Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [208,3,Mod(161,208)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(208, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("208.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 208 = 2^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 208.t (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: | \(5.66758949869\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(i)\) |
Coefficient field: | 6.0.20819026944.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 42x^{4} + 441x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 52) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 177.3 | ||
Root | \(-4.43242i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 208.177 |
Dual form | 208.3.t.d.161.3 |
$q$-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 \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 4.43242 | 1.47747 | 0.738736 | − | 0.673994i | \(-0.235423\pi\) | ||||
0.738736 | + | 0.673994i | \(0.235423\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.03938 | − | 6.03938i | −1.20788 | − | 1.20788i | −0.971714 | − | 0.236162i | \(-0.924110\pi\) |
−0.236162 | − | 0.971714i | \(-0.575890\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.393041 | + | 0.393041i | −0.0561487 | + | 0.0561487i | −0.734624 | − | 0.678475i | \(-0.762641\pi\) |
0.678475 | + | 0.734624i | \(0.262641\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 10.6463 | 1.18293 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.8648 | − | 11.8648i | 1.07862 | − | 1.07862i | 0.0819883 | − | 0.996633i | \(-0.473873\pi\) |
0.996633 | − | 0.0819883i | \(-0.0261270\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.90422 | − | 9.47180i | 0.684940 | − | 0.728600i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −26.7691 | − | 26.7691i | −1.78460 | − | 1.78460i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 10.0833i | − | 0.593138i | −0.955011 | − | 0.296569i | \(-0.904158\pi\) | ||
0.955011 | − | 0.296569i | \(-0.0958424\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.56758 | + | 8.56758i | 0.450925 | + | 0.450925i | 0.895662 | − | 0.444736i | \(-0.146703\pi\) |
−0.444736 | + | 0.895662i | \(0.646703\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.74212 | + | 1.74212i | −0.0829582 | + | 0.0829582i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 30.0788i | 1.30777i | 0.756593 | + | 0.653886i | \(0.226862\pi\) | ||||
−0.756593 | + | 0.653886i | \(0.773138\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 47.9482i | 1.91793i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.29726 | 0.270269 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −26.6733 | −0.919768 | −0.459884 | − | 0.887979i | \(-0.652109\pi\) | ||||
−0.459884 | + | 0.887979i | \(0.652109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00458 | + | 3.00458i | 0.0969220 | + | 0.0969220i | 0.753905 | − | 0.656983i | \(-0.228168\pi\) |
−0.656983 | + | 0.753905i | \(0.728168\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 52.5899 | − | 52.5899i | 1.59363 | − | 1.59363i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.74744 | 0.135641 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14.0394 | + | 14.0394i | −0.379443 | + | 0.379443i | −0.870901 | − | 0.491458i | \(-0.836464\pi\) |
0.491458 | + | 0.870901i | \(0.336464\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.4672 | − | 41.9830i | 1.01198 | − | 1.07649i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −22.4548 | − | 22.4548i | −0.547677 | − | 0.547677i | 0.378091 | − | 0.925768i | \(-0.376581\pi\) |
−0.925768 | + | 0.378091i | \(0.876581\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 49.8826i | 1.16006i | 0.814595 | + | 0.580030i | \(0.196959\pi\) | ||||
−0.814595 | + | 0.580030i | \(0.803041\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −64.2973 | − | 64.2973i | −1.42883 | − | 1.42883i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24.8300 | − | 24.8300i | 0.528299 | − | 0.528299i | −0.391766 | − | 0.920065i | \(-0.628136\pi\) |
0.920065 | + | 0.391766i | \(0.128136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.6910i | 0.993695i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 44.6936i | − | 0.876345i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 65.8084 | 1.24167 | 0.620834 | − | 0.783942i | \(-0.286794\pi\) | ||||
0.620834 | + | 0.783942i | \(0.286794\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −143.312 | −2.60568 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 37.9751 | + | 37.9751i | 0.666230 | + | 0.666230i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.62399 | + | 7.62399i | −0.129220 | + | 0.129220i | −0.768759 | − | 0.639539i | \(-0.779125\pi\) |
0.639539 | + | 0.768759i | \(0.279125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 89.6169 | 1.46913 | 0.734564 | − | 0.678539i | \(-0.237387\pi\) | ||||
0.734564 | + | 0.678539i | \(0.237387\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.18444 | + | 4.18444i | −0.0664198 | + | 0.0664198i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −110.980 | + | 3.42784i | −1.70738 | + | 0.0527360i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3806 | + | 12.3806i | 0.184785 | + | 0.184785i | 0.793437 | − | 0.608652i | \(-0.208289\pi\) |
−0.608652 | + | 0.793437i | \(0.708289\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 133.322i | 1.93220i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.79853 | + | 7.79853i | 0.109838 | + | 0.109838i | 0.759890 | − | 0.650052i | \(-0.225253\pi\) |
−0.650052 | + | 0.759890i | \(0.725253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −36.2093 | + | 36.2093i | −0.496018 | + | 0.496018i | −0.910196 | − | 0.414178i | \(-0.864069\pi\) |
0.414178 | + | 0.910196i | \(0.364069\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 212.526i | 2.83369i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.32673i | 0.121126i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.20475 | 0.0911994 | 0.0455997 | − | 0.998960i | \(-0.485480\pi\) | ||||
0.0455997 | + | 0.998960i | \(0.485480\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −63.4725 | −0.783612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 53.9095 | + | 53.9095i | 0.649513 | + | 0.649513i | 0.952875 | − | 0.303363i | \(-0.0981094\pi\) |
−0.303363 | + | 0.952875i | \(0.598109\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −60.8971 | + | 60.8971i | −0.716436 | + | 0.716436i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −118.227 | −1.35893 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 70.0269 | − | 70.0269i | 0.786819 | − | 0.786819i | −0.194152 | − | 0.980971i | \(-0.562195\pi\) |
0.980971 | + | 0.194152i | \(0.0621955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.223083 | + | 7.22252i | 0.00245146 | + | 0.0793684i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.3176 | + | 13.3176i | 0.143200 | + | 0.143200i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 103.486i | − | 1.08932i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −124.696 | − | 124.696i | −1.28552 | − | 1.28552i | −0.937478 | − | 0.348043i | \(-0.886846\pi\) |
−0.348043 | − | 0.937478i | \(-0.613154\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 126.317 | − | 126.317i | 1.27593 | − | 1.27593i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 52.1758i | 0.516592i | 0.966066 | + | 0.258296i | \(0.0831611\pi\) | ||||
−0.966066 | + | 0.258296i | \(0.916839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 129.461i | 1.25690i | 0.777849 | + | 0.628451i | \(0.216311\pi\) | ||||
−0.777849 | + | 0.628451i | \(0.783689\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21.0427 | 0.200406 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −28.4462 | −0.265852 | −0.132926 | − | 0.991126i | \(-0.542437\pi\) | ||||
−0.132926 | + | 0.991126i | \(0.542437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −33.1837 | − | 33.1837i | −0.304438 | − | 0.304438i | 0.538310 | − | 0.842747i | \(-0.319063\pi\) |
−0.842747 | + | 0.538310i | \(0.819063\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −62.2284 | + | 62.2284i | −0.560616 | + | 0.560616i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 61.0854 | 0.540579 | 0.270289 | − | 0.962779i | \(-0.412881\pi\) | ||||
0.270289 | + | 0.962779i | \(0.412881\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 181.657 | − | 181.657i | 1.57963 | − | 1.57963i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 94.7973 | − | 100.840i | 0.810233 | − | 0.861880i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.96316 | + | 3.96316i | 0.0333039 | + | 0.0333039i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 160.549i | − | 1.32685i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −99.5289 | − | 99.5289i | −0.809178 | − | 0.809178i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 138.593 | − | 138.593i | 1.10874 | − | 1.10874i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 170.483i | − | 1.34239i | −0.741282 | − | 0.671194i | \(-0.765782\pi\) | ||
0.741282 | − | 0.671194i | \(-0.234218\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 221.101i | 1.71396i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.6255 | −0.111645 | −0.0558224 | − | 0.998441i | \(-0.517778\pi\) | ||||
−0.0558224 | + | 0.998441i | \(0.517778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.73482 | −0.0506377 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −44.0709 | − | 44.0709i | −0.326451 | − | 0.326451i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0904616 | + | 0.0904616i | −0.000660304 | + | 0.000660304i | −0.707437 | − | 0.706777i | \(-0.750149\pi\) |
0.706777 | + | 0.707437i | \(0.250149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 138.968 | 0.999770 | 0.499885 | − | 0.866092i | \(-0.333376\pi\) | ||||
0.499885 | + | 0.866092i | \(0.333376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 110.057 | − | 110.057i | 0.780547 | − | 0.780547i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.73426 | − | 218.028i | −0.0470927 | − | 1.52467i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 161.090 | + | 161.090i | 1.11097 | + | 1.11097i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 215.819i | 1.46816i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 144.587 | + | 144.587i | 0.970385 | + | 0.970385i | 0.999574 | − | 0.0291887i | \(-0.00929239\pi\) |
−0.0291887 | + | 0.999574i | \(0.509292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −193.041 | + | 193.041i | −1.27842 | + | 1.27842i | −0.336868 | + | 0.941552i | \(0.609368\pi\) |
−0.941552 | + | 0.336868i | \(0.890632\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 107.351i | − | 0.701638i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 36.2916i | − | 0.234139i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −49.0487 | −0.312412 | −0.156206 | − | 0.987724i | \(-0.549926\pi\) | ||||
−0.156206 | + | 0.987724i | \(0.549926\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 291.691 | 1.83453 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.8222 | − | 11.8222i | −0.0734297 | − | 0.0734297i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −84.5828 | + | 84.5828i | −0.518913 | + | 0.518913i | −0.917242 | − | 0.398329i | \(-0.869590\pi\) |
0.398329 | + | 0.917242i | \(0.369590\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −635.221 | −3.84982 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.6174 | − | 25.6174i | 0.153398 | − | 0.153398i | −0.626236 | − | 0.779634i | \(-0.715405\pi\) |
0.779634 | + | 0.626236i | \(0.215405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4299 | − | 168.678i | −0.0617153 | − | 0.998094i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91.2134 | + | 91.2134i | 0.533411 | + | 0.533411i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 82.1184i | − | 0.474673i | −0.971428 | − | 0.237336i | \(-0.923726\pi\) | ||
0.971428 | − | 0.237336i | \(-0.0762743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.8456 | − | 18.8456i | −0.107689 | − | 0.107689i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −33.7927 | + | 33.7927i | −0.190919 | + | 0.190919i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 125.292i | − | 0.699956i | −0.936758 | − | 0.349978i | \(-0.886189\pi\) | ||
0.936758 | − | 0.349978i | \(-0.113811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 104.543i | − | 0.577587i | −0.957391 | − | 0.288794i | \(-0.906746\pi\) | ||
0.957391 | − | 0.288794i | \(-0.0932541\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 397.219 | 2.17060 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 169.578 | 0.916639 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −119.637 | − | 119.637i | −0.639771 | − | 0.639771i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.86812 | + | 2.86812i | −0.0151752 | + | 0.0151752i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −215.628 | −1.12894 | −0.564470 | − | 0.825454i | \(-0.690919\pi\) | ||||
−0.564470 | + | 0.825454i | \(0.690919\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −55.7810 | + | 55.7810i | −0.289021 | + | 0.289021i | −0.836693 | − | 0.547672i | \(-0.815514\pi\) |
0.547672 | + | 0.836693i | \(0.315514\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −491.908 | + | 15.1936i | −2.52261 | + | 0.0779159i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −49.3844 | − | 49.3844i | −0.250682 | − | 0.250682i | 0.570568 | − | 0.821250i | \(-0.306723\pi\) |
−0.821250 | + | 0.570568i | \(0.806723\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 69.7637i | 0.350572i | 0.984518 | + | 0.175286i | \(0.0560849\pi\) | ||||
−0.984518 | + | 0.175286i | \(0.943915\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 54.8760 | + | 54.8760i | 0.273015 | + | 0.273015i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.4837 | − | 10.4837i | 0.0516438 | − | 0.0516438i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 271.226i | 1.32305i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 320.229i | 1.54700i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 203.306 | 0.972756 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 197.446 | 0.935761 | 0.467881 | − | 0.883792i | \(-0.345018\pi\) | ||||
0.467881 | + | 0.883792i | \(0.345018\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.5663 | + | 34.5663i | 0.162283 | + | 0.162283i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 301.260 | − | 301.260i | 1.40121 | − | 1.40121i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.36185 | −0.0108841 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −160.495 | + | 160.495i | −0.732854 | + | 0.732854i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −95.5073 | − | 89.7842i | −0.432160 | − | 0.406263i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 163.226 | + | 163.226i | 0.731957 | + | 0.731957i | 0.971007 | − | 0.239050i | \(-0.0768360\pi\) |
−0.239050 | + | 0.971007i | \(0.576836\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 510.472i | 2.26877i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −152.446 | − | 152.446i | −0.671567 | − | 0.671567i | 0.286511 | − | 0.958077i | \(-0.407505\pi\) |
−0.958077 | + | 0.286511i | \(0.907505\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −32.6090 | + | 32.6090i | −0.142397 | + | 0.142397i | −0.774712 | − | 0.632314i | \(-0.782105\pi\) |
0.632314 | + | 0.774712i | \(0.282105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 41.3400i | 0.178961i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 381.064i | − | 1.63547i | −0.575597 | − | 0.817734i | \(-0.695230\pi\) | ||
0.575597 | − | 0.817734i | \(-0.304770\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −299.916 | −1.27624 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 31.9345 | 0.134745 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 142.133 | + | 142.133i | 0.594700 | + | 0.594700i | 0.938897 | − | 0.344197i | \(-0.111849\pi\) |
−0.344197 | + | 0.938897i | \(0.611849\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −189.679 | + | 189.679i | −0.787051 | + | 0.787051i | −0.981010 | − | 0.193959i | \(-0.937867\pi\) |
0.193959 | + | 0.981010i | \(0.437867\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −347.012 | −1.42803 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 294.064 | − | 294.064i | 1.20026 | − | 1.20026i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 157.438 | − | 4.86280i | 0.637401 | − | 0.0196874i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 238.950 | + | 238.950i | 0.959637 | + | 0.959637i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 352.293i | − | 1.40356i | −0.712395 | − | 0.701778i | \(-0.752390\pi\) | ||
0.712395 | − | 0.701778i | \(-0.247610\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 356.880 | + | 356.880i | 1.41059 | + | 1.41059i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −269.921 | + | 269.921i | −1.05852 | + | 1.05852i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5071i | 0.0408836i | 0.999791 | + | 0.0204418i | \(0.00650729\pi\) | ||||
−0.999791 | + | 0.0204418i | \(0.993493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 11.0361i | − | 0.0426104i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −283.973 | −1.08802 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −267.748 | −1.01805 | −0.509027 | − | 0.860751i | \(-0.669995\pi\) | ||||
−0.509027 | + | 0.860751i | \(0.669995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −397.442 | − | 397.442i | −1.49978 | − | 1.49978i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 310.389 | − | 310.389i | 1.16250 | − | 1.16250i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −297.780 | −1.10699 | −0.553494 | − | 0.832853i | \(-0.686706\pi\) | ||||
−0.553494 | + | 0.832853i | \(0.686706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 118.767 | − | 118.767i | 0.438255 | − | 0.438255i | −0.453170 | − | 0.891424i | \(-0.649707\pi\) |
0.891424 | + | 0.453170i | \(0.149707\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.988795 | + | 32.0132i | 0.00362196 | + | 0.117265i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 568.897 | + | 568.897i | 2.06872 | + | 2.06872i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 91.5366i | − | 0.330457i | −0.986255 | − | 0.165229i | \(-0.947164\pi\) | ||
0.986255 | − | 0.165229i | \(-0.0528362\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 31.9878 | + | 31.9878i | 0.114652 | + | 0.114652i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −297.778 | + | 297.778i | −1.05971 | + | 1.05971i | −0.0616074 | + | 0.998100i | \(0.519623\pi\) |
−0.998100 | + | 0.0616074i | \(0.980377\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 374.832i | 1.32450i | 0.749285 | + | 0.662248i | \(0.230397\pi\) | ||||
−0.749285 | + | 0.662248i | \(0.769603\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 458.692i | − | 1.60945i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.6513 | 0.0615027 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 187.326 | 0.648188 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −552.703 | − | 552.703i | −1.89932 | − | 1.89932i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −162.854 | + | 162.854i | −0.555817 | + | 0.555817i | −0.928114 | − | 0.372297i | \(-0.878570\pi\) |
0.372297 | + | 0.928114i | \(0.378570\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 92.0883 | 0.312164 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 86.5808 | − | 86.5808i | 0.291518 | − | 0.291518i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 284.900 | + | 267.828i | 0.952842 | + | 0.895745i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.6059 | − | 19.6059i | −0.0651359 | − | 0.0651359i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 231.265i | 0.763251i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −541.230 | − | 541.230i | −1.77453 | − | 1.77453i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −96.9116 | + | 96.9116i | −0.315673 | + | 0.315673i | −0.847102 | − | 0.531430i | \(-0.821655\pi\) |
0.531430 | + | 0.847102i | \(0.321655\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 573.825i | 1.85704i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0062i | 0.0386052i | 0.999814 | + | 0.0193026i | \(0.00614458\pi\) | ||||
−0.999814 | + | 0.0193026i | \(0.993855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 68.4167 | 0.218584 | 0.109292 | − | 0.994010i | \(-0.465142\pi\) | ||||
0.109292 | + | 0.994010i | \(0.465142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 50.5429 | 0.160454 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 244.393 | + | 244.393i | 0.770957 | + | 0.770957i | 0.978274 | − | 0.207317i | \(-0.0664732\pi\) |
−0.207317 | + | 0.978274i | \(0.566473\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −316.474 | + | 316.474i | −0.992082 | + | 0.992082i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −126.085 | −0.392789 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 86.3898 | − | 86.3898i | 0.267461 | − | 0.267461i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 454.155 | + | 426.941i | 1.39740 | + | 1.31366i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −147.084 | − | 147.084i | −0.449798 | − | 0.449798i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.5184i | 0.0593266i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −275.224 | − | 275.224i | −0.831491 | − | 0.831491i | 0.156230 | − | 0.987721i | \(-0.450066\pi\) |
−0.987721 | + | 0.156230i | \(0.950066\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −149.468 | + | 149.468i | −0.448853 | + | 0.448853i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 149.542i | − | 0.446395i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 647.689i | 1.92193i | 0.276678 | + | 0.960963i | \(0.410767\pi\) | ||||
−0.276678 | + | 0.960963i | \(0.589233\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 270.756 | 0.798690 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 71.2978 | 0.209084 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −38.3966 | − | 38.3966i | −0.111943 | − | 0.111943i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 805.180 | − | 805.180i | 2.33385 | − | 2.33385i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 71.7372 | 0.206736 | 0.103368 | − | 0.994643i | \(-0.467038\pi\) | ||||
0.103368 | + | 0.994643i | \(0.467038\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 442.834 | − | 442.834i | 1.26887 | − | 1.26887i | 0.322190 | − | 0.946675i | \(-0.395581\pi\) |
0.946675 | − | 0.322190i | \(-0.104419\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 64.9763 | − | 69.1181i | 0.185118 | − | 0.196918i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −177.592 | − | 177.592i | −0.503093 | − | 0.503093i | 0.409305 | − | 0.912398i | \(-0.365771\pi\) |
−0.912398 | + | 0.409305i | \(0.865771\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 94.1965i | − | 0.265342i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.5664 | + | 17.5664i | 0.0492056 | + | 0.0492056i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −201.035 | + | 201.035i | −0.559986 | + | 0.559986i | −0.929303 | − | 0.369317i | \(-0.879592\pi\) |
0.369317 | + | 0.929303i | \(0.379592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 214.193i | − | 0.593333i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 711.619i | − | 1.96038i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 437.364 | 1.19826 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 625.023 | 1.70306 | 0.851530 | − | 0.524306i | \(-0.175675\pi\) | ||||
0.851530 | + | 0.524306i | \(0.175675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −239.061 | − | 239.061i | −0.647862 | − | 0.647862i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.8654 | + | 25.8654i | −0.0697181 | + | 0.0697181i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.9411 | −0.101719 | −0.0508593 | − | 0.998706i | \(-0.516196\pi\) | ||||
−0.0508593 | + | 0.998706i | \(0.516196\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 614.301 | − | 614.301i | 1.63814 | − | 1.63814i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −237.505 | + | 252.644i | −0.629986 | + | 0.670143i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −508.424 | − | 508.424i | −1.34149 | − | 1.34149i | −0.894579 | − | 0.446910i | \(-0.852524\pi\) |
−0.446910 | − | 0.894579i | \(-0.647476\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 755.653i | − | 1.98334i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.6964 | − | 37.6964i | −0.0984239 | − | 0.0984239i | 0.656180 | − | 0.754604i | \(-0.272171\pi\) |
−0.754604 | + | 0.656180i | \(0.772171\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 56.3277 | − | 56.3277i | 0.146306 | − | 0.146306i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 531.067i | 1.37227i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 339.848i | − | 0.873646i | −0.899547 | − | 0.436823i | \(-0.856104\pi\) | ||
0.899547 | − | 0.436823i | \(-0.143896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 303.294 | 0.775689 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −64.8262 | −0.164952 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −43.5122 | − | 43.5122i | −0.110158 | − | 0.110158i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −51.8720 | + | 51.8720i | −0.130660 | + | 0.130660i | −0.769412 | − | 0.638752i | \(-0.779451\pi\) |
0.638752 | + | 0.769412i | \(0.279451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −29.8515 | −0.0748159 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −416.732 | + | 416.732i | −1.03923 | + | 1.03923i | −0.0400326 | + | 0.999198i | \(0.512746\pi\) |
−0.999198 | + | 0.0400326i | \(0.987254\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 55.2122 | − | 1.70534i | 0.137003 | − | 0.00423162i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 383.335 | + | 383.335i | 0.946505 | + | 0.946505i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 333.150i | 0.818550i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −342.563 | − | 342.563i | −0.837563 | − | 0.837563i | 0.150975 | − | 0.988538i | \(-0.451759\pi\) |
−0.988538 | + | 0.150975i | \(0.951759\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.400964 | + | 0.400964i | −0.000975581 | + | 0.000975581i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 5.99308i | − | 0.0145111i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 651.160i | − | 1.56906i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 615.964 | 1.47713 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −766.950 | −1.83043 | −0.915214 | − | 0.402967i | \(-0.867979\pi\) | ||||
−0.915214 | + | 0.402967i | \(0.867979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −513.458 | − | 513.458i | −1.21962 | − | 1.21962i | −0.967766 | − | 0.251850i | \(-0.918961\pi\) |
−0.251850 | − | 0.967766i | \(-0.581039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 264.349 | − | 264.349i | 0.624939 | − | 0.624939i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 483.478 | 1.13759 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.2231 | + | 35.2231i | −0.0824897 | + | 0.0824897i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −29.8491 | − | 966.393i | −0.0695782 | − | 2.25266i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −218.539 | − | 218.539i | −0.507052 | − | 0.507052i | 0.406569 | − | 0.913620i | \(-0.366725\pi\) |
−0.913620 | + | 0.406569i | \(0.866725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 136.399i | − | 0.315010i | −0.987518 | − | 0.157505i | \(-0.949655\pi\) | ||
0.987518 | − | 0.157505i | \(-0.0503451\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 714.018 | + | 714.018i | 1.64142 | + | 1.64142i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −257.702 | + | 257.702i | −0.589708 | + | 0.589708i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 61.3626i | 0.139778i | 0.997555 | + | 0.0698891i | \(0.0222645\pi\) | ||||
−0.997555 | + | 0.0698891i | \(0.977735\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 518.381i | 1.17547i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 810.003 | 1.82845 | 0.914224 | − | 0.405209i | \(-0.132801\pi\) | ||||
0.914224 | + | 0.405209i | \(0.132801\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −845.838 | −1.90076 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 640.872 | + | 640.872i | 1.43372 | + | 1.43372i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 158.025 | − | 158.025i | 0.351949 | − | 0.351949i | −0.508886 | − | 0.860834i | \(-0.669942\pi\) |
0.860834 | + | 0.508886i | \(0.169942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −532.844 | −1.18147 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −855.640 | + | 855.640i | −1.88883 | + | 1.88883i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 42.2723 | − | 44.9668i | 0.0929061 | − | 0.0988282i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 322.166 | + | 322.166i | 0.704959 | + | 0.704959i | 0.965471 | − | 0.260512i | \(-0.0838913\pi\) |
−0.260512 | + | 0.965471i | \(0.583891\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 73.5807i | − | 0.160307i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8270 | + | 13.8270i | 0.0299935 | + | 0.0299935i | 0.721944 | − | 0.691951i | \(-0.243249\pi\) |
−0.691951 | + | 0.721944i | \(0.743249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −53.7709 | + | 53.7709i | −0.116136 | + | 0.116136i | −0.762786 | − | 0.646651i | \(-0.776169\pi\) |
0.646651 | + | 0.762786i | \(0.276169\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 160.860i | − | 0.345935i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 694.236i | 1.48659i | 0.668966 | + | 0.743293i | \(0.266737\pi\) | ||||
−0.668966 | + | 0.743293i | \(0.733263\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.73216 | −0.0207509 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −217.404 | −0.461581 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 591.849 | + | 591.849i | 1.25127 | + | 1.25127i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −410.800 | + | 410.800i | −0.864842 | + | 0.864842i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 700.619 | 1.46880 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −552.049 | + | 552.049i | −1.15250 | + | 1.15250i | −0.166453 | + | 0.986049i | \(0.553231\pi\) |
−0.986049 | + | 0.166453i | \(0.946769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.96849 | + | 257.988i | 0.0165665 | + | 0.536357i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −52.4008 | − | 52.4008i | −0.108490 | − | 0.108490i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1506.17i | 3.10550i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −108.399 | − | 108.399i | −0.222585 | − | 0.222585i | 0.587001 | − | 0.809586i | \(-0.300308\pi\) |
−0.809586 | + | 0.587001i | \(0.800308\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −374.906 | + | 374.906i | −0.766680 | + | 0.766680i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 549.283i | 1.11870i | 0.828931 | + | 0.559351i | \(0.188950\pi\) | ||||
−0.828931 | + | 0.559351i | \(0.811050\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 268.956i | 0.545549i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1525.75 | −3.08233 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.13028 | −0.0123346 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.8430 | − | 22.8430i | −0.0457775 | − | 0.0457775i | 0.683847 | − | 0.729625i | \(-0.260305\pi\) |
−0.729625 | + | 0.683847i | \(0.760305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 113.547 | − | 113.547i | 0.226641 | − | 0.226641i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −865.245 | −1.72017 | −0.860084 | − | 0.510152i | \(-0.829589\pi\) | ||||
−0.860084 | + | 0.510152i | \(0.829589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 315.110 | − | 315.110i | 0.623979 | − | 0.623979i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −46.2296 | − | 747.651i | −0.0911826 | − | 1.47466i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −367.011 | − | 367.011i | −0.721044 | − | 0.721044i | 0.247774 | − | 0.968818i | \(-0.420301\pi\) |
−0.968818 | + | 0.247774i | \(0.920301\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 28.4635i | − | 0.0557015i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 62.5198 | + | 62.5198i | 0.121871 | + | 0.121871i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 781.863 | − | 781.863i | 1.51818 | − | 1.51818i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 589.209i | − | 1.13967i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 363.983i | − | 0.701316i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −244.720 | −0.469713 | −0.234856 | − | 0.972030i | \(-0.575462\pi\) | ||||
−0.234856 | + | 0.972030i | \(0.575462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 455.570 | 0.871071 | 0.435535 | − | 0.900172i | \(-0.356559\pi\) | ||||
0.435535 | + | 0.900172i | \(0.356559\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −83.5315 | − | 83.5315i | −0.159108 | − | 0.159108i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.2962 | − | 30.2962i | 0.0574881 | − | 0.0574881i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −375.732 | −0.710268 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −81.1675 | + | 81.1675i | −0.152858 | + | 0.152858i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −412.629 | + | 12.7449i | −0.774163 | + | 0.0239116i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 171.797 | + | 171.797i | 0.321116 | + | 0.321116i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 555.347i | − | 1.03417i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 577.711 | + | 577.711i | 1.07182 | + | 1.07182i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 283.267 | − | 283.267i | 0.523598 | − | 0.523598i | −0.395058 | − | 0.918656i | \(-0.629276\pi\) |
0.918656 | + | 0.395058i | \(0.129276\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 463.379i | − | 0.853369i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 400.818i | 0.735446i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 234.065 | 0.427908 | 0.213954 | − | 0.976844i | \(-0.431366\pi\) | ||||
0.213954 | + | 0.976844i | \(0.431366\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 954.091 | 1.73787 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −228.525 | − | 228.525i | −0.414747 | − | 0.414747i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.83176 | + | 2.83176i | −0.00512073 | + | 0.00512073i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 751.642 | 1.35431 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 534.694 | − | 534.694i | 0.959954 | − | 0.959954i | −0.0392744 | − | 0.999228i | \(-0.512505\pi\) |
0.999228 | + | 0.0392744i | \(0.0125046\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 472.478 | + | 444.165i | 0.845220 | + | 0.794572i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −530.282 | − | 530.282i | −0.945244 | − | 0.945244i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 387.128i | − | 0.687616i | −0.939040 | − | 0.343808i | \(-0.888283\pi\) | ||
0.939040 | − | 0.343808i | \(-0.111717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −368.918 | − | 368.918i | −0.652952 | − | 0.652952i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.9473 | − | 24.9473i | 0.0439988 | − | 0.0439988i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 384.213i | 0.675243i | 0.941282 | + | 0.337622i | \(0.109622\pi\) | ||||
−0.941282 | + | 0.337622i | \(0.890378\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1016.14i | 1.77958i | 0.456373 | + | 0.889789i | \(0.349148\pi\) | ||||
−0.456373 | + | 0.889789i | \(0.650852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −955.751 | −1.66798 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1442.22 | −2.50821 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 717.901 | + | 717.901i | 1.24420 | + | 1.24420i | 0.958244 | + | 0.285953i | \(0.0923101\pi\) |
0.285953 | + | 0.958244i | \(0.407690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −247.245 | + | 247.245i | −0.427020 | + | 0.427020i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.3773 | −0.0729385 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 780.806 | − | 780.806i | 1.33929 | − | 1.33929i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1181.53 | + | 36.4939i | −2.01970 | + | 0.0623827i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 348.797 | + | 348.797i | 0.594203 | + | 0.594203i | 0.938764 | − | 0.344561i | \(-0.111972\pi\) |
−0.344561 | + | 0.938764i | \(0.611972\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 51.4840i | 0.0874092i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −218.893 | − | 218.893i | −0.370376 | − | 0.370376i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 633.494 | − | 633.494i | 1.06829 | − | 1.06829i | 0.0707962 | − | 0.997491i | \(-0.477446\pi\) |
0.997491 | − | 0.0707962i | \(-0.0225540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 47.8701i | − | 0.0804539i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 309.222i | 0.517960i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1122.70 | −1.87429 | −0.937146 | − | 0.348938i | \(-0.886542\pi\) | ||||
−0.937146 | + | 0.348938i | \(0.886542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 659.039 | 1.09657 | 0.548286 | − | 0.836291i | \(-0.315281\pi\) | ||||
0.548286 | + | 0.836291i | \(0.315281\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 131.808 | + | 131.808i | 0.218587 | + | 0.218587i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −969.615 | + | 969.615i | −1.60267 | + | 1.60267i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 904.658 | 1.49038 | 0.745188 | − | 0.666854i | \(-0.232360\pi\) | ||||
0.745188 | + | 0.666854i | \(0.232360\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 46.4681 | − | 46.4681i | 0.0763023 | − | 0.0763023i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.0931 | − | 456.277i | −0.0230656 | − | 0.746771i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −348.891 | − | 348.891i | −0.569153 | − | 0.569153i | 0.362738 | − | 0.931891i | \(-0.381842\pi\) |
−0.931891 | + | 0.362738i | \(0.881842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1202.19i | 1.95477i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −74.5346 | − | 74.5346i | −0.120802 | − | 0.120802i | 0.644122 | − | 0.764923i | \(-0.277223\pi\) |
−0.764923 | + | 0.644122i | \(0.777223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 624.958 | − | 624.958i | 1.00963 | − | 1.00963i | 0.00967178 | − | 0.999953i | \(-0.496921\pi\) |
0.999953 | − | 0.00967178i | \(-0.00307867\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 219.492i | 0.353450i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55.0469i | 0.0883578i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −475.323 | −0.760517 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 901.137 | 1.43722 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 141.564 | + | 141.564i | 0.225062 | + | 0.225062i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −420.333 | + | 420.333i | −0.666139 | + | 0.666139i | −0.956820 | − | 0.290681i | \(-0.906118\pi\) |
0.290681 | + | 0.956820i | \(0.406118\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 875.162 | 1.38256 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1029.61 | + | 1029.61i | −1.62144 | + | 1.62144i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 461.192 | + | 433.556i | 0.724006 | + | 0.680621i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 83.0258 | + | 83.0258i | 0.129931 | + | 0.129931i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 270.092i | 0.421361i | 0.977555 | + | 0.210680i | \(0.0675679\pi\) | ||||
−0.977555 | + | 0.210680i | \(0.932432\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −296.047 | − | 296.047i | −0.460416 | − | 0.460416i | 0.438376 | − | 0.898792i | \(-0.355554\pi\) |
−0.898792 | + | 0.438376i | \(0.855554\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1335.31 | − | 1335.31i | 2.07025 | − | 2.07025i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 161.632i | − | 0.249818i | −0.992168 | − | 0.124909i | \(-0.960136\pi\) | ||
0.992168 | − | 0.124909i | \(-0.0398639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 180.915i | 0.278759i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.4687 | −0.0160809 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −412.304 | −0.631399 | −0.315700 | − | 0.948859i | \(-0.602239\pi\) | ||||
−0.315700 | + | 0.948859i | \(0.602239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 88.3287 | + | 88.3287i | 0.134853 | + | 0.134853i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −385.497 | + | 385.497i | −0.586753 | + | 0.586753i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 576.662 | 0.875056 | 0.437528 | − | 0.899205i | \(-0.355854\pi\) | ||||
0.437528 | + | 0.899205i | \(0.355854\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −264.568 | + | 264.568i | −0.400254 | + | 0.400254i | −0.878322 | − | 0.478069i | \(-0.841337\pi\) |
0.478069 | + | 0.878322i | \(0.341337\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −423.329 | − | 397.961i | −0.638505 | − | 0.600243i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40.6741 | + | 40.6741i | 0.0611641 | + | 0.0611641i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 802.299i | − | 1.20285i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 723.488 | + | 723.488i | 1.08145 | + | 1.08145i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1063.29 | − | 1063.29i | 1.58463 | − | 1.58463i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 547.327i | − | 0.813265i | −0.913592 | − | 0.406632i | \(-0.866703\pi\) | ||
0.913592 | − | 0.406632i | \(-0.133297\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 349.890i | 0.518356i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 658.800 | 0.973117 | 0.486558 | − | 0.873648i | \(-0.338252\pi\) | ||||
0.486558 | + | 0.873648i | \(0.338252\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 98.0209 | 0.144361 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −675.703 | − | 675.703i | −0.992221 | − | 0.992221i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −718.145 | + | 718.145i | −1.05146 | + | 1.05146i | −0.0528548 | + | 0.998602i | \(0.516832\pi\) |
−0.998602 | + | 0.0528548i | \(0.983168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.09266 | 0.00159513 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −144.537 | + | 144.537i | −0.210388 | + | 0.210388i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 585.972 | − | 623.324i | 0.850468 | − | 0.904679i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −782.796 | − | 782.796i | −1.13284 | − | 1.13284i | −0.989702 | − | 0.143142i | \(-0.954279\pi\) |
−0.143142 | − | 0.989702i | \(-0.545721\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 99.2955i | 0.143284i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −839.280 | − | 839.280i | −1.20760 | − | 1.20760i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −226.419 | + | 226.419i | −0.324848 | + | 0.324848i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1689.04i | − | 2.41636i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 135.826i | − | 0.193760i | −0.995296 | − | 0.0968798i | \(-0.969114\pi\) | ||
0.995296 | − | 0.0968798i | \(-0.0308863\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −240.567 | −0.342201 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1329.35 | −1.88561 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.5072 | − | 20.5072i | −0.0290060 | − | 0.0290060i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 463.251 | − | 463.251i | 0.653387 | − | 0.653387i | −0.300420 | − | 0.953807i | \(-0.597127\pi\) |
0.953807 | + | 0.300420i | \(0.0971269\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 76.7042 | 0.107882 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −90.3741 | + | 90.3741i | −0.126752 | + | 0.126752i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1276.09 | + | 1357.43i | −1.78473 | + | 1.89850i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 629.995 | + | 629.995i | 0.878654 | + | 0.878654i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1017.87i | − | 1.41568i | −0.706374 | − | 0.707839i | \(-0.749670\pi\) | ||
0.706374 | − | 0.707839i | \(-0.250330\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.8834 | − | 50.8834i | −0.0705734 | − | 0.0705734i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −840.738 | + | 840.738i | −1.16285 | + | 1.16285i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1278.93i | − | 1.76405i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 505.072i | 0.694734i | 0.937729 | + | 0.347367i | \(0.112924\pi\) | ||||
−0.937729 | + | 0.347367i | \(0.887076\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −966.851 | −1.32627 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 502.983 | 0.688076 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 894.499 | + | 894.499i | 1.22033 | + | 1.22033i | 0.967516 | + | 0.252811i | \(0.0813550\pi\) |
0.252811 | + | 0.967516i | \(0.418645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1303.41 | − | 1303.41i | 1.77335 | − | 1.77335i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 293.788 | 0.398626 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 439.748 | − | 439.748i | 0.595059 | − | 0.595059i | −0.343935 | − | 0.938993i | \(-0.611760\pi\) |
0.938993 | + | 0.343935i | \(0.111760\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 697.831 | − | 21.5540i | 0.941742 | − | 0.0290877i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 812.067 | + | 812.067i | 1.09296 | + | 1.09296i | 0.995211 | + | 0.0977456i | \(0.0311632\pi\) |
0.0977456 | + | 0.995211i | \(0.468837\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1746.44i | − | 2.34421i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 573.939 | + | 573.939i | 0.768325 | + | 0.768325i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.1805 | − | 11.1805i | 0.0149272 | − | 0.0149272i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 684.964i | − | 0.912070i | −0.889962 | − | 0.456035i | \(-0.849269\pi\) | ||
0.889962 | − | 0.456035i | \(-0.150731\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1561.51i | − | 2.07372i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2331.70 | 3.08834 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −215.537 | −0.284726 | −0.142363 | − | 0.989815i | \(-0.545470\pi\) | ||||
−0.142363 | + | 0.989815i | \(0.545470\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1581.84 | + | 1581.84i | 2.08411 | + | 2.08411i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −871.356 | + | 871.356i | −1.14501 | + | 1.14501i | −0.157494 | + | 0.987520i | \(0.550341\pi\) |
−0.987520 | + | 0.157494i | \(0.949659\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.0851 | 0.0341875 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −648.331 | + | 648.331i | −0.847491 | + | 0.847491i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.32723 | + | 140.098i | 0.00564176 | + | 0.182658i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 562.757 | + | 562.757i | 0.731804 | + | 0.731804i | 0.970977 | − | 0.239173i | \(-0.0768763\pi\) |
−0.239173 | + | 0.970977i | \(0.576876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 46.5718i | 0.0604045i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −97.0992 | − | 97.0992i | −0.125613 | − | 0.125613i | 0.641505 | − | 0.767119i | \(-0.278310\pi\) |
−0.767119 | + | 0.641505i | \(0.778310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −144.064 | + | 144.064i | −0.185889 | + | 0.185889i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 48.9166i | − | 0.0629557i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 384.766i | − | 0.493923i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 185.057 | 0.236948 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −194.642 | −0.248585 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 296.224 | + | 296.224i | 0.377355 | + | 0.377355i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 650.868 | − | 650.868i | 0.827025 | − | 0.827025i | −0.160080 | − | 0.987104i | \(-0.551175\pi\) |
0.987104 | + | 0.160080i | \(0.0511751\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1186.77 | −1.50415 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.0090 | + | 24.0090i | −0.0303528 | + | 0.0303528i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 797.968 | − | 848.833i | 1.00626 | − | 1.07041i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1761.63 | − | 1761.63i | −2.21589 | − | 2.21589i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 901.322i | − | 1.13089i | −0.824785 | − | 0.565447i | \(-0.808704\pi\) | ||
0.824785 | − | 0.565447i | \(-0.191296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −250.370 | − | 250.370i | −0.313354 | − | 0.313354i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 745.530 | − | 745.530i | 0.930749 | − | 0.930749i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 859.236i | 1.07003i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 142.797i | 0.177388i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1319.88 | −1.63554 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1041.59 | −1.28750 | −0.643749 | − | 0.765237i | \(-0.722622\pi\) | ||||
−0.643749 | + | 0.765237i | \(0.722622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.7958 | − | 50.7958i | −0.0626335 | − | 0.0626335i | 0.675096 | − | 0.737730i | \(-0.264102\pi\) |
−0.737730 | + | 0.675096i | \(0.764102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 526.425 | − | 526.425i | 0.647509 | − | 0.647509i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1021.66 | 1.25356 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −427.373 | + | 427.373i | −0.523101 | + | 0.523101i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.37501 | + | 76.8934i | 0.00289989 | + | 0.0938869i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −959.345 | − | 959.345i | −1.16851 | − | 1.16851i | −0.982559 | − | 0.185949i | \(-0.940464\pi\) |
−0.185949 | − | 0.982559i | \(-0.559536\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 520.691i | 0.632674i | 0.948647 | + | 0.316337i | \(0.102453\pi\) | ||||
−0.948647 | + | 0.316337i | \(0.897547\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2521.59 | + | 2521.59i | 3.05647 | + | 3.05647i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −603.369 | + | 603.369i | −0.729588 | + | 0.729588i | −0.970538 | − | 0.240950i | \(-0.922541\pi\) |
0.240950 | + | 0.970538i | \(0.422541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 889.955i | 1.07353i | 0.843732 | + | 0.536764i | \(0.180354\pi\) | ||||
−0.843732 | + | 0.536764i | \(0.819646\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 405.729i | − | 0.488241i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 490.968 | 0.589398 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −309.427 | −0.370571 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.9252 | + | 21.9252i | 0.0261950 | + | 0.0261950i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −585.049 | + | 585.049i | −0.697318 | + | 0.697318i | −0.963831 | − | 0.266514i | \(-0.914128\pi\) |
0.266514 | + | 0.963831i | \(0.414128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −129.537 | −0.154027 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1319.88 | + | 1319.88i | −1.56569 | + | 1.56569i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −955.719 | + | 1081.70i | −1.13103 | + | 1.28012i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 63.1022 | + | 63.1022i | 0.0745008 | + | 0.0745008i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1661.41i | 1.95691i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −422.287 | − | 422.287i | −0.496224 | − | 0.496224i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −294.894 | + | 294.894i | −0.345714 | + | 0.345714i | −0.858510 | − | 0.512797i | \(-0.828610\pi\) |
0.512797 | + | 0.858510i | \(0.328610\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1101.74i | − | 1.28859i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 909.483i | − | 1.06124i | −0.847610 | − | 0.530620i | \(-0.821959\pi\) | ||
0.847610 | − | 0.530620i | \(-0.178041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 826.078 | 0.961674 | 0.480837 | − | 0.876810i | \(-0.340333\pi\) | ||||
0.480837 | + | 0.876810i | \(0.340333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 78.2379 | 0.0908686 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 658.414 | + | 658.414i | 0.762936 | + | 0.762936i | 0.976852 | − | 0.213916i | \(-0.0686218\pi\) |
−0.213916 | + | 0.976852i | \(0.568622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −495.944 | + | 495.944i | −0.573346 | + | 0.573346i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 830.309 | 0.957680 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 85.4832 | − | 85.4832i | 0.0983697 | − | 0.0983697i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 227.506 | − | 7.02699i | 0.261201 | − | 0.00806773i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1327.55 | − | 1327.55i | −1.52068 | − | 1.52068i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 108.945i | 0.124509i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −768.569 | − | 768.569i | −0.876361 | − | 0.876361i | 0.116795 | − | 0.993156i | \(-0.462738\pi\) |
−0.993156 | + | 0.116795i | \(0.962738\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −721.839 | + | 721.839i | −0.821205 | + | 0.821205i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 608.060i | 0.690193i | 0.938567 | + | 0.345096i | \(0.112154\pi\) | ||||
−0.938567 | + | 0.345096i | \(0.887846\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 624.258i | − | 0.706974i | −0.935440 | − | 0.353487i | \(-0.884996\pi\) | ||
0.935440 | − | 0.353487i | \(-0.115004\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 408.174 | 0.461213 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −76.0762 | −0.0857679 | −0.0428840 | − | 0.999080i | \(-0.513655\pi\) | ||||
−0.0428840 | + | 0.999080i | \(0.513655\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 67.0068 | + | 67.0068i | 0.0753733 | + | 0.0753733i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −753.091 | + | 753.091i | −0.845220 | + | 0.845220i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 425.467 | 0.476447 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −756.687 | + | 756.687i | −0.845460 | + | 0.845460i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1262.80 | + | 1187.12i | 1.40780 | + | 1.32344i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −80.1420 | − | 80.1420i | −0.0891457 | − | 0.0891457i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 663.569i | − | 0.736480i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −86.9016 | − | 86.9016i | −0.0962365 | − | 0.0962365i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −631.376 | + | 631.376i | −0.697653 | + | 0.697653i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 595.072i | − | 0.656088i | −0.944662 | − | 0.328044i | \(-0.893611\pi\) | ||
0.944662 | − | 0.328044i | \(-0.106389\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 555.482i | 0.611091i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −604.391 | −0.663437 | −0.331718 | − | 0.943378i | \(-0.607628\pi\) | ||||
−0.331718 | + | 0.943378i | \(0.607628\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1279.26 | 1.40116 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2398.96 | − | 2398.96i | −2.62181 | − | 2.62181i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.74841 | − | 5.74841i | 0.00626871 | − | 0.00626871i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 87.7344 | 0.0954672 | 0.0477336 | − | 0.998860i | \(-0.484800\pi\) | ||||
0.0477336 | + | 0.998860i | \(0.484800\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −429.553 | + | 429.553i | −0.466398 | + | 0.466398i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 143.306 | − | 4.42630i | 0.155261 | − | 0.00479555i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −673.163 | − | 673.163i | −0.727743 | − | 0.727743i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1378.28i | 1.48682i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −72.6596 | − | 72.6596i | −0.0782127 | − | 0.0782127i | 0.666918 | − | 0.745131i | \(-0.267613\pi\) |
−0.745131 | + | 0.666918i | \(0.767613\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −417.164 | + | 417.164i | −0.448082 | + | 0.448082i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 53.2165i | 0.0570381i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1445.07i | 1.54553i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1009.60 | −1.07748 | −0.538738 | − | 0.842473i | \(-0.681099\pi\) | ||||
−0.538738 | + | 0.842473i | \(0.681099\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 303.251 | 0.322951 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 362.860 | + | 362.860i | 0.385611 | + | 0.385611i | 0.873119 | − | 0.487508i | \(-0.162094\pi\) |
−0.487508 | + | 0.873119i | \(0.662094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 675.412 | − | 675.412i | 0.716237 | − | 0.716237i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 34.6433 | 0.0366596 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −359.812 | + | 359.812i | −0.379949 | + | 0.379949i | −0.871084 | − | 0.491134i | \(-0.836582\pi\) |
0.491134 | + | 0.871084i | \(0.336582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.5517 | + | 665.383i | 0.0216562 | + | 0.701141i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1083.25 | + | 1083.25i | 1.13907 | + | 1.13907i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1294.05i | 1.35787i | 0.734198 | + | 0.678935i | \(0.237558\pi\) | ||||
−0.734198 | + | 0.678935i | \(0.762442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1302.26 | + | 1302.26i | 1.36362 | + | 1.36362i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1402.75 | + | 1402.75i | −1.46577 | + | 1.46577i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 0.0711102i | − | 7.41504e-5i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 942.945i | − | 0.981212i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −302.847 | −0.314483 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 673.765 | 0.698202 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −842.215 | − | 842.215i | −0.870957 | − | 0.870957i | 0.121620 | − | 0.992577i | \(-0.461191\pi\) |
−0.992577 | + | 0.121620i | \(0.961191\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 382.916 | − | 382.916i | 0.395166 | − | 0.395166i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1113.43 | 1.14669 | 0.573343 | − | 0.819316i | \(-0.305646\pi\) | ||||
0.573343 | + | 0.819316i | \(0.305646\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.6201 | + | 54.6201i | −0.0561358 | + | 0.0561358i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2013.01 | + | 1892.38i | 2.06462 | + | 1.94090i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −328.248 | − | 328.248i | −0.335975 | − | 0.335975i | 0.518875 | − | 0.854850i | \(-0.326351\pi\) |
−0.854850 | + | 0.518875i | \(0.826351\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1661.72i | − | 1.69736i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −353.285 | − | 353.285i | −0.360127 | − | 0.360127i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −196.292 | + | 196.292i | −0.199687 | + | 0.199687i | −0.799866 | − | 0.600179i | \(-0.795096\pi\) |
0.600179 | + | 0.799866i | \(0.295096\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 596.503i | 0.605586i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 86.5139i | 0.0876534i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1500.41 | −1.51709 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −784.869 | −0.791997 | −0.395998 | − | 0.918251i | \(-0.629601\pi\) | ||||
−0.395998 | + | 0.918251i | \(0.629601\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1219.91 | − | 1219.91i | −1.22851 | − | 1.22851i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 421.330 | − | 421.330i | 0.423447 | − | 0.423447i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 909.188 | 0.911924 | 0.455962 | − | 0.889999i | \(-0.349295\pi\) | ||||
0.455962 | + | 0.889999i | \(0.349295\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −102.449 | + | 102.449i | −0.102551 | + | 0.102551i |
(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 | 208.3.t.d.177.3 | 6 | ||
4.3 | odd | 2 | 52.3.g.a.21.1 | yes | 6 | ||
12.11 | even | 2 | 468.3.m.c.73.3 | 6 | |||
13.5 | odd | 4 | inner | 208.3.t.d.161.3 | 6 | ||
20.3 | even | 4 | 1300.3.k.a.749.1 | 6 | |||
20.7 | even | 4 | 1300.3.k.b.749.3 | 6 | |||
20.19 | odd | 2 | 1300.3.t.a.801.3 | 6 | |||
52.31 | even | 4 | 52.3.g.a.5.1 | ✓ | 6 | ||
52.47 | even | 4 | 676.3.g.b.577.1 | 6 | |||
52.51 | odd | 2 | 676.3.g.b.437.1 | 6 | |||
156.83 | odd | 4 | 468.3.m.c.109.3 | 6 | |||
260.83 | odd | 4 | 1300.3.k.b.1149.1 | 6 | |||
260.187 | odd | 4 | 1300.3.k.a.1149.3 | 6 | |||
260.239 | even | 4 | 1300.3.t.a.1201.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
52.3.g.a.5.1 | ✓ | 6 | 52.31 | even | 4 | ||
52.3.g.a.21.1 | yes | 6 | 4.3 | odd | 2 | ||
208.3.t.d.161.3 | 6 | 13.5 | odd | 4 | inner | ||
208.3.t.d.177.3 | 6 | 1.1 | even | 1 | trivial | ||
468.3.m.c.73.3 | 6 | 12.11 | even | 2 | |||
468.3.m.c.109.3 | 6 | 156.83 | odd | 4 | |||
676.3.g.b.437.1 | 6 | 52.51 | odd | 2 | |||
676.3.g.b.577.1 | 6 | 52.47 | even | 4 | |||
1300.3.k.a.749.1 | 6 | 20.3 | even | 4 | |||
1300.3.k.a.1149.3 | 6 | 260.187 | odd | 4 | |||
1300.3.k.b.749.3 | 6 | 20.7 | even | 4 | |||
1300.3.k.b.1149.1 | 6 | 260.83 | odd | 4 | |||
1300.3.t.a.801.3 | 6 | 20.19 | odd | 2 | |||
1300.3.t.a.1201.3 | 6 | 260.239 | even | 4 |