Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, 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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.993.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 950) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.25342\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0778929 | −0.0294407 | −0.0147204 | − | 0.999892i | \(-0.504686\pi\) | ||||
−0.0147204 | + | 0.999892i | \(0.504686\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.50684 | 1.35886 | 0.679431 | − | 0.733739i | \(-0.262227\pi\) | ||||
0.679431 | + | 0.733739i | \(0.262227\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.33131 | −1.47864 | −0.739320 | − | 0.673354i | \(-0.764853\pi\) | ||||
−0.739320 | + | 0.673354i | \(0.764853\pi\) | |||||||
\(14\) | 0.0778929 | 0.0208177 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.33131 | −1.77810 | −0.889052 | − | 0.457806i | \(-0.848635\pi\) | ||||
−0.889052 | + | 0.457806i | \(0.848635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.50684 | −0.960861 | ||||||||
\(23\) | −3.40920 | −0.710868 | −0.355434 | − | 0.934701i | \(-0.615667\pi\) | ||||
−0.355434 | + | 0.934701i | \(0.615667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.33131 | 1.04556 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0778929 | −0.0147204 | ||||||||
\(29\) | 1.33131 | 0.247218 | 0.123609 | − | 0.992331i | \(-0.460553\pi\) | ||||
0.123609 | + | 0.992331i | \(0.460553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50684 | −0.450241 | −0.225121 | − | 0.974331i | \(-0.572278\pi\) | ||||
−0.225121 | + | 0.974331i | \(0.572278\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.33131 | 1.25731 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.50684 | −0.905318 | −0.452659 | − | 0.891684i | \(-0.649525\pi\) | ||||
−0.452659 | + | 0.891684i | \(0.649525\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.506836 | 0.0772918 | 0.0386459 | − | 0.999253i | \(-0.487696\pi\) | ||||
0.0386459 | + | 0.999253i | \(0.487696\pi\) | |||||||
\(44\) | 4.50684 | 0.679431 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.40920 | 0.502660 | ||||||||
\(47\) | 5.66262 | 0.825978 | 0.412989 | − | 0.910736i | \(-0.364485\pi\) | ||||
0.412989 | + | 0.910736i | \(0.364485\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99393 | −0.999133 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.33131 | −0.739320 | ||||||||
\(53\) | 12.9358 | 1.77687 | 0.888433 | − | 0.459006i | \(-0.151794\pi\) | ||||
0.888433 | + | 0.459006i | \(0.151794\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.0778929 | 0.0104089 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.33131 | −0.174810 | ||||||||
\(59\) | −7.56499 | −0.984878 | −0.492439 | − | 0.870347i | \(-0.663894\pi\) | ||||
−0.492439 | + | 0.870347i | \(0.663894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.15579 | −0.276020 | −0.138010 | − | 0.990431i | \(-0.544071\pi\) | ||||
−0.138010 | + | 0.990431i | \(0.544071\pi\) | |||||||
\(62\) | 2.50684 | 0.318369 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.58473 | −0.560114 | −0.280057 | − | 0.959983i | \(-0.590353\pi\) | ||||
−0.280057 | + | 0.959983i | \(0.590353\pi\) | |||||||
\(68\) | −7.33131 | −0.889052 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.8579 | 1.28859 | 0.644297 | − | 0.764775i | \(-0.277150\pi\) | ||||
0.644297 | + | 0.764775i | \(0.277150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.09763 | −0.596633 | −0.298316 | − | 0.954467i | \(-0.596425\pi\) | ||||
−0.298316 | + | 0.954467i | \(0.596425\pi\) | |||||||
\(74\) | 5.50684 | 0.640157 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −0.351050 | −0.0400059 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.0137 | 1.91419 | 0.957094 | − | 0.289778i | \(-0.0935815\pi\) | ||||
0.957094 | + | 0.289778i | \(0.0935815\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1695 | 1.44554 | 0.722768 | − | 0.691091i | \(-0.242870\pi\) | ||||
0.722768 | + | 0.691091i | \(0.242870\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.506836 | −0.0546535 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.50684 | −0.480430 | ||||||||
\(89\) | −15.0137 | −1.59145 | −0.795723 | − | 0.605661i | \(-0.792909\pi\) | ||||
−0.795723 | + | 0.605661i | \(0.792909\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.415271 | 0.0435322 | ||||||||
\(92\) | −3.40920 | −0.355434 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.66262 | −0.584055 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.67629 | 0.779410 | 0.389705 | − | 0.920940i | \(-0.372577\pi\) | ||||
0.389705 | + | 0.920940i | \(0.372577\pi\) | |||||||
\(98\) | 6.99393 | 0.706494 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.15579 | 0.413516 | 0.206758 | − | 0.978392i | \(-0.433709\pi\) | ||||
0.206758 | + | 0.978392i | \(0.433709\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.35105 | 0.231656 | 0.115828 | − | 0.993269i | \(-0.463048\pi\) | ||||
0.115828 | + | 0.993269i | \(0.463048\pi\) | |||||||
\(104\) | 5.33131 | 0.522778 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.9358 | −1.25643 | ||||||||
\(107\) | 14.0334 | 1.35666 | 0.678331 | − | 0.734757i | \(-0.262704\pi\) | ||||
0.678331 | + | 0.734757i | \(0.262704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0778929 | −0.00746078 | −0.00373039 | − | 0.999993i | \(-0.501187\pi\) | ||||
−0.00373039 | + | 0.999993i | \(0.501187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0778929 | −0.00736018 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.33131 | 0.123609 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.56499 | 0.696414 | ||||||||
\(119\) | 0.571057 | 0.0523487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.31157 | 0.846506 | ||||||||
\(122\) | 2.15579 | 0.195176 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.50684 | −0.225121 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8321 | 1.58234 | 0.791171 | − | 0.611596i | \(-0.209472\pi\) | ||||
0.791171 | + | 0.611596i | \(0.209472\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.49316 | 0.130458 | 0.0652292 | − | 0.997870i | \(-0.479222\pi\) | ||||
0.0652292 | + | 0.997870i | \(0.479222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0778929 | −0.00675417 | ||||||||
\(134\) | 4.58473 | 0.396060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.33131 | 0.628655 | ||||||||
\(137\) | 8.42894 | 0.720133 | 0.360067 | − | 0.932927i | \(-0.382754\pi\) | ||||
0.360067 | + | 0.932927i | \(0.382754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.81841 | 0.747968 | 0.373984 | − | 0.927435i | \(-0.377992\pi\) | ||||
0.373984 | + | 0.927435i | \(0.377992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.8579 | −0.911174 | ||||||||
\(143\) | −24.0273 | −2.00927 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.09763 | 0.421883 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.50684 | −0.452659 | ||||||||
\(149\) | −17.6763 | −1.44810 | −0.724049 | − | 0.689748i | \(-0.757721\pi\) | ||||
−0.724049 | + | 0.689748i | \(0.757721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.351050 | 0.0282884 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.506836 | 0.0404499 | 0.0202250 | − | 0.999795i | \(-0.493562\pi\) | ||||
0.0202250 | + | 0.999795i | \(0.493562\pi\) | |||||||
\(158\) | −17.0137 | −1.35354 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.265553 | 0.0209285 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.830542 | 0.0650531 | 0.0325265 | − | 0.999471i | \(-0.489645\pi\) | ||||
0.0325265 | + | 0.999471i | \(0.489645\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.1695 | −1.02215 | ||||||||
\(167\) | −16.5068 | −1.27734 | −0.638669 | − | 0.769482i | \(-0.720515\pi\) | ||||
−0.638669 | + | 0.769482i | \(0.720515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.4229 | 1.18638 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.506836 | 0.0386459 | ||||||||
\(173\) | −18.8321 | −1.43178 | −0.715888 | − | 0.698215i | \(-0.753978\pi\) | ||||
−0.715888 | + | 0.698215i | \(0.753978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.50684 | 0.339716 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.0137 | 1.12532 | ||||||||
\(179\) | 7.15579 | 0.534849 | 0.267424 | − | 0.963579i | \(-0.413827\pi\) | ||||
0.267424 | + | 0.963579i | \(0.413827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.5205 | 0.930642 | 0.465321 | − | 0.885142i | \(-0.345939\pi\) | ||||
0.465321 | + | 0.885142i | \(0.345939\pi\) | |||||||
\(182\) | −0.415271 | −0.0307819 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.40920 | 0.251330 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −33.0410 | −2.41620 | ||||||||
\(188\) | 5.66262 | 0.412989 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.90237 | 0.354723 | 0.177361 | − | 0.984146i | \(-0.443244\pi\) | ||||
0.177361 | + | 0.984146i | \(0.443244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.1558 | 1.30688 | 0.653441 | − | 0.756977i | \(-0.273325\pi\) | ||||
0.653441 | + | 0.756977i | \(0.273325\pi\) | |||||||
\(194\) | −7.67629 | −0.551126 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.99393 | −0.499567 | ||||||||
\(197\) | 2.98633 | 0.212767 | 0.106384 | − | 0.994325i | \(-0.466073\pi\) | ||||
0.106384 | + | 0.994325i | \(0.466073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.06422 | −0.217217 | −0.108608 | − | 0.994085i | \(-0.534639\pi\) | ||||
−0.108608 | + | 0.994085i | \(0.534639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.15579 | −0.292400 | ||||||||
\(203\) | −0.103700 | −0.00727829 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.35105 | −0.163805 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.33131 | −0.369660 | ||||||||
\(209\) | 4.50684 | 0.311744 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2534 | 1.32546 | 0.662730 | − | 0.748858i | \(-0.269398\pi\) | ||||
0.662730 | + | 0.748858i | \(0.269398\pi\) | |||||||
\(212\) | 12.9358 | 0.888433 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.0334 | −0.959304 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.195265 | 0.0132554 | ||||||||
\(218\) | 0.0778929 | 0.00527557 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 39.0855 | 2.62918 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.5068 | −0.971450 | −0.485725 | − | 0.874112i | \(-0.661444\pi\) | ||||
−0.485725 | + | 0.874112i | \(0.661444\pi\) | |||||||
\(224\) | 0.0778929 | 0.00520444 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 21.5984 | 1.43354 | 0.716768 | − | 0.697312i | \(-0.245621\pi\) | ||||
0.716768 | + | 0.697312i | \(0.245621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.0137 | −1.25646 | −0.628229 | − | 0.778028i | \(-0.716220\pi\) | ||||
−0.628229 | + | 0.778028i | \(0.716220\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.33131 | −0.0874048 | ||||||||
\(233\) | 6.01367 | 0.393969 | 0.196984 | − | 0.980407i | \(-0.436885\pi\) | ||||
0.196984 | + | 0.980407i | \(0.436885\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.56499 | −0.492439 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.571057 | −0.0370161 | ||||||||
\(239\) | −15.4092 | −0.996739 | −0.498369 | − | 0.866965i | \(-0.666068\pi\) | ||||
−0.498369 | + | 0.866965i | \(0.666068\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.81841 | −0.310381 | −0.155190 | − | 0.987885i | \(-0.549599\pi\) | ||||
−0.155190 | + | 0.987885i | \(0.549599\pi\) | |||||||
\(242\) | −9.31157 | −0.598570 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.15579 | −0.138010 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.33131 | −0.339223 | ||||||||
\(248\) | 2.50684 | 0.159184 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.52051 | −0.0959736 | −0.0479868 | − | 0.998848i | \(-0.515281\pi\) | ||||
−0.0479868 | + | 0.998848i | \(0.515281\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.3647 | −0.965972 | ||||||||
\(254\) | −17.8321 | −1.11888 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.5068 | −1.02967 | −0.514834 | − | 0.857290i | \(-0.672146\pi\) | ||||
−0.514834 | + | 0.857290i | \(0.672146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.428943 | 0.0266532 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.49316 | −0.0922480 | ||||||||
\(263\) | 18.0273 | 1.11161 | 0.555807 | − | 0.831311i | \(-0.312409\pi\) | ||||
0.555807 | + | 0.831311i | \(0.312409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0778929 | 0.00477592 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.58473 | −0.280057 | ||||||||
\(269\) | −20.2089 | −1.23216 | −0.616080 | − | 0.787683i | \(-0.711280\pi\) | ||||
−0.616080 | + | 0.787683i | \(0.711280\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.08396 | 0.369574 | 0.184787 | − | 0.982779i | \(-0.440840\pi\) | ||||
0.184787 | + | 0.982779i | \(0.440840\pi\) | |||||||
\(272\) | −7.33131 | −0.444526 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.42894 | −0.509211 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.3647 | −1.88452 | −0.942262 | − | 0.334877i | \(-0.891305\pi\) | ||||
−0.942262 | + | 0.334877i | \(0.891305\pi\) | |||||||
\(278\) | −8.81841 | −0.528893 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.3252 | −0.675607 | −0.337804 | − | 0.941217i | \(-0.609684\pi\) | ||||
−0.337804 | + | 0.941217i | \(0.609684\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1437 | 1.55408 | 0.777039 | − | 0.629452i | \(-0.216721\pi\) | ||||
0.777039 | + | 0.629452i | \(0.216721\pi\) | |||||||
\(284\) | 10.8579 | 0.644297 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0273 | 1.42077 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.7481 | 2.16165 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.09763 | −0.298316 | ||||||||
\(293\) | −1.33131 | −0.0777760 | −0.0388880 | − | 0.999244i | \(-0.512382\pi\) | ||||
−0.0388880 | + | 0.999244i | \(0.512382\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.50684 | 0.320078 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.6763 | 1.02396 | ||||||||
\(299\) | 18.1755 | 1.05112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0394789 | −0.00227553 | ||||||||
\(302\) | −20.0000 | −1.15087 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.84421 | −0.162328 | −0.0811639 | − | 0.996701i | \(-0.525864\pi\) | ||||
−0.0811639 | + | 0.996701i | \(0.525864\pi\) | |||||||
\(308\) | −0.351050 | −0.0200030 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3895 | 0.929361 | 0.464681 | − | 0.885478i | \(-0.346169\pi\) | ||||
0.464681 | + | 0.885478i | \(0.346169\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.0471 | −1.18965 | −0.594826 | − | 0.803855i | \(-0.702779\pi\) | ||||
−0.594826 | + | 0.803855i | \(0.702779\pi\) | |||||||
\(314\) | −0.506836 | −0.0286024 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.0137 | 0.957094 | ||||||||
\(317\) | 30.8902 | 1.73497 | 0.867484 | − | 0.497465i | \(-0.165736\pi\) | ||||
0.867484 | + | 0.497465i | \(0.165736\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | 0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.265553 | −0.0147987 | ||||||||
\(323\) | −7.33131 | −0.407925 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.830542 | −0.0459995 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.441078 | −0.0243174 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.3845 | 1.56015 | 0.780076 | − | 0.625685i | \(-0.215181\pi\) | ||||
0.780076 | + | 0.625685i | \(0.215181\pi\) | |||||||
\(332\) | 13.1695 | 0.722768 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.5068 | 0.903214 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.8716 | −0.973526 | −0.486763 | − | 0.873534i | \(-0.661822\pi\) | ||||
−0.486763 | + | 0.873534i | \(0.661822\pi\) | |||||||
\(338\) | −15.4229 | −0.838894 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.2979 | −0.611816 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.09003 | 0.0588560 | ||||||||
\(344\) | −0.506836 | −0.0273268 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.8321 | 1.01242 | ||||||||
\(347\) | −33.0410 | −1.77373 | −0.886867 | − | 0.462024i | \(-0.847123\pi\) | ||||
−0.886867 | + | 0.462024i | \(0.847123\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.7158 | −1.05536 | −0.527681 | − | 0.849443i | \(-0.676938\pi\) | ||||
−0.527681 | + | 0.849443i | \(0.676938\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.50684 | −0.240215 | ||||||||
\(353\) | 5.90997 | 0.314556 | 0.157278 | − | 0.987554i | \(-0.449728\pi\) | ||||
0.157278 | + | 0.987554i | \(0.449728\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.0137 | −0.795723 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.15579 | −0.378195 | ||||||||
\(359\) | 7.00760 | 0.369847 | 0.184924 | − | 0.982753i | \(-0.440796\pi\) | ||||
0.184924 | + | 0.982753i | \(0.440796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −12.5205 | −0.658063 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.415271 | 0.0217661 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.7158 | 0.924756 | 0.462378 | − | 0.886683i | \(-0.346996\pi\) | ||||
0.462378 | + | 0.886683i | \(0.346996\pi\) | |||||||
\(368\) | −3.40920 | −0.177717 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.00760 | −0.0523122 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.4487 | 0.799902 | 0.399951 | − | 0.916536i | \(-0.369027\pi\) | ||||
0.399951 | + | 0.916536i | \(0.369027\pi\) | |||||||
\(374\) | 33.0410 | 1.70851 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.66262 | −0.292027 | ||||||||
\(377\) | −7.09763 | −0.365547 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.4563 | 1.76990 | 0.884950 | − | 0.465685i | \(-0.154192\pi\) | ||||
0.884950 | + | 0.465685i | \(0.154192\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.90237 | −0.250827 | ||||||||
\(383\) | 12.0273 | 0.614569 | 0.307284 | − | 0.951618i | \(-0.400580\pi\) | ||||
0.307284 | + | 0.951618i | \(0.400580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.1558 | −0.924105 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.67629 | 0.389705 | ||||||||
\(389\) | 15.3647 | 0.779022 | 0.389511 | − | 0.921022i | \(-0.372644\pi\) | ||||
0.389511 | + | 0.921022i | \(0.372644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9939 | 1.26400 | ||||||||
\(392\) | 6.99393 | 0.353247 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.98633 | −0.150449 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.32524 | 0.0665121 | 0.0332560 | − | 0.999447i | \(-0.489412\pi\) | ||||
0.0332560 | + | 0.999447i | \(0.489412\pi\) | |||||||
\(398\) | 3.06422 | 0.153596 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.46736 | 0.322964 | 0.161482 | − | 0.986876i | \(-0.448373\pi\) | ||||
0.161482 | + | 0.986876i | \(0.448373\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.3647 | 0.665744 | ||||||||
\(404\) | 4.15579 | 0.206758 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.103700 | 0.00514653 | ||||||||
\(407\) | −24.8184 | −1.23020 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.36472 | −0.0674812 | −0.0337406 | − | 0.999431i | \(-0.510742\pi\) | ||||
−0.0337406 | + | 0.999431i | \(0.510742\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.35105 | 0.115828 | ||||||||
\(413\) | 0.589259 | 0.0289955 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.33131 | 0.261389 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.50684 | −0.220437 | ||||||||
\(419\) | −16.6231 | −0.812094 | −0.406047 | − | 0.913852i | \(-0.633093\pi\) | ||||
−0.406047 | + | 0.913852i | \(0.633093\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.1128 | −1.51635 | −0.758174 | − | 0.652053i | \(-0.773908\pi\) | ||||
−0.758174 | + | 0.652053i | \(0.773908\pi\) | |||||||
\(422\) | −19.2534 | −0.937242 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.9358 | −0.628217 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.167920 | 0.00812623 | ||||||||
\(428\) | 14.0334 | 0.678331 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.1831 | 0.490504 | 0.245252 | − | 0.969459i | \(-0.421129\pi\) | ||||
0.245252 | + | 0.969459i | \(0.421129\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.1953 | 1.06664 | 0.533318 | − | 0.845915i | \(-0.320945\pi\) | ||||
0.533318 | + | 0.845915i | \(0.320945\pi\) | |||||||
\(434\) | −0.195265 | −0.00937300 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0778929 | −0.00373039 | ||||||||
\(437\) | −3.40920 | −0.163084 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.32524 | −0.445070 | −0.222535 | − | 0.974925i | \(-0.571433\pi\) | ||||
−0.222535 | + | 0.974925i | \(0.571433\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −39.0855 | −1.85911 | ||||||||
\(443\) | 13.9879 | 0.664584 | 0.332292 | − | 0.943177i | \(-0.392178\pi\) | ||||
0.332292 | + | 0.943177i | \(0.392178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.5068 | 0.686919 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.0778929 | −0.00368009 | ||||||||
\(449\) | −13.4932 | −0.636782 | −0.318391 | − | 0.947960i | \(-0.603142\pi\) | ||||
−0.318391 | + | 0.947960i | \(0.603142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.5984 | −1.01366 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.68236 | 0.452922 | 0.226461 | − | 0.974020i | \(-0.427284\pi\) | ||||
0.226461 | + | 0.974020i | \(0.427284\pi\) | |||||||
\(458\) | 19.0137 | 0.888451 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.66262 | −0.403459 | −0.201729 | − | 0.979441i | \(-0.564656\pi\) | ||||
−0.201729 | + | 0.979441i | \(0.564656\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.0015 | 1.30134 | 0.650671 | − | 0.759360i | \(-0.274488\pi\) | ||||
0.650671 | + | 0.759360i | \(0.274488\pi\) | |||||||
\(464\) | 1.33131 | 0.0618046 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.01367 | −0.278578 | ||||||||
\(467\) | −16.9742 | −0.785472 | −0.392736 | − | 0.919651i | \(-0.628471\pi\) | ||||
−0.392736 | + | 0.919651i | \(0.628471\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.357118 | 0.0164902 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.56499 | 0.348207 | ||||||||
\(473\) | 2.28423 | 0.105029 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.571057 | 0.0261743 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.4092 | 0.704801 | ||||||||
\(479\) | −10.0532 | −0.459340 | −0.229670 | − | 0.973269i | \(-0.573765\pi\) | ||||
−0.229670 | + | 0.973269i | \(0.573765\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.3587 | 1.33864 | ||||||||
\(482\) | 4.81841 | 0.219472 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.31157 | 0.423253 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.2089 | 0.870440 | 0.435220 | − | 0.900324i | \(-0.356671\pi\) | ||||
0.435220 | + | 0.900324i | \(0.356671\pi\) | |||||||
\(488\) | 2.15579 | 0.0975878 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.32524 | −0.240325 | −0.120162 | − | 0.992754i | \(-0.538342\pi\) | ||||
−0.120162 | + | 0.992754i | \(0.538342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.76025 | −0.439580 | ||||||||
\(494\) | 5.33131 | 0.239867 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.50684 | −0.112560 | ||||||||
\(497\) | −0.845752 | −0.0379372 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.9605 | −0.535426 | −0.267713 | − | 0.963499i | \(-0.586268\pi\) | ||||
−0.267713 | + | 0.963499i | \(0.586268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.52051 | 0.0678636 | ||||||||
\(503\) | 19.3313 | 0.861941 | 0.430970 | − | 0.902366i | \(-0.358171\pi\) | ||||
0.430970 | + | 0.902366i | \(0.358171\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.3647 | 0.683045 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.8321 | 0.791171 | ||||||||
\(509\) | 36.1573 | 1.60265 | 0.801323 | − | 0.598232i | \(-0.204130\pi\) | ||||
0.801323 | + | 0.598232i | \(0.204130\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.397069 | 0.0175653 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.5068 | 0.728085 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.5205 | 1.12239 | ||||||||
\(518\) | −0.428943 | −0.0188467 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.5205 | 1.38094 | 0.690469 | − | 0.723362i | \(-0.257404\pi\) | ||||
0.690469 | + | 0.723362i | \(0.257404\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.59840 | 0.244801 | 0.122400 | − | 0.992481i | \(-0.460941\pi\) | ||||
0.122400 | + | 0.992481i | \(0.460941\pi\) | |||||||
\(524\) | 1.49316 | 0.0652292 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.0273 | −0.786030 | ||||||||
\(527\) | 18.3784 | 0.800575 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3773 | −0.494667 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.0778929 | −0.00337708 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.58473 | 0.198030 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.2089 | 0.871269 | ||||||||
\(539\) | −31.5205 | −1.35768 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.1968 | 0.653362 | 0.326681 | − | 0.945135i | \(-0.394070\pi\) | ||||
0.326681 | + | 0.945135i | \(0.394070\pi\) | |||||||
\(542\) | −6.08396 | −0.261328 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.33131 | 0.314327 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.6505 | −1.13949 | −0.569746 | − | 0.821821i | \(-0.692959\pi\) | ||||
−0.569746 | + | 0.821821i | \(0.692959\pi\) | |||||||
\(548\) | 8.42894 | 0.360067 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.33131 | 0.0567158 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.32524 | −0.0563551 | ||||||||
\(554\) | 31.3647 | 1.33256 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.81841 | 0.373984 | ||||||||
\(557\) | −12.8458 | −0.544292 | −0.272146 | − | 0.962256i | \(-0.587733\pi\) | ||||
−0.272146 | + | 0.962256i | \(0.587733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.70210 | −0.114287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.3252 | 0.477727 | ||||||||
\(563\) | −10.1968 | −0.429744 | −0.214872 | − | 0.976642i | \(-0.568933\pi\) | ||||
−0.214872 | + | 0.976642i | \(0.568933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.1437 | −1.09890 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.8579 | −0.455587 | ||||||||
\(569\) | 24.3784 | 1.02200 | 0.510998 | − | 0.859582i | \(-0.329276\pi\) | ||||
0.510998 | + | 0.859582i | \(0.329276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.32371 | 0.348336 | 0.174168 | − | 0.984716i | \(-0.444276\pi\) | ||||
0.174168 | + | 0.984716i | \(0.444276\pi\) | |||||||
\(572\) | −24.0273 | −1.00463 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.29290 | −0.303607 | −0.151804 | − | 0.988411i | \(-0.548508\pi\) | ||||
−0.151804 | + | 0.988411i | \(0.548508\pi\) | |||||||
\(578\) | −36.7481 | −1.52852 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.02581 | −0.0425576 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 58.2994 | 2.41452 | ||||||||
\(584\) | 5.09763 | 0.210942 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.33131 | 0.0549959 | ||||||||
\(587\) | −5.53264 | −0.228357 | −0.114178 | − | 0.993460i | \(-0.536424\pi\) | ||||
−0.114178 | + | 0.993460i | \(0.536424\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.50684 | −0.103292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.50684 | −0.226330 | ||||||||
\(593\) | 26.3252 | 1.08105 | 0.540524 | − | 0.841329i | \(-0.318226\pi\) | ||||
0.540524 | + | 0.841329i | \(0.318226\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.6763 | −0.724049 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.1755 | −0.743252 | ||||||||
\(599\) | −22.2994 | −0.911130 | −0.455565 | − | 0.890202i | \(-0.650563\pi\) | ||||
−0.455565 | + | 0.890202i | \(0.650563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.4947 | 1.32549 | 0.662743 | − | 0.748847i | \(-0.269392\pi\) | ||||
0.662743 | + | 0.748847i | \(0.269392\pi\) | |||||||
\(602\) | 0.0394789 | 0.00160904 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.35105 | 0.338959 | 0.169479 | − | 0.985534i | \(-0.445791\pi\) | ||||
0.169479 | + | 0.985534i | \(0.445791\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.1892 | −1.22132 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.2994 | −1.54690 | −0.773450 | − | 0.633858i | \(-0.781471\pi\) | ||||
−0.773450 | + | 0.633858i | \(0.781471\pi\) | |||||||
\(614\) | 2.84421 | 0.114783 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.351050 | 0.0141442 | ||||||||
\(617\) | 14.3526 | 0.577813 | 0.288907 | − | 0.957357i | \(-0.406708\pi\) | ||||
0.288907 | + | 0.957357i | \(0.406708\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.62314 | −0.346593 | −0.173297 | − | 0.984870i | \(-0.555442\pi\) | ||||
−0.173297 | + | 0.984870i | \(0.555442\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16.3895 | −0.657158 | ||||||||
\(623\) | 1.16946 | 0.0468533 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.0471 | 0.841211 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.506836 | 0.0202250 | ||||||||
\(629\) | 40.3723 | 1.60975 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3374 | −0.411525 | −0.205762 | − | 0.978602i | \(-0.565967\pi\) | ||||
−0.205762 | + | 0.978602i | \(0.565967\pi\) | |||||||
\(632\) | −17.0137 | −0.676768 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30.8902 | −1.22681 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.2868 | 1.47736 | ||||||||
\(638\) | −6.00000 | −0.237542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.88369 | −0.232392 | −0.116196 | − | 0.993226i | \(-0.537070\pi\) | ||||
−0.116196 | + | 0.993226i | \(0.537070\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.5084 | −1.00595 | −0.502976 | − | 0.864300i | \(-0.667762\pi\) | ||||
−0.502976 | + | 0.864300i | \(0.667762\pi\) | |||||||
\(644\) | 0.265553 | 0.0104642 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.33131 | 0.288447 | ||||||||
\(647\) | 5.09157 | 0.200170 | 0.100085 | − | 0.994979i | \(-0.468089\pi\) | ||||
0.100085 | + | 0.994979i | \(0.468089\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34.0942 | −1.33831 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.830542 | 0.0325265 | ||||||||
\(653\) | 11.1816 | 0.437570 | 0.218785 | − | 0.975773i | \(-0.429791\pi\) | ||||
0.218785 | + | 0.975773i | \(0.429791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.441078 | 0.0171950 | ||||||||
\(659\) | 13.7542 | 0.535787 | 0.267894 | − | 0.963449i | \(-0.413672\pi\) | ||||
0.267894 | + | 0.963449i | \(0.413672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6171 | −0.490747 | −0.245374 | − | 0.969429i | \(-0.578911\pi\) | ||||
−0.245374 | + | 0.969429i | \(0.578911\pi\) | |||||||
\(662\) | −28.3845 | −1.10319 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.1695 | −0.511074 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.53871 | −0.175740 | ||||||||
\(668\) | −16.5068 | −0.638669 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.71577 | −0.375073 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.35105 | 0.0906263 | 0.0453132 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453132 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(674\) | 17.8716 | 0.688387 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.4229 | 0.593188 | ||||||||
\(677\) | 23.7663 | 0.913414 | 0.456707 | − | 0.889617i | \(-0.349029\pi\) | ||||
0.456707 | + | 0.889617i | \(0.349029\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.597928 | −0.0229464 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.2979 | 0.432619 | ||||||||
\(683\) | −28.1695 | −1.07787 | −0.538937 | − | 0.842346i | \(-0.681174\pi\) | ||||
−0.538937 | + | 0.842346i | \(0.681174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.09003 | −0.0416174 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.506836 | 0.0193229 | ||||||||
\(689\) | −68.9647 | −2.62734 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.32371 | 0.0883979 | 0.0441990 | − | 0.999023i | \(-0.485926\pi\) | ||||
0.0441990 | + | 0.999023i | \(0.485926\pi\) | |||||||
\(692\) | −18.8321 | −0.715888 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.0410 | 1.25422 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 19.7158 | 0.746253 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.7036 | −0.895274 | −0.447637 | − | 0.894215i | \(-0.647734\pi\) | ||||
−0.447637 | + | 0.894215i | \(0.647734\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.50684 | −0.207694 | ||||||||
\(704\) | 4.50684 | 0.169858 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.90997 | −0.222425 | ||||||||
\(707\) | −0.323706 | −0.0121742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.05315 | 0.339998 | 0.169999 | − | 0.985444i | \(-0.445624\pi\) | ||||
0.169999 | + | 0.985444i | \(0.445624\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.0137 | 0.562661 | ||||||||
\(713\) | 8.54631 | 0.320062 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.15579 | 0.267424 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.00760 | −0.261521 | ||||||||
\(719\) | −35.0734 | −1.30802 | −0.654008 | − | 0.756488i | \(-0.726914\pi\) | ||||
−0.654008 | + | 0.756488i | \(0.726914\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.183130 | −0.00682012 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.5205 | 0.465321 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.1386 | 1.11778 | 0.558890 | − | 0.829242i | \(-0.311227\pi\) | ||||
0.558890 | + | 0.829242i | \(0.311227\pi\) | |||||||
\(728\) | −0.415271 | −0.0153910 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.71577 | −0.137433 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.8321 | 1.76672 | 0.883359 | − | 0.468697i | \(-0.155276\pi\) | ||||
0.883359 | + | 0.468697i | \(0.155276\pi\) | |||||||
\(734\) | −17.7158 | −0.653901 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.40920 | 0.125665 | ||||||||
\(737\) | −20.6626 | −0.761117 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.4674 | −0.826475 | −0.413238 | − | 0.910623i | \(-0.635602\pi\) | ||||
−0.413238 | + | 0.910623i | \(0.635602\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.00760 | 0.0369903 | ||||||||
\(743\) | 11.7926 | 0.432629 | 0.216314 | − | 0.976324i | \(-0.430596\pi\) | ||||
0.216314 | + | 0.976324i | \(0.430596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.4487 | −0.565616 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −33.0410 | −1.20810 | ||||||||
\(749\) | −1.09310 | −0.0399411 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.03948 | −0.0744216 | −0.0372108 | − | 0.999307i | \(-0.511847\pi\) | ||||
−0.0372108 | + | 0.999307i | \(0.511847\pi\) | |||||||
\(752\) | 5.66262 | 0.206495 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.09763 | 0.258481 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.3526 | 1.57568 | 0.787838 | − | 0.615882i | \(-0.211200\pi\) | ||||
0.787838 | + | 0.615882i | \(0.211200\pi\) | |||||||
\(758\) | −34.4563 | −1.25151 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.62921 | −0.240309 | −0.120154 | − | 0.992755i | \(-0.538339\pi\) | ||||
−0.120154 | + | 0.992755i | \(0.538339\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.00606730 | 0.000219651 0 | ||||||||
\(764\) | 4.90237 | 0.177361 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.0273 | −0.434566 | ||||||||
\(767\) | 40.3313 | 1.45628 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.6429 | −0.708340 | −0.354170 | − | 0.935181i | \(-0.615237\pi\) | ||||
−0.354170 | + | 0.935181i | \(0.615237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.1558 | 0.653441 | ||||||||
\(773\) | −14.4107 | −0.518318 | −0.259159 | − | 0.965835i | \(-0.583445\pi\) | ||||
−0.259159 | + | 0.965835i | \(0.583445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.67629 | −0.275563 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.3647 | −0.550852 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.9347 | 1.75102 | ||||||||
\(782\) | −24.9939 | −0.893781 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.99393 | −0.249783 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.3176 | 0.866830 | 0.433415 | − | 0.901194i | \(-0.357308\pi\) | ||||
0.433415 | + | 0.901194i | \(0.357308\pi\) | |||||||
\(788\) | 2.98633 | 0.106384 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.467357 | −0.0166173 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.4932 | 0.408134 | ||||||||
\(794\) | −1.32524 | −0.0470311 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.06422 | −0.108608 | ||||||||
\(797\) | 7.30397 | 0.258720 | 0.129360 | − | 0.991598i | \(-0.458708\pi\) | ||||
0.129360 | + | 0.991598i | \(0.458708\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.5144 | −1.46868 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.46736 | −0.228370 | ||||||||
\(803\) | −22.9742 | −0.810742 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.3647 | −0.470752 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.15579 | −0.146200 | ||||||||
\(809\) | 0.584729 | 0.0205580 | 0.0102790 | − | 0.999947i | \(-0.496728\pi\) | ||||
0.0102790 | + | 0.999947i | \(0.496728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.90997 | 0.0670682 | 0.0335341 | − | 0.999438i | \(-0.489324\pi\) | ||||
0.0335341 | + | 0.999438i | \(0.489324\pi\) | |||||||
\(812\) | −0.103700 | −0.00363914 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24.8184 | 0.869885 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.506836 | 0.0177319 | ||||||||
\(818\) | 1.36472 | 0.0477164 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.2226 | 1.33398 | 0.666989 | − | 0.745067i | \(-0.267583\pi\) | ||||
0.666989 | + | 0.745067i | \(0.267583\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.7481 | −1.59468 | −0.797340 | − | 0.603531i | \(-0.793760\pi\) | ||||
−0.797340 | + | 0.603531i | \(0.793760\pi\) | |||||||
\(824\) | −2.35105 | −0.0819027 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.589259 | −0.0205029 | ||||||||
\(827\) | 22.6687 | 0.788268 | 0.394134 | − | 0.919053i | \(-0.371045\pi\) | ||||
0.394134 | + | 0.919053i | \(0.371045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.63028 | −0.160816 | −0.0804081 | − | 0.996762i | \(-0.525622\pi\) | ||||
−0.0804081 | + | 0.996762i | \(0.525622\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.33131 | −0.184830 | ||||||||
\(833\) | 51.2747 | 1.77656 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.50684 | 0.155872 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.6231 | 0.574237 | ||||||||
\(839\) | 50.4826 | 1.74285 | 0.871426 | − | 0.490527i | \(-0.163196\pi\) | ||||
0.871426 | + | 0.490527i | \(0.163196\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2276 | −0.938883 | ||||||||
\(842\) | 31.1128 | 1.07222 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.2534 | 0.662730 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.725305 | −0.0249218 | ||||||||
\(848\) | 12.9358 | 0.444216 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.7739 | 0.643562 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.2105 | 1.23982 | 0.619912 | − | 0.784672i | \(-0.287168\pi\) | ||||
0.619912 | + | 0.784672i | \(0.287168\pi\) | |||||||
\(854\) | −0.167920 | −0.00574611 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.0334 | −0.479652 | ||||||||
\(857\) | −25.1968 | −0.860706 | −0.430353 | − | 0.902661i | \(-0.641611\pi\) | ||||
−0.430353 | + | 0.902661i | \(0.641611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.8579 | 0.643423 | 0.321711 | − | 0.946838i | \(-0.395742\pi\) | ||||
0.321711 | + | 0.946838i | \(0.395742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.1831 | −0.346839 | ||||||||
\(863\) | −15.0137 | −0.511071 | −0.255536 | − | 0.966800i | \(-0.582252\pi\) | ||||
−0.255536 | + | 0.966800i | \(0.582252\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −22.1953 | −0.754226 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.195265 | 0.00662771 | ||||||||
\(869\) | 76.6778 | 2.60112 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4426 | 0.828206 | ||||||||
\(872\) | 0.0778929 | 0.00263779 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.40920 | 0.115318 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.1128 | 1.18568 | 0.592838 | − | 0.805322i | \(-0.298007\pi\) | ||||
0.592838 | + | 0.805322i | \(0.298007\pi\) | |||||||
\(878\) | 9.32524 | 0.314712 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.3389 | 1.39274 | 0.696372 | − | 0.717681i | \(-0.254797\pi\) | ||||
0.696372 | + | 0.717681i | \(0.254797\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.6353 | −0.425211 | −0.212605 | − | 0.977138i | \(-0.568195\pi\) | ||||
−0.212605 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(884\) | 39.0855 | 1.31459 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.9879 | −0.469932 | ||||||||
\(887\) | −4.15579 | −0.139538 | −0.0697688 | − | 0.997563i | \(-0.522226\pi\) | ||||
−0.0697688 | + | 0.997563i | \(0.522226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.38899 | −0.0465853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.5068 | −0.485725 | ||||||||
\(893\) | 5.66262 | 0.189492 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.0778929 | 0.00260222 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.4932 | 0.450273 | ||||||||
\(899\) | −3.33738 | −0.111308 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −94.8362 | −3.15945 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.7542 | −1.38643 | −0.693213 | − | 0.720733i | \(-0.743805\pi\) | ||||
−0.693213 | + | 0.720733i | \(0.743805\pi\) | |||||||
\(908\) | 21.5984 | 0.716768 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.12998 | 0.302490 | 0.151245 | − | 0.988496i | \(-0.451672\pi\) | ||||
0.151245 | + | 0.988496i | \(0.451672\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 59.3526 | 1.96428 | ||||||||
\(914\) | −9.68236 | −0.320264 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.0137 | −0.628229 | ||||||||
\(917\) | −0.116307 | −0.00384079 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.0197 | 0.627403 | 0.313702 | − | 0.949522i | \(-0.398431\pi\) | ||||
0.313702 | + | 0.949522i | \(0.398431\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.66262 | 0.285288 | ||||||||
\(923\) | −57.8868 | −1.90537 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −28.0015 | −0.920188 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.33131 | −0.0437024 | ||||||||
\(929\) | 7.77239 | 0.255004 | 0.127502 | − | 0.991838i | \(-0.459304\pi\) | ||||
0.127502 | + | 0.991838i | \(0.459304\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.99393 | −0.229217 | ||||||||
\(932\) | 6.01367 | 0.196984 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.9742 | 0.555413 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.9818 | −1.50216 | −0.751080 | − | 0.660211i | \(-0.770467\pi\) | ||||
−0.751080 | + | 0.660211i | \(0.770467\pi\) | |||||||
\(938\) | −0.357118 | −0.0116603 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.6242 | 1.32431 | 0.662156 | − | 0.749366i | \(-0.269642\pi\) | ||||
0.662156 | + | 0.749366i | \(0.269642\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −7.56499 | −0.246219 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.28423 | −0.0742666 | ||||||||
\(947\) | 2.28423 | 0.0742274 | 0.0371137 | − | 0.999311i | \(-0.488184\pi\) | ||||
0.0371137 | + | 0.999311i | \(0.488184\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.1771 | 0.882205 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.571057 | −0.0185081 | ||||||||
\(953\) | 57.5084 | 1.86288 | 0.931439 | − | 0.363896i | \(-0.118554\pi\) | ||||
0.931439 | + | 0.363896i | \(0.118554\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.4092 | −0.498369 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.0532 | 0.324803 | ||||||||
\(959\) | −0.656555 | −0.0212013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7158 | −0.797283 | ||||||||
\(962\) | −29.3587 | −0.946561 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.81841 | −0.155190 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.70210 | −0.151209 | −0.0756047 | − | 0.997138i | \(-0.524089\pi\) | ||||
−0.0756047 | + | 0.997138i | \(0.524089\pi\) | |||||||
\(968\) | −9.31157 | −0.299285 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.9863 | −0.480934 | −0.240467 | − | 0.970657i | \(-0.577301\pi\) | ||||
−0.240467 | + | 0.970657i | \(0.577301\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.686891 | −0.0220207 | ||||||||
\(974\) | −19.2089 | −0.615494 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.15579 | −0.0690050 | ||||||||
\(977\) | −8.89737 | −0.284652 | −0.142326 | − | 0.989820i | \(-0.545458\pi\) | ||||
−0.142326 | + | 0.989820i | \(0.545458\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −67.6642 | −2.16256 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.32524 | 0.169935 | ||||||||
\(983\) | 1.60947 | 0.0513341 | 0.0256671 | − | 0.999671i | \(-0.491829\pi\) | ||||
0.0256671 | + | 0.999671i | \(0.491829\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.76025 | 0.310830 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.33131 | −0.169612 | ||||||||
\(989\) | −1.72791 | −0.0549443 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8974 | 0.536763 | 0.268381 | − | 0.963313i | \(-0.413511\pi\) | ||||
0.268381 | + | 0.963313i | \(0.413511\pi\) | |||||||
\(992\) | 2.50684 | 0.0795921 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.845752 | 0.0268256 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.1558 | 0.765021 | 0.382511 | − | 0.923951i | \(-0.375060\pi\) | ||||
0.382511 | + | 0.923951i | \(0.375060\pi\) | |||||||
\(998\) | 11.9605 | 0.378604 | ||||||||
\(999\) | 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 | 8550.2.a.ci.1.2 | 3 | ||
3.2 | odd | 2 | 950.2.a.l.1.3 | yes | 3 | ||
5.4 | even | 2 | 8550.2.a.cp.1.2 | 3 | |||
12.11 | even | 2 | 7600.2.a.bk.1.1 | 3 | |||
15.2 | even | 4 | 950.2.b.h.799.4 | 6 | |||
15.8 | even | 4 | 950.2.b.h.799.3 | 6 | |||
15.14 | odd | 2 | 950.2.a.j.1.1 | ✓ | 3 | ||
60.59 | even | 2 | 7600.2.a.bz.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.j.1.1 | ✓ | 3 | 15.14 | odd | 2 | ||
950.2.a.l.1.3 | yes | 3 | 3.2 | odd | 2 | ||
950.2.b.h.799.3 | 6 | 15.8 | even | 4 | |||
950.2.b.h.799.4 | 6 | 15.2 | even | 4 | |||
7600.2.a.bk.1.1 | 3 | 12.11 | even | 2 | |||
7600.2.a.bz.1.3 | 3 | 60.59 | even | 2 | |||
8550.2.a.ci.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8550.2.a.cp.1.2 | 3 | 5.4 | even | 2 |