Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(109,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.bm (of order \(6\), degree \(2\), 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: | \(10.0611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(2.13746 + 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.289 |
Dual form | 1260.2.bm.a.109.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.13746 | + | 0.656712i | −0.955901 | + | 0.293691i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.13746 | + | 2.38876i | 0.429919 | + | 0.902867i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.63746 | − | 4.56821i | −0.795224 | − | 1.37737i | −0.922697 | − | 0.385526i | \(-0.874020\pi\) |
0.127473 | − | 0.991842i | \(-0.459313\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.62685i | − | 0.728557i | −0.931290 | − | 0.364278i | \(-0.881316\pi\) | ||
0.931290 | − | 0.364278i | \(-0.118684\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.362541 | + | 0.209313i | −0.0879292 | + | 0.0507659i | −0.543320 | − | 0.839526i | \(-0.682833\pi\) |
0.455391 | + | 0.890292i | \(0.349500\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.63746 | − | 2.83616i | 0.375659 | − | 0.650660i | −0.614767 | − | 0.788709i | \(-0.710750\pi\) |
0.990425 | + | 0.138049i | \(0.0440831\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.77492 | + | 3.91150i | 1.41267 | + | 0.815604i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.13746 | − | 2.80739i | 0.827492 | − | 0.561478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.27492 | 0.793832 | 0.396916 | − | 0.917855i | \(-0.370080\pi\) | ||||
0.396916 | + | 0.917855i | \(0.370080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.63746 | − | 2.83616i | −0.294096 | − | 0.509390i | 0.680678 | − | 0.732583i | \(-0.261685\pi\) |
−0.974774 | + | 0.223193i | \(0.928352\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | − | 4.35890i | −0.676123 | − | 0.736788i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.63746 | + | 4.98684i | 1.41999 | + | 0.819831i | 0.996297 | − | 0.0859750i | \(-0.0274005\pi\) |
0.423692 | + | 0.905806i | \(0.360734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.72508 | 0.581760 | 0.290880 | − | 0.956760i | \(-0.406052\pi\) | ||||
0.290880 | + | 0.956760i | \(0.406052\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.15068i | 0.327975i | 0.986462 | + | 0.163988i | \(0.0524357\pi\) | ||||
−0.986462 | + | 0.163988i | \(0.947564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.63746 | + | 3.25479i | 0.822308 | + | 0.474760i | 0.851212 | − | 0.524823i | \(-0.175868\pi\) |
−0.0289038 | + | 0.999582i | \(0.509202\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.41238 | + | 5.43424i | −0.630339 | + | 0.776320i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.91238 | + | 2.83616i | −0.674767 | + | 0.389577i | −0.797880 | − | 0.602816i | \(-0.794045\pi\) |
0.123114 | + | 0.992393i | \(0.460712\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.63746 | + | 8.03231i | 1.16467 | + | 1.08308i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.63746 | + | 2.83616i | 0.213179 | + | 0.369237i | 0.952708 | − | 0.303888i | \(-0.0982849\pi\) |
−0.739529 | + | 0.673125i | \(0.764952\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.77492 | − | 11.7345i | 0.867439 | − | 1.50245i | 0.00283468 | − | 0.999996i | \(-0.499098\pi\) |
0.864605 | − | 0.502453i | \(-0.167569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.72508 | + | 5.61478i | 0.213970 | + | 0.696428i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.04983 | − | 1.76082i | 0.372597 | − | 0.215119i | −0.301996 | − | 0.953309i | \(-0.597653\pi\) |
0.674592 | + | 0.738191i | \(0.264319\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.54983 | 0.539966 | 0.269983 | − | 0.962865i | \(-0.412982\pi\) | ||||
0.269983 | + | 0.962865i | \(0.412982\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.63746 | + | 3.25479i | −0.659815 | + | 0.380944i | −0.792206 | − | 0.610253i | \(-0.791068\pi\) |
0.132392 | + | 0.991197i | \(0.457734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.91238 | − | 11.4964i | 0.901699 | − | 1.31014i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.63746 | − | 6.30026i | 0.409246 | − | 0.708835i | −0.585559 | − | 0.810630i | \(-0.699125\pi\) |
0.994805 | + | 0.101795i | \(0.0324584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.40437i | − | 0.812736i | −0.913710 | − | 0.406368i | \(-0.866795\pi\) | ||
0.913710 | − | 0.406368i | \(-0.133205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.637459 | − | 0.685484i | 0.0691421 | − | 0.0743512i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.50000 | − | 6.06218i | 0.370999 | − | 0.642590i | −0.618720 | − | 0.785611i | \(-0.712349\pi\) |
0.989720 | + | 0.143022i | \(0.0456819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.27492 | − | 2.98793i | 0.657790 | − | 0.313220i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.63746 | + | 7.13752i | −0.168000 | + | 0.732294i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.92820i | − | 0.703452i | −0.936103 | − | 0.351726i | \(-0.885595\pi\) | ||
0.936103 | − | 0.351726i | \(-0.114405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.77492 | − | 11.7345i | −0.674129 | − | 1.16763i | −0.976723 | − | 0.214507i | \(-0.931186\pi\) |
0.302593 | − | 0.953120i | \(-0.402148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.77492 | + | 5.64355i | 0.963151 | + | 0.556076i | 0.897141 | − | 0.441743i | \(-0.145640\pi\) |
0.0660098 | + | 0.997819i | \(0.478973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.04983 | + | 1.76082i | 0.294839 | + | 0.170225i | 0.640122 | − | 0.768273i | \(-0.278884\pi\) |
−0.345283 | + | 0.938499i | \(0.612217\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.77492 | − | 10.0025i | −0.553137 | − | 0.958061i | −0.998046 | − | 0.0624852i | \(-0.980097\pi\) |
0.444909 | − | 0.895576i | \(-0.353236\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.30136i | 0.404637i | 0.979320 | + | 0.202319i | \(0.0648477\pi\) | ||||
−0.979320 | + | 0.202319i | \(0.935152\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.0498 | − | 3.91150i | −1.58991 | − | 0.364749i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.912376 | − | 0.627940i | −0.0836374 | − | 0.0575632i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.41238 | + | 14.5707i | −0.764761 | + | 1.32461i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.00000 | + | 8.71780i | −0.626099 | + | 0.779744i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.6460i | − | 1.38836i | −0.719802 | − | 0.694179i | \(-0.755768\pi\) | ||
0.719802 | − | 0.694179i | \(-0.244232\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.36254 | + | 9.28819i | −0.468527 | + | 0.811513i | −0.999353 | − | 0.0359678i | \(-0.988549\pi\) |
0.530826 | + | 0.847481i | \(0.321882\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.63746 | + | 0.685484i | 0.748963 | + | 0.0594390i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.4622 | − | 10.6592i | 1.57733 | − | 0.910674i | 0.582103 | − | 0.813115i | \(-0.302230\pi\) |
0.995230 | − | 0.0975588i | \(-0.0311034\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0997 | −1.11110 | −0.555550 | − | 0.831483i | \(-0.687492\pi\) | ||||
−0.555550 | + | 0.831483i | \(0.687492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0000 | + | 6.92820i | −1.00349 | + | 0.579365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.13746 | + | 2.80739i | −0.758825 | + | 0.233141i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.77492 | − | 6.53835i | 0.309253 | − | 0.535642i | −0.668946 | − | 0.743311i | \(-0.733254\pi\) |
0.978199 | + | 0.207669i | \(0.0665876\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.36254 | + | 11.0202i | 0.517776 | + | 0.896815i | 0.999787 | + | 0.0206494i | \(0.00657337\pi\) |
−0.482011 | + | 0.876165i | \(0.660093\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.36254 | + | 4.98684i | 0.430730 | + | 0.400553i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.91238 | + | 1.10411i | −0.152624 | + | 0.0881176i | −0.574367 | − | 0.818598i | \(-0.694752\pi\) |
0.421743 | + | 0.906715i | \(0.361418\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.63746 | + | 20.6328i | −0.129050 | + | 1.62610i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.91238 | + | 2.83616i | 0.384767 | + | 0.222145i | 0.679890 | − | 0.733314i | \(-0.262027\pi\) |
−0.295123 | + | 0.955459i | \(0.595361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.476171i | 0.0368472i | 0.999830 | + | 0.0184236i | \(0.00586474\pi\) | ||||
−0.999830 | + | 0.0184236i | \(0.994135\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.09967 | 0.469205 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.7371 | − | 10.2405i | −1.34853 | − | 0.778573i | −0.360488 | − | 0.932764i | \(-0.617390\pi\) |
−0.988041 | + | 0.154190i | \(0.950723\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.4124 | + | 6.69012i | 0.862695 | + | 0.505725i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.63746 | + | 6.30026i | 0.271876 | + | 0.470904i | 0.969342 | − | 0.245714i | \(-0.0790225\pi\) |
−0.697466 | + | 0.716618i | \(0.745689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.2749 | −1.80434 | −0.902170 | − | 0.431380i | \(-0.858027\pi\) | ||||
−0.902170 | + | 0.431380i | \(0.858027\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.7371 | − | 4.98684i | −1.59815 | − | 0.366640i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.91238 | + | 1.10411i | 0.139847 | + | 0.0807406i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0876242 | − | 0.151770i | 0.00634026 | − | 0.0109817i | −0.862838 | − | 0.505481i | \(-0.831315\pi\) |
0.869178 | + | 0.494499i | \(0.164648\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.4622 | + | 10.6592i | −1.32894 | + | 0.767263i | −0.985136 | − | 0.171778i | \(-0.945049\pi\) |
−0.343803 | + | 0.939042i | \(0.611715\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.60271i | − | 0.612918i | −0.951884 | − | 0.306459i | \(-0.900856\pi\) | ||
0.951884 | − | 0.306459i | \(-0.0991442\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.63746 | + | 14.9605i | 0.612293 | + | 1.06052i | 0.990853 | + | 0.134946i | \(0.0430861\pi\) |
−0.378560 | + | 0.925577i | \(0.623581\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.86254 | + | 10.2118i | 0.341284 | + | 0.716725i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.96221 | + | 2.44631i | −0.556105 | + | 0.170857i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.2749 | −1.19493 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.6495 | 1.76578 | 0.882892 | − | 0.469576i | \(-0.155593\pi\) | ||||
0.882892 | + | 0.469576i | \(0.155593\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.41238 | − | 4.59698i | −0.0963232 | − | 0.313512i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.91238 | − | 7.13752i | 0.333474 | − | 0.484526i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.549834 | + | 0.952341i | 0.0369859 | + | 0.0640614i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.71780i | 0.583787i | 0.956451 | + | 0.291893i | \(0.0942853\pi\) | ||||
−0.956451 | + | 0.291893i | \(0.905715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9124 | − | 9.76436i | 1.12251 | − | 0.648084i | 0.180472 | − | 0.983580i | \(-0.442237\pi\) |
0.942041 | + | 0.335496i | \(0.108904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.63746 | − | 2.83616i | 0.108206 | − | 0.187419i | −0.806837 | − | 0.590774i | \(-0.798823\pi\) |
0.915044 | + | 0.403355i | \(0.132156\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.3625 | − | 7.13752i | −0.809897 | − | 0.467594i | 0.0370231 | − | 0.999314i | \(-0.488212\pi\) |
−0.846920 | + | 0.531720i | \(0.821546\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.1873 | − | 3.25479i | −0.925477 | − | 0.212319i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.549834 | 0.0355658 | 0.0177829 | − | 0.999842i | \(-0.494339\pi\) | ||||
0.0177829 | + | 0.999842i | \(0.494339\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.91238 | − | 8.50848i | −0.316434 | − | 0.548080i | 0.663307 | − | 0.748347i | \(-0.269152\pi\) |
−0.979741 | + | 0.200267i | \(0.935819\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.86254 | − | 14.5131i | 0.374544 | − | 0.927209i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.45017 | − | 4.30136i | −0.474043 | − | 0.273689i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.5498 | 1.29709 | 0.648547 | − | 0.761175i | \(-0.275377\pi\) | ||||
0.648547 | + | 0.761175i | \(0.275377\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 41.2657i | − | 2.59435i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.0876 | − | 5.82409i | −0.629249 | − | 0.363297i | 0.151212 | − | 0.988501i | \(-0.451682\pi\) |
−0.780461 | + | 0.625204i | \(0.785016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.08762 | + | 26.3052i | −0.129719 | + | 1.63452i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.675248 | − | 0.389855i | 0.0416376 | − | 0.0240395i | −0.479037 | − | 0.877795i | \(-0.659014\pi\) |
0.520674 | + | 0.853755i | \(0.325681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.63746 | − | 9.28819i | 0.530595 | − | 0.570569i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.22508 | + | 12.5142i | 0.440521 | + | 0.763005i | 0.997728 | − | 0.0673687i | \(-0.0214604\pi\) |
−0.557207 | + | 0.830374i | \(0.688127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.91238 | + | 8.50848i | −0.298406 | + | 0.516854i | −0.975771 | − | 0.218793i | \(-0.929788\pi\) |
0.677366 | + | 0.735646i | \(0.263121\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.7371 | − | 11.4964i | −1.43140 | − | 0.693260i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.3625 | − | 7.13752i | 0.742793 | − | 0.428852i | −0.0802909 | − | 0.996771i | \(-0.525585\pi\) |
0.823084 | + | 0.567920i | \(0.192252\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.46221 | + | 5.46301i | −0.562470 | + | 0.324742i | −0.754136 | − | 0.656718i | \(-0.771944\pi\) |
0.191666 | + | 0.981460i | \(0.438611\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.23713 | + | 8.89834i | 0.250110 | + | 0.525252i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.41238 | + | 14.5707i | −0.494846 | + | 0.857098i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.92820i | 0.404750i | 0.979308 | + | 0.202375i | \(0.0648660\pi\) | ||||
−0.979308 | + | 0.202375i | \(0.935134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.36254 | − | 4.98684i | −0.312219 | − | 0.290345i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2749 | − | 17.7967i | 0.594214 | − | 1.02921i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.13746 | + | 2.44631i | −0.296118 | + | 0.141003i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.77492 | + | 29.5312i | −0.387931 | + | 1.69095i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.5145i | 1.51326i | 0.653843 | + | 0.756631i | \(0.273156\pi\) | ||||
−0.653843 | + | 0.756631i | \(0.726844\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.91238 | − | 8.50848i | −0.278555 | − | 0.482472i | 0.692471 | − | 0.721446i | \(-0.256522\pi\) |
−0.971026 | + | 0.238974i | \(0.923189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.0120 | − | 16.7501i | −1.63986 | − | 0.946772i | −0.980881 | − | 0.194609i | \(-0.937656\pi\) |
−0.658977 | − | 0.752163i | \(-0.729010\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.1873 | + | 12.8098i | 1.24616 | + | 0.719472i | 0.970342 | − | 0.241737i | \(-0.0777171\pi\) |
0.275821 | + | 0.961209i | \(0.411050\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.2749 | − | 19.5287i | −0.631274 | − | 1.09340i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.37097i | 0.0762827i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.37459 | − | 10.8685i | −0.409068 | − | 0.602875i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.36254 | + | 17.1687i | −0.0751193 | + | 0.946543i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.91238 | + | 15.4367i | −0.489868 | + | 0.848477i | −0.999932 | − | 0.0116596i | \(-0.996289\pi\) |
0.510064 | + | 0.860137i | \(0.329622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.36254 | + | 5.76655i | −0.292987 | + | 0.315060i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.30136i | − | 0.234310i | −0.993114 | − | 0.117155i | \(-0.962623\pi\) | ||
0.993114 | − | 0.117155i | \(-0.0373774\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.63746 | + | 14.9605i | −0.467745 | + | 0.810157i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0000 | − | 4.35890i | −0.971909 | − | 0.235358i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.5000 | + | 6.06218i | −0.563670 | + | 0.325435i | −0.754617 | − | 0.656165i | \(-0.772177\pi\) |
0.190947 | + | 0.981600i | \(0.438844\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.72508 | 0.199399 | 0.0996996 | − | 0.995018i | \(-0.468212\pi\) | ||||
0.0996996 | + | 0.995018i | \(0.468212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.08762 | − | 4.09204i | 0.377236 | − | 0.217797i | −0.299379 | − | 0.954134i | \(-0.596779\pi\) |
0.676615 | + | 0.736337i | \(0.263446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.72508 | + | 2.98793i | −0.516154 | + | 0.158583i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.1873 | + | 31.5013i | −0.959889 | + | 1.66258i | −0.237127 | + | 0.971479i | \(0.576206\pi\) |
−0.722762 | + | 0.691097i | \(0.757128\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.13746 | + | 7.16629i | 0.217761 | + | 0.377173i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.91238 | − | 10.6592i | 0.518837 | − | 0.557926i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.22508 | + | 3.01670i | −0.272747 | + | 0.157471i | −0.630135 | − | 0.776485i | \(-0.717001\pi\) |
0.357388 | + | 0.933956i | \(0.383667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.3625 | − | 8.50848i | −0.641831 | − | 0.441739i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.63746 | + | 4.98684i | 0.447231 | + | 0.258209i | 0.706660 | − | 0.707553i | \(-0.250201\pi\) |
−0.259429 | + | 0.965762i | \(0.583534\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11.2296i | − | 0.578352i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6495 | 1.11206 | 0.556030 | − | 0.831162i | \(-0.312324\pi\) | ||||
0.556030 | + | 0.831162i | \(0.312324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.32475 | + | 3.07425i | 0.272082 | + | 0.157087i | 0.629833 | − | 0.776730i | \(-0.283123\pi\) |
−0.357751 | + | 0.933817i | \(0.616456\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.36254 | + | 29.7693i | −0.477159 | + | 1.51718i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.1873 | − | 28.0372i | −0.820728 | − | 1.42154i | −0.905141 | − | 0.425112i | \(-0.860235\pi\) |
0.0844123 | − | 0.996431i | \(-0.473099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.27492 | −0.165620 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.63746 | + | 15.8553i | −0.183020 | + | 0.797767i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.36254 | − | 5.40547i | −0.469892 | − | 0.271293i | 0.246302 | − | 0.969193i | \(-0.420784\pi\) |
−0.716195 | + | 0.697901i | \(0.754118\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | − | 2.59808i | 0.0749064 | − | 0.129742i | −0.826139 | − | 0.563466i | \(-0.809468\pi\) |
0.901046 | + | 0.433724i | \(0.142801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.45017 | + | 4.30136i | −0.371119 | + | 0.214266i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 52.6103i | − | 2.60780i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0498 | − | 17.4068i | −0.496932 | − | 0.860712i | 0.503061 | − | 0.864251i | \(-0.332207\pi\) |
−0.999994 | + | 0.00353862i | \(0.998874\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.91238 | + | 7.13752i | −0.241722 | + | 0.351214i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.86254 | + | 15.8265i | 0.238693 | + | 0.776894i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0997 | −0.639961 | −0.319980 | − | 0.947424i | \(-0.603676\pi\) | ||||
−0.319980 | + | 0.947424i | \(0.603676\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.27492 | −0.208347 | −0.104173 | − | 0.994559i | \(-0.533220\pi\) | ||||
−0.104173 | + | 0.994559i | \(0.533220\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.912376 | + | 1.88382i | −0.0442567 | + | 0.0913787i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.7371 | + | 2.83616i | 1.72944 | + | 0.137251i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.18729 | − | 15.9129i | −0.442536 | − | 0.766495i | 0.555341 | − | 0.831623i | \(-0.312588\pi\) |
−0.997877 | + | 0.0651276i | \(0.979255\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1578i | 0.872606i | 0.899800 | + | 0.436303i | \(0.143712\pi\) | ||||
−0.899800 | + | 0.436303i | \(0.856288\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.1873 | − | 12.8098i | 1.06136 | − | 0.612778i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.9124 | − | 20.6328i | 0.568547 | − | 0.984752i | −0.428163 | − | 0.903701i | \(-0.640839\pi\) |
0.996710 | − | 0.0810504i | \(-0.0258275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5000 | + | 6.06218i | 0.498870 | + | 0.288023i | 0.728247 | − | 0.685315i | \(-0.240335\pi\) |
−0.229377 | + | 0.973338i | \(0.573669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.50000 | + | 15.2561i | −0.165916 | + | 0.723211i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.17525 | −0.149849 | −0.0749246 | − | 0.997189i | \(-0.523872\pi\) | ||||
−0.0749246 | + | 0.997189i | \(0.523872\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.82475 | − | 17.0170i | −0.462629 | − | 0.801298i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.4502 | + | 10.5074i | −0.536792 | + | 0.492594i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.18729 | + | 0.685484i | 0.0555392 | + | 0.0320656i | 0.527512 | − | 0.849547i | \(-0.323125\pi\) |
−0.471973 | + | 0.881613i | \(0.656458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.15068i | − | 0.0999505i | −0.998750 | − | 0.0499752i | \(-0.984086\pi\) | ||
0.998750 | − | 0.0499752i | \(-0.0159142\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.5997 | + | 7.85177i | 0.629318 | + | 0.363337i | 0.780488 | − | 0.625171i | \(-0.214971\pi\) |
−0.151170 | + | 0.988508i | \(0.548304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.67525 | + | 5.28247i | 0.354410 | + | 0.243922i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.82475 | − | 5.67232i | 0.451743 | − | 0.260814i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.18729 | − | 16.3315i | −0.0544767 | − | 0.749340i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.91238 | − | 8.50848i | −0.224452 | − | 0.388763i | 0.731703 | − | 0.681624i | \(-0.238726\pi\) |
−0.956155 | + | 0.292861i | \(0.905393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.0997 | − | 22.6893i | 0.597293 | − | 1.03454i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.54983 | + | 14.8087i | 0.206597 | + | 0.672431i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.53779 | − | 1.46519i | 0.114998 | − | 0.0663943i | −0.441398 | − | 0.897312i | \(-0.645517\pi\) |
0.556396 | + | 0.830917i | \(0.312184\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.5498 | 1.28844 | 0.644218 | − | 0.764842i | \(-0.277183\pi\) | ||||
0.644218 | + | 0.764842i | \(0.277183\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.54983 | + | 0.894797i | −0.0698010 | + | 0.0402996i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.17525 | + | 10.8685i | 0.232142 | + | 0.487518i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.812707 | − | 1.40765i | 0.0363818 | − | 0.0630151i | −0.847261 | − | 0.531177i | \(-0.821750\pi\) |
0.883643 | + | 0.468161i | \(0.155083\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.7682i | 1.41647i | 0.705975 | + | 0.708236i | \(0.250509\pi\) | ||||
−0.705975 | + | 0.708236i | \(0.749491\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.1873 | + | 20.6328i | 0.987322 | + | 0.918149i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.22508 | − | 12.5142i | 0.320246 | − | 0.554683i | −0.660293 | − | 0.751008i | \(-0.729568\pi\) |
0.980539 | + | 0.196326i | \(0.0629010\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.1873 | − | 9.76436i | −0.627609 | − | 0.431950i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.5997 | − | 5.64355i | −1.08399 | − | 0.248685i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 34.3375i | − | 1.51016i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.91238 | + | 8.50848i | 0.215215 | + | 0.372763i | 0.953339 | − | 0.301902i | \(-0.0976214\pi\) |
−0.738124 | + | 0.674665i | \(0.764288\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.36254 | + | 3.67341i | 0.278215 | + | 0.160627i | 0.632615 | − | 0.774467i | \(-0.281982\pi\) |
−0.354400 | + | 0.935094i | \(0.615315\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.18729 | + | 0.685484i | 0.0517193 | + | 0.0298602i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0997 | + | 33.0816i | 0.830420 | + | 1.43833i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9.78523i | − | 0.423845i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.67525 | − | 1.76082i | −0.331830 | − | 0.0761270i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.4622 | + | 5.82409i | 1.57054 | + | 0.250861i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.77492 | − | 15.1986i | 0.377263 | − | 0.653439i | −0.613400 | − | 0.789773i | \(-0.710199\pi\) |
0.990663 | + | 0.136334i | \(0.0435319\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.9124 | + | 17.5874i | 0.810117 | + | 0.753360i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.5386i | − | 0.878168i | −0.898446 | − | 0.439084i | \(-0.855303\pi\) | ||
0.898446 | − | 0.439084i | \(-0.144697\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.00000 | − | 12.1244i | 0.298210 | − | 0.516515i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.1873 | + | 1.52274i | 0.815927 | + | 0.0647534i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.63746 | + | 4.98684i | −0.365981 | + | 0.211299i | −0.671701 | − | 0.740822i | \(-0.734436\pi\) |
0.305720 | + | 0.952121i | \(0.401103\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.64950 | 0.238949 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5997 | + | 11.3159i | −0.826028 | + | 0.476907i | −0.852491 | − | 0.522743i | \(-0.824909\pi\) |
0.0264630 | + | 0.999650i | \(0.491576\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.82475 | − | 9.19397i | −0.118838 | − | 0.386793i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.18729 | + | 7.25260i | −0.175540 | + | 0.304045i | −0.940348 | − | 0.340214i | \(-0.889501\pi\) |
0.764808 | + | 0.644259i | \(0.222834\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.63746 | − | 6.30026i | −0.152223 | − | 0.263658i | 0.779821 | − | 0.626002i | \(-0.215310\pi\) |
−0.932044 | + | 0.362344i | \(0.881976\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 39.0120 | − | 2.83616i | 1.62691 | − | 0.118276i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.36254 | + | 1.94136i | −0.139984 | + | 0.0808200i | −0.568357 | − | 0.822782i | \(-0.692421\pi\) |
0.428372 | + | 0.903602i | \(0.359087\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.6873 | − | 8.42217i | 0.733793 | − | 0.349410i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.9124 | + | 14.9605i | 1.07318 | + | 0.619601i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 20.8997i | − | 0.862623i | −0.902203 | − | 0.431311i | \(-0.858051\pi\) | ||
0.902203 | − | 0.431311i | \(-0.141949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.7251 | −0.441919 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.9124 | − | 16.6926i | −1.18729 | − | 0.685482i | −0.229600 | − | 0.973285i | \(-0.573742\pi\) |
−0.957689 | + | 0.287804i | \(0.907075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.36254 | + | 0.743028i | 0.0968548 | + | 0.0304612i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.63746 | − | 4.56821i | −0.107764 | − | 0.186652i | 0.807100 | − | 0.590414i | \(-0.201036\pi\) |
−0.914864 | + | 0.403762i | \(0.867702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.41238 | − | 36.6687i | 0.342012 | − | 1.49079i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.87459 | − | 5.70109i | −0.400797 | − | 0.231400i | 0.286031 | − | 0.958220i | \(-0.407664\pi\) |
−0.686828 | + | 0.726820i | \(0.740997\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.54983 | − | 14.8087i | 0.345889 | − | 0.599098i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.5619 | − | 14.1808i | 0.992045 | − | 0.572757i | 0.0861600 | − | 0.996281i | \(-0.472540\pi\) |
0.905885 | + | 0.423524i | \(0.139207\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.2920i | 1.25977i | 0.776689 | + | 0.629884i | \(0.216898\pi\) | ||||
−0.776689 | + | 0.629884i | \(0.783102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.46221 | − | 7.72877i | −0.179351 | − | 0.310646i | 0.762307 | − | 0.647215i | \(-0.224067\pi\) |
−0.941659 | + | 0.336570i | \(0.890733\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.4622 | + | 1.46519i | 0.739673 | + | 0.0587017i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.23713 | − | 23.2309i | 0.369485 | − | 0.929237i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.17525 | −0.166478 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0997 | 1.31768 | 0.658839 | − | 0.752284i | \(-0.271048\pi\) | ||||
0.658839 | + | 0.752284i | \(0.271048\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.2749 | + | 33.4427i | 0.407748 | + | 1.32713i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.2749 | + | 11.5906i | 0.565593 | + | 0.459238i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.04983 | − | 1.81837i | −0.0414660 | − | 0.0718212i | 0.844548 | − | 0.535481i | \(-0.179869\pi\) |
−0.886014 | + | 0.463659i | \(0.846536\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.4071i | 1.23857i | 0.785164 | + | 0.619287i | \(0.212578\pi\) | ||||
−0.785164 | + | 0.619287i | \(0.787422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.3248 | + | 13.4666i | −0.916991 | + | 0.529425i | −0.882674 | − | 0.469986i | \(-0.844259\pi\) |
−0.0343169 | + | 0.999411i | \(0.510926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.63746 | − | 14.9605i | 0.339050 | − | 0.587252i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.5619 | − | 14.1808i | −0.961181 | − | 0.554938i | −0.0646444 | − | 0.997908i | \(-0.520591\pi\) |
−0.896536 | + | 0.442970i | \(0.853925\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.36254 | − | 23.3748i | 0.209532 | − | 0.913328i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.5498 | −1.57960 | −0.789799 | − | 0.613366i | \(-0.789815\pi\) | ||||
−0.789799 | + | 0.613366i | \(0.789815\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.225083 | + | 0.389855i | 0.00875471 | + | 0.0151636i | 0.870370 | − | 0.492399i | \(-0.163880\pi\) |
−0.861615 | + | 0.507563i | \(0.830547\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.9124 | + | 4.20713i | −0.733390 | + | 0.163145i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.9622 | + | 16.7213i | 1.12142 | + | 0.647453i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −71.4743 | −2.75923 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.2920i | 1.20622i | 0.797659 | + | 0.603109i | \(0.206072\pi\) | ||||
−0.797659 | + | 0.603109i | \(0.793928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.1873 | + | 23.2021i | 1.54452 | + | 0.891731i | 0.998545 | + | 0.0539317i | \(0.0171753\pi\) |
0.545979 | + | 0.837799i | \(0.316158\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.5498 | − | 7.88054i | 0.635124 | − | 0.302428i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.5997 | − | 9.58382i | 0.635169 | − | 0.366715i | −0.147582 | − | 0.989050i | \(-0.547149\pi\) |
0.782751 | + | 0.622335i | \(0.213816\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.4622 | + | 34.9079i | −1.24032 | + | 1.33376i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.45017 | + | 12.9041i | 0.283829 | + | 0.491606i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.1873 | + | 26.3052i | −0.577752 | + | 1.00070i | 0.417985 | + | 0.908454i | \(0.362737\pi\) |
−0.995737 | + | 0.0922416i | \(0.970597\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.0000 | − | 8.60271i | 1.06210 | − | 0.326319i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.35050 | + | 0.779710i | −0.0511537 | + | 0.0295336i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.82475 | −0.333306 | −0.166653 | − | 0.986016i | \(-0.553296\pi\) | ||||
−0.166653 | + | 0.986016i | \(0.553296\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.2870 | − | 16.3315i | 1.06686 | − | 0.615954i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.3248 | − | 29.5312i | 0.764391 | − | 1.11063i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.22508 | + | 9.05011i | −0.196232 | + | 0.339884i | −0.947304 | − | 0.320337i | \(-0.896204\pi\) |
0.751072 | + | 0.660221i | \(0.229537\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 25.6197i | − | 0.959465i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.0997 | − | 22.6893i | 0.789083 | − | 0.848531i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.1873 | − | 26.3052i | 0.566390 | − | 0.981017i | −0.430528 | − | 0.902577i | \(-0.641673\pi\) |
0.996919 | − | 0.0784400i | \(-0.0249939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.36254 | + | 29.7693i | −0.0879856 | + | 1.10867i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.6873 | − | 12.0014i | 0.656890 | − | 0.445719i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.10302i | 0.115085i | 0.998343 | + | 0.0575423i | \(0.0183264\pi\) | ||||
−0.998343 | + | 0.0575423i | \(0.981674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.450166 | − | 0.779710i | −0.0166500 | − | 0.0288386i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.6375 | + | 18.8432i | 1.20549 | + | 0.695991i | 0.961771 | − | 0.273854i | \(-0.0882986\pi\) |
0.243721 | + | 0.969845i | \(0.421632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0876 | − | 9.28819i | −0.592595 | − | 0.342135i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.4622 | − | 18.1211i | −0.384859 | − | 0.666595i | 0.606891 | − | 0.794785i | \(-0.292416\pi\) |
−0.991750 | + | 0.128190i | \(0.959083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.45203i | − | 0.236702i | −0.992972 | − | 0.118351i | \(-0.962239\pi\) | ||
0.992972 | − | 0.118351i | \(-0.0377608\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.77492 | + | 16.4545i | −0.138302 | + | 0.602846i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.737127 | + | 9.28819i | −0.0269341 | + | 0.339383i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.36254 | − | 12.7523i | 0.268663 | − | 0.465338i | −0.699854 | − | 0.714286i | \(-0.746752\pi\) |
0.968517 | + | 0.248948i | \(0.0800849\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.8368 | − | 19.3770i | −0.758329 | − | 0.705200i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.5934i | 1.29366i | 0.762633 | + | 0.646831i | \(0.223906\pi\) | ||||
−0.762633 | + | 0.646831i | \(0.776094\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.4622 | − | 19.8531i | 0.415505 | − | 0.719675i | −0.579977 | − | 0.814633i | \(-0.696938\pi\) |
0.995481 | + | 0.0949578i | \(0.0302716\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.3248 | − | 25.1723i | 0.627198 | − | 0.911298i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.45017 | − | 4.30136i | 0.269010 | − | 0.155313i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.9124 | + | 20.1567i | −1.25571 | + | 0.724985i | −0.972238 | − | 0.233995i | \(-0.924820\pi\) |
−0.283473 | + | 0.958980i | \(0.591487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.7371 | − | 7.13752i | −0.529373 | − | 0.256387i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.09967 | − | 10.5649i | 0.218543 | − | 0.378528i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | − | 20.7846i | −0.429394 | − | 0.743732i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.36254 | − | 3.61587i | 0.120014 | − | 0.129056i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.50000 | + | 0.866025i | −0.0534692 | + | 0.0308705i | −0.526496 | − | 0.850177i | \(-0.676495\pi\) |
0.473027 | + | 0.881048i | \(0.343161\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.2749 | + | 4.89261i | −0.365334 | + | 0.173961i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.8248 | − | 17.7967i | −1.09462 | − | 0.631979i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.8229i | 1.65855i | 0.558839 | + | 0.829276i | \(0.311247\pi\) | ||||
−0.558839 | + | 0.829276i | \(0.688753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.72508 | −0.0964065 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.7371 | + | 17.1687i | 1.04940 | + | 0.605872i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.0498 | − | 45.1772i | −0.354210 | − | 1.59229i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.59967 | + | 14.8951i | 0.302348 | + | 0.523683i | 0.976667 | − | 0.214757i | \(-0.0688961\pi\) |
−0.674319 | + | 0.738440i | \(0.735563\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.45017 | 0.261611 | 0.130805 | − | 0.991408i | \(-0.458244\pi\) | ||||
0.130805 | + | 0.991408i | \(0.458244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.3625 | − | 2.83616i | −0.433041 | − | 0.0993464i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.09967 | + | 3.52165i | 0.213400 | + | 0.123207i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.1873 | + | 17.6449i | −0.355539 | + | 0.615812i | −0.987210 | − | 0.159425i | \(-0.949036\pi\) |
0.631671 | + | 0.775237i | \(0.282369\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.9743 | + | 23.0791i | −1.39341 | + | 0.804488i | −0.993692 | − | 0.112147i | \(-0.964227\pi\) |
−0.399723 | + | 0.916636i | \(0.630894\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.0547i | 0.523505i | 0.965135 | + | 0.261752i | \(0.0843004\pi\) | ||||
−0.965135 | + | 0.261752i | \(0.915700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.4622 | − | 44.1018i | −0.884339 | − | 1.53172i | −0.846469 | − | 0.532438i | \(-0.821276\pi\) |
−0.0378699 | − | 0.999283i | \(-0.512057\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.462210 | − | 2.89371i | 0.0160146 | − | 0.100261i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.312707 | − | 1.01779i | −0.0108217 | − | 0.0352222i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.0997 | 1.41892 | 0.709459 | − | 0.704747i | \(-0.248939\pi\) | ||||
0.709459 | + | 0.704747i | \(0.248939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7251 | −0.369830 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.0378 | + | 4.00573i | −0.448514 | + | 0.137801i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.3746 | − | 3.52165i | −1.52473 | − | 0.121005i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.0120 | + | 67.5708i | 1.33732 | + | 2.31630i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13.1342i | − | 0.449708i | −0.974392 | − | 0.224854i | \(-0.927810\pi\) | ||
0.974392 | − | 0.224854i | \(-0.0721905\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.6375 | + | 18.8432i | −1.11487 | + | 0.643673i | −0.940087 | − | 0.340933i | \(-0.889257\pi\) |
−0.174787 | + | 0.984606i | \(0.555924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.18729 | + | 2.05645i | −0.0405099 | + | 0.0701652i | −0.885569 | − | 0.464507i | \(-0.846232\pi\) |
0.845060 | + | 0.534672i | \(0.179565\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.2251 | + | 8.21286i | 0.484227 | + | 0.279569i | 0.722177 | − | 0.691709i | \(-0.243142\pi\) |
−0.237949 | + | 0.971278i | \(0.576475\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.6375 | + | 10.2405i | 1.51772 | + | 0.348189i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.3746 | −1.30177 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.62541 | − | 8.01145i | −0.156726 | − | 0.271458i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.7870 | − | 6.80521i | −0.973177 | − | 0.230058i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.8127 | + | 11.4389i | 0.669028 | + | 0.386263i | 0.795708 | − | 0.605680i | \(-0.207099\pi\) |
−0.126681 | + | 0.991944i | \(0.540432\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.0241 | 1.44952 | 0.724759 | − | 0.689002i | \(-0.241951\pi\) | ||||
0.724759 | + | 0.689002i | \(0.241951\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 55.5407i | − | 1.86909i | −0.355840 | − | 0.934547i | \(-0.615805\pi\) | ||
0.355840 | − | 0.934547i | \(-0.384195\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.9743 | − | 19.6150i | −1.14074 | − | 0.658609i | −0.194129 | − | 0.980976i | \(-0.562188\pi\) |
−0.946615 | + | 0.322367i | \(0.895521\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.3746 | − | 17.7967i | 1.25350 | − | 0.596881i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.4622 | − | 10.6592i | 0.617814 | − | 0.356695i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.9124 | − | 11.0778i | −0.398187 | − | 0.370290i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.00000 | − | 12.1244i | −0.233463 | − | 0.404370i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.18729 | − | 2.05645i | 0.0395545 | − | 0.0685103i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51.8866 | − | 15.9416i | 1.72477 | − | 0.529918i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.2492 | + | 20.9285i | −1.20363 | + | 0.694918i | −0.961361 | − | 0.275290i | \(-0.911226\pi\) |
−0.242273 | + | 0.970208i | \(0.577893\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.0997 | 0.831589 | 0.415795 | − | 0.909459i | \(-0.363504\pi\) | ||||
0.415795 | + | 0.909459i | \(0.363504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.8248 | + | 19.5287i | −1.11944 | + | 0.646307i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.2870 | − | 2.24490i | −0.934118 | − | 0.0741332i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.4622 | + | 40.6377i | −0.773947 | + | 1.34052i | 0.161438 | + | 0.986883i | \(0.448387\pi\) |
−0.935384 | + | 0.353632i | \(0.884946\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 11.9517i | − | 0.393396i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.7371 | − | 3.61587i | 1.63535 | − | 0.118889i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0498 | − | 41.6555i | 0.789049 | − | 1.36667i | −0.137500 | − | 0.990502i | \(-0.543907\pi\) |
0.926550 | − | 0.376172i | \(-0.122760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.18729 | + | 21.4125i | 0.268328 | + | 0.701768i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.81271 | − | 1.10411i | −0.157392 | − | 0.0361083i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.3638i | 0.795931i | 0.917400 | + | 0.397965i | \(0.130284\pi\) | ||||
−0.917400 | + | 0.397965i | \(0.869716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.63746 | − | 2.83616i | −0.0533796 | − | 0.0924562i | 0.838101 | − | 0.545515i | \(-0.183666\pi\) |
−0.891481 | + | 0.453059i | \(0.850333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.2371 | + | 14.5707i | 0.821834 | + | 0.474486i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.14950 | − | 5.28247i | −0.297319 | − | 0.171657i | 0.343919 | − | 0.938999i | \(-0.388245\pi\) |
−0.641238 | + | 0.767342i | \(0.721579\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.54983 | + | 14.8087i | 0.277539 | + | 0.480712i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.6893i | 0.734978i | 0.930028 | + | 0.367489i | \(0.119782\pi\) | ||||
−0.930028 | + | 0.367489i | \(0.880218\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0876242 | + | 0.381945i | −0.00283545 | + | 0.0123594i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.4622 | + | 31.9775i | 1.50034 | + | 1.03261i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1375 | − | 17.5586i | 0.327015 | − | 0.566406i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.4622 | − | 34.9079i | 1.04500 | − | 1.12372i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.15068i | − | 0.0691611i | −0.999402 | − | 0.0345806i | \(-0.988990\pi\) | ||
0.999402 | − | 0.0345806i | \(-0.0110095\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4622 | + | 31.9775i | −0.592481 | + | 1.02621i | 0.401417 | + | 0.915896i | \(0.368518\pi\) |
−0.993897 | + | 0.110311i | \(0.964815\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.9003 | − | 31.2920i | −0.477683 | − | 1.00318i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.9124 | − | 14.9605i | 0.829010 | − | 0.478629i | −0.0245034 | − | 0.999700i | \(-0.507800\pi\) |
0.853514 | + | 0.521070i | \(0.174467\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.9244 | −1.18011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.7749 | − | 22.9641i | 1.26862 | − | 0.732440i | 0.293895 | − | 0.955838i | \(-0.405048\pi\) |
0.974727 | + | 0.223398i | \(0.0717149\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.64950 | + | 18.3879i | 0.180008 | + | 0.585888i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.41238 | + | 14.5707i | −0.267498 | + | 0.463320i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.7371 | − | 28.9896i | −0.531672 | − | 0.920884i | −0.999316 | − | 0.0369667i | \(-0.988230\pi\) |
0.467644 | − | 0.883917i | \(-0.345103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.2870 | − | 26.3052i | −0.896757 | − | 0.833930i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.362541 | − | 0.209313i | 0.0114818 | − | 0.00662902i | −0.494248 | − | 0.869321i | \(-0.664557\pi\) |
0.505730 | + | 0.862692i | \(0.331223\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1260.2.bm.a.289.1 | 4 | ||
3.2 | odd | 2 | 140.2.q.a.9.2 | ✓ | 4 | ||
5.4 | even | 2 | 1260.2.bm.b.289.2 | 4 | |||
7.4 | even | 3 | 1260.2.bm.b.109.1 | 4 | |||
12.11 | even | 2 | 560.2.bw.e.289.2 | 4 | |||
15.2 | even | 4 | 700.2.i.f.401.3 | 8 | |||
15.8 | even | 4 | 700.2.i.f.401.2 | 8 | |||
15.14 | odd | 2 | 140.2.q.b.9.1 | yes | 4 | ||
21.2 | odd | 6 | 980.2.e.f.589.1 | 4 | |||
21.5 | even | 6 | 980.2.e.c.589.4 | 4 | |||
21.11 | odd | 6 | 140.2.q.b.109.2 | yes | 4 | ||
21.17 | even | 6 | 980.2.q.b.949.1 | 4 | |||
21.20 | even | 2 | 980.2.q.g.569.1 | 4 | |||
35.4 | even | 6 | inner | 1260.2.bm.a.109.1 | 4 | ||
60.59 | even | 2 | 560.2.bw.a.289.1 | 4 | |||
84.11 | even | 6 | 560.2.bw.a.529.2 | 4 | |||
105.2 | even | 12 | 4900.2.a.be.1.1 | 4 | |||
105.23 | even | 12 | 4900.2.a.be.1.3 | 4 | |||
105.32 | even | 12 | 700.2.i.f.501.3 | 8 | |||
105.44 | odd | 6 | 980.2.e.f.589.3 | 4 | |||
105.47 | odd | 12 | 4900.2.a.bf.1.3 | 4 | |||
105.53 | even | 12 | 700.2.i.f.501.2 | 8 | |||
105.59 | even | 6 | 980.2.q.g.949.1 | 4 | |||
105.68 | odd | 12 | 4900.2.a.bf.1.1 | 4 | |||
105.74 | odd | 6 | 140.2.q.a.109.2 | yes | 4 | ||
105.89 | even | 6 | 980.2.e.c.589.2 | 4 | |||
105.104 | even | 2 | 980.2.q.b.569.2 | 4 | |||
420.179 | even | 6 | 560.2.bw.e.529.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.q.a.9.2 | ✓ | 4 | 3.2 | odd | 2 | ||
140.2.q.a.109.2 | yes | 4 | 105.74 | odd | 6 | ||
140.2.q.b.9.1 | yes | 4 | 15.14 | odd | 2 | ||
140.2.q.b.109.2 | yes | 4 | 21.11 | odd | 6 | ||
560.2.bw.a.289.1 | 4 | 60.59 | even | 2 | |||
560.2.bw.a.529.2 | 4 | 84.11 | even | 6 | |||
560.2.bw.e.289.2 | 4 | 12.11 | even | 2 | |||
560.2.bw.e.529.2 | 4 | 420.179 | even | 6 | |||
700.2.i.f.401.2 | 8 | 15.8 | even | 4 | |||
700.2.i.f.401.3 | 8 | 15.2 | even | 4 | |||
700.2.i.f.501.2 | 8 | 105.53 | even | 12 | |||
700.2.i.f.501.3 | 8 | 105.32 | even | 12 | |||
980.2.e.c.589.2 | 4 | 105.89 | even | 6 | |||
980.2.e.c.589.4 | 4 | 21.5 | even | 6 | |||
980.2.e.f.589.1 | 4 | 21.2 | odd | 6 | |||
980.2.e.f.589.3 | 4 | 105.44 | odd | 6 | |||
980.2.q.b.569.2 | 4 | 105.104 | even | 2 | |||
980.2.q.b.949.1 | 4 | 21.17 | even | 6 | |||
980.2.q.g.569.1 | 4 | 21.20 | even | 2 | |||
980.2.q.g.949.1 | 4 | 105.59 | even | 6 | |||
1260.2.bm.a.109.1 | 4 | 35.4 | even | 6 | inner | ||
1260.2.bm.a.289.1 | 4 | 1.1 | even | 1 | trivial | ||
1260.2.bm.b.109.1 | 4 | 7.4 | even | 3 | |||
1260.2.bm.b.289.2 | 4 | 5.4 | even | 2 | |||
4900.2.a.be.1.1 | 4 | 105.2 | even | 12 | |||
4900.2.a.be.1.3 | 4 | 105.23 | even | 12 | |||
4900.2.a.bf.1.1 | 4 | 105.68 | odd | 12 | |||
4900.2.a.bf.1.3 | 4 | 105.47 | odd | 12 |