Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(35,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.l (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 179.16 | ||
Character | \(\chi\) | \(=\) | 324.179 |
Dual form | 324.2.l.a.143.16 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{11}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40830 | + | 0.129170i | 0.995820 | + | 0.0913373i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.96663 | + | 0.363822i | 0.983315 | + | 0.181911i | ||||
\(5\) | −0.297855 | − | 0.0525198i | −0.133205 | − | 0.0234876i | 0.106648 | − | 0.994297i | \(-0.465988\pi\) |
−0.239853 | + | 0.970809i | \(0.577099\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.312070 | + | 0.371910i | 0.117951 | + | 0.140569i | 0.821789 | − | 0.569792i | \(-0.192976\pi\) |
−0.703838 | + | 0.710361i | \(0.748532\pi\) | |||||||
\(8\) | 2.72261 | + | 0.766402i | 0.962589 | + | 0.270964i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.412685 | − | 0.112438i | −0.130503 | − | 0.0355559i | ||||
\(11\) | −0.00722947 | − | 0.0410004i | −0.00217977 | − | 0.0123621i | 0.983698 | − | 0.179826i | \(-0.0575534\pi\) |
−0.985878 | + | 0.167464i | \(0.946442\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.05761 | − | 1.47685i | 1.12538 | − | 0.409604i | 0.288765 | − | 0.957400i | \(-0.406755\pi\) |
0.836612 | + | 0.547796i | \(0.184533\pi\) | |||||||
\(14\) | 0.391449 | + | 0.564072i | 0.104619 | + | 0.150755i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.73527 | + | 1.43101i | 0.933817 | + | 0.357752i | ||||
\(17\) | 2.14427 | + | 1.23800i | 0.520062 | + | 0.300258i | 0.736960 | − | 0.675936i | \(-0.236261\pi\) |
−0.216898 | + | 0.976194i | \(0.569594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.55326 | + | 3.78353i | −1.50342 | + | 0.868001i | −0.503430 | + | 0.864036i | \(0.667929\pi\) |
−0.999992 | + | 0.00396479i | \(0.998738\pi\) | |||||||
\(20\) | −0.566662 | − | 0.211653i | −0.126709 | − | 0.0473271i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.00488525 | − | 0.0586748i | −0.00104154 | − | 0.0125095i | ||||
\(23\) | −5.03199 | − | 4.22234i | −1.04924 | − | 0.880418i | −0.0562281 | − | 0.998418i | \(-0.517907\pi\) |
−0.993014 | + | 0.118000i | \(0.962352\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61250 | − | 1.67881i | −0.922501 | − | 0.335763i | ||||
\(26\) | 5.90510 | − | 1.55572i | 1.15809 | − | 0.305103i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.478416 | + | 0.844947i | 0.0904122 | + | 0.159680i | ||||
\(29\) | 2.40260 | − | 6.60109i | 0.446152 | − | 1.22579i | −0.489231 | − | 0.872154i | \(-0.662722\pi\) |
0.935383 | − | 0.353637i | \(-0.115055\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.30836 | + | 2.75099i | −0.414593 | + | 0.494092i | −0.932412 | − | 0.361398i | \(-0.882300\pi\) |
0.517819 | + | 0.855490i | \(0.326744\pi\) | |||||||
\(32\) | 5.07554 | + | 2.49778i | 0.897237 | + | 0.441549i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.85987 | + | 2.02045i | 0.490464 | + | 0.346504i | ||||
\(35\) | −0.0734187 | − | 0.127165i | −0.0124100 | − | 0.0214948i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.36015 | + | 5.81994i | −0.552405 | + | 0.956793i | 0.445696 | + | 0.895184i | \(0.352956\pi\) |
−0.998100 | + | 0.0616082i | \(0.980377\pi\) | |||||||
\(38\) | −9.71770 | + | 4.48186i | −1.57642 | + | 0.727054i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.770692 | − | 0.371267i | −0.121857 | − | 0.0587025i | ||||
\(41\) | −2.16312 | − | 5.94312i | −0.337823 | − | 0.928160i | −0.986011 | − | 0.166680i | \(-0.946695\pi\) |
0.648188 | − | 0.761480i | \(-0.275527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.38200 | − | 0.420011i | 0.363252 | − | 0.0640511i | 0.0109565 | − | 0.999940i | \(-0.496512\pi\) |
0.352295 | + | 0.935889i | \(0.385401\pi\) | |||||||
\(44\) | 0.000699143 | − | 0.0832628i | 0.000105400 | − | 0.0125523i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.54116 | − | 6.59631i | −0.964441 | − | 0.972573i | ||||
\(47\) | −5.51016 | + | 4.62358i | −0.803740 | + | 0.674418i | −0.949105 | − | 0.314960i | \(-0.898009\pi\) |
0.145365 | + | 0.989378i | \(0.453564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.17461 | − | 6.66153i | 0.167801 | − | 0.951647i | ||||
\(50\) | −6.27895 | − | 2.96008i | −0.887977 | − | 0.418618i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.51712 | − | 1.42817i | 1.18111 | − | 0.198051i | ||||
\(53\) | 9.90799i | 1.36097i | 0.732763 | + | 0.680484i | \(0.238230\pi\) | ||||
−0.732763 | + | 0.680484i | \(0.761770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0125918i | 0.00169788i | ||||||||
\(56\) | 0.564613 | + | 1.25174i | 0.0754495 | + | 0.167271i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.23625 | − | 8.98598i | 0.556247 | − | 1.17992i | ||||
\(59\) | 0.755918 | − | 4.28703i | 0.0984122 | − | 0.558123i | −0.895236 | − | 0.445592i | \(-0.852993\pi\) |
0.993648 | − | 0.112531i | \(-0.0358958\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.77142 | + | 4.84280i | −0.738955 | + | 0.620057i | −0.932557 | − | 0.361024i | \(-0.882427\pi\) |
0.193602 | + | 0.981080i | \(0.437983\pi\) | |||||||
\(62\) | −3.60621 | + | 3.57605i | −0.457989 | + | 0.454159i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.82526 | + | 4.17323i | 0.853157 | + | 0.521654i | ||||
\(65\) | −1.28614 | + | 0.226781i | −0.159526 | + | 0.0281287i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.80965 | − | 10.4669i | −0.465423 | − | 1.27874i | −0.921354 | − | 0.388724i | \(-0.872916\pi\) |
0.455932 | − | 0.890015i | \(-0.349306\pi\) | |||||||
\(68\) | 3.76658 | + | 3.21481i | 0.456765 | + | 0.389853i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0869698 | − | 0.188570i | −0.0103949 | − | 0.0225385i | ||||
\(71\) | 1.68932 | − | 2.92598i | 0.200485 | − | 0.347250i | −0.748200 | − | 0.663473i | \(-0.769082\pi\) |
0.948685 | + | 0.316223i | \(0.102415\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.315477 | + | 0.546421i | 0.0369237 | + | 0.0639538i | 0.883897 | − | 0.467682i | \(-0.154911\pi\) |
−0.846973 | + | 0.531636i | \(0.821577\pi\) | |||||||
\(74\) | −5.48386 | + | 7.76221i | −0.637486 | + | 0.902338i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.2644 | + | 5.05658i | −1.63624 | + | 0.580029i | ||||
\(77\) | 0.0129924 | − | 0.0154837i | 0.00148062 | − | 0.00176453i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.03548 | − | 2.84496i | 0.116501 | − | 0.320083i | −0.867714 | − | 0.497065i | \(-0.834411\pi\) |
0.984214 | + | 0.176982i | \(0.0566334\pi\) | |||||||
\(80\) | −1.03741 | − | 0.622407i | −0.115986 | − | 0.0695873i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.27865 | − | 8.64913i | −0.251635 | − | 0.955136i | ||||
\(83\) | 5.41059 | + | 1.96930i | 0.593890 | + | 0.216158i | 0.621439 | − | 0.783462i | \(-0.286548\pi\) |
−0.0275495 | + | 0.999620i | \(0.508770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.573662 | − | 0.481360i | −0.0622224 | − | 0.0522108i | ||||
\(86\) | 3.40883 | − | 0.283818i | 0.367584 | − | 0.0306049i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0117397 | − | 0.117169i | 0.00125146 | − | 0.0124902i | ||||
\(89\) | −9.00521 | + | 5.19916i | −0.954550 | + | 0.551110i | −0.894491 | − | 0.447085i | \(-0.852462\pi\) |
−0.0600588 | + | 0.998195i | \(0.519129\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.81551 | + | 1.04819i | 0.190317 | + | 0.109880i | ||||
\(92\) | −8.35988 | − | 10.1345i | −0.871577 | − | 1.05660i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.35720 | + | 5.79964i | −0.861980 | + | 0.598187i | ||||
\(95\) | 2.15063 | − | 0.782765i | 0.220650 | − | 0.0803100i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.578459 | − | 3.28061i | −0.0587337 | − | 0.333095i | 0.941256 | − | 0.337694i | \(-0.109647\pi\) |
−0.999989 | + | 0.00459941i | \(0.998536\pi\) | |||||||
\(98\) | 2.51468 | − | 9.22972i | 0.254021 | − | 0.932343i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.46030 | − | 4.97974i | −0.846030 | − | 0.497974i | ||||
\(101\) | 10.7344 | + | 12.7927i | 1.06811 | + | 1.27292i | 0.960366 | + | 0.278743i | \(0.0899177\pi\) |
0.107742 | + | 0.994179i | \(0.465638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.6512 | + | 2.75973i | 1.54216 | + | 0.271924i | 0.879098 | − | 0.476640i | \(-0.158146\pi\) |
0.663062 | + | 0.748565i | \(0.269257\pi\) | |||||||
\(104\) | 12.1792 | − | 0.911130i | 1.19426 | − | 0.0893436i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.27982 | + | 13.9534i | −0.124307 | + | 1.35528i | ||||
\(107\) | −1.00162 | −0.0968302 | −0.0484151 | − | 0.998827i | \(-0.515417\pi\) | ||||
−0.0484151 | + | 0.998827i | \(0.515417\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.26618 | 0.695973 | 0.347987 | − | 0.937499i | \(-0.386865\pi\) | ||||
0.347987 | + | 0.937499i | \(0.386865\pi\) | |||||||
\(110\) | −0.00162649 | + | 0.0177331i | −0.000155080 | + | 0.00169079i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.633458 | + | 1.83576i | 0.0598561 | + | 0.173463i | ||||
\(113\) | −14.2492 | − | 2.51252i | −1.34045 | − | 0.236358i | −0.542997 | − | 0.839735i | \(-0.682710\pi\) |
−0.797456 | + | 0.603377i | \(0.793821\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.27704 | + | 1.52192i | 0.119085 | + | 0.141920i | ||||
\(116\) | 7.12665 | − | 12.1078i | 0.661693 | − | 1.12418i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.61832 | − | 5.93979i | 0.148978 | − | 0.546802i | ||||
\(119\) | 0.208739 | + | 1.18382i | 0.0191351 | + | 0.108520i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3350 | − | 3.76163i | 0.939545 | − | 0.341966i | ||||
\(122\) | −8.75345 | + | 6.07462i | −0.792500 | + | 0.549971i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.54055 | + | 4.57035i | −0.497556 | + | 0.410430i | ||||
\(125\) | 2.59533 | + | 1.49841i | 0.232133 | + | 0.134022i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.70348 | − | 4.44760i | 0.683573 | − | 0.394661i | −0.117627 | − | 0.993058i | \(-0.537529\pi\) |
0.801200 | + | 0.598397i | \(0.204195\pi\) | |||||||
\(128\) | 9.07296 | + | 6.75879i | 0.801944 | + | 0.597399i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.84057 | + | 0.153245i | −0.161428 | + | 0.0134405i | ||||
\(131\) | 14.8870 | + | 12.4917i | 1.30068 | + | 1.09140i | 0.990027 | + | 0.140881i | \(0.0449935\pi\) |
0.310657 | + | 0.950522i | \(0.399451\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.45221 | − | 1.25650i | −0.299344 | − | 0.108952i | ||||
\(134\) | −4.01312 | − | 15.2327i | −0.346681 | − | 1.31590i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.88922 | + | 5.01396i | 0.419247 | + | 0.429943i | ||||
\(137\) | 5.24564 | − | 14.4123i | 0.448165 | − | 1.23132i | −0.485834 | − | 0.874051i | \(-0.661484\pi\) |
0.934000 | − | 0.357274i | \(-0.116294\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.74324 | + | 6.84453i | −0.487135 | + | 0.580545i | −0.952486 | − | 0.304581i | \(-0.901484\pi\) |
0.465351 | + | 0.885126i | \(0.345928\pi\) | |||||||
\(140\) | −0.0981221 | − | 0.276798i | −0.00829283 | − | 0.0233937i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.75702 | − | 3.90246i | 0.231364 | − | 0.327487i | ||||
\(143\) | −0.0898857 | − | 0.155687i | −0.00751662 | − | 0.0130192i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.06231 | + | 1.83998i | −0.0882203 | + | 0.152802i | ||||
\(146\) | 0.373705 | + | 0.810277i | 0.0309280 | + | 0.0670590i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.72559 | + | 10.2232i | −0.717239 | + | 0.840340i | ||||
\(149\) | −0.588938 | − | 1.61809i | −0.0482477 | − | 0.132559i | 0.913228 | − | 0.407448i | \(-0.133581\pi\) |
−0.961476 | + | 0.274889i | \(0.911359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.593940 | + | 0.104728i | −0.0483342 | + | 0.00852262i | −0.197763 | − | 0.980250i | \(-0.563368\pi\) |
0.149429 | + | 0.988772i | \(0.452257\pi\) | |||||||
\(152\) | −20.7417 | + | 5.27866i | −1.68238 | + | 0.428155i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0202972 | − | 0.0201275i | 0.00163560 | − | 0.00162192i | ||||
\(155\) | 0.832036 | − | 0.698161i | 0.0668307 | − | 0.0560776i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.80133 | + | 10.2158i | −0.143762 | + | 0.815313i | 0.824592 | + | 0.565729i | \(0.191405\pi\) |
−0.968353 | + | 0.249584i | \(0.919706\pi\) | |||||||
\(158\) | 1.82575 | − | 3.87281i | 0.145249 | − | 0.308104i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.38059 | − | 1.01054i | −0.109145 | − | 0.0798902i | ||||
\(161\) | − | 3.18911i | − | 0.251337i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.70430i | − | 0.446795i | −0.974727 | − | 0.223397i | \(-0.928285\pi\) | ||
0.974727 | − | 0.223397i | \(-0.0717148\pi\) | |||||||
\(164\) | −2.09182 | − | 12.4749i | −0.163344 | − | 0.974127i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.36538 | + | 3.47225i | 0.571664 | + | 0.269499i | ||||
\(167\) | −0.911752 | + | 5.17080i | −0.0705535 | + | 0.400129i | 0.928995 | + | 0.370092i | \(0.120674\pi\) |
−0.999549 | + | 0.0300372i | \(0.990437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.32450 | − | 3.62869i | 0.332654 | − | 0.279130i | ||||
\(170\) | −0.745712 | − | 0.752000i | −0.0571935 | − | 0.0576758i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.83733 | + | 0.0406182i | 0.368843 | + | 0.00309711i | ||||
\(173\) | 1.36617 | − | 0.240893i | 0.103868 | − | 0.0183148i | −0.121472 | − | 0.992595i | \(-0.538762\pi\) |
0.225341 | + | 0.974280i | \(0.427650\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.815054 | − | 2.23934i | −0.0616123 | − | 0.169278i | ||||
\(176\) | 0.0316678 | − | 0.163493i | 0.00238705 | − | 0.0123237i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.3536 | + | 6.15878i | −1.00090 | + | 0.461620i | ||||
\(179\) | −5.77179 | + | 9.99703i | −0.431403 | + | 0.747213i | −0.996994 | − | 0.0774732i | \(-0.975315\pi\) |
0.565591 | + | 0.824686i | \(0.308648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.57298 | + | 14.8488i | 0.637225 | + | 1.10371i | 0.986039 | + | 0.166514i | \(0.0532510\pi\) |
−0.348814 | + | 0.937192i | \(0.613416\pi\) | |||||||
\(182\) | 2.42139 | + | 1.71067i | 0.179486 | + | 0.126803i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.4642 | − | 15.3523i | −0.771427 | − | 1.13179i | ||||
\(185\) | 1.30650 | − | 1.55702i | 0.0960556 | − | 0.114475i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0352564 | − | 0.0968660i | 0.00257820 | − | 0.00708355i | ||||
\(188\) | −12.5186 | + | 7.08814i | −0.913014 | + | 0.516956i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.12985 | − | 0.824572i | 0.227063 | − | 0.0598208i | ||||
\(191\) | 15.5567 | + | 5.66216i | 1.12564 | + | 0.409699i | 0.836708 | − | 0.547650i | \(-0.184477\pi\) |
0.288933 | + | 0.957349i | \(0.406700\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.74355 | − | 5.65851i | −0.485411 | − | 0.407308i | 0.366967 | − | 0.930234i | \(-0.380396\pi\) |
−0.852378 | + | 0.522925i | \(0.824841\pi\) | |||||||
\(194\) | −0.390888 | − | 4.69480i | −0.0280641 | − | 0.337067i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.73363 | − | 12.6734i | 0.338116 | − | 0.905244i | ||||
\(197\) | 10.8232 | − | 6.24879i | 0.771122 | − | 0.445208i | −0.0621526 | − | 0.998067i | \(-0.519797\pi\) |
0.833275 | + | 0.552859i | \(0.186463\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.88531 | + | 2.24318i | 0.275422 | + | 0.159015i | 0.631349 | − | 0.775499i | \(-0.282501\pi\) |
−0.355927 | + | 0.934514i | \(0.615835\pi\) | |||||||
\(200\) | −11.2714 | − | 8.10580i | −0.797010 | − | 0.573166i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.4648 | + | 19.4026i | 0.947378 | + | 1.36516i | ||||
\(203\) | 3.20479 | − | 1.16645i | 0.224932 | − | 0.0818686i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.332164 | + | 1.88379i | 0.0231993 | + | 0.131570i | ||||
\(206\) | 21.6852 | + | 5.90821i | 1.51088 | + | 0.411644i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.2696 | + | 0.290040i | 1.19743 | + | 0.0201107i | ||||
\(209\) | 0.202503 | + | 0.241333i | 0.0140074 | + | 0.0166934i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.1033 | + | 3.89740i | 1.52165 | + | 0.268308i | 0.871082 | − | 0.491138i | \(-0.163419\pi\) |
0.650570 | + | 0.759446i | \(0.274530\pi\) | |||||||
\(212\) | −3.60475 | + | 19.4854i | −0.247575 | + | 1.33826i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.41058 | − | 0.129380i | −0.0964254 | − | 0.00884421i | ||||
\(215\) | −0.731549 | −0.0498912 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.74349 | −0.118356 | ||||||||
\(218\) | 10.2330 | + | 0.938575i | 0.693064 | + | 0.0635683i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.00458119 | + | 0.0247635i | −0.000308864 | + | 0.00166955i | ||||
\(221\) | 10.5289 | + | 1.85654i | 0.708253 | + | 0.124884i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.7737 | − | 14.0314i | −0.788428 | − | 0.939612i | 0.210854 | − | 0.977518i | \(-0.432376\pi\) |
−0.999281 | + | 0.0379061i | \(0.987931\pi\) | |||||||
\(224\) | 0.654974 | + | 2.66712i | 0.0437623 | + | 0.178205i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.7426 | − | 5.37896i | −1.31326 | − | 0.357803i | ||||
\(227\) | −3.40406 | − | 19.3054i | −0.225936 | − | 1.28134i | −0.860888 | − | 0.508794i | \(-0.830092\pi\) |
0.634953 | − | 0.772551i | \(-0.281020\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.32626 | + | 1.93860i | −0.351969 | + | 0.128106i | −0.511953 | − | 0.859013i | \(-0.671078\pi\) |
0.159984 | + | 0.987120i | \(0.448856\pi\) | |||||||
\(230\) | 1.60188 | + | 2.30828i | 0.105625 | + | 0.152204i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.6004 | − | 16.1309i | 0.761606 | − | 1.05904i | ||||
\(233\) | −6.50499 | − | 3.75566i | −0.426156 | − | 0.246041i | 0.271552 | − | 0.962424i | \(-0.412463\pi\) |
−0.697708 | + | 0.716383i | \(0.745797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.88406 | − | 1.08776i | 0.122902 | − | 0.0709577i | ||||
\(236\) | 3.04633 | − | 8.15597i | 0.198299 | − | 0.530909i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.141053 | + | 1.69414i | 0.00914313 | + | 0.109814i | ||||
\(239\) | −4.95760 | − | 4.15992i | −0.320680 | − | 0.269083i | 0.468209 | − | 0.883618i | \(-0.344899\pi\) |
−0.788890 | + | 0.614535i | \(0.789344\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.652071 | + | 0.237335i | 0.0420036 | + | 0.0152881i | 0.362937 | − | 0.931814i | \(-0.381774\pi\) |
−0.320933 | + | 0.947102i | \(0.603996\pi\) | |||||||
\(242\) | 15.0407 | − | 3.96253i | 0.966852 | − | 0.254721i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.1122 | + | 7.42422i | −0.839420 | + | 0.475287i | ||||
\(245\) | −0.699725 | + | 1.92248i | −0.0447038 | + | 0.122823i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.0029 | + | 25.0302i | −1.33638 | + | 1.59264i | ||||
\(248\) | −8.39312 | + | 5.72076i | −0.532964 | + | 0.363269i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.46146 | + | 2.44546i | 0.218922 | + | 0.154664i | ||||
\(251\) | 1.09113 | + | 1.88989i | 0.0688715 | + | 0.119289i | 0.898405 | − | 0.439168i | \(-0.144727\pi\) |
−0.829533 | + | 0.558457i | \(0.811393\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.136739 | + | 0.236839i | −0.00859670 | + | 0.0148899i | ||||
\(254\) | 11.4233 | − | 5.26851i | 0.716763 | − | 0.330576i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.9044 | + | 10.6904i | 0.744027 | + | 0.668149i | ||||
\(257\) | 4.92162 | + | 13.5220i | 0.307002 | + | 0.843481i | 0.993237 | + | 0.116102i | \(0.0370398\pi\) |
−0.686235 | + | 0.727380i | \(0.740738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.21309 | + | 0.566555i | −0.199652 | + | 0.0352040i | ||||
\(260\) | −2.61187 | − | 0.0219314i | −0.161981 | − | 0.00136013i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.3518 | + | 19.5150i | 1.19556 | + | 1.20564i | ||||
\(263\) | 7.84733 | − | 6.58469i | 0.483887 | − | 0.406029i | −0.367943 | − | 0.929849i | \(-0.619938\pi\) |
0.851829 | + | 0.523819i | \(0.175493\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.520366 | − | 2.95114i | 0.0319658 | − | 0.181287i | ||||
\(266\) | −4.69945 | − | 2.21546i | −0.288142 | − | 0.135838i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.68407 | − | 21.9706i | −0.225041 | − | 1.34207i | ||||
\(269\) | − | 3.15222i | − | 0.192194i | −0.995372 | − | 0.0960971i | \(-0.969364\pi\) | ||
0.995372 | − | 0.0960971i | \(-0.0306359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.33151i | − | 0.202375i | −0.994867 | − | 0.101188i | \(-0.967736\pi\) | ||
0.994867 | − | 0.101188i | \(-0.0322642\pi\) | |||||||
\(272\) | 6.23785 | + | 7.69271i | 0.378225 | + | 0.466439i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.24909 | − | 19.6193i | 0.558758 | − | 1.18524i | ||||
\(275\) | −0.0354861 | + | 0.201251i | −0.00213989 | + | 0.0121359i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.19860 | − | 2.68395i | 0.192186 | − | 0.161263i | −0.541618 | − | 0.840625i | \(-0.682188\pi\) |
0.733803 | + | 0.679362i | \(0.237743\pi\) | |||||||
\(278\) | −8.97233 | + | 8.89730i | −0.538124 | + | 0.533625i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.102431 | − | 0.402489i | −0.00612145 | − | 0.0240533i | ||||
\(281\) | −19.3295 | + | 3.40832i | −1.15310 | + | 0.203323i | −0.717330 | − | 0.696733i | \(-0.754636\pi\) |
−0.435773 | + | 0.900057i | \(0.643525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.26641 | − | 14.4693i | −0.313055 | − | 0.860113i | −0.992036 | − | 0.125956i | \(-0.959800\pi\) |
0.678980 | − | 0.734156i | \(-0.262422\pi\) | |||||||
\(284\) | 4.38680 | − | 5.13971i | 0.260309 | − | 0.304986i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.106476 | − | 0.230864i | −0.00629606 | − | 0.0136513i | ||||
\(287\) | 1.53526 | − | 2.65916i | 0.0906238 | − | 0.156965i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.43473 | − | 9.41323i | −0.319690 | − | 0.553720i | ||||
\(290\) | −1.73373 | + | 2.45403i | −0.101808 | + | 0.144106i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.421625 | + | 1.18939i | 0.0246738 | + | 0.0696036i | ||||
\(293\) | −11.9699 | + | 14.2652i | −0.699290 | + | 0.833382i | −0.992446 | − | 0.122683i | \(-0.960850\pi\) |
0.293156 | + | 0.956065i | \(0.405295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.450307 | + | 1.23721i | −0.0262179 | + | 0.0720331i | ||||
\(296\) | −13.6088 | + | 13.2702i | −0.790995 | + | 0.771317i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.620393 | − | 2.35484i | −0.0359384 | − | 0.136412i | ||||
\(299\) | −26.6536 | − | 9.70110i | −1.54142 | − | 0.561029i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.899557 | + | 0.754818i | 0.0518496 | + | 0.0435070i | ||||
\(302\) | −0.849975 | + | 0.0707687i | −0.0489106 | + | 0.00407228i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −29.8924 | + | 4.75473i | −1.71445 | + | 0.272702i | ||||
\(305\) | 1.97339 | − | 1.13934i | 0.112996 | − | 0.0652382i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.7533 | − | 10.2499i | −1.01323 | − | 0.584990i | −0.101096 | − | 0.994877i | \(-0.532235\pi\) |
−0.912136 | + | 0.409887i | \(0.865568\pi\) | |||||||
\(308\) | 0.0311845 | − | 0.0257238i | 0.00177690 | − | 0.00146575i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.26194 | − | 0.875747i | 0.0716733 | − | 0.0497391i | ||||
\(311\) | −18.8205 | + | 6.85012i | −1.06722 | + | 0.388435i | −0.815135 | − | 0.579272i | \(-0.803337\pi\) |
−0.252081 | + | 0.967706i | \(0.581115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.06340 | − | 17.3734i | −0.173154 | − | 0.982003i | −0.940253 | − | 0.340475i | \(-0.889412\pi\) |
0.767100 | − | 0.641528i | \(-0.221699\pi\) | |||||||
\(314\) | −3.85640 | + | 14.1543i | −0.217629 | + | 0.798774i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.07146 | − | 5.21825i | 0.172783 | − | 0.293549i | ||||
\(317\) | −2.76189 | − | 3.29149i | −0.155123 | − | 0.184868i | 0.682886 | − | 0.730525i | \(-0.260725\pi\) |
−0.838009 | + | 0.545657i | \(0.816280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.288017 | − | 0.0507851i | −0.0161258 | − | 0.00284342i | ||||
\(320\) | −1.81376 | − | 1.60148i | −0.101392 | − | 0.0895253i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.411939 | − | 4.49123i | 0.0229565 | − | 0.250287i | ||||
\(323\) | −18.7360 | −1.04250 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.1951 | −1.17569 | ||||||||
\(326\) | 0.736827 | − | 8.03337i | 0.0408090 | − | 0.444927i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.33452 | − | 17.8387i | −0.0736866 | − | 0.984975i | ||||
\(329\) | −3.43911 | − | 0.606408i | −0.189604 | − | 0.0334323i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9390 | + | 15.4201i | 0.711190 | + | 0.847563i | 0.993743 | − | 0.111689i | \(-0.0356259\pi\) |
−0.282554 | + | 0.959252i | \(0.591181\pi\) | |||||||
\(332\) | 9.92416 | + | 5.84137i | 0.544659 | + | 0.320587i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.95194 | + | 7.16428i | −0.106805 | + | 0.392012i | ||||
\(335\) | 0.585001 | + | 3.31770i | 0.0319620 | + | 0.181266i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4122 | + | 4.51765i | −0.676133 | + | 0.246092i | −0.657186 | − | 0.753728i | \(-0.728254\pi\) |
−0.0189468 | + | 0.999820i | \(0.506031\pi\) | |||||||
\(338\) | 6.55893 | − | 4.55169i | 0.356759 | − | 0.247579i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.953052 | − | 1.15537i | −0.0516865 | − | 0.0626586i | ||||
\(341\) | 0.129480 | + | 0.0747552i | 0.00701173 | + | 0.00404822i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.78720 | − | 3.34124i | 0.312480 | − | 0.180410i | ||||
\(344\) | 6.80717 | + | 0.682042i | 0.367018 | + | 0.0367733i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.95510 | − | 0.162781i | 0.105107 | − | 0.00875117i | ||||
\(347\) | −13.6769 | − | 11.4763i | −0.734213 | − | 0.616078i | 0.197064 | − | 0.980391i | \(-0.436859\pi\) |
−0.931277 | + | 0.364313i | \(0.881304\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.2841 | + | 4.47105i | 0.657554 | + | 0.239330i | 0.649180 | − | 0.760635i | \(-0.275112\pi\) |
0.00837388 | + | 0.999965i | \(0.497334\pi\) | |||||||
\(350\) | −0.858586 | − | 3.25895i | −0.0458933 | − | 0.174198i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0657163 | − | 0.226157i | 0.00350269 | − | 0.0120542i | ||||
\(353\) | −7.34903 | + | 20.1913i | −0.391149 | + | 1.07467i | 0.575328 | + | 0.817923i | \(0.304874\pi\) |
−0.966477 | + | 0.256751i | \(0.917348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.656843 | + | 0.782795i | −0.0348616 | + | 0.0415464i | ||||
\(356\) | −19.6015 | + | 6.94853i | −1.03888 | + | 0.368271i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.41974 | + | 13.3333i | −0.497849 | + | 0.704686i | ||||
\(359\) | −9.46695 | − | 16.3972i | −0.499647 | − | 0.865413i | 0.500353 | − | 0.865821i | \(-0.333203\pi\) |
−1.00000 | 0.000407927i | \(0.999870\pi\) | ||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.1302 | − | 33.1344i | 1.00685 | − | 1.74392i | ||||
\(362\) | 10.1553 | + | 22.0190i | 0.533752 | + | 1.15729i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.18908 | + | 2.72191i | 0.167153 | + | 0.142667i | ||||
\(365\) | −0.0652682 | − | 0.179323i | −0.00341629 | − | 0.00938619i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.4580 | + | 4.13627i | −1.22450 | + | 0.215912i | −0.748260 | − | 0.663406i | \(-0.769110\pi\) |
−0.476236 | + | 0.879317i | \(0.657999\pi\) | |||||||
\(368\) | −12.7536 | − | 22.9724i | −0.664828 | − | 1.19752i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.04106 | − | 2.02400i | 0.106110 | − | 0.105223i | ||||
\(371\) | −3.68488 | + | 3.09198i | −0.191310 | + | 0.160528i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.76380 | + | 21.3456i | −0.194882 | + | 1.10523i | 0.717705 | + | 0.696348i | \(0.245193\pi\) |
−0.912587 | + | 0.408883i | \(0.865918\pi\) | |||||||
\(374\) | 0.0621638 | − | 0.131863i | 0.00321442 | − | 0.00681845i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.5456 | + | 8.36521i | −0.956415 | + | 0.431403i | ||||
\(377\) | − | 30.3329i | − | 1.56222i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.6783i | 1.72994i | 0.501825 | + | 0.864969i | \(0.332662\pi\) | ||||
−0.501825 | + | 0.864969i | \(0.667338\pi\) | |||||||
\(380\) | 4.51428 | − | 0.756963i | 0.231578 | − | 0.0388314i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.1771 | + | 9.98349i | 1.08351 | + | 0.510800i | ||||
\(383\) | −0.261068 | + | 1.48059i | −0.0133400 | + | 0.0756548i | −0.990751 | − | 0.135693i | \(-0.956674\pi\) |
0.977411 | + | 0.211347i | \(0.0677851\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.00468303 | + | 0.00392953i | −0.000238670 | + | 0.000200268i | ||||
\(386\) | −8.76604 | − | 8.83996i | −0.446180 | − | 0.449942i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.0559413 | − | 6.66219i | 0.00283999 | − | 0.338222i | ||||
\(389\) | 3.80299 | − | 0.670570i | 0.192819 | − | 0.0339993i | −0.0764044 | − | 0.997077i | \(-0.524344\pi\) |
0.269224 | + | 0.963078i | \(0.413233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.56271 | − | 15.2834i | −0.281318 | − | 0.772916i | ||||
\(392\) | 8.30341 | − | 17.2366i | 0.419386 | − | 0.870578i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.0495 | − | 7.40214i | 0.808563 | − | 0.372914i | ||||
\(395\) | −0.457839 | + | 0.793000i | −0.0230364 | + | 0.0399002i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.80431 | − | 16.9816i | −0.492064 | − | 0.852280i | 0.507894 | − | 0.861419i | \(-0.330424\pi\) |
−0.999958 | + | 0.00913954i | \(0.997091\pi\) | |||||||
\(398\) | 5.18193 | + | 3.66095i | 0.259747 | + | 0.183507i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.8265 | − | 12.8713i | −0.741327 | − | 0.643567i | ||||
\(401\) | 13.9437 | − | 16.6175i | 0.696316 | − | 0.829838i | −0.295788 | − | 0.955254i | \(-0.595582\pi\) |
0.992104 | + | 0.125416i | \(0.0400266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.30360 | + | 14.5715i | −0.264191 | + | 0.725859i | ||||
\(404\) | 16.4562 | + | 29.0639i | 0.818728 | + | 1.44598i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.66398 | − | 1.22875i | 0.231470 | − | 0.0609817i | ||||
\(407\) | 0.262912 | + | 0.0956921i | 0.0130321 | + | 0.00474328i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.42462 | − | 7.06909i | −0.416570 | − | 0.349544i | 0.410286 | − | 0.911957i | \(-0.365429\pi\) |
−0.826857 | + | 0.562413i | \(0.809873\pi\) | |||||||
\(410\) | 0.224456 | + | 2.69586i | 0.0110851 | + | 0.133139i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 29.7761 | + | 11.1216i | 1.46696 | + | 0.547923i | ||||
\(413\) | 1.83029 | − | 1.05672i | 0.0900626 | − | 0.0519976i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.50814 | − | 0.870727i | −0.0740319 | − | 0.0427423i | ||||
\(416\) | 24.2834 | + | 2.63919i | 1.19059 | + | 0.129397i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.254012 | + | 0.366028i | 0.0124241 | + | 0.0179030i | ||||
\(419\) | 22.7569 | − | 8.28284i | 1.11175 | − | 0.404643i | 0.280114 | − | 0.959967i | \(-0.409628\pi\) |
0.831635 | + | 0.555323i | \(0.187405\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.35770 | + | 36.0563i | 0.309855 | + | 1.75728i | 0.599721 | + | 0.800209i | \(0.295278\pi\) |
−0.289866 | + | 0.957067i | \(0.593611\pi\) | |||||||
\(422\) | 30.6247 | + | 8.34381i | 1.49078 | + | 0.406170i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.59351 | + | 26.9756i | −0.368773 | + | 1.31005i | ||||
\(425\) | −7.81210 | − | 9.31010i | −0.378942 | − | 0.451606i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.60217 | − | 0.635160i | −0.174321 | − | 0.0307375i | ||||
\(428\) | −1.96981 | − | 0.364411i | −0.0952146 | − | 0.0176145i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.03024 | − | 0.0944945i | −0.0496827 | − | 0.00455693i | ||||
\(431\) | 38.5608 | 1.85741 | 0.928705 | − | 0.370820i | \(-0.120923\pi\) | ||||
0.928705 | + | 0.370820i | \(0.120923\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.56251 | −0.315374 | −0.157687 | − | 0.987489i | \(-0.550404\pi\) | ||||
−0.157687 | + | 0.987489i | \(0.550404\pi\) | |||||||
\(434\) | −2.45536 | − | 0.225207i | −0.117861 | − | 0.0108103i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.2899 | + | 2.64360i | 0.684361 | + | 0.126605i | ||||
\(437\) | 48.9513 | + | 8.63143i | 2.34166 | + | 0.412897i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.17279 | − | 1.39768i | −0.0559744 | − | 0.0667077i | 0.737331 | − | 0.675532i | \(-0.236086\pi\) |
−0.793305 | + | 0.608824i | \(0.791641\pi\) | |||||||
\(440\) | −0.00965041 | + | 0.0342827i | −0.000460065 | + | 0.00163437i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.5881 | + | 3.97459i | 0.693886 | + | 0.189052i | ||||
\(443\) | 0.302973 | + | 1.71824i | 0.0143947 | + | 0.0816362i | 0.991159 | − | 0.132681i | \(-0.0423585\pi\) |
−0.976764 | + | 0.214317i | \(0.931247\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.95530 | − | 1.07564i | 0.140095 | − | 0.0509903i | ||||
\(446\) | −14.7685 | − | 21.2813i | −0.699310 | − | 1.00770i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.577888 | + | 3.84072i | 0.0273026 | + | 0.181457i | ||||
\(449\) | −8.00158 | − | 4.61971i | −0.377618 | − | 0.218018i | 0.299164 | − | 0.954202i | \(-0.403292\pi\) |
−0.676781 | + | 0.736184i | \(0.736626\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.228032 | + | 0.131654i | −0.0107376 | + | 0.00619937i | ||||
\(452\) | −27.1088 | − | 10.1254i | −1.27509 | − | 0.476258i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.30026 | − | 27.6275i | −0.107957 | − | 1.29663i | ||||
\(455\) | −0.485708 | − | 0.407557i | −0.0227703 | − | 0.0191066i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.9190 | + | 9.43376i | 1.21244 | + | 0.441293i | 0.867550 | − | 0.497350i | \(-0.165694\pi\) |
0.344891 | + | 0.938643i | \(0.387916\pi\) | |||||||
\(458\) | −7.75140 | + | 2.04214i | −0.362199 | + | 0.0954229i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.95776 | + | 3.45767i | 0.0912812 | + | 0.161215i | ||||
\(461\) | −7.09177 | + | 19.4845i | −0.330297 | + | 0.907483i | 0.657737 | + | 0.753247i | \(0.271514\pi\) |
−0.988034 | + | 0.154236i | \(0.950709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.16175 | + | 7.34328i | −0.286361 | + | 0.341271i | −0.889979 | − | 0.456002i | \(-0.849281\pi\) |
0.603618 | + | 0.797274i | \(0.293725\pi\) | |||||||
\(464\) | 18.4206 | − | 21.2187i | 0.855153 | − | 0.985053i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.67587 | − | 6.12935i | −0.401902 | − | 0.283937i | ||||
\(467\) | 8.74737 | + | 15.1509i | 0.404780 | + | 0.701099i | 0.994296 | − | 0.106657i | \(-0.0340148\pi\) |
−0.589516 | + | 0.807757i | \(0.700681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.70388 | − | 4.68326i | 0.124854 | − | 0.216253i | ||||
\(470\) | 2.79383 | − | 1.28853i | 0.128870 | − | 0.0594355i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.34366 | − | 11.0926i | 0.245962 | − | 0.510577i | ||||
\(473\) | −0.0344412 | − | 0.0946266i | −0.00158361 | − | 0.00435093i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 36.5788 | − | 6.44983i | 1.67835 | − | 0.295938i | ||||
\(476\) | −0.0201866 | + | 2.40407i | −0.000925251 | + | 0.110191i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.44446 | − | 6.49880i | −0.294763 | − | 0.297248i | ||||
\(479\) | −20.0678 | + | 16.8388i | −0.916919 | + | 0.769386i | −0.973423 | − | 0.229016i | \(-0.926449\pi\) |
0.0565037 | + | 0.998402i | \(0.482005\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.03898 | + | 28.5775i | −0.229758 | + | 1.30302i | ||||
\(482\) | 0.887657 | + | 0.418467i | 0.0404317 | + | 0.0190607i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.6937 | − | 3.63763i | 0.986076 | − | 0.165347i | ||||
\(485\) | 1.00752i | 0.0457493i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.10957i | − | 0.322166i | −0.986941 | − | 0.161083i | \(-0.948501\pi\) | ||
0.986941 | − | 0.161083i | \(-0.0514986\pi\) | |||||||
\(488\) | −19.4249 | + | 8.76184i | −0.879323 | + | 0.396630i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.23375 | + | 2.61705i | −0.0557352 | + | 0.118226i | ||||
\(491\) | −3.43007 | + | 19.4529i | −0.154797 | + | 0.877897i | 0.804174 | + | 0.594393i | \(0.202608\pi\) |
−0.958971 | + | 0.283503i | \(0.908503\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.3239 | − | 11.1801i | 0.600081 | − | 0.503527i | ||||
\(494\) | −32.8115 | + | 32.5372i | −1.47626 | + | 1.46392i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.5590 | + | 6.97241i | −0.563916 | + | 0.313071i | ||||
\(497\) | 1.61539 | − | 0.284836i | 0.0724600 | − | 0.0127767i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.5189 | − | 37.1430i | −0.605191 | − | 1.66275i | −0.740591 | − | 0.671956i | \(-0.765454\pi\) |
0.135400 | − | 0.990791i | \(-0.456768\pi\) | |||||||
\(500\) | 4.55890 | + | 3.89106i | 0.203880 | + | 0.174014i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.29252 | + | 2.80248i | 0.0576881 | + | 0.125081i | ||||
\(503\) | 19.5426 | − | 33.8489i | 0.871364 | − | 1.50925i | 0.0107769 | − | 0.999942i | \(-0.496570\pi\) |
0.860587 | − | 0.509304i | \(-0.170097\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.52541 | − | 4.37413i | −0.112379 | − | 0.194646i | ||||
\(506\) | −0.223162 | + | 0.315878i | −0.00992077 | + | 0.0140425i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.7680 | − | 5.94410i | 0.743961 | − | 0.263727i | ||||
\(509\) | 9.47986 | − | 11.2977i | 0.420187 | − | 0.500760i | −0.513877 | − | 0.857864i | \(-0.671791\pi\) |
0.934065 | + | 0.357104i | \(0.116236\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.104769 | + | 0.287850i | −0.00463471 | + | 0.0127338i | ||||
\(512\) | 15.3842 | + | 16.5930i | 0.679891 | + | 0.733314i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.18448 | + | 19.6788i | 0.228677 | + | 0.867996i | ||||
\(515\) | −4.51685 | − | 1.64400i | −0.199036 | − | 0.0724432i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.229404 | + | 0.192493i | 0.0100892 | + | 0.00846582i | ||||
\(518\) | −4.59819 | + | 0.382844i | −0.202033 | + | 0.0168212i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.67547 | − | 0.368262i | −0.161180 | − | 0.0161494i | ||||
\(521\) | 10.1293 | − | 5.84816i | 0.443773 | − | 0.256213i | −0.261424 | − | 0.965224i | \(-0.584192\pi\) |
0.705197 | + | 0.709012i | \(0.250859\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.89969 | + | 3.98354i | 0.301702 | + | 0.174188i | 0.643207 | − | 0.765692i | \(-0.277603\pi\) |
−0.341505 | + | 0.939880i | \(0.610937\pi\) | |||||||
\(524\) | 24.7325 | + | 29.9827i | 1.08044 | + | 1.30980i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.9020 | − | 8.25959i | 0.518950 | − | 0.360135i | ||||
\(527\) | −8.35546 | + | 3.04114i | −0.363969 | + | 0.132474i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.49884 | + | 19.8429i | 0.152124 | + | 0.862736i | ||||
\(530\) | 1.11403 | − | 4.08888i | 0.0483905 | − | 0.177610i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.33207 | − | 3.72706i | −0.274530 | − | 0.161589i | ||||
\(533\) | −17.5542 | − | 20.9203i | −0.760356 | − | 0.906157i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.298337 | + | 0.0526049i | 0.0128982 | + | 0.00227431i | ||||
\(536\) | −2.35033 | − | 31.4171i | −0.101519 | − | 1.35701i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.407173 | − | 4.43928i | 0.0175545 | − | 0.191391i | ||||
\(539\) | −0.281617 | −0.0121301 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.41220 | 0.361669 | 0.180834 | − | 0.983514i | \(-0.442120\pi\) | ||||
0.180834 | + | 0.983514i | \(0.442120\pi\) | |||||||
\(542\) | 0.430333 | − | 4.69178i | 0.0184844 | − | 0.201529i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.79110 | + | 11.6394i | 0.334041 | + | 0.499036i | ||||
\(545\) | −2.16426 | − | 0.381618i | −0.0927069 | − | 0.0163467i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2369 | + | 13.3916i | 0.480453 | + | 0.572582i | 0.950763 | − | 0.309920i | \(-0.100302\pi\) |
−0.470309 | + | 0.882502i | \(0.655858\pi\) | |||||||
\(548\) | 15.5597 | − | 26.4351i | 0.664679 | − | 1.12925i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0759708 | + | 0.278839i | −0.00323941 | + | 0.0118897i | ||||
\(551\) | 9.23054 | + | 52.3490i | 0.393234 | + | 2.23014i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.38121 | − | 0.502719i | 0.0587350 | − | 0.0213778i | ||||
\(554\) | 4.85129 | − | 3.36664i | 0.206111 | − | 0.143035i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.7850 | + | 11.3711i | −0.584615 | + | 0.482243i | ||||
\(557\) | −0.688812 | − | 0.397686i | −0.0291859 | − | 0.0168505i | 0.485336 | − | 0.874328i | \(-0.338697\pi\) |
−0.514522 | + | 0.857477i | \(0.672031\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.04493 | − | 5.22209i | 0.382560 | − | 0.220871i | ||||
\(560\) | −0.0922646 | − | 0.580058i | −0.00389889 | − | 0.0245119i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27.6621 | + | 2.30314i | −1.16685 | + | 0.0971520i | ||||
\(563\) | 4.79979 | + | 4.02750i | 0.202287 | + | 0.169739i | 0.738304 | − | 0.674468i | \(-0.235627\pi\) |
−0.536017 | + | 0.844207i | \(0.680072\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.11224 | + | 1.49673i | 0.173003 | + | 0.0629680i | ||||
\(566\) | −5.54768 | − | 21.0575i | −0.233187 | − | 0.885111i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.84184 | − | 6.67163i | 0.287077 | − | 0.279935i | ||||
\(569\) | −1.85350 | + | 5.09244i | −0.0777027 | + | 0.213486i | −0.972462 | − | 0.233063i | \(-0.925125\pi\) |
0.894759 | + | 0.446550i | \(0.147347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.5951 | − | 23.3525i | 0.820029 | − | 0.977273i | −0.179950 | − | 0.983676i | \(-0.557594\pi\) |
0.999979 | + | 0.00640314i | \(0.00203820\pi\) | |||||||
\(572\) | −0.120130 | − | 0.338880i | −0.00502287 | − | 0.0141693i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.50560 | − | 3.54658i | 0.104582 | − | 0.148032i | ||||
\(575\) | 16.1215 | + | 27.9233i | 0.672315 | + | 1.16448i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.67484 | + | 16.7573i | −0.402769 | + | 0.697616i | −0.994059 | − | 0.108843i | \(-0.965286\pi\) |
0.591290 | + | 0.806459i | \(0.298619\pi\) | |||||||
\(578\) | −6.43783 | − | 13.9587i | −0.267779 | − | 0.580605i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.75860 | + | 3.23207i | −0.114545 | + | 0.134204i | ||||
\(581\) | 0.956081 | + | 2.62681i | 0.0396649 | + | 0.108979i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.406232 | − | 0.0716296i | 0.0168244 | − | 0.00296659i | ||||
\(584\) | 0.440143 | + | 1.72948i | 0.0182132 | + | 0.0715662i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.6999 | + | 18.5436i | −0.772486 | + | 0.766027i | ||||
\(587\) | 33.1376 | − | 27.8057i | 1.36773 | − | 1.14767i | 0.394227 | − | 0.919013i | \(-0.371012\pi\) |
0.973508 | − | 0.228653i | \(-0.0734320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.71881 | − | 26.7617i | 0.194435 | − | 1.10270i | ||||
\(590\) | −0.793980 | + | 1.68420i | −0.0326876 | + | 0.0693374i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.8794 | + | 16.9306i | −0.858139 | + | 0.695845i | ||||
\(593\) | 32.7916i | 1.34659i | 0.739375 | + | 0.673294i | \(0.235121\pi\) | ||||
−0.739375 | + | 0.673294i | \(0.764879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.363568i | − | 0.0149048i | ||||||
\(596\) | −0.569525 | − | 3.39646i | −0.0233286 | − | 0.139124i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −36.2832 | − | 17.1049i | −1.48373 | − | 0.699473i | ||||
\(599\) | 6.52625 | − | 37.0122i | 0.266655 | − | 1.51228i | −0.497624 | − | 0.867393i | \(-0.665794\pi\) |
0.764279 | − | 0.644885i | \(-0.223095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.65033 | − | 6.41939i | 0.312063 | − | 0.261852i | −0.473281 | − | 0.880912i | \(-0.656930\pi\) |
0.785344 | + | 0.619059i | \(0.212486\pi\) | |||||||
\(602\) | 1.16935 | + | 1.17921i | 0.0476591 | + | 0.0480609i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.20616 | − | 0.0101279i | −0.0490781 | − | 0.000412100i | ||||
\(605\) | −3.27588 | + | 0.577627i | −0.133184 | + | 0.0234839i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.92909 | + | 27.2799i | 0.403009 | + | 1.10726i | 0.960792 | + | 0.277271i | \(0.0894301\pi\) |
−0.557783 | + | 0.829987i | \(0.688348\pi\) | |||||||
\(608\) | −42.7118 | + | 2.83487i | −1.73219 | + | 0.114969i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.92629 | − | 1.34963i | 0.118482 | − | 0.0546447i | ||||
\(611\) | −15.5298 | + | 26.8983i | −0.628266 | + | 1.08819i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6465 | − | 18.4402i | −0.430007 | − | 0.744794i | 0.566866 | − | 0.823810i | \(-0.308156\pi\) |
−0.996873 | + | 0.0790155i | \(0.974822\pi\) | |||||||
\(614\) | −23.6780 | − | 16.7281i | −0.955566 | − | 0.675091i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0472399 | − | 0.0321987i | 0.00190335 | − | 0.00129732i | ||||
\(617\) | −1.59822 | + | 1.90469i | −0.0643420 | + | 0.0766798i | −0.797255 | − | 0.603642i | \(-0.793716\pi\) |
0.732913 | + | 0.680322i | \(0.238160\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.56324 | − | 12.5374i | 0.183412 | − | 0.503921i | −0.813577 | − | 0.581457i | \(-0.802483\pi\) |
0.996990 | + | 0.0775360i | \(0.0247053\pi\) | |||||||
\(620\) | 1.89031 | − | 1.07031i | 0.0759168 | − | 0.0429847i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −27.3899 | + | 7.21598i | −1.09823 | + | 0.289334i | ||||
\(623\) | −4.74387 | − | 1.72663i | −0.190059 | − | 0.0691759i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.1064 | + | 15.1931i | 0.724256 | + | 0.607723i | ||||
\(626\) | −2.07006 | − | 24.8627i | −0.0827364 | − | 0.993714i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.25929 | + | 19.4354i | −0.289677 | + | 0.775557i | ||||
\(629\) | −14.4101 | + | 8.31969i | −0.574570 | + | 0.331728i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1235 | + | 19.1238i | 1.31862 | + | 0.761308i | 0.983507 | − | 0.180868i | \(-0.0578908\pi\) |
0.335117 | + | 0.942176i | \(0.391224\pi\) | |||||||
\(632\) | 4.99959 | − | 6.95213i | 0.198873 | − | 0.276541i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.46441 | − | 4.99216i | −0.137589 | − | 0.198264i | ||||
\(635\) | −2.52810 | + | 0.920154i | −0.100325 | + | 0.0365152i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.07197 | − | 28.7646i | −0.200959 | − | 1.13969i | ||||
\(638\) | −0.399055 | − | 0.108724i | −0.0157987 | − | 0.00430443i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.34745 | − | 2.48965i | −0.0927913 | − | 0.0984120i | ||||
\(641\) | −9.13644 | − | 10.8884i | −0.360868 | − | 0.430065i | 0.554811 | − | 0.831976i | \(-0.312791\pi\) |
−0.915679 | + | 0.401911i | \(0.868346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.627325 | + | 0.110614i | 0.0247393 | + | 0.00436221i | 0.186004 | − | 0.982549i | \(-0.440446\pi\) |
−0.161265 | + | 0.986911i | \(0.551557\pi\) | |||||||
\(644\) | 1.16027 | − | 6.27180i | 0.0457210 | − | 0.247144i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26.3859 | − | 2.42013i | −1.03814 | − | 0.0952189i | ||||
\(647\) | 7.26586 | 0.285650 | 0.142825 | − | 0.989748i | \(-0.454381\pi\) | ||||
0.142825 | + | 0.989748i | \(0.454381\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.181235 | −0.00711408 | ||||||||
\(650\) | −29.8491 | − | 2.73778i | −1.17078 | − | 0.107384i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.07535 | − | 11.2182i | 0.0812769 | − | 0.439340i | ||||
\(653\) | −31.3669 | − | 5.53083i | −1.22748 | − | 0.216438i | −0.477938 | − | 0.878393i | \(-0.658616\pi\) |
−0.749543 | + | 0.661955i | \(0.769727\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.77810 | − | 4.50257i | −0.147623 | − | 0.175930i | ||||
\(656\) | 0.424819 | − | 25.2946i | 0.0165864 | − | 0.987588i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.76497 | − | 1.29824i | −0.185758 | − | 0.0506105i | ||||
\(659\) | −2.56367 | − | 14.5393i | −0.0998663 | − | 0.566370i | −0.993147 | − | 0.116871i | \(-0.962714\pi\) |
0.893281 | − | 0.449499i | \(-0.148397\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.8308 | + | 6.85385i | −0.732433 | + | 0.266584i | −0.681194 | − | 0.732103i | \(-0.738539\pi\) |
−0.0512388 | + | 0.998686i | \(0.516317\pi\) | |||||||
\(662\) | 16.2302 | + | 23.3874i | 0.630803 | + | 0.908978i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.2217 | + | 9.50832i | 0.513101 | + | 0.368994i | ||||
\(665\) | 0.962265 | + | 0.555564i | 0.0373150 | + | 0.0215438i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.9619 | + | 23.0720i | −1.54733 | + | 0.893352i | ||||
\(668\) | −3.67433 | + | 9.83734i | −0.142164 | + | 0.380618i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.395308 | + | 4.74789i | 0.0152721 | + | 0.183427i | ||||
\(671\) | 0.240281 | + | 0.201620i | 0.00927594 | + | 0.00778344i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.6670 | − | 11.8898i | −1.25922 | − | 0.458319i | −0.375713 | − | 0.926736i | \(-0.622602\pi\) |
−0.883508 | + | 0.468417i | \(0.844825\pi\) | |||||||
\(674\) | −18.0636 | + | 4.75894i | −0.695784 | + | 0.183307i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.82490 | − | 5.56294i | 0.377881 | − | 0.213959i | ||||
\(677\) | −11.4934 | + | 31.5778i | −0.441726 | + | 1.21363i | 0.496630 | + | 0.867962i | \(0.334571\pi\) |
−0.938356 | + | 0.345670i | \(0.887652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.03957 | − | 1.23891i | 0.0398951 | − | 0.0475451i | ||||
\(680\) | −1.19295 | − | 1.75021i | −0.0457474 | − | 0.0671176i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.172691 | + | 0.122003i | 0.00661267 | + | 0.00467173i | ||||
\(683\) | −12.3153 | − | 21.3308i | −0.471233 | − | 0.816200i | 0.528225 | − | 0.849104i | \(-0.322858\pi\) |
−0.999459 | + | 0.0329044i | \(0.989524\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.31937 | + | 4.01726i | −0.0886185 | + | 0.153492i | ||||
\(686\) | 8.58172 | − | 3.95794i | 0.327652 | − | 0.151115i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.49845 | + | 1.83981i | 0.362125 | + | 0.0701420i | ||||
\(689\) | 14.6326 | + | 40.2027i | 0.557458 | + | 1.53160i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.4784 | − | 2.55293i | 0.550784 | − | 0.0971181i | 0.108672 | − | 0.994078i | \(-0.465340\pi\) |
0.442113 | + | 0.896960i | \(0.354229\pi\) | |||||||
\(692\) | 2.77440 | + | 0.0232961i | 0.105467 | + | 0.000885586i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.7788 | − | 17.9287i | −0.674873 | − | 0.680564i | ||||
\(695\) | 2.07012 | − | 1.73704i | 0.0785243 | − | 0.0658897i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.71925 | − | 15.4216i | 0.102999 | − | 0.584135i | ||||
\(698\) | 16.7222 | + | 7.88334i | 0.632945 | + | 0.298389i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.788188 | − | 4.70050i | −0.0297907 | − | 0.177662i | ||||
\(701\) | − | 32.3443i | − | 1.22163i | −0.791775 | − | 0.610813i | \(-0.790843\pi\) | ||
0.791775 | − | 0.610813i | \(-0.209157\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 50.8528i | − | 1.91795i | ||||||
\(704\) | 0.121761 | − | 0.310008i | 0.00458905 | − | 0.0116839i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.9578 | + | 27.4862i | −0.487672 | + | 1.03446i | ||||
\(707\) | −1.40787 | + | 7.98443i | −0.0529484 | + | 0.300285i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.0746 | + | 25.2356i | −1.12947 | + | 0.947741i | −0.999044 | − | 0.0437162i | \(-0.986080\pi\) |
−0.130430 | + | 0.991458i | \(0.541636\pi\) | |||||||
\(710\) | −1.02615 | + | 1.01757i | −0.0385106 | + | 0.0381886i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −28.5024 | + | 7.25370i | −1.06817 | + | 0.271844i | ||||
\(713\) | 23.2312 | − | 4.09629i | 0.870016 | − | 0.153407i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0185962 | + | 0.0510927i | 0.000695460 | + | 0.00191076i | ||||
\(716\) | −14.9881 | + | 17.5605i | −0.560132 | + | 0.656268i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.2143 | − | 24.3151i | −0.418514 | − | 0.907432i | ||||
\(719\) | 0.482259 | − | 0.835298i | 0.0179852 | − | 0.0311514i | −0.856893 | − | 0.515495i | \(-0.827608\pi\) |
0.874878 | + | 0.484343i | \(0.160941\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.85790 | + | 6.68207i | 0.143676 | + | 0.248853i | ||||
\(722\) | 31.2211 | − | 44.1922i | 1.16193 | − | 1.64467i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.4575 | + | 32.3212i | 0.425816 | + | 1.20121i | ||||
\(725\) | −22.1640 | + | 26.4140i | −0.823151 | + | 0.980993i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.16819 | − | 19.6944i | 0.265854 | − | 0.730427i | −0.732892 | − | 0.680345i | \(-0.761830\pi\) |
0.998745 | − | 0.0500812i | \(-0.0159480\pi\) | |||||||
\(728\) | 4.13960 | + | 4.24521i | 0.153424 | + | 0.157338i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.0687541 | − | 0.260972i | −0.00254470 | − | 0.00965899i | ||||
\(731\) | 5.62763 | + | 2.04829i | 0.208146 | + | 0.0757588i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.37507 | + | 1.15382i | 0.0507892 | + | 0.0426172i | 0.667829 | − | 0.744315i | \(-0.267224\pi\) |
−0.617040 | + | 0.786932i | \(0.711668\pi\) | |||||||
\(734\) | −33.5702 | + | 2.79505i | −1.23910 | + | 0.103167i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.9936 | − | 33.9994i | −0.552671 | − | 1.25324i | ||||
\(737\) | −0.401606 | + | 0.231867i | −0.0147934 | + | 0.00854095i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.1448 | − | 9.89858i | −0.630683 | − | 0.364125i | 0.150333 | − | 0.988635i | \(-0.451965\pi\) |
−0.781017 | + | 0.624510i | \(0.785299\pi\) | |||||||
\(740\) | 3.13588 | − | 2.58675i | 0.115277 | − | 0.0950910i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.58882 | + | 3.87847i | −0.205172 | + | 0.142383i | ||||
\(743\) | −36.3877 | + | 13.2440i | −1.33494 | + | 0.485877i | −0.908214 | − | 0.418507i | \(-0.862554\pi\) |
−0.426721 | + | 0.904383i | \(0.640331\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.0904359 | + | 0.512888i | 0.00331332 | + | 0.0187907i | ||||
\(746\) | −8.05778 | + | 29.5748i | −0.295016 | + | 1.08281i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.104578 | − | 0.177673i | 0.00382376 | − | 0.00649635i | ||||
\(749\) | −0.312575 | − | 0.372512i | −0.0114212 | − | 0.0136113i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.7048 | + | 4.00346i | 0.828508 | + | 0.146088i | 0.571792 | − | 0.820398i | \(-0.306248\pi\) |
0.256716 | + | 0.966487i | \(0.417359\pi\) | |||||||
\(752\) | −27.1983 | + | 9.38521i | −0.991820 | + | 0.342243i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.91811 | − | 42.7179i | 0.142689 | − | 1.55569i | ||||
\(755\) | 0.182408 | 0.00663851 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.3070 | 1.21056 | 0.605281 | − | 0.796012i | \(-0.293061\pi\) | ||||
0.605281 | + | 0.796012i | \(0.293061\pi\) | |||||||
\(758\) | −4.35024 | + | 47.4292i | −0.158008 | + | 1.72271i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.45525 | − | 0.482921i | 0.234156 | − | 0.0175174i | ||||
\(761\) | −15.6353 | − | 2.75693i | −0.566780 | − | 0.0999386i | −0.117087 | − | 0.993122i | \(-0.537356\pi\) |
−0.449693 | + | 0.893183i | \(0.648467\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.26755 | + | 2.70236i | 0.0820909 | + | 0.0978322i | ||||
\(764\) | 28.5342 | + | 16.7952i | 1.03233 | + | 0.607630i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.558912 | + | 2.05140i | −0.0201943 | + | 0.0741201i | ||||
\(767\) | −3.26407 | − | 18.5114i | −0.117859 | − | 0.668409i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7088 | − | 7.53738i | 0.746777 | − | 0.271805i | 0.0595284 | − | 0.998227i | \(-0.481040\pi\) |
0.687249 | + | 0.726422i | \(0.258818\pi\) | |||||||
\(770\) | −0.00710271 | + | 0.00492906i | −0.000255964 | + | 0.000177631i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.2034 | − | 13.5816i | −0.403218 | − | 0.488814i | ||||
\(773\) | 18.9410 | + | 10.9356i | 0.681261 | + | 0.393326i | 0.800330 | − | 0.599560i | \(-0.204658\pi\) |
−0.119069 | + | 0.992886i | \(0.537991\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.2657 | − | 8.81366i | 0.548360 | − | 0.316596i | ||||
\(776\) | 0.939341 | − | 9.37516i | 0.0337204 | − | 0.336549i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.44238 | − | 0.453131i | 0.195119 | − | 0.0162455i | ||||
\(779\) | 36.6615 | + | 30.7626i | 1.31353 | + | 1.10219i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.132179 | − | 0.0481093i | −0.00472975 | − | 0.00172149i | ||||
\(782\) | −5.85981 | − | 22.2422i | −0.209546 | − | 0.795380i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.9202 | − | 23.2017i | 0.497149 | − | 0.828633i | ||||
\(785\) | 1.07307 | − | 2.94823i | 0.0382994 | − | 0.105227i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.17335 | − | 2.59010i | 0.0774716 | − | 0.0923271i | −0.725916 | − | 0.687783i | \(-0.758584\pi\) |
0.803388 | + | 0.595456i | \(0.203029\pi\) | |||||||
\(788\) | 23.5587 | − | 8.35133i | 0.839244 | − | 0.297504i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.747208 | + | 1.05764i | −0.0265845 | + | 0.0376293i | ||||
\(791\) | −3.51231 | − | 6.08351i | −0.124884 | − | 0.216305i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.2661 | + | 28.1737i | −0.577625 | + | 1.00048i | ||||
\(794\) | −11.6139 | − | 25.1816i | −0.412162 | − | 0.893661i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.82484 | + | 5.82507i | 0.241900 | + | 0.206464i | ||||
\(797\) | −16.3658 | − | 44.9646i | −0.579705 | − | 1.59273i | −0.788679 | − | 0.614805i | \(-0.789235\pi\) |
0.208974 | − | 0.977921i | \(-0.432988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.5393 | + | 3.09264i | −0.620494 | + | 0.109410i | ||||
\(800\) | −19.2177 | − | 20.0419i | −0.679447 | − | 0.708588i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.7835 | − | 21.6013i | 0.769201 | − | 0.762769i | ||||
\(803\) | 0.0201228 | − | 0.0168850i | 0.000710117 | − | 0.000595859i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.167491 | + | 0.949891i | −0.00590330 | + | 0.0334793i | ||||
\(806\) | −9.35128 | + | 19.8360i | −0.329385 | + | 0.698695i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.4212 | + | 43.0564i | 0.683234 | + | 1.51472i | ||||
\(809\) | 17.3637i | 0.610473i | 0.952277 | + | 0.305237i | \(0.0987356\pi\) | ||||
−0.952277 | + | 0.305237i | \(0.901264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.7618i | − | 0.483242i | −0.970371 | − | 0.241621i | \(-0.922321\pi\) | ||
0.970371 | − | 0.241621i | \(-0.0776791\pi\) | |||||||
\(812\) | 6.72702 | − | 1.12800i | 0.236072 | − | 0.0395850i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.357899 | + | 0.168724i | 0.0125444 | + | 0.00591377i | ||||
\(815\) | −0.299589 | + | 1.69905i | −0.0104941 | + | 0.0595152i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.0208 | + | 11.7648i | −0.490524 | + | 0.411599i | ||||
\(818\) | −10.9513 | − | 11.0436i | −0.382903 | − | 0.386131i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0321227 | + | 3.82557i | −0.00112177 | + | 0.133595i | ||||
\(821\) | 26.2703 | − | 4.63216i | 0.916840 | − | 0.161664i | 0.304732 | − | 0.952438i | \(-0.401433\pi\) |
0.612108 | + | 0.790774i | \(0.290322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0879 | + | 41.4538i | 0.525932 | + | 1.44499i | 0.863820 | + | 0.503801i | \(0.168065\pi\) |
−0.337888 | + | 0.941186i | \(0.609712\pi\) | |||||||
\(824\) | 40.4972 | + | 19.5088i | 1.41079 | + | 0.679621i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.71409 | − | 1.25176i | 0.0944354 | − | 0.0435542i | ||||
\(827\) | −5.67028 | + | 9.82121i | −0.197175 | + | 0.341517i | −0.947611 | − | 0.319426i | \(-0.896510\pi\) |
0.750436 | + | 0.660943i | \(0.229843\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.5329 | + | 25.1717i | 0.504747 | + | 0.874248i | 0.999985 | + | 0.00549015i | \(0.00174758\pi\) |
−0.495238 | + | 0.868757i | \(0.664919\pi\) | |||||||
\(830\) | −2.01145 | − | 1.42105i | −0.0698184 | − | 0.0493255i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 33.8574 | + | 6.85347i | 1.17380 | + | 0.237601i | ||||
\(833\) | 10.7656 | − | 12.8300i | 0.373007 | − | 0.444532i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.543139 | − | 1.49226i | 0.0187961 | − | 0.0516419i | ||||
\(836\) | 0.310446 | + | 0.548289i | 0.0107370 | + | 0.0189630i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33.1185 | − | 8.72523i | 1.14406 | − | 0.301408i | ||||
\(839\) | 11.0585 | + | 4.02496i | 0.381781 | + | 0.138957i | 0.525779 | − | 0.850621i | \(-0.323774\pi\) |
−0.143998 | + | 0.989578i | \(0.545996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.5866 | − | 13.0787i | −0.537469 | − | 0.450990i | ||||
\(842\) | 4.29615 | + | 51.5994i | 0.148055 | + | 1.77823i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 42.0510 | + | 15.7064i | 1.44745 | + | 0.540637i | ||||
\(845\) | −1.47865 | + | 0.853700i | −0.0508672 | + | 0.0293682i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.62422 | + | 2.66980i | 0.158890 | + | 0.0917353i | ||||
\(848\) | −14.1784 | + | 37.0090i | −0.486888 | + | 1.27089i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.79920 | − | 14.1205i | −0.336110 | − | 0.484330i | ||||
\(851\) | 41.4820 | − | 15.0982i | 1.42198 | − | 0.517560i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.59288 | − | 43.0614i | −0.259975 | − | 1.47439i | −0.782971 | − | 0.622058i | \(-0.786297\pi\) |
0.522996 | − | 0.852335i | \(-0.324814\pi\) | |||||||
\(854\) | −4.99090 | − | 1.35979i | −0.170785 | − | 0.0465311i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.72702 | − | 0.767643i | −0.0932077 | − | 0.0262375i | ||||
\(857\) | 2.62091 | + | 3.12348i | 0.0895287 | + | 0.106696i | 0.808949 | − | 0.587879i | \(-0.200037\pi\) |
−0.719420 | + | 0.694575i | \(0.755592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.3251 | − | 6.75775i | −1.30764 | − | 0.230571i | −0.523961 | − | 0.851743i | \(-0.675546\pi\) |
−0.783675 | + | 0.621171i | \(0.786657\pi\) | |||||||
\(860\) | −1.43869 | − | 0.266154i | −0.0490588 | − | 0.00907577i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 54.3053 | + | 4.98092i | 1.84965 | + | 0.169651i | ||||
\(863\) | −48.5663 | −1.65322 | −0.826608 | − | 0.562778i | \(-0.809732\pi\) | ||||
−0.826608 | + | 0.562778i | \(0.809732\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.419573 | −0.0142659 | ||||||||
\(866\) | −9.24200 | − | 0.847683i | −0.314056 | − | 0.0288054i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.42880 | − | 0.634320i | −0.116381 | − | 0.0215302i | ||||
\(869\) | −0.124130 | − | 0.0218875i | −0.00421083 | − | 0.000742483i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.9161 | − | 36.8444i | −1.04755 | − | 1.24842i | ||||
\(872\) | 19.7830 | + | 5.56881i | 0.669937 | + | 0.188584i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 67.8233 | + | 18.4787i | 2.29416 | + | 0.625052i | ||||
\(875\) | 0.252648 | + | 1.43284i | 0.00854107 | + | 0.0484388i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.9919 | − | 5.82058i | 0.540008 | − | 0.196547i | −0.0575935 | − | 0.998340i | \(-0.518343\pi\) |
0.597602 | + | 0.801793i | \(0.296120\pi\) | |||||||
\(878\) | −1.47111 | − | 2.11985i | −0.0496475 | − | 0.0715414i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0180190 | + | 0.0470339i | −0.000607421 | + | 0.00158551i | ||||
\(881\) | 2.59611 | + | 1.49886i | 0.0874651 | + | 0.0504980i | 0.543095 | − | 0.839672i | \(-0.317252\pi\) |
−0.455630 | + | 0.890169i | \(0.650586\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0858 | + | 9.86450i | −0.574984 | + | 0.331967i | −0.759137 | − | 0.650931i | \(-0.774379\pi\) |
0.184154 | + | 0.982897i | \(0.441046\pi\) | |||||||
\(884\) | 20.0311 | + | 7.48178i | 0.673718 | + | 0.251640i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.204731 | + | 2.45894i | 0.00687807 | + | 0.0826098i | ||||
\(887\) | −35.6487 | − | 29.9128i | −1.19697 | − | 1.00437i | −0.999711 | − | 0.0240206i | \(-0.992353\pi\) |
−0.197254 | − | 0.980352i | \(-0.563202\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.05813 | + | 1.47704i | 0.136105 | + | 0.0495383i | ||||
\(890\) | 4.30090 | − | 1.13309i | 0.144166 | − | 0.0379813i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.0497 | − | 31.8781i | −0.604347 | − | 1.06736i | ||||
\(893\) | 18.6161 | − | 51.1474i | 0.622965 | − | 1.71158i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.24419 | − | 2.67453i | 0.0750152 | − | 0.0893996i | ||||
\(896\) | 0.317733 | + | 5.48354i | 0.0106147 | + | 0.183192i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.6719 | − | 7.53952i | −0.356126 | − | 0.251597i | ||||
\(899\) | 12.6135 | + | 21.8472i | 0.420683 | + | 0.728645i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.2661 | + | 21.2454i | −0.408642 | + | 0.707788i | ||||
\(902\) | −0.338144 | + | 0.155954i | −0.0112590 | + | 0.00519271i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −36.8695 | − | 17.7612i | −1.22626 | − | 0.590730i | ||||
\(905\) | −1.77364 | − | 4.87305i | −0.0589579 | − | 0.161986i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.2556 | + | 6.04019i | −1.13744 | + | 0.200561i | −0.710485 | − | 0.703712i | \(-0.751524\pi\) |
−0.426954 | + | 0.904273i | \(0.640413\pi\) | |||||||
\(908\) | 0.329198 | − | 39.2051i | 0.0109248 | − | 1.30107i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.631379 | − | 0.636702i | −0.0209300 | − | 0.0211065i | ||||
\(911\) | 22.9255 | − | 19.2368i | 0.759557 | − | 0.637344i | −0.178454 | − | 0.983948i | \(-0.557110\pi\) |
0.938012 | + | 0.346604i | \(0.112665\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.0416261 | − | 0.236073i | 0.00137762 | − | 0.00781289i | ||||
\(914\) | 35.2833 | + | 16.6336i | 1.16707 | + | 0.550189i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.1801 | + | 1.87470i | −0.369401 | + | 0.0619418i | ||||
\(917\) | 9.43490i | 0.311568i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.7647i | 1.74055i | 0.492569 | + | 0.870273i | \(0.336058\pi\) | ||||
−0.492569 | + | 0.870273i | \(0.663942\pi\) | |||||||
\(920\) | 2.31049 | + | 5.12233i | 0.0761748 | + | 0.168878i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.5042 | + | 26.5240i | −0.411803 | + | 0.873521i | ||||
\(923\) | 2.53335 | − | 14.3673i | 0.0833862 | − | 0.472907i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.2693 | − | 21.2034i | 0.830849 | − | 0.697165i | ||||
\(926\) | −9.62614 | + | 9.54565i | −0.316334 | + | 0.313689i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 28.6825 | − | 27.5029i | 0.941550 | − | 0.902828i | ||||
\(929\) | 54.7677 | − | 9.65703i | 1.79687 | − | 0.316837i | 0.827321 | − | 0.561729i | \(-0.189864\pi\) |
0.969550 | + | 0.244892i | \(0.0787526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.5066 | + | 48.0989i | 0.573755 | + | 1.57638i | ||||
\(932\) | −11.4265 | − | 9.75265i | −0.374288 | − | 0.319459i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.3619 | + | 22.4669i | 0.339051 | + | 0.735140i | ||||
\(935\) | −0.0155887 | + | 0.0270003i | −0.000509803 | + | 0.000883005i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.12048 | + | 15.7971i | 0.297953 | + | 0.516070i | 0.975667 | − | 0.219255i | \(-0.0703628\pi\) |
−0.677715 | + | 0.735325i | \(0.737029\pi\) | |||||||
\(938\) | 4.41282 | − | 6.24618i | 0.144084 | − | 0.203945i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.10099 | − | 1.45376i | 0.133760 | − | 0.0474165i | ||||
\(941\) | −11.2021 | + | 13.3502i | −0.365179 | + | 0.435204i | −0.917078 | − | 0.398707i | \(-0.869459\pi\) |
0.551899 | + | 0.833911i | \(0.313903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.2091 | + | 39.0392i | −0.462712 | + | 1.27129i | ||||
\(944\) | 8.95832 | − | 14.9315i | 0.291568 | − | 0.485978i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0362807 | − | 0.137712i | −0.00117959 | − | 0.00447739i | ||||
\(947\) | −40.4292 | − | 14.7150i | −1.31377 | − | 0.478174i | −0.412315 | − | 0.911042i | \(-0.635280\pi\) |
−0.901458 | + | 0.432868i | \(0.857502\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.08706 | + | 1.75125i | 0.0677488 | + | 0.0568480i | ||||
\(950\) | 52.3471 | − | 4.35841i | 1.69837 | − | 0.141405i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.338964 | + | 3.38306i | −0.0109859 | + | 0.109645i | ||||
\(953\) | 17.5809 | − | 10.1503i | 0.569502 | − | 0.328802i | −0.187449 | − | 0.982274i | \(-0.560022\pi\) |
0.756950 | + | 0.653472i | \(0.226688\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.33625 | − | 2.50353i | −0.140318 | − | 0.0810124i | ||||
\(956\) | −8.23629 | − | 9.98471i | −0.266381 | − | 0.322929i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.4365 | + | 21.1220i | −0.983360 | + | 0.682421i | ||||
\(959\) | 6.99708 | − | 2.54673i | 0.225947 | − | 0.0822382i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.14365 | + | 17.8285i | 0.101408 | + | 0.575113i | ||||
\(962\) | −10.7878 | + | 39.5948i | −0.347811 | + | 1.27659i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.19604 | + | 0.703987i | 0.0385217 | + | 0.0226739i | ||||
\(965\) | 1.71141 | + | 2.03958i | 0.0550923 | + | 0.0656565i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.0060 | − | 8.11209i | −1.47945 | − | 0.260867i | −0.625093 | − | 0.780550i | \(-0.714939\pi\) |
−0.854359 | + | 0.519683i | \(0.826050\pi\) | |||||||
\(968\) | 31.0211 | − | 2.32071i | 0.997056 | − | 0.0745904i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.130142 | + | 1.41890i | −0.00417862 | + | 0.0455581i | ||||
\(971\) | −29.3788 | −0.942809 | −0.471405 | − | 0.881917i | \(-0.656253\pi\) | ||||
−0.471405 | + | 0.881917i | \(0.656253\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.33784 | −0.139065 | ||||||||
\(974\) | 0.918347 | − | 10.0124i | 0.0294257 | − | 0.320819i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.4879 | + | 9.83020i | −0.911875 | + | 0.314657i | ||||
\(977\) | −18.3908 | − | 3.24280i | −0.588375 | − | 0.103746i | −0.128468 | − | 0.991714i | \(-0.541006\pi\) |
−0.459907 | + | 0.887967i | \(0.652117\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.278270 | + | 0.331630i | 0.00889356 | + | 0.0105989i | ||||
\(980\) | −2.07554 | + | 3.52623i | −0.0663007 | + | 0.112641i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.34331 | + | 26.9525i | −0.234335 | + | 0.860089i | ||||
\(983\) | 4.54380 | + | 25.7692i | 0.144925 | + | 0.821909i | 0.967428 | + | 0.253148i | \(0.0814660\pi\) |
−0.822503 | + | 0.568761i | \(0.807423\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.55193 | + | 1.29280i | −0.113174 | + | 0.0411919i | ||||
\(986\) | 20.2083 | − | 14.0239i | 0.643563 | − | 0.446613i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −50.4114 | + | 41.5839i | −1.60380 | + | 1.32296i | ||||
\(989\) | −13.7596 | − | 7.94413i | −0.437531 | − | 0.252609i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.5875 | − | 14.7730i | 0.812815 | − | 0.469279i | −0.0351178 | − | 0.999383i | \(-0.511181\pi\) |
0.847932 | + | 0.530105i | \(0.177847\pi\) | |||||||
\(992\) | −18.5875 | + | 8.19701i | −0.590154 | + | 0.260255i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.31174 | − | 0.192475i | 0.0733241 | − | 0.00610495i | ||||
\(995\) | −1.03945 | − | 0.872198i | −0.0329526 | − | 0.0276505i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.2095 | − | 13.5431i | −1.17844 | − | 0.428916i | −0.322787 | − | 0.946472i | \(-0.604620\pi\) |
−0.855649 | + | 0.517556i | \(0.826842\pi\) | |||||||
\(998\) | −14.2410 | − | 54.0548i | −0.450790 | − | 1.71107i | ||||
\(999\) | 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 | 324.2.l.a.179.16 | 96 | ||
3.2 | odd | 2 | 108.2.l.a.23.1 | ✓ | 96 | ||
4.3 | odd | 2 | inner | 324.2.l.a.179.3 | 96 | ||
9.2 | odd | 6 | 972.2.l.c.215.10 | 96 | |||
9.4 | even | 3 | 972.2.l.a.863.5 | 96 | |||
9.5 | odd | 6 | 972.2.l.d.863.12 | 96 | |||
9.7 | even | 3 | 972.2.l.b.215.7 | 96 | |||
12.11 | even | 2 | 108.2.l.a.23.14 | yes | 96 | ||
27.2 | odd | 18 | 972.2.l.a.107.14 | 96 | |||
27.7 | even | 9 | 108.2.l.a.47.14 | yes | 96 | ||
27.11 | odd | 18 | 972.2.l.b.755.9 | 96 | |||
27.16 | even | 9 | 972.2.l.c.755.8 | 96 | |||
27.20 | odd | 18 | inner | 324.2.l.a.143.3 | 96 | ||
27.25 | even | 9 | 972.2.l.d.107.3 | 96 | |||
36.7 | odd | 6 | 972.2.l.b.215.9 | 96 | |||
36.11 | even | 6 | 972.2.l.c.215.8 | 96 | |||
36.23 | even | 6 | 972.2.l.d.863.3 | 96 | |||
36.31 | odd | 6 | 972.2.l.a.863.14 | 96 | |||
108.7 | odd | 18 | 108.2.l.a.47.1 | yes | 96 | ||
108.11 | even | 18 | 972.2.l.b.755.7 | 96 | |||
108.43 | odd | 18 | 972.2.l.c.755.10 | 96 | |||
108.47 | even | 18 | inner | 324.2.l.a.143.16 | 96 | ||
108.79 | odd | 18 | 972.2.l.d.107.12 | 96 | |||
108.83 | even | 18 | 972.2.l.a.107.5 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.l.a.23.1 | ✓ | 96 | 3.2 | odd | 2 | ||
108.2.l.a.23.14 | yes | 96 | 12.11 | even | 2 | ||
108.2.l.a.47.1 | yes | 96 | 108.7 | odd | 18 | ||
108.2.l.a.47.14 | yes | 96 | 27.7 | even | 9 | ||
324.2.l.a.143.3 | 96 | 27.20 | odd | 18 | inner | ||
324.2.l.a.143.16 | 96 | 108.47 | even | 18 | inner | ||
324.2.l.a.179.3 | 96 | 4.3 | odd | 2 | inner | ||
324.2.l.a.179.16 | 96 | 1.1 | even | 1 | trivial | ||
972.2.l.a.107.5 | 96 | 108.83 | even | 18 | |||
972.2.l.a.107.14 | 96 | 27.2 | odd | 18 | |||
972.2.l.a.863.5 | 96 | 9.4 | even | 3 | |||
972.2.l.a.863.14 | 96 | 36.31 | odd | 6 | |||
972.2.l.b.215.7 | 96 | 9.7 | even | 3 | |||
972.2.l.b.215.9 | 96 | 36.7 | odd | 6 | |||
972.2.l.b.755.7 | 96 | 108.11 | even | 18 | |||
972.2.l.b.755.9 | 96 | 27.11 | odd | 18 | |||
972.2.l.c.215.8 | 96 | 36.11 | even | 6 | |||
972.2.l.c.215.10 | 96 | 9.2 | odd | 6 | |||
972.2.l.c.755.8 | 96 | 27.16 | even | 9 | |||
972.2.l.c.755.10 | 96 | 108.43 | odd | 18 | |||
972.2.l.d.107.3 | 96 | 27.25 | even | 9 | |||
972.2.l.d.107.12 | 96 | 108.79 | odd | 18 | |||
972.2.l.d.863.3 | 96 | 36.23 | even | 6 | |||
972.2.l.d.863.12 | 96 | 9.5 | odd | 6 |