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 | 181.7 | ||
Root | \(1.65068 - 1.65068i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.181 |
Dual form | 1170.2.b.g.181.2 |
$q$-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 | \(0.0904790\pi\) | ||||
−0.959873 | + | 0.280436i | \(0.909521\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | − | 4.89898i | − | 1.47710i | −0.674200 | − | 0.738549i | \(-0.735511\pi\) | ||
0.674200 | − | 0.738549i | \(-0.264489\pi\) | |||||||
\(12\) | 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 | \(0.199756\pi\) | ||||
−0.809467 | + | 0.587166i | \(0.800244\pi\) | |||||||
\(20\) | − | 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 | \(0.202034\pi\) | ||||
−0.805245 | + | 0.592942i | \(0.797966\pi\) | |||||||
\(32\) | 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 | \(0.0965810\pi\) | ||||
−0.954321 | + | 0.298784i | \(0.903419\pi\) | |||||||
\(38\) | −5.11879 | −0.830378 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 1.10102i | 0.171951i | 0.996297 | + | 0.0859753i | \(0.0274006\pi\) | ||||
−0.996297 | + | 0.0859753i | \(0.972599\pi\) | |||||||
\(42\) | 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 | \(-0.746613\pi\) | ||
0.699544 | − | 0.714590i | \(-0.253387\pi\) | |||||||
\(48\) | 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 | \(0.103312\pi\) | ||||
−0.947790 | + | 0.318896i | \(0.896688\pi\) | |||||||
\(60\) | 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 | \(0.198755\pi\) | ||||
−0.811310 | + | 0.584616i | \(0.801245\pi\) | |||||||
\(68\) | −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 | \(0.0838943\pi\) | ||||
−0.965468 | + | 0.260521i | \(0.916106\pi\) | |||||||
\(74\) | −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 | \(0.180719\pi\) | ||||
−0.843115 | + | 0.537733i | \(0.819281\pi\) | |||||||
\(84\) | 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 | \(-0.803972\pi\) | ||
0.816288 | − | 0.577645i | \(-0.196028\pi\) | |||||||
\(90\) | 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 | \(-0.646166\pi\) | ||
0.443226 | − | 0.896410i | \(-0.353834\pi\) | |||||||
\(98\) | 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 | \(0.320774\pi\) | ||||
−0.533773 | + | 0.845628i | \(0.679226\pi\) | |||||||
\(110\) | 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 | \(-0.948128\pi\) | ||
0.986751 | − | 0.162241i | \(-0.0518721\pi\) | |||||||
\(138\) | 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 | \(-0.775978\pi\) | ||
0.762397 | − | 0.647110i | \(-0.224022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.60272i | − | 0.537322i | −0.963235 | − | 0.268661i | \(-0.913419\pi\) | ||
0.963235 | − | 0.268661i | \(-0.0865811\pi\) | |||||||
\(152\) | 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 | \(-0.916745\pi\) | ||
0.965989 | − | 0.258582i | \(-0.0832554\pi\) | |||||||
\(164\) | − | 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 | \(-0.780795\pi\) | ||
0.772103 | − | 0.635497i | \(-0.219205\pi\) | |||||||
\(194\) | 17.6572 | 1.26771 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.79796 | −0.342711 | ||||||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 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 | \(-0.798651\pi\) | ||
0.806519 | − | 0.591208i | \(-0.201349\pi\) | |||||||
\(224\) | −1.48393 | −0.0991491 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 5.11879i | − | 0.340497i | ||||||
\(227\) | − | 2.20204i | − | 0.146155i | −0.997326 | − | 0.0730773i | \(-0.976718\pi\) | ||
0.997326 | − | 0.0730773i | \(-0.0232820\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.48393i | 0.0980607i | 0.998797 | + | 0.0490303i | \(0.0156131\pi\) | ||||
−0.998797 | + | 0.0490303i | \(0.984387\pi\) | |||||||
\(230\) | −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 | \(0.0226890\pi\) | ||||
−0.997461 | + | 0.0712191i | \(0.977311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.93571i | 0.382353i | 0.981556 | + | 0.191176i | \(0.0612302\pi\) | ||||
−0.981556 | + | 0.191176i | \(0.938770\pi\) | |||||||
\(242\) | − | 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 | \(0.124361\pi\) | ||||
−0.924646 | + | 0.380828i | \(0.875639\pi\) | |||||||
\(272\) | 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 | \(-0.916473\pi\) | ||
0.965768 | − | 0.259408i | \(-0.0835274\pi\) | |||||||
\(282\) | 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 | \(0.176229\pi\) | ||||
−0.850617 | + | 0.525786i | \(0.823771\pi\) | |||||||
\(294\) | 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 | \(-0.911947\pi\) | ||
0.961983 | − | 0.273111i | \(-0.0880526\pi\) | |||||||
\(308\) | −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 | \(-0.875300\pi\) | ||
0.924240 | − | 0.381811i | \(-0.124700\pi\) | |||||||
\(318\) | 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 | \(0.232304\pi\) | ||||
−0.745305 | + | 0.666724i | \(0.767696\pi\) | |||||||
\(332\) | − | 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 | \(-0.830278\pi\) | ||
0.861187 | − | 0.508289i | \(-0.169722\pi\) | |||||||
\(350\) | 1.48393 | 0.0793193 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.89898 | 0.261116 | ||||||||
\(353\) | − | 6.00000i | − | 0.319348i | −0.987170 | − | 0.159674i | \(-0.948956\pi\) | ||
0.987170 | − | 0.159674i | \(-0.0510443\pi\) | |||||||
\(354\) | 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 | \(0.0832474\pi\) | ||||
−0.965996 | + | 0.258558i | \(0.916753\pi\) | |||||||
\(360\) | 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 | \(-0.896929\pi\) | ||
0.948031 | − | 0.318178i | \(-0.103071\pi\) | |||||||
\(380\) | 5.11879 | 0.262589 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.4752i | 1.04760i | ||||||||
\(383\) | − | 33.7980i | − | 1.72700i | −0.504353 | − | 0.863498i | \(-0.668269\pi\) | ||
0.504353 | − | 0.863498i | \(-0.331731\pi\) | |||||||
\(384\) | 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 | \(-0.922798\pi\) | ||
0.970732 | − | 0.240167i | \(-0.0772021\pi\) | |||||||
\(398\) | − | 20.0000i | − | 1.00251i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − | 8.69694i | − | 0.434304i | −0.976138 | − | 0.217152i | \(-0.930323\pi\) | ||
0.976138 | − | 0.217152i | \(-0.0696768\pi\) | |||||||
\(402\) | 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 | \(0.0814528\pi\) | ||||
−0.967438 | + | 0.253108i | \(0.918547\pi\) | |||||||
\(410\) | − | 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 | \(-0.965401\pi\) | ||
0.994098 | − | 0.108483i | \(-0.0345994\pi\) | |||||||
\(422\) | − | 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 | \(0.0585618\pi\) | ||||
−0.983124 | + | 0.182941i | \(0.941438\pi\) | |||||||
\(432\) | 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 | \(-0.917208\pi\) | ||
0.966364 | − | 0.257177i | \(-0.0827924\pi\) | |||||||
\(450\) | 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 | \(-0.911602\pi\) | ||
0.961686 | − | 0.274155i | \(-0.0883980\pi\) | |||||||
\(458\) | −1.48393 | −0.0693394 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 1.48393i | − | 0.0691885i | ||||||
\(461\) | 15.7980i | 0.735784i | 0.929868 | + | 0.367892i | \(0.119920\pi\) | ||||
−0.929868 | + | 0.367892i | \(0.880080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.7215i | 0.544745i | 0.962192 | + | 0.272372i | \(0.0878083\pi\) | ||||
−0.962192 | + | 0.272372i | \(0.912192\pi\) | |||||||
\(464\) | 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 | \(-0.983980\pi\) | ||
0.998734 | − | 0.0503069i | \(-0.0160199\pi\) | |||||||
\(480\) | 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 | \(0.0756240\pi\) | ||||
−0.971910 | + | 0.235351i | \(0.924376\pi\) | |||||||
\(488\) | 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 | \(-0.963450\pi\) | ||
0.993415 | − | 0.114574i | \(-0.0365504\pi\) | |||||||
\(500\) | 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 | \(0.231510\pi\) | ||||
−0.746965 | + | 0.664863i | \(0.768490\pi\) | |||||||
\(510\) | 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 | \(0.243324\pi\) | ||||
−0.721781 | + | 0.692122i | \(0.756676\pi\) | |||||||
\(542\) | −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 | \(-0.906997\pi\) | ||
0.957619 | − | 0.288039i | \(-0.0930032\pi\) | |||||||
\(558\) | 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 | \(0.173644\pi\) | ||||
−0.854858 | + | 0.518861i | \(0.826356\pi\) | |||||||
\(578\) | 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 | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 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 | \(-0.823860\pi\) | ||
0.850763 | − | 0.525549i | \(-0.176140\pi\) | |||||||
\(594\) | 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 | \(0.0233867\pi\) | ||||
−0.997302 | + | 0.0734054i | \(0.976613\pi\) | |||||||
\(614\) | 9.57058 | 0.386237 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 7.26973i | − | 0.292906i | ||||||
\(617\) | − | 39.7980i | − | 1.60221i | −0.598527 | − | 0.801103i | \(-0.704247\pi\) | ||
0.598527 | − | 0.801103i | \(-0.295753\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 46.3690i | − | 1.86373i | −0.362811 | − | 0.931863i | \(-0.618183\pi\) | ||
0.362811 | − | 0.931863i | \(-0.381817\pi\) | |||||||
\(620\) | 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 | \(0.204058\pi\) | ||||
−0.801458 | + | 0.598051i | \(0.795942\pi\) | |||||||
\(632\) | − | 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 | \(0.251072\pi\) | ||||
−0.704720 | + | 0.709485i | \(0.748928\pi\) | |||||||
\(644\) | − | 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 | \(0.120415\pi\) | ||||
−0.929296 | + | 0.369337i | \(0.879585\pi\) | |||||||
\(662\) | −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 | \(0.223819\pi\) | ||||
−0.762811 | + | 0.646621i | \(0.776181\pi\) | |||||||
\(684\) | 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 | \(0.264229\pi\) | ||||
−0.674801 | + | 0.737999i | \(0.735771\pi\) | |||||||
\(692\) | 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 | \(0.219110\pi\) | ||||
−0.772293 | + | 0.635266i | \(0.780890\pi\) | |||||||
\(710\) | 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 | \(-0.705490\pi\) | ||
0.601650 | − | 0.798760i | \(-0.294510\pi\) | |||||||
\(734\) | − | 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 | \(-0.952480\pi\) | ||
0.988877 | − | 0.148736i | \(-0.0475205\pi\) | |||||||
\(740\) | 3.63487 | 0.133620 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.79796 | 0.359694 | ||||||||
\(743\) | − | 43.5959i | − | 1.59938i | −0.600414 | − | 0.799690i | \(-0.704997\pi\) | ||
0.600414 | − | 0.799690i | \(-0.295003\pi\) | |||||||
\(744\) | 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 | \(0.396705\pi\) | ||||
−0.318844 | + | 0.947807i | \(0.603295\pi\) | |||||||
\(762\) | 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 | \(0.188880\pi\) | ||||
−0.829052 | + | 0.559171i | \(0.811120\pi\) | |||||||
\(770\) | −7.26973 | −0.261983 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.6572i | 0.635497i | ||||||||
\(773\) | − | 13.5959i | − | 0.489011i | −0.969648 | − | 0.244506i | \(-0.921374\pi\) | ||
0.969648 | − | 0.244506i | \(-0.0786257\pi\) | |||||||
\(774\) | 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 | \(-0.848267\pi\) | ||
0.888522 | − | 0.458835i | \(-0.151733\pi\) | |||||||
\(788\) | − | 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 | \(0.0286460\pi\) | ||||
−0.995953 | + | 0.0898726i | \(0.971354\pi\) | |||||||
\(812\) | − | 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 | \(-0.824625\pi\) | ||
0.852023 | − | 0.523504i | \(-0.175375\pi\) | |||||||
\(822\) | 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 | \(0.0243977\pi\) | ||||
−0.997064 | + | 0.0765725i | \(0.975602\pi\) | |||||||
\(828\) | 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 | \(-0.590684\pi\) | ||
0.281053 | − | 0.959692i | \(-0.409316\pi\) | |||||||
\(840\) | 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 | \(-0.779419\pi\) | ||
0.769349 | − | 0.638829i | \(-0.220581\pi\) | |||||||
\(854\) | 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 | \(0.0238824\pi\) | ||||
−0.997187 | + | 0.0749583i | \(0.976118\pi\) | |||||||
\(864\) | 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 | \(0.00358478\pi\) | ||||
−0.999937 | + | 0.0112617i | \(0.996415\pi\) | |||||||
\(878\) | − | 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 | \(0.0455683\pi\) | ||||
−0.989771 | + | 0.142669i | \(0.954432\pi\) | |||||||
\(930\) | 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 | \(-0.968820\pi\) | ||
0.995206 | − | 0.0977972i | \(-0.0311797\pi\) | |||||||
\(942\) | 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 | \(-0.896858\pi\) | ||
0.947960 | − | 0.318391i | \(-0.103142\pi\) | |||||||
\(948\) | 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 | \(0.201534\pi\) | ||||
−0.806174 | + | 0.591678i | \(0.798466\pi\) | |||||||
\(968\) | 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 | \(0.191577\pi\) | ||||
−0.824285 | + | 0.566175i | \(0.808423\pi\) | |||||||
\(978\) | 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 | \(0.0223747\pi\) | ||||
−0.997531 | + | 0.0702342i | \(0.977625\pi\) | |||||||
\(984\) | 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.181.7 | yes | 8 | |
3.2 | odd | 2 | inner | 1170.2.b.g.181.3 | yes | 8 | |
13.12 | even | 2 | inner | 1170.2.b.g.181.2 | ✓ | 8 | |
39.38 | odd | 2 | inner | 1170.2.b.g.181.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.b.g.181.2 | ✓ | 8 | 13.12 | even | 2 | inner | |
1170.2.b.g.181.3 | yes | 8 | 3.2 | odd | 2 | inner | |
1170.2.b.g.181.6 | yes | 8 | 39.38 | odd | 2 | inner | |
1170.2.b.g.181.7 | yes | 8 | 1.1 | even | 1 | trivial |