Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,9,Mod(23,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.23");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4434941320\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 23.10 | ||
Character | \(\chi\) | \(=\) | 33.23 |
Dual form | 33.9.b.a.23.17 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 9.43364i | − | 0.589602i | −0.955559 | − | 0.294801i | \(-0.904747\pi\) | ||
0.955559 | − | 0.294801i | \(-0.0952534\pi\) | |||||||
\(3\) | 80.9807 | + | 1.77018i | 0.999761 | + | 0.0218541i | ||||
\(4\) | 167.006 | 0.652369 | ||||||||
\(5\) | − | 654.316i | − | 1.04691i | −0.852055 | − | 0.523453i | \(-0.824644\pi\) | ||
0.852055 | − | 0.523453i | \(-0.175356\pi\) | |||||||
\(6\) | 16.6993 | − | 763.942i | 0.0128852 | − | 0.589462i | ||||
\(7\) | −1003.87 | −0.418104 | −0.209052 | − | 0.977905i | \(-0.567038\pi\) | ||||
−0.209052 | + | 0.977905i | \(0.567038\pi\) | |||||||
\(8\) | − | 3990.49i | − | 0.974241i | ||||||
\(9\) | 6554.73 | + | 286.701i | 0.999045 | + | 0.0436977i | ||||
\(10\) | −6172.58 | −0.617258 | ||||||||
\(11\) | 4414.43i | 0.301511i | ||||||||
\(12\) | 13524.3 | + | 295.632i | 0.652213 | + | 0.0142569i | ||||
\(13\) | 15683.4 | 0.549119 | 0.274559 | − | 0.961570i | \(-0.411468\pi\) | ||||
0.274559 | + | 0.961570i | \(0.411468\pi\) | |||||||
\(14\) | 9470.12i | 0.246515i | ||||||||
\(15\) | 1158.26 | − | 52987.0i | 0.0228792 | − | 1.04666i | ||||
\(16\) | 5108.80 | 0.0779541 | ||||||||
\(17\) | − | 28664.7i | − | 0.343204i | −0.985166 | − | 0.171602i | \(-0.945106\pi\) | ||
0.985166 | − | 0.171602i | \(-0.0548942\pi\) | |||||||
\(18\) | 2704.63 | − | 61835.0i | 0.0257643 | − | 0.589039i | ||||
\(19\) | −155786. | −1.19540 | −0.597699 | − | 0.801720i | \(-0.703918\pi\) | ||||
−0.597699 | + | 0.801720i | \(0.703918\pi\) | |||||||
\(20\) | − | 109275.i | − | 0.682969i | ||||||
\(21\) | −81293.8 | − | 1777.03i | −0.418004 | − | 0.00913728i | ||||
\(22\) | 41644.1 | 0.177772 | ||||||||
\(23\) | − | 398996.i | − | 1.42580i | −0.701267 | − | 0.712898i | \(-0.747382\pi\) | ||
0.701267 | − | 0.712898i | \(-0.252618\pi\) | |||||||
\(24\) | 7063.89 | − | 323153.i | 0.0212911 | − | 0.974008i | ||||
\(25\) | −37504.8 | −0.0960122 | ||||||||
\(26\) | − | 147951.i | − | 0.323762i | ||||||
\(27\) | 530299. | + | 34820.3i | 0.997851 | + | 0.0655205i | ||||
\(28\) | −167652. | −0.272758 | ||||||||
\(29\) | 841380.i | 1.18960i | 0.803875 | + | 0.594799i | \(0.202768\pi\) | ||||
−0.803875 | + | 0.594799i | \(0.797232\pi\) | |||||||
\(30\) | −499860. | − | 10926.6i | −0.617111 | − | 0.0134896i | ||||
\(31\) | 136484. | 0.147787 | 0.0738934 | − | 0.997266i | \(-0.476458\pi\) | ||||
0.0738934 | + | 0.997266i | \(0.476458\pi\) | |||||||
\(32\) | − | 1.06976e6i | − | 1.02020i | ||||||
\(33\) | −7814.34 | + | 357483.i | −0.00658926 | + | 0.301439i | ||||
\(34\) | −270413. | −0.202354 | ||||||||
\(35\) | 656847.i | 0.437715i | ||||||||
\(36\) | 1.09468e6 | + | 47880.9i | 0.651746 | + | 0.0285071i | ||||
\(37\) | 1.28540e6 | 0.685851 | 0.342925 | − | 0.939363i | \(-0.388582\pi\) | ||||
0.342925 | + | 0.939363i | \(0.388582\pi\) | |||||||
\(38\) | 1.46963e6i | 0.704810i | ||||||||
\(39\) | 1.27005e6 | + | 27762.4i | 0.548987 | + | 0.0120005i | ||||
\(40\) | −2.61104e6 | −1.01994 | ||||||||
\(41\) | 3.48304e6i | 1.23260i | 0.787510 | + | 0.616302i | \(0.211370\pi\) | ||||
−0.787510 | + | 0.616302i | \(0.788630\pi\) | |||||||
\(42\) | −16763.8 | + | 766897.i | −0.00538736 | + | 0.246456i | ||||
\(43\) | 1.46303e6 | 0.427935 | 0.213968 | − | 0.976841i | \(-0.431361\pi\) | ||||
0.213968 | + | 0.976841i | \(0.431361\pi\) | |||||||
\(44\) | 737238.i | 0.196697i | ||||||||
\(45\) | 187593. | − | 4.28887e6i | 0.0457474 | − | 1.04591i | ||||
\(46\) | −3.76399e6 | −0.840653 | ||||||||
\(47\) | 4.25096e6i | 0.871156i | 0.900151 | + | 0.435578i | \(0.143456\pi\) | ||||
−0.900151 | + | 0.435578i | \(0.856544\pi\) | |||||||
\(48\) | 413714. | + | 9043.51i | 0.0779355 | + | 0.00170362i | ||||
\(49\) | −4.75705e6 | −0.825189 | ||||||||
\(50\) | 353806.i | 0.0566090i | ||||||||
\(51\) | 50741.7 | − | 2.32129e6i | 0.00750040 | − | 0.343122i | ||||
\(52\) | 2.61922e6 | 0.358228 | ||||||||
\(53\) | 1.30571e7i | 1.65480i | 0.561616 | + | 0.827398i | \(0.310180\pi\) | ||||
−0.561616 | + | 0.827398i | \(0.689820\pi\) | |||||||
\(54\) | 328482. | − | 5.00265e6i | 0.0386311 | − | 0.588336i | ||||
\(55\) | 2.88843e6 | 0.315654 | ||||||||
\(56\) | 4.00592e6i | 0.407334i | ||||||||
\(57\) | −1.26156e7 | − | 275769.i | −1.19511 | − | 0.0261244i | ||||
\(58\) | 7.93727e6 | 0.701390 | ||||||||
\(59\) | − | 2.01517e6i | − | 0.166304i | −0.996537 | − | 0.0831520i | \(-0.973501\pi\) | ||
0.996537 | − | 0.0831520i | \(-0.0264987\pi\) | |||||||
\(60\) | 193437. | − | 8.84916e6i | 0.0149257 | − | 0.682806i | ||||
\(61\) | 1.44306e7 | 1.04223 | 0.521116 | − | 0.853486i | \(-0.325516\pi\) | ||||
0.521116 | + | 0.853486i | \(0.325516\pi\) | |||||||
\(62\) | − | 1.28754e6i | − | 0.0871354i | ||||||
\(63\) | −6.58008e6 | − | 287810.i | −0.417705 | − | 0.0182702i | ||||
\(64\) | −8.78388e6 | −0.523560 | ||||||||
\(65\) | − | 1.02619e7i | − | 0.574875i | ||||||
\(66\) | 3.37237e6 | + | 73717.7i | 0.177729 | + | 0.00388504i | ||||
\(67\) | 2.96951e7 | 1.47362 | 0.736810 | − | 0.676100i | \(-0.236331\pi\) | ||||
0.736810 | + | 0.676100i | \(0.236331\pi\) | |||||||
\(68\) | − | 4.78719e6i | − | 0.223895i | ||||||
\(69\) | 706296. | − | 3.23110e7i | 0.0311595 | − | 1.42546i | ||||
\(70\) | 6.19646e6 | 0.258078 | ||||||||
\(71\) | 1.15263e6i | 0.0453584i | 0.999743 | + | 0.0226792i | \(0.00721964\pi\) | ||||
−0.999743 | + | 0.0226792i | \(0.992780\pi\) | |||||||
\(72\) | 1.14408e6 | − | 2.61566e7i | 0.0425721 | − | 0.973310i | ||||
\(73\) | −4.15279e7 | −1.46234 | −0.731171 | − | 0.682194i | \(-0.761026\pi\) | ||||
−0.731171 | + | 0.682194i | \(0.761026\pi\) | |||||||
\(74\) | − | 1.21260e7i | − | 0.404379i | ||||||
\(75\) | −3.03716e6 | − | 66390.2i | −0.0959893 | − | 0.00209826i | ||||
\(76\) | −2.60172e7 | −0.779841 | ||||||||
\(77\) | − | 4.43150e6i | − | 0.126063i | ||||||
\(78\) | 261901. | − | 1.19812e7i | 0.00707552 | − | 0.323684i | ||||
\(79\) | −1.18060e7 | −0.303106 | −0.151553 | − | 0.988449i | \(-0.548427\pi\) | ||||
−0.151553 | + | 0.988449i | \(0.548427\pi\) | |||||||
\(80\) | − | 3.34277e6i | − | 0.0816107i | ||||||
\(81\) | 4.28823e7 | + | 3.75850e6i | 0.996181 | + | 0.0873120i | ||||
\(82\) | 3.28578e7 | 0.726746 | ||||||||
\(83\) | 8.83815e7i | 1.86230i | 0.364640 | + | 0.931149i | \(0.381192\pi\) | ||||
−0.364640 | + | 0.931149i | \(0.618808\pi\) | |||||||
\(84\) | −1.35766e7 | − | 296775.i | −0.272693 | − | 0.00596088i | ||||
\(85\) | −1.87558e7 | −0.359302 | ||||||||
\(86\) | − | 1.38017e7i | − | 0.252312i | ||||||
\(87\) | −1.48940e6 | + | 6.81355e7i | −0.0259976 | + | 1.18931i | ||||
\(88\) | 1.76157e7 | 0.293745 | ||||||||
\(89\) | 6.59288e7i | 1.05079i | 0.850859 | + | 0.525394i | \(0.176082\pi\) | ||||
−0.850859 | + | 0.525394i | \(0.823918\pi\) | |||||||
\(90\) | −4.04596e7 | − | 1.76969e6i | −0.616669 | − | 0.0269728i | ||||
\(91\) | −1.57440e7 | −0.229589 | ||||||||
\(92\) | − | 6.66350e7i | − | 0.930146i | ||||||
\(93\) | 1.10526e7 | + | 241602.i | 0.147751 | + | 0.00322975i | ||||
\(94\) | 4.01021e7 | 0.513636 | ||||||||
\(95\) | 1.01933e8i | 1.25147i | ||||||||
\(96\) | 1.89367e6 | − | 8.66299e7i | 0.0222956 | − | 1.01996i | ||||
\(97\) | −9.98285e7 | −1.12763 | −0.563816 | − | 0.825900i | \(-0.690667\pi\) | ||||
−0.563816 | + | 0.825900i | \(0.690667\pi\) | |||||||
\(98\) | 4.48763e7i | 0.486534i | ||||||||
\(99\) | −1.26562e6 | + | 2.89354e7i | −0.0131754 | + | 0.301223i | ||||
\(100\) | −6.26354e6 | −0.0626354 | ||||||||
\(101\) | 3.17394e7i | 0.305009i | 0.988303 | + | 0.152505i | \(0.0487339\pi\) | ||||
−0.988303 | + | 0.152505i | \(0.951266\pi\) | |||||||
\(102\) | −2.18982e7 | − | 478679.i | −0.202305 | − | 0.00442226i | ||||
\(103\) | 1.23434e8 | 1.09670 | 0.548348 | − | 0.836250i | \(-0.315257\pi\) | ||||
0.548348 | + | 0.836250i | \(0.315257\pi\) | |||||||
\(104\) | − | 6.25844e7i | − | 0.534974i | ||||||
\(105\) | −1.16274e6 | + | 5.31919e7i | −0.00956587 | + | 0.437611i | ||||
\(106\) | 1.23176e8 | 0.975672 | ||||||||
\(107\) | − | 4.42222e7i | − | 0.337369i | −0.985670 | − | 0.168685i | \(-0.946048\pi\) | ||
0.985670 | − | 0.168685i | \(-0.0539520\pi\) | |||||||
\(108\) | 8.85634e7 | + | 5.81521e6i | 0.650967 | + | 0.0427436i | ||||
\(109\) | −3.68722e7 | −0.261212 | −0.130606 | − | 0.991434i | \(-0.541692\pi\) | ||||
−0.130606 | + | 0.991434i | \(0.541692\pi\) | |||||||
\(110\) | − | 2.72484e7i | − | 0.186110i | ||||||
\(111\) | 1.04092e8 | + | 2.27538e6i | 0.685687 | + | 0.0149887i | ||||
\(112\) | −5.12856e6 | −0.0325929 | ||||||||
\(113\) | − | 1.09977e8i | − | 0.674509i | −0.941413 | − | 0.337255i | \(-0.890502\pi\) | ||
0.941413 | − | 0.337255i | \(-0.109498\pi\) | |||||||
\(114\) | −2.60150e6 | + | 1.19011e8i | −0.0154030 | + | 0.704642i | ||||
\(115\) | −2.61070e8 | −1.49268 | ||||||||
\(116\) | 1.40516e8i | 0.776057i | ||||||||
\(117\) | 1.02800e8 | + | 4.49644e6i | 0.548594 | + | 0.0239952i | ||||
\(118\) | −1.90103e7 | −0.0980533 | ||||||||
\(119\) | 2.87756e7i | 0.143495i | ||||||||
\(120\) | −2.11444e8 | − | 4.62202e6i | −1.01969 | − | 0.0222898i | ||||
\(121\) | −1.94872e7 | −0.0909091 | ||||||||
\(122\) | − | 1.36133e8i | − | 0.614502i | ||||||
\(123\) | −6.16562e6 | + | 2.82059e8i | −0.0269374 | + | 1.23231i | ||||
\(124\) | 2.27937e7 | 0.0964115 | ||||||||
\(125\) | − | 2.31052e8i | − | 0.946390i | ||||||
\(126\) | −2.71509e6 | + | 6.20741e7i | −0.0107722 | + | 0.246280i | ||||
\(127\) | −1.84864e8 | −0.710622 | −0.355311 | − | 0.934748i | \(-0.615625\pi\) | ||||
−0.355311 | + | 0.934748i | \(0.615625\pi\) | |||||||
\(128\) | − | 1.90995e8i | − | 0.711511i | ||||||
\(129\) | 1.18477e8 | + | 2.58982e6i | 0.427833 | + | 0.00935214i | ||||
\(130\) | −9.68069e7 | −0.338948 | ||||||||
\(131\) | − | 4.41299e8i | − | 1.49847i | −0.662306 | − | 0.749234i | \(-0.730422\pi\) | ||
0.662306 | − | 0.749234i | \(-0.269578\pi\) | |||||||
\(132\) | −1.30504e6 | + | 5.97020e7i | −0.00429863 | + | 0.196650i | ||||
\(133\) | 1.56388e8 | 0.499801 | ||||||||
\(134\) | − | 2.80133e8i | − | 0.868850i | ||||||
\(135\) | 2.27835e7 | − | 3.46983e8i | 0.0685938 | − | 1.04466i | ||||
\(136\) | −1.14386e8 | −0.334363 | ||||||||
\(137\) | − | 6.76817e8i | − | 1.92127i | −0.277808 | − | 0.960637i | \(-0.589608\pi\) | ||
0.277808 | − | 0.960637i | \(-0.410392\pi\) | |||||||
\(138\) | −3.04810e8 | − | 6.66294e6i | −0.840453 | − | 0.0183717i | ||||
\(139\) | 5.01294e8 | 1.34287 | 0.671434 | − | 0.741064i | \(-0.265679\pi\) | ||||
0.671434 | + | 0.741064i | \(0.265679\pi\) | |||||||
\(140\) | 1.09698e8i | 0.285552i | ||||||||
\(141\) | −7.52498e6 | + | 3.44246e8i | −0.0190383 | + | 0.870948i | ||||
\(142\) | 1.08735e7 | 0.0267434 | ||||||||
\(143\) | 6.92331e7i | 0.165565i | ||||||||
\(144\) | 3.34868e7 | + | 1.46470e6i | 0.0778797 | + | 0.00340642i | ||||
\(145\) | 5.50529e8 | 1.24540 | ||||||||
\(146\) | 3.91760e8i | 0.862200i | ||||||||
\(147\) | −3.85229e8 | − | 8.42084e6i | −0.824992 | − | 0.0180338i | ||||
\(148\) | 2.14669e8 | 0.447428 | ||||||||
\(149\) | 7.36083e7i | 0.149342i | 0.997208 | + | 0.0746709i | \(0.0237906\pi\) | ||||
−0.997208 | + | 0.0746709i | \(0.976209\pi\) | |||||||
\(150\) | −626302. | + | 2.86515e7i | −0.00123714 | + | 0.0565955i | ||||
\(151\) | −5.08352e8 | −0.977815 | −0.488908 | − | 0.872336i | \(-0.662604\pi\) | ||||
−0.488908 | + | 0.872336i | \(0.662604\pi\) | |||||||
\(152\) | 6.21661e8i | 1.16461i | ||||||||
\(153\) | 8.21820e6 | − | 1.87889e8i | 0.0149972 | − | 0.342876i | ||||
\(154\) | −4.18052e7 | −0.0743271 | ||||||||
\(155\) | − | 8.93038e7i | − | 0.154719i | ||||||
\(156\) | 2.12107e8 | + | 4.63650e6i | 0.358142 | + | 0.00782875i | ||||
\(157\) | 3.24316e8 | 0.533789 | 0.266894 | − | 0.963726i | \(-0.414002\pi\) | ||||
0.266894 | + | 0.963726i | \(0.414002\pi\) | |||||||
\(158\) | 1.11373e8i | 0.178712i | ||||||||
\(159\) | −2.31135e7 | + | 1.05738e9i | −0.0361641 | + | 1.65440i | ||||
\(160\) | −6.99961e8 | −1.06806 | ||||||||
\(161\) | 4.00540e8i | 0.596131i | ||||||||
\(162\) | 3.54563e7 | − | 4.04536e8i | 0.0514794 | − | 0.587351i | ||||
\(163\) | 3.36024e8 | 0.476014 | 0.238007 | − | 0.971263i | \(-0.423506\pi\) | ||||
0.238007 | + | 0.971263i | \(0.423506\pi\) | |||||||
\(164\) | 5.81690e8i | 0.804112i | ||||||||
\(165\) | 2.33907e8 | + | 5.11305e6i | 0.315579 | + | 0.00689833i | ||||
\(166\) | 8.33759e8 | 1.09802 | ||||||||
\(167\) | − | 4.84943e8i | − | 0.623484i | −0.950167 | − | 0.311742i | \(-0.899088\pi\) | ||
0.950167 | − | 0.311742i | \(-0.100912\pi\) | |||||||
\(168\) | −7.09121e6 | + | 3.24402e8i | −0.00890191 | + | 0.407237i | ||||
\(169\) | −5.69762e8 | −0.698469 | ||||||||
\(170\) | 1.76935e8i | 0.211845i | ||||||||
\(171\) | −1.02113e9 | − | 4.46639e7i | −1.19426 | − | 0.0522362i | ||||
\(172\) | 2.44335e8 | 0.279172 | ||||||||
\(173\) | 1.16065e9i | 1.29574i | 0.761750 | + | 0.647871i | \(0.224340\pi\) | ||||
−0.761750 | + | 0.647871i | \(0.775660\pi\) | |||||||
\(174\) | 6.42766e8 | + | 1.40504e7i | 0.701222 | + | 0.0153282i | ||||
\(175\) | 3.76498e7 | 0.0401431 | ||||||||
\(176\) | 2.25524e7i | 0.0235041i | ||||||||
\(177\) | 3.56721e6 | − | 1.63189e8i | 0.00363442 | − | 0.166264i | ||||
\(178\) | 6.21949e8 | 0.619547 | ||||||||
\(179\) | − | 1.30016e9i | − | 1.26644i | −0.773971 | − | 0.633222i | \(-0.781732\pi\) | ||
0.773971 | − | 0.633222i | \(-0.218268\pi\) | |||||||
\(180\) | 3.13293e7 | − | 7.16269e8i | 0.0298442 | − | 0.682317i | ||||
\(181\) | −1.93174e9 | −1.79984 | −0.899921 | − | 0.436053i | \(-0.856376\pi\) | ||||
−0.899921 | + | 0.436053i | \(0.856376\pi\) | |||||||
\(182\) | 1.48523e8i | 0.135366i | ||||||||
\(183\) | 1.16860e9 | + | 2.55447e7i | 1.04198 | + | 0.0227770i | ||||
\(184\) | −1.59219e9 | −1.38907 | ||||||||
\(185\) | − | 8.41055e8i | − | 0.718022i | ||||||
\(186\) | 2.27918e6 | − | 1.04266e8i | 0.00190427 | − | 0.0871146i | ||||
\(187\) | 1.26538e8 | 0.103480 | ||||||||
\(188\) | 7.09938e8i | 0.568315i | ||||||||
\(189\) | −5.32350e8 | − | 3.49550e7i | −0.417205 | − | 0.0273944i | ||||
\(190\) | 9.61600e8 | 0.737870 | ||||||||
\(191\) | 7.40802e8i | 0.556633i | 0.960489 | + | 0.278316i | \(0.0897764\pi\) | ||||
−0.960489 | + | 0.278316i | \(0.910224\pi\) | |||||||
\(192\) | −7.11324e8 | − | 1.55491e7i | −0.523435 | − | 0.0114419i | ||||
\(193\) | −1.73481e9 | −1.25032 | −0.625161 | − | 0.780496i | \(-0.714967\pi\) | ||||
−0.625161 | + | 0.780496i | \(0.714967\pi\) | |||||||
\(194\) | 9.41746e8i | 0.664855i | ||||||||
\(195\) | 1.81654e7 | − | 8.31014e8i | 0.0125634 | − | 0.574738i | ||||
\(196\) | −7.94458e8 | −0.538328 | ||||||||
\(197\) | 3.66287e8i | 0.243196i | 0.992579 | + | 0.121598i | \(0.0388019\pi\) | ||||
−0.992579 | + | 0.121598i | \(0.961198\pi\) | |||||||
\(198\) | 2.72966e8 | + | 1.19394e7i | 0.177602 | + | 0.00776823i | ||||
\(199\) | 2.81373e9 | 1.79419 | 0.897097 | − | 0.441833i | \(-0.145672\pi\) | ||||
0.897097 | + | 0.441833i | \(0.145672\pi\) | |||||||
\(200\) | 1.49662e8i | 0.0935390i | ||||||||
\(201\) | 2.40473e9 | + | 5.25657e7i | 1.47327 | + | 0.0322046i | ||||
\(202\) | 2.99418e8 | 0.179834 | ||||||||
\(203\) | − | 8.44634e8i | − | 0.497375i | ||||||
\(204\) | 8.47420e6 | − | 3.87670e8i | 0.00489303 | − | 0.223842i | ||||
\(205\) | 2.27901e9 | 1.29042 | ||||||||
\(206\) | − | 1.16443e9i | − | 0.646615i | ||||||
\(207\) | 1.14393e8 | − | 2.61532e9i | 0.0623041 | − | 1.42444i | ||||
\(208\) | 8.01233e7 | 0.0428061 | ||||||||
\(209\) | − | 6.87704e8i | − | 0.360426i | ||||||
\(210\) | 5.01793e8 | + | 1.09689e7i | 0.258016 | + | 0.00564006i | ||||
\(211\) | −2.34269e9 | −1.18191 | −0.590957 | − | 0.806703i | \(-0.701250\pi\) | ||||
−0.590957 | + | 0.806703i | \(0.701250\pi\) | |||||||
\(212\) | 2.18063e9i | 1.07954i | ||||||||
\(213\) | −2.04037e6 | + | 9.33410e7i | −0.000991267 | + | 0.0453476i | ||||
\(214\) | −4.17177e8 | −0.198914 | ||||||||
\(215\) | − | 9.57281e8i | − | 0.448008i | ||||||
\(216\) | 1.38950e8 | − | 2.11615e9i | 0.0638328 | − | 0.972147i | ||||
\(217\) | −1.37012e8 | −0.0617902 | ||||||||
\(218\) | 3.47839e8i | 0.154011i | ||||||||
\(219\) | −3.36296e9 | − | 7.35120e7i | −1.46199 | − | 0.0319582i | ||||
\(220\) | 4.82387e8 | 0.205923 | ||||||||
\(221\) | − | 4.49559e8i | − | 0.188459i | ||||||
\(222\) | 2.14651e7 | − | 9.81968e8i | 0.00883735 | − | 0.404283i | ||||
\(223\) | 7.59300e8 | 0.307039 | 0.153520 | − | 0.988146i | \(-0.450939\pi\) | ||||
0.153520 | + | 0.988146i | \(0.450939\pi\) | |||||||
\(224\) | 1.07390e9i | 0.426551i | ||||||||
\(225\) | −2.45834e8 | − | 1.07526e7i | −0.0959205 | − | 0.00419552i | ||||
\(226\) | −1.03748e9 | −0.397692 | ||||||||
\(227\) | − | 4.54793e9i | − | 1.71282i | −0.516300 | − | 0.856408i | \(-0.672691\pi\) | ||
0.516300 | − | 0.856408i | \(-0.327309\pi\) | |||||||
\(228\) | −2.10689e9 | − | 4.60552e7i | −0.779655 | − | 0.0170427i | ||||
\(229\) | −1.86293e9 | −0.677413 | −0.338707 | − | 0.940892i | \(-0.609989\pi\) | ||||
−0.338707 | + | 0.940892i | \(0.609989\pi\) | |||||||
\(230\) | 2.46284e9i | 0.880085i | ||||||||
\(231\) | 7.84456e6 | − | 3.58866e8i | 0.00275499 | − | 0.126033i | ||||
\(232\) | 3.35752e9 | 1.15895 | ||||||||
\(233\) | 4.67187e9i | 1.58514i | 0.609783 | + | 0.792568i | \(0.291256\pi\) | ||||
−0.609783 | + | 0.792568i | \(0.708744\pi\) | |||||||
\(234\) | 4.24178e7 | − | 9.69781e8i | 0.0141477 | − | 0.323452i | ||||
\(235\) | 2.78147e9 | 0.912019 | ||||||||
\(236\) | − | 3.36546e8i | − | 0.108492i | ||||||
\(237\) | −9.56057e8 | − | 2.08987e7i | −0.303033 | − | 0.00662410i | ||||
\(238\) | 2.71458e8 | 0.0846049 | ||||||||
\(239\) | 1.52975e9i | 0.468844i | 0.972135 | + | 0.234422i | \(0.0753197\pi\) | ||||
−0.972135 | + | 0.234422i | \(0.924680\pi\) | |||||||
\(240\) | 5.91731e6 | − | 2.70700e8i | 0.00178353 | − | 0.0815912i | ||||
\(241\) | −3.94692e9 | −1.17001 | −0.585006 | − | 0.811029i | \(-0.698908\pi\) | ||||
−0.585006 | + | 0.811029i | \(0.698908\pi\) | |||||||
\(242\) | 1.83835e8i | 0.0536002i | ||||||||
\(243\) | 3.46599e9 | + | 3.80275e8i | 0.994035 | + | 0.109062i | ||||
\(244\) | 2.41000e9 | 0.679920 | ||||||||
\(245\) | 3.11262e9i | 0.863895i | ||||||||
\(246\) | 2.66084e9 | + | 5.81642e7i | 0.726572 | + | 0.0158824i | ||||
\(247\) | −2.44324e9 | −0.656416 | ||||||||
\(248\) | − | 5.44639e8i | − | 0.143980i | ||||||
\(249\) | −1.56451e8 | + | 7.15719e9i | −0.0406988 | + | 1.86185i | ||||
\(250\) | −2.17966e9 | −0.557994 | ||||||||
\(251\) | − | 6.72012e8i | − | 0.169310i | −0.996410 | − | 0.0846549i | \(-0.973021\pi\) | ||
0.996410 | − | 0.0846549i | \(-0.0269788\pi\) | |||||||
\(252\) | −1.09892e9 | − | 4.80661e7i | −0.272497 | − | 0.0119189i | ||||
\(253\) | 1.76134e9 | 0.429894 | ||||||||
\(254\) | 1.74394e9i | 0.418984i | ||||||||
\(255\) | −1.51886e9 | − | 3.32011e7i | −0.359216 | − | 0.00785222i | ||||
\(256\) | −4.05045e9 | −0.943068 | ||||||||
\(257\) | 2.66110e9i | 0.609998i | 0.952353 | + | 0.304999i | \(0.0986560\pi\) | ||||
−0.952353 | + | 0.304999i | \(0.901344\pi\) | |||||||
\(258\) | 2.44314e7 | − | 1.11767e9i | 0.00551404 | − | 0.252251i | ||||
\(259\) | −1.29037e9 | −0.286757 | ||||||||
\(260\) | − | 1.71380e9i | − | 0.375031i | ||||||
\(261\) | −2.41224e8 | + | 5.51502e9i | −0.0519827 | + | 1.18846i | ||||
\(262\) | −4.16305e9 | −0.883500 | ||||||||
\(263\) | − | 6.79769e9i | − | 1.42082i | −0.703789 | − | 0.710409i | \(-0.748510\pi\) | ||
0.703789 | − | 0.710409i | \(-0.251490\pi\) | |||||||
\(264\) | 1.42653e9 | + | 3.11830e7i | 0.293674 | + | 0.00641952i | ||||
\(265\) | 8.54350e9 | 1.73242 | ||||||||
\(266\) | − | 1.47531e9i | − | 0.294684i | ||||||
\(267\) | −1.16706e8 | + | 5.33896e9i | −0.0229640 | + | 1.05054i | ||||
\(268\) | 4.95927e9 | 0.961344 | ||||||||
\(269\) | 7.24354e9i | 1.38338i | 0.722194 | + | 0.691690i | \(0.243134\pi\) | ||||
−0.722194 | + | 0.691690i | \(0.756866\pi\) | |||||||
\(270\) | −3.27332e9 | − | 2.14931e8i | −0.615932 | − | 0.0404431i | ||||
\(271\) | 9.63308e9 | 1.78603 | 0.893013 | − | 0.450030i | \(-0.148587\pi\) | ||||
0.893013 | + | 0.450030i | \(0.148587\pi\) | |||||||
\(272\) | − | 1.46442e8i | − | 0.0267541i | ||||||
\(273\) | −1.27496e9 | − | 2.78698e7i | −0.229534 | − | 0.00501745i | ||||
\(274\) | −6.38485e9 | −1.13279 | ||||||||
\(275\) | − | 1.65562e8i | − | 0.0289488i | ||||||
\(276\) | 1.17956e8 | − | 5.39614e9i | 0.0203275 | − | 0.929923i | ||||
\(277\) | −2.47506e9 | −0.420404 | −0.210202 | − | 0.977658i | \(-0.567412\pi\) | ||||
−0.210202 | + | 0.977658i | \(0.567412\pi\) | |||||||
\(278\) | − | 4.72903e9i | − | 0.791758i | ||||||
\(279\) | 8.94617e8 | + | 3.91301e7i | 0.147646 | + | 0.00645795i | ||||
\(280\) | 2.62114e9 | 0.426440 | ||||||||
\(281\) | − | 6.69017e9i | − | 1.07303i | −0.843891 | − | 0.536515i | \(-0.819740\pi\) | ||
0.843891 | − | 0.536515i | \(-0.180260\pi\) | |||||||
\(282\) | 3.24749e9 | + | 7.09879e7i | 0.513513 | + | 0.0112250i | ||||
\(283\) | 7.61999e8 | 0.118798 | 0.0593989 | − | 0.998234i | \(-0.481082\pi\) | ||||
0.0593989 | + | 0.998234i | \(0.481082\pi\) | |||||||
\(284\) | 1.92497e8i | 0.0295904i | ||||||||
\(285\) | −1.80440e8 | + | 8.25460e9i | −0.0273498 | + | 1.25117i | ||||
\(286\) | 6.53120e8 | 0.0976178 | ||||||||
\(287\) | − | 3.49651e9i | − | 0.515356i | ||||||
\(288\) | 3.06701e8 | − | 7.01199e9i | 0.0445806 | − | 1.01923i | ||||
\(289\) | 6.15409e9 | 0.882211 | ||||||||
\(290\) | − | 5.19349e9i | − | 0.734289i | ||||||
\(291\) | −8.08417e9 | − | 1.76714e8i | −1.12736 | − | 0.0246434i | ||||
\(292\) | −6.93543e9 | −0.953986 | ||||||||
\(293\) | − | 3.45422e9i | − | 0.468683i | −0.972154 | − | 0.234341i | \(-0.924707\pi\) | ||
0.972154 | − | 0.234341i | \(-0.0752934\pi\) | |||||||
\(294\) | −7.94392e7 | + | 3.63411e9i | −0.0106328 | + | 0.486417i | ||||
\(295\) | −1.31856e9 | −0.174105 | ||||||||
\(296\) | − | 5.12936e9i | − | 0.668184i | ||||||
\(297\) | −1.53712e8 | + | 2.34097e9i | −0.0197552 | + | 0.300863i | ||||
\(298\) | 6.94394e8 | 0.0880523 | ||||||||
\(299\) | − | 6.25761e9i | − | 0.782932i | ||||||
\(300\) | −5.07225e8 | − | 1.10876e7i | −0.0626204 | − | 0.00136884i | ||||
\(301\) | −1.46868e9 | −0.178921 | ||||||||
\(302\) | 4.79561e9i | 0.576522i | ||||||||
\(303\) | −5.61845e7 | + | 2.57028e9i | −0.00666571 | + | 0.304937i | ||||
\(304\) | −7.95878e8 | −0.0931863 | ||||||||
\(305\) | − | 9.44216e9i | − | 1.09112i | ||||||
\(306\) | −1.77248e9 | − | 7.75275e7i | −0.202160 | − | 0.00884240i | ||||
\(307\) | −7.57987e9 | −0.853313 | −0.426657 | − | 0.904414i | \(-0.640309\pi\) | ||||
−0.426657 | + | 0.904414i | \(0.640309\pi\) | |||||||
\(308\) | − | 7.40089e8i | − | 0.0822396i | ||||||
\(309\) | 9.99578e9 | + | 2.18501e8i | 1.09643 | + | 0.0239673i | ||||
\(310\) | −8.42460e8 | −0.0912226 | ||||||||
\(311\) | − | 4.30352e9i | − | 0.460026i | −0.973188 | − | 0.230013i | \(-0.926123\pi\) | ||
0.973188 | − | 0.230013i | \(-0.0738769\pi\) | |||||||
\(312\) | 1.10786e8 | − | 5.06812e9i | 0.0116914 | − | 0.534846i | ||||
\(313\) | −1.37328e10 | −1.43081 | −0.715407 | − | 0.698708i | \(-0.753758\pi\) | ||||
−0.715407 | + | 0.698708i | \(0.753758\pi\) | |||||||
\(314\) | − | 3.05948e9i | − | 0.314723i | ||||||
\(315\) | −1.88319e8 | + | 4.30546e9i | −0.0191272 | + | 0.437297i | ||||
\(316\) | −1.97168e9 | −0.197737 | ||||||||
\(317\) | 1.29241e10i | 1.27986i | 0.768432 | + | 0.639931i | \(0.221037\pi\) | ||||
−0.768432 | + | 0.639931i | \(0.778963\pi\) | |||||||
\(318\) | 9.97490e9 | + | 2.18044e8i | 0.975439 | + | 0.0213224i | ||||
\(319\) | −3.71421e9 | −0.358677 | ||||||||
\(320\) | 5.74743e9i | 0.548118i | ||||||||
\(321\) | 7.82814e7 | − | 3.58115e9i | 0.00737290 | − | 0.337289i | ||||
\(322\) | 3.77855e9 | 0.351480 | ||||||||
\(323\) | 4.46555e9i | 0.410265i | ||||||||
\(324\) | 7.16162e9 | + | 6.27693e8i | 0.649878 | + | 0.0569596i | ||||
\(325\) | −5.88201e8 | −0.0527221 | ||||||||
\(326\) | − | 3.16993e9i | − | 0.280659i | ||||||
\(327\) | −2.98594e9 | − | 6.52705e7i | −0.261150 | − | 0.00570855i | ||||
\(328\) | 1.38990e10 | 1.20085 | ||||||||
\(329\) | − | 4.26740e9i | − | 0.364234i | ||||||
\(330\) | 4.82347e7 | − | 2.20660e9i | 0.00406727 | − | 0.186066i | ||||
\(331\) | −1.16501e10 | −0.970551 | −0.485275 | − | 0.874361i | \(-0.661281\pi\) | ||||
−0.485275 | + | 0.874361i | \(0.661281\pi\) | |||||||
\(332\) | 1.47603e10i | 1.21490i | ||||||||
\(333\) | 8.42542e9 | + | 3.68524e8i | 0.685196 | + | 0.0299701i | ||||
\(334\) | −4.57478e9 | −0.367608 | ||||||||
\(335\) | − | 1.94300e10i | − | 1.54274i | ||||||
\(336\) | −4.15314e8 | − | 9.07848e6i | −0.0325851 | − | 0.000712289i | ||||
\(337\) | 1.16754e10 | 0.905218 | 0.452609 | − | 0.891709i | \(-0.350493\pi\) | ||||
0.452609 | + | 0.891709i | \(0.350493\pi\) | |||||||
\(338\) | 5.37493e9i | 0.411819i | ||||||||
\(339\) | 1.94679e8 | − | 8.90601e9i | 0.0147408 | − | 0.674348i | ||||
\(340\) | −3.13234e9 | −0.234397 | ||||||||
\(341\) | 6.02499e8i | 0.0445594i | ||||||||
\(342\) | −4.21343e8 | + | 9.63300e9i | −0.0307986 | + | 0.704137i | ||||
\(343\) | 1.05625e10 | 0.763119 | ||||||||
\(344\) | − | 5.83819e9i | − | 0.416912i | ||||||
\(345\) | −2.11416e10 | − | 4.62141e8i | −1.49232 | − | 0.0326211i | ||||
\(346\) | 1.09492e10 | 0.763972 | ||||||||
\(347\) | 1.30223e10i | 0.898195i | 0.893483 | + | 0.449097i | \(0.148254\pi\) | ||||
−0.893483 | + | 0.449097i | \(0.851746\pi\) | |||||||
\(348\) | −2.48739e8 | + | 1.13791e10i | −0.0169600 | + | 0.775871i | ||||
\(349\) | −1.26647e9 | −0.0853676 | −0.0426838 | − | 0.999089i | \(-0.513591\pi\) | ||||
−0.0426838 | + | 0.999089i | \(0.513591\pi\) | |||||||
\(350\) | − | 3.55175e8i | − | 0.0236685i | ||||||
\(351\) | 8.31688e9 | + | 5.46100e8i | 0.547939 | + | 0.0359785i | ||||
\(352\) | 4.72238e9 | 0.307603 | ||||||||
\(353\) | 2.70283e9i | 0.174068i | 0.996205 | + | 0.0870341i | \(0.0277389\pi\) | ||||
−0.996205 | + | 0.0870341i | \(0.972261\pi\) | |||||||
\(354\) | −1.53947e9 | − | 3.36518e7i | −0.0980298 | − | 0.00214287i | ||||
\(355\) | 7.54187e8 | 0.0474860 | ||||||||
\(356\) | 1.10105e10i | 0.685502i | ||||||||
\(357\) | −5.09380e7 | + | 2.33026e9i | −0.00313595 | + | 0.143460i | ||||
\(358\) | −1.22653e10 | −0.746698 | ||||||||
\(359\) | − | 1.50990e10i | − | 0.909016i | −0.890743 | − | 0.454508i | \(-0.849815\pi\) | ||
0.890743 | − | 0.454508i | \(-0.150185\pi\) | |||||||
\(360\) | −1.71147e10 | − | 7.48588e8i | −1.01896 | − | 0.0445690i | ||||
\(361\) | 7.28559e9 | 0.428979 | ||||||||
\(362\) | 1.82233e10i | 1.06119i | ||||||||
\(363\) | −1.57808e9 | − | 3.44958e7i | −0.0908874 | − | 0.00198674i | ||||
\(364\) | −2.62935e9 | −0.149776 | ||||||||
\(365\) | 2.71724e10i | 1.53093i | ||||||||
\(366\) | 2.40980e8 | − | 1.10241e10i | 0.0134294 | − | 0.614356i | ||||
\(367\) | −5.03372e9 | −0.277475 | −0.138738 | − | 0.990329i | \(-0.544305\pi\) | ||||
−0.138738 | + | 0.990329i | \(0.544305\pi\) | |||||||
\(368\) | − | 2.03839e9i | − | 0.111147i | ||||||
\(369\) | −9.98591e8 | + | 2.28304e10i | −0.0538620 | + | 1.23143i | ||||
\(370\) | −7.93421e9 | −0.423347 | ||||||||
\(371\) | − | 1.31076e10i | − | 0.691877i | ||||||
\(372\) | 1.84585e9 | + | 4.03491e7i | 0.0963885 | + | 0.00210699i | ||||
\(373\) | 2.28499e10 | 1.18045 | 0.590226 | − | 0.807238i | \(-0.299038\pi\) | ||||
0.590226 | + | 0.807238i | \(0.299038\pi\) | |||||||
\(374\) | − | 1.19372e9i | − | 0.0610119i | ||||||
\(375\) | 4.09005e8 | − | 1.87108e10i | 0.0206825 | − | 0.946164i | ||||
\(376\) | 1.69634e10 | 0.848716 | ||||||||
\(377\) | 1.31957e10i | 0.653230i | ||||||||
\(378\) | −3.29753e8 | + | 5.02200e9i | −0.0161518 | + | 0.245985i | ||||
\(379\) | −2.78517e9 | −0.134988 | −0.0674940 | − | 0.997720i | \(-0.521500\pi\) | ||||
−0.0674940 | + | 0.997720i | \(0.521500\pi\) | |||||||
\(380\) | 1.70235e10i | 0.816420i | ||||||||
\(381\) | −1.49704e10 | − | 3.27244e8i | −0.710452 | − | 0.0155300i | ||||
\(382\) | 6.98846e9 | 0.328192 | ||||||||
\(383\) | 1.49315e10i | 0.693920i | 0.937880 | + | 0.346960i | \(0.112786\pi\) | ||||
−0.937880 | + | 0.346960i | \(0.887214\pi\) | |||||||
\(384\) | 3.38095e8 | − | 1.54669e10i | 0.0155494 | − | 0.711341i | ||||
\(385\) | −2.89960e9 | −0.131976 | ||||||||
\(386\) | 1.63655e10i | 0.737193i | ||||||||
\(387\) | 9.58974e9 | + | 4.19451e8i | 0.427526 | + | 0.0186998i | ||||
\(388\) | −1.66720e10 | −0.735632 | ||||||||
\(389\) | − | 1.14426e10i | − | 0.499719i | −0.968282 | − | 0.249859i | \(-0.919616\pi\) | ||
0.968282 | − | 0.249859i | \(-0.0803844\pi\) | |||||||
\(390\) | −7.83949e9 | − | 1.71366e8i | −0.338867 | − | 0.00740740i | ||||
\(391\) | −1.14371e10 | −0.489339 | ||||||||
\(392\) | 1.89830e10i | 0.803933i | ||||||||
\(393\) | 7.81179e8 | − | 3.57367e10i | 0.0327477 | − | 1.49811i | ||||
\(394\) | 3.45542e9 | 0.143389 | ||||||||
\(395\) | 7.72485e9i | 0.317323i | ||||||||
\(396\) | −2.11367e8 | + | 4.83240e9i | −0.00859520 | + | 0.196509i | ||||
\(397\) | −2.19883e10 | −0.885176 | −0.442588 | − | 0.896725i | \(-0.645940\pi\) | ||||
−0.442588 | + | 0.896725i | \(0.645940\pi\) | |||||||
\(398\) | − | 2.65437e10i | − | 1.05786i | ||||||
\(399\) | 1.26644e10 | + | 2.76835e8i | 0.499682 | + | 0.0109227i | ||||
\(400\) | −1.91604e8 | −0.00748455 | ||||||||
\(401\) | − | 3.25761e10i | − | 1.25986i | −0.776653 | − | 0.629929i | \(-0.783084\pi\) | ||
0.776653 | − | 0.629929i | \(-0.216916\pi\) | |||||||
\(402\) | 4.95886e8 | − | 2.26853e10i | 0.0189879 | − | 0.868642i | ||||
\(403\) | 2.14053e9 | 0.0811524 | ||||||||
\(404\) | 5.30069e9i | 0.198979i | ||||||||
\(405\) | 2.45925e9 | − | 2.80586e10i | 0.0914075 | − | 1.04291i | ||||
\(406\) | −7.96797e9 | −0.293254 | ||||||||
\(407\) | 5.67428e9i | 0.206792i | ||||||||
\(408\) | −9.26307e9 | − | 2.02484e8i | −0.334283 | − | 0.00730720i | ||||
\(409\) | −2.21604e10 | −0.791926 | −0.395963 | − | 0.918267i | \(-0.629589\pi\) | ||||
−0.395963 | + | 0.918267i | \(0.629589\pi\) | |||||||
\(410\) | − | 2.14994e10i | − | 0.760835i | ||||||
\(411\) | 1.19809e9 | − | 5.48091e10i | 0.0419877 | − | 1.92081i | ||||
\(412\) | 2.06143e10 | 0.715451 | ||||||||
\(413\) | 2.02296e9i | 0.0695324i | ||||||||
\(414\) | −2.46719e10 | − | 1.07914e9i | −0.839850 | − | 0.0367347i | ||||
\(415\) | 5.78295e10 | 1.94965 | ||||||||
\(416\) | − | 1.67774e10i | − | 0.560212i | ||||||
\(417\) | 4.05951e10 | + | 8.87381e8i | 1.34255 | + | 0.0293472i | ||||
\(418\) | −6.48755e9 | −0.212508 | ||||||||
\(419\) | − | 1.97226e10i | − | 0.639893i | −0.947436 | − | 0.319946i | \(-0.896335\pi\) | ||
0.947436 | − | 0.319946i | \(-0.103665\pi\) | |||||||
\(420\) | −1.94185e8 | + | 8.88339e9i | −0.00624048 | + | 0.285484i | ||||
\(421\) | −2.56754e10 | −0.817315 | −0.408658 | − | 0.912688i | \(-0.634003\pi\) | ||||
−0.408658 | + | 0.912688i | \(0.634003\pi\) | |||||||
\(422\) | 2.21001e10i | 0.696859i | ||||||||
\(423\) | −1.21876e9 | + | 2.78639e10i | −0.0380676 | + | 0.870324i | ||||
\(424\) | 5.21044e10 | 1.61217 | ||||||||
\(425\) | 1.07506e9i | 0.0329517i | ||||||||
\(426\) | 8.80546e8 | + | 1.92481e7i | 0.0267371 | + | 0.000584454i | ||||
\(427\) | −1.44864e10 | −0.435761 | ||||||||
\(428\) | − | 7.38540e9i | − | 0.220089i | ||||||
\(429\) | −1.22555e8 | + | 5.60654e9i | −0.00361828 | + | 0.165526i | ||||
\(430\) | −9.03065e9 | −0.264147 | ||||||||
\(431\) | − | 2.02786e10i | − | 0.587664i | −0.955857 | − | 0.293832i | \(-0.905069\pi\) | ||
0.955857 | − | 0.293832i | \(-0.0949307\pi\) | |||||||
\(432\) | 2.70919e9 | + | 1.77890e8i | 0.0777866 | + | 0.00510760i | ||||
\(433\) | −1.50102e10 | −0.427007 | −0.213504 | − | 0.976942i | \(-0.568488\pi\) | ||||
−0.213504 | + | 0.976942i | \(0.568488\pi\) | |||||||
\(434\) | 1.29252e9i | 0.0364317i | ||||||||
\(435\) | 4.45822e10 | + | 9.74536e8i | 1.24510 | + | 0.0272170i | ||||
\(436\) | −6.15790e9 | −0.170407 | ||||||||
\(437\) | 6.21579e10i | 1.70440i | ||||||||
\(438\) | −6.93486e8 | + | 3.17250e10i | −0.0188426 | + | 0.861995i | ||||
\(439\) | −3.61916e10 | −0.974427 | −0.487213 | − | 0.873283i | \(-0.661987\pi\) | ||||
−0.487213 | + | 0.873283i | \(0.661987\pi\) | |||||||
\(440\) | − | 1.15263e10i | − | 0.307523i | ||||||
\(441\) | −3.11812e10 | − | 1.36385e9i | −0.824401 | − | 0.0360589i | ||||
\(442\) | −4.24098e9 | −0.111116 | ||||||||
\(443\) | − | 1.99664e8i | − | 0.00518423i | −0.999997 | − | 0.00259212i | \(-0.999175\pi\) | ||
0.999997 | − | 0.00259212i | \(-0.000825097\pi\) | |||||||
\(444\) | 1.73841e10 | + | 3.80004e8i | 0.447321 | + | 0.00977813i | ||||
\(445\) | 4.31383e10 | 1.10008 | ||||||||
\(446\) | − | 7.16296e9i | − | 0.181031i | ||||||
\(447\) | −1.30300e8 | + | 5.96085e9i | −0.00326373 | + | 0.149306i | ||||
\(448\) | 8.81785e9 | 0.218902 | ||||||||
\(449\) | 4.72852e10i | 1.16343i | 0.813393 | + | 0.581715i | \(0.197618\pi\) | ||||
−0.813393 | + | 0.581715i | \(0.802382\pi\) | |||||||
\(450\) | −1.01437e8 | + | 2.31911e9i | −0.00247369 | + | 0.0565550i | ||||
\(451\) | −1.53756e10 | −0.371644 | ||||||||
\(452\) | − | 1.83669e10i | − | 0.440029i | ||||||
\(453\) | −4.11667e10 | − | 8.99875e8i | −0.977582 | − | 0.0213693i | ||||
\(454\) | −4.29036e10 | −1.00988 | ||||||||
\(455\) | 1.03016e10i | 0.240358i | ||||||||
\(456\) | −1.10045e9 | + | 5.03425e10i | −0.0254514 | + | 1.16433i | ||||
\(457\) | 6.39052e10 | 1.46511 | 0.732557 | − | 0.680706i | \(-0.238327\pi\) | ||||
0.732557 | + | 0.680706i | \(0.238327\pi\) | |||||||
\(458\) | 1.75742e10i | 0.399405i | ||||||||
\(459\) | 9.98114e8 | − | 1.52009e10i | 0.0224869 | − | 0.342466i | ||||
\(460\) | −4.36003e10 | −0.973775 | ||||||||
\(461\) | − | 5.51990e10i | − | 1.22216i | −0.791570 | − | 0.611079i | \(-0.790736\pi\) | ||
0.791570 | − | 0.611079i | \(-0.209264\pi\) | |||||||
\(462\) | −3.38541e9 | − | 7.40027e7i | −0.0743093 | − | 0.00162435i | ||||
\(463\) | −4.87768e10 | −1.06142 | −0.530712 | − | 0.847552i | \(-0.678075\pi\) | ||||
−0.530712 | + | 0.847552i | \(0.678075\pi\) | |||||||
\(464\) | 4.29844e9i | 0.0927341i | ||||||||
\(465\) | 1.58084e8 | − | 7.23188e9i | 0.00338124 | − | 0.154682i | ||||
\(466\) | 4.40727e10 | 0.934600 | ||||||||
\(467\) | − | 1.40745e10i | − | 0.295914i | −0.988994 | − | 0.147957i | \(-0.952730\pi\) | ||
0.988994 | − | 0.147957i | \(-0.0472697\pi\) | |||||||
\(468\) | 1.71683e10 | + | 7.50934e8i | 0.357886 | + | 0.0156538i | ||||
\(469\) | −2.98099e10 | −0.616126 | ||||||||
\(470\) | − | 2.62394e10i | − | 0.537728i | ||||||
\(471\) | 2.62633e10 | + | 5.74098e8i | 0.533661 | + | 0.0116655i | ||||
\(472\) | −8.04150e9 | −0.162020 | ||||||||
\(473\) | 6.45842e9i | 0.129027i | ||||||||
\(474\) | −1.97151e8 | + | 9.01910e9i | −0.00390559 | + | 0.178669i | ||||
\(475\) | 5.84270e9 | 0.114773 | ||||||||
\(476\) | 4.80570e9i | 0.0936115i | ||||||||
\(477\) | −3.74349e9 | + | 8.55860e10i | −0.0723108 | + | 1.65322i | ||||
\(478\) | 1.44311e10 | 0.276431 | ||||||||
\(479\) | − | 3.32933e10i | − | 0.632432i | −0.948687 | − | 0.316216i | \(-0.897587\pi\) | ||
0.948687 | − | 0.316216i | \(-0.102413\pi\) | |||||||
\(480\) | −5.66833e10 | − | 1.23906e9i | −1.06780 | − | 0.0233414i | ||||
\(481\) | 2.01593e10 | 0.376613 | ||||||||
\(482\) | 3.72339e10i | 0.689842i | ||||||||
\(483\) | −7.09028e8 | + | 3.24360e10i | −0.0130279 | + | 0.595989i | ||||
\(484\) | −3.25448e9 | −0.0593063 | ||||||||
\(485\) | 6.53194e10i | 1.18052i | ||||||||
\(486\) | 3.58738e9 | − | 3.26969e10i | 0.0643031 | − | 0.586085i | ||||
\(487\) | −1.01082e11 | −1.79705 | −0.898523 | − | 0.438926i | \(-0.855359\pi\) | ||||
−0.898523 | + | 0.438926i | \(0.855359\pi\) | |||||||
\(488\) | − | 5.75851e10i | − | 1.01538i | ||||||
\(489\) | 2.72114e10 | + | 5.94823e8i | 0.475900 | + | 0.0104029i | ||||
\(490\) | 2.93633e10 | 0.509355 | ||||||||
\(491\) | − | 5.12897e10i | − | 0.882478i | −0.897390 | − | 0.441239i | \(-0.854539\pi\) | ||
0.897390 | − | 0.441239i | \(-0.145461\pi\) | |||||||
\(492\) | −1.02970e9 | + | 4.71057e10i | −0.0175731 | + | 0.803920i | ||||
\(493\) | 2.41179e10 | 0.408274 | ||||||||
\(494\) | 2.30487e10i | 0.387024i | ||||||||
\(495\) | 1.89329e10 | + | 8.28116e8i | 0.315353 | + | 0.0137934i | ||||
\(496\) | 6.97271e8 | 0.0115206 | ||||||||
\(497\) | − | 1.15709e9i | − | 0.0189645i | ||||||
\(498\) | 6.75184e10 | + | 1.47591e9i | 1.09775 | + | 0.0239961i | ||||
\(499\) | 1.03716e11 | 1.67279 | 0.836397 | − | 0.548124i | \(-0.184658\pi\) | ||||
0.836397 | + | 0.548124i | \(0.184658\pi\) | |||||||
\(500\) | − | 3.85872e10i | − | 0.617396i | ||||||
\(501\) | 8.58438e8 | − | 3.92710e10i | 0.0136257 | − | 0.623335i | ||||
\(502\) | −6.33952e9 | −0.0998255 | ||||||||
\(503\) | 5.73744e10i | 0.896284i | 0.893962 | + | 0.448142i | \(0.147914\pi\) | ||||
−0.893962 | + | 0.448142i | \(0.852086\pi\) | |||||||
\(504\) | −1.14850e9 | + | 2.62578e10i | −0.0177996 | + | 0.406945i | ||||
\(505\) | 2.07676e10 | 0.319316 | ||||||||
\(506\) | − | 1.66159e10i | − | 0.253467i | ||||||
\(507\) | −4.61397e10 | − | 1.00858e9i | −0.698302 | − | 0.0152644i | ||||
\(508\) | −3.08735e10 | −0.463587 | ||||||||
\(509\) | 1.24239e11i | 1.85092i | 0.378848 | + | 0.925459i | \(0.376320\pi\) | ||||
−0.378848 | + | 0.925459i | \(0.623680\pi\) | |||||||
\(510\) | −3.13208e8 | + | 1.43283e10i | −0.00462969 | + | 0.211795i | ||||
\(511\) | 4.16885e10 | 0.611411 | ||||||||
\(512\) | − | 1.06842e10i | − | 0.155475i | ||||||
\(513\) | −8.26130e10 | − | 5.42450e9i | −1.19283 | − | 0.0783232i | ||||
\(514\) | 2.51038e10 | 0.359656 | ||||||||
\(515\) | − | 8.07650e10i | − | 1.14814i | ||||||
\(516\) | 1.97864e10 | + | 4.32517e8i | 0.279105 | + | 0.00610104i | ||||
\(517\) | −1.87656e10 | −0.262663 | ||||||||
\(518\) | 1.21729e10i | 0.169073i | ||||||||
\(519\) | −2.05457e9 | + | 9.39905e10i | −0.0283173 | + | 1.29543i | ||||
\(520\) | −4.09500e10 | −0.560067 | ||||||||
\(521\) | − | 1.99173e10i | − | 0.270321i | −0.990824 | − | 0.135160i | \(-0.956845\pi\) | ||
0.990824 | − | 0.135160i | \(-0.0431550\pi\) | |||||||
\(522\) | 5.20267e10 | + | 2.27562e9i | 0.700720 | + | 0.0306492i | ||||
\(523\) | 9.32432e9 | 0.124626 | 0.0623132 | − | 0.998057i | \(-0.480152\pi\) | ||||
0.0623132 | + | 0.998057i | \(0.480152\pi\) | |||||||
\(524\) | − | 7.36997e10i | − | 0.977554i | ||||||
\(525\) | 3.04891e9 | + | 6.66470e7i | 0.0401335 | + | 0.000877290i | ||||
\(526\) | −6.41270e10 | −0.837718 | ||||||||
\(527\) | − | 3.91228e9i | − | 0.0507209i | ||||||
\(528\) | −3.99219e7 | + | 1.82631e9i | −0.000513660 | + | 0.0234984i | ||||
\(529\) | −8.08872e10 | −1.03290 | ||||||||
\(530\) | − | 8.05963e10i | − | 1.02144i | ||||||
\(531\) | 5.77750e8 | − | 1.32089e10i | 0.00726711 | − | 0.166145i | ||||
\(532\) | 2.61178e10 | 0.326055 | ||||||||
\(533\) | 5.46258e10i | 0.676845i | ||||||||
\(534\) | 5.03658e10 | + | 1.10096e9i | 0.619399 | + | 0.0135396i | ||||
\(535\) | −2.89353e10 | −0.353194 | ||||||||
\(536\) | − | 1.18498e11i | − | 1.43566i | ||||||
\(537\) | 2.30152e9 | − | 1.05288e11i | 0.0276770 | − | 1.26614i | ||||
\(538\) | 6.83329e10 | 0.815645 | ||||||||
\(539\) | − | 2.09997e10i | − | 0.248804i | ||||||
\(540\) | 3.80499e9 | − | 5.79484e10i | 0.0447485 | − | 0.681501i | ||||
\(541\) | 1.15274e11 | 1.34568 | 0.672839 | − | 0.739789i | \(-0.265075\pi\) | ||||
0.672839 | + | 0.739789i | \(0.265075\pi\) | |||||||
\(542\) | − | 9.08750e10i | − | 1.05305i | ||||||
\(543\) | −1.56434e11 | − | 3.41953e9i | −1.79941 | − | 0.0393339i | ||||
\(544\) | −3.06644e10 | −0.350137 | ||||||||
\(545\) | 2.41261e10i | 0.273464i | ||||||||
\(546\) | −2.62914e8 | + | 1.20275e10i | −0.00295830 | + | 0.135334i | ||||
\(547\) | 2.41200e10 | 0.269419 | 0.134710 | − | 0.990885i | \(-0.456990\pi\) | ||||
0.134710 | + | 0.990885i | \(0.456990\pi\) | |||||||
\(548\) | − | 1.13033e11i | − | 1.25338i | ||||||
\(549\) | 9.45886e10 | + | 4.13726e9i | 1.04124 | + | 0.0455432i | ||||
\(550\) | −1.56185e9 | −0.0170683 | ||||||||
\(551\) | − | 1.31075e11i | − | 1.42204i | ||||||
\(552\) | −1.28937e11 | − | 2.81847e9i | −1.38874 | − | 0.0303569i | ||||
\(553\) | 1.18516e10 | 0.126730 | ||||||||
\(554\) | 2.33488e10i | 0.247871i | ||||||||
\(555\) | 1.48882e9 | − | 6.81092e10i | 0.0156917 | − | 0.717850i | ||||
\(556\) | 8.37193e10 | 0.876045 | ||||||||
\(557\) | 1.16076e11i | 1.20593i | 0.797767 | + | 0.602966i | \(0.206015\pi\) | ||||
−0.797767 | + | 0.602966i | \(0.793985\pi\) | |||||||
\(558\) | 3.69140e8 | − | 8.43950e9i | 0.00380762 | − | 0.0870522i | ||||
\(559\) | 2.29452e10 | 0.234987 | ||||||||
\(560\) | 3.35570e9i | 0.0341217i | ||||||||
\(561\) | 1.02472e10 | + | 2.23996e8i | 0.103455 | + | 0.00226146i | ||||
\(562\) | −6.31127e10 | −0.632662 | ||||||||
\(563\) | 1.43539e11i | 1.42869i | 0.699794 | + | 0.714345i | \(0.253275\pi\) | ||||
−0.699794 | + | 0.714345i | \(0.746725\pi\) | |||||||
\(564\) | −1.25672e9 | + | 5.74913e10i | −0.0124200 | + | 0.568179i | ||||
\(565\) | −7.19597e10 | −0.706148 | ||||||||
\(566\) | − | 7.18843e9i | − | 0.0700435i | ||||||
\(567\) | −4.30482e10 | − | 3.77303e9i | −0.416507 | − | 0.0365055i | ||||
\(568\) | 4.59957e9 | 0.0441900 | ||||||||
\(569\) | 5.95031e9i | 0.0567663i | 0.999597 | + | 0.0283832i | \(0.00903585\pi\) | ||||
−0.999597 | + | 0.0283832i | \(0.990964\pi\) | |||||||
\(570\) | 7.78710e10 | + | 1.70221e9i | 0.737694 | + | 0.0161255i | ||||
\(571\) | −1.46668e10 | −0.137972 | −0.0689862 | − | 0.997618i | \(-0.521976\pi\) | ||||
−0.0689862 | + | 0.997618i | \(0.521976\pi\) | |||||||
\(572\) | 1.15624e10i | 0.108010i | ||||||||
\(573\) | −1.31135e9 | + | 5.99907e10i | −0.0121647 | + | 0.556500i | ||||
\(574\) | −3.29848e10 | −0.303855 | ||||||||
\(575\) | 1.49643e10i | 0.136894i | ||||||||
\(576\) | −5.75760e10 | − | 2.51835e9i | −0.523060 | − | 0.0228784i | ||||
\(577\) | 8.14507e9 | 0.0734838 | 0.0367419 | − | 0.999325i | \(-0.488302\pi\) | ||||
0.0367419 | + | 0.999325i | \(0.488302\pi\) | |||||||
\(578\) | − | 5.80555e10i | − | 0.520154i | ||||||
\(579\) | −1.40486e11 | − | 3.07092e9i | −1.25002 | − | 0.0273246i | ||||
\(580\) | 9.19418e10 | 0.812458 | ||||||||
\(581\) | − | 8.87233e10i | − | 0.778634i | ||||||
\(582\) | −1.66706e9 | + | 7.62632e10i | −0.0145298 | + | 0.664696i | ||||
\(583\) | −5.76398e10 | −0.498940 | ||||||||
\(584\) | 1.65717e11i | 1.42467i | ||||||||
\(585\) | 2.94209e9 | − | 6.72639e10i | 0.0251208 | − | 0.574326i | ||||
\(586\) | −3.25858e10 | −0.276337 | ||||||||
\(587\) | 9.70196e10i | 0.817160i | 0.912722 | + | 0.408580i | \(0.133976\pi\) | ||||
−0.912722 | + | 0.408580i | \(0.866024\pi\) | |||||||
\(588\) | −6.43357e10 | − | 1.40634e9i | −0.538199 | − | 0.0117647i | ||||
\(589\) | −2.12623e10 | −0.176664 | ||||||||
\(590\) | 1.24388e10i | 0.102653i | ||||||||
\(591\) | −6.48395e8 | + | 2.96622e10i | −0.00531484 | + | 0.243138i | ||||
\(592\) | 6.56683e9 | 0.0534649 | ||||||||
\(593\) | − | 1.70701e10i | − | 0.138044i | −0.997615 | − | 0.0690219i | \(-0.978012\pi\) | ||
0.997615 | − | 0.0690219i | \(-0.0219878\pi\) | |||||||
\(594\) | 2.20838e10 | + | 1.45006e9i | 0.177390 | + | 0.0116477i | ||||
\(595\) | 1.88283e10 | 0.150226 | ||||||||
\(596\) | 1.22931e10i | 0.0974260i | ||||||||
\(597\) | 2.27857e11 | + | 4.98081e9i | 1.79377 | + | 0.0392105i | ||||
\(598\) | −5.90320e10 | −0.461618 | ||||||||
\(599\) | 2.38404e11i | 1.85185i | 0.377708 | + | 0.925925i | \(0.376712\pi\) | ||||
−0.377708 | + | 0.925925i | \(0.623288\pi\) | |||||||
\(600\) | −2.64930e8 | + | 1.21198e10i | −0.00204421 | + | 0.0935167i | ||||
\(601\) | 1.82138e11 | 1.39606 | 0.698028 | − | 0.716071i | \(-0.254061\pi\) | ||||
0.698028 | + | 0.716071i | \(0.254061\pi\) | |||||||
\(602\) | 1.38550e10i | 0.105492i | ||||||||
\(603\) | 1.94643e11 | + | 8.51361e9i | 1.47221 | + | 0.0643939i | ||||
\(604\) | −8.48981e10 | −0.637896 | ||||||||
\(605\) | 1.27508e10i | 0.0951733i | ||||||||
\(606\) | 2.42471e10 | + | 5.30024e8i | 0.179791 | + | 0.00393012i | ||||
\(607\) | 2.63810e11 | 1.94329 | 0.971643 | − | 0.236453i | \(-0.0759848\pi\) | ||||
0.971643 | + | 0.236453i | \(0.0759848\pi\) | |||||||
\(608\) | 1.66653e11i | 1.21955i | ||||||||
\(609\) | 1.49516e9 | − | 6.83990e10i | 0.0108697 | − | 0.497257i | ||||
\(610\) | −8.90739e10 | −0.643326 | ||||||||
\(611\) | 6.66695e10i | 0.478368i | ||||||||
\(612\) | 1.37249e9 | − | 3.13788e10i | 0.00978372 | − | 0.223681i | ||||
\(613\) | −1.61834e11 | −1.14612 | −0.573058 | − | 0.819515i | \(-0.694243\pi\) | ||||
−0.573058 | + | 0.819515i | \(0.694243\pi\) | |||||||
\(614\) | 7.15058e10i | 0.503116i | ||||||||
\(615\) | 1.84556e11 | + | 4.03426e9i | 1.29011 | + | 0.0282010i | ||||
\(616\) | −1.76839e10 | −0.122816 | ||||||||
\(617\) | − | 7.79064e10i | − | 0.537567i | −0.963201 | − | 0.268783i | \(-0.913378\pi\) | ||
0.963201 | − | 0.268783i | \(-0.0866216\pi\) | |||||||
\(618\) | 2.06126e9 | − | 9.42966e10i | 0.0141312 | − | 0.646461i | ||||
\(619\) | −9.39221e10 | −0.639743 | −0.319871 | − | 0.947461i | \(-0.603640\pi\) | ||||
−0.319871 | + | 0.947461i | \(0.603640\pi\) | |||||||
\(620\) | − | 1.49143e10i | − | 0.100934i | ||||||
\(621\) | 1.38932e10 | − | 2.11587e11i | 0.0934190 | − | 1.42273i | ||||
\(622\) | −4.05979e10 | −0.271232 | ||||||||
\(623\) | − | 6.61838e10i | − | 0.439339i | ||||||
\(624\) | 6.48843e9 | + | 1.41833e8i | 0.0427958 | + | 0.000935488i | ||||
\(625\) | −1.65832e11 | −1.08679 | ||||||||
\(626\) | 1.29551e11i | 0.843611i | ||||||||
\(627\) | 1.21736e9 | − | 5.56907e10i | 0.00787679 | − | 0.360340i | ||||
\(628\) | 5.41628e10 | 0.348227 | ||||||||
\(629\) | − | 3.68455e10i | − | 0.235387i | ||||||
\(630\) | 4.06161e10 | + | 1.77653e9i | 0.257832 | + | 0.0112774i | ||||
\(631\) | −1.25718e11 | −0.793012 | −0.396506 | − | 0.918032i | \(-0.629777\pi\) | ||||
−0.396506 | + | 0.918032i | \(0.629777\pi\) | |||||||
\(632\) | 4.71117e10i | 0.295298i | ||||||||
\(633\) | −1.89713e11 | − | 4.14699e9i | −1.18163 | − | 0.0258296i | ||||
\(634\) | 1.21921e11 | 0.754610 | ||||||||
\(635\) | 1.20960e11i | 0.743954i | ||||||||
\(636\) | −3.86010e9 | + | 1.76588e11i | −0.0235923 | + | 1.07928i | ||||
\(637\) | −7.46066e10 | −0.453127 | ||||||||
\(638\) | 3.50385e10i | 0.211477i | ||||||||
\(639\) | −3.30461e8 | + | 7.55521e9i | −0.00198206 | + | 0.0453151i | ||||
\(640\) | −1.24971e11 | −0.744885 | ||||||||
\(641\) | − | 2.55401e11i | − | 1.51283i | −0.654092 | − | 0.756415i | \(-0.726949\pi\) | ||
0.654092 | − | 0.756415i | \(-0.273051\pi\) | |||||||
\(642\) | −3.37832e10 | − | 7.38479e8i | −0.198866 | − | 0.00434708i | ||||
\(643\) | 1.62943e11 | 0.953219 | 0.476610 | − | 0.879115i | \(-0.341866\pi\) | ||||
0.476610 | + | 0.879115i | \(0.341866\pi\) | |||||||
\(644\) | 6.68927e10i | 0.388897i | ||||||||
\(645\) | 1.69456e9 | − | 7.75213e10i | 0.00979081 | − | 0.447901i | ||||
\(646\) | 4.21264e10 | 0.241893 | ||||||||
\(647\) | 2.50710e11i | 1.43072i | 0.698755 | + | 0.715361i | \(0.253738\pi\) | ||||
−0.698755 | + | 0.715361i | \(0.746262\pi\) | |||||||
\(648\) | 1.49982e10 | − | 1.71122e11i | 0.0850629 | − | 0.970520i | ||||
\(649\) | 8.89580e9 | 0.0501425 | ||||||||
\(650\) | 5.54888e9i | 0.0310851i | ||||||||
\(651\) | −1.10953e10 | − | 2.42536e8i | −0.0617755 | − | 0.00135037i | ||||
\(652\) | 5.61182e10 | 0.310537 | ||||||||
\(653\) | 3.60027e10i | 0.198008i | 0.995087 | + | 0.0990038i | \(0.0315656\pi\) | ||||
−0.995087 | + | 0.0990038i | \(0.968434\pi\) | |||||||
\(654\) | −6.15738e8 | + | 2.81682e10i | −0.00336578 | + | 0.153974i | ||||
\(655\) | −2.88749e11 | −1.56875 | ||||||||
\(656\) | 1.77942e10i | 0.0960865i | ||||||||
\(657\) | −2.72205e11 | − | 1.19061e10i | −1.46095 | − | 0.0639011i | ||||
\(658\) | −4.02572e10 | −0.214753 | ||||||||
\(659\) | − | 1.05976e11i | − | 0.561910i | −0.959721 | − | 0.280955i | \(-0.909349\pi\) | ||
0.959721 | − | 0.280955i | \(-0.0906512\pi\) | |||||||
\(660\) | 3.90640e10 | + | 8.53912e8i | 0.205874 | + | 0.00450026i | ||||
\(661\) | −5.55412e10 | −0.290944 | −0.145472 | − | 0.989362i | \(-0.546470\pi\) | ||||
−0.145472 | + | 0.989362i | \(0.546470\pi\) | |||||||
\(662\) | 1.09903e11i | 0.572239i | ||||||||
\(663\) | 7.95802e8 | − | 3.64056e10i | 0.00411861 | − | 0.188414i | ||||
\(664\) | 3.52686e11 | 1.81433 | ||||||||
\(665\) | − | 1.02327e11i | − | 0.523245i | ||||||
\(666\) | 3.47652e9 | − | 7.94824e10i | 0.0176705 | − | 0.403993i | ||||
\(667\) | 3.35708e11 | 1.69612 | ||||||||
\(668\) | − | 8.09887e10i | − | 0.406741i | ||||||
\(669\) | 6.14886e10 | + | 1.34410e9i | 0.306966 | + | 0.00671006i | ||||
\(670\) | −1.83295e11 | −0.909604 | ||||||||
\(671\) | 6.37027e10i | 0.314245i | ||||||||
\(672\) | −1.90099e9 | + | 8.69649e10i | −0.00932188 | + | 0.426449i | ||||
\(673\) | 3.64622e11 | 1.77739 | 0.888696 | − | 0.458498i | \(-0.151612\pi\) | ||||
0.888696 | + | 0.458498i | \(0.151612\pi\) | |||||||
\(674\) | − | 1.10142e11i | − | 0.533719i | ||||||
\(675\) | −1.98887e10 | − | 1.30593e9i | −0.0958059 | − | 0.00629077i | ||||
\(676\) | −9.51540e10 | −0.455659 | ||||||||
\(677\) | − | 3.08651e11i | − | 1.46931i | −0.678441 | − | 0.734655i | \(-0.737344\pi\) | ||
0.678441 | − | 0.734655i | \(-0.262656\pi\) | |||||||
\(678\) | −8.40161e10 | − | 1.83653e9i | −0.397597 | − | 0.00869121i | ||||
\(679\) | 1.00215e11 | 0.471467 | ||||||||
\(680\) | 7.48448e10i | 0.350047i | ||||||||
\(681\) | 8.05067e9 | − | 3.68295e11i | 0.0374320 | − | 1.71241i | ||||
\(682\) | 5.68376e9 | 0.0262723 | ||||||||
\(683\) | − | 1.10656e11i | − | 0.508502i | −0.967138 | − | 0.254251i | \(-0.918171\pi\) | ||
0.967138 | − | 0.254251i | \(-0.0818289\pi\) | |||||||
\(684\) | −1.70536e11 | − | 7.45915e9i | −0.779096 | − | 0.0340773i | ||||
\(685\) | −4.42853e11 | −2.01139 | ||||||||
\(686\) | − | 9.96432e10i | − | 0.449937i | ||||||
\(687\) | −1.50861e11 | − | 3.29772e9i | −0.677252 | − | 0.0148043i | ||||
\(688\) | 7.47431e9 | 0.0333593 | ||||||||
\(689\) | 2.04780e11i | 0.908679i | ||||||||
\(690\) | −4.35967e9 | + | 1.99442e11i | −0.0192335 | + | 0.879875i | ||||
\(691\) | 6.52617e10 | 0.286251 | 0.143125 | − | 0.989705i | \(-0.454285\pi\) | ||||
0.143125 | + | 0.989705i | \(0.454285\pi\) | |||||||
\(692\) | 1.93837e11i | 0.845302i | ||||||||
\(693\) | 1.27052e9 | − | 2.90473e10i | 0.00550867 | − | 0.125943i | ||||
\(694\) | 1.22848e11 | 0.529578 | ||||||||
\(695\) | − | 3.28005e11i | − | 1.40586i | ||||||
\(696\) | 2.71894e11 | + | 5.94342e9i | 1.15868 | + | 0.0253279i | ||||
\(697\) | 9.98404e10 | 0.423034 | ||||||||
\(698\) | 1.19474e10i | 0.0503329i | ||||||||
\(699\) | −8.27005e9 | + | 3.78331e11i | −0.0346417 | + | 1.58476i | ||||
\(700\) | 6.28776e9 | 0.0261881 | ||||||||
\(701\) | − | 3.10663e11i | − | 1.28652i | −0.765646 | − | 0.643262i | \(-0.777581\pi\) | ||
0.765646 | − | 0.643262i | \(-0.222419\pi\) | |||||||
\(702\) | 5.15171e9 | − | 7.84584e10i | 0.0212130 | − | 0.323066i | ||||
\(703\) | −2.00246e11 | −0.819866 | ||||||||
\(704\) | − | 3.87758e10i | − | 0.157859i | ||||||
\(705\) | 2.25246e11 | + | 4.92372e9i | 0.911801 | + | 0.0199313i | ||||
\(706\) | 2.54975e10 | 0.102631 | ||||||||
\(707\) | − | 3.18622e10i | − | 0.127526i | ||||||
\(708\) | 5.95747e8 | − | 2.72537e10i | 0.00237099 | − | 0.108466i | ||||
\(709\) | −1.69788e11 | −0.671927 | −0.335964 | − | 0.941875i | \(-0.609062\pi\) | ||||
−0.335964 | + | 0.941875i | \(0.609062\pi\) | |||||||
\(710\) | − | 7.11473e9i | − | 0.0279979i | ||||||
\(711\) | −7.73851e10 | − | 3.38479e9i | −0.302816 | − | 0.0132450i | ||||
\(712\) | 2.63088e11 | 1.02372 | ||||||||
\(713\) | − | 5.44567e10i | − | 0.210714i | ||||||
\(714\) | 2.19829e10 | + | 4.80530e8i | 0.0845847 | + | 0.00184896i | ||||
\(715\) | 4.53004e10 | 0.173331 | ||||||||
\(716\) | − | 2.17136e11i | − | 0.826188i | ||||||
\(717\) | −2.70793e9 | + | 1.23880e11i | −0.0102462 | + | 0.468732i | ||||
\(718\) | −1.42439e11 | −0.535958 | ||||||||
\(719\) | − | 1.37855e11i | − | 0.515829i | −0.966168 | − | 0.257914i | \(-0.916965\pi\) | ||
0.966168 | − | 0.257914i | \(-0.0830353\pi\) | |||||||
\(720\) | 9.58376e8 | − | 2.19110e10i | 0.00356620 | − | 0.0815327i | ||||
\(721\) | −1.23912e11 | −0.458533 | ||||||||
\(722\) | − | 6.87296e10i | − | 0.252927i | ||||||
\(723\) | −3.19625e11 | − | 6.98677e9i | −1.16973 | − | 0.0255696i | ||||
\(724\) | −3.22613e11 | −1.17416 | ||||||||
\(725\) | − | 3.15558e10i | − | 0.114216i | ||||||
\(726\) | −3.25421e8 | + | 1.48871e10i | −0.00117138 | + | 0.0535874i | ||||
\(727\) | 3.86044e11 | 1.38197 | 0.690985 | − | 0.722869i | \(-0.257177\pi\) | ||||
0.690985 | + | 0.722869i | \(0.257177\pi\) | |||||||
\(728\) | 6.28264e10i | 0.223675i | ||||||||
\(729\) | 2.80005e11 | + | 3.69303e10i | 0.991414 | + | 0.130759i | ||||
\(730\) | 2.56335e11 | 0.902643 | ||||||||
\(731\) | − | 4.19372e10i | − | 0.146869i | ||||||
\(732\) | 1.95163e11 | + | 4.26614e9i | 0.679757 | + | 0.0148590i | ||||
\(733\) | 5.36395e11 | 1.85810 | 0.929049 | − | 0.369956i | \(-0.120627\pi\) | ||||
0.929049 | + | 0.369956i | \(0.120627\pi\) | |||||||
\(734\) | 4.74863e10i | 0.163600i | ||||||||
\(735\) | −5.50990e9 | + | 2.52062e11i | −0.0188797 | + | 0.863689i | ||||
\(736\) | −4.26830e11 | −1.45460 | ||||||||
\(737\) | 1.31087e11i | 0.444313i | ||||||||
\(738\) | 2.15374e11 | + | 9.42035e9i | 0.726052 | + | 0.0317572i | ||||
\(739\) | −2.66131e11 | −0.892314 | −0.446157 | − | 0.894955i | \(-0.647208\pi\) | ||||
−0.446157 | + | 0.894955i | \(0.647208\pi\) | |||||||
\(740\) | − | 1.40462e11i | − | 0.468415i | ||||||
\(741\) | −1.97855e11 | − | 4.32499e9i | −0.656259 | − | 0.0143454i | ||||
\(742\) | −1.23653e11 | −0.407932 | ||||||||
\(743\) | 4.53817e11i | 1.48911i | 0.667563 | + | 0.744553i | \(0.267337\pi\) | ||||
−0.667563 | + | 0.744553i | \(0.732663\pi\) | |||||||
\(744\) | 9.64109e8 | − | 4.41052e10i | 0.00314655 | − | 0.143945i | ||||
\(745\) | 4.81631e10 | 0.156347 | ||||||||
\(746\) | − | 2.15558e11i | − | 0.695998i | ||||||
\(747\) | −2.53391e10 | + | 5.79317e11i | −0.0813782 | + | 1.86052i | ||||
\(748\) | 2.11327e10 | 0.0675070 | ||||||||
\(749\) | 4.43933e10i | 0.141055i | ||||||||
\(750\) | −1.76511e11 | − | 3.85840e9i | −0.557861 | − | 0.0121945i | ||||
\(751\) | 1.24898e11 | 0.392640 | 0.196320 | − | 0.980540i | \(-0.437101\pi\) | ||||
0.196320 | + | 0.980540i | \(0.437101\pi\) | |||||||
\(752\) | 2.17173e10i | 0.0679102i | ||||||||
\(753\) | 1.18958e9 | − | 5.44200e10i | 0.00370011 | − | 0.169269i | ||||
\(754\) | 1.24483e11 | 0.385146 | ||||||||
\(755\) | 3.32623e11i | 1.02368i | ||||||||
\(756\) | −8.89059e10 | − | 5.83770e9i | −0.272172 | − | 0.0178712i | ||||
\(757\) | −1.51106e11 | −0.460148 | −0.230074 | − | 0.973173i | \(-0.573897\pi\) | ||||
−0.230074 | + | 0.973173i | \(0.573897\pi\) | |||||||
\(758\) | 2.62743e10i | 0.0795892i | ||||||||
\(759\) | 1.42635e11 | + | 3.11789e9i | 0.429791 | + | 0.00939494i | ||||
\(760\) | 4.06763e11 | 1.21923 | ||||||||
\(761\) | 1.81909e11i | 0.542395i | 0.962524 | + | 0.271197i | \(0.0874196\pi\) | ||||
−0.962524 | + | 0.271197i | \(0.912580\pi\) | |||||||
\(762\) | −3.08710e9 | + | 1.41226e11i | −0.00915652 | + | 0.418884i | ||||
\(763\) | 3.70148e10 | 0.109214 | ||||||||
\(764\) | 1.23719e11i | 0.363130i | ||||||||
\(765\) | −1.22939e11 | − | 5.37730e9i | −0.358959 | − | 0.0157007i | ||||
\(766\) | 1.40859e11 | 0.409137 | ||||||||
\(767\) | − | 3.16046e10i | − | 0.0913206i | ||||||
\(768\) | −3.28008e11 | − | 7.17003e9i | −0.942843 | − | 0.0206099i | ||||
\(769\) | −4.38439e11 | −1.25373 | −0.626864 | − | 0.779128i | \(-0.715662\pi\) | ||||
−0.626864 | + | 0.779128i | \(0.715662\pi\) | |||||||
\(770\) | 2.73538e10i | 0.0778135i | ||||||||
\(771\) | −4.71062e9 | + | 2.15497e11i | −0.0133309 | + | 0.609852i | ||||
\(772\) | −2.89724e11 | −0.815671 | ||||||||
\(773\) | 1.20107e11i | 0.336396i | 0.985753 | + | 0.168198i | \(0.0537948\pi\) | ||||
−0.985753 | + | 0.168198i | \(0.946205\pi\) | |||||||
\(774\) | 3.95695e9 | − | 9.04662e10i | 0.0110255 | − | 0.252071i | ||||
\(775\) | −5.11881e9 | −0.0141893 | ||||||||
\(776\) | 3.98364e11i | 1.09859i | ||||||||
\(777\) | −1.04495e11 | − | 2.28418e9i | −0.286688 | − | 0.00626681i | ||||
\(778\) | −1.07945e11 | −0.294635 | ||||||||
\(779\) | − | 5.42608e11i | − | 1.47345i | ||||||
\(780\) | 3.03374e9 | − | 1.38785e11i | 0.00819596 | − | 0.374941i | ||||
\(781\) | −5.08822e9 | −0.0136761 | ||||||||
\(782\) | 1.07894e11i | 0.288515i | ||||||||
\(783\) | −2.92971e10 | + | 4.46183e11i | −0.0779431 | + | 1.18704i | ||||
\(784\) | −2.43028e10 | −0.0643269 | ||||||||
\(785\) | − | 2.12205e11i | − | 0.558827i | ||||||
\(786\) | −3.37127e11 | − | 7.36936e9i | −0.883289 | − | 0.0193081i | ||||
\(787\) | −7.26524e11 | −1.89387 | −0.946937 | − | 0.321418i | \(-0.895840\pi\) | ||||
−0.946937 | + | 0.321418i | \(0.895840\pi\) | |||||||
\(788\) | 6.11723e10i | 0.158654i | ||||||||
\(789\) | 1.20332e10 | − | 5.50482e11i | 0.0310507 | − | 1.42048i | ||||
\(790\) | 7.28735e10 | 0.187095 | ||||||||
\(791\) | 1.10402e11i | 0.282015i | ||||||||
\(792\) | 1.15466e11 | + | 5.05045e9i | 0.293464 | + | 0.0128360i | ||||
\(793\) | 2.26320e11 | 0.572309 | ||||||||
\(794\) | 2.07430e11i | 0.521902i | ||||||||
\(795\) | 6.91858e11 | + | 1.51235e10i | 1.73200 | + | 0.0378604i | ||||
\(796\) | 4.69910e11 | 1.17048 | ||||||||
\(797\) | − | 1.76890e11i | − | 0.438400i | −0.975680 | − | 0.219200i | \(-0.929655\pi\) | ||
0.975680 | − | 0.219200i | \(-0.0703447\pi\) | |||||||
\(798\) | 2.61156e9 | − | 1.19471e11i | 0.00644005 | − | 0.294613i | ||||
\(799\) | 1.21853e11 | 0.298984 | ||||||||
\(800\) | 4.01211e10i | 0.0979519i | ||||||||
\(801\) | −1.89019e10 | + | 4.32146e11i | −0.0459171 | + | 1.04978i | ||||
\(802\) | −3.07311e11 | −0.742815 | ||||||||
\(803\) | − | 1.83322e11i | − | 0.440913i | ||||||
\(804\) | 4.01605e11 | + | 8.77881e9i | 0.961114 | + | 0.0210093i | ||||
\(805\) | 2.62080e11 | 0.624093 | ||||||||
\(806\) | − | 2.01930e10i | − | 0.0478477i | ||||||
\(807\) | −1.28224e10 | + | 5.86586e11i | −0.0302325 | + | 1.38305i | ||||
\(808\) | 1.26656e11 | 0.297153 | ||||||||
\(809\) | − | 5.66801e11i | − | 1.32323i | −0.749842 | − | 0.661617i | \(-0.769871\pi\) | ||
0.749842 | − | 0.661617i | \(-0.230129\pi\) | |||||||
\(810\) | −2.64695e11 | − | 2.31996e10i | −0.614901 | − | 0.0538941i | ||||
\(811\) | −1.10981e11 | −0.256545 | −0.128273 | − | 0.991739i | \(-0.540943\pi\) | ||||
−0.128273 | + | 0.991739i | \(0.540943\pi\) | |||||||
\(812\) | − | 1.41059e11i | − | 0.324472i | ||||||
\(813\) | 7.80093e11 | + | 1.70523e10i | 1.78560 | + | 0.0390320i | ||||
\(814\) | 5.35291e10 | 0.121925 | ||||||||
\(815\) | − | 2.19866e11i | − | 0.498342i | ||||||
\(816\) | 2.59230e8 | − | 1.18590e10i | 0.000584688 | − | 0.0267478i | ||||
\(817\) | −2.27918e11 | −0.511553 | ||||||||
\(818\) | 2.09053e11i | 0.466921i | ||||||||
\(819\) | −1.03198e11 | − | 4.51383e9i | −0.229369 | − | 0.0100325i | ||||
\(820\) | 3.80610e11 | 0.841830 | ||||||||
\(821\) | − | 1.68985e11i | − | 0.371943i | −0.982555 | − | 0.185971i | \(-0.940457\pi\) | ||
0.982555 | − | 0.185971i | \(-0.0595432\pi\) | |||||||
\(822\) | −5.17049e11 | − | 1.13023e10i | −1.13252 | − | 0.0247560i | ||||
\(823\) | 3.90269e11 | 0.850677 | 0.425339 | − | 0.905034i | \(-0.360155\pi\) | ||||
0.425339 | + | 0.905034i | \(0.360155\pi\) | |||||||
\(824\) | − | 4.92563e11i | − | 1.06845i | ||||||
\(825\) | 2.93075e8 | − | 1.34073e10i | 0.000632649 | − | 0.0289419i | ||||
\(826\) | 1.90839e10 | 0.0409964 | ||||||||
\(827\) | − | 6.26831e11i | − | 1.34007i | −0.742328 | − | 0.670037i | \(-0.766278\pi\) | ||
0.742328 | − | 0.670037i | \(-0.233722\pi\) | |||||||
\(828\) | 1.91043e10 | − | 4.36774e11i | 0.0406453 | − | 0.929257i | ||||
\(829\) | 2.19781e11 | 0.465341 | 0.232671 | − | 0.972556i | \(-0.425254\pi\) | ||||
0.232671 | + | 0.972556i | \(0.425254\pi\) | |||||||
\(830\) | − | 5.45542e11i | − | 1.14952i | ||||||
\(831\) | −2.00432e11 | − | 4.38130e9i | −0.420303 | − | 0.00918754i | ||||
\(832\) | −1.37761e11 | −0.287496 | ||||||||
\(833\) | 1.36359e11i | 0.283208i | ||||||||
\(834\) | 8.37124e9 | − | 3.82960e11i | 0.0173032 | − | 0.791569i | ||||
\(835\) | −3.17306e11 | −0.652729 | ||||||||
\(836\) | − | 1.14851e11i | − | 0.235131i | ||||||
\(837\) | 7.23774e10 | + | 4.75242e9i | 0.147469 | + | 0.00968307i | ||||
\(838\) | −1.86055e11 | −0.377282 | ||||||||
\(839\) | 9.65408e10i | 0.194833i | 0.995244 | + | 0.0974166i | \(0.0310579\pi\) | ||||
−0.995244 | + | 0.0974166i | \(0.968942\pi\) | |||||||
\(840\) | 2.12262e11 | + | 4.63989e9i | 0.426338 | + | 0.00931947i | ||||
\(841\) | −2.07674e11 | −0.415143 | ||||||||
\(842\) | 2.42213e11i | 0.481891i | ||||||||
\(843\) | 1.18428e10 | − | 5.41775e11i | 0.0234501 | − | 1.07277i | ||||
\(844\) | −3.91245e11 | −0.771043 | ||||||||
\(845\) | 3.72805e11i | 0.731231i | ||||||||
\(846\) | 2.62858e11 | + | 1.14973e10i | 0.513145 | + | 0.0224447i | ||||
\(847\) | 1.95625e10 | 0.0380094 | ||||||||
\(848\) | 6.67063e10i | 0.128998i | ||||||||
\(849\) | 6.17072e10 | + | 1.34888e9i | 0.118770 | + | 0.00259622i | ||||
\(850\) | 1.01418e10 | 0.0194284 | ||||||||
\(851\) | − | 5.12868e11i | − | 0.977884i | ||||||
\(852\) | −3.40755e8 | + | 1.55886e10i | −0.000646672 | + | 0.0295834i | ||||
\(853\) | −5.28926e11 | −0.999076 | −0.499538 | − | 0.866292i | \(-0.666497\pi\) | ||||
−0.499538 | + | 0.866292i | \(0.666497\pi\) | |||||||
\(854\) | 1.36659e11i | 0.256926i | ||||||||
\(855\) | −2.92243e10 | + | 6.68144e11i | −0.0546864 | + | 1.25027i | ||||
\(856\) | −1.76468e11 | −0.328679 | ||||||||
\(857\) | 5.60134e11i | 1.03841i | 0.854650 | + | 0.519205i | \(0.173772\pi\) | ||||
−0.854650 | + | 0.519205i | \(0.826228\pi\) | |||||||
\(858\) | 5.28901e10 | + | 1.15614e9i | 0.0975945 | + | 0.00213335i | ||||
\(859\) | −6.65910e11 | −1.22305 | −0.611523 | − | 0.791227i | \(-0.709443\pi\) | ||||
−0.611523 | + | 0.791227i | \(0.709443\pi\) | |||||||
\(860\) | − | 1.59872e11i | − | 0.292266i | ||||||
\(861\) | 6.18946e9 | − | 2.83150e11i | 0.0112626 | − | 0.515233i | ||||
\(862\) | −1.91301e11 | −0.346488 | ||||||||
\(863\) | 7.17319e11i | 1.29321i | 0.762825 | + | 0.646605i | \(0.223812\pi\) | ||||
−0.762825 | + | 0.646605i | \(0.776188\pi\) | |||||||
\(864\) | 3.72494e10 | − | 5.67293e11i | 0.0668442 | − | 1.01801i | ||||
\(865\) | 7.59435e11 | 1.35652 | ||||||||
\(866\) | 1.41601e11i | 0.251765i | ||||||||
\(867\) | 4.98362e11 | + | 1.08939e10i | 0.882001 | + | 0.0192799i | ||||
\(868\) | −2.28819e10 | −0.0403100 | ||||||||
\(869\) | − | 5.21167e10i | − | 0.0913898i | ||||||
\(870\) | 9.19342e9 | − | 4.20572e11i | 0.0160472 | − | 0.734114i | ||||
\(871\) | 4.65719e11 | 0.809192 | ||||||||
\(872\) | 1.47138e11i | 0.254483i | ||||||||
\(873\) | −6.54349e11 | − | 2.86209e10i | −1.12655 | − | 0.0492750i | ||||
\(874\) | 5.86375e11 | 1.00492 | ||||||||
\(875\) | 2.31946e11i | 0.395689i | ||||||||
\(876\) | −5.61636e11 | − | 1.22770e10i | −0.953759 | − | 0.0208485i | ||||
\(877\) | 3.53642e11 | 0.597813 | 0.298907 | − | 0.954282i | \(-0.403378\pi\) | ||||
0.298907 | + | 0.954282i | \(0.403378\pi\) | |||||||
\(878\) | 3.41418e11i | 0.574524i | ||||||||
\(879\) | 6.11459e9 | − | 2.79725e11i | 0.0102426 | − | 0.468571i | ||||
\(880\) | 1.47564e10 | 0.0246065 | ||||||||
\(881\) | 1.08549e12i | 1.80187i | 0.433956 | + | 0.900934i | \(0.357117\pi\) | ||||
−0.433956 | + | 0.900934i | \(0.642883\pi\) | |||||||
\(882\) | −1.28661e10 | + | 2.94152e11i | −0.0212604 | + | 0.486069i | ||||
\(883\) | 1.71060e11 | 0.281388 | 0.140694 | − | 0.990053i | \(-0.455067\pi\) | ||||
0.140694 | + | 0.990053i | \(0.455067\pi\) | |||||||
\(884\) | − | 7.50793e10i | − | 0.122945i | ||||||
\(885\) | −1.06778e11 | − | 2.33408e9i | −0.174063 | − | 0.00380490i | ||||
\(886\) | −1.88356e9 | −0.00305664 | ||||||||
\(887\) | − | 7.24330e11i | − | 1.17015i | −0.810978 | − | 0.585076i | \(-0.801065\pi\) | ||
0.810978 | − | 0.585076i | \(-0.198935\pi\) | |||||||
\(888\) | 9.07989e9 | − | 4.15379e11i | 0.0146026 | − | 0.668024i | ||||
\(889\) | 1.85579e11 | 0.297114 | ||||||||
\(890\) | − | 4.06951e11i | − | 0.648608i | ||||||
\(891\) | −1.65916e10 | + | 1.89301e11i | −0.0263256 | + | 0.300360i | ||||
\(892\) | 1.26808e11 | 0.200303 | ||||||||
\(893\) | − | 6.62239e11i | − | 1.04138i | ||||||
\(894\) | 5.62325e10 | + | 1.22920e9i | 0.0880313 | + | 0.00192430i | ||||
\(895\) | −8.50718e11 | −1.32585 | ||||||||
\(896\) | 1.91733e11i | 0.297485i | ||||||||
\(897\) | 1.10771e10 | − | 5.06745e11i | 0.0171103 | − | 0.782745i | ||||
\(898\) | 4.46072e11 | 0.685961 | ||||||||
\(899\) | 1.14835e11i | 0.175807i | ||||||||
\(900\) | −4.10558e10 | − | 1.79576e9i | −0.0625755 | − | 0.00273702i | ||||
\(901\) | 3.74279e11 | 0.567932 | ||||||||
\(902\) | 1.45048e11i | 0.219122i | ||||||||
\(903\) | −1.18935e11 | − | 2.59984e9i | −0.178879 | − | 0.00391016i | ||||
\(904\) | −4.38862e11 | −0.657135 | ||||||||
\(905\) | 1.26397e12i | 1.88426i | ||||||||
\(906\) | −8.48910e9 | + | 3.88352e11i | −0.0125994 | + | 0.576385i | ||||
\(907\) | −6.42137e11 | −0.948852 | −0.474426 | − | 0.880295i | \(-0.657344\pi\) | ||||
−0.474426 | + | 0.880295i | \(0.657344\pi\) | |||||||
\(908\) | − | 7.59534e11i | − | 1.11739i | ||||||
\(909\) | −9.09972e9 | + | 2.08043e11i | −0.0133282 | + | 0.304718i | ||||
\(910\) | 9.71813e10 | 0.141715 | ||||||||
\(911\) | 1.53902e11i | 0.223445i | 0.993739 | + | 0.111723i | \(0.0356368\pi\) | ||||
−0.993739 | + | 0.111723i | \(0.964363\pi\) | |||||||
\(912\) | −6.44507e10 | − | 1.40885e9i | −0.0931640 | − | 0.00203650i | ||||
\(913\) | −3.90154e11 | −0.561504 | ||||||||
\(914\) | − | 6.02858e11i | − | 0.863834i | ||||||
\(915\) | 1.67143e10 | − | 7.64632e11i | 0.0238454 | − | 1.09086i | ||||
\(916\) | −3.11121e11 | −0.441923 | ||||||||
\(917\) | 4.43005e11i | 0.626515i | ||||||||
\(918\) | −1.43399e11 | − | 9.41584e9i | −0.201919 | − | 0.0132583i | ||||
\(919\) | −1.90278e11 | −0.266763 | −0.133382 | − | 0.991065i | \(-0.542584\pi\) | ||||
−0.133382 | + | 0.991065i | \(0.542584\pi\) | |||||||
\(920\) | 1.04180e12i | 1.45423i | ||||||||
\(921\) | −6.13823e11 | − | 1.34178e10i | −0.853109 | − | 0.0186484i | ||||
\(922\) | −5.20727e11 | −0.720587 | ||||||||
\(923\) | 1.80772e10i | 0.0249072i | ||||||||
\(924\) | 1.31009e9 | − | 5.99329e10i | 0.00179727 | − | 0.0822200i | ||||
\(925\) | −4.82084e10 | −0.0658501 | ||||||||
\(926\) | 4.60142e11i | 0.625818i | ||||||||
\(927\) | 8.09078e11 | + | 3.53887e10i | 1.09565 | + | 0.0479232i | ||||
\(928\) | 9.00075e11 | 1.21363 | ||||||||
\(929\) | 8.05848e11i | 1.08191i | 0.841052 | + | 0.540954i | \(0.181937\pi\) | ||||
−0.841052 | + | 0.540954i | \(0.818063\pi\) | |||||||
\(930\) | −6.82230e10 | − | 1.49131e9i | −0.0912008 | − | 0.00199359i | ||||
\(931\) | 7.41080e11 | 0.986430 | ||||||||
\(932\) | 7.80232e11i | 1.03409i | ||||||||
\(933\) | 7.61801e9 | − | 3.48502e11i | 0.0100535 | − | 0.459916i | ||||
\(934\) | −1.32774e11 | −0.174471 | ||||||||
\(935\) | − | 8.27960e10i | − | 0.108334i | ||||||
\(936\) | 1.79430e10 | − | 4.10224e11i | 0.0233771 | − | 0.534463i | ||||
\(937\) | 1.34399e12 | 1.74356 | 0.871779 | − | 0.489899i | \(-0.162967\pi\) | ||||
0.871779 | + | 0.489899i | \(0.162967\pi\) | |||||||
\(938\) | 2.81216e11i | 0.363269i | ||||||||
\(939\) | −1.11209e12 | − | 2.43096e10i | −1.43047 | − | 0.0312691i | ||||
\(940\) | 4.64524e11 | 0.594973 | ||||||||
\(941\) | 1.55227e11i | 0.197975i | 0.995089 | + | 0.0989874i | \(0.0315604\pi\) | ||||
−0.995089 | + | 0.0989874i | \(0.968440\pi\) | |||||||
\(942\) | 5.41583e9 | − | 2.47759e11i | 0.00687799 | − | 0.314648i | ||||
\(943\) | 1.38972e12 | 1.75744 | ||||||||
\(944\) | − | 1.02951e10i | − | 0.0129641i | ||||||
\(945\) | −2.28716e10 | + | 3.48325e11i | −0.0286793 | + | 0.436775i | ||||
\(946\) | 6.09264e10 | 0.0760748 | ||||||||
\(947\) | − | 8.72752e11i | − | 1.08515i | −0.840007 | − | 0.542576i | \(-0.817449\pi\) | ||
0.840007 | − | 0.542576i | \(-0.182551\pi\) | |||||||
\(948\) | −1.59668e11 | − | 3.49023e9i | −0.197689 | − | 0.00432136i | ||||
\(949\) | −6.51298e11 | −0.802999 | ||||||||
\(950\) | − | 5.51179e10i | − | 0.0676704i | ||||||
\(951\) | −2.28780e10 | + | 1.04660e12i | −0.0279702 | + | 1.27956i | ||||
\(952\) | 1.14829e11 | 0.139798 | ||||||||
\(953\) | 5.23143e11i | 0.634233i | 0.948387 | + | 0.317117i | \(0.102715\pi\) | ||||
−0.948387 | + | 0.317117i | \(0.897285\pi\) | |||||||
\(954\) | 8.07388e11 | + | 3.53148e10i | 0.974740 | + | 0.0426347i | ||||
\(955\) | 4.84719e11 | 0.582742 | ||||||||
\(956\) | 2.55478e11i | 0.305859i | ||||||||
\(957\) | −3.00779e11 | − | 6.57483e9i | −0.358592 | − | 0.00783857i | ||||
\(958\) | −3.14077e11 | −0.372884 | ||||||||
\(959\) | 6.79435e11i | 0.803292i | ||||||||
\(960\) | −1.01740e10 | + | 4.65431e11i | −0.0119786 | + | 0.547987i | ||||
\(961\) | −8.34263e11 | −0.978159 | ||||||||
\(962\) | − | 1.90176e11i | − | 0.222052i | ||||||
\(963\) | 1.26786e10 | − | 2.89865e11i | 0.0147423 | − | 0.337047i | ||||
\(964\) | −6.59162e11 | −0.763280 | ||||||||
\(965\) | 1.13511e12i | 1.30897i | ||||||||
\(966\) | 3.05989e11 | + | 6.68871e9i | 0.351397 | + | 0.00768129i | ||||
\(967\) | 5.27384e11 | 0.603145 | 0.301572 | − | 0.953443i | \(-0.402489\pi\) | ||||
0.301572 | + | 0.953443i | \(0.402489\pi\) | |||||||
\(968\) | 7.77634e10i | 0.0885673i | ||||||||
\(969\) | −7.90483e9 | + | 3.61623e11i | −0.00896597 | + | 0.410167i | ||||
\(970\) | 6.16200e11 | 0.696040 | ||||||||
\(971\) | − | 9.85260e11i | − | 1.10834i | −0.832403 | − | 0.554171i | \(-0.813035\pi\) | ||
0.832403 | − | 0.554171i | \(-0.186965\pi\) | |||||||
\(972\) | 5.78842e11 | + | 6.35084e10i | 0.648478 | + | 0.0711485i | ||||
\(973\) | −5.03233e11 | −0.561458 | ||||||||
\(974\) | 9.53574e11i | 1.05954i | ||||||||
\(975\) | −4.76329e10 | − | 1.04122e9i | −0.0527095 | − | 0.00115219i | ||||
\(976\) | 7.37230e10 | 0.0812463 | ||||||||
\(977\) | − | 1.10638e12i | − | 1.21430i | −0.794588 | − | 0.607148i | \(-0.792313\pi\) | ||
0.794588 | − | 0.607148i | \(-0.207687\pi\) | |||||||
\(978\) | 5.61135e9 | − | 2.56703e11i | 0.00613355 | − | 0.280592i | ||||
\(979\) | −2.91038e11 | −0.316825 | ||||||||
\(980\) | 5.19827e11i | 0.563579i | ||||||||
\(981\) | −2.41688e11 | − | 1.05713e10i | −0.260963 | − | 0.0114144i | ||||
\(982\) | −4.83848e11 | −0.520311 | ||||||||
\(983\) | 1.56145e11i | 0.167230i | 0.996498 | + | 0.0836152i | \(0.0266466\pi\) | ||||
−0.996498 | + | 0.0836152i | \(0.973353\pi\) | |||||||
\(984\) | 1.12555e12 | + | 2.46038e10i | 1.20057 | + | 0.0262435i | ||||
\(985\) | 2.39668e11 | 0.254604 | ||||||||
\(986\) | − | 2.27520e11i | − | 0.240719i | ||||||
\(987\) | 7.55408e9 | − | 3.45577e11i | 0.00796000 | − | 0.364147i | ||||
\(988\) | −4.08037e11 | −0.428225 | ||||||||
\(989\) | − | 5.83742e11i | − | 0.610149i | ||||||
\(990\) | 7.81215e9 | − | 1.78606e11i | 0.00813261 | − | 0.185933i | ||||
\(991\) | −1.22532e12 | −1.27045 | −0.635223 | − | 0.772329i | \(-0.719092\pi\) | ||||
−0.635223 | + | 0.772329i | \(0.719092\pi\) | |||||||
\(992\) | − | 1.46005e11i | − | 0.150772i | ||||||
\(993\) | −9.43434e11 | − | 2.06228e10i | −0.970319 | − | 0.0212105i | ||||
\(994\) | −1.09156e10 | −0.0111815 | ||||||||
\(995\) | − | 1.84107e12i | − | 1.87835i | ||||||
\(996\) | −2.61284e10 | + | 1.19530e12i | −0.0265506 | + | 1.21461i | ||||
\(997\) | −7.31861e11 | −0.740710 | −0.370355 | − | 0.928890i | \(-0.620764\pi\) | ||||
−0.370355 | + | 0.928890i | \(0.620764\pi\) | |||||||
\(998\) | − | 9.78417e11i | − | 0.986284i | ||||||
\(999\) | 6.81644e11 | + | 4.47578e10i | 0.684377 | + | 0.0449373i |
(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 | 33.9.b.a.23.10 | ✓ | 26 | |
3.2 | odd | 2 | inner | 33.9.b.a.23.17 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.9.b.a.23.10 | ✓ | 26 | 1.1 | even | 1 | trivial | |
33.9.b.a.23.17 | yes | 26 | 3.2 | odd | 2 | inner |