(-0.566168\pi\) | ||||
−0.206380 | + | 0.978472i | \(0.566168\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 13.4121i | − | 0.467517i | −0.972295 | − | 0.233758i | \(-0.924898\pi\) | ||
0.972295 | − | 0.233758i | \(-0.0751025\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3.09487i | − | 0.107750i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.8208 | 1.55857 | 0.779286 | − | 0.626668i | \(-0.215582\pi\) | ||||
0.779286 | + | 0.626668i | \(0.215582\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.5431 | −1.37339 | −0.686694 | − | 0.726947i | \(-0.740939\pi\) | ||||
−0.686694 | + | 0.726947i | \(0.740939\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.8559i | 0.862241i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 17.2812i | − | 0.598756i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.3234 | 0.530289 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.08441 | −0.106613 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.1962 | 1.80201 | 0.901007 | − | 0.433805i | \(-0.142829\pi\) | ||||
0.901007 | + | 0.433805i | \(0.142829\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0188 | −0.793751 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.4409 | 0.635138 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 7.53751i | − | 0.259298i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.88751 | 0.236658 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.823367i | 0.0282579i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.367801 | + | 18.1507i | 0.0126081 | + | 0.622197i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 57.1046 | 1.95522 | 0.977612 | − | 0.210415i | \(-0.0674815\pi\) | ||||
0.977612 | + | 0.210415i | \(0.0674815\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 3.05893i | − | 0.104613i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.0004 | −1.12727 | −0.563636 | − | 0.826024i | \(-0.690598\pi\) | ||||
−0.563636 | + | 0.826024i | \(0.690598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 46.3157i | − | 1.58027i | −0.612932 | − | 0.790135i | \(-0.710010\pi\) | ||
0.612932 | − | 0.790135i | \(-0.289990\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.6004i | 0.667978i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.8658i | 0.982604i | 0.870989 | + | 0.491302i | \(0.163479\pi\) | ||||
−0.870989 | + | 0.491302i | \(0.836521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 3.12803i | − | 0.106356i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 15.8987i | − | 0.539948i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.22806 | 0.109505 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.1261 | 0.580295 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.72909i | − | 0.193900i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.84428i | − | 0.163767i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.1171 | −0.848145 | −0.424072 | − | 0.905628i | \(-0.639400\pi\) | ||||
−0.424072 | + | 0.905628i | \(0.639400\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.91225 | 0.233144 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.8946i | 1.64730i | 0.567098 | + | 0.823650i | \(0.308066\pi\) | ||||
−0.567098 | + | 0.823650i | \(0.691934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 39.3348i | − | 1.32372i | −0.749627 | − | 0.661860i | \(-0.769767\pi\) | ||
0.749627 | − | 0.661860i | \(-0.230233\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 4.64825i | − | 0.156249i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 56.2201i | 1.88769i | 0.330393 | + | 0.943843i | \(0.392819\pi\) | ||||
−0.330393 | + | 0.943843i | \(0.607181\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.49554i | − | 0.217853i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.09487 | −0.103682 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7377i | 0.392786i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.9800 | 0.868417 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.440321 | − | 21.7294i | −0.0147019 | − | 0.725525i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7.54340i | − | 0.251587i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.54536 | −0.284687 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 12.2618i | − | 0.408047i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.3758 | 0.511110 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.5550 | −1.24699 | −0.623496 | − | 0.781826i | \(-0.714288\pi\) | ||||
−0.623496 | + | 0.781826i | \(0.714288\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.97419 | −0.131816 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.2173 | −0.338513 | −0.169256 | − | 0.985572i | \(-0.554137\pi\) | ||||
−0.169256 | + | 0.985572i | \(0.554137\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.1524 | −0.435281 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 11.3650i | − | 0.375716i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 62.1157i | − | 2.05124i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4425 | 1.16914 | 0.584569 | − | 0.811344i | \(-0.301263\pi\) | ||||
0.584569 | + | 0.811344i | \(0.301263\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.2075 | −0.995372 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 60.1543i | 1.98000i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.78545i | 0.124465i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.3249 | 0.437648 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.3376 | 0.896918 | 0.448459 | − | 0.893803i | \(-0.351973\pi\) | ||||
0.448459 | + | 0.893803i | \(0.351973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −50.3716 | −1.65086 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.6281 | −0.544381 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.24787 | 0.106217 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.1261i | − | 0.918838i | −0.888220 | − | 0.459419i | \(-0.848058\pi\) | ||
0.888220 | − | 0.459419i | \(-0.151942\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.9251 | −1.04183 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.1173i | 1.60118i | 0.599214 | + | 0.800589i | \(0.295480\pi\) | ||||
−0.599214 | + | 0.800589i | \(0.704520\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.4003 | + | 0.393124i | −0.631762 | + | 0.0128019i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.84428 | −0.157585 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.22418i | 0.0397804i | 0.999802 | + | 0.0198902i | \(0.00633166\pi\) | ||||
−0.999802 | + | 0.0198902i | \(0.993668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.4946 | −0.373131 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.2873i | − | 0.690287i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31.8279i | − | 1.03101i | −0.856887 | − | 0.515504i | \(-0.827605\pi\) | ||
0.856887 | − | 0.515504i | \(-0.172395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.659707i | 0.0213476i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 7.56898i | − | 0.244670i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.7907i | 0.574490i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.4864 | 0.693110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.4779 | −0.369871 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 13.2828i | − | 0.427590i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.01006i | 0.0967971i | 0.998828 | + | 0.0483985i | \(0.0154118\pi\) | ||||
−0.998828 | + | 0.0483985i | \(0.984588\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.21015 | 0.103125 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.278352 | 0.00893273 | 0.00446636 | − | 0.999990i | \(-0.498578\pi\) | ||||
0.00446636 | + | 0.999990i | \(0.498578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 56.0286i | − | 1.79619i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 4.53183i | − | 0.145135i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.5047i | 1.42383i | 0.702264 | + | 0.711916i | \(0.252173\pi\) | ||||
−0.702264 | + | 0.711916i | \(0.747827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0593i | 0.385417i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.3604i | 0.426566i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.02437 | −0.224043 | −0.112021 | − | 0.993706i | \(-0.535733\pi\) | ||||
−0.112021 | + | 0.993706i | \(0.535733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.33165i | 0.0424299i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.5884 | 0.591675 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.1367 | − | 0.245934i | 0.385923 | − | 0.00782026i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 51.5501i | − | 1.63754i | −0.574119 | − | 0.818772i | \(-0.694655\pi\) | ||
0.574119 | − | 0.818772i | \(-0.305345\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.0651 | 0.605012 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 3.42710i | − | 0.108646i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.3647 | −0.423264 | −0.211632 | − | 0.977349i | \(-0.567878\pi\) | ||||
−0.211632 | + | 0.977349i | \(0.567878\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.78545 | 0.119766 |
(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 | 5520.2.be.b.1471.1 | yes | 16 | |
4.3 | odd | 2 | 5520.2.be.a.1471.16 | yes | 16 | ||
23.22 | odd | 2 | 5520.2.be.a.1471.8 | ✓ | 16 | ||
92.91 | even | 2 | inner | 5520.2.be.b.1471.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.a.1471.8 | ✓ | 16 | 23.22 | odd | 2 | ||
5520.2.be.a.1471.16 | yes | 16 | 4.3 | odd | 2 | ||
5520.2.be.b.1471.1 | yes | 16 | 1.1 | even | 1 | trivial | |
5520.2.be.b.1471.9 | yes | 16 | 92.91 | even | 2 | inner |