Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(161,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.j (of order \(4\), degree \(2\), 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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.1 | ||
Character | \(\chi\) | \(=\) | 1152.737 |
Dual form | 1152.3.j.a.161.1 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.08688 | + | 6.08688i | −1.21738 | + | 1.21738i | −0.248829 | + | 0.968547i | \(0.580046\pi\) |
−0.968547 | + | 0.248829i | \(0.919954\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 9.40026i | − | 1.34289i | −0.741053 | − | 0.671447i | \(-0.765673\pi\) | ||
0.741053 | − | 0.671447i | \(-0.234327\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.9531 | − | 11.9531i | 1.08665 | − | 1.08665i | 0.0907749 | − | 0.995871i | \(-0.471066\pi\) |
0.995871 | − | 0.0907749i | \(-0.0289344\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.47284 | + | 3.47284i | −0.267142 | + | 0.267142i | −0.827947 | − | 0.560806i | \(-0.810491\pi\) |
0.560806 | + | 0.827947i | \(0.310491\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 28.5398i | 1.67881i | 0.543506 | + | 0.839405i | \(0.317097\pi\) | ||||
−0.543506 | + | 0.839405i | \(0.682903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.08620 | − | 3.08620i | 0.162431 | − | 0.162431i | −0.621212 | − | 0.783643i | \(-0.713359\pi\) |
0.783643 | + | 0.621212i | \(0.213359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.57437 | −0.111929 | −0.0559645 | − | 0.998433i | \(-0.517823\pi\) | ||||
−0.0559645 | + | 0.998433i | \(0.517823\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 49.1003i | − | 1.96401i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.49628 | + | 3.49628i | 0.120561 | + | 0.120561i | 0.764813 | − | 0.644252i | \(-0.222831\pi\) |
−0.644252 | + | 0.764813i | \(0.722831\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −21.0909 | −0.680351 | −0.340176 | − | 0.940362i | \(-0.610487\pi\) | ||||
−0.340176 | + | 0.940362i | \(0.610487\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 57.2183 | + | 57.2183i | 1.63481 | + | 1.63481i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.2847 | + | 13.2847i | 0.359047 | + | 0.359047i | 0.863462 | − | 0.504414i | \(-0.168292\pi\) |
−0.504414 | + | 0.863462i | \(0.668292\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2365 | 0.274060 | 0.137030 | − | 0.990567i | \(-0.456244\pi\) | ||||
0.137030 | + | 0.990567i | \(0.456244\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.19150 | − | 8.19150i | −0.190500 | − | 0.190500i | 0.605412 | − | 0.795912i | \(-0.293008\pi\) |
−0.795912 | + | 0.605412i | \(0.793008\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17.2381i | 0.366769i | 0.983041 | + | 0.183384i | \(0.0587053\pi\) | ||||
−0.983041 | + | 0.183384i | \(0.941295\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −39.3649 | −0.803364 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −30.5182 | + | 30.5182i | −0.575816 | + | 0.575816i | −0.933748 | − | 0.357932i | \(-0.883482\pi\) |
0.357932 | + | 0.933748i | \(0.383482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 145.514i | 2.64572i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.7367 | − | 14.7367i | 0.249774 | − | 0.249774i | −0.571104 | − | 0.820878i | \(-0.693485\pi\) |
0.820878 | + | 0.571104i | \(0.193485\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −39.3037 | + | 39.3037i | −0.644323 | + | 0.644323i | −0.951615 | − | 0.307292i | \(-0.900577\pi\) |
0.307292 | + | 0.951615i | \(0.400577\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 42.2775i | − | 0.650424i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −79.6470 | + | 79.6470i | −1.18876 | + | 1.18876i | −0.211351 | + | 0.977410i | \(0.567786\pi\) |
−0.977410 | + | 0.211351i | \(0.932214\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −73.1921 | −1.03087 | −0.515437 | − | 0.856927i | \(-0.672370\pi\) | ||||
−0.515437 | + | 0.856927i | \(0.672370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.23261i | 0.0168851i | 0.999964 | + | 0.00844256i | \(0.00268738\pi\) | ||||
−0.999964 | + | 0.00844256i | \(0.997313\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −112.362 | − | 112.362i | −1.45925 | − | 1.45925i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −110.191 | −1.39482 | −0.697411 | − | 0.716672i | \(-0.745665\pi\) | ||||
−0.697411 | + | 0.716672i | \(0.745665\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.7800 | − | 13.7800i | −0.166025 | − | 0.166025i | 0.619205 | − | 0.785229i | \(-0.287455\pi\) |
−0.785229 | + | 0.619205i | \(0.787455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −173.718 | − | 173.718i | −2.04374 | − | 2.04374i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 39.2555 | 0.441073 | 0.220537 | − | 0.975379i | \(-0.429219\pi\) | ||||
0.220537 | + | 0.975379i | \(0.429219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 32.6456 | + | 32.6456i | 0.358743 | + | 0.358743i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 37.5706i | 0.395480i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −109.383 | −1.12766 | −0.563830 | − | 0.825891i | \(-0.690673\pi\) | ||||
−0.563830 | + | 0.825891i | \(0.690673\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −102.843 | + | 102.843i | −1.01824 | + | 1.01824i | −0.0184123 | + | 0.999830i | \(0.505861\pi\) |
−0.999830 | + | 0.0184123i | \(0.994139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 66.0152i | 0.640924i | 0.947261 | + | 0.320462i | \(0.103838\pi\) | ||||
−0.947261 | + | 0.320462i | \(0.896162\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −87.3982 | + | 87.3982i | −0.816805 | + | 0.816805i | −0.985644 | − | 0.168838i | \(-0.945998\pi\) |
0.168838 | + | 0.985644i | \(0.445998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.493298 | + | 0.493298i | −0.00452567 | + | 0.00452567i | −0.709366 | − | 0.704840i | \(-0.751019\pi\) |
0.704840 | + | 0.709366i | \(0.251019\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 181.667i | 1.60768i | 0.594848 | + | 0.803838i | \(0.297212\pi\) | ||||
−0.594848 | + | 0.803838i | \(0.702788\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.6699 | − | 15.6699i | 0.136260 | − | 0.136260i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 268.281 | 2.25447 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 164.754i | − | 1.36160i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 146.696 | + | 146.696i | 1.17356 | + | 1.17356i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 188.223 | 1.48207 | 0.741035 | − | 0.671466i | \(-0.234335\pi\) | ||||
0.741035 | + | 0.671466i | \(0.234335\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 79.5518 | + | 79.5518i | 0.607266 | + | 0.607266i | 0.942231 | − | 0.334965i | \(-0.108725\pi\) |
−0.334965 | + | 0.942231i | \(0.608725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −29.0110 | − | 29.0110i | −0.218128 | − | 0.218128i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −204.894 | −1.49557 | −0.747787 | − | 0.663939i | \(-0.768883\pi\) | ||||
−0.747787 | + | 0.663939i | \(0.768883\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −153.586 | − | 153.586i | −1.10494 | − | 1.10494i | −0.993806 | − | 0.111133i | \(-0.964552\pi\) |
−0.111133 | − | 0.993806i | \(-0.535448\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 83.0225i | 0.580577i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −42.5629 | −0.293537 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 24.6527 | − | 24.6527i | 0.165455 | − | 0.165455i | −0.619523 | − | 0.784978i | \(-0.712674\pi\) |
0.784978 | + | 0.619523i | \(0.212674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 56.2047i | − | 0.372216i | −0.982529 | − | 0.186108i | \(-0.940412\pi\) | ||
0.982529 | − | 0.186108i | \(-0.0595875\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 128.378 | − | 128.378i | 0.828244 | − | 0.828244i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 152.225 | − | 152.225i | 0.969589 | − | 0.969589i | −0.0299624 | − | 0.999551i | \(-0.509539\pi\) |
0.999551 | + | 0.0299624i | \(0.00953875\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.1997i | 0.150309i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −147.071 | + | 147.071i | −0.902276 | + | 0.902276i | −0.995633 | − | 0.0933563i | \(-0.970240\pi\) |
0.0933563 | + | 0.995633i | \(0.470240\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 100.239 | 0.600232 | 0.300116 | − | 0.953903i | \(-0.402975\pi\) | ||||
0.300116 | + | 0.953903i | \(0.402975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 144.879i | 0.857271i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 179.056 | + | 179.056i | 1.03501 | + | 1.03501i | 0.999365 | + | 0.0356433i | \(0.0113480\pi\) |
0.0356433 | + | 0.999365i | \(0.488652\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −461.555 | −2.63746 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.84637 | − | 8.84637i | −0.0494211 | − | 0.0494211i | 0.681964 | − | 0.731385i | \(-0.261126\pi\) |
−0.731385 | + | 0.681964i | \(0.761126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 135.353 | + | 135.353i | 0.747807 | + | 0.747807i | 0.974067 | − | 0.226260i | \(-0.0726499\pi\) |
−0.226260 | + | 0.974067i | \(0.572650\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −161.725 | −0.874191 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 341.139 | + | 341.139i | 1.82427 | + | 1.82427i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 117.914i | − | 0.617351i | −0.951167 | − | 0.308675i | \(-0.900114\pi\) | ||
0.951167 | − | 0.308675i | \(-0.0998856\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 65.1940 | 0.337793 | 0.168896 | − | 0.985634i | \(-0.445980\pi\) | ||||
0.168896 | + | 0.985634i | \(0.445980\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.9481 | − | 26.9481i | 0.136793 | − | 0.136793i | −0.635395 | − | 0.772187i | \(-0.719163\pi\) |
0.772187 | + | 0.635395i | \(0.219163\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 290.806i | − | 1.46133i | −0.682734 | − | 0.730667i | \(-0.739209\pi\) | ||
0.682734 | − | 0.730667i | \(-0.260791\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 32.8660 | − | 32.8660i | 0.161901 | − | 0.161901i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −68.3951 | + | 68.3951i | −0.333634 | + | 0.333634i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 73.7793i | − | 0.353011i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −143.972 | + | 143.972i | −0.682334 | + | 0.682334i | −0.960526 | − | 0.278192i | \(-0.910265\pi\) |
0.278192 | + | 0.960526i | \(0.410265\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 99.7214 | 0.463821 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 198.260i | 0.913640i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −99.1141 | − | 99.1141i | −0.448480 | − | 0.448480i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 200.870 | 0.900761 | 0.450381 | − | 0.892837i | \(-0.351288\pi\) | ||||
0.450381 | + | 0.892837i | \(0.351288\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 37.3792 | + | 37.3792i | 0.164666 | + | 0.164666i | 0.784630 | − | 0.619964i | \(-0.212853\pi\) |
−0.619964 | + | 0.784630i | \(0.712853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −101.806 | − | 101.806i | −0.444569 | − | 0.444569i | 0.448975 | − | 0.893544i | \(-0.351789\pi\) |
−0.893544 | + | 0.448975i | \(0.851789\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −80.6982 | −0.346344 | −0.173172 | − | 0.984892i | \(-0.555402\pi\) | ||||
−0.173172 | + | 0.984892i | \(0.555402\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −104.927 | − | 104.927i | −0.446496 | − | 0.446496i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 301.011i | 1.25946i | 0.776814 | + | 0.629730i | \(0.216834\pi\) | ||||
−0.776814 | + | 0.629730i | \(0.783166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 159.477 | 0.661732 | 0.330866 | − | 0.943678i | \(-0.392659\pi\) | ||||
0.330866 | + | 0.943678i | \(0.392659\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 239.609 | − | 239.609i | 0.977997 | − | 0.977997i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.4357i | 0.0867844i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −291.951 | + | 291.951i | −1.16315 | + | 1.16315i | −0.179368 | + | 0.983782i | \(0.557405\pi\) |
−0.983782 | + | 0.179368i | \(0.942595\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.7717 | + | 30.7717i | −0.121627 | + | 0.121627i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 136.807i | − | 0.532323i | −0.963929 | − | 0.266161i | \(-0.914245\pi\) | ||
0.963929 | − | 0.266161i | \(-0.0857554\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 124.880 | − | 124.880i | 0.482162 | − | 0.482162i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −449.794 | −1.71024 | −0.855121 | − | 0.518429i | \(-0.826517\pi\) | ||||
−0.855121 | + | 0.518429i | \(0.826517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 371.522i | − | 1.40197i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −77.2032 | − | 77.2032i | −0.287001 | − | 0.287001i | 0.548892 | − | 0.835893i | \(-0.315050\pi\) |
−0.835893 | + | 0.548892i | \(0.815050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 496.378 | 1.83165 | 0.915827 | − | 0.401574i | \(-0.131537\pi\) | ||||
0.915827 | + | 0.401574i | \(0.131537\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −586.901 | − | 586.901i | −2.13419 | − | 2.13419i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.7238 | + | 25.7238i | 0.0928658 | + | 0.0928658i | 0.752014 | − | 0.659148i | \(-0.229083\pi\) |
−0.659148 | + | 0.752014i | \(0.729083\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 380.796 | 1.35515 | 0.677573 | − | 0.735456i | \(-0.263032\pi\) | ||||
0.677573 | + | 0.735456i | \(0.263032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 36.5558 | + | 36.5558i | 0.129172 | + | 0.129172i | 0.768737 | − | 0.639565i | \(-0.220885\pi\) |
−0.639565 | + | 0.768737i | \(0.720885\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 105.626i | − | 0.368034i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −525.519 | −1.81841 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 119.828 | − | 119.828i | 0.408970 | − | 0.408970i | −0.472409 | − | 0.881379i | \(-0.656615\pi\) |
0.881379 | + | 0.472409i | \(0.156615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 179.401i | 0.608138i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.94036 | − | 8.94036i | 0.0299009 | − | 0.0299009i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −77.0023 | + | 77.0023i | −0.255821 | + | 0.255821i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 478.474i | − | 1.56877i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 368.177 | − | 368.177i | 1.19927 | − | 1.19927i | 0.224889 | − | 0.974384i | \(-0.427798\pi\) |
0.974384 | − | 0.224889i | \(-0.0722021\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −82.3959 | −0.264939 | −0.132469 | − | 0.991187i | \(-0.542291\pi\) | ||||
−0.132469 | + | 0.991187i | \(0.542291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 368.385i | 1.17695i | 0.808516 | + | 0.588474i | \(0.200271\pi\) | ||||
−0.808516 | + | 0.588474i | \(0.799729\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −185.382 | − | 185.382i | −0.584800 | − | 0.584800i | 0.351419 | − | 0.936218i | \(-0.385699\pi\) |
−0.936218 | + | 0.351419i | \(0.885699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 83.5829 | 0.262015 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 88.0794 | + | 88.0794i | 0.272692 | + | 0.272692i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 170.517 | + | 170.517i | 0.524669 | + | 0.524669i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 162.043 | 0.492532 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −209.678 | − | 209.678i | −0.633467 | − | 0.633467i | 0.315469 | − | 0.948936i | \(-0.397838\pi\) |
−0.948936 | + | 0.315469i | \(0.897838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 969.604i | − | 2.89434i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 417.353 | 1.23844 | 0.619218 | − | 0.785219i | \(-0.287450\pi\) | ||||
0.619218 | + | 0.785219i | \(0.287450\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −252.102 | + | 252.102i | −0.739301 | + | 0.739301i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 90.5729i | − | 0.264061i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −99.3706 | + | 99.3706i | −0.286371 | + | 0.286371i | −0.835643 | − | 0.549273i | \(-0.814905\pi\) |
0.549273 | + | 0.835643i | \(0.314905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.95933 | − | 9.95933i | 0.0285368 | − | 0.0285368i | −0.692694 | − | 0.721231i | \(-0.743577\pi\) |
0.721231 | + | 0.692694i | \(0.243577\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 509.355i | 1.44293i | 0.692451 | + | 0.721465i | \(0.256531\pi\) | ||||
−0.692451 | + | 0.721465i | \(0.743469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 445.511 | − | 445.511i | 1.25496 | − | 1.25496i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −401.516 | −1.11843 | −0.559214 | − | 0.829023i | \(-0.688897\pi\) | ||||
−0.559214 | + | 0.829023i | \(0.688897\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 341.951i | 0.947232i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.50278 | − | 7.50278i | −0.0205556 | − | 0.0205556i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −338.335 | −0.921894 | −0.460947 | − | 0.887428i | \(-0.652490\pi\) | ||||
−0.460947 | + | 0.887428i | \(0.652490\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 286.879 | + | 286.879i | 0.773259 | + | 0.773259i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 342.158 | + | 342.158i | 0.917314 | + | 0.917314i | 0.996833 | − | 0.0795197i | \(-0.0253387\pi\) |
−0.0795197 | + | 0.996833i | \(0.525339\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.2841 | −0.0644140 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −400.188 | − | 400.188i | −1.05591 | − | 1.05591i | −0.998342 | − | 0.0575645i | \(-0.981667\pi\) |
−0.0575645 | − | 0.998342i | \(-0.518333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 595.773i | 1.55554i | 0.628548 | + | 0.777771i | \(0.283650\pi\) | ||||
−0.628548 | + | 0.777771i | \(0.716350\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1367.87 | 3.55292 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −83.6879 | + | 83.6879i | −0.215136 | + | 0.215136i | −0.806445 | − | 0.591309i | \(-0.798611\pi\) |
0.591309 | + | 0.806445i | \(0.298611\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 73.4718i | − | 0.187908i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 670.719 | − | 670.719i | 1.69802 | − | 1.69802i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 311.065 | − | 311.065i | 0.783539 | − | 0.783539i | −0.196887 | − | 0.980426i | \(-0.563083\pi\) |
0.980426 | + | 0.196887i | \(0.0630832\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 279.299i | − | 0.696505i | −0.937401 | − | 0.348253i | \(-0.886775\pi\) | ||
0.937401 | − | 0.348253i | \(-0.113225\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 73.2453 | − | 73.2453i | 0.181750 | − | 0.181750i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 317.588 | 0.780315 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 446.244i | 1.09106i | 0.838091 | + | 0.545530i | \(0.183672\pi\) | ||||
−0.838091 | + | 0.545530i | \(0.816328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −138.529 | − | 138.529i | −0.335420 | − | 0.335420i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 167.755 | 0.404229 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 331.372 | + | 331.372i | 0.790864 | + | 0.790864i | 0.981635 | − | 0.190770i | \(-0.0610986\pi\) |
−0.190770 | + | 0.981635i | \(0.561099\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 74.8932 | + | 74.8932i | 0.177893 | + | 0.177893i | 0.790437 | − | 0.612543i | \(-0.209854\pi\) |
−0.612543 | + | 0.790437i | \(0.709854\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1401.31 | 3.29720 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 369.465 | + | 369.465i | 0.865258 | + | 0.865258i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 433.486i | − | 1.00577i | −0.864354 | − | 0.502884i | \(-0.832272\pi\) | ||
0.864354 | − | 0.502884i | \(-0.167728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −279.207 | −0.644820 | −0.322410 | − | 0.946600i | \(-0.604493\pi\) | ||||
−0.322410 | + | 0.946600i | \(0.604493\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.94500 | + | 7.94500i | −0.0181808 | + | 0.0181808i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 564.253i | − | 1.28531i | −0.766154 | − | 0.642657i | \(-0.777832\pi\) | ||
0.766154 | − | 0.642657i | \(-0.222168\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.2113 | − | 39.2113i | 0.0885131 | − | 0.0885131i | −0.661464 | − | 0.749977i | \(-0.730065\pi\) |
0.749977 | + | 0.661464i | \(0.230065\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −238.944 | + | 238.944i | −0.536952 | + | 0.536952i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 277.135i | − | 0.617228i | −0.951187 | − | 0.308614i | \(-0.900135\pi\) | ||
0.951187 | − | 0.308614i | \(-0.0998651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 134.311 | − | 134.311i | 0.297806 | − | 0.297806i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −397.420 | −0.873450 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 631.173i | − | 1.38112i | −0.723274 | − | 0.690561i | \(-0.757364\pi\) | ||
0.723274 | − | 0.690561i | \(-0.242636\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 494.475 | + | 494.475i | 1.07261 | + | 1.07261i | 0.997149 | + | 0.0754643i | \(0.0240439\pi\) |
0.0754643 | + | 0.997149i | \(0.475956\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 394.376 | 0.851784 | 0.425892 | − | 0.904774i | \(-0.359960\pi\) | ||||
0.425892 | + | 0.904774i | \(0.359960\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −214.554 | − | 214.554i | −0.459430 | − | 0.459430i | 0.439039 | − | 0.898468i | \(-0.355319\pi\) |
−0.898468 | + | 0.439039i | \(0.855319\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 748.702 | + | 748.702i | 1.59638 | + | 1.59638i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −195.828 | −0.414012 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −151.533 | − | 151.533i | −0.319017 | − | 0.319017i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 636.488i | 1.32879i | 0.747383 | + | 0.664393i | \(0.231310\pi\) | ||||
−0.747383 | + | 0.664393i | \(0.768690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −92.2716 | −0.191833 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 665.802 | − | 665.802i | 1.37279 | − | 1.37279i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 550.556i | 1.13051i | 0.824918 | + | 0.565253i | \(0.191221\pi\) | ||||
−0.824918 | + | 0.565253i | \(0.808779\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −192.006 | + | 192.006i | −0.391051 | + | 0.391051i | −0.875062 | − | 0.484011i | \(-0.839179\pi\) |
0.484011 | + | 0.875062i | \(0.339179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −99.7832 | + | 99.7832i | −0.202400 | + | 0.202400i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 688.024i | 1.38435i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −156.794 | + | 156.794i | −0.314215 | + | 0.314215i | −0.846540 | − | 0.532325i | \(-0.821319\pi\) |
0.532325 | + | 0.846540i | \(0.321319\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −88.5520 | −0.176048 | −0.0880239 | − | 0.996118i | \(-0.528055\pi\) | ||||
−0.0880239 | + | 0.996118i | \(0.528055\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1251.98i | − | 2.47917i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −430.228 | − | 430.228i | −0.845242 | − | 0.845242i | 0.144293 | − | 0.989535i | \(-0.453909\pi\) |
−0.989535 | + | 0.144293i | \(0.953909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.5869 | 0.0226749 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −401.827 | − | 401.827i | −0.780246 | − | 0.780246i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 206.049 | + | 206.049i | 0.398548 | + | 0.398548i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −889.748 | −1.70777 | −0.853885 | − | 0.520462i | \(-0.825760\pi\) | ||||
−0.853885 | + | 0.520462i | \(0.825760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −134.417 | − | 134.417i | −0.257012 | − | 0.257012i | 0.566826 | − | 0.823838i | \(-0.308171\pi\) |
−0.823838 | + | 0.566826i | \(0.808171\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 601.929i | − | 1.14218i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −522.373 | −0.987472 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −39.0225 | + | 39.0225i | −0.0732129 | + | 0.0732129i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1063.96i | − | 1.98872i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −470.532 | + | 470.532i | −0.872973 | + | 0.872973i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −309.758 | + | 309.758i | −0.572565 | + | 0.572565i | −0.932844 | − | 0.360279i | \(-0.882681\pi\) |
0.360279 | + | 0.932844i | \(0.382681\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6.00529i | − | 0.0110189i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 609.425 | − | 609.425i | 1.11412 | − | 1.11412i | 0.121535 | − | 0.992587i | \(-0.461218\pi\) |
0.992587 | − | 0.121535i | \(-0.0387815\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.5804 | 0.0391659 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1035.82i | 1.87310i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −605.408 | − | 605.408i | −1.08691 | − | 1.08691i | −0.995845 | − | 0.0910624i | \(-0.970974\pi\) |
−0.0910624 | − | 0.995845i | \(-0.529026\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 56.8956 | 0.101781 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −68.2515 | − | 68.2515i | −0.121228 | − | 0.121228i | 0.643890 | − | 0.765118i | \(-0.277319\pi\) |
−0.765118 | + | 0.643890i | \(0.777319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1105.79 | − | 1105.79i | −1.95715 | − | 1.95715i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −758.298 | −1.33269 | −0.666343 | − | 0.745646i | \(-0.732141\pi\) | ||||
−0.666343 | + | 0.745646i | \(0.732141\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 663.635 | + | 663.635i | 1.16223 | + | 1.16223i | 0.983986 | + | 0.178248i | \(0.0570429\pi\) |
0.178248 | + | 0.983986i | \(0.442957\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 126.402i | 0.219830i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −68.8744 | −0.119366 | −0.0596832 | − | 0.998217i | \(-0.519009\pi\) | ||||
−0.0596832 | + | 0.998217i | \(0.519009\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −129.536 | + | 129.536i | −0.222953 | + | 0.222953i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 729.575i | 1.25142i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 720.353 | − | 720.353i | 1.22718 | − | 1.22718i | 0.262151 | − | 0.965027i | \(-0.415568\pi\) |
0.965027 | − | 0.262151i | \(-0.0844317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −65.0906 | + | 65.0906i | −0.110510 | + | 0.110510i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 585.630i | − | 0.987572i | −0.869583 | − | 0.493786i | \(-0.835613\pi\) | ||
0.869583 | − | 0.493786i | \(-0.164387\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1633.00 | + | 1633.00i | −2.74453 | + | 2.74453i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1006.31 | −1.67999 | −0.839995 | − | 0.542594i | \(-0.817442\pi\) | ||||
−0.839995 | + | 0.542594i | \(0.817442\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 534.875i | 0.889976i | 0.895537 | + | 0.444988i | \(0.146792\pi\) | ||||
−0.895537 | + | 0.444988i | \(0.853208\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1002.84 | + | 1002.84i | 1.65758 | + | 1.65758i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −219.896 | −0.362267 | −0.181133 | − | 0.983459i | \(-0.557977\pi\) | ||||
−0.181133 | + | 0.983459i | \(0.557977\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −59.8653 | − | 59.8653i | −0.0979792 | − | 0.0979792i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −389.389 | − | 389.389i | −0.635219 | − | 0.635219i | 0.314153 | − | 0.949372i | \(-0.398279\pi\) |
−0.949372 | + | 0.314153i | \(0.898279\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −261.466 | −0.423771 | −0.211885 | − | 0.977295i | \(-0.567960\pi\) | ||||
−0.211885 | + | 0.977295i | \(0.567960\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 275.915 | + | 275.915i | 0.445743 | + | 0.445743i | 0.893937 | − | 0.448193i | \(-0.147932\pi\) |
−0.448193 | + | 0.893937i | \(0.647932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 369.012i | − | 0.592315i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −558.331 | −0.893329 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −379.144 | + | 379.144i | −0.602772 | + | 0.602772i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 237.889i | − | 0.377003i | −0.982073 | − | 0.188501i | \(-0.939637\pi\) | ||
0.982073 | − | 0.188501i | \(-0.0603630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1145.69 | + | 1145.69i | −1.80424 | + | 1.80424i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 136.708 | − | 136.708i | 0.214612 | − | 0.214612i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 858.416i | − | 1.33918i | −0.742730 | − | 0.669591i | \(-0.766469\pi\) | ||
0.742730 | − | 0.669591i | \(-0.233531\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 643.410 | − | 643.410i | 1.00064 | − | 1.00064i | 0.000638349 | − | 1.00000i | \(-0.499797\pi\) |
1.00000 | 0.000638349i | \(-0.000203193\pi\) | ||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 597.840 | 0.924019 | 0.462009 | − | 0.886875i | \(-0.347129\pi\) | ||||
0.462009 | + | 0.886875i | \(0.347129\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 352.298i | − | 0.542832i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −91.3671 | − | 91.3671i | −0.139919 | − | 0.139919i | 0.633678 | − | 0.773597i | \(-0.281544\pi\) |
−0.773597 | + | 0.633678i | \(0.781544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −968.445 | −1.47854 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −445.487 | − | 445.487i | −0.676004 | − | 0.676004i | 0.283089 | − | 0.959094i | \(-0.408641\pi\) |
−0.959094 | + | 0.283089i | \(0.908641\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −387.304 | − | 387.304i | −0.585937 | − | 0.585937i | 0.350592 | − | 0.936528i | \(-0.385981\pi\) |
−0.936528 | + | 0.350592i | \(0.885981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 353.174 | 0.531088 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00071 | − | 9.00071i | −0.0134943 | − | 0.0134943i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 939.603i | 1.40030i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −845.703 | −1.25662 | −0.628309 | − | 0.777964i | \(-0.716252\pi\) | ||||
−0.628309 | + | 0.777964i | \(0.716252\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 311.755 | − | 311.755i | 0.460495 | − | 0.460495i | −0.438323 | − | 0.898818i | \(-0.644427\pi\) |
0.898818 | + | 0.438323i | \(0.144427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1028.23i | 1.51433i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 214.466 | − | 214.466i | 0.314005 | − | 0.314005i | −0.532454 | − | 0.846459i | \(-0.678730\pi\) |
0.846459 | + | 0.532454i | \(0.178730\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1247.16 | − | 1247.16i | 1.82068 | − | 1.82068i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 211.970i | − | 0.307649i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −812.184 | + | 812.184i | −1.17537 | + | 1.17537i | −0.194465 | + | 0.980909i | \(0.562297\pi\) |
−0.980909 | + | 0.194465i | \(0.937703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1869.72 | 2.69025 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 320.686i | 0.460095i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 105.563 | + | 105.563i | 0.150589 | + | 0.150589i | 0.778381 | − | 0.627792i | \(-0.216041\pi\) |
−0.627792 | + | 0.778381i | \(0.716041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.9987 | 0.116641 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 966.746 | + | 966.746i | 1.36739 | + | 1.36739i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 106.375 | + | 106.375i | 0.150035 | + | 0.150035i | 0.778134 | − | 0.628099i | \(-0.216167\pi\) |
−0.628099 | + | 0.778134i | \(0.716167\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 54.2957 | 0.0761510 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −505.348 | − | 505.348i | −0.706781 | − | 0.706781i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1119.16i | 1.55656i | 0.627919 | + | 0.778278i | \(0.283907\pi\) | ||||
−0.627919 | + | 0.778278i | \(0.716093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 620.560 | 0.860693 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 171.668 | − | 171.668i | 0.236784 | − | 0.236784i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 334.759i | − | 0.460466i | −0.973136 | − | 0.230233i | \(-0.926051\pi\) | ||
0.973136 | − | 0.230233i | \(-0.0739489\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 233.784 | − | 233.784i | 0.319814 | − | 0.319814i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −97.8371 | + | 97.8371i | −0.133475 | + | 0.133475i | −0.770688 | − | 0.637213i | \(-0.780087\pi\) |
0.637213 | + | 0.770688i | \(0.280087\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1904.06i | 2.58353i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −249.678 | + | 249.678i | −0.337860 | + | 0.337860i | −0.855561 | − | 0.517702i | \(-0.826788\pi\) |
0.517702 | + | 0.855561i | \(0.326788\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1176.88 | 1.58396 | 0.791981 | − | 0.610545i | \(-0.209050\pi\) | ||||
0.791981 | + | 0.610545i | \(0.209050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 300.117i | 0.402841i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 821.565 | + | 821.565i | 1.09688 | + | 1.09688i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 909.942 | 1.21164 | 0.605821 | − | 0.795601i | \(-0.292845\pi\) | ||||
0.605821 | + | 0.795601i | \(0.292845\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 342.111 | + | 342.111i | 0.453128 | + | 0.453128i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −418.277 | − | 418.277i | −0.552545 | − | 0.552545i | 0.374629 | − | 0.927175i | \(-0.377770\pi\) |
−0.927175 | + | 0.374629i | \(0.877770\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −670.931 | −0.881644 | −0.440822 | − | 0.897594i | \(-0.645313\pi\) | ||||
−0.440822 | + | 0.897594i | \(0.645313\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.63713 | + | 4.63713i | 0.00607750 | + | 0.00607750i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 102.356i | 0.133450i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1054.59 | 1.37138 | 0.685689 | − | 0.727895i | \(-0.259501\pi\) | ||||
0.685689 | + | 0.727895i | \(0.259501\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −877.952 | + | 877.952i | −1.13577 | + | 1.13577i | −0.146573 | + | 0.989200i | \(0.546824\pi\) |
−0.989200 | + | 0.146573i | \(0.953176\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1035.57i | 1.33622i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.6780 | − | 34.6780i | 0.0445160 | − | 0.0445160i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −874.873 | + | 874.873i | −1.12020 | + | 1.12020i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1853.16i | 2.36071i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.3967 | + | 18.3967i | −0.0233758 | + | 0.0233758i | −0.718698 | − | 0.695322i | \(-0.755262\pi\) |
0.695322 | + | 0.718698i | \(0.255262\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1707.72 | 2.15894 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 272.991i | − | 0.344251i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.8374 | − | 27.8374i | −0.0349278 | − | 0.0349278i | 0.689427 | − | 0.724355i | \(-0.257862\pi\) |
−0.724355 | + | 0.689427i | \(0.757862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −491.973 | −0.615736 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.7336 | + | 14.7336i | 0.0183482 | + | 0.0183482i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −147.301 | − | 147.301i | −0.182982 | − | 0.182982i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −416.938 | −0.515374 | −0.257687 | − | 0.966228i | \(-0.582960\pi\) | ||||
−0.257687 | + | 0.966228i | \(0.582960\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −699.525 | − | 699.525i | −0.862546 | − | 0.862546i | 0.129087 | − | 0.991633i | \(-0.458795\pi\) |
−0.991633 | + | 0.129087i | \(0.958795\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1790.41i | − | 2.19682i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −50.5612 | −0.0618864 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −200.751 | + | 200.751i | −0.244520 | + | 0.244520i | −0.818717 | − | 0.574197i | \(-0.805314\pi\) |
0.574197 | + | 0.818717i | \(0.305314\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 159.123i | − | 0.193345i | −0.995316 | − | 0.0966724i | \(-0.969180\pi\) | ||
0.995316 | − | 0.0966724i | \(-0.0308199\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −790.803 | + | 790.803i | −0.956231 | + | 0.956231i | −0.999081 | − | 0.0428505i | \(-0.986356\pi\) |
0.0428505 | + | 0.999081i | \(0.486356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 827.815 | − | 827.815i | 0.998570 | − | 0.998570i | −0.00142868 | − | 0.999999i | \(-0.500455\pi\) |
0.999999 | + | 0.00142868i | \(0.000454762\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1123.46i | − | 1.34870i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −610.141 | + | 610.141i | −0.730708 | + | 0.730708i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −65.9441 | −0.0785985 | −0.0392992 | − | 0.999227i | \(-0.512513\pi\) | ||||
−0.0392992 | + | 0.999227i | \(0.512513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 816.552i | − | 0.970930i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −881.860 | − | 881.860i | −1.04362 | − | 1.04362i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1548.73 | −1.82849 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.1998 | − | 34.1998i | −0.0401878 | − | 0.0401878i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.8417 | + | 22.8417i | 0.0267780 | + | 0.0267780i | 0.720369 | − | 0.693591i | \(-0.243972\pi\) |
−0.693591 | + | 0.720369i | \(0.743972\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 630.654 | 0.735886 | 0.367943 | − | 0.929848i | \(-0.380062\pi\) | ||||
0.367943 | + | 0.929848i | \(0.380062\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −161.861 | − | 161.861i | −0.188430 | − | 0.188430i | 0.606587 | − | 0.795017i | \(-0.292538\pi\) |
−0.795017 | + | 0.606587i | \(0.792538\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1070.23i | 1.24013i | 0.784549 | + | 0.620066i | \(0.212894\pi\) | ||||
−0.784549 | + | 0.620066i | \(0.787106\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2179.79 | −2.51999 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1317.12 | + | 1317.12i | −1.51568 | + | 1.51568i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 553.203i | − | 0.635135i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1378.98 | − | 1378.98i | 1.57597 | − | 1.57597i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −773.573 | + | 773.573i | −0.882067 | + | 0.882067i | −0.993745 | − | 0.111677i | \(-0.964378\pi\) |
0.111677 | + | 0.993745i | \(0.464378\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 495.482i | 0.562408i | 0.959648 | + | 0.281204i | \(0.0907338\pi\) | ||||
−0.959648 | + | 0.281204i | \(0.909266\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 119.779 | − | 119.779i | 0.135650 | − | 0.135650i | −0.636021 | − | 0.771671i | \(-0.719421\pi\) |
0.771671 | + | 0.636021i | \(0.219421\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −895.932 | −1.01007 | −0.505035 | − | 0.863099i | \(-0.668520\pi\) | ||||
−0.505035 | + | 0.863099i | \(0.668520\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1769.34i | − | 1.99026i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 53.2003 | + | 53.2003i | 0.0595748 | + | 0.0595748i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 107.694 | 0.120328 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −73.7397 | − | 73.7397i | −0.0820242 | − | 0.0820242i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −870.984 | − | 870.984i | −0.966686 | − | 0.966686i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1647.76 | −1.82073 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 852.347 | + | 852.347i | 0.939743 | + | 0.939743i | 0.998285 | − | 0.0585418i | \(-0.0186451\pi\) |
−0.0585418 | + | 0.998285i | \(0.518645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 748.289i | − | 0.821393i | −0.911772 | − | 0.410697i | \(-0.865286\pi\) | ||
0.911772 | − | 0.410697i | \(-0.134714\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −329.429 | −0.360820 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 747.807 | − | 747.807i | 0.815493 | − | 0.815493i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 85.7074i | 0.0932616i | 0.998912 | + | 0.0466308i | \(0.0148484\pi\) | ||||
−0.998912 | + | 0.0466308i | \(0.985152\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 254.184 | − | 254.184i | 0.275389 | − | 0.275389i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 652.285 | − | 652.285i | 0.705173 | − | 0.705173i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 119.970i | − | 0.129139i | −0.997913 | − | 0.0645696i | \(-0.979433\pi\) | ||
0.997913 | − | 0.0645696i | \(-0.0205675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −121.488 | + | 121.488i | −0.130492 | + | 0.130492i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4152.95 | −4.44166 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 631.867i | 0.674351i | 0.941442 | + | 0.337176i | \(0.109472\pi\) | ||||
−0.941442 | + | 0.337176i | \(0.890528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 370.590 | + | 370.590i | 0.393825 | + | 0.393825i | 0.876048 | − | 0.482223i | \(-0.160171\pi\) |
−0.482223 | + | 0.876048i | \(0.660171\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.9268 | −0.0306753 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.2368 | − | 16.2368i | −0.0171455 | − | 0.0171455i | 0.698482 | − | 0.715628i | \(-0.253859\pi\) |
−0.715628 | + | 0.698482i | \(0.753859\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.28067 | − | 4.28067i | −0.00451072 | − | 0.00451072i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1216.35 | 1.27634 | 0.638168 | − | 0.769897i | \(-0.279693\pi\) | ||||
0.638168 | + | 0.769897i | \(0.279693\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 717.728 | + | 717.728i | 0.751548 | + | 0.751548i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1926.05i | 2.00840i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −516.174 | −0.537122 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −396.828 | + | 396.828i | −0.411221 | + | 0.411221i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 781.540i | 0.808211i | 0.914712 | + | 0.404105i | \(0.132417\pi\) | ||||
−0.914712 | + | 0.404105i | \(0.867583\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.3700 | − | 15.3700i | 0.0158290 | − | 0.0158290i | −0.699148 | − | 0.714977i | \(-0.746437\pi\) |
0.714977 | + | 0.699148i | \(0.246437\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1443.75 | + | 1443.75i | −1.48381 | + | 1.48381i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 806.751i | − | 0.825743i | −0.910789 | − | 0.412871i | \(-0.864526\pi\) | ||
0.910789 | − | 0.412871i | \(-0.135474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 469.226 | − | 469.226i | 0.479291 | − | 0.479291i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1060.81 | 1.07916 | 0.539579 | − | 0.841935i | \(-0.318583\pi\) | ||||
0.539579 | + | 0.841935i | \(0.318583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 328.060i | 0.333056i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.0879 | + | 21.0879i | 0.0213225 | + | 0.0213225i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1036.12 | 1.04553 | 0.522766 | − | 0.852476i | \(-0.324900\pi\) | ||||
0.522766 | + | 0.852476i | \(0.324900\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1770.10 | + | 1770.10i | 1.77899 | + | 1.77899i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.6898 | − | 44.6898i | −0.0448242 | − | 0.0448242i | 0.684339 | − | 0.729164i | \(-0.260091\pi\) |
−0.729164 | + | 0.684339i | \(0.760091\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.3.j.a.737.1 | 32 | ||
3.2 | odd | 2 | inner | 1152.3.j.a.737.16 | 32 | ||
4.3 | odd | 2 | 1152.3.j.b.737.1 | 32 | |||
8.3 | odd | 2 | 576.3.j.a.305.16 | 32 | |||
8.5 | even | 2 | 144.3.j.a.53.14 | yes | 32 | ||
12.11 | even | 2 | 1152.3.j.b.737.16 | 32 | |||
16.3 | odd | 4 | 1152.3.j.b.161.16 | 32 | |||
16.5 | even | 4 | 144.3.j.a.125.3 | yes | 32 | ||
16.11 | odd | 4 | 576.3.j.a.17.1 | 32 | |||
16.13 | even | 4 | inner | 1152.3.j.a.161.16 | 32 | ||
24.5 | odd | 2 | 144.3.j.a.53.3 | ✓ | 32 | ||
24.11 | even | 2 | 576.3.j.a.305.1 | 32 | |||
48.5 | odd | 4 | 144.3.j.a.125.14 | yes | 32 | ||
48.11 | even | 4 | 576.3.j.a.17.16 | 32 | |||
48.29 | odd | 4 | inner | 1152.3.j.a.161.1 | 32 | ||
48.35 | even | 4 | 1152.3.j.b.161.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.j.a.53.3 | ✓ | 32 | 24.5 | odd | 2 | ||
144.3.j.a.53.14 | yes | 32 | 8.5 | even | 2 | ||
144.3.j.a.125.3 | yes | 32 | 16.5 | even | 4 | ||
144.3.j.a.125.14 | yes | 32 | 48.5 | odd | 4 | ||
576.3.j.a.17.1 | 32 | 16.11 | odd | 4 | |||
576.3.j.a.17.16 | 32 | 48.11 | even | 4 | |||
576.3.j.a.305.1 | 32 | 24.11 | even | 2 | |||
576.3.j.a.305.16 | 32 | 8.3 | odd | 2 | |||
1152.3.j.a.161.1 | 32 | 48.29 | odd | 4 | inner | ||
1152.3.j.a.161.16 | 32 | 16.13 | even | 4 | inner | ||
1152.3.j.a.737.1 | 32 | 1.1 | even | 1 | trivial | ||
1152.3.j.a.737.16 | 32 | 3.2 | odd | 2 | inner | ||
1152.3.j.b.161.1 | 32 | 48.35 | even | 4 | |||
1152.3.j.b.161.16 | 32 | 16.3 | odd | 4 | |||
1152.3.j.b.737.1 | 32 | 4.3 | odd | 2 | |||
1152.3.j.b.737.16 | 32 | 12.11 | even | 2 |