Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 3 x^{10} - 19 x^{9} + 55 x^{8} + 128 x^{7} - 361 x^{6} - 343 x^{5} + 1012 x^{4} + 215 x^{3} - 1090 x^{2} + 240 x + 160 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.48144\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 2.48144 | 1.43266 | 0.716331 | − | 0.697761i | \(-0.245820\pi\) | ||||
0.716331 | + | 0.697761i | \(0.245820\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.56116 | 0.698173 | 0.349087 | − | 0.937090i | \(-0.386492\pi\) | ||||
0.349087 | + | 0.937090i | \(0.386492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.15756 | 1.05252 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.87394 | 1.00025 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.17712 | 0.285494 | 0.142747 | − | 0.989759i | \(-0.454406\pi\) | ||||
0.142747 | + | 0.989759i | \(0.454406\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.31074 | 1.44778 | 0.723892 | − | 0.689914i | \(-0.242351\pi\) | ||||
0.723892 | + | 0.689914i | \(0.242351\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.48144 | −0.541495 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.27004 | 0.890366 | 0.445183 | − | 0.895440i | \(-0.353139\pi\) | ||||
0.445183 | + | 0.895440i | \(0.353139\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56277 | −0.512554 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.390980 | 0.0752440 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.71487 | −1.24692 | −0.623460 | − | 0.781855i | \(-0.714274\pi\) | ||||
−0.623460 | + | 0.781855i | \(0.714274\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.78667 | −0.680106 | −0.340053 | − | 0.940406i | \(-0.610445\pi\) | ||||
−0.340053 | + | 0.940406i | \(0.610445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.48144 | 0.431964 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.56116 | −0.263885 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.14323 | 0.352345 | 0.176172 | − | 0.984359i | \(-0.443628\pi\) | ||||
0.176172 | + | 0.984359i | \(0.443628\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.48144 | 0.397349 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.7416 | 1.83372 | 0.916861 | − | 0.399206i | \(-0.130714\pi\) | ||||
0.916861 | + | 0.399206i | \(0.130714\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.31235 | −0.657627 | −0.328814 | − | 0.944395i | \(-0.606649\pi\) | ||||
−0.328814 | + | 0.944395i | \(0.606649\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.92947 | 0.734842 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.97107 | −0.579240 | −0.289620 | − | 0.957142i | \(-0.593529\pi\) | ||||
−0.289620 | + | 0.957142i | \(0.593529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.92097 | 0.409017 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.15591 | 0.570858 | 0.285429 | − | 0.958400i | \(-0.407864\pi\) | ||||
0.285429 | + | 0.958400i | \(0.407864\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.56116 | 0.210507 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.6597 | 2.07418 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.96907 | 0.777106 | 0.388553 | − | 0.921426i | \(-0.372975\pi\) | ||||
0.388553 | + | 0.921426i | \(0.372975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.28945 | 0.805282 | 0.402641 | − | 0.915358i | \(-0.368092\pi\) | ||||
0.402641 | + | 0.915358i | \(0.368092\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.15756 | −0.397815 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.56116 | 0.193638 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.3339 | 1.75116 | 0.875582 | − | 0.483070i | \(-0.160478\pi\) | ||||
0.875582 | + | 0.483070i | \(0.160478\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.5959 | 1.27559 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0156182 | −0.00185353 | −0.000926767 | − | 1.00000i | \(-0.500295\pi\) | ||||
−0.000926767 | 1.00000i | \(0.500295\pi\) | ||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.3588 | 1.91466 | 0.957328 | − | 0.289002i | \(-0.0933235\pi\) | ||||
0.957328 | + | 0.289002i | \(0.0933235\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.35937 | −0.734317 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.88084 | −0.324119 | −0.162060 | − | 0.986781i | \(-0.551814\pi\) | ||||
−0.162060 | + | 0.986781i | \(0.551814\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.50249 | −0.944721 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.75310 | −0.521720 | −0.260860 | − | 0.965377i | \(-0.584006\pi\) | ||||
−0.260860 | + | 0.965377i | \(0.584006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.83768 | 0.199325 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.6626 | −1.78641 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.87297 | 0.622533 | 0.311267 | − | 0.950323i | \(-0.399247\pi\) | ||||
0.311267 | + | 0.950323i | \(0.399247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.39640 | −0.974362 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.85210 | 1.01080 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2741 | −1.34778 | −0.673892 | − | 0.738830i | \(-0.735379\pi\) | ||||
−0.673892 | + | 0.738830i | \(0.735379\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.15756 | 0.317347 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.8013 | 1.07477 | 0.537384 | − | 0.843338i | \(-0.319413\pi\) | ||||
0.537384 | + | 0.843338i | \(0.319413\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9337 | 1.66852 | 0.834262 | − | 0.551368i | \(-0.185894\pi\) | ||||
0.834262 | + | 0.551368i | \(0.185894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.87394 | −0.378058 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.72746 | 0.747041 | 0.373521 | − | 0.927622i | \(-0.378150\pi\) | ||||
0.373521 | + | 0.927622i | \(0.378150\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.625583 | 0.0599200 | 0.0299600 | − | 0.999551i | \(-0.490462\pi\) | ||||
0.0299600 | + | 0.999551i | \(0.490462\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.31830 | 0.504791 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.6749 | −1.28643 | −0.643213 | − | 0.765688i | \(-0.722399\pi\) | ||||
−0.643213 | + | 0.765688i | \(0.722399\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.66623 | 0.621630 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.15756 | 0.291917 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.17712 | −0.107907 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 29.1360 | 2.62710 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8067 | −1.05602 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.30079 | −0.204162 | −0.102081 | − | 0.994776i | \(-0.532550\pi\) | ||||
−0.102081 | + | 0.994776i | \(0.532550\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.7009 | −0.942158 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.90098 | 0.602941 | 0.301471 | − | 0.953475i | \(-0.402522\pi\) | ||||
0.301471 | + | 0.953475i | \(0.402522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.31074 | −0.547211 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.610383 | 0.0525334 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.25875 | −0.534721 | −0.267361 | − | 0.963597i | \(-0.586151\pi\) | ||||
−0.267361 | + | 0.963597i | \(0.586151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.04281 | −0.173269 | −0.0866346 | − | 0.996240i | \(-0.527611\pi\) | ||||
−0.0866346 | + | 0.996240i | \(0.527611\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.85398 | −0.829855 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4830 | −0.870566 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.48144 | 0.204666 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.3696 | −1.25913 | −0.629564 | − | 0.776949i | \(-0.716766\pi\) | ||||
−0.629564 | + | 0.776949i | \(0.716766\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.7034 | −1.60344 | −0.801722 | − | 0.597697i | \(-0.796082\pi\) | ||||
−0.801722 | + | 0.597697i | \(0.796082\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.71684 | 0.300489 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.91161 | −0.474832 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.8416 | −0.865256 | −0.432628 | − | 0.901572i | \(-0.642414\pi\) | ||||
−0.432628 | + | 0.901572i | \(0.642414\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.3126 | 0.817846 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.27004 | −0.336527 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3512 | −0.967423 | −0.483711 | − | 0.875228i | \(-0.660712\pi\) | ||||
−0.483711 | + | 0.875228i | \(0.660712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.87394 | 0.301586 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.57583 | −0.276706 | −0.138353 | − | 0.990383i | \(-0.544181\pi\) | ||||
−0.138353 | + | 0.990383i | \(0.544181\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.9266 | 1.52382 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.10474 | 0.388106 | 0.194053 | − | 0.980991i | \(-0.437837\pi\) | ||||
0.194053 | + | 0.980991i | \(0.437837\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.56277 | 0.193727 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.8119 | 1.11333 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.46690 | −0.184385 | −0.0921924 | − | 0.995741i | \(-0.529387\pi\) | ||||
−0.0921924 | + | 0.995741i | \(0.529387\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5309 | −0.782755 | −0.391378 | − | 0.920230i | \(-0.628001\pi\) | ||||
−0.391378 | + | 0.920230i | \(0.628001\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.6069 | 1.15370 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.34593 | 0.245998 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.17712 | 0.0860798 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.390980 | −0.0284396 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.58755 | 0.404301 | 0.202150 | − | 0.979354i | \(-0.435207\pi\) | ||||
0.202150 | + | 0.979354i | \(0.435207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5914 | 0.762389 | 0.381194 | − | 0.924495i | \(-0.375513\pi\) | ||||
0.381194 | + | 0.924495i | \(0.375513\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.87394 | 0.277418 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.2836 | 1.30265 | 0.651326 | − | 0.758798i | \(-0.274213\pi\) | ||||
0.651326 | + | 0.758798i | \(0.274213\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2091 | 0.936368 | 0.468184 | − | 0.883631i | \(-0.344908\pi\) | ||||
0.468184 | + | 0.883631i | \(0.344908\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 35.5687 | 2.50883 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.71487 | 0.471291 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.3305 | 1.28026 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.4829 | 0.937128 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.31074 | 0.436523 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.59626 | 0.247577 | 0.123788 | − | 0.992309i | \(-0.460496\pi\) | ||||
0.123788 | + | 0.992309i | \(0.460496\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0387556 | −0.00265549 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.73228 | −0.459138 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.78667 | 0.257056 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 40.5935 | 2.74306 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.17712 | 0.0791819 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.67011 | −0.111839 | −0.0559194 | − | 0.998435i | \(-0.517809\pi\) | ||||
−0.0559194 | + | 0.998435i | \(0.517809\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.09211 | −0.539474 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.32857 | 0.353670 | 0.176835 | − | 0.984241i | \(-0.443414\pi\) | ||||
0.176835 | + | 0.984241i | \(0.443414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.02612 | 0.0678078 | 0.0339039 | − | 0.999425i | \(-0.489206\pi\) | ||||
0.0339039 | + | 0.999425i | \(0.489206\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.48144 | −0.163267 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.41024 | 0.288924 | 0.144462 | − | 0.989510i | \(-0.453855\pi\) | ||||
0.144462 | + | 0.989510i | \(0.453855\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.19948 | −0.404410 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.14863 | −0.464354 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.3307 | −1.31508 | −0.657542 | − | 0.753417i | \(-0.728404\pi\) | ||||
−0.657542 | + | 0.753417i | \(0.728404\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7834 | 0.759036 | 0.379518 | − | 0.925184i | \(-0.376090\pi\) | ||||
0.379518 | + | 0.925184i | \(0.376090\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2714 | −1.42871 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.56116 | 0.0997390 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.31074 | 0.401543 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.7945 | −0.747448 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.399012 | −0.0251854 | −0.0125927 | − | 0.999921i | \(-0.504008\pi\) | ||||
−0.0125927 | + | 0.999921i | \(0.504008\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.27004 | 0.268455 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.56010 | 0.285565 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.1347 | −1.13121 | −0.565605 | − | 0.824676i | \(-0.691357\pi\) | ||||
−0.565605 | + | 0.824676i | \(0.691357\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.14323 | −0.133174 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.2026 | −1.31241 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.5704 | −0.960110 | −0.480055 | − | 0.877238i | \(-0.659383\pi\) | ||||
−0.480055 | + | 0.877238i | \(0.659383\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.48805 | 0.398558 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5734 | 0.891880 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.238391 | 0.0145350 | 0.00726748 | − | 0.999974i | \(-0.497687\pi\) | ||||
0.00726748 | + | 0.999974i | \(0.497687\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.7051 | 1.74371 | 0.871857 | − | 0.489761i | \(-0.162916\pi\) | ||||
0.871857 | + | 0.489761i | \(0.162916\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.48144 | −0.150184 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.56277 | −0.154541 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.48559 | 0.509850 | 0.254925 | − | 0.966961i | \(-0.417949\pi\) | ||||
0.254925 | + | 0.966961i | \(0.417949\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.9566 | −0.715825 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.618209 | −0.0368792 | −0.0184396 | − | 0.999830i | \(-0.505870\pi\) | ||||
−0.0184396 | + | 0.999830i | \(0.505870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.1327 | 1.67231 | 0.836157 | − | 0.548490i | \(-0.184797\pi\) | ||||
0.836157 | + | 0.548490i | \(0.184797\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.4474 | 1.44814 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.7416 | −0.693082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6144 | −0.918493 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.9390 | −1.93092 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.3144 | −0.719413 | −0.359707 | − | 0.933065i | \(-0.617123\pi\) | ||||
−0.359707 | + | 0.933065i | \(0.617123\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.31868 | 0.542555 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.390980 | 0.0226869 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.27004 | 0.246943 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.31235 | 0.248560 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.8028 | 1.53978 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.81886 | 0.562226 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5236 | −1.00013 | −0.500064 | − | 0.865989i | \(-0.666690\pi\) | ||||
−0.500064 | + | 0.865989i | \(0.666690\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 42.0199 | 2.39043 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.0147336 | 0.000835468 0 | 0.000417734 | − | 1.00000i | \(-0.499867\pi\) | ||||
0.000417734 | 1.00000i | \(0.499867\pi\) | ||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.73651 | −0.0981531 | −0.0490766 | − | 0.998795i | \(-0.515628\pi\) | ||||
−0.0490766 | + | 0.998795i | \(0.515628\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.92947 | −0.277744 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.6520 | −0.879104 | −0.439552 | − | 0.898217i | \(-0.644863\pi\) | ||||
−0.439552 | + | 0.898217i | \(0.644863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.71487 | −0.375960 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.1752 | 1.07026 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.42852 | 0.413334 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.56277 | −0.142157 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.55235 | 0.0858451 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.97107 | 0.218932 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.0136 | −1.26494 | −0.632471 | − | 0.774584i | \(-0.717959\pi\) | ||||
−0.632471 | + | 0.774584i | \(0.717959\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.76738 | 0.370850 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.3775 | 1.22262 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7006 | 0.909738 | 0.454869 | − | 0.890558i | \(-0.349686\pi\) | ||||
0.454869 | + | 0.890558i | \(0.349686\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −33.9335 | −1.84301 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.78667 | −0.205060 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.5419 | 0.890585 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4530 | 0.936927 | 0.468463 | − | 0.883483i | \(-0.344808\pi\) | ||||
0.468463 | + | 0.883483i | \(0.344808\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.0812 | −1.82432 | −0.912161 | − | 0.409831i | \(-0.865588\pi\) | ||||
−0.912161 | + | 0.409831i | \(0.865588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.390980 | 0.0208689 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.72405 | −0.144986 | −0.0724932 | − | 0.997369i | \(-0.523096\pi\) | ||||
−0.0724932 | + | 0.997369i | \(0.523096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0243825 | −0.00129409 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.92097 | −0.154594 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.3466 | 0.651630 | 0.325815 | − | 0.945433i | \(-0.394361\pi\) | ||||
0.325815 | + | 0.945433i | \(0.394361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.8255 | 1.09608 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.48144 | 0.130242 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.5388 | 1.33676 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.46233 | 0.180732 | 0.0903662 | − | 0.995909i | \(-0.471196\pi\) | ||||
0.0903662 | + | 0.995909i | \(0.471196\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 37.0747 | 1.93003 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.15591 | −0.215764 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6744 | −0.552701 | −0.276350 | − | 0.961057i | \(-0.589125\pi\) | ||||
−0.276350 | + | 0.961057i | \(0.589125\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.2977 | −1.51293 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.71487 | −0.345833 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6381 | −0.803276 | −0.401638 | − | 0.915799i | \(-0.631559\pi\) | ||||
−0.401638 | + | 0.915799i | \(0.631559\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.70928 | −0.292495 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.9362 | 0.967594 | 0.483797 | − | 0.875180i | \(-0.339257\pi\) | ||||
0.483797 | + | 0.875180i | \(0.339257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.56116 | −0.0795642 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.6165 | −0.692166 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.50949 | 0.127236 | 0.0636182 | − | 0.997974i | \(-0.479736\pi\) | ||||
0.0636182 | + | 0.997974i | \(0.479736\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.02637 | 0.254194 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.1244 | 0.863811 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.49745 | −0.226292 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.6202 | −0.633390 | −0.316695 | − | 0.948528i | \(-0.602573\pi\) | ||||
−0.316695 | + | 0.948528i | \(0.602573\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.6597 | −0.783968 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.6824 | 0.783139 | 0.391570 | − | 0.920148i | \(-0.371932\pi\) | ||||
0.391570 | + | 0.920148i | \(0.371932\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.78667 | −0.188627 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.2738 | −0.659579 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.14323 | 0.106236 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5252 | −0.668780 | −0.334390 | − | 0.942435i | \(-0.608530\pi\) | ||||
−0.334390 | + | 0.942435i | \(0.608530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.5307 | −0.766075 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.96907 | −0.293719 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.42036 | −0.364251 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.06913 | −0.248236 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.3526 | 1.38512 | 0.692558 | − | 0.721362i | \(-0.256484\pi\) | ||||
0.692558 | + | 0.721362i | \(0.256484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.94894 | 0.484882 | 0.242441 | − | 0.970166i | \(-0.422052\pi\) | ||||
0.242441 | + | 0.970166i | \(0.422052\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.5389 | −0.609662 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.01670 | −0.146331 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.28945 | −0.304368 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.48144 | 0.119805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.81615 | −0.472827 | −0.236414 | − | 0.971652i | \(-0.575972\pi\) | ||||
−0.236414 | + | 0.971652i | \(0.575972\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.8631 | 1.09873 | 0.549366 | − | 0.835582i | \(-0.314869\pi\) | ||||
0.549366 | + | 0.835582i | \(0.314869\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −26.0130 | −1.24723 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.9471 | 1.28906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.74098 | 0.464912 | 0.232456 | − | 0.972607i | \(-0.425324\pi\) | ||||
0.232456 | + | 0.972607i | \(0.425324\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.15756 | 0.150360 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −41.0526 | −1.95047 | −0.975233 | − | 0.221178i | \(-0.929010\pi\) | ||||
−0.975233 | + | 0.221178i | \(0.929010\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.16866 | 0.434636 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −38.1388 | −1.80390 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.43267 | 0.445155 | 0.222578 | − | 0.974915i | \(-0.428553\pi\) | ||||
0.222578 | + | 0.974915i | \(0.428553\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.7416 | 0.552888 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −48.8930 | −2.29719 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.56116 | −0.0731884 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.5005 | −0.631528 | −0.315764 | − | 0.948838i | \(-0.602261\pi\) | ||||
−0.315764 | + | 0.948838i | \(0.602261\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.460231 | 0.0214818 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.78455 | −0.0831148 | −0.0415574 | − | 0.999136i | \(-0.513232\pi\) | ||||
−0.0415574 | + | 0.999136i | \(0.513232\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.84604 | −0.178741 | −0.0893704 | − | 0.995998i | \(-0.528485\pi\) | ||||
−0.0893704 | + | 0.995998i | \(0.528485\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.6693 | −0.680273 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.33881 | −0.247050 | −0.123525 | − | 0.992341i | \(-0.539420\pi\) | ||||
−0.123525 | + | 0.992341i | \(0.539420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.3339 | −0.661878 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.9029 | −1.23962 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.31235 | −0.198282 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.1730 | −0.742067 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.1225 | 0.600839 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.7598 | −0.674395 | −0.337197 | − | 0.941434i | \(-0.609479\pi\) | ||||
−0.337197 | + | 0.941434i | \(0.609479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.14323 | 0.0977229 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.5959 | −0.482129 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.7231 | −0.940987 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6715 | −0.755456 | −0.377728 | − | 0.925917i | \(-0.623295\pi\) | ||||
−0.377728 | + | 0.925917i | \(0.623295\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.6489 | −1.38599 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.3758 | 1.55136 | 0.775680 | − | 0.631127i | \(-0.217407\pi\) | ||||
0.775680 | + | 0.631127i | \(0.217407\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.90423 | −0.355989 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.92947 | 0.221563 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0156182 | 0.000700570 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.2659 | 1.17582 | 0.587912 | − | 0.808925i | \(-0.299950\pi\) | ||||
0.587912 | + | 0.808925i | \(0.299950\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.87322 | −0.396426 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.2508 | 1.83928 | 0.919640 | − | 0.392762i | \(-0.128480\pi\) | ||||
0.919640 | + | 0.392762i | \(0.128480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.8626 | 0.750374 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.48144 | 0.110205 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.2542 | 0.498833 | 0.249417 | − | 0.968396i | \(-0.419761\pi\) | ||||
0.249417 | + | 0.968396i | \(0.419761\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.3588 | −0.723672 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.46737 | 0.108937 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.4362 | 1.16492 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.97107 | −0.174647 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.6671 | 0.556025 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.82010 | 0.0797399 | 0.0398700 | − | 0.999205i | \(-0.487306\pi\) | ||||
0.0398700 | + | 0.999205i | \(0.487306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6531 | 0.684463 | 0.342231 | − | 0.939616i | \(-0.388817\pi\) | ||||
0.342231 | + | 0.939616i | \(0.388817\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.35937 | 0.277546 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.45738 | −0.194166 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.76672 | −0.207249 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.8477 | 0.817920 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.7416 | 0.508583 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0638 | 0.521564 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.12147 | −0.264161 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.1889 | −1.46990 | −0.734948 | − | 0.678123i | \(-0.762794\pi\) | ||||
−0.734948 | + | 0.678123i | \(0.762794\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.1318 | −1.12142 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.976637 | 0.0418345 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.5322 | 1.56200 | 0.781001 | − | 0.624529i | \(-0.214709\pi\) | ||||
0.781001 | + | 0.624529i | \(0.214709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.8593 | 0.847575 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.3758 | −1.80527 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.88084 | 0.122506 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.30274 | 0.352432 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.84658 | −0.162985 | −0.0814925 | − | 0.996674i | \(-0.525969\pi\) | ||||
−0.0814925 | + | 0.996674i | \(0.525969\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.31235 | −0.182393 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.92097 | 0.123323 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.2475 | −0.769038 | −0.384519 | − | 0.923117i | \(-0.625633\pi\) | ||||
−0.384519 | + | 0.923117i | \(0.625633\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.3487 | −0.898148 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.50249 | 0.357071 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.5637 | −1.23937 | −0.619687 | − | 0.784849i | \(-0.712740\pi\) | ||||
−0.619687 | + | 0.784849i | \(0.712740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.2496 | 0.470781 | 0.235390 | − | 0.971901i | \(-0.424363\pi\) | ||||
0.235390 | + | 0.971901i | \(0.424363\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8652 | 0.579226 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.9431 | −0.456361 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.2782 | −0.802562 | −0.401281 | − | 0.915955i | \(-0.631435\pi\) | ||||
−0.401281 | + | 0.915955i | \(0.631435\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.2821 | 1.09225 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.75310 | 0.197192 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.15591 | 0.172120 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.92947 | 0.203808 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.8675 | −1.02639 | −0.513196 | − | 0.858271i | \(-0.671539\pi\) | ||||
−0.513196 | + | 0.858271i | \(0.671539\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.8967 | −0.984646 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 45.3697 | 1.86626 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.3691 | 1.49350 | 0.746749 | − | 0.665106i | \(-0.231614\pi\) | ||||
0.746749 | + | 0.665106i | \(0.231614\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.83768 | −0.0753376 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 32.7776 | 1.34150 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.250843 | 0.0102492 | 0.00512458 | − | 0.999987i | \(-0.498369\pi\) | ||||
0.00512458 | + | 0.999987i | \(0.498369\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.7065 | 1.08938 | 0.544691 | − | 0.838637i | \(-0.316647\pi\) | ||||
0.544691 | + | 0.838637i | \(0.316647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.2601 | 1.84314 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.56116 | 0.0634703 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.2503 | 1.51194 | 0.755972 | − | 0.654604i | \(-0.227165\pi\) | ||||
0.755972 | + | 0.654604i | \(0.227165\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.6626 | 0.675201 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.97107 | −0.160652 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.9308 | −1.33006 | −0.665032 | − | 0.746815i | \(-0.731582\pi\) | ||||
−0.665032 | + | 0.746815i | \(0.731582\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 45.4860 | 1.83417 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.9539 | −1.12538 | −0.562691 | − | 0.826667i | \(-0.690234\pi\) | ||||
−0.562691 | + | 0.826667i | \(0.690234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.3143 | −1.25863 | −0.629313 | − | 0.777152i | \(-0.716664\pi\) | ||||
−0.629313 | + | 0.777152i | \(0.716664\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.66950 | 0.0669947 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.87297 | −0.235295 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.61835 | −0.224734 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.6597 | 0.625390 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.52285 | 0.100592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.55579 | 0.101744 | 0.0508722 | − | 0.998705i | \(-0.483800\pi\) | ||||
0.0508722 | + | 0.998705i | \(0.483800\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.92392 | 0.354694 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.59191 | −0.142541 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0493153 | −0.00195088 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.5791 | −1.60278 | −0.801389 | − | 0.598144i | \(-0.795905\pi\) | ||||
−0.801389 | + | 0.598144i | \(0.795905\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.4614 | 0.451992 | 0.225996 | − | 0.974128i | \(-0.427436\pi\) | ||||
0.225996 | + | 0.974128i | \(0.427436\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.7058 | −0.657789 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.1042 | −1.06557 | −0.532787 | − | 0.846249i | \(-0.678855\pi\) | ||||
−0.532787 | + | 0.846249i | \(0.678855\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.96907 | 0.234306 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.39640 | 0.368274 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.9089 | −1.48349 | −0.741745 | − | 0.670682i | \(-0.766002\pi\) | ||||
−0.741745 | + | 0.670682i | \(0.766002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.7736 | 0.420957 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 51.6540 | 2.01522 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.2350 | −0.905105 | −0.452553 | − | 0.891738i | \(-0.649487\pi\) | ||||
−0.452553 | + | 0.891738i | \(0.649487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.7507 | −0.729318 | −0.364659 | − | 0.931141i | \(-0.618814\pi\) | ||||
−0.364659 | + | 0.931141i | \(0.618814\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.92097 | 0.113441 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.85210 | −0.382048 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.6728 | −1.11021 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.14428 | −0.160227 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.28945 | 0.242802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.2275 | 1.12664 | 0.563318 | − | 0.826240i | \(-0.309525\pi\) | ||||
0.563318 | + | 0.826240i | \(0.309525\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00199 | −0.0385666 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.2094 | −0.930441 | −0.465221 | − | 0.885195i | \(-0.654025\pi\) | ||||
−0.465221 | + | 0.885195i | \(0.654025\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.2741 | 0.509415 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.2226 | 0.506689 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.4345 | 1.58545 | 0.792724 | − | 0.609581i | \(-0.208662\pi\) | ||||
0.792724 | + | 0.609581i | \(0.208662\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.77093 | −0.373328 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.54625 | 0.0971456 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.15591 | 0.158327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.8913 | 0.756701 | 0.378351 | − | 0.925662i | \(-0.376491\pi\) | ||||
0.378351 | + | 0.925662i | \(0.376491\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.15756 | −0.119946 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.18917 | −0.120972 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.8213 | 0.523518 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.9438 | 0.413931 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.82418 | 0.144437 | 0.0722187 | − | 0.997389i | \(-0.476992\pi\) | ||||
0.0722187 | + | 0.997389i | \(0.476992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.5254 | 0.510119 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.3837 | −0.579383 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.8013 | −0.406224 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.53919 | 0.208029 | 0.104014 | − | 0.994576i | \(-0.466831\pi\) | ||||
0.104014 | + | 0.994576i | \(0.466831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.09642 | −0.341142 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.1692 | −0.605543 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.56116 | 0.0583842 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −50.4495 | −1.88407 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.1864 | 1.68517 | 0.842585 | − | 0.538564i | \(-0.181033\pi\) | ||||
0.842585 | + | 0.538564i | \(0.181033\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.9337 | −0.630643 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.2399 | 1.08744 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.2087 | 0.639114 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.6293 | −1.76647 | −0.883236 | − | 0.468929i | \(-0.844640\pi\) | ||||
−0.883236 | + | 0.468929i | \(0.844640\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.7577 | −1.10214 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.07617 | −0.187749 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.7008 | 0.875408 | 0.437704 | − | 0.899119i | \(-0.355792\pi\) | ||||
0.437704 | + | 0.899119i | \(0.355792\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.87394 | 0.142892 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.3339 | 0.527996 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.6597 | −1.90033 | −0.950167 | − | 0.311741i | \(-0.899088\pi\) | ||||
−0.950167 | + | 0.311741i | \(0.899088\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.6597 | 0.575275 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.3330 | −1.33293 | −0.666464 | − | 0.745537i | \(-0.732193\pi\) | ||||
−0.666464 | + | 0.745537i | \(0.732193\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.9945 | −0.879089 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.0082 | −0.549121 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.72746 | −0.282355 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.3407 | −0.669263 | −0.334631 | − | 0.942349i | \(-0.608612\pi\) | ||||
−0.334631 | + | 0.942349i | \(0.608612\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.990125 | −0.0360821 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.7603 | −1.11948 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.9776 | −1.34397 | −0.671987 | − | 0.740563i | \(-0.734559\pi\) | ||||
−0.671987 | + | 0.740563i | \(0.734559\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.5959 | 0.384606 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.89156 | −0.104819 | −0.0524094 | − | 0.998626i | \(-0.516690\pi\) | ||||
−0.0524094 | + | 0.998626i | \(0.516690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.625583 | −0.0226476 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.80259 | 0.209793 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.96907 | 0.215530 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.38294 | −0.158053 | −0.0790265 | − | 0.996873i | \(-0.525181\pi\) | ||||
−0.0790265 | + | 0.996873i | \(0.525181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.0002 | −1.62064 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.1000 | −1.01069 | −0.505344 | − | 0.862918i | \(-0.668634\pi\) | ||||
−0.505344 | + | 0.862918i | \(0.668634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.70436 | 0.348591 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.31830 | −0.190793 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 74.0979 | 2.65483 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0156182 | −0.000558862 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.62538 | −0.0938233 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.9255 | −0.604099 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.36322 | 0.262471 | 0.131235 | − | 0.991351i | \(-0.458106\pi\) | ||||
0.131235 | + | 0.991351i | \(0.458106\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.6370 | −1.37551 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6749 | 0.486223 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.28945 | 0.223345 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.0997 | 0.570998 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.93083 | 0.174659 | 0.0873295 | − | 0.996179i | \(-0.472167\pi\) | ||||
0.0873295 | + | 0.996179i | \(0.472167\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.67444 | −0.165370 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.5442 | 0.655229 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.3588 | 0.577291 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.66623 | −0.234954 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.591554 | 0.0208237 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.58531 | 0.0908945 | 0.0454473 | − | 0.998967i | \(-0.485529\pi\) | ||||
0.0454473 | + | 0.998967i | \(0.485529\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.721237 | −0.0253260 | −0.0126630 | − | 0.999920i | \(-0.504031\pi\) | ||||
−0.0126630 | + | 0.999920i | \(0.504031\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 71.2302 | 2.49815 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.2823 | −0.675429 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.2141 | −0.952102 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.15756 | −0.110334 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.9930 | −1.74477 | −0.872384 | − | 0.488821i | \(-0.837427\pi\) | ||||
−0.872384 | + | 0.488821i | \(0.837427\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.705645 | 0.0245972 | 0.0122986 | − | 0.999924i | \(-0.496085\pi\) | ||||
0.0122986 | + | 0.999924i | \(0.496085\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.35937 | −0.221405 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.4921 | 0.434393 | 0.217197 | − | 0.976128i | \(-0.430309\pi\) | ||||
0.217197 | + | 0.976128i | \(0.430309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.70790 | −0.0940493 | −0.0470246 | − | 0.998894i | \(-0.514974\pi\) | ||||
−0.0470246 | + | 0.998894i | \(0.514974\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.0565 | 0.730443 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.17712 | 0.0407849 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.58245 | −0.193189 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.48051 | −0.0511739 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.5682 | −0.537475 | −0.268738 | − | 0.963213i | \(-0.586606\pi\) | ||||
−0.268738 | + | 0.963213i | \(0.586606\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.0894 | 0.554809 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.53405 | −0.0528355 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.56116 | 0.0537056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 69.8096 | 2.39586 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.15169 | 0.313716 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.41907 | −0.322503 | −0.161251 | − | 0.986913i | \(-0.551553\pi\) | ||||
−0.161251 | + | 0.986913i | \(0.551553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.1086 | 1.06389 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.3585 | 0.524638 | 0.262319 | − | 0.964981i | \(-0.415513\pi\) | ||||
0.262319 | + | 0.964981i | \(0.415513\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.74147 | 0.298255 | 0.149128 | − | 0.988818i | \(-0.452354\pi\) | ||||
0.149128 | + | 0.988818i | \(0.452354\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.1360 | −0.992952 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.63880 | −0.157907 | −0.0789533 | − | 0.996878i | \(-0.525158\pi\) | ||||
−0.0789533 | + | 0.996878i | \(0.525158\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.96933 | 0.270965 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38.7462 | −1.31589 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.88084 | −0.0977257 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.3339 | 0.485685 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −41.9139 | −1.41857 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.8067 | 0.399140 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.5610 | −1.60602 | −0.803010 | − | 0.595966i | \(-0.796769\pi\) | ||||
−0.803010 | + | 0.595966i | \(0.796769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.5574 | −1.03068 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.7015 | 1.27020 | 0.635098 | − | 0.772432i | \(-0.280960\pi\) | ||||
0.635098 | + | 0.772432i | \(0.280960\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.9623 | 0.907353 | 0.453676 | − | 0.891167i | \(-0.350112\pi\) | ||||
0.453676 | + | 0.891167i | \(0.350112\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.1238 | 0.777298 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.7931 | 0.933200 | 0.466600 | − | 0.884468i | \(-0.345479\pi\) | ||||
0.466600 | + | 0.884468i | \(0.345479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.30079 | 0.0771661 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.50249 | −0.284844 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.0604 | −0.838614 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.85123 | −0.128733 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.5959 | 0.353786 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.4270 | 0.848037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.89202 | 0.162977 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.7009 | 0.356102 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.4404 | −0.546499 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.5750 | −1.34727 | −0.673636 | − | 0.739063i | \(-0.735268\pi\) | ||||
−0.673636 | + | 0.739063i | \(0.735268\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 34.1057 | 1.13121 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −59.0732 | −1.95718 | −0.978591 | − | 0.205813i | \(-0.934016\pi\) | ||||
−0.978591 | + | 0.205813i | \(0.934016\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.75310 | −0.157304 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.3649 | 0.805480 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.90098 | −0.227890 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.4062 | −0.343269 | −0.171634 | − | 0.985161i | \(-0.554905\pi\) | ||||
−0.171634 | + | 0.985161i | \(0.554905\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.4839 | −1.43284 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0156182 | −0.000514078 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.49261 | −0.180596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 53.4691 | 1.75616 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.4171 | −1.32604 | −0.663021 | − | 0.748601i | \(-0.730726\pi\) | ||||
−0.663021 | + | 0.748601i | \(0.730726\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.31074 | 0.206826 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.0365607 | 0.00119694 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.83768 | 0.0600986 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.3396 | −1.02382 | −0.511910 | − | 0.859039i | \(-0.671062\pi\) | ||||
−0.511910 | + | 0.859039i | \(0.671062\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.30904 | −0.140620 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.9408 | −0.617451 | −0.308726 | − | 0.951151i | \(-0.599902\pi\) | ||||
−0.308726 | + | 0.951151i | \(0.599902\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.1369 | 1.63268 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.610383 | −0.0198557 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.62876 | −0.247901 | −0.123951 | − | 0.992288i | \(-0.539556\pi\) | ||||
−0.123951 | + | 0.992288i | \(0.539556\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.3588 | 0.531030 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.8396 | −1.25946 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.2639 | 0.559232 | 0.279616 | − | 0.960112i | \(-0.409793\pi\) | ||||
0.279616 | + | 0.960112i | \(0.409793\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.72307 | 0.282272 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.6626 | −0.538624 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.25875 | 0.202106 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.6611 | −0.537456 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.3999 | 0.786276 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.5350 | 0.532279 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.96313 | −0.127446 | −0.0637228 | − | 0.997968i | \(-0.520297\pi\) | ||||
−0.0637228 | + | 0.997968i | \(0.520297\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.4335 | 0.592168 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.4619 | −0.367830 | −0.183915 | − | 0.982942i | \(-0.558877\pi\) | ||||
−0.183915 | + | 0.982942i | \(0.558877\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.04281 | 0.0654896 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.35937 | −0.203663 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.3767 | −1.22778 | −0.613890 | − | 0.789392i | \(-0.710396\pi\) | ||||
−0.613890 | + | 0.789392i | \(0.710396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.87297 | 0.187701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.97532 | 0.0630670 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.8034 | 0.823000 | 0.411500 | − | 0.911410i | \(-0.365005\pi\) | ||||
0.411500 | + | 0.911410i | \(0.365005\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.5437 | 0.909476 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.85398 | 0.313656 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.4139 | −0.585529 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.47383 | 0.237414 | 0.118707 | − | 0.992929i | \(-0.462125\pi\) | ||||
0.118707 | + | 0.992929i | \(0.462125\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −57.1069 | −1.81223 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.6215 | 0.653747 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.9687 | −1.10747 | −0.553734 | − | 0.832693i | \(-0.686798\pi\) | ||||
−0.553734 | + | 0.832693i | \(0.686798\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.837959 | 0.0265118 |
(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 | 8008.2.a.w.1.9 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.w.1.9 | ✓ | 11 | 1.1 | even | 1 | trivial |