Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,3,Mod(31,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.h (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.97549476762\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 95.3 | ||
Character | \(\chi\) | \(=\) | 256.95 |
Dual form | 256.3.h.a.159.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.10785 | + | 2.67458i | −0.369282 | + | 0.891526i | 0.624586 | + | 0.780956i | \(0.285268\pi\) |
−0.993868 | + | 0.110570i | \(0.964732\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.95565 | − | 7.13556i | −0.591129 | − | 1.42711i | −0.882413 | − | 0.470475i | \(-0.844083\pi\) |
0.291284 | − | 0.956637i | \(-0.405917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.18452 | + | 4.18452i | 0.597788 | + | 0.597788i | 0.939723 | − | 0.341935i | \(-0.111082\pi\) |
−0.341935 | + | 0.939723i | \(0.611082\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.437918 | + | 0.437918i | 0.0486575 | + | 0.0486575i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.42655 | + | 3.44399i | 0.129686 | + | 0.313090i | 0.975363 | − | 0.220605i | \(-0.0708031\pi\) |
−0.845677 | + | 0.533695i | \(0.820803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.39996 | + | 20.2793i | −0.646151 | + | 1.55995i | 0.172096 | + | 0.985080i | \(0.444946\pi\) |
−0.818247 | + | 0.574866i | \(0.805054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 22.3590 | 1.49060 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73115i | 0.101832i | 0.998703 | + | 0.0509161i | \(0.0162141\pi\) | ||||
−0.998703 | + | 0.0509161i | \(0.983786\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.2459 | + | 5.90085i | 0.749785 | + | 0.310571i | 0.724654 | − | 0.689113i | \(-0.242000\pi\) |
0.0251314 | + | 0.999684i | \(0.492000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −15.8276 | + | 6.55601i | −0.753696 | + | 0.312191i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.1565 | + | 15.1565i | −0.658979 | + | 0.658979i | −0.955139 | − | 0.296159i | \(-0.904294\pi\) |
0.296159 | + | 0.955139i | \(0.404294\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.5027 | + | 24.5027i | −0.980107 | + | 0.980107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −25.7276 | + | 10.6567i | −0.952874 | + | 0.394693i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.74107 | + | 2.79224i | 0.232451 | + | 0.0962842i | 0.495869 | − | 0.868398i | \(-0.334850\pi\) |
−0.263418 | + | 0.964682i | \(0.584850\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.1695i | 1.00547i | 0.864442 | + | 0.502733i | \(0.167672\pi\) | ||||
−0.864442 | + | 0.502733i | \(0.832328\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.7916 | −0.327019 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.4909 | − | 42.2268i | 0.499740 | − | 1.20648i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.30038 | − | 12.7962i | −0.143253 | − | 0.345844i | 0.835926 | − | 0.548843i | \(-0.184931\pi\) |
−0.979179 | + | 0.202998i | \(0.934931\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −44.9327 | − | 44.9327i | −1.15212 | − | 1.15212i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.5776 | − | 18.5776i | −0.453111 | − | 0.453111i | 0.443275 | − | 0.896386i | \(-0.353817\pi\) |
−0.896386 | + | 0.443275i | \(0.853817\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.0691 | + | 75.0074i | 0.722537 | + | 1.74436i | 0.665993 | + | 0.745958i | \(0.268008\pi\) |
0.0565443 | + | 0.998400i | \(0.481992\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.83046 | − | 4.41911i | 0.0406768 | − | 0.0982026i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16.2824 | 0.346435 | 0.173217 | − | 0.984884i | \(-0.444584\pi\) | ||||
0.173217 | + | 0.984884i | \(0.444584\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 13.9797i | − | 0.285299i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.63009 | − | 1.91784i | −0.0907860 | − | 0.0376048i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 29.0670 | − | 12.0399i | 0.548434 | − | 0.227169i | −0.0912216 | − | 0.995831i | \(-0.529077\pi\) |
0.639655 | + | 0.768662i | \(0.279077\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.3584 | − | 20.3584i | 0.370153 | − | 0.370153i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −31.5646 | + | 31.5646i | −0.553765 | + | 0.553765i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34.1002 | − | 14.1248i | 0.577969 | − | 0.239403i | −0.0744962 | − | 0.997221i | \(-0.523735\pi\) |
0.652465 | + | 0.757819i | \(0.273735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 68.7647 | + | 28.4833i | 1.12729 | + | 0.466939i | 0.866859 | − | 0.498553i | \(-0.166135\pi\) |
0.260432 | + | 0.965492i | \(0.416135\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.66495i | 0.0581737i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 169.531 | 2.60818 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5147 | − | 25.3846i | 0.156935 | − | 0.378875i | −0.825782 | − | 0.563990i | \(-0.809266\pi\) |
0.982717 | + | 0.185115i | \(0.0592657\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −23.7462 | − | 57.3284i | −0.344148 | − | 0.830847i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 32.2012 | + | 32.2012i | 0.453538 | + | 0.453538i | 0.896527 | − | 0.442989i | \(-0.146082\pi\) |
−0.442989 | + | 0.896527i | \(0.646082\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −28.5494 | − | 28.5494i | −0.391088 | − | 0.391088i | 0.483987 | − | 0.875075i | \(-0.339188\pi\) |
−0.875075 | + | 0.483987i | \(0.839188\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −38.3891 | − | 92.6796i | −0.511855 | − | 1.23573i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.44203 | + | 20.3809i | −0.109637 | + | 0.264686i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −22.4049 | −0.283606 | −0.141803 | − | 0.989895i | \(-0.545290\pi\) | ||||
−0.141803 | + | 0.989895i | \(0.545290\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 75.0427i | − | 0.926453i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −123.286 | − | 51.0669i | −1.48538 | − | 0.615264i | −0.515073 | − | 0.857146i | \(-0.672235\pi\) |
−0.970306 | + | 0.241882i | \(0.922235\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.3527 | − | 5.11665i | 0.145326 | − | 0.0601959i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.9361 | + | 14.9361i | −0.171680 | + | 0.171680i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 61.0281 | − | 61.0281i | 0.685709 | − | 0.685709i | −0.275572 | − | 0.961280i | \(-0.588867\pi\) |
0.961280 | + | 0.275572i | \(0.0888672\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −120.009 | + | 49.7093i | −1.31878 | + | 0.546256i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −83.3652 | − | 34.5310i | −0.896400 | − | 0.371301i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 119.093i | − | 1.25362i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −69.9064 | −0.720684 | −0.360342 | − | 0.932820i | \(-0.617340\pi\) | ||||
−0.360342 | + | 0.932820i | \(0.617340\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.883474 | + | 2.13290i | −0.00892398 | + | 0.0215444i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4825 | + | 25.3069i | 0.103787 | + | 0.250564i | 0.967239 | − | 0.253867i | \(-0.0817025\pi\) |
−0.863452 | + | 0.504431i | \(0.831702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −116.721 | − | 116.721i | −1.13322 | − | 1.13322i | −0.989639 | − | 0.143579i | \(-0.954139\pi\) |
−0.143579 | − | 0.989639i | \(-0.545861\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 93.5616 | + | 93.5616i | 0.891063 | + | 0.891063i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −21.6236 | − | 52.2039i | −0.202090 | − | 0.487887i | 0.790047 | − | 0.613046i | \(-0.210056\pi\) |
−0.992137 | + | 0.125159i | \(0.960056\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 28.8284 | − | 69.5980i | 0.264481 | − | 0.638514i | −0.734725 | − | 0.678366i | \(-0.762689\pi\) |
0.999206 | + | 0.0398518i | \(0.0126886\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 40.0965 | 0.361230 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 130.141i | 1.15169i | 0.817559 | + | 0.575845i | \(0.195327\pi\) | ||||
−0.817559 | + | 0.575845i | \(0.804673\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 152.948 | + | 63.3530i | 1.32998 | + | 0.550895i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.5592 | + | 5.20217i | −0.107343 | + | 0.0444630i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.24401 | + | 7.24401i | −0.0608740 | + | 0.0608740i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 75.7339 | − | 75.7339i | 0.625900 | − | 0.625900i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 70.2682 | − | 29.1060i | 0.571286 | − | 0.236635i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 68.8726 | + | 28.5280i | 0.550981 | + | 0.228224i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 56.3580i | 0.443764i | 0.975074 | + | 0.221882i | \(0.0712200\pi\) | ||||
−0.975074 | + | 0.221882i | \(0.928780\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −235.033 | −1.82196 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −39.2631 | + | 94.7895i | −0.299718 | + | 0.723584i | 0.700235 | + | 0.713912i | \(0.253079\pi\) |
−0.999953 | + | 0.00967128i | \(0.996921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34.9201 | + | 84.3045i | 0.262557 | + | 0.633868i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 152.083 | + | 152.083i | 1.12654 | + | 1.12654i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 62.6423 | + | 62.6423i | 0.457243 | + | 0.457243i | 0.897750 | − | 0.440506i | \(-0.145201\pi\) |
−0.440506 | + | 0.897750i | \(0.645201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6343 | + | 28.0877i | 0.0837000 | + | 0.202070i | 0.960188 | − | 0.279353i | \(-0.0901201\pi\) |
−0.876488 | + | 0.481423i | \(0.840120\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.0384 | + | 43.5487i | −0.127932 | + | 0.308856i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −81.8247 | −0.572201 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 56.3542i | − | 0.388649i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 37.3897 | + | 15.4873i | 0.254352 | + | 0.105356i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 52.6977 | − | 21.8281i | 0.353676 | − | 0.146497i | −0.198770 | − | 0.980046i | \(-0.563695\pi\) |
0.552446 | + | 0.833549i | \(0.313695\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 48.5998 | − | 48.5998i | 0.321853 | − | 0.321853i | −0.527625 | − | 0.849478i | \(-0.676917\pi\) |
0.849478 | + | 0.527625i | \(0.176917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.758099 | + | 0.758099i | −0.00495490 | + | 0.00495490i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 222.412 | − | 92.1259i | 1.43491 | − | 0.594361i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −121.622 | − | 50.3774i | −0.774661 | − | 0.320875i | −0.0399023 | − | 0.999204i | \(-0.512705\pi\) |
−0.734759 | + | 0.678328i | \(0.762705\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 91.0803i | 0.572832i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −126.845 | −0.787860 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.0161 | + | 31.4236i | −0.0798533 | + | 0.192783i | −0.958764 | − | 0.284203i | \(-0.908271\pi\) |
0.878911 | + | 0.476986i | \(0.158271\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 31.8962 | + | 77.0043i | 0.193310 | + | 0.466692i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 138.734 | + | 138.734i | 0.830744 | + | 0.830744i | 0.987619 | − | 0.156875i | \(-0.0501419\pi\) |
−0.156875 | + | 0.987619i | \(0.550142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −221.190 | − | 221.190i | −1.30881 | − | 1.30881i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.65445 | + | 8.82263i | 0.0213711 | + | 0.0515943i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 69.7574 | − | 168.409i | 0.403222 | − | 0.973464i | −0.583656 | − | 0.812001i | \(-0.698379\pi\) |
0.986879 | − | 0.161464i | \(-0.0516215\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −205.064 | −1.17179 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 106.852i | 0.603682i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 45.0027 | + | 18.6407i | 0.251411 | + | 0.104138i | 0.504830 | − | 0.863219i | \(-0.331555\pi\) |
−0.253419 | + | 0.967357i | \(0.581555\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −118.928 | + | 49.2615i | −0.657060 | + | 0.272163i | −0.686201 | − | 0.727412i | \(-0.740723\pi\) |
0.0291408 | + | 0.999575i | \(0.490723\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −152.362 | + | 152.362i | −0.832577 | + | 0.832577i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −75.6423 | + | 75.6423i | −0.408877 | + | 0.408877i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.96206 | + | 2.46956i | −0.0318827 | + | 0.0132062i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −152.251 | − | 63.0643i | −0.805559 | − | 0.333674i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 179.282i | − | 0.938649i | −0.883026 | − | 0.469325i | \(-0.844497\pi\) | ||
0.883026 | − | 0.469325i | \(-0.155503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 179.924 | 0.932249 | 0.466125 | − | 0.884719i | \(-0.345650\pi\) | ||||
0.466125 | + | 0.884719i | \(0.345650\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −187.815 | + | 453.425i | −0.963153 | + | 2.32526i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 93.2938 | + | 225.231i | 0.473573 | + | 1.14331i | 0.962573 | + | 0.271022i | \(0.0873617\pi\) |
−0.489000 | + | 0.872284i | \(0.662638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 131.782 | + | 131.782i | 0.662220 | + | 0.662220i | 0.955903 | − | 0.293683i | \(-0.0948810\pi\) |
−0.293683 | + | 0.955903i | \(0.594881\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 56.2446 | + | 56.2446i | 0.279824 | + | 0.279824i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.5239 | + | 39.8923i | 0.0813987 | + | 0.196514i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −77.6526 | + | 187.470i | −0.378793 | + | 0.914487i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.2746 | −0.0641286 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 57.4807i | 0.275027i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −182.694 | − | 75.6743i | −0.865848 | − | 0.358646i | −0.0948559 | − | 0.995491i | \(-0.530239\pi\) |
−0.770992 | + | 0.636845i | \(0.780239\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −121.799 | + | 50.4506i | −0.571824 | + | 0.236857i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 443.391 | − | 443.391i | 2.06228 | − | 2.06228i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −130.429 | + | 130.429i | −0.601056 | + | 0.601056i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 107.986 | − | 44.7293i | 0.493087 | − | 0.204243i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −35.1064 | − | 14.5416i | −0.158853 | − | 0.0657989i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 175.414i | 0.786612i | 0.919408 | + | 0.393306i | \(0.128669\pi\) | ||||
−0.919408 | + | 0.393306i | \(0.871331\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.4603 | −0.0953792 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 157.825 | − | 381.024i | 0.695265 | − | 1.67852i | −0.0386277 | − | 0.999254i | \(-0.512299\pi\) |
0.733893 | − | 0.679265i | \(-0.237701\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −57.0597 | − | 137.754i | −0.249169 | − | 0.601547i | 0.748965 | − | 0.662610i | \(-0.230551\pi\) |
−0.998134 | + | 0.0610623i | \(0.980551\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −45.1577 | − | 45.1577i | −0.195488 | − | 0.195488i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 275.512 | + | 275.512i | 1.18246 | + | 1.18246i | 0.979106 | + | 0.203349i | \(0.0651826\pi\) |
0.203349 | + | 0.979106i | \(0.434817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −48.1251 | − | 116.184i | −0.204788 | − | 0.494401i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.8212 | − | 59.9236i | 0.104731 | − | 0.252842i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 63.0374 | 0.263755 | 0.131877 | − | 0.991266i | \(-0.457899\pi\) | ||||
0.131877 | + | 0.991266i | \(0.457899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 194.368i | 0.806507i | 0.915088 | + | 0.403253i | \(0.132121\pi\) | ||||
−0.915088 | + | 0.403253i | \(0.867879\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −30.8408 | − | 12.7747i | −0.126917 | − | 0.0525708i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −99.7526 | + | 41.3189i | −0.407154 | + | 0.168649i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −239.330 | + | 239.330i | −0.968949 | + | 0.968949i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 273.165 | − | 273.165i | 1.09705 | − | 1.09705i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −317.091 | + | 131.343i | −1.26331 | + | 0.523281i | −0.910924 | − | 0.412574i | \(-0.864630\pi\) |
−0.352387 | + | 0.935854i | \(0.614630\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −73.8205 | − | 30.5774i | −0.291781 | − | 0.120859i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 38.7067i | 0.151791i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −180.756 | −0.703330 | −0.351665 | − | 0.936126i | \(-0.614384\pi\) | ||||
−0.351665 | + | 0.936126i | \(0.614384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.3666 | − | 75.7256i | 0.121106 | − | 0.292377i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.72926 | + | 4.17480i | 0.00662552 | + | 0.0159954i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −266.626 | − | 266.626i | −1.01379 | − | 1.01379i | −0.999904 | − | 0.0138830i | \(-0.995581\pi\) |
−0.0138830 | − | 0.999904i | \(-0.504419\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −171.823 | − | 171.823i | −0.648390 | − | 0.648390i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 95.6146 | + | 230.834i | 0.358107 | + | 0.864547i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 156.911 | − | 378.816i | 0.583311 | − | 1.40824i | −0.306483 | − | 0.951876i | \(-0.599152\pi\) |
0.889794 | − | 0.456362i | \(-0.150848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 323.931 | 1.19532 | 0.597659 | − | 0.801750i | \(-0.296098\pi\) | ||||
0.597659 | + | 0.801750i | \(0.296098\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 376.043i | − | 1.37745i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −119.341 | − | 49.4328i | −0.433969 | − | 0.179756i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 289.883 | − | 120.073i | 1.04651 | − | 0.433478i | 0.207864 | − | 0.978158i | \(-0.433349\pi\) |
0.838644 | + | 0.544680i | \(0.183349\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.6497 | + | 13.6497i | −0.0489235 | + | 0.0489235i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 297.826 | − | 297.826i | 1.05988 | − | 1.05988i | 0.0617901 | − | 0.998089i | \(-0.480319\pi\) |
0.998089 | − | 0.0617901i | \(-0.0196809\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −132.389 | + | 54.8372i | −0.467804 | + | 0.193771i | −0.604118 | − | 0.796895i | \(-0.706474\pi\) |
0.136314 | + | 0.990666i | \(0.456474\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 318.525 | + | 131.937i | 1.11763 | + | 0.462938i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 155.476i | − | 0.541729i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 286.003 | 0.989630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 77.4455 | − | 186.970i | 0.266136 | − | 0.642509i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.1180 | − | 43.7407i | −0.0618361 | − | 0.149286i | 0.889941 | − | 0.456075i | \(-0.150745\pi\) |
−0.951777 | + | 0.306790i | \(0.900745\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −201.576 | − | 201.576i | −0.683309 | − | 0.683309i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −73.4033 | − | 73.4033i | −0.247149 | − | 0.247149i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −180.050 | − | 434.678i | −0.602172 | − | 1.45377i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −183.861 | + | 443.879i | −0.610833 | + | 1.47468i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −79.2984 | −0.261711 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 574.861i | − | 1.88479i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 532.332 | + | 220.499i | 1.73398 | + | 0.718239i | 0.999202 | + | 0.0399320i | \(0.0127141\pi\) |
0.734779 | + | 0.678307i | \(0.237286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 441.490 | − | 182.871i | 1.42877 | − | 0.591816i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −383.582 | + | 383.582i | −1.23338 | + | 1.23338i | −0.270725 | + | 0.962657i | \(0.587263\pi\) |
−0.962657 | + | 0.270725i | \(0.912737\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −362.165 | + | 362.165i | −1.15708 | + | 1.15708i | −0.171974 | + | 0.985101i | \(0.555015\pi\) |
−0.985101 | + | 0.171974i | \(0.944985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.1514 | − | 10.8323i | 0.0830204 | − | 0.0343882i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 487.277 | + | 201.837i | 1.53715 | + | 0.636709i | 0.980936 | − | 0.194329i | \(-0.0622529\pi\) |
0.556215 | + | 0.831038i | \(0.312253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.1995i | 0.0852648i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 163.579 | 0.509592 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.2152 | + | 24.6618i | −0.0316261 | + | 0.0763523i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −291.076 | − | 702.719i | −0.895618 | − | 2.16221i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 154.208 | + | 154.208i | 0.471584 | + | 0.471584i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 68.1341 | + | 68.1341i | 0.207095 | + | 0.207095i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.5475 | + | 49.6062i | 0.0620772 | + | 0.149868i | 0.951874 | − | 0.306489i | \(-0.0991542\pi\) |
−0.889797 | + | 0.456356i | \(0.849154\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.28257 | − | 7.92483i | 0.00985757 | − | 0.0237983i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −212.211 | −0.633466 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 627.680i | 1.86255i | 0.364315 | + | 0.931276i | \(0.381303\pi\) | ||||
−0.364315 | + | 0.931276i | \(0.618697\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −348.072 | − | 144.176i | −1.02676 | − | 0.425299i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −107.347 | + | 44.4648i | −0.314802 | + | 0.130395i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 263.539 | − | 263.539i | 0.768336 | − | 0.768336i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −338.885 | + | 338.885i | −0.982275 | + | 0.982275i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 320.625 | − | 132.807i | 0.923992 | − | 0.382730i | 0.130596 | − | 0.991436i | \(-0.458311\pi\) |
0.793396 | + | 0.608706i | \(0.208311\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.5498 | − | 6.02674i | −0.0416901 | − | 0.0172686i | 0.361741 | − | 0.932279i | \(-0.382182\pi\) |
−0.403431 | + | 0.915010i | \(0.632182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 611.254i | − | 1.74146i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 283.828 | 0.804045 | 0.402023 | − | 0.915630i | \(-0.368307\pi\) | ||||
0.402023 | + | 0.915630i | \(0.368307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 134.598 | − | 324.949i | 0.379150 | − | 0.915349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.3494 | − | 27.3999i | −0.0317911 | − | 0.0767505i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −388.417 | − | 388.417i | −1.08194 | − | 1.08194i | −0.996329 | − | 0.0856121i | \(-0.972715\pi\) |
−0.0856121 | − | 0.996329i | \(-0.527285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −87.1393 | − | 87.1393i | −0.241383 | − | 0.241383i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 118.655 | + | 286.458i | 0.326872 | + | 0.789140i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −119.334 | + | 288.098i | −0.326943 | + | 0.789309i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 529.617 | 1.44310 | 0.721548 | − | 0.692364i | \(-0.243431\pi\) | ||||
0.721548 | + | 0.692364i | \(0.243431\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 16.2709i | − | 0.0440945i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 172.013 | + | 71.2499i | 0.463646 | + | 0.192048i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.8515 | − | 15.2644i | 0.0987975 | − | 0.0409233i | −0.332737 | − | 0.943020i | \(-0.607972\pi\) |
0.431535 | + | 0.902096i | \(0.357972\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −152.601 | + | 152.601i | −0.406935 | + | 0.406935i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −113.249 | + | 113.249i | −0.300396 | + | 0.300396i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −463.955 | + | 192.176i | −1.22415 | + | 0.507061i | −0.898728 | − | 0.438506i | \(-0.855508\pi\) |
−0.325426 | + | 0.945567i | \(0.605508\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −150.734 | − | 62.4361i | −0.395627 | − | 0.163874i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 304.650i | 0.795432i | 0.917509 | + | 0.397716i | \(0.130197\pi\) | ||||
−0.917509 | + | 0.397716i | \(0.869803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 170.380 | 0.442547 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.2414 | + | 46.4528i | −0.0497193 | + | 0.120033i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 72.6039 | + | 175.281i | 0.186642 | + | 0.450594i | 0.989309 | − | 0.145833i | \(-0.0465863\pi\) |
−0.802667 | + | 0.596428i | \(0.796586\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.2382 | − | 26.2382i | −0.0671053 | − | 0.0671053i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −210.024 | − | 210.024i | −0.534413 | − | 0.534413i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 66.2209 | + | 159.871i | 0.167648 | + | 0.404737i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −79.4405 | + | 191.786i | −0.200102 | + | 0.483089i | −0.991796 | − | 0.127829i | \(-0.959199\pi\) |
0.791694 | + | 0.610917i | \(0.209199\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −264.165 | −0.662068 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 58.9969i | − | 0.147124i | −0.997291 | − | 0.0735622i | \(-0.976563\pi\) | ||
0.997291 | − | 0.0735622i | \(-0.0234368\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −632.095 | − | 261.822i | −1.56847 | − | 0.649683i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −535.471 | + | 221.800i | −1.32215 | + | 0.547653i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.5089 | − | 36.5089i | 0.0897025 | − | 0.0897025i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 110.309 | − | 110.309i | 0.269704 | − | 0.269704i | −0.559277 | − | 0.828981i | \(-0.688921\pi\) |
0.828981 | + | 0.559277i | \(0.188921\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −236.940 | + | 98.1437i | −0.576496 | + | 0.238792i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 201.798 | + | 83.5875i | 0.488615 | + | 0.202391i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1030.65i | 2.48350i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −88.0117 | −0.211059 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.61960 | − | 11.1527i | 0.0110253 | − | 0.0266174i | −0.918271 | − | 0.395952i | \(-0.870415\pi\) |
0.929296 | + | 0.369335i | \(0.120415\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.5432 | − | 78.5662i | −0.0772998 | − | 0.186618i | 0.880506 | − | 0.474036i | \(-0.157203\pi\) |
−0.957805 | + | 0.287418i | \(0.907203\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.13037 | + | 7.13037i | 0.0168567 | + | 0.0168567i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −42.4177 | − | 42.4177i | −0.0998064 | − | 0.0998064i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 168.558 | + | 406.936i | 0.394750 | + | 0.953012i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 90.6492 | − | 218.847i | 0.211304 | − | 0.510132i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 201.982 | 0.468636 | 0.234318 | − | 0.972160i | \(-0.424714\pi\) | ||||
0.234318 | + | 0.972160i | \(0.424714\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 643.404i | − | 1.48592i | −0.669334 | − | 0.742961i | \(-0.733421\pi\) | ||
0.669334 | − | 0.742961i | \(-0.266579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 150.724 | + | 62.4318i | 0.346491 | + | 0.143521i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −305.355 | + | 126.482i | −0.698753 | + | 0.289433i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 218.953 | − | 218.953i | 0.498753 | − | 0.498753i | −0.412296 | − | 0.911050i | \(-0.635273\pi\) |
0.911050 | + | 0.412296i | \(0.135273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.12194 | − | 6.12194i | 0.0138819 | − | 0.0138819i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 275.767 | − | 114.227i | 0.622499 | − | 0.257848i | −0.0490630 | − | 0.998796i | \(-0.515624\pi\) |
0.671562 | + | 0.740948i | \(0.265624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −615.847 | − | 255.092i | −1.38392 | − | 0.573240i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 165.126i | 0.369410i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −264.162 | −0.588334 | −0.294167 | − | 0.955754i | \(-0.595042\pi\) | ||||
−0.294167 | + | 0.955754i | \(0.595042\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.4792 | − | 90.4828i | 0.0831024 | − | 0.200627i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 76.1428 | + | 183.825i | 0.168086 | + | 0.405795i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 709.407 | + | 709.407i | 1.55914 | + | 1.55914i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 324.484 | + | 324.484i | 0.710030 | + | 0.710030i | 0.966541 | − | 0.256511i | \(-0.0825731\pi\) |
−0.256511 | + | 0.966541i | \(0.582573\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.4483 | − | 44.5382i | −0.0401925 | − | 0.0970332i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 46.5472 | − | 112.375i | 0.100970 | − | 0.243763i | −0.865320 | − | 0.501220i | \(-0.832885\pi\) |
0.966290 | + | 0.257457i | \(0.0828846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 602.217 | 1.30069 | 0.650343 | − | 0.759641i | \(-0.274625\pi\) | ||||
0.650343 | + | 0.759641i | \(0.274625\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 696.918i | 1.49875i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 327.171 | + | 135.519i | 0.700580 | + | 0.290190i | 0.704400 | − | 0.709803i | \(-0.251216\pi\) |
−0.00382006 | + | 0.999993i | \(0.501216\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 150.221 | − | 62.2237i | 0.320301 | − | 0.132673i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 269.477 | − | 269.477i | 0.572137 | − | 0.572137i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −214.003 | + | 214.003i | −0.452439 | + | 0.452439i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −493.650 | + | 204.477i | −1.03926 | + | 0.430477i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0014 | + | 7.45644i | 0.0377389 | + | 0.0156320i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 151.023i | − | 0.315289i | −0.987496 | − | 0.157644i | \(-0.949610\pi\) | ||
0.987496 | − | 0.157644i | \(-0.0503900\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 304.022 | 0.632062 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 140.525 | − | 339.258i | 0.290943 | − | 0.702398i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 206.618 | + | 498.821i | 0.426017 | + | 1.02850i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −382.894 | − | 382.894i | −0.786231 | − | 0.786231i | 0.194643 | − | 0.980874i | \(-0.437645\pi\) |
−0.980874 | + | 0.194643i | \(0.937645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −69.6251 | − | 69.6251i | −0.142383 | − | 0.142383i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 205.776 | + | 496.786i | 0.419095 | + | 1.01178i | 0.982610 | + | 0.185679i | \(0.0594484\pi\) |
−0.563516 | + | 0.826105i | \(0.690552\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.83378 | + | 11.6698i | −0.00980483 | + | 0.0236709i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.8306 | 0.0360215 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 269.493i | 0.542239i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 604.867 | + | 250.544i | 1.21216 | + | 0.502093i | 0.894909 | − | 0.446249i | \(-0.147240\pi\) |
0.317250 | + | 0.948342i | \(0.397240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −524.752 | + | 217.359i | −1.04741 | + | 0.433851i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −324.203 | + | 324.203i | −0.644539 | + | 0.644539i | −0.951668 | − | 0.307129i | \(-0.900632\pi\) |
0.307129 | + | 0.951668i | \(0.400632\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 149.597 | − | 149.597i | 0.296231 | − | 0.296231i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 836.633 | − | 346.545i | 1.65016 | − | 0.683521i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −734.614 | − | 304.287i | −1.44325 | − | 0.597813i | −0.482666 | − | 0.875805i | \(-0.660331\pi\) |
−0.960584 | + | 0.277991i | \(0.910331\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 238.931i | − | 0.467575i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −429.397 | −0.837031 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −487.886 | + | 1177.86i | −0.947351 | + | 2.28711i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.2277 | + | 56.0766i | 0.0449278 | + | 0.108465i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 373.143 | + | 373.143i | 0.718966 | + | 0.718966i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.7805 | − | 16.7805i | −0.0322082 | − | 0.0322082i | 0.690819 | − | 0.723027i | \(-0.257250\pi\) |
−0.723027 | + | 0.690819i | \(0.757250\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −250.400 | − | 604.519i | −0.478776 | − | 1.15587i | −0.960183 | − | 0.279371i | \(-0.909874\pi\) |
0.481407 | − | 0.876497i | \(-0.340126\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 227.179 | − | 548.459i | 0.432722 | − | 1.04468i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −53.9589 | −0.102389 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 69.5595i | 0.131492i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.1185 | + | 8.74759i | 0.0397713 | + | 0.0164738i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 532.791 | − | 220.689i | 0.999607 | − | 0.414051i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −308.593 | + | 308.593i | −0.576809 | + | 0.576809i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −99.7121 | + | 99.7121i | −0.185684 | + | 0.185684i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 48.1458 | − | 19.9427i | 0.0893244 | − | 0.0369994i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 870.996 | + | 360.778i | 1.60997 | + | 0.666873i | 0.992781 | − | 0.119939i | \(-0.0382700\pi\) |
0.617192 | + | 0.786812i | \(0.288270\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 372.656i | − | 0.686291i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −581.827 | −1.06757 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.1835 | − | 87.3546i | 0.0661489 | − | 0.159698i | −0.887348 | − | 0.461100i | \(-0.847455\pi\) |
0.953497 | + | 0.301403i | \(0.0974548\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.6400 | + | 42.5866i | 0.0321311 | + | 0.0775713i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 79.5561 | + | 79.5561i | 0.144385 | + | 0.144385i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −93.7536 | − | 93.7536i | −0.169536 | − | 0.169536i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −118.511 | − | 286.111i | −0.213534 | − | 0.515516i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −288.342 | + | 696.118i | −0.517669 | + | 1.24976i | 0.421663 | + | 0.906753i | \(0.361447\pi\) |
−0.939332 | + | 0.343010i | \(0.888553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1782.08 | −3.18797 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 18.6819i | − | 0.0333010i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −609.320 | − | 252.389i | −1.08227 | − | 0.448293i | −0.230968 | − | 0.972961i | \(-0.574189\pi\) |
−0.851306 | + | 0.524669i | \(0.824189\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 928.629 | − | 384.651i | 1.64359 | − | 0.680797i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 314.017 | − | 314.017i | 0.553822 | − | 0.553822i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 256.311 | − | 256.311i | 0.450459 | − | 0.450459i | −0.445047 | − | 0.895507i | \(-0.646813\pi\) |
0.895507 | + | 0.445047i | \(0.146813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 346.136 | − | 143.374i | 0.606193 | − | 0.251094i | −0.0584066 | − | 0.998293i | \(-0.518602\pi\) |
0.664600 | + | 0.747199i | \(0.268602\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 479.504 | + | 198.617i | 0.836830 | + | 0.346626i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 742.751i | − | 1.29174i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −354.659 | −0.614661 | −0.307330 | − | 0.951603i | \(-0.599436\pi\) | ||||
−0.307330 | + | 0.951603i | \(0.599436\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −199.328 | + | 481.221i | −0.344263 | + | 0.831124i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −302.204 | − | 729.584i | −0.520144 | − | 1.25574i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 82.9309 | + | 82.9309i | 0.142249 | + | 0.142249i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 74.2408 | + | 74.2408i | 0.126907 | + | 0.126907i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −230.018 | − | 555.312i | −0.391853 | − | 0.946018i | −0.989536 | − | 0.144285i | \(-0.953912\pi\) |
0.597683 | − | 0.801733i | \(-0.296088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −183.926 | + | 444.038i | −0.312269 | + | 0.753884i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −705.754 | −1.19417 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 458.661i | − | 0.773460i | −0.922193 | − | 0.386730i | \(-0.873605\pi\) | ||
0.922193 | − | 0.386730i | \(-0.126395\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 73.1008 | + | 30.2793i | 0.122858 | + | 0.0508896i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −498.454 | + | 206.467i | −0.834932 | + | 0.345840i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −265.583 | + | 265.583i | −0.443377 | + | 0.443377i | −0.893145 | − | 0.449768i | \(-0.851507\pi\) |
0.449768 | + | 0.893145i | \(0.351507\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 466.600 | − | 466.600i | 0.776373 | − | 0.776373i | −0.202839 | − | 0.979212i | \(-0.565017\pi\) |
0.979212 | + | 0.202839i | \(0.0650168\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.7209 | − | 6.51182i | 0.0260712 | − | 0.0107990i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −764.246 | − | 316.561i | −1.26322 | − | 0.523241i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 90.4302i | − | 0.148979i | −0.997222 | − | 0.0744894i | \(-0.976267\pi\) | ||
0.997222 | − | 0.0744894i | \(-0.0237327\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −125.001 | −0.205256 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −136.772 | + | 330.197i | −0.223849 | + | 0.540420i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −63.5389 | − | 153.397i | −0.103652 | − | 0.250239i | 0.863542 | − | 0.504277i | \(-0.168241\pi\) |
−0.967194 | + | 0.254038i | \(0.918241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −415.376 | − | 415.376i | −0.675408 | − | 0.675408i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 181.842 | + | 181.842i | 0.294720 | + | 0.294720i | 0.838942 | − | 0.544221i | \(-0.183175\pi\) |
−0.544221 | + | 0.838942i | \(0.683175\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −388.636 | − | 938.250i | −0.627844 | − | 1.51575i | −0.842296 | − | 0.539016i | \(-0.818796\pi\) |
0.214451 | − | 0.976735i | \(-0.431204\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 228.422 | − | 551.460i | 0.367829 | − | 0.888019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 510.746 | 0.819817 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 290.538i | 0.464860i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −153.737 | − | 63.6798i | −0.245194 | − | 0.101563i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.1522 | − | 9.17573i | 0.0352181 | − | 0.0145878i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 241.593 | − | 241.593i | 0.382873 | − | 0.382873i | −0.489263 | − | 0.872136i | \(-0.662734\pi\) |
0.872136 | + | 0.489263i | \(0.162734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 404.793 | − | 404.793i | 0.639484 | − | 0.639484i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 402.146 | − | 166.574i | 0.633301 | − | 0.262322i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 283.498 | + | 117.429i | 0.445051 | + | 0.184346i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.2029i | 0.0441361i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −385.038 | −0.600684 | −0.300342 | − | 0.953832i | \(-0.597101\pi\) | ||||
−0.300342 | + | 0.953832i | \(0.597101\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 144.485 | − | 348.818i | 0.224705 | − | 0.542486i | −0.770813 | − | 0.637062i | \(-0.780150\pi\) |
0.995518 | + | 0.0945760i | \(0.0301495\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 694.674 | + | 1677.09i | 1.07701 | + | 2.60014i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 580.537 | + | 580.537i | 0.897276 | + | 0.897276i | 0.995194 | − | 0.0979186i | \(-0.0312185\pi\) |
−0.0979186 | + | 0.995194i | \(0.531218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 97.2911 | + | 97.2911i | 0.149909 | + | 0.149909i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −204.347 | − | 493.338i | −0.313898 | − | 0.757816i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 467.055 | − | 1127.57i | 0.715246 | − | 1.72676i | 0.0287882 | − | 0.999586i | \(-0.490835\pi\) |
0.686457 | − | 0.727170i | \(-0.259165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 792.423 | 1.20981 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 25.0046i | − | 0.0380587i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −287.435 | − | 119.060i | −0.436169 | − | 0.180667i | 0.153784 | − | 0.988104i | \(-0.450854\pi\) |
−0.589953 | + | 0.807437i | \(0.700854\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 478.625 | − | 198.253i | 0.724093 | − | 0.299929i | 0.00997082 | − | 0.999950i | \(-0.496826\pi\) |
0.714122 | + | 0.700021i | \(0.246826\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 77.7851 | − | 77.7851i | 0.117323 | − | 0.117323i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 498.348 | − | 498.348i | 0.749396 | − | 0.749396i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −144.492 | + | 59.8505i | −0.216629 | + | 0.0897309i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −469.160 | − | 194.332i | −0.701285 | − | 0.290482i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 277.458i | 0.413499i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 831.026 | 1.23481 | 0.617405 | − | 0.786646i | \(-0.288184\pi\) | ||||
0.617405 | + | 0.786646i | \(0.288184\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 369.277 | − | 891.513i | 0.547077 | − | 1.32076i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.6301 | + | 40.1487i | 0.0245644 | + | 0.0593038i | 0.935686 | − | 0.352834i | \(-0.114782\pi\) |
−0.911121 | + | 0.412138i | \(0.864782\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −292.524 | − | 292.524i | −0.430816 | − | 0.430816i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 844.232 | + | 844.232i | 1.23969 | + | 1.23969i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 411.955 | + | 994.547i | 0.603155 | + | 1.45614i | 0.870317 | + | 0.492493i | \(0.163914\pi\) |
−0.267162 | + | 0.963652i | \(0.586086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 261.839 | − | 632.136i | 0.382247 | − | 0.922827i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 431.648 | 0.628309 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 690.593i | 1.00231i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 657.136 | + | 272.195i | 0.950993 | + | 0.393914i | 0.803604 | − | 0.595164i | \(-0.202913\pi\) |
0.147389 | + | 0.989079i | \(0.452913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.6220 | + | 5.22822i | −0.0182136 | + | 0.00754433i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 166.034 | − | 166.034i | 0.238898 | − | 0.238898i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.1605 | − | 32.1605i | 0.0461413 | − | 0.0461413i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1042.10 | + | 431.653i | −1.49085 | + | 0.617530i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −57.0623 | − | 23.6360i | −0.0814012 | − | 0.0337175i | 0.341611 | − | 0.939841i | \(-0.389027\pi\) |
−0.423013 | + | 0.906124i | \(0.639027\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 213.571i | − | 0.303799i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 364.059 | 0.516396 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −62.0332 | + | 149.761i | −0.0877414 | + | 0.211827i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 167.767 | + | 405.025i | 0.236625 | + | 0.571262i | 0.996930 | − | 0.0783041i | \(-0.0249505\pi\) |
−0.760305 | + | 0.649566i | \(0.774951\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.81149 | − | 9.81149i | −0.0137996 | − | 0.0137996i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −472.421 | − | 472.421i | −0.662582 | − | 0.662582i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 241.845 | + | 583.865i | 0.338245 | + | 0.816595i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −69.8358 | + | 168.598i | −0.0973999 | + | 0.235144i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1154.30 | −1.60542 | −0.802712 | − | 0.596367i | \(-0.796610\pi\) | ||||
−0.802712 | + | 0.596367i | \(0.796610\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 976.846i | − | 1.35485i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −519.853 | − | 215.330i | −0.719022 | − | 0.297829i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −233.592 | + | 96.7569i | −0.322195 | + | 0.133458i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 644.722 | − | 644.722i | 0.886825 | − | 0.886825i | −0.107392 | − | 0.994217i | \(-0.534250\pi\) |
0.994217 | + | 0.107392i | \(0.0342500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 545.902 | − | 545.902i | 0.748837 | − | 0.748837i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −129.849 | + | 53.7851i | −0.177632 | + | 0.0735775i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −508.297 | − | 210.544i | −0.693448 | − | 0.287235i | 0.00798801 | − | 0.999968i | \(-0.497457\pi\) |
−0.701436 | + | 0.712733i | \(0.747457\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 312.571i | − | 0.425267i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 102.424 | 0.138974 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −479.243 | + | 1157.00i | −0.648503 | + | 1.56562i | 0.166421 | + | 0.986055i | \(0.446779\pi\) |
−0.814923 | + | 0.579569i | \(0.803221\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −374.967 | − | 905.249i | −0.506028 | − | 1.22166i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 106.350 | + | 106.350i | 0.143136 | + | 0.143136i | 0.775044 | − | 0.631908i | \(-0.217728\pi\) |
−0.631908 | + | 0.775044i | \(0.717728\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −311.511 | − | 311.511i | −0.418136 | − | 0.418136i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31.6262 | − | 76.3524i | −0.0423376 | − | 0.102212i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 127.964 | − | 308.932i | 0.170846 | − | 0.412460i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 186.540 | 0.248389 | 0.124195 | − | 0.992258i | \(-0.460365\pi\) | ||||
0.124195 | + | 0.992258i | \(0.460365\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 993.594i | − | 1.31951i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −490.430 | − | 203.143i | −0.649577 | − | 0.269064i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1190.57 | + | 493.151i | −1.57275 | + | 0.651454i | −0.987244 | − | 0.159214i | \(-0.949104\pi\) |
−0.585506 | + | 0.810668i | \(0.699104\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 163.564 | − | 163.564i | 0.215499 | − | 0.215499i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1042.65 | + | 1042.65i | −1.37010 | + | 1.37010i | −0.509823 | + | 0.860279i | \(0.670289\pi\) |
−0.860279 | + | 0.509823i | \(0.829711\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 411.867 | − | 170.601i | 0.539800 | − | 0.223592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.65014 | + | 3.16879i | 0.0100002 | + | 0.00414221i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 810.175i | 1.05629i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 362.542 | 0.471446 | 0.235723 | − | 0.971820i | \(-0.424254\pi\) | ||||
0.235723 | + | 0.971820i | \(0.424254\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 200.250 | − | 483.445i | 0.259727 | − | 0.627037i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −259.669 | − | 626.896i | −0.335924 | − | 0.810991i | −0.998098 | − | 0.0616419i | \(-0.980366\pi\) |
0.662175 | − | 0.749350i | \(-0.269634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −763.736 | − | 763.736i | −0.985465 | − | 0.985465i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 167.785 | + | 167.785i | 0.215939 | + | 0.215939i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −155.031 | − | 374.278i | −0.199013 | − | 0.480459i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −64.9641 | + | 156.837i | −0.0831807 | + | 0.200816i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −203.188 | −0.259499 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1016.74i | 1.29521i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −148.037 | − | 61.3188i | −0.188103 | − | 0.0779147i | 0.286644 | − | 0.958037i | \(-0.407460\pi\) |
−0.474747 | + | 0.880122i | \(0.657460\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1008.49 | − | 417.731i | 1.27819 | − | 0.529444i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −544.577 | + | 544.577i | −0.688466 | + | 0.688466i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1155.24 | + | 1155.24i | −1.45680 | + | 1.45680i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 649.909 | − | 269.201i | 0.817495 | − | 0.338618i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 173.793 | + | 71.9875i | 0.218059 | + | 0.0903231i | 0.489039 | − | 0.872262i | \(-0.337348\pi\) |
−0.270980 | + | 0.962585i | \(0.587348\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.1873i | 0.0352782i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 53.4505 | 0.0667297 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 57.5968 | − | 139.051i | 0.0717271 | − | 0.173164i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 374.910 | + | 905.113i | 0.465727 | + | 1.12436i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 839.340 | + | 839.340i | 1.04007 | + | 1.04007i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −679.446 | − | 679.446i | −0.839859 | − | 0.839859i | 0.148981 | − | 0.988840i | \(-0.452401\pi\) |
−0.988840 | + | 0.148981i | \(0.952401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.19630 | + | 10.1308i | 0.00517422 | + | 0.0124917i | 0.926446 | − | 0.376429i | \(-0.122848\pi\) |
−0.921271 | + | 0.388921i | \(0.872848\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −358.866 | + | 866.379i | −0.441410 | + | 1.06566i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 262.696 | 0.322326 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1251.88i | 1.53229i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −74.3225 | − | 30.7854i | −0.0907479 | − | 0.0375890i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −114.507 | + | 47.4303i | −0.139472 | + | 0.0577714i | −0.451328 | − | 0.892358i | \(-0.649050\pi\) |
0.311855 | + | 0.950130i | \(0.399050\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −701.981 | + | 701.981i | −0.852954 | + | 0.852954i | −0.990496 | − | 0.137542i | \(-0.956080\pi\) |
0.137542 | + | 0.990496i | \(0.456080\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 264.424 | − | 264.424i | 0.320514 | − | 0.320514i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −420.620 | + | 174.226i | −0.508609 | + | 0.210673i | −0.622205 | − | 0.782854i | \(-0.713763\pi\) |
0.113596 | + | 0.993527i | \(0.463763\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 917.677 | + | 380.114i | 1.10697 | + | 0.458521i | 0.859893 | − | 0.510475i | \(-0.170530\pi\) |
0.247076 | + | 0.968996i | \(0.420530\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 908.337i | 1.09306i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.2008 | 0.0290526 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 579.897 | − | 1400.00i | 0.694487 | − | 1.67664i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −332.164 | − | 801.915i | −0.396851 | − | 0.958083i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −125.592 | − | 125.592i | −0.149693 | − | 0.149693i | 0.628288 | − | 0.777981i | \(-0.283756\pi\) |
−0.777981 | + | 0.628288i | \(0.783756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −557.031 | − | 557.031i | −0.662344 | − | 0.662344i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 466.613 | + | 1126.50i | 0.553515 | + | 1.33630i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −924.554 | + | 2232.07i | −1.09415 | + | 2.64150i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 633.819 | 0.748311 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 414.835i | − | 0.488616i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 274.282 | + | 113.611i | 0.322305 | + | 0.133503i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −866.692 | + | 358.995i | −1.01605 | + | 0.420862i | −0.827659 | − | 0.561232i | \(-0.810328\pi\) |
−0.188392 | + | 0.982094i | \(0.560328\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 52.1531 | − | 52.1531i | 0.0609978 | − | 0.0609978i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −559.264 | + | 559.264i | −0.652584 | + | 0.652584i | −0.953614 | − | 0.301031i | \(-0.902669\pi\) |
0.301031 | + | 0.953614i | \(0.402669\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 552.858 | − | 229.001i | 0.643607 | − | 0.266591i | −0.0369150 | − | 0.999318i | \(-0.511753\pi\) |
0.680522 | + | 0.732728i | \(0.261753\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 415.833 | + | 172.244i | 0.482965 | + | 0.200051i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 106.004i | − | 0.122833i | −0.998112 | − | 0.0614163i | \(-0.980438\pi\) | ||
0.998112 | − | 0.0614163i | \(-0.0195617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1407.87 | −1.62760 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −316.848 | + | 764.938i | −0.365453 | + | 0.882281i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.9616 | − | 77.1622i | −0.0367798 | − | 0.0887943i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 426.460 | + | 426.460i | 0.489621 | + | 0.489621i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30.6132 | − | 30.6132i | −0.0350667 | − | 0.0350667i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 168.823 | + | 407.574i | 0.192940 | + | 0.465799i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −135.124 | + | 326.217i | −0.154075 | + | 0.371969i | −0.982003 | − | 0.188864i | \(-0.939519\pi\) |
0.827928 | + | 0.560834i | \(0.189519\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 137.060 | 0.155927 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 628.648i | − | 0.713562i | −0.934188 | − | 0.356781i | \(-0.883874\pi\) | ||
0.934188 | − | 0.356781i | \(-0.116126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 816.843 | + | 338.347i | 0.925077 | + | 0.383179i | 0.793809 | − | 0.608167i | \(-0.208095\pi\) |
0.131268 | + | 0.991347i | \(0.458095\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 762.446 | − | 315.815i | 0.861521 | − | 0.356854i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.4622 | + | 22.4622i | −0.0253238 | + | 0.0253238i | −0.719655 | − | 0.694332i | \(-0.755700\pi\) |
0.694332 | + | 0.719655i | \(0.255700\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −235.831 | + | 235.831i | −0.265277 | + | 0.265277i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 258.446 | − | 107.052i | 0.290063 | − | 0.120148i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 231.958 | + | 96.0803i | 0.259752 | + | 0.107593i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 376.214i | − | 0.420351i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1362.05 | 1.51845 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −87.0327 | + | 210.116i | −0.0968106 | + | 0.233721i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.8429 | + | 50.3192i | 0.0231331 | + | 0.0558482i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −983.499 | − | 983.499i | −1.08915 | − | 1.08915i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 703.017 | + | 703.017i | 0.776814 | + | 0.776814i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 554.178 | + | 1337.90i | 0.611001 | + | 1.47509i | 0.861903 | + | 0.507074i | \(0.169273\pi\) |
−0.250902 | + | 0.968012i | \(0.580727\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.49189 | + | 15.6728i | −0.00714180 | + | 0.0172418i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 267.709 | 0.293863 | 0.146931 | − | 0.989147i | \(-0.453060\pi\) | ||||
0.146931 | + | 0.989147i | \(0.453060\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 497.447i | − | 0.544849i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1537.51 | + | 636.858i | 1.68034 | + | 0.696020i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −560.945 | + | 232.351i | −0.611717 | + | 0.253382i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 191.361 | − | 191.361i | 0.208227 | − | 0.208227i | −0.595286 | − | 0.803514i | \(-0.702961\pi\) |
0.803514 | + | 0.595286i | \(0.202961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1179.48 | + | 1179.48i | −1.28066 | + | 1.28066i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −923.507 | + | 382.529i | −1.00055 | + | 0.414441i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 443.416 | + | 183.669i | 0.479368 | + | 0.198561i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 102.229i | − | 0.110279i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −459.352 | −0.494458 | −0.247229 | − | 0.968957i | \(-0.579520\pi\) | ||||
−0.247229 | + | 0.968957i | \(0.579520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 82.4919 | − | 199.153i | 0.0886057 | − | 0.213913i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −600.970 | − | 1450.87i | −0.644126 | − | 1.55506i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 35.2434 | + | 35.2434i | 0.0376935 | + | 0.0376935i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −135.689 | − | 135.689i | −0.144812 | − | 0.144812i | 0.630984 | − | 0.775796i | \(-0.282651\pi\) |
−0.775796 | + | 0.630984i | \(0.782651\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −567.415 | − | 1369.86i | −0.604276 | − | 1.45885i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 471.321 | − | 1137.87i | 0.500873 | − | 1.20921i | −0.448136 | − | 0.893965i | \(-0.647912\pi\) |
0.949009 | − | 0.315249i | \(-0.102088\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 563.142 | 0.597182 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1272.79i | 1.34687i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 300.223 | + | 124.357i | 0.317026 | + | 0.131316i | 0.535522 | − | 0.844521i | \(-0.320115\pi\) |
−0.218496 | + | 0.975838i | \(0.570115\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 818.776 | − | 339.148i | 0.862778 | − | 0.357374i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1079.66 | + | 1079.66i | −1.13529 | + | 1.13529i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 362.517 | − | 362.517i | 0.380395 | − | 0.380395i | −0.490849 | − | 0.871245i | \(-0.663313\pi\) |
0.871245 | + | 0.490849i | \(0.163313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1279.28 | + | 529.894i | −1.33956 | + | 0.554863i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −72.7471 | − | 30.1328i | −0.0760158 | − | 0.0314868i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 524.256i | 0.546669i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.5357 | −0.0109633 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.3917 | − | 32.3304i | 0.0139062 | − | 0.0335725i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −531.792 | − | 1283.86i | −0.551079 | − | 1.33042i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −642.315 | − | 642.315i | −0.664235 | − | 0.664235i | 0.292141 | − | 0.956375i | \(-0.405632\pi\) |
−0.956375 | + | 0.292141i | \(0.905632\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −54.6429 | − | 54.6429i | −0.0563910 | − | 0.0563910i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 114.682 | + | 276.867i | 0.118107 | + | 0.285136i | 0.971867 | − | 0.235532i | \(-0.0756832\pi\) |
−0.853760 | + | 0.520667i | \(0.825683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −68.8494 | + | 166.217i | −0.0707599 | + | 0.170830i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2201.94 | 2.25840 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1952.32i | − | 1.99828i | −0.0414975 | − | 0.999139i | \(-0.513213\pi\) | ||
0.0414975 | − | 0.999139i | \(-0.486787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 297.240 | + | 123.121i | 0.303616 | + | 0.125762i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.1027 | − | 17.8537i | 0.0439375 | − | 0.0181995i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −437.102 | + | 437.102i | −0.444661 | + | 0.444661i | −0.893575 | − | 0.448914i | \(-0.851811\pi\) |
0.448914 | + | 0.893575i | \(0.351811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1331.41 | − | 1331.41i | 1.35168 | − | 1.35168i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −257.712 | + | 106.748i | −0.261107 | + | 0.108154i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1607.75 | − | 665.952i | −1.62563 | − | 0.673359i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 238.251i | 0.240415i | 0.992749 | + | 0.120208i | \(0.0383560\pi\) | ||||
−0.992749 | + | 0.120208i | \(0.961644\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −155.439 | −0.156535 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 550.836 | − | 1329.84i | 0.553604 | − | 1.33652i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 262.900 | + | 634.696i | 0.263691 | + | 0.636606i | 0.999161 | − | 0.0409509i | \(-0.0130387\pi\) |
−0.735470 | + | 0.677557i | \(0.763039\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 272.732 | + | 272.732i | 0.273005 | + | 0.273005i |
(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 | 256.3.h.a.95.3 | 28 | ||
4.3 | odd | 2 | 256.3.h.b.95.5 | 28 | |||
8.3 | odd | 2 | 32.3.h.a.3.1 | ✓ | 28 | ||
8.5 | even | 2 | 128.3.h.a.47.5 | 28 | |||
24.11 | even | 2 | 288.3.u.a.163.7 | 28 | |||
32.5 | even | 8 | 32.3.h.a.11.1 | yes | 28 | ||
32.11 | odd | 8 | inner | 256.3.h.a.159.3 | 28 | ||
32.21 | even | 8 | 256.3.h.b.159.5 | 28 | |||
32.27 | odd | 8 | 128.3.h.a.79.5 | 28 | |||
96.5 | odd | 8 | 288.3.u.a.235.7 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.3.1 | ✓ | 28 | 8.3 | odd | 2 | ||
32.3.h.a.11.1 | yes | 28 | 32.5 | even | 8 | ||
128.3.h.a.47.5 | 28 | 8.5 | even | 2 | |||
128.3.h.a.79.5 | 28 | 32.27 | odd | 8 | |||
256.3.h.a.95.3 | 28 | 1.1 | even | 1 | trivial | ||
256.3.h.a.159.3 | 28 | 32.11 | odd | 8 | inner | ||
256.3.h.b.95.5 | 28 | 4.3 | odd | 2 | |||
256.3.h.b.159.5 | 28 | 32.21 | even | 8 | |||
288.3.u.a.163.7 | 28 | 24.11 | even | 2 | |||
288.3.u.a.235.7 | 28 | 96.5 | odd | 8 |