Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, 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("1840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(14.6924739719\) |
Analytic rank: | \(1\) |
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: | no (minimal twist has level 920) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.14510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | \(-0.287442\pi\) | ||||
0.619238 | + | 0.785204i | \(0.287442\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.14510 | 0.432808 | 0.216404 | − | 0.976304i | \(-0.430567\pi\) | ||||
0.216404 | + | 0.976304i | \(0.430567\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.60147 | 0.533822 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.89167 | −1.77641 | −0.888203 | − | 0.459452i | \(-0.848046\pi\) | ||||
−0.888203 | + | 0.459452i | \(0.848046\pi\) | |||||||
\(12\) | 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 | \(-0.413195\pi\) | ||||
0.269338 | + | 0.963046i | \(0.413195\pi\) | |||||||
\(20\) | 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 | \(-0.670674\pi\) | ||||
−0.510864 | + | 0.859662i | \(0.670674\pi\) | |||||||
\(32\) | 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 | \(-0.840024\pi\) | ||||
−0.876343 | + | 0.481687i | \(0.840024\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.60147 | −0.238732 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.74657 | −1.12995 | −0.564977 | − | 0.825107i | \(-0.691115\pi\) | ||||
−0.564977 | + | 0.825107i | \(0.691115\pi\) | |||||||
\(48\) | 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 | \(-0.516523\pi\) | ||||
−0.0518848 | + | 0.998653i | \(0.516523\pi\) | |||||||
\(60\) | 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 | \(-0.100175\pi\) | ||||
0.950887 | + | 0.309540i | \(0.100175\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.14510 | −0.258240 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.94217 | −0.349172 | −0.174586 | − | 0.984642i | \(-0.555859\pi\) | ||||
−0.174586 | + | 0.984642i | \(0.555859\pi\) | |||||||
\(72\) | 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 | \(-0.484048\pi\) | ||||
0.0500923 | + | 0.998745i | \(0.484048\pi\) | |||||||
\(84\) | 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 | \(-0.337972\pi\) | ||||
0.487328 | + | 0.873219i | \(0.337972\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.45636 | −0.239716 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.6961 | −1.22738 | −0.613688 | − | 0.789549i | \(-0.710315\pi\) | ||||
−0.613688 | + | 0.789549i | \(0.710315\pi\) | |||||||
\(108\) | 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 | \(-0.681265\pi\) | ||||
−0.539177 | + | 0.842193i | \(0.681265\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.6540 | −2.17066 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.94950 | 0.607181 | 0.303590 | − | 0.952803i | \(-0.401815\pi\) | ||||
0.303590 | + | 0.952803i | \(0.401815\pi\) | |||||||
\(132\) | 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 | \(-0.628165\pi\) | ||||
−0.391851 | + | 0.920029i | \(0.628165\pi\) | |||||||
\(140\) | 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 | \(-0.624202\pi\) | ||||
−0.380366 | + | 0.924836i | \(0.624202\pi\) | |||||||
\(152\) | 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 | \(-0.813049\pi\) | ||||
−0.832427 | + | 0.554135i | \(0.813049\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.6382 | 0.983886 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.9863 | 0.850143 | 0.425072 | − | 0.905160i | \(-0.360249\pi\) | ||||
0.425072 | + | 0.905160i | \(0.360249\pi\) | |||||||
\(168\) | 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 | \(-0.623874\pi\) | ||||
−0.379414 | + | 0.925227i | \(0.623874\pi\) | |||||||
\(180\) | 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 | \(-0.321559\pi\) | ||||
0.531685 | + | 0.846942i | \(0.321559\pi\) | |||||||
\(192\) | 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 | \(-0.721314\pi\) | ||||
−0.640600 | + | 0.767875i | \(0.721314\pi\) | |||||||
\(200\) | 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 | \(-0.365675\pi\) | ||||
0.409580 | + | 0.912274i | \(0.365675\pi\) | |||||||
\(212\) | 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 | \(-0.549011\pi\) | ||||
−0.153363 | + | 0.988170i | \(0.549011\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.60147 | 0.106764 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.21666 | −0.147125 | −0.0735624 | − | 0.997291i | \(-0.523437\pi\) | ||||
−0.0735624 | + | 0.997291i | \(0.523437\pi\) | |||||||
\(228\) | 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 | \(-0.736961\pi\) | ||||
−0.677555 | + | 0.735472i | \(0.736961\pi\) | |||||||
\(240\) | 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 | \(-0.420554\pi\) | ||||
0.247003 | + | 0.969015i | \(0.420554\pi\) | |||||||
\(252\) | 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 | \(-0.350399\pi\) | ||||
0.452873 | + | 0.891575i | \(0.350399\pi\) | |||||||
\(264\) | 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 | \(-0.296912\pi\) | ||||
0.595607 | + | 0.803276i | \(0.296912\pi\) | |||||||
\(272\) | 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 | \(-0.681336\pi\) | ||||
−0.539366 | + | 0.842071i | \(0.681336\pi\) | |||||||
\(284\) | 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 | \(-0.774176\pi\) | ||||
−0.758721 | + | 0.651415i | \(0.774176\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.2186 | 1.20709 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5299 | −0.767211 | −0.383605 | − | 0.923497i | \(-0.625318\pi\) | ||||
−0.383605 | + | 0.923497i | \(0.625318\pi\) | |||||||
\(312\) | 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 | \(-0.380768\pi\) | ||||
0.365881 | + | 0.930662i | \(0.380768\pi\) | |||||||
\(332\) | 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 | \(-0.434595\pi\) | ||||
0.204034 | + | 0.978964i | \(0.434595\pi\) | |||||||
\(348\) | 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 | \(-0.589428\pi\) | ||||
−0.277266 | + | 0.960793i | \(0.589428\pi\) | |||||||
\(360\) | 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 | \(-0.842886\pi\) | ||||
−0.880639 | + | 0.473788i | \(0.842886\pi\) | |||||||
\(368\) | 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 | \(-0.170887\pi\) | ||||
0.859320 | + | 0.511438i | \(0.170887\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.0682 | −1.33551 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.0873 | −0.668728 | −0.334364 | − | 0.942444i | \(-0.608522\pi\) | ||||
−0.334364 | + | 0.942444i | \(0.608522\pi\) | |||||||
\(384\) | 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 | \(-0.455790\pi\) | ||||
0.138442 | + | 0.990371i | \(0.455790\pi\) | |||||||
\(420\) | 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 | \(-0.749894\pi\) | ||||
−0.706870 | + | 0.707343i | \(0.749894\pi\) | |||||||
\(432\) | 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 | \(-0.334749\pi\) | ||||
0.496142 | + | 0.868241i | \(0.334749\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.11032 | −0.433825 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.2975 | −1.01188 | −0.505938 | − | 0.862570i | \(-0.668854\pi\) | ||||
−0.505938 | + | 0.862570i | \(0.668854\pi\) | |||||||
\(444\) | 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 | \(-0.368624\pi\) | ||||
0.401112 | + | 0.916029i | \(0.368624\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.2029 | 0.565897 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.4510 | 0.992635 | 0.496318 | − | 0.868141i | \(-0.334685\pi\) | ||||
0.496318 | + | 0.868141i | \(0.334685\pi\) | |||||||
\(468\) | 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 | \(-0.569587\pi\) | ||||
−0.216876 | + | 0.976199i | \(0.569587\pi\) | |||||||
\(480\) | 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 | \(-0.834839\pi\) | ||||
−0.868381 | + | 0.495898i | \(0.834839\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −45.5951 | −2.06188 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.9947 | 0.631570 | 0.315785 | − | 0.948831i | \(-0.397732\pi\) | ||||
0.315785 | + | 0.948831i | \(0.397732\pi\) | |||||||
\(492\) | 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 | \(-0.499542\pi\) | ||||
0.00143761 | + | 0.999999i | \(0.499542\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.5667 | 1.05288 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.2785 | 1.08252 | 0.541262 | − | 0.840854i | \(-0.317947\pi\) | ||||
0.541262 | + | 0.840854i | \(0.317947\pi\) | |||||||
\(504\) | 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 | \(-0.374523\pi\) | ||||
0.384069 | + | 0.923305i | \(0.374523\pi\) | |||||||
\(524\) | 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 | \(-0.383439\pi\) | ||||
0.358058 | + | 0.933699i | \(0.383439\pi\) | |||||||
\(548\) | 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 | \(-0.759604\pi\) | ||||
−0.728117 | + | 0.685453i | \(0.759604\pi\) | |||||||
\(564\) | 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 | \(-0.599546\pi\) | ||||
−0.307659 | + | 0.951497i | \(0.599546\pi\) | |||||||
\(572\) | 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 | \(-0.491240\pi\) | ||||
0.0275172 | + | 0.999621i | \(0.491240\pi\) | |||||||
\(588\) | 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 | \(-0.147846\pi\) | ||||
0.894058 | + | 0.447951i | \(0.147846\pi\) | |||||||
\(600\) | 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 | \(-0.539992\pi\) | ||||
−0.125309 | + | 0.992118i | \(0.539992\pi\) | |||||||
\(608\) | 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 | \(-0.572001\pi\) | ||||
−0.224274 | + | 0.974526i | \(0.572001\pi\) | |||||||
\(620\) | 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 | \(-0.469092\pi\) | ||||
0.0969481 | + | 0.995289i | \(0.469092\pi\) | |||||||
\(632\) | 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 | \(-0.894561\pi\) | ||||
−0.945637 | + | 0.325223i | \(0.894561\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.6540 | 0.970749 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.1103 | −0.476106 | −0.238053 | − | 0.971252i | \(-0.576509\pi\) | ||||
−0.238053 | + | 0.971252i | \(0.576509\pi\) | |||||||
\(648\) | 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 | \(-0.630290\pi\) | ||||
−0.397984 | + | 0.917392i | \(0.630290\pi\) | |||||||
\(660\) | 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 | \(-0.362532\pi\) | ||||
0.418568 | + | 0.908185i | \(0.362532\pi\) | |||||||
\(684\) | 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 | \(-0.479983\pi\) | ||||
0.0628438 | + | 0.998023i | \(0.479983\pi\) | |||||||
\(692\) | 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 | \(-0.572275\pi\) | ||||
−0.225114 | + | 0.974332i | \(0.572275\pi\) | |||||||
\(720\) | 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 | \(-0.567965\pi\) | ||||
−0.211900 | + | 0.977291i | \(0.567965\pi\) | |||||||
\(728\) | 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 | \(-0.450807\pi\) | ||||
0.153931 | + | 0.988082i | \(0.450807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.6382 | −0.905108 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.1598 | −0.556158 | −0.278079 | − | 0.960558i | \(-0.589698\pi\) | ||||
−0.278079 | + | 0.960558i | \(0.589698\pi\) | |||||||
\(744\) | 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 | \(-0.289340\pi\) | ||||
0.614543 | + | 0.788883i | \(0.289340\pi\) | |||||||
\(752\) | 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 | \(-0.621770\pi\) | ||||
−0.373289 | + | 0.927715i | \(0.621770\pi\) | |||||||
\(788\) | 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 | \(-0.378967\pi\) | ||||
0.371140 | + | 0.928577i | \(0.378967\pi\) | |||||||
\(812\) | 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 | \(-0.643027\pi\) | ||||
−0.434364 | + | 0.900737i | \(0.643027\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.6382 | −0.440007 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.62252 | 0.230288 | 0.115144 | − | 0.993349i | \(-0.463267\pi\) | ||||
0.115144 | + | 0.993349i | \(0.463267\pi\) | |||||||
\(828\) | 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 | \(-0.762946\pi\) | ||||
−0.735272 | + | 0.677772i | \(0.762946\pi\) | |||||||
\(840\) | 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 | \(-0.421250\pi\) | ||||
0.244883 | + | 0.969553i | \(0.421250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.59841 | −0.0885536 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.9211 | −0.541961 | −0.270981 | − | 0.962585i | \(-0.587348\pi\) | ||||
−0.270981 | + | 0.962585i | \(0.587348\pi\) | |||||||
\(864\) | 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 | \(-0.639905\pi\) | ||||
−0.425508 | + | 0.904955i | \(0.639905\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.70979 | 0.0574741 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.2849 | 1.08402 | 0.542010 | − | 0.840372i | \(-0.317664\pi\) | ||||
0.542010 | + | 0.840372i | \(0.317664\pi\) | |||||||
\(888\) | 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 | \(-0.492186\pi\) | ||||
0.0245461 | + | 0.999699i | \(0.492186\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.47941 | 0.148573 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.70979 | −0.189174 | −0.0945870 | − | 0.995517i | \(-0.530153\pi\) | ||||
−0.0945870 | + | 0.995517i | \(0.530153\pi\) | |||||||
\(912\) | 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 | \(-0.621736\pi\) | ||||
−0.373190 | + | 0.927755i | \(0.621736\pi\) | |||||||
\(920\) | 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 | \(-0.323086\pi\) | ||||
0.527616 | + | 0.849483i | \(0.323086\pi\) | |||||||
\(948\) | 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 | \(-0.623736\pi\) | ||||
−0.379013 | + | 0.925392i | \(0.623736\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.6750 | −0.953299 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.9368 | −0.415163 | −0.207581 | − | 0.978218i | \(-0.566559\pi\) | ||||
−0.207581 | + | 0.978218i | \(0.566559\pi\) | |||||||
\(972\) | 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 | \(-0.637106\pi\) | ||||
−0.417536 | + | 0.908660i | \(0.637106\pi\) | |||||||
\(984\) | 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 | \(-0.147573\pi\) | ||||
0.894442 | + | 0.447185i | \(0.147573\pi\) | |||||||
\(992\) | 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 | 1840.2.a.t.1.3 | 3 | ||
4.3 | odd | 2 | 920.2.a.g.1.1 | ✓ | 3 | ||
5.4 | even | 2 | 9200.2.a.cd.1.1 | 3 | |||
8.3 | odd | 2 | 7360.2.a.cb.1.3 | 3 | |||
8.5 | even | 2 | 7360.2.a.ca.1.1 | 3 | |||
12.11 | even | 2 | 8280.2.a.bo.1.1 | 3 | |||
20.3 | even | 4 | 4600.2.e.r.4049.2 | 6 | |||
20.7 | even | 4 | 4600.2.e.r.4049.5 | 6 | |||
20.19 | odd | 2 | 4600.2.a.y.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.g.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
1840.2.a.t.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4600.2.a.y.1.3 | 3 | 20.19 | odd | 2 | |||
4600.2.e.r.4049.2 | 6 | 20.3 | even | 4 | |||
4600.2.e.r.4049.5 | 6 | 20.7 | even | 4 | |||
7360.2.a.ca.1.1 | 3 | 8.5 | even | 2 | |||
7360.2.a.cb.1.3 | 3 | 8.3 | odd | 2 | |||
8280.2.a.bo.1.1 | 3 | 12.11 | even | 2 | |||
9200.2.a.cd.1.1 | 3 | 5.4 | even | 2 |