Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(1,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, 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("1792.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 448) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.73205 | −1.57735 | −0.788675 | − | 0.614810i | \(-0.789233\pi\) | ||||
−0.788675 | + | 0.614810i | \(0.789233\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.73205 | 1.22181 | 0.610905 | − | 0.791704i | \(-0.290806\pi\) | ||||
0.610905 | + | 0.791704i | \(0.290806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.46410 | 1.64749 | 0.823744 | − | 0.566961i | \(-0.191881\pi\) | ||||
0.823744 | + | 0.566961i | \(0.191881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.73205 | 1.86713 | 0.933567 | − | 0.358402i | \(-0.116678\pi\) | ||||
0.933567 | + | 0.358402i | \(0.116678\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.46410 | −1.92722 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26795 | 0.290887 | 0.145444 | − | 0.989367i | \(-0.453539\pi\) | ||||
0.145444 | + | 0.989367i | \(0.453539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.73205 | −0.596182 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.46410 | −0.722315 | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361158 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.46410 | 0.492820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.46410 | −0.271877 | −0.135938 | − | 0.990717i | \(-0.543405\pi\) | ||||
−0.135938 | + | 0.990717i | \(0.543405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14.9282 | −2.59867 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.73205 | 0.461801 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.46410 | −0.240697 | −0.120348 | − | 0.992732i | \(-0.538401\pi\) | ||||
−0.120348 | + | 0.992732i | \(0.538401\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18.3923 | −2.94513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.46410 | 0.833268 | 0.416634 | − | 0.909074i | \(-0.363210\pi\) | ||||
0.416634 | + | 0.909074i | \(0.363210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.1962 | 1.81810 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.92820 | −0.427122 | −0.213561 | − | 0.976930i | \(-0.568506\pi\) | ||||
−0.213561 | + | 0.976930i | \(0.568506\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.46410 | −0.765127 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0000 | 1.64833 | 0.824163 | − | 0.566352i | \(-0.191646\pi\) | ||||
0.824163 | + | 0.566352i | \(0.191646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.9282 | 2.01292 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.66025 | −1.25766 | −0.628829 | − | 0.777544i | \(-0.716465\pi\) | ||||
−0.628829 | + | 0.777544i | \(0.716465\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1244 | −1.42433 | −0.712164 | − | 0.702013i | \(-0.752285\pi\) | ||||
−0.712164 | + | 0.702013i | \(0.752285\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.46410 | 0.562424 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.3923 | 2.28128 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.46410 | 1.13934 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.92820 | 0.347514 | 0.173757 | − | 0.984789i | \(-0.444409\pi\) | ||||
0.173757 | + | 0.984789i | \(0.444409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.9282 | −1.51313 | −0.756566 | − | 0.653917i | \(-0.773124\pi\) | ||||
−0.756566 | + | 0.653917i | \(0.773124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.73205 | −0.777350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.46410 | 0.622692 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9282 | 1.22952 | 0.614759 | − | 0.788715i | \(-0.289253\pi\) | ||||
0.614759 | + | 0.788715i | \(0.289253\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.66025 | 0.621294 | 0.310647 | − | 0.950525i | \(-0.399454\pi\) | ||||
0.310647 | + | 0.950525i | \(0.399454\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.46410 | 0.592665 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8564 | −1.25678 | −0.628388 | − | 0.777900i | \(-0.716285\pi\) | ||||
−0.628388 | + | 0.777900i | \(0.716285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.73205 | 0.705711 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9282 | 1.13320 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.46410 | 0.355409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.92820 | 0.906522 | 0.453261 | − | 0.891378i | \(-0.350261\pi\) | ||||
0.453261 | + | 0.891378i | \(0.350261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.3923 | 2.45152 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.66025 | −0.165201 | −0.0826007 | − | 0.996583i | \(-0.526323\pi\) | ||||
−0.0826007 | + | 0.996583i | \(0.526323\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.85641 | 0.971181 | 0.485590 | − | 0.874187i | \(-0.338605\pi\) | ||||
0.485590 | + | 0.874187i | \(0.338605\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.46410 | −0.728422 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.07180 | 0.490309 | 0.245155 | − | 0.969484i | \(-0.421161\pi\) | ||||
0.245155 | + | 0.969484i | \(0.421161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3923 | 1.18697 | 0.593484 | − | 0.804846i | \(-0.297752\pi\) | ||||
0.593484 | + | 0.804846i | \(0.297752\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.53590 | −0.614846 | −0.307423 | − | 0.951573i | \(-0.599467\pi\) | ||||
−0.307423 | + | 0.951573i | \(0.599467\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.46410 | −0.882532 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 30.0526 | 2.77836 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8564 | 1.71422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.46410 | −0.492681 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.4641 | 1.01727 | 0.508637 | − | 0.860981i | \(-0.330149\pi\) | ||||
0.508637 | + | 0.860981i | \(0.330149\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.9282 | −1.31436 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7321 | 0.937664 | 0.468832 | − | 0.883287i | \(-0.344675\pi\) | ||||
0.468832 | + | 0.883287i | \(0.344675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.26795 | 0.109945 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.9282 | −0.940550 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8564 | −1.69645 | −0.848224 | − | 0.529638i | \(-0.822328\pi\) | ||||
−0.848224 | + | 0.529638i | \(0.822328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.26795 | −0.786097 | −0.393049 | − | 0.919518i | \(-0.628580\pi\) | ||||
−0.393049 | + | 0.919518i | \(0.628580\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 36.7846 | 3.07608 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.73205 | −0.225336 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.07180 | 0.0878050 | 0.0439025 | − | 0.999036i | \(-0.486021\pi\) | ||||
0.0439025 | + | 0.999036i | \(0.486021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.39230 | −0.194683 | −0.0973415 | − | 0.995251i | \(-0.531034\pi\) | ||||
−0.0973415 | + | 0.995251i | \(0.531034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.92820 | 0.721802 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.9282 | −0.877774 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1962 | −0.973359 | −0.486679 | − | 0.873581i | \(-0.661792\pi\) | ||||
−0.486679 | + | 0.873581i | \(0.661792\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −32.7846 | −2.59999 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.46410 | −0.273009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4641 | 1.05459 | 0.527295 | − | 0.849682i | \(-0.323206\pi\) | ||||
0.527295 | + | 0.849682i | \(0.323206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −40.7846 | −3.17508 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.07180 | −0.392467 | −0.196234 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196234 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.3205 | 2.48619 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.66025 | 0.432850 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.80385 | 0.289201 | 0.144601 | − | 0.989490i | \(-0.453810\pi\) | ||||
0.144601 | + | 0.989490i | \(0.453810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.46410 | 0.186269 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.3923 | 1.98377 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.92820 | 0.218864 | 0.109432 | − | 0.993994i | \(-0.465097\pi\) | ||||
0.109432 | + | 0.993994i | \(0.465097\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.7321 | −0.797707 | −0.398854 | − | 0.917015i | \(-0.630592\pi\) | ||||
−0.398854 | + | 0.917015i | \(0.630592\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.3923 | 2.24666 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.9282 | 0.799149 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.00000 | −0.290957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.53590 | 0.470464 | 0.235232 | − | 0.971939i | \(-0.424415\pi\) | ||||
0.235232 | + | 0.971939i | \(0.424415\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −50.2487 | −3.59838 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.8564 | 1.84219 | 0.921096 | − | 0.389335i | \(-0.127295\pi\) | ||||
0.921096 | + | 0.389335i | \(0.127295\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.8564 | 1.54163 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.46410 | −0.102760 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.46410 | 0.381629 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.4641 | −1.07483 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.92820 | 0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.7846 | −1.15550 | −0.577750 | − | 0.816214i | \(-0.696069\pi\) | ||||
−0.577750 | + | 0.816214i | \(0.696069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.00000 | −0.548151 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.9282 | 1.01810 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 35.3205 | 2.38674 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.4641 | 0.905693 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.92820 | 0.463947 | 0.231973 | − | 0.972722i | \(-0.425482\pi\) | ||||
0.231973 | + | 0.972722i | \(0.425482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.0000 | 0.733333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.80385 | −0.252470 | −0.126235 | − | 0.992000i | \(-0.540289\pi\) | ||||
−0.126235 | + | 0.992000i | \(0.540289\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2679 | −1.14110 | −0.570549 | − | 0.821263i | \(-0.693270\pi\) | ||||
−0.570549 | + | 0.821263i | \(0.693270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.9282 | −0.982204 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.8564 | −1.93938 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.5359 | 0.810880 | 0.405440 | − | 0.914122i | \(-0.367118\pi\) | ||||
0.405440 | + | 0.914122i | \(0.367118\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.7846 | −1.21002 | −0.605012 | − | 0.796217i | \(-0.706832\pi\) | ||||
−0.605012 | + | 0.796217i | \(0.706832\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.7321 | 1.20166 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.73205 | 0.174544 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.53590 | 0.543126 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.4641 | −0.979998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.8038 | −0.997530 | −0.498765 | − | 0.866737i | \(-0.666213\pi\) | ||||
−0.498765 | + | 0.866737i | \(0.666213\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.9282 | −1.19001 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.9282 | −0.934840 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.46410 | −0.0909748 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.53590 | −0.404562 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.9282 | 0.673862 | 0.336931 | − | 0.941529i | \(-0.390611\pi\) | ||||
0.336931 | + | 0.941529i | \(0.390611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.7846 | 2.01394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.3923 | 1.98238 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.5885 | 0.767532 | 0.383766 | − | 0.923430i | \(-0.374627\pi\) | ||||
0.383766 | + | 0.923430i | \(0.374627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.9282 | −0.906824 | −0.453412 | − | 0.891301i | \(-0.649793\pi\) | ||||
−0.453412 | + | 0.891301i | \(0.649793\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.3923 | −1.11315 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.4641 | 0.811916 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | −0.240337 | −0.120168 | − | 0.992754i | \(-0.538343\pi\) | ||||
−0.120168 | + | 0.992754i | \(0.538343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.8564 | −1.06904 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.5885 | 0.986081 | 0.493041 | − | 0.870006i | \(-0.335885\pi\) | ||||
0.493041 | + | 0.870006i | \(0.335885\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.46410 | −0.560605 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.3923 | −1.42990 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1962 | 0.712507 | 0.356253 | − | 0.934389i | \(-0.384054\pi\) | ||||
0.356253 | + | 0.934389i | \(0.384054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.3923 | −1.53662 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.8564 | −1.26824 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.3205 | −1.34866 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.46410 | 0.314946 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.53590 | 0.260581 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.3923 | −1.74026 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.58846 | 0.490169 | 0.245085 | − | 0.969502i | \(-0.421184\pi\) | ||||
0.245085 | + | 0.969502i | \(0.421184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.9282 | −1.53189 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.85641 | −0.332086 | −0.166043 | − | 0.986118i | \(-0.553099\pi\) | ||||
−0.166043 | + | 0.986118i | \(0.553099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.8564 | −1.12235 | −0.561175 | − | 0.827697i | \(-0.689651\pi\) | ||||
−0.561175 | + | 0.827697i | \(0.689651\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.1962 | 0.687175 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.7846 | 1.61670 | 0.808352 | − | 0.588699i | \(-0.200360\pi\) | ||||
0.808352 | + | 0.588699i | \(0.200360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.8564 | −0.773389 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.53590 | 0.141101 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.5885 | 0.920162 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.8564 | −1.87226 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.92820 | −0.161437 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3923 | −0.901003 | −0.450501 | − | 0.892776i | \(-0.648755\pi\) | ||||
−0.450501 | + | 0.892776i | \(0.648755\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.53590 | −0.358165 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.8564 | −1.19414 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3923 | 0.892946 | 0.446473 | − | 0.894797i | \(-0.352680\pi\) | ||||
0.446473 | + | 0.894797i | \(0.352680\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.8564 | 0.969827 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.8564 | −1.18359 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.8564 | 1.39206 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35.3205 | −1.89610 | −0.948052 | − | 0.318115i | \(-0.896950\pi\) | ||||
−0.948052 | + | 0.318115i | \(0.896950\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0526 | 0.752216 | 0.376108 | − | 0.926576i | \(-0.377262\pi\) | ||||
0.376108 | + | 0.926576i | \(0.377262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.9282 | −1.43732 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.928203 | 0.0494033 | 0.0247016 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247016 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.46410 | −0.289191 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.4641 | −1.44950 | −0.724750 | − | 0.689012i | \(-0.758045\pi\) | ||||
−0.724750 | + | 0.689012i | \(0.758045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3923 | −0.915384 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −51.5167 | −2.70392 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −35.3205 | −1.84876 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.7846 | −1.08495 | −0.542474 | − | 0.840073i | \(-0.682512\pi\) | ||||
−0.542474 | + | 0.840073i | \(0.682512\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.92820 | 0.464784 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | 0.623009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.9282 | −1.60140 | −0.800701 | − | 0.599064i | \(-0.795539\pi\) | ||||
−0.800701 | + | 0.599064i | \(0.795539\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.9282 | 0.977448 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.85641 | −0.507631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.2487 | −0.731907 | −0.365954 | − | 0.930633i | \(-0.619257\pi\) | ||||
−0.365954 | + | 0.930633i | \(0.619257\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −31.3205 | −1.60460 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.7846 | 1.67522 | 0.837608 | − | 0.546272i | \(-0.183954\pi\) | ||||
0.837608 | + | 0.546272i | \(0.183954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.9282 | 0.760812 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.3923 | 1.23993 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.3205 | 1.18240 | 0.591198 | − | 0.806526i | \(-0.298655\pi\) | ||||
0.591198 | + | 0.806526i | \(0.298655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.92820 | −0.350374 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.3205 | −1.47902 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.8564 | 1.50224 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.87564 | −0.244702 | −0.122351 | − | 0.992487i | \(-0.539043\pi\) | ||||
−0.122351 | + | 0.992487i | \(0.539043\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.46410 | −0.173422 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4641 | 0.672365 | 0.336183 | − | 0.941797i | \(-0.390864\pi\) | ||||
0.336183 | + | 0.941797i | \(0.390864\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.9282 | −1.34139 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.73205 | −0.334518 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.07180 | 0.151891 | 0.0759453 | − | 0.997112i | \(-0.475803\pi\) | ||||
0.0759453 | + | 0.997112i | \(0.475803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 54.2487 | 2.67589 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.66025 | −0.475350 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.4641 | 0.759103 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.3205 | 1.23995 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.8038 | −1.16289 | −0.581447 | − | 0.813584i | \(-0.697513\pi\) | ||||
−0.581447 | + | 0.813584i | \(0.697513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.8564 | −1.26016 | −0.630082 | − | 0.776529i | \(-0.716979\pi\) | ||||
−0.630082 | + | 0.776529i | \(0.716979\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.0718 | −0.635573 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.92820 | 0.239053 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.1244 | −0.538345 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −100.497 | −4.85206 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.4641 | 1.70825 | 0.854123 | − | 0.520071i | \(-0.174095\pi\) | ||||
0.854123 | + | 0.520071i | \(0.174095\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.8564 | 0.762010 | 0.381005 | − | 0.924573i | \(-0.375578\pi\) | ||||
0.381005 | + | 0.924573i | \(0.375578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.9282 | 0.523967 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.39230 | −0.210112 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.9282 | 1.47612 | 0.738061 | − | 0.674734i | \(-0.235742\pi\) | ||||
0.738061 | + | 0.674734i | \(0.235742\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.46410 | 0.212576 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.3923 | −1.53554 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.92820 | −0.138499 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9282 | 0.514589 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.53590 | 0.307083 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.3923 | 0.862245 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3205 | −0.716663 | −0.358332 | − | 0.933594i | \(-0.616654\pi\) | ||||
−0.358332 | + | 0.933594i | \(0.616654\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.00000 | −0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.1962 | 1.12693 | 0.563464 | − | 0.826141i | \(-0.309469\pi\) | ||||
0.563464 | + | 0.826141i | \(0.309469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 29.8564 | 1.38456 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.875644 | −0.0405200 | −0.0202600 | − | 0.999795i | \(-0.506449\pi\) | ||||
−0.0202600 | + | 0.999795i | \(0.506449\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.3205 | 1.53533 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.8564 | 1.37280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.12436 | 0.143355 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 53.5692 | 2.45277 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.85641 | 0.450351 | 0.225175 | − | 0.974318i | \(-0.427705\pi\) | ||||
0.225175 | + | 0.974318i | \(0.427705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.85641 | −0.449413 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.46410 | 0.430632 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.3923 | 1.10760 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.6077 | −0.979138 | −0.489569 | − | 0.871965i | \(-0.662846\pi\) | ||||
−0.489569 | + | 0.871965i | \(0.662846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −36.7846 | −1.66346 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.7846 | 1.47955 | 0.739774 | − | 0.672855i | \(-0.234932\pi\) | ||||
0.739774 | + | 0.672855i | \(0.234932\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.92820 | −0.131880 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 66.6410 | 2.99529 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.92820 | 0.131348 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0718 | 0.585174 | 0.292587 | − | 0.956239i | \(-0.405484\pi\) | ||||
0.292587 | + | 0.956239i | \(0.405484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.8564 | 0.619059 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.9282 | 1.37902 | 0.689510 | − | 0.724276i | \(-0.257826\pi\) | ||||
0.689510 | + | 0.724276i | \(0.257826\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.53590 | −0.201845 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −88.3013 | −3.92160 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.12436 | 0.138485 | 0.0692423 | − | 0.997600i | \(-0.477942\pi\) | ||||
0.0692423 | + | 0.997600i | \(0.477942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.9282 | −0.571910 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.07180 | −0.223925 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.9282 | 1.18660 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0000 | −0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3923 | −0.456172 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.7846 | 0.647726 | 0.323863 | − | 0.946104i | \(-0.395018\pi\) | ||||
0.323863 | + | 0.946104i | \(0.395018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.41154 | 0.149176 | 0.0745882 | − | 0.997214i | \(-0.476236\pi\) | ||||
0.0745882 | + | 0.997214i | \(0.476236\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.73205 | −0.293811 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | −0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −43.1244 | −1.87144 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.4641 | 0.583195 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.8564 | 0.599065 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.46410 | 0.235356 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.00000 | 0.171973 | 0.0859867 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859867 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.3205 | 1.25826 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.8564 | 1.45025 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 46.2487 | 1.97745 | 0.988726 | − | 0.149736i | \(-0.0478423\pi\) | ||||
0.988726 | + | 0.149736i | \(0.0478423\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −49.6603 | −2.11945 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.85641 | −0.0790856 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.9282 | 0.464714 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.9282 | 0.463876 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.7128 | −1.00474 | −0.502372 | − | 0.864652i | \(-0.667539\pi\) | ||||
−0.502372 | + | 0.864652i | \(0.667539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.7846 | 1.55582 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.8564 | −1.26054 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.0526 | −1.43514 | −0.717572 | − | 0.696484i | \(-0.754747\pi\) | ||||
−0.717572 | + | 0.696484i | \(0.754747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.8564 | −0.751225 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.46410 | −0.103483 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.46410 | 0.229067 | 0.114534 | − | 0.993419i | \(-0.463463\pi\) | ||||
0.114534 | + | 0.993419i | \(0.463463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.1769 | 1.05362 | 0.526811 | − | 0.849983i | \(-0.323388\pi\) | ||||
0.526811 | + | 0.849983i | \(0.323388\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43.7128 | 1.82613 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.53590 | −0.355972 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.0718 | −1.29354 | −0.646768 | − | 0.762687i | \(-0.723880\pi\) | ||||
−0.646768 | + | 0.762687i | \(0.723880\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.8564 | −0.742087 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.66025 | 0.234827 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 65.5692 | 2.71560 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 82.1051 | 3.39463 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.2679 | −1.37312 | −0.686558 | − | 0.727075i | \(-0.740879\pi\) | ||||
−0.686558 | + | 0.727075i | \(0.740879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.07180 | −0.208980 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −70.6410 | −2.90578 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.1436 | 0.498678 | 0.249339 | − | 0.968416i | \(-0.419787\pi\) | ||||
0.249339 | + | 0.968416i | \(0.419787\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.46410 | 0.224006 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.9282 | 0.447262 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.7128 | 1.13231 | 0.566157 | − | 0.824297i | \(-0.308429\pi\) | ||||
0.566157 | + | 0.824297i | \(0.308429\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −35.7128 | −1.45434 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 51.5167 | 2.09445 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.7128 | 1.12483 | 0.562414 | − | 0.826856i | \(-0.309873\pi\) | ||||
0.562414 | + | 0.826856i | \(0.309873\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7128 | −0.797495 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3205 | 1.58814 | 0.794070 | − | 0.607826i | \(-0.207958\pi\) | ||||
0.794070 | + | 0.607826i | \(0.207958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.9282 | −0.601963 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.3923 | 0.981997 | 0.490999 | − | 0.871160i | \(-0.336632\pi\) | ||||
0.490999 | + | 0.871160i | \(0.336632\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.1962 | −0.972525 | −0.486263 | − | 0.873813i | \(-0.661640\pi\) | ||||
−0.486263 | + | 0.873813i | \(0.661640\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.8564 | 0.556038 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.8564 | −0.475017 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.9282 | −0.755920 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.92820 | −0.116755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.5692 | −1.97332 | −0.986660 | − | 0.162796i | \(-0.947949\pi\) | ||||
−0.986660 | + | 0.162796i | \(0.947949\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.8564 | 1.82263 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.3205 | 1.24292 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.73205 | 0.266734 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.0718 | 0.517112 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.2487 | −0.878771 | −0.439386 | − | 0.898299i | \(-0.644804\pi\) | ||||
−0.439386 | + | 0.898299i | \(0.644804\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.3397 | −0.565504 | −0.282752 | − | 0.959193i | \(-0.591247\pi\) | ||||
−0.282752 | + | 0.959193i | \(0.591247\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.7846 | −1.60589 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.85641 | −0.0729829 | −0.0364914 | − | 0.999334i | \(-0.511618\pi\) | ||||
−0.0364914 | + | 0.999334i | \(0.511618\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −52.7846 | −2.07198 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.9282 | 0.428310 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.5359 | 1.50803 | 0.754013 | − | 0.656859i | \(-0.228115\pi\) | ||||
0.754013 | + | 0.656859i | \(0.228115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.3205 | 1.14565 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −57.7128 | −2.25159 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.32051 | −0.129349 | −0.0646743 | − | 0.997906i | \(-0.520601\pi\) | ||||
−0.0646743 | + | 0.997906i | \(0.520601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.9808 | 1.12722 | 0.563611 | − | 0.826041i | \(-0.309412\pi\) | ||||
0.563611 | + | 0.826041i | \(0.309412\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −36.7846 | −1.42860 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.46410 | 0.134332 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.07180 | 0.196381 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.9282 | −0.731807 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −60.7846 | −2.34656 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.14359 | 0.159724 | 0.0798619 | − | 0.996806i | \(-0.474552\pi\) | ||||
0.0798619 | + | 0.996806i | \(0.474552\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.85641 | −0.379373 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.4449 | −0.555161 | −0.277581 | − | 0.960702i | \(-0.589533\pi\) | ||||
−0.277581 | + | 0.960702i | \(0.589533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.92820 | 0.342633 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.3923 | 0.398234 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.6410 | 1.17245 | 0.586223 | − | 0.810150i | \(-0.300614\pi\) | ||||
0.586223 | + | 0.810150i | \(0.300614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −54.2487 | −2.07274 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 47.1769 | 1.79991 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 80.7846 | 3.07765 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1244 | −0.423190 | −0.211595 | − | 0.977357i | \(-0.567866\pi\) | ||||
−0.211595 | + | 0.977357i | \(0.567866\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.3923 | 0.926587 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.3205 | −0.960462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.3923 | 0.620014 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.6077 | 0.740572 | 0.370286 | − | 0.928918i | \(-0.379260\pi\) | ||||
0.370286 | + | 0.928918i | \(0.379260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.85641 | −0.0700157 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.8564 | 0.823160 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.66025 | −0.0624403 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 48.1051 | 1.80663 | 0.903313 | − | 0.428982i | \(-0.141128\pi\) | ||||
0.903313 | + | 0.428982i | \(0.141128\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.7846 | 1.82957 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8564 | 0.518927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 100.497 | 3.75839 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34.2487 | −1.27904 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.0718 | −0.785845 | −0.392923 | − | 0.919572i | \(-0.628536\pi\) | ||||
−0.392923 | + | 0.919572i | \(0.628536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.85641 | 0.367072 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 51.3205 | 1.90863 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.60770 | −0.133986 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.9282 | 0.405305 | 0.202652 | − | 0.979251i | \(-0.435044\pi\) | ||||
0.202652 | + | 0.979251i | \(0.435044\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9282 | 0.404194 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.6603 | 0.504553 | 0.252276 | − | 0.967655i | \(-0.418821\pi\) | ||||
0.252276 | + | 0.967655i | \(0.418821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.46410 | −0.275318 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.7128 | −1.61018 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.32051 | 0.122147 | 0.0610734 | − | 0.998133i | \(-0.480548\pi\) | ||||
0.0610734 | + | 0.998133i | \(0.480548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.3205 | −0.856700 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.2487 | 1.18309 | 0.591545 | − | 0.806272i | \(-0.298518\pi\) | ||||
0.591545 | + | 0.806272i | \(0.298518\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.92820 | 0.107281 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.2679 | 0.924506 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.07180 | 0.185319 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.2487 | −0.884848 | −0.442424 | − | 0.896806i | \(-0.645881\pi\) | ||||
−0.442424 | + | 0.896806i | \(0.645881\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 43.1769 | 1.57345 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.53590 | −0.237866 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.2487 | −0.372496 | −0.186248 | − | 0.982503i | \(-0.559633\pi\) | ||||
−0.186248 | + | 0.982503i | \(0.559633\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 51.7128 | 1.87706 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.7128 | 0.787089 | 0.393544 | − | 0.919306i | \(-0.371249\pi\) | ||||
0.393544 | + | 0.919306i | \(0.371249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.3923 | 0.448632 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 24.3923 | 0.881906 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −65.0333 | −2.34822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7846 | −0.388903 | −0.194451 | − | 0.980912i | \(-0.562293\pi\) | ||||
−0.194451 | + | 0.980912i | \(0.562293\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.3923 | 0.590354 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.8756 | 0.750845 | 0.375422 | − | 0.926854i | \(-0.377498\pi\) | ||||
0.375422 | + | 0.926854i | \(0.377498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.85641 | −0.354053 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.00000 | 0.143499 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.53590 | 0.0908580 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | 0.572525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.85641 | 0.209291 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.3205 | −1.18926 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.5885 | −0.733899 | −0.366950 | − | 0.930241i | \(-0.619598\pi\) | ||||
−0.366950 | + | 0.930241i | \(0.619598\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.8564 | −1.06292 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.53590 | −0.232390 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −74.8897 | −2.65941 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −89.5692 | −3.17669 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.9808 | −0.459802 | −0.229901 | − | 0.973214i | \(-0.573840\pi\) | ||||
−0.229901 | + | 0.973214i | \(0.573840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.85641 | −0.207185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −52.9282 | −1.87013 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −70.6410 | −2.49287 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.46410 | −0.333566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.3923 | −1.21067 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.3205 | −0.819905 | −0.409953 | − | 0.912107i | \(-0.634455\pi\) | ||||
−0.409953 | + | 0.912107i | \(0.634455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.1244 | −0.952465 | −0.476232 | − | 0.879319i | \(-0.657998\pi\) | ||||
−0.476232 | + | 0.879319i | \(0.657998\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.7846 | 1.43038 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.7846 | 1.28851 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.92820 | 0.242387 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.0526 | 1.05012 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.92820 | −0.241796 | −0.120898 | − | 0.992665i | \(-0.538577\pi\) | ||||
−0.120898 | + | 0.992665i | \(0.538577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.92820 | −0.102071 | −0.0510354 | − | 0.998697i | \(-0.516252\pi\) | ||||
−0.0510354 | + | 0.998697i | \(0.516252\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −36.7846 | −1.28068 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.8564 | −0.481834 | −0.240917 | − | 0.970546i | \(-0.577448\pi\) | ||||
−0.240917 | + | 0.970546i | \(0.577448\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.9808 | −1.42332 | −0.711660 | − | 0.702524i | \(-0.752056\pi\) | ||||
−0.711660 | + | 0.702524i | \(0.752056\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.9282 | 0.379095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000 | 0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.8564 | −0.479521 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0000 | 0.553041 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.7128 | −1.37104 | −0.685519 | − | 0.728054i | \(-0.740425\pi\) | ||||
−0.685519 | + | 0.728054i | \(0.740425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8564 | −0.926083 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.46410 | 0.188194 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 88.3013 | 3.03766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.8564 | 0.647914 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −45.3205 | −1.55540 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.07180 | 0.173859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.98076 | −0.170538 | −0.0852690 | − | 0.996358i | \(-0.527175\pi\) | ||||
−0.0852690 | + | 0.996358i | \(0.527175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.4641 | 0.528861 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.7846 | 1.05158 | 0.525791 | − | 0.850614i | \(-0.323769\pi\) | ||||
0.525791 | + | 0.850614i | \(0.323769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.4449 | −1.03877 | −0.519383 | − | 0.854542i | \(-0.673838\pi\) | ||||
−0.519383 | + | 0.854542i | \(0.673838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.46410 | −0.186216 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.3923 | 0.353349 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.5167 | 1.20621 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 59.7128 | 2.02562 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.8564 | −1.82485 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 39.8564 | 1.34893 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.92820 | −0.234216 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3923 | −0.688599 | −0.344300 | − | 0.938860i | \(-0.611884\pi\) | ||||
−0.344300 | + | 0.938860i | \(0.611884\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −33.3205 | −1.12387 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.7846 | −1.71098 | −0.855488 | − | 0.517822i | \(-0.826743\pi\) | ||||
−0.855488 | + | 0.517822i | \(0.826743\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.07180 | −0.170680 | −0.0853398 | − | 0.996352i | \(-0.527198\pi\) | ||||
−0.0853398 | + | 0.996352i | \(0.527198\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 72.1051 | 2.42379 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.6410 | −1.56605 | −0.783026 | − | 0.621989i | \(-0.786325\pi\) | ||||
−0.783026 | + | 0.621989i | \(0.786325\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.4641 | 0.384494 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.4641 | −0.451064 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.71281 | −0.124245 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 63.7128 | 2.12731 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.85641 | 0.195322 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000 | 0.799556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.9282 | −0.496779 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.3205 | −0.974647 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.7128 | −1.45146 | −0.725730 | − | 0.687980i | \(-0.758498\pi\) | ||||
−0.725730 | + | 0.687980i | \(0.758498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.41154 | −0.245825 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.53590 | 0.150281 | 0.0751405 | − | 0.997173i | \(-0.476059\pi\) | ||||
0.0751405 | + | 0.997173i | \(0.476059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.9282 | 1.02357 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 83.0333 | 2.74500 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7321 | 0.354404 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.21539 | −0.238014 | −0.119007 | − | 0.992893i | \(-0.537971\pi\) | ||||
−0.119007 | + | 0.992893i | \(0.537971\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.4641 | −0.773168 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.7128 | 0.648855 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.60770 | −0.118620 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 44.0000 | 1.44515 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.7128 | 1.23732 | 0.618659 | − | 0.785660i | \(-0.287676\pi\) | ||||
0.618659 | + | 0.785660i | \(0.287676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.26795 | 0.0415554 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.0000 | 0.523816 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.8564 | 0.976409 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.64102 | −0.282290 | −0.141145 | − | 0.989989i | \(-0.545078\pi\) | ||||
−0.141145 | + | 0.989989i | \(0.545078\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54.2487 | 1.77034 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.9808 | 1.46633 | 0.733165 | − | 0.680050i | \(-0.238042\pi\) | ||||
0.733165 | + | 0.680050i | \(0.238042\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.92820 | −0.225613 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.9282 | −0.355494 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.3923 | 0.792643 | 0.396322 | − | 0.918112i | \(-0.370286\pi\) | ||||
0.396322 | + | 0.918112i | \(0.370286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −87.0333 | −2.82522 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −78.6410 | −2.55011 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.8564 | 0.643212 | 0.321606 | − | 0.946874i | \(-0.395777\pi\) | ||||
0.321606 | + | 0.946874i | \(0.395777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43.7128 | −1.41451 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.8564 | 0.706517 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.8564 | −0.641197 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.6410 | 0.729597 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.8564 | 0.574818 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.1769 | −0.488057 | −0.244028 | − | 0.969768i | \(-0.578469\pi\) | ||||
−0.244028 | + | 0.969768i | \(0.578469\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.92820 | −0.222566 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55.5167 | −1.78161 | −0.890807 | − | 0.454381i | \(-0.849860\pi\) | ||||
−0.890807 | + | 0.454381i | \(0.849860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.26795 | −0.297117 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −45.3205 | −1.45142 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.1436 | −0.900393 | −0.450197 | − | 0.892929i | \(-0.648646\pi\) | ||||
−0.450197 | + | 0.892929i | \(0.648646\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64.7846 | −2.07053 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 55.3205 | 1.76625 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.7128 | −1.52180 | −0.760901 | − | 0.648868i | \(-0.775243\pi\) | ||||
−0.760901 | + | 0.648868i | \(0.775243\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 70.6410 | 2.25081 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.00000 | 0.254643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.9282 | −0.601882 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.7846 | −0.787309 | −0.393655 | − | 0.919258i | \(-0.628789\pi\) | ||||
−0.393655 | + | 0.919258i | \(0.628789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 44.7846 | 1.42120 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.9282 | −0.346447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.26795 | −0.166838 | −0.0834188 | − | 0.996515i | \(-0.526584\pi\) | ||||
−0.0834188 | + | 0.996515i | \(0.526584\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.85641 | 0.185289 |
(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 | 1792.2.a.k.1.1 | 2 | ||
4.3 | odd | 2 | 1792.2.a.s.1.2 | 2 | |||
8.3 | odd | 2 | 1792.2.a.i.1.1 | 2 | |||
8.5 | even | 2 | 1792.2.a.q.1.2 | 2 | |||
16.3 | odd | 4 | 448.2.b.d.225.4 | yes | 4 | ||
16.5 | even | 4 | 448.2.b.c.225.4 | yes | 4 | ||
16.11 | odd | 4 | 448.2.b.d.225.1 | yes | 4 | ||
16.13 | even | 4 | 448.2.b.c.225.1 | ✓ | 4 | ||
48.5 | odd | 4 | 4032.2.c.k.2017.1 | 4 | |||
48.11 | even | 4 | 4032.2.c.n.2017.1 | 4 | |||
48.29 | odd | 4 | 4032.2.c.k.2017.4 | 4 | |||
48.35 | even | 4 | 4032.2.c.n.2017.4 | 4 | |||
112.13 | odd | 4 | 3136.2.b.g.1569.4 | 4 | |||
112.27 | even | 4 | 3136.2.b.h.1569.4 | 4 | |||
112.69 | odd | 4 | 3136.2.b.g.1569.1 | 4 | |||
112.83 | even | 4 | 3136.2.b.h.1569.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
448.2.b.c.225.1 | ✓ | 4 | 16.13 | even | 4 | ||
448.2.b.c.225.4 | yes | 4 | 16.5 | even | 4 | ||
448.2.b.d.225.1 | yes | 4 | 16.11 | odd | 4 | ||
448.2.b.d.225.4 | yes | 4 | 16.3 | odd | 4 | ||
1792.2.a.i.1.1 | 2 | 8.3 | odd | 2 | |||
1792.2.a.k.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1792.2.a.q.1.2 | 2 | 8.5 | even | 2 | |||
1792.2.a.s.1.2 | 2 | 4.3 | odd | 2 | |||
3136.2.b.g.1569.1 | 4 | 112.69 | odd | 4 | |||
3136.2.b.g.1569.4 | 4 | 112.13 | odd | 4 | |||
3136.2.b.h.1569.1 | 4 | 112.83 | even | 4 | |||
3136.2.b.h.1569.4 | 4 | 112.27 | even | 4 | |||
4032.2.c.k.2017.1 | 4 | 48.5 | odd | 4 | |||
4032.2.c.k.2017.4 | 4 | 48.29 | odd | 4 | |||
4032.2.c.n.2017.1 | 4 | 48.11 | even | 4 | |||
4032.2.c.n.2017.4 | 4 | 48.35 | even | 4 |