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: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.20087896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 21x^{3} + 5x^{2} + 84x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.0475116\) 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 | ||||||||
\(7\) | −5.02263 | −1.89837 | −0.949187 | − | 0.314712i | \(-0.898092\pi\) | ||||
−0.949187 | + | 0.314712i | \(0.898092\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.71008 | −1.11863 | −0.559316 | − | 0.828955i | \(-0.688936\pi\) | ||||
−0.559316 | + | 0.828955i | \(0.688936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.49408 | −1.80113 | −0.900566 | − | 0.434719i | \(-0.856848\pi\) | ||||
−0.900566 | + | 0.434719i | \(0.856848\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.37642 | 1.30397 | 0.651987 | − | 0.758230i | \(-0.273936\pi\) | ||||
0.651987 | + | 0.758230i | \(0.273936\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.39905 | −1.92687 | −0.963437 | − | 0.267934i | \(-0.913659\pi\) | ||||
−0.963437 | + | 0.267934i | \(0.913659\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.02263 | 1.09603 | ||||||||
\(22\) | 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 | ||||||||
\(29\) | 3.31255 | 0.615124 | 0.307562 | − | 0.951528i | \(-0.400487\pi\) | ||||
0.307562 | + | 0.951528i | \(0.400487\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.18153 | 1.28984 | 0.644920 | − | 0.764250i | \(-0.276891\pi\) | ||||
0.644920 | + | 0.764250i | \(0.276891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.71008 | 0.645842 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.02263 | −0.848979 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.02263 | −0.496917 | −0.248458 | − | 0.968643i | \(-0.579924\pi\) | ||||
−0.248458 | + | 0.968643i | \(0.579924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.49408 | 1.03988 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.782477 | 0.122202 | 0.0611012 | − | 0.998132i | \(-0.480539\pi\) | ||||
0.0611012 | + | 0.998132i | \(0.480539\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0950231 | −0.0144909 | −0.00724544 | − | 0.999974i | \(-0.502306\pi\) | ||||
−0.00724544 | + | 0.999974i | \(0.502306\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.39905 | 1.22513 | 0.612564 | − | 0.790421i | \(-0.290138\pi\) | ||||
0.612564 | + | 0.790421i | \(0.290138\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.2268 | 2.60383 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.37642 | −0.752850 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.82773 | 0.937861 | 0.468930 | − | 0.883235i | \(-0.344639\pi\) | ||||
0.468930 | + | 0.883235i | \(0.344639\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.71008 | −0.500267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.39905 | 1.11248 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.2628 | 1.46629 | 0.733144 | − | 0.680073i | \(-0.238052\pi\) | ||||
0.733144 | + | 0.680073i | \(0.238052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.6032 | −1.86975 | −0.934875 | − | 0.354978i | \(-0.884488\pi\) | ||||
−0.934875 | + | 0.354978i | \(0.884488\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.02263 | −0.632792 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.49408 | −0.805491 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.71160 | −1.18646 | −0.593230 | − | 0.805033i | \(-0.702148\pi\) | ||||
−0.593230 | + | 0.805033i | \(0.702148\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.73271 | 1.03638 | 0.518191 | − | 0.855265i | \(-0.326606\pi\) | ||||
0.518191 | + | 0.855265i | \(0.326606\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.64620 | 0.426756 | 0.213378 | − | 0.976970i | \(-0.431553\pi\) | ||||
0.213378 | + | 0.976970i | \(0.431553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.6344 | 2.12358 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.59395 | 0.966895 | 0.483447 | − | 0.875373i | \(-0.339384\pi\) | ||||
0.483447 | + | 0.875373i | \(0.339384\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.37642 | −0.809668 | −0.404834 | − | 0.914390i | \(-0.632671\pi\) | ||||
−0.404834 | + | 0.914390i | \(0.632671\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.37642 | 0.583155 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.31255 | −0.355142 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.29918 | −0.667712 | −0.333856 | − | 0.942624i | \(-0.608350\pi\) | ||||
−0.333856 | + | 0.942624i | \(0.608350\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 32.6173 | 3.41922 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.18153 | −0.744690 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.39905 | −0.861725 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.32514 | −0.540686 | −0.270343 | − | 0.962764i | \(-0.587137\pi\) | ||||
−0.270343 | + | 0.962764i | \(0.587137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.71008 | −0.372877 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0654 | 1.00154 | 0.500772 | − | 0.865579i | \(-0.333049\pi\) | ||||
0.500772 | + | 0.865579i | \(0.333049\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.15890 | 0.212723 | 0.106361 | − | 0.994328i | \(-0.466080\pi\) | ||||
0.106361 | + | 0.994328i | \(0.466080\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.02263 | 0.490158 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.00152 | −0.193494 | −0.0967470 | − | 0.995309i | \(-0.530844\pi\) | ||||
−0.0967470 | + | 0.995309i | \(0.530844\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4302 | 1.19060 | 0.595298 | − | 0.803505i | \(-0.297034\pi\) | ||||
0.595298 | + | 0.803505i | \(0.297034\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.02263 | 0.286895 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0468 | −1.32141 | −0.660705 | − | 0.750646i | \(-0.729742\pi\) | ||||
−0.660705 | + | 0.750646i | \(0.729742\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.49408 | −0.600377 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.0038 | −2.47543 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.76470 | 0.251336 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.782477 | −0.0705536 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.9142 | −1.05722 | −0.528609 | − | 0.848866i | \(-0.677286\pi\) | ||||
−0.528609 | + | 0.848866i | \(0.677286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0950231 | 0.00836632 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 42.1853 | 3.65793 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.2494 | −1.73002 | −0.865012 | − | 0.501751i | \(-0.832689\pi\) | ||||
−0.865012 | + | 0.501751i | \(0.832689\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.61658 | −0.476392 | −0.238196 | − | 0.971217i | \(-0.576556\pi\) | ||||
−0.238196 | + | 0.971217i | \(0.576556\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.39905 | −0.707328 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.0935 | 2.01480 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.31255 | 0.275092 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.2268 | −1.50332 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.226041 | 0.0185180 | 0.00925898 | − | 0.999957i | \(-0.497053\pi\) | ||||
0.00925898 | + | 0.999957i | \(0.497053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2353 | 0.832937 | 0.416468 | − | 0.909150i | \(-0.363268\pi\) | ||||
0.416468 | + | 0.909150i | \(0.363268\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.37642 | 0.434658 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.18153 | 0.576834 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7755 | 1.09940 | 0.549701 | − | 0.835361i | \(-0.314742\pi\) | ||||
0.549701 | + | 0.835361i | \(0.314742\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.82773 | −0.541474 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.02263 | 0.395838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.33269 | −0.261036 | −0.130518 | − | 0.991446i | \(-0.541664\pi\) | ||||
−0.130518 | + | 0.991446i | \(0.541664\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.71008 | 0.288829 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5014 | 1.50906 | 0.754532 | − | 0.656263i | \(-0.227864\pi\) | ||||
0.754532 | + | 0.656263i | \(0.227864\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.1730 | 2.24408 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.39905 | −0.642292 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.0453 | −1.21990 | −0.609949 | − | 0.792441i | \(-0.708810\pi\) | ||||
−0.609949 | + | 0.792441i | \(0.708810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.02263 | −0.379675 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.2628 | −0.846562 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.1730 | 1.05934 | 0.529670 | − | 0.848204i | \(-0.322316\pi\) | ||||
0.529670 | + | 0.848204i | \(0.322316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.03114 | 0.299633 | 0.149816 | − | 0.988714i | \(-0.452132\pi\) | ||||
0.149816 | + | 0.988714i | \(0.452132\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.6032 | 1.07950 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.02263 | −0.222228 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.9470 | −1.45867 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.02263 | 0.365342 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.58910 | 0.621485 | 0.310743 | − | 0.950494i | \(-0.399422\pi\) | ||||
0.310743 | + | 0.950494i | \(0.399422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8434 | −1.21241 | −0.606206 | − | 0.795308i | \(-0.707309\pi\) | ||||
−0.606206 | + | 0.795308i | \(0.707309\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.49408 | 0.465050 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0422192 | 0.00300800 | 0.00150400 | − | 0.999999i | \(-0.499521\pi\) | ||||
0.00150400 | + | 0.999999i | \(0.499521\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.1589 | 1.00370 | 0.501849 | − | 0.864955i | \(-0.332653\pi\) | ||||
0.501849 | + | 0.864955i | \(0.332653\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.71160 | 0.685003 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.6377 | −1.16774 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.782477 | 0.0546506 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31.1612 | 2.15546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6166 | 0.937404 | 0.468702 | − | 0.883356i | \(-0.344722\pi\) | ||||
0.468702 | + | 0.883356i | \(0.344722\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.73271 | −0.598355 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0950231 | −0.00648052 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −36.0701 | −2.44860 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.64620 | −0.246388 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −34.9149 | −2.34863 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.3133 | −1.89600 | −0.947999 | − | 0.318273i | \(-0.896897\pi\) | ||||
−0.947999 | + | 0.318273i | \(0.896897\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9118 | 0.856983 | 0.428492 | − | 0.903546i | \(-0.359045\pi\) | ||||
0.428492 | + | 0.903546i | \(0.359045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.6814 | 1.23450 | 0.617252 | − | 0.786766i | \(-0.288246\pi\) | ||||
0.617252 | + | 0.786766i | \(0.288246\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.6344 | −1.22605 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.2353 | −0.801561 | −0.400781 | − | 0.916174i | \(-0.631261\pi\) | ||||
−0.400781 | + | 0.916174i | \(0.631261\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.39905 | 0.547894 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.59395 | −0.558237 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.2977 | 0.924839 | 0.462419 | − | 0.886661i | \(-0.346981\pi\) | ||||
0.462419 | + | 0.886661i | \(0.346981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.22604 | 0.272223 | 0.136112 | − | 0.990694i | \(-0.456539\pi\) | ||||
0.136112 | + | 0.990694i | \(0.456539\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.2268 | 1.16447 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 54.5441 | 3.47056 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.37642 | 0.467462 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.4015 | −0.972136 | −0.486068 | − | 0.873921i | \(-0.661569\pi\) | ||||
−0.486068 | + | 0.873921i | \(0.661569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.71008 | 0.233251 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.37642 | −0.336685 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.7367 | 1.23114 | 0.615571 | − | 0.788081i | \(-0.288925\pi\) | ||||
0.615571 | + | 0.788081i | \(0.288925\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.1815 | 0.943334 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.31255 | 0.205041 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.81588 | 0.605273 | 0.302637 | − | 0.953106i | \(-0.402133\pi\) | ||||
0.302637 | + | 0.953106i | \(0.402133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.82773 | 0.419424 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.29918 | 0.385503 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.92275 | −0.422088 | −0.211044 | − | 0.977477i | \(-0.567686\pi\) | ||||
−0.211044 | + | 0.977477i | \(0.567686\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.22678 | −0.560487 | −0.280244 | − | 0.959929i | \(-0.590415\pi\) | ||||
−0.280244 | + | 0.959929i | \(0.590415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −32.6173 | −1.97409 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.71008 | −0.223726 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.33032 | −0.500521 | −0.250260 | − | 0.968179i | \(-0.580516\pi\) | ||||
−0.250260 | + | 0.968179i | \(0.580516\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.18153 | 0.429947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1451 | −0.963138 | −0.481569 | − | 0.876408i | \(-0.659933\pi\) | ||||
−0.481569 | + | 0.876408i | \(0.659933\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.5550 | 1.69742 | 0.848708 | − | 0.528862i | \(-0.177381\pi\) | ||||
0.848708 | + | 0.528862i | \(0.177381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.39905 | 0.497517 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.93009 | −0.231986 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.9059 | 0.700350 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.32514 | 0.312165 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.5836 | 1.49461 | 0.747305 | − | 0.664481i | \(-0.231347\pi\) | ||||
0.747305 | + | 0.664481i | \(0.231347\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2628 | 0.655744 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.71008 | 0.215281 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.49408 | 0.375562 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.477266 | 0.0275091 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.0654 | −0.578242 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.6032 | −0.836177 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.58910 | −0.261914 | −0.130957 | − | 0.991388i | \(-0.541805\pi\) | ||||
−0.130957 | + | 0.991388i | \(0.541805\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.15890 | −0.122816 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.8360 | −1.35162 | −0.675808 | − | 0.737077i | \(-0.736205\pi\) | ||||
−0.675808 | + | 0.737077i | \(0.736205\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.0747 | 1.47383 | 0.736913 | − | 0.675987i | \(-0.236283\pi\) | ||||
0.736913 | + | 0.675987i | \(0.236283\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.02263 | −0.282993 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.7367 | 0.883862 | 0.441931 | − | 0.897049i | \(-0.354294\pi\) | ||||
0.441931 | + | 0.897049i | \(0.354294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.2898 | −0.688098 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.00152 | 0.111714 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −45.1569 | −2.51260 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.49408 | −0.360226 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.4302 | −0.687391 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −42.1853 | −2.32575 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.3427 | −1.88764 | −0.943822 | − | 0.330453i | \(-0.892799\pi\) | ||||
−0.943822 | + | 0.330453i | \(0.892799\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.02263 | −0.165639 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.71160 | −0.530601 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.23767 | 0.503208 | 0.251604 | − | 0.967830i | \(-0.419042\pi\) | ||||
0.251604 | + | 0.967830i | \(0.419042\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.0468 | 0.762916 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.6441 | −1.44286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −56.3879 | −3.04466 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.4803 | 0.884709 | 0.442354 | − | 0.896840i | \(-0.354143\pi\) | ||||
0.442354 | + | 0.896840i | \(0.354143\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.48882 | 0.186752 | 0.0933761 | − | 0.995631i | \(-0.470234\pi\) | ||||
0.0933761 | + | 0.995631i | \(0.470234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.49408 | 0.346628 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.7503 | 1.58345 | 0.791723 | − | 0.610880i | \(-0.209184\pi\) | ||||
0.791723 | + | 0.610880i | \(0.209184\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.73271 | 0.463484 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.0038 | 1.42919 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.5014 | 0.607021 | 0.303511 | − | 0.952828i | \(-0.401841\pi\) | ||||
0.303511 | + | 0.952828i | \(0.401841\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51.5441 | 2.71285 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.76470 | −0.145109 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.64620 | 0.190851 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.58758 | 0.135071 | 0.0675353 | − | 0.997717i | \(-0.478486\pi\) | ||||
0.0675353 | + | 0.997717i | \(0.478486\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.782477 | 0.0407341 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.2931 | −1.78041 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6392 | −0.654433 | −0.327217 | − | 0.944949i | \(-0.606111\pi\) | ||||
−0.327217 | + | 0.944949i | \(0.606111\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.5119 | −1.10792 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.8858 | 0.713265 | 0.356633 | − | 0.934245i | \(-0.383925\pi\) | ||||
0.356633 | + | 0.934245i | \(0.383925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.9142 | 0.610385 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.20264 | 0.316940 | 0.158470 | − | 0.987364i | \(-0.449344\pi\) | ||||
0.158470 | + | 0.987364i | \(0.449344\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.6344 | 0.949695 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.0950231 | −0.00483030 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.147827 | 0.00749513 | 0.00374756 | − | 0.999993i | \(-0.498807\pi\) | ||||
0.00374756 | + | 0.999993i | \(0.498807\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.37642 | −0.271897 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.59395 | 0.432408 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.0259 | 1.45677 | 0.728383 | − | 0.685170i | \(-0.240272\pi\) | ||||
0.728383 | + | 0.685170i | \(0.240272\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −42.1853 | −2.11191 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.2145 | 0.859652 | 0.429826 | − | 0.902912i | \(-0.358575\pi\) | ||||
0.429826 | + | 0.902912i | \(0.358575\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −46.6374 | −2.32317 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.2142 | 0.555867 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.8348 | −1.17856 | −0.589279 | − | 0.807930i | \(-0.700588\pi\) | ||||
−0.589279 | + | 0.807930i | \(0.700588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.2494 | 0.998830 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −56.5687 | −2.78357 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.37642 | −0.362094 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.61658 | 0.275045 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.99064 | 0.390368 | 0.195184 | − | 0.980767i | \(-0.437470\pi\) | ||||
0.195184 | + | 0.980767i | \(0.437470\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5326 | −0.562062 | −0.281031 | − | 0.959699i | \(-0.590676\pi\) | ||||
−0.281031 | + | 0.959699i | \(0.590676\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.39905 | 0.408376 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.37642 | 0.260795 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 73.3465 | 3.54948 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.0935 | −1.16325 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.3661 | −1.27001 | −0.635005 | − | 0.772508i | \(-0.719002\pi\) | ||||
−0.635005 | + | 0.772508i | \(0.719002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.24618 | 0.107945 | 0.0539723 | − | 0.998542i | \(-0.482812\pi\) | ||||
0.0539723 | + | 0.998542i | \(0.482812\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.31255 | −0.158824 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.39905 | 0.401781 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3512 | −0.732673 | −0.366337 | − | 0.930482i | \(-0.619388\pi\) | ||||
−0.366337 | + | 0.930482i | \(0.619388\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.2268 | 0.867942 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.0948 | −1.23980 | −0.619901 | − | 0.784680i | \(-0.712827\pi\) | ||||
−0.619901 | + | 0.784680i | \(0.712827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.29918 | −0.298610 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.226041 | −0.0106914 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.67109 | 0.267635 | 0.133818 | − | 0.991006i | \(-0.457276\pi\) | ||||
0.133818 | + | 0.991006i | \(0.457276\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.90305 | −0.136699 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.2353 | −0.480896 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.6173 | 1.52912 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.2024 | 1.41281 | 0.706405 | − | 0.707808i | \(-0.250316\pi\) | ||||
0.706405 | + | 0.707808i | \(0.250316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.37642 | −0.250950 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.0526 | −1.25996 | −0.629982 | − | 0.776609i | \(-0.716938\pi\) | ||||
−0.629982 | + | 0.776609i | \(0.716938\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6671 | 0.495742 | 0.247871 | − | 0.968793i | \(-0.420269\pi\) | ||||
0.247871 | + | 0.968793i | \(0.420269\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.18153 | −0.333035 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.9696 | −0.970357 | −0.485179 | − | 0.874415i | \(-0.661245\pi\) | ||||
−0.485179 | + | 0.874415i | \(0.661245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.7777 | 2.25235 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.7755 | −0.634740 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.352543 | 0.0162100 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.39905 | −0.385375 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.82773 | 0.312620 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.7218 | −0.855422 | −0.427711 | − | 0.903916i | \(-0.640680\pi\) | ||||
−0.427711 | + | 0.903916i | \(0.640680\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.6292 | 0.895013 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.02263 | −0.228537 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.32514 | −0.241802 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.5363 | −0.477445 | −0.238723 | − | 0.971088i | \(-0.576729\pi\) | ||||
−0.238723 | + | 0.971088i | \(0.576729\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.33269 | 0.150709 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.77063 | 0.350683 | 0.175342 | − | 0.984508i | \(-0.443897\pi\) | ||||
0.175342 | + | 0.984508i | \(0.443897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.8097 | 0.802107 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.71008 | −0.166756 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.8611 | −1.96744 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8370 | 0.932792 | 0.466396 | − | 0.884576i | \(-0.345552\pi\) | ||||
0.466396 | + | 0.884576i | \(0.345552\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.5014 | −0.871259 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.6377 | −0.741838 | −0.370919 | − | 0.928665i | \(-0.620957\pi\) | ||||
−0.370919 | + | 0.928665i | \(0.620957\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0654 | 0.447904 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29.1730 | −1.29562 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.9235 | 1.14904 | 0.574519 | − | 0.818491i | \(-0.305189\pi\) | ||||
0.574519 | + | 0.818491i | \(0.305189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.3135 | −0.810142 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.39905 | 0.370827 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.15890 | 0.0951326 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.1612 | −1.37047 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.0453 | 0.704308 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.91501 | −0.390574 | −0.195287 | − | 0.980746i | \(-0.562564\pi\) | ||||
−0.195287 | + | 0.980746i | \(0.562564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.6481 | −0.640518 | −0.320259 | − | 0.947330i | \(-0.603770\pi\) | ||||
−0.320259 | + | 0.947330i | \(0.603770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.02263 | 0.219205 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 38.6110 | 1.68192 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2628 | 0.488763 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.08146 | −0.220103 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.00152 | −0.0865331 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.1730 | −0.611611 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −67.6228 | −2.91272 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0571 | −0.819329 | −0.409664 | − | 0.912236i | \(-0.634354\pi\) | ||||
−0.409664 | + | 0.912236i | \(0.634354\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.03114 | −0.172993 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.4302 | 0.532451 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.84032 | 0.121443 | 0.0607217 | − | 0.998155i | \(-0.480660\pi\) | ||||
0.0607217 | + | 0.998155i | \(0.480660\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.6032 | −0.623250 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.8222 | −1.18527 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43.1642 | −1.83553 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.02263 | 0.128303 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.1365 | 1.48878 | 0.744391 | − | 0.667744i | \(-0.232740\pi\) | ||||
0.744391 | + | 0.667744i | \(0.232740\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.617087 | 0.0261000 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.9470 | 0.842162 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.96960 | 0.209444 | 0.104722 | − | 0.994502i | \(-0.466605\pi\) | ||||
0.104722 | + | 0.994502i | \(0.466605\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0468 | −0.590952 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.02263 | −0.210931 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.6769 | −1.45373 | −0.726866 | − | 0.686780i | \(-0.759024\pi\) | ||||
−0.726866 | + | 0.686780i | \(0.759024\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.2514 | −0.470858 | −0.235429 | − | 0.971892i | \(-0.575650\pi\) | ||||
−0.235429 | + | 0.971892i | \(0.575650\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.58910 | −0.358815 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.2872 | −0.594785 | −0.297392 | − | 0.954755i | \(-0.596117\pi\) | ||||
−0.297392 | + | 0.954755i | \(0.596117\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.8434 | 0.699986 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.0490 | 1.53705 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.3314 | −1.04912 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.49408 | −0.268497 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.8856 | 1.19224 | 0.596118 | − | 0.802897i | \(-0.296709\pi\) | ||||
0.596118 | + | 0.802897i | \(0.296709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.3180 | −2.48536 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0422192 | −0.00173667 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.6225 | −1.54497 | −0.772486 | − | 0.635032i | \(-0.780987\pi\) | ||||
−0.772486 | + | 0.635032i | \(0.780987\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.0038 | −1.10705 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.1589 | −0.579485 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.7483 | 1.09291 | 0.546454 | − | 0.837489i | \(-0.315977\pi\) | ||||
0.546454 | + | 0.837489i | \(0.315977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.4621 | 0.875457 | 0.437728 | − | 0.899107i | \(-0.355783\pi\) | ||||
0.437728 | + | 0.899107i | \(0.355783\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.71160 | −0.395487 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.76470 | 0.112401 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.1644 | 1.02139 | 0.510696 | − | 0.859761i | \(-0.329388\pi\) | ||||
0.510696 | + | 0.859761i | \(0.329388\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.6377 | 0.674193 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −54.5441 | −2.20662 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.62432 | −0.388723 | −0.194361 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194361 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.782477 | −0.0315525 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.2368 | −1.21729 | −0.608644 | − | 0.793443i | \(-0.708286\pi\) | ||||
−0.608644 | + | 0.793443i | \(0.708286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6503 | −0.910391 | −0.455196 | − | 0.890391i | \(-0.650431\pi\) | ||||
−0.455196 | + | 0.890391i | \(0.650431\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.6384 | 1.26757 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −31.1612 | −1.24446 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.2509 | −0.647967 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.3188 | 1.56526 | 0.782629 | − | 0.622489i | \(-0.213878\pi\) | ||||
0.782629 | + | 0.622489i | \(0.213878\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.6166 | −0.541210 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.9142 | −0.472802 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −118.366 | −4.68984 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.73271 | 0.345461 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.9826 | −0.631276 | −0.315638 | − | 0.948880i | \(-0.602219\pi\) | ||||
−0.315638 | + | 0.948880i | \(0.602219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.36706 | 0.132784 | 0.0663919 | − | 0.997794i | \(-0.478851\pi\) | ||||
0.0663919 | + | 0.997794i | \(0.478851\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0950231 | 0.00374153 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.5839 | 0.534039 | 0.267019 | − | 0.963691i | \(-0.413961\pi\) | ||||
0.267019 | + | 0.963691i | \(0.413961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.7858 | −1.64024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.0701 | 1.41370 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.3754 | −0.953881 | −0.476941 | − | 0.878936i | \(-0.658254\pi\) | ||||
−0.476941 | + | 0.878936i | \(0.658254\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.64620 | 0.142252 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.9766 | 1.63518 | 0.817589 | − | 0.575803i | \(-0.195310\pi\) | ||||
0.817589 | + | 0.575803i | \(0.195310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.8004 | −1.54805 | −0.774027 | − | 0.633152i | \(-0.781761\pi\) | ||||
−0.774027 | + | 0.633152i | \(0.781761\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.9149 | 1.35598 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 42.1853 | 1.63588 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.31255 | −0.128262 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.3133 | 1.09465 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 54.1791 | 2.09156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.60095 | 0.0617120 | 0.0308560 | − | 0.999524i | \(-0.490177\pi\) | ||||
0.0308560 | + | 0.999524i | \(0.490177\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.52044 | 0.327467 | 0.163734 | − | 0.986505i | \(-0.447646\pi\) | ||||
0.163734 | + | 0.986505i | \(0.447646\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.7462 | 1.02642 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.9118 | −0.494779 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.7050 | −1.59580 | −0.797899 | − | 0.602791i | \(-0.794055\pi\) | ||||
−0.797899 | + | 0.602791i | \(0.794055\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.2494 | −0.773690 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.6814 | −0.712741 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −44.3398 | −1.68921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.01703 | −0.228899 | −0.114449 | − | 0.993429i | \(-0.536510\pi\) | ||||
−0.114449 | + | 0.993429i | \(0.536510\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.6344 | 0.707861 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.61658 | −0.213049 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.20693 | 0.159349 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.2353 | 0.462782 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.51347 | −0.359319 | −0.179659 | − | 0.983729i | \(-0.557500\pi\) | ||||
−0.179659 | + | 0.983729i | \(0.557500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.3872 | 0.957496 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.39905 | −0.316327 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −50.5547 | −1.90131 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.8187 | 1.04475 | 0.522376 | − | 0.852715i | \(-0.325046\pi\) | ||||
0.522376 | + | 0.852715i | \(0.325046\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.59395 | 0.322298 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.18153 | −0.268950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0935 | 0.901047 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.2977 | −0.533956 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.1729 | 1.42361 | 0.711805 | − | 0.702377i | \(-0.247878\pi\) | ||||
0.711805 | + | 0.702377i | \(0.247878\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8434 | −0.403828 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.22604 | −0.157168 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.31255 | 0.123025 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.3738 | −1.64573 | −0.822867 | − | 0.568234i | \(-0.807627\pi\) | ||||
−0.822867 | + | 0.568234i | \(0.807627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.510885 | −0.0188957 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.5639 | 1.42439 | 0.712195 | − | 0.701982i | \(-0.247701\pi\) | ||||
0.712195 | + | 0.701982i | \(0.247701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.2268 | −0.672305 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.0308 | 1.32721 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.9275 | −1.21126 | −0.605629 | − | 0.795747i | \(-0.707078\pi\) | ||||
−0.605629 | + | 0.795747i | \(0.707078\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −54.5441 | −2.00373 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.09739 | 0.187005 | 0.0935025 | − | 0.995619i | \(-0.470194\pi\) | ||||
0.0935025 | + | 0.995619i | \(0.470194\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.226041 | 0.00828149 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.37642 | −0.269889 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.0529 | 0.367324 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.9611 | −0.436466 | −0.218233 | − | 0.975897i | \(-0.570029\pi\) | ||||
−0.218233 | + | 0.975897i | \(0.570029\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.4015 | 0.561263 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.2353 | 0.372501 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.87805 | −0.359024 | −0.179512 | − | 0.983756i | \(-0.557452\pi\) | ||||
−0.179512 | + | 0.983756i | \(0.557452\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.71008 | −0.134667 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.9064 | 1.15661 | 0.578303 | − | 0.815822i | \(-0.303715\pi\) | ||||
0.578303 | + | 0.815822i | \(0.303715\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −62.4322 | −2.26020 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.37642 | 0.194385 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −73.1413 | −2.64098 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.75907 | −0.315860 | −0.157930 | − | 0.987450i | \(-0.550482\pi\) | ||||
−0.157930 | + | 0.987450i | \(0.550482\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.7367 | −0.710800 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.1997 | −0.366859 | −0.183430 | − | 0.983033i | \(-0.558720\pi\) | ||||
−0.183430 | + | 0.983033i | \(0.558720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.18153 | 0.257968 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.1815 | −0.544634 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.57206 | −0.235469 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.3991 | −1.15933 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.31255 | −0.118381 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7755 | 0.491668 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.4576 | 0.836172 | 0.418086 | − | 0.908407i | \(-0.362701\pi\) | ||||
0.418086 | + | 0.908407i | \(0.362701\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.81588 | −0.349455 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 70.5517 | 2.50853 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 94.8343 | 3.36767 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.82773 | −0.242155 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.5265 | 1.71890 | 0.859449 | − | 0.511222i | \(-0.170807\pi\) | ||||
0.859449 | + | 0.511222i | \(0.170807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.1569 | 1.59754 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.29918 | −0.222571 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.5277 | −0.477382 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.02263 | 0.177024 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.92275 | 0.243692 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.1619 | 1.13075 | 0.565376 | − | 0.824833i | \(-0.308731\pi\) | ||||
0.565376 | + | 0.824833i | \(0.308731\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.2522 | 0.781380 | 0.390690 | − | 0.920522i | \(-0.372236\pi\) | ||||
0.390690 | + | 0.920522i | \(0.372236\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.22678 | 0.323597 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.33269 | −0.116739 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.798104 | 0.0279221 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 32.6173 | 1.13974 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.10472 | 0.0734553 | 0.0367277 | − | 0.999325i | \(-0.488307\pi\) | ||||
0.0367277 | + | 0.999325i | \(0.488307\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.1922 | −0.424993 | −0.212497 | − | 0.977162i | \(-0.568159\pi\) | ||||
−0.212497 | + | 0.977162i | \(0.568159\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.71008 | 0.129168 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.9593 | 0.415866 | 0.207933 | − | 0.978143i | \(-0.433326\pi\) | ||||
0.207933 | + | 0.978143i | \(0.433326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.71590 | −0.0943271 | −0.0471635 | − | 0.998887i | \(-0.515018\pi\) | ||||
−0.0471635 | + | 0.998887i | \(0.515018\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.33032 | 0.288976 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 97.9949 | 3.39532 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.5014 | 0.674874 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.18153 | −0.248230 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.9457 | 1.03384 | 0.516920 | − | 0.856033i | \(-0.327078\pi\) | ||||
0.516920 | + | 0.856033i | \(0.327078\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.0270 | −0.621622 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.1451 | 0.556068 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.1730 | 1.00358 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.8861 | −0.477130 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.5550 | −0.980004 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.02263 | 0.103614 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.02437 | 0.240510 | 0.120255 | − | 0.992743i | \(-0.461629\pi\) | ||||
0.120255 | + | 0.992743i | \(0.461629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.39905 | −0.287242 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.56799 | −0.121880 | −0.0609401 | − | 0.998141i | \(-0.519410\pi\) | ||||
−0.0609401 | + | 0.998141i | \(0.519410\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.5711 | 0.770116 | 0.385058 | − | 0.922892i | \(-0.374181\pi\) | ||||
0.385058 | + | 0.922892i | \(0.374181\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.93009 | 0.133937 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.2607 | −0.655642 | −0.327821 | − | 0.944740i | \(-0.606314\pi\) | ||||
−0.327821 | + | 0.944740i | \(0.606314\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.0453 | −0.545555 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.9059 | −0.404347 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.8842 | −1.08160 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.0678 | 2.13697 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.32514 | −0.180229 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.02263 | −0.169796 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.4441 | 0.892953 | 0.446477 | − | 0.894795i | \(-0.352679\pi\) | ||||
0.446477 | + | 0.894795i | \(0.352679\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.5836 | −0.862914 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.2630 | 0.918513 | 0.459256 | − | 0.888304i | \(-0.348116\pi\) | ||||
0.459256 | + | 0.888304i | \(0.348116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.3469 | 0.852992 | 0.426496 | − | 0.904490i | \(-0.359748\pi\) | ||||
0.426496 | + | 0.904490i | \(0.359748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.2628 | −0.378594 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.1308 | 1.61607 | 0.808037 | − | 0.589132i | \(-0.200530\pi\) | ||||
0.808037 | + | 0.589132i | \(0.200530\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 59.8408 | 2.00699 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.71008 | −0.124292 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −70.5441 | −2.36067 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.1730 | 0.473752 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.49408 | −0.216831 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.7891 | 0.793412 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.7088 | 1.22295 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.477266 | −0.0158824 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.03114 | 0.134000 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.4071 | 0.611199 | 0.305599 | − | 0.952160i | \(-0.401143\pi\) | ||||
0.305599 | + | 0.952160i | \(0.401143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0654 | 0.333848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.5984 | 1.34508 | 0.672542 | − | 0.740059i | \(-0.265203\pi\) | ||||
0.672542 | + | 0.740059i | \(0.265203\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.3671 | 0.905720 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.6032 | 0.482767 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.5485 | 0.842767 | 0.421383 | − | 0.906883i | \(-0.361545\pi\) | ||||
0.421383 | + | 0.906883i | \(0.361545\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.58910 | 0.151216 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −56.7109 | −1.86666 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.02263 | −0.0993834 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.15890 | 0.0709076 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.7588 | 0.615456 | 0.307728 | − | 0.951474i | \(-0.400431\pi\) | ||||
0.307728 | + | 0.951474i | \(0.400431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −153.088 | −5.01725 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.8360 | 0.780356 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.9470 | −0.652336 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.4697 | 0.342031 | 0.171015 | − | 0.985268i | \(-0.445295\pi\) | ||||
0.171015 | + | 0.985268i | \(0.445295\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.0747 | −0.850914 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.1569 | −0.494100 | −0.247050 | − | 0.969003i | \(-0.579461\pi\) | ||||
−0.247050 | + | 0.969003i | \(0.579461\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.782477 | −0.0254810 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.02263 | 0.163386 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.2362 | −0.365127 | −0.182563 | − | 0.983194i | \(-0.558440\pi\) | ||||
−0.182563 | + | 0.983194i | \(0.558440\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.6787 | −0.768643 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.7367 | −0.510298 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.5317 | −0.470727 | −0.235363 | − | 0.971907i | \(-0.575628\pi\) | ||||
−0.235363 | + | 0.971907i | \(0.575628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.58910 | 0.277937 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.2898 | 0.397273 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 101.705 | 3.28423 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.5744 | 0.663689 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.00152 | −0.0644980 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.8434 | −0.542207 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.8670 | −0.767512 | −0.383756 | − | 0.923434i | \(-0.625370\pi\) | ||||
−0.383756 | + | 0.923434i | \(0.625370\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 45.1569 | 1.45065 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.8670 | 0.541286 | 0.270643 | − | 0.962680i | \(-0.412764\pi\) | ||||
0.270643 | + | 0.962680i | \(0.412764\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.2100 | 0.904370 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.49408 | 0.207977 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.3073 | −0.905629 | −0.452815 | − | 0.891605i | \(-0.649580\pi\) | ||||
−0.452815 | + | 0.891605i | \(0.649580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.3705 | 0.746923 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.4302 | 0.396866 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.45949 | 0.237921 | 0.118960 | − | 0.992899i | \(-0.462044\pi\) | ||||
0.118960 | + | 0.992899i | \(0.462044\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0422192 | 0.00134522 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.1853 | 1.34277 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0950231 | 0.00302156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.6469 | 1.03706 | 0.518532 | − | 0.855058i | \(-0.326479\pi\) | ||||
0.518532 | + | 0.855058i | \(0.326479\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.3427 | 1.08983 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.1589 | 0.448867 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.7800 | 0.911473 | 0.455737 | − | 0.890115i | \(-0.349376\pi\) | ||||
0.455737 | + | 0.890115i | \(0.349376\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.02263 | 0.0956317 |
(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.w.1.1 | ✓ | 5 | |
3.2 | odd | 2 | 8280.2.a.br.1.1 | 5 | |||
4.3 | odd | 2 | 5520.2.a.cc.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.w.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
5520.2.a.cc.1.5 | 5 | 4.3 | odd | 2 | |||
8280.2.a.br.1.1 | 5 | 3.2 | odd | 2 |