Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(181,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3057647616.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 30x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.2 | ||
Root | \(1.65068 + 1.65068i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.181 |
Dual form | 1170.2.b.g.181.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.48393i | − | 0.560872i | −0.959873 | − | 0.280436i | \(-0.909521\pi\) | ||
0.959873 | − | 0.280436i | \(-0.0904790\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 4.89898i | 1.47710i | 0.674200 | + | 0.738549i | \(0.264489\pi\) | ||||
−0.674200 | + | 0.738549i | \(0.735511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.44949 | + | 3.30136i | 0.402016 | + | 0.915633i | ||||
\(14\) | −1.48393 | −0.396596 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 8.08665 | 1.96130 | 0.980650 | − | 0.195769i | \(-0.0627201\pi\) | ||||
0.980650 | + | 0.195769i | \(0.0627201\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.11879i | − | 1.17433i | −0.809467 | − | 0.587166i | \(-0.800244\pi\) | ||
0.809467 | − | 0.587166i | \(-0.199756\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.89898 | 1.04447 | ||||||||
\(23\) | 1.48393 | 0.309420 | 0.154710 | − | 0.987960i | \(-0.450556\pi\) | ||||
0.154710 | + | 0.987960i | \(0.450556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.30136 | − | 1.44949i | 0.647450 | − | 0.284268i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.48393i | 0.280436i | ||||||||
\(29\) | 5.11879 | 0.950536 | 0.475268 | − | 0.879841i | \(-0.342351\pi\) | ||||
0.475268 | + | 0.879841i | \(0.342351\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.60272i | − | 1.18588i | −0.805245 | − | 0.592942i | \(-0.797966\pi\) | ||
0.805245 | − | 0.592942i | \(-0.202034\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 8.08665i | − | 1.38685i | ||||||
\(35\) | −1.48393 | −0.250830 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.63487i | − | 0.597568i | −0.954321 | − | 0.298784i | \(-0.903419\pi\) | ||
0.954321 | − | 0.298784i | \(-0.0965810\pi\) | |||||||
\(38\) | −5.11879 | −0.830378 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | − | 1.10102i | − | 0.171951i | −0.996297 | − | 0.0859753i | \(-0.972599\pi\) | ||
0.996297 | − | 0.0859753i | \(-0.0274006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | − | 4.89898i | − | 0.738549i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 1.48393i | − | 0.218793i | ||||||
\(47\) | 9.79796i | 1.42918i | 0.699544 | + | 0.714590i | \(0.253387\pi\) | ||||
−0.699544 | + | 0.714590i | \(0.746613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.79796 | 0.685423 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.44949 | − | 3.30136i | −0.201008 | − | 0.457816i | ||||
\(53\) | −6.60272 | −0.906953 | −0.453477 | − | 0.891268i | \(-0.649816\pi\) | ||||
−0.453477 | + | 0.891268i | \(0.649816\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.89898 | 0.660578 | ||||||||
\(56\) | 1.48393 | 0.198298 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 5.11879i | − | 0.672130i | ||||||
\(59\) | − | 4.89898i | − | 0.637793i | −0.947790 | − | 0.318896i | \(-0.896688\pi\) | ||
0.947790 | − | 0.318896i | \(-0.103312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | −6.60272 | −0.838546 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.30136 | − | 1.44949i | 0.409483 | − | 0.179787i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.57058i | − | 1.16923i | −0.811310 | − | 0.584616i | \(-0.801245\pi\) | ||
0.811310 | − | 0.584616i | \(-0.198755\pi\) | |||||||
\(68\) | −8.08665 | −0.980650 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.48393i | 0.177363i | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.45178i | − | 0.521042i | −0.965468 | − | 0.260521i | \(-0.916106\pi\) | ||
0.965468 | − | 0.260521i | \(-0.0838943\pi\) | |||||||
\(74\) | −3.63487 | −0.422545 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.11879i | 0.587166i | ||||||||
\(77\) | 7.26973 | 0.828463 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7980 | 1.55239 | 0.776196 | − | 0.630492i | \(-0.217147\pi\) | ||||
0.776196 | + | 0.630492i | \(0.217147\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.10102 | −0.121587 | ||||||||
\(83\) | − | 9.79796i | − | 1.07547i | −0.843115 | − | 0.537733i | \(-0.819281\pi\) | ||
0.843115 | − | 0.537733i | \(-0.180719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 8.08665i | − | 0.877120i | ||||||
\(86\) | 4.00000i | 0.431331i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.89898 | −0.522233 | ||||||||
\(89\) | 10.8990i | 1.15529i | 0.816288 | + | 0.577645i | \(0.196028\pi\) | ||||
−0.816288 | + | 0.577645i | \(0.803972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.89898 | − | 2.15094i | 0.513553 | − | 0.225480i | ||||
\(92\) | −1.48393 | −0.154710 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.79796 | 1.01058 | ||||||||
\(95\) | −5.11879 | −0.525177 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.6572i | 1.79282i | 0.443226 | + | 0.896410i | \(0.353834\pi\) | ||||
−0.443226 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(98\) | − | 4.79796i | − | 0.484667i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 18.3242 | 1.82333 | 0.911665 | − | 0.410935i | \(-0.134798\pi\) | ||||
0.911665 | + | 0.410935i | \(0.134798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8990 | 1.27097 | 0.635487 | − | 0.772111i | \(-0.280799\pi\) | ||||
0.635487 | + | 0.772111i | \(0.280799\pi\) | |||||||
\(104\) | −3.30136 | + | 1.44949i | −0.323725 | + | 0.142134i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.60272i | 0.641313i | ||||||||
\(107\) | 5.93571 | 0.573827 | 0.286913 | − | 0.957957i | \(-0.407371\pi\) | ||||
0.286913 | + | 0.957957i | \(0.407371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.6572i | − | 1.69126i | −0.533773 | − | 0.845628i | \(-0.679226\pi\) | ||
0.533773 | − | 0.845628i | \(-0.320774\pi\) | |||||||
\(110\) | − | 4.89898i | − | 0.467099i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.48393i | − | 0.140218i | ||||||
\(113\) | −5.11879 | −0.481536 | −0.240768 | − | 0.970583i | \(-0.577399\pi\) | ||||
−0.240768 | + | 0.970583i | \(0.577399\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.48393i | − | 0.138377i | ||||||
\(116\) | −5.11879 | −0.475268 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.89898 | −0.450988 | ||||||||
\(119\) | − | 12.0000i | − | 1.10004i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.0000 | −1.18182 | ||||||||
\(122\) | 2.00000i | 0.181071i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.60272i | 0.592942i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8990 | −1.14460 | −0.572300 | − | 0.820045i | \(-0.693949\pi\) | ||||
−0.572300 | + | 0.820045i | \(0.693949\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.44949 | − | 3.30136i | −0.127129 | − | 0.289548i | ||||
\(131\) | 11.0545 | 0.965836 | 0.482918 | − | 0.875665i | \(-0.339577\pi\) | ||||
0.482918 | + | 0.875665i | \(0.339577\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.59592 | −0.658650 | ||||||||
\(134\) | −9.57058 | −0.826772 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.08665i | 0.693424i | ||||||||
\(137\) | 3.79796i | 0.324482i | 0.986751 | + | 0.162241i | \(0.0518721\pi\) | ||||
−0.986751 | + | 0.162241i | \(0.948128\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.7980 | −1.17033 | −0.585164 | − | 0.810915i | \(-0.698970\pi\) | ||||
−0.585164 | + | 0.810915i | \(0.698970\pi\) | |||||||
\(140\) | 1.48393 | 0.125415 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.1733 | + | 7.10102i | −1.35248 | + | 0.593817i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.11879i | − | 0.425093i | ||||||
\(146\) | −4.45178 | −0.368432 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.63487i | 0.298784i | ||||||||
\(149\) | 15.7980i | 1.29422i | 0.762397 | + | 0.647110i | \(0.224022\pi\) | ||||
−0.762397 | + | 0.647110i | \(0.775978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.60272i | 0.537322i | 0.963235 | + | 0.268661i | \(0.0865811\pi\) | ||||
−0.963235 | + | 0.268661i | \(0.913419\pi\) | |||||||
\(152\) | 5.11879 | 0.415189 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 7.26973i | − | 0.585812i | ||||||
\(155\) | −6.60272 | −0.530343 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.10102 | 0.726341 | 0.363170 | − | 0.931723i | \(-0.381694\pi\) | ||||
0.363170 | + | 0.931723i | \(0.381694\pi\) | |||||||
\(158\) | − | 13.7980i | − | 1.09771i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | − | 2.20204i | − | 0.173545i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.60272i | 0.517165i | 0.965989 | + | 0.258582i | \(0.0832554\pi\) | ||||
−0.965989 | + | 0.258582i | \(0.916745\pi\) | |||||||
\(164\) | 1.10102i | 0.0859753i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.79796 | −0.760469 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.79796 | + | 9.57058i | −0.676766 | + | 0.736198i | ||||
\(170\) | −8.08665 | −0.620218 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | 0.304997 | ||||||||
\(173\) | −12.5384 | −0.953279 | −0.476640 | − | 0.879099i | \(-0.658145\pi\) | ||||
−0.476640 | + | 0.879099i | \(0.658145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.48393i | 0.112174i | ||||||||
\(176\) | 4.89898i | 0.369274i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.8990 | 0.816913 | ||||||||
\(179\) | −21.2921 | −1.59145 | −0.795723 | − | 0.605661i | \(-0.792909\pi\) | ||||
−0.795723 | + | 0.605661i | \(0.792909\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.7980 | 1.76889 | 0.884444 | − | 0.466646i | \(-0.154538\pi\) | ||||
0.884444 | + | 0.466646i | \(0.154538\pi\) | |||||||
\(182\) | −2.15094 | − | 4.89898i | −0.159438 | − | 0.363137i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.48393i | 0.109397i | ||||||||
\(185\) | −3.63487 | −0.267241 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 39.6163i | 2.89703i | ||||||||
\(188\) | − | 9.79796i | − | 0.714590i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.11879i | 0.371356i | ||||||||
\(191\) | 20.4752 | 1.48153 | 0.740766 | − | 0.671763i | \(-0.234463\pi\) | ||||
0.740766 | + | 0.671763i | \(0.234463\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.6572i | 1.27099i | 0.772103 | + | 0.635497i | \(0.219205\pi\) | ||||
−0.772103 | + | 0.635497i | \(0.780795\pi\) | |||||||
\(194\) | 17.6572 | 1.26771 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.79796 | −0.342711 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 18.3242i | − | 1.28929i | ||||||
\(203\) | − | 7.59592i | − | 0.533129i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.10102 | −0.0768986 | ||||||||
\(206\) | − | 12.8990i | − | 0.898714i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.44949 | + | 3.30136i | 0.100504 | + | 0.228908i | ||||
\(209\) | 25.0769 | 1.73460 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.79796 | −0.399148 | −0.199574 | − | 0.979883i | \(-0.563956\pi\) | ||||
−0.199574 | + | 0.979883i | \(0.563956\pi\) | |||||||
\(212\) | 6.60272 | 0.453477 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 5.93571i | − | 0.405757i | ||||||
\(215\) | 4.00000i | 0.272798i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.79796 | −0.665129 | ||||||||
\(218\) | −17.6572 | −1.19590 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.89898 | −0.330289 | ||||||||
\(221\) | 11.7215 | + | 26.6969i | 0.788474 | + | 1.79583i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6572i | 1.18242i | 0.806519 | + | 0.591208i | \(0.201349\pi\) | ||||
−0.806519 | + | 0.591208i | \(0.798651\pi\) | |||||||
\(224\) | −1.48393 | −0.0991491 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.11879i | 0.340497i | ||||||||
\(227\) | 2.20204i | 0.146155i | 0.997326 | + | 0.0730773i | \(0.0232820\pi\) | ||||
−0.997326 | + | 0.0730773i | \(0.976718\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.48393i | − | 0.0980607i | −0.998797 | − | 0.0490303i | \(-0.984387\pi\) | ||
0.998797 | − | 0.0490303i | \(-0.0156131\pi\) | |||||||
\(230\) | −1.48393 | −0.0978473 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.11879i | 0.336065i | ||||||||
\(233\) | −5.11879 | −0.335343 | −0.167672 | − | 0.985843i | \(-0.553625\pi\) | ||||
−0.167672 | + | 0.985843i | \(0.553625\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.79796 | 0.639148 | ||||||||
\(236\) | 4.89898i | 0.318896i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.0000 | −0.777844 | ||||||||
\(239\) | − | 2.20204i | − | 0.142438i | −0.997461 | − | 0.0712191i | \(-0.977311\pi\) | ||
0.997461 | − | 0.0712191i | \(-0.0226890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.93571i | − | 0.382353i | −0.981556 | − | 0.191176i | \(-0.938770\pi\) | ||
0.981556 | − | 0.191176i | \(-0.0612302\pi\) | |||||||
\(242\) | 13.0000i | 0.835672i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | − | 4.79796i | − | 0.306530i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.8990 | − | 7.41964i | 1.07526 | − | 0.472100i | ||||
\(248\) | 6.60272 | 0.419273 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −8.08665 | −0.510425 | −0.255212 | − | 0.966885i | \(-0.582145\pi\) | ||||
−0.255212 | + | 0.966885i | \(0.582145\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.26973i | 0.457044i | ||||||||
\(254\) | 12.8990i | 0.809354i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.0545 | 0.689561 | 0.344780 | − | 0.938683i | \(-0.387953\pi\) | ||||
0.344780 | + | 0.938683i | \(0.387953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.39388 | −0.335159 | ||||||||
\(260\) | −3.30136 | + | 1.44949i | −0.204742 | + | 0.0898935i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 11.0545i | − | 0.682949i | ||||||
\(263\) | −11.7215 | −0.722779 | −0.361390 | − | 0.932415i | \(-0.617698\pi\) | ||||
−0.361390 | + | 0.932415i | \(0.617698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.60272i | 0.405602i | ||||||||
\(266\) | 7.59592i | 0.465736i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.57058i | 0.584616i | ||||||||
\(269\) | 14.0224 | 0.854958 | 0.427479 | − | 0.904025i | \(-0.359402\pi\) | ||||
0.427479 | + | 0.904025i | \(0.359402\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.5384i | − | 0.761655i | −0.924646 | − | 0.380828i | \(-0.875639\pi\) | ||
0.924646 | − | 0.380828i | \(-0.124361\pi\) | |||||||
\(272\) | 8.08665 | 0.490325 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.79796 | 0.229443 | ||||||||
\(275\) | − | 4.89898i | − | 0.295420i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.6969 | −1.48390 | −0.741948 | − | 0.670458i | \(-0.766098\pi\) | ||||
−0.741948 | + | 0.670458i | \(0.766098\pi\) | |||||||
\(278\) | 13.7980i | 0.827547i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 1.48393i | − | 0.0886816i | ||||||
\(281\) | 8.69694i | 0.518816i | 0.965768 | + | 0.259408i | \(0.0835274\pi\) | ||||
−0.965768 | + | 0.259408i | \(0.916473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.7980 | −1.77130 | −0.885652 | − | 0.464349i | \(-0.846288\pi\) | ||||
−0.885652 | + | 0.464349i | \(0.846288\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.10102 | + | 16.1733i | 0.419892 | + | 0.956347i | ||||
\(287\) | −1.63383 | −0.0964422 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 48.3939 | 2.84670 | ||||||||
\(290\) | −5.11879 | −0.300586 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.45178i | 0.260521i | ||||||||
\(293\) | − | 18.0000i | − | 1.05157i | −0.850617 | − | 0.525786i | \(-0.823771\pi\) | ||
0.850617 | − | 0.525786i | \(-0.176229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.89898 | −0.285230 | ||||||||
\(296\) | 3.63487 | 0.211272 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.7980 | 0.915151 | ||||||||
\(299\) | 2.15094 | + | 4.89898i | 0.124392 | + | 0.283315i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.93571i | 0.342129i | ||||||||
\(302\) | 6.60272 | 0.379944 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 5.11879i | − | 0.293583i | ||||||
\(305\) | 2.00000i | 0.114520i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.57058i | 0.546222i | 0.961983 | + | 0.273111i | \(0.0880526\pi\) | ||||
−0.961983 | + | 0.273111i | \(0.911947\pi\) | |||||||
\(308\) | −7.26973 | −0.414231 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.60272i | 0.375009i | ||||||||
\(311\) | 5.93571 | 0.336583 | 0.168292 | − | 0.985737i | \(-0.446175\pi\) | ||||
0.168292 | + | 0.985737i | \(0.446175\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.3939 | −1.77449 | −0.887243 | − | 0.461302i | \(-0.847383\pi\) | ||||
−0.887243 | + | 0.461302i | \(0.847383\pi\) | |||||||
\(314\) | − | 9.10102i | − | 0.513600i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.7980 | −0.776196 | ||||||||
\(317\) | 13.5959i | 0.763623i | 0.924240 | + | 0.381811i | \(0.124700\pi\) | ||||
−0.924240 | + | 0.381811i | \(0.875300\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.0769i | 1.40403i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.20204 | −0.122715 | ||||||||
\(323\) | − | 41.3939i | − | 2.30322i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.44949 | − | 3.30136i | −0.0804032 | − | 0.183127i | ||||
\(326\) | 6.60272 | 0.365691 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.10102 | 0.0607937 | ||||||||
\(329\) | 14.5395 | 0.801586 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.2599i | − | 1.33345i | −0.745305 | − | 0.666724i | \(-0.767696\pi\) | ||
0.745305 | − | 0.666724i | \(-0.232304\pi\) | |||||||
\(332\) | 9.79796i | 0.537733i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.57058 | −0.522896 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0000 | 0.544735 | 0.272367 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272367 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(338\) | 9.57058 | + | 8.79796i | 0.520571 | + | 0.478546i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.08665i | 0.438560i | ||||||||
\(341\) | 32.3466 | 1.75167 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.5073i | − | 0.945306i | ||||||
\(344\) | − | 4.00000i | − | 0.215666i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.5384i | 0.674070i | ||||||||
\(347\) | −35.3144 | −1.89578 | −0.947889 | − | 0.318599i | \(-0.896788\pi\) | ||||
−0.947889 | + | 0.318599i | \(0.896788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.9912i | 1.01658i | 0.861187 | + | 0.508289i | \(0.169722\pi\) | ||||
−0.861187 | + | 0.508289i | \(0.830278\pi\) | |||||||
\(350\) | 1.48393 | 0.0793193 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.89898 | 0.261116 | ||||||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 10.8990i | − | 0.577645i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.2921i | 1.12532i | ||||||||
\(359\) | − | 9.79796i | − | 0.517116i | −0.965996 | − | 0.258558i | \(-0.916753\pi\) | ||
0.965996 | − | 0.258558i | \(-0.0832474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.20204 | −0.379055 | ||||||||
\(362\) | − | 23.7980i | − | 1.25079i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.89898 | + | 2.15094i | −0.256776 | + | 0.112740i | ||||
\(365\) | −4.45178 | −0.233017 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.69694 | −0.349577 | −0.174789 | − | 0.984606i | \(-0.555924\pi\) | ||||
−0.174789 | + | 0.984606i | \(0.555924\pi\) | |||||||
\(368\) | 1.48393 | 0.0773551 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.63487i | 0.188968i | ||||||||
\(371\) | 9.79796i | 0.508685i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.6969 | 0.657423 | 0.328711 | − | 0.944430i | \(-0.393386\pi\) | ||||
0.328711 | + | 0.944430i | \(0.393386\pi\) | |||||||
\(374\) | 39.6163 | 2.04851 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.79796 | −0.505291 | ||||||||
\(377\) | 7.41964 | + | 16.8990i | 0.382131 | + | 0.870342i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.3885i | 0.636356i | 0.948031 | + | 0.318178i | \(0.103071\pi\) | ||||
−0.948031 | + | 0.318178i | \(0.896929\pi\) | |||||||
\(380\) | 5.11879 | 0.262589 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 20.4752i | − | 1.04760i | ||||||
\(383\) | 33.7980i | 1.72700i | 0.504353 | + | 0.863498i | \(0.331731\pi\) | ||||
−0.504353 | + | 0.863498i | \(0.668269\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 7.26973i | − | 0.370500i | ||||||
\(386\) | 17.6572 | 0.898729 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 17.6572i | − | 0.896410i | ||||||
\(389\) | −14.0224 | −0.710962 | −0.355481 | − | 0.934684i | \(-0.615683\pi\) | ||||
−0.355481 | + | 0.934684i | \(0.615683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 4.79796i | 0.242334i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | − | 13.7980i | − | 0.694251i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.57058i | 0.480333i | 0.970732 | + | 0.240167i | \(0.0772021\pi\) | ||||
−0.970732 | + | 0.240167i | \(0.922798\pi\) | |||||||
\(398\) | 20.0000i | 1.00251i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 8.69694i | 0.434304i | 0.976138 | + | 0.217152i | \(0.0696768\pi\) | ||||
−0.976138 | + | 0.217152i | \(0.930323\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.7980 | − | 9.57058i | 1.08583 | − | 0.476744i | ||||
\(404\) | −18.3242 | −0.911665 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.59592 | −0.376979 | ||||||||
\(407\) | 17.8071 | 0.882667 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.2376i | − | 0.506216i | −0.967438 | − | 0.253108i | \(-0.918547\pi\) | ||
0.967438 | − | 0.253108i | \(-0.0814528\pi\) | |||||||
\(410\) | 1.10102i | 0.0543755i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.8990 | −0.635487 | ||||||||
\(413\) | −7.26973 | −0.357720 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.79796 | −0.480963 | ||||||||
\(416\) | 3.30136 | − | 1.44949i | 0.161863 | − | 0.0710671i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 25.0769i | − | 1.22655i | ||||||
\(419\) | −27.2278 | −1.33017 | −0.665083 | − | 0.746770i | \(-0.731604\pi\) | ||||
−0.665083 | + | 0.746770i | \(0.731604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.45178i | 0.216967i | 0.994098 | + | 0.108483i | \(0.0345994\pi\) | ||||
−0.994098 | + | 0.108483i | \(0.965401\pi\) | |||||||
\(422\) | 5.79796i | 0.282240i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 6.60272i | − | 0.320656i | ||||||
\(425\) | −8.08665 | −0.392260 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.96786i | 0.143625i | ||||||||
\(428\) | −5.93571 | −0.286913 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | − | 7.59592i | − | 0.365882i | −0.983124 | − | 0.182941i | \(-0.941438\pi\) | ||
0.983124 | − | 0.182941i | \(-0.0585618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 9.79796i | 0.470317i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.6572i | 0.845628i | ||||||||
\(437\) | − | 7.59592i | − | 0.363362i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.5959 | −0.553443 | −0.276721 | − | 0.960950i | \(-0.589248\pi\) | ||||
−0.276721 | + | 0.960950i | \(0.589248\pi\) | |||||||
\(440\) | 4.89898i | 0.233550i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.6969 | − | 11.7215i | 1.26984 | − | 0.557536i | ||||
\(443\) | −30.7128 | −1.45921 | −0.729604 | − | 0.683870i | \(-0.760295\pi\) | ||||
−0.729604 | + | 0.683870i | \(0.760295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.8990 | 0.516661 | ||||||||
\(446\) | 17.6572 | 0.836094 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.48393i | 0.0701090i | ||||||||
\(449\) | 10.8990i | 0.514355i | 0.966364 | + | 0.257177i | \(0.0827924\pi\) | ||||
−0.966364 | + | 0.257177i | \(0.917208\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.39388 | 0.253988 | ||||||||
\(452\) | 5.11879 | 0.240768 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.20204 | 0.103347 | ||||||||
\(455\) | −2.15094 | − | 4.89898i | −0.100838 | − | 0.229668i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.7215i | 0.548309i | 0.961686 | + | 0.274155i | \(0.0883980\pi\) | ||||
−0.961686 | + | 0.274155i | \(0.911602\pi\) | |||||||
\(458\) | −1.48393 | −0.0693394 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.48393i | 0.0691885i | ||||||||
\(461\) | − | 15.7980i | − | 0.735784i | −0.929868 | − | 0.367892i | \(-0.880080\pi\) | ||
0.929868 | − | 0.367892i | \(-0.119920\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11.7215i | − | 0.544745i | −0.962192 | − | 0.272372i | \(-0.912192\pi\) | ||
0.962192 | − | 0.272372i | \(-0.0878083\pi\) | |||||||
\(464\) | 5.11879 | 0.237634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.11879i | 0.237124i | ||||||||
\(467\) | −13.2054 | −0.611075 | −0.305537 | − | 0.952180i | \(-0.598836\pi\) | ||||
−0.305537 | + | 0.952180i | \(0.598836\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.2020 | −0.655789 | ||||||||
\(470\) | − | 9.79796i | − | 0.451946i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.89898 | 0.225494 | ||||||||
\(473\) | − | 19.5959i | − | 0.901021i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.11879i | 0.234866i | ||||||||
\(476\) | 12.0000i | 0.550019i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.20204 | −0.100719 | ||||||||
\(479\) | 2.20204i | 0.100614i | 0.998734 | + | 0.0503069i | \(0.0160199\pi\) | ||||
−0.998734 | + | 0.0503069i | \(0.983980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | − | 5.26870i | 0.547153 | − | 0.240232i | ||||
\(482\) | −5.93571 | −0.270364 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.0000 | 0.590909 | ||||||||
\(485\) | 17.6572 | 0.801773 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.3875i | − | 0.470702i | −0.971910 | − | 0.235351i | \(-0.924376\pi\) | ||
0.971910 | − | 0.235351i | \(-0.0756240\pi\) | |||||||
\(488\) | − | 2.00000i | − | 0.0905357i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.79796 | −0.216750 | ||||||||
\(491\) | −18.3242 | −0.826961 | −0.413481 | − | 0.910513i | \(-0.635687\pi\) | ||||
−0.413481 | + | 0.910513i | \(0.635687\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.3939 | 1.86429 | ||||||||
\(494\) | −7.41964 | − | 16.8990i | −0.333825 | − | 0.760321i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.60272i | − | 0.296471i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.11879i | 0.229149i | 0.993415 | + | 0.114574i | \(0.0365504\pi\) | ||||
−0.993415 | + | 0.114574i | \(0.963450\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.08665i | 0.360925i | ||||||||
\(503\) | −17.6572 | −0.787297 | −0.393648 | − | 0.919261i | \(-0.628787\pi\) | ||||
−0.393648 | + | 0.919261i | \(0.628787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 18.3242i | − | 0.815418i | ||||||
\(506\) | 7.26973 | 0.323179 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.8990 | 0.572300 | ||||||||
\(509\) | − | 30.0000i | − | 1.32973i | −0.746965 | − | 0.664863i | \(-0.768490\pi\) | ||
0.746965 | − | 0.664863i | \(-0.231510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.60612 | −0.292238 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 11.0545i | − | 0.487593i | ||||||
\(515\) | − | 12.8990i | − | 0.568397i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −48.0000 | −2.11104 | ||||||||
\(518\) | 5.39388i | 0.236993i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.44949 | + | 3.30136i | 0.0635643 | + | 0.144774i | ||||
\(521\) | −35.3144 | −1.54715 | −0.773577 | − | 0.633702i | \(-0.781534\pi\) | ||||
−0.773577 | + | 0.633702i | \(0.781534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.7980 | 1.82770 | 0.913849 | − | 0.406055i | \(-0.133096\pi\) | ||||
0.913849 | + | 0.406055i | \(0.133096\pi\) | |||||||
\(524\) | −11.0545 | −0.482918 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.7215i | 0.511082i | ||||||||
\(527\) | − | 53.3939i | − | 2.32587i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.7980 | −0.904259 | ||||||||
\(530\) | 6.60272 | 0.286804 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.59592 | 0.329325 | ||||||||
\(533\) | 3.63487 | − | 1.59592i | 0.157443 | − | 0.0691269i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5.93571i | − | 0.256623i | ||||||
\(536\) | 9.57058 | 0.413386 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 14.0224i | − | 0.604547i | ||||||
\(539\) | 23.5051i | 1.01244i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 32.1967i | − | 1.38424i | −0.721781 | − | 0.692122i | \(-0.756676\pi\) | ||
0.721781 | − | 0.692122i | \(-0.243324\pi\) | |||||||
\(542\) | −12.5384 | −0.538572 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 8.08665i | − | 0.346712i | ||||||
\(545\) | −17.6572 | −0.756352 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000 | 1.36822 | 0.684111 | − | 0.729378i | \(-0.260191\pi\) | ||||
0.684111 | + | 0.729378i | \(0.260191\pi\) | |||||||
\(548\) | − | 3.79796i | − | 0.162241i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.89898 | −0.208893 | ||||||||
\(551\) | − | 26.2020i | − | 1.11624i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 20.4752i | − | 0.870693i | ||||||
\(554\) | 24.6969i | 1.04927i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.7980 | 0.585164 | ||||||||
\(557\) | 13.5959i | 0.576078i | 0.957619 | + | 0.288039i | \(0.0930032\pi\) | ||||
−0.957619 | + | 0.288039i | \(0.906997\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.79796 | − | 13.2054i | −0.245228 | − | 0.558531i | ||||
\(560\) | −1.48393 | −0.0627074 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.69694 | 0.366858 | ||||||||
\(563\) | −36.6485 | −1.54455 | −0.772274 | − | 0.635289i | \(-0.780881\pi\) | ||||
−0.772274 | + | 0.635289i | \(0.780881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.11879i | 0.215349i | ||||||||
\(566\) | 29.7980i | 1.25250i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.96786 | 0.124419 | 0.0622095 | − | 0.998063i | \(-0.480185\pi\) | ||||
0.0622095 | + | 0.998063i | \(0.480185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.5959 | 0.987458 | 0.493729 | − | 0.869616i | \(-0.335633\pi\) | ||||
0.493729 | + | 0.869616i | \(0.335633\pi\) | |||||||
\(572\) | 16.1733 | − | 7.10102i | 0.676239 | − | 0.296909i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.63383i | 0.0681949i | ||||||||
\(575\) | −1.48393 | −0.0618841 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 24.9270i | − | 1.03772i | −0.854858 | − | 0.518861i | \(-0.826356\pi\) | ||
0.854858 | − | 0.518861i | \(-0.173644\pi\) | |||||||
\(578\) | − | 48.3939i | − | 2.01292i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.11879i | 0.212546i | ||||||||
\(581\) | −14.5395 | −0.603199 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 32.3466i | − | 1.33966i | ||||||
\(584\) | 4.45178 | 0.184216 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.7980 | −1.39262 | ||||||||
\(590\) | 4.89898i | 0.201688i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 3.63487i | − | 0.149392i | ||||||
\(593\) | 25.5959i | 1.05110i | 0.850763 | + | 0.525549i | \(0.176140\pi\) | ||||
−0.850763 | + | 0.525549i | \(0.823860\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | − | 15.7980i | − | 0.647110i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.89898 | − | 2.15094i | 0.200334 | − | 0.0879584i | ||||
\(599\) | 11.8714 | 0.485053 | 0.242527 | − | 0.970145i | \(-0.422024\pi\) | ||||
0.242527 | + | 0.970145i | \(0.422024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.3939 | 1.60691 | 0.803455 | − | 0.595366i | \(-0.202993\pi\) | ||||
0.803455 | + | 0.595366i | \(0.202993\pi\) | |||||||
\(602\) | 5.93571 | 0.241921 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 6.60272i | − | 0.268661i | ||||||
\(605\) | 13.0000i | 0.528525i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.30306 | −0.0528896 | −0.0264448 | − | 0.999650i | \(-0.508419\pi\) | ||||
−0.0264448 | + | 0.999650i | \(0.508419\pi\) | |||||||
\(608\) | −5.11879 | −0.207594 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.00000 | 0.0809776 | ||||||||
\(611\) | −32.3466 | + | 14.2020i | −1.30860 | + | 0.574553i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.63487i | − | 0.146811i | −0.997302 | − | 0.0734054i | \(-0.976613\pi\) | ||
0.997302 | − | 0.0734054i | \(-0.0233867\pi\) | |||||||
\(614\) | 9.57058 | 0.386237 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.26973i | 0.292906i | ||||||||
\(617\) | 39.7980i | 1.60221i | 0.598527 | + | 0.801103i | \(0.295753\pi\) | ||||
−0.598527 | + | 0.801103i | \(0.704247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.3690i | 1.86373i | 0.362811 | + | 0.931863i | \(0.381817\pi\) | ||||
−0.362811 | + | 0.931863i | \(0.618183\pi\) | |||||||
\(620\) | 6.60272 | 0.265172 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 5.93571i | − | 0.238000i | ||||||
\(623\) | 16.1733 | 0.647969 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 31.3939i | 1.25475i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.10102 | −0.363170 | ||||||||
\(629\) | − | 29.3939i | − | 1.17201i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.0457i | − | 1.19610i | −0.801458 | − | 0.598051i | \(-0.795942\pi\) | ||
0.801458 | − | 0.598051i | \(-0.204058\pi\) | |||||||
\(632\) | 13.7980i | 0.548853i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.5959 | 0.539963 | ||||||||
\(635\) | 12.8990i | 0.511880i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.95459 | + | 15.8398i | 0.275551 | + | 0.627595i | ||||
\(638\) | 25.0769 | 0.992802 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 20.4752 | 0.808721 | 0.404360 | − | 0.914600i | \(-0.367494\pi\) | ||||
0.404360 | + | 0.914600i | \(0.367494\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 35.9815i | − | 1.41897i | −0.704720 | − | 0.709485i | \(-0.748928\pi\) | ||
0.704720 | − | 0.709485i | \(-0.251072\pi\) | |||||||
\(644\) | 2.20204i | 0.0867726i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −41.3939 | −1.62862 | ||||||||
\(647\) | 11.7215 | 0.460820 | 0.230410 | − | 0.973094i | \(-0.425993\pi\) | ||||
0.230410 | + | 0.973094i | \(0.425993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | −3.30136 | + | 1.44949i | −0.129490 | + | 0.0568537i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 6.60272i | − | 0.258582i | ||||||
\(653\) | 10.9046 | 0.426730 | 0.213365 | − | 0.976973i | \(-0.431558\pi\) | ||||
0.213365 | + | 0.976973i | \(0.431558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 11.0545i | − | 0.431935i | ||||||
\(656\) | − | 1.10102i | − | 0.0429876i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 14.5395i | − | 0.566807i | ||||||
\(659\) | −2.15094 | −0.0837886 | −0.0418943 | − | 0.999122i | \(-0.513339\pi\) | ||||
−0.0418943 | + | 0.999122i | \(0.513339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 18.9912i | − | 0.738674i | −0.929296 | − | 0.369337i | \(-0.879585\pi\) | ||
0.929296 | − | 0.369337i | \(-0.120415\pi\) | |||||||
\(662\) | −24.2599 | −0.942890 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.79796 | 0.380235 | ||||||||
\(665\) | 7.59592i | 0.294557i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.59592 | 0.294115 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.57058i | 0.369744i | ||||||||
\(671\) | − | 9.79796i | − | 0.378246i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | − | 10.0000i | − | 0.385186i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.79796 | − | 9.57058i | 0.338383 | − | 0.368099i | ||||
\(677\) | −2.30084 | −0.0884287 | −0.0442143 | − | 0.999022i | \(-0.514078\pi\) | ||||
−0.0442143 | + | 0.999022i | \(0.514078\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.2020 | 1.00554 | ||||||||
\(680\) | 8.08665 | 0.310109 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 32.3466i | − | 1.23862i | ||||||
\(683\) | − | 33.7980i | − | 1.29324i | −0.762811 | − | 0.646621i | \(-0.776181\pi\) | ||
0.762811 | − | 0.646621i | \(-0.223819\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.79796 | 0.145113 | ||||||||
\(686\) | −17.5073 | −0.668432 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | −9.57058 | − | 21.7980i | −0.364610 | − | 0.830436i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 38.7994i | − | 1.47600i | −0.674801 | − | 0.737999i | \(-0.735771\pi\) | ||
0.674801 | − | 0.737999i | \(-0.264229\pi\) | |||||||
\(692\) | 12.5384 | 0.476640 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.3144i | 1.34052i | ||||||||
\(695\) | 13.7980i | 0.523386i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.90357i | − | 0.337247i | ||||||
\(698\) | 18.9912 | 0.718829 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 1.48393i | − | 0.0560872i | ||||||
\(701\) | 25.5940 | 0.966671 | 0.483335 | − | 0.875435i | \(-0.339425\pi\) | ||||
0.483335 | + | 0.875435i | \(0.339425\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.6061 | −0.701743 | ||||||||
\(704\) | − | 4.89898i | − | 0.184637i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | 0.225813 | ||||||||
\(707\) | − | 27.1918i | − | 1.02265i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 33.8305i | − | 1.27053i | −0.772293 | − | 0.635266i | \(-0.780890\pi\) | ||
0.772293 | − | 0.635266i | \(-0.219110\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.8990 | −0.408457 | ||||||||
\(713\) | − | 9.79796i | − | 0.366936i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.10102 | + | 16.1733i | 0.265563 | + | 0.604847i | ||||
\(716\) | 21.2921 | 0.795723 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.79796 | −0.365657 | ||||||||
\(719\) | −10.2376 | −0.381798 | −0.190899 | − | 0.981610i | \(-0.561140\pi\) | ||||
−0.190899 | + | 0.981610i | \(0.561140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 19.1412i | − | 0.712854i | ||||||
\(722\) | 7.20204i | 0.268032i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.7980 | −0.884444 | ||||||||
\(725\) | −5.11879 | −0.190107 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.6969 | −0.841783 | −0.420891 | − | 0.907111i | \(-0.638283\pi\) | ||||
−0.420891 | + | 0.907111i | \(0.638283\pi\) | |||||||
\(728\) | 2.15094 | + | 4.89898i | 0.0797191 | + | 0.181568i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.45178i | 0.164768i | ||||||||
\(731\) | −32.3466 | −1.19638 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.2512i | 1.59752i | 0.601650 | + | 0.798760i | \(0.294510\pi\) | ||||
−0.601650 | + | 0.798760i | \(0.705490\pi\) | |||||||
\(734\) | 6.69694i | 0.247189i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.48393i | − | 0.0546983i | ||||||
\(737\) | 46.8861 | 1.72707 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.08665i | 0.297472i | 0.988877 | + | 0.148736i | \(0.0475205\pi\) | ||||
−0.988877 | + | 0.148736i | \(0.952480\pi\) | |||||||
\(740\) | 3.63487 | 0.133620 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.79796 | 0.359694 | ||||||||
\(743\) | 43.5959i | 1.59938i | 0.600414 | + | 0.799690i | \(0.295003\pi\) | ||||
−0.600414 | + | 0.799690i | \(0.704997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.7980 | 0.578792 | ||||||||
\(746\) | − | 12.6969i | − | 0.464868i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 39.6163i | − | 1.44852i | ||||||
\(749\) | − | 8.80816i | − | 0.321843i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.7980 | −0.941381 | −0.470690 | − | 0.882298i | \(-0.655995\pi\) | ||||
−0.470690 | + | 0.882298i | \(0.655995\pi\) | |||||||
\(752\) | 9.79796i | 0.357295i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.8990 | − | 7.41964i | 0.615425 | − | 0.270207i | ||||
\(755\) | 6.60272 | 0.240298 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.8990 | 1.41381 | 0.706904 | − | 0.707310i | \(-0.250091\pi\) | ||||
0.706904 | + | 0.707310i | \(0.250091\pi\) | |||||||
\(758\) | 12.3885 | 0.449971 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 5.11879i | − | 0.185678i | ||||||
\(761\) | − | 52.2929i | − | 1.89561i | −0.318844 | − | 0.947807i | \(-0.603295\pi\) | ||
0.318844 | − | 0.947807i | \(-0.396705\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.2020 | −0.948578 | ||||||||
\(764\) | −20.4752 | −0.740766 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.7980 | 1.22117 | ||||||||
\(767\) | 16.1733 | − | 7.10102i | 0.583984 | − | 0.256403i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.0126i | − | 1.11834i | −0.829052 | − | 0.559171i | \(-0.811120\pi\) | ||
0.829052 | − | 0.559171i | \(-0.188880\pi\) | |||||||
\(770\) | −7.26973 | −0.261983 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 17.6572i | − | 0.635497i | ||||||
\(773\) | 13.5959i | 0.489011i | 0.969648 | + | 0.244506i | \(0.0786257\pi\) | ||||
−0.969648 | + | 0.244506i | \(0.921374\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.60272i | 0.237177i | ||||||||
\(776\) | −17.6572 | −0.633857 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.0224i | 0.502726i | ||||||||
\(779\) | −5.63590 | −0.201927 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 12.0000i | − | 0.429119i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.79796 | 0.171356 | ||||||||
\(785\) | − | 9.10102i | − | 0.324829i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.7439i | 0.917670i | 0.888522 | + | 0.458835i | \(0.151733\pi\) | ||||
−0.888522 | + | 0.458835i | \(0.848267\pi\) | |||||||
\(788\) | 18.0000i | 0.641223i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.7980 | −0.490909 | ||||||||
\(791\) | 7.59592i | 0.270080i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.89898 | − | 6.60272i | −0.102946 | − | 0.234469i | ||||
\(794\) | 9.57058 | 0.339647 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.0000 | 0.708881 | ||||||||
\(797\) | −46.2190 | −1.63716 | −0.818581 | − | 0.574391i | \(-0.805239\pi\) | ||||
−0.818581 | + | 0.574391i | \(0.805239\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 79.2326i | 2.80305i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.69694 | 0.307100 | ||||||||
\(803\) | 21.8092 | 0.769630 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.20204 | −0.0776117 | ||||||||
\(806\) | −9.57058 | − | 21.7980i | −0.337109 | − | 0.767800i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.3242i | 0.644644i | ||||||||
\(809\) | −32.3466 | −1.13725 | −0.568623 | − | 0.822598i | \(-0.692524\pi\) | ||||
−0.568623 | + | 0.822598i | \(0.692524\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.11879i | − | 0.179745i | −0.995953 | − | 0.0898726i | \(-0.971354\pi\) | ||
0.995953 | − | 0.0898726i | \(-0.0286460\pi\) | |||||||
\(812\) | 7.59592i | 0.266564i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 17.8071i | − | 0.624140i | ||||||
\(815\) | 6.60272 | 0.231283 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.4752i | 0.716336i | ||||||||
\(818\) | −10.2376 | −0.357949 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.10102 | 0.0384493 | ||||||||
\(821\) | 30.0000i | 1.04701i | 0.852023 | + | 0.523504i | \(0.175375\pi\) | ||||
−0.852023 | + | 0.523504i | \(0.824625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.30306 | −0.0454219 | −0.0227109 | − | 0.999742i | \(-0.507230\pi\) | ||||
−0.0227109 | + | 0.999742i | \(0.507230\pi\) | |||||||
\(824\) | 12.8990i | 0.449357i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.26973i | 0.252946i | ||||||||
\(827\) | − | 4.40408i | − | 0.153145i | −0.997064 | − | 0.0765725i | \(-0.975602\pi\) | ||
0.997064 | − | 0.0765725i | \(-0.0243977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.7980 | 0.687612 | 0.343806 | − | 0.939041i | \(-0.388284\pi\) | ||||
0.343806 | + | 0.939041i | \(0.388284\pi\) | |||||||
\(830\) | 9.79796i | 0.340092i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.44949 | − | 3.30136i | −0.0502520 | − | 0.114454i | ||||
\(833\) | 38.7994 | 1.34432 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −25.0769 | −0.867301 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.2278i | 0.940569i | ||||||||
\(839\) | 55.5959i | 1.91938i | 0.281053 | + | 0.959692i | \(0.409316\pi\) | ||||
−0.281053 | + | 0.959692i | \(0.590684\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.79796 | −0.0964813 | ||||||||
\(842\) | 4.45178 | 0.153419 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.79796 | 0.199574 | ||||||||
\(845\) | 9.57058 | + | 8.79796i | 0.329238 | + | 0.302659i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.2911i | 0.662849i | ||||||||
\(848\) | −6.60272 | −0.226738 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.08665i | 0.277370i | ||||||||
\(851\) | − | 5.39388i | − | 0.184900i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.3155i | 1.27766i | 0.769349 | + | 0.638829i | \(0.220581\pi\) | ||||
−0.769349 | + | 0.638829i | \(0.779419\pi\) | |||||||
\(854\) | 2.96786 | 0.101558 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.93571i | 0.202878i | ||||||||
\(857\) | −2.15094 | −0.0734746 | −0.0367373 | − | 0.999325i | \(-0.511696\pi\) | ||||
−0.0367373 | + | 0.999325i | \(0.511696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.3939 | −0.866428 | −0.433214 | − | 0.901291i | \(-0.642621\pi\) | ||||
−0.433214 | + | 0.901291i | \(0.642621\pi\) | |||||||
\(860\) | − | 4.00000i | − | 0.136399i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.59592 | −0.258718 | ||||||||
\(863\) | − | 4.40408i | − | 0.149917i | −0.997187 | − | 0.0749583i | \(-0.976118\pi\) | ||
0.997187 | − | 0.0749583i | \(-0.0238824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.5384i | 0.426319i | ||||||||
\(866\) | 14.0000i | 0.475739i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.79796 | 0.332564 | ||||||||
\(869\) | 67.5959i | 2.29303i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.5959 | − | 13.8725i | 1.07059 | − | 0.470050i | ||||
\(872\) | 17.6572 | 0.597949 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.59592 | −0.256936 | ||||||||
\(875\) | 1.48393 | 0.0501659 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 0.667010i | − | 0.0225233i | −0.999937 | − | 0.0112617i | \(-0.996415\pi\) | ||
0.999937 | − | 0.0112617i | \(-0.00358478\pi\) | |||||||
\(878\) | 11.5959i | 0.391343i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.89898 | 0.165145 | ||||||||
\(881\) | 2.96786 | 0.0999896 | 0.0499948 | − | 0.998749i | \(-0.484080\pi\) | ||||
0.0499948 | + | 0.998749i | \(0.484080\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.3939 | −0.450740 | −0.225370 | − | 0.974273i | \(-0.572359\pi\) | ||||
−0.225370 | + | 0.974273i | \(0.572359\pi\) | |||||||
\(884\) | −11.7215 | − | 26.6969i | −0.394237 | − | 0.897915i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.7128i | 1.03182i | ||||||||
\(887\) | 4.45178 | 0.149476 | 0.0747381 | − | 0.997203i | \(-0.476188\pi\) | ||||
0.0747381 | + | 0.997203i | \(0.476188\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.1412i | 0.641974i | ||||||||
\(890\) | − | 10.8990i | − | 0.365335i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 17.6572i | − | 0.591208i | ||||||
\(893\) | 50.1537 | 1.67833 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.2921i | 0.711716i | ||||||||
\(896\) | 1.48393 | 0.0495745 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.8990 | 0.363704 | ||||||||
\(899\) | − | 33.7980i | − | 1.12723i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.3939 | −1.77881 | ||||||||
\(902\) | − | 5.39388i | − | 0.179596i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 5.11879i | − | 0.170249i | ||||||
\(905\) | − | 23.7980i | − | 0.791071i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.5959 | −1.31476 | −0.657380 | − | 0.753559i | \(-0.728336\pi\) | ||||
−0.657380 | + | 0.753559i | \(0.728336\pi\) | |||||||
\(908\) | − | 2.20204i | − | 0.0730773i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.89898 | + | 2.15094i | −0.162400 | + | 0.0713029i | ||||
\(911\) | 42.5842 | 1.41088 | 0.705438 | − | 0.708771i | \(-0.250750\pi\) | ||||
0.705438 | + | 0.708771i | \(0.250750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.0000 | 1.58857 | ||||||||
\(914\) | 11.7215 | 0.387713 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.48393i | 0.0490303i | ||||||||
\(917\) | − | 16.4041i | − | 0.541711i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.7980 | −0.587100 | −0.293550 | − | 0.955944i | \(-0.594837\pi\) | ||||
−0.293550 | + | 0.955944i | \(0.594837\pi\) | |||||||
\(920\) | 1.48393 | 0.0489236 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.7980 | −0.520278 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.63487i | 0.119514i | ||||||||
\(926\) | −11.7215 | −0.385193 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 5.11879i | − | 0.168033i | ||||||
\(929\) | − | 8.69694i | − | 0.285337i | −0.989771 | − | 0.142669i | \(-0.954432\pi\) | ||
0.989771 | − | 0.142669i | \(-0.0455683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 24.5598i | − | 0.804914i | ||||||
\(932\) | 5.11879 | 0.167672 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.2054i | 0.432095i | ||||||||
\(935\) | 39.6163 | 1.29559 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.3939 | −0.633570 | −0.316785 | − | 0.948497i | \(-0.602603\pi\) | ||||
−0.316785 | + | 0.948497i | \(0.602603\pi\) | |||||||
\(938\) | 14.2020i | 0.463713i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.79796 | −0.319574 | ||||||||
\(941\) | 6.00000i | 0.195594i | 0.995206 | + | 0.0977972i | \(0.0311797\pi\) | ||||
−0.995206 | + | 0.0977972i | \(0.968820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.63383i | − | 0.0532050i | ||||||
\(944\) | − | 4.89898i | − | 0.159448i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −19.5959 | −0.637118 | ||||||||
\(947\) | 19.5959i | 0.636782i | 0.947960 | + | 0.318391i | \(0.103142\pi\) | ||||
−0.947960 | + | 0.318391i | \(0.896858\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.6969 | − | 6.45281i | 0.477083 | − | 0.209467i | ||||
\(950\) | 5.11879 | 0.166076 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.0000 | 0.388922 | ||||||||
\(953\) | 22.6261 | 0.732932 | 0.366466 | − | 0.930432i | \(-0.380568\pi\) | ||||
0.366466 | + | 0.930432i | \(0.380568\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 20.4752i | − | 0.662561i | ||||||
\(956\) | 2.20204i | 0.0712191i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.20204 | 0.0711447 | ||||||||
\(959\) | 5.63590 | 0.181993 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5959 | −0.406320 | ||||||||
\(962\) | −5.26870 | − | 12.0000i | −0.169870 | − | 0.386896i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.93571i | 0.191176i | ||||||||
\(965\) | 17.6572 | 0.568406 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 36.7984i | − | 1.18336i | −0.806174 | − | 0.591678i | \(-0.798466\pi\) | ||
0.806174 | − | 0.591678i | \(-0.201534\pi\) | |||||||
\(968\) | − | 13.0000i | − | 0.417836i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 17.6572i | − | 0.566939i | ||||||
\(971\) | −38.7994 | −1.24513 | −0.622566 | − | 0.782567i | \(-0.713910\pi\) | ||||
−0.622566 | + | 0.782567i | \(0.713910\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.4752i | 0.656404i | ||||||||
\(974\) | −10.3875 | −0.332837 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | − | 35.3939i | − | 1.13235i | −0.824285 | − | 0.566175i | \(-0.808423\pi\) | ||
0.824285 | − | 0.566175i | \(-0.191577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.3939 | −1.70648 | ||||||||
\(980\) | 4.79796i | 0.153265i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.3242i | 0.584750i | ||||||||
\(983\) | − | 4.40408i | − | 0.140468i | −0.997531 | − | 0.0702342i | \(-0.977625\pi\) | ||
0.997531 | − | 0.0702342i | \(-0.0223747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.0000 | −0.573528 | ||||||||
\(986\) | − | 41.3939i | − | 1.31825i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.8990 | + | 7.41964i | −0.537628 | + | 0.236050i | ||||
\(989\) | −5.93571 | −0.188745 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | −6.60272 | −0.209637 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.0000i | 0.634043i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.89898 | 0.218493 | 0.109246 | − | 0.994015i | \(-0.465156\pi\) | ||||
0.109246 | + | 0.994015i | \(0.465156\pi\) | |||||||
\(998\) | 5.11879 | 0.162033 | ||||||||
\(999\) | 0 | 0 |
(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 | 1170.2.b.g.181.2 | ✓ | 8 | |
3.2 | odd | 2 | inner | 1170.2.b.g.181.6 | yes | 8 | |
13.12 | even | 2 | inner | 1170.2.b.g.181.7 | yes | 8 | |
39.38 | odd | 2 | inner | 1170.2.b.g.181.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.b.g.181.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1170.2.b.g.181.3 | yes | 8 | 39.38 | odd | 2 | inner | |
1170.2.b.g.181.6 | yes | 8 | 3.2 | odd | 2 | inner | |
1170.2.b.g.181.7 | yes | 8 | 13.12 | even | 2 | inner |