Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5544,2,Mod(1,5544)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5544, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("5544.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5544 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5544.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: | \(44.2690628806\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1848) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5544.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.56155 | 0.698348 | 0.349174 | − | 0.937058i | \(-0.386462\pi\) | ||||
0.349174 | + | 0.937058i | \(0.386462\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.56155 | 0.987797 | 0.493899 | − | 0.869520i | \(-0.335571\pi\) | ||||
0.493899 | + | 0.869520i | \(0.335571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.12311 | −0.757464 | −0.378732 | − | 0.925506i | \(-0.623640\pi\) | ||||
−0.378732 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.438447 | −0.100587 | −0.0502933 | − | 0.998734i | \(-0.516016\pi\) | ||||
−0.0502933 | + | 0.998734i | \(0.516016\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56155 | −0.512311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.56155 | −0.661364 | −0.330682 | − | 0.943742i | \(-0.607279\pi\) | ||||
−0.330682 | + | 0.943742i | \(0.607279\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.56155 | −0.263951 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.438447 | −0.0720803 | −0.0360401 | − | 0.999350i | \(-0.511474\pi\) | ||||
−0.0360401 | + | 0.999350i | \(0.511474\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.24621 | 0.975494 | 0.487747 | − | 0.872985i | \(-0.337819\pi\) | ||||
0.487747 | + | 0.872985i | \(0.337819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.24621 | 0.952538 | 0.476269 | − | 0.879300i | \(-0.341989\pi\) | ||||
0.476269 | + | 0.879300i | \(0.341989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.31534 | 0.191862 | 0.0959311 | − | 0.995388i | \(-0.469417\pi\) | ||||
0.0959311 | + | 0.995388i | \(0.469417\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.12311 | 0.703713 | 0.351856 | − | 0.936054i | \(-0.385551\pi\) | ||||
0.351856 | + | 0.936054i | \(0.385551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.56155 | 0.210560 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.9309 | 1.94383 | 0.971917 | − | 0.235325i | \(-0.0756153\pi\) | ||||
0.971917 | + | 0.235325i | \(0.0756153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.56155 | 0.689826 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.56155 | −0.190774 | −0.0953870 | − | 0.995440i | \(-0.530409\pi\) | ||||
−0.0953870 | + | 0.995440i | \(0.530409\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.2462 | 1.69071 | 0.845357 | − | 0.534202i | \(-0.179388\pi\) | ||||
0.845357 | + | 0.534202i | \(0.179388\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.68466 | −1.01646 | −0.508231 | − | 0.861221i | \(-0.669700\pi\) | ||||
−0.508231 | + | 0.861221i | \(0.669700\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.246211 | −0.0270252 | −0.0135126 | − | 0.999909i | \(-0.504301\pi\) | ||||
−0.0135126 | + | 0.999909i | \(0.504301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.87689 | −0.528973 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.246211 | −0.0260983 | −0.0130492 | − | 0.999915i | \(-0.504154\pi\) | ||||
−0.0130492 | + | 0.999915i | \(0.504154\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.56155 | −0.373352 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.684658 | −0.0702445 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.12311 | −0.114034 | −0.0570170 | − | 0.998373i | \(-0.518159\pi\) | ||||
−0.0570170 | + | 0.998373i | \(0.518159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.2462 | −1.61656 | −0.808279 | − | 0.588799i | \(-0.799601\pi\) | ||||
−0.808279 | + | 0.588799i | \(0.799601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.24621 | −0.812523 | −0.406262 | − | 0.913757i | \(-0.633168\pi\) | ||||
−0.406262 | + | 0.913757i | \(0.633168\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.8078 | 1.91489 | 0.957444 | − | 0.288618i | \(-0.0931957\pi\) | ||||
0.957444 | + | 0.288618i | \(0.0931957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.24621 | 0.582462 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.12311 | 0.286295 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8078 | −1.05612 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.12311 | 0.277131 | 0.138565 | − | 0.990353i | \(-0.455751\pi\) | ||||
0.138565 | + | 0.990353i | \(0.455751\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.87689 | 0.600837 | 0.300419 | − | 0.953807i | \(-0.402874\pi\) | ||||
0.300419 | + | 0.953807i | \(0.402874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.438447 | 0.0380182 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.3693 | 1.98216 | 0.991080 | − | 0.133270i | \(-0.0425477\pi\) | ||||
0.991080 | + | 0.133270i | \(0.0425477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.56155 | 0.297832 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.56155 | −0.461862 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.43845 | 0.691305 | 0.345652 | − | 0.938363i | \(-0.387658\pi\) | ||||
0.345652 | + | 0.938363i | \(0.387658\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3693 | −1.41349 | −0.706747 | − | 0.707466i | \(-0.749838\pi\) | ||||
−0.706747 | + | 0.707466i | \(0.749838\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.12311 | 0.250854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.2462 | 1.77544 | 0.887720 | − | 0.460383i | \(-0.152288\pi\) | ||||
0.887720 | + | 0.460383i | \(0.152288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0540 | −1.72740 | −0.863700 | − | 0.504006i | \(-0.831859\pi\) | ||||
−0.863700 | + | 0.504006i | \(0.831859\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.2462 | 1.41193 | 0.705967 | − | 0.708245i | \(-0.250513\pi\) | ||||
0.705967 | + | 0.708245i | \(0.250513\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.315342 | −0.0242570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.36932 | −0.560279 | −0.280139 | − | 0.959959i | \(-0.590381\pi\) | ||||
−0.280139 | + | 0.959959i | \(0.590381\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.56155 | 0.193635 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.4924 | 1.23270 | 0.616351 | − | 0.787472i | \(-0.288610\pi\) | ||||
0.616351 | + | 0.787472i | \(0.288610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.24621 | −0.166960 | −0.0834798 | − | 0.996509i | \(-0.526603\pi\) | ||||
−0.0834798 | + | 0.996509i | \(0.526603\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.684658 | −0.0503371 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.12311 | −0.228384 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.36932 | −0.388510 | −0.194255 | − | 0.980951i | \(-0.562229\pi\) | ||||
−0.194255 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.1231 | −1.23255 | −0.616274 | − | 0.787532i | \(-0.711359\pi\) | ||||
−0.616274 | + | 0.787532i | \(0.711359\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2462 | 1.15749 | 0.578747 | − | 0.815507i | \(-0.303542\pi\) | ||||
0.578747 | + | 0.815507i | \(0.303542\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.12311 | 0.646720 | 0.323360 | − | 0.946276i | \(-0.395188\pi\) | ||||
0.323360 | + | 0.946276i | \(0.395188\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.56155 | 0.249972 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.75379 | 0.681234 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.438447 | −0.0303280 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1231 | 0.765746 | 0.382873 | − | 0.923801i | \(-0.374935\pi\) | ||||
0.382873 | + | 0.923801i | \(0.374935\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.75379 | 0.665203 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.1231 | −0.748221 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.75379 | 0.251372 | 0.125686 | − | 0.992070i | \(-0.459887\pi\) | ||||
0.125686 | + | 0.992070i | \(0.459887\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.246211 | 0.0163416 | 0.00817081 | − | 0.999967i | \(-0.497399\pi\) | ||||
0.00817081 | + | 0.999967i | \(0.497399\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2462 | 0.677089 | 0.338544 | − | 0.940950i | \(-0.390065\pi\) | ||||
0.338544 | + | 0.940950i | \(0.390065\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.75379 | −0.507968 | −0.253984 | − | 0.967208i | \(-0.581741\pi\) | ||||
−0.253984 | + | 0.967208i | \(0.581741\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.05398 | 0.133987 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.0540 | −0.650338 | −0.325169 | − | 0.945656i | \(-0.605421\pi\) | ||||
−0.325169 | + | 0.945656i | \(0.605421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.9309 | 0.961782 | 0.480891 | − | 0.876780i | \(-0.340313\pi\) | ||||
0.480891 | + | 0.876780i | \(0.340313\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.56155 | 0.0997639 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.56155 | −0.0993592 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.9309 | −0.942428 | −0.471214 | − | 0.882019i | \(-0.656184\pi\) | ||||
−0.471214 | + | 0.882019i | \(0.656184\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6847 | 0.916004 | 0.458002 | − | 0.888951i | \(-0.348565\pi\) | ||||
0.458002 | + | 0.888951i | \(0.348565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.438447 | 0.0272438 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.06913 | 0.0659254 | 0.0329627 | − | 0.999457i | \(-0.489506\pi\) | ||||
0.0329627 | + | 0.999457i | \(0.489506\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.3693 | 0.815142 | 0.407571 | − | 0.913174i | \(-0.366376\pi\) | ||||
0.407571 | + | 0.913174i | \(0.366376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.43845 | 0.391108 | 0.195554 | − | 0.980693i | \(-0.437350\pi\) | ||||
0.195554 | + | 0.980693i | \(0.437350\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.56155 | −0.154467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.12311 | 0.307818 | 0.153909 | − | 0.988085i | \(-0.450814\pi\) | ||||
0.153909 | + | 0.988085i | \(0.450814\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.6847 | 1.11463 | 0.557317 | − | 0.830300i | \(-0.311831\pi\) | ||||
0.557317 | + | 0.830300i | \(0.311831\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1771 | −0.902184 | −0.451092 | − | 0.892478i | \(-0.648965\pi\) | ||||
−0.451092 | + | 0.892478i | \(0.648965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.24621 | −0.368702 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.24621 | −0.426248 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.8769 | −1.10280 | −0.551400 | − | 0.834241i | \(-0.685906\pi\) | ||||
−0.551400 | + | 0.834241i | \(0.685906\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.3153 | 1.35747 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.2462 | 0.823880 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.24621 | −0.360026 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.12311 | −0.178829 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.63068 | 0.264287 | 0.132144 | − | 0.991231i | \(-0.457814\pi\) | ||||
0.132144 | + | 0.991231i | \(0.457814\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.1231 | −0.744143 | −0.372072 | − | 0.928204i | \(-0.621352\pi\) | ||||
−0.372072 | + | 0.928204i | \(0.621352\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.00000 | −0.113047 | −0.0565233 | − | 0.998401i | \(-0.518002\pi\) | ||||
−0.0565233 | + | 0.998401i | \(0.518002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.87689 | 0.386245 | 0.193122 | − | 0.981175i | \(-0.438139\pi\) | ||||
0.193122 | + | 0.981175i | \(0.438139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.56155 | −0.199409 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.36932 | 0.0761908 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.12311 | −0.506059 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.31534 | −0.0725171 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.2462 | 1.00290 | 0.501451 | − | 0.865186i | \(-0.332800\pi\) | ||||
0.501451 | + | 0.865186i | \(0.332800\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.43845 | −0.133227 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.87689 | −0.374608 | −0.187304 | − | 0.982302i | \(-0.559975\pi\) | ||||
−0.187304 | + | 0.982302i | \(0.559975\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.00000 | 0.429463 | 0.214731 | − | 0.976673i | \(-0.431112\pi\) | ||||
0.214731 | + | 0.976673i | \(0.431112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.06913 | 0.164287 | 0.0821434 | − | 0.996621i | \(-0.473823\pi\) | ||||
0.0821434 | + | 0.996621i | \(0.473823\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.6847 | −0.994484 | −0.497242 | − | 0.867612i | \(-0.665654\pi\) | ||||
−0.497242 | + | 0.867612i | \(0.665654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.2462 | 1.18071 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.2462 | −0.751886 | −0.375943 | − | 0.926643i | \(-0.622681\pi\) | ||||
−0.375943 | + | 0.926643i | \(0.622681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8078 | −0.989882 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.5616 | −0.709844 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.12311 | −0.265978 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7386 | 1.28092 | 0.640459 | − | 0.767992i | \(-0.278744\pi\) | ||||
0.640459 | + | 0.767992i | \(0.278744\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.6847 | −0.653293 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.0540 | 1.54377 | 0.771885 | − | 0.635763i | \(-0.219314\pi\) | ||||
0.771885 | + | 0.635763i | \(0.219314\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.8617 | 1.42367 | 0.711834 | − | 0.702348i | \(-0.247865\pi\) | ||||
0.711834 | + | 0.702348i | \(0.247865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.56155 | −0.0795841 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.36932 | 0.373639 | 0.186820 | − | 0.982394i | \(-0.440182\pi\) | ||||
0.186820 | + | 0.982394i | \(0.440182\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.4924 | −0.631769 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.4924 | −0.628562 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.36932 | −0.0687240 | −0.0343620 | − | 0.999409i | \(-0.510940\pi\) | ||||
−0.0343620 | + | 0.999409i | \(0.510940\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.61553 | 0.480177 | 0.240088 | − | 0.970751i | \(-0.422824\pi\) | ||||
0.240088 | + | 0.970751i | \(0.422824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.12311 | 0.354827 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.438447 | −0.0217330 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.876894 | 0.0433596 | 0.0216798 | − | 0.999765i | \(-0.493099\pi\) | ||||
0.0216798 | + | 0.999765i | \(0.493099\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.9309 | −0.734700 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.384472 | −0.0188730 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.19224 | −0.400217 | −0.200108 | − | 0.979774i | \(-0.564129\pi\) | ||||
−0.200108 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.05398 | −0.197579 | −0.0987893 | − | 0.995108i | \(-0.531497\pi\) | ||||
−0.0987893 | + | 0.995108i | \(0.531497\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.00000 | 0.388057 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000 | 0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.56155 | 0.267891 | 0.133945 | − | 0.990989i | \(-0.457235\pi\) | ||||
0.133945 | + | 0.990989i | \(0.457235\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.63068 | −0.222536 | −0.111268 | − | 0.993790i | \(-0.535491\pi\) | ||||
−0.111268 | + | 0.993790i | \(0.535491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.75379 | −0.0838951 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.05398 | −0.288940 | −0.144470 | − | 0.989509i | \(-0.546148\pi\) | ||||
−0.144470 | + | 0.989509i | \(0.546148\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.4924 | −0.783579 | −0.391789 | − | 0.920055i | \(-0.628144\pi\) | ||||
−0.391789 | + | 0.920055i | \(0.628144\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.384472 | −0.0182257 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.87689 | 0.324541 | 0.162270 | − | 0.986746i | \(-0.448118\pi\) | ||||
0.162270 | + | 0.986746i | \(0.448118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.24621 | 0.294123 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.56155 | −0.260730 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.8769 | −0.508800 | −0.254400 | − | 0.967099i | \(-0.581878\pi\) | ||||
−0.254400 | + | 0.967099i | \(0.581878\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.8769 | −0.692886 | −0.346443 | − | 0.938071i | \(-0.612611\pi\) | ||||
−0.346443 | + | 0.938071i | \(0.612611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.6847 | 1.51898 | 0.759492 | − | 0.650516i | \(-0.225447\pi\) | ||||
0.759492 | + | 0.650516i | \(0.225447\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.4384 | 0.668132 | 0.334066 | − | 0.942550i | \(-0.391579\pi\) | ||||
0.334066 | + | 0.942550i | \(0.391579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.56155 | 0.0721058 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.24621 | 0.287201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.12311 | 0.0515316 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.12311 | −0.142698 | −0.0713492 | − | 0.997451i | \(-0.522730\pi\) | ||||
−0.0713492 | + | 0.997451i | \(0.522730\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.56155 | −0.0712007 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.75379 | −0.0796354 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.7386 | 1.03039 | 0.515193 | − | 0.857074i | \(-0.327720\pi\) | ||||
0.515193 | + | 0.857074i | \(0.327720\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.9309 | −1.21537 | −0.607687 | − | 0.794177i | \(-0.707902\pi\) | ||||
−0.607687 | + | 0.794177i | \(0.707902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.1231 | 0.500959 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.2462 | −0.639030 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.4233 | −1.76483 | −0.882414 | − | 0.470473i | \(-0.844083\pi\) | ||||
−0.882414 | + | 0.470473i | \(0.844083\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.3693 | −1.12892 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.36932 | 0.237991 | 0.118995 | − | 0.992895i | \(-0.462033\pi\) | ||||
0.118995 | + | 0.992895i | \(0.462033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.68466 | 0.384187 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.8769 | −0.567424 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.31534 | 0.0578487 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.80776 | −0.254443 | −0.127221 | − | 0.991874i | \(-0.540606\pi\) | ||||
−0.127221 | + | 0.991874i | \(0.540606\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.5616 | −1.38009 | −0.690045 | − | 0.723766i | \(-0.742409\pi\) | ||||
−0.690045 | + | 0.723766i | \(0.742409\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.24621 | −0.272089 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.2462 | 0.963590 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.9309 | 1.33726 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.3693 | 0.660779 | 0.330389 | − | 0.943845i | \(-0.392820\pi\) | ||||
0.330389 | + | 0.943845i | \(0.392820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.12311 | 0.133779 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2462 | 0.780152 | 0.390076 | − | 0.920783i | \(-0.372449\pi\) | ||||
0.390076 | + | 0.920783i | \(0.372449\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.56155 | 0.0665244 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.80776 | −0.0765974 | −0.0382987 | − | 0.999266i | \(-0.512194\pi\) | ||||
−0.0382987 | + | 0.999266i | \(0.512194\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2462 | 0.940914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.36932 | 0.142000 | 0.0709999 | − | 0.997476i | \(-0.477381\pi\) | ||||
0.0709999 | + | 0.997476i | \(0.477381\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.12311 | 0.131390 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.9848 | −1.63433 | −0.817165 | − | 0.576404i | \(-0.804455\pi\) | ||||
−0.817165 | + | 0.576404i | \(0.804455\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.7386 | −0.616793 | −0.308396 | − | 0.951258i | \(-0.599792\pi\) | ||||
−0.308396 | + | 0.951258i | \(0.599792\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.2462 | −0.427297 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.2462 | −1.34243 | −0.671214 | − | 0.741264i | \(-0.734227\pi\) | ||||
−0.671214 | + | 0.741264i | \(0.734227\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.246211 | 0.0102146 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.12311 | 0.212177 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.82292 | 0.116514 | 0.0582572 | − | 0.998302i | \(-0.481446\pi\) | ||||
0.0582572 | + | 0.998302i | \(0.481446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.876894 | −0.0361318 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.0000 | 1.64260 | 0.821302 | − | 0.570494i | \(-0.193248\pi\) | ||||
0.821302 | + | 0.570494i | \(0.193248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.87689 | 0.199933 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.0000 | 1.63436 | 0.817178 | − | 0.576386i | \(-0.195537\pi\) | ||||
0.817178 | + | 0.576386i | \(0.195537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.8078 | 0.644812 | 0.322406 | − | 0.946601i | \(-0.395508\pi\) | ||||
0.322406 | + | 0.946601i | \(0.395508\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.56155 | 0.0634861 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.8078 | −1.12868 | −0.564341 | − | 0.825542i | \(-0.690870\pi\) | ||||
−0.564341 | + | 0.825542i | \(0.690870\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.68466 | 0.189521 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0000 | −1.05013 | −0.525065 | − | 0.851062i | \(-0.675959\pi\) | ||||
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.0000 | 0.563619 | 0.281809 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281809 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.12311 | 0.286302 | 0.143151 | − | 0.989701i | \(-0.454277\pi\) | ||||
0.143151 | + | 0.989701i | \(0.454277\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.246211 | 0.00986425 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.63068 | −0.225227 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.36932 | 0.0545982 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.87689 | 0.193534 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.56155 | 0.141114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.7386 | −0.503146 | −0.251573 | − | 0.967838i | \(-0.580948\pi\) | ||||
−0.251573 | + | 0.967838i | \(0.580948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.7538 | −0.700141 | −0.350071 | − | 0.936723i | \(-0.613842\pi\) | ||||
−0.350071 | + | 0.936723i | \(0.613842\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.06913 | −0.120660 | −0.0603300 | − | 0.998178i | \(-0.519215\pi\) | ||||
−0.0603300 | + | 0.998178i | \(0.519215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.9309 | 0.586088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.630683 | −0.0246805 | −0.0123403 | − | 0.999924i | \(-0.503928\pi\) | ||||
−0.0123403 | + | 0.999924i | \(0.503928\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.7386 | 0.419593 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.05398 | 0.0800115 | 0.0400058 | − | 0.999199i | \(-0.487262\pi\) | ||||
0.0400058 | + | 0.999199i | \(0.487262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0000 | 0.466746 | 0.233373 | − | 0.972387i | \(-0.425024\pi\) | ||||
0.233373 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.684658 | 0.0265499 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.2462 | −0.551616 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.6155 | 0.833217 | 0.416609 | − | 0.909086i | \(-0.363219\pi\) | ||||
0.416609 | + | 0.909086i | \(0.363219\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.4924 | 1.78685 | 0.893424 | − | 0.449213i | \(-0.148296\pi\) | ||||
0.893424 | + | 0.449213i | \(0.148296\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.12311 | 0.0431008 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.1231 | −0.884781 | −0.442391 | − | 0.896823i | \(-0.645869\pi\) | ||||
−0.442391 | + | 0.896823i | \(0.645869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.6155 | 0.596639 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.2462 | 0.695125 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.6155 | 1.50705 | 0.753523 | − | 0.657422i | \(-0.228353\pi\) | ||||
0.753523 | + | 0.657422i | \(0.228353\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.4924 | 1.38424 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.5076 | −0.738902 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.00000 | −0.0755390 | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.192236 | 0.00725032 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.2462 | 0.611002 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.0540 | −0.903366 | −0.451683 | − | 0.892178i | \(-0.649176\pi\) | ||||
−0.451683 | + | 0.892178i | \(0.649176\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.00000 | 0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.56155 | 0.207990 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.68466 | 0.249296 | 0.124648 | − | 0.992201i | \(-0.460220\pi\) | ||||
0.124648 | + | 0.992201i | \(0.460220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.24621 | 0.307105 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.12311 | 0.338824 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.6307 | 0.913501 | 0.456751 | − | 0.889595i | \(-0.349013\pi\) | ||||
0.456751 | + | 0.889595i | \(0.349013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.5076 | −0.721514 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.4773 | −1.75361 | −0.876806 | − | 0.480843i | \(-0.840331\pi\) | ||||
−0.876806 | + | 0.480843i | \(0.840331\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.56155 | −0.0575205 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.24621 | 0.0826282 | 0.0413141 | − | 0.999146i | \(-0.486846\pi\) | ||||
0.0413141 | + | 0.999146i | \(0.486846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.05398 | 0.0753530 | 0.0376765 | − | 0.999290i | \(-0.488004\pi\) | ||||
0.0376765 | + | 0.999290i | \(0.488004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.1771 | 0.482771 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.8078 | −0.723760 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.94602 | 0.0710114 | 0.0355057 | − | 0.999369i | \(-0.488696\pi\) | ||||
0.0355057 | + | 0.999369i | \(0.488696\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.1231 | −0.987111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.9460 | −0.434186 | −0.217093 | − | 0.976151i | \(-0.569657\pi\) | ||||
−0.217093 | + | 0.976151i | \(0.569657\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.24621 | 0.0814251 | 0.0407125 | − | 0.999171i | \(-0.487037\pi\) | ||||
0.0407125 | + | 0.999171i | \(0.487037\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | −0.0724049 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53.1771 | 1.92011 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.3153 | −0.408042 | −0.204021 | − | 0.978967i | \(-0.565401\pi\) | ||||
−0.204021 | + | 0.978967i | \(0.565401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −51.4233 | −1.84957 | −0.924784 | − | 0.380493i | \(-0.875754\pi\) | ||||
−0.924784 | + | 0.380493i | \(0.875754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.12311 | −0.184027 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.73863 | −0.0981217 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.2462 | 0.509770 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.7386 | 1.23988 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.3153 | −1.33015 | −0.665074 | − | 0.746777i | \(-0.731600\pi\) | ||||
−0.665074 | + | 0.746777i | \(0.731600\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.12311 | −0.252949 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.0540 | −0.356130 | −0.178065 | − | 0.984019i | \(-0.556984\pi\) | ||||
−0.178065 | + | 0.984019i | \(0.556984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.10795 | −0.145329 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.68466 | −0.306475 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.24621 | −0.220150 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.80776 | −0.204190 | −0.102095 | − | 0.994775i | \(-0.532555\pi\) | ||||
−0.102095 | + | 0.994775i | \(0.532555\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.5464 | −1.70469 | −0.852347 | − | 0.522976i | \(-0.824822\pi\) | ||||
−0.852347 | + | 0.522976i | \(0.824822\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.4384 | −1.20633 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.73863 | −0.0958127 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.6847 | −1.76891 | −0.884453 | − | 0.466629i | \(-0.845468\pi\) | ||||
−0.884453 | + | 0.466629i | \(0.845468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.56155 | −0.0544323 | −0.0272162 | − | 0.999630i | \(-0.508664\pi\) | ||||
−0.0272162 | + | 0.999630i | \(0.508664\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.93087 | −0.101916 | −0.0509582 | − | 0.998701i | \(-0.516228\pi\) | ||||
−0.0509582 | + | 0.998701i | \(0.516228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7538 | 0.477689 | 0.238844 | − | 0.971058i | \(-0.423231\pi\) | ||||
0.238844 | + | 0.971058i | \(0.423231\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.12311 | −0.108209 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.4924 | 0.986021 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.42329 | −0.187233 | −0.0936164 | − | 0.995608i | \(-0.529843\pi\) | ||||
−0.0936164 | + | 0.995608i | \(0.529843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.3153 | −0.562598 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.492423 | −0.0169398 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.75379 | −0.0601191 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.26137 | 0.111667 | 0.0558335 | − | 0.998440i | \(-0.482218\pi\) | ||||
0.0558335 | + | 0.998440i | \(0.482218\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.3693 | 1.54979 | 0.774893 | − | 0.632092i | \(-0.217804\pi\) | ||||
0.774893 | + | 0.632092i | \(0.217804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.4924 | 0.972149 | 0.486074 | − | 0.873917i | \(-0.338428\pi\) | ||||
0.486074 | + | 0.873917i | \(0.338428\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.7386 | −1.59100 | −0.795501 | − | 0.605953i | \(-0.792792\pi\) | ||||
−0.795501 | + | 0.605953i | \(0.792792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5076 | −0.391269 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.00000 | −0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.56155 | −0.188446 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.8078 | 0.399175 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.3693 | −1.05927 | −0.529633 | − | 0.848227i | \(-0.677670\pi\) | ||||
−0.529633 | + | 0.848227i | \(0.677670\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.9157 | 1.68170 | 0.840852 | − | 0.541266i | \(-0.182055\pi\) | ||||
0.840852 | + | 0.541266i | \(0.182055\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.93087 | −0.0986316 | −0.0493158 | − | 0.998783i | \(-0.515704\pi\) | ||||
−0.0493158 | + | 0.998783i | \(0.515704\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.1231 | 0.642091 | 0.321046 | − | 0.947064i | \(-0.395966\pi\) | ||||
0.321046 | + | 0.947064i | \(0.395966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.12311 | −0.104746 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.576708 | −0.0192988 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.7538 | 0.860854 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.12311 | −0.237569 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0000 | −0.533037 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.50758 | −0.116596 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.9848 | −1.75933 | −0.879666 | − | 0.475591i | \(-0.842234\pi\) | ||||
−0.879666 | + | 0.475591i | \(0.842234\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.1231 | −0.501051 | −0.250525 | − | 0.968110i | \(-0.580603\pi\) | ||||
−0.250525 | + | 0.968110i | \(0.580603\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.246211 | −0.00814840 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.87689 | −0.227095 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.2462 | −0.997730 | −0.498865 | − | 0.866680i | \(-0.666250\pi\) | ||||
−0.498865 | + | 0.866680i | \(0.666250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 50.7386 | 1.67008 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12311 | 0.0369275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.6695 | −0.907807 | −0.453903 | − | 0.891051i | \(-0.649969\pi\) | ||||
−0.453903 | + | 0.891051i | \(0.649969\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.438447 | −0.0143695 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.87689 | −0.159492 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.6155 | −1.55553 | −0.777766 | − | 0.628554i | \(-0.783647\pi\) | ||||
−0.777766 | + | 0.628554i | \(0.783647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.61553 | −0.183061 | −0.0915305 | − | 0.995802i | \(-0.529176\pi\) | ||||
−0.0915305 | + | 0.995802i | \(0.529176\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.9848 | 0.813618 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.1231 | −1.27133 | −0.635665 | − | 0.771965i | \(-0.719274\pi\) | ||||
−0.635665 | + | 0.771965i | \(0.719274\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.9309 | −1.00406 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.8078 | −1.22471 | −0.612357 | − | 0.790582i | \(-0.709778\pi\) | ||||
−0.612357 | + | 0.790582i | \(0.709778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.38447 | −0.271315 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.0000 | −0.322917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.7386 | −0.860747 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.63068 | 0.213228 | 0.106614 | − | 0.994300i | \(-0.465999\pi\) | ||||
0.106614 | + | 0.994300i | \(0.465999\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.5616 | 1.59051 | 0.795253 | − | 0.606278i | \(-0.207338\pi\) | ||||
0.795253 | + | 0.606278i | \(0.207338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.3693 | −0.749186 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.38447 | 0.204257 | 0.102129 | − | 0.994771i | \(-0.467435\pi\) | ||||
0.102129 | + | 0.994771i | \(0.467435\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.246211 | −0.00786895 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.3693 | −1.25569 | −0.627843 | − | 0.778340i | \(-0.716062\pi\) | ||||
−0.627843 | + | 0.778340i | \(0.716062\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.3693 | 0.808334 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.9848 | 0.794472 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.6847 | 1.03826 | 0.519131 | − | 0.854695i | \(-0.326256\pi\) | ||||
0.519131 | + | 0.854695i | \(0.326256\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.2462 | 0.451635 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.0000 | −1.71020 | −0.855099 | − | 0.518465i | \(-0.826503\pi\) | ||||
−0.855099 | + | 0.518465i | \(0.826503\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5544.2.a.bd.1.2 | 2 | ||
3.2 | odd | 2 | 1848.2.a.p.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 3696.2.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1848.2.a.p.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
3696.2.a.bi.1.1 | 2 | 12.11 | even | 2 | |||
5544.2.a.bd.1.2 | 2 | 1.1 | even | 1 | trivial |