Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4275,2,Mod(1,4275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4275.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4275.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: | \(34.1360468641\) |
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: | \(\Z[a_1, a_2]\) |
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 | \(2.65109\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4275.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.65109 | 1.16750 | 0.583750 | − | 0.811934i | \(-0.301585\pi\) | ||||
0.583750 | + | 0.811934i | \(0.301585\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.726109 | 0.363055 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.377203 | −0.142569 | −0.0712846 | − | 0.997456i | \(-0.522710\pi\) | ||||
−0.0712846 | + | 0.997456i | \(0.522710\pi\) | |||||||
\(8\) | −2.10331 | −0.743633 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(-0.372027\pi\) | ||||
0.391295 | + | 0.920265i | \(0.372027\pi\) | |||||||
\(14\) | −0.622797 | −0.166450 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.92498 | −1.23125 | ||||||||
\(17\) | −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 | 0 | ||||||||
\(22\) | 2.27389 | 0.484795 | ||||||||
\(23\) | −6.19887 | −1.29255 | −0.646277 | − | 0.763103i | \(-0.723675\pi\) | ||||
−0.646277 | + | 0.763103i | \(0.723675\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.65884 | 0.913674 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.273891 | −0.0517604 | ||||||||
\(29\) | 3.37720 | 0.627131 | 0.313565 | − | 0.949567i | \(-0.398476\pi\) | ||||
0.313565 | + | 0.949567i | \(0.398476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.48052 | 0.445514 | 0.222757 | − | 0.974874i | \(-0.428494\pi\) | ||||
0.222757 | + | 0.974874i | \(0.428494\pi\) | |||||||
\(32\) | −3.92498 | −0.693846 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.5294 | −1.80577 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.58383 | 0.917976 | 0.458988 | − | 0.888443i | \(-0.348212\pi\) | ||||
0.458988 | + | 0.888443i | \(0.348212\pi\) | |||||||
\(38\) | 1.65109 | 0.267843 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.50106 | −1.32764 | −0.663821 | − | 0.747891i | \(-0.731066\pi\) | ||||
−0.663821 | + | 0.747891i | \(0.731066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1522 | −1.85319 | −0.926593 | − | 0.376065i | \(-0.877277\pi\) | ||||
−0.926593 | + | 0.376065i | \(0.877277\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.2349 | −1.50906 | ||||||||
\(47\) | 6.87826 | 1.00330 | 0.501649 | − | 0.865071i | \(-0.332727\pi\) | ||||
0.501649 | + | 0.865071i | \(0.332727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.85772 | −0.979674 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.04884 | 0.284123 | ||||||||
\(53\) | −11.5478 | −1.58621 | −0.793105 | − | 0.609085i | \(-0.791537\pi\) | ||||
−0.793105 | + | 0.609085i | \(0.791537\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.793375 | 0.106019 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.57608 | 0.732175 | ||||||||
\(59\) | −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 | \(0.395677\pi\) | |||||||
\(62\) | 4.09556 | 0.520137 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.36945 | 0.421182 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.22717 | 0.394262 | 0.197131 | − | 0.980377i | \(-0.436838\pi\) | ||||
0.197131 | + | 0.980377i | \(0.436838\pi\) | |||||||
\(68\) | −4.63055 | −0.561536 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.559941\pi\) | ||||
−0.187200 | + | 0.982322i | \(0.559941\pi\) | |||||||
\(74\) | 9.21942 | 1.07174 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.726109 | 0.0832905 | ||||||||
\(77\) | −0.519485 | −0.0592008 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.71836 | −0.755874 | −0.377937 | − | 0.925831i | \(-0.623366\pi\) | ||||
−0.377937 | + | 0.925831i | \(0.623366\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.0360 | −1.55002 | ||||||||
\(83\) | −18.2165 | −1.99952 | −0.999760 | − | 0.0218996i | \(-0.993029\pi\) | ||||
−0.999760 | + | 0.0218996i | \(0.993029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −20.0643 | −2.16359 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.89669 | −0.308788 | ||||||||
\(89\) | −1.50106 | −0.159112 | −0.0795561 | − | 0.996830i | \(-0.525350\pi\) | ||||
−0.0795561 | + | 0.996830i | \(0.525350\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.06434 | −0.111573 | ||||||||
\(92\) | −4.50106 | −0.469268 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.3567 | 1.17135 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.7827 | −1.19635 | −0.598176 | − | 0.801365i | \(-0.704108\pi\) | ||||
−0.598176 | + | 0.801365i | \(0.704108\pi\) | |||||||
\(98\) | −11.3227 | −1.14377 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.18820 | 0.914260 | 0.457130 | − | 0.889400i | \(-0.348877\pi\) | ||||
0.457130 | + | 0.889400i | \(0.348877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.47277 | −0.933379 | −0.466690 | − | 0.884421i | \(-0.654553\pi\) | ||||
−0.466690 | + | 0.884421i | \(0.654553\pi\) | |||||||
\(104\) | −5.93486 | −0.581961 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.0665 | −1.85190 | ||||||||
\(107\) | 15.3510 | 1.48404 | 0.742020 | − | 0.670378i | \(-0.233868\pi\) | ||||
0.742020 | + | 0.670378i | \(0.233868\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.7643 | −1.60573 | −0.802863 | − | 0.596163i | \(-0.796691\pi\) | ||||
−0.802863 | + | 0.596163i | \(0.796691\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.85772 | 0.175538 | ||||||||
\(113\) | 13.3305 | 1.25403 | 0.627013 | − | 0.779009i | \(-0.284277\pi\) | ||||
0.627013 | + | 0.779009i | \(0.284277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.45222 | 0.227683 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.0000 | −0.920575 | ||||||||
\(119\) | 2.40550 | 0.220512 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.10331 | −0.827574 | ||||||||
\(122\) | 8.30219 | 0.751645 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.80113 | 0.161746 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.04672 | −0.270353 | −0.135176 | − | 0.990822i | \(-0.543160\pi\) | ||||
−0.135176 | + | 0.990822i | \(0.543160\pi\) | |||||||
\(128\) | 13.4132 | 1.18557 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(134\) | 5.32836 | 0.460300 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.4132 | 1.15018 | ||||||||
\(137\) | −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 | \(-0.641911\pi\) | ||||
−0.431205 | + | 0.902254i | \(0.641911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.80113 | 0.318983 | ||||||||
\(143\) | 3.88601 | 0.324965 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.28164 | −0.437112 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.05447 | 0.333275 | ||||||||
\(149\) | 5.54003 | 0.453857 | 0.226929 | − | 0.973911i | \(-0.427132\pi\) | ||||
0.226929 | + | 0.973911i | \(0.427132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.12386 | 0.416974 | 0.208487 | − | 0.978025i | \(-0.433146\pi\) | ||||
0.208487 | + | 0.978025i | \(0.433146\pi\) | |||||||
\(152\) | −2.10331 | −0.170601 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.857718 | −0.0691169 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.7643 | 1.57736 | 0.788681 | − | 0.614803i | \(-0.210765\pi\) | ||||
0.788681 | + | 0.614803i | \(0.210765\pi\) | |||||||
\(158\) | −11.0926 | −0.882483 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | \(0.322393\pi\) | |||||||
\(164\) | −6.17270 | −0.482007 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −30.0771 | −2.33444 | ||||||||
\(167\) | −13.1054 | −1.01413 | −0.507065 | − | 0.861908i | \(-0.669269\pi\) | ||||
−0.507065 | + | 0.861908i | \(0.669269\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.03817 | −0.387551 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.82379 | −0.672808 | ||||||||
\(173\) | −1.48827 | −0.113151 | −0.0565754 | − | 0.998398i | \(-0.518018\pi\) | ||||
−0.0565754 | + | 0.998398i | \(0.518018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.78270 | −0.511265 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.47839 | −0.185763 | ||||||||
\(179\) | 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 | \(0.568416\pi\) | |||||||
\(182\) | −1.75733 | −0.130262 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.0382 | 0.961187 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.78270 | −0.642255 | ||||||||
\(188\) | 4.99437 | 0.364252 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(-0.779283\pi\) | ||||
−0.769075 | + | 0.639159i | \(0.779283\pi\) | |||||||
\(194\) | −19.4543 | −1.39674 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.97945 | −0.355675 | ||||||||
\(197\) | −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 | \(-0.525130\pi\) | ||||
−0.0788647 | + | 0.996885i | \(0.525130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.1706 | 1.06740 | ||||||||
\(203\) | −1.27389 | −0.0894096 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.6404 | −1.08972 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.8967 | −0.963562 | ||||||||
\(209\) | 1.37720 | 0.0952631 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.75441 | −0.671521 | −0.335760 | − | 0.941947i | \(-0.608993\pi\) | ||||
−0.335760 | + | 0.941947i | \(0.608993\pi\) | |||||||
\(212\) | −8.38495 | −0.575881 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.3460 | 1.73262 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.935657 | −0.0635166 | ||||||||
\(218\) | −27.6794 | −1.87468 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | \(0.714585\pi\) | |||||||
\(224\) | 1.48052 | 0.0989211 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 22.0099 | 1.46407 | ||||||||
\(227\) | 8.04672 | 0.534080 | 0.267040 | − | 0.963686i | \(-0.413954\pi\) | ||||
0.267040 | + | 0.963686i | \(0.413954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1415 | 1.33099 | 0.665493 | − | 0.746404i | \(-0.268221\pi\) | ||||
0.665493 | + | 0.746404i | \(0.268221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.10331 | −0.466355 | ||||||||
\(233\) | 1.73386 | 0.113589 | 0.0567945 | − | 0.998386i | \(-0.481912\pi\) | ||||
0.0567945 | + | 0.998386i | \(0.481912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.39775 | −0.286269 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.97170 | 0.257447 | ||||||||
\(239\) | 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 | \(0.522540\pi\) | |||||||
\(242\) | −15.0304 | −0.966192 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.65109 | 0.233737 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.82167 | 0.179539 | ||||||||
\(248\) | −5.21730 | −0.331299 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(254\) | −5.03042 | −0.315637 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.4076 | 0.962976 | ||||||||
\(257\) | −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 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.3772 | 0.888227 | ||||||||
\(263\) | −5.36945 | −0.331095 | −0.165547 | − | 0.986202i | \(-0.552939\pi\) | ||||
−0.165547 | + | 0.986202i | \(0.552939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.622797 | −0.0381861 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.34328 | 0.143139 | ||||||||
\(269\) | −7.06727 | −0.430899 | −0.215449 | − | 0.976515i | \(-0.569122\pi\) | ||||
−0.215449 | + | 0.976515i | \(0.569122\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.6970 | 1.31800 | 0.659000 | − | 0.752143i | \(-0.270980\pi\) | ||||
0.659000 | + | 0.752143i | \(0.270980\pi\) | |||||||
\(272\) | 31.4076 | 1.90437 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.8881 | −0.657776 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1132 | 1.50891 | 0.754453 | − | 0.656355i | \(-0.227902\pi\) | ||||
0.754453 | + | 0.656355i | \(0.227902\pi\) | |||||||
\(278\) | −16.7877 | −1.00686 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0411 | 0.599001 | 0.299501 | − | 0.954096i | \(-0.403180\pi\) | ||||
0.299501 | + | 0.954096i | \(0.403180\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.9143 | −1.24323 | −0.621613 | − | 0.783324i | \(-0.713522\pi\) | ||||
−0.621613 | + | 0.783324i | \(0.713522\pi\) | |||||||
\(284\) | 1.67164 | 0.0991936 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.41617 | 0.379396 | ||||||||
\(287\) | 3.20662 | 0.189281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.6687 | 1.39228 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.32273 | −0.135928 | ||||||||
\(293\) | 0.818748 | 0.0478318 | 0.0239159 | − | 0.999714i | \(-0.492387\pi\) | ||||
0.0239159 | + | 0.999714i | \(0.492387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.7445 | −0.682637 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.14711 | 0.529878 | ||||||||
\(299\) | −17.4912 | −1.01154 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.58383 | 0.264207 | ||||||||
\(302\) | 8.45997 | 0.486817 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.92498 | −0.282467 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.44447 | −0.424878 | −0.212439 | − | 0.977174i | \(-0.568141\pi\) | ||||
−0.212439 | + | 0.977174i | \(0.568141\pi\) | |||||||
\(308\) | −0.377203 | −0.0214931 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.445930\pi\) | ||||
0.169049 | + | 0.985608i | \(0.445930\pi\) | |||||||
\(314\) | 32.6327 | 1.84157 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.87826 | −0.274424 | ||||||||
\(317\) | −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 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.86064 | 0.215145 | ||||||||
\(323\) | −6.37720 | −0.354837 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.3219 | 1.23630 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.8804 | 0.987279 | ||||||||
\(329\) | −2.59450 | −0.143039 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.16283 | 0.228810 | 0.114405 | − | 0.993434i | \(-0.463504\pi\) | ||||
0.114405 | + | 0.993434i | \(0.463504\pi\) | |||||||
\(332\) | −13.2272 | −0.725935 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.6383 | −1.18399 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0304 | −0.982180 | −0.491090 | − | 0.871109i | \(-0.663401\pi\) | ||||
−0.491090 | + | 0.871109i | \(0.663401\pi\) | |||||||
\(338\) | −8.31849 | −0.452466 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.41617 | 0.184996 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.22717 | 0.282241 | ||||||||
\(344\) | 25.5598 | 1.37809 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.45726 | −0.132103 | ||||||||
\(347\) | −7.43380 | −0.399067 | −0.199534 | − | 0.979891i | \(-0.563943\pi\) | ||||
−0.199534 | + | 0.979891i | \(0.563943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.9194 | 1.17332 | 0.586658 | − | 0.809835i | \(-0.300443\pi\) | ||||
0.586658 | + | 0.809835i | \(0.300443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.40550 | −0.288114 | ||||||||
\(353\) | −10.3695 | −0.551910 | −0.275955 | − | 0.961171i | \(-0.588994\pi\) | ||||
−0.275955 | + | 0.961171i | \(0.588994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.08993 | −0.0577664 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 28.2555 | 1.49335 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | −9.47547 | −0.498020 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.772829 | −0.0405073 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.0275 | 1.82842 | 0.914210 | − | 0.405240i | \(-0.132812\pi\) | ||||
0.914210 | + | 0.405240i | \(0.132812\pi\) | |||||||
\(368\) | 30.5294 | 1.59145 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.35586 | 0.226145 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.8003 | 1.59478 | 0.797390 | − | 0.603464i | \(-0.206213\pi\) | ||||
0.797390 | + | 0.603464i | \(0.206213\pi\) | |||||||
\(374\) | −14.5011 | −0.749832 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.4671 | −0.746086 | ||||||||
\(377\) | 9.52936 | 0.490787 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.671640 | 0.0344998 | 0.0172499 | − | 0.999851i | \(-0.494509\pi\) | ||||
0.0172499 | + | 0.999851i | \(0.494509\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −36.9759 | −1.89185 | ||||||||
\(383\) | 30.1805 | 1.54215 | 0.771075 | − | 0.636745i | \(-0.219720\pi\) | ||||
0.771075 | + | 0.636745i | \(0.219720\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −35.2816 | −1.79579 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.55553 | −0.434341 | ||||||||
\(389\) | 31.5109 | 1.59767 | 0.798834 | − | 0.601552i | \(-0.205451\pi\) | ||||
0.798834 | + | 0.601552i | \(0.205451\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.5315 | 1.99919 | ||||||||
\(392\) | 14.4239 | 0.728518 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.83929 | −0.0926623 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5761 | −0.631175 | −0.315588 | − | 0.948896i | \(-0.602202\pi\) | ||||
−0.315588 | + | 0.948896i | \(0.602202\pi\) | |||||||
\(398\) | −3.67376 | −0.184149 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.6036 | −1.22864 | −0.614322 | − | 0.789056i | \(-0.710570\pi\) | ||||
−0.614322 | + | 0.789056i | \(0.710570\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.99920 | 0.348655 | ||||||||
\(404\) | 6.67164 | 0.331926 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.10331 | −0.104386 | ||||||||
\(407\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.87826 | −0.338868 | ||||||||
\(413\) | 2.28456 | 0.112416 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.0750 | −0.542997 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.27389 | 0.111220 | ||||||||
\(419\) | −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 | \(0.248181\pi\) | |||||||
\(422\) | −16.1054 | −0.784000 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 24.2886 | 1.17956 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.89669 | −0.0917872 | ||||||||
\(428\) | 11.1465 | 0.538788 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.536503\pi\) | ||||
−0.114427 | + | 0.993432i | \(0.536503\pi\) | |||||||
\(434\) | −1.54486 | −0.0741555 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1727 | −0.582967 | ||||||||
\(437\) | −6.19887 | −0.296532 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.88601 | 0.328652 | 0.164326 | − | 0.986406i | \(-0.447455\pi\) | ||||
0.164326 | + | 0.986406i | \(0.447455\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −29.7104 | −1.41318 | ||||||||
\(443\) | −8.65109 | −0.411026 | −0.205513 | − | 0.978654i | \(-0.565886\pi\) | ||||
−0.205513 | + | 0.978654i | \(0.565886\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −30.7819 | −1.45757 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.27097 | −0.0600476 | ||||||||
\(449\) | −8.63055 | −0.407301 | −0.203650 | − | 0.979044i | \(-0.565281\pi\) | ||||
−0.203650 | + | 0.979044i | \(0.565281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7077 | −0.551293 | ||||||||
\(452\) | 9.67939 | 0.455280 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.2859 | 0.623538 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.6092 | −1.33828 | −0.669141 | − | 0.743135i | \(-0.733338\pi\) | ||||
−0.669141 | + | 0.743135i | \(0.733338\pi\) | |||||||
\(458\) | 33.2555 | 1.55393 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.1025 | 1.82119 | 0.910593 | − | 0.413305i | \(-0.135626\pi\) | ||||
0.910593 | + | 0.413305i | \(0.135626\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.04380 | −0.373827 | −0.186913 | − | 0.982376i | \(-0.559848\pi\) | ||||
−0.186913 | + | 0.982376i | \(0.559848\pi\) | |||||||
\(464\) | −16.6327 | −0.772152 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.86276 | 0.132615 | ||||||||
\(467\) | −17.0488 | −0.788926 | −0.394463 | − | 0.918912i | \(-0.629069\pi\) | ||||
−0.394463 | + | 0.918912i | \(0.629069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.21730 | −0.0562096 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.7389 | 0.586356 | ||||||||
\(473\) | −16.7360 | −0.769521 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.74666 | 0.0800578 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 30.2397 | 1.38313 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | −3.62704 | −0.165207 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.61000 | −0.300455 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.5577 | −1.11281 | −0.556407 | − | 0.830910i | \(-0.687820\pi\) | ||||
−0.556407 | + | 0.830910i | \(0.687820\pi\) | |||||||
\(488\) | −10.5761 | −0.478757 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(494\) | 4.65884 | 0.209611 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.2165 | −0.548537 | ||||||||
\(497\) | −0.868391 | −0.0389527 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.418295 | 0.0187255 | 0.00936273 | − | 0.999956i | \(-0.497020\pi\) | ||||
0.00936273 | + | 0.999956i | \(0.497020\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.5732 | 1.00749 | ||||||||
\(503\) | 12.5993 | 0.561776 | 0.280888 | − | 0.959741i | \(-0.409371\pi\) | ||||
0.280888 | + | 0.959741i | \(0.409371\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14.0956 | −0.626624 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.21225 | −0.0981528 | ||||||||
\(509\) | −12.8209 | −0.568275 | −0.284138 | − | 0.958784i | \(-0.591707\pi\) | ||||
−0.284138 | + | 0.958784i | \(0.591707\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.20662 | 0.0533779 | ||||||||
\(512\) | −1.38708 | −0.0613007 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −47.0403 | −2.07486 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.47277 | 0.416612 | ||||||||
\(518\) | −3.47759 | −0.152797 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.3743 | −0.498316 | −0.249158 | − | 0.968463i | \(-0.580154\pi\) | ||||
−0.249158 | + | 0.968463i | \(0.580154\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.0948 | 1.44713 | 0.723566 | − | 0.690255i | \(-0.242502\pi\) | ||||
0.723566 | + | 0.690255i | \(0.242502\pi\) | |||||||
\(524\) | 6.32273 | 0.276210 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.86547 | −0.386553 | ||||||||
\(527\) | −15.8187 | −0.689075 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.4260 | 0.670698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.273891 | −0.0118747 | ||||||||
\(533\) | −23.9872 | −1.03900 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.78775 | −0.293186 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.6687 | −0.503074 | ||||||||
\(539\) | −9.44447 | −0.406802 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.4338 | 1.35144 | 0.675722 | − | 0.737156i | \(-0.263832\pi\) | ||||
0.675722 | + | 0.737156i | \(0.263832\pi\) | |||||||
\(542\) | 35.8238 | 1.53876 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 25.0304 | 1.07317 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.3460 | −0.998202 | −0.499101 | − | 0.866544i | \(-0.666336\pi\) | ||||
−0.499101 | + | 0.866544i | \(0.666336\pi\) | |||||||
\(548\) | −4.78833 | −0.204547 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.37720 | 0.143874 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.53418 | 0.107764 | ||||||||
\(554\) | 41.4642 | 1.76165 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.38283 | −0.313102 | ||||||||
\(557\) | −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 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.5788 | 0.699334 | ||||||||
\(563\) | 29.6404 | 1.24919 | 0.624597 | − | 0.780947i | \(-0.285263\pi\) | ||||
0.624597 | + | 0.780947i | \(0.285263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −34.5315 | −1.45147 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.84222 | −0.203175 | ||||||||
\(569\) | 7.64334 | 0.320426 | 0.160213 | − | 0.987082i | \(-0.448782\pi\) | ||||
0.160213 | + | 0.987082i | \(0.448782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5577 | −0.441824 | −0.220912 | − | 0.975294i | \(-0.570903\pi\) | ||||
−0.220912 | + | 0.975294i | \(0.570903\pi\) | |||||||
\(572\) | 2.82167 | 0.117980 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.29444 | 0.220986 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.9447 | 1.62129 | 0.810645 | − | 0.585538i | \(-0.199117\pi\) | ||||
0.810645 | + | 0.585538i | \(0.199117\pi\) | |||||||
\(578\) | 39.0793 | 1.62548 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.87131 | 0.285070 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.9036 | −0.658661 | ||||||||
\(584\) | 6.72823 | 0.278416 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.35183 | 0.0558436 | ||||||||
\(587\) | 10.9992 | 0.453986 | 0.226993 | − | 0.973896i | \(-0.427111\pi\) | ||||
0.226993 | + | 0.973896i | \(0.427111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.48052 | 0.102208 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −27.5003 | −1.13025 | ||||||||
\(593\) | −26.7848 | −1.09992 | −0.549960 | − | 0.835191i | \(-0.685357\pi\) | ||||
−0.549960 | + | 0.835191i | \(0.685357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.02267 | 0.164775 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −28.8796 | −1.18097 | ||||||||
\(599\) | 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 | \(0.772863\pi\) | |||||||
\(602\) | 7.56833 | 0.308462 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.72048 | 0.151384 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8732 | −0.603685 | −0.301843 | − | 0.953358i | \(-0.597602\pi\) | ||||
−0.301843 | + | 0.953358i | \(0.597602\pi\) | |||||||
\(608\) | −3.92498 | −0.159179 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.4082 | 0.785172 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −40.4671 | −1.63445 | −0.817226 | − | 0.576317i | \(-0.804489\pi\) | ||||
−0.817226 | + | 0.576317i | \(0.804489\pi\) | |||||||
\(614\) | −12.2915 | −0.496045 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.09264 | 0.0440237 | ||||||||
\(617\) | −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 | \(-0.277224\pi\) | ||||
0.644119 | + | 0.764926i | \(0.277224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.57878 | 0.0633034 | ||||||||
\(623\) | 0.566205 | 0.0226845 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.87614 | 0.394730 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.3510 | 0.572668 | ||||||||
\(629\) | −35.6092 | −1.41983 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.9709 | −0.755220 | −0.377610 | − | 0.925965i | \(-0.623254\pi\) | ||||
−0.377610 | + | 0.925965i | \(0.623254\pi\) | |||||||
\(632\) | 14.1308 | 0.562093 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −37.3991 | −1.48531 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.3502 | −0.766684 | ||||||||
\(638\) | 7.67939 | 0.304030 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.3433 | 1.75145 | 0.875727 | − | 0.482806i | \(-0.160383\pi\) | ||||
0.875727 | + | 0.482806i | \(0.160383\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.9397 | 1.69338 | 0.846688 | − | 0.532090i | \(-0.178593\pi\) | ||||
0.846688 | + | 0.532090i | \(0.178593\pi\) | |||||||
\(644\) | 1.69781 | 0.0669032 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5294 | −0.414272 | ||||||||
\(647\) | −17.9864 | −0.707118 | −0.353559 | − | 0.935412i | \(-0.615029\pi\) | ||||
−0.353559 | + | 0.935412i | \(0.615029\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.34116 | −0.327419 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.81663 | 0.384449 | ||||||||
\(653\) | 21.7274 | 0.850260 | 0.425130 | − | 0.905132i | \(-0.360228\pi\) | ||||
0.425130 | + | 0.905132i | \(0.360228\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.8676 | 1.63465 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.28376 | −0.166998 | ||||||||
\(659\) | 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 | \(0.272273\pi\) | |||||||
\(662\) | 6.87322 | 0.267135 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 38.3150 | 1.48691 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.9349 | −0.810601 | ||||||||
\(668\) | −9.51598 | −0.368184 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.92498 | 0.267336 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0622 | −0.426417 | −0.213209 | − | 0.977007i | \(-0.568391\pi\) | ||||
−0.213209 | + | 0.977007i | \(0.568391\pi\) | |||||||
\(674\) | −29.7699 | −1.14669 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.65826 | −0.140702 | ||||||||
\(677\) | 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 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.64042 | 0.215983 | ||||||||
\(683\) | 13.6073 | 0.520669 | 0.260334 | − | 0.965519i | \(-0.416167\pi\) | ||||
0.260334 | + | 0.965519i | \(0.416167\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.63055 | 0.329516 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 59.8492 | 2.28173 | ||||||||
\(689\) | −32.5840 | −1.24135 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.3043 | −1.53325 | −0.766624 | − | 0.642096i | \(-0.778065\pi\) | ||||
−0.766624 | + | 0.642096i | \(0.778065\pi\) | |||||||
\(692\) | −1.08064 | −0.0410799 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.2739 | −0.465911 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.2130 | 2.05346 | ||||||||
\(698\) | 36.1909 | 1.36985 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.23704 | 0.122261 | 0.0611307 | − | 0.998130i | \(-0.480529\pi\) | ||||
0.0611307 | + | 0.998130i | \(0.480529\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.58383 | 0.210598 | ||||||||
\(704\) | 4.64042 | 0.174892 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.1209 | −0.644355 | ||||||||
\(707\) | −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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.15720 | 0.118321 | ||||||||
\(713\) | −15.3764 | −0.575851 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.4260 | 0.464383 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 39.6086 | 1.47818 | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 1.65109 | 0.0614473 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.16707 | −0.154868 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.7926 | 0.659890 | 0.329945 | − | 0.944000i | \(-0.392970\pi\) | ||||
0.329945 | + | 0.944000i | \(0.392970\pi\) | |||||||
\(728\) | 2.23864 | 0.0829697 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 77.4968 | 2.86632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.66097 | −0.209093 | −0.104546 | − | 0.994520i | \(-0.533339\pi\) | ||||
−0.104546 | + | 0.994520i | \(0.533339\pi\) | |||||||
\(734\) | 57.8337 | 2.13468 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.3305 | 0.896834 | ||||||||
\(737\) | 4.44447 | 0.163714 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.59955 | −0.205983 | −0.102991 | − | 0.994682i | \(-0.532841\pi\) | ||||
−0.102991 | + | 0.994682i | \(0.532841\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.19193 | 0.264024 | ||||||||
\(743\) | −5.81663 | −0.213391 | −0.106696 | − | 0.994292i | \(-0.534027\pi\) | ||||
−0.106696 | + | 0.994292i | \(0.534027\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 50.8542 | 1.86191 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.37720 | −0.233174 | ||||||||
\(749\) | −5.79045 | −0.211579 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.1797 | −1.50267 | −0.751333 | − | 0.659923i | \(-0.770589\pi\) | ||||
−0.751333 | + | 0.659923i | \(0.770589\pi\) | |||||||
\(752\) | −33.8753 | −1.23531 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.7339 | 0.572993 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.5208 | −1.21833 | −0.609167 | − | 0.793042i | \(-0.708496\pi\) | ||||
−0.609167 | + | 0.793042i | \(0.708496\pi\) | |||||||
\(758\) | 1.10894 | 0.0402785 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.5032 | −1.14199 | −0.570995 | − | 0.820954i | \(-0.693442\pi\) | ||||
−0.570995 | + | 0.820954i | \(0.693442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.32353 | 0.228927 | ||||||||
\(764\) | −16.2611 | −0.588306 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 49.8307 | 1.80046 | ||||||||
\(767\) | −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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.5160 | −0.558432 | ||||||||
\(773\) | −40.6687 | −1.46275 | −0.731376 | − | 0.681974i | \(-0.761122\pi\) | ||||
−0.731376 | + | 0.681974i | \(0.761122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.7827 | 0.889647 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 52.0275 | 1.86528 | ||||||||
\(779\) | −8.50106 | −0.304582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.17058 | 0.113452 | ||||||||
\(782\) | 65.2702 | 2.33406 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 33.7742 | 1.20622 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.9525 | −1.42415 | −0.712076 | − | 0.702102i | \(-0.752245\pi\) | ||||
−0.712076 | + | 0.702102i | \(0.752245\pi\) | |||||||
\(788\) | −0.808876 | −0.0288150 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.02830 | −0.178786 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.1882 | 0.503838 | ||||||||
\(794\) | −20.7643 | −0.736897 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.61563 | −0.0572644 | ||||||||
\(797\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −40.6228 | −1.43444 | ||||||||
\(803\) | −4.40550 | −0.155467 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.5563 | 0.407054 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19.3257 | −0.679874 | ||||||||
\(809\) | −55.5958 | −1.95465 | −0.977323 | − | 0.211756i | \(-0.932082\pi\) | ||||
−0.977323 | + | 0.211756i | \(0.932082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.3326 | 1.48650 | 0.743249 | − | 0.669014i | \(-0.233284\pi\) | ||||
0.743249 | + | 0.669014i | \(0.233284\pi\) | |||||||
\(812\) | −0.924984 | −0.0324606 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.6970 | 0.445030 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.1522 | −0.425150 | ||||||||
\(818\) | 22.5648 | 0.788961 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.10543 | 0.108380 | 0.0541902 | − | 0.998531i | \(-0.482742\pi\) | ||||
0.0541902 | + | 0.998531i | \(0.482742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.2002 | −1.57558 | −0.787790 | − | 0.615944i | \(-0.788775\pi\) | ||||
−0.787790 | + | 0.615944i | \(0.788775\pi\) | |||||||
\(824\) | 19.9242 | 0.694092 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.77203 | 0.131246 | ||||||||
\(827\) | 35.6503 | 1.23968 | 0.619841 | − | 0.784727i | \(-0.287197\pi\) | ||||
0.619841 | + | 0.784727i | \(0.287197\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.4330 | −0.640204 | −0.320102 | − | 0.947383i | \(-0.603717\pi\) | ||||
−0.320102 | + | 0.947383i | \(0.603717\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.50749 | 0.329613 | ||||||||
\(833\) | 43.7331 | 1.51526 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.00000 | 0.0345857 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.9512 | −0.723746 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 48.1832 | 1.66050 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.08277 | −0.243799 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.43380 | 0.117987 | ||||||||
\(848\) | 56.8726 | 1.95301 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.6134 | −1.18653 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.6639 | 1.46078 | 0.730392 | − | 0.683028i | \(-0.239337\pi\) | ||||
0.730392 | + | 0.683028i | \(0.239337\pi\) | |||||||
\(854\) | −3.13161 | −0.107161 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −32.2880 | −1.10358 | ||||||||
\(857\) | 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 | \(-0.545108\pi\) | ||||
−0.141237 | + | 0.989976i | \(0.545108\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 49.5024 | 1.68606 | ||||||||
\(863\) | −30.4154 | −1.03535 | −0.517676 | − | 0.855577i | \(-0.673203\pi\) | ||||
−0.517676 | + | 0.855577i | \(0.673203\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.86276 | −0.267188 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.679390 | −0.0230600 | ||||||||
\(869\) | −9.25254 | −0.313871 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.10602 | 0.308546 | ||||||||
\(872\) | 35.2605 | 1.19407 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.2349 | −0.346201 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.8484 | 1.95340 | 0.976700 | − | 0.214608i | \(-0.0688474\pi\) | ||||
0.976700 | + | 0.214608i | \(0.0688474\pi\) | |||||||
\(878\) | 11.3695 | 0.383700 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.4055 | −0.620097 | −0.310049 | − | 0.950721i | \(-0.600345\pi\) | ||||
−0.310049 | + | 0.950721i | \(0.600345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.7947 | −0.632492 | −0.316246 | − | 0.948677i | \(-0.602422\pi\) | ||||
−0.316246 | + | 0.948677i | \(0.602422\pi\) | |||||||
\(884\) | −13.0659 | −0.439453 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.2838 | −0.479872 | ||||||||
\(887\) | 11.1471 | 0.374283 | 0.187142 | − | 0.982333i | \(-0.440078\pi\) | ||||
0.187142 | + | 0.982333i | \(0.440078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.14923 | 0.0385440 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.5371 | −0.453256 | ||||||||
\(893\) | 6.87826 | 0.230172 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.05952 | −0.169027 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.2498 | −0.475523 | ||||||||
\(899\) | 8.37720 | 0.279395 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 73.6425 | 2.45339 | ||||||||
\(902\) | −19.3305 | −0.643635 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.0382 | −0.932536 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.5598 | 1.28036 | 0.640178 | − | 0.768226i | \(-0.278861\pi\) | ||||
0.640178 | + | 0.768226i | \(0.278861\pi\) | |||||||
\(908\) | 5.84280 | 0.193900 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(914\) | −47.2365 | −1.56244 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.6249 | 0.483221 | ||||||||
\(917\) | −3.28456 | −0.108466 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.4458 | −1.07029 | −0.535144 | − | 0.844761i | \(-0.679743\pi\) | ||||
−0.535144 | + | 0.844761i | \(0.679743\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 64.5619 | 2.12623 | ||||||||
\(923\) | 6.49602 | 0.213819 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.2811 | −0.436443 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.2555 | −0.435132 | ||||||||
\(929\) | 18.4231 | 0.604443 | 0.302222 | − | 0.953238i | \(-0.402272\pi\) | ||||
0.302222 | + | 0.953238i | \(0.402272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.85772 | −0.224753 | ||||||||
\(932\) | 1.25897 | 0.0412390 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.1492 | −0.921071 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.29926 | 0.271125 | 0.135563 | − | 0.990769i | \(-0.456716\pi\) | ||||
0.135563 | + | 0.990769i | \(0.456716\pi\) | |||||||
\(938\) | −2.00987 | −0.0656247 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.6687 | −1.09757 | −0.548784 | − | 0.835964i | \(-0.684909\pi\) | ||||
−0.548784 | + | 0.835964i | \(0.684909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.6970 | 1.71605 | ||||||||
\(944\) | 29.8286 | 0.970839 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.6327 | −0.898416 | ||||||||
\(947\) | −1.35103 | −0.0439026 | −0.0219513 | − | 0.999759i | \(-0.506988\pi\) | ||||
−0.0219513 | + | 0.999759i | \(0.506988\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.02617 | −0.293002 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.05952 | −0.163980 | ||||||||
\(953\) | 6.70769 | 0.217283 | 0.108642 | − | 0.994081i | \(-0.465350\pi\) | ||||
0.108642 | + | 0.994081i | \(0.465350\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.2987 | 0.430110 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.2285 | −1.20280 | ||||||||
\(959\) | 2.48746 | 0.0803244 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8470 | −0.801518 | ||||||||
\(962\) | 26.0142 | 0.838731 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.59508 | −0.0513741 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.5174 | 0.627636 | 0.313818 | − | 0.949483i | \(-0.398392\pi\) | ||||
0.313818 | + | 0.949483i | \(0.398392\pi\) | |||||||
\(968\) | 19.1471 | 0.615411 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(974\) | −40.5470 | −1.29921 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.7643 | −0.792685 | ||||||||
\(977\) | −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 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27.9527 | 0.892006 | ||||||||
\(983\) | 12.4677 | 0.397658 | 0.198829 | − | 0.980034i | \(-0.436286\pi\) | ||||
0.198829 | + | 0.980034i | \(0.436286\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −35.5598 | −1.13245 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.04884 | 0.0651824 | ||||||||
\(989\) | 75.3297 | 2.39534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.0841 | 0.796822 | 0.398411 | − | 0.917207i | \(-0.369562\pi\) | ||||
0.398411 | + | 0.917207i | \(0.369562\pi\) | |||||||
\(992\) | −9.73598 | −0.309118 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.43380 | −0.0454772 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.8775 | 0.376163 | 0.188082 | − | 0.982153i | \(-0.439773\pi\) | ||||
0.188082 | + | 0.982153i | \(0.439773\pi\) | |||||||
\(998\) | 0.690644 | 0.0218620 | ||||||||
\(999\) | 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 | 4275.2.a.ba.1.3 | 3 | ||
3.2 | odd | 2 | 475.2.a.g.1.1 | yes | 3 | ||
5.4 | even | 2 | 4275.2.a.bm.1.1 | 3 | |||
12.11 | even | 2 | 7600.2.a.bh.1.1 | 3 | |||
15.2 | even | 4 | 475.2.b.b.324.2 | 6 | |||
15.8 | even | 4 | 475.2.b.b.324.5 | 6 | |||
15.14 | odd | 2 | 475.2.a.e.1.3 | ✓ | 3 | ||
57.56 | even | 2 | 9025.2.a.y.1.3 | 3 | |||
60.59 | even | 2 | 7600.2.a.cc.1.3 | 3 | |||
285.284 | even | 2 | 9025.2.a.bc.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.e.1.3 | ✓ | 3 | 15.14 | odd | 2 | ||
475.2.a.g.1.1 | yes | 3 | 3.2 | odd | 2 | ||
475.2.b.b.324.2 | 6 | 15.2 | even | 4 | |||
475.2.b.b.324.5 | 6 | 15.8 | even | 4 | |||
4275.2.a.ba.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4275.2.a.bm.1.1 | 3 | 5.4 | even | 2 | |||
7600.2.a.bh.1.1 | 3 | 12.11 | even | 2 | |||
7600.2.a.cc.1.3 | 3 | 60.59 | even | 2 | |||
9025.2.a.y.1.3 | 3 | 57.56 | even | 2 | |||
9025.2.a.bc.1.1 | 3 | 285.284 | even | 2 |