Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(127,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.b (of order \(2\), degree \(1\), not 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: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.8 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.127 |
Dual form | 768.3.b.f.127.5 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.29253i | 0.858506i | 0.903184 | + | 0.429253i | \(0.141223\pi\) | ||||
−0.903184 | + | 0.429253i | \(0.858777\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.75787i | 0.393982i | 0.980405 | + | 0.196991i | \(0.0631170\pi\) | ||||
−0.980405 | + | 0.196991i | \(0.936883\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.7980 | 1.25436 | 0.627180 | − | 0.778874i | \(-0.284209\pi\) | ||||
0.627180 | + | 0.778874i | \(0.284209\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 14.5266i | − 1.11743i | −0.829359 | − | 0.558716i | \(-0.811294\pi\) | ||||
0.829359 | − | 0.558716i | \(-0.188706\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.43488i | 0.495659i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.8673 | 1.34513 | 0.672567 | − | 0.740037i | \(-0.265192\pi\) | ||||
0.672567 | + | 0.740037i | \(0.265192\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.0399 | −0.844204 | −0.422102 | − | 0.906548i | \(-0.638708\pi\) | ||||
−0.422102 | + | 0.906548i | \(0.638708\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.77678i | 0.227466i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 17.1117i | − 0.743986i | −0.928236 | − | 0.371993i | \(-0.878675\pi\) | ||||
0.928236 | − | 0.371993i | \(-0.121325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.57420 | 0.262968 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 21.8667i | 0.754025i | 0.926208 | + | 0.377013i | \(0.123049\pi\) | ||||
−0.926208 | + | 0.377013i | \(0.876951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.6944i | 1.24821i | 0.781341 | + | 0.624104i | \(0.214536\pi\) | ||||
−0.781341 | + | 0.624104i | \(0.785464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 23.8988 | 0.724205 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.8383 | −0.338236 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66.4204i | 1.79515i | 0.440866 | + | 0.897573i | \(0.354671\pi\) | ||||
−0.440866 | + | 0.897573i | \(0.645329\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 25.1608i | − 0.645149i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −23.2392 | −0.566809 | −0.283405 | − | 0.959000i | \(-0.591464\pi\) | ||||
−0.283405 | + | 0.959000i | \(0.591464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 47.9230 | 1.11449 | 0.557244 | − | 0.830349i | \(-0.311859\pi\) | ||||
0.557244 | + | 0.830349i | \(0.311859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.8776i | 0.286169i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14.8512i | 0.315983i | 0.987441 | + | 0.157991i | \(0.0505018\pi\) | ||||
−0.987441 | + | 0.157991i | \(0.949498\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41.3941 | 0.844778 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 39.6073 | 0.776613 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 65.5589i | 1.23696i | 0.785800 | + | 0.618480i | \(0.212251\pi\) | ||||
−0.785800 | + | 0.618480i | \(0.787749\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 59.2281i | 1.07688i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −27.7819 | −0.487401 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −65.8428 | −1.11598 | −0.557990 | − | 0.829848i | \(-0.688427\pi\) | ||||
−0.557990 | + | 0.829848i | \(0.688427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40.1123i | 0.657579i | 0.944403 | + | 0.328790i | \(0.106641\pi\) | ||||
−0.944403 | + | 0.328790i | \(0.893359\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.27362i | 0.131327i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 62.3559 | 0.959321 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −74.8105 | −1.11657 | −0.558287 | − | 0.829648i | \(-0.688541\pi\) | ||||
−0.558287 | + | 0.829648i | \(0.688541\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 29.6383i | − 0.429540i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 122.681i | − 1.72790i | −0.503578 | − | 0.863950i | \(-0.667983\pi\) | ||||
0.503578 | − | 0.863950i | \(-0.332017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 144.904 | 1.98498 | 0.992492 | − | 0.122312i | \(-0.0390307\pi\) | ||||
0.992492 | + | 0.122312i | \(0.0390307\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.3868 | 0.151825 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 38.0530i | 0.494195i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 128.657i | − 1.62857i | −0.580467 | − | 0.814284i | \(-0.697130\pi\) | ||||
0.580467 | − | 0.814284i | \(-0.302870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −22.0417 | −0.265563 | −0.132781 | − | 0.991145i | \(-0.542391\pi\) | ||||
−0.132781 | + | 0.991145i | \(0.542391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 98.1584i | 1.15480i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 37.8743i | 0.435337i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 122.075 | 1.37163 | 0.685813 | − | 0.727778i | \(-0.259447\pi\) | ||||
0.685813 | + | 0.727778i | \(0.259447\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 40.0626 | 0.440248 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 67.0208i | 0.720653i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 68.8516i | − 0.724754i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −88.3072 | −0.910384 | −0.455192 | − | 0.890393i | \(-0.650429\pi\) | ||||
−0.455192 | + | 0.890393i | \(0.650429\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 41.3939 | 0.418120 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 104.345i | − 1.03312i | −0.856251 | − | 0.516560i | \(-0.827212\pi\) | ||||
0.856251 | − | 0.516560i | \(-0.172788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 69.0609i | 0.670494i | 0.942130 | + | 0.335247i | \(0.108820\pi\) | ||||
−0.942130 | + | 0.335247i | \(0.891180\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −20.5045 | −0.195281 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −149.429 | −1.39653 | −0.698265 | − | 0.715839i | \(-0.746044\pi\) | ||||
−0.698265 | + | 0.715839i | \(0.746044\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 54.3341i | − 0.498478i | −0.968442 | − | 0.249239i | \(-0.919820\pi\) | ||||
0.968442 | − | 0.249239i | \(-0.0801805\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 115.044i | 1.03643i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.32846 | 0.0560041 | 0.0280021 | − | 0.999608i | \(-0.491086\pi\) | ||||
0.0280021 | + | 0.999608i | \(0.491086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 73.4523 | 0.638716 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 43.5798i | − 0.372477i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 63.0651i | 0.529958i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 69.3837 | 0.573419 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −40.2514 | −0.327247 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 135.533i | 1.08427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 16.5228i | − 0.130101i | −0.997882 | − | 0.0650504i | \(-0.979279\pi\) | ||||
0.997882 | − | 0.0650504i | \(-0.0207208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 83.0050 | 0.643450 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 50.9799 | 0.389159 | 0.194580 | − | 0.980887i | \(-0.437666\pi\) | ||||
0.194580 | + | 0.980887i | \(0.437666\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 44.2360i | − 0.332601i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 22.3046i | 0.165220i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0157 | −0.0731070 | −0.0365535 | − | 0.999332i | \(-0.511638\pi\) | ||||
−0.0365535 | + | 0.999332i | \(0.511638\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 65.7088 | 0.472725 | 0.236363 | − | 0.971665i | \(-0.424045\pi\) | ||||
0.236363 | + | 0.971665i | \(0.424045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25.7230i | 0.182433i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 200.438i | − 1.40166i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −93.8635 | −0.647335 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 71.6967 | 0.487733 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 94.7716i | − 0.636051i | −0.948082 | − | 0.318026i | \(-0.896980\pi\) | ||||
0.948082 | − | 0.318026i | \(-0.103020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 269.769i | 1.78655i | 0.449508 | + | 0.893276i | \(0.351599\pi\) | ||||
−0.449508 | + | 0.893276i | \(0.648401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 68.6018 | 0.448378 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −166.097 | −1.07159 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 31.5058i | − 0.200674i | −0.994954 | − | 0.100337i | \(-0.968008\pi\) | ||||
0.994954 | − | 0.100337i | \(-0.0319921\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 113.551i | 0.714159i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 47.1918 | 0.293117 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 201.159 | 1.23410 | 0.617051 | − | 0.786923i | \(-0.288327\pi\) | ||||
0.617051 | + | 0.786923i | \(0.288327\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 102.586i | 0.621734i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 266.393i | − 1.59517i | −0.603208 | − | 0.797584i | \(-0.706111\pi\) | ||||
0.603208 | − | 0.797584i | \(-0.293889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −42.0224 | −0.248653 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −48.1196 | −0.281401 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 43.8456i | 0.253443i | 0.991938 | + | 0.126721i | \(0.0404454\pi\) | ||||
−0.991938 | + | 0.126721i | \(0.959555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.1308i | 0.103605i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −114.043 | −0.644311 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −275.778 | −1.54066 | −0.770330 | − | 0.637646i | \(-0.779908\pi\) | ||||
−0.770330 | + | 0.637646i | \(0.779908\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 79.0033i | − 0.436482i | −0.975895 | − | 0.218241i | \(-0.929968\pi\) | ||||
0.975895 | − | 0.218241i | \(-0.0700319\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 69.4766i | 0.379654i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −285.111 | −1.54114 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 315.522 | 1.68728 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.3303i | 0.0758219i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 142.409i | 0.745598i | 0.927912 | + | 0.372799i | \(0.121602\pi\) | ||||
−0.927912 | + | 0.372799i | \(0.878398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −277.818 | −1.43947 | −0.719736 | − | 0.694248i | \(-0.755737\pi\) | ||||
−0.719736 | + | 0.694248i | \(0.755737\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 108.004 | 0.553864 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.40848i | 0.0173019i | 0.999963 | + | 0.00865095i | \(0.00275372\pi\) | ||||
−0.999963 | + | 0.00865095i | \(0.997246\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 314.323i | − 1.57951i | −0.613421 | − | 0.789756i | \(-0.710207\pi\) | ||||
0.613421 | − | 0.789756i | \(-0.289793\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −129.576 | −0.644654 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −60.3057 | −0.297072 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 99.7548i | − 0.486609i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 51.3350i | − 0.247995i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −221.317 | −1.05894 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.54933 | 0.00734281 | 0.00367140 | − | 0.999993i | \(-0.498831\pi\) | ||||
0.00367140 | + | 0.999993i | \(0.498831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 212.490i | − 0.997603i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 205.711i | 0.956794i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −106.714 | −0.491772 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 250.981 | 1.14603 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 332.184i | − 1.50309i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 148.964i | 0.668001i | 0.942573 | + | 0.334000i | \(0.108399\pi\) | ||||
−0.942573 | + | 0.334000i | \(0.891601\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.7226 | 0.0876560 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −237.803 | −1.04759 | −0.523796 | − | 0.851844i | \(-0.675485\pi\) | ||||
−0.523796 | + | 0.851844i | \(0.675485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 70.0590i | 0.305935i | 0.988231 | + | 0.152967i | \(0.0488829\pi\) | ||||
−0.988231 | + | 0.152967i | \(0.951117\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 65.9098i | 0.285324i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.18107 | −0.0308200 | −0.0154100 | − | 0.999881i | \(-0.504905\pi\) | ||||
−0.0154100 | + | 0.999881i | \(0.504905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −63.7491 | −0.271273 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 222.840i | − 0.940254i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 216.620i | − 0.906359i | −0.891419 | − | 0.453180i | \(-0.850290\pi\) | ||||
0.891419 | − | 0.453180i | \(-0.149710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 385.001 | 1.59751 | 0.798757 | − | 0.601653i | \(-0.205491\pi\) | ||||
0.798757 | + | 0.601653i | \(0.205491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 177.685i | 0.725247i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 233.005i | 0.943340i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −38.1774 | −0.153323 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 85.4882 | 0.340590 | 0.170295 | − | 0.985393i | \(-0.445528\pi\) | ||||
0.170295 | + | 0.985393i | \(0.445528\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 236.106i | − 0.933226i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 170.015i | 0.666727i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −54.2981 | −0.211277 | −0.105638 | − | 0.994405i | \(-0.533689\pi\) | ||||
−0.105638 | + | 0.994405i | \(0.533689\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −183.179 | −0.707255 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 65.6002i | 0.251342i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 501.827i | − 1.90809i | −0.299670 | − | 0.954043i | \(-0.596877\pi\) | ||||
0.299670 | − | 0.954043i | \(-0.403123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −281.413 | −1.06194 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 211.440 | 0.791909 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 284.911i | − 1.05915i | −0.848264 | − | 0.529574i | \(-0.822352\pi\) | ||||
0.848264 | − | 0.529574i | \(-0.177648\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 241.190i | 0.889998i | 0.895531 | + | 0.444999i | \(0.146796\pi\) | ||||
−0.895531 | + | 0.444999i | \(0.853204\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 69.3904 | 0.254177 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 90.7105 | 0.329856 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 242.877i | − 0.876813i | −0.898777 | − | 0.438407i | \(-0.855543\pi\) | ||||
0.898777 | − | 0.438407i | \(-0.144457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 116.083i | 0.416069i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −105.341 | −0.374880 | −0.187440 | − | 0.982276i | \(-0.560019\pi\) | ||||
−0.187440 | + | 0.982276i | \(0.560019\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −223.867 | −0.791049 | −0.395525 | − | 0.918455i | \(-0.629437\pi\) | ||||
−0.395525 | + | 0.918455i | \(0.629437\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 119.254i | − 0.418437i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 64.0907i | − 0.223313i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 233.912 | 0.809384 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −152.953 | −0.525610 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 421.057i | − 1.43705i | −0.695499 | − | 0.718527i | \(-0.744817\pi\) | ||||
0.695499 | − | 0.718527i | \(-0.255183\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 282.632i | − 0.958075i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 71.6963 | 0.241402 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −248.575 | −0.831353 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 132.166i | 0.439088i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 180.731i | − 0.596472i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −172.183 | −0.564536 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −122.865 | −0.400211 | −0.200106 | − | 0.979774i | \(-0.564129\pi\) | ||||
−0.200106 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 119.617i | 0.387110i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 437.535i | − 1.40686i | −0.710762 | − | 0.703432i | \(-0.751650\pi\) | ||||
0.710762 | − | 0.703432i | \(-0.248350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −375.413 | −1.19940 | −0.599702 | − | 0.800223i | \(-0.704714\pi\) | ||||
−0.599702 | + | 0.800223i | \(0.704714\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −35.5148 | −0.112745 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 388.867i | − 1.22671i | −0.789808 | − | 0.613355i | \(-0.789820\pi\) | ||||
0.789808 | − | 0.613355i | \(-0.210180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 301.716i | 0.945819i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −258.818 | −0.806287 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −366.788 | −1.13557 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 95.5008i | − 0.293849i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 94.1094i | − 0.287796i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −40.9577 | −0.124491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.4690 | 0.0467341 | 0.0233670 | − | 0.999727i | \(-0.492561\pi\) | ||||
0.0233670 | + | 0.999727i | \(0.492561\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 199.261i | 0.598382i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 321.126i | − 0.958585i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −88.0105 | −0.261159 | −0.130579 | − | 0.991438i | \(-0.541684\pi\) | ||||
−0.130579 | + | 0.991438i | \(0.541684\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.9612 | 0.0323340 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 533.904i | 1.56570i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 249.296i | 0.726810i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 127.223 | 0.368763 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 183.589 | 0.529076 | 0.264538 | − | 0.964375i | \(-0.414781\pi\) | ||||
0.264538 | + | 0.964375i | \(0.414781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 242.556i | 0.695003i | 0.937679 | + | 0.347501i | \(0.112970\pi\) | ||||
−0.937679 | + | 0.347501i | \(0.887030\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 75.4825i | − 0.215050i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.2850 | 0.0291360 | 0.0145680 | − | 0.999894i | \(-0.495363\pi\) | ||||
0.0145680 | + | 0.999894i | \(0.495363\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 526.611 | 1.48341 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 109.232i | 0.305972i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 137.976i | 0.384334i | 0.981362 | + | 0.192167i | \(0.0615515\pi\) | ||||
−0.981362 | + | 0.192167i | \(0.938448\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −103.723 | −0.287320 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 120.176 | 0.331063 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 622.004i | 1.70412i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 400.180i | 1.09041i | 0.838303 | + | 0.545205i | \(0.183548\pi\) | ||||
−0.838303 | + | 0.545205i | \(0.816452\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −69.7175 | −0.188936 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −180.803 | −0.487340 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 644.881i | − 1.72890i | −0.502717 | − | 0.864451i | \(-0.667666\pi\) | ||||
0.502717 | − | 0.864451i | \(-0.332334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 234.750i | 0.626001i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 317.649 | 0.842571 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −485.900 | −1.28206 | −0.641029 | − | 0.767517i | \(-0.721492\pi\) | ||||
−0.641029 | + | 0.767517i | \(0.721492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 28.6183i | − 0.0751137i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 168.828i | − 0.440804i | −0.975409 | − | 0.220402i | \(-0.929263\pi\) | ||||
0.975409 | − | 0.220402i | \(-0.0707370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −163.344 | −0.424270 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 143.769 | 0.371496 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 192.592i | − 0.495095i | −0.968876 | − | 0.247548i | \(-0.920375\pi\) | ||||
0.968876 | − | 0.247548i | \(-0.0796247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 391.297i | − 1.00076i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 88.2998 | 0.224681 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 552.263 | 1.39813 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 62.0483i | 0.156293i | 0.996942 | + | 0.0781465i | \(0.0249002\pi\) | ||||
−0.996942 | + | 0.0781465i | \(0.975100\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 76.6189i | − 0.192027i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 353.066 | 0.880464 | 0.440232 | − | 0.897884i | \(-0.354896\pi\) | ||||
0.440232 | + | 0.897884i | \(0.354896\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 562.099 | 1.39479 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 38.6328i | 0.0953895i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 916.466i | 2.25176i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 62.9725 | 0.153967 | 0.0769835 | − | 0.997032i | \(-0.475471\pi\) | ||||
0.0769835 | + | 0.997032i | \(0.475471\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.3476 | −0.0422084 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 181.586i | − 0.439676i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 94.6146i | − 0.227987i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 113.811 | 0.272928 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 398.741 | 0.951650 | 0.475825 | − | 0.879540i | \(-0.342150\pi\) | ||||
0.475825 | + | 0.879540i | \(0.342150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 533.059i | 1.26617i | 0.774081 | + | 0.633086i | \(0.218212\pi\) | ||||
−0.774081 | + | 0.633086i | \(0.781788\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 44.5535i | 0.105328i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 150.334 | 0.353727 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −110.625 | −0.259075 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 347.168i | − 0.809250i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 284.282i | − 0.659587i | −0.944053 | − | 0.329793i | \(-0.893021\pi\) | ||||
0.944053 | − | 0.329793i | \(-0.106979\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −304.599 | −0.703462 | −0.351731 | − | 0.936101i | \(-0.614407\pi\) | ||||
−0.351731 | + | 0.936101i | \(0.614407\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −162.576 | −0.373739 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 274.469i | 0.628075i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 204.615i | 0.466094i | 0.972465 | + | 0.233047i | \(0.0748696\pi\) | ||||
−0.972465 | + | 0.233047i | \(0.925130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 124.182 | 0.281593 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −625.828 | −1.41270 | −0.706352 | − | 0.707861i | \(-0.749660\pi\) | ||||
−0.706352 | + | 0.707861i | \(0.749660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 524.009i | 1.17755i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 164.149i | − 0.367224i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −557.532 | −1.24172 | −0.620860 | − | 0.783921i | \(-0.713217\pi\) | ||||
−0.620860 | + | 0.783921i | \(0.713217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −320.653 | −0.710983 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 467.254i | 1.03147i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 171.970i | 0.377955i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 312.142 | 0.683024 | 0.341512 | − | 0.939877i | \(-0.389061\pi\) | ||||
0.341512 | + | 0.939877i | \(0.389061\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 118.822 | 0.258871 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 603.187i | 1.30843i | 0.756308 | + | 0.654216i | \(0.227001\pi\) | ||||
−0.756308 | + | 0.654216i | \(0.772999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 707.866i | − 1.52887i | −0.644702 | − | 0.764434i | \(-0.723019\pi\) | ||||
0.644702 | − | 0.764434i | \(-0.276981\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −287.689 | −0.618685 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 195.220 | 0.418031 | 0.209015 | − | 0.977912i | \(-0.432974\pi\) | ||||
0.209015 | + | 0.977912i | \(0.432974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 206.318i | − 0.439910i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 54.5696i | − 0.115859i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 661.239 | 1.39797 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −105.449 | −0.221998 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 196.677i | 0.412320i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 233.729i | 0.487952i | 0.969781 | + | 0.243976i | \(0.0784517\pi\) | ||||
−0.969781 | + | 0.243976i | \(0.921548\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 964.863 | 2.00595 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 81.7387 | 0.169231 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 379.061i | − 0.781569i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 224.058i | − 0.460078i | −0.973181 | − | 0.230039i | \(-0.926115\pi\) | ||||
0.973181 | − | 0.230039i | \(-0.0738854\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 348.417 | 0.712510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −194.772 | −0.396684 | −0.198342 | − | 0.980133i | \(-0.563556\pi\) | ||||
−0.198342 | + | 0.980133i | \(0.563556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 500.032i | 1.01426i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 177.684i | 0.358958i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 338.339 | 0.680762 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 99.7462 | 0.199892 | 0.0999461 | − | 0.994993i | \(-0.468133\pi\) | ||||
0.0999461 | + | 0.994993i | \(0.468133\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 461.406i | − 0.920970i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 772.172i | 1.53513i | 0.640969 | + | 0.767567i | \(0.278533\pi\) | ||||
−0.640969 | + | 0.767567i | \(0.721467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 447.904 | 0.886939 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −72.7849 | −0.143560 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 292.306i | 0.574276i | 0.957889 | + | 0.287138i | \(0.0927038\pi\) | ||||
−0.957889 | + | 0.287138i | \(0.907296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 399.627i | 0.782048i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −83.3456 | −0.162467 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −296.446 | −0.575623 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 204.916i | 0.396356i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 75.9428i | 0.146325i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 412.035 | 0.790853 | 0.395427 | − | 0.918498i | \(-0.370597\pi\) | ||||
0.395427 | + | 0.918498i | \(0.370597\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 124.693 | 0.238420 | 0.119210 | − | 0.992869i | \(-0.461964\pi\) | ||||
0.119210 | + | 0.992869i | \(0.461964\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 31.4035i | 0.0598162i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 884.836i | 1.67901i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 236.191 | 0.446486 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −197.528 | −0.371993 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 337.586i | 0.633370i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 641.427i | − 1.19893i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −477.662 | −0.889500 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 571.154 | 1.05966 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 572.988i | 1.05913i | 0.848270 | + | 0.529564i | \(0.177644\pi\) | ||||
−0.848270 | + | 0.529564i | \(0.822356\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 136.838i | − 0.252003i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 233.231 | 0.427946 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 682.433 | 1.24759 | 0.623796 | − | 0.781587i | \(-0.285590\pi\) | ||||
0.623796 | + | 0.781587i | \(0.285590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 120.337i | 0.219193i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 350.739i | − 0.636551i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 354.820 | 0.641627 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −493.828 | −0.889779 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 856.125i | − 1.53703i | −0.639832 | − | 0.768515i | \(-0.720996\pi\) | ||||
0.639832 | − | 0.768515i | \(-0.279004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 696.158i | − 1.24536i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 546.499 | 0.974152 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 680.745 | 1.20914 | 0.604570 | − | 0.796552i | \(-0.293345\pi\) | ||||
0.604570 | + | 0.796552i | \(0.293345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.1651i | 0.0480798i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.8209i | 0.0437758i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −343.401 | −0.603516 | −0.301758 | − | 0.953384i | \(-0.597574\pi\) | ||||
−0.301758 | + | 0.953384i | \(0.597574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 329.137 | 0.576422 | 0.288211 | − | 0.957567i | \(-0.406940\pi\) | ||||
0.288211 | + | 0.957567i | \(0.406940\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 246.660i | 0.430471i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 112.495i | − 0.195644i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 734.738 | 1.27338 | 0.636688 | − | 0.771122i | \(-0.280304\pi\) | ||||
0.636688 | + | 0.771122i | \(0.280304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −481.195 | −0.831079 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 60.7883i | − 0.104627i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 904.579i | 1.55159i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 187.068 | 0.319774 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 433.815 | 0.739037 | 0.369519 | − | 0.929223i | \(-0.379523\pi\) | ||||
0.369519 | + | 0.929223i | \(0.379523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 620.654i | − 1.05374i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.90365i | 0.00998926i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −425.075 | −0.716822 | −0.358411 | − | 0.933564i | \(-0.616681\pi\) | ||||
−0.358411 | + | 0.933564i | \(0.616681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −270.709 | −0.454972 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 544.424i | − 0.911932i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1048.73i | − 1.75081i | −0.483394 | − | 0.875403i | \(-0.660596\pi\) | ||||
0.483394 | − | 0.875403i | \(-0.339404\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 478.816 | 0.796699 | 0.398349 | − | 0.917234i | \(-0.369583\pi\) | ||||
0.398349 | + | 0.917234i | \(0.369583\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −224.431 | −0.372191 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 297.831i | 0.492283i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 18.7009i | − 0.0308088i | −0.999881 | − | 0.0154044i | \(-0.995096\pi\) | ||||
0.999881 | − | 0.0154044i | \(-0.00490356\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −104.453 | −0.171515 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 215.737 | 0.353089 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 314.964i | 0.513807i | 0.966437 | + | 0.256904i | \(0.0827023\pi\) | ||||
−0.966437 | + | 0.256904i | \(0.917298\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 172.780i | − 0.280944i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −786.590 | −1.27486 | −0.637431 | − | 0.770507i | \(-0.720003\pi\) | ||||
−0.637431 | + | 0.770507i | \(0.720003\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −505.431 | −0.816528 | −0.408264 | − | 0.912864i | \(-0.633866\pi\) | ||||
−0.408264 | + | 0.912864i | \(0.633866\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 88.9148i | − 0.143180i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 336.667i | 0.540396i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −417.425 | −0.667880 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −383.333 | −0.611377 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1518.85i | 2.41471i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 682.834i | − 1.08215i | −0.840976 | − | 0.541073i | \(-0.818018\pi\) | ||||
0.840976 | − | 0.541073i | \(-0.181982\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.68352 | 0.00423937 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 70.9246 | 0.111692 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 601.316i | − 0.943982i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 368.043i | − 0.575967i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 816.719 | 1.27413 | 0.637066 | − | 0.770809i | \(-0.280148\pi\) | ||||
0.637066 | + | 0.770809i | \(0.280148\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1164.05 | −1.81034 | −0.905172 | − | 0.425045i | \(-0.860258\pi\) | ||||
−0.905172 | + | 0.425045i | \(0.860258\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 356.301i | 0.552405i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 471.519i | 0.728778i | 0.931247 | + | 0.364389i | \(0.118722\pi\) | ||||
−0.931247 | + | 0.364389i | \(0.881278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −908.496 | −1.39984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −184.835 | −0.283924 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1187.25i | 1.81814i | 0.416642 | + | 0.909071i | \(0.363207\pi\) | ||||
−0.416642 | + | 0.909071i | \(0.636793\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 218.833i | 0.334096i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 434.711 | 0.661661 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 245.640 | 0.372747 | 0.186373 | − | 0.982479i | \(-0.440327\pi\) | ||||
0.186373 | + | 0.982479i | \(0.440327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1244.70i | 1.88305i | 0.336936 | + | 0.941527i | \(0.390609\pi\) | ||||
−0.336936 | + | 0.941527i | \(0.609391\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 575.359i | − 0.867812i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 189.884 | 0.285540 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 374.176 | 0.560984 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 258.013i | 0.385670i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 553.468i | 0.824841i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −852.278 | −1.26639 | −0.633193 | − | 0.773994i | \(-0.718256\pi\) | ||||
−0.633193 | + | 0.773994i | \(0.718256\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 34.1605 | 0.0506082 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 555.765i | − 0.820923i | −0.911878 | − | 0.410461i | \(-0.865368\pi\) | ||||
0.911878 | − | 0.410461i | \(-0.134632\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 243.540i | − 0.358675i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −411.888 | −0.604828 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −335.241 | −0.490836 | −0.245418 | − | 0.969417i | \(-0.578925\pi\) | ||||
−0.245418 | + | 0.969417i | \(0.578925\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 42.9925i | − 0.0627628i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 121.346i | 0.176631i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 952.349 | 1.38222 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1274.20 | −1.84400 | −0.921999 | − | 0.387192i | \(-0.873445\pi\) | ||||
−0.921999 | + | 0.387192i | \(0.873445\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 114.159i | 0.164732i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 282.057i | 0.405837i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −531.416 | −0.762434 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.4380 | −0.0177940 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 676.056i | − 0.964416i | −0.876057 | − | 0.482208i | \(-0.839835\pi\) | ||||
0.876057 | − | 0.482208i | \(-0.160165\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1065.37i | − 1.51547i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −110.417 | −0.156619 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 287.771 | 0.407031 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 62.3418i | − 0.0879292i | −0.999033 | − | 0.0439646i | \(-0.986001\pi\) | ||||
0.999033 | − | 0.0439646i | \(-0.0139989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 385.971i | − 0.542856i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 662.127 | 0.928649 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 860.384 | 1.20333 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 375.197i | − 0.523287i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 322.341i | 0.448318i | 0.974553 | + | 0.224159i | \(0.0719636\pi\) | ||||
−0.974553 | + | 0.224159i | \(0.928036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −190.461 | −0.264163 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 666.841 | 0.922326 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 143.756i | 0.198284i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 368.070i | − 0.506287i | −0.967429 | − | 0.253143i | \(-0.918536\pi\) | ||||
0.967429 | − | 0.253143i | \(-0.0814644\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1095.87 | 1.49913 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 430.587i | − 0.587431i | −0.955893 | − | 0.293715i | \(-0.905108\pi\) | ||||
0.955893 | − | 0.293715i | \(-0.0948918\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 307.760i | 0.418721i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1032.23 | −1.40059 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −818.050 | −1.10697 | −0.553485 | − | 0.832859i | \(-0.686702\pi\) | ||||
−0.553485 | + | 0.832859i | \(0.686702\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 403.576i | 0.544638i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 685.438i | 0.922528i | 0.887263 | + | 0.461264i | \(0.152604\pi\) | ||||
−0.887263 | + | 0.461264i | \(0.847396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 406.810 | 0.546053 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −66.1251 | −0.0885209 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 412.106i | − 0.550208i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 104.336i | − 0.138929i | −0.997584 | − | 0.0694647i | \(-0.977871\pi\) | ||||
0.997584 | − | 0.0694647i | \(-0.0221291\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 148.070 | 0.196640 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1157.99 | −1.53377 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 539.949i | − 0.713274i | −0.934243 | − | 0.356637i | \(-0.883923\pi\) | ||||
0.934243 | − | 0.356637i | \(-0.116077\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 408.948i | − 0.538798i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1192.21 | −1.56663 | −0.783317 | − | 0.621623i | \(-0.786474\pi\) | ||||
−0.783317 | + | 0.621623i | \(0.786474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 149.847 | 0.196391 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 294.475i | 0.384935i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 956.473i | 1.24703i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −321.506 | −0.418083 | −0.209042 | − | 0.977907i | \(-0.567034\pi\) | ||||
−0.209042 | + | 0.977907i | \(0.567034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −94.0471 | −0.121981 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1453.29i | − 1.88006i | −0.341094 | − | 0.940029i | \(-0.610798\pi\) | ||||
0.341094 | − | 0.940029i | \(-0.389202\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 254.385i | 0.328239i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −317.276 | −0.408334 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 372.753 | 0.478502 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1692.75i | − 2.16741i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 113.623i | 0.145112i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 135.240 | 0.172280 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −231.223 | −0.293802 | −0.146901 | − | 0.989151i | \(-0.546930\pi\) | ||||
−0.146901 | + | 0.989151i | \(0.546930\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 869.189i | − 1.10163i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.4531i | 0.0220646i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 582.696 | 0.734800 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −487.422 | −0.613110 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 51.5068i | − 0.0646259i | −0.999478 | − | 0.0323129i | \(-0.989713\pi\) | ||||
0.999478 | − | 0.0323129i | \(-0.0102873\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 339.606i | 0.425039i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 366.224 | 0.457209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1999.38 | 2.48988 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 202.572i | 0.251643i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 493.480i | − 0.611499i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −580.914 | −0.718065 | −0.359032 | − | 0.933325i | \(-0.616893\pi\) | ||||
−0.359032 | + | 0.933325i | \(0.616893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1351.98 | −1.66706 | −0.833529 | − | 0.552475i | \(-0.813683\pi\) | ||||
−0.833529 | + | 0.552475i | \(0.813683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 417.753i | 0.513841i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 863.480i | 1.05948i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −768.678 | −0.940855 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 120.188 | 0.146749 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 179.511i | 0.218650i | 0.994006 | + | 0.109325i | \(0.0348688\pi\) | ||||
−0.994006 | + | 0.109325i | \(0.965131\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 665.446i | 0.808561i | 0.914635 | + | 0.404281i | \(0.132478\pi\) | ||||
−0.914635 | + | 0.404281i | \(0.867522\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 157.115 | 0.190443 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 901.166 | 1.08968 | 0.544840 | − | 0.838540i | \(-0.316590\pi\) | ||||
0.544840 | + | 0.838540i | \(0.316590\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 183.151i | 0.220930i | 0.993880 | + | 0.110465i | \(0.0352340\pi\) | ||||
−0.993880 | + | 0.110465i | \(0.964766\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 420.676i | − 0.506228i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 946.571 | 1.13634 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1143.50 | 1.36946 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 201.062i | 0.240218i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 846.082i | 1.00844i | 0.863575 | + | 0.504220i | \(0.168220\pi\) | ||||
−0.863575 | + | 0.504220i | \(0.831780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 362.846 | 0.431446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −182.457 | −0.216437 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 180.382i | − 0.213470i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 191.351i | 0.225917i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −387.749 | −0.456713 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1136.56 | 1.33556 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 540.635i | − 0.633804i | −0.948458 | − | 0.316902i | \(-0.897357\pi\) | ||||
0.948458 | − | 0.316902i | \(-0.102643\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 206.555i | − 0.241585i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1333.41 | −1.55590 | −0.777952 | − | 0.628323i | \(-0.783742\pi\) | ||||
−0.777952 | + | 0.628323i | \(0.783742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −439.034 | −0.511099 | −0.255549 | − | 0.966796i | \(-0.582256\pi\) | ||||
−0.255549 | + | 0.966796i | \(0.582256\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 111.008i | − 0.128930i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1164.41i | − 1.34926i | −0.738155 | − | 0.674631i | \(-0.764303\pi\) | ||||
0.738155 | − | 0.674631i | \(-0.235697\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −188.208 | −0.217582 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 405.147 | 0.467298 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1775.20i | − 2.04281i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1086.74i | 1.24769i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −264.922 | −0.303461 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −373.783 | −0.427181 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 404.456i | − 0.461181i | −0.973051 | − | 0.230591i | \(-0.925934\pi\) | ||||
0.973051 | − | 0.230591i | \(-0.0740658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 729.292i | − 0.829684i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −227.084 | −0.257757 | −0.128879 | − | 0.991660i | \(-0.541138\pi\) | ||||
−0.128879 | + | 0.991660i | \(0.541138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −673.730 | −0.763001 | −0.381501 | − | 0.924369i | \(-0.624593\pi\) | ||||
−0.381501 | + | 0.924369i | \(0.624593\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 489.533i | − 0.553145i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1370.95i | − 1.54560i | −0.634648 | − | 0.772801i | \(-0.718855\pi\) | ||||
0.634648 | − | 0.772801i | \(-0.281145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.5678 | 0.0512574 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 124.182 | 0.139373 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 238.211i | − 0.266754i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1183.79i | − 1.32267i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −430.544 | −0.479982 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −846.121 | −0.941180 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1499.15i | 1.66388i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 228.917i | 0.253508i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 339.124 | 0.374723 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1469.46 | 1.62013 | 0.810063 | − | 0.586342i | \(-0.199433\pi\) | ||||
0.810063 | + | 0.586342i | \(0.199433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 313.035i | − 0.344373i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 871.203i | 0.956315i | 0.878274 | + | 0.478157i | \(0.158695\pi\) | ||||
−0.878274 | + | 0.478157i | \(0.841305\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −304.131 | −0.333111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −298.230 | −0.325935 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 140.596i | 0.153322i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 256.361i | − 0.278957i | −0.990225 | − | 0.139478i | \(-0.955457\pi\) | ||||
0.990225 | − | 0.139478i | \(-0.0445426\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −212.808 | −0.231062 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1782.14 | −1.93081 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 436.661i | 0.472066i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 207.183i | 0.223498i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1399.93 | −1.50692 | −0.753462 | − | 0.657491i | \(-0.771618\pi\) | ||||
−0.753462 | + | 0.657491i | \(0.771618\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −663.956 | −0.713165 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 757.832i | − 0.812253i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1354.39i | 1.44854i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −365.610 | −0.390192 | −0.195096 | − | 0.980784i | \(-0.562502\pi\) | ||||
−0.195096 | + | 0.980784i | \(0.562502\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −650.235 | −0.692476 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 407.498i | 0.433048i | 0.976277 | + | 0.216524i | \(0.0694720\pi\) | ||||
−0.976277 | + | 0.216524i | \(0.930528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 397.661i | 0.421698i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −61.5134 | −0.0650935 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1150.64 | 1.21503 | 0.607516 | − | 0.794307i | \(-0.292166\pi\) | ||||
0.607516 | + | 0.794307i | \(0.292166\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2104.96i | − 2.21808i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 673.537i | − 0.708241i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1341.53 | 1.40769 | 0.703844 | − | 0.710355i | \(-0.251466\pi\) | ||||
0.703844 | + | 0.710355i | \(0.251466\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −611.295 | −0.640100 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 522.588i | 0.546069i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 27.6219i | − 0.0288029i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −536.260 | −0.558023 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −448.286 | −0.465510 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1192.54i | − 1.23579i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1227.25i | 1.26914i | 0.772867 | + | 0.634568i | \(0.218822\pi\) | ||||
−0.772867 | + | 0.634568i | \(0.781178\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −635.295 | −0.655620 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1864.31 | 1.91999 | 0.959994 | − | 0.280020i | \(-0.0903413\pi\) | ||||
0.959994 | + | 0.280020i | \(0.0903413\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 181.217i | 0.186245i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 165.412i | − 0.169654i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1209.56 | −1.23803 | −0.619017 | − | 0.785378i | \(-0.712469\pi\) | ||||
−0.619017 | + | 0.785378i | \(0.712469\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1684.38 | 1.72051 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 163.002i | − 0.166159i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1018.26i | − 1.03587i | −0.855420 | − | 0.517935i | \(-0.826701\pi\) | ||||
0.855420 | − | 0.517935i | \(-0.173299\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.6310 | −0.0148538 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −70.9408 | −0.0718752 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 820.042i | − 0.829163i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1627.52i | − 1.64230i | −0.570712 | − | 0.821150i | \(-0.693333\pi\) | ||||
0.570712 | − | 0.821150i | \(-0.306667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.7931 | 0.0269819 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1349.24 | 1.35602 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 540.192i | 0.541817i | 0.962605 | + | 0.270909i | \(0.0873241\pi\) | ||||
−0.962605 | + | 0.270909i | \(0.912676\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 345.131i | 0.345476i |
(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 | 768.3.b.f.127.8 | 8 | ||
3.2 | odd | 2 | 2304.3.b.q.127.2 | 8 | |||
4.3 | odd | 2 | 768.3.b.e.127.4 | 8 | |||
8.3 | odd | 2 | inner | 768.3.b.f.127.5 | 8 | ||
8.5 | even | 2 | 768.3.b.e.127.1 | 8 | |||
12.11 | even | 2 | 2304.3.b.t.127.2 | 8 | |||
16.3 | odd | 4 | 384.3.g.a.127.4 | ✓ | 8 | ||
16.5 | even | 4 | 384.3.g.b.127.1 | yes | 8 | ||
16.11 | odd | 4 | 384.3.g.b.127.5 | yes | 8 | ||
16.13 | even | 4 | 384.3.g.a.127.8 | yes | 8 | ||
24.5 | odd | 2 | 2304.3.b.t.127.7 | 8 | |||
24.11 | even | 2 | 2304.3.b.q.127.7 | 8 | |||
48.5 | odd | 4 | 1152.3.g.c.127.7 | 8 | |||
48.11 | even | 4 | 1152.3.g.c.127.8 | 8 | |||
48.29 | odd | 4 | 1152.3.g.f.127.1 | 8 | |||
48.35 | even | 4 | 1152.3.g.f.127.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.g.a.127.4 | ✓ | 8 | 16.3 | odd | 4 | ||
384.3.g.a.127.8 | yes | 8 | 16.13 | even | 4 | ||
384.3.g.b.127.1 | yes | 8 | 16.5 | even | 4 | ||
384.3.g.b.127.5 | yes | 8 | 16.11 | odd | 4 | ||
768.3.b.e.127.1 | 8 | 8.5 | even | 2 | |||
768.3.b.e.127.4 | 8 | 4.3 | odd | 2 | |||
768.3.b.f.127.5 | 8 | 8.3 | odd | 2 | inner | ||
768.3.b.f.127.8 | 8 | 1.1 | even | 1 | trivial | ||
1152.3.g.c.127.7 | 8 | 48.5 | odd | 4 | |||
1152.3.g.c.127.8 | 8 | 48.11 | even | 4 | |||
1152.3.g.f.127.1 | 8 | 48.29 | odd | 4 | |||
1152.3.g.f.127.2 | 8 | 48.35 | even | 4 | |||
2304.3.b.q.127.2 | 8 | 3.2 | odd | 2 | |||
2304.3.b.q.127.7 | 8 | 24.11 | even | 2 | |||
2304.3.b.t.127.2 | 8 | 12.11 | even | 2 | |||
2304.3.b.t.127.7 | 8 | 24.5 | odd | 2 |