Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.10 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.b.1609.22 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.45456 | − | 1.69831i | 0.650497 | − | 0.759509i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.243187i | − | 0.0919159i | −0.998943 | − | 0.0459580i | \(-0.985366\pi\) | ||
0.998943 | − | 0.0459580i | \(-0.0146340\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.348249 | 0.105001 | 0.0525005 | − | 0.998621i | \(-0.483281\pi\) | ||||
0.0525005 | + | 0.998621i | \(0.483281\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62829i | 0.728955i | 0.931212 | + | 0.364478i | \(0.118752\pi\) | ||||
−0.931212 | + | 0.364478i | \(0.881248\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.69831 | − | 1.45456i | −0.438502 | − | 0.375565i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.29103i | 0.313121i | 0.987668 | + | 0.156561i | \(0.0500406\pi\) | ||||
−0.987668 | + | 0.156561i | \(0.949959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.36602 | 0.313386 | 0.156693 | − | 0.987647i | \(-0.449917\pi\) | ||||
0.156693 | + | 0.987647i | \(0.449917\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.243187 | −0.0530677 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.600572i | − | 0.125228i | −0.998038 | − | 0.0626140i | \(-0.980056\pi\) | ||
0.998038 | − | 0.0626140i | \(-0.0199437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.768532 | − | 4.94058i | −0.153706 | − | 0.988117i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.99937 | −0.742664 | −0.371332 | − | 0.928500i | \(-0.621099\pi\) | ||||
−0.371332 | + | 0.928500i | \(0.621099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.23948 | −0.581827 | −0.290914 | − | 0.956749i | \(-0.593959\pi\) | ||||
−0.290914 | + | 0.956749i | \(0.593959\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.348249i | − | 0.0606223i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.413007 | − | 0.353729i | −0.0698109 | − | 0.0597910i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.96539i | − | 1.30950i | −0.755845 | − | 0.654751i | \(-0.772773\pi\) | ||
0.755845 | − | 0.654751i | \(-0.227227\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.62829 | 0.420863 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.27937 | 0.355978 | 0.177989 | − | 0.984032i | \(-0.443041\pi\) | ||||
0.177989 | + | 0.984032i | \(0.443041\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.24187i | − | 1.25687i | −0.777860 | − | 0.628437i | \(-0.783695\pi\) | ||
0.777860 | − | 0.628437i | \(-0.216305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.45456 | + | 1.69831i | −0.216832 | + | 0.253170i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.05568i | − | 1.32091i | −0.750867 | − | 0.660454i | \(-0.770364\pi\) | ||
0.750867 | − | 0.660454i | \(-0.229636\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.94086 | 0.991551 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.29103 | 0.180781 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.5701i | − | 1.45192i | −0.687738 | − | 0.725959i | \(-0.741396\pi\) | ||
0.687738 | − | 0.725959i | \(-0.258604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.506548 | − | 0.591435i | 0.0683029 | − | 0.0797491i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.36602i | − | 0.180933i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00319 | 0.781549 | 0.390775 | − | 0.920486i | \(-0.372207\pi\) | ||||
0.390775 | + | 0.920486i | \(0.372207\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.78086 | −0.484090 | −0.242045 | − | 0.970265i | \(-0.577818\pi\) | ||||
−0.242045 | + | 0.970265i | \(0.577818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.243187i | 0.0306386i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.46365 | + | 3.82299i | 0.553648 | + | 0.474184i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.600572 | −0.0723004 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.45872 | −0.529152 | −0.264576 | − | 0.964365i | \(-0.585232\pi\) | ||||
−0.264576 | + | 0.964365i | \(0.585232\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.87821i | − | 1.03912i | −0.854435 | − | 0.519558i | \(-0.826097\pi\) | ||
0.854435 | − | 0.519558i | \(-0.173903\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.94058 | + | 0.768532i | −0.570489 | + | 0.0887425i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.0846895i | − | 0.00965126i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.2980 | −1.83367 | −0.916837 | − | 0.399263i | \(-0.869266\pi\) | ||||
−0.916837 | + | 0.399263i | \(0.869266\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.3876i | 1.14019i | 0.821580 | + | 0.570093i | \(0.193093\pi\) | ||||
−0.821580 | + | 0.570093i | \(0.806907\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.19257 | + | 1.87788i | 0.237818 | + | 0.203684i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.99937i | 0.428777i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.64400 | 0.916262 | 0.458131 | − | 0.888885i | \(-0.348519\pi\) | ||||
0.458131 | + | 0.888885i | \(0.348519\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.639164 | 0.0670026 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.23948i | 0.335918i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.98695 | − | 2.31992i | 0.203857 | − | 0.238019i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.828410i | 0.0841123i | 0.999115 | + | 0.0420562i | \(0.0133908\pi\) | ||||
−0.999115 | + | 0.0420562i | \(0.986609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.348249 | −0.0350003 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.67000 | −0.365178 | −0.182589 | − | 0.983189i | \(-0.558448\pi\) | ||||
−0.182589 | + | 0.983189i | \(0.558448\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 18.2295i | − | 1.79620i | −0.439788 | − | 0.898102i | \(-0.644946\pi\) | ||
0.439788 | − | 0.898102i | \(-0.355054\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.353729 | + | 0.413007i | −0.0345204 | + | 0.0403053i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 19.0797i | − | 1.84450i | −0.386590 | − | 0.922252i | \(-0.626347\pi\) | ||
0.386590 | − | 0.922252i | \(-0.373653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.89028 | 0.755752 | 0.377876 | − | 0.925856i | \(-0.376655\pi\) | ||||
0.377876 | + | 0.925856i | \(0.376655\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.96539 | −0.756041 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.54739i | 0.521854i | 0.965359 | + | 0.260927i | \(0.0840282\pi\) | ||||
−0.965359 | + | 0.260927i | \(0.915972\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.01996 | − | 0.873566i | −0.0951117 | − | 0.0814604i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.62829i | − | 0.242985i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.313962 | 0.0287808 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8787 | −0.988975 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 2.27937i | − | 0.205524i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.50853 | − | 5.88115i | −0.850469 | − | 0.526026i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.3276i | − | 1.00516i | −0.864530 | − | 0.502581i | \(-0.832384\pi\) | ||
0.864530 | − | 0.502581i | \(-0.167616\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.24187 | −0.725657 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.32162 | −0.727064 | −0.363532 | − | 0.931582i | \(-0.618429\pi\) | ||||
−0.363532 | + | 0.931582i | \(0.618429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.332197i | − | 0.0288051i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.69831 | + | 1.45456i | 0.146167 | + | 0.125188i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.4140i | 1.14603i | 0.819544 | + | 0.573016i | \(0.194227\pi\) | ||||
−0.819544 | + | 0.573016i | \(0.805773\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2582 | −1.12454 | −0.562272 | − | 0.826952i | \(-0.690073\pi\) | ||||
−0.562272 | + | 0.826952i | \(0.690073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.05568 | −0.762626 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.915298i | 0.0765410i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.81731 | + | 6.79218i | −0.483101 | + | 0.564060i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 6.94086i | − | 0.572473i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.1304 | 1.64914 | 0.824572 | − | 0.565757i | \(-0.191416\pi\) | ||||
0.824572 | + | 0.565757i | \(0.191416\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.0072 | 1.87230 | 0.936150 | − | 0.351602i | \(-0.114363\pi\) | ||||
0.936150 | + | 0.351602i | \(0.114363\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.29103i | − | 0.104374i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.71200 | + | 5.50164i | −0.378477 | + | 0.441903i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.04826i | 0.163469i | 0.996654 | + | 0.0817345i | \(0.0260460\pi\) | ||||
−0.996654 | + | 0.0817345i | \(0.973954\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.5701 | −0.838266 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.146051 | −0.0115104 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8378i | 0.848880i | 0.905456 | + | 0.424440i | \(0.139529\pi\) | ||||
−0.905456 | + | 0.424440i | \(0.860471\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.591435 | − | 0.506548i | −0.0460432 | − | 0.0394347i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.7540i | 1.21908i | 0.792755 | + | 0.609541i | \(0.208646\pi\) | ||||
−0.792755 | + | 0.609541i | \(0.791354\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.09211 | 0.468624 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.36602 | −0.104462 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.79373i | 0.744604i | 0.928112 | + | 0.372302i | \(0.121431\pi\) | ||||
−0.928112 | + | 0.372302i | \(0.878569\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.20148 | + | 0.186897i | −0.0908236 | + | 0.0141281i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.00319i | − | 0.451228i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.38131 | −0.402218 | −0.201109 | − | 0.979569i | \(-0.564455\pi\) | ||||
−0.201109 | + | 0.979569i | \(0.564455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.76426 | −0.279796 | −0.139898 | − | 0.990166i | \(-0.544677\pi\) | ||||
−0.139898 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.78086i | 0.279490i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.5277 | − | 11.5861i | −0.994578 | − | 0.851828i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.449600i | 0.0328780i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.243187 | 0.0176892 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.6591 | −1.63956 | −0.819778 | − | 0.572682i | \(-0.805903\pi\) | ||||
−0.819778 | + | 0.572682i | \(0.805903\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 2.56499i | − | 0.184632i | −0.995730 | − | 0.0923160i | \(-0.970573\pi\) | ||
0.995730 | − | 0.0923160i | \(-0.0294270\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.82299 | − | 4.46365i | 0.273770 | − | 0.319649i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.115117i | 0.00820173i | 0.999992 | + | 0.00410087i | \(0.00130535\pi\) | ||||
−0.999992 | + | 0.00410087i | \(0.998695\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.63561 | 0.541274 | 0.270637 | − | 0.962681i | \(-0.412766\pi\) | ||||
0.270637 | + | 0.962681i | \(0.412766\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.972593i | 0.0682626i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.31547 | − | 3.87109i | 0.231563 | − | 0.270368i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.600572i | 0.0417426i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.475714 | 0.0329058 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.669505 | 0.0460906 | 0.0230453 | − | 0.999734i | \(-0.492664\pi\) | ||||
0.0230453 | + | 0.999734i | \(0.492664\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.45872i | 0.305506i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.9973 | − | 11.9883i | −0.954607 | − | 0.817593i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.787797i | 0.0534792i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.87821 | −0.599934 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.39320 | −0.228251 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.2148i | 1.75547i | 0.479144 | + | 0.877736i | \(0.340947\pi\) | ||||
−0.479144 | + | 0.877736i | \(0.659053\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.768532 | + | 4.94058i | 0.0512355 | + | 0.329372i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 14.2115i | − | 0.943248i | −0.881800 | − | 0.471624i | \(-0.843668\pi\) | ||
0.881800 | − | 0.471624i | \(-0.156332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.41350 | 0.423816 | 0.211908 | − | 0.977290i | \(-0.432032\pi\) | ||||
0.211908 | + | 0.977290i | \(0.432032\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0846895 | −0.00557216 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.2402i | 0.736372i | 0.929752 | + | 0.368186i | \(0.120021\pi\) | ||||
−0.929752 | + | 0.368186i | \(0.879979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.3794 | − | 13.1720i | −1.00324 | − | 0.859247i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.2980i | 1.05867i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.7654 | 0.696354 | 0.348177 | − | 0.937429i | \(-0.386801\pi\) | ||||
0.348177 | + | 0.937429i | \(0.386801\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.229596 | −0.0147896 | −0.00739478 | − | 0.999973i | \(-0.502354\pi\) | ||||
−0.00739478 | + | 0.999973i | \(0.502354\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.0959 | − | 11.7878i | 0.645002 | − | 0.753092i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.59028i | 0.228444i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.3876 | 0.658287 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.71115 | −0.360484 | −0.180242 | − | 0.983622i | \(-0.557688\pi\) | ||||
−0.180242 | + | 0.983622i | \(0.557688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.209149i | − | 0.0131491i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.87788 | − | 2.19257i | 0.117597 | − | 0.137304i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.8726i | 0.802968i | 0.915866 | + | 0.401484i | \(0.131506\pi\) | ||||
−0.915866 | + | 0.401484i | \(0.868494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.93708 | −0.120364 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.99937 | 0.247555 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 21.7586i | − | 1.34169i | −0.741598 | − | 0.670845i | \(-0.765932\pi\) | ||
0.741598 | − | 0.670845i | \(-0.234068\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.9514 | − | 15.3748i | −1.10274 | − | 0.944469i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.64400i | − | 0.529004i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.9686 | −1.88819 | −0.944096 | − | 0.329672i | \(-0.893062\pi\) | ||||
−0.944096 | + | 0.329672i | \(0.893062\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.6020 | 1.12999 | 0.564996 | − | 0.825094i | \(-0.308878\pi\) | ||||
0.564996 | + | 0.825094i | \(0.308878\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.639164i | − | 0.0386840i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.267641 | − | 1.72055i | −0.0161393 | − | 0.103753i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.97556i | 0.298952i | 0.988765 | + | 0.149476i | \(0.0477587\pi\) | ||||
−0.988765 | + | 0.149476i | \(0.952241\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.23948 | 0.193942 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.6486 | 0.635242 | 0.317621 | − | 0.948218i | \(-0.397116\pi\) | ||||
0.317621 | + | 0.948218i | \(0.397116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.1137i | − | 1.19563i | −0.801633 | − | 0.597817i | \(-0.796035\pi\) | ||
0.801633 | − | 0.597817i | \(-0.203965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.31992 | − | 1.98695i | −0.137420 | − | 0.117697i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.554313i | − | 0.0327200i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.3332 | 0.901955 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.828410 | 0.0485623 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.53165i | − | 0.323163i | −0.986859 | − | 0.161581i | \(-0.948341\pi\) | ||
0.986859 | − | 0.161581i | \(-0.0516594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.73198 | − | 10.1953i | 0.508396 | − | 0.593593i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.348249i | 0.0202074i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.57847 | 0.0912856 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00431 | −0.115527 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.67000i | 0.210836i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.49948 | + | 6.42109i | −0.314899 | + | 0.367671i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 30.4742i | − | 1.73926i | −0.493708 | − | 0.869628i | \(-0.664359\pi\) | ||
0.493708 | − | 0.869628i | \(-0.335641\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.2295 | −1.03704 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.1197 | −1.36770 | −0.683851 | − | 0.729622i | \(-0.739696\pi\) | ||||
−0.683851 | + | 0.729622i | \(0.739696\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.01994i | 0.170697i | 0.996351 | + | 0.0853485i | \(0.0272004\pi\) | ||||
−0.996351 | + | 0.0853485i | \(0.972800\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.413007 | + | 0.353729i | 0.0232703 | + | 0.0199303i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.4860i | 1.93693i | 0.249158 | + | 0.968463i | \(0.419846\pi\) | ||||
−0.249158 | + | 0.968463i | \(0.580154\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.39278 | −0.0779804 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.0797 | −1.06492 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.76357i | 0.0981277i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.9853 | − | 2.01992i | 0.720293 | − | 0.112045i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7.89028i | − | 0.436334i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.20222 | −0.121412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.2865 | −1.11505 | −0.557523 | − | 0.830162i | \(-0.688248\pi\) | ||||
−0.557523 | + | 0.830162i | \(0.688248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.96539i | 0.436501i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.69831 | + | 1.45456i | 0.0927887 | + | 0.0794709i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.7605i | − | 0.967474i | −0.875213 | − | 0.483737i | \(-0.839279\pi\) | ||
0.875213 | − | 0.483737i | \(-0.160721\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.54739 | 0.301293 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.12814 | −0.0610924 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.39023i | − | 0.183055i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.873566 | + | 1.01996i | −0.0470312 | + | 0.0549128i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 5.05750i | − | 0.271501i | −0.990743 | − | 0.135750i | \(-0.956655\pi\) | ||
0.990743 | − | 0.135750i | \(-0.0433446\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.9805 | 0.855415 | 0.427707 | − | 0.903917i | \(-0.359321\pi\) | ||||
0.427707 | + | 0.903917i | \(0.359321\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.62829 | −0.140288 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.2131i | 1.07583i | 0.842998 | + | 0.537916i | \(0.180788\pi\) | ||||
−0.842998 | + | 0.537916i | \(0.819212\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.48545 | + | 7.57230i | −0.344212 | + | 0.401896i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.313962i | − | 0.0166166i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.11759 | 0.0589840 | 0.0294920 | − | 0.999565i | \(-0.490611\pi\) | ||||
0.0294920 | + | 0.999565i | \(0.490611\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1340 | −0.901789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8787i | 0.570985i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.0780 | − | 12.9139i | −0.789217 | − | 0.675942i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.5732i | − | 0.865113i | −0.901607 | − | 0.432556i | \(-0.857612\pi\) | ||
0.901607 | − | 0.432556i | \(-0.142388\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.27937 | −0.118659 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.57051 | −0.133454 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 11.1433i | − | 0.576977i | −0.957483 | − | 0.288489i | \(-0.906847\pi\) | ||
0.957483 | − | 0.288489i | \(-0.0931527\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.88115 | + | 9.50853i | −0.303701 | + | 0.491018i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 10.5115i | − | 0.541369i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.3738 | 1.71430 | 0.857148 | − | 0.515070i | \(-0.172234\pi\) | ||||
0.857148 | + | 0.515070i | \(0.172234\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3276 | −0.580330 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 14.6887i | − | 0.750557i | −0.926912 | − | 0.375279i | \(-0.877547\pi\) | ||
0.926912 | − | 0.375279i | \(-0.122453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.143829 | − | 0.123186i | −0.00733021 | − | 0.00627812i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.24187i | 0.418958i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.7047 | 1.81030 | 0.905149 | − | 0.425094i | \(-0.139759\pi\) | ||||
0.905149 | + | 0.425094i | \(0.139759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.775357 | 0.0392115 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.32162i | 0.419770i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.7064 | + | 27.6792i | −1.19280 | + | 1.39269i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 19.8878i | − | 0.998139i | −0.866562 | − | 0.499070i | \(-0.833675\pi\) | ||
0.866562 | − | 0.499070i | \(-0.166325\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.332197 | −0.0166307 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.0058 | 1.59829 | 0.799147 | − | 0.601136i | \(-0.205285\pi\) | ||||
0.799147 | + | 0.601136i | \(0.205285\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.51427i | − | 0.424126i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.45456 | − | 1.69831i | 0.0722775 | − | 0.0843898i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.77394i | − | 0.137499i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5485 | 0.867715 | 0.433858 | − | 0.900981i | \(-0.357152\pi\) | ||||
0.433858 | + | 0.900981i | \(0.357152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.4140 | 0.661662 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.45990i | − | 0.0718368i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.6414 | + | 15.1093i | 0.865981 | + | 0.741688i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.2582i | 0.649256i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.89826 | −0.483562 | −0.241781 | − | 0.970331i | \(-0.577731\pi\) | ||||
−0.241781 | + | 0.970331i | \(0.577731\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.12038 | −0.103341 | −0.0516705 | − | 0.998664i | \(-0.516455\pi\) | ||||
−0.0516705 | + | 0.998664i | \(0.516455\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.05568i | 0.440302i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.37845 | − | 0.992199i | 0.309400 | − | 0.0481287i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.919456i | 0.0444956i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.915298 | 0.0441910 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.5843 | −0.895173 | −0.447587 | − | 0.894241i | \(-0.647716\pi\) | ||||
−0.447587 | + | 0.894241i | \(0.647716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.8648i | 1.29104i | 0.763743 | + | 0.645520i | \(0.223359\pi\) | ||||
−0.763743 | + | 0.645520i | \(0.776641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.79218 | + | 5.81731i | 0.325660 | + | 0.278918i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.820392i | − | 0.0392447i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5212 | −0.597606 | −0.298803 | − | 0.954315i | \(-0.596587\pi\) | ||||
−0.298803 | + | 0.954315i | \(0.596587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.94086 | −0.330517 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 18.2936i | − | 0.869155i | −0.900634 | − | 0.434578i | \(-0.856898\pi\) | ||
0.900634 | − | 0.434578i | \(-0.143102\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.5732 | − | 14.6802i | 0.596026 | − | 0.695909i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 20.1304i | − | 0.952134i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.7717 | −0.791505 | −0.395752 | − | 0.918357i | \(-0.629516\pi\) | ||||
−0.395752 | + | 0.918357i | \(0.629516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.793789 | 0.0373780 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 23.0072i | − | 1.08097i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.929700 | − | 1.08550i | 0.0435850 | − | 0.0508890i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 34.3782i | − | 1.60815i | −0.594531 | − | 0.804073i | \(-0.702662\pi\) | ||
0.594531 | − | 0.804073i | \(-0.297338\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.29103 | −0.0602602 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.5010 | −1.65344 | −0.826722 | − | 0.562610i | \(-0.809797\pi\) | ||||
−0.826722 | + | 0.562610i | \(0.809797\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.2881i | 0.571079i | 0.958367 | + | 0.285539i | \(0.0921727\pi\) | ||||
−0.958367 | + | 0.285539i | \(0.907827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.50164 | + | 4.71200i | 0.255133 | + | 0.218514i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.76116i | 0.405418i | 0.979239 | + | 0.202709i | \(0.0649746\pi\) | ||||
−0.979239 | + | 0.202709i | \(0.935025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.243187 | 0.0112293 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.04826 | 0.0943789 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.87022i | − | 0.131973i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.04983 | − | 6.74892i | −0.0481694 | − | 0.309662i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.5701i | 0.483973i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.8588 | −1.22721 | −0.613604 | − | 0.789614i | \(-0.710281\pi\) | ||||
−0.613604 | + | 0.789614i | \(0.710281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.9353 | 0.954569 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.146051i | 0.00664555i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.40690 | + | 1.20497i | 0.0638840 | + | 0.0547148i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.2493i | 1.09884i | 0.835547 | + | 0.549419i | \(0.185151\pi\) | ||||
−0.835547 | + | 0.549419i | \(0.814849\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.8378 | 0.490101 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.62812 | −0.163735 | −0.0818675 | − | 0.996643i | \(-0.526088\pi\) | ||||
−0.0818675 | + | 0.996643i | \(0.526088\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.16331i | − | 0.232544i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.506548 | + | 0.591435i | −0.0227676 | + | 0.0265830i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.08430i | 0.0486375i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.73744 | −0.301609 | −0.150805 | − | 0.988564i | \(-0.548186\pi\) | ||||
−0.150805 | + | 0.988564i | \(0.548186\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.7540 | 0.703837 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.52703i | 0.424789i | 0.977184 | + | 0.212395i | \(0.0681262\pi\) | ||||
−0.977184 | + | 0.212395i | \(0.931874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.33822 | + | 6.23280i | −0.237548 | + | 0.277356i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 6.09211i | − | 0.270560i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.5611 | 0.645408 | 0.322704 | − | 0.946500i | \(-0.395408\pi\) | ||||
0.322704 | + | 0.946500i | \(0.395408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.15906 | −0.0955113 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.36602i | 0.0603111i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −30.9593 | − | 26.5158i | −1.36423 | − | 1.16843i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.15363i | − | 0.138697i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.79373 | 0.429897 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0602 | 1.05410 | 0.527048 | − | 0.849836i | \(-0.323299\pi\) | ||||
0.527048 | + | 0.849836i | \(0.323299\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.8445i | 0.998919i | 0.866337 | + | 0.499460i | \(0.166468\pi\) | ||||
−0.866337 | + | 0.499460i | \(0.833532\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.186897 | + | 1.20148i | 0.00815684 | + | 0.0524370i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.18227i | − | 0.182182i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.6393 | 0.984318 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00319 | −0.260516 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.99084i | 0.259492i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.4033 | − | 27.7525i | −1.40092 | − | 1.19984i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.38131i | 0.232221i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.41715 | 0.104114 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.8419 | 1.66994 | 0.834971 | − | 0.550294i | \(-0.185484\pi\) | ||||
0.834971 | + | 0.550294i | \(0.185484\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.76426i | 0.161540i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.4769 | − | 13.4002i | 0.491615 | − | 0.574000i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.4692i | − | 1.08899i | −0.838765 | − | 0.544493i | \(-0.816722\pi\) | ||
0.838765 | − | 0.544493i | \(-0.183278\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.78086 | 0.161363 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.46321 | −0.232740 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.96347i | 0.168544i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.5861 | + | 13.5277i | −0.491803 | + | 0.574220i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 5.56886i | − | 0.235960i | −0.993016 | − | 0.117980i | \(-0.962358\pi\) | ||
0.993016 | − | 0.117980i | \(-0.0376419\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.6620 | 0.916205 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.449600 | 0.0189821 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 3.52200i | − | 0.148435i | −0.997242 | − | 0.0742173i | \(-0.976354\pi\) | ||
0.997242 | − | 0.0742173i | \(-0.0236458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.42120 | + | 8.06898i | 0.396353 | + | 0.339465i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.243187i | − | 0.0102129i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.7892 | 0.536151 | 0.268076 | − | 0.963398i | \(-0.413612\pi\) | ||||
0.268076 | + | 0.963398i | \(0.413612\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0643 | 1.34185 | 0.670924 | − | 0.741526i | \(-0.265898\pi\) | ||||
0.670924 | + | 0.741526i | \(0.265898\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.6591i | 0.946598i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.96718 | + | 0.461559i | −0.123740 | + | 0.0192483i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 7.73038i | − | 0.321820i | −0.986969 | − | 0.160910i | \(-0.948557\pi\) | ||
0.986969 | − | 0.160910i | \(-0.0514428\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.56499 | −0.106597 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.52612 | 0.104801 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.68104i | − | 0.152453i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.46365 | − | 3.82299i | −0.184549 | − | 0.158061i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.7972i | 1.35368i | 0.736128 | + | 0.676842i | \(0.236652\pi\) | ||||
−0.736128 | + | 0.676842i | \(0.763348\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.42518 | −0.182336 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.115117 | 0.00473527 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.1119i | 0.702702i | 0.936244 | + | 0.351351i | \(0.114278\pi\) | ||||
−0.936244 | + | 0.351351i | \(0.885722\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.456675 | − | 0.533205i | 0.0187218 | − | 0.0218593i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 7.63561i | − | 0.312505i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.88400 | 0.403849 | 0.201925 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201925 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.34260 | 0.340302 | 0.170151 | − | 0.985418i | \(-0.445575\pi\) | ||||
0.170151 | + | 0.985418i | \(0.445575\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.00000i | − | 0.0407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.8237 | + | 18.4755i | −0.643325 | + | 0.751135i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.58194i | − | 0.388919i | −0.980911 | − | 0.194460i | \(-0.937705\pi\) | ||
0.980911 | − | 0.194460i | \(-0.0622953\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.972593 | 0.0394114 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.8009 | 0.962882 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 43.4482i | − | 1.75486i | −0.479709 | − | 0.877428i | \(-0.659258\pi\) | ||
0.479709 | − | 0.877428i | \(-0.340742\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.87109 | − | 3.31547i | −0.156097 | − | 0.133693i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.09240i | 0.245271i | 0.992452 | + | 0.122635i | \(0.0391346\pi\) | ||||
−0.992452 | + | 0.122635i | \(0.960865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0361608 | −0.00145343 | −0.000726713 | − | 1.00000i | \(-0.500231\pi\) | ||||
−0.000726713 | 1.00000i | \(0.500231\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.600572 | 0.0241001 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.10210i | − | 0.0842190i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.8187 | + | 7.59400i | −0.952749 | + | 0.303760i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 0.475714i | − | 0.0189982i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.2836 | 0.410033 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0856 | −1.59578 | −0.797890 | − | 0.602802i | \(-0.794051\pi\) | ||||
−0.797890 | + | 0.602802i | \(0.794051\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 0.669505i | − | 0.0266104i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.2378 | − | 16.4766i | −0.763429 | − | 0.653855i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.2426i | 0.722797i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.45872 | 0.176384 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.1783 | −1.82393 | −0.911967 | − | 0.410263i | \(-0.865437\pi\) | ||||
−0.911967 | + | 0.410263i | \(0.865437\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.4979i | 0.966104i | 0.875592 | + | 0.483052i | \(0.160472\pi\) | ||||
−0.875592 | + | 0.483052i | \(0.839528\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.9883 | + | 13.9973i | −0.472038 | + | 0.551142i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.6660i | 1.48080i | 0.672166 | + | 0.740401i | \(0.265364\pi\) | ||||
−0.672166 | + | 0.740401i | \(0.734636\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.09061 | 0.0820634 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.787797 | 0.0308762 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.1227i | 0.513530i | 0.966474 | + | 0.256765i | \(0.0826566\pi\) | ||||
−0.966474 | + | 0.256765i | \(0.917343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.1043 | + | 14.1327i | −0.472953 | + | 0.552211i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.87821i | 0.346372i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.7196 | 0.885029 | 0.442514 | − | 0.896761i | \(-0.354087\pi\) | ||||
0.442514 | + | 0.896761i | \(0.354087\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.6427 | 1.81419 | 0.907095 | − | 0.420926i | \(-0.138295\pi\) | ||||
0.907095 | + | 0.420926i | \(0.138295\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.39320i | 0.131781i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.564175 | − | 0.483199i | −0.0218778 | − | 0.0187377i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.40191i | 0.0930023i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.2148 | 1.01352 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.31668 | −0.0508299 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3729i | 0.631129i | 0.948904 | + | 0.315565i | \(0.102194\pi\) | ||||
−0.948904 | + | 0.315565i | \(0.897806\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.94058 | − | 0.768532i | 0.190163 | − | 0.0295808i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.1803i | 0.890893i | 0.895309 | + | 0.445446i | \(0.146955\pi\) | ||||
−0.895309 | + | 0.445446i | \(0.853045\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.201458 | 0.00773126 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.2115 | −0.544585 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 9.81125i | − | 0.375417i | −0.982225 | − | 0.187709i | \(-0.939894\pi\) | ||
0.982225 | − | 0.187709i | \(-0.0601060\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.7811 | + | 19.5114i | 0.870421 | + | 0.745491i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6.41350i | − | 0.244690i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.7813 | 1.05838 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.8801 | 0.604107 | 0.302054 | − | 0.953291i | \(-0.402328\pi\) | ||||
0.302054 | + | 0.953291i | \(0.402328\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0846895i | 0.00321709i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.2848 | + | 22.5165i | −0.731513 | + | 0.854101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.94274i | 0.111464i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.2402 | 0.425145 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.7019 | 1.08405 | 0.542027 | − | 0.840361i | \(-0.317657\pi\) | ||||
0.542027 | + | 0.840361i | \(0.317657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 10.8809i | − | 0.410380i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.1720 | + | 15.3794i | −0.496086 | + | 0.579221i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.892494i | 0.0335657i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.0371 | 1.35340 | 0.676702 | − | 0.736257i | \(-0.263409\pi\) | ||||
0.676702 | + | 0.736257i | \(0.263409\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.2980 | 0.611224 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.94554i | 0.0728610i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.55446 | + | 1.33135i | 0.0581336 | + | 0.0497897i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 10.7654i | − | 0.402040i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.8888 | 0.406084 | 0.203042 | − | 0.979170i | \(-0.434917\pi\) | ||||
0.203042 | + | 0.979170i | \(0.434917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.43316 | −0.165100 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.229596i | 0.00853876i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.07364 | + | 19.7592i | 0.114152 | + | 0.733839i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.1718i | 0.488515i | 0.969710 | + | 0.244258i | \(0.0785443\pi\) | ||||
−0.969710 | + | 0.244258i | \(0.921456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.6405 | 0.393554 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 8.79199i | − | 0.324740i | −0.986730 | − | 0.162370i | \(-0.948086\pi\) | ||
0.986730 | − | 0.162370i | \(-0.0519138\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.7878 | − | 10.0959i | −0.434798 | − | 0.372392i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.348249i | 0.0128279i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.8812 | 1.79813 | 0.899063 | − | 0.437819i | \(-0.144249\pi\) | ||||
0.899063 | + | 0.437819i | \(0.144249\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.59028 | 0.131892 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.5643i | 1.26804i | 0.773316 | + | 0.634021i | \(0.218597\pi\) | ||||
−0.773316 | + | 0.634021i | \(0.781403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.2808 | − | 34.1877i | 1.07276 | − | 1.25254i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 10.3876i | − | 0.380062i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.63993 | −0.169539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.8582 | −1.85584 | −0.927921 | − | 0.372776i | \(-0.878406\pi\) | ||||
−0.927921 | + | 0.372776i | \(0.878406\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.71115i | 0.208126i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.4653 | − | 39.0734i | 1.21793 | − | 1.42203i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0671i | 0.547621i | 0.961784 | + | 0.273811i | \(0.0882842\pi\) | ||||
−0.961784 | + | 0.273811i | \(0.911716\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.209149 | −0.00759161 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.8857 | −1.11961 | −0.559803 | − | 0.828626i | \(-0.689123\pi\) | ||||
−0.559803 | + | 0.828626i | \(0.689123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.91881i | − | 0.0694656i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.19257 | − | 1.87788i | −0.0792727 | − | 0.0678948i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.7781i | 0.569715i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.7448 | 0.856258 | 0.428129 | − | 0.903718i | \(-0.359173\pi\) | ||||
0.428129 | + | 0.903718i | \(0.359173\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.8726 | 0.463594 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.2043i | 0.690730i | 0.938469 | + | 0.345365i | \(0.112245\pi\) | ||||
−0.938469 | + | 0.345365i | \(0.887755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.48964 | + | 16.0049i | 0.0894306 | + | 0.574913i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.93708i | 0.0694922i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.11366 | 0.111559 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.55274 | −0.0555615 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.99937i | − | 0.142926i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.47859 | + | 2.97931i | 0.124156 | + | 0.106336i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.5866i | 0.769478i | 0.923025 | + | 0.384739i | \(0.125709\pi\) | ||||
−0.923025 | + | 0.384739i | \(0.874291\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.7586 | −0.774625 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.34905 | 0.0479667 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9.93719i | − | 0.352880i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.3748 | + | 17.9514i | −0.545290 | + | 0.636670i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 0.628606i | − | 0.0222664i | −0.999938 | − | 0.0111332i | \(-0.996456\pi\) | ||
0.999938 | − | 0.0111332i | \(-0.00354388\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.6912 | 0.413604 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.64400 | −0.305421 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 3.09183i | − | 0.109108i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.212439 | + | 0.248040i | −0.00748751 | + | 0.00874228i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.9686i | 1.09015i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.66456 | −0.234314 | −0.117157 | − | 0.993113i | \(-0.537378\pi\) | ||||
−0.117157 | + | 0.993113i | \(0.537378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.1579 | 0.532266 | 0.266133 | − | 0.963936i | \(-0.414254\pi\) | ||||
0.266133 | + | 0.963936i | \(0.414254\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 18.6020i | − | 0.652401i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.4059 | + | 15.7642i | 0.644732 | + | 0.552194i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 11.2585i | − | 0.393887i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.639164 | −0.0223342 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.66243 | −0.127820 | −0.0639099 | − | 0.997956i | \(-0.520357\pi\) | ||||
−0.0639099 | + | 0.997956i | \(0.520357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.5049i | − | 1.13305i | −0.824044 | − | 0.566526i | \(-0.808287\pi\) | ||
0.824044 | − | 0.566526i | \(-0.191713\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.72055 | + | 0.267641i | −0.0599019 | + | 0.00931805i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.2718i | − | 0.391958i | −0.980608 | − | 0.195979i | \(-0.937212\pi\) | ||
0.980608 | − | 0.195979i | \(-0.0627884\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.7842 | 1.41649 | 0.708247 | − | 0.705965i | \(-0.249487\pi\) | ||||
0.708247 | + | 0.705965i | \(0.249487\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.97556 | 0.172600 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.96087i | 0.310476i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.7552 | + | 22.9151i | 0.925903 | + | 0.793009i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3.23948i | − | 0.111973i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.6090 | −0.953170 | −0.476585 | − | 0.879129i | \(-0.658125\pi\) | ||||
−0.476585 | + | 0.879129i | \(0.658125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0051 | −0.448450 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 10.6486i | − | 0.366757i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.86132 | − | 10.3463i | 0.304839 | − | 0.355924i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.64556i | 0.0909025i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.1137 | −0.690299 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.78379 | −0.163986 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.4575i | 0.358056i | 0.983844 | + | 0.179028i | \(0.0572953\pi\) | ||||
−0.983844 | + | 0.179028i | \(0.942705\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.98695 | + | 2.31992i | −0.0679522 | + | 0.0793398i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.36756i | 0.0467149i | 0.999727 | + | 0.0233574i | \(0.00743558\pi\) | ||||
−0.999727 | + | 0.0233574i | \(0.992564\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.6188 | 1.11294 | 0.556470 | − | 0.830868i | \(-0.312156\pi\) | ||||
0.556470 | + | 0.830868i | \(0.312156\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.554313 | −0.0188909 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 17.9528i | − | 0.611119i | −0.952173 | − | 0.305559i | \(-0.901157\pi\) | ||
0.952173 | − | 0.305559i | \(-0.0988435\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6328 | + | 14.2455i | 0.565533 | + | 0.484363i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 15.3332i | − | 0.520744i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.67577 | −0.192537 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.62829 | −0.0890561 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.828410i | − | 0.0280374i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.43022 | + | 2.31235i | −0.0483501 | + | 0.0781716i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.5206i | 1.60466i | 0.596884 | + | 0.802328i | \(0.296405\pi\) | ||||
−0.596884 | + | 0.802328i | \(0.703595\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.53165 | −0.186578 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.2506 | 0.581189 | 0.290594 | − | 0.956846i | \(-0.406147\pi\) | ||||
0.290594 | + | 0.956846i | \(0.406147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2789i | 0.413218i | 0.978424 | + | 0.206609i | \(0.0662428\pi\) | ||||
−0.978424 | + | 0.206609i | \(0.933757\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.1953 | − | 8.73198i | −0.342711 | − | 0.293522i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.2768i | 0.445792i | 0.974842 | + | 0.222896i | \(0.0715510\pi\) | ||||
−0.974842 | + | 0.222896i | \(0.928449\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.75472 | −0.0923904 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.348249 | 0.0116668 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 12.3702i | − | 0.413954i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.82742 | + | 9.13915i | −0.261642 | + | 0.305488i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.57847i | − | 0.0527037i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.9559 | 0.432102 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.6464 | 0.454626 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.00431i | 0.0666994i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.47533 | + | 6.39290i | −0.182006 | + | 0.212507i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 26.5941i | − | 0.883043i | −0.897251 | − | 0.441521i | \(-0.854439\pi\) | ||
0.897251 | − | 0.441521i | \(-0.145561\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.67000 | 0.121726 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3603 | 0.343253 | 0.171627 | − | 0.985162i | \(-0.445098\pi\) | ||||
0.171627 | + | 0.985162i | \(0.445098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.61747i | 0.119721i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.42109 | + | 5.49948i | 0.212275 | + | 0.181807i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.02371i | 0.0668287i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.2996 | 0.702610 | 0.351305 | − | 0.936261i | \(-0.385738\pi\) | ||||
0.351305 | + | 0.936261i | \(0.385738\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.4742 | −1.00416 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 11.7188i | − | 0.385728i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.3537 | + | 6.12166i | −1.29394 | + | 0.201279i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.2295i | 0.598734i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.73373 | 0.220927 | 0.110463 | − | 0.993880i | \(-0.464767\pi\) | ||||
0.110463 | + | 0.993880i | \(0.464767\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.48134 | 0.310738 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.1197i | 0.789643i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.763562 | + | 0.653969i | 0.0249711 | + | 0.0213871i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.0134i | 1.82988i | 0.403592 | + | 0.914939i | \(0.367761\pi\) | ||||
−0.403592 | + | 0.914939i | \(0.632239\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.01994 | 0.0985520 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.54236 | 0.148077 | 0.0740384 | − | 0.997255i | \(-0.476411\pi\) | ||||
0.0740384 | + | 0.997255i | \(0.476411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.36893i | − | 0.0445784i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.353729 | − | 0.413007i | 0.0115068 | − | 0.0134351i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.5803i | 0.831247i | 0.909537 | + | 0.415623i | \(0.136437\pi\) | ||||
−0.909537 | + | 0.415623i | \(0.863563\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.3345 | 0.757469 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.4860 | 1.11828 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.2314i | 1.20604i | 0.797725 | + | 0.603022i | \(0.206037\pi\) | ||||
−0.797725 | + | 0.603022i | \(0.793963\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.9589 | + | 38.4822i | −1.06653 | + | 1.24526i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.39278i | 0.0450220i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.26210 | 0.105339 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5058 | −0.661477 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.0797i | 0.614835i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.35616 | − | 3.73092i | −0.140230 | − | 0.120103i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 36.0430i | − | 1.15907i | −0.814949 | − | 0.579533i | \(-0.803235\pi\) | ||
0.814949 | − | 0.579533i | \(-0.196765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.76357 | 0.0566541 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.3875 | −1.36028 | −0.680140 | − | 0.733082i | \(-0.738081\pi\) | ||||
−0.680140 | + | 0.733082i | \(0.738081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.22421i | 0.103363i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.01992 | − | 12.9853i | −0.0646893 | − | 0.415861i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.1608i | 1.25286i | 0.779476 | + | 0.626432i | \(0.215485\pi\) | ||||
−0.779476 | + | 0.626432i | \(0.784515\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.01026 | 0.0962084 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.89028 | −0.251917 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 20.7388i | − | 0.661466i | −0.943724 | − | 0.330733i | \(-0.892704\pi\) | ||
0.943724 | − | 0.330733i | \(-0.107296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.195504 | + | 0.167444i | 0.00622929 | + | 0.00533520i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.20222i | 0.0700975i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.94984 | −0.157396 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.90436 | 0.0922601 | 0.0461301 | − | 0.998935i | \(-0.485311\pi\) | ||||
0.0461301 | + | 0.998935i | \(0.485311\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.2865i | 0.643772i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.1064 | − | 12.9677i | 0.352097 | − | 0.411102i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.01155i | 0.285399i | 0.989766 | + | 0.142699i | \(0.0455782\pi\) | ||||
−0.989766 | + | 0.142699i | \(0.954422\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.96539 | 0.252014 |
(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 | 4020.2.g.b.1609.10 | ✓ | 24 | |
5.4 | even | 2 | inner | 4020.2.g.b.1609.22 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.b.1609.10 | ✓ | 24 | 1.1 | even | 1 | trivial | |
4020.2.g.b.1609.22 | yes | 24 | 5.4 | even | 2 | inner |