Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(401,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1200.401");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.l (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: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.2 | ||
Root | \(0.500000 - 1.65831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.401 |
Dual form | 1200.3.l.s.401.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 2.50000 | + | 1.65831i | 0.833333 | + | 0.552771i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.50000 | + | 8.29156i | 0.388889 | + | 0.921285i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.5831i | 1.50756i | 0.657129 | + | 0.753778i | \(0.271771\pi\) | ||||
−0.657129 | + | 0.753778i | \(0.728229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.0000 | −0.769231 | −0.384615 | − | 0.923077i | \(-0.625666\pi\) | ||||
−0.384615 | + | 0.923077i | \(0.625666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.31662i | − | 0.195096i | −0.995231 | − | 0.0975478i | \(-0.968900\pi\) | ||
0.995231 | − | 0.0975478i | \(-0.0310999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00000 | −0.368421 | −0.184211 | − | 0.982887i | \(-0.558973\pi\) | ||||
−0.184211 | + | 0.982887i | \(0.558973\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19.8997i | 0.865206i | 0.901584 | + | 0.432603i | \(0.142405\pi\) | ||||
−0.901584 | + | 0.432603i | \(0.857595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | + | 26.5330i | −0.185185 | + | 0.982704i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 33.1662i | − | 1.14366i | −0.820371 | − | 0.571832i | \(-0.806233\pi\) | ||
0.820371 | − | 0.571832i | \(-0.193767\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −42.0000 | −1.35484 | −0.677419 | − | 0.735597i | \(-0.736902\pi\) | ||||
−0.677419 | + | 0.735597i | \(0.736902\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −27.5000 | + | 41.4578i | −0.833333 | + | 1.25630i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.0000 | 1.08108 | 0.540541 | − | 0.841318i | \(-0.318220\pi\) | ||||
0.540541 | + | 0.841318i | \(0.318220\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −25.0000 | − | 16.5831i | −0.641026 | − | 0.425208i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.5831i | 0.404466i | 0.979337 | + | 0.202233i | \(0.0648199\pi\) | ||||
−0.979337 | + | 0.202233i | \(0.935180\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −50.0000 | −1.16279 | −0.581395 | − | 0.813621i | \(-0.697493\pi\) | ||||
−0.581395 | + | 0.813621i | \(0.697493\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 46.4327i | − | 0.987931i | −0.869482 | − | 0.493965i | \(-0.835547\pi\) | ||
0.869482 | − | 0.493965i | \(-0.164453\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.50000 | − | 8.29156i | 0.107843 | − | 0.162580i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 46.4327i | 0.876090i | 0.898953 | + | 0.438045i | \(0.144329\pi\) | ||||
−0.898953 | + | 0.438045i | \(0.855671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.5000 | − | 11.6082i | −0.307018 | − | 0.203652i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 66.3325i | 1.12428i | 0.827042 | + | 0.562140i | \(0.190022\pi\) | ||||
−0.827042 | + | 0.562140i | \(0.809978\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.00000 | −0.131148 | −0.0655738 | − | 0.997848i | \(-0.520888\pi\) | ||||
−0.0655738 | + | 0.997848i | \(0.520888\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 45.0000 | 0.671642 | 0.335821 | − | 0.941926i | \(-0.390986\pi\) | ||||
0.335821 | + | 0.941926i | \(0.390986\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −33.0000 | + | 49.7494i | −0.478261 | + | 0.721005i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 33.1662i | 0.467130i | 0.972341 | + | 0.233565i | \(0.0750392\pi\) | ||||
−0.972341 | + | 0.233565i | \(0.924961\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 35.0000 | 0.479452 | 0.239726 | − | 0.970841i | \(-0.422942\pi\) | ||||
0.239726 | + | 0.970841i | \(0.422942\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −0.151899 | −0.0759494 | − | 0.997112i | \(-0.524199\pi\) | ||||
−0.0759494 | + | 0.997112i | \(0.524199\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −56.5000 | + | 58.0409i | −0.697531 | + | 0.716555i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 69.6491i | 0.839146i | 0.907722 | + | 0.419573i | \(0.137820\pi\) | ||||
−0.907722 | + | 0.419573i | \(0.862180\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 55.0000 | − | 82.9156i | 0.632184 | − | 0.953053i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 149.248i | 1.67695i | 0.544944 | + | 0.838473i | \(0.316551\pi\) | ||||
−0.544944 | + | 0.838473i | \(0.683449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −105.000 | − | 69.6491i | −1.12903 | − | 0.748915i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 70.0000 | 0.721649 | 0.360825 | − | 0.932634i | \(-0.382495\pi\) | ||||
0.360825 | + | 0.932634i | \(0.382495\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −137.500 | + | 58.0409i | −1.38889 | + | 0.586272i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −70.0000 | −0.679612 | −0.339806 | − | 0.940496i | \(-0.610361\pi\) | ||||
−0.339806 | + | 0.940496i | \(0.610361\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 69.6491i | 0.650926i | 0.945555 | + | 0.325463i | \(0.105520\pi\) | ||||
−0.945555 | + | 0.325463i | \(0.894480\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −88.0000 | −0.807339 | −0.403670 | − | 0.914905i | \(-0.632266\pi\) | ||||
−0.403670 | + | 0.914905i | \(0.632266\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 100.000 | + | 66.3325i | 0.900901 | + | 0.597590i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 102.815i | − | 0.909871i | −0.890525 | − | 0.454935i | \(-0.849662\pi\) | ||
0.890525 | − | 0.454935i | \(-0.150338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −35.0000 | − | 82.9156i | −0.299145 | − | 0.708681i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −154.000 | −1.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −27.5000 | + | 41.4578i | −0.223577 | + | 0.337055i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 190.000 | 1.49606 | 0.748031 | − | 0.663663i | \(-0.230999\pi\) | ||||
0.748031 | + | 0.663663i | \(0.230999\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −125.000 | − | 82.9156i | −0.968992 | − | 0.642757i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 198.997i | − | 1.51906i | −0.650469 | − | 0.759532i | \(-0.725428\pi\) | ||
0.650469 | − | 0.759532i | \(-0.274572\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 69.6491i | − | 0.508388i | −0.967153 | − | 0.254194i | \(-0.918190\pi\) | ||
0.967153 | − | 0.254194i | \(-0.0818101\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −77.0000 | −0.553957 | −0.276978 | − | 0.960876i | \(-0.589333\pi\) | ||||
−0.276978 | + | 0.960876i | \(0.589333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 77.0000 | − | 116.082i | 0.546099 | − | 0.823276i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 165.831i | − | 1.15966i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −122.500 | − | 81.2573i | −0.833333 | − | 0.552771i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 165.831i | 1.11296i | 0.830861 | + | 0.556481i | \(0.187849\pi\) | ||||
−0.830861 | + | 0.556481i | \(0.812151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −172.000 | −1.13907 | −0.569536 | − | 0.821966i | \(-0.692877\pi\) | ||||
−0.569536 | + | 0.821966i | \(0.692877\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 27.5000 | − | 11.6082i | 0.179739 | − | 0.0758705i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 250.000 | 1.59236 | 0.796178 | − | 0.605062i | \(-0.206852\pi\) | ||||
0.796178 | + | 0.605062i | \(0.206852\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −77.0000 | + | 116.082i | −0.484277 | + | 0.730075i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 35.0000 | 0.214724 | 0.107362 | − | 0.994220i | \(-0.465760\pi\) | ||||
0.107362 | + | 0.994220i | \(0.465760\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 179.098i | − | 1.07244i | −0.844078 | − | 0.536221i | \(-0.819851\pi\) | ||
0.844078 | − | 0.536221i | \(-0.180149\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −69.0000 | −0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.5000 | − | 58.0409i | −0.143275 | − | 0.339421i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 278.596i | 1.61038i | 0.593014 | + | 0.805192i | \(0.297938\pi\) | ||||
−0.593014 | + | 0.805192i | \(0.702062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −110.000 | + | 165.831i | −0.621469 | + | 0.936900i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 116.082i | 0.648502i | 0.945971 | + | 0.324251i | \(0.105112\pi\) | ||||
−0.945971 | + | 0.324251i | \(0.894888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 182.000 | 1.00552 | 0.502762 | − | 0.864425i | \(-0.332317\pi\) | ||||
0.502762 | + | 0.864425i | \(0.332317\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.0000 | − | 13.2665i | −0.109290 | − | 0.0724945i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 55.0000 | 0.294118 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 232.164i | 1.21552i | 0.794122 | + | 0.607758i | \(0.207931\pi\) | ||||
−0.794122 | + | 0.607758i | \(0.792069\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.0000 | 0.129534 | 0.0647668 | − | 0.997900i | \(-0.479370\pi\) | ||||
0.0647668 | + | 0.997900i | \(0.479370\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 218.897i | − | 1.11115i | −0.831465 | − | 0.555577i | \(-0.812498\pi\) | ||
0.831465 | − | 0.555577i | \(-0.187502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 68.0000 | 0.341709 | 0.170854 | − | 0.985296i | \(-0.445347\pi\) | ||||
0.170854 | + | 0.985296i | \(0.445347\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 112.500 | + | 74.6241i | 0.559701 | + | 0.371264i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −165.000 | + | 69.6491i | −0.797101 | + | 0.336469i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 116.082i | − | 0.555416i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −77.0000 | −0.364929 | −0.182464 | − | 0.983212i | \(-0.558407\pi\) | ||||
−0.182464 | + | 0.983212i | \(0.558407\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −55.0000 | + | 82.9156i | −0.258216 | + | 0.389275i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 87.5000 | + | 58.0409i | 0.399543 | + | 0.265027i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.1662i | 0.150074i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 140.000 | 0.627803 | 0.313901 | − | 0.949456i | \(-0.398364\pi\) | ||||
0.313901 | + | 0.949456i | \(0.398364\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 185.731i | 0.818198i | 0.912490 | + | 0.409099i | \(0.134157\pi\) | ||||
−0.912490 | + | 0.409099i | \(0.865843\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 372.000 | 1.62445 | 0.812227 | − | 0.583341i | \(-0.198255\pi\) | ||||
0.812227 | + | 0.583341i | \(0.198255\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 119.398i | − | 0.512440i | −0.966619 | − | 0.256220i | \(-0.917523\pi\) | ||
0.966619 | − | 0.256220i | \(-0.0824771\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30.0000 | − | 19.8997i | −0.126582 | − | 0.0839652i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 232.164i | − | 0.971396i | −0.874127 | − | 0.485698i | \(-0.838565\pi\) | ||
0.874127 | − | 0.485698i | \(-0.161435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −413.000 | −1.71369 | −0.856846 | − | 0.515572i | \(-0.827580\pi\) | ||||
−0.856846 | + | 0.515572i | \(0.827580\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −237.500 | + | 51.4077i | −0.977366 | + | 0.211554i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 70.0000 | 0.283401 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −115.500 | + | 174.123i | −0.463855 | + | 0.699288i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 248.747i | 0.991023i | 0.868601 | + | 0.495512i | \(0.165019\pi\) | ||||
−0.868601 | + | 0.495512i | \(0.834981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −330.000 | −1.30435 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 278.596i | 1.08403i | 0.840368 | + | 0.542017i | \(0.182339\pi\) | ||||
−0.840368 | + | 0.542017i | \(0.817661\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 275.000 | − | 116.082i | 1.05364 | − | 0.444758i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 285.230i | 1.08452i | 0.840210 | + | 0.542262i | \(0.182432\pi\) | ||||
−0.840210 | + | 0.542262i | \(0.817568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −247.500 | + | 373.120i | −0.926966 | + | 1.39745i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 464.327i | − | 1.72612i | −0.505098 | − | 0.863062i | \(-0.668544\pi\) | ||
0.505098 | − | 0.863062i | \(-0.331456\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.0000 | −0.0811808 | −0.0405904 | − | 0.999176i | \(-0.512924\pi\) | ||||
−0.0405904 | + | 0.999176i | \(0.512924\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 210.000 | 0.758123 | 0.379061 | − | 0.925372i | \(-0.376247\pi\) | ||||
0.379061 | + | 0.925372i | \(0.376247\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −147.000 | − | 348.246i | −0.526882 | − | 1.24819i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 198.997i | 0.708176i | 0.935212 | + | 0.354088i | \(0.115209\pi\) | ||||
−0.935212 | + | 0.354088i | \(0.884791\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 345.000 | 1.21908 | 0.609541 | − | 0.792755i | \(-0.291354\pi\) | ||||
0.609541 | + | 0.792755i | \(0.291354\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 278.000 | 0.961938 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 175.000 | + | 116.082i | 0.601375 | + | 0.398907i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 318.396i | − | 1.08668i | −0.839514 | − | 0.543338i | \(-0.817160\pi\) | ||
0.839514 | − | 0.543338i | \(-0.182840\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −440.000 | − | 82.9156i | −1.48148 | − | 0.279177i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 198.997i | − | 0.665543i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 325.000 | 1.05863 | 0.529316 | − | 0.848425i | \(-0.322449\pi\) | ||||
0.529316 | + | 0.848425i | \(0.322449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −175.000 | − | 116.082i | −0.566343 | − | 0.375669i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 397.995i | − | 1.27973i | −0.768489 | − | 0.639863i | \(-0.778991\pi\) | ||
0.768489 | − | 0.639863i | \(-0.221009\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 490.000 | 1.56550 | 0.782748 | − | 0.622339i | \(-0.213818\pi\) | ||||
0.782748 | + | 0.622339i | \(0.213818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 212.264i | 0.669602i | 0.942289 | + | 0.334801i | \(0.108669\pi\) | ||||
−0.942289 | + | 0.334801i | \(0.891331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 550.000 | 1.72414 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −115.500 | + | 174.123i | −0.359813 | + | 0.542439i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.2164i | 0.0718773i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −220.000 | − | 145.931i | −0.672783 | − | 0.446274i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 243.000 | 0.734139 | 0.367069 | − | 0.930194i | \(-0.380361\pi\) | ||||
0.367069 | + | 0.930194i | \(0.380361\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 140.000 | + | 331.662i | 0.420420 | + | 0.995983i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −385.000 | −1.14243 | −0.571217 | − | 0.820799i | \(-0.693528\pi\) | ||||
−0.571217 | + | 0.820799i | \(0.693528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 170.500 | − | 257.038i | 0.502950 | − | 0.758225i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 696.491i | − | 2.04250i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 295.180i | − | 0.850662i | −0.905038 | − | 0.425331i | \(-0.860158\pi\) | ||
0.905038 | − | 0.425331i | \(-0.139842\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 532.000 | 1.52436 | 0.762178 | − | 0.647368i | \(-0.224130\pi\) | ||||
0.762178 | + | 0.647368i | \(0.224130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 50.0000 | − | 265.330i | 0.142450 | − | 0.755926i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 278.596i | 0.789225i | 0.918848 | + | 0.394613i | \(0.129121\pi\) | ||||
−0.918848 | + | 0.394613i | \(0.870879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 397.995i | 1.10862i | 0.832310 | + | 0.554311i | \(0.187018\pi\) | ||||
−0.832310 | + | 0.554311i | \(0.812982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −312.000 | −0.864266 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −385.000 | − | 255.380i | −1.06061 | − | 0.703526i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −180.000 | −0.490463 | −0.245232 | − | 0.969465i | \(-0.578864\pi\) | ||||
−0.245232 | + | 0.969465i | \(0.578864\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −137.500 | + | 58.0409i | −0.372629 | + | 0.157293i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 110.000 | 0.294906 | 0.147453 | − | 0.989069i | \(-0.452892\pi\) | ||||
0.147453 | + | 0.989069i | \(0.452892\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 331.662i | 0.879741i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 533.000 | 1.40633 | 0.703166 | − | 0.711025i | \(-0.251769\pi\) | ||||
0.703166 | + | 0.711025i | \(0.251769\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 475.000 | + | 315.079i | 1.24672 | + | 0.826980i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 79.5990i | − | 0.207830i | −0.994586 | − | 0.103915i | \(-0.966863\pi\) | ||
0.994586 | − | 0.103915i | \(-0.0331370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −175.000 | − | 414.578i | −0.452196 | − | 1.07126i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 99.4987i | − | 0.255781i | −0.991788 | − | 0.127890i | \(-0.959179\pi\) | ||
0.991788 | − | 0.127890i | \(-0.0408206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 66.0000 | 0.168798 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 330.000 | − | 497.494i | 0.839695 | − | 1.26589i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.0000 | 0.0503778 | 0.0251889 | − | 0.999683i | \(-0.491981\pi\) | ||||
0.0251889 | + | 0.999683i | \(0.491981\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 746.241i | 1.86095i | 0.366357 | + | 0.930475i | \(0.380605\pi\) | ||||
−0.366357 | + | 0.930475i | \(0.619395\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 420.000 | 1.04218 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 663.325i | 1.62979i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 77.0000 | 0.188264 | 0.0941320 | − | 0.995560i | \(-0.469992\pi\) | ||||
0.0941320 | + | 0.995560i | \(0.469992\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 115.500 | − | 174.123i | 0.281022 | − | 0.423656i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −192.500 | − | 127.690i | −0.461631 | − | 0.306211i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 116.082i | − | 0.277045i | −0.990359 | − | 0.138523i | \(-0.955765\pi\) | ||
0.990359 | − | 0.138523i | \(-0.0442353\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 412.000 | 0.978622 | 0.489311 | − | 0.872109i | \(-0.337248\pi\) | ||||
0.489311 | + | 0.872109i | \(0.337248\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 385.000 | − | 162.515i | 0.910165 | − | 0.384195i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 275.000 | − | 414.578i | 0.641026 | − | 0.966383i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 198.997i | − | 0.461711i | −0.972988 | − | 0.230856i | \(-0.925848\pi\) | ||
0.972988 | − | 0.230856i | \(-0.0741525\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 455.000 | 1.05081 | 0.525404 | − | 0.850853i | \(-0.323914\pi\) | ||||
0.525404 | + | 0.850853i | \(0.323914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 139.298i | − | 0.318760i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0000 | −0.0501139 | −0.0250569 | − | 0.999686i | \(-0.507977\pi\) | ||||
−0.0250569 | + | 0.999686i | \(0.507977\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −171.500 | − | 406.287i | −0.388889 | − | 0.921285i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 527.343i | − | 1.19039i | −0.803581 | − | 0.595196i | \(-0.797075\pi\) | ||
0.803581 | − | 0.595196i | \(-0.202925\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −275.000 | + | 414.578i | −0.615213 | + | 0.927468i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 82.9156i | 0.184667i | 0.995728 | + | 0.0923337i | \(0.0294326\pi\) | ||||
−0.995728 | + | 0.0923337i | \(0.970567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −275.000 | −0.609756 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −430.000 | − | 285.230i | −0.949227 | − | 0.629646i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 275.000 | 0.601751 | 0.300875 | − | 0.953663i | \(-0.402721\pi\) | ||||
0.300875 | + | 0.953663i | \(0.402721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 88.0000 | + | 16.5831i | 0.191721 | + | 0.0361288i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 596.992i | − | 1.29499i | −0.762068 | − | 0.647497i | \(-0.775816\pi\) | ||
0.762068 | − | 0.647497i | \(-0.224184\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −240.000 | −0.518359 | −0.259179 | − | 0.965829i | \(-0.583452\pi\) | ||||
−0.259179 | + | 0.965829i | \(0.583452\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 13.2665i | − | 0.0284079i | −0.999899 | − | 0.0142040i | \(-0.995479\pi\) | ||
0.999899 | − | 0.0142040i | \(-0.00452141\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 625.000 | + | 414.578i | 1.32696 | + | 0.880208i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 829.156i | − | 1.75297i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −385.000 | + | 162.515i | −0.807128 | + | 0.340701i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 298.496i | − | 0.623165i | −0.950219 | − | 0.311583i | \(-0.899141\pi\) | ||
0.950219 | − | 0.311583i | \(-0.100859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −400.000 | −0.831601 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 410.000 | 0.841889 | 0.420945 | − | 0.907086i | \(-0.361699\pi\) | ||||
0.420945 | + | 0.907086i | \(0.361699\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 87.5000 | + | 58.0409i | 0.178937 | + | 0.118693i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 265.330i | − | 0.540387i | −0.962806 | − | 0.270193i | \(-0.912912\pi\) | ||
0.962806 | − | 0.270193i | \(-0.0870877\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −110.000 | −0.223124 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −322.000 | −0.645291 | −0.322645 | − | 0.946520i | \(-0.604572\pi\) | ||||
−0.322645 | + | 0.946520i | \(0.604572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 297.000 | − | 447.744i | 0.592814 | − | 0.893701i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 411.261i | − | 0.817617i | −0.912620 | − | 0.408809i | \(-0.865944\pi\) | ||
0.912620 | − | 0.408809i | \(-0.134056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −172.500 | − | 114.424i | −0.340237 | − | 0.225687i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 431.161i | 0.847075i | 0.905879 | + | 0.423538i | \(0.139212\pi\) | ||||
−0.905879 | + | 0.423538i | \(0.860788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.0000 | − | 185.731i | 0.0682261 | − | 0.362049i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 770.000 | 1.48936 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −462.000 | + | 696.491i | −0.890173 | + | 1.34199i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 281.913i | − | 0.541100i | −0.962706 | − | 0.270550i | \(-0.912794\pi\) | ||
0.962706 | − | 0.270550i | \(-0.0872055\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1015.00 | 1.94073 | 0.970363 | − | 0.241651i | \(-0.0776888\pi\) | ||||
0.970363 | + | 0.241651i | \(0.0776888\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 139.298i | 0.264323i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 133.000 | 0.251418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −550.000 | + | 232.164i | −1.03578 | + | 0.437220i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 165.831i | − | 0.311128i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −192.500 | + | 290.205i | −0.358473 | + | 0.540418i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 812.573i | − | 1.50756i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 912.000 | 1.68577 | 0.842884 | − | 0.538096i | \(-0.180856\pi\) | ||||
0.842884 | + | 0.538096i | \(0.180856\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 455.000 | + | 301.813i | 0.837937 | + | 0.555825i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 55.0000 | 0.100548 | 0.0502742 | − | 0.998735i | \(-0.483990\pi\) | ||||
0.0502742 | + | 0.998735i | \(0.483990\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.0000 | − | 66.3325i | −0.0510018 | − | 0.120824i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 232.164i | 0.421350i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1014.89i | − | 1.82206i | −0.412341 | − | 0.911030i | \(-0.635289\pi\) | ||
0.412341 | − | 0.911030i | \(-0.364711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 500.000 | 0.894454 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 137.500 | + | 91.2072i | 0.245098 | + | 0.162580i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 119.398i | 0.212075i | 0.994362 | + | 0.106038i | \(0.0338164\pi\) | ||||
−0.994362 | + | 0.106038i | \(0.966184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 49.7494i | − | 0.0874330i | −0.999044 | − | 0.0437165i | \(-0.986080\pi\) | ||
0.999044 | − | 0.0437165i | \(-0.0139198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −242.000 | −0.423818 | −0.211909 | − | 0.977289i | \(-0.567968\pi\) | ||||
−0.211909 | + | 0.977289i | \(0.567968\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −385.000 | + | 580.409i | −0.671902 | + | 1.01293i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −665.000 | −1.15251 | −0.576256 | − | 0.817269i | \(-0.695487\pi\) | ||||
−0.576256 | + | 0.817269i | \(0.695487\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 62.5000 | + | 41.4578i | 0.107945 | + | 0.0716024i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −770.000 | −1.32075 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 626.842i | − | 1.06787i | −0.845524 | − | 0.533937i | \(-0.820712\pi\) | ||
0.845524 | − | 0.533937i | \(-0.179288\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 294.000 | 0.499151 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 363.000 | − | 547.243i | 0.614213 | − | 0.925961i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 859.006i | 1.44858i | 0.689497 | + | 0.724288i | \(0.257831\pi\) | ||||
−0.689497 | + | 0.724288i | \(0.742169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 170.000 | + | 112.765i | 0.284757 | + | 0.188887i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 331.662i | 0.553694i | 0.960914 | + | 0.276847i | \(0.0892895\pi\) | ||||
−0.960914 | + | 0.276847i | \(0.910711\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −343.000 | −0.570715 | −0.285358 | − | 0.958421i | \(-0.592112\pi\) | ||||
−0.285358 | + | 0.958421i | \(0.592112\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 157.500 | + | 373.120i | 0.261194 | + | 0.618773i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1100.00 | −1.81219 | −0.906096 | − | 0.423073i | \(-0.860951\pi\) | ||||
−0.906096 | + | 0.423073i | \(0.860951\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 464.327i | 0.759947i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 290.000 | 0.473083 | 0.236542 | − | 0.971621i | \(-0.423986\pi\) | ||||
0.236542 | + | 0.971621i | \(0.423986\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 79.5990i | 0.129010i | 0.997917 | + | 0.0645049i | \(0.0205468\pi\) | ||||
−0.997917 | + | 0.0645049i | \(0.979453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 58.0000 | 0.0936995 | 0.0468498 | − | 0.998902i | \(-0.485082\pi\) | ||||
0.0468498 | + | 0.998902i | \(0.485082\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −528.000 | − | 99.4987i | −0.850242 | − | 0.160223i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 192.500 | − | 290.205i | 0.307018 | − | 0.462846i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 132.665i | − | 0.210914i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −862.000 | −1.36609 | −0.683043 | − | 0.730378i | \(-0.739344\pi\) | ||||
−0.683043 | + | 0.730378i | \(0.739344\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −192.500 | − | 127.690i | −0.304107 | − | 0.201722i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 490.000 | 0.769231 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −275.000 | + | 116.082i | −0.430360 | + | 0.181662i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 596.992i | 0.931345i | 0.884957 | + | 0.465673i | \(0.154188\pi\) | ||||
−0.884957 | + | 0.465673i | \(0.845812\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1050.00 | −1.63297 | −0.816485 | − | 0.577366i | \(-0.804080\pi\) | ||||
−0.816485 | + | 0.577366i | \(0.804080\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 252.063i | 0.389588i | 0.980844 | + | 0.194794i | \(0.0624038\pi\) | ||||
−0.980844 | + | 0.194794i | \(0.937596\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1100.00 | −1.69492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1207.25i | 1.84878i | 0.381452 | + | 0.924389i | \(0.375424\pi\) | ||||
−0.381452 | + | 0.924389i | \(0.624576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 122.500 | + | 290.205i | 0.186454 | + | 0.441712i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 812.573i | 1.23304i | 0.787339 | + | 0.616520i | \(0.211458\pi\) | ||||
−0.787339 | + | 0.616520i | \(0.788542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −98.0000 | −0.148260 | −0.0741301 | − | 0.997249i | \(-0.523618\pi\) | ||||
−0.0741301 | + | 0.997249i | \(0.523618\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −55.0000 | + | 82.9156i | −0.0829563 | + | 0.125061i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 660.000 | 0.989505 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 350.000 | + | 232.164i | 0.523169 | + | 0.347031i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 132.665i | − | 0.197712i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 210.000 | 0.312036 | 0.156018 | − | 0.987754i | \(-0.450134\pi\) | ||||
0.156018 | + | 0.987754i | \(0.450134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 79.5990i | 0.117576i | 0.998270 | + | 0.0587880i | \(0.0187236\pi\) | ||||
−0.998270 | + | 0.0587880i | \(0.981276\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −308.000 | + | 464.327i | −0.452276 | + | 0.681832i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 169.148i | 0.247654i | 0.992304 | + | 0.123827i | \(0.0395168\pi\) | ||||
−0.992304 | + | 0.123827i | \(0.960483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 930.000 | + | 616.892i | 1.35371 | + | 0.897951i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 464.327i | − | 0.673915i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 713.000 | 1.03184 | 0.515919 | − | 0.856637i | \(-0.327451\pi\) | ||||
0.515919 | + | 0.856637i | \(0.327451\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 55.0000 | 0.0789096 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 198.000 | − | 298.496i | 0.283262 | − | 0.427033i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1160.82i | 1.65595i | 0.560767 | + | 0.827973i | \(0.310506\pi\) | ||||
−0.560767 | + | 0.827973i | \(0.689494\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −280.000 | −0.398293 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −248.000 | −0.349788 | −0.174894 | − | 0.984587i | \(-0.555958\pi\) | ||||
−0.174894 | + | 0.984587i | \(0.555958\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −42.0000 | − | 99.4987i | −0.0590717 | − | 0.139942i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 835.789i | − | 1.17222i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 385.000 | − | 580.409i | 0.536960 | − | 0.809497i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 198.997i | − | 0.276770i | −0.990379 | − | 0.138385i | \(-0.955809\pi\) | ||
0.990379 | − | 0.138385i | \(-0.0441911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1032.50 | − | 684.883i | −1.42808 | − | 0.947279i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.0000 | −0.0137552 | −0.00687758 | − | 0.999976i | \(-0.502189\pi\) | ||||
−0.00687758 | + | 0.999976i | \(0.502189\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −679.000 | − | 265.330i | −0.931413 | − | 0.363964i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 165.831i | 0.226855i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −770.000 | −1.05048 | −0.525239 | − | 0.850955i | \(-0.676024\pi\) | ||||
−0.525239 | + | 0.850955i | \(0.676024\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 746.241i | 1.01254i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −802.000 | −1.08525 | −0.542625 | − | 0.839975i | \(-0.682570\pi\) | ||||
−0.542625 | + | 0.839975i | \(0.682570\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 175.000 | + | 116.082i | 0.236167 | + | 0.156656i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1346.55i | 1.81231i | 0.422941 | + | 0.906157i | \(0.360998\pi\) | ||||
−0.422941 | + | 0.906157i | \(0.639002\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −577.500 | + | 243.772i | −0.773092 | + | 0.326335i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −322.000 | −0.428762 | −0.214381 | − | 0.976750i | \(-0.568773\pi\) | ||||
−0.214381 | + | 0.976750i | \(0.568773\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −412.500 | + | 621.867i | −0.547809 | + | 0.825853i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −400.000 | −0.528402 | −0.264201 | − | 0.964468i | \(-0.585108\pi\) | ||||
−0.264201 | + | 0.964468i | \(0.585108\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −825.000 | − | 547.243i | −1.08696 | − | 0.721005i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 348.246i | − | 0.457616i | −0.973472 | − | 0.228808i | \(-0.926517\pi\) | ||
0.973472 | − | 0.228808i | \(-0.0734828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 663.325i | − | 0.864830i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −193.000 | −0.250975 | −0.125488 | − | 0.992095i | \(-0.540050\pi\) | ||||
−0.125488 | + | 0.992095i | \(0.540050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −462.000 | + | 696.491i | −0.599222 | + | 0.903361i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 417.895i | − | 0.540614i | −0.962774 | − | 0.270307i | \(-0.912875\pi\) | ||
0.962774 | − | 0.270307i | \(-0.0871252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 116.082i | − | 0.149014i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −550.000 | −0.704225 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 880.000 | + | 165.831i | 1.12388 | + | 0.211790i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 910.000 | 1.15629 | 0.578145 | − | 0.815934i | \(-0.303777\pi\) | ||||
0.578145 | + | 0.815934i | \(0.303777\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −473.000 | + | 713.074i | −0.599493 | + | 0.903770i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 80.0000 | 0.100883 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1107.75i | 1.38990i | 0.719057 | + | 0.694951i | \(0.244574\pi\) | ||||
−0.719057 | + | 0.694951i | \(0.755426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −154.000 | −0.192741 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1237.50 | + | 522.368i | −1.54494 | + | 0.652145i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 580.409i | 0.722801i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 770.000 | − | 1160.82i | 0.954151 | − | 1.43844i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1260.32i | 1.55787i | 0.627104 | + | 0.778935i | \(0.284240\pi\) | ||||
−0.627104 | + | 0.778935i | \(0.715760\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 858.000 | 1.05795 | 0.528977 | − | 0.848636i | \(-0.322576\pi\) | ||||
0.528977 | + | 0.848636i | \(0.322576\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −55.0000 | − | 36.4829i | −0.0676507 | − | 0.0448744i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 350.000 | 0.428397 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 696.491i | − | 0.848345i | −0.905581 | − | 0.424172i | \(-0.860565\pi\) | ||
0.905581 | − | 0.424172i | \(-0.139435\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1060.00 | −1.28797 | −0.643985 | − | 0.765038i | \(-0.722720\pi\) | ||||
−0.643985 | + | 0.765038i | \(0.722720\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 500.810i | 0.605575i | 0.953058 | + | 0.302787i | \(0.0979172\pi\) | ||||
−0.953058 | + | 0.302787i | \(0.902083\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1038.00 | −1.25211 | −0.626055 | − | 0.779779i | \(-0.715332\pi\) | ||||
−0.626055 | + | 0.779779i | \(0.715332\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 525.000 | + | 348.246i | 0.631769 | + | 0.419068i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 162.515i | 0.195096i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 210.000 | − | 1114.39i | 0.250896 | − | 1.33140i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 928.655i | 1.10686i | 0.832896 | + | 0.553430i | \(0.186681\pi\) | ||||
−0.832896 | + | 0.553430i | \(0.813319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −259.000 | −0.307967 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −330.000 | + | 497.494i | −0.391459 | + | 0.590147i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 862.500 | + | 572.118i | 1.01590 | + | 0.673873i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 795.990i | 0.935358i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −630.000 | −0.738570 | −0.369285 | − | 0.929316i | \(-0.620397\pi\) | ||||
−0.369285 | + | 0.929316i | \(0.620397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1296.80i | − | 1.51319i | −0.653886 | − | 0.756593i | \(-0.726862\pi\) | ||
0.653886 | − | 0.756593i | \(-0.273138\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −307.000 | −0.357392 | −0.178696 | − | 0.983904i | \(-0.557188\pi\) | ||||
−0.178696 | + | 0.983904i | \(0.557188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 484.227i | 0.561098i | 0.959840 | + | 0.280549i | \(0.0905165\pi\) | ||||
−0.959840 | + | 0.280549i | \(0.909484\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 695.000 | + | 461.011i | 0.801615 | + | 0.531731i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 198.997i | − | 0.228996i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −450.000 | −0.516648 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 245.000 | + | 580.409i | 0.280641 | + | 0.664845i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −840.000 | −0.957811 | −0.478905 | − | 0.877867i | \(-0.658966\pi\) | ||||
−0.478905 | + | 0.877867i | \(0.658966\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 528.000 | − | 795.990i | 0.600683 | − | 0.905563i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 464.327i | − | 0.527046i | −0.964653 | − | 0.263523i | \(-0.915116\pi\) | ||
0.964653 | − | 0.263523i | \(-0.0848845\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 995.000 | 1.12684 | 0.563420 | − | 0.826171i | \(-0.309485\pi\) | ||||
0.563420 | + | 0.826171i | \(0.309485\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 477.594i | − | 0.538437i | −0.963079 | − | 0.269219i | \(-0.913235\pi\) | ||
0.963079 | − | 0.269219i | \(-0.0867654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −962.500 | − | 936.947i | −1.08025 | − | 1.05157i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 325.029i | 0.363975i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 330.000 | − | 497.494i | 0.367893 | − | 0.554620i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1392.98i | 1.54948i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 154.000 | 0.170921 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1050.00 | −1.15766 | −0.578831 | − | 0.815447i | \(-0.696491\pi\) | ||||
−0.578831 | + | 0.815447i | \(0.696491\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 729.657i | − | 0.800941i | −0.916310 | − | 0.400471i | \(-0.868847\pi\) | ||
0.916310 | − | 0.400471i | \(-0.131153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1155.00 | −1.26506 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1342.00 | −1.46028 | −0.730141 | − | 0.683296i | \(-0.760546\pi\) | ||||
−0.730141 | + | 0.683296i | \(0.760546\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 812.500 | + | 538.952i | 0.882193 | + | 0.585181i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 331.662i | − | 0.359331i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −245.000 | − | 580.409i | −0.264293 | − | 0.626116i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 464.327i | 0.499814i | 0.968270 | + | 0.249907i | \(0.0804001\pi\) | ||||
−0.968270 | + | 0.249907i | \(0.919600\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 343.000 | 0.368421 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 660.000 | − | 994.987i | 0.707395 | − | 1.06644i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 165.000 | 0.176094 | 0.0880470 | − | 0.996116i | \(-0.471937\pi\) | ||||
0.0880470 | + | 0.996116i | \(0.471937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1225.00 | + | 812.573i | 1.30458 | + | 0.865360i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 232.164i | − | 0.246720i | −0.992362 | − | 0.123360i | \(-0.960633\pi\) | ||
0.992362 | − | 0.123360i | \(-0.0393670\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −330.000 | −0.349947 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 278.596i | − | 0.294188i | −0.989122 | − | 0.147094i | \(-0.953008\pi\) | ||
0.989122 | − | 0.147094i | \(-0.0469921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −350.000 | −0.368809 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −352.000 | + | 530.660i | −0.370137 | + | 0.558002i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 195.681i | 0.205331i | 0.994716 | + | 0.102666i | \(0.0327372\pi\) | ||||
−0.994716 | + | 0.102666i | \(0.967263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1375.00 | + | 912.072i | 1.43678 | + | 0.953053i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 803.000 | 0.835588 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −577.500 | + | 243.772i | −0.599688 | + | 0.253138i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −280.000 | −0.289555 | −0.144778 | − | 0.989464i | \(-0.546247\pi\) | ||||
−0.144778 | + | 0.989464i | \(0.546247\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38.5000 | + | 58.0409i | −0.0397317 | + | 0.0598978i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1044.74i | − | 1.07594i | −0.842964 | − | 0.537970i | \(-0.819192\pi\) | ||
0.842964 | − | 0.537970i | \(-0.180808\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1097.80i | − | 1.12365i | −0.827257 | − | 0.561823i | \(-0.810100\pi\) | ||
0.827257 | − | 0.561823i | \(-0.189900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2475.00 | −2.52809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −308.000 | − | 729.657i | −0.313965 | − | 0.743789i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1671.58i | − | 1.70049i | −0.526389 | − | 0.850244i | \(-0.676455\pi\) | ||
0.526389 | − | 0.850244i | \(-0.323545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 994.987i | − | 1.00605i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −452.000 | −0.456105 | −0.228052 | − | 0.973649i | \(-0.573236\pi\) | ||||
−0.228052 | + | 0.973649i | \(0.573236\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 607.500 | + | 402.970i | 0.611782 | + | 0.405811i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 420.000 | 0.421264 | 0.210632 | − | 0.977565i | \(-0.432448\pi\) | ||||
0.210632 | + | 0.977565i | \(0.432448\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −200.000 | + | 1061.32i | −0.200200 | + | 1.06238i |
(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 | 1200.3.l.s.401.2 | 2 | ||
3.2 | odd | 2 | inner | 1200.3.l.s.401.1 | 2 | ||
4.3 | odd | 2 | 75.3.c.c.26.1 | ✓ | 2 | ||
5.2 | odd | 4 | 1200.3.c.d.449.3 | 4 | |||
5.3 | odd | 4 | 1200.3.c.d.449.2 | 4 | |||
5.4 | even | 2 | 1200.3.l.f.401.1 | 2 | |||
12.11 | even | 2 | 75.3.c.c.26.2 | yes | 2 | ||
15.2 | even | 4 | 1200.3.c.d.449.1 | 4 | |||
15.8 | even | 4 | 1200.3.c.d.449.4 | 4 | |||
15.14 | odd | 2 | 1200.3.l.f.401.2 | 2 | |||
20.3 | even | 4 | 75.3.d.c.74.1 | 4 | |||
20.7 | even | 4 | 75.3.d.c.74.4 | 4 | |||
20.19 | odd | 2 | 75.3.c.f.26.2 | yes | 2 | ||
60.23 | odd | 4 | 75.3.d.c.74.3 | 4 | |||
60.47 | odd | 4 | 75.3.d.c.74.2 | 4 | |||
60.59 | even | 2 | 75.3.c.f.26.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.c.c.26.1 | ✓ | 2 | 4.3 | odd | 2 | ||
75.3.c.c.26.2 | yes | 2 | 12.11 | even | 2 | ||
75.3.c.f.26.1 | yes | 2 | 60.59 | even | 2 | ||
75.3.c.f.26.2 | yes | 2 | 20.19 | odd | 2 | ||
75.3.d.c.74.1 | 4 | 20.3 | even | 4 | |||
75.3.d.c.74.2 | 4 | 60.47 | odd | 4 | |||
75.3.d.c.74.3 | 4 | 60.23 | odd | 4 | |||
75.3.d.c.74.4 | 4 | 20.7 | even | 4 | |||
1200.3.c.d.449.1 | 4 | 15.2 | even | 4 | |||
1200.3.c.d.449.2 | 4 | 5.3 | odd | 4 | |||
1200.3.c.d.449.3 | 4 | 5.2 | odd | 4 | |||
1200.3.c.d.449.4 | 4 | 15.8 | even | 4 | |||
1200.3.l.f.401.1 | 2 | 5.4 | even | 2 | |||
1200.3.l.f.401.2 | 2 | 15.14 | odd | 2 | |||
1200.3.l.s.401.1 | 2 | 3.2 | odd | 2 | inner | ||
1200.3.l.s.401.2 | 2 | 1.1 | even | 1 | trivial |