Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2760,2,Mod(1,2760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2760.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: | \(22.0387109579\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.54764.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 3x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.339102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2760.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.845563 | −0.319593 | −0.159796 | − | 0.987150i | \(-0.551084\pi\) | ||||
−0.159796 | + | 0.987150i | \(0.551084\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.55883 | −1.37454 | −0.687270 | − | 0.726402i | \(-0.741191\pi\) | ||||
−0.687270 | + | 0.726402i | \(0.741191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.23704 | 1.45249 | 0.726246 | − | 0.687435i | \(-0.241263\pi\) | ||||
0.726246 | + | 0.687435i | \(0.241263\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.72619 | 1.14627 | 0.573135 | − | 0.819461i | \(-0.305727\pi\) | ||||
0.573135 | + | 0.819461i | \(0.305727\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.54591 | −1.27232 | −0.636159 | − | 0.771558i | \(-0.719478\pi\) | ||||
−0.636159 | + | 0.771558i | \(0.719478\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.845563 | 0.184517 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.06968 | 1.31281 | 0.656403 | − | 0.754411i | \(-0.272077\pi\) | ||||
0.656403 | + | 0.754411i | \(0.272077\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.83264 | −0.329152 | −0.164576 | − | 0.986364i | \(-0.552626\pi\) | ||||
−0.164576 | + | 0.986364i | \(0.552626\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.55883 | 0.793591 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.845563 | 0.142926 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.93738 | −1.63370 | −0.816848 | − | 0.576854i | \(-0.804280\pi\) | ||||
−0.816848 | + | 0.576854i | \(0.804280\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.23704 | −0.838597 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.71327 | 0.892263 | 0.446131 | − | 0.894968i | \(-0.352801\pi\) | ||||
0.446131 | + | 0.894968i | \(0.352801\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.78294 | 0.729392 | 0.364696 | − | 0.931127i | \(-0.381173\pi\) | ||||
0.364696 | + | 0.931127i | \(0.381173\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.54591 | 0.808954 | 0.404477 | − | 0.914548i | \(-0.367454\pi\) | ||||
0.404477 | + | 0.914548i | \(0.367454\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.28502 | −0.897860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.72619 | −0.661799 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.4962 | −1.99121 | −0.995604 | − | 0.0936641i | \(-0.970142\pi\) | ||||
−0.995604 | + | 0.0936641i | \(0.970142\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.55883 | 0.614713 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.54591 | 0.734573 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.06968 | 0.660015 | 0.330008 | − | 0.943978i | \(-0.392949\pi\) | ||||
0.330008 | + | 0.943978i | \(0.392949\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.22411 | −0.796916 | −0.398458 | − | 0.917187i | \(-0.630455\pi\) | ||||
−0.398458 | + | 0.917187i | \(0.630455\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.845563 | −0.106531 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.23704 | −0.649574 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.85849 | −0.960067 | −0.480033 | − | 0.877250i | \(-0.659375\pi\) | ||||
−0.480033 | + | 0.877250i | \(0.659375\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.71327 | 0.440684 | 0.220342 | − | 0.975423i | \(-0.429283\pi\) | ||||
0.220342 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.23704 | 0.144784 | 0.0723920 | − | 0.997376i | \(-0.476937\pi\) | ||||
0.0723920 | + | 0.997376i | \(0.476937\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.85478 | 0.439293 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.7700 | −1.54925 | −0.774624 | − | 0.632422i | \(-0.782061\pi\) | ||||
−0.774624 | + | 0.632422i | \(0.782061\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.50913 | 0.824235 | 0.412117 | − | 0.911131i | \(-0.364789\pi\) | ||||
0.412117 | + | 0.911131i | \(0.364789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.72619 | −0.512627 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.06968 | −0.757949 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.98708 | 0.316630 | 0.158315 | − | 0.987389i | \(-0.449394\pi\) | ||||
0.158315 | + | 0.987389i | \(0.449394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.42825 | −0.464206 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.83264 | 0.190036 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.54591 | 0.568998 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.33472 | −0.237055 | −0.118527 | − | 0.992951i | \(-0.537817\pi\) | ||||
−0.118527 | + | 0.992951i | \(0.537817\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.55883 | −0.458180 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.1873 | −1.21269 | −0.606343 | − | 0.795203i | \(-0.707364\pi\) | ||||
−0.606343 | + | 0.795203i | \(0.707364\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.1047 | −1.78391 | −0.891956 | − | 0.452121i | \(-0.850667\pi\) | ||||
−0.891956 | + | 0.452121i | \(0.850667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.845563 | −0.0825185 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.39147 | −0.617887 | −0.308943 | − | 0.951080i | \(-0.599975\pi\) | ||||
−0.308943 | + | 0.951080i | \(0.599975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.55883 | 0.628222 | 0.314111 | − | 0.949386i | \(-0.398294\pi\) | ||||
0.314111 | + | 0.949386i | \(0.398294\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.93738 | 0.943214 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0826 | −1.32478 | −0.662390 | − | 0.749159i | \(-0.730458\pi\) | ||||
−0.662390 | + | 0.749159i | \(0.730458\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.23704 | 0.484164 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.99629 | −0.366340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.78294 | 0.889358 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.71327 | −0.515148 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.2629 | −1.17689 | −0.588445 | − | 0.808537i | \(-0.700260\pi\) | ||||
−0.588445 | + | 0.808537i | \(0.700260\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.78294 | −0.421115 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.38225 | −0.644991 | −0.322495 | − | 0.946571i | \(-0.604522\pi\) | ||||
−0.322495 | + | 0.946571i | \(0.604522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.68942 | 0.406624 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.1306 | 0.865514 | 0.432757 | − | 0.901511i | \(-0.357541\pi\) | ||||
0.432757 | + | 0.901511i | \(0.357541\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7332 | 0.995201 | 0.497600 | − | 0.867406i | \(-0.334215\pi\) | ||||
0.497600 | + | 0.867406i | \(0.334215\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.54591 | −0.467050 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.8748 | −1.99651 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.06968 | −0.587105 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.28502 | 0.518380 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5934 | −0.867849 | −0.433924 | − | 0.900949i | \(-0.642871\pi\) | ||||
−0.433924 | + | 0.900949i | \(0.642871\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.16520 | 0.664474 | 0.332237 | − | 0.943196i | \(-0.392197\pi\) | ||||
0.332237 | + | 0.943196i | \(0.392197\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.72619 | 0.382090 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.83264 | 0.147201 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.6068 | −0.846516 | −0.423258 | − | 0.906009i | \(-0.639114\pi\) | ||||
−0.423258 | + | 0.906009i | \(0.639114\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.4962 | 1.14962 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.845563 | −0.0666397 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.6653 | −1.22700 | −0.613500 | − | 0.789695i | \(-0.710239\pi\) | ||||
−0.613500 | + | 0.789695i | \(0.710239\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.55883 | −0.354905 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.16365 | −0.167429 | −0.0837143 | − | 0.996490i | \(-0.526678\pi\) | ||||
−0.0837143 | + | 0.996490i | \(0.526678\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4265 | 1.10973 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.54591 | −0.424106 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.30887 | −0.631712 | −0.315856 | − | 0.948807i | \(-0.602292\pi\) | ||||
−0.315856 | + | 0.948807i | \(0.602292\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.845563 | −0.0639186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.06968 | −0.381060 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.7571 | −0.804023 | −0.402012 | − | 0.915635i | \(-0.631689\pi\) | ||||
−0.402012 | + | 0.915635i | \(0.631689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.2482 | 1.43071 | 0.715356 | − | 0.698761i | \(-0.246265\pi\) | ||||
0.715356 | + | 0.698761i | \(0.246265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.22411 | 0.460100 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.93738 | 0.730611 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.5459 | −1.57559 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.845563 | 0.0615057 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.78465 | 0.129133 | 0.0645665 | − | 0.997913i | \(-0.479434\pi\) | ||||
0.0645665 | + | 0.997913i | \(0.479434\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4524 | −0.824361 | −0.412180 | − | 0.911102i | \(-0.635233\pi\) | ||||
−0.412180 | + | 0.911102i | \(0.635233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.23704 | 0.375032 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.23874 | 0.159504 | 0.0797520 | − | 0.996815i | \(-0.474587\pi\) | ||||
0.0797520 | + | 0.996815i | \(0.474587\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.5530 | 1.31518 | 0.657592 | − | 0.753374i | \(-0.271575\pi\) | ||||
0.657592 | + | 0.753374i | \(0.271575\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.85849 | 0.554295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.97786 | −0.419563 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.71327 | −0.399032 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.2829 | 1.74885 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0204 | −1.72248 | −0.861239 | − | 0.508201i | \(-0.830311\pi\) | ||||
−0.861239 | + | 0.508201i | \(0.830311\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.71327 | −0.254429 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.78294 | −0.326194 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.54961 | 0.105195 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.23704 | −0.0835911 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.7512 | 1.66495 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.71697 | −0.516767 | −0.258383 | − | 0.966042i | \(-0.583190\pi\) | ||||
−0.258383 | + | 0.966042i | \(0.583190\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.4395 | −0.958381 | −0.479190 | − | 0.877711i | \(-0.659070\pi\) | ||||
−0.479190 | + | 0.877711i | \(0.659070\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8660 | 1.04845 | 0.524227 | − | 0.851578i | \(-0.324354\pi\) | ||||
0.524227 | + | 0.851578i | \(0.324354\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.85478 | −0.253626 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.36057 | −0.547719 | −0.273859 | − | 0.961770i | \(-0.588300\pi\) | ||||
−0.273859 | + | 0.961770i | \(0.588300\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.54591 | −0.361775 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.7700 | 0.894459 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6173 | 0.751460 | 0.375730 | − | 0.926729i | \(-0.377392\pi\) | ||||
0.375730 | + | 0.926729i | \(0.377392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.0675 | −1.61474 | −0.807370 | − | 0.590045i | \(-0.799110\pi\) | ||||
−0.807370 | + | 0.590045i | \(0.799110\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.28502 | 0.401535 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.0441 | −1.84803 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.50913 | −0.475872 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.4870 | −0.851291 | −0.425646 | − | 0.904890i | \(-0.639953\pi\) | ||||
−0.425646 | + | 0.904890i | \(0.639953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.55883 | −0.286611 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.72619 | 0.295966 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.85478 | −0.115698 | −0.0578490 | − | 0.998325i | \(-0.518424\pi\) | ||||
−0.0578490 | + | 0.998325i | \(0.518424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.40269 | 0.522117 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.06968 | 0.437602 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.2132 | 0.999748 | 0.499874 | − | 0.866098i | \(-0.333380\pi\) | ||||
0.499874 | + | 0.866098i | \(0.333380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.4962 | 0.890495 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.98708 | −0.182806 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.80508 | −0.536855 | −0.268428 | − | 0.963300i | \(-0.586504\pi\) | ||||
−0.268428 | + | 0.963300i | \(0.586504\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.23333 | 0.196411 | 0.0982054 | − | 0.995166i | \(-0.468690\pi\) | ||||
0.0982054 | + | 0.995166i | \(0.468690\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.42825 | 0.268010 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.55883 | −0.274908 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.61775 | 0.157285 | 0.0786426 | − | 0.996903i | \(-0.474941\pi\) | ||||
0.0786426 | + | 0.996903i | \(0.474941\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.83264 | −0.109717 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.6031 | −0.871149 | −0.435574 | − | 0.900153i | \(-0.643455\pi\) | ||||
−0.435574 | + | 0.900153i | \(0.643455\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.7808 | −1.35418 | −0.677088 | − | 0.735902i | \(-0.736759\pi\) | ||||
−0.677088 | + | 0.735902i | \(0.736759\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.54591 | −0.328511 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.83093 | −0.285161 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.33688 | 0.313934 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.33472 | 0.136864 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.5880 | −1.49487 | −0.747434 | − | 0.664336i | \(-0.768715\pi\) | ||||
−0.747434 | + | 0.664336i | \(0.768715\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.06968 | −0.295168 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.55883 | 0.264530 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.23704 | 0.302866 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.04428 | −0.233109 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.1873 | 0.700144 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.22411 | 0.356392 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4507 | 0.710597 | 0.355299 | − | 0.934753i | \(-0.384379\pi\) | ||||
0.355299 | + | 0.934753i | \(0.384379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.1047 | 1.02994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.9048 | 0.618352 | 0.309176 | − | 0.951005i | \(-0.399947\pi\) | ||||
0.309176 | + | 0.951005i | \(0.399947\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.7549 | −1.73837 | −0.869186 | − | 0.494486i | \(-0.835356\pi\) | ||||
−0.869186 | + | 0.494486i | \(0.835356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.845563 | 0.0476421 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.9983 | 1.40404 | 0.702022 | − | 0.712155i | \(-0.252281\pi\) | ||||
0.702022 | + | 0.712155i | \(0.252281\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.2295 | −1.80450 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.39147 | 0.356737 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.2110 | −1.45842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.23704 | 0.290498 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.55883 | −0.362704 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.68942 | −0.258536 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.59390 | −0.527328 | −0.263664 | − | 0.964615i | \(-0.584931\pi\) | ||||
−0.263664 | + | 0.964615i | \(0.584931\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.93738 | −0.544565 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.85849 | 0.429355 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.97415 | 0.216486 | 0.108243 | − | 0.994124i | \(-0.465478\pi\) | ||||
0.108243 | + | 0.994124i | \(0.465478\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.0826 | 0.764862 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.35470 | 0.452432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.2333 | 0.606543 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.1177 | 0.704193 | 0.352097 | − | 0.935964i | \(-0.385469\pi\) | ||||
0.352097 | + | 0.935964i | \(0.385469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.80679 | 0.524946 | 0.262473 | − | 0.964939i | \(-0.415462\pi\) | ||||
0.262473 | + | 0.964939i | \(0.415462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.23704 | −0.279532 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.55007 | −0.455074 | −0.227537 | − | 0.973769i | \(-0.573067\pi\) | ||||
−0.227537 | + | 0.973769i | \(0.573067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.71327 | −0.197080 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.99629 | 0.211506 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.3990 | 1.49884 | 0.749420 | − | 0.662094i | \(-0.230332\pi\) | ||||
0.749420 | + | 0.662094i | \(0.230332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.7571 | 0.618795 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.78294 | −0.513471 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.23704 | −0.0647494 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.3121 | 1.26908 | 0.634539 | − | 0.772890i | \(-0.281190\pi\) | ||||
0.634539 | + | 0.772890i | \(0.281190\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.71327 | 0.297421 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2575 | 0.636376 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3435 | −1.05335 | −0.526673 | − | 0.850068i | \(-0.676561\pi\) | ||||
−0.526673 | + | 0.850068i | \(0.676561\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.0241 | 1.90684 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.33056 | 0.376546 | 0.188273 | − | 0.982117i | \(-0.439711\pi\) | ||||
0.188273 | + | 0.982117i | \(0.439711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.2629 | 0.679478 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.2575 | 1.44389 | 0.721945 | − | 0.691951i | \(-0.243249\pi\) | ||||
0.721945 | + | 0.691951i | \(0.243249\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.85478 | −0.196458 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.78294 | 0.243131 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.9966 | 1.21667 | 0.608337 | − | 0.793678i | \(-0.291837\pi\) | ||||
0.608337 | + | 0.793678i | \(0.291837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.72619 | 0.239014 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.38225 | 0.372385 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.7700 | 0.692845 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.02169 | −0.151654 | −0.0758271 | − | 0.997121i | \(-0.524160\pi\) | ||||
−0.0758271 | + | 0.997121i | \(0.524160\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.68942 | −0.234765 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.6263 | −1.47947 | −0.739735 | − | 0.672899i | \(-0.765049\pi\) | ||||
−0.739735 | + | 0.672899i | \(0.765049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.59760 | −0.478091 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.3028 | 2.24558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.42437 | −0.367112 | −0.183556 | − | 0.983009i | \(-0.558761\pi\) | ||||
−0.183556 | + | 0.983009i | \(0.558761\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1306 | −0.499705 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.28673 | −0.210936 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.50913 | −0.368609 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.7332 | −0.574580 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.20568 | −0.107754 | −0.0538772 | − | 0.998548i | \(-0.517158\pi\) | ||||
−0.0538772 | + | 0.998548i | \(0.517158\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0989 | 1.66188 | 0.830939 | − | 0.556364i | \(-0.187804\pi\) | ||||
0.830939 | + | 0.556364i | \(0.187804\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.54591 | 0.269651 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.72619 | 0.229254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.26288 | 0.254689 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.8748 | 1.15268 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.16952 | 0.200839 | 0.100419 | − | 0.994945i | \(-0.467982\pi\) | ||||
0.100419 | + | 0.994945i | \(0.467982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.08965 | 0.340707 | 0.170353 | − | 0.985383i | \(-0.445509\pi\) | ||||
0.170353 | + | 0.985383i | \(0.445509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.06968 | 0.338965 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.54591 | −0.265297 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.7537 | −1.75416 | −0.877079 | − | 0.480347i | \(-0.840511\pi\) | ||||
−0.877079 | + | 0.480347i | \(0.840511\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.28502 | −0.299287 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.3505 | 1.10942 | 0.554709 | − | 0.832045i | \(-0.312830\pi\) | ||||
0.554709 | + | 0.832045i | \(0.312830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.98708 | −0.141601 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5934 | 0.501053 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0437 | 1.41785 | 0.708924 | − | 0.705285i | \(-0.249181\pi\) | ||||
0.708924 | + | 0.705285i | \(0.249181\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.0458 | −1.22645 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.16520 | −0.383634 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.42825 | 0.207599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5496 | 0.914492 | 0.457246 | − | 0.889340i | \(-0.348836\pi\) | ||||
0.457246 | + | 0.889340i | \(0.348836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.72619 | −0.220600 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.6577 | −1.05527 | −0.527637 | − | 0.849470i | \(-0.676922\pi\) | ||||
−0.527637 | + | 0.849470i | \(0.676922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.7037 | −1.00866 | −0.504328 | − | 0.863512i | \(-0.668260\pi\) | ||||
−0.504328 | + | 0.863512i | \(0.668260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.83264 | −0.0849867 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.2003 | 1.16613 | 0.583065 | − | 0.812426i | \(-0.301853\pi\) | ||||
0.583065 | + | 0.812426i | \(0.301853\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.64485 | 0.306831 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.6068 | 0.488736 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.8046 | −1.00258 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.54591 | −0.254464 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.4962 | −0.663736 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.1635 | −0.875602 | −0.437801 | − | 0.899072i | \(-0.644243\pi\) | ||||
−0.437801 | + | 0.899072i | \(0.644243\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52.0424 | −2.37293 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.845563 | 0.0384745 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.33472 | 0.106014 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.3805 | 0.651645 | 0.325822 | − | 0.945431i | \(-0.394359\pi\) | ||||
0.325822 | + | 0.945431i | \(0.394359\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.6653 | 0.708408 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.3267 | −0.736813 | −0.368407 | − | 0.929665i | \(-0.620097\pi\) | ||||
−0.368407 | + | 0.929665i | \(0.620097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.4126 | 1.50483 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.55883 | 0.204904 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.13980 | −0.140839 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.8726 | 1.33728 | 0.668641 | − | 0.743586i | \(-0.266877\pi\) | ||||
0.668641 | + | 0.743586i | \(0.266877\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.16365 | 0.0966649 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.6831 | 1.50186 | 0.750928 | − | 0.660385i | \(-0.229607\pi\) | ||||
0.750928 | + | 0.660385i | \(0.229607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1873 | 0.542329 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.4265 | −0.640705 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.9265 | −1.32647 | −0.663233 | − | 0.748413i | \(-0.730816\pi\) | ||||
−0.663233 | + | 0.748413i | \(0.730816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.04599 | −0.0462719 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.54591 | 0.244858 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.1047 | 0.797790 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.2829 | −1.11194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.30887 | 0.364719 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.19827 | −0.359173 | −0.179586 | − | 0.983742i | \(-0.557476\pi\) | ||||
−0.179586 | + | 0.983742i | \(0.557476\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.15779 | −0.356715 | −0.178358 | − | 0.983966i | \(-0.557078\pi\) | ||||
−0.178358 | + | 0.983966i | \(0.557078\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.845563 | 0.0369034 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.66141 | −0.377297 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.06968 | 0.220005 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.9206 | 1.29600 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.39147 | 0.276327 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.7571 | 0.464203 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.6524 | 1.23414 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.4406 | −1.86766 | −0.933830 | − | 0.357718i | \(-0.883555\pi\) | ||||
−0.933830 | + | 0.357718i | \(0.883555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.2482 | −0.826021 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.55883 | −0.280949 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.5659 | −1.60620 | −0.803101 | − | 0.595843i | \(-0.796818\pi\) | ||||
−0.803101 | + | 0.595843i | \(0.796818\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.22411 | −0.265639 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.2078 | −1.67031 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.6434 | 0.495129 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.93738 | −0.421818 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.0438 | 0.552685 | 0.276342 | − | 0.961059i | \(-0.410878\pi\) | ||||
0.276342 | + | 0.961059i | \(0.410878\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.0484 | 1.05944 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.5459 | 0.909669 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.25212 | −0.179206 | −0.0896028 | − | 0.995978i | \(-0.528560\pi\) | ||||
−0.0896028 | + | 0.995978i | \(0.528560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0826 | 0.592459 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.845563 | −0.0355103 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.8358 | 1.92154 | 0.960769 | − | 0.277350i | \(-0.0894563\pi\) | ||||
0.960769 | + | 0.277350i | \(0.0894563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.7595 | 0.952457 | 0.476229 | − | 0.879321i | \(-0.342003\pi\) | ||||
0.476229 | + | 0.879321i | \(0.342003\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.78465 | −0.0745549 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.2310 | 1.67484 | 0.837419 | − | 0.546561i | \(-0.184063\pi\) | ||||
0.837419 | + | 0.546561i | \(0.184063\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.4524 | 0.475945 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.34945 | −0.263420 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 66.0858 | 2.73699 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.23704 | −0.216525 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −42.7278 | −1.76357 | −0.881783 | − | 0.471655i | \(-0.843657\pi\) | ||||
−0.881783 | + | 0.471655i | \(0.843657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.1637 | 0.418786 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.23874 | −0.0920897 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.1852 | 0.911036 | 0.455518 | − | 0.890227i | \(-0.349454\pi\) | ||||
0.455518 | + | 0.890227i | \(0.349454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.99629 | 0.163832 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.5530 | −0.759322 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.85632 | −0.402718 | −0.201359 | − | 0.979517i | \(-0.564536\pi\) | ||||
−0.201359 | + | 0.979517i | \(0.564536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.1157 | 0.494208 | 0.247104 | − | 0.968989i | \(-0.420521\pi\) | ||||
0.247104 | + | 0.968989i | \(0.420521\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.85849 | −0.320022 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.78294 | −0.397733 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.4984 | 0.588471 | 0.294235 | − | 0.955733i | \(-0.404935\pi\) | ||||
0.294235 | + | 0.955733i | \(0.404935\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.97786 | 0.242235 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.0441 | 1.17500 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.0312 | −1.45529 | −0.727643 | − | 0.685956i | \(-0.759384\pi\) | ||||
−0.727643 | + | 0.685956i | \(0.759384\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.71327 | 0.230381 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.0792 | −1.77456 | −0.887280 | − | 0.461230i | \(-0.847408\pi\) | ||||
−0.887280 | + | 0.461230i | \(0.847408\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.9998 | 1.32638 | 0.663188 | − | 0.748453i | \(-0.269203\pi\) | ||||
0.663188 | + | 0.748453i | \(0.269203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.52576 | −0.101193 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.2829 | −1.00970 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −46.9660 | −1.87266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8200 | −0.510356 | −0.255178 | − | 0.966894i | \(-0.582134\pi\) | ||||
−0.255178 | + | 0.966894i | \(0.582134\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.0204 | 0.994473 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.2629 | 0.526321 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.9149 | −1.30414 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.71327 | 0.146895 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.8126 | 1.53301 | 0.766503 | − | 0.642241i | \(-0.221995\pi\) | ||||
0.766503 | + | 0.642241i | \(0.221995\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.1339 | −1.30667 | −0.653337 | − | 0.757067i | \(-0.726632\pi\) | ||||
−0.653337 | + | 0.757067i | \(0.726632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.78294 | 0.188328 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.3547 | 0.957482 | 0.478741 | − | 0.877956i | \(-0.341093\pi\) | ||||
0.478741 | + | 0.877956i | \(0.341093\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.1118 | −0.907217 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.54961 | −0.0607341 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.5943 | 0.492855 | 0.246427 | − | 0.969161i | \(-0.420743\pi\) | ||||
0.246427 | + | 0.969161i | \(0.420743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.38225 | 0.288449 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.23704 | 0.0482613 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.9259 | −1.63320 | −0.816601 | − | 0.577202i | \(-0.804144\pi\) | ||||
−0.816601 | + | 0.577202i | \(0.804144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.1664 | 1.75677 | 0.878384 | − | 0.477955i | \(-0.158622\pi\) | ||||
0.878384 | + | 0.477955i | \(0.158622\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.7512 | −0.961258 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.68942 | −0.181848 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.06968 | 0.273739 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.71697 | 0.298355 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.3747 | 1.09539 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.4022 | −0.516618 | −0.258309 | − | 0.966062i | \(-0.583165\pi\) | ||||
−0.258309 | + | 0.966062i | \(0.583165\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.5662 | −1.59752 | −0.798759 | − | 0.601651i | \(-0.794510\pi\) | ||||
−0.798759 | + | 0.601651i | \(0.794510\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.97415 | 0.0757611 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.4395 | 0.553321 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.1778 | −0.925136 | −0.462568 | − | 0.886584i | \(-0.653072\pi\) | ||||
−0.462568 | + | 0.886584i | \(0.653072\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.1306 | −0.387070 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.8660 | −0.605325 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −75.9172 | −2.89221 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.99242 | 0.189921 | 0.0949603 | − | 0.995481i | \(-0.469728\pi\) | ||||
0.0949603 | + | 0.995481i | \(0.469728\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.85478 | 0.146431 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.7332 | −0.445067 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.0020 | 1.02277 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.36057 | 0.316226 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.0384 | 1.05900 | 0.529498 | − | 0.848311i | \(-0.322380\pi\) | ||||
0.529498 | + | 0.848311i | \(0.322380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 55.1118 | 2.07858 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.54591 | 0.208871 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3052 | 0.387566 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.9594 | 1.53826 | 0.769130 | − | 0.639092i | \(-0.220690\pi\) | ||||
0.769130 | + | 0.639092i | \(0.220690\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.7700 | −0.516416 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.83264 | −0.0686329 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.8748 | 0.892865 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.6173 | −0.433856 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.8568 | 1.00159 | 0.500794 | − | 0.865566i | \(-0.333041\pi\) | ||||
0.500794 | + | 0.865566i | \(0.333041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3087 | 0.570126 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.0675 | 0.932271 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.06968 | 0.262561 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.9849 | −1.29752 | −0.648759 | − | 0.760994i | \(-0.724712\pi\) | ||||
−0.648759 | + | 0.760994i | \(0.724712\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.6051 | 0.836080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.2170 | 1.04222 | 0.521109 | − | 0.853490i | \(-0.325518\pi\) | ||||
0.521109 | + | 0.853490i | \(0.325518\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.28502 | −0.231827 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.8255 | 1.31965 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.8251 | 1.13392 | 0.566959 | − | 0.823746i | \(-0.308120\pi\) | ||||
0.566959 | + | 0.823746i | \(0.308120\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.0441 | 1.06696 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.2093 | 1.95206 | 0.976030 | − | 0.217635i | \(-0.0698343\pi\) | ||||
0.976030 | + | 0.217635i | \(0.0698343\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5934 | 0.388114 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.50913 | 0.274745 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.40439 | 0.197472 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0513 | 0.914136 | 0.457068 | − | 0.889432i | \(-0.348900\pi\) | ||||
0.457068 | + | 0.889432i | \(0.348900\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.4870 | 0.491493 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.16520 | −0.297162 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.72032 | 0.0988718 | 0.0494359 | − | 0.998777i | \(-0.484258\pi\) | ||||
0.0494359 | + | 0.998777i | \(0.484258\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.55883 | 0.165475 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.9779 | −0.434197 | −0.217099 | − | 0.976150i | \(-0.569659\pi\) | ||||
−0.217099 | + | 0.976150i | \(0.569659\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.54591 | −0.200775 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.72619 | −0.170876 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.5501 | 0.958667 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.2412 | 0.513551 | 0.256775 | − | 0.966471i | \(-0.417340\pi\) | ||||
0.256775 | + | 0.966471i | \(0.417340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.85478 | 0.0667983 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.0660 | 0.541885 | 0.270943 | − | 0.962595i | \(-0.412665\pi\) | ||||
0.270943 | + | 0.962595i | \(0.412665\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.83264 | −0.0658304 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.40269 | −0.301445 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.6853 | −1.13524 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.9282 | −0.605737 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.06968 | −0.252650 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.6068 | 0.378574 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.79922 | 0.171074 | 0.0855368 | − | 0.996335i | \(-0.472739\pi\) | ||||
0.0855368 | + | 0.996335i | \(0.472739\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.2132 | −0.577205 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.9077 | 0.423390 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.5959 | −1.15751 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.4962 | −0.514128 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.6538 | 1.82967 | 0.914836 | − | 0.403825i | \(-0.132320\pi\) | ||||
0.914836 | + | 0.403825i | \(0.132320\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.2110 | 0.927279 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.98708 | 0.105543 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.63943 | −0.199011 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.845563 | 0.0298022 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.80508 | 0.309954 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.30500 | −0.327146 | −0.163573 | − | 0.986531i | \(-0.552302\pi\) | ||||
−0.163573 | + | 0.986531i | \(0.552302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.2041 | −1.37664 | −0.688320 | − | 0.725407i | \(-0.741652\pi\) | ||||
−0.688320 | + | 0.725407i | \(0.741652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.23333 | −0.113398 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.6653 | 0.548731 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.5258 | −0.928019 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.42825 | −0.154735 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.23948 | −0.322460 | −0.161230 | − | 0.986917i | \(-0.551546\pi\) | ||||
−0.161230 | + | 0.986917i | \(0.551546\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.3931 | −0.920006 | −0.460003 | − | 0.887917i | \(-0.652152\pi\) | ||||
−0.460003 | + | 0.887917i | \(0.652152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.55883 | 0.158718 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.7520 | −0.582525 | −0.291263 | − | 0.956643i | \(-0.594075\pi\) | ||||
−0.291263 | + | 0.956643i | \(0.594075\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.1381 | −1.11620 | −0.558101 | − | 0.829773i | \(-0.688470\pi\) | ||||
−0.558101 | + | 0.829773i | \(0.688470\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.61775 | −0.0908086 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.7042 | −1.02919 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.16365 | 0.0748763 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.83264 | 0.0633453 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.8748 | 0.548058 | 0.274029 | − | 0.961721i | \(-0.411644\pi\) | ||||
0.274029 | + | 0.961721i | \(0.411644\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.9803 | 0.723459 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.6031 | 0.502958 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.4265 | −0.496288 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.27210 | −0.284233 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.7808 | 0.781834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.93738 | −0.340649 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.4481 | −0.939804 | −0.469902 | − | 0.882719i | \(-0.655711\pi\) | ||||
−0.469902 | + | 0.882719i | \(0.655711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.54591 | 0.189666 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −49.3929 | −1.68723 | −0.843615 | − | 0.536948i | \(-0.819577\pi\) | ||||
−0.843615 | + | 0.536948i | \(0.819577\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.5863 | −0.634157 | −0.317078 | − | 0.948399i | \(-0.602702\pi\) | ||||
−0.317078 | + | 0.948399i | \(0.602702\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.83093 | 0.164638 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.6619 | −1.14586 | −0.572932 | − | 0.819603i | \(-0.694194\pi\) | ||||
−0.572932 | + | 0.819603i | \(0.694194\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.30887 | 0.282510 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.33688 | −0.181250 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 62.7752 | 2.12950 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.1552 | −1.39449 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.33472 | −0.0790183 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.845563 | 0.0285853 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.2321 | 0.987097 | 0.493548 | − | 0.869718i | \(-0.335700\pi\) | ||||
0.493548 | + | 0.869718i | \(0.335700\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.5880 | 0.863063 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.20242 | 0.0405107 | 0.0202553 | − | 0.999795i | \(-0.493552\pi\) | ||||
0.0202553 | + | 0.999795i | \(0.493552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.82877 | −0.0951956 | −0.0475978 | − | 0.998867i | \(-0.515157\pi\) | ||||
−0.0475978 | + | 0.998867i | \(0.515157\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.06968 | 0.170415 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.86048 | −0.230352 | −0.115176 | − | 0.993345i | \(-0.536743\pi\) | ||||
−0.115176 | + | 0.993345i | \(0.536743\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.2146 | 0.376126 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.55883 | −0.152727 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.7571 | −1.02925 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.7571 | 0.359570 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.23704 | −0.174860 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.9562 | −0.432113 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −68.5119 | −2.28246 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.04428 | 0.134585 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.2482 | −0.639833 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.1198 | −0.502046 | −0.251023 | − | 0.967981i | \(-0.580767\pi\) | ||||
−0.251023 | + | 0.967981i | \(0.580767\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.1873 | −0.404228 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.3931 | −1.66960 | −0.834799 | − | 0.550555i | \(-0.814416\pi\) | ||||
−0.834799 | + | 0.550555i | \(0.814416\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.2329 | −1.13294 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.22411 | −0.205763 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.24216 | 0.206134 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0053 | −1.31965 | −0.659827 | − | 0.751417i | \(-0.729371\pi\) | ||||
−0.659827 | + | 0.751417i | \(0.729371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.4507 | −0.410264 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.4465 | 0.640090 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.93738 | −0.326739 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.1047 | −0.594638 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.0921 | 1.28257 | 0.641285 | − | 0.767303i | \(-0.278402\pi\) | ||||
0.641285 | + | 0.767303i | \(0.278402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.8562 | 1.14236 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.9048 | −0.357006 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.5459 | 0.704627 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.2310 | 1.57564 | 0.787819 | − | 0.615907i | \(-0.211210\pi\) | ||||
0.787819 | + | 0.615907i | \(0.211210\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.7549 | 1.00365 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.7337 | 0.349909 | 0.174954 | − | 0.984577i | \(-0.444022\pi\) | ||||
0.174954 | + | 0.984577i | \(0.444022\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.71327 | 0.186050 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.845563 | −0.0275062 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.9257 | −0.420029 | −0.210015 | − | 0.977698i | \(-0.567351\pi\) | ||||
−0.210015 | + | 0.977698i | \(0.567351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.47840 | 0.210298 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.9983 | −0.810625 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.4051 | −1.72996 | −0.864981 | − | 0.501805i | \(-0.832670\pi\) | ||||
−0.864981 | + | 0.501805i | \(0.832670\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.78465 | −0.0577500 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.2295 | 1.04183 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.56605 | −0.276612 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6414 | −0.891659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.39147 | −0.205962 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.4524 | 0.368665 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.1852 | −0.906374 | −0.453187 | − | 0.891415i | \(-0.649713\pi\) | ||||
−0.453187 | + | 0.891415i | \(0.649713\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.2110 | 0.842019 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.1922 | 1.06519 | 0.532595 | − | 0.846370i | \(-0.321217\pi\) | ||||
0.532595 | + | 0.846370i | \(0.321217\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.92120 | −0.318059 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.23704 | −0.167719 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.0750 | 0.354321 | 0.177161 | − | 0.984182i | \(-0.443309\pi\) | ||||
0.177161 | + | 0.984182i | \(0.443309\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.6176 | −0.435220 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.55883 | 0.209407 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.8785 | −0.378864 | −0.189432 | − | 0.981894i | \(-0.560665\pi\) | ||||
−0.189432 | + | 0.981894i | \(0.560665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.23874 | −0.0713323 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.68942 | 0.149266 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.78294 | 0.152089 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.8800 | −1.07623 | −0.538117 | − | 0.842870i | \(-0.680864\pi\) | ||||
−0.538117 | + | 0.842870i | \(0.680864\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.59390 | 0.304453 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.5530 | −0.588168 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.33797 | −0.295737 | −0.147868 | − | 0.989007i | \(-0.547241\pi\) | ||||
−0.147868 | + | 0.989007i | \(0.547241\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.93738 | 0.314405 |
(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 | 2760.2.a.v.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 8280.2.a.bq.1.2 | 4 | |||
4.3 | odd | 2 | 5520.2.a.cb.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.v.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
5520.2.a.cb.1.3 | 4 | 4.3 | odd | 2 | |||
8280.2.a.bq.1.2 | 4 | 3.2 | odd | 2 |