Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,2,Mod(199,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.19588605559\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.199 |
Dual form | 275.2.b.d.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214i | 0.292893i | 0.989219 | + | 0.146447i | \(0.0467837\pi\) | ||||
−0.989219 | + | 0.146447i | \(0.953216\pi\) | |||||||
\(3\) | 2.82843i | 1.63299i | 0.577350 | + | 0.816497i | \(0.304087\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 1.82843 | 0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.17157 | −0.478293 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 1.58579i | 0.560660i | ||||||||
\(9\) | −5.00000 | −1.66667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 5.17157i | 1.49290i | ||||||||
\(13\) | − 6.82843i | − 1.89386i | −0.321433 | − | 0.946932i | \(-0.604164\pi\) | ||||
0.321433 | − | 0.946932i | \(-0.395836\pi\) | |||||||
\(14\) | −0.828427 | −0.221406 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | − 1.17157i | − 0.284148i | −0.989856 | − | 0.142074i | \(-0.954623\pi\) | ||||
0.989856 | − | 0.142074i | \(-0.0453771\pi\) | |||||||
\(18\) | − 2.07107i | − 0.488155i | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.65685 | −1.23443 | ||||||||
\(22\) | 0.414214i | 0.0883106i | ||||||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | −4.48528 | −0.915554 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.82843 | 0.554700 | ||||||||
\(27\) | − 5.65685i | − 1.08866i | ||||||||
\(28\) | 3.65685i | 0.691080i | ||||||||
\(29\) | −7.65685 | −1.42184 | −0.710921 | − | 0.703272i | \(-0.751722\pi\) | ||||
−0.710921 | + | 0.703272i | \(0.751722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 4.41421i | 0.780330i | ||||||||
\(33\) | 2.82843i | 0.492366i | ||||||||
\(34\) | 0.485281 | 0.0832251 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.14214 | −1.52369 | ||||||||
\(37\) | − 3.65685i | − 0.601183i | −0.953753 | − | 0.300592i | \(-0.902816\pi\) | ||||
0.953753 | − | 0.300592i | \(-0.0971841\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19.3137 | 3.09267 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | − 2.34315i | − 0.361555i | ||||||||
\(43\) | − 6.00000i | − 0.914991i | −0.889212 | − | 0.457496i | \(-0.848747\pi\) | ||||
0.889212 | − | 0.457496i | \(-0.151253\pi\) | |||||||
\(44\) | 1.82843 | 0.275646 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.17157 | −0.172739 | ||||||||
\(47\) | 2.82843i | 0.412568i | 0.978492 | + | 0.206284i | \(0.0661372\pi\) | ||||
−0.978492 | + | 0.206284i | \(0.933863\pi\) | |||||||
\(48\) | 8.48528i | 1.22474i | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.31371 | 0.464012 | ||||||||
\(52\) | − 12.4853i | − 1.73140i | ||||||||
\(53\) | 0.343146i | 0.0471347i | 0.999722 | + | 0.0235673i | \(0.00750241\pi\) | ||||
−0.999722 | + | 0.0235673i | \(0.992498\pi\) | |||||||
\(54\) | 2.34315 | 0.318862 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.17157 | −0.423819 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 3.17157i | − 0.416448i | ||||||||
\(59\) | 9.65685 | 1.25722 | 0.628608 | − | 0.777723i | \(-0.283625\pi\) | ||||
0.628608 | + | 0.777723i | \(0.283625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3137 | 1.70465 | 0.852323 | − | 0.523016i | \(-0.175193\pi\) | ||||
0.852323 | + | 0.523016i | \(0.175193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 10.0000i | − 1.25988i | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.17157 | −0.144211 | ||||||||
\(67\) | 4.48528i | 0.547964i | 0.961735 | + | 0.273982i | \(0.0883409\pi\) | ||||
−0.961735 | + | 0.273982i | \(0.911659\pi\) | |||||||
\(68\) | − 2.14214i | − 0.259772i | ||||||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | −1.34269 | −0.671345 | − | 0.741145i | \(-0.734283\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(72\) | − 7.92893i | − 0.934434i | ||||||||
\(73\) | − 6.82843i | − 0.799207i | −0.916688 | − | 0.399603i | \(-0.869148\pi\) | ||||
0.916688 | − | 0.399603i | \(-0.130852\pi\) | |||||||
\(74\) | 1.51472 | 0.176082 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 8.00000i | 0.905822i | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.48528i | 0.274453i | ||||||||
\(83\) | − 6.00000i | − 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | −10.3431 | −1.12853 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.48528 | 0.267995 | ||||||||
\(87\) | − 21.6569i | − 2.32186i | ||||||||
\(88\) | 1.58579i | 0.169045i | ||||||||
\(89\) | −9.31371 | −0.987251 | −0.493626 | − | 0.869675i | \(-0.664329\pi\) | ||||
−0.493626 | + | 0.869675i | \(0.664329\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.6569 | 1.43163 | ||||||||
\(92\) | 5.17157i | 0.539174i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.17157 | −0.120839 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −12.4853 | −1.27427 | ||||||||
\(97\) | 7.65685i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(98\) | 1.24264i | 0.125526i | ||||||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3137 | −1.32476 | −0.662382 | − | 0.749166i | \(-0.730454\pi\) | ||||
−0.662382 | + | 0.749166i | \(0.730454\pi\) | |||||||
\(102\) | 1.37258i | 0.135906i | ||||||||
\(103\) | 1.17157i | 0.115439i | 0.998333 | + | 0.0577193i | \(0.0183828\pi\) | ||||
−0.998333 | + | 0.0577193i | \(0.981617\pi\) | |||||||
\(104\) | 10.8284 | 1.06181 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.142136 | −0.0138054 | ||||||||
\(107\) | 3.65685i | 0.353521i | 0.984254 | + | 0.176761i | \(0.0565619\pi\) | ||||
−0.984254 | + | 0.176761i | \(0.943438\pi\) | |||||||
\(108\) | − 10.3431i | − 0.995270i | ||||||||
\(109\) | −3.65685 | −0.350263 | −0.175132 | − | 0.984545i | \(-0.556035\pi\) | ||||
−0.175132 | + | 0.984545i | \(0.556035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3431 | 0.981728 | ||||||||
\(112\) | 6.00000i | 0.566947i | ||||||||
\(113\) | 8.34315i | 0.784857i | 0.919782 | + | 0.392429i | \(0.128365\pi\) | ||||
−0.919782 | + | 0.392429i | \(0.871635\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −14.0000 | −1.29987 | ||||||||
\(117\) | 34.1421i | 3.15644i | ||||||||
\(118\) | 4.00000i | 0.368230i | ||||||||
\(119\) | 2.34315 | 0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.51472i | 0.499279i | ||||||||
\(123\) | 16.9706i | 1.53018i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.14214 | 0.369011 | ||||||||
\(127\) | − 15.6569i | − 1.38932i | −0.719338 | − | 0.694661i | \(-0.755555\pi\) | ||||
0.719338 | − | 0.694661i | \(-0.244445\pi\) | |||||||
\(128\) | 10.5563i | 0.933058i | ||||||||
\(129\) | 16.9706 | 1.49417 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3137 | 0.988483 | 0.494242 | − | 0.869325i | \(-0.335446\pi\) | ||||
0.494242 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(132\) | 5.17157i | 0.450128i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.85786 | −0.160495 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.85786 | 0.159311 | ||||||||
\(137\) | − 22.9706i | − 1.96251i | −0.192720 | − | 0.981254i | \(-0.561731\pi\) | ||||
0.192720 | − | 0.981254i | \(-0.438269\pi\) | |||||||
\(138\) | − 3.31371i | − 0.282082i | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | − 4.68629i | − 0.393265i | ||||||||
\(143\) | − 6.82843i | − 0.571022i | ||||||||
\(144\) | −15.0000 | −1.25000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.82843 | 0.234082 | ||||||||
\(147\) | 8.48528i | 0.699854i | ||||||||
\(148\) | − 6.68629i | − 0.549610i | ||||||||
\(149\) | −11.6569 | −0.954967 | −0.477483 | − | 0.878641i | \(-0.658451\pi\) | ||||
−0.477483 | + | 0.878641i | \(0.658451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.85786i | 0.473580i | ||||||||
\(154\) | −0.828427 | −0.0667566 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 35.3137 | 2.82736 | ||||||||
\(157\) | 14.0000i | 1.11732i | 0.829396 | + | 0.558661i | \(0.188685\pi\) | ||||
−0.829396 | + | 0.558661i | \(0.811315\pi\) | |||||||
\(158\) | − 1.65685i | − 0.131812i | ||||||||
\(159\) | −0.970563 | −0.0769706 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.65685 | −0.445823 | ||||||||
\(162\) | 0.414214i | 0.0325437i | ||||||||
\(163\) | − 0.485281i | − 0.0380102i | −0.999819 | − | 0.0190051i | \(-0.993950\pi\) | ||||
0.999819 | − | 0.0190051i | \(-0.00604987\pi\) | |||||||
\(164\) | 10.9706 | 0.856657 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.48528 | 0.192895 | ||||||||
\(167\) | − 10.9706i | − 0.848928i | −0.905445 | − | 0.424464i | \(-0.860463\pi\) | ||||
0.905445 | − | 0.424464i | \(-0.139537\pi\) | |||||||
\(168\) | − 8.97056i | − 0.692094i | ||||||||
\(169\) | −33.6274 | −2.58672 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 10.9706i | − 0.836498i | ||||||||
\(173\) | 6.14214i | 0.466978i | 0.972359 | + | 0.233489i | \(0.0750143\pi\) | ||||
−0.972359 | + | 0.233489i | \(0.924986\pi\) | |||||||
\(174\) | 8.97056 | 0.680057 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 27.3137i | 2.05302i | ||||||||
\(178\) | − 3.85786i | − 0.289159i | ||||||||
\(179\) | 1.65685 | 0.123839 | 0.0619196 | − | 0.998081i | \(-0.480278\pi\) | ||||
0.0619196 | + | 0.998081i | \(0.480278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.31371 | −0.0976472 | −0.0488236 | − | 0.998807i | \(-0.515547\pi\) | ||||
−0.0488236 | + | 0.998807i | \(0.515547\pi\) | |||||||
\(182\) | 5.65685i | 0.419314i | ||||||||
\(183\) | 37.6569i | 2.78367i | ||||||||
\(184\) | −4.48528 | −0.330659 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.17157i | − 0.0856739i | ||||||||
\(188\) | 5.17157i | 0.377176i | ||||||||
\(189\) | 11.3137 | 0.822951 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.3137 | −1.39749 | −0.698745 | − | 0.715370i | \(-0.746258\pi\) | ||||
−0.698745 | + | 0.715370i | \(0.746258\pi\) | |||||||
\(192\) | 11.7990i | 0.851519i | ||||||||
\(193\) | − 6.82843i | − 0.491521i | −0.969331 | − | 0.245760i | \(-0.920962\pi\) | ||||
0.969331 | − | 0.245760i | \(-0.0790377\pi\) | |||||||
\(194\) | −3.17157 | −0.227706 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.48528 | 0.391806 | ||||||||
\(197\) | 5.17157i | 0.368459i | 0.982883 | + | 0.184230i | \(0.0589790\pi\) | ||||
−0.982883 | + | 0.184230i | \(0.941021\pi\) | |||||||
\(198\) | − 2.07107i | − 0.147184i | ||||||||
\(199\) | −21.6569 | −1.53521 | −0.767607 | − | 0.640921i | \(-0.778553\pi\) | ||||
−0.767607 | + | 0.640921i | \(0.778553\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.6863 | −0.894822 | ||||||||
\(202\) | − 5.51472i | − 0.388014i | ||||||||
\(203\) | − 15.3137i | − 1.07481i | ||||||||
\(204\) | 6.05887 | 0.424206 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.485281 | −0.0338112 | ||||||||
\(207\) | − 14.1421i | − 0.982946i | ||||||||
\(208\) | − 20.4853i | − 1.42040i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0.627417i | 0.0430912i | ||||||||
\(213\) | − 32.0000i | − 2.19260i | ||||||||
\(214\) | −1.51472 | −0.103544 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.97056 | 0.610369 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 1.51472i | − 0.102590i | ||||||||
\(219\) | 19.3137 | 1.30510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 4.28427i | 0.287541i | ||||||||
\(223\) | − 5.17157i | − 0.346314i | −0.984894 | − | 0.173157i | \(-0.944603\pi\) | ||||
0.984894 | − | 0.173157i | \(-0.0553968\pi\) | |||||||
\(224\) | −8.82843 | −0.589874 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.45584 | −0.229879 | ||||||||
\(227\) | − 2.68629i | − 0.178295i | −0.996018 | − | 0.0891477i | \(-0.971586\pi\) | ||||
0.996018 | − | 0.0891477i | \(-0.0284143\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.3137 | 1.40845 | 0.704225 | − | 0.709977i | \(-0.251295\pi\) | ||||
0.704225 | + | 0.709977i | \(0.251295\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | − 12.1421i | − 0.797170i | ||||||||
\(233\) | 22.1421i | 1.45058i | 0.688444 | + | 0.725290i | \(0.258294\pi\) | ||||
−0.688444 | + | 0.725290i | \(0.741706\pi\) | |||||||
\(234\) | −14.1421 | −0.924500 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 17.6569 | 1.14936 | ||||||||
\(237\) | − 11.3137i | − 0.734904i | ||||||||
\(238\) | 0.970563i | 0.0629122i | ||||||||
\(239\) | 0.686292 | 0.0443925 | 0.0221963 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221963 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0.414214i | 0.0266267i | ||||||||
\(243\) | − 14.1421i | − 0.907218i | ||||||||
\(244\) | 24.3431 | 1.55841 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.02944 | −0.448181 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.9706 | 1.07547 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | − 18.2843i | − 1.15180i | ||||||||
\(253\) | 2.82843i | 0.177822i | ||||||||
\(254\) | 6.48528 | 0.406923 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | − 13.3137i | − 0.830486i | −0.909710 | − | 0.415243i | \(-0.863696\pi\) | ||||
0.909710 | − | 0.415243i | \(-0.136304\pi\) | |||||||
\(258\) | 7.02944i | 0.437634i | ||||||||
\(259\) | 7.31371 | 0.454452 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 38.2843 | 2.36974 | ||||||||
\(262\) | 4.68629i | 0.289520i | ||||||||
\(263\) | 22.9706i | 1.41643i | 0.705999 | + | 0.708213i | \(0.250498\pi\) | ||||
−0.705999 | + | 0.708213i | \(0.749502\pi\) | |||||||
\(264\) | −4.48528 | −0.276050 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 26.3431i | − 1.61217i | ||||||||
\(268\) | 8.20101i | 0.500956i | ||||||||
\(269\) | 5.31371 | 0.323983 | 0.161991 | − | 0.986792i | \(-0.448208\pi\) | ||||
0.161991 | + | 0.986792i | \(0.448208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3137 | −0.930242 | −0.465121 | − | 0.885247i | \(-0.653989\pi\) | ||||
−0.465121 | + | 0.885247i | \(0.653989\pi\) | |||||||
\(272\) | − 3.51472i | − 0.213111i | ||||||||
\(273\) | 38.6274i | 2.33784i | ||||||||
\(274\) | 9.51472 | 0.574805 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.6274 | −0.880467 | ||||||||
\(277\) | − 1.17157i | − 0.0703930i | −0.999380 | − | 0.0351965i | \(-0.988794\pi\) | ||||
0.999380 | − | 0.0351965i | \(-0.0112057\pi\) | |||||||
\(278\) | 1.65685i | 0.0993715i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.31371 | −0.316989 | −0.158495 | − | 0.987360i | \(-0.550664\pi\) | ||||
−0.158495 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(282\) | − 3.31371i | − 0.197328i | ||||||||
\(283\) | − 12.6274i | − 0.750622i | −0.926899 | − | 0.375311i | \(-0.877536\pi\) | ||||
0.926899 | − | 0.375311i | \(-0.122464\pi\) | |||||||
\(284\) | −20.6863 | −1.22751 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.82843 | 0.167248 | ||||||||
\(287\) | 12.0000i | 0.708338i | ||||||||
\(288\) | − 22.0711i | − 1.30055i | ||||||||
\(289\) | 15.6274 | 0.919260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.6569 | −1.26955 | ||||||||
\(292\) | − 12.4853i | − 0.730646i | ||||||||
\(293\) | − 14.8284i | − 0.866286i | −0.901325 | − | 0.433143i | \(-0.857405\pi\) | ||||
0.901325 | − | 0.433143i | \(-0.142595\pi\) | |||||||
\(294\) | −3.51472 | −0.204983 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.79899 | 0.337059 | ||||||||
\(297\) | − 5.65685i | − 0.328244i | ||||||||
\(298\) | − 4.82843i | − 0.279703i | ||||||||
\(299\) | 19.3137 | 1.11694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | − 4.97056i | − 0.286024i | ||||||||
\(303\) | − 37.6569i | − 2.16333i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.42641 | −0.138708 | ||||||||
\(307\) | 27.6569i | 1.57846i | 0.614098 | + | 0.789230i | \(0.289520\pi\) | ||||
−0.614098 | + | 0.789230i | \(0.710480\pi\) | |||||||
\(308\) | 3.65685i | 0.208369i | ||||||||
\(309\) | −3.31371 | −0.188510 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.3137 | 1.54882 | 0.774409 | − | 0.632685i | \(-0.218047\pi\) | ||||
0.774409 | + | 0.632685i | \(0.218047\pi\) | |||||||
\(312\) | 30.6274i | 1.73394i | ||||||||
\(313\) | 21.3137i | 1.20472i | 0.798224 | + | 0.602361i | \(0.205773\pi\) | ||||
−0.798224 | + | 0.602361i | \(0.794227\pi\) | |||||||
\(314\) | −5.79899 | −0.327256 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.31371 | −0.411428 | ||||||||
\(317\) | − 21.3137i | − 1.19710i | −0.801087 | − | 0.598549i | \(-0.795744\pi\) | ||||
0.801087 | − | 0.598549i | \(-0.204256\pi\) | |||||||
\(318\) | − 0.402020i | − 0.0225442i | ||||||||
\(319\) | −7.65685 | −0.428702 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3431 | −0.577298 | ||||||||
\(322\) | − 2.34315i | − 0.130578i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.82843 | 0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.201010 | 0.0111329 | ||||||||
\(327\) | − 10.3431i | − 0.571977i | ||||||||
\(328\) | 9.51472i | 0.525362i | ||||||||
\(329\) | −5.65685 | −0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3137 | 0.841718 | 0.420859 | − | 0.907126i | \(-0.361729\pi\) | ||||
0.420859 | + | 0.907126i | \(0.361729\pi\) | |||||||
\(332\) | − 10.9706i | − 0.602088i | ||||||||
\(333\) | 18.2843i | 1.00197i | ||||||||
\(334\) | 4.54416 | 0.248645 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −16.9706 | −0.925820 | ||||||||
\(337\) | 3.51472i | 0.191459i | 0.995407 | + | 0.0957295i | \(0.0305184\pi\) | ||||
−0.995407 | + | 0.0957295i | \(0.969482\pi\) | |||||||
\(338\) | − 13.9289i | − 0.757634i | ||||||||
\(339\) | −23.5980 | −1.28167 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 9.51472 | 0.512999 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.54416 | −0.136775 | ||||||||
\(347\) | 22.9706i | 1.23312i | 0.787306 | + | 0.616562i | \(0.211475\pi\) | ||||
−0.787306 | + | 0.616562i | \(0.788525\pi\) | |||||||
\(348\) | − 39.5980i | − 2.12267i | ||||||||
\(349\) | 6.97056 | 0.373126 | 0.186563 | − | 0.982443i | \(-0.440265\pi\) | ||||
0.186563 | + | 0.982443i | \(0.440265\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −38.6274 | −2.06178 | ||||||||
\(352\) | 4.41421i | 0.235278i | ||||||||
\(353\) | − 1.31371i | − 0.0699216i | −0.999389 | − | 0.0349608i | \(-0.988869\pi\) | ||||
0.999389 | − | 0.0349608i | \(-0.0111306\pi\) | |||||||
\(354\) | −11.3137 | −0.601317 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −17.0294 | −0.902558 | ||||||||
\(357\) | 6.62742i | 0.350760i | ||||||||
\(358\) | 0.686292i | 0.0362716i | ||||||||
\(359\) | −23.3137 | −1.23045 | −0.615225 | − | 0.788351i | \(-0.710935\pi\) | ||||
−0.615225 | + | 0.788351i | \(0.710935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | − 0.544156i | − 0.0286002i | ||||||||
\(363\) | 2.82843i | 0.148454i | ||||||||
\(364\) | 24.9706 | 1.30881 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −15.5980 | −0.815319 | ||||||||
\(367\) | − 8.48528i | − 0.442928i | −0.975169 | − | 0.221464i | \(-0.928916\pi\) | ||||
0.975169 | − | 0.221464i | \(-0.0710835\pi\) | |||||||
\(368\) | 8.48528i | 0.442326i | ||||||||
\(369\) | −30.0000 | −1.56174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.686292 | −0.0356305 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3.79899i | − 0.196704i | −0.995152 | − | 0.0983521i | \(-0.968643\pi\) | ||||
0.995152 | − | 0.0983521i | \(-0.0313571\pi\) | |||||||
\(374\) | 0.485281 | 0.0250933 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.48528 | −0.231311 | ||||||||
\(377\) | 52.2843i | 2.69278i | ||||||||
\(378\) | 4.68629i | 0.241037i | ||||||||
\(379\) | −22.3431 | −1.14769 | −0.573845 | − | 0.818964i | \(-0.694549\pi\) | ||||
−0.573845 | + | 0.818964i | \(0.694549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 44.2843 | 2.26875 | ||||||||
\(382\) | − 8.00000i | − 0.409316i | ||||||||
\(383\) | − 34.1421i | − 1.74458i | −0.488987 | − | 0.872291i | \(-0.662634\pi\) | ||||
0.488987 | − | 0.872291i | \(-0.337366\pi\) | |||||||
\(384\) | −29.8579 | −1.52368 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.82843 | 0.143963 | ||||||||
\(387\) | 30.0000i | 1.52499i | ||||||||
\(388\) | 14.0000i | 0.710742i | ||||||||
\(389\) | 24.6274 | 1.24866 | 0.624330 | − | 0.781161i | \(-0.285372\pi\) | ||||
0.624330 | + | 0.781161i | \(0.285372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.31371 | 0.167581 | ||||||||
\(392\) | 4.75736i | 0.240283i | ||||||||
\(393\) | 32.0000i | 1.61419i | ||||||||
\(394\) | −2.14214 | −0.107919 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.14214 | −0.459410 | ||||||||
\(397\) | − 13.3137i | − 0.668196i | −0.942538 | − | 0.334098i | \(-0.891568\pi\) | ||||
0.942538 | − | 0.334098i | \(-0.108432\pi\) | |||||||
\(398\) | − 8.97056i | − 0.449654i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3137 | 0.864605 | 0.432303 | − | 0.901729i | \(-0.357701\pi\) | ||||
0.432303 | + | 0.901729i | \(0.357701\pi\) | |||||||
\(402\) | − 5.25483i | − 0.262087i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −24.3431 | −1.21112 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.34315 | 0.314805 | ||||||||
\(407\) | − 3.65685i | − 0.181264i | ||||||||
\(408\) | 5.25483i | 0.260153i | ||||||||
\(409\) | −34.9706 | −1.72918 | −0.864592 | − | 0.502475i | \(-0.832423\pi\) | ||||
−0.864592 | + | 0.502475i | \(0.832423\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 64.9706 | 3.20476 | ||||||||
\(412\) | 2.14214i | 0.105535i | ||||||||
\(413\) | 19.3137i | 0.950365i | ||||||||
\(414\) | 5.85786 | 0.287898 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 30.1421 | 1.47784 | ||||||||
\(417\) | 11.3137i | 0.554035i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.3431 | 0.700709 | 0.350354 | − | 0.936617i | \(-0.386061\pi\) | ||||
0.350354 | + | 0.936617i | \(0.386061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | − 6.62742i | − 0.322618i | ||||||||
\(423\) | − 14.1421i | − 0.687614i | ||||||||
\(424\) | −0.544156 | −0.0264265 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.2548 | 0.642199 | ||||||||
\(427\) | 26.6274i | 1.28859i | ||||||||
\(428\) | 6.68629i | 0.323194i | ||||||||
\(429\) | 19.3137 | 0.932475 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3137 | 0.544962 | 0.272481 | − | 0.962161i | \(-0.412156\pi\) | ||||
0.272481 | + | 0.962161i | \(0.412156\pi\) | |||||||
\(432\) | − 16.9706i | − 0.816497i | ||||||||
\(433\) | 3.65685i | 0.175737i | 0.996132 | + | 0.0878686i | \(0.0280056\pi\) | ||||
−0.996132 | + | 0.0878686i | \(0.971994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.68629 | −0.320215 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 8.00000i | 0.382255i | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | − 3.31371i | − 0.157617i | ||||||||
\(443\) | − 21.1716i | − 1.00589i | −0.864318 | − | 0.502946i | \(-0.832249\pi\) | ||||
0.864318 | − | 0.502946i | \(-0.167751\pi\) | |||||||
\(444\) | 18.9117 | 0.897509 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.14214 | 0.101433 | ||||||||
\(447\) | − 32.9706i | − 1.55945i | ||||||||
\(448\) | 8.34315i | 0.394177i | ||||||||
\(449\) | 16.6274 | 0.784696 | 0.392348 | − | 0.919817i | \(-0.371663\pi\) | ||||
0.392348 | + | 0.919817i | \(0.371663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | 0.282529 | ||||||||
\(452\) | 15.2548i | 0.717527i | ||||||||
\(453\) | − 33.9411i | − 1.59469i | ||||||||
\(454\) | 1.11270 | 0.0522215 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.4853i | 0.771149i | 0.922677 | + | 0.385574i | \(0.125997\pi\) | ||||
−0.922677 | + | 0.385574i | \(0.874003\pi\) | |||||||
\(458\) | 8.82843i | 0.412525i | ||||||||
\(459\) | −6.62742 | −0.309341 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.6274 | −1.51961 | −0.759805 | − | 0.650151i | \(-0.774706\pi\) | ||||
−0.759805 | + | 0.650151i | \(0.774706\pi\) | |||||||
\(462\) | − 2.34315i | − 0.109013i | ||||||||
\(463\) | 22.1421i | 1.02903i | 0.857481 | + | 0.514516i | \(0.172028\pi\) | ||||
−0.857481 | + | 0.514516i | \(0.827972\pi\) | |||||||
\(464\) | −22.9706 | −1.06638 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.17157 | −0.424865 | ||||||||
\(467\) | 9.17157i | 0.424410i | 0.977225 | + | 0.212205i | \(0.0680644\pi\) | ||||
−0.977225 | + | 0.212205i | \(0.931936\pi\) | |||||||
\(468\) | 62.4264i | 2.88566i | ||||||||
\(469\) | −8.97056 | −0.414222 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −39.5980 | −1.82458 | ||||||||
\(472\) | 15.3137i | 0.704871i | ||||||||
\(473\) | − 6.00000i | − 0.275880i | ||||||||
\(474\) | 4.68629 | 0.215248 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.28427 | 0.196369 | ||||||||
\(477\) | − 1.71573i | − 0.0785578i | ||||||||
\(478\) | 0.284271i | 0.0130023i | ||||||||
\(479\) | 36.0000 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.9706 | −1.13856 | ||||||||
\(482\) | 2.48528i | 0.113201i | ||||||||
\(483\) | − 16.0000i | − 0.728025i | ||||||||
\(484\) | 1.82843 | 0.0831103 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.85786 | 0.265718 | ||||||||
\(487\) | 7.51472i | 0.340524i | 0.985399 | + | 0.170262i | \(0.0544615\pi\) | ||||
−0.985399 | + | 0.170262i | \(0.945539\pi\) | |||||||
\(488\) | 21.1127i | 0.955727i | ||||||||
\(489\) | 1.37258 | 0.0620703 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.3137 | −1.05213 | −0.526066 | − | 0.850443i | \(-0.676334\pi\) | ||||
−0.526066 | + | 0.850443i | \(0.676334\pi\) | |||||||
\(492\) | 31.0294i | 1.39892i | ||||||||
\(493\) | 8.97056i | 0.404014i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 22.6274i | − 1.01498i | ||||||||
\(498\) | 7.02944i | 0.314997i | ||||||||
\(499\) | 1.65685 | 0.0741710 | 0.0370855 | − | 0.999312i | \(-0.488193\pi\) | ||||
0.0370855 | + | 0.999312i | \(0.488193\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.0294 | 1.38629 | ||||||||
\(502\) | 4.97056i | 0.221847i | ||||||||
\(503\) | − 28.6274i | − 1.27643i | −0.769857 | − | 0.638217i | \(-0.779672\pi\) | ||||
0.769857 | − | 0.638217i | \(-0.220328\pi\) | |||||||
\(504\) | 15.8579 | 0.706365 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.17157 | −0.0520828 | ||||||||
\(507\) | − 95.1127i | − 4.22410i | ||||||||
\(508\) | − 28.6274i | − 1.27014i | ||||||||
\(509\) | −9.31371 | −0.412823 | −0.206411 | − | 0.978465i | \(-0.566179\pi\) | ||||
−0.206411 | + | 0.978465i | \(0.566179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6569 | 0.604144 | ||||||||
\(512\) | 22.7574i | 1.00574i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.51472 | 0.243244 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 31.0294 | 1.36599 | ||||||||
\(517\) | 2.82843i | 0.124394i | ||||||||
\(518\) | 3.02944i | 0.133106i | ||||||||
\(519\) | −17.3726 | −0.762572 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.68629 | 0.117689 | 0.0588443 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588443 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(522\) | 15.8579i | 0.694080i | ||||||||
\(523\) | 37.5980i | 1.64404i | 0.569455 | + | 0.822022i | \(0.307154\pi\) | ||||
−0.569455 | + | 0.822022i | \(0.692846\pi\) | |||||||
\(524\) | 20.6863 | 0.903685 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.51472 | −0.414861 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 8.48528i | 0.369274i | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −48.2843 | −2.09536 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 40.9706i | − 1.77463i | ||||||||
\(534\) | 10.9117 | 0.472195 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.11270 | −0.307222 | ||||||||
\(537\) | 4.68629i | 0.202228i | ||||||||
\(538\) | 2.20101i | 0.0948923i | ||||||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | − 6.34315i | − 0.272461i | ||||||||
\(543\) | − 3.71573i | − 0.159457i | ||||||||
\(544\) | 5.17157 | 0.221729 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.0000 | −0.684737 | ||||||||
\(547\) | 34.0000i | 1.45374i | 0.686778 | + | 0.726868i | \(0.259025\pi\) | ||||
−0.686778 | + | 0.726868i | \(0.740975\pi\) | |||||||
\(548\) | − 42.0000i | − 1.79415i | ||||||||
\(549\) | −66.5685 | −2.84108 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − 12.6863i | − 0.539964i | ||||||||
\(553\) | − 8.00000i | − 0.340195i | ||||||||
\(554\) | 0.485281 | 0.0206176 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.31371 | 0.310170 | ||||||||
\(557\) | − 38.1421i | − 1.61613i | −0.589090 | − | 0.808067i | \(-0.700514\pi\) | ||||
0.589090 | − | 0.808067i | \(-0.299486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.9706 | −1.73287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.31371 | 0.139905 | ||||||||
\(562\) | − 2.20101i | − 0.0928440i | ||||||||
\(563\) | 11.6569i | 0.491278i | 0.969361 | + | 0.245639i | \(0.0789977\pi\) | ||||
−0.969361 | + | 0.245639i | \(0.921002\pi\) | |||||||
\(564\) | −14.6274 | −0.615925 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.23045 | 0.219852 | ||||||||
\(567\) | 2.00000i | 0.0839921i | ||||||||
\(568\) | − 17.9411i | − 0.752793i | ||||||||
\(569\) | −20.3431 | −0.852829 | −0.426415 | − | 0.904528i | \(-0.640224\pi\) | ||||
−0.426415 | + | 0.904528i | \(0.640224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.9411 | 1.92258 | 0.961288 | − | 0.275545i | \(-0.0888584\pi\) | ||||
0.961288 | + | 0.275545i | \(0.0888584\pi\) | |||||||
\(572\) | − 12.4853i | − 0.522036i | ||||||||
\(573\) | − 54.6274i | − 2.28209i | ||||||||
\(574\) | −4.97056 | −0.207467 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −20.8579 | −0.869078 | ||||||||
\(577\) | − 6.97056i | − 0.290188i | −0.989418 | − | 0.145094i | \(-0.953651\pi\) | ||||
0.989418 | − | 0.145094i | \(-0.0463485\pi\) | |||||||
\(578\) | 6.47309i | 0.269245i | ||||||||
\(579\) | 19.3137 | 0.802650 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | − 8.97056i | − 0.371842i | ||||||||
\(583\) | 0.343146i | 0.0142116i | ||||||||
\(584\) | 10.8284 | 0.448084 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.14214 | 0.253729 | ||||||||
\(587\) | − 26.1421i | − 1.07900i | −0.841985 | − | 0.539501i | \(-0.818613\pi\) | ||||
0.841985 | − | 0.539501i | \(-0.181387\pi\) | |||||||
\(588\) | 15.5147i | 0.639816i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.6274 | −0.601692 | ||||||||
\(592\) | − 10.9706i | − 0.450887i | ||||||||
\(593\) | 20.4853i | 0.841230i | 0.907239 | + | 0.420615i | \(0.138186\pi\) | ||||
−0.907239 | + | 0.420615i | \(0.861814\pi\) | |||||||
\(594\) | 2.34315 | 0.0961404 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.3137 | −0.873044 | ||||||||
\(597\) | − 61.2548i | − 2.50699i | ||||||||
\(598\) | 8.00000i | 0.327144i | ||||||||
\(599\) | −5.65685 | −0.231133 | −0.115566 | − | 0.993300i | \(-0.536868\pi\) | ||||
−0.115566 | + | 0.993300i | \(0.536868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.9411 | −1.79240 | −0.896198 | − | 0.443654i | \(-0.853682\pi\) | ||||
−0.896198 | + | 0.443654i | \(0.853682\pi\) | |||||||
\(602\) | 4.97056i | 0.202585i | ||||||||
\(603\) | − 22.4264i | − 0.913274i | ||||||||
\(604\) | −21.9411 | −0.892772 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15.5980 | 0.633625 | ||||||||
\(607\) | 18.2843i | 0.742136i | 0.928606 | + | 0.371068i | \(0.121008\pi\) | ||||
−0.928606 | + | 0.371068i | \(0.878992\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 43.3137 | 1.75516 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.3137 | 0.781349 | ||||||||
\(612\) | 10.7107i | 0.432954i | ||||||||
\(613\) | 25.4558i | 1.02815i | 0.857745 | + | 0.514076i | \(0.171865\pi\) | ||||
−0.857745 | + | 0.514076i | \(0.828135\pi\) | |||||||
\(614\) | −11.4558 | −0.462320 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.17157 | −0.127786 | ||||||||
\(617\) | − 11.6569i | − 0.469287i | −0.972081 | − | 0.234644i | \(-0.924608\pi\) | ||||
0.972081 | − | 0.234644i | \(-0.0753923\pi\) | |||||||
\(618\) | − 1.37258i | − 0.0552134i | ||||||||
\(619\) | 25.6569 | 1.03124 | 0.515618 | − | 0.856819i | \(-0.327562\pi\) | ||||
0.515618 | + | 0.856819i | \(0.327562\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0000 | 0.642058 | ||||||||
\(622\) | 11.3137i | 0.453638i | ||||||||
\(623\) | − 18.6274i | − 0.746292i | ||||||||
\(624\) | 57.9411 | 2.31950 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.82843 | −0.352855 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 25.5980i | 1.02147i | ||||||||
\(629\) | −4.28427 | −0.170825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | − 6.34315i | − 0.252317i | ||||||||
\(633\) | − 45.2548i | − 1.79872i | ||||||||
\(634\) | 8.82843 | 0.350622 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.77460 | −0.0703676 | ||||||||
\(637\) | − 20.4853i | − 0.811656i | ||||||||
\(638\) | − 3.17157i | − 0.125564i | ||||||||
\(639\) | 56.5685 | 2.23782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | − 4.28427i | − 0.169087i | ||||||||
\(643\) | 49.4558i | 1.95035i | 0.221440 | + | 0.975174i | \(0.428924\pi\) | ||||
−0.221440 | + | 0.975174i | \(0.571076\pi\) | |||||||
\(644\) | −10.3431 | −0.407577 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.1127i | 1.38042i | 0.723608 | + | 0.690211i | \(0.242482\pi\) | ||||
−0.723608 | + | 0.690211i | \(0.757518\pi\) | |||||||
\(648\) | 1.58579i | 0.0622956i | ||||||||
\(649\) | 9.65685 | 0.379065 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 0.887302i | − 0.0347494i | ||||||||
\(653\) | 0.343146i | 0.0134283i | 0.999977 | + | 0.00671417i | \(0.00213720\pi\) | ||||
−0.999977 | + | 0.00671417i | \(0.997863\pi\) | |||||||
\(654\) | 4.28427 | 0.167528 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 18.0000 | 0.702782 | ||||||||
\(657\) | 34.1421i | 1.33201i | ||||||||
\(658\) | − 2.34315i | − 0.0913453i | ||||||||
\(659\) | 21.9411 | 0.854705 | 0.427352 | − | 0.904085i | \(-0.359446\pi\) | ||||
0.427352 | + | 0.904085i | \(0.359446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.627417 | −0.0244037 | −0.0122018 | − | 0.999926i | \(-0.503884\pi\) | ||||
−0.0122018 | + | 0.999926i | \(0.503884\pi\) | |||||||
\(662\) | 6.34315i | 0.246533i | ||||||||
\(663\) | − 22.6274i | − 0.878776i | ||||||||
\(664\) | 9.51472 | 0.369243 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.57359 | −0.293471 | ||||||||
\(667\) | − 21.6569i | − 0.838557i | ||||||||
\(668\) | − 20.0589i | − 0.776101i | ||||||||
\(669\) | 14.6274 | 0.565529 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.3137 | 0.513970 | ||||||||
\(672\) | − 24.9706i | − 0.963260i | ||||||||
\(673\) | 4.48528i | 0.172895i | 0.996256 | + | 0.0864474i | \(0.0275515\pi\) | ||||
−0.996256 | + | 0.0864474i | \(0.972449\pi\) | |||||||
\(674\) | −1.45584 | −0.0560770 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −61.4853 | −2.36482 | ||||||||
\(677\) | − 17.1716i | − 0.659957i | −0.943988 | − | 0.329979i | \(-0.892958\pi\) | ||||
0.943988 | − | 0.329979i | \(-0.107042\pi\) | |||||||
\(678\) | − 9.77460i | − 0.375391i | ||||||||
\(679\) | −15.3137 | −0.587686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.59798 | 0.291155 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.7990i | 1.21675i | 0.793648 | + | 0.608377i | \(0.208179\pi\) | ||||
−0.793648 | + | 0.608377i | \(0.791821\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.28427 | −0.316295 | ||||||||
\(687\) | 60.2843i | 2.29999i | ||||||||
\(688\) | − 18.0000i | − 0.686244i | ||||||||
\(689\) | 2.34315 | 0.0892667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.6863 | −0.634776 | −0.317388 | − | 0.948296i | \(-0.602806\pi\) | ||||
−0.317388 | + | 0.948296i | \(0.602806\pi\) | |||||||
\(692\) | 11.2304i | 0.426918i | ||||||||
\(693\) | − 10.0000i | − 0.379869i | ||||||||
\(694\) | −9.51472 | −0.361174 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 34.3431 | 1.30177 | ||||||||
\(697\) | − 7.02944i | − 0.266259i | ||||||||
\(698\) | 2.88730i | 0.109286i | ||||||||
\(699\) | −62.6274 | −2.36879 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.6274 | 1.23232 | 0.616160 | − | 0.787621i | \(-0.288687\pi\) | ||||
0.616160 | + | 0.787621i | \(0.288687\pi\) | |||||||
\(702\) | − 16.0000i | − 0.603881i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.17157 | 0.157222 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.544156 | 0.0204796 | ||||||||
\(707\) | − 26.6274i | − 1.00143i | ||||||||
\(708\) | 49.9411i | 1.87690i | ||||||||
\(709\) | 20.6274 | 0.774679 | 0.387339 | − | 0.921937i | \(-0.373394\pi\) | ||||
0.387339 | + | 0.921937i | \(0.373394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.0000 | 0.750059 | ||||||||
\(712\) | − 14.7696i | − 0.553512i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −2.74517 | −0.102735 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.02944 | 0.113215 | ||||||||
\(717\) | 1.94113i | 0.0724927i | ||||||||
\(718\) | − 9.65685i | − 0.360391i | ||||||||
\(719\) | −29.6569 | −1.10601 | −0.553007 | − | 0.833177i | \(-0.686520\pi\) | ||||
−0.553007 | + | 0.833177i | \(0.686520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.34315 | −0.0872633 | ||||||||
\(722\) | − 7.87006i | − 0.292893i | ||||||||
\(723\) | 16.9706i | 0.631142i | ||||||||
\(724\) | −2.40202 | −0.0892704 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.17157 | −0.0434811 | ||||||||
\(727\) | 36.4853i | 1.35316i | 0.736367 | + | 0.676582i | \(0.236540\pi\) | ||||
−0.736367 | + | 0.676582i | \(0.763460\pi\) | |||||||
\(728\) | 21.6569i | 0.802656i | ||||||||
\(729\) | 43.0000 | 1.59259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.02944 | −0.259993 | ||||||||
\(732\) | 68.8528i | 2.54487i | ||||||||
\(733\) | 33.4558i | 1.23572i | 0.786288 | + | 0.617860i | \(0.212000\pi\) | ||||
−0.786288 | + | 0.617860i | \(0.788000\pi\) | |||||||
\(734\) | 3.51472 | 0.129731 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.4853 | −0.460214 | ||||||||
\(737\) | 4.48528i | 0.165217i | ||||||||
\(738\) | − 12.4264i | − 0.457422i | ||||||||
\(739\) | 37.9411 | 1.39569 | 0.697843 | − | 0.716250i | \(-0.254143\pi\) | ||||
0.697843 | + | 0.716250i | \(0.254143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 0.284271i | − 0.0104359i | ||||||||
\(743\) | 29.5980i | 1.08584i | 0.839783 | + | 0.542922i | \(0.182682\pi\) | ||||
−0.839783 | + | 0.542922i | \(0.817318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.57359 | 0.0576133 | ||||||||
\(747\) | 30.0000i | 1.09764i | ||||||||
\(748\) | − 2.14214i | − 0.0783242i | ||||||||
\(749\) | −7.31371 | −0.267237 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | 8.48528i | 0.309426i | ||||||||
\(753\) | 33.9411i | 1.23688i | ||||||||
\(754\) | −21.6569 | −0.788696 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 20.6863 | 0.752353 | ||||||||
\(757\) | 9.31371i | 0.338512i | 0.985572 | + | 0.169256i | \(0.0541365\pi\) | ||||
−0.985572 | + | 0.169256i | \(0.945863\pi\) | |||||||
\(758\) | − 9.25483i | − 0.336151i | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 18.3431i | 0.664502i | ||||||||
\(763\) | − 7.31371i | − 0.264774i | ||||||||
\(764\) | −35.3137 | −1.27761 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.1421 | 0.510976 | ||||||||
\(767\) | − 65.9411i | − 2.38100i | ||||||||
\(768\) | 11.2304i | 0.405244i | ||||||||
\(769\) | −14.9706 | −0.539852 | −0.269926 | − | 0.962881i | \(-0.586999\pi\) | ||||
−0.269926 | + | 0.962881i | \(0.586999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.6569 | 1.35618 | ||||||||
\(772\) | − 12.4853i | − 0.449355i | ||||||||
\(773\) | − 30.2843i | − 1.08925i | −0.838680 | − | 0.544625i | \(-0.816672\pi\) | ||||
0.838680 | − | 0.544625i | \(-0.183328\pi\) | |||||||
\(774\) | −12.4264 | −0.446658 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.1421 | −0.435877 | ||||||||
\(777\) | 20.6863i | 0.742117i | ||||||||
\(778\) | 10.2010i | 0.365724i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.3137 | −0.404836 | ||||||||
\(782\) | 1.37258i | 0.0490835i | ||||||||
\(783\) | 43.3137i | 1.54791i | ||||||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.2548 | −0.472784 | ||||||||
\(787\) | − 18.9706i | − 0.676228i | −0.941105 | − | 0.338114i | \(-0.890211\pi\) | ||||
0.941105 | − | 0.338114i | \(-0.109789\pi\) | |||||||
\(788\) | 9.45584i | 0.336850i | ||||||||
\(789\) | −64.9706 | −2.31301 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.6863 | −0.593296 | ||||||||
\(792\) | − 7.92893i | − 0.281742i | ||||||||
\(793\) | − 90.9117i | − 3.22837i | ||||||||
\(794\) | 5.51472 | 0.195710 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −39.5980 | −1.40351 | ||||||||
\(797\) | 12.6274i | 0.447286i | 0.974671 | + | 0.223643i | \(0.0717950\pi\) | ||||
−0.974671 | + | 0.223643i | \(0.928205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.31371 | 0.117231 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 46.5685 | 1.64542 | ||||||||
\(802\) | 7.17157i | 0.253237i | ||||||||
\(803\) | − 6.82843i | − 0.240970i | ||||||||
\(804\) | −23.1960 | −0.818058 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.0294i | 0.529061i | ||||||||
\(808\) | − 21.1127i | − 0.742742i | ||||||||
\(809\) | −22.9706 | −0.807602 | −0.403801 | − | 0.914847i | \(-0.632311\pi\) | ||||
−0.403801 | + | 0.914847i | \(0.632311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.9411 | −0.489539 | −0.244770 | − | 0.969581i | \(-0.578712\pi\) | ||||
−0.244770 | + | 0.969581i | \(0.578712\pi\) | |||||||
\(812\) | − 28.0000i | − 0.982607i | ||||||||
\(813\) | − 43.3137i | − 1.51908i | ||||||||
\(814\) | 1.51472 | 0.0530909 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.94113 | 0.348009 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − 14.4853i | − 0.506466i | ||||||||
\(819\) | −68.2843 | −2.38605 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.6863 | −0.652156 | −0.326078 | − | 0.945343i | \(-0.605727\pi\) | ||||
−0.326078 | + | 0.945343i | \(0.605727\pi\) | |||||||
\(822\) | 26.9117i | 0.938653i | ||||||||
\(823\) | 36.4853i | 1.27180i | 0.771773 | + | 0.635898i | \(0.219370\pi\) | ||||
−0.771773 | + | 0.635898i | \(0.780630\pi\) | |||||||
\(824\) | −1.85786 | −0.0647218 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 34.2843i | 1.19218i | 0.802917 | + | 0.596090i | \(0.203280\pi\) | ||||
−0.802917 | + | 0.596090i | \(0.796720\pi\) | |||||||
\(828\) | − 25.8579i | − 0.898623i | ||||||||
\(829\) | −18.0000 | −0.625166 | −0.312583 | − | 0.949890i | \(-0.601194\pi\) | ||||
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.31371 | 0.114951 | ||||||||
\(832\) | − 28.4853i | − 0.987549i | ||||||||
\(833\) | − 3.51472i | − 0.121778i | ||||||||
\(834\) | −4.68629 | −0.162273 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.94113i | 0.205233i | ||||||||
\(839\) | −37.6569 | −1.30006 | −0.650029 | − | 0.759909i | \(-0.725243\pi\) | ||||
−0.650029 | + | 0.759909i | \(0.725243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | − 2.48528i | − 0.0856485i | ||||||||
\(843\) | − 15.0294i | − 0.517641i | ||||||||
\(844\) | −29.2548 | −1.00699 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.85786 | 0.201398 | ||||||||
\(847\) | 2.00000i | 0.0687208i | ||||||||
\(848\) | 1.02944i | 0.0353510i | ||||||||
\(849\) | 35.7157 | 1.22576 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.3431 | 0.354558 | ||||||||
\(852\) | − 58.5097i | − 2.00451i | ||||||||
\(853\) | − 32.4853i | − 1.11227i | −0.831090 | − | 0.556137i | \(-0.812283\pi\) | ||||
0.831090 | − | 0.556137i | \(-0.187717\pi\) | |||||||
\(854\) | −11.0294 | −0.377420 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.79899 | −0.198205 | ||||||||
\(857\) | 48.7696i | 1.66594i | 0.553321 | + | 0.832968i | \(0.313360\pi\) | ||||
−0.553321 | + | 0.832968i | \(0.686640\pi\) | |||||||
\(858\) | 8.00000i | 0.273115i | ||||||||
\(859\) | 32.2843 | 1.10153 | 0.550763 | − | 0.834662i | \(-0.314337\pi\) | ||||
0.550763 | + | 0.834662i | \(0.314337\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −33.9411 | −1.15671 | ||||||||
\(862\) | 4.68629i | 0.159616i | ||||||||
\(863\) | − 14.8284i | − 0.504766i | −0.967627 | − | 0.252383i | \(-0.918786\pi\) | ||||
0.967627 | − | 0.252383i | \(-0.0812142\pi\) | |||||||
\(864\) | 24.9706 | 0.849516 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.51472 | −0.0514722 | ||||||||
\(867\) | 44.2010i | 1.50115i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.00000 | −0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.6274 | 1.03777 | ||||||||
\(872\) | − 5.79899i | − 0.196379i | ||||||||
\(873\) | − 38.2843i | − 1.29573i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 35.3137 | 1.19314 | ||||||||
\(877\) | − 1.45584i | − 0.0491604i | −0.999698 | − | 0.0245802i | \(-0.992175\pi\) | ||||
0.999698 | − | 0.0245802i | \(-0.00782490\pi\) | |||||||
\(878\) | 6.62742i | 0.223664i | ||||||||
\(879\) | 41.9411 | 1.41464 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.6274 | −1.77306 | −0.886531 | − | 0.462668i | \(-0.846892\pi\) | ||||
−0.886531 | + | 0.462668i | \(0.846892\pi\) | |||||||
\(882\) | − 6.21320i | − 0.209209i | ||||||||
\(883\) | 42.8284i | 1.44129i | 0.693304 | + | 0.720646i | \(0.256155\pi\) | ||||
−0.693304 | + | 0.720646i | \(0.743845\pi\) | |||||||
\(884\) | −14.6274 | −0.491973 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.76955 | 0.294619 | ||||||||
\(887\) | 18.2843i | 0.613926i | 0.951721 | + | 0.306963i | \(0.0993127\pi\) | ||||
−0.951721 | + | 0.306963i | \(0.900687\pi\) | |||||||
\(888\) | 16.4020i | 0.550416i | ||||||||
\(889\) | 31.3137 | 1.05023 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | − 9.45584i | − 0.316605i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 13.6569 | 0.456754 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21.1127 | −0.705326 | ||||||||
\(897\) | 54.6274i | 1.82396i | ||||||||
\(898\) | 6.88730i | 0.229832i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.402020 | 0.0133932 | ||||||||
\(902\) | 2.48528i | 0.0827508i | ||||||||
\(903\) | 33.9411i | 1.12949i | ||||||||
\(904\) | −13.2304 | −0.440038 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 14.0589 | 0.467075 | ||||||||
\(907\) | 44.4853i | 1.47711i | 0.674193 | + | 0.738555i | \(0.264491\pi\) | ||||
−0.674193 | + | 0.738555i | \(0.735509\pi\) | |||||||
\(908\) | − 4.91169i | − 0.163000i | ||||||||
\(909\) | 66.5685 | 2.20794 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.9411 | 1.91968 | 0.959838 | − | 0.280556i | \(-0.0905189\pi\) | ||||
0.959838 | + | 0.280556i | \(0.0905189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 6.00000i | − 0.198571i | ||||||||
\(914\) | −6.82843 | −0.225864 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 38.9706 | 1.28762 | ||||||||
\(917\) | 22.6274i | 0.747223i | ||||||||
\(918\) | − 2.74517i | − 0.0906040i | ||||||||
\(919\) | 32.0000 | 1.05558 | 0.527791 | − | 0.849374i | \(-0.323020\pi\) | ||||
0.527791 | + | 0.849374i | \(0.323020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −78.2254 | −2.57761 | ||||||||
\(922\) | − 13.5147i | − 0.445084i | ||||||||
\(923\) | 77.2548i | 2.54287i | ||||||||
\(924\) | −10.3431 | −0.340265 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.17157 | −0.301397 | ||||||||
\(927\) | − 5.85786i | − 0.192398i | ||||||||
\(928\) | − 33.7990i | − 1.10951i | ||||||||
\(929\) | 17.3137 | 0.568044 | 0.284022 | − | 0.958818i | \(-0.408331\pi\) | ||||
0.284022 | + | 0.958818i | \(0.408331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 40.4853i | 1.32614i | ||||||||
\(933\) | 77.2548i | 2.52921i | ||||||||
\(934\) | −3.79899 | −0.124307 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −54.1421 | −1.76969 | ||||||||
\(937\) | − 49.4558i | − 1.61565i | −0.589421 | − | 0.807826i | \(-0.700644\pi\) | ||||
0.589421 | − | 0.807826i | \(-0.299356\pi\) | |||||||
\(938\) | − 3.71573i | − 0.121323i | ||||||||
\(939\) | −60.2843 | −1.96730 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.3137 | −0.955600 | −0.477800 | − | 0.878469i | \(-0.658566\pi\) | ||||
−0.477800 | + | 0.878469i | \(0.658566\pi\) | |||||||
\(942\) | − 16.4020i | − 0.534407i | ||||||||
\(943\) | 16.9706i | 0.552638i | ||||||||
\(944\) | 28.9706 | 0.942912 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.48528 | 0.0808035 | ||||||||
\(947\) | − 46.8284i | − 1.52172i | −0.648916 | − | 0.760860i | \(-0.724778\pi\) | ||||
0.648916 | − | 0.760860i | \(-0.275222\pi\) | |||||||
\(948\) | − 20.6863i | − 0.671860i | ||||||||
\(949\) | −46.6274 | −1.51359 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 60.2843 | 1.95485 | ||||||||
\(952\) | 3.71573i | 0.120427i | ||||||||
\(953\) | 58.8284i | 1.90564i | 0.303536 | + | 0.952820i | \(0.401833\pi\) | ||||
−0.303536 | + | 0.952820i | \(0.598167\pi\) | |||||||
\(954\) | 0.710678 | 0.0230091 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.25483 | 0.0405842 | ||||||||
\(957\) | − 21.6569i | − 0.700067i | ||||||||
\(958\) | 14.9117i | 0.481775i | ||||||||
\(959\) | 45.9411 | 1.48352 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | − 10.3431i | − 0.333476i | ||||||||
\(963\) | − 18.2843i | − 0.589202i | ||||||||
\(964\) | 10.9706 | 0.353338 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.62742 | 0.213234 | ||||||||
\(967\) | − 18.9706i | − 0.610052i | −0.952344 | − | 0.305026i | \(-0.901335\pi\) | ||||
0.952344 | − | 0.305026i | \(-0.0986652\pi\) | |||||||
\(968\) | 1.58579i | 0.0509691i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.3137 | −1.00490 | −0.502452 | − | 0.864605i | \(-0.667569\pi\) | ||||
−0.502452 | + | 0.864605i | \(0.667569\pi\) | |||||||
\(972\) | − 25.8579i | − 0.829391i | ||||||||
\(973\) | 8.00000i | 0.256468i | ||||||||
\(974\) | −3.11270 | −0.0997373 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39.9411 | 1.27848 | ||||||||
\(977\) | − 43.6569i | − 1.39671i | −0.715753 | − | 0.698353i | \(-0.753916\pi\) | ||||
0.715753 | − | 0.698353i | \(-0.246084\pi\) | |||||||
\(978\) | 0.568542i | 0.0181800i | ||||||||
\(979\) | −9.31371 | −0.297667 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.2843 | 0.583772 | ||||||||
\(982\) | − 9.65685i | − 0.308163i | ||||||||
\(983\) | − 50.1421i | − 1.59929i | −0.600476 | − | 0.799643i | \(-0.705022\pi\) | ||||
0.600476 | − | 0.799643i | \(-0.294978\pi\) | |||||||
\(984\) | −26.9117 | −0.857913 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.71573 | −0.118333 | ||||||||
\(987\) | − 16.0000i | − 0.509286i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706 | 0.539633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.94113 | 0.315790 | 0.157895 | − | 0.987456i | \(-0.449529\pi\) | ||||
0.157895 | + | 0.987456i | \(0.449529\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.3137i | 1.37452i | ||||||||
\(994\) | 9.37258 | 0.297280 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 31.0294 | 0.983205 | ||||||||
\(997\) | − 9.45584i | − 0.299470i | −0.988726 | − | 0.149735i | \(-0.952158\pi\) | ||||
0.988726 | − | 0.149735i | \(-0.0478420\pi\) | |||||||
\(998\) | 0.686292i | 0.0217242i | ||||||||
\(999\) | −20.6863 | −0.654485 |
(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 | 275.2.b.d.199.3 | 4 | ||
3.2 | odd | 2 | 2475.2.c.l.199.2 | 4 | |||
4.3 | odd | 2 | 4400.2.b.q.4049.1 | 4 | |||
5.2 | odd | 4 | 55.2.a.b.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 275.2.a.c.1.2 | 2 | |||
5.4 | even | 2 | inner | 275.2.b.d.199.2 | 4 | ||
15.2 | even | 4 | 495.2.a.b.1.2 | 2 | |||
15.8 | even | 4 | 2475.2.a.x.1.1 | 2 | |||
15.14 | odd | 2 | 2475.2.c.l.199.3 | 4 | |||
20.3 | even | 4 | 4400.2.a.bn.1.2 | 2 | |||
20.7 | even | 4 | 880.2.a.m.1.1 | 2 | |||
20.19 | odd | 2 | 4400.2.b.q.4049.4 | 4 | |||
35.27 | even | 4 | 2695.2.a.f.1.1 | 2 | |||
40.27 | even | 4 | 3520.2.a.bo.1.2 | 2 | |||
40.37 | odd | 4 | 3520.2.a.bn.1.1 | 2 | |||
55.2 | even | 20 | 605.2.g.l.81.1 | 8 | |||
55.7 | even | 20 | 605.2.g.l.511.2 | 8 | |||
55.17 | even | 20 | 605.2.g.l.366.1 | 8 | |||
55.27 | odd | 20 | 605.2.g.f.366.2 | 8 | |||
55.32 | even | 4 | 605.2.a.d.1.2 | 2 | |||
55.37 | odd | 20 | 605.2.g.f.511.1 | 8 | |||
55.42 | odd | 20 | 605.2.g.f.81.2 | 8 | |||
55.43 | even | 4 | 3025.2.a.o.1.1 | 2 | |||
55.47 | odd | 20 | 605.2.g.f.251.1 | 8 | |||
55.52 | even | 20 | 605.2.g.l.251.2 | 8 | |||
60.47 | odd | 4 | 7920.2.a.ch.1.1 | 2 | |||
65.12 | odd | 4 | 9295.2.a.g.1.2 | 2 | |||
165.32 | odd | 4 | 5445.2.a.y.1.1 | 2 | |||
220.87 | odd | 4 | 9680.2.a.bn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.b.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
275.2.a.c.1.2 | 2 | 5.3 | odd | 4 | |||
275.2.b.d.199.2 | 4 | 5.4 | even | 2 | inner | ||
275.2.b.d.199.3 | 4 | 1.1 | even | 1 | trivial | ||
495.2.a.b.1.2 | 2 | 15.2 | even | 4 | |||
605.2.a.d.1.2 | 2 | 55.32 | even | 4 | |||
605.2.g.f.81.2 | 8 | 55.42 | odd | 20 | |||
605.2.g.f.251.1 | 8 | 55.47 | odd | 20 | |||
605.2.g.f.366.2 | 8 | 55.27 | odd | 20 | |||
605.2.g.f.511.1 | 8 | 55.37 | odd | 20 | |||
605.2.g.l.81.1 | 8 | 55.2 | even | 20 | |||
605.2.g.l.251.2 | 8 | 55.52 | even | 20 | |||
605.2.g.l.366.1 | 8 | 55.17 | even | 20 | |||
605.2.g.l.511.2 | 8 | 55.7 | even | 20 | |||
880.2.a.m.1.1 | 2 | 20.7 | even | 4 | |||
2475.2.a.x.1.1 | 2 | 15.8 | even | 4 | |||
2475.2.c.l.199.2 | 4 | 3.2 | odd | 2 | |||
2475.2.c.l.199.3 | 4 | 15.14 | odd | 2 | |||
2695.2.a.f.1.1 | 2 | 35.27 | even | 4 | |||
3025.2.a.o.1.1 | 2 | 55.43 | even | 4 | |||
3520.2.a.bn.1.1 | 2 | 40.37 | odd | 4 | |||
3520.2.a.bo.1.2 | 2 | 40.27 | even | 4 | |||
4400.2.a.bn.1.2 | 2 | 20.3 | even | 4 | |||
4400.2.b.q.4049.1 | 4 | 4.3 | odd | 2 | |||
4400.2.b.q.4049.4 | 4 | 20.19 | odd | 2 | |||
5445.2.a.y.1.1 | 2 | 165.32 | odd | 4 | |||
7920.2.a.ch.1.1 | 2 | 60.47 | odd | 4 | |||
9295.2.a.g.1.2 | 2 | 65.12 | odd | 4 | |||
9680.2.a.bn.1.1 | 2 | 220.87 | odd | 4 |