Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,16,Mod(28,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(41.3811164790\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 28.2 | ||
Character | \(\chi\) | \(=\) | 29.28 |
Dual form | 29.16.b.a.28.35 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 327.159i | − | 1.80731i | −0.428257 | − | 0.903657i | \(-0.640872\pi\) | ||
0.428257 | − | 0.903657i | \(-0.359128\pi\) | |||||||
\(3\) | − | 2163.79i | − | 0.571224i | −0.958345 | − | 0.285612i | \(-0.907803\pi\) | ||
0.958345 | − | 0.285612i | \(-0.0921968\pi\) | |||||||
\(4\) | −74264.8 | −2.26638 | ||||||||
\(5\) | 235169. | 1.34618 | 0.673092 | − | 0.739559i | \(-0.264966\pi\) | ||||
0.673092 | + | 0.739559i | \(0.264966\pi\) | |||||||
\(6\) | −707903. | −1.03238 | ||||||||
\(7\) | 2.51260e6 | 1.15316 | 0.576578 | − | 0.817042i | \(-0.304388\pi\) | ||||
0.576578 | + | 0.817042i | \(0.304388\pi\) | |||||||
\(8\) | 1.35760e7i | 2.28875i | ||||||||
\(9\) | 9.66691e6 | 0.673704 | ||||||||
\(10\) | − | 7.69374e7i | − | 2.43298i | ||||||
\(11\) | − | 7.17284e7i | − | 1.10980i | −0.831916 | − | 0.554902i | \(-0.812756\pi\) | ||
0.831916 | − | 0.554902i | \(-0.187244\pi\) | |||||||
\(12\) | 1.60694e8i | 1.29461i | ||||||||
\(13\) | −4.51020e8 | −1.99352 | −0.996760 | − | 0.0804354i | \(-0.974369\pi\) | ||||
−0.996760 | + | 0.0804354i | \(0.974369\pi\) | |||||||
\(14\) | − | 8.22019e8i | − | 2.08411i | ||||||
\(15\) | − | 5.08856e8i | − | 0.768972i | ||||||
\(16\) | 2.00801e9 | 1.87011 | ||||||||
\(17\) | 1.32955e9i | 0.785849i | 0.919571 | + | 0.392925i | \(0.128537\pi\) | ||||
−0.919571 | + | 0.392925i | \(0.871463\pi\) | |||||||
\(18\) | − | 3.16261e9i | − | 1.21759i | ||||||
\(19\) | 3.49440e8i | 0.0896851i | 0.998994 | + | 0.0448425i | \(0.0142786\pi\) | ||||
−0.998994 | + | 0.0448425i | \(0.985721\pi\) | |||||||
\(20\) | −1.74648e10 | −3.05097 | ||||||||
\(21\) | − | 5.43674e9i | − | 0.658709i | ||||||
\(22\) | −2.34666e10 | −2.00576 | ||||||||
\(23\) | −2.49620e10 | −1.52869 | −0.764347 | − | 0.644805i | \(-0.776938\pi\) | ||||
−0.764347 | + | 0.644805i | \(0.776938\pi\) | |||||||
\(24\) | 2.93757e10 | 1.30739 | ||||||||
\(25\) | 2.47867e10 | 0.812209 | ||||||||
\(26\) | 1.47555e11i | 3.60292i | ||||||||
\(27\) | − | 5.19652e10i | − | 0.956059i | ||||||
\(28\) | −1.86598e11 | −2.61349 | ||||||||
\(29\) | −2.92440e10 | − | 8.81702e10i | −0.314813 | − | 0.949154i | ||||
\(30\) | −1.66477e11 | −1.38977 | ||||||||
\(31\) | − | 2.04746e11i | − | 1.33660i | −0.743891 | − | 0.668301i | \(-0.767022\pi\) | ||
0.743891 | − | 0.668301i | \(-0.232978\pi\) | |||||||
\(32\) | − | 2.12079e11i | − | 1.09112i | ||||||
\(33\) | −1.55205e11 | −0.633946 | ||||||||
\(34\) | 4.34975e11 | 1.42028 | ||||||||
\(35\) | 5.90884e11 | 1.55236 | ||||||||
\(36\) | −7.17912e11 | −1.52687 | ||||||||
\(37\) | − | 7.75922e11i | − | 1.34371i | −0.740684 | − | 0.671854i | \(-0.765498\pi\) | ||
0.740684 | − | 0.671854i | \(-0.234502\pi\) | |||||||
\(38\) | 1.14322e11 | 0.162089 | ||||||||
\(39\) | 9.75913e11i | 1.13875i | ||||||||
\(40\) | 3.19266e12i | 3.08108i | ||||||||
\(41\) | − | 9.31848e11i | − | 0.747250i | −0.927580 | − | 0.373625i | \(-0.878115\pi\) | ||
0.927580 | − | 0.373625i | \(-0.121885\pi\) | |||||||
\(42\) | −1.77868e12 | −1.19049 | ||||||||
\(43\) | 1.23664e12i | 0.693794i | 0.937903 | + | 0.346897i | \(0.112765\pi\) | ||||
−0.937903 | + | 0.346897i | \(0.887235\pi\) | |||||||
\(44\) | 5.32690e12i | 2.51524i | ||||||||
\(45\) | 2.27335e12 | 0.906929 | ||||||||
\(46\) | 8.16653e12i | 2.76283i | ||||||||
\(47\) | − | 2.93435e12i | − | 0.844848i | −0.906398 | − | 0.422424i | \(-0.861179\pi\) | ||
0.906398 | − | 0.422424i | \(-0.138821\pi\) | |||||||
\(48\) | − | 4.34492e12i | − | 1.06825i | ||||||
\(49\) | 1.56559e12 | 0.329767 | ||||||||
\(50\) | − | 8.10917e12i | − | 1.46792i | ||||||
\(51\) | 2.87688e12 | 0.448896 | ||||||||
\(52\) | 3.34949e13 | 4.51808 | ||||||||
\(53\) | −8.73122e12 | −1.02095 | −0.510477 | − | 0.859892i | \(-0.670531\pi\) | ||||
−0.510477 | + | 0.859892i | \(0.670531\pi\) | |||||||
\(54\) | −1.70009e13 | −1.72790 | ||||||||
\(55\) | − | 1.68683e13i | − | 1.49400i | ||||||
\(56\) | 3.41112e13i | 2.63929i | ||||||||
\(57\) | 7.56115e11 | 0.0512302 | ||||||||
\(58\) | −2.88456e13 | + | 9.56744e12i | −1.71542 | + | 0.568965i | ||||
\(59\) | −2.99957e12 | −0.156917 | −0.0784584 | − | 0.996917i | \(-0.525000\pi\) | ||||
−0.0784584 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(60\) | 3.77901e13i | 1.74278i | ||||||||
\(61\) | 4.29433e13i | 1.74953i | 0.484547 | + | 0.874765i | \(0.338984\pi\) | ||||
−0.484547 | + | 0.874765i | \(0.661016\pi\) | |||||||
\(62\) | −6.69844e13 | −2.41566 | ||||||||
\(63\) | 2.42891e13 | 0.776885 | ||||||||
\(64\) | −3.58492e12 | −0.101890 | ||||||||
\(65\) | −1.06066e14 | −2.68364 | ||||||||
\(66\) | 5.07768e13i | 1.14574i | ||||||||
\(67\) | 5.77645e13 | 1.16439 | 0.582197 | − | 0.813048i | \(-0.302193\pi\) | ||||
0.582197 | + | 0.813048i | \(0.302193\pi\) | |||||||
\(68\) | − | 9.87391e13i | − | 1.78103i | ||||||
\(69\) | 5.40126e13i | 0.873226i | ||||||||
\(70\) | − | 1.93313e14i | − | 2.80560i | ||||||
\(71\) | 4.14492e13 | 0.540852 | 0.270426 | − | 0.962741i | \(-0.412835\pi\) | ||||
0.270426 | + | 0.962741i | \(0.412835\pi\) | |||||||
\(72\) | 1.31238e14i | 1.54194i | ||||||||
\(73\) | 5.77169e12i | 0.0611479i | 0.999533 | + | 0.0305740i | \(0.00973351\pi\) | ||||
−0.999533 | + | 0.0305740i | \(0.990266\pi\) | |||||||
\(74\) | −2.53850e14 | −2.42850 | ||||||||
\(75\) | − | 5.36332e13i | − | 0.463953i | ||||||
\(76\) | − | 2.59511e13i | − | 0.203261i | ||||||
\(77\) | − | 1.80225e14i | − | 1.27978i | ||||||
\(78\) | 3.19279e14 | 2.05807 | ||||||||
\(79\) | 5.65194e13i | 0.331127i | 0.986199 | + | 0.165563i | \(0.0529442\pi\) | ||||
−0.986199 | + | 0.165563i | \(0.947056\pi\) | |||||||
\(80\) | 4.72221e14 | 2.51751 | ||||||||
\(81\) | 2.62676e13 | 0.127580 | ||||||||
\(82\) | −3.04862e14 | −1.35052 | ||||||||
\(83\) | 1.19422e14 | 0.483058 | 0.241529 | − | 0.970394i | \(-0.422351\pi\) | ||||
0.241529 | + | 0.970394i | \(0.422351\pi\) | |||||||
\(84\) | 4.03759e14i | 1.49289i | ||||||||
\(85\) | 3.12669e14i | 1.05790i | ||||||||
\(86\) | 4.04578e14 | 1.25390 | ||||||||
\(87\) | −1.90782e14 | + | 6.32780e13i | −0.542179 | + | 0.179828i | ||||
\(88\) | 9.73788e14 | 2.54006 | ||||||||
\(89\) | − | 6.03893e14i | − | 1.44722i | −0.690209 | − | 0.723610i | \(-0.742481\pi\) | ||
0.690209 | − | 0.723610i | \(-0.257519\pi\) | |||||||
\(90\) | − | 7.43747e14i | − | 1.63910i | ||||||
\(91\) | −1.13323e15 | −2.29884 | ||||||||
\(92\) | 1.85380e15 | 3.46460 | ||||||||
\(93\) | −4.43027e14 | −0.763499 | ||||||||
\(94\) | −9.60000e14 | −1.52691 | ||||||||
\(95\) | 8.21772e13i | 0.120733i | ||||||||
\(96\) | −4.58895e14 | −0.623274 | ||||||||
\(97\) | 5.20879e14i | 0.654560i | 0.944927 | + | 0.327280i | \(0.106132\pi\) | ||||
−0.944927 | + | 0.327280i | \(0.893868\pi\) | |||||||
\(98\) | − | 5.12196e14i | − | 0.595993i | ||||||
\(99\) | − | 6.93392e14i | − | 0.747679i | ||||||
\(100\) | −1.84078e15 | −1.84078 | ||||||||
\(101\) | 1.58634e14i | 0.147227i | 0.997287 | + | 0.0736134i | \(0.0234531\pi\) | ||||
−0.997287 | + | 0.0736134i | \(0.976547\pi\) | |||||||
\(102\) | − | 9.41196e14i | − | 0.811295i | ||||||
\(103\) | 1.58250e15 | 1.26784 | 0.633920 | − | 0.773398i | \(-0.281445\pi\) | ||||
0.633920 | + | 0.773398i | \(0.281445\pi\) | |||||||
\(104\) | − | 6.12307e15i | − | 4.56267i | ||||||
\(105\) | − | 1.27855e15i | − | 0.886744i | ||||||
\(106\) | 2.85650e15i | 1.84518i | ||||||||
\(107\) | 4.49153e14 | 0.270406 | 0.135203 | − | 0.990818i | \(-0.456831\pi\) | ||||
0.135203 | + | 0.990818i | \(0.456831\pi\) | |||||||
\(108\) | 3.85919e15i | 2.16680i | ||||||||
\(109\) | −4.05225e14 | −0.212323 | −0.106162 | − | 0.994349i | \(-0.533856\pi\) | ||||
−0.106162 | + | 0.994349i | \(0.533856\pi\) | |||||||
\(110\) | −5.51860e15 | −2.70012 | ||||||||
\(111\) | −1.67893e15 | −0.767558 | ||||||||
\(112\) | 5.04533e15 | 2.15652 | ||||||||
\(113\) | − | 3.22452e15i | − | 1.28937i | −0.764449 | − | 0.644684i | \(-0.776989\pi\) | ||
0.764449 | − | 0.644684i | \(-0.223011\pi\) | |||||||
\(114\) | − | 2.47370e14i | − | 0.0925891i | ||||||
\(115\) | −5.87027e15 | −2.05790 | ||||||||
\(116\) | 2.17180e15 | + | 6.54794e15i | 0.713486 | + | 2.15115i | ||||
\(117\) | −4.35997e15 | −1.34304 | ||||||||
\(118\) | 9.81337e14i | 0.283598i | ||||||||
\(119\) | 3.34064e15i | 0.906206i | ||||||||
\(120\) | 6.90825e15 | 1.75998 | ||||||||
\(121\) | −9.67716e14 | −0.231663 | ||||||||
\(122\) | 1.40493e16 | 3.16195 | ||||||||
\(123\) | −2.01632e15 | −0.426847 | ||||||||
\(124\) | 1.52054e16i | 3.02925i | ||||||||
\(125\) | −1.34773e15 | −0.252801 | ||||||||
\(126\) | − | 7.94638e15i | − | 1.40407i | ||||||
\(127\) | − | 5.35389e15i | − | 0.891541i | −0.895147 | − | 0.445771i | \(-0.852930\pi\) | ||
0.895147 | − | 0.445771i | \(-0.147070\pi\) | |||||||
\(128\) | − | 5.77657e15i | − | 0.906974i | ||||||
\(129\) | 2.67584e15 | 0.396312 | ||||||||
\(130\) | 3.47003e16i | 4.85018i | ||||||||
\(131\) | − | 7.30720e14i | − | 0.0964309i | −0.998837 | − | 0.0482155i | \(-0.984647\pi\) | ||
0.998837 | − | 0.0482155i | \(-0.0153534\pi\) | |||||||
\(132\) | 1.15263e16 | 1.43676 | ||||||||
\(133\) | 8.78002e14i | 0.103421i | ||||||||
\(134\) | − | 1.88982e16i | − | 2.10442i | ||||||
\(135\) | − | 1.22206e16i | − | 1.28703i | ||||||
\(136\) | −1.80501e16 | −1.79861 | ||||||||
\(137\) | 1.35058e15i | 0.127384i | 0.997970 | + | 0.0636920i | \(0.0202875\pi\) | ||||
−0.997970 | + | 0.0636920i | \(0.979712\pi\) | |||||||
\(138\) | 1.76707e16 | 1.57819 | ||||||||
\(139\) | 3.09087e15 | 0.261499 | 0.130750 | − | 0.991415i | \(-0.458262\pi\) | ||||
0.130750 | + | 0.991415i | \(0.458262\pi\) | |||||||
\(140\) | −4.38819e16 | −3.51824 | ||||||||
\(141\) | −6.34933e15 | −0.482597 | ||||||||
\(142\) | − | 1.35605e16i | − | 0.977489i | ||||||
\(143\) | 3.23509e16i | 2.21241i | ||||||||
\(144\) | 1.94113e16 | 1.25990 | ||||||||
\(145\) | −6.87727e15 | − | 2.07348e16i | −0.423795 | − | 1.27773i | ||||
\(146\) | 1.88826e15 | 0.110513 | ||||||||
\(147\) | − | 3.38761e15i | − | 0.188371i | ||||||
\(148\) | 5.76237e16i | 3.04536i | ||||||||
\(149\) | 3.06651e16 | 1.54080 | 0.770402 | − | 0.637558i | \(-0.220055\pi\) | ||||
0.770402 | + | 0.637558i | \(0.220055\pi\) | |||||||
\(150\) | −1.75466e16 | −0.838509 | ||||||||
\(151\) | −6.06041e14 | −0.0275534 | −0.0137767 | − | 0.999905i | \(-0.504385\pi\) | ||||
−0.0137767 | + | 0.999905i | \(0.504385\pi\) | |||||||
\(152\) | −4.74401e15 | −0.205267 | ||||||||
\(153\) | 1.28527e16i | 0.529429i | ||||||||
\(154\) | −5.89621e16 | −2.31296 | ||||||||
\(155\) | − | 4.81498e16i | − | 1.79931i | ||||||
\(156\) | − | 7.24760e16i | − | 2.58083i | ||||||
\(157\) | 2.17662e16i | 0.738813i | 0.929268 | + | 0.369406i | \(0.120439\pi\) | ||||
−0.929268 | + | 0.369406i | \(0.879561\pi\) | |||||||
\(158\) | 1.84908e16 | 0.598450 | ||||||||
\(159\) | 1.88925e16i | 0.583193i | ||||||||
\(160\) | − | 4.98743e16i | − | 1.46885i | ||||||
\(161\) | −6.27195e16 | −1.76282 | ||||||||
\(162\) | − | 8.59369e15i | − | 0.230578i | ||||||
\(163\) | − | 3.94701e16i | − | 1.01126i | −0.862752 | − | 0.505628i | \(-0.831261\pi\) | ||
0.862752 | − | 0.505628i | \(-0.168739\pi\) | |||||||
\(164\) | 6.92035e16i | 1.69355i | ||||||||
\(165\) | −3.64994e16 | −0.853407 | ||||||||
\(166\) | − | 3.90700e16i | − | 0.873037i | ||||||
\(167\) | −1.76634e16 | −0.377312 | −0.188656 | − | 0.982043i | \(-0.560413\pi\) | ||||
−0.188656 | + | 0.982043i | \(0.560413\pi\) | |||||||
\(168\) | 7.38095e16 | 1.50762 | ||||||||
\(169\) | 1.52233e17 | 2.97412 | ||||||||
\(170\) | 1.02293e17 | 1.91195 | ||||||||
\(171\) | 3.37800e15i | 0.0604212i | ||||||||
\(172\) | − | 9.18390e16i | − | 1.57240i | ||||||
\(173\) | 8.81767e16 | 1.44547 | 0.722733 | − | 0.691127i | \(-0.242885\pi\) | ||||
0.722733 | + | 0.691127i | \(0.242885\pi\) | |||||||
\(174\) | 2.07019e16 | + | 6.24160e16i | 0.325006 | + | 0.979888i | ||||
\(175\) | 6.22789e16 | 0.936603 | ||||||||
\(176\) | − | 1.44032e17i | − | 2.07545i | ||||||
\(177\) | 6.49045e15i | 0.0896346i | ||||||||
\(178\) | −1.97569e17 | −2.61558 | ||||||||
\(179\) | 1.26571e16 | 0.160670 | 0.0803352 | − | 0.996768i | \(-0.474401\pi\) | ||||
0.0803352 | + | 0.996768i | \(0.474401\pi\) | |||||||
\(180\) | −1.68830e17 | −2.05545 | ||||||||
\(181\) | −2.79960e16 | −0.326969 | −0.163484 | − | 0.986546i | \(-0.552273\pi\) | ||||
−0.163484 | + | 0.986546i | \(0.552273\pi\) | |||||||
\(182\) | 3.70747e17i | 4.15472i | ||||||||
\(183\) | 9.29203e16 | 0.999373 | ||||||||
\(184\) | − | 3.38885e17i | − | 3.49880i | ||||||
\(185\) | − | 1.82472e17i | − | 1.80888i | ||||||
\(186\) | 1.44940e17i | 1.37988i | ||||||||
\(187\) | 9.53668e16 | 0.872138 | ||||||||
\(188\) | 2.17919e17i | 1.91475i | ||||||||
\(189\) | − | 1.30568e17i | − | 1.10248i | ||||||
\(190\) | 2.68850e16 | 0.218202 | ||||||||
\(191\) | 1.90007e17i | 1.48259i | 0.671181 | + | 0.741293i | \(0.265787\pi\) | ||||
−0.671181 | + | 0.741293i | \(0.734213\pi\) | |||||||
\(192\) | 7.75703e15i | 0.0582018i | ||||||||
\(193\) | 4.58576e16i | 0.330926i | 0.986216 | + | 0.165463i | \(0.0529119\pi\) | ||||
−0.986216 | + | 0.165463i | \(0.947088\pi\) | |||||||
\(194\) | 1.70410e17 | 1.18299 | ||||||||
\(195\) | 2.29504e17i | 1.53296i | ||||||||
\(196\) | −1.16268e17 | −0.747378 | ||||||||
\(197\) | 2.76867e16 | 0.171306 | 0.0856532 | − | 0.996325i | \(-0.472702\pi\) | ||||
0.0856532 | + | 0.996325i | \(0.472702\pi\) | |||||||
\(198\) | −2.26849e17 | −1.35129 | ||||||||
\(199\) | 2.11201e17 | 1.21143 | 0.605715 | − | 0.795682i | \(-0.292887\pi\) | ||||
0.605715 | + | 0.795682i | \(0.292887\pi\) | |||||||
\(200\) | 3.36505e17i | 1.85894i | ||||||||
\(201\) | − | 1.24990e17i | − | 0.665129i | ||||||
\(202\) | 5.18986e16 | 0.266085 | ||||||||
\(203\) | −7.34785e16 | − | 2.21536e17i | −0.363028 | − | 1.09452i | ||||
\(204\) | −2.13651e17 | −1.01737 | ||||||||
\(205\) | − | 2.19141e17i | − | 1.00594i | ||||||
\(206\) | − | 5.17729e17i | − | 2.29139i | ||||||
\(207\) | −2.41305e17 | −1.02989 | ||||||||
\(208\) | −9.05654e17 | −3.72810 | ||||||||
\(209\) | 2.50647e16 | 0.0995328 | ||||||||
\(210\) | −4.18289e17 | −1.60262 | ||||||||
\(211\) | 4.99204e17i | 1.84569i | 0.385167 | + | 0.922847i | \(0.374144\pi\) | ||||
−0.385167 | + | 0.922847i | \(0.625856\pi\) | |||||||
\(212\) | 6.48423e17 | 2.31387 | ||||||||
\(213\) | − | 8.96874e16i | − | 0.308947i | ||||||
\(214\) | − | 1.46944e17i | − | 0.488708i | ||||||
\(215\) | 2.90819e17i | 0.933974i | ||||||||
\(216\) | 7.05483e17 | 2.18818 | ||||||||
\(217\) | − | 5.14444e17i | − | 1.54131i | ||||||
\(218\) | 1.32573e17i | 0.383735i | ||||||||
\(219\) | 1.24887e16 | 0.0349291 | ||||||||
\(220\) | 1.25272e18i | 3.38597i | ||||||||
\(221\) | − | 5.99655e17i | − | 1.56661i | ||||||
\(222\) | 5.49278e17i | 1.38722i | ||||||||
\(223\) | −1.26404e17 | −0.308655 | −0.154328 | − | 0.988020i | \(-0.549321\pi\) | ||||
−0.154328 | + | 0.988020i | \(0.549321\pi\) | |||||||
\(224\) | − | 5.32869e17i | − | 1.25823i | ||||||
\(225\) | 2.39610e17 | 0.547188 | ||||||||
\(226\) | −1.05493e18 | −2.33029 | ||||||||
\(227\) | −4.35843e16 | −0.0931400 | −0.0465700 | − | 0.998915i | \(-0.514829\pi\) | ||||
−0.0465700 | + | 0.998915i | \(0.514829\pi\) | |||||||
\(228\) | −5.61527e16 | −0.116107 | ||||||||
\(229\) | − | 5.46694e16i | − | 0.109390i | −0.998503 | − | 0.0546951i | \(-0.982581\pi\) | ||
0.998503 | − | 0.0546951i | \(-0.0174187\pi\) | |||||||
\(230\) | 1.92051e18i | 3.71927i | ||||||||
\(231\) | −3.89969e17 | −0.731038 | ||||||||
\(232\) | 1.19700e18 | − | 3.97018e17i | 2.17238 | − | 0.720528i | ||||
\(233\) | −3.80048e17 | −0.667835 | −0.333918 | − | 0.942602i | \(-0.608371\pi\) | ||||
−0.333918 | + | 0.942602i | \(0.608371\pi\) | |||||||
\(234\) | 1.42640e18i | 2.42730i | ||||||||
\(235\) | − | 6.90068e17i | − | 1.13732i | ||||||
\(236\) | 2.22763e17 | 0.355634 | ||||||||
\(237\) | 1.22296e17 | 0.189147 | ||||||||
\(238\) | 1.09292e18 | 1.63780 | ||||||||
\(239\) | 2.99102e17 | 0.434346 | 0.217173 | − | 0.976133i | \(-0.430316\pi\) | ||||
0.217173 | + | 0.976133i | \(0.430316\pi\) | |||||||
\(240\) | − | 1.02179e18i | − | 1.43806i | ||||||
\(241\) | 5.50081e17 | 0.750411 | 0.375205 | − | 0.926942i | \(-0.377572\pi\) | ||||
0.375205 | + | 0.926942i | \(0.377572\pi\) | |||||||
\(242\) | 3.16597e17i | 0.418689i | ||||||||
\(243\) | − | 8.02482e17i | − | 1.02894i | ||||||
\(244\) | − | 3.18918e18i | − | 3.96511i | ||||||
\(245\) | 3.68177e17 | 0.443927 | ||||||||
\(246\) | 6.59658e17i | 0.771446i | ||||||||
\(247\) | − | 1.57604e17i | − | 0.178789i | ||||||
\(248\) | 2.77964e18 | 3.05915 | ||||||||
\(249\) | − | 2.58405e17i | − | 0.275934i | ||||||
\(250\) | 4.40922e17i | 0.456890i | ||||||||
\(251\) | − | 1.15107e18i | − | 1.15757i | −0.815480 | − | 0.578786i | \(-0.803527\pi\) | ||
0.815480 | − | 0.578786i | \(-0.196473\pi\) | |||||||
\(252\) | −1.80382e18 | −1.76072 | ||||||||
\(253\) | 1.79048e18i | 1.69655i | ||||||||
\(254\) | −1.75157e18 | −1.61129 | ||||||||
\(255\) | 6.76551e17 | 0.604296 | ||||||||
\(256\) | −2.00732e18 | −1.74108 | ||||||||
\(257\) | −1.74711e18 | −1.47171 | −0.735853 | − | 0.677141i | \(-0.763219\pi\) | ||||
−0.735853 | + | 0.677141i | \(0.763219\pi\) | |||||||
\(258\) | − | 8.75423e17i | − | 0.716259i | ||||||
\(259\) | − | 1.94958e18i | − | 1.54950i | ||||||
\(260\) | 7.87695e18 | 6.08216 | ||||||||
\(261\) | −2.82699e17 | − | 8.52333e17i | −0.212090 | − | 0.639448i | ||||
\(262\) | −2.39061e17 | −0.174281 | ||||||||
\(263\) | 1.12024e18i | 0.793672i | 0.917889 | + | 0.396836i | \(0.129892\pi\) | ||||
−0.917889 | + | 0.396836i | \(0.870108\pi\) | |||||||
\(264\) | − | 2.10708e18i | − | 1.45094i | ||||||
\(265\) | −2.05331e18 | −1.37439 | ||||||||
\(266\) | 2.87246e17 | 0.186914 | ||||||||
\(267\) | −1.30670e18 | −0.826687 | ||||||||
\(268\) | −4.28987e18 | −2.63896 | ||||||||
\(269\) | − | 9.86319e17i | − | 0.590031i | −0.955492 | − | 0.295016i | \(-0.904675\pi\) | ||
0.955492 | − | 0.295016i | \(-0.0953249\pi\) | |||||||
\(270\) | −3.99807e18 | −2.32607 | ||||||||
\(271\) | 2.35022e18i | 1.32996i | 0.746861 | + | 0.664980i | \(0.231560\pi\) | ||||
−0.746861 | + | 0.664980i | \(0.768440\pi\) | |||||||
\(272\) | 2.66976e18i | 1.46962i | ||||||||
\(273\) | 2.45208e18i | 1.31315i | ||||||||
\(274\) | 4.41853e17 | 0.230223 | ||||||||
\(275\) | − | 1.77791e18i | − | 0.901392i | ||||||
\(276\) | − | 4.01123e18i | − | 1.97906i | ||||||
\(277\) | −2.17959e18 | −1.04659 | −0.523296 | − | 0.852151i | \(-0.675298\pi\) | ||||
−0.523296 | + | 0.852151i | \(0.675298\pi\) | |||||||
\(278\) | − | 1.01121e18i | − | 0.472611i | ||||||
\(279\) | − | 1.97926e18i | − | 0.900474i | ||||||
\(280\) | 8.02187e18i | 3.55296i | ||||||||
\(281\) | 1.10254e18 | 0.475441 | 0.237721 | − | 0.971334i | \(-0.423600\pi\) | ||||
0.237721 | + | 0.971334i | \(0.423600\pi\) | |||||||
\(282\) | 2.07724e18i | 0.872204i | ||||||||
\(283\) | 1.44966e17 | 0.0592744 | 0.0296372 | − | 0.999561i | \(-0.490565\pi\) | ||||
0.0296372 | + | 0.999561i | \(0.490565\pi\) | |||||||
\(284\) | −3.07822e18 | −1.22578 | ||||||||
\(285\) | 1.77814e17 | 0.0689653 | ||||||||
\(286\) | 1.05839e19 | 3.99853 | ||||||||
\(287\) | − | 2.34136e18i | − | 0.861695i | ||||||
\(288\) | − | 2.05015e18i | − | 0.735092i | ||||||
\(289\) | 1.09471e18 | 0.382441 | ||||||||
\(290\) | −6.78359e18 | + | 2.24996e18i | −2.30927 | + | 0.765931i | ||||
\(291\) | 1.12707e18 | 0.373900 | ||||||||
\(292\) | − | 4.28634e17i | − | 0.138585i | ||||||
\(293\) | − | 2.55227e18i | − | 0.804304i | −0.915573 | − | 0.402152i | \(-0.868262\pi\) | ||
0.915573 | − | 0.402152i | \(-0.131738\pi\) | |||||||
\(294\) | −1.10829e18 | −0.340445 | ||||||||
\(295\) | −7.05405e17 | −0.211239 | ||||||||
\(296\) | 1.05340e19 | 3.07541 | ||||||||
\(297\) | −3.72738e18 | −1.06104 | ||||||||
\(298\) | − | 1.00324e19i | − | 2.78472i | ||||||
\(299\) | 1.12584e19 | 3.04748 | ||||||||
\(300\) | 3.98306e18i | 1.05150i | ||||||||
\(301\) | 3.10719e18i | 0.800053i | ||||||||
\(302\) | 1.98271e17i | 0.0497976i | ||||||||
\(303\) | 3.43252e17 | 0.0840994 | ||||||||
\(304\) | 7.01679e17i | 0.167721i | ||||||||
\(305\) | 1.00989e19i | 2.35519i | ||||||||
\(306\) | 4.20487e18 | 0.956845 | ||||||||
\(307\) | − | 2.33832e18i | − | 0.519238i | −0.965711 | − | 0.259619i | \(-0.916403\pi\) | ||
0.965711 | − | 0.259619i | \(-0.0835969\pi\) | |||||||
\(308\) | 1.33844e19i | 2.90046i | ||||||||
\(309\) | − | 3.42420e18i | − | 0.724221i | ||||||
\(310\) | −1.57526e19 | −3.25192 | ||||||||
\(311\) | 3.07645e18i | 0.619936i | 0.950747 | + | 0.309968i | \(0.100318\pi\) | ||||
−0.950747 | + | 0.309968i | \(0.899682\pi\) | |||||||
\(312\) | −1.32490e19 | −2.60630 | ||||||||
\(313\) | 5.67516e18 | 1.08992 | 0.544961 | − | 0.838461i | \(-0.316545\pi\) | ||||
0.544961 | + | 0.838461i | \(0.316545\pi\) | |||||||
\(314\) | 7.12099e18 | 1.33527 | ||||||||
\(315\) | 5.71202e18 | 1.04583 | ||||||||
\(316\) | − | 4.19740e18i | − | 0.750460i | ||||||
\(317\) | 5.76163e18i | 1.00601i | 0.864284 | + | 0.503004i | \(0.167772\pi\) | ||||
−0.864284 | + | 0.503004i | \(0.832228\pi\) | |||||||
\(318\) | 6.18086e18 | 1.05401 | ||||||||
\(319\) | −6.32430e18 | + | 2.09763e18i | −1.05337 | + | 0.349380i | ||||
\(320\) | −8.43061e17 | −0.137162 | ||||||||
\(321\) | − | 9.71874e17i | − | 0.154462i | ||||||
\(322\) | 2.05192e19i | 3.18597i | ||||||||
\(323\) | −4.64599e17 | −0.0704789 | ||||||||
\(324\) | −1.95076e18 | −0.289146 | ||||||||
\(325\) | −1.11793e19 | −1.61915 | ||||||||
\(326\) | −1.29130e19 | −1.82766 | ||||||||
\(327\) | 8.76823e17i | 0.121284i | ||||||||
\(328\) | 1.26508e19 | 1.71027 | ||||||||
\(329\) | − | 7.37285e18i | − | 0.974241i | ||||||
\(330\) | 1.19411e19i | 1.54237i | ||||||||
\(331\) | − | 8.00495e18i | − | 1.01076i | −0.862896 | − | 0.505381i | \(-0.831352\pi\) | ||
0.862896 | − | 0.505381i | \(-0.168648\pi\) | |||||||
\(332\) | −8.86886e18 | −1.09479 | ||||||||
\(333\) | − | 7.50077e18i | − | 0.905261i | ||||||
\(334\) | 5.77873e18i | 0.681920i | ||||||||
\(335\) | 1.35844e19 | 1.56749 | ||||||||
\(336\) | − | 1.09170e19i | − | 1.23186i | ||||||
\(337\) | 2.22591e18i | 0.245631i | 0.992429 | + | 0.122816i | \(0.0391924\pi\) | ||||
−0.992429 | + | 0.122816i | \(0.960808\pi\) | |||||||
\(338\) | − | 4.98044e19i | − | 5.37517i | ||||||
\(339\) | −6.97719e18 | −0.736517 | ||||||||
\(340\) | − | 2.32203e19i | − | 2.39760i | ||||||
\(341\) | −1.46861e19 | −1.48337 | ||||||||
\(342\) | 1.10514e18 | 0.109200 | ||||||||
\(343\) | −7.99502e18 | −0.772883 | ||||||||
\(344\) | −1.67887e19 | −1.58792 | ||||||||
\(345\) | 1.27021e19i | 1.17552i | ||||||||
\(346\) | − | 2.88478e19i | − | 2.61241i | ||||||
\(347\) | 6.46966e18 | 0.573337 | 0.286669 | − | 0.958030i | \(-0.407452\pi\) | ||||
0.286669 | + | 0.958030i | \(0.407452\pi\) | |||||||
\(348\) | 1.41684e19 | − | 4.69933e18i | 1.22879 | − | 0.407560i | ||||
\(349\) | 9.75878e17 | 0.0828333 | 0.0414166 | − | 0.999142i | \(-0.486813\pi\) | ||||
0.0414166 | + | 0.999142i | \(0.486813\pi\) | |||||||
\(350\) | − | 2.03751e19i | − | 1.69274i | ||||||
\(351\) | 2.34374e19i | 1.90592i | ||||||||
\(352\) | −1.52121e19 | −1.21093 | ||||||||
\(353\) | 2.03484e19 | 1.58569 | 0.792847 | − | 0.609421i | \(-0.208598\pi\) | ||||
0.792847 | + | 0.609421i | \(0.208598\pi\) | |||||||
\(354\) | 2.12341e18 | 0.161998 | ||||||||
\(355\) | 9.74755e18 | 0.728086 | ||||||||
\(356\) | 4.48480e19i | 3.27996i | ||||||||
\(357\) | 7.22844e18 | 0.517646 | ||||||||
\(358\) | − | 4.14088e18i | − | 0.290382i | ||||||
\(359\) | 7.87831e18i | 0.541034i | 0.962715 | + | 0.270517i | \(0.0871947\pi\) | ||||
−0.962715 | + | 0.270517i | \(0.912805\pi\) | |||||||
\(360\) | 3.08632e19i | 2.07573i | ||||||||
\(361\) | 1.50590e19 | 0.991957 | ||||||||
\(362\) | 9.15913e18i | 0.590935i | ||||||||
\(363\) | 2.09394e18i | 0.132332i | ||||||||
\(364\) | 8.41593e19 | 5.21005 | ||||||||
\(365\) | 1.35732e18i | 0.0823163i | ||||||||
\(366\) | − | 3.03997e19i | − | 1.80618i | ||||||
\(367\) | 2.06114e19i | 1.19981i | 0.800072 | + | 0.599904i | \(0.204794\pi\) | ||||
−0.800072 | + | 0.599904i | \(0.795206\pi\) | |||||||
\(368\) | −5.01240e19 | −2.85882 | ||||||||
\(369\) | − | 9.00809e18i | − | 0.503425i | ||||||
\(370\) | −5.96974e19 | −3.26921 | ||||||||
\(371\) | −2.19381e19 | −1.17732 | ||||||||
\(372\) | 3.29013e19 | 1.73038 | ||||||||
\(373\) | −3.40029e17 | −0.0175267 | −0.00876335 | − | 0.999962i | \(-0.502789\pi\) | ||||
−0.00876335 | + | 0.999962i | \(0.502789\pi\) | |||||||
\(374\) | − | 3.12001e19i | − | 1.57623i | ||||||
\(375\) | 2.91621e18i | 0.144406i | ||||||||
\(376\) | 3.98369e19 | 1.93365 | ||||||||
\(377\) | 1.31896e19 | + | 3.97665e19i | 0.627585 | + | 1.89216i | ||||
\(378\) | −4.27164e19 | −1.99254 | ||||||||
\(379\) | − | 2.05464e19i | − | 0.939598i | −0.882773 | − | 0.469799i | \(-0.844326\pi\) | ||
0.882773 | − | 0.469799i | \(-0.155674\pi\) | |||||||
\(380\) | − | 6.10288e18i | − | 0.273626i | ||||||
\(381\) | −1.15847e19 | −0.509269 | ||||||||
\(382\) | 6.21625e19 | 2.67950 | ||||||||
\(383\) | −1.59681e19 | −0.674934 | −0.337467 | − | 0.941337i | \(-0.609570\pi\) | ||||
−0.337467 | + | 0.941337i | \(0.609570\pi\) | |||||||
\(384\) | −1.24993e19 | −0.518085 | ||||||||
\(385\) | − | 4.23832e19i | − | 1.72281i | ||||||
\(386\) | 1.50027e19 | 0.598087 | ||||||||
\(387\) | 1.19545e19i | 0.467412i | ||||||||
\(388\) | − | 3.86830e19i | − | 1.48348i | ||||||
\(389\) | 1.23416e19i | 0.464248i | 0.972686 | + | 0.232124i | \(0.0745676\pi\) | ||||
−0.972686 | + | 0.232124i | \(0.925432\pi\) | |||||||
\(390\) | 7.50843e19 | 2.77054 | ||||||||
\(391\) | − | 3.31883e19i | − | 1.20132i | ||||||
\(392\) | 2.12545e19i | 0.754755i | ||||||||
\(393\) | −1.58113e18 | −0.0550836 | ||||||||
\(394\) | − | 9.05793e18i | − | 0.309605i | ||||||
\(395\) | 1.32916e19i | 0.445757i | ||||||||
\(396\) | 5.14946e19i | 1.69453i | ||||||||
\(397\) | −1.49827e19 | −0.483793 | −0.241897 | − | 0.970302i | \(-0.577769\pi\) | ||||
−0.241897 | + | 0.970302i | \(0.577769\pi\) | |||||||
\(398\) | − | 6.90963e19i | − | 2.18943i | ||||||
\(399\) | 1.89981e18 | 0.0590764 | ||||||||
\(400\) | 4.97719e19 | 1.51892 | ||||||||
\(401\) | −5.42271e19 | −1.62418 | −0.812089 | − | 0.583533i | \(-0.801670\pi\) | ||||
−0.812089 | + | 0.583533i | \(0.801670\pi\) | |||||||
\(402\) | −4.08917e19 | −1.20210 | ||||||||
\(403\) | 9.23444e19i | 2.66454i | ||||||||
\(404\) | − | 1.17809e19i | − | 0.333672i | ||||||
\(405\) | 6.17732e18 | 0.171746 | ||||||||
\(406\) | −7.24775e19 | + | 2.40391e19i | −1.97814 | + | 0.656105i | ||||
\(407\) | −5.56556e19 | −1.49125 | ||||||||
\(408\) | 3.90567e19i | 1.02741i | ||||||||
\(409\) | − | 5.51035e19i | − | 1.42316i | −0.702604 | − | 0.711581i | \(-0.747980\pi\) | ||
0.702604 | − | 0.711581i | \(-0.252020\pi\) | |||||||
\(410\) | −7.16940e19 | −1.81804 | ||||||||
\(411\) | 2.92236e18 | 0.0727647 | ||||||||
\(412\) | −1.17524e20 | −2.87341 | ||||||||
\(413\) | −7.53673e18 | −0.180949 | ||||||||
\(414\) | 7.89451e19i | 1.86133i | ||||||||
\(415\) | 2.80843e19 | 0.650284 | ||||||||
\(416\) | 9.56518e19i | 2.17517i | ||||||||
\(417\) | − | 6.68801e18i | − | 0.149374i | ||||||
\(418\) | − | 8.20015e18i | − | 0.179887i | ||||||
\(419\) | −5.59770e19 | −1.20616 | −0.603079 | − | 0.797681i | \(-0.706060\pi\) | ||||
−0.603079 | + | 0.797681i | \(0.706060\pi\) | |||||||
\(420\) | 9.49513e19i | 2.00970i | ||||||||
\(421\) | − | 6.28392e19i | − | 1.30652i | −0.757135 | − | 0.653258i | \(-0.773402\pi\) | ||
0.757135 | − | 0.653258i | \(-0.226598\pi\) | |||||||
\(422\) | 1.63319e20 | 3.33575 | ||||||||
\(423\) | − | 2.83661e19i | − | 0.569177i | ||||||
\(424\) | − | 1.18535e20i | − | 2.33671i | ||||||
\(425\) | 3.29552e19i | 0.638274i | ||||||||
\(426\) | −2.93420e19 | −0.558365 | ||||||||
\(427\) | 1.07899e20i | 2.01748i | ||||||||
\(428\) | −3.33563e19 | −0.612843 | ||||||||
\(429\) | 7.00007e19 | 1.26378 | ||||||||
\(430\) | 9.51441e19 | 1.68798 | ||||||||
\(431\) | 5.94346e19 | 1.03624 | 0.518120 | − | 0.855308i | \(-0.326632\pi\) | ||||
0.518120 | + | 0.855308i | \(0.326632\pi\) | |||||||
\(432\) | − | 1.04347e20i | − | 1.78793i | ||||||
\(433\) | 4.78947e19i | 0.806544i | 0.915080 | + | 0.403272i | \(0.132127\pi\) | ||||
−0.915080 | + | 0.403272i | \(0.867873\pi\) | |||||||
\(434\) | −1.68305e20 | −2.78563 | ||||||||
\(435\) | −4.48659e19 | + | 1.48810e19i | −0.729872 | + | 0.242082i | ||||
\(436\) | 3.00940e19 | 0.481206 | ||||||||
\(437\) | − | 8.72271e18i | − | 0.137101i | ||||||
\(438\) | − | 4.08580e18i | − | 0.0631279i | ||||||
\(439\) | 7.83901e19 | 1.19063 | 0.595315 | − | 0.803492i | \(-0.297027\pi\) | ||||
0.595315 | + | 0.803492i | \(0.297027\pi\) | |||||||
\(440\) | 2.29004e20 | 3.41939 | ||||||||
\(441\) | 1.51344e19 | 0.222165 | ||||||||
\(442\) | −1.96183e20 | −2.83135 | ||||||||
\(443\) | − | 6.22916e19i | − | 0.883897i | −0.897041 | − | 0.441948i | \(-0.854287\pi\) | ||
0.897041 | − | 0.441948i | \(-0.145713\pi\) | |||||||
\(444\) | 1.24686e20 | 1.73958 | ||||||||
\(445\) | − | 1.42017e20i | − | 1.94822i | ||||||
\(446\) | 4.13541e19i | 0.557837i | ||||||||
\(447\) | − | 6.63529e19i | − | 0.880144i | ||||||
\(448\) | −9.00748e18 | −0.117495 | ||||||||
\(449\) | 3.96064e19i | 0.508063i | 0.967196 | + | 0.254031i | \(0.0817567\pi\) | ||||
−0.967196 | + | 0.254031i | \(0.918243\pi\) | |||||||
\(450\) | − | 7.83906e19i | − | 0.988941i | ||||||
\(451\) | −6.68399e19 | −0.829301 | ||||||||
\(452\) | 2.39468e20i | 2.92220i | ||||||||
\(453\) | 1.31135e18i | 0.0157391i | ||||||||
\(454\) | 1.42590e19i | 0.168333i | ||||||||
\(455\) | −2.66500e20 | −3.09466 | ||||||||
\(456\) | 1.02651e19i | 0.117253i | ||||||||
\(457\) | −1.05440e20 | −1.18477 | −0.592384 | − | 0.805655i | \(-0.701813\pi\) | ||||
−0.592384 | + | 0.805655i | \(0.701813\pi\) | |||||||
\(458\) | −1.78856e19 | −0.197702 | ||||||||
\(459\) | 6.90906e19 | 0.751318 | ||||||||
\(460\) | 4.35955e20 | 4.66399 | ||||||||
\(461\) | − | 1.39084e20i | − | 1.46393i | −0.681341 | − | 0.731966i | \(-0.738603\pi\) | ||
0.681341 | − | 0.731966i | \(-0.261397\pi\) | |||||||
\(462\) | 1.27582e20i | 1.32121i | ||||||||
\(463\) | 1.69920e20 | 1.73136 | 0.865681 | − | 0.500596i | \(-0.166886\pi\) | ||||
0.865681 | + | 0.500596i | \(0.166886\pi\) | |||||||
\(464\) | −5.87224e19 | − | 1.77047e20i | −0.588734 | − | 1.77502i | ||||
\(465\) | −1.04186e20 | −1.02781 | ||||||||
\(466\) | 1.24336e20i | 1.20699i | ||||||||
\(467\) | − | 1.35865e20i | − | 1.29787i | −0.760845 | − | 0.648933i | \(-0.775215\pi\) | ||
0.760845 | − | 0.648933i | \(-0.224785\pi\) | |||||||
\(468\) | 3.23792e20 | 3.04385 | ||||||||
\(469\) | 1.45139e20 | 1.34273 | ||||||||
\(470\) | −2.25762e20 | −2.05549 | ||||||||
\(471\) | 4.70974e19 | 0.422027 | ||||||||
\(472\) | − | 4.07224e19i | − | 0.359144i | ||||||
\(473\) | 8.87024e19 | 0.769975 | ||||||||
\(474\) | − | 4.00103e19i | − | 0.341849i | ||||||
\(475\) | 8.66144e18i | 0.0728430i | ||||||||
\(476\) | − | 2.48092e20i | − | 2.05381i | ||||||
\(477\) | −8.44039e19 | −0.687820 | ||||||||
\(478\) | − | 9.78539e19i | − | 0.784999i | ||||||
\(479\) | 3.91138e19i | 0.308897i | 0.988001 | + | 0.154449i | \(0.0493601\pi\) | ||||
−0.988001 | + | 0.154449i | \(0.950640\pi\) | |||||||
\(480\) | −1.07918e20 | −0.839041 | ||||||||
\(481\) | 3.49956e20i | 2.67871i | ||||||||
\(482\) | − | 1.79964e20i | − | 1.35623i | ||||||
\(483\) | 1.35712e20i | 1.00696i | ||||||||
\(484\) | 7.18672e19 | 0.525038 | ||||||||
\(485\) | 1.22494e20i | 0.881157i | ||||||||
\(486\) | −2.62539e20 | −1.85961 | ||||||||
\(487\) | −1.79076e18 | −0.0124902 | −0.00624512 | − | 0.999980i | \(-0.501988\pi\) | ||||
−0.00624512 | + | 0.999980i | \(0.501988\pi\) | |||||||
\(488\) | −5.83000e20 | −4.00424 | ||||||||
\(489\) | −8.54051e19 | −0.577653 | ||||||||
\(490\) | − | 1.20452e20i | − | 0.802315i | ||||||
\(491\) | 1.22992e20i | 0.806799i | 0.915024 | + | 0.403399i | \(0.132171\pi\) | ||||
−0.915024 | + | 0.403399i | \(0.867829\pi\) | |||||||
\(492\) | 1.49742e20 | 0.967398 | ||||||||
\(493\) | 1.17227e20 | − | 3.88815e19i | 0.745892 | − | 0.247395i | ||||
\(494\) | −5.15616e19 | −0.323128 | ||||||||
\(495\) | − | 1.63064e20i | − | 1.00651i | ||||||
\(496\) | − | 4.11132e20i | − | 2.49959i | ||||||
\(497\) | 1.04145e20 | 0.623686 | ||||||||
\(498\) | −8.45393e19 | −0.498699 | ||||||||
\(499\) | −7.83398e19 | −0.455227 | −0.227614 | − | 0.973751i | \(-0.573092\pi\) | ||||
−0.227614 | + | 0.973751i | \(0.573092\pi\) | |||||||
\(500\) | 1.00089e20 | 0.572944 | ||||||||
\(501\) | 3.82199e19i | 0.215529i | ||||||||
\(502\) | −3.76582e20 | −2.09210 | ||||||||
\(503\) | − | 1.94868e20i | − | 1.06655i | −0.845943 | − | 0.533274i | \(-0.820961\pi\) | ||
0.845943 | − | 0.533274i | \(-0.179039\pi\) | |||||||
\(504\) | 3.29750e20i | 1.77810i | ||||||||
\(505\) | 3.73058e19i | 0.198194i | ||||||||
\(506\) | 5.85772e20 | 3.06620 | ||||||||
\(507\) | − | 3.29401e20i | − | 1.69889i | ||||||
\(508\) | 3.97606e20i | 2.02057i | ||||||||
\(509\) | 2.58584e20 | 1.29485 | 0.647423 | − | 0.762131i | \(-0.275847\pi\) | ||||
0.647423 | + | 0.762131i | \(0.275847\pi\) | |||||||
\(510\) | − | 2.21340e20i | − | 1.09215i | ||||||
\(511\) | 1.45019e19i | 0.0705130i | ||||||||
\(512\) | 4.67427e20i | 2.23970i | ||||||||
\(513\) | 1.81587e19 | 0.0857442 | ||||||||
\(514\) | 5.71581e20i | 2.65983i | ||||||||
\(515\) | 3.72154e20 | 1.70675 | ||||||||
\(516\) | −1.98721e20 | −0.898194 | ||||||||
\(517\) | −2.10477e20 | −0.937615 | ||||||||
\(518\) | −6.37822e20 | −2.80044 | ||||||||
\(519\) | − | 1.90796e20i | − | 0.825685i | ||||||
\(520\) | − | 1.43995e21i | − | 6.14219i | ||||||
\(521\) | 1.57085e20 | 0.660466 | 0.330233 | − | 0.943899i | \(-0.392873\pi\) | ||||
0.330233 | + | 0.943899i | \(0.392873\pi\) | |||||||
\(522\) | −2.78848e20 | + | 9.24876e19i | −1.15568 | + | 0.383314i | ||||
\(523\) | −2.90825e20 | −1.18814 | −0.594071 | − | 0.804412i | \(-0.702480\pi\) | ||||
−0.594071 | + | 0.804412i | \(0.702480\pi\) | |||||||
\(524\) | 5.42668e19i | 0.218549i | ||||||||
\(525\) | − | 1.34759e20i | − | 0.535010i | ||||||
\(526\) | 3.66495e20 | 1.43441 | ||||||||
\(527\) | 2.72221e20 | 1.05037 | ||||||||
\(528\) | −3.11654e20 | −1.18555 | ||||||||
\(529\) | 3.56466e20 | 1.33690 | ||||||||
\(530\) | 6.71758e20i | 2.48395i | ||||||||
\(531\) | −2.89966e19 | −0.105715 | ||||||||
\(532\) | − | 6.52046e19i | − | 0.234391i | ||||||
\(533\) | 4.20282e20i | 1.48966i | ||||||||
\(534\) | 4.27498e20i | 1.49408i | ||||||||
\(535\) | 1.05627e20 | 0.364016 | ||||||||
\(536\) | 7.84214e20i | 2.66501i | ||||||||
\(537\) | − | 2.73873e19i | − | 0.0917787i | ||||||
\(538\) | −3.22683e20 | −1.06637 | ||||||||
\(539\) | − | 1.12297e20i | − | 0.365977i | ||||||
\(540\) | 9.07560e20i | 2.91690i | ||||||||
\(541\) | − | 5.99080e20i | − | 1.89892i | −0.313895 | − | 0.949458i | \(-0.601634\pi\) | ||
0.313895 | − | 0.949458i | \(-0.398366\pi\) | |||||||
\(542\) | 7.68895e20 | 2.40366 | ||||||||
\(543\) | 6.05775e19i | 0.186772i | ||||||||
\(544\) | 2.81971e20 | 0.857456 | ||||||||
\(545\) | −9.52962e19 | −0.285826 | ||||||||
\(546\) | 8.02219e20 | 2.37327 | ||||||||
\(547\) | −2.28999e19 | −0.0668235 | −0.0334117 | − | 0.999442i | \(-0.510637\pi\) | ||||
−0.0334117 | + | 0.999442i | \(0.510637\pi\) | |||||||
\(548\) | − | 1.00300e20i | − | 0.288701i | ||||||
\(549\) | 4.15129e20i | 1.17866i | ||||||||
\(550\) | −5.81658e20 | −1.62910 | ||||||||
\(551\) | 3.08101e19 | − | 1.02190e19i | 0.0851249 | − | 0.0282340i | ||||
\(552\) | −7.33277e20 | −1.99860 | ||||||||
\(553\) | 1.42011e20i | 0.381840i | ||||||||
\(554\) | 7.13073e20i | 1.89152i | ||||||||
\(555\) | −3.94832e20 | −1.03327 | ||||||||
\(556\) | −2.29543e20 | −0.592657 | ||||||||
\(557\) | 4.96235e20 | 1.26408 | 0.632039 | − | 0.774937i | \(-0.282218\pi\) | ||||
0.632039 | + | 0.774937i | \(0.282218\pi\) | |||||||
\(558\) | −6.47532e20 | −1.62744 | ||||||||
\(559\) | − | 5.57750e20i | − | 1.38309i | ||||||
\(560\) | 1.18650e21 | 2.90308 | ||||||||
\(561\) | − | 2.06354e20i | − | 0.498186i | ||||||
\(562\) | − | 3.60705e20i | − | 0.859271i | ||||||
\(563\) | 7.15855e20i | 1.68272i | 0.540475 | + | 0.841360i | \(0.318245\pi\) | ||||
−0.540475 | + | 0.841360i | \(0.681755\pi\) | |||||||
\(564\) | 4.71532e20 | 1.09375 | ||||||||
\(565\) | − | 7.58306e20i | − | 1.73572i | ||||||
\(566\) | − | 4.74268e19i | − | 0.107127i | ||||||
\(567\) | 6.60000e19 | 0.147120 | ||||||||
\(568\) | 5.62716e20i | 1.23788i | ||||||||
\(569\) | − | 1.89760e20i | − | 0.411967i | −0.978555 | − | 0.205984i | \(-0.933961\pi\) | ||
0.978555 | − | 0.205984i | \(-0.0660394\pi\) | |||||||
\(570\) | − | 5.81735e19i | − | 0.124642i | ||||||
\(571\) | 1.16175e20 | 0.245665 | 0.122832 | − | 0.992427i | \(-0.460802\pi\) | ||||
0.122832 | + | 0.992427i | \(0.460802\pi\) | |||||||
\(572\) | − | 2.40254e21i | − | 5.01418i | ||||||
\(573\) | 4.11136e20 | 0.846888 | ||||||||
\(574\) | −7.65996e20 | −1.55735 | ||||||||
\(575\) | −6.18724e20 | −1.24162 | ||||||||
\(576\) | −3.46551e19 | −0.0686435 | ||||||||
\(577\) | − | 7.40630e20i | − | 1.44805i | −0.689775 | − | 0.724024i | \(-0.742291\pi\) | ||
0.689775 | − | 0.724024i | \(-0.257709\pi\) | |||||||
\(578\) | − | 3.58143e20i | − | 0.691191i | ||||||
\(579\) | 9.92262e19 | 0.189033 | ||||||||
\(580\) | 5.10740e20 | + | 1.53987e21i | 0.960483 | + | 2.89584i | ||||
\(581\) | 3.00060e20 | 0.557040 | ||||||||
\(582\) | − | 3.68732e20i | − | 0.675754i | ||||||
\(583\) | 6.26277e20i | 1.13306i | ||||||||
\(584\) | −7.83568e19 | −0.139952 | ||||||||
\(585\) | −1.02533e21 | −1.80798 | ||||||||
\(586\) | −8.34999e20 | −1.45363 | ||||||||
\(587\) | −3.25073e19 | −0.0558721 | −0.0279360 | − | 0.999610i | \(-0.508893\pi\) | ||||
−0.0279360 | + | 0.999610i | \(0.508893\pi\) | |||||||
\(588\) | 2.51580e20i | 0.426920i | ||||||||
\(589\) | 7.15463e19 | 0.119873 | ||||||||
\(590\) | 2.30780e20i | 0.381775i | ||||||||
\(591\) | − | 5.99082e19i | − | 0.0978543i | ||||||
\(592\) | − | 1.55806e21i | − | 2.51288i | ||||||
\(593\) | −9.11421e20 | −1.45147 | −0.725736 | − | 0.687973i | \(-0.758501\pi\) | ||||
−0.725736 | + | 0.687973i | \(0.758501\pi\) | |||||||
\(594\) | 1.21945e21i | 1.91763i | ||||||||
\(595\) | 7.85612e20i | 1.21992i | ||||||||
\(596\) | −2.27734e21 | −3.49205 | ||||||||
\(597\) | − | 4.56996e20i | − | 0.691998i | ||||||
\(598\) | − | 3.68327e21i | − | 5.50775i | ||||||
\(599\) | 4.11734e20i | 0.608017i | 0.952669 | + | 0.304008i | \(0.0983251\pi\) | ||||
−0.952669 | + | 0.304008i | \(0.901675\pi\) | |||||||
\(600\) | 7.28127e20 | 1.06187 | ||||||||
\(601\) | − | 1.02932e20i | − | 0.148250i | −0.997249 | − | 0.0741248i | \(-0.976384\pi\) | ||
0.997249 | − | 0.0741248i | \(-0.0236163\pi\) | |||||||
\(602\) | 1.01654e21 | 1.44595 | ||||||||
\(603\) | 5.58404e20 | 0.784456 | ||||||||
\(604\) | 4.50075e19 | 0.0624465 | ||||||||
\(605\) | −2.27576e20 | −0.311861 | ||||||||
\(606\) | − | 1.12298e20i | − | 0.151994i | ||||||
\(607\) | 5.96092e20i | 0.796889i | 0.917192 | + | 0.398445i | \(0.130450\pi\) | ||||
−0.917192 | + | 0.398445i | \(0.869550\pi\) | |||||||
\(608\) | 7.41088e19 | 0.0978573 | ||||||||
\(609\) | −4.79358e20 | + | 1.58992e20i | −0.625217 | + | 0.207370i | ||||
\(610\) | 3.30395e21 | 4.25656 | ||||||||
\(611\) | 1.32345e21i | 1.68422i | ||||||||
\(612\) | − | 9.54502e20i | − | 1.19989i | ||||||
\(613\) | −8.45979e20 | −1.05052 | −0.525262 | − | 0.850941i | \(-0.676033\pi\) | ||||
−0.525262 | + | 0.850941i | \(0.676033\pi\) | |||||||
\(614\) | −7.65002e20 | −0.938426 | ||||||||
\(615\) | −4.74176e20 | −0.574614 | ||||||||
\(616\) | 2.44674e21 | 2.92909 | ||||||||
\(617\) | − | 4.79571e20i | − | 0.567172i | −0.958947 | − | 0.283586i | \(-0.908476\pi\) | ||
0.958947 | − | 0.283586i | \(-0.0915241\pi\) | |||||||
\(618\) | −1.12026e21 | −1.30889 | ||||||||
\(619\) | 4.08621e20i | 0.471673i | 0.971793 | + | 0.235836i | \(0.0757829\pi\) | ||||
−0.971793 | + | 0.235836i | \(0.924217\pi\) | |||||||
\(620\) | 3.57583e21i | 4.07793i | ||||||||
\(621\) | 1.29716e21i | 1.46152i | ||||||||
\(622\) | 1.00649e21 | 1.12042 | ||||||||
\(623\) | − | 1.51734e21i | − | 1.66887i | ||||||
\(624\) | 1.95965e21i | 2.12958i | ||||||||
\(625\) | −1.07337e21 | −1.15253 | ||||||||
\(626\) | − | 1.85668e21i | − | 1.96983i | ||||||
\(627\) | − | 5.42349e19i | − | 0.0568555i | ||||||
\(628\) | − | 1.61646e21i | − | 1.67443i | ||||||
\(629\) | 1.03163e21 | 1.05595 | ||||||||
\(630\) | − | 1.86874e21i | − | 1.89014i | ||||||
\(631\) | −1.92987e21 | −1.92889 | −0.964447 | − | 0.264275i | \(-0.914867\pi\) | ||||
−0.964447 | + | 0.264275i | \(0.914867\pi\) | |||||||
\(632\) | −7.67310e20 | −0.757867 | ||||||||
\(633\) | 1.08017e21 | 1.05430 | ||||||||
\(634\) | 1.88497e21 | 1.81817 | ||||||||
\(635\) | − | 1.25907e21i | − | 1.20018i | ||||||
\(636\) | − | 1.40305e21i | − | 1.32174i | ||||||
\(637\) | −7.06112e20 | −0.657397 | ||||||||
\(638\) | 6.86257e20 | + | 2.06905e21i | 0.631439 | + | 1.90378i | ||||
\(639\) | 4.00686e20 | 0.364374 | ||||||||
\(640\) | − | 1.35847e21i | − | 1.22095i | ||||||
\(641\) | 5.62278e20i | 0.499477i | 0.968313 | + | 0.249739i | \(0.0803447\pi\) | ||||
−0.968313 | + | 0.249739i | \(0.919655\pi\) | |||||||
\(642\) | −3.17957e20 | −0.279162 | ||||||||
\(643\) | −1.15662e21 | −1.00371 | −0.501857 | − | 0.864951i | \(-0.667350\pi\) | ||||
−0.501857 | + | 0.864951i | \(0.667350\pi\) | |||||||
\(644\) | 4.65785e21 | 3.99523 | ||||||||
\(645\) | 6.29273e20 | 0.533508 | ||||||||
\(646\) | 1.51998e20i | 0.127378i | ||||||||
\(647\) | 1.67194e21 | 1.38496 | 0.692482 | − | 0.721435i | \(-0.256517\pi\) | ||||
0.692482 | + | 0.721435i | \(0.256517\pi\) | |||||||
\(648\) | 3.56611e20i | 0.291999i | ||||||||
\(649\) | 2.15155e20i | 0.174147i | ||||||||
\(650\) | 3.65740e21i | 2.92632i | ||||||||
\(651\) | −1.11315e21 | −0.880433 | ||||||||
\(652\) | 2.93124e21i | 2.29189i | ||||||||
\(653\) | − | 2.32854e21i | − | 1.79985i | −0.436048 | − | 0.899923i | \(-0.643622\pi\) | ||
0.436048 | − | 0.899923i | \(-0.356378\pi\) | |||||||
\(654\) | 2.86860e20 | 0.219198 | ||||||||
\(655\) | − | 1.71842e20i | − | 0.129814i | ||||||
\(656\) | − | 1.87116e21i | − | 1.39744i | ||||||
\(657\) | 5.57944e19i | 0.0411956i | ||||||||
\(658\) | −2.41209e21 | −1.76076 | ||||||||
\(659\) | 8.29636e20i | 0.598752i | 0.954135 | + | 0.299376i | \(0.0967784\pi\) | ||||
−0.954135 | + | 0.299376i | \(0.903222\pi\) | |||||||
\(660\) | 2.71062e21 | 1.93415 | ||||||||
\(661\) | −1.11973e20 | −0.0789958 | −0.0394979 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394979 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(662\) | −2.61889e21 | −1.82676 | ||||||||
\(663\) | −1.29753e21 | −0.894882 | ||||||||
\(664\) | 1.62128e21i | 1.10560i | ||||||||
\(665\) | 2.06478e20i | 0.139223i | ||||||||
\(666\) | −2.45394e21 | −1.63609 | ||||||||
\(667\) | 7.29989e20 | + | 2.20090e21i | 0.481252 | + | 1.45097i | ||||
\(668\) | 1.31177e21 | 0.855132 | ||||||||
\(669\) | 2.73511e20i | 0.176311i | ||||||||
\(670\) | − | 4.44425e21i | − | 2.83294i | ||||||
\(671\) | 3.08025e21 | 1.94163 | ||||||||
\(672\) | −1.15302e21 | −0.718732 | ||||||||
\(673\) | 4.93200e20 | 0.304025 | 0.152013 | − | 0.988379i | \(-0.451425\pi\) | ||||
0.152013 | + | 0.988379i | \(0.451425\pi\) | |||||||
\(674\) | 7.28227e20 | 0.443933 | ||||||||
\(675\) | − | 1.28804e21i | − | 0.776520i | ||||||
\(676\) | −1.13056e22 | −6.74050 | ||||||||
\(677\) | − | 9.22814e20i | − | 0.544126i | −0.962279 | − | 0.272063i | \(-0.912294\pi\) | ||
0.962279 | − | 0.272063i | \(-0.0877059\pi\) | |||||||
\(678\) | 2.28265e21i | 1.33112i | ||||||||
\(679\) | 1.30876e21i | 0.754809i | ||||||||
\(680\) | −4.24481e21 | −2.42126 | ||||||||
\(681\) | 9.43074e19i | 0.0532038i | ||||||||
\(682\) | 4.80468e21i | 2.68091i | ||||||||
\(683\) | −2.54799e21 | −1.40619 | −0.703093 | − | 0.711098i | \(-0.748198\pi\) | ||||
−0.703093 | + | 0.711098i | \(0.748198\pi\) | |||||||
\(684\) | − | 2.50867e20i | − | 0.136937i | ||||||
\(685\) | 3.17613e20i | 0.171482i | ||||||||
\(686\) | 2.61564e21i | 1.39684i | ||||||||
\(687\) | −1.18293e20 | −0.0624863 | ||||||||
\(688\) | 2.48319e21i | 1.29747i | ||||||||
\(689\) | 3.93795e21 | 2.03529 | ||||||||
\(690\) | 4.15559e21 | 2.12454 | ||||||||
\(691\) | 2.67015e21 | 1.35036 | 0.675182 | − | 0.737651i | \(-0.264065\pi\) | ||||
0.675182 | + | 0.737651i | \(0.264065\pi\) | |||||||
\(692\) | −6.54843e21 | −3.27598 | ||||||||
\(693\) | − | 1.74222e21i | − | 0.862189i | ||||||
\(694\) | − | 2.11660e21i | − | 1.03620i | ||||||
\(695\) | 7.26876e20 | 0.352026 | ||||||||
\(696\) | −8.59065e20 | − | 2.59006e21i | −0.411582 | − | 1.24091i | ||||
\(697\) | 1.23894e21 | 0.587226 | ||||||||
\(698\) | − | 3.19267e20i | − | 0.149706i | ||||||
\(699\) | 8.22346e20i | 0.381483i | ||||||||
\(700\) | −4.62513e21 | −2.12270 | ||||||||
\(701\) | −3.48455e21 | −1.58220 | −0.791099 | − | 0.611688i | \(-0.790491\pi\) | ||||
−0.791099 | + | 0.611688i | \(0.790491\pi\) | |||||||
\(702\) | 7.66773e21 | 3.44460 | ||||||||
\(703\) | 2.71138e20 | 0.120511 | ||||||||
\(704\) | 2.57141e20i | 0.113078i | ||||||||
\(705\) | −1.49316e21 | −0.649664 | ||||||||
\(706\) | − | 6.65715e21i | − | 2.86585i | ||||||
\(707\) | 3.98584e20i | 0.169775i | ||||||||
\(708\) | − | 4.82013e20i | − | 0.203146i | ||||||
\(709\) | −1.65286e21 | −0.689269 | −0.344634 | − | 0.938737i | \(-0.611997\pi\) | ||||
−0.344634 | + | 0.938737i | \(0.611997\pi\) | |||||||
\(710\) | − | 3.18899e21i | − | 1.31588i | ||||||
\(711\) | 5.46368e20i | 0.223081i | ||||||||
\(712\) | 8.19848e21 | 3.31233 | ||||||||
\(713\) | 5.11086e21i | 2.04326i | ||||||||
\(714\) | − | 2.36485e21i | − | 0.935549i | ||||||
\(715\) | 7.60792e21i | 2.97832i | ||||||||
\(716\) | −9.39976e20 | −0.364141 | ||||||||
\(717\) | − | 6.47195e20i | − | 0.248108i | ||||||
\(718\) | 2.57746e21 | 0.977819 | ||||||||
\(719\) | −2.42457e20 | −0.0910267 | −0.0455133 | − | 0.998964i | \(-0.514492\pi\) | ||||
−0.0455133 | + | 0.998964i | \(0.514492\pi\) | |||||||
\(720\) | 4.56492e21 | 1.69605 | ||||||||
\(721\) | 3.97619e21 | 1.46202 | ||||||||
\(722\) | − | 4.92669e21i | − | 1.79278i | ||||||
\(723\) | − | 1.19026e21i | − | 0.428652i | ||||||
\(724\) | 2.07912e21 | 0.741037 | ||||||||
\(725\) | −7.24862e20 | − | 2.18544e21i | −0.255694 | − | 0.770911i | ||||
\(726\) | 6.85049e20 | 0.239165 | ||||||||
\(727\) | 3.97979e21i | 1.37516i | 0.726110 | + | 0.687578i | \(0.241326\pi\) | ||||
−0.726110 | + | 0.687578i | \(0.758674\pi\) | |||||||
\(728\) | − | 1.53848e22i | − | 5.26147i | ||||||
\(729\) | −1.35949e21 | −0.460172 | ||||||||
\(730\) | 4.44059e20 | 0.148771 | ||||||||
\(731\) | −1.64418e21 | −0.545218 | ||||||||
\(732\) | −6.90071e21 | −2.26496 | ||||||||
\(733\) | − | 2.41996e21i | − | 0.786192i | −0.919497 | − | 0.393096i | \(-0.871404\pi\) | ||
0.919497 | − | 0.393096i | \(-0.128596\pi\) | |||||||
\(734\) | 6.74319e21 | 2.16843 | ||||||||
\(735\) | − | 7.96659e20i | − | 0.253582i | ||||||
\(736\) | 5.29391e21i | 1.66799i | ||||||||
\(737\) | − | 4.14335e21i | − | 1.29225i | ||||||
\(738\) | −2.94707e21 | −0.909847 | ||||||||
\(739\) | 6.28024e21i | 1.91930i | 0.281196 | + | 0.959650i | \(0.409269\pi\) | ||||
−0.281196 | + | 0.959650i | \(0.590731\pi\) | |||||||
\(740\) | 1.35513e22i | 4.09961i | ||||||||
\(741\) | −3.41023e20 | −0.102128 | ||||||||
\(742\) | 7.17723e21i | 2.12778i | ||||||||
\(743\) | 1.61237e21i | 0.473204i | 0.971607 | + | 0.236602i | \(0.0760337\pi\) | ||||
−0.971607 | + | 0.236602i | \(0.923966\pi\) | |||||||
\(744\) | − | 6.01456e21i | − | 1.74746i | ||||||
\(745\) | 7.21147e21 | 2.07421 | ||||||||
\(746\) | 1.11244e20i | 0.0316762i | ||||||||
\(747\) | 1.15444e21 | 0.325438 | ||||||||
\(748\) | −7.08240e21 | −1.97660 | ||||||||
\(749\) | 1.12854e21 | 0.311820 | ||||||||
\(750\) | 9.54064e20 | 0.260987 | ||||||||
\(751\) | − | 4.01567e21i | − | 1.08757i | −0.839223 | − | 0.543787i | \(-0.816990\pi\) | ||
0.839223 | − | 0.543787i | \(-0.183010\pi\) | |||||||
\(752\) | − | 5.89222e21i | − | 1.57996i | ||||||
\(753\) | −2.49067e21 | −0.661232 | ||||||||
\(754\) | 1.30100e22 | − | 4.31510e21i | 3.41972 | − | 1.13424i | ||||
\(755\) | −1.42522e20 | −0.0370919 | ||||||||
\(756\) | 9.69659e21i | 2.49865i | ||||||||
\(757\) | 2.70758e21i | 0.690816i | 0.938453 | + | 0.345408i | \(0.112259\pi\) | ||||
−0.938453 | + | 0.345408i | \(0.887741\pi\) | |||||||
\(758\) | −6.72194e21 | −1.69815 | ||||||||
\(759\) | 3.87423e21 | 0.969109 | ||||||||
\(760\) | −1.11564e21 | −0.276327 | ||||||||
\(761\) | 4.07331e21 | 0.998993 | 0.499496 | − | 0.866316i | \(-0.333518\pi\) | ||||
0.499496 | + | 0.866316i | \(0.333518\pi\) | |||||||
\(762\) | 3.79004e21i | 0.920410i | ||||||||
\(763\) | −1.01817e21 | −0.244842 | ||||||||
\(764\) | − | 1.41109e22i | − | 3.36011i | ||||||
\(765\) | 3.02255e21i | 0.712709i | ||||||||
\(766\) | 5.22409e21i | 1.21982i | ||||||||
\(767\) | 1.35287e21 | 0.312817 | ||||||||
\(768\) | 4.34343e21i | 0.994544i | ||||||||
\(769\) | − | 7.92015e21i | − | 1.79591i | −0.440083 | − | 0.897957i | \(-0.645051\pi\) | ||
0.440083 | − | 0.897957i | \(-0.354949\pi\) | |||||||
\(770\) | −1.38660e22 | −3.11366 | ||||||||
\(771\) | 3.78038e21i | 0.840673i | ||||||||
\(772\) | − | 3.40560e21i | − | 0.750005i | ||||||
\(773\) | − | 1.66043e19i | − | 0.00362138i | −0.999998 | − | 0.00181069i | \(-0.999424\pi\) | ||
0.999998 | − | 0.00181069i | \(-0.000576360\pi\) | |||||||
\(774\) | 3.91102e21 | 0.844760 | ||||||||
\(775\) | − | 5.07496e21i | − | 1.08560i | ||||||
\(776\) | −7.07149e21 | −1.49812 | ||||||||
\(777\) | −4.21848e21 | −0.885113 | ||||||||
\(778\) | 4.03767e21 | 0.839042 | ||||||||
\(779\) | 3.25625e20 | 0.0670172 | ||||||||
\(780\) | − | 1.70441e22i | − | 3.47427i | ||||||
\(781\) | − | 2.97308e21i | − | 0.600239i | ||||||
\(782\) | −1.08578e22 | −2.17117 | ||||||||
\(783\) | −4.58178e21 | + | 1.51967e21i | −0.907447 | + | 0.300979i | ||||
\(784\) | 3.14372e21 | 0.616700 | ||||||||
\(785\) | 5.11872e21i | 0.994577i | ||||||||
\(786\) | 5.17279e20i | 0.0995534i | ||||||||
\(787\) | −7.49421e21 | −1.42862 | −0.714308 | − | 0.699831i | \(-0.753259\pi\) | ||||
−0.714308 | + | 0.699831i | \(0.753259\pi\) | |||||||
\(788\) | −2.05614e21 | −0.388246 | ||||||||
\(789\) | 2.42396e21 | 0.453364 | ||||||||
\(790\) | 4.34846e21 | 0.805623 | ||||||||
\(791\) | − | 8.10192e21i | − | 1.48684i | ||||||
\(792\) | 9.41353e21 | 1.71125 | ||||||||
\(793\) | − | 1.93683e22i | − | 3.48772i | ||||||
\(794\) | 4.90170e21i | 0.874366i | ||||||||
\(795\) | 4.44293e21i | 0.785084i | ||||||||
\(796\) | −1.56848e22 | −2.74556 | ||||||||
\(797\) | 6.10504e20i | 0.105865i | 0.998598 | + | 0.0529323i | \(0.0168568\pi\) | ||||
−0.998598 | + | 0.0529323i | \(0.983143\pi\) | |||||||
\(798\) | − | 6.21540e20i | − | 0.106770i | ||||||
\(799\) | 3.90138e21 | 0.663923 | ||||||||
\(800\) | − | 5.25673e21i | − | 0.886218i | ||||||
\(801\) | − | 5.83778e21i | − | 0.974998i | ||||||
\(802\) | 1.77409e22i | 2.93540i | ||||||||
\(803\) | 4.13994e20 | 0.0678621 | ||||||||
\(804\) | 9.28239e21i | 1.50744i | ||||||||
\(805\) | −1.47496e22 | −2.37308 | ||||||||
\(806\) | 3.02113e22 | 4.81567 | ||||||||
\(807\) | −2.13419e21 | −0.337040 | ||||||||
\(808\) | −2.15363e21 | −0.336965 | ||||||||
\(809\) | 1.81825e21i | 0.281863i | 0.990019 | + | 0.140932i | \(0.0450098\pi\) | ||||
−0.990019 | + | 0.140932i | \(0.954990\pi\) | |||||||
\(810\) | − | 2.02097e21i | − | 0.310400i | ||||||
\(811\) | 1.03501e22 | 1.57503 | 0.787513 | − | 0.616299i | \(-0.211369\pi\) | ||||
0.787513 | + | 0.616299i | \(0.211369\pi\) | |||||||
\(812\) | 5.45687e21 | + | 1.64523e22i | 0.822760 | + | 2.48061i | ||||
\(813\) | 5.08539e21 | 0.759705 | ||||||||
\(814\) | 1.82082e22i | 2.69516i | ||||||||
\(815\) | − | 9.28212e21i | − | 1.36134i | ||||||
\(816\) | 5.77681e21 | 0.839483 | ||||||||
\(817\) | −4.32132e20 | −0.0622230 | ||||||||
\(818\) | −1.80276e22 | −2.57210 | ||||||||
\(819\) | −1.09549e22 | −1.54874 | ||||||||
\(820\) | 1.62745e22i | 2.27984i | ||||||||
\(821\) | −1.06971e22 | −1.48489 | −0.742445 | − | 0.669907i | \(-0.766334\pi\) | ||||
−0.742445 | + | 0.669907i | \(0.766334\pi\) | |||||||
\(822\) | − | 9.56077e20i | − | 0.131509i | ||||||
\(823\) | − | 4.45050e21i | − | 0.606611i | −0.952893 | − | 0.303306i | \(-0.901910\pi\) | ||
0.952893 | − | 0.303306i | \(-0.0980903\pi\) | |||||||
\(824\) | 2.14841e22i | 2.90177i | ||||||||
\(825\) | −3.84702e21 | −0.514897 | ||||||||
\(826\) | 2.46571e21i | 0.327032i | ||||||||
\(827\) | 1.05576e22i | 1.38762i | 0.720156 | + | 0.693812i | \(0.244070\pi\) | ||||
−0.720156 | + | 0.693812i | \(0.755930\pi\) | |||||||
\(828\) | 1.79205e22 | 2.33412 | ||||||||
\(829\) | − | 7.28068e21i | − | 0.939752i | −0.882733 | − | 0.469876i | \(-0.844299\pi\) | ||
0.882733 | − | 0.469876i | \(-0.155701\pi\) | |||||||
\(830\) | − | 9.18803e21i | − | 1.17527i | ||||||
\(831\) | 4.71619e21i | 0.597838i | ||||||||
\(832\) | 1.61687e21 | 0.203119 | ||||||||
\(833\) | 2.08154e21i | 0.259147i | ||||||||
\(834\) | −2.18804e21 | −0.269967 | ||||||||
\(835\) | −4.15387e21 | −0.507930 | ||||||||
\(836\) | −1.86143e21 | −0.225579 | ||||||||
\(837\) | −1.06397e22 | −1.27787 | ||||||||
\(838\) | 1.83134e22i | 2.17991i | ||||||||
\(839\) | − | 7.55611e21i | − | 0.891422i | −0.895177 | − | 0.445711i | \(-0.852951\pi\) | ||
0.895177 | − | 0.445711i | \(-0.147049\pi\) | |||||||
\(840\) | 1.73577e22 | 2.02954 | ||||||||
\(841\) | −6.91876e21 | + | 5.15690e21i | −0.801786 | + | 0.597611i | ||||
\(842\) | −2.05584e22 | −2.36129 | ||||||||
\(843\) | − | 2.38567e21i | − | 0.271583i | ||||||
\(844\) | − | 3.70733e22i | − | 4.18305i | ||||||
\(845\) | 3.58004e22 | 4.00371 | ||||||||
\(846\) | −9.28023e21 | −1.02868 | ||||||||
\(847\) | −2.43148e21 | −0.267144 | ||||||||
\(848\) | −1.75324e22 | −1.90929 | ||||||||
\(849\) | − | 3.13676e20i | − | 0.0338589i | ||||||
\(850\) | 1.07816e22 | 1.15356 | ||||||||
\(851\) | 1.93685e22i | 2.05412i | ||||||||
\(852\) | 6.66062e21i | 0.700193i | ||||||||
\(853\) | 1.32017e22i | 1.37566i | 0.725871 | + | 0.687831i | \(0.241437\pi\) | ||||
−0.725871 | + | 0.687831i | \(0.758563\pi\) | |||||||
\(854\) | 3.53002e22 | 3.64622 | ||||||||
\(855\) | 7.94400e20i | 0.0813380i | ||||||||
\(856\) | 6.09772e21i | 0.618892i | ||||||||
\(857\) | 9.64988e21 | 0.970880 | 0.485440 | − | 0.874270i | \(-0.338659\pi\) | ||||
0.485440 | + | 0.874270i | \(0.338659\pi\) | |||||||
\(858\) | − | 2.29013e22i | − | 2.28405i | ||||||
\(859\) | − | 1.83155e22i | − | 1.81080i | −0.424557 | − | 0.905401i | \(-0.639570\pi\) | ||
0.424557 | − | 0.905401i | \(-0.360430\pi\) | |||||||
\(860\) | − | 2.15977e22i | − | 2.11674i | ||||||
\(861\) | −5.06621e21 | −0.492221 | ||||||||
\(862\) | − | 1.94446e22i | − | 1.87281i | ||||||
\(863\) | 7.59763e21 | 0.725433 | 0.362717 | − | 0.931899i | \(-0.381849\pi\) | ||||
0.362717 | + | 0.931899i | \(0.381849\pi\) | |||||||
\(864\) | −1.10207e22 | −1.04318 | ||||||||
\(865\) | 2.07364e22 | 1.94586 | ||||||||
\(866\) | 1.56692e22 | 1.45768 | ||||||||
\(867\) | − | 2.36872e21i | − | 0.218459i | ||||||
\(868\) | 3.82051e22i | 3.49320i | ||||||||
\(869\) | 4.05404e21 | 0.367486 | ||||||||
\(870\) | 4.86845e21 | + | 1.46783e22i | 0.437518 | + | 1.31911i | ||||
\(871\) | −2.60529e22 | −2.32124 | ||||||||
\(872\) | − | 5.50136e21i | − | 0.485955i | ||||||
\(873\) | 5.03530e21i | 0.440979i | ||||||||
\(874\) | −2.85371e21 | −0.247784 | ||||||||
\(875\) | −3.38631e21 | −0.291519 | ||||||||
\(876\) | −9.27474e20 | −0.0791628 | ||||||||
\(877\) | −2.63914e21 | −0.223339 | −0.111670 | − | 0.993745i | \(-0.535620\pi\) | ||||
−0.111670 | + | 0.993745i | \(0.535620\pi\) | |||||||
\(878\) | − | 2.56460e22i | − | 2.15184i | ||||||
\(879\) | −5.52259e21 | −0.459437 | ||||||||
\(880\) | − | 3.38717e22i | − | 2.79394i | ||||||
\(881\) | − | 5.24190e21i | − | 0.428716i | −0.976755 | − | 0.214358i | \(-0.931234\pi\) | ||
0.976755 | − | 0.214358i | \(-0.0687659\pi\) | |||||||
\(882\) | − | 4.95136e21i | − | 0.401522i | ||||||
\(883\) | 3.28609e20 | 0.0264225 | 0.0132113 | − | 0.999913i | \(-0.495795\pi\) | ||||
0.0132113 | + | 0.999913i | \(0.495795\pi\) | |||||||
\(884\) | 4.45333e22i | 3.55053i | ||||||||
\(885\) | 1.52635e21i | 0.120665i | ||||||||
\(886\) | −2.03792e22 | −1.59748 | ||||||||
\(887\) | 4.93296e21i | 0.383425i | 0.981451 | + | 0.191713i | \(0.0614042\pi\) | ||||
−0.981451 | + | 0.191713i | \(0.938596\pi\) | |||||||
\(888\) | − | 2.27933e22i | − | 1.75675i | ||||||
\(889\) | − | 1.34522e22i | − | 1.02809i | ||||||
\(890\) | −4.64620e22 | −3.52105 | ||||||||
\(891\) | − | 1.88414e21i | − | 0.141589i | ||||||
\(892\) | 9.38735e21 | 0.699531 | ||||||||
\(893\) | 1.02538e21 | 0.0757703 | ||||||||
\(894\) | −2.17079e22 | −1.59070 | ||||||||
\(895\) | 2.97655e21 | 0.216292 | ||||||||
\(896\) | − | 1.45142e22i | − | 1.04588i | ||||||
\(897\) | − | 2.43607e22i | − | 1.74079i | ||||||
\(898\) | 1.29576e22 | 0.918229 | ||||||||
\(899\) | −1.80525e22 | + | 5.98759e21i | −1.26864 | + | 0.420779i | ||||
\(900\) | −1.77946e22 | −1.24014 | ||||||||
\(901\) | − | 1.16086e22i | − | 0.802315i | ||||||
\(902\) | 2.18673e22i | 1.49881i | ||||||||
\(903\) | 6.72330e21 | 0.457009 | ||||||||
\(904\) | 4.37762e22 | 2.95104 | ||||||||
\(905\) | −6.58378e21 | −0.440160 | ||||||||
\(906\) | 4.29018e20 | 0.0284455 | ||||||||
\(907\) | 1.71728e22i | 1.12924i | 0.825350 | + | 0.564621i | \(0.190978\pi\) | ||||
−0.825350 | + | 0.564621i | \(0.809022\pi\) | |||||||
\(908\) | 3.23678e21 | 0.211091 | ||||||||
\(909\) | 1.53350e21i | 0.0991872i | ||||||||
\(910\) | 8.71879e22i | 5.59302i | ||||||||
\(911\) | 1.64359e22i | 1.04570i | 0.852425 | + | 0.522849i | \(0.175131\pi\) | ||||
−0.852425 | + | 0.522849i | \(0.824869\pi\) | |||||||
\(912\) | 1.51829e21 | 0.0958061 | ||||||||
\(913\) | − | 8.56595e21i | − | 0.536099i | ||||||
\(914\) | 3.44956e22i | 2.14125i | ||||||||
\(915\) | 2.18519e22 | 1.34534 | ||||||||
\(916\) | 4.06002e21i | 0.247920i | ||||||||
\(917\) | − | 1.83601e21i | − | 0.111200i | ||||||
\(918\) | − | 2.26036e22i | − | 1.35787i | ||||||
\(919\) | 2.38784e21 | 0.142278 | 0.0711391 | − | 0.997466i | \(-0.477337\pi\) | ||||
0.0711391 | + | 0.997466i | \(0.477337\pi\) | |||||||
\(920\) | − | 7.96951e22i | − | 4.71002i | ||||||
\(921\) | −5.05964e21 | −0.296601 | ||||||||
\(922\) | −4.55026e22 | −2.64579 | ||||||||
\(923\) | −1.86944e22 | −1.07820 | ||||||||
\(924\) | 2.89610e22 | 1.65681 | ||||||||
\(925\) | − | 1.92325e22i | − | 1.09137i | ||||||
\(926\) | − | 5.55909e22i | − | 3.12911i | ||||||
\(927\) | 1.52979e22 | 0.854149 | ||||||||
\(928\) | −1.86990e22 | + | 6.20204e21i | −1.03564 | + | 0.343499i | ||||
\(929\) | 3.05558e22 | 1.67871 | 0.839356 | − | 0.543582i | \(-0.182932\pi\) | ||||
0.839356 | + | 0.543582i | \(0.182932\pi\) | |||||||
\(930\) | 3.40854e22i | 1.85757i | ||||||||
\(931\) | 5.47079e20i | 0.0295752i | ||||||||
\(932\) | 2.82242e22 | 1.51357 | ||||||||
\(933\) | 6.65680e21 | 0.354122 | ||||||||
\(934\) | −4.44493e22 | −2.34565 | ||||||||
\(935\) | 2.24273e22 | 1.17406 | ||||||||
\(936\) | − | 5.91912e22i | − | 3.07389i | ||||||
\(937\) | 6.94788e21 | 0.357936 | 0.178968 | − | 0.983855i | \(-0.442724\pi\) | ||||
0.178968 | + | 0.983855i | \(0.442724\pi\) | |||||||
\(938\) | − | 4.74835e22i | − | 2.42673i | ||||||
\(939\) | − | 1.22799e22i | − | 0.622589i | ||||||
\(940\) | 5.12478e22i | 2.57760i | ||||||||
\(941\) | 2.12028e22 | 1.05796 | 0.528982 | − | 0.848633i | \(-0.322574\pi\) | ||||
0.528982 | + | 0.848633i | \(0.322574\pi\) | |||||||
\(942\) | − | 1.54083e22i | − | 0.762736i | ||||||
\(943\) | 2.32608e22i | 1.14232i | ||||||||
\(944\) | −6.02318e21 | −0.293451 | ||||||||
\(945\) | − | 3.07054e22i | − | 1.48415i | ||||||
\(946\) | − | 2.90198e22i | − | 1.39159i | ||||||
\(947\) | − | 6.87679e21i | − | 0.327161i | −0.986530 | − | 0.163580i | \(-0.947696\pi\) | ||
0.986530 | − | 0.163580i | \(-0.0523043\pi\) | |||||||
\(948\) | −9.08231e21 | −0.428680 | ||||||||
\(949\) | − | 2.60315e21i | − | 0.121900i | ||||||
\(950\) | 2.83367e21 | 0.131650 | ||||||||
\(951\) | 1.24670e22 | 0.574655 | ||||||||
\(952\) | −4.53526e22 | −2.07408 | ||||||||
\(953\) | −2.90857e21 | −0.131972 | −0.0659861 | − | 0.997821i | \(-0.521019\pi\) | ||||
−0.0659861 | + | 0.997821i | \(0.521019\pi\) | |||||||
\(954\) | 2.76135e22i | 1.24311i | ||||||||
\(955\) | 4.46837e22i | 1.99583i | ||||||||
\(956\) | −2.22128e22 | −0.984393 | ||||||||
\(957\) | 4.53883e21 | + | 1.36845e22i | 0.199574 | + | 0.601712i | ||||
\(958\) | 1.27964e22 | 0.558274 | ||||||||
\(959\) | 3.39345e21i | 0.146893i | ||||||||
\(960\) | 1.82421e21i | 0.0783503i | ||||||||
\(961\) | −1.84556e22 | −0.786506 | ||||||||
\(962\) | 1.14491e23 | 4.84127 | ||||||||
\(963\) | 4.34192e21 | 0.182173 | ||||||||
\(964\) | −4.08517e22 | −1.70072 | ||||||||
\(965\) | 1.07843e22i | 0.445487i | ||||||||
\(966\) | 4.43993e22 | 1.81990 | ||||||||
\(967\) | 2.37638e22i | 0.966535i | 0.875473 | + | 0.483268i | \(0.160550\pi\) | ||||
−0.875473 | + | 0.483268i | \(0.839450\pi\) | |||||||
\(968\) | − | 1.31378e22i | − | 0.530220i | ||||||
\(969\) | 1.00530e21i | 0.0402592i | ||||||||
\(970\) | 4.00751e22 | 1.59253 | ||||||||
\(971\) | 8.25082e21i | 0.325352i | 0.986680 | + | 0.162676i | \(0.0520125\pi\) | ||||
−0.986680 | + | 0.162676i | \(0.947988\pi\) | |||||||
\(972\) | 5.95962e22i | 2.33196i | ||||||||
\(973\) | 7.76613e21 | 0.301549 | ||||||||
\(974\) | 5.85863e20i | 0.0225738i | ||||||||
\(975\) | 2.41896e22i | 0.924899i | ||||||||
\(976\) | 8.62307e22i | 3.27181i | ||||||||
\(977\) | 1.38690e22 | 0.522199 | 0.261100 | − | 0.965312i | \(-0.415915\pi\) | ||||
0.261100 | + | 0.965312i | \(0.415915\pi\) | |||||||
\(978\) | 2.79410e22i | 1.04400i | ||||||||
\(979\) | −4.33163e22 | −1.60613 | ||||||||
\(980\) | −2.73426e22 | −1.00611 | ||||||||
\(981\) | −3.91728e21 | −0.143043 | ||||||||
\(982\) | 4.02379e22 | 1.45814 | ||||||||
\(983\) | 4.26234e22i | 1.53284i | 0.642340 | + | 0.766420i | \(0.277964\pi\) | ||||
−0.642340 | + | 0.766420i | \(0.722036\pi\) | |||||||
\(984\) | − | 2.73737e22i | − | 0.976946i | ||||||
\(985\) | 6.51103e21 | 0.230610 | ||||||||
\(986\) | −1.27204e22 | − | 3.83518e22i | −0.447121 | − | 1.34806i | ||||
\(987\) | −1.59533e22 | −0.556509 | ||||||||
\(988\) | 1.17045e22i | 0.405204i | ||||||||
\(989\) | − | 3.08691e22i | − | 1.06060i | ||||||
\(990\) | −5.33478e22 | −1.81908 | ||||||||
\(991\) | −3.97845e22 | −1.34636 | −0.673181 | − | 0.739478i | \(-0.735073\pi\) | ||||
−0.673181 | + | 0.739478i | \(0.735073\pi\) | |||||||
\(992\) | −4.34223e22 | −1.45839 | ||||||||
\(993\) | −1.73211e22 | −0.577371 | ||||||||
\(994\) | − | 3.40720e22i | − | 1.12720i | ||||||
\(995\) | 4.96679e22 | 1.63081 | ||||||||
\(996\) | 1.91904e22i | 0.625372i | ||||||||
\(997\) | 1.13283e22i | 0.366397i | 0.983076 | + | 0.183199i | \(0.0586452\pi\) | ||||
−0.983076 | + | 0.183199i | \(0.941355\pi\) | |||||||
\(998\) | 2.56296e22i | 0.822739i | ||||||||
\(999\) | −4.03210e22 | −1.28466 |
(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 | 29.16.b.a.28.2 | ✓ | 36 | |
29.28 | even | 2 | inner | 29.16.b.a.28.35 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.16.b.a.28.2 | ✓ | 36 | 1.1 | even | 1 | trivial | |
29.16.b.a.28.35 | yes | 36 | 29.28 | even | 2 | inner |