Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3312,2,Mod(1,3312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3312.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3312.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: | \(26.4464531494\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.44688.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 5x^{2} + 6x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1656) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.92812\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3312.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.64575 | −1.63043 | −0.815215 | − | 0.579159i | \(-0.803381\pi\) | ||||
−0.815215 | + | 0.579159i | \(0.803381\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.81895 | 1.82139 | 0.910696 | − | 0.413076i | \(-0.135546\pi\) | ||||
0.910696 | + | 0.413076i | \(0.135546\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.68303 | 0.808965 | 0.404482 | − | 0.914546i | \(-0.367452\pi\) | ||||
0.404482 | + | 0.914546i | \(0.367452\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.85623 | −1.06953 | −0.534763 | − | 0.845002i | \(-0.679599\pi\) | ||||
−0.534763 | + | 0.845002i | \(0.679599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.962718 | −0.233494 | −0.116747 | − | 0.993162i | \(-0.537247\pi\) | ||||
−0.116747 | + | 0.993162i | \(0.537247\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.21048 | −0.965951 | −0.482975 | − | 0.875634i | \(-0.660444\pi\) | ||||
−0.482975 | + | 0.875634i | \(0.660444\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.29150 | 1.65830 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.85623 | −1.45887 | −0.729433 | − | 0.684052i | \(-0.760216\pi\) | ||||
−0.729433 | + | 0.684052i | \(0.760216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.85623 | −1.41102 | −0.705511 | − | 0.708699i | \(-0.749282\pi\) | ||||
−0.705511 | + | 0.708699i | \(0.749282\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17.5687 | −2.96965 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.0294 | 1.81323 | 0.906614 | − | 0.421961i | \(-0.138658\pi\) | ||||
0.906614 | + | 0.421961i | \(0.138658\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.564731 | −0.0881962 | −0.0440981 | − | 0.999027i | \(-0.514041\pi\) | ||||
−0.0440981 | + | 0.999027i | \(0.514041\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.57655 | 0.850416 | 0.425208 | − | 0.905096i | \(-0.360201\pi\) | ||||
0.425208 | + | 0.905096i | \(0.360201\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.63790 | 1.11410 | 0.557051 | − | 0.830478i | \(-0.311933\pi\) | ||||
0.557051 | + | 0.830478i | \(0.311933\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.2223 | 2.31747 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.99215 | −1.37253 | −0.686264 | − | 0.727353i | \(-0.740750\pi\) | ||||
−0.686264 | + | 0.727353i | \(0.740750\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.78167 | −1.31896 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15.0732 | −1.96236 | −0.981180 | − | 0.193095i | \(-0.938147\pi\) | ||||
−0.981180 | + | 0.193095i | \(0.938147\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.683033 | −0.0874534 | −0.0437267 | − | 0.999044i | \(-0.513923\pi\) | ||||
−0.0437267 | + | 0.999044i | \(0.513923\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.0589 | 1.74379 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7935 | 1.31863 | 0.659317 | − | 0.751865i | \(-0.270845\pi\) | ||||
0.659317 | + | 0.751865i | \(0.270845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.43527 | −0.407691 | −0.203846 | − | 0.979003i | \(-0.565344\pi\) | ||||
−0.203846 | + | 0.979003i | \(0.565344\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0692033 | 0.00809963 | 0.00404981 | − | 0.999992i | \(-0.498711\pi\) | ||||
0.00404981 | + | 0.999992i | \(0.498711\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.9294 | 1.47344 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.89352 | −0.775581 | −0.387791 | − | 0.921748i | \(-0.626762\pi\) | ||||
−0.387791 | + | 0.921748i | \(0.626762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.31697 | −0.144556 | −0.0722780 | − | 0.997385i | \(-0.523027\pi\) | ||||
−0.0722780 | + | 0.997385i | \(0.523027\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.50983 | 0.380695 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.0413 | −1.91237 | −0.956184 | − | 0.292765i | \(-0.905425\pi\) | ||||
−0.956184 | + | 0.292765i | \(0.905425\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.5830 | −1.94803 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.3504 | 1.57491 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.34640 | −0.441310 | −0.220655 | − | 0.975352i | \(-0.570820\pi\) | ||||
−0.220655 | + | 0.975352i | \(0.570820\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.21833 | −0.220732 | −0.110366 | − | 0.993891i | \(-0.535202\pi\) | ||||
−0.110366 | + | 0.993891i | \(0.535202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.54711 | −0.448040 | −0.224020 | − | 0.974584i | \(-0.571918\pi\) | ||||
−0.224020 | + | 0.974584i | \(0.571918\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.336631 | −0.0325434 | −0.0162717 | − | 0.999868i | \(-0.505180\pi\) | ||||
−0.0162717 | + | 0.999868i | \(0.505180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2660 | −1.07909 | −0.539545 | − | 0.841957i | \(-0.681404\pi\) | ||||
−0.539545 | + | 0.841957i | \(0.681404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.9667 | 1.87831 | 0.939154 | − | 0.343496i | \(-0.111611\pi\) | ||||
0.939154 | + | 0.343496i | \(0.111611\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.64575 | 0.339968 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.63929 | −0.425283 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.80133 | −0.345576 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.94510 | −0.438807 | −0.219403 | − | 0.975634i | \(-0.570411\pi\) | ||||
−0.219403 | + | 0.975634i | \(0.570411\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3464 | −0.903969 | −0.451985 | − | 0.892026i | \(-0.649284\pi\) | ||||
−0.451985 | + | 0.892026i | \(0.649284\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.2901 | −1.75938 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.82431 | 0.412169 | 0.206084 | − | 0.978534i | \(-0.433928\pi\) | ||||
0.206084 | + | 0.978534i | \(0.433928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.3464 | −0.865210 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.6419 | 2.37858 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.20512 | −0.344497 | −0.172249 | − | 0.985054i | \(-0.555103\pi\) | ||||
−0.172249 | + | 0.985054i | \(0.555103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.91113 | −0.236905 | −0.118452 | − | 0.992960i | \(-0.537793\pi\) | ||||
−0.118452 | + | 0.992960i | \(0.537793\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 28.6419 | 2.30057 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.6124 | −1.72486 | −0.862430 | − | 0.506176i | \(-0.831059\pi\) | ||||
−0.862430 | + | 0.506176i | \(0.831059\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.81895 | −0.379787 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0236 | −1.72502 | −0.862512 | − | 0.506036i | \(-0.831110\pi\) | ||||
−0.862512 | + | 0.506036i | \(0.831110\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.415605 | 0.0321605 | 0.0160802 | − | 0.999871i | \(-0.494881\pi\) | ||||
0.0160802 | + | 0.999871i | \(0.494881\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.87054 | 0.143888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.8759 | −1.43511 | −0.717554 | − | 0.696503i | \(-0.754738\pi\) | ||||
−0.717554 | + | 0.696503i | \(0.754738\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 39.9564 | 3.02042 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.87590 | 0.663416 | 0.331708 | − | 0.943382i | \(-0.392375\pi\) | ||||
0.331708 | + | 0.943382i | \(0.392375\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.66337 | 0.123637 | 0.0618186 | − | 0.998087i | \(-0.480310\pi\) | ||||
0.0618186 | + | 0.998087i | \(0.480310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −40.2106 | −2.95634 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.58301 | −0.188888 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.92941 | 0.356679 | 0.178340 | − | 0.983969i | \(-0.442927\pi\) | ||||
0.178340 | + | 0.983969i | \(0.442927\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.35176 | −0.457210 | −0.228605 | − | 0.973519i | \(-0.573416\pi\) | ||||
−0.228605 | + | 0.973519i | \(0.573416\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.20264 | 0.441919 | 0.220960 | − | 0.975283i | \(-0.429081\pi\) | ||||
0.220960 | + | 0.975283i | \(0.429081\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.66983 | −0.614588 | −0.307294 | − | 0.951615i | \(-0.599423\pi\) | ||||
−0.307294 | + | 0.951615i | \(0.599423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −37.8588 | −2.65717 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.05887 | 0.143798 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.2969 | −0.781420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9843 | −0.825034 | −0.412517 | − | 0.910950i | \(-0.635350\pi\) | ||||
−0.412517 | + | 0.910950i | \(0.635350\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.3307 | −1.38654 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37.8588 | −2.57002 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.71247 | 0.249728 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0771 | −1.61232 | −0.806162 | − | 0.591694i | \(-0.798459\pi\) | ||||
−0.806162 | + | 0.591694i | \(0.798459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.9196 | −0.990251 | −0.495126 | − | 0.868821i | \(-0.664878\pi\) | ||||
−0.495126 | + | 0.868821i | \(0.664878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.2660 | 1.00881 | 0.504404 | − | 0.863468i | \(-0.331712\pi\) | ||||
0.504404 | + | 0.863468i | \(0.331712\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.2758 | −0.738703 | −0.369351 | − | 0.929290i | \(-0.620420\pi\) | ||||
−0.369351 | + | 0.929290i | \(0.620420\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −27.8459 | −1.81647 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.2758 | −1.24685 | −0.623424 | − | 0.781884i | \(-0.714259\pi\) | ||||
−0.623424 | + | 0.781884i | \(0.714259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.6419 | 1.20083 | 0.600414 | − | 0.799689i | \(-0.295002\pi\) | ||||
0.600414 | + | 0.799689i | \(0.295002\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −59.1425 | −3.77847 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.2366 | 1.03311 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.44643 | −0.154417 | −0.0772086 | − | 0.997015i | \(-0.524601\pi\) | ||||
−0.0772086 | + | 0.997015i | \(0.524601\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.68303 | −0.168681 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.9986 | 1.68413 | 0.842064 | − | 0.539378i | \(-0.181341\pi\) | ||||
0.842064 | + | 0.539378i | \(0.181341\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 53.1503 | 3.30260 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.71247 | −0.228921 | −0.114460 | − | 0.993428i | \(-0.536514\pi\) | ||||
−0.114460 | + | 0.993428i | \(0.536514\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.4289 | 2.23781 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.8053 | 1.45144 | 0.725718 | − | 0.687993i | \(-0.241508\pi\) | ||||
0.725718 | + | 0.687993i | \(0.241508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.63790 | −0.585461 | −0.292730 | − | 0.956195i | \(-0.594564\pi\) | ||||
−0.292730 | + | 0.956195i | \(0.594564\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.2464 | 1.34151 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.63393 | −0.518763 | −0.259381 | − | 0.965775i | \(-0.583519\pi\) | ||||
−0.259381 | + | 0.965775i | \(0.583519\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.9118 | 1.24749 | 0.623746 | − | 0.781627i | \(-0.285610\pi\) | ||||
0.623746 | + | 0.781627i | \(0.285610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.4863 | 1.39612 | 0.698058 | − | 0.716042i | \(-0.254048\pi\) | ||||
0.698058 | + | 0.716042i | \(0.254048\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.72141 | −0.160640 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0732 | −0.945481 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.0471 | −0.995899 | −0.497950 | − | 0.867206i | \(-0.665914\pi\) | ||||
−0.497950 | + | 0.867206i | \(0.665914\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 54.9530 | 3.19949 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.85623 | 0.223012 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.8731 | 1.54894 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.49017 | 0.142587 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.1334 | 1.14908 | 0.574538 | − | 0.818478i | \(-0.305182\pi\) | ||||
0.574538 | + | 0.818478i | \(0.305182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.96338 | −0.508266 | −0.254133 | − | 0.967169i | \(-0.581790\pi\) | ||||
−0.254133 | + | 0.967169i | \(0.581790\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.6222 | 1.10911 | 0.554556 | − | 0.832146i | \(-0.312888\pi\) | ||||
0.554556 | + | 0.832146i | \(0.312888\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.8642 | 1.22801 | 0.614007 | − | 0.789300i | \(-0.289557\pi\) | ||||
0.614007 | + | 0.789300i | \(0.289557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.0785 | −1.18017 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.05351 | 0.225543 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −31.9740 | −1.77360 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.8067 | 2.02922 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.87451 | −0.322892 | −0.161446 | − | 0.986882i | \(-0.551616\pi\) | ||||
−0.161446 | + | 0.986882i | \(0.551616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −39.3504 | −2.14994 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.2561 | −1.43026 | −0.715132 | − | 0.698990i | \(-0.753633\pi\) | ||||
−0.715132 | + | 0.698990i | \(0.753633\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.0785 | −1.14147 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44.4418 | 2.39963 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.5776 | 0.889935 | 0.444967 | − | 0.895547i | \(-0.353215\pi\) | ||||
0.444967 | + | 0.895547i | \(0.353215\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0535 | −0.752267 | −0.376134 | − | 0.926565i | \(-0.622747\pi\) | ||||
−0.376134 | + | 0.926565i | \(0.622747\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.3504 | 1.34926 | 0.674632 | − | 0.738154i | \(-0.264302\pi\) | ||||
0.674632 | + | 0.738154i | \(0.264302\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.5241 | 0.664712 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.78306 | 0.146884 | 0.0734422 | − | 0.997299i | \(-0.476602\pi\) | ||||
0.0734422 | + | 0.997299i | \(0.476602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.27184 | −0.0669389 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.252298 | −0.0132059 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.47652 | −0.285872 | −0.142936 | − | 0.989732i | \(-0.545654\pi\) | ||||
−0.142936 | + | 0.989732i | \(0.545654\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −48.1517 | −2.49991 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1786 | −0.578804 | −0.289402 | − | 0.957208i | \(-0.593456\pi\) | ||||
−0.289402 | + | 0.957208i | \(0.593456\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.2955 | 1.56030 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.6354 | 0.803137 | 0.401569 | − | 0.915829i | \(-0.368465\pi\) | ||||
0.401569 | + | 0.915829i | \(0.368465\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.7125 | 0.802870 | 0.401435 | − | 0.915888i | \(-0.368512\pi\) | ||||
0.401435 | + | 0.915888i | \(0.368512\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −47.1374 | −2.40234 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.215842 | −0.0109436 | −0.00547182 | − | 0.999985i | \(-0.501742\pi\) | ||||
−0.00547182 | + | 0.999985i | \(0.501742\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.962718 | 0.0486868 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.1320 | 1.26453 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.870538 | −0.0436910 | −0.0218455 | − | 0.999761i | \(-0.506954\pi\) | ||||
−0.0218455 | + | 0.999761i | \(0.506954\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.962718 | −0.0480759 | −0.0240379 | − | 0.999711i | \(-0.507652\pi\) | ||||
−0.0240379 | + | 0.999711i | \(0.507652\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.2955 | 1.50912 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.5923 | 1.46684 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.2420 | −0.803113 | −0.401557 | − | 0.915834i | \(-0.631531\pi\) | ||||
−0.401557 | + | 0.915834i | \(0.631531\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −72.6369 | −3.57423 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.80133 | 0.235688 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.5250 | 0.758444 | 0.379222 | − | 0.925306i | \(-0.376192\pi\) | ||||
0.379222 | + | 0.925306i | \(0.376192\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.246374 | 0.0120075 | 0.00600377 | − | 0.999982i | \(-0.498089\pi\) | ||||
0.00600377 | + | 0.999982i | \(0.498089\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.98238 | −0.387202 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.29150 | −0.159287 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.50447 | 0.265141 | 0.132571 | − | 0.991174i | \(-0.457677\pi\) | ||||
0.132571 | + | 0.991174i | \(0.457677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.62499 | 0.462547 | 0.231274 | − | 0.972889i | \(-0.425711\pi\) | ||||
0.231274 | + | 0.972889i | \(0.425711\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.21048 | 0.201415 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6928 | 0.605794 | 0.302897 | − | 0.953023i | \(-0.402046\pi\) | ||||
0.302897 | + | 0.953023i | \(0.402046\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.2955 | 1.43938 | 0.719691 | − | 0.694295i | \(-0.244284\pi\) | ||||
0.719691 | + | 0.694295i | \(0.244284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 65.7739 | 3.11798 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.4067 | 0.821471 | 0.410736 | − | 0.911755i | \(-0.365272\pi\) | ||||
0.410736 | + | 0.911755i | \(0.365272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.51519 | −0.0713476 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 67.7490 | 3.17612 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.3464 | −1.51310 | −0.756550 | − | 0.653935i | \(-0.773117\pi\) | ||||
−0.756550 | + | 0.653935i | \(0.773117\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.2302 | 1.82713 | 0.913567 | − | 0.406688i | \(-0.133316\pi\) | ||||
0.913567 | + | 0.406688i | \(0.133316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.7007 | −1.61268 | −0.806340 | − | 0.591452i | \(-0.798555\pi\) | ||||
−0.806340 | + | 0.591452i | \(0.798555\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.9079 | 1.01378 | 0.506889 | − | 0.862012i | \(-0.330796\pi\) | ||||
0.506889 | + | 0.862012i | \(0.330796\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 52.0133 | 2.40175 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.9621 | 0.687956 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.9112 | −1.60184 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −42.0079 | −1.91939 | −0.959696 | − | 0.281041i | \(-0.909320\pi\) | ||||
−0.959696 | + | 0.281041i | \(0.909320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.5321 | −1.93930 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.8459 | 0.719525 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.89020 | −0.0856532 | −0.0428266 | − | 0.999083i | \(-0.513636\pi\) | ||||
−0.0428266 | + | 0.999083i | \(0.513636\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.8562 | 0.805841 | 0.402920 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402920 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.56334 | 0.340636 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.5544 | −0.742566 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1227 | −0.542687 | −0.271344 | − | 0.962483i | \(-0.587468\pi\) | ||||
−0.271344 | + | 0.962483i | \(0.587468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.3740 | −1.39890 | −0.699449 | − | 0.714683i | \(-0.746571\pi\) | ||||
−0.699449 | + | 0.714683i | \(0.746571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.08748 | 0.359888 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.0222 | −0.577201 | −0.288600 | − | 0.957450i | \(-0.593190\pi\) | ||||
−0.288600 | + | 0.957450i | \(0.593190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.333487 | 0.0147526 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.5776 | 0.730498 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.4927 | 0.901270 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.14708 | 0.0502545 | 0.0251272 | − | 0.999684i | \(-0.492001\pi\) | ||||
0.0251272 | + | 0.999684i | \(0.492001\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.4314 | −1.59303 | −0.796517 | − | 0.604616i | \(-0.793326\pi\) | ||||
−0.796517 | + | 0.604616i | \(0.793326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.56334 | 0.329464 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.17773 | 0.0943282 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.22727 | 0.0530597 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 43.5250 | 1.87475 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.0642 | −0.948615 | −0.474308 | − | 0.880359i | \(-0.657302\pi\) | ||||
−0.474308 | + | 0.880359i | \(0.657302\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 41.0732 | 1.75938 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8942 | 1.40645 | 0.703227 | − | 0.710966i | \(-0.251742\pi\) | ||||
0.703227 | + | 0.710966i | \(0.251742\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.0785 | 1.40919 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.2195 | −1.41264 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.7046 | 0.580683 | 0.290342 | − | 0.956923i | \(-0.406231\pi\) | ||||
0.290342 | + | 0.956923i | \(0.406231\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.5045 | −0.909542 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.52496 | −0.148559 | −0.0742797 | − | 0.997237i | \(-0.523666\pi\) | ||||
−0.0742797 | + | 0.997237i | \(0.523666\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −72.7936 | −3.06245 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.3131 | −0.935413 | −0.467707 | − | 0.883884i | \(-0.654920\pi\) | ||||
−0.467707 | + | 0.883884i | \(0.654920\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.7935 | −0.619088 | −0.309544 | − | 0.950885i | \(-0.600176\pi\) | ||||
−0.309544 | + | 0.950885i | \(0.600176\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.29150 | −0.345780 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.6968 | 1.31955 | 0.659777 | − | 0.751461i | \(-0.270651\pi\) | ||||
0.659777 | + | 0.751461i | \(0.270651\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.34640 | −0.263293 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.8093 | −1.11033 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.2080 | 0.916622 | 0.458311 | − | 0.888792i | \(-0.348455\pi\) | ||||
0.458311 | + | 0.888792i | \(0.348455\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.0785 | 1.36298 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.7504 | 0.687857 | 0.343928 | − | 0.938996i | \(-0.388242\pi\) | ||||
0.343928 | + | 0.938996i | \(0.388242\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.9137 | 0.693395 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.5830 | 1.57646 | 0.788229 | − | 0.615381i | \(-0.210998\pi\) | ||||
0.788229 | + | 0.615381i | \(0.210998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5308 | 0.755886 | 0.377943 | − | 0.925829i | \(-0.376632\pi\) | ||||
0.377943 | + | 0.925829i | \(0.376632\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.8587 | 0.563437 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.5138 | −0.507920 | −0.253960 | − | 0.967215i | \(-0.581733\pi\) | ||||
−0.253960 | + | 0.967215i | \(0.581733\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.4535 | −1.19156 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.3955 | 1.30844 | 0.654221 | − | 0.756303i | \(-0.272997\pi\) | ||||
0.654221 | + | 0.756303i | \(0.272997\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.3367 | −0.657692 | −0.328846 | − | 0.944384i | \(-0.606660\pi\) | ||||
−0.328846 | + | 0.944384i | \(0.606660\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.1007 | −0.727528 | −0.363764 | − | 0.931491i | \(-0.618509\pi\) | ||||
−0.363764 | + | 0.931491i | \(0.618509\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −86.9399 | −3.48317 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.29150 | 0.0916601 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.6182 | −0.423377 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.1381 | 1.47844 | 0.739221 | − | 0.673463i | \(-0.235194\pi\) | ||||
0.739221 | + | 0.673463i | \(0.235194\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.0286 | 0.715444 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −62.5570 | −2.47860 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.1091 | −1.07074 | −0.535372 | − | 0.844616i | \(-0.679829\pi\) | ||||
−0.535372 | + | 0.844616i | \(0.679829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.4235 | −0.726550 | −0.363275 | − | 0.931682i | \(-0.618341\pi\) | ||||
−0.363275 | + | 0.931682i | \(0.618341\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.6276 | −1.71518 | −0.857588 | − | 0.514337i | \(-0.828038\pi\) | ||||
−0.857588 | + | 0.514337i | \(0.828038\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.4418 | −1.58748 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.76201 | 0.108086 | 0.0540428 | − | 0.998539i | \(-0.482789\pi\) | ||||
0.0540428 | + | 0.998539i | \(0.482789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.7204 | 1.47386 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.4320 | −1.65292 | −0.826459 | − | 0.562997i | \(-0.809648\pi\) | ||||
−0.826459 | + | 0.562997i | \(0.809648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1276 | 1.36631 | 0.683153 | − | 0.730275i | \(-0.260608\pi\) | ||||
0.683153 | + | 0.730275i | \(0.260608\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 73.9727 | 2.86854 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.85623 | 0.304195 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.83260 | −0.0707467 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.9843 | 0.770338 | 0.385169 | − | 0.922846i | \(-0.374143\pi\) | ||||
0.385169 | + | 0.922846i | \(0.374143\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.0864 | −1.34848 | −0.674240 | − | 0.738513i | \(-0.735528\pi\) | ||||
−0.674240 | + | 0.738513i | \(0.735528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.9451 | −0.803799 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.51519 | −0.364089 | −0.182044 | − | 0.983290i | \(-0.558271\pi\) | ||||
−0.182044 | + | 0.983290i | \(0.558271\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.5882 | −0.672012 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.5321 | 1.46796 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.14238 | −0.119542 | −0.0597708 | − | 0.998212i | \(-0.519037\pi\) | ||||
−0.0597708 | + | 0.998212i | \(0.519037\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.5830 | 0.553165 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.543677 | 0.0205932 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.5555 | −1.26737 | −0.633687 | − | 0.773590i | \(-0.718459\pi\) | ||||
−0.633687 | + | 0.773590i | \(0.718459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46.4392 | −1.75149 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.6900 | −0.402040 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.95090 | 0.223491 | 0.111745 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111745 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.85623 | 0.294218 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.7204 | 1.41066 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.9348 | −0.556973 | −0.278486 | − | 0.960440i | \(-0.589833\pi\) | ||||
−0.278486 | + | 0.960440i | \(0.589833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.9123 | −0.816058 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −65.1400 | −2.41924 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.1783 | 1.08216 | 0.541081 | − | 0.840970i | \(-0.318015\pi\) | ||||
0.541081 | + | 0.840970i | \(0.318015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.36865 | −0.198567 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.21789 | 0.340470 | 0.170235 | − | 0.985403i | \(-0.445547\pi\) | ||||
0.170235 | + | 0.985403i | \(0.445547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.9593 | 1.06673 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.6900 | −1.57038 | −0.785189 | − | 0.619256i | \(-0.787434\pi\) | ||||
−0.785189 | + | 0.619256i | \(0.787434\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.2848 | −0.817548 | −0.408774 | − | 0.912636i | \(-0.634044\pi\) | ||||
−0.408774 | + | 0.912636i | \(0.634044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.3308 | 0.561678 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.62221 | −0.0592743 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.56268 | 0.202985 | 0.101493 | − | 0.994836i | \(-0.467638\pi\) | ||||
0.101493 | + | 0.994836i | \(0.467638\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.6133 | 0.386256 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.3052 | 0.665315 | 0.332658 | − | 0.943048i | \(-0.392055\pi\) | ||||
0.332658 | + | 0.943048i | \(0.392055\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.9137 | −0.758121 | −0.379061 | − | 0.925372i | \(-0.623753\pi\) | ||||
−0.379061 | + | 0.925372i | \(0.623753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −54.2905 | −1.96545 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.1257 | 2.09880 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.51241 | −0.0545390 | −0.0272695 | − | 0.999628i | \(-0.508681\pi\) | ||||
−0.0272695 | + | 0.999628i | \(0.508681\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.3662 | 1.34397 | 0.671984 | − | 0.740566i | \(-0.265443\pi\) | ||||
0.671984 | + | 0.740566i | \(0.265443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −65.1400 | −2.33990 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.37779 | 0.0851932 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.21694 | −0.329808 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 78.7936 | 2.81226 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.5256 | 0.909890 | 0.454945 | − | 0.890520i | \(-0.349659\pi\) | ||||
0.454945 | + | 0.890520i | \(0.349659\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 96.2185 | 3.42114 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.63393 | 0.0935337 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.7764 | 1.05473 | 0.527367 | − | 0.849637i | \(-0.323179\pi\) | ||||
0.527367 | + | 0.849637i | \(0.323179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.35315 | −0.260136 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.185675 | 0.00655232 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.5687 | 0.619215 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.6379 | 1.74518 | 0.872588 | − | 0.488457i | \(-0.162440\pi\) | ||||
0.872588 | + | 0.488457i | \(0.162440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.8538 | 1.61015 | 0.805073 | − | 0.593176i | \(-0.202126\pi\) | ||||
0.805073 | + | 0.593176i | \(0.202126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 80.2927 | 2.81253 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.4800 | −0.821460 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.5138 | 1.13474 | 0.567370 | − | 0.823463i | \(-0.307961\pi\) | ||||
0.567370 | + | 0.823463i | \(0.307961\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.41163 | −0.188638 | −0.0943189 | − | 0.995542i | \(-0.530067\pi\) | ||||
−0.0943189 | + | 0.995542i | \(0.530067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.2384 | 0.425572 | 0.212786 | − | 0.977099i | \(-0.431746\pi\) | ||||
0.212786 | + | 0.977099i | \(0.431746\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.6169 | 1.44541 | 0.722706 | − | 0.691155i | \(-0.242898\pi\) | ||||
0.722706 | + | 0.691155i | \(0.242898\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.6175 | −0.541115 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.51519 | −0.0524354 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.4525 | −1.25848 | −0.629241 | − | 0.777210i | \(-0.716634\pi\) | ||||
−0.629241 | + | 0.777210i | \(0.716634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.7204 | 1.12829 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.81952 | −0.234598 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3184 | −0.629429 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0294 | −0.378084 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.2561 | 0.898993 | 0.449497 | − | 0.893282i | \(-0.351603\pi\) | ||||
0.449497 | + | 0.893282i | \(0.351603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.1463 | 0.619867 | 0.309934 | − | 0.950758i | \(-0.399693\pi\) | ||||
0.309934 | + | 0.950758i | \(0.399693\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.1374 | 1.06239 | 0.531197 | − | 0.847248i | \(-0.321742\pi\) | ||||
0.531197 | + | 0.847248i | \(0.321742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.9240 | −0.644182 | −0.322091 | − | 0.946709i | \(-0.604386\pi\) | ||||
−0.322091 | + | 0.946709i | \(0.604386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 68.8168 | 2.33984 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.4955 | −0.627418 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.6222 | −1.41031 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −57.8274 | −1.95492 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.0471 | −1.18346 | −0.591729 | − | 0.806137i | \(-0.701554\pi\) | ||||
−0.591729 | + | 0.806137i | \(0.701554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.1600 | 1.31933 | 0.659667 | − | 0.751558i | \(-0.270697\pi\) | ||||
0.659667 | + | 0.751558i | \(0.270697\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.8548 | 0.903737 | 0.451869 | − | 0.892084i | \(-0.350758\pi\) | ||||
0.451869 | + | 0.892084i | \(0.350758\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.1139 | −0.608205 | −0.304102 | − | 0.952639i | \(-0.598357\pi\) | ||||
−0.304102 | + | 0.952639i | \(0.598357\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.8302 | −0.799239 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.1593 | −1.07617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.3593 | −1.08165 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 61.7204 | 2.05849 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.61963 | 0.320476 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.06423 | −0.201582 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.95553 | −0.297363 | −0.148682 | − | 0.988885i | \(-0.547503\pi\) | ||||
−0.148682 | + | 0.988885i | \(0.547503\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.89008 | 0.228278 | 0.114139 | − | 0.993465i | \(-0.463589\pi\) | ||||
0.114139 | + | 0.993465i | \(0.463589\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.53347 | −0.116941 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.8588 | −1.64648 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.0779 | −0.497373 | −0.248687 | − | 0.968584i | \(-0.579999\pi\) | ||||
−0.248687 | + | 0.968584i | \(0.579999\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.2472 | 0.436037 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 91.4506 | 3.00688 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.6717 | −0.940690 | −0.470345 | − | 0.882483i | \(-0.655870\pi\) | ||||
−0.470345 | + | 0.882483i | \(0.655870\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −68.3037 | −2.23856 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.41699 | 0.307969 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.0079 | 1.04565 | 0.522827 | − | 0.852439i | \(-0.324877\pi\) | ||||
0.522827 | + | 0.852439i | \(0.324877\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.8587 | 0.451781 | 0.225891 | − | 0.974153i | \(-0.427471\pi\) | ||||
0.225891 | + | 0.974153i | \(0.427471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.564731 | 0.0183902 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.8080 | −1.32608 | −0.663040 | − | 0.748584i | \(-0.730734\pi\) | ||||
−0.663040 | + | 0.748584i | \(0.730734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.266864 | −0.00866277 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.74181 | −0.153602 | −0.0768011 | − | 0.997046i | \(-0.524471\pi\) | ||||
−0.0768011 | + | 0.997046i | \(0.524471\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.9714 | −0.581541 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.2481 | 0.750721 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7204 | 0.990981 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.1569 | 0.745448 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.1517 | −0.969614 | −0.484807 | − | 0.874621i | \(-0.661110\pi\) | ||||
−0.484807 | + | 0.874621i | \(0.661110\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.6035 | −1.04630 | −0.523148 | − | 0.852242i | \(-0.675242\pi\) | ||||
−0.523148 | + | 0.852242i | \(0.675242\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.2758 | −0.617954 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.4349 | −1.80551 | −0.902757 | − | 0.430152i | \(-0.858460\pi\) | ||||
−0.902757 | + | 0.430152i | \(0.858460\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.4053 | −1.54704 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.4838 | 1.70587 | 0.852934 | − | 0.522018i | \(-0.174821\pi\) | ||||
0.852934 | + | 0.522018i | \(0.174821\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.6133 | −0.720519 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.57655 | −0.177324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.8838 | 0.790461 | 0.395231 | − | 0.918582i | \(-0.370665\pi\) | ||||
0.395231 | + | 0.918582i | \(0.370665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.6080 | 1.00204 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6365 | 0.906928 | 0.453464 | − | 0.891275i | \(-0.350188\pi\) | ||||
0.453464 | + | 0.891275i | \(0.350188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3312.2.a.bg.1.2 | 4 | ||
3.2 | odd | 2 | 3312.2.a.bh.1.4 | 4 | |||
4.3 | odd | 2 | 1656.2.a.o.1.1 | ✓ | 4 | ||
12.11 | even | 2 | 1656.2.a.p.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1656.2.a.o.1.1 | ✓ | 4 | 4.3 | odd | 2 | ||
1656.2.a.p.1.3 | yes | 4 | 12.11 | even | 2 | ||
3312.2.a.bg.1.2 | 4 | 1.1 | even | 1 | trivial | ||
3312.2.a.bh.1.4 | 4 | 3.2 | odd | 2 |