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 | 1.2 | ||
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 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.732051 | −0.327383 | −0.163692 | − | 0.986512i | \(-0.552340\pi\) | ||||
−0.163692 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.46410 | −0.441443 | −0.220722 | − | 0.975337i | \(-0.570841\pi\) | ||||
−0.220722 | + | 0.975337i | \(0.570841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.26795 | 0.906366 | 0.453183 | − | 0.891417i | \(-0.350288\pi\) | ||||
0.453183 | + | 0.891417i | \(0.350288\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.535898 | −0.138368 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.73205 | 1.08561 | 0.542803 | − | 0.839860i | \(-0.317363\pi\) | ||||
0.542803 | + | 0.839860i | \(0.317363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.732051 | 0.159747 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410 | 0.722315 | 0.361158 | − | 0.932505i | \(-0.382382\pi\) | ||||
0.361158 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.46410 | −0.892820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.46410 | 1.01466 | 0.507329 | − | 0.861752i | \(-0.330633\pi\) | ||||
0.507329 | + | 0.861752i | \(0.330633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.07180 | −0.186576 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.732051 | −0.123739 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.46410 | 0.898293 | 0.449146 | − | 0.893458i | \(-0.351728\pi\) | ||||
0.449146 | + | 0.893458i | \(0.351728\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.39230 | 0.383075 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.46410 | −0.223273 | −0.111637 | − | 0.993749i | \(-0.535609\pi\) | ||||
−0.111637 | + | 0.993749i | \(0.535609\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.80385 | 0.268902 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9282 | 1.59404 | 0.797021 | − | 0.603951i | \(-0.206408\pi\) | ||||
0.797021 | + | 0.603951i | \(0.206408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.46410 | 0.205015 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0000 | 1.64833 | 0.824163 | − | 0.566352i | \(-0.191646\pi\) | ||||
0.824163 | + | 0.566352i | \(0.191646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.07180 | 0.144521 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.46410 | 0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.66025 | 0.997280 | 0.498640 | − | 0.866809i | \(-0.333833\pi\) | ||||
0.498640 | + | 0.866809i | \(0.333833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1244 | 1.68040 | 0.840201 | − | 0.542275i | \(-0.182437\pi\) | ||||
0.840201 | + | 0.542275i | \(0.182437\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.46410 | −0.310448 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.39230 | −0.296729 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.53590 | 0.305286 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.9282 | −1.29694 | −0.648470 | − | 0.761241i | \(-0.724591\pi\) | ||||
−0.648470 | + | 0.761241i | \(0.724591\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.928203 | 0.108638 | 0.0543190 | − | 0.998524i | \(-0.482701\pi\) | ||||
0.0543190 | + | 0.998524i | \(0.482701\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.26795 | −0.377350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.46410 | −0.166850 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.92820 | −0.329449 | −0.164724 | − | 0.986340i | \(-0.552673\pi\) | ||||
−0.164724 | + | 0.986340i | \(0.552673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.6603 | −1.27988 | −0.639940 | − | 0.768425i | \(-0.721041\pi\) | ||||
−0.639940 | + | 0.768425i | \(0.721041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.46410 | −0.158804 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8564 | 1.68078 | 0.840388 | − | 0.541985i | \(-0.182327\pi\) | ||||
0.840388 | + | 0.541985i | \(0.182327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.26795 | 0.342574 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.92820 | −0.303641 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.46410 | −0.355409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.92820 | −0.500383 | −0.250192 | − | 0.968196i | \(-0.580494\pi\) | ||||
−0.250192 | + | 0.968196i | \(0.580494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.60770 | 0.362587 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6603 | 1.55825 | 0.779127 | − | 0.626866i | \(-0.215663\pi\) | ||||
0.779127 | + | 0.626866i | \(0.215663\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.8564 | −1.75944 | −0.879722 | − | 0.475488i | \(-0.842271\pi\) | ||||
−0.879722 | + | 0.475488i | \(0.842271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.535898 | −0.0522983 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.9282 | 1.82986 | 0.914929 | − | 0.403614i | \(-0.132246\pi\) | ||||
0.914929 | + | 0.403614i | \(0.132246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.39230 | −0.803837 | −0.401919 | − | 0.915675i | \(-0.631656\pi\) | ||||
−0.401919 | + | 0.915675i | \(0.631656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.4641 | −1.26660 | −0.633298 | − | 0.773908i | \(-0.718299\pi\) | ||||
−0.633298 | + | 0.773908i | \(0.718299\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.53590 | −0.236474 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.05256 | −0.744459 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.46410 | 0.132014 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.53590 | 0.402496 | 0.201248 | − | 0.979540i | \(-0.435500\pi\) | ||||
0.201248 | + | 0.979540i | \(0.435500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.07180 | −0.0943664 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.26795 | 0.635004 | 0.317502 | − | 0.948258i | \(-0.397156\pi\) | ||||
0.317502 | + | 0.948258i | \(0.397156\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.73205 | 0.410321 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.92820 | 0.252020 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.85641 | 0.671218 | 0.335609 | − | 0.942001i | \(-0.391058\pi\) | ||||
0.335609 | + | 0.942001i | \(0.391058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7321 | −1.07992 | −0.539959 | − | 0.841691i | \(-0.681560\pi\) | ||||
−0.539959 | + | 0.841691i | \(0.681560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.78461 | −0.400109 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.732051 | 0.0603785 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.9282 | 1.22297 | 0.611483 | − | 0.791258i | \(-0.290573\pi\) | ||||
0.611483 | + | 0.791258i | \(0.290573\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3923 | 1.49674 | 0.748372 | − | 0.663279i | \(-0.230836\pi\) | ||||
0.748372 | + | 0.663279i | \(0.230836\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.92820 | −0.398422 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.92820 | 0.235199 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.80385 | −0.143963 | −0.0719814 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719814 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.78461 | 0.696665 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.46410 | 0.273009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.53590 | 0.511931 | 0.255966 | − | 0.966686i | \(-0.417607\pi\) | ||||
0.255966 | + | 0.966686i | \(0.417607\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.784610 | 0.0610818 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.9282 | −1.46471 | −0.732354 | − | 0.680924i | \(-0.761578\pi\) | ||||
−0.732354 | + | 0.680924i | \(0.761578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.32051 | −0.178501 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.6603 | −0.891682 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1962 | 1.07931 | 0.539657 | − | 0.841885i | \(-0.318554\pi\) | ||||
0.539657 | + | 0.841885i | \(0.318554\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.46410 | −0.337454 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.60770 | 0.421500 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.9282 | −0.816812 | −0.408406 | − | 0.912800i | \(-0.633915\pi\) | ||||
−0.408406 | + | 0.912800i | \(0.633915\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.26795 | −0.540222 | −0.270111 | − | 0.962829i | \(-0.587060\pi\) | ||||
−0.270111 | + | 0.962829i | \(0.587060\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.60770 | 0.710221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.92820 | −0.214131 | ||||||||
\(188\) | 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 | ||||||||
\(193\) | 13.4641 | 0.969167 | 0.484584 | − | 0.874745i | \(-0.338971\pi\) | ||||
0.484584 | + | 0.874745i | \(0.338971\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.75129 | −0.125412 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.85641 | −0.132263 | −0.0661317 | − | 0.997811i | \(-0.521066\pi\) | ||||
−0.0661317 | + | 0.997811i | \(0.521066\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.85641 | −0.413079 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.46410 | 0.383505 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.46410 | −0.102257 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.53590 | −0.593286 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.92820 | −0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.7846 | 1.70624 | 0.853121 | − | 0.521712i | \(-0.174707\pi\) | ||||
0.853121 | + | 0.521712i | \(0.174707\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.00000 | −0.548151 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.07180 | 0.0730959 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.679492 | 0.0459158 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.53590 | 0.439652 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.92820 | −0.463947 | −0.231973 | − | 0.972722i | \(-0.574518\pi\) | ||||
−0.231973 | + | 0.972722i | \(0.574518\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.0000 | 0.733333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.1962 | −0.942232 | −0.471116 | − | 0.882071i | \(-0.656149\pi\) | ||||
−0.471116 | + | 0.882071i | \(0.656149\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.7321 | −1.37001 | −0.685006 | − | 0.728537i | \(-0.740201\pi\) | ||||
−0.685006 | + | 0.728537i | \(0.740201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.07180 | −0.0705191 | ||||||||
\(232\) | 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 | ||||||||
\(237\) | −2.14359 | −0.139241 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.4641 | 1.25903 | 0.629514 | − | 0.776989i | \(-0.283254\pi\) | ||||
0.629514 | + | 0.776989i | \(0.283254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.7846 | 1.46769 | 0.733843 | − | 0.679319i | \(-0.237725\pi\) | ||||
0.733843 | + | 0.679319i | \(0.237725\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.732051 | −0.0467690 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.4641 | 0.983957 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.53590 | −0.540941 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.1962 | −1.65349 | −0.826743 | − | 0.562579i | \(-0.809809\pi\) | ||||
−0.826743 | + | 0.562579i | \(0.809809\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.07180 | −0.318861 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.07180 | −0.0671185 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.46410 | 0.339523 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.4641 | −0.833407 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.92820 | −0.180561 | −0.0902804 | − | 0.995916i | \(-0.528776\pi\) | ||||
−0.0902804 | + | 0.995916i | \(0.528776\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.78461 | −0.539634 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.6077 | 0.710379 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.5885 | −1.13336 | −0.566679 | − | 0.823939i | \(-0.691772\pi\) | ||||
−0.566679 | + | 0.823939i | \(0.691772\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.07180 | −0.0651070 | −0.0325535 | − | 0.999470i | \(-0.510364\pi\) | ||||
−0.0325535 | + | 0.999470i | \(0.510364\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.39230 | 0.144789 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.53590 | 0.394130 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | −0.240337 | −0.120168 | − | 0.992754i | \(-0.538343\pi\) | ||||
−0.120168 | + | 0.992754i | \(0.538343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.85641 | 0.590088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5885 | −0.867194 | −0.433597 | − | 0.901107i | \(-0.642756\pi\) | ||||
−0.433597 | + | 0.901107i | \(0.642756\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.53590 | −0.150214 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.60770 | −0.211487 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.80385 | 0.105382 | 0.0526910 | − | 0.998611i | \(-0.483220\pi\) | ||||
0.0526910 | + | 0.998611i | \(0.483220\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.60770 | −0.326493 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.85641 | 0.339823 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.3205 | 0.654682 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.46410 | −0.0843894 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.4641 | 0.658595 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.60770 | −0.550135 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.5885 | −1.28919 | −0.644596 | − | 0.764524i | \(-0.722974\pi\) | ||||
−0.644596 | + | 0.764524i | \(0.722974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.0718 | −0.743629 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.8564 | 1.23936 | 0.619682 | − | 0.784853i | \(-0.287262\pi\) | ||||
0.619682 | + | 0.784853i | \(0.287262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.85641 | 0.444070 | 0.222035 | − | 0.975039i | \(-0.428730\pi\) | ||||
0.222035 | + | 0.975039i | \(0.428730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.80385 | 0.101635 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.7846 | −0.718055 | −0.359028 | − | 0.933327i | \(-0.616892\pi\) | ||||
−0.359028 | + | 0.933327i | \(0.616892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.8564 | 0.773389 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.46410 | 0.526597 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.5885 | −0.809222 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.14359 | −0.339741 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.9282 | 0.602491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.39230 | 0.241423 | 0.120711 | − | 0.992688i | \(-0.461482\pi\) | ||||
0.120711 | + | 0.992688i | \(0.461482\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.4641 | −0.737828 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.85641 | 0.319970 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.39230 | −0.239264 | −0.119632 | − | 0.992818i | \(-0.538171\pi\) | ||||
−0.119632 | + | 0.992818i | \(0.538171\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.85641 | −0.535327 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.85641 | 0.317142 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.85641 | −0.0999456 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.679492 | −0.0364770 | −0.0182385 | − | 0.999834i | \(-0.505806\pi\) | ||||
−0.0182385 | + | 0.999834i | \(0.505806\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0526 | −1.28750 | −0.643752 | − | 0.765234i | \(-0.722623\pi\) | ||||
−0.643752 | + | 0.765234i | \(0.722623\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.0718 | −0.697721 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9282 | −0.688099 | −0.344049 | − | 0.938952i | \(-0.611799\pi\) | ||||
−0.344049 | + | 0.938952i | \(0.611799\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.46410 | 0.0774885 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5359 | −1.08384 | −0.541922 | − | 0.840429i | \(-0.682303\pi\) | ||||
−0.541922 | + | 0.840429i | \(0.682303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.39230 | 0.178542 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.48334 | −0.340287 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.679492 | −0.0355662 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.7846 | 1.08495 | 0.542474 | − | 0.840073i | \(-0.317488\pi\) | ||||
0.542474 | + | 0.840073i | \(0.317488\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.92820 | −0.256552 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | 0.623009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.0718 | −0.883944 | −0.441972 | − | 0.897029i | \(-0.645721\pi\) | ||||
−0.441972 | + | 0.897029i | \(0.645721\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.07180 | 0.261906 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.8564 | 0.919652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.2487 | 1.75924 | 0.879619 | − | 0.475679i | \(-0.157798\pi\) | ||||
0.879619 | + | 0.475679i | \(0.157798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.32051 | 0.170115 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.78461 | −0.448873 | −0.224436 | − | 0.974489i | \(-0.572054\pi\) | ||||
−0.224436 | + | 0.974489i | \(0.572054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.07180 | 0.0546238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.60770 | 0.183389 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.3205 | −0.573973 | −0.286986 | − | 0.957935i | \(-0.592653\pi\) | ||||
−0.286986 | + | 0.957935i | \(0.592653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.92820 | 0.350374 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.32051 | 0.268384 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.14359 | 0.107856 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.1244 | −1.46171 | −0.730855 | − | 0.682533i | \(-0.760878\pi\) | ||||
−0.730855 | + | 0.682533i | \(0.760878\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.46410 | 0.173422 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.53590 | 0.326387 | 0.163194 | − | 0.986594i | \(-0.447820\pi\) | ||||
0.163194 | + | 0.986594i | \(0.447820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.0718 | −0.651153 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.26795 | −0.162386 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9282 | 0.837046 | 0.418523 | − | 0.908206i | \(-0.362548\pi\) | ||||
0.418523 | + | 0.908206i | \(0.362548\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.75129 | 0.283690 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.66025 | 0.376936 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.53590 | 0.419011 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.32051 | −0.456427 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.1962 | −1.67059 | −0.835296 | − | 0.549801i | \(-0.814704\pi\) | ||||
−0.835296 | + | 0.549801i | \(0.814704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.85641 | 0.0904757 | 0.0452379 | − | 0.998976i | \(-0.485595\pi\) | ||||
0.0452379 | + | 0.998976i | \(0.485595\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.9282 | −1.30929 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.92820 | −0.433081 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.1244 | 0.635132 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.50258 | −0.169106 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.5359 | 1.37453 | 0.687263 | − | 0.726409i | \(-0.258812\pi\) | ||||
0.687263 | + | 0.726409i | \(0.258812\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.8564 | −0.569783 | −0.284891 | − | 0.958560i | \(-0.591957\pi\) | ||||
−0.284891 | + | 0.958560i | \(0.591957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.92820 | −0.140397 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.3923 | 0.784150 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.0718 | 0.814792 | 0.407396 | − | 0.913252i | \(-0.366437\pi\) | ||||
0.407396 | + | 0.913252i | \(0.366437\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46410 | −0.117338 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.6077 | −0.550258 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.9282 | 0.516886 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.92820 | −0.137884 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.4641 | 0.632599 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.39230 | −0.112153 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3205 | 0.903775 | 0.451888 | − | 0.892075i | \(-0.350751\pi\) | ||||
0.451888 | + | 0.892075i | \(0.350751\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.00000 | −0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8038 | 0.642909 | 0.321455 | − | 0.946925i | \(-0.395828\pi\) | ||||
0.321455 | + | 0.946925i | \(0.395828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.14359 | 0.0994068 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.1244 | −1.16262 | −0.581308 | − | 0.813683i | \(-0.697459\pi\) | ||||
−0.581308 | + | 0.813683i | \(0.697459\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.32051 | −0.0608458 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.14359 | 0.0985625 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.1244 | −0.969252 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.5692 | −1.35388 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.8564 | −0.815880 | −0.407940 | − | 0.913009i | \(-0.633753\pi\) | ||||
−0.407940 | + | 0.913009i | \(0.633753\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.8564 | 0.814182 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.53590 | 0.115387 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.60770 | 0.163817 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −42.3923 | −1.92098 | −0.960489 | − | 0.278317i | \(-0.910224\pi\) | ||||
−0.960489 | + | 0.278317i | \(0.910224\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.78461 | 0.216368 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.78461 | −0.396444 | −0.198222 | − | 0.980157i | \(-0.563517\pi\) | ||||
−0.198222 | + | 0.980157i | \(0.563517\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.9282 | 0.492182 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.64102 | −0.118705 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.9282 | −0.490197 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.9282 | 1.20547 | 0.602736 | − | 0.797941i | \(-0.294077\pi\) | ||||
0.602736 | + | 0.797941i | \(0.294077\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.8564 | −0.619059 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.0718 | 0.761194 | 0.380597 | − | 0.924741i | \(-0.375719\pi\) | ||||
0.380597 | + | 0.924741i | \(0.375719\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.4641 | −0.510146 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.69873 | −0.0754432 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.1244 | −0.936321 | −0.468160 | − | 0.883644i | \(-0.655083\pi\) | ||||
−0.468160 | + | 0.883644i | \(0.655083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.928203 | 0.0410613 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.9282 | −0.835701 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.0718 | 0.576012 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0000 | −0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.3923 | 0.456172 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.7846 | −1.17346 | −0.586728 | − | 0.809784i | \(-0.699584\pi\) | ||||
−0.586728 | + | 0.809784i | \(0.699584\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.5885 | 1.51245 | 0.756224 | − | 0.654313i | \(-0.227042\pi\) | ||||
0.756224 | + | 0.654313i | \(0.227042\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.26795 | −0.142625 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | −0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.8756 | −0.819133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.53590 | 0.283101 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.8564 | −0.599065 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.46410 | −0.0630633 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.00000 | 0.171973 | 0.0859867 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859867 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.32051 | −0.228325 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.14359 | 0.263163 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.24871 | −0.0961480 | −0.0480740 | − | 0.998844i | \(-0.515308\pi\) | ||||
−0.0480740 | + | 0.998844i | \(0.515308\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −32.3397 | −1.38023 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.8564 | 1.10152 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.92820 | −0.124520 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.92820 | −0.124295 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.7128 | 1.34372 | 0.671858 | − | 0.740680i | \(-0.265497\pi\) | ||||
0.671858 | + | 0.740680i | \(0.265497\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.78461 | −0.202367 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.14359 | −0.0905026 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.05256 | 0.170795 | 0.0853975 | − | 0.996347i | \(-0.472784\pi\) | ||||
0.0853975 | + | 0.996347i | \(0.472784\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.85641 | 0.414662 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.46410 | 0.187475 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.46410 | −0.0613783 | −0.0306892 | − | 0.999529i | \(-0.509770\pi\) | ||||
−0.0306892 | + | 0.999529i | \(0.509770\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.1769 | −1.55581 | −0.777903 | − | 0.628385i | \(-0.783716\pi\) | ||||
−0.777903 | + | 0.628385i | \(0.783716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.7128 | −0.489310 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.4641 | −0.644898 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.9282 | −1.87039 | −0.935193 | − | 0.354139i | \(-0.884774\pi\) | ||||
−0.935193 | + | 0.354139i | \(0.884774\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.85641 | 0.409618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.6603 | −0.483749 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.5692 | −0.727643 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.89488 | 0.243723 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.7321 | −1.51609 | −0.758047 | − | 0.652200i | \(-0.773846\pi\) | ||||
−0.758047 | + | 0.652200i | \(0.773846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.9282 | −0.779923 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.35898 | −0.0559011 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.8564 | 1.63671 | 0.818353 | − | 0.574716i | \(-0.194887\pi\) | ||||
0.818353 | + | 0.574716i | \(0.194887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.46410 | −0.0600223 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.92820 | −0.119843 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.7128 | −1.13231 | −0.566157 | − | 0.824297i | \(-0.691571\pi\) | ||||
−0.566157 | + | 0.824297i | \(0.691571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.7128 | 0.802768 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.48334 | 0.263585 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.7128 | −1.12483 | −0.562414 | − | 0.826856i | \(-0.690127\pi\) | ||||
−0.562414 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.7128 | 1.44479 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.67949 | 0.189003 | 0.0945014 | − | 0.995525i | \(-0.469874\pi\) | ||||
0.0945014 | + | 0.995525i | \(0.469874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.07180 | −0.0432190 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.60770 | 0.145240 | 0.0726202 | − | 0.997360i | \(-0.476864\pi\) | ||||
0.0726202 | + | 0.997360i | \(0.476864\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.8038 | −0.554823 | −0.277412 | − | 0.960751i | \(-0.589477\pi\) | ||||
−0.277412 | + | 0.960751i | \(0.589477\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.8564 | −0.556038 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.8564 | 0.635274 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.07180 | −0.202548 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.9282 | 0.435736 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.5692 | 1.33637 | 0.668185 | − | 0.743995i | \(-0.267072\pi\) | ||||
0.668185 | + | 0.743995i | \(0.267072\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.1436 | 0.721143 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.32051 | −0.131770 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.26795 | 0.129481 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.9282 | 1.06526 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.2487 | 1.03676 | 0.518381 | − | 0.855150i | \(-0.326535\pi\) | ||||
0.518381 | + | 0.855150i | \(0.326535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.6603 | −1.24856 | −0.624279 | − | 0.781201i | \(-0.714607\pi\) | ||||
−0.624279 | + | 0.781201i | \(0.714607\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.784610 | 0.0308940 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.8564 | 1.01652 | 0.508260 | − | 0.861204i | \(-0.330289\pi\) | ||||
0.508260 | + | 0.861204i | \(0.330289\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.2154 | −0.440243 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.92820 | −0.114765 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.4641 | 1.77915 | 0.889574 | − | 0.456791i | \(-0.151001\pi\) | ||||
0.889574 | + | 0.456791i | \(0.151001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.32051 | −0.207889 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.28719 | −0.0892317 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.3205 | 1.22007 | 0.610037 | − | 0.792373i | \(-0.291155\pi\) | ||||
0.610037 | + | 0.792373i | \(0.291155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.9808 | −0.893848 | −0.446924 | − | 0.894572i | \(-0.647481\pi\) | ||||
−0.446924 | + | 0.894572i | \(0.647481\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.78461 | 0.185819 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.46410 | −0.134332 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.9282 | 0.732903 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.07180 | −0.196087 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.2154 | −0.741802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8564 | 1.22797 | 0.613987 | − | 0.789316i | \(-0.289565\pi\) | ||||
0.613987 | + | 0.789316i | \(0.289565\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.8564 | 0.687293 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.4449 | 1.70815 | 0.854077 | − | 0.520146i | \(-0.174122\pi\) | ||||
0.854077 | + | 0.520146i | \(0.174122\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.92820 | −0.189127 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.3923 | −0.398234 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.6410 | −1.47856 | −0.739279 | − | 0.673400i | \(-0.764833\pi\) | ||||
−0.739279 | + | 0.673400i | \(0.764833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.75129 | −0.219745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.1769 | −0.579035 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.2154 | 1.49399 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1244 | 0.499274 | 0.249637 | − | 0.968339i | \(-0.419689\pi\) | ||||
0.249637 | + | 0.968339i | \(0.419689\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.60770 | 0.137045 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.32051 | 0.353547 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.39230 | −0.166132 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.3923 | 1.52560 | 0.762798 | − | 0.646637i | \(-0.223825\pi\) | ||||
0.762798 | + | 0.646637i | \(0.223825\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.8564 | 0.975193 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.85641 | −0.220565 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.6603 | 0.588964 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.1051 | −1.05551 | −0.527755 | − | 0.849397i | \(-0.676966\pi\) | ||||
−0.527755 | + | 0.849397i | \(0.676966\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.21539 | 0.270598 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8564 | −0.518927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.50258 | 0.130989 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.2487 | 0.532128 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.9282 | −1.30260 | −0.651301 | − | 0.758819i | \(-0.725777\pi\) | ||||
−0.651301 | + | 0.758819i | \(0.725777\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.8564 | −0.665007 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.6795 | 0.620317 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.3923 | −0.905907 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.92820 | −0.108601 | −0.0543005 | − | 0.998525i | \(-0.517293\pi\) | ||||
−0.0543005 | + | 0.998525i | \(0.517293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.92820 | −0.108304 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.66025 | −0.135195 | −0.0675973 | − | 0.997713i | \(-0.521533\pi\) | ||||
−0.0675973 | + | 0.997713i | \(0.521533\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.535898 | −0.0197669 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.7128 | 0.431447 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.3205 | −1.15214 | −0.576072 | − | 0.817399i | \(-0.695415\pi\) | ||||
−0.576072 | + | 0.817399i | \(0.695415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.3205 | 0.415869 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.2487 | −0.596107 | −0.298054 | − | 0.954549i | \(-0.596337\pi\) | ||||
−0.298054 | + | 0.954549i | \(0.596337\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.9282 | −0.400378 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.7321 | 1.05125 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.9282 | 0.691621 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2487 | 0.884848 | 0.442424 | − | 0.896806i | \(-0.354119\pi\) | ||||
0.442424 | + | 0.896806i | \(0.354119\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.1769 | −0.698846 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.4641 | −0.490009 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.2487 | 1.39017 | 0.695087 | − | 0.718926i | \(-0.255366\pi\) | ||||
0.695087 | + | 0.718926i | \(0.255366\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.71281 | −0.134767 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.7128 | −1.22209 | −0.611044 | − | 0.791596i | \(-0.709250\pi\) | ||||
−0.611044 | + | 0.791596i | \(0.709250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.39230 | −0.303822 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.60770 | 0.130436 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.0333 | 0.903901 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.7846 | 1.11012 | 0.555061 | − | 0.831810i | \(-0.312695\pi\) | ||||
0.555061 | + | 0.831810i | \(0.312695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.39230 | −0.158185 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.1244 | 1.62301 | 0.811505 | − | 0.584345i | \(-0.198649\pi\) | ||||
0.811505 | + | 0.584345i | \(0.198649\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.8564 | 0.641421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.00000 | 0.143499 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.46410 | 0.339087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | 0.572525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.8564 | −0.781084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.32051 | 0.0471310 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5885 | 0.377438 | 0.188719 | − | 0.982031i | \(-0.439567\pi\) | ||||
0.188719 | + | 0.982031i | \(0.439567\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.14359 | −0.0763140 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.4641 | −0.478728 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.8897 | 1.52306 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.43078 | −0.228076 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.9808 | 1.38077 | 0.690385 | − | 0.723442i | \(-0.257441\pi\) | ||||
0.690385 | + | 0.723442i | \(0.257441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.8564 | 0.773224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.0718 | −1.38053 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.35898 | −0.0479575 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.53590 | −0.0893787 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.6077 | −0.479014 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.3205 | 0.398008 | 0.199004 | − | 0.979999i | \(-0.436229\pi\) | ||||
0.199004 | + | 0.979999i | \(0.436229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.87564 | −0.100978 | −0.0504888 | − | 0.998725i | \(-0.516078\pi\) | ||||
−0.0504888 | + | 0.998725i | \(0.516078\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.784610 | −0.0275175 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.78461 | −0.167598 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.92820 | −0.242387 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.05256 | −0.281379 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.92820 | 0.241796 | 0.120898 | − | 0.992665i | \(-0.461423\pi\) | ||||
0.120898 | + | 0.992665i | \(0.461423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.9282 | 0.380933 | 0.190467 | − | 0.981694i | \(-0.439000\pi\) | ||||
0.190467 | + | 0.981694i | \(0.439000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.78461 | 0.166579 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.8564 | 0.481834 | 0.240917 | − | 0.970546i | \(-0.422552\pi\) | ||||
0.240917 | + | 0.970546i | \(0.422552\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.9808 | 0.381378 | 0.190689 | − | 0.981651i | \(-0.438928\pi\) | ||||
0.190689 | + | 0.981651i | \(0.438928\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.92820 | −0.101578 | ||||||||
\(832\) | 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 | ||||||||
\(839\) | 15.7128 | 0.542467 | 0.271233 | − | 0.962514i | \(-0.412569\pi\) | ||||
0.271233 | + | 0.962514i | \(0.412569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.856406 | 0.0295313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.46410 | −0.0504263 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.69873 | 0.0584381 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.85641 | −0.304310 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.6795 | −0.366519 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.9282 | 0.648850 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.9808 | 1.60859 | 0.804295 | − | 0.594230i | \(-0.202543\pi\) | ||||
0.804295 | + | 0.594230i | \(0.202543\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.53590 | 0.291922 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.7846 | −0.368395 | −0.184198 | − | 0.982889i | \(-0.558969\pi\) | ||||
−0.184198 | + | 0.982889i | \(0.558969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.4449 | 0.970526 | 0.485263 | − | 0.874368i | \(-0.338724\pi\) | ||||
0.485263 | + | 0.874368i | \(0.338724\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.46410 | 0.0498964 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | −9.51666 | −0.323203 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.28719 | 0.145433 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.1436 | −0.885842 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.1436 | 0.410998 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.92820 | 0.234216 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.392305 | 0.0132472 | 0.00662360 | − | 0.999978i | \(-0.497892\pi\) | ||||
0.00662360 | + | 0.999978i | \(0.497892\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.32051 | 0.0445396 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.21539 | −0.310474 | −0.155237 | − | 0.987877i | \(-0.549614\pi\) | ||||
−0.155237 | + | 0.987877i | \(0.549614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.9282 | −0.636985 | −0.318492 | − | 0.947925i | \(-0.603177\pi\) | ||||
−0.318492 | + | 0.947925i | \(0.603177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.10512 | −0.137992 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.6410 | 0.760211 | 0.380105 | − | 0.924943i | \(-0.375888\pi\) | ||||
0.380105 | + | 0.924943i | \(0.375888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.53590 | 0.152129 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.53590 | −0.218961 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.7128 | 1.73050 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.28719 | 0.276701 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.8564 | −0.728952 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000 | 0.799556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.07180 | −0.0356672 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.32051 | 0.176860 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.7128 | 0.388918 | 0.194459 | − | 0.980911i | \(-0.437705\pi\) | ||||
0.194459 | + | 0.980911i | \(0.437705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −38.5885 | −1.27990 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.4641 | 0.379823 | 0.189911 | − | 0.981801i | \(-0.439180\pi\) | ||||
0.189911 | + | 0.981801i | \(0.439180\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.0718 | 0.564994 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.03332 | −0.232514 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.26795 | 0.240009 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.7846 | −1.60926 | −0.804628 | − | 0.593779i | \(-0.797635\pi\) | ||||
−0.804628 | + | 0.593779i | \(0.797635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.5359 | −0.544876 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.7128 | −1.17550 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.3923 | −0.802014 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 44.0000 | 1.44515 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.7128 | −0.581139 | −0.290569 | − | 0.956854i | \(-0.593845\pi\) | ||||
−0.290569 | + | 0.956854i | \(0.593845\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.73205 | 0.155087 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.0000 | 0.523816 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.14359 | 0.0701030 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.6410 | 1.98106 | 0.990528 | − | 0.137312i | \(-0.0438463\pi\) | ||||
0.990528 | + | 0.137312i | \(0.0438463\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.75129 | 0.187686 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.98076 | −0.227566 | −0.113783 | − | 0.993506i | \(-0.536297\pi\) | ||||
−0.113783 | + | 0.993506i | \(0.536297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.92820 | 0.225613 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.92820 | 0.0952545 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.60770 | 0.117234 | 0.0586172 | − | 0.998281i | \(-0.481331\pi\) | ||||
0.0586172 | + | 0.998281i | \(0.481331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.03332 | 0.0984658 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.35898 | −0.303486 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.85641 | −0.254494 | −0.127247 | − | 0.991871i | \(-0.540614\pi\) | ||||
−0.127247 | + | 0.991871i | \(0.540614\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.7128 | 0.379018 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.85641 | −0.189311 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.85641 | 0.253697 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −46.6410 | −1.50299 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.85641 | −0.317289 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.1769 | 1.51711 | 0.758554 | − | 0.651611i | \(-0.225906\pi\) | ||||
0.758554 | + | 0.651611i | \(0.225906\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.92820 | 0.222566 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.4833 | −0.336426 | −0.168213 | − | 0.985751i | \(-0.553800\pi\) | ||||
−0.168213 | + | 0.985751i | \(0.553800\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7321 | −0.408171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.6795 | −0.342017 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −55.8564 | −1.78700 | −0.893502 | − | 0.449058i | \(-0.851759\pi\) | ||||
−0.893502 | + | 0.449058i | \(0.851759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.2154 | −0.741967 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.6795 | 0.660245 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.71281 | 0.246001 | 0.123000 | − | 0.992407i | \(-0.460748\pi\) | ||||
0.123000 | + | 0.992407i | \(0.460748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.35898 | 0.0433008 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.00000 | 0.254643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.07180 | −0.161274 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.7846 | 0.533181 | 0.266590 | − | 0.963810i | \(-0.414103\pi\) | ||||
0.266590 | + | 0.963810i | \(0.414103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.21539 | 0.102037 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.92820 | 0.0928303 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.73205 | −0.276547 | −0.138273 | − | 0.990394i | \(-0.544155\pi\) | ||||
−0.138273 | + | 0.990394i | \(0.544155\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.8564 | −0.691506 |
(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.1.2 | 2 | ||
4.3 | odd | 2 | 1792.2.a.s.1.1 | 2 | |||
8.3 | odd | 2 | 1792.2.a.i.1.2 | 2 | |||
8.5 | even | 2 | 1792.2.a.q.1.1 | 2 | |||
16.3 | odd | 4 | 448.2.b.d.225.2 | yes | 4 | ||
16.5 | even | 4 | 448.2.b.c.225.2 | ✓ | 4 | ||
16.11 | odd | 4 | 448.2.b.d.225.3 | yes | 4 | ||
16.13 | even | 4 | 448.2.b.c.225.3 | yes | 4 | ||
48.5 | odd | 4 | 4032.2.c.k.2017.3 | 4 | |||
48.11 | even | 4 | 4032.2.c.n.2017.3 | 4 | |||
48.29 | odd | 4 | 4032.2.c.k.2017.2 | 4 | |||
48.35 | even | 4 | 4032.2.c.n.2017.2 | 4 | |||
112.13 | odd | 4 | 3136.2.b.g.1569.2 | 4 | |||
112.27 | even | 4 | 3136.2.b.h.1569.2 | 4 | |||
112.69 | odd | 4 | 3136.2.b.g.1569.3 | 4 | |||
112.83 | even | 4 | 3136.2.b.h.1569.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
448.2.b.c.225.2 | ✓ | 4 | 16.5 | even | 4 | ||
448.2.b.c.225.3 | yes | 4 | 16.13 | even | 4 | ||
448.2.b.d.225.2 | yes | 4 | 16.3 | odd | 4 | ||
448.2.b.d.225.3 | yes | 4 | 16.11 | odd | 4 | ||
1792.2.a.i.1.2 | 2 | 8.3 | odd | 2 | |||
1792.2.a.k.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1792.2.a.q.1.1 | 2 | 8.5 | even | 2 | |||
1792.2.a.s.1.1 | 2 | 4.3 | odd | 2 | |||
3136.2.b.g.1569.2 | 4 | 112.13 | odd | 4 | |||
3136.2.b.g.1569.3 | 4 | 112.69 | odd | 4 | |||
3136.2.b.h.1569.2 | 4 | 112.27 | even | 4 | |||
3136.2.b.h.1569.3 | 4 | 112.83 | even | 4 | |||
4032.2.c.k.2017.2 | 4 | 48.29 | odd | 4 | |||
4032.2.c.k.2017.3 | 4 | 48.5 | odd | 4 | |||
4032.2.c.n.2017.2 | 4 | 48.35 | even | 4 | |||
4032.2.c.n.2017.3 | 4 | 48.11 | even | 4 |