Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(1,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.14510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.1 |
$q$-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 | ||||||||
\(3\) | −2.14510 | −1.23848 | −0.619238 | − | 0.785204i | \(-0.712558\pi\) | ||||
−0.619238 | + | 0.785204i | \(0.712558\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.14510 | −0.432808 | −0.216404 | − | 0.976304i | \(-0.569433\pi\) | ||||
−0.216404 | + | 0.976304i | \(0.569433\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.60147 | 0.533822 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.89167 | 1.77641 | 0.888203 | − | 0.459452i | \(-0.151954\pi\) | ||||
0.888203 | + | 0.459452i | \(0.151954\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.89167 | −1.35671 | −0.678353 | − | 0.734736i | \(-0.737306\pi\) | ||||
−0.678353 | + | 0.734736i | \(0.737306\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.14510 | 0.553863 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.89167 | −1.42894 | −0.714470 | − | 0.699666i | \(-0.753332\pi\) | ||||
−0.714470 | + | 0.699666i | \(0.753332\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.34803 | −0.538676 | −0.269338 | − | 0.963046i | \(-0.586805\pi\) | ||||
−0.269338 | + | 0.963046i | \(0.586805\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.45636 | 0.536022 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.00000 | 0.577350 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.74657 | 0.695720 | 0.347860 | − | 0.937546i | \(-0.386908\pi\) | ||||
0.347860 | + | 0.937546i | \(0.386908\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.68874 | 1.02173 | 0.510864 | − | 0.859662i | \(-0.329326\pi\) | ||||
0.510864 | + | 0.859662i | \(0.329326\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.6382 | −2.20004 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.14510 | 0.193558 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.4931 | 1.68025 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.05783 | −0.165205 | −0.0826025 | − | 0.996583i | \(-0.526323\pi\) | ||||
−0.0826025 | + | 0.996583i | \(0.526323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4931 | 1.75269 | 0.876343 | − | 0.481687i | \(-0.159976\pi\) | ||||
0.876343 | + | 0.481687i | \(0.159976\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.60147 | −0.238732 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.74657 | 1.12995 | 0.564977 | − | 0.825107i | \(-0.308885\pi\) | ||||
0.564977 | + | 0.825107i | \(0.308885\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.68874 | −0.812677 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.6382 | 1.76971 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.9863 | 1.78380 | 0.891901 | − | 0.452231i | \(-0.149372\pi\) | ||||
0.891901 | + | 0.452231i | \(0.149372\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.89167 | −0.794433 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.03677 | 0.667137 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.797069 | 0.103770 | 0.0518848 | − | 0.998653i | \(-0.483477\pi\) | ||||
0.0518848 | + | 0.998653i | \(0.483477\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8917 | 1.77865 | 0.889323 | − | 0.457279i | \(-0.151176\pi\) | ||||
0.889323 | + | 0.457279i | \(0.151176\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.83384 | −0.231042 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.89167 | 0.606737 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5667 | −1.90177 | −0.950887 | − | 0.309540i | \(-0.899825\pi\) | ||||
−0.950887 | + | 0.309540i | \(0.899825\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.14510 | −0.258240 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.94217 | 0.349172 | 0.174586 | − | 0.984642i | \(-0.444141\pi\) | ||||
0.174586 | + | 0.984642i | \(0.444141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.32698 | 0.740517 | 0.370258 | − | 0.928929i | \(-0.379269\pi\) | ||||
0.370258 | + | 0.928929i | \(0.379269\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.14510 | −0.247695 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.74657 | −0.768843 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2397 | −1.24886 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.912726 | −0.100185 | −0.0500923 | − | 0.998745i | \(-0.515952\pi\) | ||||
−0.0500923 | + | 0.998745i | \(0.515952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.89167 | 0.639041 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.03677 | −0.861633 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.4931 | −1.64227 | −0.821135 | − | 0.570735i | \(-0.806659\pi\) | ||||
−0.821135 | + | 0.570735i | \(0.806659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.60147 | 0.587193 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.2029 | −1.26539 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.34803 | 0.240903 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3848 | 1.35902 | 0.679511 | − | 0.733666i | \(-0.262192\pi\) | ||||
0.679511 | + | 0.733666i | \(0.262192\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.43531 | 0.948284 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.79707 | 0.278319 | 0.139159 | − | 0.990270i | \(-0.455560\pi\) | ||||
0.139159 | + | 0.990270i | \(0.455560\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.89167 | −0.974655 | −0.487328 | − | 0.873219i | \(-0.662028\pi\) | ||||
−0.487328 | + | 0.873219i | \(0.662028\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.45636 | −0.239716 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.6961 | 1.22738 | 0.613688 | − | 0.789549i | \(-0.289685\pi\) | ||||
0.613688 | + | 0.789549i | \(0.289685\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.65197 | 0.349795 | 0.174897 | − | 0.984587i | \(-0.444041\pi\) | ||||
0.174897 | + | 0.984587i | \(0.444041\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.58041 | −0.814417 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.83384 | −0.724239 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.74657 | 0.618457 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.7118 | 2.15562 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.26915 | 0.204602 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.1524 | 1.07835 | 0.539177 | − | 0.842193i | \(-0.318735\pi\) | ||||
0.539177 | + | 0.842193i | \(0.318735\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.6540 | −2.17066 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.94950 | −0.607181 | −0.303590 | − | 0.952803i | \(-0.598185\pi\) | ||||
−0.303590 | + | 0.952803i | \(0.598185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.68874 | 0.233143 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.00000 | −0.258199 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.44904 | −0.209235 | −0.104618 | − | 0.994513i | \(-0.533362\pi\) | ||||
−0.104618 | + | 0.994513i | \(0.533362\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.23970 | 0.783702 | 0.391851 | − | 0.920029i | \(-0.371835\pi\) | ||||
0.391851 | + | 0.920029i | \(0.371835\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.6172 | −1.39942 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −28.8201 | −2.41006 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.74657 | −0.311136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.2029 | 1.00648 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.05783 | −0.168584 | −0.0842919 | − | 0.996441i | \(-0.526863\pi\) | ||||
−0.0842919 | + | 0.996441i | \(0.526863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.34803 | 0.760732 | 0.380366 | − | 0.924836i | \(-0.375798\pi\) | ||||
0.380366 | + | 0.924836i | \(0.375798\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.43531 | −0.762799 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.68874 | −0.456931 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.60879 | −0.288013 | −0.144007 | − | 0.989577i | \(-0.545999\pi\) | ||||
−0.144007 | + | 0.989577i | \(0.545999\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27.8569 | −2.20920 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.14510 | −0.0902467 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.2554 | 1.66485 | 0.832427 | − | 0.554135i | \(-0.186951\pi\) | ||||
0.832427 | + | 0.554135i | \(0.186951\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.6382 | 0.983886 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.9863 | −0.850143 | −0.425072 | − | 0.905160i | \(-0.639751\pi\) | ||||
−0.425072 | + | 0.905160i | \(0.639751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.9284 | 0.840650 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.76030 | −0.287557 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.28288 | −0.477678 | −0.238839 | − | 0.971059i | \(-0.576767\pi\) | ||||
−0.238839 | + | 0.971059i | \(0.576767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.14510 | −0.0865616 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.70979 | −0.128516 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.1524 | 0.758828 | 0.379414 | − | 0.925227i | \(-0.376126\pi\) | ||||
0.379414 | + | 0.925227i | \(0.376126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1451 | 0.828409 | 0.414204 | − | 0.910184i | \(-0.364060\pi\) | ||||
0.414204 | + | 0.910184i | \(0.364060\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.7991 | −2.20281 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −34.7118 | −2.53838 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.43531 | −0.249882 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6961 | −1.06337 | −0.531685 | − | 0.846942i | \(-0.678441\pi\) | ||||
−0.531685 | + | 0.846942i | \(0.678441\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.4005 | −1.90035 | −0.950176 | − | 0.311715i | \(-0.899097\pi\) | ||||
−0.950176 | + | 0.311715i | \(0.899097\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.4931 | −0.751429 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.26076 | −0.303567 | −0.151783 | − | 0.988414i | \(-0.548502\pi\) | ||||
−0.151783 | + | 0.988414i | \(0.548502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0735 | 1.28120 | 0.640600 | − | 0.767875i | \(-0.278686\pi\) | ||||
0.640600 | + | 0.767875i | \(0.278686\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 33.3921 | 2.35530 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.29021 | −0.301113 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.05783 | 0.0738819 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.60147 | 0.111310 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.8338 | −0.956907 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.8990 | −0.819161 | −0.409580 | − | 0.912274i | \(-0.634325\pi\) | ||||
−0.409580 | + | 0.912274i | \(0.634325\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.31126 | −0.432440 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.4931 | −0.783825 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.51419 | −0.442212 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.5720 | −0.917112 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.8201 | 1.93865 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.58041 | 0.306727 | 0.153363 | − | 0.988170i | \(-0.450989\pi\) | ||||
0.153363 | + | 0.988170i | \(0.450989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.60147 | 0.106764 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.21666 | 0.147125 | 0.0735624 | − | 0.997291i | \(-0.476563\pi\) | ||||
0.0735624 | + | 0.997291i | \(0.476563\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.1608 | −1.26618 | −0.633091 | − | 0.774077i | \(-0.718214\pi\) | ||||
−0.633091 | + | 0.774077i | \(0.718214\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.4721 | 0.952193 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.7466 | −1.42467 | −0.712333 | − | 0.701842i | \(-0.752361\pi\) | ||||
−0.712333 | + | 0.701842i | \(0.752361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.74657 | −0.505330 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.9495 | 1.35511 | 0.677555 | − | 0.735472i | \(-0.263039\pi\) | ||||
0.677555 | + | 0.735472i | \(0.263039\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.0735 | 1.55071 | 0.775357 | − | 0.631523i | \(-0.217570\pi\) | ||||
0.775357 | + | 0.631523i | \(0.217570\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1103 | 0.969328 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.68874 | 0.363440 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4858 | 0.730825 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.95789 | 0.124076 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.82651 | −0.494005 | −0.247003 | − | 0.969015i | \(-0.579446\pi\) | ||||
−0.247003 | + | 0.969015i | \(0.579446\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.89167 | 0.370406 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.6382 | −0.791437 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.82012 | 0.612562 | 0.306281 | − | 0.951941i | \(-0.400915\pi\) | ||||
0.306281 | + | 0.951941i | \(0.400915\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.58041 | −0.284613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.6887 | −0.905746 | −0.452873 | − | 0.891575i | \(-0.649601\pi\) | ||||
−0.452873 | + | 0.891575i | \(0.649601\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.9863 | −0.797740 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.2344 | 2.03391 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.253432 | −0.0154520 | −0.00772600 | − | 0.999970i | \(-0.502459\pi\) | ||||
−0.00772600 | + | 0.999970i | \(0.502459\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.6099 | −1.19121 | −0.595607 | − | 0.803276i | \(-0.703088\pi\) | ||||
−0.595607 | + | 0.803276i | \(0.703088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0157 | −0.727224 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.89167 | 0.355281 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.1976 | 1.75431 | 0.877157 | − | 0.480204i | \(-0.159437\pi\) | ||||
0.877157 | + | 0.480204i | \(0.159437\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.11032 | 0.545421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.1755 | −1.62115 | −0.810577 | − | 0.585633i | \(-0.800846\pi\) | ||||
−0.810577 | + | 0.585633i | \(0.800846\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.1471 | 1.07873 | 0.539366 | − | 0.842071i | \(-0.318664\pi\) | ||||
0.539366 | + | 0.842071i | \(0.318664\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.03677 | −0.298353 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.21132 | 0.0715021 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.7118 | 1.04187 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.7118 | −1.68311 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.681412 | 0.0398085 | 0.0199043 | − | 0.999802i | \(-0.493664\pi\) | ||||
0.0199043 | + | 0.999802i | \(0.493664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.797069 | −0.0464071 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.6750 | 1.02561 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.89167 | −0.282893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.1608 | −0.758577 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.00000 | −0.344691 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.8917 | −0.795435 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.5877 | 1.51744 | 0.758721 | − | 0.651415i | \(-0.225824\pi\) | ||||
0.758721 | + | 0.651415i | \(0.225824\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.2186 | 1.20709 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5299 | 0.767211 | 0.383605 | − | 0.923497i | \(-0.374682\pi\) | ||||
0.383605 | + | 0.923497i | \(0.374682\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8412 | 1.12149 | 0.560745 | − | 0.827989i | \(-0.310515\pi\) | ||||
0.560745 | + | 0.827989i | \(0.310515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.83384 | 0.103325 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.55096 | 0.199442 | 0.0997210 | − | 0.995015i | \(-0.468205\pi\) | ||||
0.0997210 | + | 0.995015i | \(0.468205\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.0735 | 1.23588 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.2344 | −1.52007 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.8338 | 0.769736 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.89167 | −0.271341 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.83384 | −0.433212 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.87062 | −0.489053 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.3133 | −0.731763 | −0.365881 | − | 0.930662i | \(-0.619232\pi\) | ||||
−0.365881 | + | 0.930662i | \(0.619232\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.40586 | 0.351039 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.5667 | 0.850499 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4951 | −1.11644 | −0.558220 | − | 0.829693i | \(-0.688516\pi\) | ||||
−0.558220 | + | 0.829693i | \(0.688516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.4510 | 1.16506 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.5162 | 1.81500 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5299 | 0.784541 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.14510 | 0.115488 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.60147 | −0.408068 | −0.204034 | − | 0.978964i | \(-0.565405\pi\) | ||||
−0.204034 | + | 0.978964i | \(0.565405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.55736 | 0.297479 | 0.148739 | − | 0.988876i | \(-0.452478\pi\) | ||||
0.148739 | + | 0.988876i | \(0.452478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.6750 | −0.783294 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.96323 | 0.104492 | 0.0522460 | − | 0.998634i | \(-0.483362\pi\) | ||||
0.0522460 | + | 0.998634i | \(0.483362\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.94217 | −0.156154 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.4721 | −0.765944 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.5069 | 0.554531 | 0.277266 | − | 0.960793i | \(-0.410572\pi\) | ||||
0.277266 | + | 0.960793i | \(0.410572\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4867 | −0.709828 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −50.8642 | −2.66968 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.32698 | −0.331169 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.7412 | 1.76128 | 0.880639 | − | 0.473788i | \(-0.157114\pi\) | ||||
0.880639 | + | 0.473788i | \(0.157114\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.69408 | −0.0881901 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.8706 | −0.772044 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.4510 | −0.903580 | −0.451790 | − | 0.892124i | \(-0.649214\pi\) | ||||
−0.451790 | + | 0.892124i | \(0.649214\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.14510 | 0.110773 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.3270 | −0.943887 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.4584 | −1.71864 | −0.859320 | − | 0.511438i | \(-0.829113\pi\) | ||||
−0.859320 | + | 0.511438i | \(0.829113\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.0682 | −1.33551 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.0873 | 0.668728 | 0.334364 | − | 0.942444i | \(-0.391478\pi\) | ||||
0.334364 | + | 0.942444i | \(0.391478\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.74657 | 0.343837 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.4059 | 0.935623 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.1083 | 0.715321 | 0.357660 | − | 0.933852i | \(-0.383575\pi\) | ||||
0.357660 | + | 0.933852i | \(0.383575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.89167 | −0.297955 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.9074 | 0.751978 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6245 | 0.834360 | 0.417180 | − | 0.908824i | \(-0.363018\pi\) | ||||
0.417180 | + | 0.908824i | \(0.363018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.76762 | −0.288742 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.2628 | 1.11175 | 0.555874 | − | 0.831266i | \(-0.312384\pi\) | ||||
0.555874 | + | 0.831266i | \(0.312384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.8274 | −1.38618 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.2397 | 0.558505 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.5667 | 1.16816 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6887 | 0.775758 | 0.387879 | − | 0.921710i | \(-0.373208\pi\) | ||||
0.387879 | + | 0.921710i | \(0.373208\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.25343 | 0.259133 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.912726 | −0.0449123 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.912726 | 0.0448039 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.8201 | −0.970595 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.66769 | −0.276885 | −0.138442 | − | 0.990371i | \(-0.544210\pi\) | ||||
−0.138442 | + | 0.990371i | \(0.544210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0716 | 0.734543 | 0.367271 | − | 0.930114i | \(-0.380292\pi\) | ||||
0.367271 | + | 0.930114i | \(0.380292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.4059 | 0.603194 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.89167 | −0.285788 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.9074 | −0.769813 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 61.8221 | 2.98480 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.3500 | 1.41374 | 0.706870 | − | 0.707343i | \(-0.250106\pi\) | ||||
0.706870 | + | 0.707343i | \(0.250106\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.6245 | 1.42366 | 0.711832 | − | 0.702350i | \(-0.247866\pi\) | ||||
0.711832 | + | 0.702350i | \(0.247866\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.03677 | 0.385334 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.34803 | −0.112322 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.7907 | −0.992285 | −0.496142 | − | 0.868241i | \(-0.665251\pi\) | ||||
−0.496142 | + | 0.868241i | \(0.665251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.11032 | −0.433825 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.2975 | 1.01188 | 0.505938 | − | 0.862570i | \(-0.331146\pi\) | ||||
0.505938 | + | 0.862570i | \(0.331146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.4931 | 0.734445 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.41425 | 0.208787 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.3197 | −0.911751 | −0.455875 | − | 0.890044i | \(-0.650674\pi\) | ||||
−0.455875 | + | 0.890044i | \(0.650674\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.23238 | −0.293471 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.0525 | −0.942148 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.60147 | −0.262601 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.912726 | 0.0426955 | 0.0213478 | − | 0.999772i | \(-0.493204\pi\) | ||||
0.0213478 | + | 0.999772i | \(0.493204\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.6750 | −0.824999 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.83384 | 0.131985 | 0.0659926 | − | 0.997820i | \(-0.478979\pi\) | ||||
0.0659926 | + | 0.997820i | \(0.478979\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.2618 | −0.802225 | −0.401112 | − | 0.916029i | \(-0.631376\pi\) | ||||
−0.401112 | + | 0.916029i | \(0.631376\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.2029 | 0.565897 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.4510 | −0.992635 | −0.496318 | − | 0.868141i | \(-0.665315\pi\) | ||||
−0.496318 | + | 0.868141i | \(0.665315\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.8255 | 0.823103 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.74123 | 0.356697 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 67.7138 | 3.11348 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.34803 | −0.107735 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.7971 | 0.952232 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.49314 | 0.433752 | 0.216876 | − | 0.976199i | \(-0.430413\pi\) | ||||
0.216876 | + | 0.976199i | \(0.430413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.5667 | −0.892164 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.45636 | 0.111768 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.3848 | −0.607773 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.3270 | 1.73676 | 0.868381 | − | 0.495898i | \(-0.165161\pi\) | ||||
0.868381 | + | 0.495898i | \(0.165161\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −45.5951 | −2.06188 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.9947 | −0.631570 | −0.315785 | − | 0.948831i | \(-0.602268\pi\) | ||||
−0.315785 | + | 0.948831i | \(0.602268\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.0735 | −0.994143 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.43531 | −0.424086 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.36909 | −0.151124 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.0642277 | −0.00287522 | −0.00143761 | − | 0.999999i | \(-0.500458\pi\) | ||||
−0.00143761 | + | 0.999999i | \(0.500458\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.5667 | 1.05288 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.2785 | −1.08252 | −0.541262 | − | 0.840854i | \(-0.682053\pi\) | ||||
−0.541262 | + | 0.840854i | \(0.682053\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.79707 | −0.124468 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.4426 | −1.04112 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.65929 | −0.117871 | −0.0589356 | − | 0.998262i | \(-0.518771\pi\) | ||||
−0.0589356 | + | 0.998262i | \(0.518771\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.24504 | −0.320502 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.04410 | −0.311005 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.89167 | 0.435879 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.6402 | 2.00726 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.4774 | 0.591593 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0598 | −0.747404 | −0.373702 | − | 0.927549i | \(-0.621912\pi\) | ||||
−0.373702 | + | 0.927549i | \(0.621912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.5667 | −0.768137 | −0.384069 | − | 0.923305i | \(-0.625477\pi\) | ||||
−0.384069 | + | 0.923305i | \(0.625477\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.45636 | 0.107204 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.5162 | −1.45999 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.27648 | 0.0553944 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.17455 | 0.224135 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.6961 | −0.548899 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.7780 | −0.939790 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −33.5162 | −1.44364 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.36909 | −0.359815 | −0.179908 | − | 0.983684i | \(-0.557580\pi\) | ||||
−0.179908 | + | 0.983684i | \(0.557580\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.9074 | −1.02596 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.65197 | −0.156433 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.7486 | −0.716117 | −0.358058 | − | 0.933699i | \(-0.616561\pi\) | ||||
−0.358058 | + | 0.933699i | \(0.616561\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.2470 | 0.949480 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.79707 | −0.374768 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.58041 | 0.364218 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.26182 | −0.307693 | −0.153847 | − | 0.988095i | \(-0.549166\pi\) | ||||
−0.153847 | + | 0.988095i | \(0.549166\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.2206 | −2.37788 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 74.4603 | 3.14372 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.5530 | 1.45623 | 0.728117 | − | 0.685453i | \(-0.240396\pi\) | ||||
0.728117 | + | 0.685453i | \(0.240396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | 0.420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.8706 | 0.540515 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.7275 | 1.45585 | 0.727926 | − | 0.685655i | \(-0.240484\pi\) | ||||
0.727926 | + | 0.685655i | \(0.240484\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.7034 | 0.615318 | 0.307659 | − | 0.951497i | \(-0.400454\pi\) | ||||
0.307659 | + | 0.951497i | \(0.400454\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.5246 | 1.31696 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.13777 | −0.255519 | −0.127759 | − | 0.991805i | \(-0.540779\pi\) | ||||
−0.127759 | + | 0.991805i | \(0.540779\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 56.6318 | 2.35354 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.04516 | 0.0433607 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 76.5108 | 3.16876 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.83384 | 0.323890 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.33338 | −0.0550344 | −0.0275172 | − | 0.999621i | \(-0.508760\pi\) | ||||
−0.0275172 | + | 0.999621i | \(0.508760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.3574 | −0.550380 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.13977 | 0.375960 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.88434 | 0.0773807 | 0.0386903 | − | 0.999251i | \(-0.487681\pi\) | ||||
0.0386903 | + | 0.999251i | \(0.487681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.74657 | −0.276582 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.7696 | −1.58673 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −43.7632 | −1.78812 | −0.894058 | − | 0.447951i | \(-0.852154\pi\) | ||||
−0.894058 | + | 0.447951i | \(0.852154\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.50046 | 0.183578 | 0.0917889 | − | 0.995778i | \(-0.470742\pi\) | ||||
0.0917889 | + | 0.995778i | \(0.470742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.9295 | −1.01521 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.7118 | −0.964021 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.17455 | 0.250617 | 0.125309 | − | 0.992118i | \(-0.460008\pi\) | ||||
0.125309 | + | 0.992118i | \(0.460008\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.20293 | 0.372922 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.8937 | −1.53301 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.72445 | −0.392767 | −0.196383 | − | 0.980527i | \(-0.562920\pi\) | ||||
−0.196383 | + | 0.980527i | \(0.562920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.26915 | −0.0915010 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.730849 | −0.0294229 | −0.0147114 | − | 0.999892i | \(-0.504683\pi\) | ||||
−0.0147114 | + | 0.999892i | \(0.504683\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1598 | 0.448549 | 0.224274 | − | 0.974526i | \(-0.427999\pi\) | ||||
0.224274 | + | 0.974526i | \(0.427999\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | 0.120386 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.7412 | 0.710787 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.6750 | 1.18511 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.5667 | −0.939665 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.87062 | −0.193896 | −0.0969481 | − | 0.995289i | \(-0.530908\pi\) | ||||
−0.0969481 | + | 0.995289i | \(0.530908\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.5246 | 1.01451 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.1524 | −0.482254 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.8274 | 1.10256 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.71179 | 0.186395 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.6540 | 1.28975 | 0.644877 | − | 0.764286i | \(-0.276909\pi\) | ||||
0.644877 | + | 0.764286i | \(0.276909\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.9579 | 1.89127 | 0.945637 | − | 0.325223i | \(-0.105439\pi\) | ||||
0.945637 | + | 0.325223i | \(0.105439\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.6540 | 0.970749 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.1103 | 0.476106 | 0.238053 | − | 0.971252i | \(-0.423491\pi\) | ||||
0.238053 | + | 0.971252i | \(0.423491\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.69607 | 0.184337 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.9736 | 0.547669 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.2133 | −1.69107 | −0.845534 | − | 0.533922i | \(-0.820718\pi\) | ||||
−0.845534 | + | 0.533922i | \(0.820718\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.94950 | 0.271539 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.1324 | 0.395304 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.4333 | 0.795969 | 0.397984 | − | 0.917392i | \(-0.369710\pi\) | ||||
0.397984 | + | 0.917392i | \(0.369710\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.1398 | 1.87242 | 0.936210 | − | 0.351441i | \(-0.114308\pi\) | ||||
0.936210 | + | 0.351441i | \(0.114308\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −61.8221 | −2.40097 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.68874 | −0.104265 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.74657 | 0.145068 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.82545 | −0.379874 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 81.8452 | 3.15960 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.5436 | 0.637710 | 0.318855 | − | 0.947803i | \(-0.396702\pi\) | ||||
0.318855 | + | 0.947803i | \(0.396702\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.00000 | 0.115470 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.9863 | −1.88270 | −0.941348 | − | 0.337438i | \(-0.890440\pi\) | ||||
−0.941348 | + | 0.337438i | \(0.890440\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.3270 | −0.588195 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.75496 | −0.182210 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.8779 | −0.837136 | −0.418568 | − | 0.908185i | \(-0.637468\pi\) | ||||
−0.418568 | + | 0.908185i | \(0.637468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.44904 | 0.0935728 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.1019 | 1.56814 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −63.5246 | −2.42009 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.30393 | −0.125688 | −0.0628438 | − | 0.998023i | \(-0.520017\pi\) | ||||
−0.0628438 | + | 0.998023i | \(0.520017\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.8044 | −0.410425 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.23970 | −0.350482 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.23238 | 0.236068 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 46.6486 | 1.76441 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.46369 | −0.168591 | −0.0842956 | − | 0.996441i | \(-0.526864\pi\) | ||||
−0.0842956 | + | 0.996441i | \(0.526864\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.39214 | −0.354231 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.6172 | 0.625839 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.20293 | −0.120459 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.39853 | −0.0900789 | −0.0450394 | − | 0.998985i | \(-0.514341\pi\) | ||||
−0.0450394 | + | 0.998985i | \(0.514341\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.68874 | 0.213045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.8201 | 1.07781 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −44.9388 | −1.67827 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0725 | 0.450228 | 0.225114 | − | 0.974332i | \(-0.427725\pi\) | ||||
0.225114 | + | 0.974332i | \(0.427725\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.3270 | 0.421839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −51.6402 | −1.92052 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.74657 | 0.139144 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.4269 | 0.423801 | 0.211900 | − | 0.977291i | \(-0.432035\pi\) | ||||
0.211900 | + | 0.977291i | \(0.432035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.30592 | 0.0483676 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −67.7138 | −2.50448 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.08727 | −0.114031 | −0.0570155 | − | 0.998373i | \(-0.518158\pi\) | ||||
−0.0570155 | + | 0.998373i | \(0.518158\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.2029 | −0.450112 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −91.7138 | −3.37832 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.36909 | −0.307862 | −0.153931 | − | 0.988082i | \(-0.549193\pi\) | ||||
−0.153931 | + | 0.988082i | \(0.549193\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.6382 | −0.905108 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.1598 | 0.556158 | 0.278079 | − | 0.960558i | \(-0.410302\pi\) | ||||
0.278079 | + | 0.960558i | \(0.410302\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.05783 | 0.0753930 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.46170 | −0.0534808 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.5383 | −0.531218 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.6823 | −1.22909 | −0.614543 | − | 0.788883i | \(-0.710660\pi\) | ||||
−0.614543 | + | 0.788883i | \(0.710660\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.7887 | 0.611813 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.34803 | −0.340210 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.1608 | −1.05987 | −0.529934 | − | 0.848039i | \(-0.677783\pi\) | ||||
−0.529934 | + | 0.848039i | \(0.677783\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.6382 | −0.458739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.91912 | −0.250818 | −0.125409 | − | 0.992105i | \(-0.540024\pi\) | ||||
−0.125409 | + | 0.992105i | \(0.540024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.18188 | −0.151394 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.43531 | 0.341134 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.89900 | −0.140785 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.3491 | −0.517442 | −0.258721 | − | 0.965952i | \(-0.583301\pi\) | ||||
−0.258721 | + | 0.965952i | \(0.583301\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.0652 | −0.758643 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.6265 | 1.82091 | 0.910454 | − | 0.413609i | \(-0.135732\pi\) | ||||
0.910454 | + | 0.413609i | \(0.135732\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.68874 | 0.204346 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.82545 | 0.352486 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.48382 | 0.0889920 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.3343 | 0.620270 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.2397 | 0.401674 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.60879 | 0.128803 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.9442 | 0.746579 | 0.373289 | − | 0.927715i | \(-0.378230\pi\) | ||||
0.373289 | + | 0.927715i | \(0.378230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.5089 | 1.12174 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.4510 | 0.407152 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −67.9535 | −2.41310 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.8569 | 0.987982 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.0009 | 0.673047 | 0.336524 | − | 0.941675i | \(-0.390749\pi\) | ||||
0.336524 | + | 0.941675i | \(0.390749\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.6402 | −1.61464 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.8117 | −0.876679 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.2765 | 1.31546 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.14510 | 0.0403596 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.543637 | 0.0191369 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.4300 | 0.647963 | 0.323982 | − | 0.946063i | \(-0.394978\pi\) | ||||
0.323982 | + | 0.946063i | \(0.394978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.1387 | −0.742280 | −0.371140 | − | 0.928577i | \(-0.621033\pi\) | ||||
−0.371140 | + | 0.928577i | \(0.621033\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 42.0652 | 1.47529 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.2554 | −0.744545 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.9863 | −0.944130 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.97055 | 0.313457 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.7550 | −0.584752 | −0.292376 | − | 0.956303i | \(-0.594446\pi\) | ||||
−0.292376 | + | 0.956303i | \(0.594446\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.9220 | 0.868728 | 0.434364 | − | 0.900737i | \(-0.356973\pi\) | ||||
0.434364 | + | 0.900737i | \(0.356973\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.6382 | −0.440007 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.62252 | −0.230288 | −0.115144 | − | 0.993349i | \(-0.536733\pi\) | ||||
−0.115144 | + | 0.993349i | \(0.536733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.7001 | 1.83035 | 0.915174 | − | 0.403058i | \(-0.132053\pi\) | ||||
0.915174 | + | 0.403058i | \(0.132053\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −62.6318 | −2.17267 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.5162 | 1.16127 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.9863 | 0.380196 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.0662 | 0.589895 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.5951 | 1.47054 | 0.735272 | − | 0.677772i | \(-0.237054\pi\) | ||||
0.735272 | + | 0.677772i | \(0.237054\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.9632 | −0.515973 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 58.2942 | 2.00776 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.9284 | −0.375950 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.1524 | −0.932969 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.9274 | −1.33598 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | 0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −57.7255 | −1.97648 | −0.988242 | − | 0.152898i | \(-0.951139\pi\) | ||||
−0.988242 | + | 0.152898i | \(0.951139\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.76030 | 0.128599 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −55.3721 | −1.89148 | −0.945738 | − | 0.324930i | \(-0.894659\pi\) | ||||
−0.945738 | + | 0.324930i | \(0.894659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.3544 | −0.489767 | −0.244883 | − | 0.969553i | \(-0.578750\pi\) | ||||
−0.244883 | + | 0.969553i | \(0.578750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.59841 | −0.0885536 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.9211 | 0.541961 | 0.270981 | − | 0.962585i | \(-0.412652\pi\) | ||||
0.270981 | + | 0.962585i | \(0.412652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.28288 | 0.213624 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.9936 | −1.29033 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 76.1471 | 2.58015 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.4353 | 0.725475 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.14510 | 0.0387115 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.2975 | −1.02308 | −0.511538 | − | 0.859261i | \(-0.670924\pi\) | ||||
−0.511538 | + | 0.859261i | \(0.670924\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.46170 | −0.0493019 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.1883 | −0.376943 | −0.188471 | − | 0.982079i | \(-0.560353\pi\) | ||||
−0.188471 | + | 0.982079i | \(0.560353\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.2882 | 0.851016 | 0.425508 | − | 0.904955i | \(-0.360095\pi\) | ||||
0.425508 | + | 0.904955i | \(0.360095\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.70979 | 0.0574741 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.2849 | −1.08402 | −0.542010 | − | 0.840372i | \(-0.682336\pi\) | ||||
−0.542010 | + | 0.840372i | \(0.682336\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.9158 | −0.466720 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −66.2206 | −2.21847 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.1892 | −0.608679 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.1524 | −0.339358 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.4931 | 0.350356 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.3133 | 0.710837 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −76.5108 | −2.54895 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.2313 | 0.939479 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.1451 | −0.370476 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.47848 | −0.0490922 | −0.0245461 | − | 0.999699i | \(-0.507814\pi\) | ||||
−0.0245461 | + | 0.999699i | \(0.507814\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.47941 | 0.148573 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.70979 | 0.189174 | 0.0945870 | − | 0.995517i | \(-0.469847\pi\) | ||||
0.0945870 | + | 0.995517i | \(0.469847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.37748 | −0.177969 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.7991 | 0.985127 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.95789 | 0.262793 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.6265 | 0.746379 | 0.373190 | − | 0.927755i | \(-0.378264\pi\) | ||||
0.373190 | + | 0.927755i | \(0.378264\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −57.0334 | −1.87932 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.3921 | −0.473723 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.8412 | −0.520292 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.0829 | −1.64317 | −0.821583 | − | 0.570089i | \(-0.806909\pi\) | ||||
−0.821583 | + | 0.570089i | \(0.806909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.3574 | 0.437770 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.0230 | −0.950172 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34.7118 | 1.13520 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.98428 | 0.326172 | 0.163086 | − | 0.986612i | \(-0.447855\pi\) | ||||
0.163086 | + | 0.986612i | \(0.447855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −42.5613 | −1.38894 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.0809 | −1.17620 | −0.588101 | − | 0.808787i | \(-0.700124\pi\) | ||||
−0.588101 | + | 0.808787i | \(0.700124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.05783 | −0.0344476 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.43531 | 0.111751 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.4730 | −1.05523 | −0.527616 | − | 0.849483i | \(-0.676914\pi\) | ||||
−0.527616 | + | 0.849483i | \(0.676914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.9495 | −1.00466 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.61718 | −0.247004 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.3427 | −1.27443 | −0.637217 | − | 0.770684i | \(-0.719915\pi\) | ||||
−0.637217 | + | 0.770684i | \(0.719915\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.6961 | 0.475554 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.3500 | −1.53061 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.80440 | 0.0905587 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.36176 | 0.0439278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.3323 | 0.655200 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.4005 | 0.849863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.5720 | 0.758025 | 0.379013 | − | 0.925392i | \(-0.376264\pi\) | ||||
0.379013 | + | 0.925392i | \(0.376264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.6750 | −0.953299 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.9368 | 0.415163 | 0.207581 | − | 0.978218i | \(-0.433441\pi\) | ||||
0.207581 | + | 0.978218i | \(0.433441\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.5804 | −0.339192 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.4931 | 0.336049 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.7118 | −0.726614 | −0.363307 | − | 0.931669i | \(-0.618352\pi\) | ||||
−0.363307 | + | 0.931669i | \(0.618352\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −91.2805 | −2.91734 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.84850 | 0.186728 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.1819 | 0.835072 | 0.417536 | − | 0.908660i | \(-0.362894\pi\) | ||||
0.417536 | + | 0.908660i | \(0.362894\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.26076 | 0.135759 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.0284 | 0.605680 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.4931 | 0.365460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.3143 | −1.78888 | −0.894442 | − | 0.447185i | \(-0.852427\pi\) | ||||
−0.894442 | + | 0.447185i | \(0.852427\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.5583 | 0.906270 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.0735 | −0.572970 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.74123 | −0.118486 | −0.0592430 | − | 0.998244i | \(-0.518869\pi\) | ||||
−0.0592430 | + | 0.998244i | \(0.518869\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.0000 | 0.379663 |
(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 | 920.2.a.g.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bo.1.1 | 3 | |||
4.3 | odd | 2 | 1840.2.a.t.1.3 | 3 | |||
5.2 | odd | 4 | 4600.2.e.r.4049.5 | 6 | |||
5.3 | odd | 4 | 4600.2.e.r.4049.2 | 6 | |||
5.4 | even | 2 | 4600.2.a.y.1.3 | 3 | |||
8.3 | odd | 2 | 7360.2.a.ca.1.1 | 3 | |||
8.5 | even | 2 | 7360.2.a.cb.1.3 | 3 | |||
20.19 | odd | 2 | 9200.2.a.cd.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.g.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1840.2.a.t.1.3 | 3 | 4.3 | odd | 2 | |||
4600.2.a.y.1.3 | 3 | 5.4 | even | 2 | |||
4600.2.e.r.4049.2 | 6 | 5.3 | odd | 4 | |||
4600.2.e.r.4049.5 | 6 | 5.2 | odd | 4 | |||
7360.2.a.ca.1.1 | 3 | 8.3 | odd | 2 | |||
7360.2.a.cb.1.3 | 3 | 8.5 | even | 2 | |||
8280.2.a.bo.1.1 | 3 | 3.2 | odd | 2 | |||
9200.2.a.cd.1.1 | 3 | 20.19 | odd | 2 |