Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,4,Mod(1,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.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: | \(76.4664753674\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 162) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1296.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −21.0000 | −1.87830 | −0.939149 | − | 0.343511i | \(-0.888384\pi\) | ||||
−0.939149 | + | 0.343511i | \(0.888384\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.00000 | −0.431959 | −0.215980 | − | 0.976398i | \(-0.569295\pi\) | ||||
−0.215980 | + | 0.976398i | \(0.569295\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.0000 | 0.986764 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −49.0000 | −1.04540 | −0.522698 | − | 0.852518i | \(-0.675075\pi\) | ||||
−0.522698 | + | 0.852518i | \(0.675075\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −21.0000 | −0.299603 | −0.149801 | − | 0.988716i | \(-0.547863\pi\) | ||||
−0.149801 | + | 0.988716i | \(0.547863\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 112.000 | 1.35235 | 0.676173 | − | 0.736743i | \(-0.263637\pi\) | ||||
0.676173 | + | 0.736743i | \(0.263637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 180.000 | 1.63185 | 0.815926 | − | 0.578156i | \(-0.196228\pi\) | ||||
0.815926 | + | 0.578156i | \(0.196228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 316.000 | 2.52800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 135.000 | 0.864444 | 0.432222 | − | 0.901767i | \(-0.357730\pi\) | ||||
0.432222 | + | 0.901767i | \(0.357730\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −308.000 | −1.78447 | −0.892233 | − | 0.451576i | \(-0.850862\pi\) | ||||
−0.892233 | + | 0.451576i | \(0.850862\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 168.000 | 0.811348 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.00444322 | −0.00222161 | − | 0.999998i | \(-0.500707\pi\) | ||||
−0.00222161 | + | 0.999998i | \(0.500707\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 42.0000 | 0.159983 | 0.0799914 | − | 0.996796i | \(-0.474511\pi\) | ||||
0.0799914 | + | 0.996796i | \(0.474511\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20.0000 | −0.0709296 | −0.0354648 | − | 0.999371i | \(-0.511291\pi\) | ||||
−0.0354648 | + | 0.999371i | \(0.511291\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 84.0000 | 0.260695 | 0.130347 | − | 0.991468i | \(-0.458391\pi\) | ||||
0.130347 | + | 0.991468i | \(0.458391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 174.000 | 0.450957 | 0.225479 | − | 0.974248i | \(-0.427605\pi\) | ||||
0.225479 | + | 0.974248i | \(0.427605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −756.000 | −1.85344 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 504.000 | 1.11212 | 0.556061 | − | 0.831141i | \(-0.312312\pi\) | ||||
0.556061 | + | 0.831141i | \(0.312312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −385.000 | −0.808102 | −0.404051 | − | 0.914737i | \(-0.632398\pi\) | ||||
−0.404051 | + | 0.914737i | \(0.632398\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1029.00 | 1.96357 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −272.000 | −0.495971 | −0.247986 | − | 0.968764i | \(-0.579769\pi\) | ||||
−0.247986 | + | 0.968764i | \(0.579769\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −888.000 | −1.48431 | −0.742156 | − | 0.670227i | \(-0.766197\pi\) | ||||
−0.742156 | + | 0.670227i | \(0.766197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 371.000 | 0.594826 | 0.297413 | − | 0.954749i | \(-0.403876\pi\) | ||||
0.297413 | + | 0.954749i | \(0.403876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −288.000 | −0.426242 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 652.000 | 0.928554 | 0.464277 | − | 0.885690i | \(-0.346314\pi\) | ||||
0.464277 | + | 0.885690i | \(0.346314\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 84.0000 | 0.111087 | 0.0555434 | − | 0.998456i | \(-0.482311\pi\) | ||||
0.0555434 | + | 0.998456i | \(0.482311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 441.000 | 0.562743 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −21.0000 | −0.0250112 | −0.0125056 | − | 0.999922i | \(-0.503981\pi\) | ||||
−0.0125056 | + | 0.999922i | \(0.503981\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 392.000 | 0.451569 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2352.00 | −2.54011 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1246.00 | −1.30425 | −0.652124 | − | 0.758112i | \(-0.726122\pi\) | ||||
−0.652124 | + | 0.758112i | \(0.726122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −546.000 | −0.537911 | −0.268956 | − | 0.963153i | \(-0.586678\pi\) | ||||
−0.268956 | + | 0.963153i | \(0.586678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 196.000 | 0.187500 | 0.0937498 | − | 0.995596i | \(-0.470115\pi\) | ||||
0.0937498 | + | 0.995596i | \(0.470115\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −300.000 | −0.271048 | −0.135524 | − | 0.990774i | \(-0.543272\pi\) | ||||
−0.135524 | + | 0.990774i | \(0.543272\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1069.00 | −0.939373 | −0.469686 | − | 0.882833i | \(-0.655633\pi\) | ||||
−0.469686 | + | 0.882833i | \(0.655633\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −897.000 | −0.746749 | −0.373375 | − | 0.927681i | \(-0.621799\pi\) | ||||
−0.373375 | + | 0.927681i | \(0.621799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3780.00 | −3.06510 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 168.000 | 0.129416 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0000 | −0.0262960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4011.00 | −2.87004 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1532.00 | −1.07042 | −0.535209 | − | 0.844720i | \(-0.679767\pi\) | ||||
−0.535209 | + | 0.844720i | \(0.679767\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 840.000 | 0.560238 | 0.280119 | − | 0.959965i | \(-0.409626\pi\) | ||||
0.280119 | + | 0.959965i | \(0.409626\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −896.000 | −0.584158 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −729.000 | −0.454618 | −0.227309 | − | 0.973823i | \(-0.572993\pi\) | ||||
−0.227309 | + | 0.973823i | \(0.572993\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2044.00 | 1.24726 | 0.623632 | − | 0.781718i | \(-0.285656\pi\) | ||||
0.623632 | + | 0.781718i | \(0.285656\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1764.00 | −1.03156 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2835.00 | −1.62368 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1287.00 | 0.707618 | 0.353809 | − | 0.935318i | \(-0.384886\pi\) | ||||
0.353809 | + | 0.935318i | \(0.384886\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 736.000 | 0.396655 | 0.198327 | − | 0.980136i | \(-0.436449\pi\) | ||||
0.198327 | + | 0.980136i | \(0.436449\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6468.00 | 3.35176 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2149.00 | −1.09241 | −0.546207 | − | 0.837650i | \(-0.683929\pi\) | ||||
−0.546207 | + | 0.837650i | \(0.683929\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1440.00 | −0.704894 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3088.00 | 1.48387 | 0.741935 | − | 0.670472i | \(-0.233908\pi\) | ||||
0.741935 | + | 0.670472i | \(0.233908\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 168.000 | 0.0778457 | 0.0389228 | − | 0.999242i | \(-0.487607\pi\) | ||||
0.0389228 | + | 0.999242i | \(0.487607\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 204.000 | 0.0928539 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3003.00 | 1.31973 | 0.659867 | − | 0.751383i | \(-0.270613\pi\) | ||||
0.659867 | + | 0.751383i | \(0.270613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2528.00 | −1.09199 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1164.00 | −0.486042 | −0.243021 | − | 0.970021i | \(-0.578138\pi\) | ||||
−0.243021 | + | 0.970021i | \(0.578138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1666.00 | −0.684159 | −0.342080 | − | 0.939671i | \(-0.611131\pi\) | ||||
−0.342080 | + | 0.939671i | \(0.611131\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.0000 | 0.00834568 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −756.000 | −0.295637 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2064.00 | −0.781915 | −0.390958 | − | 0.920409i | \(-0.627856\pi\) | ||||
−0.390958 | + | 0.920409i | \(0.627856\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −565.000 | −0.210723 | −0.105362 | − | 0.994434i | \(-0.533600\pi\) | ||||
−0.105362 | + | 0.994434i | \(0.533600\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4731.00 | 1.71101 | 0.855507 | − | 0.517791i | \(-0.173246\pi\) | ||||
0.855507 | + | 0.517791i | \(0.173246\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4676.00 | −1.66569 | −0.832846 | − | 0.553504i | \(-0.813290\pi\) | ||||
−0.832846 | + | 0.553504i | \(0.813290\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1080.00 | −0.373405 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −882.000 | −0.300495 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4032.00 | 1.33445 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3380.00 | −1.10279 | −0.551395 | − | 0.834244i | \(-0.685904\pi\) | ||||
−0.551395 | + | 0.834244i | \(0.685904\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 420.000 | 0.133227 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2464.00 | 0.770817 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1029.00 | 0.313204 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5236.00 | 1.57233 | 0.786163 | − | 0.618020i | \(-0.212065\pi\) | ||||
0.786163 | + | 0.618020i | \(0.212065\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3864.00 | 1.12979 | 0.564896 | − | 0.825162i | \(-0.308916\pi\) | ||||
0.564896 | + | 0.825162i | \(0.308916\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3913.00 | −1.12916 | −0.564581 | − | 0.825377i | \(-0.690962\pi\) | ||||
−0.564581 | + | 0.825377i | \(0.690962\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6333.00 | −1.78064 | −0.890319 | − | 0.455337i | \(-0.849519\pi\) | ||||
−0.890319 | + | 0.455337i | \(0.849519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1764.00 | −0.489662 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3828.00 | −1.03604 | −0.518018 | − | 0.855370i | \(-0.673330\pi\) | ||||
−0.518018 | + | 0.855370i | \(0.673330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1477.00 | −0.394780 | −0.197390 | − | 0.980325i | \(-0.563246\pi\) | ||||
−0.197390 | + | 0.980325i | \(0.563246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5859.00 | 1.52783 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5488.00 | −1.41374 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3612.00 | −0.908316 | −0.454158 | − | 0.890921i | \(-0.650060\pi\) | ||||
−0.454158 | + | 0.890921i | \(0.650060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6480.00 | 1.61025 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 399.000 | 0.0968441 | 0.0484221 | − | 0.998827i | \(-0.484581\pi\) | ||||
0.0484221 | + | 0.998827i | \(0.484581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | 0.00191929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3228.00 | 0.756833 | 0.378416 | − | 0.925635i | \(-0.376469\pi\) | ||||
0.378416 | + | 0.925635i | \(0.376469\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3654.00 | −0.847032 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 147.000 | 0.0333188 | 0.0166594 | − | 0.999861i | \(-0.494697\pi\) | ||||
0.0166594 | + | 0.999861i | \(0.494697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3332.00 | −0.746880 | −0.373440 | − | 0.927654i | \(-0.621822\pi\) | ||||
−0.373440 | + | 0.927654i | \(0.621822\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11376.0 | 2.49454 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2414.00 | 0.523622 | 0.261811 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261811 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3555.00 | 0.754710 | 0.377355 | − | 0.926069i | \(-0.376834\pi\) | ||||
0.377355 | + | 0.926069i | \(0.376834\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5348.00 | −1.12334 | −0.561671 | − | 0.827361i | \(-0.689841\pi\) | ||||
−0.561671 | + | 0.827361i | \(0.689841\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −336.000 | −0.0691061 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4472.00 | −0.910238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6489.00 | −1.29383 | −0.646914 | − | 0.762563i | \(-0.723941\pi\) | ||||
−0.646914 | + | 0.762563i | \(0.723941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10584.0 | −2.08890 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8820.00 | −1.70593 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 160.000 | 0.0306387 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8085.00 | 1.51785 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1204.00 | 0.223830 | 0.111915 | − | 0.993718i | \(-0.464302\pi\) | ||||
0.111915 | + | 0.993718i | \(0.464302\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3192.00 | −0.581999 | −0.291000 | − | 0.956723i | \(-0.593988\pi\) | ||||
−0.291000 | + | 0.956723i | \(0.593988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3241.00 | −0.585278 | −0.292639 | − | 0.956223i | \(-0.594533\pi\) | ||||
−0.292639 | + | 0.956223i | \(0.594533\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5325.00 | −0.943476 | −0.471738 | − | 0.881739i | \(-0.656373\pi\) | ||||
−0.471738 | + | 0.881739i | \(0.656373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4860.00 | 0.853002 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2352.00 | −0.405167 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15484.0 | −2.64276 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −672.000 | −0.112610 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −968.000 | −0.160743 | −0.0803717 | − | 0.996765i | \(-0.525611\pi\) | ||||
−0.0803717 | + | 0.996765i | \(0.525611\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5712.00 | 0.931582 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9890.00 | 1.59864 | 0.799321 | − | 0.600904i | \(-0.205192\pi\) | ||||
0.799321 | + | 0.600904i | \(0.205192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11088.0 | −1.76085 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4976.00 | 0.783320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1560.00 | −0.241341 | −0.120670 | − | 0.992693i | \(-0.538504\pi\) | ||||
−0.120670 | + | 0.992693i | \(0.538504\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2870.00 | 0.440194 | 0.220097 | − | 0.975478i | \(-0.429363\pi\) | ||||
0.220097 | + | 0.975478i | \(0.429363\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7182.00 | −1.08289 | −0.541444 | − | 0.840737i | \(-0.682122\pi\) | ||||
−0.541444 | + | 0.840737i | \(0.682122\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18648.0 | 2.78798 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8100.00 | 1.19081 | 0.595406 | − | 0.803425i | \(-0.296991\pi\) | ||||
0.595406 | + | 0.803425i | \(0.296991\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5685.00 | 0.828838 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7791.00 | −1.11726 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11144.0 | −1.58505 | −0.792523 | − | 0.609842i | \(-0.791233\pi\) | ||||
−0.792523 | + | 0.609842i | \(0.791233\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1392.00 | −0.194795 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13838.0 | 1.92092 | 0.960462 | − | 0.278412i | \(-0.0898080\pi\) | ||||
0.960462 | + | 0.278412i | \(0.0898080\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6615.00 | −0.903687 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1196.00 | −0.162096 | −0.0810480 | − | 0.996710i | \(-0.525827\pi\) | ||||
−0.0810480 | + | 0.996710i | \(0.525827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3864.00 | 0.515512 | 0.257756 | − | 0.966210i | \(-0.417017\pi\) | ||||
0.257756 | + | 0.966210i | \(0.417017\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6048.00 | 0.800609 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5070.00 | 0.660821 | 0.330410 | − | 0.943837i | \(-0.392813\pi\) | ||||
0.330410 | + | 0.943837i | \(0.392813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3780.00 | −0.488907 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13692.0 | −1.74410 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15239.0 | 1.92651 | 0.963254 | − | 0.268593i | \(-0.0865587\pi\) | ||||
0.963254 | + | 0.268593i | \(0.0865587\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1707.00 | 0.212577 | 0.106289 | − | 0.994335i | \(-0.466103\pi\) | ||||
0.106289 | + | 0.994335i | \(0.466103\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15092.0 | 1.86547 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.0000 | −0.00438441 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13321.0 | −1.61047 | −0.805234 | − | 0.592958i | \(-0.797960\pi\) | ||||
−0.805234 | + | 0.592958i | \(0.797960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4032.00 | −0.480392 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1764.00 | −0.208654 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13944.0 | −1.62580 | −0.812899 | − | 0.582405i | \(-0.802112\pi\) | ||||
−0.812899 | + | 0.582405i | \(0.802112\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10837.0 | −1.25454 | −0.627272 | − | 0.778800i | \(-0.715829\pi\) | ||||
−0.627272 | + | 0.778800i | \(0.715829\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6636.00 | −0.757396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3080.00 | 0.349067 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12612.0 | 1.40951 | 0.704755 | − | 0.709451i | \(-0.251057\pi\) | ||||
0.704755 | + | 0.709451i | \(0.251057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9709.00 | −1.07756 | −0.538781 | − | 0.842446i | \(-0.681115\pi\) | ||||
−0.538781 | + | 0.842446i | \(0.681115\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20160.0 | 2.20683 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10388.0 | −1.12937 | −0.564684 | − | 0.825307i | \(-0.691002\pi\) | ||||
−0.564684 | + | 0.825307i | \(0.691002\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2508.00 | −0.268981 | −0.134491 | − | 0.990915i | \(-0.542940\pi\) | ||||
−0.134491 | + | 0.990915i | \(0.542940\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 441.000 | 0.0469784 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13698.0 | 1.43975 | 0.719876 | − | 0.694103i | \(-0.244199\pi\) | ||||
0.719876 | + | 0.694103i | \(0.244199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1512.00 | 0.157865 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8232.00 | −0.848180 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9745.00 | −0.997488 | −0.498744 | − | 0.866749i | \(-0.666205\pi\) | ||||
−0.498744 | + | 0.866749i | \(0.666205\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17514.0 | −1.76943 | −0.884716 | − | 0.466130i | \(-0.845648\pi\) | ||||
−0.884716 | + | 0.466130i | \(0.845648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4640.00 | −0.465743 | −0.232872 | − | 0.972507i | \(-0.574812\pi\) | ||||
−0.232872 | + | 0.972507i | \(0.574812\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4368.00 | −0.432820 | −0.216410 | − | 0.976303i | \(-0.569435\pi\) | ||||
−0.216410 | + | 0.976303i | \(0.569435\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2176.00 | 0.214240 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −720.000 | −0.0699908 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35392.0 | 3.41873 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18816.0 | −1.79483 | −0.897416 | − | 0.441184i | \(-0.854558\pi\) | ||||
−0.897416 | + | 0.441184i | \(0.854558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.0000 | 0.00464492 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26166.0 | 2.44977 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13756.0 | 1.27997 | 0.639983 | − | 0.768389i | \(-0.278941\pi\) | ||||
0.639983 | + | 0.768389i | \(0.278941\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7740.00 | 0.711408 | 0.355704 | − | 0.934599i | \(-0.384241\pi\) | ||||
0.355704 | + | 0.934599i | \(0.384241\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2835.00 | −0.258990 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7104.00 | 0.641163 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2396.00 | −0.214949 | −0.107475 | − | 0.994208i | \(-0.534276\pi\) | ||||
−0.107475 | + | 0.994208i | \(0.534276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12096.0 | 1.07223 | 0.536117 | − | 0.844144i | \(-0.319890\pi\) | ||||
0.536117 | + | 0.844144i | \(0.319890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11466.0 | 1.01036 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1722.00 | −0.149953 | −0.0749767 | − | 0.997185i | \(-0.523888\pi\) | ||||
−0.0749767 | + | 0.997185i | \(0.523888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2968.00 | −0.256940 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4116.00 | −0.352180 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3024.00 | 0.257244 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2982.00 | −0.250756 | −0.125378 | − | 0.992109i | \(-0.540014\pi\) | ||||
−0.125378 | + | 0.992109i | \(0.540014\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −812.000 | −0.0678896 | −0.0339448 | − | 0.999424i | \(-0.510807\pi\) | ||||
−0.0339448 | + | 0.999424i | \(0.510807\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6468.00 | 0.534631 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20233.0 | 1.66294 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2058.00 | −0.167246 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6300.00 | 0.509108 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10044.0 | −0.802645 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7055.00 | 0.560662 | 0.280331 | − | 0.959903i | \(-0.409556\pi\) | ||||
0.280331 | + | 0.959903i | \(0.409556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22449.0 | 1.76442 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14596.0 | 1.14091 | 0.570457 | − | 0.821328i | \(-0.306766\pi\) | ||||
0.570457 | + | 0.821328i | \(0.306766\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15120.0 | 1.16903 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5216.00 | −0.401097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7755.00 | 0.589928 | 0.294964 | − | 0.955508i | \(-0.404692\pi\) | ||||
0.294964 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 980.000 | 0.0741495 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16044.0 | 1.20102 | 0.600510 | − | 0.799617i | \(-0.294964\pi\) | ||||
0.600510 | + | 0.799617i | \(0.294964\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18837.0 | 1.40262 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17025.0 | −1.25435 | −0.627175 | − | 0.778878i | \(-0.715789\pi\) | ||||
−0.627175 | + | 0.778878i | \(0.715789\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3320.00 | −0.243323 | −0.121662 | − | 0.992572i | \(-0.538822\pi\) | ||||
−0.121662 | + | 0.992572i | \(0.538822\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 56880.0 | 4.12532 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1127.00 | 0.0813130 | 0.0406565 | − | 0.999173i | \(-0.487055\pi\) | ||||
0.0406565 | + | 0.999173i | \(0.487055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −672.000 | −0.0479850 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6264.00 | 0.444989 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −84.0000 | −0.00590639 | −0.00295320 | − | 0.999996i | \(-0.500940\pi\) | ||||
−0.00295320 | + | 0.999996i | \(0.500940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34496.0 | −2.41321 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1743.00 | 0.120702 | 0.0603511 | − | 0.998177i | \(-0.480778\pi\) | ||||
0.0603511 | + | 0.998177i | \(0.480778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3528.00 | −0.243082 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16092.0 | −1.09766 | −0.548832 | − | 0.835932i | \(-0.684928\pi\) | ||||
−0.548832 | + | 0.835932i | \(0.684928\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21035.0 | 1.42768 | 0.713840 | − | 0.700309i | \(-0.246954\pi\) | ||||
0.713840 | + | 0.700309i | \(0.246954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 735.000 | 0.0493917 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6776.00 | −0.453096 | −0.226548 | − | 0.974000i | \(-0.572744\pi\) | ||||
−0.226548 | + | 0.974000i | \(0.572744\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4116.00 | −0.272530 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23794.0 | −1.56775 | −0.783875 | − | 0.620919i | \(-0.786760\pi\) | ||||
−0.783875 | + | 0.620919i | \(0.786760\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21621.0 | −1.41074 | −0.705372 | − | 0.708838i | \(-0.749220\pi\) | ||||
−0.705372 | + | 0.708838i | \(0.749220\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22232.0 | −1.44359 | −0.721793 | − | 0.692109i | \(-0.756682\pi\) | ||||
−0.721793 | + | 0.692109i | \(0.756682\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 168.000 | 0.0108038 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 44731.0 | 2.86278 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.0000 | 0.00133120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9280.00 | 0.585469 | 0.292735 | − | 0.956194i | \(-0.405435\pi\) | ||||
0.292735 | + | 0.956194i | \(0.405435\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32172.0 | 2.01056 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13671.0 | 0.850337 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19179.0 | 1.18179 | 0.590893 | − | 0.806750i | \(-0.298775\pi\) | ||||
0.590893 | + | 0.806750i | \(0.298775\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3220.00 | 0.197487 | 0.0987437 | − | 0.995113i | \(-0.468518\pi\) | ||||
0.0987437 | + | 0.995113i | \(0.468518\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14112.0 | 0.857496 | 0.428748 | − | 0.903424i | \(-0.358955\pi\) | ||||
0.428748 | + | 0.903424i | \(0.358955\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18144.0 | 1.09740 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22842.0 | −1.36888 | −0.684438 | − | 0.729071i | \(-0.739953\pi\) | ||||
−0.684438 | + | 0.729071i | \(0.739953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17640.0 | −1.05229 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21720.0 | −1.28390 | −0.641951 | − | 0.766746i | \(-0.721875\pi\) | ||||
−0.641951 | + | 0.766746i | \(0.721875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26327.0 | 1.54917 | 0.774585 | − | 0.632470i | \(-0.217959\pi\) | ||||
0.774585 | + | 0.632470i | \(0.217959\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18816.0 | 1.09722 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24300.0 | 1.41064 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13860.0 | −0.797406 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19741.0 | −1.13070 | −0.565349 | − | 0.824852i | \(-0.691258\pi\) | ||||
−0.565349 | + | 0.824852i | \(0.691258\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12642.0 | −0.717683 | −0.358842 | − | 0.933398i | \(-0.616828\pi\) | ||||
−0.358842 | + | 0.933398i | \(0.616828\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9968.00 | 0.563383 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26172.0 | −1.46624 | −0.733121 | − | 0.680098i | \(-0.761937\pi\) | ||||
−0.733121 | + | 0.680098i | \(0.761937\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15309.0 | 0.853908 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8526.00 | −0.471429 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9520.00 | 0.524107 | 0.262053 | − | 0.965053i | \(-0.415600\pi\) | ||||
0.262053 | + | 0.965053i | \(0.415600\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −42924.0 | −2.34273 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −882.000 | −0.0479313 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16773.0 | −0.903720 | −0.451860 | − | 0.892089i | \(-0.649239\pi\) | ||||
−0.451860 | + | 0.892089i | \(0.649239\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −112.000 | −0.00600876 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4368.00 | 0.232356 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12767.0 | 0.676269 | 0.338135 | − | 0.941098i | \(-0.390204\pi\) | ||||
0.338135 | + | 0.941098i | \(0.390204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −55440.0 | −2.91198 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37044.0 | 1.93758 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24948.0 | −1.29402 | −0.647012 | − | 0.762480i | \(-0.723982\pi\) | ||||
−0.647012 | + | 0.762480i | \(0.723982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1568.00 | −0.0809922 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 42660.0 | 2.18531 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −56.0000 | −0.00285684 | −0.00142842 | − | 0.999999i | \(-0.500455\pi\) | ||||
−0.00142842 | + | 0.999999i | \(0.500455\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 420.000 | 0.0212507 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1190.00 | 0.0599641 | 0.0299820 | − | 0.999550i | \(-0.490455\pi\) | ||||
0.0299820 | + | 0.999550i | \(0.490455\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9792.00 | −0.489407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26692.0 | 1.32866 | 0.664331 | − | 0.747439i | \(-0.268717\pi\) | ||||
0.664331 | + | 0.747439i | \(0.268717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18852.0 | 0.930838 | 0.465419 | − | 0.885090i | \(-0.345904\pi\) | ||||
0.465419 | + | 0.885090i | \(0.345904\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27027.0 | −1.32912 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2400.00 | 0.117082 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22616.0 | −1.09889 | −0.549447 | − | 0.835528i | \(-0.685162\pi\) | ||||
−0.549447 | + | 0.835528i | \(0.685162\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15456.0 | −0.745035 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9326.00 | 0.447766 | 0.223883 | − | 0.974616i | \(-0.428127\pi\) | ||||
0.223883 | + | 0.974616i | \(0.428127\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20769.0 | −0.989324 | −0.494662 | − | 0.869085i | \(-0.664708\pi\) | ||||
−0.494662 | + | 0.869085i | \(0.664708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8552.00 | 0.405771 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24696.0 | −1.16261 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −301.000 | −0.0141149 | −0.00705744 | − | 0.999975i | \(-0.502246\pi\) | ||||
−0.00705744 | + | 0.999975i | \(0.502246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17955.0 | 0.835442 | 0.417721 | − | 0.908575i | \(-0.362829\pi\) | ||||
0.417721 | + | 0.908575i | \(0.362829\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −97328.0 | −4.51113 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4704.00 | 0.216352 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31968.0 | −1.46467 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 45129.0 | 2.05188 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27412.0 | 1.24159 | 0.620796 | − | 0.783972i | \(-0.286810\pi\) | ||||
0.620796 | + | 0.783972i | \(0.286810\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7176.00 | 0.322565 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18865.0 | 0.844787 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22533.0 | −1.00146 | −0.500728 | − | 0.865605i | \(-0.666934\pi\) | ||||
−0.500728 | + | 0.865605i | \(0.666934\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1764.00 | −0.0781049 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13356.0 | 0.586953 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30240.0 | 1.32400 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6105.00 | −0.265316 | −0.132658 | − | 0.991162i | \(-0.542351\pi\) | ||||
−0.132658 | + | 0.991162i | \(0.542351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3472.00 | 0.150331 | 0.0751655 | − | 0.997171i | \(-0.476051\pi\) | ||||
0.0751655 | + | 0.997171i | \(0.476051\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −64848.0 | −2.78715 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2240.00 | −0.0959213 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4929.00 | −0.209529 | −0.104764 | − | 0.994497i | \(-0.533409\pi\) | ||||
−0.104764 | + | 0.994497i | \(0.533409\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39524.0 | −1.67402 | −0.837011 | − | 0.547186i | \(-0.815699\pi\) | ||||
−0.837011 | + | 0.547186i | \(0.815699\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38676.0 | 1.62623 | 0.813117 | − | 0.582100i | \(-0.197769\pi\) | ||||
0.813117 | + | 0.582100i | \(0.197769\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16646.0 | 0.697394 | 0.348697 | − | 0.937236i | \(-0.386624\pi\) | ||||
0.348697 | + | 0.937236i | \(0.386624\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5859.00 | 0.243700 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3528.00 | −0.146217 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6636.00 | 0.273063 | 0.136532 | − | 0.990636i | \(-0.456404\pi\) | ||||
0.136532 | + | 0.990636i | \(0.456404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6164.00 | −0.252737 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4284.00 | −0.174407 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 280.000 | 0.0113588 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −180.000 | −0.00725067 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9394.00 | −0.377074 | −0.188537 | − | 0.982066i | \(-0.560375\pi\) | ||||
−0.188537 | + | 0.982066i | \(0.560375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7287.00 | 0.290454 | 0.145227 | − | 0.989398i | \(-0.453609\pi\) | ||||
0.145227 | + | 0.989398i | \(0.453609\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25732.0 | 1.02208 | 0.511039 | − | 0.859558i | \(-0.329261\pi\) | ||||
0.511039 | + | 0.859558i | \(0.329261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7188.00 | −0.283525 | −0.141763 | − | 0.989901i | \(-0.545277\pi\) | ||||
−0.141763 | + | 0.989901i | \(0.545277\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −63063.0 | −2.47885 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23472.0 | 0.916264 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13328.0 | 0.518487 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32088.0 | 1.23974 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12601.0 | −0.485183 | −0.242592 | − | 0.970129i | \(-0.577997\pi\) | ||||
−0.242592 | + | 0.970129i | \(0.577997\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 210.000 | 0.00803074 | 0.00401537 | − | 0.999992i | \(-0.498722\pi\) | ||||
0.00401537 | + | 0.999992i | \(0.498722\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47524.0 | 1.81122 | 0.905612 | − | 0.424108i | \(-0.139412\pi\) | ||||
0.905612 | + | 0.424108i | \(0.139412\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41748.0 | −1.58034 | −0.790169 | − | 0.612888i | \(-0.790008\pi\) | ||||
−0.790169 | + | 0.612888i | \(0.790008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12256.0 | 0.462377 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9408.00 | 0.352550 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24444.0 | 0.912931 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41580.0 | −1.54257 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3654.00 | −0.135108 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34986.0 | 1.28505 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14720.0 | −0.538886 | −0.269443 | − | 0.963016i | \(-0.586840\pi\) | ||||
−0.269443 | + | 0.963016i | \(0.586840\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17652.0 | 0.641972 | 0.320986 | − | 0.947084i | \(-0.395986\pi\) | ||||
0.320986 | + | 0.947084i | \(0.395986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3024.00 | 0.109616 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6720.00 | −0.242000 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17156.0 | −0.615804 | −0.307902 | − | 0.951418i | \(-0.599627\pi\) | ||||
−0.307902 | + | 0.951418i | \(0.599627\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 43512.0 | 1.55170 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −316.000 | −0.0112324 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24213.0 | −0.855116 | −0.427558 | − | 0.903988i | \(-0.640626\pi\) | ||||
−0.427558 | + | 0.903988i | \(0.640626\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31248.0 | −1.10001 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15876.0 | 0.555295 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15085.0 | −0.525940 | −0.262970 | − | 0.964804i | \(-0.584702\pi\) | ||||
−0.262970 | + | 0.964804i | \(0.584702\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5229.00 | −0.181148 | −0.0905741 | − | 0.995890i | \(-0.528870\pi\) | ||||
−0.0905741 | + | 0.995890i | \(0.528870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7560.00 | 0.261068 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28488.0 | 0.977546 | 0.488773 | − | 0.872411i | \(-0.337445\pi\) | ||||
0.488773 | + | 0.872411i | \(0.337445\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18179.0 | −0.621829 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1143.00 | 0.0388514 | 0.0194257 | − | 0.999811i | \(-0.493816\pi\) | ||||
0.0194257 | + | 0.999811i | \(0.493816\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43344.0 | 1.46867 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5832.00 | 0.196377 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65073.0 | 2.18432 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11865.0 | 0.395801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36416.0 | −1.21102 | −0.605512 | − | 0.795836i | \(-0.707032\pi\) | ||||
−0.605512 | + | 0.795836i | \(0.707032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25200.0 | 0.832859 | 0.416430 | − | 0.909168i | \(-0.363281\pi\) | ||||
0.416430 | + | 0.909168i | \(0.363281\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16352.0 | −0.538768 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23742.0 | −0.777455 | −0.388728 | − | 0.921353i | \(-0.627085\pi\) | ||||
−0.388728 | + | 0.921353i | \(0.627085\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −756.000 | −0.0246801 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4704.00 | 0.152629 | 0.0763145 | − | 0.997084i | \(-0.475685\pi\) | ||||
0.0763145 | + | 0.997084i | \(0.475685\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −99351.0 | −3.21379 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3600.00 | −0.115747 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6280.00 | 0.201302 | 0.100651 | − | 0.994922i | \(-0.467907\pi\) | ||||
0.100651 | + | 0.994922i | \(0.467907\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 98196.0 | 3.12867 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8701.00 | −0.276393 | −0.138196 | − | 0.990405i | \(-0.544130\pi\) | ||||
−0.138196 | + | 0.990405i | \(0.544130\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1296.4.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 1296.4.a.h.1.1 | 1 | |||
4.3 | odd | 2 | 162.4.a.c.1.1 | yes | 1 | ||
12.11 | even | 2 | 162.4.a.b.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 162.4.c.d.109.1 | 2 | |||
36.11 | even | 6 | 162.4.c.e.109.1 | 2 | |||
36.23 | even | 6 | 162.4.c.e.55.1 | 2 | |||
36.31 | odd | 6 | 162.4.c.d.55.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.4.a.b.1.1 | ✓ | 1 | 12.11 | even | 2 | ||
162.4.a.c.1.1 | yes | 1 | 4.3 | odd | 2 | ||
162.4.c.d.55.1 | 2 | 36.31 | odd | 6 | |||
162.4.c.d.109.1 | 2 | 36.7 | odd | 6 | |||
162.4.c.e.55.1 | 2 | 36.23 | even | 6 | |||
162.4.c.e.109.1 | 2 | 36.11 | even | 6 | |||
1296.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1296.4.a.h.1.1 | 1 | 3.2 | odd | 2 |