Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.3829849.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 6x^{4} + 15x^{3} - 5x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.22391\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45784 | 1.73795 | 0.868977 | − | 0.494853i | \(-0.164778\pi\) | ||||
0.868977 | + | 0.494853i | \(0.164778\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.04096 | 2.02048 | ||||||||
\(5\) | −2.05098 | −0.917224 | −0.458612 | − | 0.888637i | \(-0.651653\pi\) | ||||
−0.458612 | + | 0.888637i | \(0.651653\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 5.01636 | 1.77355 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.04096 | −1.59409 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.206501 | −0.0572731 | −0.0286365 | − | 0.999590i | \(-0.509117\pi\) | ||||
−0.0286365 | + | 0.999590i | \(0.509117\pi\) | |||||||
\(14\) | −2.45784 | −0.656885 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.24747 | 1.06187 | ||||||||
\(17\) | 0.813723 | 0.197357 | 0.0986785 | − | 0.995119i | \(-0.468538\pi\) | ||||
0.0986785 | + | 0.995119i | \(0.468538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.28843 | −1.44266 | −0.721332 | − | 0.692589i | \(-0.756470\pi\) | ||||
−0.721332 | + | 0.692589i | \(0.756470\pi\) | |||||||
\(20\) | −8.28792 | −1.85324 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.11704 | 1.06698 | 0.533489 | − | 0.845807i | \(-0.320881\pi\) | ||||
0.533489 | + | 0.845807i | \(0.320881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.793499 | −0.158700 | ||||||||
\(26\) | −0.507546 | −0.0995380 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.04096 | −0.763671 | ||||||||
\(29\) | −3.87979 | −0.720459 | −0.360230 | − | 0.932864i | \(-0.617302\pi\) | ||||
−0.360230 | + | 0.932864i | \(0.617302\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.49493 | 1.16652 | 0.583262 | − | 0.812284i | \(-0.301776\pi\) | ||||
0.583262 | + | 0.812284i | \(0.301776\pi\) | |||||||
\(32\) | 0.406862 | 0.0719237 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 2.05098 | 0.346678 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.79350 | 0.294849 | 0.147425 | − | 0.989073i | \(-0.452902\pi\) | ||||
0.147425 | + | 0.989073i | \(0.452902\pi\) | |||||||
\(38\) | −15.4559 | −2.50728 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.2884 | −1.62674 | ||||||||
\(41\) | −1.82882 | −0.285613 | −0.142807 | − | 0.989751i | \(-0.545613\pi\) | ||||
−0.142807 | + | 0.989751i | \(0.545613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0819 | −1.53748 | −0.768740 | − | 0.639562i | \(-0.779116\pi\) | ||||
−0.768740 | + | 0.639562i | \(0.779116\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.5769 | 1.85436 | ||||||||
\(47\) | −8.79547 | −1.28295 | −0.641475 | − | 0.767144i | \(-0.721677\pi\) | ||||
−0.641475 | + | 0.767144i | \(0.721677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.95029 | −0.275813 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.834464 | −0.115719 | ||||||||
\(53\) | −3.08686 | −0.424013 | −0.212006 | − | 0.977268i | \(-0.568000\pi\) | ||||
−0.212006 | + | 0.977268i | \(0.568000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.01636 | −0.670339 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.53590 | −1.25212 | ||||||||
\(59\) | 2.66333 | 0.346736 | 0.173368 | − | 0.984857i | \(-0.444535\pi\) | ||||
0.173368 | + | 0.984857i | \(0.444535\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.58700 | −0.459268 | −0.229634 | − | 0.973277i | \(-0.573753\pi\) | ||||
−0.229634 | + | 0.973277i | \(0.573753\pi\) | |||||||
\(62\) | 15.9635 | 2.02736 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.49493 | −0.936866 | ||||||||
\(65\) | 0.423529 | 0.0525323 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.2884 | 1.25693 | 0.628466 | − | 0.777837i | \(-0.283683\pi\) | ||||
0.628466 | + | 0.777837i | \(0.283683\pi\) | |||||||
\(68\) | 3.28823 | 0.398756 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.04096 | 0.602511 | ||||||||
\(71\) | −15.5607 | −1.84672 | −0.923361 | − | 0.383934i | \(-0.874569\pi\) | ||||
−0.923361 | + | 0.383934i | \(0.874569\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.79350 | −0.912160 | −0.456080 | − | 0.889939i | \(-0.650747\pi\) | ||||
−0.456080 | + | 0.889939i | \(0.650747\pi\) | |||||||
\(74\) | 4.40813 | 0.512435 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −25.4113 | −2.91488 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1639 | 1.36854 | 0.684270 | − | 0.729228i | \(-0.260121\pi\) | ||||
0.684270 | + | 0.729228i | \(0.260121\pi\) | |||||||
\(80\) | −8.71145 | −0.973970 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.49493 | −0.496382 | ||||||||
\(83\) | −14.9484 | −1.64080 | −0.820400 | − | 0.571791i | \(-0.806249\pi\) | ||||
−0.820400 | + | 0.571791i | \(0.806249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.66893 | −0.181021 | ||||||||
\(86\) | −24.7797 | −2.67207 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.72940 | −0.607315 | −0.303657 | − | 0.952781i | \(-0.598208\pi\) | ||||
−0.303657 | + | 0.952781i | \(0.598208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.206501 | 0.0216472 | ||||||||
\(92\) | 20.6778 | 2.15581 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.6178 | −2.22971 | ||||||||
\(95\) | 12.8974 | 1.32325 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.49493 | −0.862530 | −0.431265 | − | 0.902225i | \(-0.641933\pi\) | ||||
−0.431265 | + | 0.902225i | \(0.641933\pi\) | |||||||
\(98\) | 2.45784 | 0.248279 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.20650 | −0.320650 | ||||||||
\(101\) | −10.6451 | −1.05922 | −0.529612 | − | 0.848240i | \(-0.677663\pi\) | ||||
−0.529612 | + | 0.848240i | \(0.677663\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.7509 | −1.55198 | −0.775989 | − | 0.630746i | \(-0.782749\pi\) | ||||
−0.775989 | + | 0.630746i | \(0.782749\pi\) | |||||||
\(104\) | −1.03588 | −0.101577 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.58700 | −0.736914 | ||||||||
\(107\) | 1.43862 | 0.139077 | 0.0695384 | − | 0.997579i | \(-0.477847\pi\) | ||||
0.0695384 | + | 0.997579i | \(0.477847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.49493 | 0.238971 | 0.119486 | − | 0.992836i | \(-0.461875\pi\) | ||||
0.119486 | + | 0.992836i | \(0.461875\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.24747 | −0.401348 | ||||||||
\(113\) | 17.5909 | 1.65482 | 0.827408 | − | 0.561602i | \(-0.189815\pi\) | ||||
0.827408 | + | 0.561602i | \(0.189815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.4949 | −0.978657 | ||||||||
\(116\) | −15.6781 | −1.45567 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.54603 | 0.602611 | ||||||||
\(119\) | −0.813723 | −0.0745939 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.81626 | −0.798186 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 26.2458 | 2.35694 | ||||||||
\(125\) | 11.8823 | 1.06279 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9079 | −0.967923 | −0.483961 | − | 0.875089i | \(-0.660802\pi\) | ||||
−0.483961 | + | 0.875089i | \(0.660802\pi\) | |||||||
\(128\) | −19.2350 | −1.70015 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.04096 | 0.0912986 | ||||||||
\(131\) | 5.72940 | 0.500580 | 0.250290 | − | 0.968171i | \(-0.419474\pi\) | ||||
0.250290 | + | 0.968171i | \(0.419474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.28843 | 0.545276 | ||||||||
\(134\) | 25.2873 | 2.18449 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.08193 | 0.350023 | ||||||||
\(137\) | −6.34175 | −0.541813 | −0.270906 | − | 0.962606i | \(-0.587323\pi\) | ||||
−0.270906 | + | 0.962606i | \(0.587323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.16386 | 0.353174 | 0.176587 | − | 0.984285i | \(-0.443494\pi\) | ||||
0.176587 | + | 0.984285i | \(0.443494\pi\) | |||||||
\(140\) | 8.28792 | 0.700457 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −38.2458 | −3.20952 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.95736 | 0.660823 | ||||||||
\(146\) | −19.1552 | −1.58529 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.24747 | 0.595738 | ||||||||
\(149\) | 16.1856 | 1.32598 | 0.662990 | − | 0.748628i | \(-0.269287\pi\) | ||||
0.662990 | + | 0.748628i | \(0.269287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.66893 | −0.135815 | −0.0679077 | − | 0.997692i | \(-0.521632\pi\) | ||||
−0.0679077 | + | 0.997692i | \(0.521632\pi\) | |||||||
\(152\) | −31.5450 | −2.55864 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.3209 | −1.06996 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.5769 | −1.48259 | −0.741297 | − | 0.671177i | \(-0.765789\pi\) | ||||
−0.741297 | + | 0.671177i | \(0.765789\pi\) | |||||||
\(158\) | 29.8968 | 2.37846 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.834464 | −0.0659701 | ||||||||
\(161\) | −5.11704 | −0.403280 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2884 | 0.805852 | 0.402926 | − | 0.915233i | \(-0.367993\pi\) | ||||
0.402926 | + | 0.915233i | \(0.367993\pi\) | |||||||
\(164\) | −7.39018 | −0.577076 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −36.7407 | −2.85163 | ||||||||
\(167\) | −23.5550 | −1.82274 | −0.911372 | − | 0.411585i | \(-0.864975\pi\) | ||||
−0.911372 | + | 0.411585i | \(0.864975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9574 | −0.996720 | ||||||||
\(170\) | −4.10195 | −0.314605 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −40.7407 | −3.10645 | ||||||||
\(173\) | 5.93077 | 0.450908 | 0.225454 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225454 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.793499 | 0.0599829 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.0819 | −1.05549 | ||||||||
\(179\) | 16.4078 | 1.22638 | 0.613188 | − | 0.789937i | \(-0.289887\pi\) | ||||
0.613188 | + | 0.789937i | \(0.289887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.50507 | −0.260530 | −0.130265 | − | 0.991479i | \(-0.541583\pi\) | ||||
−0.130265 | + | 0.991479i | \(0.541583\pi\) | |||||||
\(182\) | 0.507546 | 0.0376218 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 25.6689 | 1.89234 | ||||||||
\(185\) | −3.67842 | −0.270443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −35.5422 | −2.59218 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 31.6998 | 2.29974 | ||||||||
\(191\) | 18.6476 | 1.34929 | 0.674647 | − | 0.738141i | \(-0.264296\pi\) | ||||
0.674647 | + | 0.738141i | \(0.264296\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50507 | −0.396264 | −0.198132 | − | 0.980175i | \(-0.563487\pi\) | ||||
−0.198132 | + | 0.980175i | \(0.563487\pi\) | |||||||
\(194\) | −20.8792 | −1.49904 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.04096 | 0.288640 | ||||||||
\(197\) | 18.2366 | 1.29931 | 0.649653 | − | 0.760231i | \(-0.274914\pi\) | ||||
0.649653 | + | 0.760231i | \(0.274914\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.90793 | −0.489690 | −0.244845 | − | 0.969562i | \(-0.578737\pi\) | ||||
−0.244845 | + | 0.969562i | \(0.578737\pi\) | |||||||
\(200\) | −3.98048 | −0.281462 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −26.1639 | −1.84088 | ||||||||
\(203\) | 3.87979 | 0.272308 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.75086 | 0.261971 | ||||||||
\(206\) | −38.7130 | −2.69727 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.877106 | −0.0608164 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.17400 | −0.493878 | −0.246939 | − | 0.969031i | \(-0.579425\pi\) | ||||
−0.246939 | + | 0.969031i | \(0.579425\pi\) | |||||||
\(212\) | −12.4739 | −0.856710 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.53590 | 0.241709 | ||||||||
\(215\) | 20.6778 | 1.41021 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.49493 | −0.440905 | ||||||||
\(218\) | 6.13214 | 0.415321 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.168035 | −0.0113032 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.16386 | 0.546692 | 0.273346 | − | 0.961916i | \(-0.411870\pi\) | ||||
0.273346 | + | 0.961916i | \(0.411870\pi\) | |||||||
\(224\) | −0.406862 | −0.0271846 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 43.2357 | 2.87599 | ||||||||
\(227\) | −3.69921 | −0.245525 | −0.122763 | − | 0.992436i | \(-0.539175\pi\) | ||||
−0.122763 | + | 0.992436i | \(0.539175\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.2458 | −1.33788 | −0.668940 | − | 0.743317i | \(-0.733252\pi\) | ||||
−0.668940 | + | 0.743317i | \(0.733252\pi\) | |||||||
\(230\) | −25.7948 | −1.70086 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.4624 | −1.27777 | ||||||||
\(233\) | 13.6903 | 0.896885 | 0.448442 | − | 0.893812i | \(-0.351979\pi\) | ||||
0.448442 | + | 0.893812i | \(0.351979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0393 | 1.17675 | ||||||||
\(236\) | 10.7624 | 0.700574 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.00000 | −0.129641 | ||||||||
\(239\) | 16.5966 | 1.07355 | 0.536773 | − | 0.843726i | \(-0.319643\pi\) | ||||
0.536773 | + | 0.843726i | \(0.319643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.9574 | 0.770241 | 0.385121 | − | 0.922866i | \(-0.374160\pi\) | ||||
0.385121 | + | 0.922866i | \(0.374160\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.4949 | −0.927943 | ||||||||
\(245\) | −2.05098 | −0.131032 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.29857 | 0.0826259 | ||||||||
\(248\) | 32.5809 | 2.06889 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 29.2048 | 1.84708 | ||||||||
\(251\) | 5.54057 | 0.349718 | 0.174859 | − | 0.984594i | \(-0.444053\pi\) | ||||
0.174859 | + | 0.984594i | \(0.444053\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −26.8099 | −1.68220 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.2868 | −2.01792 | ||||||||
\(257\) | 27.8458 | 1.73697 | 0.868487 | − | 0.495712i | \(-0.165093\pi\) | ||||
0.868487 | + | 0.495712i | \(0.165093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.79350 | −0.111443 | ||||||||
\(260\) | 1.71146 | 0.106141 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.0819 | 0.869984 | ||||||||
\(263\) | −7.16802 | −0.441999 | −0.220999 | − | 0.975274i | \(-0.570932\pi\) | ||||
−0.220999 | + | 0.975274i | \(0.570932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.33107 | 0.388915 | ||||||||
\(266\) | 15.4559 | 0.947664 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 41.5752 | 2.53961 | ||||||||
\(269\) | −11.9031 | −0.725746 | −0.362873 | − | 0.931839i | \(-0.618204\pi\) | ||||
−0.362873 | + | 0.931839i | \(0.618204\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.2884 | −1.83989 | −0.919946 | − | 0.392046i | \(-0.871767\pi\) | ||||
−0.919946 | + | 0.392046i | \(0.871767\pi\) | |||||||
\(272\) | 3.45626 | 0.209567 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.5870 | −0.941645 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.5769 | −1.71702 | −0.858509 | − | 0.512799i | \(-0.828609\pi\) | ||||
−0.858509 | + | 0.512799i | \(0.828609\pi\) | |||||||
\(278\) | 10.2341 | 0.613800 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.2884 | 0.614851 | ||||||||
\(281\) | 4.72685 | 0.281980 | 0.140990 | − | 0.990011i | \(-0.454971\pi\) | ||||
0.140990 | + | 0.990011i | \(0.454971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.4523 | −0.621324 | −0.310662 | − | 0.950520i | \(-0.600551\pi\) | ||||
−0.310662 | + | 0.950520i | \(0.600551\pi\) | |||||||
\(284\) | −62.8804 | −3.73127 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.82882 | 0.107952 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3379 | −0.961050 | ||||||||
\(290\) | 19.5579 | 1.14848 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −31.4933 | −1.84300 | ||||||||
\(293\) | 32.1699 | 1.87939 | 0.939693 | − | 0.342018i | \(-0.111110\pi\) | ||||
0.939693 | + | 0.342018i | \(0.111110\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.46243 | −0.318035 | ||||||||
\(296\) | 8.99683 | 0.522930 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 39.7817 | 2.30449 | ||||||||
\(299\) | −1.05667 | −0.0611091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0819 | 0.581113 | ||||||||
\(302\) | −4.10195 | −0.236041 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −26.7099 | −1.53192 | ||||||||
\(305\) | 7.35685 | 0.421252 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.3277 | 1.38846 | 0.694228 | − | 0.719755i | \(-0.255746\pi\) | ||||
0.694228 | + | 0.719755i | \(0.255746\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −32.7407 | −1.85955 | ||||||||
\(311\) | 21.6929 | 1.23009 | 0.615045 | − | 0.788492i | \(-0.289138\pi\) | ||||
0.615045 | + | 0.788492i | \(0.289138\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.25592 | −0.410129 | −0.205065 | − | 0.978748i | \(-0.565740\pi\) | ||||
−0.205065 | + | 0.978748i | \(0.565740\pi\) | |||||||
\(314\) | −45.6589 | −2.57668 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 49.1537 | 2.76511 | ||||||||
\(317\) | 30.9119 | 1.73618 | 0.868092 | − | 0.496403i | \(-0.165346\pi\) | ||||
0.868092 | + | 0.496403i | \(0.165346\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 15.3719 | 0.859317 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.5769 | −0.700881 | ||||||||
\(323\) | −5.11704 | −0.284720 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.163858 | 0.00908923 | ||||||||
\(326\) | 25.2873 | 1.40053 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.17400 | −0.506549 | ||||||||
\(329\) | 8.79547 | 0.484910 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.3277 | 1.11731 | 0.558656 | − | 0.829399i | \(-0.311317\pi\) | ||||
0.558656 | + | 0.829399i | \(0.311317\pi\) | |||||||
\(332\) | −60.4059 | −3.31521 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −57.8944 | −3.16784 | ||||||||
\(335\) | −21.1013 | −1.15289 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.8226 | 1.46112 | 0.730561 | − | 0.682847i | \(-0.239258\pi\) | ||||
0.730561 | + | 0.682847i | \(0.239258\pi\) | |||||||
\(338\) | −31.8471 | −1.73225 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.74408 | −0.365749 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −50.5746 | −2.72680 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.5769 | 0.783657 | ||||||||
\(347\) | −24.9478 | −1.33927 | −0.669633 | − | 0.742692i | \(-0.733549\pi\) | ||||
−0.669633 | + | 0.742692i | \(0.733549\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.9574 | 1.06829 | 0.534146 | − | 0.845392i | \(-0.320633\pi\) | ||||
0.534146 | + | 0.845392i | \(0.320633\pi\) | |||||||
\(350\) | 1.95029 | 0.104247 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.89803 | −0.154247 | −0.0771234 | − | 0.997022i | \(-0.524574\pi\) | ||||
−0.0771234 | + | 0.997022i | \(0.524574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.9147 | 1.69386 | ||||||||
\(356\) | −23.1523 | −1.22707 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 40.3277 | 2.13139 | ||||||||
\(359\) | −26.2392 | −1.38485 | −0.692425 | − | 0.721490i | \(-0.743458\pi\) | ||||
−0.692425 | + | 0.721490i | \(0.743458\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.5444 | 1.08128 | ||||||||
\(362\) | −8.61489 | −0.452789 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.834464 | 0.0437378 | ||||||||
\(365\) | 15.9843 | 0.836655 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.3379 | 1.21823 | 0.609113 | − | 0.793083i | \(-0.291526\pi\) | ||||
0.609113 | + | 0.793083i | \(0.291526\pi\) | |||||||
\(368\) | 21.7345 | 1.13299 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.04096 | −0.470017 | ||||||||
\(371\) | 3.08686 | 0.160262 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.08193 | 0.107798 | 0.0538991 | − | 0.998546i | \(-0.482835\pi\) | ||||
0.0538991 | + | 0.998546i | \(0.482835\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −44.1212 | −2.27538 | ||||||||
\(377\) | 0.801181 | 0.0412629 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.45229 | −0.331432 | −0.165716 | − | 0.986174i | \(-0.552993\pi\) | ||||
−0.165716 | + | 0.986174i | \(0.552993\pi\) | |||||||
\(380\) | 52.1180 | 2.67360 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 45.8328 | 2.34501 | ||||||||
\(383\) | −6.97919 | −0.356620 | −0.178310 | − | 0.983974i | \(-0.557063\pi\) | ||||
−0.178310 | + | 0.983974i | \(0.557063\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.5306 | −0.688688 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −34.3277 | −1.74273 | ||||||||
\(389\) | −8.16232 | −0.413846 | −0.206923 | − | 0.978357i | \(-0.566345\pi\) | ||||
−0.206923 | + | 0.978357i | \(0.566345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.16386 | 0.210575 | ||||||||
\(392\) | 5.01636 | 0.253364 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 44.8226 | 2.25813 | ||||||||
\(395\) | −24.9478 | −1.25526 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.4198 | −1.37616 | −0.688080 | − | 0.725635i | \(-0.741546\pi\) | ||||
−0.688080 | + | 0.725635i | \(0.741546\pi\) | |||||||
\(398\) | −16.9786 | −0.851059 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.37036 | −0.168518 | ||||||||
\(401\) | −23.9327 | −1.19514 | −0.597571 | − | 0.801816i | \(-0.703867\pi\) | ||||
−0.597571 | + | 0.801816i | \(0.703867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.34121 | −0.0668104 | ||||||||
\(404\) | −43.0164 | −2.14014 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.53590 | 0.473259 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.7509 | −1.17440 | −0.587202 | − | 0.809440i | \(-0.699771\pi\) | ||||
−0.587202 | + | 0.809440i | \(0.699771\pi\) | |||||||
\(410\) | 9.21899 | 0.455294 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −63.6487 | −3.13574 | ||||||||
\(413\) | −2.66333 | −0.131054 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.6588 | 1.50498 | ||||||||
\(416\) | −0.0840174 | −0.00411929 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.2844 | 1.08867 | 0.544333 | − | 0.838869i | \(-0.316783\pi\) | ||||
0.544333 | + | 0.838869i | \(0.316783\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.38050 | 0.457177 | 0.228589 | − | 0.973523i | \(-0.426589\pi\) | ||||
0.228589 | + | 0.973523i | \(0.426589\pi\) | |||||||
\(422\) | −17.6325 | −0.858337 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.4848 | −0.752008 | ||||||||
\(425\) | −0.645689 | −0.0313205 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.58700 | 0.173587 | ||||||||
\(428\) | 5.81342 | 0.281002 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 50.8226 | 2.45089 | ||||||||
\(431\) | −5.94331 | −0.286279 | −0.143140 | − | 0.989703i | \(-0.545720\pi\) | ||||
−0.143140 | + | 0.989703i | \(0.545720\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.42314 | −0.260619 | −0.130310 | − | 0.991473i | \(-0.541597\pi\) | ||||
−0.130310 | + | 0.991473i | \(0.541597\pi\) | |||||||
\(434\) | −15.9635 | −0.766272 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.0819 | 0.482837 | ||||||||
\(437\) | −32.1782 | −1.53929 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.0393 | 1.24279 | 0.621394 | − | 0.783499i | \(-0.286567\pi\) | ||||
0.621394 | + | 0.783499i | \(0.286567\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.413002 | −0.0196445 | ||||||||
\(443\) | 7.35685 | 0.349534 | 0.174767 | − | 0.984610i | \(-0.444083\pi\) | ||||
0.174767 | + | 0.984610i | \(0.444083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.7509 | 0.557044 | ||||||||
\(446\) | 20.0654 | 0.950126 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.49493 | 0.354102 | ||||||||
\(449\) | −11.4172 | −0.538812 | −0.269406 | − | 0.963027i | \(-0.586827\pi\) | ||||
−0.269406 | + | 0.963027i | \(0.586827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 71.0843 | 3.34353 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.09207 | −0.426712 | ||||||||
\(455\) | −0.423529 | −0.0198553 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.3209 | −0.529571 | −0.264786 | − | 0.964307i | \(-0.585301\pi\) | ||||
−0.264786 | + | 0.964307i | \(0.585301\pi\) | |||||||
\(458\) | −49.7609 | −2.32517 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −42.4096 | −1.97736 | ||||||||
\(461\) | −0.604106 | −0.0281360 | −0.0140680 | − | 0.999901i | \(-0.504478\pi\) | ||||
−0.0140680 | + | 0.999901i | \(0.504478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.8653 | −1.62033 | −0.810164 | − | 0.586204i | \(-0.800622\pi\) | ||||
−0.810164 | + | 0.586204i | \(0.800622\pi\) | |||||||
\(464\) | −16.4793 | −0.765031 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 33.6487 | 1.55874 | ||||||||
\(467\) | −28.4582 | −1.31689 | −0.658443 | − | 0.752630i | \(-0.728785\pi\) | ||||
−0.658443 | + | 0.752630i | \(0.728785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2884 | −0.475076 | ||||||||
\(470\) | 44.3376 | 2.04514 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.3602 | 0.614954 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.98986 | 0.228951 | ||||||||
\(476\) | −3.28823 | −0.150716 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 40.7918 | 1.86577 | ||||||||
\(479\) | 30.1064 | 1.37560 | 0.687798 | − | 0.725902i | \(-0.258577\pi\) | ||||
0.687798 | + | 0.725902i | \(0.258577\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.370359 | −0.0168869 | ||||||||
\(482\) | 29.3892 | 1.33864 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.4229 | 0.791133 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.1537 | −1.50234 | −0.751169 | − | 0.660110i | \(-0.770510\pi\) | ||||
−0.751169 | + | 0.660110i | \(0.770510\pi\) | |||||||
\(488\) | −17.9937 | −0.814535 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.04096 | −0.227728 | ||||||||
\(491\) | −10.8257 | −0.488555 | −0.244277 | − | 0.969705i | \(-0.578551\pi\) | ||||
−0.244277 | + | 0.969705i | \(0.578551\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.15708 | −0.142188 | ||||||||
\(494\) | 3.19167 | 0.143600 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.5870 | 1.23869 | ||||||||
\(497\) | 15.5607 | 0.697995 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.8653 | 1.73985 | 0.869925 | − | 0.493185i | \(-0.164167\pi\) | ||||
0.869925 | + | 0.493185i | \(0.164167\pi\) | |||||||
\(500\) | 48.0161 | 2.14734 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.6178 | 0.607793 | ||||||||
\(503\) | 10.4437 | 0.465662 | 0.232831 | − | 0.972517i | \(-0.425201\pi\) | ||||
0.232831 | + | 0.972517i | \(0.425201\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.8328 | 0.971546 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −44.0786 | −1.95567 | ||||||||
\(509\) | 41.7999 | 1.85275 | 0.926374 | − | 0.376605i | \(-0.122908\pi\) | ||||
0.926374 | + | 0.376605i | \(0.122908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.79350 | 0.344764 | ||||||||
\(512\) | −40.8855 | −1.80690 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 68.4405 | 3.01878 | ||||||||
\(515\) | 32.3046 | 1.42351 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.40813 | −0.193682 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.12457 | 0.0931686 | ||||||||
\(521\) | −27.8874 | −1.22177 | −0.610884 | − | 0.791720i | \(-0.709186\pi\) | ||||
−0.610884 | + | 0.791720i | \(0.709186\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.6161 | 1.33875 | 0.669375 | − | 0.742924i | \(-0.266562\pi\) | ||||
0.669375 | + | 0.742924i | \(0.266562\pi\) | |||||||
\(524\) | 23.1523 | 1.01141 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.6178 | −0.768174 | ||||||||
\(527\) | 5.28508 | 0.230222 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.18413 | 0.138441 | ||||||||
\(530\) | 15.5607 | 0.675916 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 25.4113 | 1.10172 | ||||||||
\(533\) | 0.377652 | 0.0163579 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.95058 | −0.127565 | ||||||||
\(536\) | 51.6105 | 2.22923 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.2559 | −1.26131 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.7407 | 0.719740 | 0.359870 | − | 0.933003i | \(-0.382821\pi\) | ||||
0.359870 | + | 0.933003i | \(0.382821\pi\) | |||||||
\(542\) | −74.4440 | −3.19765 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.331073 | 0.0141946 | ||||||||
\(545\) | −5.11704 | −0.219190 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.4029 | −0.915120 | −0.457560 | − | 0.889179i | \(-0.651277\pi\) | ||||
−0.457560 | + | 0.889179i | \(0.651277\pi\) | |||||||
\(548\) | −25.6268 | −1.09472 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.3978 | 1.03938 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.1639 | −0.517260 | ||||||||
\(554\) | −70.2373 | −2.98410 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.8260 | 0.713582 | ||||||||
\(557\) | −7.53742 | −0.319371 | −0.159685 | − | 0.987168i | \(-0.551048\pi\) | ||||
−0.159685 | + | 0.987168i | \(0.551048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.08193 | 0.0880562 | ||||||||
\(560\) | 8.71145 | 0.368126 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.6178 | 0.490068 | ||||||||
\(563\) | −14.9900 | −0.631752 | −0.315876 | − | 0.948800i | \(-0.602298\pi\) | ||||
−0.315876 | + | 0.948800i | \(0.602298\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.0786 | −1.51784 | ||||||||
\(566\) | −25.6900 | −1.07983 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −78.0583 | −3.27525 | ||||||||
\(569\) | −17.8339 | −0.747635 | −0.373818 | − | 0.927502i | \(-0.621951\pi\) | ||||
−0.373818 | + | 0.927502i | \(0.621951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4130 | 0.686863 | 0.343431 | − | 0.939178i | \(-0.388411\pi\) | ||||
0.343431 | + | 0.939178i | \(0.388411\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.49493 | 0.187615 | ||||||||
\(575\) | −4.06037 | −0.169329 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.2357 | 1.05057 | 0.525287 | − | 0.850925i | \(-0.323958\pi\) | ||||
0.525287 | + | 0.850925i | \(0.323958\pi\) | |||||||
\(578\) | −40.1558 | −1.67026 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 32.1554 | 1.33518 | ||||||||
\(581\) | 14.9484 | 0.620164 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −39.0950 | −1.61776 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 79.0684 | 3.26629 | ||||||||
\(587\) | 30.4883 | 1.25839 | 0.629194 | − | 0.777248i | \(-0.283385\pi\) | ||||
0.629194 | + | 0.777248i | \(0.283385\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.8429 | −1.68290 | ||||||||
\(590\) | −13.4258 | −0.552730 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.61783 | 0.313091 | ||||||||
\(593\) | 36.2719 | 1.48951 | 0.744754 | − | 0.667340i | \(-0.232567\pi\) | ||||
0.744754 | + | 0.667340i | \(0.232567\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.66893 | 0.0684193 | ||||||||
\(596\) | 65.4056 | 2.67912 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.59714 | −0.106205 | ||||||||
\(599\) | −2.03018 | −0.0829511 | −0.0414755 | − | 0.999140i | \(-0.513206\pi\) | ||||
−0.0414755 | + | 0.999140i | \(0.513206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.7834 | −1.17410 | −0.587049 | − | 0.809551i | \(-0.699710\pi\) | ||||
−0.587049 | + | 0.809551i | \(0.699710\pi\) | |||||||
\(602\) | 24.7797 | 1.00995 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.74408 | −0.274413 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.4422 | −0.951488 | −0.475744 | − | 0.879584i | \(-0.657821\pi\) | ||||
−0.475744 | + | 0.879584i | \(0.657821\pi\) | |||||||
\(608\) | −2.55852 | −0.103762 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.0819 | 0.732116 | ||||||||
\(611\) | 1.81627 | 0.0734785 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.2458 | −1.22162 | −0.610808 | − | 0.791779i | \(-0.709155\pi\) | ||||
−0.610808 | + | 0.791779i | \(0.709155\pi\) | |||||||
\(614\) | 59.7936 | 2.41307 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.8968 | 1.20360 | 0.601800 | − | 0.798647i | \(-0.294451\pi\) | ||||
0.601800 | + | 0.798647i | \(0.294451\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.0718 | 0.927334 | 0.463667 | − | 0.886010i | \(-0.346533\pi\) | ||||
0.463667 | + | 0.886010i | \(0.346533\pi\) | |||||||
\(620\) | −53.8295 | −2.16184 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 53.3176 | 2.13784 | ||||||||
\(623\) | 5.72940 | 0.229543 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.4029 | −0.816115 | ||||||||
\(626\) | −17.8339 | −0.712785 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −75.0684 | −2.99556 | ||||||||
\(629\) | 1.45941 | 0.0581906 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.3277 | −0.968471 | −0.484236 | − | 0.874938i | \(-0.660902\pi\) | ||||
−0.484236 | + | 0.874938i | \(0.660902\pi\) | |||||||
\(632\) | 61.0183 | 2.42718 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 75.9764 | 3.01741 | ||||||||
\(635\) | 22.3719 | 0.887802 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.206501 | −0.00818187 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 39.4506 | 1.55942 | ||||||||
\(641\) | −0.168035 | −0.00663697 | −0.00331849 | − | 0.999994i | \(-0.501056\pi\) | ||||
−0.00331849 | + | 0.999994i | \(0.501056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.2357 | 0.443091 | 0.221545 | − | 0.975150i | \(-0.428890\pi\) | ||||
0.221545 | + | 0.975150i | \(0.428890\pi\) | |||||||
\(644\) | −20.6778 | −0.814819 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.5769 | −0.494830 | ||||||||
\(647\) | 33.4072 | 1.31337 | 0.656686 | − | 0.754164i | \(-0.271958\pi\) | ||||
0.656686 | + | 0.754164i | \(0.271958\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.402737 | 0.0157967 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 41.5752 | 1.62821 | ||||||||
\(653\) | 4.94901 | 0.193670 | 0.0968348 | − | 0.995300i | \(-0.469128\pi\) | ||||
0.0968348 | + | 0.995300i | \(0.469128\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.7509 | −0.459144 | ||||||||
\(656\) | −7.76783 | −0.303283 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.6178 | 0.842751 | ||||||||
\(659\) | 12.8974 | 0.502412 | 0.251206 | − | 0.967934i | \(-0.419173\pi\) | ||||
0.251206 | + | 0.967934i | \(0.419173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.8978 | 1.00731 | 0.503654 | − | 0.863906i | \(-0.331989\pi\) | ||||
0.503654 | + | 0.863906i | \(0.331989\pi\) | |||||||
\(662\) | 49.9622 | 1.94184 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −74.9865 | −2.91004 | ||||||||
\(665\) | −12.8974 | −0.500140 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.8531 | −0.768714 | ||||||||
\(668\) | −95.1851 | −3.68282 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −51.8636 | −2.00367 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.0718 | −1.81448 | −0.907242 | − | 0.420609i | \(-0.861817\pi\) | ||||
−0.907242 | + | 0.420609i | \(0.861817\pi\) | |||||||
\(674\) | 65.9257 | 2.53936 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −52.3602 | −2.01385 | ||||||||
\(677\) | 5.97235 | 0.229536 | 0.114768 | − | 0.993392i | \(-0.463388\pi\) | ||||
0.114768 | + | 0.993392i | \(0.463388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.49493 | 0.326006 | ||||||||
\(680\) | −8.37194 | −0.321049 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.26999 | −0.163386 | −0.0816932 | − | 0.996658i | \(-0.526033\pi\) | ||||
−0.0816932 | + | 0.996658i | \(0.526033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.0068 | 0.496964 | ||||||||
\(686\) | −2.45784 | −0.0938407 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −42.8226 | −1.63260 | ||||||||
\(689\) | 0.637440 | 0.0242845 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.3379 | −0.735647 | −0.367823 | − | 0.929896i | \(-0.619897\pi\) | ||||
−0.367823 | + | 0.929896i | \(0.619897\pi\) | |||||||
\(692\) | 23.9660 | 0.911051 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −61.3176 | −2.32758 | ||||||||
\(695\) | −8.53997 | −0.323940 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.48815 | −0.0563677 | ||||||||
\(698\) | 49.0519 | 1.85664 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.20650 | 0.121194 | ||||||||
\(701\) | 22.3135 | 0.842769 | 0.421384 | − | 0.906882i | \(-0.361544\pi\) | ||||
0.421384 | + | 0.906882i | \(0.361544\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.2783 | −0.425369 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.12289 | −0.268074 | ||||||||
\(707\) | 10.6451 | 0.400349 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.0325 | 0.564558 | 0.282279 | − | 0.959332i | \(-0.408910\pi\) | ||||
0.282279 | + | 0.959332i | \(0.408910\pi\) | |||||||
\(710\) | 78.4412 | 2.94384 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −28.7407 | −1.07710 | ||||||||
\(713\) | 33.2348 | 1.24465 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 66.3034 | 2.47787 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −64.4916 | −2.40680 | ||||||||
\(719\) | −20.2958 | −0.756907 | −0.378454 | − | 0.925620i | \(-0.623544\pi\) | ||||
−0.378454 | + | 0.925620i | \(0.623544\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.7509 | 0.586593 | ||||||||
\(722\) | 50.4947 | 1.87922 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.1639 | −0.526396 | ||||||||
\(725\) | 3.07861 | 0.114337 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.9865 | −1.00087 | −0.500437 | − | 0.865773i | \(-0.666827\pi\) | ||||
−0.500437 | + | 0.865773i | \(0.666827\pi\) | |||||||
\(728\) | 1.03588 | 0.0383924 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 39.2868 | 1.45407 | ||||||||
\(731\) | −8.20390 | −0.303432 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.41300 | 0.162998 | 0.0814990 | − | 0.996673i | \(-0.474029\pi\) | ||||
0.0814990 | + | 0.996673i | \(0.474029\pi\) | |||||||
\(734\) | 57.3607 | 2.11722 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.08193 | 0.0767409 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.1808 | 1.33093 | 0.665466 | − | 0.746428i | \(-0.268233\pi\) | ||||
0.665466 | + | 0.746428i | \(0.268233\pi\) | |||||||
\(740\) | −14.8644 | −0.546425 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.58700 | 0.278527 | ||||||||
\(743\) | −22.7703 | −0.835363 | −0.417682 | − | 0.908593i | \(-0.637157\pi\) | ||||
−0.417682 | + | 0.908593i | \(0.637157\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.1964 | −1.21622 | ||||||||
\(746\) | 5.11704 | 0.187348 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.43862 | −0.0525661 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.0291 | −0.548421 | −0.274211 | − | 0.961670i | \(-0.588417\pi\) | ||||
−0.274211 | + | 0.961670i | \(0.588417\pi\) | |||||||
\(752\) | −37.3584 | −1.36232 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.96917 | 0.0717130 | ||||||||
\(755\) | 3.42293 | 0.124573 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.6094 | 0.858097 | 0.429048 | − | 0.903281i | \(-0.358849\pi\) | ||||
0.429048 | + | 0.903281i | \(0.358849\pi\) | |||||||
\(758\) | −15.8587 | −0.576013 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 64.6981 | 2.34685 | ||||||||
\(761\) | −50.9440 | −1.84672 | −0.923359 | − | 0.383938i | \(-0.874568\pi\) | ||||
−0.923359 | + | 0.383938i | \(0.874568\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.49493 | −0.0903226 | ||||||||
\(764\) | 75.3543 | 2.72622 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.1537 | −0.619789 | ||||||||
\(767\) | −0.549981 | −0.0198586 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.3602 | −0.626026 | −0.313013 | − | 0.949749i | \(-0.601338\pi\) | ||||
−0.313013 | + | 0.949749i | \(0.601338\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.2458 | −0.800643 | ||||||||
\(773\) | 35.2442 | 1.26765 | 0.633824 | − | 0.773478i | \(-0.281485\pi\) | ||||
0.633824 | + | 0.773478i | \(0.281485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.15372 | −0.185127 | ||||||||
\(776\) | −42.6136 | −1.52974 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.0617 | −0.719245 | ||||||||
\(779\) | 11.5004 | 0.412044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 10.2341 | 0.365970 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.24747 | 0.151695 | ||||||||
\(785\) | 38.1007 | 1.35987 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.8754 | −1.06494 | −0.532472 | − | 0.846448i | \(-0.678737\pi\) | ||||
−0.532472 | + | 0.846448i | \(0.678737\pi\) | |||||||
\(788\) | 73.6935 | 2.62522 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −61.3176 | −2.18158 | ||||||||
\(791\) | −17.5909 | −0.625462 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.740719 | 0.0263037 | ||||||||
\(794\) | −67.3934 | −2.39170 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.9147 | −0.989411 | ||||||||
\(797\) | 12.2851 | 0.435159 | 0.217580 | − | 0.976043i | \(-0.430184\pi\) | ||||
0.217580 | + | 0.976043i | \(0.430184\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.15708 | −0.253199 | ||||||||
\(800\) | −0.322844 | −0.0114143 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −58.8226 | −2.07710 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.4949 | 0.369898 | ||||||||
\(806\) | −3.29648 | −0.116113 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −53.3995 | −1.87859 | ||||||||
\(809\) | −32.6350 | −1.14739 | −0.573693 | − | 0.819070i | \(-0.694490\pi\) | ||||
−0.573693 | + | 0.819070i | \(0.694490\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.8754 | −0.487232 | −0.243616 | − | 0.969872i | \(-0.578334\pi\) | ||||
−0.243616 | + | 0.969872i | \(0.578334\pi\) | |||||||
\(812\) | 15.6781 | 0.550193 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.1013 | −0.739147 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 63.3995 | 2.21807 | ||||||||
\(818\) | −58.3757 | −2.04106 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.1571 | 0.529308 | ||||||||
\(821\) | 8.42606 | 0.294072 | 0.147036 | − | 0.989131i | \(-0.453027\pi\) | ||||
0.147036 | + | 0.989131i | \(0.453027\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.4422 | 1.37487 | 0.687433 | − | 0.726247i | \(-0.258737\pi\) | ||||
0.687433 | + | 0.726247i | \(0.258737\pi\) | |||||||
\(824\) | −79.0120 | −2.75251 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.54603 | −0.227766 | ||||||||
\(827\) | −0.591563 | −0.0205707 | −0.0102853 | − | 0.999947i | \(-0.503274\pi\) | ||||
−0.0102853 | + | 0.999947i | \(0.503274\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.5667 | 0.818506 | 0.409253 | − | 0.912421i | \(-0.365789\pi\) | ||||
0.409253 | + | 0.912421i | \(0.365789\pi\) | |||||||
\(830\) | 75.3543 | 2.61559 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.54771 | 0.0536572 | ||||||||
\(833\) | 0.813723 | 0.0281938 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.3108 | 1.67186 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 54.7715 | 1.89205 | ||||||||
\(839\) | 38.6507 | 1.33437 | 0.667185 | − | 0.744892i | \(-0.267499\pi\) | ||||
0.667185 | + | 0.744892i | \(0.267499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9472 | −0.480939 | ||||||||
\(842\) | 23.0557 | 0.794553 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.9899 | −0.997872 | ||||||||
\(845\) | 26.5752 | 0.914216 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −13.1113 | −0.450245 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.58700 | −0.0544336 | ||||||||
\(851\) | 9.17741 | 0.314598 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.3927 | −1.31454 | −0.657271 | − | 0.753654i | \(-0.728289\pi\) | ||||
−0.657271 | + | 0.753654i | \(0.728289\pi\) | |||||||
\(854\) | 8.81626 | 0.301686 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.21664 | 0.246660 | ||||||||
\(857\) | −3.49785 | −0.119484 | −0.0597421 | − | 0.998214i | \(-0.519028\pi\) | ||||
−0.0597421 | + | 0.998214i | \(0.519028\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.1740 | −1.06364 | −0.531822 | − | 0.846856i | \(-0.678492\pi\) | ||||
−0.531822 | + | 0.846856i | \(0.678492\pi\) | |||||||
\(860\) | 83.5582 | 2.84931 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.6077 | −0.497540 | ||||||||
\(863\) | 30.9119 | 1.05225 | 0.526126 | − | 0.850406i | \(-0.323644\pi\) | ||||
0.526126 | + | 0.850406i | \(0.323644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.1639 | −0.413584 | ||||||||
\(866\) | −13.3292 | −0.452944 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −26.2458 | −0.890840 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.12457 | −0.0719884 | ||||||||
\(872\) | 12.5155 | 0.423827 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −79.0887 | −2.67522 | ||||||||
\(875\) | −11.8823 | −0.401696 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.5118 | −0.895242 | −0.447621 | − | 0.894223i | \(-0.647729\pi\) | ||||
−0.447621 | + | 0.894223i | \(0.647729\pi\) | |||||||
\(878\) | 64.0003 | 2.15991 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.0604 | −0.372633 | −0.186316 | − | 0.982490i | \(-0.559655\pi\) | ||||
−0.186316 | + | 0.982490i | \(0.559655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.8754 | 0.601556 | 0.300778 | − | 0.953694i | \(-0.402754\pi\) | ||||
0.300778 | + | 0.953694i | \(0.402754\pi\) | |||||||
\(884\) | −0.679023 | −0.0228380 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.0819 | 0.607474 | ||||||||
\(887\) | −24.7382 | −0.830626 | −0.415313 | − | 0.909679i | \(-0.636328\pi\) | ||||
−0.415313 | + | 0.909679i | \(0.636328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.9079 | 0.365840 | ||||||||
\(890\) | 28.8817 | 0.968117 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 32.9899 | 1.10458 | ||||||||
\(893\) | 55.3097 | 1.85087 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.6520 | −1.12486 | ||||||||
\(896\) | 19.2350 | 0.642598 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.0617 | −0.936430 | ||||||||
\(899\) | −25.1990 | −0.840433 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.51185 | −0.0836818 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 88.2424 | 2.93490 | ||||||||
\(905\) | 7.18881 | 0.238964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.3176 | 0.840656 | 0.420328 | − | 0.907372i | \(-0.361915\pi\) | ||||
0.420328 | + | 0.907372i | \(0.361915\pi\) | |||||||
\(908\) | −14.9484 | −0.496080 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.04096 | −0.0345076 | ||||||||
\(911\) | 48.7124 | 1.61391 | 0.806957 | − | 0.590610i | \(-0.201113\pi\) | ||||
0.806957 | + | 0.590610i | \(0.201113\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −27.8250 | −0.920370 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −81.8125 | −2.70316 | ||||||||
\(917\) | −5.72940 | −0.189201 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.0068 | −1.22074 | −0.610371 | − | 0.792116i | \(-0.708979\pi\) | ||||
−0.610371 | + | 0.792116i | \(0.708979\pi\) | |||||||
\(920\) | −52.6463 | −1.73570 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.48479 | −0.0488991 | ||||||||
\(923\) | 3.21331 | 0.105767 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.42314 | −0.0467925 | ||||||||
\(926\) | −85.6932 | −2.81605 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.57854 | −0.0518181 | ||||||||
\(929\) | −13.4682 | −0.441877 | −0.220938 | − | 0.975288i | \(-0.570912\pi\) | ||||
−0.220938 | + | 0.975288i | \(0.570912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.28843 | −0.206095 | ||||||||
\(932\) | 55.3222 | 1.81214 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −69.9455 | −2.28869 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.7204 | 1.78764 | 0.893819 | − | 0.448427i | \(-0.148016\pi\) | ||||
0.893819 | + | 0.448427i | \(0.148016\pi\) | |||||||
\(938\) | −25.2873 | −0.825659 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 72.8961 | 2.37761 | ||||||||
\(941\) | 32.9919 | 1.07551 | 0.537753 | − | 0.843103i | \(-0.319273\pi\) | ||||
0.537753 | + | 0.843103i | \(0.319273\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.35813 | −0.304743 | ||||||||
\(944\) | 11.3124 | 0.368187 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.5513 | 0.667829 | 0.333914 | − | 0.942603i | \(-0.391630\pi\) | ||||
0.333914 | + | 0.942603i | \(0.391630\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.60937 | 0.0522422 | ||||||||
\(950\) | 12.2643 | 0.397905 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.08193 | −0.132296 | ||||||||
\(953\) | 55.9138 | 1.81123 | 0.905613 | − | 0.424106i | \(-0.139412\pi\) | ||||
0.905613 | + | 0.424106i | \(0.139412\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.2458 | −1.23760 | ||||||||
\(956\) | 67.0664 | 2.16908 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 73.9966 | 2.39072 | ||||||||
\(959\) | 6.34175 | 0.204786 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.1841 | 0.360778 | ||||||||
\(962\) | −0.910283 | −0.0293487 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 48.3193 | 1.55626 | ||||||||
\(965\) | 11.2908 | 0.363462 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.9046 | −0.929509 | −0.464754 | − | 0.885440i | \(-0.653857\pi\) | ||||
−0.464754 | + | 0.885440i | \(0.653857\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 42.8226 | 1.37495 | ||||||||
\(971\) | 36.6621 | 1.17654 | 0.588271 | − | 0.808664i | \(-0.299809\pi\) | ||||
0.588271 | + | 0.808664i | \(0.299809\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.16386 | −0.133487 | ||||||||
\(974\) | −81.4865 | −2.61099 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.2357 | −0.487681 | ||||||||
\(977\) | 14.5457 | 0.465357 | 0.232678 | − | 0.972554i | \(-0.425251\pi\) | ||||
0.232678 | + | 0.972554i | \(0.425251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −8.28792 | −0.264748 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.6077 | −0.849085 | ||||||||
\(983\) | 17.6325 | 0.562390 | 0.281195 | − | 0.959651i | \(-0.409269\pi\) | ||||
0.281195 | + | 0.959651i | \(0.409269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.4029 | −1.19175 | ||||||||
\(986\) | −7.75958 | −0.247115 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.24747 | 0.166944 | ||||||||
\(989\) | −51.5897 | −1.64046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.1144 | 0.480126 | 0.240063 | − | 0.970757i | \(-0.422832\pi\) | ||||
0.240063 | + | 0.970757i | \(0.422832\pi\) | |||||||
\(992\) | 2.64254 | 0.0839007 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 38.2458 | 1.21308 | ||||||||
\(995\) | 14.1680 | 0.449156 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.5769 | 0.778357 | 0.389178 | − | 0.921162i | \(-0.372759\pi\) | ||||
0.389178 | + | 0.921162i | \(0.372759\pi\) | |||||||
\(998\) | 95.5246 | 3.02378 | ||||||||
\(999\) | 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 | 7623.2.a.cq.1.6 | yes | 6 | |
3.2 | odd | 2 | inner | 7623.2.a.cq.1.1 | ✓ | 6 | |
11.10 | odd | 2 | 7623.2.a.cr.1.1 | yes | 6 | ||
33.32 | even | 2 | 7623.2.a.cr.1.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7623.2.a.cq.1.1 | ✓ | 6 | 3.2 | odd | 2 | inner | |
7623.2.a.cq.1.6 | yes | 6 | 1.1 | even | 1 | trivial | |
7623.2.a.cr.1.1 | yes | 6 | 11.10 | odd | 2 | ||
7623.2.a.cr.1.6 | yes | 6 | 33.32 | even | 2 |