Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 4x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 475) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.37720\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | ||||||||
\(3\) | 2.37720 | 1.37248 | 0.686239 | − | 0.727376i | \(-0.259260\pi\) | ||||
0.686239 | + | 0.727376i | \(0.259260\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.377203 | −0.142569 | −0.0712846 | − | 0.997456i | \(-0.522710\pi\) | ||||
−0.0712846 | + | 0.997456i | \(0.522710\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.65109 | 0.883698 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.37720 | 0.415242 | 0.207621 | − | 0.978209i | \(-0.433428\pi\) | ||||
0.207621 | + | 0.978209i | \(0.433428\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82167 | −0.782591 | −0.391295 | − | 0.920265i | \(-0.627973\pi\) | ||||
−0.391295 | + | 0.920265i | \(0.627973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.37720 | −1.54670 | −0.773349 | − | 0.633980i | \(-0.781420\pi\) | ||||
−0.773349 | + | 0.633980i | \(0.781420\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.896688 | −0.195673 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.19887 | 1.29255 | 0.646277 | − | 0.763103i | \(-0.276325\pi\) | ||||
0.646277 | + | 0.763103i | \(0.276325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.829422 | −0.159622 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.37720 | −0.627131 | −0.313565 | − | 0.949567i | \(-0.601524\pi\) | ||||
−0.313565 | + | 0.949567i | \(0.601524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.48052 | −0.445514 | −0.222757 | − | 0.974874i | \(-0.571506\pi\) | ||||
−0.222757 | + | 0.974874i | \(0.571506\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.27389 | 0.569911 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.58383 | −0.917976 | −0.458988 | − | 0.888443i | \(-0.651788\pi\) | ||||
−0.458988 | + | 0.888443i | \(0.651788\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.70769 | −1.07409 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.50106 | 1.32764 | 0.663821 | − | 0.747891i | \(-0.268934\pi\) | ||||
0.663821 | + | 0.747891i | \(0.268934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1522 | −1.85319 | −0.926593 | − | 0.376065i | \(-0.877277\pi\) | ||||
−0.926593 | + | 0.376065i | \(0.877277\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.87826 | −1.00330 | −0.501649 | − | 0.865071i | \(-0.667273\pi\) | ||||
−0.501649 | + | 0.865071i | \(0.667273\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.85772 | −0.979674 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.1599 | −2.12281 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.5478 | −1.58621 | −0.793105 | − | 0.609085i | \(-0.791537\pi\) | ||||
−0.793105 | + | 0.609085i | \(0.791537\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.37720 | −0.314868 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.05659 | −0.788501 | −0.394251 | − | 0.919003i | \(-0.628996\pi\) | ||||
−0.394251 | + | 0.919003i | \(0.628996\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.02830 | 0.643807 | 0.321904 | − | 0.946772i | \(-0.395677\pi\) | ||||
0.321904 | + | 0.946772i | \(0.395677\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.22717 | 0.394262 | 0.197131 | − | 0.980377i | \(-0.436838\pi\) | ||||
0.197131 | + | 0.980377i | \(0.436838\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.7360 | 1.77400 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.30219 | 0.273219 | 0.136610 | − | 0.990625i | \(-0.456379\pi\) | ||||
0.136610 | + | 0.990625i | \(0.456379\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.19887 | 0.374400 | 0.187200 | − | 0.982322i | \(-0.440059\pi\) | ||||
0.187200 | + | 0.982322i | \(0.440059\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.519485 | −0.0592008 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.71836 | 0.755874 | 0.377937 | − | 0.925831i | \(-0.376634\pi\) | ||||
0.377937 | + | 0.925831i | \(0.376634\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.92498 | −1.10278 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.2165 | 1.99952 | 0.999760 | − | 0.0218996i | \(-0.00697141\pi\) | ||||
0.999760 | + | 0.0218996i | \(0.00697141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.02830 | −0.860724 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.50106 | 0.159112 | 0.0795561 | − | 0.996830i | \(-0.474650\pi\) | ||||
0.0795561 | + | 0.996830i | \(0.474650\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.06434 | 0.111573 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.89669 | −0.611458 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7827 | 1.19635 | 0.598176 | − | 0.801365i | \(-0.295892\pi\) | ||||
0.598176 | + | 0.801365i | \(0.295892\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.65109 | 0.366949 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.18820 | −0.914260 | −0.457130 | − | 0.889400i | \(-0.651123\pi\) | ||||
−0.457130 | + | 0.889400i | \(0.651123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.47277 | −0.933379 | −0.466690 | − | 0.884421i | \(-0.654553\pi\) | ||||
−0.466690 | + | 0.884421i | \(0.654553\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.3510 | −1.48404 | −0.742020 | − | 0.670378i | \(-0.766132\pi\) | ||||
−0.742020 | + | 0.670378i | \(0.766132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.7643 | −1.60573 | −0.802863 | − | 0.596163i | \(-0.796691\pi\) | ||||
−0.802863 | + | 0.596163i | \(0.796691\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.2739 | −1.25990 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3305 | 1.25403 | 0.627013 | − | 0.779009i | \(-0.284277\pi\) | ||||
0.627013 | + | 0.779009i | \(0.284277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.48052 | −0.691574 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.40550 | 0.220512 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.10331 | −0.827574 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.2087 | 1.82216 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.04672 | −0.270353 | −0.135176 | − | 0.990822i | \(-0.543160\pi\) | ||||
−0.135176 | + | 0.990822i | \(0.543160\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −28.8881 | −2.54346 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.70769 | 0.760794 | 0.380397 | − | 0.924823i | \(-0.375787\pi\) | ||||
0.380397 | + | 0.924823i | \(0.375787\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.377203 | 0.0327076 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.59450 | −0.563406 | −0.281703 | − | 0.959502i | \(-0.590899\pi\) | ||||
−0.281703 | + | 0.959502i | \(0.590899\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1677 | 0.862409 | 0.431205 | − | 0.902254i | \(-0.358089\pi\) | ||||
0.431205 | + | 0.902254i | \(0.358089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.3510 | −1.37701 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.88601 | −0.324965 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.3022 | −1.34458 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.54003 | −0.453857 | −0.226929 | − | 0.973911i | \(-0.572868\pi\) | ||||
−0.226929 | + | 0.973911i | \(0.572868\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12386 | −0.416974 | −0.208487 | − | 0.978025i | \(-0.566854\pi\) | ||||
−0.208487 | + | 0.978025i | \(0.566854\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.9066 | −1.36681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.7643 | −1.57736 | −0.788681 | − | 0.614803i | \(-0.789235\pi\) | ||||
−0.788681 | + | 0.614803i | \(0.789235\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27.4514 | −2.17704 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.33823 | −0.184279 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.5195 | 1.05893 | 0.529464 | − | 0.848332i | \(-0.322393\pi\) | ||||
0.529464 | + | 0.848332i | \(0.322393\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.1054 | 1.01413 | 0.507065 | − | 0.861908i | \(-0.330731\pi\) | ||||
0.507065 | + | 0.861908i | \(0.330731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.03817 | −0.387551 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.65109 | −0.202734 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.48827 | −0.113151 | −0.0565754 | − | 0.998398i | \(-0.518018\pi\) | ||||
−0.0565754 | + | 0.998398i | \(0.518018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.3977 | −1.08220 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.1132 | 1.27910 | 0.639550 | − | 0.768750i | \(-0.279121\pi\) | ||||
0.639550 | + | 0.768750i | \(0.279121\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.73891 | −0.426569 | −0.213285 | − | 0.976990i | \(-0.568416\pi\) | ||||
−0.213285 | + | 0.976990i | \(0.568416\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9533 | 0.883612 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.78270 | −0.642255 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.312860 | 0.0227572 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.3948 | −1.62043 | −0.810216 | − | 0.586131i | \(-0.800650\pi\) | ||||
−0.810216 | + | 0.586131i | \(0.800650\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.3687 | 1.53815 | 0.769075 | − | 0.639159i | \(-0.220717\pi\) | ||||
0.769075 | + | 0.639159i | \(0.220717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.11399 | −0.0793682 | −0.0396841 | − | 0.999212i | \(-0.512635\pi\) | ||||
−0.0396841 | + | 0.999212i | \(0.512635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.22505 | 0.157729 | 0.0788647 | − | 0.996885i | \(-0.474870\pi\) | ||||
0.0788647 | + | 0.996885i | \(0.474870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.67164 | 0.541116 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.27389 | 0.0894096 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.4338 | 1.14223 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.37720 | −0.0952631 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.75441 | 0.671521 | 0.335760 | − | 0.941947i | \(-0.391007\pi\) | ||||
0.335760 | + | 0.941947i | \(0.391007\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.47277 | 0.374988 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.935657 | 0.0635166 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.60437 | 0.513856 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.9944 | 1.21043 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.6433 | −1.24845 | −0.624225 | − | 0.781244i | \(-0.714585\pi\) | ||||
−0.624225 | + | 0.781244i | \(0.714585\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.04672 | −0.534080 | −0.267040 | − | 0.963686i | \(-0.586046\pi\) | ||||
−0.267040 | + | 0.963686i | \(0.586046\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1415 | 1.33099 | 0.665493 | − | 0.746404i | \(-0.268221\pi\) | ||||
0.665493 | + | 0.746404i | \(0.268221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.23492 | −0.0812518 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.73386 | 0.113589 | 0.0567945 | − | 0.998386i | \(-0.481912\pi\) | ||||
0.0567945 | + | 0.998386i | \(0.481912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.9709 | 1.03742 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3150 | 1.18470 | 0.592349 | − | 0.805682i | \(-0.298201\pi\) | ||||
0.592349 | + | 0.805682i | \(0.298201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.19675 | −0.141505 | −0.0707526 | − | 0.997494i | \(-0.522540\pi\) | ||||
−0.0707526 | + | 0.997494i | \(0.522540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.1054 | −1.35391 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.82167 | 0.179539 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 43.3043 | 2.74430 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.6716 | 0.862946 | 0.431473 | − | 0.902126i | \(-0.357994\pi\) | ||||
0.431473 | + | 0.902126i | \(0.357994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.53711 | 0.536723 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.4904 | −1.77718 | −0.888591 | − | 0.458701i | \(-0.848315\pi\) | ||||
−0.888591 | + | 0.458701i | \(0.848315\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.10624 | 0.130875 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.95328 | −0.554194 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.36945 | 0.331095 | 0.165547 | − | 0.986202i | \(-0.447061\pi\) | ||||
0.165547 | + | 0.986202i | \(0.447061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.56833 | 0.218378 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.06727 | 0.430899 | 0.215449 | − | 0.976515i | \(-0.430878\pi\) | ||||
0.215449 | + | 0.976515i | \(0.430878\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.6970 | −1.31800 | −0.659000 | − | 0.752143i | \(-0.729020\pi\) | ||||
−0.659000 | + | 0.752143i | \(0.729020\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.53016 | 0.153132 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.1132 | −1.50891 | −0.754453 | − | 0.656355i | \(-0.772098\pi\) | ||||
−0.754453 | + | 0.656355i | \(0.772098\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.57608 | −0.393699 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0411 | −0.599001 | −0.299501 | − | 0.954096i | \(-0.596820\pi\) | ||||
−0.299501 | + | 0.954096i | \(0.596820\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.9143 | −1.24323 | −0.621613 | − | 0.783324i | \(-0.713522\pi\) | ||||
−0.621613 | + | 0.783324i | \(0.713522\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.20662 | −0.189281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.6687 | 1.39228 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.0099 | 1.64197 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.818748 | 0.0478318 | 0.0239159 | − | 0.999714i | \(-0.492387\pi\) | ||||
0.0239159 | + | 0.999714i | \(0.492387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.14228 | −0.0662819 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.4912 | −1.01154 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.58383 | 0.264207 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.8422 | −1.25480 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.44447 | −0.424878 | −0.212439 | − | 0.977174i | \(-0.568141\pi\) | ||||
−0.212439 | + | 0.977174i | \(0.568141\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.5187 | −1.28104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.956204 | 0.0542213 | 0.0271107 | − | 0.999632i | \(-0.491369\pi\) | ||||
0.0271107 | + | 0.999632i | \(0.491369\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.98158 | −0.338099 | −0.169049 | − | 0.985608i | \(-0.554070\pi\) | ||||
−0.169049 | + | 0.985608i | \(0.554070\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.6511 | −1.27221 | −0.636106 | − | 0.771602i | \(-0.719456\pi\) | ||||
−0.636106 | + | 0.771602i | \(0.719456\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.65109 | −0.260411 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.4925 | −2.03681 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.37720 | 0.354837 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −39.8521 | −2.20383 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.59450 | 0.143039 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.16283 | −0.228810 | −0.114405 | − | 0.993434i | \(-0.536496\pi\) | ||||
−0.114405 | + | 0.993434i | \(0.536496\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.8032 | −0.811213 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0304 | 0.982180 | 0.491090 | − | 0.871109i | \(-0.336599\pi\) | ||||
0.491090 | + | 0.871109i | \(0.336599\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.6893 | 1.72112 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.41617 | −0.184996 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.22717 | 0.282241 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.43380 | 0.399067 | 0.199534 | − | 0.979891i | \(-0.436057\pi\) | ||||
0.199534 | + | 0.979891i | \(0.436057\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.9194 | 1.17332 | 0.586658 | − | 0.809835i | \(-0.300443\pi\) | ||||
0.586658 | + | 0.809835i | \(0.300443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.34036 | 0.124919 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.3695 | −0.551910 | −0.275955 | − | 0.961171i | \(-0.588994\pi\) | ||||
−0.275955 | + | 0.961171i | \(0.588994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.71836 | 0.302648 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.9893 | 1.26611 | 0.633054 | − | 0.774108i | \(-0.281801\pi\) | ||||
0.633054 | + | 0.774108i | \(0.281801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.6404 | −1.13583 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.0275 | 1.82842 | 0.914210 | − | 0.405240i | \(-0.132812\pi\) | ||||
0.914210 | + | 0.405240i | \(0.132812\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.5371 | 1.17323 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.35586 | 0.226145 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.8003 | −1.59478 | −0.797390 | − | 0.603464i | \(-0.793787\pi\) | ||||
−0.797390 | + | 0.603464i | \(0.793787\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.52936 | 0.490787 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.671640 | −0.0344998 | −0.0172499 | − | 0.999851i | \(-0.505491\pi\) | ||||
−0.0172499 | + | 0.999851i | \(0.505491\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.24267 | −0.371053 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.1805 | −1.54215 | −0.771075 | − | 0.636745i | \(-0.780280\pi\) | ||||
−0.771075 | + | 0.636745i | \(0.780280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.2165 | −1.63766 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.5109 | −1.59767 | −0.798834 | − | 0.601552i | \(-0.794549\pi\) | ||||
−0.798834 | + | 0.601552i | \(0.794549\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.5315 | −1.99919 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.6999 | 1.04417 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5761 | 0.631175 | 0.315588 | − | 0.948896i | \(-0.397798\pi\) | ||||
0.315588 | + | 0.948896i | \(0.397798\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.896688 | 0.0448905 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.6036 | 1.22864 | 0.614322 | − | 0.789056i | \(-0.289430\pi\) | ||||
0.614322 | + | 0.789056i | \(0.289430\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.99920 | 0.348655 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.69006 | −0.381182 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6666 | 0.675770 | 0.337885 | − | 0.941187i | \(-0.390289\pi\) | ||||
0.337885 | + | 0.941187i | \(0.390289\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.6765 | −0.773263 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.28456 | 0.112416 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.1706 | 1.18364 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6893 | −0.619911 | −0.309956 | − | 0.950751i | \(-0.600314\pi\) | ||||
−0.309956 | + | 0.950751i | \(0.600314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.1826 | 1.42227 | 0.711136 | − | 0.703055i | \(-0.248181\pi\) | ||||
0.711136 | + | 0.703055i | \(0.248181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.2349 | −0.886612 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.89669 | −0.0917872 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.23784 | −0.446007 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.9816 | 1.44416 | 0.722081 | − | 0.691809i | \(-0.243186\pi\) | ||||
0.722081 | + | 0.691809i | \(0.243186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.76216 | 0.228855 | 0.114427 | − | 0.993432i | \(-0.463497\pi\) | ||||
0.114427 | + | 0.993432i | \(0.463497\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.19887 | −0.296532 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.88601 | −0.328652 | −0.164326 | − | 0.986406i | \(-0.552545\pi\) | ||||
−0.164326 | + | 0.986406i | \(0.552545\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.1805 | −0.865736 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.65109 | 0.411026 | 0.205513 | − | 0.978654i | \(-0.434114\pi\) | ||||
0.205513 | + | 0.978654i | \(0.434114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.1698 | −0.622909 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.63055 | 0.407301 | 0.203650 | − | 0.979044i | \(-0.434719\pi\) | ||||
0.203650 | + | 0.979044i | \(0.434719\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.7077 | 0.551293 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.1805 | −0.572288 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.6092 | 1.33828 | 0.669141 | − | 0.743135i | \(-0.266662\pi\) | ||||
0.669141 | + | 0.743135i | \(0.266662\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.28939 | 0.246888 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.1025 | −1.82119 | −0.910593 | − | 0.413305i | \(-0.864374\pi\) | ||||
−0.910593 | + | 0.413305i | \(0.864374\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.04380 | −0.373827 | −0.186913 | − | 0.982376i | \(-0.559848\pi\) | ||||
−0.186913 | + | 0.982376i | \(0.559848\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0488 | 0.788926 | 0.394463 | − | 0.918912i | \(-0.370931\pi\) | ||||
0.394463 | + | 0.918912i | \(0.370931\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.21730 | −0.0562096 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −46.9837 | −2.16489 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.7360 | −0.769521 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.6142 | −1.40173 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.5478 | −1.03023 | −0.515117 | − | 0.857120i | \(-0.672252\pi\) | ||||
−0.515117 | + | 0.857120i | \(0.672252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7557 | 0.718399 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.55845 | −0.252918 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.5577 | −1.11281 | −0.556407 | − | 0.830910i | \(-0.687820\pi\) | ||||
−0.556407 | + | 0.830910i | \(0.687820\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.1386 | 1.45336 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9298 | 0.764032 | 0.382016 | − | 0.924156i | \(-0.375230\pi\) | ||||
0.382016 | + | 0.924156i | \(0.375230\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.5371 | 0.969983 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.868391 | −0.0389527 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.418295 | −0.0187255 | −0.00936273 | − | 0.999956i | \(-0.502980\pi\) | ||||
−0.00936273 | + | 0.999956i | \(0.502980\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.1543 | 1.39187 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.5993 | −0.561776 | −0.280888 | − | 0.959741i | \(-0.590629\pi\) | ||||
−0.280888 | + | 0.959741i | \(0.590629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.9767 | −0.531906 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8209 | 0.568275 | 0.284138 | − | 0.958784i | \(-0.408293\pi\) | ||||
0.284138 | + | 0.958784i | \(0.408293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.20662 | −0.0533779 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.829422 | 0.0366199 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.47277 | −0.416612 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.53791 | −0.155297 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.3743 | 0.498316 | 0.249158 | − | 0.968463i | \(-0.419846\pi\) | ||||
0.249158 | + | 0.968463i | \(0.419846\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.0948 | 1.44713 | 0.723566 | − | 0.690255i | \(-0.242502\pi\) | ||||
0.723566 | + | 0.690255i | \(0.242502\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.8187 | 0.689075 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.4260 | 0.670698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.0566 | −0.696797 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.9872 | −1.03900 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.6815 | 1.75554 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.44447 | −0.406802 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.4338 | 1.35144 | 0.675722 | − | 0.737156i | \(-0.263832\pi\) | ||||
0.675722 | + | 0.737156i | \(0.263832\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.6425 | −0.585458 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.3460 | −0.998202 | −0.499101 | − | 0.866544i | \(-0.666336\pi\) | ||||
−0.499101 | + | 0.866544i | \(0.666336\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.3305 | 0.568931 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.37720 | 0.143874 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.53418 | −0.107764 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.9229 | −0.674673 | −0.337337 | − | 0.941384i | \(-0.609526\pi\) | ||||
−0.337337 | + | 0.941384i | \(0.609526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.2894 | 1.45029 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.8783 | −0.881481 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.6404 | −1.24919 | −0.624597 | − | 0.780947i | \(-0.714737\pi\) | ||||
−0.624597 | + | 0.780947i | \(0.714737\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.74373 | 0.157222 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.64334 | −0.320426 | −0.160213 | − | 0.987082i | \(-0.551218\pi\) | ||||
−0.160213 | + | 0.987082i | \(0.551218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5577 | 0.441824 | 0.220912 | − | 0.975294i | \(-0.429097\pi\) | ||||
0.220912 | + | 0.975294i | \(0.429097\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −53.2370 | −2.22401 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.9447 | −1.62129 | −0.810645 | − | 0.585538i | \(-0.800883\pi\) | ||||
−0.810645 | + | 0.585538i | \(0.800883\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 50.7976 | 2.11108 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.87131 | −0.285070 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.9036 | −0.658661 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.9992 | −0.453986 | −0.226993 | − | 0.973896i | \(-0.572889\pi\) | ||||
−0.226993 | + | 0.973896i | \(0.572889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.48052 | 0.102208 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.64817 | −0.108931 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.7848 | −1.09992 | −0.549960 | − | 0.835191i | \(-0.685357\pi\) | ||||
−0.549960 | + | 0.835191i | \(0.685357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.28939 | 0.216480 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.44930 | 0.140934 | 0.0704672 | − | 0.997514i | \(-0.477551\pi\) | ||||
0.0704672 | + | 0.997514i | \(0.477551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.0686 | −1.51206 | −0.756030 | − | 0.654537i | \(-0.772863\pi\) | ||||
−0.756030 | + | 0.654537i | \(0.772863\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.55553 | 0.348408 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8732 | −0.603685 | −0.301843 | − | 0.953358i | \(-0.597602\pi\) | ||||
−0.301843 | + | 0.953358i | \(0.597602\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.02830 | 0.122713 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.4082 | 0.785172 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.4671 | 1.63445 | 0.817226 | − | 0.576317i | \(-0.195511\pi\) | ||||
0.817226 | + | 0.576317i | \(0.195511\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.76991 | −0.353063 | −0.176532 | − | 0.984295i | \(-0.556488\pi\) | ||||
−0.176532 | + | 0.984295i | \(0.556488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.0510 | −1.28824 | −0.644119 | − | 0.764926i | \(-0.722776\pi\) | ||||
−0.644119 | + | 0.764926i | \(0.722776\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.14148 | −0.206321 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.566205 | −0.0226845 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.27389 | −0.130747 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.6092 | 1.41983 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.9709 | 0.755220 | 0.377610 | − | 0.925965i | \(-0.376746\pi\) | ||||
0.377610 | + | 0.925965i | \(0.376746\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.1882 | 0.921648 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.3502 | 0.766684 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.10331 | 0.241443 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.3433 | −1.75145 | −0.875727 | − | 0.482806i | \(-0.839617\pi\) | ||||
−0.875727 | + | 0.482806i | \(0.839617\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.9397 | 1.69338 | 0.846688 | − | 0.532090i | \(-0.178593\pi\) | ||||
0.846688 | + | 0.532090i | \(0.178593\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.9864 | 0.707118 | 0.353559 | − | 0.935412i | \(-0.384971\pi\) | ||||
0.353559 | + | 0.935412i | \(0.384971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.34116 | −0.327419 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.22425 | 0.0871751 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.7274 | 0.850260 | 0.425130 | − | 0.905132i | \(-0.360228\pi\) | ||||
0.425130 | + | 0.905132i | \(0.360228\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.48052 | 0.330856 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.8590 | 1.59164 | 0.795821 | − | 0.605532i | \(-0.207040\pi\) | ||||
0.795821 | + | 0.605532i | \(0.207040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.7282 | 1.31188 | 0.655938 | − | 0.754815i | \(-0.272273\pi\) | ||||
0.655938 | + | 0.754815i | \(0.272273\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 42.7763 | 1.66129 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.9349 | −0.810601 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −44.3190 | −1.71347 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.92498 | 0.267336 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0622 | 0.426417 | 0.213209 | − | 0.977007i | \(-0.431609\pi\) | ||||
0.213209 | + | 0.977007i | \(0.431609\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.14711 | 0.236253 | 0.118126 | − | 0.992999i | \(-0.462311\pi\) | ||||
0.118126 | + | 0.992999i | \(0.462311\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.44447 | −0.170563 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.1287 | −0.733013 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.6073 | −0.520669 | −0.260334 | − | 0.965519i | \(-0.583833\pi\) | ||||
−0.260334 | + | 0.965519i | \(0.583833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 47.8804 | 1.82675 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.5840 | 1.24135 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.3043 | 1.53325 | 0.766624 | − | 0.642096i | \(-0.221935\pi\) | ||||
0.766624 | + | 0.642096i | \(0.221935\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.37720 | −0.0523156 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −54.2130 | −2.05346 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.12174 | 0.155898 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.23704 | −0.122261 | −0.0611307 | − | 0.998130i | \(-0.519471\pi\) | ||||
−0.0611307 | + | 0.998130i | \(0.519471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.58383 | 0.210598 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.46582 | 0.130345 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.2370 | 0.760018 | 0.380009 | − | 0.924983i | \(-0.375921\pi\) | ||||
0.380009 | + | 0.924983i | \(0.375921\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.8110 | 0.667965 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.3764 | −0.575851 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 43.5384 | 1.62597 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −47.8804 | −1.78564 | −0.892819 | − | 0.450416i | \(-0.851276\pi\) | ||||
−0.892819 | + | 0.450416i | \(0.851276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.57315 | 0.133071 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.22212 | −0.194213 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.7926 | 0.659890 | 0.329945 | − | 0.944000i | \(-0.392970\pi\) | ||||
0.329945 | + | 0.944000i | \(0.392970\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.3969 | −0.755443 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 77.4968 | 2.86632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.66097 | 0.209093 | 0.104546 | − | 0.994520i | \(-0.466661\pi\) | ||||
0.104546 | + | 0.994520i | \(0.466661\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.44447 | 0.163714 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.59955 | 0.205983 | 0.102991 | − | 0.994682i | \(-0.467159\pi\) | ||||
0.102991 | + | 0.994682i | \(0.467159\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.70769 | 0.246413 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.81663 | 0.213391 | 0.106696 | − | 0.994292i | \(-0.465973\pi\) | ||||
0.106696 | + | 0.994292i | \(0.465973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 48.2936 | 1.76697 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.79045 | 0.211579 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.1797 | 1.50267 | 0.751333 | − | 0.659923i | \(-0.229411\pi\) | ||||
0.751333 | + | 0.659923i | \(0.229411\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.5003 | 1.18438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5208 | 1.21833 | 0.609167 | − | 0.793042i | \(-0.291504\pi\) | ||||
0.609167 | + | 0.793042i | \(0.291504\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.2944 | 0.736641 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.5032 | 1.14199 | 0.570995 | − | 0.820954i | \(-0.306558\pi\) | ||||
0.570995 | + | 0.820954i | \(0.306558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.32353 | 0.228927 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.0897 | 0.617074 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.22425 | −0.0441475 | −0.0220737 | − | 0.999756i | \(-0.507027\pi\) | ||||
−0.0220737 | + | 0.999756i | \(0.507027\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −67.7274 | −2.43914 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.6687 | −1.46275 | −0.731376 | − | 0.681974i | \(-0.761122\pi\) | ||||
−0.731376 | + | 0.681974i | \(0.761122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.00695 | 0.179623 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.50106 | −0.304582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.17058 | 0.113452 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.80113 | 0.100104 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.9525 | −1.42415 | −0.712076 | − | 0.702102i | \(-0.752245\pi\) | ||||
−0.712076 | + | 0.702102i | \(0.752245\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.7643 | 0.454420 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.02830 | −0.178786 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.1882 | −0.503838 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.53791 | 0.160741 | 0.0803705 | − | 0.996765i | \(-0.474390\pi\) | ||||
0.0803705 | + | 0.996765i | \(0.474390\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.8641 | 1.55180 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.97945 | 0.140607 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.40550 | 0.155467 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.8003 | 0.591399 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 55.5958 | 1.95465 | 0.977323 | − | 0.211756i | \(-0.0679183\pi\) | ||||
0.977323 | + | 0.211756i | \(0.0679183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.3326 | −1.48650 | −0.743249 | − | 0.669014i | \(-0.766716\pi\) | ||||
−0.743249 | + | 0.669014i | \(0.766716\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −51.5782 | −1.80893 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.1522 | 0.425150 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.82167 | 0.0985972 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.10543 | −0.108380 | −0.0541902 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541902 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.2002 | −1.57558 | −0.787790 | − | 0.615944i | \(-0.788775\pi\) | ||||
−0.787790 | + | 0.615944i | \(0.788775\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.6503 | −1.23968 | −0.619841 | − | 0.784727i | \(-0.712803\pi\) | ||||
−0.619841 | + | 0.784727i | \(0.712803\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.4330 | −0.640204 | −0.320102 | − | 0.947383i | \(-0.603717\pi\) | ||||
−0.320102 | + | 0.947383i | \(0.603717\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −59.6991 | −2.07094 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.7331 | 1.51526 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.05739 | 0.0711139 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.1805 | 0.489564 | 0.244782 | − | 0.969578i | \(-0.421284\pi\) | ||||
0.244782 | + | 0.969578i | \(0.421284\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5945 | −0.606707 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.8697 | −0.822117 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.43380 | 0.117987 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −49.7176 | −1.70630 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.6134 | −1.18653 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.6639 | −1.46078 | −0.730392 | − | 0.683028i | \(-0.760663\pi\) | ||||
−0.730392 | + | 0.683028i | \(0.760663\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.42392 | 0.0486403 | 0.0243201 | − | 0.999704i | \(-0.492258\pi\) | ||||
0.0243201 | + | 0.999704i | \(0.492258\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.27894 | 0.282474 | 0.141237 | − | 0.989976i | \(-0.454892\pi\) | ||||
0.141237 | + | 0.989976i | \(0.454892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.62280 | −0.259784 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.4154 | 1.03535 | 0.517676 | − | 0.855577i | \(-0.326797\pi\) | ||||
0.517676 | + | 0.855577i | \(0.326797\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 56.2653 | 1.91087 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.25254 | 0.313871 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.10602 | −0.308546 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.2370 | 1.05721 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.8484 | −1.95340 | −0.976700 | − | 0.214608i | \(-0.931153\pi\) | ||||
−0.976700 | + | 0.214608i | \(0.931153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.94633 | 0.0656481 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.4055 | 0.620097 | 0.310049 | − | 0.950721i | \(-0.399655\pi\) | ||||
0.310049 | + | 0.950721i | \(0.399655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.7947 | −0.632492 | −0.316246 | − | 0.948677i | \(-0.602422\pi\) | ||||
−0.316246 | + | 0.948677i | \(0.602422\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.1471 | −0.374283 | −0.187142 | − | 0.982333i | \(-0.559922\pi\) | ||||
−0.187142 | + | 0.982333i | \(0.559922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.14923 | 0.0385440 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.6687 | −0.457919 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.87826 | 0.230172 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −41.5801 | −1.38832 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.37720 | 0.279395 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 73.6425 | 2.45339 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.8967 | 0.362619 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.5598 | 1.28036 | 0.640178 | − | 0.768226i | \(-0.278861\pi\) | ||||
0.640178 | + | 0.768226i | \(0.278861\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.3588 | −0.807930 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.79820 | 0.0595771 | 0.0297885 | − | 0.999556i | \(-0.490517\pi\) | ||||
0.0297885 | + | 0.999556i | \(0.490517\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.0878 | 0.830285 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.28456 | −0.108466 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.4458 | 1.07029 | 0.535144 | − | 0.844761i | \(-0.320257\pi\) | ||||
0.535144 | + | 0.844761i | \(0.320257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.6970 | −0.583136 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.49602 | −0.213819 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.1132 | −0.824825 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.4231 | −0.604443 | −0.302222 | − | 0.953238i | \(-0.597728\pi\) | ||||
−0.302222 | + | 0.953238i | \(0.597728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.85772 | 0.224753 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.27309 | 0.0744176 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.29926 | −0.271125 | −0.135563 | − | 0.990769i | \(-0.543284\pi\) | ||||
−0.135563 | + | 0.990769i | \(0.543284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.2194 | −0.464033 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.6687 | 1.09757 | 0.548784 | − | 0.835964i | \(-0.315091\pi\) | ||||
0.548784 | + | 0.835964i | \(0.315091\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.6970 | 1.71605 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.35103 | 0.0439026 | 0.0219513 | − | 0.999759i | \(-0.493012\pi\) | ||||
0.0219513 | + | 0.999759i | \(0.493012\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.02617 | −0.293002 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −53.8462 | −1.74608 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.70769 | 0.217283 | 0.108642 | − | 0.994081i | \(-0.465350\pi\) | ||||
0.108642 | + | 0.994081i | \(0.465350\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.0566 | −0.357409 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.48746 | 0.0803244 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8470 | −0.801518 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40.6970 | −1.31144 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.5174 | 0.627636 | 0.313818 | − | 0.949483i | \(-0.398392\pi\) | ||||
0.313818 | + | 0.949483i | \(0.398392\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.1599 | 0.487006 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.50669 | 0.272993 | 0.136496 | − | 0.990641i | \(-0.456416\pi\) | ||||
0.136496 | + | 0.990641i | \(0.456416\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.83527 | −0.122953 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.7048 | −0.630411 | −0.315206 | − | 0.949023i | \(-0.602073\pi\) | ||||
−0.315206 | + | 0.949023i | \(0.602073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.06727 | 0.0660701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.4437 | −1.41898 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.4677 | −0.397658 | −0.198829 | − | 0.980034i | \(-0.563714\pi\) | ||||
−0.198829 | + | 0.980034i | \(0.563714\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.16765 | 0.196319 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −75.3297 | −2.39534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.0841 | −0.796822 | −0.398411 | − | 0.917207i | \(-0.630438\pi\) | ||||
−0.398411 | + | 0.917207i | \(0.630438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.89589 | −0.314036 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.8775 | −0.376163 | −0.188082 | − | 0.982153i | \(-0.560227\pi\) | ||||
−0.188082 | + | 0.982153i | \(0.560227\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.63135 | 0.146529 |
(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 | 7600.2.a.cc.1.3 | 3 | ||
4.3 | odd | 2 | 475.2.a.e.1.3 | ✓ | 3 | ||
5.4 | even | 2 | 7600.2.a.bh.1.1 | 3 | |||
12.11 | even | 2 | 4275.2.a.bm.1.1 | 3 | |||
20.3 | even | 4 | 475.2.b.b.324.2 | 6 | |||
20.7 | even | 4 | 475.2.b.b.324.5 | 6 | |||
20.19 | odd | 2 | 475.2.a.g.1.1 | yes | 3 | ||
60.59 | even | 2 | 4275.2.a.ba.1.3 | 3 | |||
76.75 | even | 2 | 9025.2.a.bc.1.1 | 3 | |||
380.379 | even | 2 | 9025.2.a.y.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.e.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
475.2.a.g.1.1 | yes | 3 | 20.19 | odd | 2 | ||
475.2.b.b.324.2 | 6 | 20.3 | even | 4 | |||
475.2.b.b.324.5 | 6 | 20.7 | even | 4 | |||
4275.2.a.ba.1.3 | 3 | 60.59 | even | 2 | |||
4275.2.a.bm.1.1 | 3 | 12.11 | even | 2 | |||
7600.2.a.bh.1.1 | 3 | 5.4 | even | 2 | |||
7600.2.a.cc.1.3 | 3 | 1.1 | even | 1 | trivial | ||
9025.2.a.y.1.3 | 3 | 380.379 | even | 2 | |||
9025.2.a.bc.1.1 | 3 | 76.75 | even | 2 |