Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7280,2,Mod(1,7280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7280.a (trivial) |
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: | yes |
Analytic conductor: | \(58.1310926715\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3640) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7280.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 2.30278 | 1.32951 | 0.664754 | − | 0.747062i | \(-0.268536\pi\) | ||||
0.664754 | + | 0.747062i | \(0.268536\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.30278 | 0.767592 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.60555 | −0.785603 | −0.392802 | − | 0.919623i | \(-0.628494\pi\) | ||||
−0.392802 | + | 0.919623i | \(0.628494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.30278 | 0.594574 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.69722 | 0.654173 | 0.327086 | − | 0.944994i | \(-0.393933\pi\) | ||||
0.327086 | + | 0.944994i | \(0.393933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.69722 | 0.618786 | 0.309393 | − | 0.950934i | \(-0.399874\pi\) | ||||
0.309393 | + | 0.950934i | \(0.399874\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.30278 | −0.502507 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.60555 | −0.308988 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.90833 | −1.65423 | −0.827117 | − | 0.562029i | \(-0.810021\pi\) | ||||
−0.827117 | + | 0.562029i | \(0.810021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.30278 | 0.772801 | 0.386401 | − | 0.922331i | \(-0.373718\pi\) | ||||
0.386401 | + | 0.922331i | \(0.373718\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.00000 | −1.04447 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.90833 | 1.13572 | 0.567861 | − | 0.823124i | \(-0.307771\pi\) | ||||
0.567861 | + | 0.823124i | \(0.307771\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.30278 | −0.368739 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.697224 | −0.108888 | −0.0544441 | − | 0.998517i | \(-0.517339\pi\) | ||||
−0.0544441 | + | 0.998517i | \(0.517339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.30278 | 0.343278 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.60555 | −0.380059 | −0.190029 | − | 0.981778i | \(-0.560858\pi\) | ||||
−0.190029 | + | 0.981778i | \(0.560858\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.21110 | 0.869728 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.60555 | 0.632621 | 0.316311 | − | 0.948656i | \(-0.397556\pi\) | ||||
0.316311 | + | 0.948656i | \(0.397556\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.60555 | −0.351332 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.21110 | 0.822681 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1194 | 1.83819 | 0.919097 | − | 0.394032i | \(-0.128920\pi\) | ||||
0.919097 | + | 0.394032i | \(0.128920\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.2111 | 1.69151 | 0.845754 | − | 0.533573i | \(-0.179151\pi\) | ||||
0.845754 | + | 0.533573i | \(0.179151\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.30278 | −0.290122 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.90833 | 0.233139 | 0.116570 | − | 0.993183i | \(-0.462810\pi\) | ||||
0.116570 | + | 0.993183i | \(0.462810\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18.4222 | 2.21777 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.60555 | −0.546578 | −0.273289 | − | 0.961932i | \(-0.588112\pi\) | ||||
−0.273289 | + | 0.961932i | \(0.588112\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.39445 | −0.163208 | −0.0816039 | − | 0.996665i | \(-0.526004\pi\) | ||||
−0.0816039 | + | 0.996665i | \(0.526004\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.30278 | 0.265902 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.60555 | 0.296930 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5139 | 1.63294 | 0.816469 | − | 0.577389i | \(-0.195928\pi\) | ||||
0.816469 | + | 0.577389i | \(0.195928\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6056 | −1.17839 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.81665 | −1.07752 | −0.538759 | − | 0.842460i | \(-0.681107\pi\) | ||||
−0.538759 | + | 0.842460i | \(0.681107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.69722 | 0.292555 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.5139 | −2.19932 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.69722 | −0.391905 | −0.195952 | − | 0.980613i | \(-0.562780\pi\) | ||||
−0.195952 | + | 0.980613i | \(0.562780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.90833 | 1.02745 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.69722 | 0.276729 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.21110 | 0.122969 | 0.0614844 | − | 0.998108i | \(-0.480417\pi\) | ||||
0.0614844 | + | 0.998108i | \(0.480417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.90833 | −0.188033 | −0.0940165 | − | 0.995571i | \(-0.529971\pi\) | ||||
−0.0940165 | + | 0.995571i | \(0.529971\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.30278 | −0.224728 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.9083 | 1.50995 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.8167 | −1.29976 | −0.649881 | − | 0.760036i | \(-0.725181\pi\) | ||||
−0.649881 | + | 0.760036i | \(0.725181\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.30278 | −0.212892 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.69722 | −0.247254 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.21110 | −0.382828 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.60555 | −0.144768 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.39445 | 0.123737 | 0.0618687 | − | 0.998084i | \(-0.480294\pi\) | ||||
0.0618687 | + | 0.998084i | \(0.480294\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.60555 | 0.405496 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.69722 | −0.233879 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.60555 | −0.138184 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.30278 | 0.538482 | 0.269241 | − | 0.963073i | \(-0.413227\pi\) | ||||
0.269241 | + | 0.963073i | \(0.413227\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.4222 | 1.05364 | 0.526819 | − | 0.849978i | \(-0.323385\pi\) | ||||
0.526819 | + | 0.849978i | \(0.323385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.60555 | 0.217887 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.90833 | −0.739796 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.30278 | 0.189930 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.00000 | 0.655386 | 0.327693 | − | 0.944784i | \(-0.393729\pi\) | ||||
0.327693 | + | 0.944784i | \(0.393729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.21110 | 0.502138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.30278 | 0.345607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.51388 | −0.599673 | −0.299836 | − | 0.953991i | \(-0.596932\pi\) | ||||
−0.299836 | + | 0.953991i | \(0.596932\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.6056 | 0.841075 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.119429 | 0.00935444 | 0.00467722 | − | 0.999989i | \(-0.498511\pi\) | ||||
0.00467722 | + | 0.999989i | \(0.498511\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | −0.467099 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.78890 | 0.680105 | 0.340053 | − | 0.940406i | \(-0.389555\pi\) | ||||
0.340053 | + | 0.940406i | \(0.389555\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.21110 | 0.474975 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.3028 | 1.69565 | 0.847824 | − | 0.530277i | \(-0.177912\pi\) | ||||
0.847824 | + | 0.530277i | \(0.177912\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32.5139 | 2.44389 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.9083 | 1.48802 | 0.744009 | − | 0.668169i | \(-0.232922\pi\) | ||||
0.744009 | + | 0.668169i | \(0.232922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8167 | −0.878325 | −0.439162 | − | 0.898408i | \(-0.644725\pi\) | ||||
−0.439162 | + | 0.898408i | \(0.644725\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.4222 | 2.24887 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.90833 | 0.507910 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.02776 | −0.513920 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.60555 | 0.116787 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.51388 | −0.109540 | −0.0547702 | − | 0.998499i | \(-0.517443\pi\) | ||||
−0.0547702 | + | 0.998499i | \(0.517443\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0916731 | 0.00659877 | 0.00329939 | − | 0.999995i | \(-0.498950\pi\) | ||||
0.00329939 | + | 0.999995i | \(0.498950\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.30278 | −0.164905 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.1194 | −0.863474 | −0.431737 | − | 0.902000i | \(-0.642099\pi\) | ||||
−0.431737 | + | 0.902000i | \(0.642099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2111 | 0.936510 | 0.468255 | − | 0.883593i | \(-0.344883\pi\) | ||||
0.468255 | + | 0.883593i | \(0.344883\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.39445 | 0.309961 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.90833 | 0.625242 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.697224 | −0.0486963 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.4222 | 1.28043 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.02776 | −0.486120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.51388 | 0.448434 | 0.224217 | − | 0.974539i | \(-0.428018\pi\) | ||||
0.224217 | + | 0.974539i | \(0.428018\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.6056 | −0.726680 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.30278 | −0.292091 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.21110 | −0.216986 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.69722 | −0.181435 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.21110 | 0.0811014 | 0.0405507 | − | 0.999177i | \(-0.487089\pi\) | ||||
0.0405507 | + | 0.999177i | \(0.487089\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.30278 | 0.153518 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.81665 | −0.120576 | −0.0602878 | − | 0.998181i | \(-0.519202\pi\) | ||||
−0.0602878 | + | 0.998181i | \(0.519202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.30278 | 0.218254 | 0.109127 | − | 0.994028i | \(-0.465195\pi\) | ||||
0.109127 | + | 0.994028i | \(0.465195\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | 0.394771 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8167 | 1.29823 | 0.649116 | − | 0.760689i | \(-0.275139\pi\) | ||||
0.649116 | + | 0.760689i | \(0.275139\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.60555 | −0.169967 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33.4222 | 2.17101 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.6333 | 1.39934 | 0.699671 | − | 0.714465i | \(-0.253330\pi\) | ||||
0.699671 | + | 0.714465i | \(0.253330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.09167 | −0.392399 | −0.196200 | − | 0.980564i | \(-0.562860\pi\) | ||||
−0.196200 | + | 0.980564i | \(0.562860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.6056 | −1.25770 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.69722 | −0.171620 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.6056 | −1.43257 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6333 | −0.986766 | −0.493383 | − | 0.869812i | \(-0.664240\pi\) | ||||
−0.493383 | + | 0.869812i | \(0.664240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.8444 | −1.31048 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.21110 | 0.388954 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.6333 | −1.34945 | −0.674724 | − | 0.738070i | \(-0.735737\pi\) | ||||
−0.674724 | + | 0.738070i | \(0.735737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.90833 | −0.429263 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.5139 | −1.26978 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.6333 | 1.70394 | 0.851971 | − | 0.523588i | \(-0.175407\pi\) | ||||
0.851971 | + | 0.523588i | \(0.175407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.60555 | 0.282917 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.51388 | −0.521041 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.81665 | 0.232705 | 0.116353 | − | 0.993208i | \(-0.462880\pi\) | ||||
0.116353 | + | 0.993208i | \(0.462880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.30278 | 0.139370 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.60555 | −0.157121 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.2111 | −0.793778 | −0.396889 | − | 0.917867i | \(-0.629910\pi\) | ||||
−0.396889 | + | 0.917867i | \(0.629910\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.90833 | 0.593196 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.0000 | −1.90896 | −0.954480 | − | 0.298275i | \(-0.903589\pi\) | ||||
−0.954480 | + | 0.298275i | \(0.903589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.9083 | 1.54009 | 0.770045 | − | 0.637989i | \(-0.220234\pi\) | ||||
0.770045 | + | 0.637989i | \(0.220234\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.21110 | 0.367914 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.697224 | 0.0411559 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.72498 | −0.572058 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.78890 | 0.163488 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.4222 | −1.54360 | −0.771801 | − | 0.635864i | \(-0.780644\pi\) | ||||
−0.771801 | + | 0.635864i | \(0.780644\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1194 | 0.822065 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.18335 | 0.242742 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.00000 | −0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.8167 | 0.793746 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.2111 | 0.756466 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.6056 | −0.833583 | −0.416791 | − | 0.909002i | \(-0.636845\pi\) | ||||
−0.416791 | + | 0.909002i | \(0.636845\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.39445 | −0.249991 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0278 | −0.738736 | −0.369368 | − | 0.929283i | \(-0.620426\pi\) | ||||
−0.369368 | + | 0.929283i | \(0.620426\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.33053 | 0.527393 | 0.263696 | − | 0.964606i | \(-0.415058\pi\) | ||||
0.263696 | + | 0.964606i | \(0.415058\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.30278 | −0.129747 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.4222 | 0.697701 | 0.348850 | − | 0.937178i | \(-0.386572\pi\) | ||||
0.348850 | + | 0.937178i | \(0.386572\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.2111 | 1.29957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.8167 | 0.771170 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.27502 | 0.404793 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.21110 | −0.509375 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.60555 | 0.143649 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0000 | −0.989369 | −0.494685 | − | 0.869072i | \(-0.664716\pi\) | ||||
−0.494685 | + | 0.869072i | \(0.664716\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.9083 | 0.871771 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.90833 | 0.104263 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.42221 | 0.240893 | 0.120446 | − | 0.992720i | \(-0.461567\pi\) | ||||
0.120446 | + | 0.992720i | \(0.461567\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.8167 | −1.72804 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.2111 | −0.607115 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.4222 | 0.991818 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.18335 | 0.439305 | 0.219653 | − | 0.975578i | \(-0.429508\pi\) | ||||
0.219653 | + | 0.975578i | \(0.429508\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9361 | 1.28127 | 0.640635 | − | 0.767846i | \(-0.278671\pi\) | ||||
0.640635 | + | 0.767846i | \(0.278671\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.60555 | 0.0856980 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.6333 | −1.36432 | −0.682162 | − | 0.731201i | \(-0.738960\pi\) | ||||
−0.682162 | + | 0.731201i | \(0.738960\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.60555 | −0.244437 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.21110 | −0.328726 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.0278 | 0.582023 | 0.291011 | − | 0.956720i | \(-0.406008\pi\) | ||||
0.291011 | + | 0.956720i | \(0.406008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.7250 | −0.617104 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.69722 | −0.508972 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.39445 | −0.0729888 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.57779 | −0.0823602 | −0.0411801 | − | 0.999152i | \(-0.513112\pi\) | ||||
−0.0411801 | + | 0.999152i | \(0.513112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.60555 | −0.0835817 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.60555 | −0.239108 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0000 | −0.724893 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.30278 | 0.118915 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.90833 | 0.458802 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.6333 | −0.700296 | −0.350148 | − | 0.936694i | \(-0.613869\pi\) | ||||
−0.350148 | + | 0.936694i | \(0.613869\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.21110 | 0.164510 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.2389 | −1.34074 | −0.670372 | − | 0.742026i | \(-0.733865\pi\) | ||||
−0.670372 | + | 0.742026i | \(0.733865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.60555 | 0.132791 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.60555 | 0.234113 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.51388 | −0.431671 | −0.215835 | − | 0.976430i | \(-0.569247\pi\) | ||||
−0.215835 | + | 0.976430i | \(0.569247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.5778 | 1.09124 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.5139 | 0.730272 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.18335 | 0.410710 | 0.205355 | − | 0.978688i | \(-0.434165\pi\) | ||||
0.205355 | + | 0.978688i | \(0.434165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.21110 | −0.310944 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.0000 | −1.19850 | −0.599251 | − | 0.800561i | \(-0.704535\pi\) | ||||
−0.599251 | + | 0.800561i | \(0.704535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.30278 | −0.214337 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.6056 | −0.526994 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.0000 | −0.892227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.00000 | −0.0988936 | −0.0494468 | − | 0.998777i | \(-0.515746\pi\) | ||||
−0.0494468 | + | 0.998777i | \(0.515746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.5139 | 0.715917 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.1194 | −0.694772 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.81665 | −0.481881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.6056 | 1.40082 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.6333 | 0.763737 | 0.381869 | − | 0.924217i | \(-0.375281\pi\) | ||||
0.381869 | + | 0.924217i | \(0.375281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4222 | −0.605421 | −0.302711 | − | 0.953083i | \(-0.597892\pi\) | ||||
−0.302711 | + | 0.953083i | \(0.597892\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.69722 | 0.130835 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.2111 | −0.639330 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00000 | 0.289683 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.0000 | 1.63772 | 0.818861 | − | 0.573992i | \(-0.194606\pi\) | ||||
0.818861 | + | 0.573992i | \(0.194606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.9361 | −1.19835 | −0.599176 | − | 0.800617i | \(-0.704505\pi\) | ||||
−0.599176 | + | 0.800617i | \(0.704505\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.5139 | −0.983565 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.5778 | 1.03221 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.2111 | −0.916896 | −0.458448 | − | 0.888721i | \(-0.651594\pi\) | ||||
−0.458448 | + | 0.888721i | \(0.651594\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.30278 | 0.109656 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.6056 | −0.788954 | −0.394477 | − | 0.918906i | \(-0.629074\pi\) | ||||
−0.394477 | + | 0.918906i | \(0.629074\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.69722 | −0.175265 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.4222 | 0.871340 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.0278 | −1.65306 | −0.826531 | − | 0.562891i | \(-0.809689\pi\) | ||||
−0.826531 | + | 0.562891i | \(0.809689\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.81665 | 0.0855429 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.0278 | 1.08194 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5139 | 1.28704 | 0.643522 | − | 0.765427i | \(-0.277472\pi\) | ||||
0.643522 | + | 0.765427i | \(0.277472\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.33053 | −0.202132 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.9083 | 1.16010 | 0.580048 | − | 0.814582i | \(-0.303034\pi\) | ||||
0.580048 | + | 0.814582i | \(0.303034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.72498 | −0.266062 | −0.133031 | − | 0.991112i | \(-0.542471\pi\) | ||||
−0.133031 | + | 0.991112i | \(0.542471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.90833 | 0.459488 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.4861 | 0.901710 | 0.450855 | − | 0.892597i | \(-0.351119\pi\) | ||||
0.450855 | + | 0.892597i | \(0.351119\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.90833 | −0.0881183 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.3028 | −0.797270 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.21110 | −0.239607 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.69722 | 0.123757 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6056 | 0.485595 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.9083 | −1.86915 | −0.934575 | − | 0.355767i | \(-0.884220\pi\) | ||||
−0.934575 | + | 0.355767i | \(0.884220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.90833 | −0.314993 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.4222 | −0.838239 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.21110 | 0.0549933 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.3028 | −1.37315 | −0.686575 | − | 0.727059i | \(-0.740887\pi\) | ||||
−0.686575 | + | 0.727059i | \(0.740887\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.275019 | 0.0124368 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.4222 | 1.37293 | 0.686467 | − | 0.727161i | \(-0.259160\pi\) | ||||
0.686467 | + | 0.727161i | \(0.259160\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.0278 | −1.08216 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.00000 | −0.269680 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.60555 | 0.206587 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.0000 | −1.16392 | −0.581960 | − | 0.813217i | \(-0.697714\pi\) | ||||
−0.581960 | + | 0.813217i | \(0.697714\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.2389 | 0.904206 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.6333 | 1.23211 | 0.616054 | − | 0.787704i | \(-0.288730\pi\) | ||||
0.616054 | + | 0.787704i | \(0.288730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.30278 | 0.102270 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.3305 | −1.07843 | −0.539216 | − | 0.842168i | \(-0.681279\pi\) | ||||
−0.539216 | + | 0.842168i | \(0.681279\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39445 | 0.0616868 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.33053 | −0.191198 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.90833 | −0.0840909 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.78890 | 0.298575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 51.3583 | 2.25438 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.2389 | −0.974302 | −0.487151 | − | 0.873318i | \(-0.661964\pi\) | ||||
−0.487151 | + | 0.873318i | \(0.661964\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.4222 | −1.50518 | −0.752589 | − | 0.658491i | \(-0.771195\pi\) | ||||
−0.752589 | + | 0.658491i | \(0.771195\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.30278 | −0.100501 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.6056 | 0.505546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.5139 | 1.41098 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.697224 | 0.0302001 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | 0.259403 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 45.8444 | 1.97833 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.60555 | −0.112229 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.0555 | 1.63613 | 0.818067 | − | 0.575123i | \(-0.195046\pi\) | ||||
0.818067 | + | 0.575123i | \(0.195046\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.2111 | −1.16774 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00000 | −0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.6333 | 1.60908 | 0.804542 | − | 0.593896i | \(-0.202411\pi\) | ||||
0.804542 | + | 0.593896i | \(0.202411\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.4222 | 1.29839 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.0278 | −1.02362 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.5139 | −0.617193 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.9083 | 0.675271 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.09167 | 0.173370 | 0.0866849 | − | 0.996236i | \(-0.472373\pi\) | ||||
0.0866849 | + | 0.996236i | \(0.472373\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.1833 | −0.683261 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.5416 | −1.75077 | −0.875386 | − | 0.483425i | \(-0.839392\pi\) | ||||
−0.875386 | + | 0.483425i | \(0.839392\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.8167 | −0.581271 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.6056 | 0.445391 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.7527 | 1.91805 | 0.959027 | − | 0.283314i | \(-0.0914338\pi\) | ||||
0.959027 | + | 0.283314i | \(0.0914338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.7250 | 0.448826 | 0.224413 | − | 0.974494i | \(-0.427953\pi\) | ||||
0.224413 | + | 0.974494i | \(0.427953\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.48612 | −0.145635 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.6056 | −0.608037 | −0.304019 | − | 0.952666i | \(-0.598328\pi\) | ||||
−0.304019 | + | 0.952666i | \(0.598328\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.211103 | 0.00877312 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.81665 | 0.407263 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | −0.496989 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.30278 | −0.0952081 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.81665 | −0.0749813 | −0.0374907 | − | 0.999297i | \(-0.511936\pi\) | ||||
−0.0374907 | + | 0.999297i | \(0.511936\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.6056 | 0.478198 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.9083 | −1.14800 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.1833 | −0.910961 | −0.455480 | − | 0.890246i | \(-0.650532\pi\) | ||||
−0.455480 | + | 0.890246i | \(0.650532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.69722 | −0.110575 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.4222 | 1.24510 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.4222 | −0.752711 | −0.376355 | − | 0.926475i | \(-0.622823\pi\) | ||||
−0.376355 | + | 0.926475i | \(0.622823\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.2111 | 1.51787 | 0.758936 | − | 0.651165i | \(-0.225719\pi\) | ||||
0.758936 | + | 0.651165i | \(0.225719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.39445 | 0.178956 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.21110 | −0.171206 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5139 | 0.467334 | 0.233667 | − | 0.972317i | \(-0.424927\pi\) | ||||
0.233667 | + | 0.972317i | \(0.424927\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.5139 | 0.831264 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.60555 | 0.105409 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.8444 | −0.761119 | −0.380559 | − | 0.924757i | \(-0.624269\pi\) | ||||
−0.380559 | + | 0.924757i | \(0.624269\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.60555 | −0.0647421 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.90833 | 0.157343 | 0.0786717 | − | 0.996901i | \(-0.474932\pi\) | ||||
0.0786717 | + | 0.996901i | \(0.474932\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.7250 | −0.431073 | −0.215537 | − | 0.976496i | \(-0.569150\pi\) | ||||
−0.215537 | + | 0.976496i | \(0.569150\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.8444 | −0.515428 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.69722 | 0.148126 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.1833 | −0.646301 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.6333 | 0.742959 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.81665 | −0.231557 | −0.115779 | − | 0.993275i | \(-0.536936\pi\) | ||||
−0.115779 | + | 0.993275i | \(0.536936\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.0000 | 0.596196 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.39445 | 0.0553370 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.6056 | −0.419549 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.7250 | −1.52954 | −0.764772 | − | 0.644301i | \(-0.777149\pi\) | ||||
−0.764772 | + | 0.644301i | \(0.777149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.8444 | −1.68962 | −0.844809 | − | 0.535068i | \(-0.820286\pi\) | ||||
−0.844809 | + | 0.535068i | \(0.820286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.60555 | 0.181343 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.486122 | −0.0191114 | −0.00955571 | − | 0.999954i | \(-0.503042\pi\) | ||||
−0.00955571 | + | 0.999954i | \(0.503042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.7889 | −1.44409 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.90833 | −0.388338 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.42221 | 0.0947882 | 0.0473941 | − | 0.998876i | \(-0.484908\pi\) | ||||
0.0473941 | + | 0.998876i | \(0.484908\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.21110 | −0.125277 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.1472 | 1.17437 | 0.587184 | − | 0.809454i | \(-0.300237\pi\) | ||||
0.587184 | + | 0.809454i | \(0.300237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.4861 | 0.602340 | 0.301170 | − | 0.953570i | \(-0.402623\pi\) | ||||
0.301170 | + | 0.953570i | \(0.402623\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.21110 | −0.241219 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.69722 | −0.104594 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −71.2666 | −2.75945 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.78890 | 0.107825 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.4222 | −1.32885 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.81665 | 0.301310 | 0.150655 | − | 0.988586i | \(-0.451862\pi\) | ||||
0.150655 | + | 0.988586i | \(0.451862\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.60555 | −0.0617977 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.42221 | −0.323692 | −0.161846 | − | 0.986816i | \(-0.551745\pi\) | ||||
−0.161846 | + | 0.986816i | \(0.551745\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.21110 | −0.0464779 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.18335 | −0.160306 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.93608 | −0.112346 | −0.0561731 | − | 0.998421i | \(-0.517890\pi\) | ||||
−0.0561731 | + | 0.998421i | \(0.517890\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.30278 | 0.240817 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.60555 | 0.290170 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.60555 | −0.175458 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.09167 | 0.117613 | 0.0588064 | − | 0.998269i | \(-0.481271\pi\) | ||||
0.0588064 | + | 0.998269i | \(0.481271\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.00000 | 0.227921 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.4222 | 0.471201 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.88057 | −0.0712317 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 45.6333 | 1.72601 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.1194 | −1.32644 | −0.663221 | − | 0.748423i | \(-0.730811\pi\) | ||||
−0.663221 | + | 0.748423i | \(0.730811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.6333 | 0.702769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | −0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.2111 | 1.09705 | 0.548523 | − | 0.836135i | \(-0.315190\pi\) | ||||
0.548523 | + | 0.836135i | \(0.315190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 33.4222 | 1.25343 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34.4222 | 1.28912 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.60555 | 0.0974421 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 49.8167 | 1.86044 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.42221 | 0.0903330 | 0.0451665 | − | 0.998979i | \(-0.485618\pi\) | ||||
0.0451665 | + | 0.998979i | \(0.485618\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.90833 | 0.0710698 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.0278 | −0.521698 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.90833 | −0.330847 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.6972 | 0.953057 | 0.476529 | − | 0.879159i | \(-0.341895\pi\) | ||||
0.476529 | + | 0.879159i | \(0.341895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.3305 | −0.493723 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.39445 | 0.199521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0000 | 0.443230 | 0.221615 | − | 0.975134i | \(-0.428867\pi\) | ||||
0.221615 | + | 0.975134i | \(0.428867\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.30278 | 0.0849392 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.97224 | −0.183155 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.0555 | −1.69418 | −0.847090 | − | 0.531450i | \(-0.821647\pi\) | ||||
−0.847090 | + | 0.531450i | \(0.821647\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.21110 | −0.228171 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.0917 | −0.957211 | −0.478605 | − | 0.878030i | \(-0.658858\pi\) | ||||
−0.478605 | + | 0.878030i | \(0.658858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.00000 | 0.293097 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −22.6056 | −0.827094 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | −0.219235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.51388 | 0.201204 | 0.100602 | − | 0.994927i | \(-0.467923\pi\) | ||||
0.100602 | + | 0.994927i | \(0.467923\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.0000 | −1.31191 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0000 | 0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1833 | 0.878959 | 0.439479 | − | 0.898253i | \(-0.355163\pi\) | ||||
0.439479 | + | 0.898253i | \(0.355163\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −48.0000 | −1.74229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.48612 | −0.235122 | −0.117561 | − | 0.993066i | \(-0.537508\pi\) | ||||
−0.117561 | + | 0.993066i | \(0.537508\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.00000 | 0.144810 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.21110 | 0.224563 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.1194 | −0.509823 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.4222 | −1.60191 | −0.800953 | − | 0.598727i | \(-0.795673\pi\) | ||||
−0.800953 | + | 0.598727i | \(0.795673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.8167 | −1.79410 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.8167 | 1.36017 | 0.680085 | − | 0.733133i | \(-0.261943\pi\) | ||||
0.680085 | + | 0.733133i | \(0.261943\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.30278 | 0.154560 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.9083 | −0.570708 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.88057 | −0.0673784 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | 0.429394 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.3028 | 0.511140 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.51388 | −0.268182 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.4222 | −0.514096 | −0.257048 | − | 0.966399i | \(-0.582750\pi\) | ||||
−0.257048 | + | 0.966399i | \(0.582750\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 63.6333 | 2.26541 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.8167 | 0.491264 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.2111 | −0.469140 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.6056 | 0.376140 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.5416 | 0.373404 | 0.186702 | − | 0.982417i | \(-0.440220\pi\) | ||||
0.186702 | + | 0.982417i | \(0.440220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.02776 | −0.248624 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.51388 | −0.300823 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.63331 | 0.128217 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | −0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.78890 | 0.309384 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.48612 | −0.122566 | −0.0612828 | − | 0.998120i | \(-0.519519\pi\) | ||||
−0.0612828 | + | 0.998120i | \(0.519519\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.6333 | −0.408501 | −0.204250 | − | 0.978919i | \(-0.565476\pi\) | ||||
−0.204250 | + | 0.978919i | \(0.565476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.119429 | 0.00418343 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.39445 | 0.188728 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.30278 | 0.0804655 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.4777 | −1.90129 | −0.950643 | − | 0.310288i | \(-0.899575\pi\) | ||||
−0.950643 | + | 0.310288i | \(0.899575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.0278 | −1.15128 | −0.575638 | − | 0.817705i | \(-0.695246\pi\) | ||||
−0.575638 | + | 0.817705i | \(0.695246\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.00000 | −0.208893 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.6333 | −1.37819 | −0.689093 | − | 0.724673i | \(-0.741991\pi\) | ||||
−0.689093 | + | 0.724673i | \(0.741991\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.21110 | −0.180989 | −0.0904945 | − | 0.995897i | \(-0.528845\pi\) | ||||
−0.0904945 | + | 0.995897i | \(0.528845\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.4222 | −1.05533 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.69722 | 0.0934533 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.78890 | 0.304152 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.90833 | −0.238787 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.8444 | −0.719629 | −0.359814 | − | 0.933024i | \(-0.617160\pi\) | ||||
−0.359814 | + | 0.933024i | \(0.617160\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.3583 | 1.73649 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −73.6888 | −2.53798 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.21110 | 0.144695 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 59.6611 | 2.04756 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 55.2666 | 1.89452 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.8167 | 1.56873 | 0.784366 | − | 0.620298i | \(-0.212988\pi\) | ||||
0.784366 | + | 0.620298i | \(0.212988\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.21110 | 0.212415 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.6972 | 1.56099 | 0.780494 | − | 0.625164i | \(-0.214968\pi\) | ||||
0.780494 | + | 0.625164i | \(0.214968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4222 | 0.355601 | 0.177801 | − | 0.984067i | \(-0.443102\pi\) | ||||
0.177801 | + | 0.984067i | \(0.443102\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.60555 | 0.0547170 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.2750 | −0.622089 | −0.311044 | − | 0.950395i | \(-0.600679\pi\) | ||||
−0.311044 | + | 0.950395i | \(0.600679\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.3028 | 0.758317 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.3944 | −0.760555 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.8167 | −1.28284 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.90833 | −0.0646612 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.78890 | 0.0943899 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.9083 | 1.07747 | 0.538734 | − | 0.842476i | \(-0.318903\pi\) | ||||
0.538734 | + | 0.842476i | \(0.318903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −60.8444 | −2.05223 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.4500 | −1.19434 | −0.597170 | − | 0.802115i | \(-0.703708\pi\) | ||||
−0.597170 | + | 0.802115i | \(0.703708\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.3944 | −0.719981 | −0.359990 | − | 0.932956i | \(-0.617220\pi\) | ||||
−0.359990 | + | 0.932956i | \(0.617220\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.5139 | 1.09294 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.1472 | 1.18013 | 0.590064 | − | 0.807357i | \(-0.299103\pi\) | ||||
0.590064 | + | 0.807357i | \(0.299103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.39445 | −0.0467683 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.6333 | 0.925751 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.02776 | −0.235175 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.9083 | 0.665462 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.4222 | −0.615100 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.3305 | −1.27839 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.4222 | 0.413844 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.60555 | −0.153263 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.8167 | −0.392799 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.60555 | 0.152925 | 0.0764624 | − | 0.997072i | \(-0.475637\pi\) | ||||
0.0764624 | + | 0.997072i | \(0.475637\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.8167 | 0.458269 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.9083 | 0.792118 | 0.396059 | − | 0.918225i | \(-0.370378\pi\) | ||||
0.396059 | + | 0.918225i | \(0.370378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.5778 | 0.846501 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.4222 | 1.00573 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.5416 | 1.07345 | 0.536725 | − | 0.843757i | \(-0.319661\pi\) | ||||
0.536725 | + | 0.843757i | \(0.319661\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.6333 | −1.10826 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.60555 | 0.151594 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.90833 | 0.227144 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.39445 | −0.144333 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.7527 | −1.10739 | −0.553696 | − | 0.832719i | \(-0.686783\pi\) | ||||
−0.553696 | + | 0.832719i | \(0.686783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.69722 | 0.0883980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.0000 | −0.982156 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.02776 | −0.229832 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.3028 | −1.21863 | −0.609314 | − | 0.792929i | \(-0.708555\pi\) | ||||
−0.609314 | + | 0.792929i | \(0.708555\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.4861 | 0.701173 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.1194 | −0.884068 | −0.442034 | − | 0.896998i | \(-0.645743\pi\) | ||||
−0.442034 | + | 0.896998i | \(0.645743\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.57779 | −0.181638 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.60555 | 0.0522286 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56.1472 | 1.82454 | 0.912269 | − | 0.409591i | \(-0.134329\pi\) | ||||
0.912269 | + | 0.409591i | \(0.134329\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.39445 | 0.0452657 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.6056 | 0.927599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.0278 | 0.357224 | 0.178612 | − | 0.983920i | \(-0.442839\pi\) | ||||
0.178612 | + | 0.983920i | \(0.442839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.51388 | −0.0489879 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 53.4500 | 1.72779 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.30278 | −0.203527 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.4861 | −0.402778 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.8167 | 0.445235 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0916731 | 0.00295106 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.4861 | −0.401527 | −0.200763 | − | 0.979640i | \(-0.564342\pi\) | ||||
−0.200763 | + | 0.979640i | \(0.564342\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.7527 | 0.538175 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.0278 | −1.57338 | −0.786688 | − | 0.617351i | \(-0.788206\pi\) | ||||
−0.786688 | + | 0.617351i | \(0.788206\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.4222 | −0.398238 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.30278 | −0.0737478 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.90833 | −0.253010 | −0.126505 | − | 0.991966i | \(-0.540376\pi\) | ||||
−0.126505 | + | 0.991966i | \(0.540376\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.63331 | 0.307882 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.21110 | −0.294088 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.4500 | 1.70479 | 0.852395 | − | 0.522899i | \(-0.175150\pi\) | ||||
0.852395 | + | 0.522899i | \(0.175150\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.1194 | −0.386157 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | 0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0000 | 0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.1472 | 1.08472 | 0.542361 | − | 0.840146i | \(-0.317531\pi\) | ||||
0.542361 | + | 0.840146i | \(0.317531\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −41.4500 | −1.31537 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.2111 | 0.418820 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.14719 | −0.194683 | −0.0973417 | − | 0.995251i | \(-0.531034\pi\) | ||||
−0.0973417 | + | 0.995251i | \(0.531034\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.0917 | −0.350925 |
(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 | 7280.2.a.bh.1.2 | 2 | ||
4.3 | odd | 2 | 3640.2.a.l.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.l.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
7280.2.a.bh.1.2 | 2 | 1.1 | even | 1 | trivial |