Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2432,2,Mod(1217,2432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2432.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2432 = 2^{7} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2432.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(19.4196177716\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} - 8 x^{13} - 3 x^{12} + 20 x^{11} - 24 x^{10} + 28 x^{8} - 96 x^{6} + 160 x^{5} - 48 x^{4} - 256 x^{3} + 512 x^{2} - 512 x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.15 | ||
Root | \(0.569934 - 1.29429i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2432.1217 |
Dual form | 2432.2.c.i.1217.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2432\mathbb{Z}\right)^\times\).
\(n\) | \(1407\) | \(1921\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.63640i | 1.52213i | 0.648676 | + | 0.761065i | \(0.275323\pi\) | ||||
−0.648676 | + | 0.761065i | \(0.724677\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.63403i | − 1.17798i | −0.808142 | − | 0.588988i | \(-0.799527\pi\) | ||||
0.808142 | − | 0.588988i | \(-0.200473\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.88603 | 1.46878 | 0.734391 | − | 0.678727i | \(-0.237468\pi\) | ||||
0.734391 | + | 0.678727i | \(0.237468\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.95063 | −1.31688 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.95063i | − 1.79418i | −0.441845 | − | 0.897091i | \(-0.645676\pi\) | ||||
0.441845 | − | 0.897091i | \(-0.354324\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.14940i | 1.15084i | 0.817859 | + | 0.575418i | \(0.195161\pi\) | ||||
−0.817859 | + | 0.575418i | \(0.804839\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.94438 | 1.79303 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.82843 | 0.443459 | 0.221729 | − | 0.975108i | \(-0.428830\pi\) | ||||
0.221729 | + | 0.975108i | \(0.428830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.2452i | 2.23568i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.14940 | −0.865210 | −0.432605 | − | 0.901584i | \(-0.642406\pi\) | ||||
−0.432605 | + | 0.901584i | \(0.642406\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.93813 | −0.387627 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2.50625i | − 0.482328i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.19638i | − 1.52203i | −0.648735 | − | 0.761015i | \(-0.724702\pi\) | ||||
0.648735 | − | 0.761015i | \(-0.275298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.67631 | −0.301075 | −0.150537 | − | 0.988604i | \(-0.548100\pi\) | ||||
−0.150537 | + | 0.988604i | \(0.548100\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.6883 | 2.73098 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 10.2359i | − 1.73019i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.14452i | 1.33895i | 0.742834 | + | 0.669476i | \(0.233481\pi\) | ||||
−0.742834 | + | 0.669476i | \(0.766519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.9395 | −1.75172 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.514201 | 0.0803047 | 0.0401524 | − | 0.999194i | \(-0.487216\pi\) | ||||
0.0401524 | + | 0.999194i | \(0.487216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 10.9631i | − 1.67186i | −0.548835 | − | 0.835931i | \(-0.684929\pi\) | ||||
0.548835 | − | 0.835931i | \(-0.315071\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.4061i | 1.55125i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.3035 | 1.94051 | 0.970257 | − | 0.242075i | \(-0.0778281\pi\) | ||||
0.970257 | + | 0.242075i | \(0.0778281\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.10124 | 1.15732 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.82047i | 0.675001i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.62446i | − 0.223137i | −0.993757 | − | 0.111568i | \(-0.964413\pi\) | ||||
0.993757 | − | 0.111568i | \(-0.0355874\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.6742 | −2.11350 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.63640 | 0.349200 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 12.2234i | − 1.59136i | −0.605720 | − | 0.795678i | \(-0.707115\pi\) | ||||
0.605720 | − | 0.795678i | \(-0.292885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.98666i | − 0.766513i | −0.923642 | − | 0.383257i | \(-0.874803\pi\) | ||||
0.923642 | − | 0.383257i | \(-0.125197\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.3523 | −1.93420 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.9297 | 1.35566 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.09328i | − 0.500074i | −0.968236 | − | 0.250037i | \(-0.919557\pi\) | ||||
0.968236 | − | 0.250037i | \(-0.0804428\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 10.9395i | − 1.31696i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.8696 | 1.40866 | 0.704332 | − | 0.709871i | \(-0.251247\pi\) | ||||
0.704332 | + | 0.709871i | \(0.251247\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.28531 | 1.08676 | 0.543381 | − | 0.839486i | \(-0.317144\pi\) | ||||
0.543381 | + | 0.839486i | \(0.317144\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 5.10971i | − 0.590018i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 23.1243i | − 2.63526i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.42124 | 0.272410 | 0.136205 | − | 0.990681i | \(-0.456509\pi\) | ||||
0.136205 | + | 0.990681i | \(0.456509\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.24441 | −0.582712 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.987504i | 0.108393i | 0.998530 | + | 0.0541963i | \(0.0172597\pi\) | ||||
−0.998530 | + | 0.0541963i | \(0.982740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 4.81614i | − 0.522384i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.6090 | 2.31672 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.25389 | 0.238912 | 0.119456 | − | 0.992840i | \(-0.461885\pi\) | ||||
0.119456 | + | 0.992840i | \(0.461885\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.1247i | 1.69033i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.41944i | − 0.458274i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.63403 | −0.270246 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.27281 | 0.941511 | 0.470756 | − | 0.882264i | \(-0.343981\pi\) | ||||
0.470756 | + | 0.882264i | \(0.343981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23.5087i | 2.36272i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3620i | 1.32957i | 0.747034 | + | 0.664785i | \(0.231477\pi\) | ||||
−0.747034 | + | 0.664785i | \(0.768523\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0094 | −0.986255 | −0.493127 | − | 0.869957i | \(-0.664146\pi\) | ||||
−0.493127 | + | 0.869957i | \(0.664146\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 26.9861 | 2.63357 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.85189i | 0.469050i | 0.972110 | + | 0.234525i | \(0.0753535\pi\) | ||||
−0.972110 | + | 0.234525i | \(0.924646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.1198i | 1.44822i | 0.689687 | + | 0.724108i | \(0.257748\pi\) | ||||
−0.689687 | + | 0.724108i | \(0.742252\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.4723 | −2.03806 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.10175 | −0.291789 | −0.145894 | − | 0.989300i | \(-0.546606\pi\) | ||||
−0.145894 | + | 0.989300i | \(0.546606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.9297i | 1.01920i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 16.3928i | − 1.51551i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.10532 | 0.651344 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.4100 | −2.21909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.35564i | 0.122234i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 8.06506i | − 0.721361i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.59176 | −0.318717 | −0.159358 | − | 0.987221i | \(-0.550943\pi\) | ||||
−0.159358 | + | 0.987221i | \(0.550943\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28.9032 | 2.54479 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 9.76906i | − 0.853527i | −0.904363 | − | 0.426763i | \(-0.859654\pi\) | ||||
0.904363 | − | 0.426763i | \(-0.140346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.88603i | − 0.336962i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.60154 | −0.568170 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.25690 | −0.363692 | −0.181846 | − | 0.983327i | \(-0.558207\pi\) | ||||
−0.181846 | + | 0.983327i | \(0.558207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.50875i | 0.806521i | 0.915085 | + | 0.403261i | \(0.132123\pi\) | ||||
−0.915085 | + | 0.403261i | \(0.867877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 35.0734i | 2.95371i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.6916 | 2.06481 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.5895 | −1.79291 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.3581i | 1.76159i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.13803i | − 0.420924i | −0.977602 | − | 0.210462i | \(-0.932503\pi\) | ||||
0.977602 | − | 0.210462i | \(-0.0674968\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.26807 | 0.428709 | 0.214355 | − | 0.976756i | \(-0.431235\pi\) | ||||
0.214355 | + | 0.976756i | \(0.431235\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.22344 | −0.583981 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.41546i | 0.354659i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.12828i | 0.568899i | 0.958691 | + | 0.284449i | \(0.0918108\pi\) | ||||
−0.958691 | + | 0.284449i | \(0.908189\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.28273 | 0.339643 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.1247 | −1.27080 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 12.4060i | − 0.971712i | −0.874039 | − | 0.485856i | \(-0.838508\pi\) | ||||
0.874039 | − | 0.485856i | \(-0.161492\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 41.3234i | − 3.21703i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.80460 | −0.681320 | −0.340660 | − | 0.940187i | \(-0.610651\pi\) | ||||
−0.340660 | + | 0.940187i | \(0.610651\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.21753 | −0.324426 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.95063i | 0.302112i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.52203i | 0.115718i | 0.998325 | + | 0.0578590i | \(0.0184274\pi\) | ||||
−0.998325 | + | 0.0578590i | \(0.981573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.53165 | −0.569339 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32.2259 | 2.42225 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.6599i | 1.39470i | 0.716729 | + | 0.697352i | \(0.245639\pi\) | ||||
−0.716729 | + | 0.697352i | \(0.754361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 11.3132i | − 0.840907i | −0.907314 | − | 0.420453i | \(-0.861871\pi\) | ||||
0.907314 | − | 0.420453i | \(-0.138129\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.7833 | 1.16673 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.4530 | 1.57725 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 10.8803i | − 0.795646i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 9.73936i | − 0.708434i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.5963 | −0.839078 | −0.419539 | − | 0.907737i | \(-0.637808\pi\) | ||||
−0.419539 | + | 0.907737i | \(0.637808\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.78701 | −0.272595 | −0.136298 | − | 0.990668i | \(-0.543520\pi\) | ||||
−0.136298 | + | 0.990668i | \(0.543520\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 28.8150i | 2.06349i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0803i | 1.85814i | 0.369902 | + | 0.929071i | \(0.379391\pi\) | ||||
−0.369902 | + | 0.929071i | \(0.620609\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.53452 | −0.250555 | −0.125278 | − | 0.992122i | \(-0.539982\pi\) | ||||
−0.125278 | + | 0.992122i | \(0.539982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.7916 | 0.761178 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 31.8514i | − 2.23553i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.35442i | − 0.0945970i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.3928 | 1.13938 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.95063 | −0.411614 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.84939i | 0.196160i | 0.995179 | + | 0.0980802i | \(0.0312702\pi\) | ||||
−0.995179 | + | 0.0980802i | \(0.968730\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 31.2931i | 2.14417i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.8772 | −1.96941 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.51420 | −0.442213 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.4798i | 1.65419i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.58688i | 0.510349i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.4383 | 1.56954 | 0.784772 | − | 0.619785i | \(-0.212780\pi\) | ||||
0.784772 | + | 0.619785i | \(0.212780\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.65685 | 0.510457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.43341i | 0.493373i | 0.969095 | + | 0.246686i | \(0.0793418\pi\) | ||||
−0.969095 | + | 0.246686i | \(0.920658\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.2316i | 1.27086i | 0.772157 | + | 0.635431i | \(0.219178\pi\) | ||||
−0.772157 | + | 0.635431i | \(0.780822\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 60.9651 | 4.01121 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.9306 | 1.96082 | 0.980411 | − | 0.196965i | \(-0.0631084\pi\) | ||||
0.980411 | + | 0.196965i | \(0.0631084\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 35.0419i | − 2.28588i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.38336i | 0.414644i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0479 | −1.03805 | −0.519026 | − | 0.854758i | \(-0.673705\pi\) | ||||
−0.519026 | + | 0.854758i | \(0.673705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9168 | 1.54061 | 0.770307 | − | 0.637673i | \(-0.220103\pi\) | ||||
0.770307 | + | 0.637673i | \(0.220103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 21.3451i | − 1.36929i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 21.3389i | − 1.36329i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.14940 | 0.264020 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.60346 | −0.164988 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 10.1950i | − 0.643505i | −0.946824 | − | 0.321753i | \(-0.895728\pi\) | ||||
0.946824 | − | 0.321753i | \(-0.104272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6916i | 1.55234i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.6973 | 0.795135 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.1866 | 1.25920 | 0.629602 | − | 0.776918i | \(-0.283218\pi\) | ||||
0.629602 | + | 0.776918i | \(0.283218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.6499i | 1.96663i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 32.3809i | 2.00432i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.32659 | 0.328451 | 0.164226 | − | 0.986423i | \(-0.447487\pi\) | ||||
0.164226 | + | 0.986423i | \(0.447487\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.27888 | −0.262850 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.94216i | 0.363654i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 14.0564i | − 0.857032i | −0.903534 | − | 0.428516i | \(-0.859037\pi\) | ||||
0.903534 | − | 0.428516i | \(-0.140963\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.56884 | −0.520520 | −0.260260 | − | 0.965539i | \(-0.583808\pi\) | ||||
−0.260260 | + | 0.965539i | \(0.583808\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −42.5112 | −2.57290 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.5331i | 0.695474i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.7013i | 1.36399i | 0.731357 | + | 0.681995i | \(0.238887\pi\) | ||||
−0.731357 | + | 0.681995i | \(0.761113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.62249 | 0.396478 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.26940 | −0.493311 | −0.246656 | − | 0.969103i | \(-0.579332\pi\) | ||||
−0.246656 | + | 0.969103i | \(0.579332\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 21.7941i | − 1.29552i | −0.761844 | − | 0.647761i | \(-0.775706\pi\) | ||||
0.761844 | − | 0.647761i | \(-0.224294\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 6.94438i | − 0.411350i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.99820 | 0.117950 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6569 | −0.803344 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.4469i | 1.43310i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.64036i | − 0.504775i | −0.967626 | − | 0.252388i | \(-0.918784\pi\) | ||||
0.967626 | − | 0.252388i | \(-0.0812158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.1970 | −1.87458 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.9138 | −0.865384 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 17.2175i | − 0.995716i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 42.6031i | − 2.45560i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −35.2277 | −2.02378 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.7691 | −0.902934 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 11.3871i | − 0.649894i | −0.945732 | − | 0.324947i | \(-0.894654\pi\) | ||||
0.945732 | − | 0.324947i | \(-0.105346\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 26.3888i | − 1.50121i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3199 | −0.641893 | −0.320947 | − | 0.947097i | \(-0.604001\pi\) | ||||
−0.320947 | + | 0.947097i | \(0.604001\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.3052 | −1.03467 | −0.517337 | − | 0.855782i | \(-0.673076\pi\) | ||||
−0.517337 | + | 0.855782i | \(0.673076\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 40.4384i | 2.27845i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.0999i | 1.46592i | 0.680273 | + | 0.732959i | \(0.261861\pi\) | ||||
−0.680273 | + | 0.732959i | \(0.738139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −48.7736 | −2.73080 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.7916 | −0.713955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.82843i | − 0.101736i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 8.04210i | − 0.446095i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −39.8619 | −2.20437 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 51.6978 | 2.85019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.2799i | 0.674962i | 0.941332 | + | 0.337481i | \(0.109575\pi\) | ||||
−0.941332 | + | 0.337481i | \(0.890425\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 32.1760i | − 1.76323i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.7818 | −0.589075 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5263 | 0.845772 | 0.422886 | − | 0.906183i | \(-0.361017\pi\) | ||||
0.422886 | + | 0.906183i | \(0.361017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 8.17748i | − 0.444140i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.97512i | 0.540183i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.27944 | 0.231068 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −28.8150 | −1.55135 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5212i | 0.672176i | 0.941831 | + | 0.336088i | \(0.109104\pi\) | ||||
−0.941831 | + | 0.336088i | \(0.890896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.36237i | 0.0729259i | 0.999335 | + | 0.0364630i | \(0.0116091\pi\) | ||||
−0.999335 | + | 0.0364630i | \(0.988391\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.3994 | 0.555081 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.3247 | −1.18822 | −0.594111 | − | 0.804383i | \(-0.702496\pi\) | ||||
−0.594111 | + | 0.804383i | \(0.702496\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 31.2650i | − 1.65937i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.7325i | 0.991430i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.2824 | 0.859351 | 0.429676 | − | 0.902983i | \(-0.358628\pi\) | ||||
0.429676 | + | 0.902983i | \(0.358628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 64.3547i | − 3.37774i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 24.4578i | − 1.28018i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.6214 | 1.54623 | 0.773113 | − | 0.634268i | \(-0.218698\pi\) | ||||
0.773113 | + | 0.634268i | \(0.218698\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.03142 | −0.105751 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 6.31270i | − 0.327739i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.18659i | − 0.268551i | −0.990944 | − | 0.134276i | \(-0.957129\pi\) | ||||
0.990944 | − | 0.134276i | \(-0.0428708\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.2628 | 1.09800 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.0101 | 1.75161 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 11.6485i | − 0.598344i | −0.954199 | − | 0.299172i | \(-0.903290\pi\) | ||||
0.954199 | − | 0.299172i | \(-0.0967104\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 9.46932i | − 0.485128i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.3465 | −1.70393 | −0.851964 | − | 0.523600i | \(-0.824589\pi\) | ||||
−0.851964 | + | 0.523600i | \(0.824589\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −60.9103 | −3.10428 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 43.3113i | 2.20164i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.51874i | 0.0770033i | 0.999259 | + | 0.0385016i | \(0.0122585\pi\) | ||||
−0.999259 | + | 0.0385016i | \(0.987742\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.58688 | −0.383685 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.7552 | 1.29918 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6.37762i | − 0.320893i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.4592i | 1.47852i | 0.673422 | + | 0.739258i | \(0.264824\pi\) | ||||
−0.673422 | + | 0.739258i | \(0.735176\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.2452 | 0.512899 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.0523 | −1.60062 | −0.800308 | − | 0.599589i | \(-0.795331\pi\) | ||||
−0.800308 | + | 0.599589i | \(0.795331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6.95569i | − 0.346488i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.8139i | 0.686421i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.4651 | 2.40232 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7427 | 0.531192 | 0.265596 | − | 0.964084i | \(-0.414431\pi\) | ||||
0.265596 | + | 0.964084i | \(0.414431\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 11.2229i | − 0.553586i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 47.5007i | − 2.33736i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.60112 | 0.127684 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.0689 | −1.22763 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.9990i | 0.977013i | 0.872560 | + | 0.488507i | \(0.162458\pi\) | ||||
−0.872560 | + | 0.488507i | \(0.837542\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5670i | 0.515006i | 0.966277 | + | 0.257503i | \(0.0828997\pi\) | ||||
−0.966277 | + | 0.257503i | \(0.917100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −52.5572 | −2.55542 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.54374 | −0.171897 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 23.2643i | − 1.12584i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 65.0969i | 3.14291i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.24892 | 0.156495 | 0.0782474 | − | 0.996934i | \(-0.475068\pi\) | ||||
0.0782474 | + | 0.996934i | \(0.475068\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.4848 | −1.22472 | −0.612360 | − | 0.790579i | \(-0.709780\pi\) | ||||
−0.612360 | + | 0.790579i | \(0.709780\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 56.9188i | − 2.72905i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.14940i | 0.198493i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.9520 | −0.856804 | −0.428402 | − | 0.903588i | \(-0.640923\pi\) | ||||
−0.428402 | + | 0.903588i | \(0.640923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.0050 | −1.52405 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.68123i | 0.0798777i | 0.999202 | + | 0.0399388i | \(0.0127163\pi\) | ||||
−0.999202 | + | 0.0399388i | \(0.987284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 5.93682i | − 0.281432i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.5459 | 0.640700 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.8275 | −1.03010 | −0.515052 | − | 0.857159i | \(-0.672227\pi\) | ||||
−0.515052 | + | 0.857159i | \(0.672227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 3.05982i | − 0.144081i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8888i | 0.652551i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 42.4730 | 1.99117 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.04431 | −0.376297 | −0.188148 | − | 0.982141i | \(-0.560249\pi\) | ||||
−0.188148 | + | 0.982141i | \(0.560249\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 4.58249i | − 0.213892i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 6.79339i | − 0.316400i | −0.987407 | − | 0.158200i | \(-0.949431\pi\) | ||||
0.987407 | − | 0.158200i | \(-0.0505690\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.2479 | 1.45221 | 0.726107 | − | 0.687582i | \(-0.241328\pi\) | ||||
0.726107 | + | 0.687582i | \(0.241328\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.6409 | −0.539836 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 36.9113i | − 1.70805i | −0.520230 | − | 0.854026i | \(-0.674154\pi\) | ||||
0.520230 | − | 0.854026i | \(-0.325846\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 15.9066i | − 0.734500i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.7930 | −0.865938 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −65.2375 | −2.99962 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.93813i | 0.0889277i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.41764i | 0.293844i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.26161 | −0.331792 | −0.165896 | − | 0.986143i | \(-0.553052\pi\) | ||||
−0.165896 | + | 0.986143i | \(0.553052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.7949 | −1.54091 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 42.5112i | − 1.93433i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 24.4249i | − 1.10908i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00500 | −0.0455411 | −0.0227705 | − | 0.999741i | \(-0.507249\pi\) | ||||
−0.0227705 | + | 0.999741i | \(0.507249\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.7072 | 1.47907 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 9.12714i | − 0.411902i | −0.978562 | − | 0.205951i | \(-0.933971\pi\) | ||||
0.978562 | − | 0.205951i | \(-0.0660288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 14.9865i | − 0.674957i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 61.9228 | 2.78322 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.1257 | 2.06902 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 19.8928i | − 0.890524i | −0.895400 | − | 0.445262i | \(-0.853111\pi\) | ||||
0.895400 | − | 0.445262i | \(-0.146889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 23.2125i | − 1.03706i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.9716 | −0.845904 | −0.422952 | − | 0.906152i | \(-0.639006\pi\) | ||||
−0.422952 | + | 0.906152i | \(0.639006\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.1960 | 1.56620 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 11.1191i | − 0.493818i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.2981i | 1.07700i | 0.842627 | + | 0.538498i | \(0.181008\pi\) | ||||
−0.842627 | + | 0.538498i | \(0.818992\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.0830 | 1.59622 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.50625 | −0.110654 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.3651i | 1.16178i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 79.1642i | − 3.48164i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.01270 | −0.176138 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.1930 | 0.446563 | 0.223282 | − | 0.974754i | \(-0.428323\pi\) | ||||
0.223282 | + | 0.974754i | \(0.428323\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.42683i | 0.0623907i | 0.999513 | + | 0.0311954i | \(0.00993140\pi\) | ||||
−0.999513 | + | 0.0311954i | \(0.990069\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 19.8565i | − 0.866608i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.06501 | −0.133514 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.78247 | −0.251412 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 48.2903i | 2.09562i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.13363i | 0.0924176i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.7801 | 0.552530 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −49.1950 | −2.12292 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 48.2075i | − 2.07644i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 28.1257i | − 1.20922i | −0.796522 | − | 0.604610i | \(-0.793329\pi\) | ||||
0.796522 | − | 0.604610i | \(-0.206671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.8263 | 1.27997 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.8261 | 1.70596 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 45.2937i | − 1.93662i | −0.249753 | − | 0.968310i | \(-0.580349\pi\) | ||||
0.249753 | − | 0.968310i | \(-0.419651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.6511i | 1.00940i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.19638 | −0.349177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.40900 | 0.400111 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 56.5587i | 2.40078i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 13.9151i | − 0.589601i | −0.955559 | − | 0.294801i | \(-0.904747\pi\) | ||||
0.955559 | − | 0.294801i | \(-0.0952533\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.4904 | 1.92404 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.6849 | 1.21108 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 10.3367i | − 0.435641i | −0.975989 | − | 0.217820i | \(-0.930105\pi\) | ||||
0.975989 | − | 0.217820i | \(-0.0698947\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.17013i | 0.343720i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.3799 | −0.855877 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.2369 | −1.64490 | −0.822448 | − | 0.568840i | \(-0.807392\pi\) | ||||
−0.822448 | + | 0.568840i | \(0.807392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.4374i | 1.39931i | 0.714479 | + | 0.699657i | \(0.246664\pi\) | ||||
−0.714479 | + | 0.699657i | \(0.753336\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 30.5725i | − 1.27718i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.04210 | 0.335379 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.3203 | −0.929206 | −0.464603 | − | 0.885519i | \(-0.653803\pi\) | ||||
−0.464603 | + | 0.885519i | \(0.653803\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 9.98409i | − 0.414925i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.83747i | 0.159205i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.66656 | −0.400348 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −43.1791 | −1.78523 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.6753i | 1.80267i | 0.433119 | + | 0.901337i | \(0.357413\pi\) | ||||
−0.433119 | + | 0.901337i | \(0.642587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.67631i | 0.0690712i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −68.7581 | −2.82833 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.6978 | −0.808890 | −0.404445 | − | 0.914562i | \(-0.632535\pi\) | ||||
−0.404445 | + | 0.914562i | \(0.632535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 18.7157i | − 0.767267i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 9.31842i | − 0.381377i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.2570 | −1.39970 | −0.699851 | − | 0.714289i | \(-0.746750\pi\) | ||||
−0.699851 | + | 0.714289i | \(0.746750\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.1801 | 0.782373 | 0.391186 | − | 0.920311i | \(-0.372065\pi\) | ||||
0.391186 | + | 0.920311i | \(0.372065\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.1711i | 0.658536i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 64.2968i | 2.61404i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.1796 | 0.697297 | 0.348649 | − | 0.937253i | \(-0.386641\pi\) | ||||
0.348649 | + | 0.937253i | \(0.386641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 83.9731 | 3.40276 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 55.2016i | 2.23322i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 13.4502i | − 0.543247i | −0.962404 | − | 0.271623i | \(-0.912439\pi\) | ||||
0.962404 | − | 0.271623i | \(-0.0875605\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.57081 | 0.143989 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.2065 | 0.612191 | 0.306095 | − | 0.952001i | \(-0.400977\pi\) | ||||
0.306095 | + | 0.952001i | \(0.400977\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.1696i | 1.61455i | 0.590173 | + | 0.807277i | \(0.299060\pi\) | ||||
−0.590173 | + | 0.807277i | \(0.700940\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.3994i | 0.417315i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.75868 | 0.350909 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9343 | −1.23737 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 15.6883i | − 0.626529i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.8917i | 0.593770i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0318 | 0.478980 | 0.239490 | − | 0.970899i | \(-0.423020\pi\) | ||||
0.239490 | + | 0.970899i | \(0.423020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.51216 | −0.298581 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.46081i | 0.375441i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.6153i | 1.33189i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −46.8925 | −1.85504 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.1707 | 1.11267 | 0.556337 | − | 0.830957i | \(-0.312206\pi\) | ||||
0.556337 | + | 0.830957i | \(0.312206\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 38.2190i | − 1.50721i | −0.657327 | − | 0.753605i | \(-0.728313\pi\) | ||||
0.657327 | − | 0.753605i | \(-0.271687\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 76.1321i | − 2.99770i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.26170 | 0.285487 | 0.142743 | − | 0.989760i | \(-0.454408\pi\) | ||||
0.142743 | + | 0.989760i | \(0.454408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −72.7372 | −2.85518 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 17.1741i | − 0.673105i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.0972i | 0.629932i | 0.949103 | + | 0.314966i | \(0.101993\pi\) | ||||
−0.949103 | + | 0.314966i | \(0.898007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.7320 | −1.00543 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.6828 | −1.43113 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.8679i | 0.696035i | 0.937488 | + | 0.348018i | \(0.113145\pi\) | ||||
−0.937488 | + | 0.348018i | \(0.886855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6386i | 0.841644i | 0.907143 | + | 0.420822i | \(0.138258\pi\) | ||||
−0.907143 | + | 0.420822i | \(0.861742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.0021 | −0.776817 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.2359 | −0.396933 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.0101i | 1.31687i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 61.7928i | 2.38905i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.6244 | −1.37526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.9881 | −1.69561 | −0.847807 | − | 0.530304i | \(-0.822078\pi\) | ||||
−0.847807 | + | 0.530304i | \(0.822078\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.85745i | 0.186963i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.6983i | 1.14140i | 0.821160 | + | 0.570699i | \(0.193328\pi\) | ||||
−0.821160 | + | 0.570699i | \(0.806672\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.0344 | 1.38287 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.5975 | −0.750977 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 6.20351i | − 0.237371i | −0.992932 | − | 0.118685i | \(-0.962132\pi\) | ||||
0.992932 | − | 0.118685i | \(-0.0378680\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2128i | 0.428420i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −50.7024 | −1.93442 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.74053 | 0.256794 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.1172i | 1.06963i | 0.844970 | + | 0.534814i | \(0.179618\pi\) | ||||
−0.844970 | + | 0.534814i | \(0.820382\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 91.3557i | 3.47032i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.0464 | 0.950063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.940179 | 0.0356118 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 78.9093i | 2.98462i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 8.35403i | − 0.315527i | −0.987477 | − | 0.157764i | \(-0.949572\pi\) | ||||
0.987477 | − | 0.157764i | \(-0.0504284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.14452 | 0.307177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 92.3846 | 3.47940 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 51.9252i | 1.95285i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 31.7187i | − 1.19122i | −0.803274 | − | 0.595610i | \(-0.796910\pi\) | ||||
0.803274 | − | 0.595610i | \(-0.203090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.56541 | −0.358731 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.95569 | 0.260493 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 65.0384i | − 2.43230i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 42.3088i | − 1.58005i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.7972 | −1.26042 | −0.630211 | − | 0.776424i | \(-0.717032\pi\) | ||||
−0.630211 | + | 0.776424i | \(0.717032\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.8968 | −1.44859 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 63.0543i | 2.34501i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.8857i | 0.589979i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.8637 | 1.21885 | 0.609423 | − | 0.792845i | \(-0.291401\pi\) | ||||
0.609423 | + | 0.792845i | \(0.291401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 40.5412 | 1.50153 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 20.0453i | − 0.741401i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.3118i | 0.528618i | 0.964438 | + | 0.264309i | \(0.0851439\pi\) | ||||
−0.964438 | + | 0.264309i | \(0.914856\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 56.2581 | 2.07511 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.3576 | −0.897225 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.6101i | 0.831726i | 0.909427 | + | 0.415863i | \(0.136520\pi\) | ||||
−0.909427 | + | 0.415863i | \(0.863480\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.9395i | 0.401873i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.6222 | 0.463062 | 0.231531 | − | 0.972828i | \(-0.425627\pi\) | ||||
0.231531 | + | 0.972828i | \(0.425627\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.5337 | −0.495838 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 3.90126i | − 0.142740i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.8546i | 0.688932i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.69943 | 0.171485 | 0.0857423 | − | 0.996317i | \(-0.472674\pi\) | ||||
0.0857423 | + | 0.996317i | \(0.472674\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.8783 | 0.979498 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 13.8763i | − 0.505009i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8920i | 0.795679i | 0.917455 | + | 0.397839i | \(0.130240\pi\) | ||||
−0.917455 | + | 0.397839i | \(0.869760\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −65.0969 | −2.36287 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.164985 | 0.00598068 | 0.00299034 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00299034 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.7560i | 2.12711i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.0268i | 0.687915i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 50.7200 | 1.83139 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.55812 | −0.308614 | −0.154307 | − | 0.988023i | \(-0.549314\pi\) | ||||
−0.154307 | + | 0.988023i | \(0.549314\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53.2200i | 1.91667i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.49557i | 0.341532i | 0.985312 | + | 0.170766i | \(0.0546242\pi\) | ||||
−0.985312 | + | 0.170766i | \(0.945376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.24892 | 0.116705 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −83.4419 | −2.99346 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 0.514201i | − 0.0184232i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 70.6317i | − 2.52740i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.5422 | −0.734117 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.7761 | 0.670149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 8.59840i | − 0.306500i | −0.988187 | − | 0.153250i | \(-0.951026\pi\) | ||||
0.988187 | − | 0.153250i | \(-0.0489739\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.0430i | 0.499945i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0535 | −0.428574 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.8410 | 0.882131 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 11.2809i | − 0.400091i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 23.3568i | − 0.827340i | −0.910427 | − | 0.413670i | \(-0.864247\pi\) | ||||
0.910427 | − | 0.413670i | \(-0.135753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.3245 | 0.860538 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.90428 | −0.314617 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 55.2534i | − 1.94985i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 42.4730i | 1.49698i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.0583 | 1.30451 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0634 | 0.388968 | 0.194484 | − | 0.980906i | \(-0.437697\pi\) | ||||
0.194484 | + | 0.980906i | \(0.437697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 12.9630i | − 0.455193i | −0.973756 | − | 0.227596i | \(-0.926913\pi\) | ||||
0.973756 | − | 0.227596i | \(-0.0730866\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 22.5909i | − 0.792299i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.6778 | −1.14465 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.9631 | −0.383551 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 63.7028i | − 2.22595i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 14.8255i | − 0.517415i | −0.965956 | − | 0.258707i | \(-0.916703\pi\) | ||||
0.965956 | − | 0.258707i | \(-0.0832965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.04240 | 0.140909 | 0.0704547 | − | 0.997515i | \(-0.477555\pi\) | ||||
0.0704547 | + | 0.997515i | \(0.477555\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.4060 | −1.05860 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.6070i | 1.16863i | 0.811527 | + | 0.584314i | \(0.198636\pi\) | ||||
−0.811527 | + | 0.584314i | \(0.801364\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.3399i | 1.33160i | 0.746130 | + | 0.665800i | \(0.231910\pi\) | ||||
−0.746130 | + | 0.665800i | \(0.768090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −59.8498 | −2.07617 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.8125 | 0.513223 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.1916i | 0.802579i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.20125i | 0.145217i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.6832 | −1.30097 | −0.650484 | − | 0.759520i | \(-0.725434\pi\) | ||||
−0.650484 | + | 0.759520i | \(0.725434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −38.1806 | −1.31657 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 21.8015i | − 0.750883i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.1091i | 0.382165i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −94.8581 | −3.25936 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 57.4580 | 1.97195 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 33.7949i | − 1.15847i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7.06647i | − 0.241951i | −0.992655 | − | 0.120976i | \(-0.961398\pi\) | ||||
0.992655 | − | 0.120976i | \(-0.0386023\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.4061 | 0.355881 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.95910 | −0.271878 | −0.135939 | − | 0.990717i | \(-0.543405\pi\) | ||||
−0.135939 | + | 0.990717i | \(0.543405\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 13.1466i | − 0.448558i | −0.974525 | − | 0.224279i | \(-0.927997\pi\) | ||||
0.974525 | − | 0.224279i | \(-0.0720026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.26807i | 0.179535i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.9886 | −1.19102 | −0.595512 | − | 0.803346i | \(-0.703051\pi\) | ||||
−0.595512 | + | 0.803346i | \(0.703051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.00909 | 0.136313 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 36.0050i | − 1.22279i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 14.4079i | − 0.488754i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9847 | 0.575504 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36.6335 | −1.23985 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 31.3411i | − 1.05952i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.1816i | 1.66075i | 0.557208 | + | 0.830373i | \(0.311873\pi\) | ||||
−0.557208 | + | 0.830373i | \(0.688127\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.7795 | 0.768333 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.58658 | −0.255598 | −0.127799 | − | 0.991800i | \(-0.540791\pi\) | ||||
−0.127799 | + | 0.991800i | \(0.540791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.1875i | 0.511101i | 0.966796 | + | 0.255551i | \(0.0822568\pi\) | ||||
−0.966796 | + | 0.255551i | \(0.917743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 84.8842i | − 2.85335i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.9000 | 1.10467 | 0.552337 | − | 0.833621i | \(-0.313736\pi\) | ||||
0.552337 | + | 0.833621i | \(0.313736\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.9577 | −0.468125 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.2075i | 1.04549i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 13.3035i | − 0.445185i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 49.1507 | 1.64293 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 45.3924 | 1.51561 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.7397i | 0.458244i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.97021i | − 0.0989519i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 112.319 | 3.73774 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.7995 | −0.990568 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.9392i | 1.85743i | 0.370793 | + | 0.928715i | \(0.379086\pi\) | ||||
−0.370793 | + | 0.928715i | \(0.620914\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 52.7884i | − 1.75088i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.6551 | 1.47949 | 0.739745 | − | 0.672887i | \(-0.234946\pi\) | ||||
0.739745 | + | 0.672887i | \(0.234946\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.87627 | 0.194476 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 41.5736i | − 1.37438i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 37.9629i | − 1.25364i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.52507 | 0.248229 | 0.124115 | − | 0.992268i | \(-0.460391\pi\) | ||||
0.124115 | + | 0.992268i | \(0.460391\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.0209 | 0.989222 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 49.2518i | 1.62114i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 15.7852i | − 0.519014i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 39.5434 | 1.29878 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.4360 | −0.342395 | −0.171198 | − | 0.985237i | \(-0.554764\pi\) | ||||
−0.171198 | + | 0.985237i | \(0.554764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 8.10124i | − 0.265507i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 29.8439i | − 0.977044i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −28.6591 | −0.937252 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.1073 | 0.624207 | 0.312104 | − | 0.950048i | \(-0.398966\pi\) | ||||
0.312104 | + | 0.950048i | \(0.398966\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 48.2600i | − 1.57491i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.2146i | 1.40875i | 0.709826 | + | 0.704377i | \(0.248774\pi\) | ||||
−0.709826 | + | 0.704377i | \(0.751226\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.13363 | −0.0694804 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25.6538 | −0.834518 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.25385i | 0.0407446i | 0.999792 | + | 0.0203723i | \(0.00648516\pi\) | ||||
−0.999792 | + | 0.0203723i | \(0.993515\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.5285i | 1.25069i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −68.8100 | −2.23132 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.0739 | 1.13616 | 0.568078 | − | 0.822975i | \(-0.307687\pi\) | ||||
0.568078 | + | 0.822975i | \(0.307687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.5450i | 0.988413i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 128.587i | − 4.15663i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.5425 | −0.534184 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.1900 | −0.909354 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 19.1680i | − 0.617681i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.97512i | 0.321110i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.66764 | 0.0536275 | 0.0268138 | − | 0.999640i | \(-0.491464\pi\) | ||||
0.0268138 | + | 0.999640i | \(0.491464\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.82047 | 0.154856 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 16.1136i | − 0.517110i | −0.965996 | − | 0.258555i | \(-0.916754\pi\) | ||||
0.965996 | − | 0.258555i | \(-0.0832464\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.9513i | 1.18460i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.2022 | 0.679015 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.8857 | 1.08410 | 0.542051 | − | 0.840346i | \(-0.317648\pi\) | ||||
0.542051 | + | 0.840346i | \(0.317648\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 13.4121i | − 0.428651i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 59.7328i | − 1.90712i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.89492 | 0.315599 | 0.157799 | − | 0.987471i | \(-0.449560\pi\) | ||||
0.157799 | + | 0.987471i | \(0.449560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68.6963 | 2.18885 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 136.296i | 4.33836i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45.4904i | 1.44651i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3693 | 0.996478 | 0.498239 | − | 0.867040i | \(-0.333980\pi\) | ||||
0.498239 | + | 0.867040i | \(0.333980\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.3747 | −1.02738 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.31004i | 0.295148i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.55606i | − 0.144292i | −0.997394 | − | 0.0721459i | \(-0.977015\pi\) | ||||
0.997394 | − | 0.0721459i | \(-0.0229847\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.4122 | 0.645813 |
(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 | 2432.2.c.i.1217.15 | yes | 16 | |
4.3 | odd | 2 | inner | 2432.2.c.i.1217.1 | ✓ | 16 | |
8.3 | odd | 2 | inner | 2432.2.c.i.1217.16 | yes | 16 | |
8.5 | even | 2 | inner | 2432.2.c.i.1217.2 | yes | 16 | |
16.3 | odd | 4 | 4864.2.a.br.1.7 | 8 | |||
16.5 | even | 4 | 4864.2.a.br.1.8 | 8 | |||
16.11 | odd | 4 | 4864.2.a.bm.1.2 | 8 | |||
16.13 | even | 4 | 4864.2.a.bm.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.i.1217.1 | ✓ | 16 | 4.3 | odd | 2 | inner | |
2432.2.c.i.1217.2 | yes | 16 | 8.5 | even | 2 | inner | |
2432.2.c.i.1217.15 | yes | 16 | 1.1 | even | 1 | trivial | |
2432.2.c.i.1217.16 | yes | 16 | 8.3 | odd | 2 | inner | |
4864.2.a.bm.1.1 | 8 | 16.13 | even | 4 | |||
4864.2.a.bm.1.2 | 8 | 16.11 | odd | 4 | |||
4864.2.a.br.1.7 | 8 | 16.3 | odd | 4 | |||
4864.2.a.br.1.8 | 8 | 16.5 | even | 4 |