Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2004,2,Mod(1,2004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2004, 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("2004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2004.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: | \(16.0020205651\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.161121.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.31991\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2004.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.28459 | 0.574487 | 0.287244 | − | 0.957858i | \(-0.407261\pi\) | ||||
0.287244 | + | 0.957858i | \(0.407261\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.96468 | −0.742579 | −0.371290 | − | 0.928517i | \(-0.621084\pi\) | ||||
−0.371290 | + | 0.928517i | \(0.621084\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.40916 | −0.726390 | −0.363195 | − | 0.931713i | \(-0.618314\pi\) | ||||
−0.363195 | + | 0.931713i | \(0.618314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.92621 | −1.08893 | −0.544467 | − | 0.838782i | \(-0.683268\pi\) | ||||
−0.544467 | + | 0.838782i | \(0.683268\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.28459 | 0.331680 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.63982 | −0.882787 | −0.441393 | − | 0.897314i | \(-0.645516\pi\) | ||||
−0.441393 | + | 0.897314i | \(0.645516\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.30861 | 0.529632 | 0.264816 | − | 0.964299i | \(-0.414689\pi\) | ||||
0.264816 | + | 0.964299i | \(0.414689\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.96468 | −0.428728 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.55057 | −0.948860 | −0.474430 | − | 0.880293i | \(-0.657346\pi\) | ||||
−0.474430 | + | 0.880293i | \(0.657346\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.34982 | −0.669965 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.81156 | −1.07918 | −0.539590 | − | 0.841928i | \(-0.681421\pi\) | ||||
−0.539590 | + | 0.841928i | \(0.681421\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.65708 | −0.836436 | −0.418218 | − | 0.908347i | \(-0.637345\pi\) | ||||
−0.418218 | + | 0.908347i | \(0.637345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.40916 | −0.419381 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.52381 | −0.426602 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.09300 | 0.672885 | 0.336442 | − | 0.941704i | \(-0.390776\pi\) | ||||
0.336442 | + | 0.941704i | \(0.390776\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.92621 | −0.628697 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.34227 | 1.14667 | 0.573335 | − | 0.819321i | \(-0.305649\pi\) | ||||
0.573335 | + | 0.819321i | \(0.305649\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.88636 | −0.592664 | −0.296332 | − | 0.955085i | \(-0.595763\pi\) | ||||
−0.296332 | + | 0.955085i | \(0.595763\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.28459 | 0.191496 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.51721 | 1.09650 | 0.548249 | − | 0.836315i | \(-0.315295\pi\) | ||||
0.548249 | + | 0.836315i | \(0.315295\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.14003 | −0.448576 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.63982 | −0.509677 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.6471 | −1.46250 | −0.731248 | − | 0.682111i | \(-0.761062\pi\) | ||||
−0.731248 | + | 0.682111i | \(0.761062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.09479 | −0.417302 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.30861 | 0.305783 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8022 | 1.40633 | 0.703164 | − | 0.711028i | \(-0.251770\pi\) | ||||
0.703164 | + | 0.711028i | \(0.251770\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0025 | −1.79284 | −0.896418 | − | 0.443209i | \(-0.853840\pi\) | ||||
−0.896418 | + | 0.443209i | \(0.853840\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.96468 | −0.247526 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.04358 | −0.625579 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.286799 | 0.0350381 | 0.0175191 | − | 0.999847i | \(-0.494423\pi\) | ||||
0.0175191 | + | 0.999847i | \(0.494423\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.55057 | −0.547825 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1569 | −1.20540 | −0.602699 | − | 0.797968i | \(-0.705908\pi\) | ||||
−0.602699 | + | 0.797968i | \(0.705908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.44823 | 0.403585 | 0.201792 | − | 0.979428i | \(-0.435323\pi\) | ||||
0.201792 | + | 0.979428i | \(0.435323\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.34982 | −0.386804 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.73323 | 0.539402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.99698 | 0.674713 | 0.337356 | − | 0.941377i | \(-0.390467\pi\) | ||||
0.337356 | + | 0.941377i | \(0.390467\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0713 | 1.10547 | 0.552737 | − | 0.833356i | \(-0.313583\pi\) | ||||
0.552737 | + | 0.833356i | \(0.313583\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.67569 | −0.507150 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.81156 | −0.623064 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.05989 | −0.960346 | −0.480173 | − | 0.877174i | \(-0.659426\pi\) | ||||
−0.480173 | + | 0.877174i | \(0.659426\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.71375 | 0.808620 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.65708 | −0.482916 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.96563 | 0.304267 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.02676 | 0.408855 | 0.204428 | − | 0.978882i | \(-0.434467\pi\) | ||||
0.204428 | + | 0.978882i | \(0.434467\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.40916 | −0.242130 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.06980 | 0.106450 | 0.0532248 | − | 0.998583i | \(-0.483050\pi\) | ||||
0.0532248 | + | 0.998583i | \(0.483050\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5422 | 1.53142 | 0.765709 | − | 0.643188i | \(-0.222388\pi\) | ||||
0.765709 | + | 0.643188i | \(0.222388\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.52381 | −0.246299 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.54641 | −0.246171 | −0.123085 | − | 0.992396i | \(-0.539279\pi\) | ||||
−0.123085 | + | 0.992396i | \(0.539279\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.5695 | 1.49129 | 0.745646 | − | 0.666343i | \(-0.232141\pi\) | ||||
0.745646 | + | 0.666343i | \(0.232141\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.09300 | 0.388490 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.22887 | −0.303746 | −0.151873 | − | 0.988400i | \(-0.548531\pi\) | ||||
−0.151873 | + | 0.988400i | \(0.548531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.84563 | −0.545108 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.92621 | −0.362978 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.15109 | 0.655539 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.19594 | −0.472358 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.34227 | 0.662030 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.7261 | −0.959373 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.940660 | 0.0834701 | 0.0417351 | − | 0.999129i | \(-0.486711\pi\) | ||||
0.0417351 | + | 0.999129i | \(0.486711\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.88636 | −0.342175 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7284 | −1.19946 | −0.599729 | − | 0.800203i | \(-0.704725\pi\) | ||||
−0.599729 | + | 0.800203i | \(0.704725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.53569 | −0.393294 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.28459 | 0.110560 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.2672 | −1.47524 | −0.737620 | − | 0.675216i | \(-0.764050\pi\) | ||||
−0.737620 | + | 0.675216i | \(0.764050\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0634 | 0.853570 | 0.426785 | − | 0.904353i | \(-0.359646\pi\) | ||||
0.426785 | + | 0.904353i | \(0.359646\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.51721 | 0.633063 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.45888 | 0.790991 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.46548 | −0.619975 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.14003 | −0.258985 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.8300 | −1.54261 | −0.771306 | − | 0.636464i | \(-0.780396\pi\) | ||||
−0.771306 | + | 0.636464i | \(0.780396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6354 | 0.865498 | 0.432749 | − | 0.901514i | \(-0.357544\pi\) | ||||
0.432749 | + | 0.901514i | \(0.357544\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.63982 | −0.294262 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.98244 | −0.480521 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.2179 | 1.77318 | 0.886592 | − | 0.462553i | \(-0.153066\pi\) | ||||
0.886592 | + | 0.462553i | \(0.153066\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.6471 | −0.844373 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.94042 | 0.704604 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.9987 | −1.72307 | −0.861535 | − | 0.507699i | \(-0.830496\pi\) | ||||
−0.861535 | + | 0.507699i | \(0.830496\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.09479 | −0.240929 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.41512 | 0.185778 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.30861 | 0.176544 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8426 | 1.20449 | 0.602246 | − | 0.798311i | \(-0.294273\pi\) | ||||
0.602246 | + | 0.798311i | \(0.294273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.58133 | 0.497502 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.8022 | 0.811944 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.43373 | −0.256649 | −0.128324 | − | 0.991732i | \(-0.540960\pi\) | ||||
−0.128324 | + | 0.991732i | \(0.540960\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.3243 | −0.841725 | −0.420863 | − | 0.907124i | \(-0.638273\pi\) | ||||
−0.420863 | + | 0.907124i | \(0.638273\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.0025 | −1.03509 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.25783 | 0.386564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.76893 | 0.641247 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.96468 | −0.142909 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.0824 | −1.88726 | −0.943628 | − | 0.331007i | \(-0.892612\pi\) | ||||
−0.943628 | + | 0.331007i | \(0.892612\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.5074 | 1.83606 | 0.918031 | − | 0.396508i | \(-0.129778\pi\) | ||||
0.918031 | + | 0.396508i | \(0.129778\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.04358 | −0.361178 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.73730 | −0.337519 | −0.168759 | − | 0.985657i | \(-0.553976\pi\) | ||||
−0.168759 | + | 0.985657i | \(0.553976\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8698 | −0.983206 | −0.491603 | − | 0.870819i | \(-0.663589\pi\) | ||||
−0.491603 | + | 0.870819i | \(0.663589\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.286799 | 0.0202293 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.4179 | 0.801376 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.43182 | 0.658747 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.55057 | −0.316287 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.56182 | −0.384719 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.5267 | 1.20659 | 0.603294 | − | 0.797519i | \(-0.293854\pi\) | ||||
0.603294 | + | 0.797519i | \(0.293854\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.1569 | −0.695937 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.99238 | −0.340478 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.14967 | 0.621120 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.44823 | 0.233010 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.2907 | 0.961297 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.9825 | 1.20420 | 0.602099 | − | 0.798422i | \(-0.294331\pi\) | ||||
0.602099 | + | 0.798422i | \(0.294331\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.34982 | −0.223322 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.80164 | 0.318696 | 0.159348 | − | 0.987222i | \(-0.449061\pi\) | ||||
0.159348 | + | 0.987222i | \(0.449061\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.8758 | −1.84208 | −0.921041 | − | 0.389465i | \(-0.872660\pi\) | ||||
−0.921041 | + | 0.389465i | \(0.872660\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.73323 | 0.311424 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.52381 | 0.361877 | 0.180939 | − | 0.983494i | \(-0.442086\pi\) | ||||
0.180939 | + | 0.983494i | \(0.442086\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.65655 | 0.629924 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.99698 | 0.389546 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.2120 | −1.50146 | −0.750729 | − | 0.660611i | \(-0.770297\pi\) | ||||
−0.750729 | + | 0.660611i | \(0.770297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.27780 | 0.211142 | 0.105571 | − | 0.994412i | \(-0.466333\pi\) | ||||
0.105571 | + | 0.994412i | \(0.466333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.03366 | −0.257701 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.06410 | −0.576735 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.0713 | 0.638246 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.2250 | −0.708518 | −0.354259 | − | 0.935147i | \(-0.615267\pi\) | ||||
−0.354259 | + | 0.935147i | \(0.615267\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.9631 | 0.689242 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.67569 | −0.292803 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.9517 | 0.807907 | 0.403954 | − | 0.914779i | \(-0.367636\pi\) | ||||
0.403954 | + | 0.914779i | \(0.367636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.04143 | −0.499670 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.81156 | −0.359726 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.16998 | −0.257132 | −0.128566 | − | 0.991701i | \(-0.541037\pi\) | ||||
−0.128566 | + | 0.991701i | \(0.541037\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.6772 | −0.840185 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.05989 | −0.554456 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.2329 | −1.90430 | −0.952152 | − | 0.305625i | \(-0.901135\pi\) | ||||
−0.952152 | + | 0.305625i | \(0.901135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.9256 | 1.21039 | 0.605197 | − | 0.796076i | \(-0.293095\pi\) | ||||
0.605197 | + | 0.796076i | \(0.293095\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.71375 | 0.466857 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.07027 | 0.486655 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.20031 | 0.132204 | 0.0661021 | − | 0.997813i | \(-0.478944\pi\) | ||||
0.0661021 | + | 0.997813i | \(0.478944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.65708 | −0.278812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.4717 | 1.57917 | 0.789585 | − | 0.613641i | \(-0.210296\pi\) | ||||
0.789585 | + | 0.613641i | \(0.210296\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.2466 | 0.846870 | 0.423435 | − | 0.905926i | \(-0.360824\pi\) | ||||
0.423435 | + | 0.905926i | \(0.360824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.96563 | 0.175669 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.4252 | −0.851494 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.75169 | −0.220687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.02676 | 0.236053 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.2255 | 0.714221 | 0.357111 | − | 0.934062i | \(-0.383762\pi\) | ||||
0.357111 | + | 0.934062i | \(0.383762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.8764 | 0.807917 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.40916 | −0.139794 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.8665 | 1.03325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.63545 | 0.440100 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.06980 | 0.0614587 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.9875 | −1.02996 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.04146 | 0.0594395 | 0.0297197 | − | 0.999558i | \(-0.490539\pi\) | ||||
0.0297197 | + | 0.999558i | \(0.490539\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.5422 | 0.884164 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.61814 | −0.0917564 | −0.0458782 | − | 0.998947i | \(-0.514609\pi\) | ||||
−0.0458782 | + | 0.998947i | \(0.514609\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.1205 | −1.41990 | −0.709948 | − | 0.704254i | \(-0.751281\pi\) | ||||
−0.709948 | + | 0.704254i | \(0.751281\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.52381 | −0.142201 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.6518 | −1.44075 | −0.720374 | − | 0.693586i | \(-0.756030\pi\) | ||||
−0.720374 | + | 0.693586i | \(0.756030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0010 | 0.783905 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.54641 | −0.142127 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.40294 | −0.467552 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.1521 | 0.729547 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.5695 | 0.860998 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.7689 | −0.814236 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.7667 | 0.976544 | 0.488272 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488272 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.09300 | 0.224295 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.368420 | 0.0201290 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.2213 | −1.04705 | −0.523526 | − | 0.852010i | \(-0.675384\pi\) | ||||
−0.523526 | + | 0.852010i | \(0.675384\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.22887 | −0.175368 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.2197 | 0.607578 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9219 | 1.07568 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.84563 | −0.314718 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.1326 | 0.758677 | 0.379339 | − | 0.925258i | \(-0.376152\pi\) | ||||
0.379339 | + | 0.925258i | \(0.376152\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.1862 | −1.50877 | −0.754387 | − | 0.656429i | \(-0.772066\pi\) | ||||
−0.754387 | + | 0.656429i | \(0.772066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.92621 | −0.209566 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.0991 | −0.856870 | −0.428435 | − | 0.903573i | \(-0.640935\pi\) | ||||
−0.428435 | + | 0.903573i | \(0.640935\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.0474 | −0.692486 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.15109 | 0.378476 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.09816 | −0.163515 | −0.0817574 | − | 0.996652i | \(-0.526053\pi\) | ||||
−0.0817574 | + | 0.996652i | \(0.526053\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.6703 | −0.719490 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.19594 | −0.272716 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.42957 | 0.231854 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5041 | −0.809307 | −0.404654 | − | 0.914470i | \(-0.632608\pi\) | ||||
−0.404654 | + | 0.914470i | \(0.632608\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.34227 | 0.382223 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.9182 | 1.08602 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.04456 | −0.416532 | −0.208266 | − | 0.978072i | \(-0.566782\pi\) | ||||
−0.208266 | + | 0.978072i | \(0.566782\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.7261 | −0.553894 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.8174 | 1.17516 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3818 | 0.944210 | 0.472105 | − | 0.881542i | \(-0.343494\pi\) | ||||
0.472105 | + | 0.881542i | \(0.343494\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.940660 | 0.0481915 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.38490 | 0.0707649 | 0.0353825 | − | 0.999374i | \(-0.488735\pi\) | ||||
0.0353825 | + | 0.999374i | \(0.488735\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.08028 | 0.309880 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.88636 | −0.197555 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.6320 | 0.944680 | 0.472340 | − | 0.881416i | \(-0.343409\pi\) | ||||
0.472340 | + | 0.881416i | \(0.343409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.5633 | 0.837641 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.7284 | −0.692507 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.70367 | 0.387614 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.8598 | 1.84994 | 0.924969 | − | 0.380042i | \(-0.124090\pi\) | ||||
0.924969 | + | 0.380042i | \(0.124090\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.53569 | −0.227068 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.06368 | −0.252868 | −0.126434 | − | 0.991975i | \(-0.540353\pi\) | ||||
−0.126434 | + | 0.991975i | \(0.540353\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.2847 | 0.910824 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.28459 | 0.0638319 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.86070 | −0.488777 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0361 | 1.18851 | 0.594254 | − | 0.804278i | \(-0.297447\pi\) | ||||
0.594254 | + | 0.804278i | \(0.297447\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.2672 | −0.851730 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.2229 | −1.04431 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9376 | 0.635080 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.0634 | 0.492809 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.8318 | 0.529170 | 0.264585 | − | 0.964362i | \(-0.414765\pi\) | ||||
0.264585 | + | 0.964362i | \(0.414765\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.18637 | 0.106557 | 0.0532785 | − | 0.998580i | \(-0.483033\pi\) | ||||
0.0532785 | + | 0.998580i | \(0.483033\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.51721 | 0.365499 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.1928 | 0.591436 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.5104 | 1.33132 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.45888 | 0.456679 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.3902 | 0.933994 | 0.466997 | − | 0.884259i | \(-0.345336\pi\) | ||||
0.466997 | + | 0.884259i | \(0.345336\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.7996 | 0.903449 | 0.451725 | − | 0.892157i | \(-0.350809\pi\) | ||||
0.451725 | + | 0.892157i | \(0.350809\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.46548 | −0.357942 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.5055 | −0.502547 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.05917 | −0.384643 | −0.192322 | − | 0.981332i | \(-0.561602\pi\) | ||||
−0.192322 | + | 0.981332i | \(0.561602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.14003 | −0.149525 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.1425 | −1.33709 | −0.668546 | − | 0.743671i | \(-0.733083\pi\) | ||||
−0.668546 | + | 0.743671i | \(0.733083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.6383 | −0.551706 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.8300 | −0.890627 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.9364 | 1.36559 | 0.682797 | − | 0.730608i | \(-0.260763\pi\) | ||||
0.682797 | + | 0.730608i | \(0.260763\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.6887 | −0.832929 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.6354 | 0.499696 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.90902 | 0.464542 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.80085 | −0.364909 | −0.182454 | − | 0.983214i | \(-0.558404\pi\) | ||||
−0.182454 | + | 0.983214i | \(0.558404\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.63982 | −0.169892 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.6981 | −0.637984 | −0.318992 | − | 0.947757i | \(-0.603344\pi\) | ||||
−0.318992 | + | 0.947757i | \(0.603344\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.1886 | 1.82125 | 0.910625 | − | 0.413235i | \(-0.135601\pi\) | ||||
0.910625 | + | 0.413235i | \(0.135601\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.98244 | −0.277429 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.2581 | 0.798610 | 0.399305 | − | 0.916818i | \(-0.369252\pi\) | ||||
0.399305 | + | 0.916818i | \(0.369252\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.563469 | −0.0260186 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.2179 | 1.02375 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.36287 | 0.430505 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.73344 | −0.354835 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.6471 | −0.487499 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.46912 | −0.112817 | −0.0564084 | − | 0.998408i | \(-0.517965\pi\) | ||||
−0.0564084 | + | 0.998408i | \(0.517965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0700 | −0.732727 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.94042 | 0.406803 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.17274 | 0.234882 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.6955 | 0.801861 | 0.400930 | − | 0.916108i | \(-0.368687\pi\) | ||||
0.400930 | + | 0.916108i | \(0.368687\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.9987 | −0.994814 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9043 | 0.672623 | 0.336312 | − | 0.941751i | \(-0.390820\pi\) | ||||
0.336312 | + | 0.941751i | \(0.390820\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.1530 | 0.952685 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.09479 | −0.139101 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.9550 | 0.895104 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7483 | 0.660226 | 0.330113 | − | 0.943941i | \(-0.392913\pi\) | ||||
0.330113 | + | 0.943941i | \(0.392913\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.6170 | 0.963856 | 0.481928 | − | 0.876211i | \(-0.339937\pi\) | ||||
0.481928 | + | 0.876211i | \(0.339937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.37426 | 0.0611539 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.41512 | 0.107259 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.3422 | −0.502735 | −0.251368 | − | 0.967892i | \(-0.580880\pi\) | ||||
−0.251368 | + | 0.967892i | \(0.580880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.77467 | −0.299694 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.30861 | 0.101928 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.9654 | 0.879779 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.1102 | −0.796484 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.8426 | 0.695413 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.90072 | −0.258515 | −0.129258 | − | 0.991611i | \(-0.541259\pi\) | ||||
−0.129258 | + | 0.991611i | \(0.541259\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.21958 | 0.315690 | 0.157845 | − | 0.987464i | \(-0.449545\pi\) | ||||
0.157845 | + | 0.987464i | \(0.449545\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.58133 | 0.287233 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.9509 | 0.738394 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.29229 | −0.0996648 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.8022 | 0.468776 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.8273 | −1.24865 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.27110 | −0.141422 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.43373 | −0.148176 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.56484 | 0.325841 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.15094 | −0.178463 | −0.0892314 | − | 0.996011i | \(-0.528441\pi\) | ||||
−0.0892314 | + | 0.996011i | \(0.528441\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.3243 | −0.485970 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.0005 | 0.856728 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.37704 | −0.229906 | −0.114953 | − | 0.993371i | \(-0.536672\pi\) | ||||
−0.114953 | + | 0.993371i | \(0.536672\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.0025 | −0.597612 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.4166 | −0.571568 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.7822 | −0.501028 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.25783 | 0.223183 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.1551 | −0.557399 | −0.278700 | − | 0.960378i | \(-0.589903\pi\) | ||||
−0.278700 | + | 0.960378i | \(0.589903\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.2587 | 0.645372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.76893 | 0.370224 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.08117 | 0.214146 | 0.107073 | − | 0.994251i | \(-0.465852\pi\) | ||||
0.107073 | + | 0.994251i | \(0.465852\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.14778 | −0.174498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.96468 | −0.0825088 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.5777 | −0.694972 | −0.347486 | − | 0.937685i | \(-0.612965\pi\) | ||||
−0.347486 | + | 0.937685i | \(0.612965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.5518 | 1.27855 | 0.639277 | − | 0.768977i | \(-0.279234\pi\) | ||||
0.639277 | + | 0.768977i | \(0.279234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.0824 | −1.08961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.2436 | 0.635703 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.2441 | −0.967663 | −0.483832 | − | 0.875161i | \(-0.660755\pi\) | ||||
−0.483832 | + | 0.875161i | \(0.660755\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.5074 | 1.06005 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.7870 | −0.820902 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.6507 | 1.06234 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.04358 | −0.208526 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.3846 | −0.800088 | −0.400044 | − | 0.916496i | \(-0.631005\pi\) | ||||
−0.400044 | + | 0.916496i | \(0.631005\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.7514 | −0.443003 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.73730 | −0.194867 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.34754 | 0.383857 | 0.191929 | − | 0.981409i | \(-0.438526\pi\) | ||||
0.191929 | + | 0.981409i | \(0.438526\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.18623 | 0.376599 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8698 | −0.567654 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.66606 | 0.0680732 | 0.0340366 | − | 0.999421i | \(-0.489164\pi\) | ||||
0.0340366 | + | 0.999421i | \(0.489164\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.5815 | −1.08428 | −0.542141 | − | 0.840287i | \(-0.682386\pi\) | ||||
−0.542141 | + | 0.840287i | \(0.682386\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.286799 | 0.0116794 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.67466 | −0.271363 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.8790 | −1.25334 | −0.626670 | − | 0.779285i | \(-0.715583\pi\) | ||||
−0.626670 | + | 0.779285i | \(0.715583\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.4179 | 0.462675 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.5141 | −1.19401 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.9530 | 0.603947 | 0.301973 | − | 0.953316i | \(-0.402355\pi\) | ||||
0.301973 | + | 0.953316i | \(0.402355\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.43182 | 0.380328 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.3705 | 0.820087 | 0.410043 | − | 0.912066i | \(-0.365514\pi\) | ||||
0.410043 | + | 0.912066i | \(0.365514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.534153 | 0.0214694 | 0.0107347 | − | 0.999942i | \(-0.496583\pi\) | ||||
0.0107347 | + | 0.999942i | \(0.496583\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.55057 | −0.182608 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.7998 | 0.713133 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.97043 | 0.118817 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.56182 | −0.222118 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.8978 | −0.594014 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.3425 | −0.650583 | −0.325292 | − | 0.945614i | \(-0.605462\pi\) | ||||
−0.325292 | + | 0.945614i | \(0.605462\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.5267 | 0.696624 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.20836 | 0.0479525 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.3284 | 0.488470 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.1569 | −0.401800 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.9146 | 1.81352 | 0.906759 | − | 0.421649i | \(-0.138548\pi\) | ||||
0.906759 | + | 0.421649i | \(0.138548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.16517 | −0.0853860 | −0.0426930 | − | 0.999088i | \(-0.513594\pi\) | ||||
−0.0426930 | + | 0.999088i | \(0.513594\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.99238 | −0.196575 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.7954 | −1.17138 | −0.585688 | − | 0.810536i | \(-0.699176\pi\) | ||||
−0.585688 | + | 0.810536i | \(0.699176\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.0243 | −1.02154 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.14967 | 0.358604 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.26237 | 0.362464 | 0.181232 | − | 0.983440i | \(-0.441991\pi\) | ||||
0.181232 | + | 0.983440i | \(0.441991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.6354 | −0.689073 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.44823 | 0.134528 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.492474 | 0.0191841 | 0.00959203 | − | 0.999954i | \(-0.496947\pi\) | ||||
0.00959203 | + | 0.999954i | \(0.496947\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.06786 | −0.313804 | −0.156902 | − | 0.987614i | \(-0.550151\pi\) | ||||
−0.156902 | + | 0.987614i | \(0.550151\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.2907 | 0.555005 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.82651 | −0.225942 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.4459 | 1.02399 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.9825 | 0.695244 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.7343 | 1.30230 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.59943 | 0.254389 | 0.127195 | − | 0.991878i | \(-0.459403\pi\) | ||||
0.127195 | + | 0.991878i | \(0.459403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.34982 | −0.128935 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.6380 | −0.562584 | −0.281292 | − | 0.959622i | \(-0.590763\pi\) | ||||
−0.281292 | + | 0.959622i | \(0.590763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.91130 | −0.303608 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.80164 | 0.183999 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.3419 | −0.395724 | −0.197862 | − | 0.980230i | \(-0.563400\pi\) | ||||
−0.197862 | + | 0.980230i | \(0.563400\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.1814 | −0.847506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.8758 | −1.06353 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41.8029 | 1.59256 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.5829 | −1.31559 | −0.657797 | − | 0.753195i | \(-0.728512\pi\) | ||||
−0.657797 | + | 0.753195i | \(0.728512\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.73323 | 0.179801 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9274 | 0.490365 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.7246 | −1.01227 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.52381 | 0.208930 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.5480 | −1.45594 | −0.727969 | − | 0.685610i | \(-0.759535\pi\) | ||||
−0.727969 | + | 0.685610i | \(0.759535\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.44915 | 0.356381 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.65655 | 0.363687 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.10183 | −0.0790473 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.9239 | 0.635592 | 0.317796 | − | 0.948159i | \(-0.397057\pi\) | ||||
0.317796 | + | 0.948159i | \(0.397057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.99698 | 0.224904 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.1924 | 0.793660 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1508 | 0.454414 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.2120 | −0.866867 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.1218 | 0.601241 | 0.300621 | − | 0.953744i | \(-0.402806\pi\) | ||||
0.300621 | + | 0.953744i | \(0.402806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.5354 | −1.13720 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.27780 | 0.121903 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.4677 | 0.723012 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.8925 | 0.403980 | 0.201990 | − | 0.979388i | \(-0.435259\pi\) | ||||
0.201990 | + | 0.979388i | \(0.435259\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.1457 | 0.523196 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.2054 | 1.44809 | 0.724043 | − | 0.689755i | \(-0.242282\pi\) | ||||
0.724043 | + | 0.689755i | \(0.242282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.03366 | −0.148784 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.690946 | −0.0254513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.8075 | −1.72184 | −0.860921 | − | 0.508738i | \(-0.830112\pi\) | ||||
−0.860921 | + | 0.508738i | \(0.830112\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.06410 | −0.332978 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.4808 | −1.22829 | −0.614145 | − | 0.789193i | \(-0.710499\pi\) | ||||
−0.614145 | + | 0.789193i | \(0.710499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.1888 | −0.886211 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.0713 | 0.368491 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.00289 | 0.182801 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.7166 | −0.901922 | −0.450961 | − | 0.892544i | \(-0.648919\pi\) | ||||
−0.450961 | + | 0.892544i | \(0.648919\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.2250 | −0.409063 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.6622 | 0.497218 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.5140 | −0.963667 | −0.481834 | − | 0.876263i | \(-0.660029\pi\) | ||||
−0.481834 | + | 0.876263i | \(0.660029\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.9631 | 0.397934 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.2602 | 0.915681 | 0.457840 | − | 0.889034i | \(-0.348623\pi\) | ||||
0.457840 | + | 0.889034i | \(0.348623\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.5892 | −1.10740 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.67569 | −0.169050 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −42.4117 | −1.53140 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.6768 | −0.709564 | −0.354782 | − | 0.934949i | \(-0.615445\pi\) | ||||
−0.354782 | + | 0.934949i | \(0.615445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.9517 | 0.466446 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.8440 | −1.32519 | −0.662594 | − | 0.748979i | \(-0.730544\pi\) | ||||
−0.662594 | + | 0.748979i | \(0.730544\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.6004 | 0.560382 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.04143 | −0.288485 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.9505 | 0.607313 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.4695 | 0.875589 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.81156 | −0.207688 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.5410 | 1.01867 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.36433 | 0.191218 | 0.0956088 | − | 0.995419i | \(-0.469520\pi\) | ||||
0.0956088 | + | 0.995419i | \(0.469520\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.16998 | −0.148455 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.34369 | 0.225556 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.9767 | 1.95228 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.6772 | −0.485081 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.20815 | −0.255326 | −0.127663 | − | 0.991818i | \(-0.540748\pi\) | ||||
−0.127663 | + | 0.991818i | \(0.540748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.3613 | −0.967973 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.05989 | −0.320115 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.30734 | −0.293160 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.4848 | 0.404786 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.2329 | −1.09945 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.3611 | 0.821334 | 0.410667 | − | 0.911785i | \(-0.365296\pi\) | ||||
0.410667 | + | 0.911785i | \(0.365296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.5681 | 1.67034 | 0.835170 | − | 0.549991i | \(-0.185369\pi\) | ||||
0.835170 | + | 0.549991i | \(0.185369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.9256 | 0.698821 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.2593 | −0.989881 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.97209 | −0.313894 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.71375 | 0.269540 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.28529 | 0.0448568 | 0.0224284 | − | 0.999748i | \(-0.492860\pi\) | ||||
0.0224284 | + | 0.999748i | \(0.492860\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.1103 | 0.526712 | 0.263356 | − | 0.964699i | \(-0.415171\pi\) | ||||
0.263356 | + | 0.964699i | \(0.415171\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.07027 | 0.280971 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.1009 | −1.11626 | −0.558129 | − | 0.829754i | \(-0.688481\pi\) | ||||
−0.558129 | + | 0.829754i | \(0.688481\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.5385 | −1.37323 | −0.686614 | − | 0.727022i | \(-0.740904\pi\) | ||||
−0.686614 | + | 0.727022i | \(0.740904\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.20031 | 0.0763281 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.4292 | 0.395997 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.28459 | −0.0444551 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.65708 | −0.160972 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.69426 | −0.0930161 | −0.0465081 | − | 0.998918i | \(-0.514809\pi\) | ||||
−0.0465081 | + | 0.998918i | \(0.514809\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.77421 | 0.164628 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.4717 | 0.911735 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.10244 | 0.106727 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.2084 | 0.350763 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.2466 | 0.488941 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.6255 | −0.638473 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.3525 | 1.65556 | 0.827779 | − | 0.561054i | \(-0.189604\pi\) | ||||
0.827779 | + | 0.561054i | \(0.189604\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.96563 | 0.101422 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.9684 | −1.26282 | −0.631408 | − | 0.775450i | \(-0.717523\pi\) | ||||
−0.631408 | + | 0.775450i | \(0.717523\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.7504 | 1.97042 | 0.985210 | − | 0.171352i | \(-0.0548136\pi\) | ||||
0.985210 | + | 0.171352i | \(0.0548136\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.4252 | −0.491610 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.667087 | 0.0227079 | 0.0113540 | − | 0.999936i | \(-0.496386\pi\) | ||||
0.0113540 | + | 0.999936i | \(0.496386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.3513 | 0.691965 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.75169 | −0.127414 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.4477 | −0.490105 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.12603 | −0.0381542 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.02676 | 0.136285 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.0734 | 0.712411 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.1291 | −0.578407 | −0.289204 | − | 0.957268i | \(-0.593390\pi\) | ||||
−0.289204 | + | 0.957268i | \(0.593390\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.2255 | 0.412356 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.5491 | −0.624935 | −0.312468 | − | 0.949928i | \(-0.601156\pi\) | ||||
−0.312468 | + | 0.949928i | \(0.601156\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.0598 | −0.607761 | −0.303880 | − | 0.952710i | \(-0.598282\pi\) | ||||
−0.303880 | + | 0.952710i | \(0.598282\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.8764 | 0.466451 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.4311 | −0.484549 | −0.242274 | − | 0.970208i | \(-0.577893\pi\) | ||||
−0.242274 | + | 0.970208i | \(0.577893\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.84810 | −0.0619832 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.40916 | −0.0807100 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.3543 | 0.580740 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.41094 | −0.147442 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.8665 | 0.596545 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.0649 | 0.902664 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.7537 | 1.29107 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.63545 | 0.254092 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.5470 | −0.483560 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.6448 | 1.78125 | 0.890624 | − | 0.454741i | \(-0.150268\pi\) | ||||
0.890624 | + | 0.454741i | \(0.150268\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.06980 | 0.0354832 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.7916 | −1.31835 | −0.659177 | − | 0.751988i | \(-0.729095\pi\) | ||||
−0.659177 | + | 0.751988i | \(0.729095\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.2635 | −0.803005 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.9875 | −0.594648 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.9720 | 0.890693 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.7644 | −0.849889 | −0.424945 | − | 0.905219i | \(-0.639706\pi\) | ||||
−0.424945 | + | 0.905219i | \(0.639706\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.04146 | 0.0343174 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.8780 | 1.31260 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.7108 | −0.450809 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5422 | 0.510472 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.8575 | −0.815549 | −0.407775 | − | 0.913083i | \(-0.633695\pi\) | ||||
−0.407775 | + | 0.913083i | \(0.633695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.24911 | −0.237580 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.61814 | −0.0529756 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.2645 | 0.368388 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.4739 | 0.407505 | 0.203752 | − | 0.979022i | \(-0.434686\pi\) | ||||
0.203752 | + | 0.979022i | \(0.434686\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.1205 | −0.819777 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.43127 | −0.274852 | −0.137426 | − | 0.990512i | \(-0.543883\pi\) | ||||
−0.137426 | + | 0.990512i | \(0.543883\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.4115 | −1.08803 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.52381 | −0.0820997 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.1816 | −1.50070 | −0.750350 | − | 0.661041i | \(-0.770115\pi\) | ||||
−0.750350 | + | 0.661041i | \(0.770115\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.5385 | −0.439477 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.6518 | −0.831816 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.1218 | −0.878563 | −0.439281 | − | 0.898350i | \(-0.644767\pi\) | ||||
−0.439281 | + | 0.898350i | \(0.644767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.5053 | −1.08420 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.0010 | 0.452588 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.9246 | 1.09548 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.31164 | −0.300375 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.54641 | −0.0820570 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.7666 | 1.05479 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.9680 | −1.67118 | −0.835590 | − | 0.549354i | \(-0.814874\pi\) | ||||
−0.835590 | + | 0.549354i | \(0.814874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.40294 | −0.269941 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.3326 | −1.16597 | −0.582985 | − | 0.812483i | \(-0.698115\pi\) | ||||
−0.582985 | + | 0.812483i | \(0.698115\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.7714 | −0.633843 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.1521 | 0.421204 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.2379 | −1.79921 | −0.899605 | − | 0.436704i | \(-0.856146\pi\) | ||||
−0.899605 | + | 0.436704i | \(0.856146\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.8267 | 0.697586 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.5695 | 0.497097 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.9094 | −1.46428 | −0.732141 | − | 0.681153i | \(-0.761479\pi\) | ||||
−0.732141 | + | 0.681153i | \(0.761479\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.08550 | −0.193900 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.7689 | −0.470100 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.6852 | 0.562355 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.0349 | −0.731726 | −0.365863 | − | 0.930669i | \(-0.619226\pi\) | ||||
−0.365863 | + | 0.930669i | \(0.619226\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.7667 | 0.563808 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.8171 | −0.564839 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.2868 | −1.56093 | −0.780464 | − | 0.625201i | \(-0.785017\pi\) | ||||
−0.780464 | + | 0.625201i | \(0.785017\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.09300 | 0.129497 |
(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 | 2004.2.a.b.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 6012.2.a.f.1.1 | 5 | |||
4.3 | odd | 2 | 8016.2.a.q.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.b.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
6012.2.a.f.1.1 | 5 | 3.2 | odd | 2 | |||
8016.2.a.q.1.5 | 5 | 4.3 | odd | 2 |