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 | 23.3 | ||
Character | \(\chi\) | \(=\) | 33.23 |
Dual form | 33.9.b.a.23.24 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 27.3024i | − | 1.70640i | −0.521582 | − | 0.853201i | \(-0.674658\pi\) | ||
0.521582 | − | 0.853201i | \(-0.325342\pi\) | |||||||
\(3\) | −36.6798 | − | 72.2191i | −0.452837 | − | 0.891593i | ||||
\(4\) | −489.423 | −1.91181 | ||||||||
\(5\) | 131.340i | 0.210144i | 0.994465 | + | 0.105072i | \(0.0335072\pi\) | ||||
−0.994465 | + | 0.105072i | \(0.966493\pi\) | |||||||
\(6\) | −1971.76 | + | 1001.45i | −1.52142 | + | 0.772722i | ||||
\(7\) | −44.0163 | −0.0183325 | −0.00916625 | − | 0.999958i | \(-0.502918\pi\) | ||||
−0.00916625 | + | 0.999958i | \(0.502918\pi\) | |||||||
\(8\) | 6373.03i | 1.55592i | ||||||||
\(9\) | −3870.19 | + | 5297.96i | −0.589877 | + | 0.807493i | ||||
\(10\) | 3585.90 | 0.358590 | ||||||||
\(11\) | 4414.43i | 0.301511i | ||||||||
\(12\) | 17951.9 | + | 35345.7i | 0.865738 | + | 1.70456i | ||||
\(13\) | −6563.79 | −0.229816 | −0.114908 | − | 0.993376i | \(-0.536657\pi\) | ||||
−0.114908 | + | 0.993376i | \(0.536657\pi\) | |||||||
\(14\) | 1201.75i | 0.0312826i | ||||||||
\(15\) | 9485.24 | − | 4817.52i | 0.187363 | − | 0.0951608i | ||||
\(16\) | 48706.9 | 0.743208 | ||||||||
\(17\) | − | 105271.i | − | 1.26041i | −0.776429 | − | 0.630204i | \(-0.782971\pi\) | ||
0.776429 | − | 0.630204i | \(-0.217029\pi\) | |||||||
\(18\) | 144647. | + | 105666.i | 1.37791 | + | 1.00657i | ||||
\(19\) | −82626.7 | −0.634024 | −0.317012 | − | 0.948421i | \(-0.602680\pi\) | ||||
−0.317012 | + | 0.948421i | \(0.602680\pi\) | |||||||
\(20\) | − | 64280.8i | − | 0.401755i | ||||||
\(21\) | 1614.51 | + | 3178.82i | 0.00830164 | + | 0.0163451i | ||||
\(22\) | 120525. | 0.514500 | ||||||||
\(23\) | 20607.9i | 0.0736414i | 0.999322 | + | 0.0368207i | \(0.0117230\pi\) | ||||
−0.999322 | + | 0.0368207i | \(0.988277\pi\) | |||||||
\(24\) | 460254. | − | 233761.i | 1.38724 | − | 0.704576i | ||||
\(25\) | 373375. | 0.955840 | ||||||||
\(26\) | 179207.i | 0.392159i | ||||||||
\(27\) | 524571. | + | 85173.1i | 0.987074 | + | 0.160268i | ||||
\(28\) | 21542.6 | 0.0350483 | ||||||||
\(29\) | 1.04815e6i | 1.48195i | 0.671533 | + | 0.740975i | \(0.265636\pi\) | ||||
−0.671533 | + | 0.740975i | \(0.734364\pi\) | |||||||
\(30\) | −131530. | − | 258970.i | −0.162383 | − | 0.319716i | ||||
\(31\) | −1.11820e6 | −1.21080 | −0.605399 | − | 0.795922i | \(-0.706986\pi\) | ||||
−0.605399 | + | 0.795922i | \(0.706986\pi\) | |||||||
\(32\) | 301679.i | 0.287704i | ||||||||
\(33\) | 318806. | − | 161920.i | 0.268826 | − | 0.136535i | ||||
\(34\) | −2.87414e6 | −2.15076 | ||||||||
\(35\) | − | 5781.10i | − | 0.00385246i | ||||||
\(36\) | 1.89416e6 | − | 2.59295e6i | 1.12773 | − | 1.54377i | ||||
\(37\) | −1.77509e6 | −0.947138 | −0.473569 | − | 0.880757i | \(-0.657035\pi\) | ||||
−0.473569 | + | 0.880757i | \(0.657035\pi\) | |||||||
\(38\) | 2.25591e6i | 1.08190i | ||||||||
\(39\) | 240758. | + | 474030.i | 0.104069 | + | 0.204903i | ||||
\(40\) | −837032. | −0.326966 | ||||||||
\(41\) | 4.15439e6i | 1.47019i | 0.677967 | + | 0.735093i | \(0.262861\pi\) | ||||
−0.677967 | + | 0.735093i | \(0.737139\pi\) | |||||||
\(42\) | 86789.5 | − | 44080.1i | 0.0278914 | − | 0.0141659i | ||||
\(43\) | 606228. | 0.177322 | 0.0886609 | − | 0.996062i | \(-0.471741\pi\) | ||||
0.0886609 | + | 0.996062i | \(0.471741\pi\) | |||||||
\(44\) | − | 2.16052e6i | − | 0.576432i | ||||||
\(45\) | −695833. | − | 508309.i | −0.169689 | − | 0.123959i | ||||
\(46\) | 562645. | 0.125662 | ||||||||
\(47\) | − | 7.81050e6i | − | 1.60062i | −0.599589 | − | 0.800308i | \(-0.704669\pi\) | ||
0.599589 | − | 0.800308i | \(-0.295331\pi\) | |||||||
\(48\) | −1.78656e6 | − | 3.51756e6i | −0.336552 | − | 0.662639i | ||||
\(49\) | −5.76286e6 | −0.999664 | ||||||||
\(50\) | − | 1.01940e7i | − | 1.63105i | ||||||
\(51\) | −7.60254e6 | + | 3.86130e6i | −1.12377 | + | 0.570760i | ||||
\(52\) | 3.21247e6 | 0.439365 | ||||||||
\(53\) | − | 490682.i | − | 0.0621866i | −0.999516 | − | 0.0310933i | \(-0.990101\pi\) | ||
0.999516 | − | 0.0310933i | \(-0.00989890\pi\) | |||||||
\(54\) | 2.32543e6 | − | 1.43221e7i | 0.273482 | − | 1.68434i | ||||
\(55\) | −579790. | −0.0633607 | ||||||||
\(56\) | − | 280517.i | − | 0.0285238i | ||||||
\(57\) | 3.03073e6 | + | 5.96722e6i | 0.287110 | + | 0.565292i | ||||
\(58\) | 2.86172e7 | 2.52880 | ||||||||
\(59\) | 1.98365e7i | 1.63703i | 0.574484 | + | 0.818516i | \(0.305203\pi\) | ||||
−0.574484 | + | 0.818516i | \(0.694797\pi\) | |||||||
\(60\) | −4.64230e6 | + | 2.35780e6i | −0.358202 | + | 0.181929i | ||||
\(61\) | −1.67301e7 | −1.20831 | −0.604155 | − | 0.796867i | \(-0.706489\pi\) | ||||
−0.604155 | + | 0.796867i | \(0.706489\pi\) | |||||||
\(62\) | 3.05295e7i | 2.06611i | ||||||||
\(63\) | 170351. | − | 233197.i | 0.0108139 | − | 0.0148034i | ||||
\(64\) | 2.07055e7 | 1.23415 | ||||||||
\(65\) | − | 862086.i | − | 0.0482945i | ||||||
\(66\) | −4.42082e6 | − | 8.70418e6i | −0.232985 | − | 0.458725i | ||||
\(67\) | 1.41991e7 | 0.704630 | 0.352315 | − | 0.935881i | \(-0.385395\pi\) | ||||
0.352315 | + | 0.935881i | \(0.385395\pi\) | |||||||
\(68\) | 5.15219e7i | 2.40966i | ||||||||
\(69\) | 1.48828e6 | − | 755893.i | 0.0656582 | − | 0.0333475i | ||||
\(70\) | −157838. | −0.00657385 | ||||||||
\(71\) | − | 1.70553e7i | − | 0.671160i | −0.942012 | − | 0.335580i | \(-0.891068\pi\) | ||
0.942012 | − | 0.335580i | \(-0.108932\pi\) | |||||||
\(72\) | −3.37641e7 | − | 2.46648e7i | −1.25639 | − | 0.917799i | ||||
\(73\) | −1.82226e7 | −0.641680 | −0.320840 | − | 0.947133i | \(-0.603965\pi\) | ||||
−0.320840 | + | 0.947133i | \(0.603965\pi\) | |||||||
\(74\) | 4.84643e7i | 1.61620i | ||||||||
\(75\) | −1.36953e7 | − | 2.69648e7i | −0.432840 | − | 0.852220i | ||||
\(76\) | 4.04394e7 | 1.21213 | ||||||||
\(77\) | − | 194307.i | − | 0.00552746i | ||||||
\(78\) | 1.29422e7 | − | 6.57329e6i | 0.349647 | − | 0.177584i | ||||
\(79\) | −2.20505e7 | −0.566123 | −0.283062 | − | 0.959102i | \(-0.591350\pi\) | ||||
−0.283062 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(80\) | 6.39715e6i | 0.156180i | ||||||||
\(81\) | −1.30900e7 | − | 4.10082e7i | −0.304089 | − | 0.952644i | ||||
\(82\) | 1.13425e8 | 2.50873 | ||||||||
\(83\) | − | 4.39847e7i | − | 0.926807i | −0.886147 | − | 0.463404i | \(-0.846628\pi\) | ||
0.886147 | − | 0.463404i | \(-0.153372\pi\) | |||||||
\(84\) | −790179. | − | 1.55579e6i | −0.0158711 | − | 0.0312488i | ||||
\(85\) | 1.38262e7 | 0.264867 | ||||||||
\(86\) | − | 1.65515e7i | − | 0.302582i | ||||||
\(87\) | 7.56967e7 | − | 3.84461e7i | 1.32130 | − | 0.671081i | ||||
\(88\) | −2.81333e7 | −0.469126 | ||||||||
\(89\) | − | 9.75343e7i | − | 1.55452i | −0.629177 | − | 0.777262i | \(-0.716608\pi\) | ||
0.629177 | − | 0.777262i | \(-0.283392\pi\) | |||||||
\(90\) | −1.38781e7 | + | 1.89979e7i | −0.211524 | + | 0.289559i | ||||
\(91\) | 288914. | 0.00421311 | ||||||||
\(92\) | − | 1.00860e7i | − | 0.140788i | ||||||
\(93\) | 4.10152e7 | + | 8.07551e7i | 0.548294 | + | 1.07954i | ||||
\(94\) | −2.13246e8 | −2.73130 | ||||||||
\(95\) | − | 1.08522e7i | − | 0.133236i | ||||||
\(96\) | 2.17870e7 | − | 1.10655e7i | 0.256515 | − | 0.130283i | ||||
\(97\) | −1.33932e8 | −1.51286 | −0.756430 | − | 0.654074i | \(-0.773058\pi\) | ||||
−0.756430 | + | 0.654074i | \(0.773058\pi\) | |||||||
\(98\) | 1.57340e8i | 1.70583i | ||||||||
\(99\) | −2.33875e7 | − | 1.70847e7i | −0.243468 | − | 0.177855i | ||||
\(100\) | −1.82738e8 | −1.82738 | ||||||||
\(101\) | − | 5.67481e7i | − | 0.545338i | −0.962108 | − | 0.272669i | \(-0.912094\pi\) | ||
0.962108 | − | 0.272669i | \(-0.0879064\pi\) | |||||||
\(102\) | 1.05423e8 | + | 2.07568e8i | 0.973946 | + | 1.91761i | ||||
\(103\) | 2.31177e7 | 0.205398 | 0.102699 | − | 0.994712i | \(-0.467252\pi\) | ||||
0.102699 | + | 0.994712i | \(0.467252\pi\) | |||||||
\(104\) | − | 4.18312e7i | − | 0.357575i | ||||||
\(105\) | −417505. | + | 212049.i | −0.00343483 | + | 0.00174454i | ||||
\(106\) | −1.33968e7 | −0.106115 | ||||||||
\(107\) | − | 1.15379e8i | − | 0.880224i | −0.897943 | − | 0.440112i | \(-0.854939\pi\) | ||
0.897943 | − | 0.440112i | \(-0.145061\pi\) | |||||||
\(108\) | −2.56737e8 | − | 4.16857e7i | −1.88710 | − | 0.306402i | ||||
\(109\) | −1.63794e8 | −1.16036 | −0.580180 | − | 0.814488i | \(-0.697018\pi\) | ||||
−0.580180 | + | 0.814488i | \(0.697018\pi\) | |||||||
\(110\) | 1.58297e7i | 0.108119i | ||||||||
\(111\) | 6.51099e7 | + | 1.28195e8i | 0.428899 | + | 0.844462i | ||||
\(112\) | −2.14390e6 | −0.0136249 | ||||||||
\(113\) | 2.60072e8i | 1.59507i | 0.603273 | + | 0.797535i | \(0.293863\pi\) | ||||
−0.603273 | + | 0.797535i | \(0.706137\pi\) | |||||||
\(114\) | 1.62920e8 | − | 8.27463e7i | 0.964615 | − | 0.489925i | ||||
\(115\) | −2.70663e6 | −0.0154753 | ||||||||
\(116\) | − | 5.12991e8i | − | 2.83321i | ||||||
\(117\) | 2.54031e7 | − | 3.47747e7i | 0.135563 | − | 0.185575i | ||||
\(118\) | 5.41585e8 | 2.79343 | ||||||||
\(119\) | 4.63363e6i | 0.0231064i | ||||||||
\(120\) | 3.07022e7 | + | 6.04497e7i | 0.148062 | + | 0.291520i | ||||
\(121\) | −1.94872e7 | −0.0909091 | ||||||||
\(122\) | 4.56772e8i | 2.06186i | ||||||||
\(123\) | 3.00026e8 | − | 1.52382e8i | 1.31081 | − | 0.665754i | ||||
\(124\) | 5.47272e8 | 2.31481 | ||||||||
\(125\) | 1.00344e8i | 0.411007i | ||||||||
\(126\) | −6.36684e6 | − | 4.65101e6i | −0.0252605 | − | 0.0184529i | ||||
\(127\) | −3.39607e8 | −1.30545 | −0.652727 | − | 0.757593i | \(-0.726375\pi\) | ||||
−0.652727 | + | 0.757593i | \(0.726375\pi\) | |||||||
\(128\) | − | 4.88082e8i | − | 1.81825i | ||||||
\(129\) | −2.22363e7 | − | 4.37812e7i | −0.0802979 | − | 0.158099i | ||||
\(130\) | −2.35371e7 | −0.0824098 | ||||||||
\(131\) | 9.39738e7i | 0.319096i | 0.987190 | + | 0.159548i | \(0.0510037\pi\) | ||||
−0.987190 | + | 0.159548i | \(0.948996\pi\) | |||||||
\(132\) | −1.56031e8 | + | 7.92476e7i | −0.513943 | + | 0.261030i | ||||
\(133\) | 3.63692e6 | 0.0116233 | ||||||||
\(134\) | − | 3.87670e8i | − | 1.20238i | ||||||
\(135\) | −1.11866e7 | + | 6.88971e7i | −0.0336793 | + | 0.207427i | ||||
\(136\) | 6.70892e8 | 1.96109 | ||||||||
\(137\) | 6.33508e7i | 0.179833i | 0.995949 | + | 0.0899166i | \(0.0286601\pi\) | ||||
−0.995949 | + | 0.0899166i | \(0.971340\pi\) | |||||||
\(138\) | −2.06377e7 | − | 4.06337e7i | −0.0569043 | − | 0.112039i | ||||
\(139\) | −4.69989e8 | −1.25901 | −0.629505 | − | 0.776997i | \(-0.716742\pi\) | ||||
−0.629505 | + | 0.776997i | \(0.716742\pi\) | |||||||
\(140\) | 2.82940e6i | 0.00736517i | ||||||||
\(141\) | −5.64067e8 | + | 2.86487e8i | −1.42710 | + | 0.724818i | ||||
\(142\) | −4.65652e8 | −1.14527 | ||||||||
\(143\) | − | 2.89754e7i | − | 0.0692923i | ||||||
\(144\) | −1.88505e8 | + | 2.58047e8i | −0.438401 | + | 0.600135i | ||||
\(145\) | −1.37664e8 | −0.311422 | ||||||||
\(146\) | 4.97521e8i | 1.09496i | ||||||||
\(147\) | 2.11381e8 | + | 4.16189e8i | 0.452685 | + | 0.891294i | ||||
\(148\) | 8.68770e8 | 1.81075 | ||||||||
\(149\) | − | 2.91586e7i | − | 0.0591592i | −0.999562 | − | 0.0295796i | \(-0.990583\pi\) | ||
0.999562 | − | 0.0295796i | \(-0.00941685\pi\) | |||||||
\(150\) | −7.36204e8 | + | 3.73915e8i | −1.45423 | + | 0.738599i | ||||
\(151\) | 9.83817e8 | 1.89237 | 0.946186 | − | 0.323623i | \(-0.104901\pi\) | ||||
0.946186 | + | 0.323623i | \(0.104901\pi\) | |||||||
\(152\) | − | 5.26582e8i | − | 0.986488i | ||||||
\(153\) | 5.57719e8 | + | 4.07417e8i | 1.01777 | + | 0.743487i | ||||
\(154\) | −5.30505e6 | −0.00943207 | ||||||||
\(155\) | − | 1.46864e8i | − | 0.254441i | ||||||
\(156\) | −1.17833e8 | − | 2.32002e8i | −0.198961 | − | 0.391735i | ||||
\(157\) | −2.39574e8 | −0.394313 | −0.197156 | − | 0.980372i | \(-0.563171\pi\) | ||||
−0.197156 | + | 0.980372i | \(0.563171\pi\) | |||||||
\(158\) | 6.02034e8i | 0.966034i | ||||||||
\(159\) | −3.54366e7 | + | 1.79981e7i | −0.0554451 | + | 0.0281604i | ||||
\(160\) | −3.96225e7 | −0.0604591 | ||||||||
\(161\) | − | 907084.i | − | 0.00135003i | ||||||
\(162\) | −1.11962e9 | + | 3.57390e8i | −1.62559 | + | 0.518899i | ||||
\(163\) | 4.51535e8 | 0.639647 | 0.319824 | − | 0.947477i | \(-0.396376\pi\) | ||||
0.319824 | + | 0.947477i | \(0.396376\pi\) | |||||||
\(164\) | − | 2.03326e9i | − | 2.81071i | ||||||
\(165\) | 2.12666e7 | + | 4.18719e7i | 0.0286921 | + | 0.0564920i | ||||
\(166\) | −1.20089e9 | −1.58151 | ||||||||
\(167\) | 5.15624e8i | 0.662930i | 0.943468 | + | 0.331465i | \(0.107543\pi\) | ||||
−0.943468 | + | 0.331465i | \(0.892457\pi\) | |||||||
\(168\) | −2.02587e7 | + | 1.02893e7i | −0.0254316 | + | 0.0129166i | ||||
\(169\) | −7.72647e8 | −0.947184 | ||||||||
\(170\) | − | 3.77489e8i | − | 0.451970i | ||||||
\(171\) | 3.19781e8 | − | 4.37753e8i | 0.373997 | − | 0.511970i | ||||
\(172\) | −2.96702e8 | −0.339006 | ||||||||
\(173\) | − | 3.97074e8i | − | 0.443289i | −0.975128 | − | 0.221645i | \(-0.928858\pi\) | ||
0.975128 | − | 0.221645i | \(-0.0711425\pi\) | |||||||
\(174\) | −1.04967e9 | − | 2.06671e9i | −1.14513 | − | 2.25466i | ||||
\(175\) | −1.64346e7 | −0.0175229 | ||||||||
\(176\) | 2.15013e8i | 0.224086i | ||||||||
\(177\) | 1.43257e9 | − | 7.27599e8i | 1.45957 | − | 0.741308i | ||||
\(178\) | −2.66293e9 | −2.65264 | ||||||||
\(179\) | − | 7.85792e8i | − | 0.765412i | −0.923870 | − | 0.382706i | \(-0.874992\pi\) | ||
0.923870 | − | 0.382706i | \(-0.125008\pi\) | |||||||
\(180\) | 3.40557e8 | + | 2.48778e8i | 0.324414 | + | 0.236986i | ||||
\(181\) | 1.59130e9 | 1.48265 | 0.741325 | − | 0.671146i | \(-0.234198\pi\) | ||||
0.741325 | + | 0.671146i | \(0.234198\pi\) | |||||||
\(182\) | − | 7.88805e6i | − | 0.00718926i | ||||||
\(183\) | 6.13655e8 | + | 1.20823e9i | 0.547167 | + | 1.07732i | ||||
\(184\) | −1.31335e8 | −0.114580 | ||||||||
\(185\) | − | 2.33140e8i | − | 0.199035i | ||||||
\(186\) | 2.20481e9 | − | 1.11982e9i | 1.84213 | − | 0.935610i | ||||
\(187\) | 4.64709e8 | 0.380027 | ||||||||
\(188\) | 3.82264e9i | 3.06007i | ||||||||
\(189\) | −2.30897e7 | − | 3.74901e6i | −0.0180955 | − | 0.00293812i | ||||
\(190\) | −2.96291e8 | −0.227355 | ||||||||
\(191\) | 7.23571e8i | 0.543685i | 0.962342 | + | 0.271843i | \(0.0876330\pi\) | ||||
−0.962342 | + | 0.271843i | \(0.912367\pi\) | |||||||
\(192\) | −7.59475e8 | − | 1.49533e9i | −0.558867 | − | 1.10036i | ||||
\(193\) | −4.55812e8 | −0.328516 | −0.164258 | − | 0.986417i | \(-0.552523\pi\) | ||||
−0.164258 | + | 0.986417i | \(0.552523\pi\) | |||||||
\(194\) | 3.65668e9i | 2.58155i | ||||||||
\(195\) | −6.22591e7 | + | 3.16211e7i | −0.0430590 | + | 0.0218695i | ||||
\(196\) | 2.82048e9 | 1.91117 | ||||||||
\(197\) | − | 2.55244e9i | − | 1.69469i | −0.531040 | − | 0.847347i | \(-0.678199\pi\) | ||
0.531040 | − | 0.847347i | \(-0.321801\pi\) | |||||||
\(198\) | −4.66453e8 | + | 6.38535e8i | −0.303492 | + | 0.415455i | ||||
\(199\) | 2.10450e8 | 0.134195 | 0.0670974 | − | 0.997746i | \(-0.478626\pi\) | ||||
0.0670974 | + | 0.997746i | \(0.478626\pi\) | |||||||
\(200\) | 2.37953e9i | 1.48721i | ||||||||
\(201\) | −5.20820e8 | − | 1.02545e9i | −0.319083 | − | 0.628244i | ||||
\(202\) | −1.54936e9 | −0.930567 | ||||||||
\(203\) | − | 4.61359e7i | − | 0.0271678i | ||||||
\(204\) | 3.72086e9 | − | 1.88981e9i | 2.14844 | − | 1.09118i | ||||
\(205\) | −5.45637e8 | −0.308950 | ||||||||
\(206\) | − | 6.31170e8i | − | 0.350491i | ||||||
\(207\) | −1.09180e8 | − | 7.97563e7i | −0.0594649 | − | 0.0434394i | ||||
\(208\) | −3.19701e8 | −0.170801 | ||||||||
\(209\) | − | 3.64749e8i | − | 0.191165i | ||||||
\(210\) | 5.78947e6 | + | 1.13989e7i | 0.00297688 | + | 0.00586120i | ||||
\(211\) | 3.76856e8 | 0.190128 | 0.0950638 | − | 0.995471i | \(-0.469694\pi\) | ||||
0.0950638 | + | 0.995471i | \(0.469694\pi\) | |||||||
\(212\) | 2.40151e8i | 0.118889i | ||||||||
\(213\) | −1.23172e9 | + | 6.25585e8i | −0.598402 | + | 0.303926i | ||||
\(214\) | −3.15014e9 | −1.50202 | ||||||||
\(215\) | 7.96218e7i | 0.0372630i | ||||||||
\(216\) | −5.42810e8 | + | 3.34311e9i | −0.249364 | + | 1.53580i | ||||
\(217\) | 4.92189e7 | 0.0221969 | ||||||||
\(218\) | 4.47199e9i | 1.98004i | ||||||||
\(219\) | 6.68401e8 | + | 1.31602e9i | 0.290577 | + | 0.572118i | ||||
\(220\) | 2.83763e8 | 0.121134 | ||||||||
\(221\) | 6.90974e8i | 0.289663i | ||||||||
\(222\) | 3.50004e9 | − | 1.77766e9i | 1.44099 | − | 0.731875i | ||||
\(223\) | −1.78266e9 | −0.720856 | −0.360428 | − | 0.932787i | \(-0.617369\pi\) | ||||
−0.360428 | + | 0.932787i | \(0.617369\pi\) | |||||||
\(224\) | − | 1.32788e7i | − | 0.00527433i | ||||||
\(225\) | −1.44503e9 | + | 1.97813e9i | −0.563828 | + | 0.771834i | ||||
\(226\) | 7.10060e9 | 2.72183 | ||||||||
\(227\) | − | 2.32944e9i | − | 0.877302i | −0.898658 | − | 0.438651i | \(-0.855457\pi\) | ||
0.898658 | − | 0.438651i | \(-0.144543\pi\) | |||||||
\(228\) | −1.48331e9 | − | 2.92050e9i | −0.548899 | − | 1.08073i | ||||
\(229\) | 4.82444e9 | 1.75430 | 0.877152 | − | 0.480212i | \(-0.159440\pi\) | ||||
0.877152 | + | 0.480212i | \(0.159440\pi\) | |||||||
\(230\) | 7.38977e7i | 0.0264070i | ||||||||
\(231\) | −1.40327e7 | + | 7.12714e6i | −0.00492824 | + | 0.00250304i | ||||
\(232\) | −6.67992e9 | −2.30579 | ||||||||
\(233\) | 1.02242e9i | 0.346899i | 0.984843 | + | 0.173450i | \(0.0554914\pi\) | ||||
−0.984843 | + | 0.173450i | \(0.944509\pi\) | |||||||
\(234\) | −9.49434e8 | − | 6.93566e8i | −0.316666 | − | 0.231326i | ||||
\(235\) | 1.02583e9 | 0.336359 | ||||||||
\(236\) | − | 9.70845e9i | − | 3.12969i | ||||||
\(237\) | 8.08809e8 | + | 1.59247e9i | 0.256361 | + | 0.504752i | ||||
\(238\) | 1.26509e8 | 0.0394289 | ||||||||
\(239\) | − | 2.32559e9i | − | 0.712757i | −0.934342 | − | 0.356379i | \(-0.884011\pi\) | ||
0.934342 | − | 0.356379i | \(-0.115989\pi\) | |||||||
\(240\) | 4.61996e8 | − | 2.34646e8i | 0.139249 | − | 0.0707242i | ||||
\(241\) | −3.50877e9 | −1.04013 | −0.520063 | − | 0.854128i | \(-0.674092\pi\) | ||||
−0.520063 | + | 0.854128i | \(0.674092\pi\) | |||||||
\(242\) | 5.32047e8i | 0.155128i | ||||||||
\(243\) | −2.48143e9 | + | 2.44952e9i | −0.711668 | + | 0.702516i | ||||
\(244\) | 8.18808e9 | 2.31006 | ||||||||
\(245\) | − | 7.56893e8i | − | 0.210073i | ||||||
\(246\) | −4.16041e9 | − | 8.19145e9i | −1.13604 | − | 2.23677i | ||||
\(247\) | 5.42344e8 | 0.145709 | ||||||||
\(248\) | − | 7.12630e9i | − | 1.88390i | ||||||
\(249\) | −3.17654e9 | + | 1.61335e9i | −0.826335 | + | 0.419693i | ||||
\(250\) | 2.73962e9 | 0.701344 | ||||||||
\(251\) | 4.49017e9i | 1.13127i | 0.824655 | + | 0.565637i | \(0.191370\pi\) | ||||
−0.824655 | + | 0.565637i | \(0.808630\pi\) | |||||||
\(252\) | −8.33740e7 | + | 1.14132e8i | −0.0206742 | + | 0.0283012i | ||||
\(253\) | −9.09720e7 | −0.0222037 | ||||||||
\(254\) | 9.27210e9i | 2.22763i | ||||||||
\(255\) | −5.07143e8 | − | 9.98516e8i | −0.119942 | − | 0.236154i | ||||
\(256\) | −8.02521e9 | −1.86851 | ||||||||
\(257\) | − | 2.12580e9i | − | 0.487293i | −0.969864 | − | 0.243646i | \(-0.921656\pi\) | ||
0.969864 | − | 0.243646i | \(-0.0783436\pi\) | |||||||
\(258\) | −1.19533e9 | + | 6.07106e8i | −0.269780 | + | 0.137020i | ||||
\(259\) | 7.81329e7 | 0.0173634 | ||||||||
\(260\) | 4.21925e8i | 0.0923298i | ||||||||
\(261\) | −5.55308e9 | − | 4.05655e9i | −1.19666 | − | 0.874168i | ||||
\(262\) | 2.56571e9 | 0.544507 | ||||||||
\(263\) | 4.54665e9i | 0.950317i | 0.879900 | + | 0.475159i | \(0.157609\pi\) | ||||
−0.879900 | + | 0.475159i | \(0.842391\pi\) | |||||||
\(264\) | 1.03192e9 | + | 2.03176e9i | 0.212438 | + | 0.418270i | ||||
\(265\) | 6.44461e7 | 0.0130681 | ||||||||
\(266\) | − | 9.92969e7i | − | 0.0198339i | ||||||
\(267\) | −7.04384e9 | + | 3.57754e9i | −1.38600 | + | 0.703946i | ||||
\(268\) | −6.94937e9 | −1.34712 | ||||||||
\(269\) | − | 2.48249e9i | − | 0.474109i | −0.971496 | − | 0.237055i | \(-0.923818\pi\) | ||
0.971496 | − | 0.237055i | \(-0.0761820\pi\) | |||||||
\(270\) | 1.88106e9 | + | 3.05422e8i | 0.353954 | + | 0.0574705i | ||||
\(271\) | 9.49043e9 | 1.75958 | 0.879790 | − | 0.475363i | \(-0.157683\pi\) | ||||
0.879790 | + | 0.475363i | \(0.157683\pi\) | |||||||
\(272\) | − | 5.12740e9i | − | 0.936745i | ||||||
\(273\) | −1.05973e7 | − | 2.08651e7i | −0.00190785 | − | 0.00375638i | ||||
\(274\) | 1.72963e9 | 0.306868 | ||||||||
\(275\) | 1.64824e9i | 0.288196i | ||||||||
\(276\) | −7.28400e8 | + | 3.69952e8i | −0.125526 | + | 0.0637542i | ||||
\(277\) | −4.51936e9 | −0.767641 | −0.383820 | − | 0.923408i | \(-0.625392\pi\) | ||||
−0.383820 | + | 0.923408i | \(0.625392\pi\) | |||||||
\(278\) | 1.28319e10i | 2.14838i | ||||||||
\(279\) | 4.32763e9 | − | 5.92416e9i | 0.714222 | − | 0.977710i | ||||
\(280\) | 3.68431e7 | 0.00599410 | ||||||||
\(281\) | − | 7.64027e9i | − | 1.22542i | −0.790309 | − | 0.612708i | \(-0.790080\pi\) | ||
0.790309 | − | 0.612708i | \(-0.209920\pi\) | |||||||
\(282\) | 7.82181e9 | + | 1.54004e10i | 1.23683 | + | 2.43521i | ||||
\(283\) | −5.96187e9 | −0.929474 | −0.464737 | − | 0.885449i | \(-0.653851\pi\) | ||||
−0.464737 | + | 0.885449i | \(0.653851\pi\) | |||||||
\(284\) | 8.34727e9i | 1.28313i | ||||||||
\(285\) | −7.83733e8 | + | 3.98055e8i | −0.118792 | + | 0.0603343i | ||||
\(286\) | −7.91098e8 | −0.118240 | ||||||||
\(287\) | − | 1.82861e8i | − | 0.0269522i | ||||||
\(288\) | −1.59828e9 | − | 1.16755e9i | −0.232319 | − | 0.169710i | ||||
\(289\) | −4.10614e9 | −0.588630 | ||||||||
\(290\) | 3.75857e9i | 0.531412i | ||||||||
\(291\) | 4.91262e9 | + | 9.67248e9i | 0.685079 | + | 1.34886i | ||||
\(292\) | 8.91856e9 | 1.22677 | ||||||||
\(293\) | − | 6.54569e9i | − | 0.888147i | −0.895990 | − | 0.444074i | \(-0.853533\pi\) | ||
0.895990 | − | 0.444074i | \(-0.146467\pi\) | |||||||
\(294\) | 1.13630e10 | − | 5.77121e9i | 1.52091 | − | 0.772462i | ||||
\(295\) | −2.60532e9 | −0.344012 | ||||||||
\(296\) | − | 1.13127e10i | − | 1.47367i | ||||||
\(297\) | −3.75990e8 | + | 2.31568e9i | −0.0483227 | + | 0.297614i | ||||
\(298\) | −7.96102e8 | −0.100949 | ||||||||
\(299\) | − | 1.35266e8i | − | 0.0169240i | ||||||
\(300\) | 6.70281e9 | + | 1.31972e10i | 0.827507 | + | 1.62928i | ||||
\(301\) | −2.66839e7 | −0.00325075 | ||||||||
\(302\) | − | 2.68606e10i | − | 3.22915i | ||||||
\(303\) | −4.09830e9 | + | 2.08151e9i | −0.486220 | + | 0.246949i | ||||
\(304\) | −4.02449e9 | −0.471212 | ||||||||
\(305\) | − | 2.19732e9i | − | 0.253919i | ||||||
\(306\) | 1.11235e10 | − | 1.52271e10i | 1.26869 | − | 1.73673i | ||||
\(307\) | 1.21591e10 | 1.36882 | 0.684412 | − | 0.729096i | \(-0.260059\pi\) | ||||
0.684412 | + | 0.729096i | \(0.260059\pi\) | |||||||
\(308\) | 9.50984e7i | 0.0105674i | ||||||||
\(309\) | −8.47952e8 | − | 1.66954e9i | −0.0930117 | − | 0.183131i | ||||
\(310\) | −4.00974e9 | −0.434179 | ||||||||
\(311\) | − | 1.56012e10i | − | 1.66769i | −0.551997 | − | 0.833846i | \(-0.686134\pi\) | ||
0.551997 | − | 0.833846i | \(-0.313866\pi\) | |||||||
\(312\) | −3.02101e9 | + | 1.53436e9i | −0.318811 | + | 0.161923i | ||||
\(313\) | 5.51545e9 | 0.574650 | 0.287325 | − | 0.957833i | \(-0.407234\pi\) | ||||
0.287325 | + | 0.957833i | \(0.407234\pi\) | |||||||
\(314\) | 6.54095e9i | 0.672856i | ||||||||
\(315\) | 3.06280e7 | + | 2.23739e7i | 0.00311083 | + | 0.00227248i | ||||
\(316\) | 1.07921e10 | 1.08232 | ||||||||
\(317\) | − | 1.20811e9i | − | 0.119638i | −0.998209 | − | 0.0598192i | \(-0.980948\pi\) | ||
0.998209 | − | 0.0598192i | \(-0.0190524\pi\) | |||||||
\(318\) | 4.91393e8 | + | 9.67506e8i | 0.0480530 | + | 0.0946117i | ||||
\(319\) | −4.62700e9 | −0.446824 | ||||||||
\(320\) | 2.71946e9i | 0.259348i | ||||||||
\(321\) | −8.33260e9 | + | 4.23210e9i | −0.784802 | + | 0.398598i | ||||
\(322\) | −2.47656e7 | −0.00230370 | ||||||||
\(323\) | 8.69816e9i | 0.799130i | ||||||||
\(324\) | 6.40658e9 | + | 2.00704e10i | 0.581361 | + | 1.82127i | ||||
\(325\) | −2.45075e9 | −0.219668 | ||||||||
\(326\) | − | 1.23280e10i | − | 1.09150i | ||||||
\(327\) | 6.00794e9 | + | 1.18291e10i | 0.525454 | + | 1.03457i | ||||
\(328\) | −2.64761e10 | −2.28748 | ||||||||
\(329\) | 3.43790e8i | 0.0293433i | ||||||||
\(330\) | 1.14320e9 | − | 5.80629e8i | 0.0963981 | − | 0.0489602i | ||||
\(331\) | 1.60134e10 | 1.33405 | 0.667026 | − | 0.745034i | \(-0.267567\pi\) | ||||
0.667026 | + | 0.745034i | \(0.267567\pi\) | |||||||
\(332\) | 2.15272e10i | 1.77188i | ||||||||
\(333\) | 6.86992e9 | − | 9.40435e9i | 0.558695 | − | 0.764807i | ||||
\(334\) | 1.40778e10 | 1.13122 | ||||||||
\(335\) | 1.86491e9i | 0.148074i | ||||||||
\(336\) | 7.86377e7 | + | 1.54830e8i | 0.00616984 | + | 0.0121478i | ||||
\(337\) | −2.02686e10 | −1.57146 | −0.785730 | − | 0.618569i | \(-0.787713\pi\) | ||||
−0.785730 | + | 0.618569i | \(0.787713\pi\) | |||||||
\(338\) | 2.10952e10i | 1.61628i | ||||||||
\(339\) | 1.87821e10 | − | 9.53938e9i | 1.42215 | − | 0.722307i | ||||
\(340\) | −6.76687e9 | −0.506375 | ||||||||
\(341\) | − | 4.93620e9i | − | 0.365069i | ||||||
\(342\) | −1.19517e10 | − | 8.73079e9i | −0.873627 | − | 0.638189i | ||||
\(343\) | 5.07406e8 | 0.0366588 | ||||||||
\(344\) | 3.86351e9i | 0.275898i | ||||||||
\(345\) | 9.92788e7 | + | 1.95471e8i | 0.00700777 | + | 0.0137976i | ||||
\(346\) | −1.08411e10 | −0.756430 | ||||||||
\(347\) | − | 1.24843e10i | − | 0.861085i | −0.902570 | − | 0.430542i | \(-0.858322\pi\) | ||
0.902570 | − | 0.430542i | \(-0.141678\pi\) | |||||||
\(348\) | −3.70477e10 | + | 1.88164e10i | −2.52607 | + | 1.28298i | ||||
\(349\) | −2.54367e10 | −1.71458 | −0.857292 | − | 0.514830i | \(-0.827855\pi\) | ||||
−0.857292 | + | 0.514830i | \(0.827855\pi\) | |||||||
\(350\) | 4.48705e8i | 0.0299012i | ||||||||
\(351\) | −3.44317e9 | − | 5.59058e8i | −0.226846 | − | 0.0368322i | ||||
\(352\) | −1.33174e9 | −0.0867459 | ||||||||
\(353\) | 1.97543e10i | 1.27222i | 0.771598 | + | 0.636110i | \(0.219458\pi\) | ||||
−0.771598 | + | 0.636110i | \(0.780542\pi\) | |||||||
\(354\) | −1.98652e10 | − | 3.91127e10i | −1.26497 | − | 2.49061i | ||||
\(355\) | 2.24004e9 | 0.141040 | ||||||||
\(356\) | 4.77356e10i | 2.97196i | ||||||||
\(357\) | 3.34636e8 | − | 1.69960e8i | 0.0206016 | − | 0.0104635i | ||||
\(358\) | −2.14540e10 | −1.30610 | ||||||||
\(359\) | − | 5.92821e9i | − | 0.356899i | −0.983949 | − | 0.178450i | \(-0.942892\pi\) | ||
0.983949 | − | 0.178450i | \(-0.0571082\pi\) | |||||||
\(360\) | 3.23947e9 | − | 4.43456e9i | 0.192870 | − | 0.264022i | ||||
\(361\) | −1.01564e10 | −0.598013 | ||||||||
\(362\) | − | 4.34465e10i | − | 2.53000i | ||||||
\(363\) | 7.14785e8 | + | 1.40735e9i | 0.0411670 | + | 0.0810539i | ||||
\(364\) | −1.41401e8 | −0.00805467 | ||||||||
\(365\) | − | 2.39335e9i | − | 0.134845i | ||||||
\(366\) | 3.29876e10 | − | 1.67543e10i | 1.83834 | − | 0.933688i | ||||
\(367\) | 2.46231e10 | 1.35731 | 0.678655 | − | 0.734457i | \(-0.262563\pi\) | ||||
0.678655 | + | 0.734457i | \(0.262563\pi\) | |||||||
\(368\) | 1.00375e9i | 0.0547309i | ||||||||
\(369\) | −2.20098e10 | − | 1.60783e10i | −1.18716 | − | 0.867229i | ||||
\(370\) | −6.36529e9 | −0.339634 | ||||||||
\(371\) | 2.15980e7i | 0.00114004i | ||||||||
\(372\) | −2.00738e10 | − | 3.95234e10i | −1.04823 | − | 2.06387i | ||||
\(373\) | 2.71718e10 | 1.40373 | 0.701863 | − | 0.712312i | \(-0.252352\pi\) | ||||
0.701863 | + | 0.712312i | \(0.252352\pi\) | |||||||
\(374\) | − | 1.26877e10i | − | 0.648480i | ||||||
\(375\) | 7.24672e9 | − | 3.68058e9i | 0.366451 | − | 0.186119i | ||||
\(376\) | 4.97765e10 | 2.49042 | ||||||||
\(377\) | − | 6.87986e9i | − | 0.340576i | ||||||
\(378\) | −1.02357e8 | + | 6.30406e8i | −0.00501361 | + | 0.0308783i | ||||
\(379\) | 1.99323e10 | 0.966051 | 0.483026 | − | 0.875606i | \(-0.339538\pi\) | ||||
0.483026 | + | 0.875606i | \(0.339538\pi\) | |||||||
\(380\) | 5.31130e9i | 0.254722i | ||||||||
\(381\) | 1.24567e10 | + | 2.45261e10i | 0.591158 | + | 1.16393i | ||||
\(382\) | 1.97552e10 | 0.927746 | ||||||||
\(383\) | 1.73119e10i | 0.804545i | 0.915520 | + | 0.402272i | \(0.131780\pi\) | ||||
−0.915520 | + | 0.402272i | \(0.868220\pi\) | |||||||
\(384\) | −3.52488e10 | + | 1.79027e10i | −1.62114 | + | 0.823369i | ||||
\(385\) | 2.55202e7 | 0.00116156 | ||||||||
\(386\) | 1.24448e10i | 0.560580i | ||||||||
\(387\) | −2.34621e9 | + | 3.21177e9i | −0.104598 | + | 0.143186i | ||||
\(388\) | 6.55497e10 | 2.89230 | ||||||||
\(389\) | − | 4.43612e9i | − | 0.193734i | −0.995297 | − | 0.0968668i | \(-0.969118\pi\) | ||
0.995297 | − | 0.0968668i | \(-0.0308821\pi\) | |||||||
\(390\) | 8.63335e8 | + | 1.69982e9i | 0.0373182 | + | 0.0734760i | ||||
\(391\) | 2.16940e9 | 0.0928182 | ||||||||
\(392\) | − | 3.67269e10i | − | 1.55539i | ||||||
\(393\) | 6.78670e9 | − | 3.44694e9i | 0.284504 | − | 0.144499i | ||||
\(394\) | −6.96879e10 | −2.89183 | ||||||||
\(395\) | − | 2.89611e9i | − | 0.118967i | ||||||
\(396\) | 1.14464e10 | + | 8.36163e9i | 0.465465 | + | 0.340024i | ||||
\(397\) | 4.61270e9 | 0.185692 | 0.0928460 | − | 0.995680i | \(-0.470404\pi\) | ||||
0.0928460 | + | 0.995680i | \(0.470404\pi\) | |||||||
\(398\) | − | 5.74579e9i | − | 0.228991i | ||||||
\(399\) | −1.33402e8 | − | 2.62655e8i | −0.00526344 | − | 0.0103632i | ||||
\(400\) | 1.81859e10 | 0.710387 | ||||||||
\(401\) | 3.92776e10i | 1.51903i | 0.650487 | + | 0.759517i | \(0.274565\pi\) | ||||
−0.650487 | + | 0.759517i | \(0.725435\pi\) | |||||||
\(402\) | −2.79972e10 | + | 1.42197e10i | −1.07204 | + | 0.544484i | ||||
\(403\) | 7.33960e9 | 0.278261 | ||||||||
\(404\) | 2.77739e10i | 1.04258i | ||||||||
\(405\) | 5.38601e9 | − | 1.71924e9i | 0.200192 | − | 0.0639024i | ||||
\(406\) | −1.25962e9 | −0.0463593 | ||||||||
\(407\) | − | 7.83600e9i | − | 0.285573i | ||||||
\(408\) | −2.46082e10 | − | 4.84512e10i | −0.888053 | − | 1.74849i | ||||
\(409\) | −4.04898e10 | −1.44695 | −0.723474 | − | 0.690352i | \(-0.757456\pi\) | ||||
−0.723474 | + | 0.690352i | \(0.757456\pi\) | |||||||
\(410\) | 1.48972e10i | 0.527193i | ||||||||
\(411\) | 4.57514e9 | − | 2.32370e9i | 0.160338 | − | 0.0814352i | ||||
\(412\) | −1.13143e10 | −0.392681 | ||||||||
\(413\) | − | 8.73130e8i | − | 0.0300109i | ||||||
\(414\) | −2.17754e9 | + | 2.98087e9i | −0.0741251 | + | 0.101471i | ||||
\(415\) | 5.77694e9 | 0.194763 | ||||||||
\(416\) | − | 1.98016e9i | − | 0.0661190i | ||||||
\(417\) | 1.72391e10 | + | 3.39422e10i | 0.570126 | + | 1.12252i | ||||
\(418\) | −9.95855e9 | −0.326205 | ||||||||
\(419\) | 3.01067e10i | 0.976805i | 0.872619 | + | 0.488402i | \(0.162420\pi\) | ||||
−0.872619 | + | 0.488402i | \(0.837580\pi\) | |||||||
\(420\) | 2.04337e8 | − | 1.03782e8i | 0.00656674 | − | 0.00333522i | ||||
\(421\) | −3.18581e10 | −1.01413 | −0.507063 | − | 0.861909i | \(-0.669269\pi\) | ||||
−0.507063 | + | 0.861909i | \(0.669269\pi\) | |||||||
\(422\) | − | 1.02891e10i | − | 0.324434i | ||||||
\(423\) | 4.13797e10 | + | 3.02281e10i | 1.29249 | + | 0.944167i | ||||
\(424\) | 3.12713e9 | 0.0967571 | ||||||||
\(425\) | − | 3.93054e10i | − | 1.20475i | ||||||
\(426\) | 1.70800e10 | + | 3.36289e10i | 0.518621 | + | 1.02112i | ||||
\(427\) | 7.36396e8 | 0.0221513 | ||||||||
\(428\) | 5.64694e10i | 1.68282i | ||||||||
\(429\) | −2.09257e9 | + | 1.06281e9i | −0.0617805 | + | 0.0313781i | ||||
\(430\) | 2.17387e9 | 0.0635858 | ||||||||
\(431\) | 2.29512e10i | 0.665115i | 0.943083 | + | 0.332558i | \(0.107912\pi\) | ||||
−0.943083 | + | 0.332558i | \(0.892088\pi\) | |||||||
\(432\) | 2.55502e10 | + | 4.14851e9i | 0.733601 | + | 0.119113i | ||||
\(433\) | −1.91534e10 | −0.544872 | −0.272436 | − | 0.962174i | \(-0.587829\pi\) | ||||
−0.272436 | + | 0.962174i | \(0.587829\pi\) | |||||||
\(434\) | − | 1.34380e9i | − | 0.0378769i | ||||||
\(435\) | 5.04950e9 | + | 9.94199e9i | 0.141023 | + | 0.277662i | ||||
\(436\) | 8.01648e10 | 2.21839 | ||||||||
\(437\) | − | 1.70276e9i | − | 0.0466904i | ||||||
\(438\) | 3.59305e10 | − | 1.82490e10i | 0.976263 | − | 0.495841i | ||||
\(439\) | −1.76811e10 | −0.476048 | −0.238024 | − | 0.971259i | \(-0.576500\pi\) | ||||
−0.238024 | + | 0.971259i | \(0.576500\pi\) | |||||||
\(440\) | − | 3.69502e9i | − | 0.0985839i | ||||||
\(441\) | 2.23034e10 | − | 3.05314e10i | 0.589679 | − | 0.807221i | ||||
\(442\) | 1.88653e10 | 0.494281 | ||||||||
\(443\) | 4.22211e10i | 1.09626i | 0.836392 | + | 0.548131i | \(0.184661\pi\) | ||||
−0.836392 | + | 0.548131i | \(0.815339\pi\) | |||||||
\(444\) | −3.18663e10 | − | 6.27418e10i | −0.819974 | − | 1.61445i | ||||
\(445\) | 1.28101e10 | 0.326673 | ||||||||
\(446\) | 4.86709e10i | 1.23007i | ||||||||
\(447\) | −2.10581e9 | + | 1.06953e9i | −0.0527459 | + | 0.0267895i | ||||
\(448\) | −9.11382e8 | −0.0226250 | ||||||||
\(449\) | 4.43622e10i | 1.09151i | 0.837945 | + | 0.545754i | \(0.183757\pi\) | ||||
−0.837945 | + | 0.545754i | \(0.816243\pi\) | |||||||
\(450\) | 5.40077e10 | + | 3.94528e10i | 1.31706 | + | 0.962118i | ||||
\(451\) | −1.83393e10 | −0.443278 | ||||||||
\(452\) | − | 1.27285e11i | − | 3.04947i | ||||||
\(453\) | −3.60862e10 | − | 7.10503e10i | −0.856936 | − | 1.68723i | ||||
\(454\) | −6.35995e10 | −1.49703 | ||||||||
\(455\) | 3.79459e7i | 0.000885358i | ||||||||
\(456\) | −3.80293e10 | + | 1.93149e10i | −0.879546 | + | 0.446718i | ||||
\(457\) | −6.38635e10 | −1.46416 | −0.732079 | − | 0.681220i | \(-0.761450\pi\) | ||||
−0.732079 | + | 0.681220i | \(0.761450\pi\) | |||||||
\(458\) | − | 1.31719e11i | − | 2.99355i | ||||||
\(459\) | 8.96622e9 | − | 5.52219e10i | 0.202003 | − | 1.24412i | ||||
\(460\) | 1.32469e9 | 0.0295858 | ||||||||
\(461\) | 7.38538e9i | 0.163519i | 0.996652 | + | 0.0817596i | \(0.0260540\pi\) | ||||
−0.996652 | + | 0.0817596i | \(0.973946\pi\) | |||||||
\(462\) | 1.94588e8 | + | 3.83126e8i | 0.00427119 | + | 0.00840957i | ||||
\(463\) | 5.59667e10 | 1.21788 | 0.608942 | − | 0.793215i | \(-0.291594\pi\) | ||||
0.608942 | + | 0.793215i | \(0.291594\pi\) | |||||||
\(464\) | 5.10523e10i | 1.10140i | ||||||||
\(465\) | −1.06064e10 | + | 5.38693e9i | −0.226858 | + | 0.115220i | ||||
\(466\) | 2.79144e10 | 0.591950 | ||||||||
\(467\) | − | 5.32082e10i | − | 1.11869i | −0.828934 | − | 0.559347i | \(-0.811052\pi\) | ||
0.828934 | − | 0.559347i | \(-0.188948\pi\) | |||||||
\(468\) | −1.24329e10 | + | 1.70195e10i | −0.259172 | + | 0.354784i | ||||
\(469\) | −6.24992e8 | −0.0129176 | ||||||||
\(470\) | − | 2.80076e10i | − | 0.573965i | ||||||
\(471\) | 8.78752e9 | + | 1.73018e10i | 0.178559 | + | 0.351567i | ||||
\(472\) | −1.26419e11 | −2.54708 | ||||||||
\(473\) | 2.67615e9i | 0.0534645i | ||||||||
\(474\) | 4.34783e10 | − | 2.20825e10i | 0.861309 | − | 0.437456i | ||||
\(475\) | −3.08507e10 | −0.606025 | ||||||||
\(476\) | − | 2.26780e9i | − | 0.0441751i | ||||||
\(477\) | 2.59961e9 | + | 1.89903e9i | 0.0502152 | + | 0.0366825i | ||||
\(478\) | −6.34943e10 | −1.21625 | ||||||||
\(479\) | − | 2.22266e10i | − | 0.422213i | −0.977463 | − | 0.211106i | \(-0.932293\pi\) | ||
0.977463 | − | 0.211106i | \(-0.0677067\pi\) | |||||||
\(480\) | 1.45334e9 | + | 2.86150e9i | 0.0273781 | + | 0.0539049i | ||||
\(481\) | 1.16513e10 | 0.217668 | ||||||||
\(482\) | 9.57979e10i | 1.77487i | ||||||||
\(483\) | −6.55087e7 | + | 3.32716e7i | −0.00120368 | + | 0.000611344i | ||||
\(484\) | 9.53748e9 | 0.173801 | ||||||||
\(485\) | − | 1.75907e10i | − | 0.317918i | ||||||
\(486\) | 6.68780e10 | + | 6.77492e10i | 1.19878 | + | 1.21439i | ||||
\(487\) | −1.07915e11 | −1.91851 | −0.959257 | − | 0.282534i | \(-0.908825\pi\) | ||||
−0.959257 | + | 0.282534i | \(0.908825\pi\) | |||||||
\(488\) | − | 1.06621e11i | − | 1.88003i | ||||||
\(489\) | −1.65622e10 | − | 3.26094e10i | −0.289656 | − | 0.570305i | ||||
\(490\) | −2.06650e10 | −0.358469 | ||||||||
\(491\) | 3.87397e10i | 0.666547i | 0.942830 | + | 0.333274i | \(0.108153\pi\) | ||||
−0.942830 | + | 0.333274i | \(0.891847\pi\) | |||||||
\(492\) | −1.46840e11 | + | 7.45794e10i | −2.50601 | + | 1.27280i | ||||
\(493\) | 1.10340e11 | 1.86786 | ||||||||
\(494\) | − | 1.48073e10i | − | 0.248638i | ||||||
\(495\) | 2.24389e9 | − | 3.07170e9i | 0.0373750 | − | 0.0511633i | ||||
\(496\) | −5.44639e10 | −0.899874 | ||||||||
\(497\) | 7.50713e8i | 0.0123041i | ||||||||
\(498\) | 4.40484e10 | + | 8.67272e10i | 0.716165 | + | 1.41006i | ||||
\(499\) | −3.37873e10 | −0.544943 | −0.272471 | − | 0.962164i | \(-0.587841\pi\) | ||||
−0.272471 | + | 0.962164i | \(0.587841\pi\) | |||||||
\(500\) | − | 4.91105e10i | − | 0.785768i | ||||||
\(501\) | 3.72379e10 | − | 1.89130e10i | 0.591064 | − | 0.300199i | ||||
\(502\) | 1.22593e11 | 1.93041 | ||||||||
\(503\) | − | 3.41165e10i | − | 0.532957i | −0.963841 | − | 0.266479i | \(-0.914140\pi\) | ||
0.963841 | − | 0.266479i | \(-0.0858602\pi\) | |||||||
\(504\) | 1.48617e9 | + | 1.08565e9i | 0.0230328 | + | 0.0168256i | ||||
\(505\) | 7.45329e9 | 0.114599 | ||||||||
\(506\) | 2.48376e9i | 0.0378885i | ||||||||
\(507\) | 2.83405e10 | + | 5.57999e10i | 0.428920 | + | 0.844503i | ||||
\(508\) | 1.66212e11 | 2.49578 | ||||||||
\(509\) | − | 8.29669e10i | − | 1.23604i | −0.786161 | − | 0.618022i | \(-0.787934\pi\) | ||
0.786161 | − | 0.618022i | \(-0.212066\pi\) | |||||||
\(510\) | −2.72619e10 | + | 1.38462e10i | −0.402973 | + | 0.204669i | ||||
\(511\) | 8.02092e8 | 0.0117636 | ||||||||
\(512\) | 9.41589e10i | 1.37019i | ||||||||
\(513\) | −4.33436e10 | − | 7.03757e9i | −0.625828 | − | 0.101614i | ||||
\(514\) | −5.80395e10 | −0.831518 | ||||||||
\(515\) | 3.03627e9i | 0.0431630i | ||||||||
\(516\) | 1.08830e10 | + | 2.14275e10i | 0.153514 | + | 0.302255i | ||||
\(517\) | 3.44789e10 | 0.482604 | ||||||||
\(518\) | − | 2.13322e9i | − | 0.0296290i | ||||||
\(519\) | −2.86763e10 | + | 1.45646e10i | −0.395234 | + | 0.200738i | ||||
\(520\) | 5.49410e9 | 0.0751421 | ||||||||
\(521\) | 6.81143e9i | 0.0924458i | 0.998931 | + | 0.0462229i | \(0.0147184\pi\) | ||||
−0.998931 | + | 0.0462229i | \(0.985282\pi\) | |||||||
\(522\) | −1.10754e11 | + | 1.51613e11i | −1.49168 | + | 2.04199i | ||||
\(523\) | 5.27677e9 | 0.0705280 | 0.0352640 | − | 0.999378i | \(-0.488773\pi\) | ||||
0.0352640 | + | 0.999378i | \(0.488773\pi\) | |||||||
\(524\) | − | 4.59930e10i | − | 0.610051i | ||||||
\(525\) | 6.02818e8 | + | 1.18689e9i | 0.00793503 | + | 0.0156233i | ||||
\(526\) | 1.24135e11 | 1.62162 | ||||||||
\(527\) | 1.17713e11i | 1.52610i | ||||||||
\(528\) | 1.55280e10 | − | 7.88663e9i | 0.199793 | − | 0.101474i | ||||
\(529\) | 7.78863e10 | 0.994577 | ||||||||
\(530\) | − | 1.75954e9i | − | 0.0222995i | ||||||
\(531\) | −1.05093e11 | − | 7.67709e10i | −1.32189 | − | 0.965648i | ||||
\(532\) | −1.78000e9 | −0.0222214 | ||||||||
\(533\) | − | 2.72685e10i | − | 0.337873i | ||||||
\(534\) | 9.76756e10 | + | 1.92314e11i | 1.20122 | + | 2.36508i | ||||
\(535\) | 1.51539e10 | 0.184974 | ||||||||
\(536\) | 9.04912e10i | 1.09635i | ||||||||
\(537\) | −5.67492e10 | + | 2.88227e10i | −0.682437 | + | 0.346607i | ||||
\(538\) | −6.77780e10 | −0.809021 | ||||||||
\(539\) | − | 2.54397e10i | − | 0.301410i | ||||||
\(540\) | 5.47499e9 | − | 3.37198e10i | 0.0643885 | − | 0.396561i | ||||
\(541\) | −6.44764e10 | −0.752682 | −0.376341 | − | 0.926481i | \(-0.622818\pi\) | ||||
−0.376341 | + | 0.926481i | \(0.622818\pi\) | |||||||
\(542\) | − | 2.59112e11i | − | 3.00255i | ||||||
\(543\) | −5.83687e10 | − | 1.14922e11i | −0.671399 | − | 1.32192i | ||||
\(544\) | 3.17579e10 | 0.362624 | ||||||||
\(545\) | − | 2.15127e10i | − | 0.243842i | ||||||
\(546\) | −5.69668e8 | + | 2.89332e8i | −0.00640990 | + | 0.00325556i | ||||
\(547\) | 1.11191e11 | 1.24199 | 0.620996 | − | 0.783814i | \(-0.286728\pi\) | ||||
0.620996 | + | 0.783814i | \(0.286728\pi\) | |||||||
\(548\) | − | 3.10054e10i | − | 0.343807i | ||||||
\(549\) | 6.47484e10 | − | 8.86352e10i | 0.712754 | − | 0.975701i | ||||
\(550\) | 4.50009e10 | 0.491779 | ||||||||
\(551\) | − | 8.66055e10i | − | 0.939592i | ||||||
\(552\) | 4.81733e9 | + | 9.48486e9i | 0.0518859 | + | 0.102159i | ||||
\(553\) | 9.70584e8 | 0.0103785 | ||||||||
\(554\) | 1.23390e11i | 1.30990i | ||||||||
\(555\) | −1.68371e10 | + | 8.55152e9i | −0.177458 | + | 0.0901304i | ||||
\(556\) | 2.30024e11 | 2.40699 | ||||||||
\(557\) | 1.69283e11i | 1.75870i | 0.476175 | + | 0.879351i | \(0.342023\pi\) | ||||
−0.476175 | + | 0.879351i | \(0.657977\pi\) | |||||||
\(558\) | −1.61744e11 | − | 1.18155e11i | −1.66837 | − | 1.21875i | ||||
\(559\) | −3.97915e9 | −0.0407515 | ||||||||
\(560\) | − | 2.81579e8i | − | 0.00286318i | ||||||
\(561\) | −1.70454e10 | − | 3.35609e10i | −0.172090 | − | 0.338830i | ||||
\(562\) | −2.08598e11 | −2.09105 | ||||||||
\(563\) | − | 1.35792e11i | − | 1.35157i | −0.737097 | − | 0.675787i | \(-0.763804\pi\) | ||
0.737097 | − | 0.675787i | \(-0.236196\pi\) | |||||||
\(564\) | 2.76067e11 | − | 1.40214e11i | 2.72834 | − | 1.38571i | ||||
\(565\) | −3.41578e10 | −0.335194 | ||||||||
\(566\) | 1.62774e11i | 1.58606i | ||||||||
\(567\) | 5.76176e8 | + | 1.80503e9i | 0.00557472 | + | 0.0174643i | ||||
\(568\) | 1.08694e11 | 1.04427 | ||||||||
\(569\) | 8.05901e10i | 0.768834i | 0.923160 | + | 0.384417i | \(0.125597\pi\) | ||||
−0.923160 | + | 0.384417i | \(0.874403\pi\) | |||||||
\(570\) | 1.08679e10 | + | 2.13978e10i | 0.102955 | + | 0.202708i | ||||
\(571\) | 2.68487e9 | 0.0252569 | 0.0126284 | − | 0.999920i | \(-0.495980\pi\) | ||||
0.0126284 | + | 0.999920i | \(0.495980\pi\) | |||||||
\(572\) | 1.41812e10i | 0.132474i | ||||||||
\(573\) | 5.22556e10 | − | 2.65404e10i | 0.484746 | − | 0.246201i | ||||
\(574\) | −4.99256e9 | −0.0459913 | ||||||||
\(575\) | 7.69446e9i | 0.0703894i | ||||||||
\(576\) | −8.01342e10 | + | 1.09697e11i | −0.727995 | + | 0.996564i | ||||
\(577\) | −2.53602e10 | −0.228796 | −0.114398 | − | 0.993435i | \(-0.536494\pi\) | ||||
−0.114398 | + | 0.993435i | \(0.536494\pi\) | |||||||
\(578\) | 1.12108e11i | 1.00444i | ||||||||
\(579\) | 1.67191e10 | + | 3.29183e10i | 0.148764 | + | 0.292903i | ||||
\(580\) | 6.73762e10 | 0.595380 | ||||||||
\(581\) | 1.93605e9i | 0.0169907i | ||||||||
\(582\) | 2.64082e11 | − | 1.34126e11i | 2.30169 | − | 1.16902i | ||||
\(583\) | 2.16608e9 | 0.0187500 | ||||||||
\(584\) | − | 1.16133e11i | − | 0.998400i | ||||||
\(585\) | 4.56730e9 | + | 3.33643e9i | 0.0389974 | + | 0.0284878i | ||||
\(586\) | −1.78713e11 | −1.51554 | ||||||||
\(587\) | 5.37419e10i | 0.452648i | 0.974052 | + | 0.226324i | \(0.0726709\pi\) | ||||
−0.974052 | + | 0.226324i | \(0.927329\pi\) | |||||||
\(588\) | −1.03455e11 | − | 2.03692e11i | −0.865447 | − | 1.70398i | ||||
\(589\) | 9.23929e10 | 0.767675 | ||||||||
\(590\) | 7.11316e10i | 0.587023i | ||||||||
\(591\) | −1.84335e11 | + | 9.36231e10i | −1.51098 | + | 0.767420i | ||||
\(592\) | −8.64590e10 | −0.703920 | ||||||||
\(593\) | − | 1.91782e10i | − | 0.155092i | −0.996989 | − | 0.0775459i | \(-0.975292\pi\) | ||
0.996989 | − | 0.0775459i | \(-0.0247084\pi\) | |||||||
\(594\) | 6.32238e10 | + | 1.02655e10i | 0.507849 | + | 0.0824579i | ||||
\(595\) | −6.08579e8 | −0.00485567 | ||||||||
\(596\) | 1.42709e10i | 0.113101i | ||||||||
\(597\) | −7.71925e9 | − | 1.51985e10i | −0.0607684 | − | 0.119647i | ||||
\(598\) | −3.69308e9 | −0.0288792 | ||||||||
\(599\) | 1.07951e11i | 0.838530i | 0.907864 | + | 0.419265i | \(0.137712\pi\) | ||||
−0.907864 | + | 0.419265i | \(0.862288\pi\) | |||||||
\(600\) | 1.71847e11 | − | 8.72806e10i | 1.32598 | − | 0.673462i | ||||
\(601\) | 3.28941e10 | 0.252128 | 0.126064 | − | 0.992022i | \(-0.459766\pi\) | ||||
0.126064 | + | 0.992022i | \(0.459766\pi\) | |||||||
\(602\) | 7.28537e8i | 0.00554709i | ||||||||
\(603\) | −5.49531e10 | + | 7.52262e10i | −0.415646 | + | 0.568984i | ||||
\(604\) | −4.81503e11 | −3.61786 | ||||||||
\(605\) | − | 2.55944e9i | − | 0.0191040i | ||||||
\(606\) | 5.68303e10 | + | 1.11893e11i | 0.421395 | + | 0.829687i | ||||
\(607\) | −1.99786e11 | −1.47167 | −0.735836 | − | 0.677159i | \(-0.763211\pi\) | ||||
−0.735836 | + | 0.677159i | \(0.763211\pi\) | |||||||
\(608\) | − | 2.49267e10i | − | 0.182411i | ||||||
\(609\) | −3.33189e9 | + | 1.69226e9i | −0.0242227 | + | 0.0123026i | ||||
\(610\) | −5.99923e10 | −0.433287 | ||||||||
\(611\) | 5.12664e10i | 0.367848i | ||||||||
\(612\) | −2.72961e11 | − | 1.99399e11i | −1.94578 | − | 1.42141i | ||||
\(613\) | −1.94014e10 | −0.137402 | −0.0687008 | − | 0.997637i | \(-0.521885\pi\) | ||||
−0.0687008 | + | 0.997637i | \(0.521885\pi\) | |||||||
\(614\) | − | 3.31973e11i | − | 2.33576i | ||||||
\(615\) | 2.00139e10 | + | 3.94054e10i | 0.139904 | + | 0.275458i | ||||
\(616\) | 1.23832e9 | 0.00860026 | ||||||||
\(617\) | 2.03207e11i | 1.40216i | 0.713083 | + | 0.701080i | \(0.247298\pi\) | ||||
−0.713083 | + | 0.701080i | \(0.752702\pi\) | |||||||
\(618\) | −4.55825e10 | + | 2.31512e10i | −0.312496 | + | 0.158715i | ||||
\(619\) | 1.64997e10 | 0.112386 | 0.0561932 | − | 0.998420i | \(-0.482104\pi\) | ||||
0.0561932 | + | 0.998420i | \(0.482104\pi\) | |||||||
\(620\) | 7.18785e10i | 0.486444i | ||||||||
\(621\) | −1.75524e9 | + | 1.08103e10i | −0.0118024 | + | 0.0726895i | ||||
\(622\) | −4.25950e11 | −2.84576 | ||||||||
\(623\) | 4.29310e9i | 0.0284983i | ||||||||
\(624\) | 1.17266e10 | + | 2.30885e10i | 0.0773451 | + | 0.152285i | ||||
\(625\) | 1.32670e11 | 0.869469 | ||||||||
\(626\) | − | 1.50585e11i | − | 0.980585i | ||||||
\(627\) | −2.63419e10 | + | 1.33789e10i | −0.170442 | + | 0.0865668i | ||||
\(628\) | 1.17253e11 | 0.753851 | ||||||||
\(629\) | 1.86865e11i | 1.19378i | ||||||||
\(630\) | 6.10863e8 | − | 8.36220e8i | 0.00387776 | − | 0.00530833i | ||||
\(631\) | 7.99871e10 | 0.504548 | 0.252274 | − | 0.967656i | \(-0.418822\pi\) | ||||
0.252274 | + | 0.967656i | \(0.418822\pi\) | |||||||
\(632\) | − | 1.40529e11i | − | 0.880840i | ||||||
\(633\) | −1.38230e10 | − | 2.72162e10i | −0.0860968 | − | 0.169517i | ||||
\(634\) | −3.29844e10 | −0.204151 | ||||||||
\(635\) | − | 4.46039e10i | − | 0.274333i | ||||||
\(636\) | 1.73435e10 | − | 8.80870e9i | 0.106001 | − | 0.0538373i | ||||
\(637\) | 3.78262e10 | 0.229739 | ||||||||
\(638\) | 1.26328e11i | 0.762462i | ||||||||
\(639\) | 9.03584e10 | + | 6.60072e10i | 0.541957 | + | 0.395902i | ||||
\(640\) | 6.41045e10 | 0.382093 | ||||||||
\(641\) | 2.36630e11i | 1.40165i | 0.713335 | + | 0.700823i | \(0.247184\pi\) | ||||
−0.713335 | + | 0.700823i | \(0.752816\pi\) | |||||||
\(642\) | 1.15547e11 | + | 2.27500e11i | 0.680169 | + | 1.33919i | ||||
\(643\) | 5.35545e10 | 0.313294 | 0.156647 | − | 0.987655i | \(-0.449931\pi\) | ||||
0.156647 | + | 0.987655i | \(0.449931\pi\) | |||||||
\(644\) | 4.43948e8i | 0.00258100i | ||||||||
\(645\) | 5.75021e9 | − | 2.92051e9i | 0.0332235 | − | 0.0168741i | ||||
\(646\) | 2.37481e11 | 1.36364 | ||||||||
\(647\) | − | 5.97099e10i | − | 0.340745i | −0.985380 | − | 0.170372i | \(-0.945503\pi\) | ||
0.985380 | − | 0.170372i | \(-0.0544970\pi\) | |||||||
\(648\) | 2.61346e11 | − | 8.34233e10i | 1.48223 | − | 0.473137i | ||||
\(649\) | −8.75668e10 | −0.493583 | ||||||||
\(650\) | 6.69115e10i | 0.374841i | ||||||||
\(651\) | −1.80534e9 | − | 3.55455e9i | −0.0100516 | − | 0.0197907i | ||||
\(652\) | −2.20992e11 | −1.22288 | ||||||||
\(653\) | − | 2.94711e11i | − | 1.62085i | −0.585841 | − | 0.810426i | \(-0.699236\pi\) | ||
0.585841 | − | 0.810426i | \(-0.300764\pi\) | |||||||
\(654\) | 3.22963e11 | − | 1.64032e11i | 1.76539 | − | 0.896636i | ||||
\(655\) | −1.23425e10 | −0.0670560 | ||||||||
\(656\) | 2.02347e11i | 1.09265i | ||||||||
\(657\) | 7.05248e10 | − | 9.65426e10i | 0.378513 | − | 0.518152i | ||||
\(658\) | 9.38629e9 | 0.0500715 | ||||||||
\(659\) | − | 3.57804e10i | − | 0.189716i | −0.995491 | − | 0.0948579i | \(-0.969760\pi\) | ||
0.995491 | − | 0.0948579i | \(-0.0302397\pi\) | |||||||
\(660\) | −1.04084e10 | − | 2.04931e10i | −0.0548538 | − | 0.108002i | ||||
\(661\) | 1.26426e11 | 0.662263 | 0.331132 | − | 0.943585i | \(-0.392570\pi\) | ||||
0.331132 | + | 0.943585i | \(0.392570\pi\) | |||||||
\(662\) | − | 4.37206e11i | − | 2.27643i | ||||||
\(663\) | 4.99015e10 | − | 2.53448e10i | 0.258261 | − | 0.131170i | ||||
\(664\) | 2.80316e11 | 1.44203 | ||||||||
\(665\) | 4.77673e8i | 0.00244255i | ||||||||
\(666\) | −2.56762e11 | − | 1.87566e11i | −1.30507 | − | 0.953359i | ||||
\(667\) | −2.16002e10 | −0.109133 | ||||||||
\(668\) | − | 2.52359e11i | − | 1.26740i | ||||||
\(669\) | 6.53876e10 | + | 1.28742e11i | 0.326430 | + | 0.642711i | ||||
\(670\) | 5.09165e10 | 0.252673 | ||||||||
\(671\) | − | 7.38536e10i | − | 0.364319i | ||||||
\(672\) | −9.58983e8 | + | 4.87064e8i | −0.00470255 | + | 0.00238841i | ||||
\(673\) | −7.02840e10 | −0.342607 | −0.171304 | − | 0.985218i | \(-0.554798\pi\) | ||||
−0.171304 | + | 0.985218i | \(0.554798\pi\) | |||||||
\(674\) | 5.53382e11i | 2.68154i | ||||||||
\(675\) | 1.95862e11 | + | 3.18015e10i | 0.943484 | + | 0.153191i | ||||
\(676\) | 3.78152e11 | 1.81084 | ||||||||
\(677\) | − | 9.16109e10i | − | 0.436106i | −0.975937 | − | 0.218053i | \(-0.930029\pi\) | ||
0.975937 | − | 0.218053i | \(-0.0699706\pi\) | |||||||
\(678\) | −2.60448e11 | − | 5.12799e11i | −1.23255 | − | 2.42677i | ||||
\(679\) | 5.89522e9 | 0.0277345 | ||||||||
\(680\) | 8.81149e10i | 0.412110i | ||||||||
\(681\) | −1.68230e11 | + | 8.54435e10i | −0.782196 | + | 0.397275i | ||||
\(682\) | −1.34770e11 | −0.622955 | ||||||||
\(683\) | − | 1.83141e11i | − | 0.841596i | −0.907154 | − | 0.420798i | \(-0.861750\pi\) | ||
0.907154 | − | 0.420798i | \(-0.138250\pi\) | |||||||
\(684\) | −1.56508e11 | + | 2.14246e11i | −0.715010 | + | 0.978789i | ||||
\(685\) | −8.32049e9 | −0.0377908 | ||||||||
\(686\) | − | 1.38534e10i | − | 0.0625548i | ||||||
\(687\) | −1.76959e11 | − | 3.48417e11i | −0.794414 | − | 1.56413i | ||||
\(688\) | 2.95275e10 | 0.131787 | ||||||||
\(689\) | 3.22073e9i | 0.0142915i | ||||||||
\(690\) | 5.33683e9 | − | 2.71055e9i | 0.0235443 | − | 0.0119581i | ||||
\(691\) | −1.70702e11 | −0.748731 | −0.374366 | − | 0.927281i | \(-0.622140\pi\) | ||||
−0.374366 | + | 0.927281i | \(0.622140\pi\) | |||||||
\(692\) | 1.94337e11i | 0.847485i | ||||||||
\(693\) | 1.02943e9 | + | 7.52004e8i | 0.00446338 | + | 0.00326052i | ||||
\(694\) | −3.40852e11 | −1.46936 | ||||||||
\(695\) | − | 6.17283e10i | − | 0.264573i | ||||||
\(696\) | 2.45018e11 | + | 4.82417e11i | 1.04415 | + | 2.05582i | ||||
\(697\) | 4.37335e11 | 1.85303 | ||||||||
\(698\) | 6.94484e11i | 2.92577i | ||||||||
\(699\) | 7.38379e10 | − | 3.75020e10i | 0.309293 | − | 0.157089i | ||||
\(700\) | 8.04348e9 | 0.0335005 | ||||||||
\(701\) | 2.78433e11i | 1.15305i | 0.817079 | + | 0.576526i | \(0.195592\pi\) | ||||
−0.817079 | + | 0.576526i | \(0.804408\pi\) | |||||||
\(702\) | −1.52636e10 | + | 9.40071e10i | −0.0628506 | + | 0.387090i | ||||
\(703\) | 1.46670e11 | 0.600508 | ||||||||
\(704\) | 9.14031e10i | 0.372109i | ||||||||
\(705\) | −3.76272e10 | − | 7.40844e10i | −0.152316 | − | 0.299896i | ||||
\(706\) | 5.39340e11 | 2.17092 | ||||||||
\(707\) | 2.49784e9i | 0.00999742i | ||||||||
\(708\) | −7.01135e11 | + | 3.56104e11i | −2.79041 | + | 1.41724i | ||||
\(709\) | 2.55436e11 | 1.01088 | 0.505438 | − | 0.862863i | \(-0.331331\pi\) | ||||
0.505438 | + | 0.862863i | \(0.331331\pi\) | |||||||
\(710\) | − | 6.11586e10i | − | 0.240671i | ||||||
\(711\) | 8.53397e10 | − | 1.16823e11i | 0.333943 | − | 0.457140i | ||||
\(712\) | 6.21589e11 | 2.41871 | ||||||||
\(713\) | − | 2.30437e10i | − | 0.0891648i | ||||||
\(714\) | −4.64034e9 | − | 9.13638e9i | −0.0178549 | − | 0.0351545i | ||||
\(715\) | 3.80562e9 | 0.0145613 | ||||||||
\(716\) | 3.84585e11i | 1.46332i | ||||||||
\(717\) | −1.67952e11 | + | 8.53022e10i | −0.635490 | + | 0.322763i | ||||
\(718\) | −1.61855e11 | −0.609014 | ||||||||
\(719\) | − | 4.37975e11i | − | 1.63883i | −0.573201 | − | 0.819415i | \(-0.694299\pi\) | ||
0.573201 | − | 0.819415i | \(-0.305701\pi\) | |||||||
\(720\) | −3.38918e10 | − | 2.47582e10i | −0.126115 | − | 0.0921273i | ||||
\(721\) | −1.01756e9 | −0.00376545 | ||||||||
\(722\) | 2.77294e11i | 1.02045i | ||||||||
\(723\) | 1.28701e11 | + | 2.53400e11i | 0.471008 | + | 0.927370i | ||||
\(724\) | −7.78821e11 | −2.83455 | ||||||||
\(725\) | 3.91355e11i | 1.41651i | ||||||||
\(726\) | 3.84240e10 | − | 1.95154e10i | 0.138311 | − | 0.0702475i | ||||
\(727\) | −3.88581e11 | −1.39105 | −0.695527 | − | 0.718500i | \(-0.744829\pi\) | ||||
−0.695527 | + | 0.718500i | \(0.744829\pi\) | |||||||
\(728\) | 1.84126e9i | 0.00655524i | ||||||||
\(729\) | 2.67921e11 | + | 8.93587e10i | 0.948628 | + | 0.316393i | ||||
\(730\) | −6.53443e10 | −0.230100 | ||||||||
\(731\) | − | 6.38180e10i | − | 0.223498i | ||||||
\(732\) | −3.00337e11 | − | 5.91336e11i | −1.04608 | − | 2.05963i | ||||
\(733\) | 3.28148e11 | 1.13672 | 0.568360 | − | 0.822780i | \(-0.307578\pi\) | ||||
0.568360 | + | 0.822780i | \(0.307578\pi\) | |||||||
\(734\) | − | 6.72272e11i | − | 2.31612i | ||||||
\(735\) | −5.46621e10 | + | 2.77627e10i | −0.187300 | + | 0.0951288i | ||||
\(736\) | −6.21697e9 | −0.0211869 | ||||||||
\(737\) | 6.26809e10i | 0.212454i | ||||||||
\(738\) | −4.38976e11 | + | 6.00921e11i | −1.47984 | + | 2.02578i | ||||
\(739\) | 1.11991e11 | 0.375497 | 0.187748 | − | 0.982217i | \(-0.439881\pi\) | ||||
0.187748 | + | 0.982217i | \(0.439881\pi\) | |||||||
\(740\) | 1.14104e11i | 0.380517i | ||||||||
\(741\) | −1.98931e10 | − | 3.91676e10i | −0.0659825 | − | 0.129913i | ||||
\(742\) | 5.89679e8 | 0.00194536 | ||||||||
\(743\) | − | 5.06571e11i | − | 1.66221i | −0.556118 | − | 0.831103i | \(-0.687710\pi\) | ||
0.556118 | − | 0.831103i | \(-0.312290\pi\) | |||||||
\(744\) | −5.14655e11 | + | 2.61391e11i | −1.67967 | + | 0.853099i | ||||
\(745\) | 3.82969e9 | 0.0124319 | ||||||||
\(746\) | − | 7.41855e11i | − | 2.39532i | ||||||
\(747\) | 2.33029e11 | + | 1.70229e11i | 0.748390 | + | 0.546703i | ||||
\(748\) | −2.27440e11 | −0.726540 | ||||||||
\(749\) | 5.07858e9i | 0.0161367i | ||||||||
\(750\) | −1.00489e11 | − | 1.97853e11i | −0.317594 | − | 0.625314i | ||||
\(751\) | 2.89932e11 | 0.911458 | 0.455729 | − | 0.890119i | \(-0.349379\pi\) | ||||
0.455729 | + | 0.890119i | \(0.349379\pi\) | |||||||
\(752\) | − | 3.80425e11i | − | 1.18959i | ||||||
\(753\) | 3.24276e11 | − | 1.64698e11i | 1.00864 | − | 0.512282i | ||||
\(754\) | −1.87837e11 | −0.581160 | ||||||||
\(755\) | 1.29214e11i | 0.397670i | ||||||||
\(756\) | 1.13006e10 | + | 1.83485e9i | 0.0345952 | + | 0.00561712i | ||||
\(757\) | −5.49298e11 | −1.67273 | −0.836363 | − | 0.548176i | \(-0.815322\pi\) | ||||
−0.836363 | + | 0.548176i | \(0.815322\pi\) | |||||||
\(758\) | − | 5.44200e11i | − | 1.64847i | ||||||
\(759\) | 3.33683e9 | + | 6.56991e9i | 0.0100547 | + | 0.0197967i | ||||
\(760\) | 6.91612e10 | 0.207304 | ||||||||
\(761\) | − | 3.35949e11i | − | 1.00169i | −0.865536 | − | 0.500847i | \(-0.833022\pi\) | ||
0.865536 | − | 0.500847i | \(-0.166978\pi\) | |||||||
\(762\) | 6.69622e11 | − | 3.40099e11i | 1.98614 | − | 1.00875i | ||||
\(763\) | 7.20963e9 | 0.0212723 | ||||||||
\(764\) | − | 3.54132e11i | − | 1.03942i | ||||||
\(765\) | −5.35100e10 | + | 7.32507e10i | −0.156239 | + | 0.213878i | ||||
\(766\) | 4.72658e11 | 1.37288 | ||||||||
\(767\) | − | 1.30203e11i | − | 0.376217i | ||||||
\(768\) | 2.94363e11 | + | 5.79573e11i | 0.846132 | + | 1.66595i | ||||
\(769\) | −4.79303e11 | −1.37058 | −0.685290 | − | 0.728270i | \(-0.740325\pi\) | ||||
−0.685290 | + | 0.728270i | \(0.740325\pi\) | |||||||
\(770\) | − | 6.96765e8i | − | 0.00198209i | ||||||
\(771\) | −1.53523e11 | + | 7.79739e10i | −0.434467 | + | 0.220664i | ||||
\(772\) | 2.23085e11 | 0.628060 | ||||||||
\(773\) | 5.74251e10i | 0.160836i | 0.996761 | + | 0.0804180i | \(0.0256255\pi\) | ||||
−0.996761 | + | 0.0804180i | \(0.974374\pi\) | |||||||
\(774\) | 8.76892e10 | + | 6.40574e10i | 0.244333 | + | 0.178487i | ||||
\(775\) | −4.17507e11 | −1.15733 | ||||||||
\(776\) | − | 8.53556e11i | − | 2.35388i | ||||||
\(777\) | −2.86590e9 | − | 5.64269e9i | −0.00786280 | − | 0.0154811i | ||||
\(778\) | −1.21117e11 | −0.330588 | ||||||||
\(779\) | − | 3.43264e11i | − | 0.932133i | ||||||
\(780\) | 3.04710e10 | − | 1.54761e10i | 0.0823207 | − | 0.0418104i | ||||
\(781\) | 7.52895e10 | 0.202362 | ||||||||
\(782\) | − | 5.92300e10i | − | 0.158385i | ||||||
\(783\) | −8.92745e10 | + | 5.49832e11i | −0.237509 | + | 1.46279i | ||||
\(784\) | −2.80691e11 | −0.742958 | ||||||||
\(785\) | − | 3.14656e10i | − | 0.0828623i | ||||||
\(786\) | −9.41099e10 | − | 1.85293e11i | −0.246573 | − | 0.485478i | ||||
\(787\) | −3.28821e10 | −0.0857158 | −0.0428579 | − | 0.999081i | \(-0.513646\pi\) | ||||
−0.0428579 | + | 0.999081i | \(0.513646\pi\) | |||||||
\(788\) | 1.24923e12i | 3.23993i | ||||||||
\(789\) | 3.28355e11 | − | 1.66770e11i | 0.847297 | − | 0.430339i | ||||
\(790\) | −7.90710e10 | −0.203006 | ||||||||
\(791\) | − | 1.14474e10i | − | 0.0292416i | ||||||
\(792\) | 1.08881e11 | − | 1.49049e11i | 0.276727 | − | 0.378816i | ||||
\(793\) | 1.09813e11 | 0.277689 | ||||||||
\(794\) | − | 1.25938e11i | − | 0.316865i | ||||||
\(795\) | −2.36387e9 | − | 4.65424e9i | −0.00591773 | − | 0.0116514i | ||||
\(796\) | −1.02999e11 | −0.256555 | ||||||||
\(797\) | 3.68934e11i | 0.914357i | 0.889375 | + | 0.457178i | \(0.151140\pi\) | ||||
−0.889375 | + | 0.457178i | \(0.848860\pi\) | |||||||
\(798\) | −7.17113e9 | + | 3.64219e9i | −0.0176838 | + | 0.00898154i | ||||
\(799\) | −8.22216e11 | −2.01743 | ||||||||
\(800\) | 1.12639e11i | 0.274998i | ||||||||
\(801\) | 5.16733e11 | + | 3.77476e11i | 1.25527 | + | 0.916979i | ||||
\(802\) | 1.07237e12 | 2.59208 | ||||||||
\(803\) | − | 8.04423e10i | − | 0.193474i | ||||||
\(804\) | 2.54901e11 | + | 5.01877e11i | 0.610025 | + | 1.20108i | ||||
\(805\) | 1.19136e8 | 0.000283700 | ||||||||
\(806\) | − | 2.00389e11i | − | 0.474825i | ||||||
\(807\) | −1.79283e11 | + | 9.10572e10i | −0.422712 | + | 0.214694i | ||||
\(808\) | 3.61657e11 | 0.848500 | ||||||||
\(809\) | − | 2.83299e11i | − | 0.661380i | −0.943739 | − | 0.330690i | \(-0.892719\pi\) | ||
0.943739 | − | 0.330690i | \(-0.107281\pi\) | |||||||
\(810\) | −4.69396e10 | − | 1.47051e11i | −0.109043 | − | 0.341608i | ||||
\(811\) | −6.40995e11 | −1.48174 | −0.740868 | − | 0.671650i | \(-0.765586\pi\) | ||||
−0.740868 | + | 0.671650i | \(0.765586\pi\) | |||||||
\(812\) | 2.25800e10i | 0.0519397i | ||||||||
\(813\) | −3.48107e11 | − | 6.85390e11i | −0.796803 | − | 1.56883i | ||||
\(814\) | −2.13942e11 | −0.487302 | ||||||||
\(815\) | 5.93045e10i | 0.134418i | ||||||||
\(816\) | −3.70296e11 | + | 1.88072e11i | −0.835196 | + | 0.424193i | ||||
\(817\) | −5.00906e10 | −0.112426 | ||||||||
\(818\) | 1.10547e12i | 2.46907i | ||||||||
\(819\) | −1.11815e9 | + | 1.53065e9i | −0.00248522 | + | 0.00340206i | ||||
\(820\) | 2.67047e11 | 0.590654 | ||||||||
\(821\) | 2.09233e11i | 0.460530i | 0.973128 | + | 0.230265i | \(0.0739593\pi\) | ||||
−0.973128 | + | 0.230265i | \(0.926041\pi\) | |||||||
\(822\) | −6.34426e10 | − | 1.24912e11i | −0.138961 | − | 0.273601i | ||||
\(823\) | −1.50852e11 | −0.328815 | −0.164408 | − | 0.986393i | \(-0.552571\pi\) | ||||
−0.164408 | + | 0.986393i | \(0.552571\pi\) | |||||||
\(824\) | 1.47330e11i | 0.319581i | ||||||||
\(825\) | 1.19034e11 | − | 6.04570e10i | 0.256954 | − | 0.130506i | ||||
\(826\) | −2.38386e10 | −0.0512106 | ||||||||
\(827\) | 7.27889e11i | 1.55612i | 0.628189 | + | 0.778060i | \(0.283796\pi\) | ||||
−0.628189 | + | 0.778060i | \(0.716204\pi\) | |||||||
\(828\) | 5.34351e10 | + | 3.90346e10i | 0.113686 | + | 0.0830479i | ||||
\(829\) | −4.15800e11 | −0.880372 | −0.440186 | − | 0.897907i | \(-0.645088\pi\) | ||||
−0.440186 | + | 0.897907i | \(0.645088\pi\) | |||||||
\(830\) | − | 1.57725e11i | − | 0.332344i | ||||||
\(831\) | 1.65769e11 | + | 3.26384e11i | 0.347616 | + | 0.684423i | ||||
\(832\) | −1.35907e11 | −0.283627 | ||||||||
\(833\) | 6.06660e11i | 1.25998i | ||||||||
\(834\) | 9.26705e11 | − | 4.70670e11i | 1.91548 | − | 0.972864i | ||||
\(835\) | −6.77220e10 | −0.139310 | ||||||||
\(836\) | 1.78517e11i | 0.365472i | ||||||||
\(837\) | −5.86574e11 | − | 9.52402e10i | −1.19515 | − | 0.194052i | ||||
\(838\) | 8.21988e11 | 1.66682 | ||||||||
\(839\) | − | 1.98754e11i | − | 0.401114i | −0.979682 | − | 0.200557i | \(-0.935725\pi\) | ||
0.979682 | − | 0.200557i | \(-0.0642752\pi\) | |||||||
\(840\) | −1.35140e9 | − | 2.66077e9i | −0.00271435 | − | 0.00534430i | ||||
\(841\) | −5.98381e11 | −1.19617 | ||||||||
\(842\) | 8.69805e11i | 1.73051i | ||||||||
\(843\) | −5.51773e11 | + | 2.80244e11i | −1.09257 | + | 0.554914i | ||||
\(844\) | −1.84442e11 | −0.363488 | ||||||||
\(845\) | − | 1.01479e11i | − | 0.199045i | ||||||
\(846\) | 8.25300e11 | − | 1.12977e12i | 1.61113 | − | 2.20550i | ||||
\(847\) | 8.57754e8 | 0.00166659 | ||||||||
\(848\) | − | 2.38996e10i | − | 0.0462176i | ||||||
\(849\) | 2.18680e11 | + | 4.30561e11i | 0.420900 | + | 0.828713i | ||||
\(850\) | −1.07313e12 | −2.05579 | ||||||||
\(851\) | − | 3.65808e10i | − | 0.0697486i | ||||||
\(852\) | 6.02832e11 | − | 3.06176e11i | 1.14403 | − | 0.581049i | ||||
\(853\) | 5.03229e11 | 0.950538 | 0.475269 | − | 0.879841i | \(-0.342351\pi\) | ||||
0.475269 | + | 0.879841i | \(0.342351\pi\) | |||||||
\(854\) | − | 2.01054e10i | − | 0.0377991i | ||||||
\(855\) | 5.74944e10 | + | 4.19999e10i | 0.107587 | + | 0.0785930i | ||||
\(856\) | 7.35317e11 | 1.36955 | ||||||||
\(857\) | − | 3.25995e10i | − | 0.0604348i | −0.999543 | − | 0.0302174i | \(-0.990380\pi\) | ||
0.999543 | − | 0.0302174i | \(-0.00961997\pi\) | |||||||
\(858\) | 2.90173e10 | + | 5.71324e10i | 0.0535437 | + | 0.105422i | ||||
\(859\) | 4.46503e11 | 0.820071 | 0.410036 | − | 0.912070i | \(-0.365516\pi\) | ||||
0.410036 | + | 0.912070i | \(0.365516\pi\) | |||||||
\(860\) | − | 3.89688e10i | − | 0.0712399i | ||||||
\(861\) | −1.32061e10 | + | 6.70731e9i | −0.0240304 | + | 0.0122049i | ||||
\(862\) | 6.26625e11 | 1.13495 | ||||||||
\(863\) | − | 3.19673e11i | − | 0.576319i | −0.957582 | − | 0.288159i | \(-0.906957\pi\) | ||
0.957582 | − | 0.288159i | \(-0.0930433\pi\) | |||||||
\(864\) | −2.56949e10 | + | 1.58252e11i | −0.0461097 | + | 0.283985i | ||||
\(865\) | 5.21516e10 | 0.0931544 | ||||||||
\(866\) | 5.22935e11i | 0.929771i | ||||||||
\(867\) | 1.50612e11 | + | 2.96541e11i | 0.266553 | + | 0.524818i | ||||
\(868\) | −2.40889e10 | −0.0424363 | ||||||||
\(869\) | − | 9.73405e10i | − | 0.170693i | ||||||
\(870\) | 2.71441e11 | − | 1.37864e11i | 0.473803 | − | 0.240643i | ||||
\(871\) | −9.31998e10 | −0.161936 | ||||||||
\(872\) | − | 1.04387e12i | − | 1.80542i | ||||||
\(873\) | 5.18344e11 | − | 7.09569e11i | 0.892402 | − | 1.22162i | ||||
\(874\) | −4.64895e10 | −0.0796727 | ||||||||
\(875\) | − | 4.41676e9i | − | 0.00753479i | ||||||
\(876\) | −3.27131e11 | − | 6.44090e11i | −0.555527 | − | 1.09378i | ||||
\(877\) | 4.26579e11 | 0.721109 | 0.360555 | − | 0.932738i | \(-0.382587\pi\) | ||||
0.360555 | + | 0.932738i | \(0.382587\pi\) | |||||||
\(878\) | 4.82737e11i | 0.812330i | ||||||||
\(879\) | −4.72723e11 | + | 2.40095e11i | −0.791866 | + | 0.402186i | ||||
\(880\) | −2.82397e10 | −0.0470902 | ||||||||
\(881\) | − | 1.14290e12i | − | 1.89717i | −0.316528 | − | 0.948583i | \(-0.602517\pi\) | ||
0.316528 | − | 0.948583i | \(-0.397483\pi\) | |||||||
\(882\) | −8.33582e11 | − | 6.08936e11i | −1.37744 | − | 1.00623i | ||||
\(883\) | 1.50217e11 | 0.247102 | 0.123551 | − | 0.992338i | \(-0.460572\pi\) | ||||
0.123551 | + | 0.992338i | \(0.460572\pi\) | |||||||
\(884\) | − | 3.38179e11i | − | 0.553780i | ||||||
\(885\) | 9.55626e10 | + | 1.88154e11i | 0.155781 | + | 0.306719i | ||||
\(886\) | 1.15274e12 | 1.87066 | ||||||||
\(887\) | 2.38490e11i | 0.385280i | 0.981270 | + | 0.192640i | \(0.0617049\pi\) | ||||
−0.981270 | + | 0.192640i | \(0.938295\pi\) | |||||||
\(888\) | −8.16992e11 | + | 4.14947e11i | −1.31391 | + | 0.667331i | ||||
\(889\) | 1.49483e10 | 0.0239322 | ||||||||
\(890\) | − | 3.49748e11i | − | 0.557436i | ||||||
\(891\) | 1.81028e11 | − | 5.77851e10i | 0.287233 | − | 0.0916864i | ||||
\(892\) | 8.72475e11 | 1.37814 | ||||||||
\(893\) | 6.45355e11i | 1.01483i | ||||||||
\(894\) | 2.92009e10 | + | 5.74937e10i | 0.0457136 | + | 0.0900058i | ||||
\(895\) | 1.03206e11 | 0.160847 | ||||||||
\(896\) | 2.14836e10i | 0.0333330i | ||||||||
\(897\) | −9.76876e9 | + | 4.96152e9i | −0.0150893 | + | 0.00766381i | ||||
\(898\) | 1.21120e12 | 1.86255 | ||||||||
\(899\) | − | 1.17204e12i | − | 1.79434i | ||||||
\(900\) | 7.07231e11 | − | 9.68141e11i | 1.07793 | − | 1.47560i | ||||
\(901\) | −5.16544e10 | −0.0783805 | ||||||||
\(902\) | 5.00707e11i | 0.756410i | ||||||||
\(903\) | 9.78761e8 | + | 1.92709e9i | 0.00147206 | + | 0.00289835i | ||||
\(904\) | −1.65745e12 | −2.48179 | ||||||||
\(905\) | 2.09002e11i | 0.311570i | ||||||||
\(906\) | −1.93985e12 | + | 9.85242e11i | −2.87909 | + | 1.46228i | ||||
\(907\) | 1.46391e11 | 0.216315 | 0.108157 | − | 0.994134i | \(-0.465505\pi\) | ||||
0.108157 | + | 0.994134i | \(0.465505\pi\) | |||||||
\(908\) | 1.14008e12i | 1.67723i | ||||||||
\(909\) | 3.00649e11 | + | 2.19626e11i | 0.440357 | + | 0.321683i | ||||
\(910\) | 1.03602e9 | 0.00151078 | ||||||||
\(911\) | − | 5.04419e11i | − | 0.732349i | −0.930546 | − | 0.366175i | \(-0.880667\pi\) | ||
0.930546 | − | 0.366175i | \(-0.119333\pi\) | |||||||
\(912\) | 1.47617e11 | + | 2.90645e11i | 0.213382 | + | 0.420129i | ||||
\(913\) | 1.94167e11 | 0.279443 | ||||||||
\(914\) | 1.74363e12i | 2.49844i | ||||||||
\(915\) | −1.58689e11 | + | 8.05973e10i | −0.226392 | + | 0.114984i | ||||
\(916\) | −2.36119e12 | −3.35390 | ||||||||
\(917\) | − | 4.13638e9i | − | 0.00584983i | ||||||
\(918\) | −1.50769e12 | − | 2.44800e11i | −2.12296 | − | 0.344699i | ||||
\(919\) | 5.64585e11 | 0.791530 | 0.395765 | − | 0.918352i | \(-0.370479\pi\) | ||||
0.395765 | + | 0.918352i | \(0.370479\pi\) | |||||||
\(920\) | − | 1.72495e10i | − | 0.0240782i | ||||||
\(921\) | −4.45993e11 | − | 8.78118e11i | −0.619854 | − | 1.22043i | ||||
\(922\) | 2.01639e11 | 0.279030 | ||||||||
\(923\) | 1.11947e11i | 0.154244i | ||||||||
\(924\) | 6.86791e9 | − | 3.48819e9i | 0.00942187 | − | 0.00478533i | ||||
\(925\) | −6.62774e11 | −0.905312 | ||||||||
\(926\) | − | 1.52803e12i | − | 2.07820i | ||||||
\(927\) | −8.94698e10 | + | 1.22477e11i | −0.121159 | + | 0.165857i | ||||
\(928\) | −3.16206e11 | −0.426362 | ||||||||
\(929\) | − | 2.13830e11i | − | 0.287081i | −0.989644 | − | 0.143541i | \(-0.954151\pi\) | ||
0.989644 | − | 0.143541i | \(-0.0458488\pi\) | |||||||
\(930\) | 1.47076e11 | + | 2.89580e11i | 0.196613 | + | 0.387112i | ||||
\(931\) | 4.76166e11 | 0.633811 | ||||||||
\(932\) | − | 5.00394e11i | − | 0.663206i | ||||||
\(933\) | −1.12670e12 | + | 5.72248e11i | −1.48690 | + | 0.755193i | ||||
\(934\) | −1.45271e12 | −1.90894 | ||||||||
\(935\) | 6.10348e10i | 0.0798604i | ||||||||
\(936\) | 2.21620e11 | + | 1.61894e11i | 0.288739 | + | 0.210925i | ||||
\(937\) | 1.29643e12 | 1.68187 | 0.840934 | − | 0.541138i | \(-0.182006\pi\) | ||||
0.840934 | + | 0.541138i | \(0.182006\pi\) | |||||||
\(938\) | 1.70638e10i | 0.0220427i | ||||||||
\(939\) | −2.02306e11 | − | 3.98321e11i | −0.260223 | − | 0.512354i | ||||
\(940\) | −5.02065e11 | −0.643055 | ||||||||
\(941\) | − | 1.08479e12i | − | 1.38352i | −0.722126 | − | 0.691762i | \(-0.756835\pi\) | ||
0.722126 | − | 0.691762i | \(-0.243165\pi\) | |||||||
\(942\) | 4.72381e11 | − | 2.39921e11i | 0.599914 | − | 0.304694i | ||||
\(943\) | −8.56132e10 | −0.108266 | ||||||||
\(944\) | 9.66174e11i | 1.21665i | ||||||||
\(945\) | 4.92394e8 | − | 3.03260e9i | 0.000617426 | − | 0.00380266i | ||||
\(946\) | 7.30654e10 | 0.0912320 | ||||||||
\(947\) | − | 8.10922e11i | − | 1.00828i | −0.863623 | − | 0.504138i | \(-0.831810\pi\) | ||
0.863623 | − | 0.504138i | \(-0.168190\pi\) | |||||||
\(948\) | −3.95850e11 | − | 7.79392e11i | −0.490114 | − | 0.964989i | ||||
\(949\) | 1.19609e11 | 0.147469 | ||||||||
\(950\) | 8.42300e11i | 1.03412i | ||||||||
\(951\) | −8.72487e10 | + | 4.43133e10i | −0.106669 | + | 0.0541766i | ||||
\(952\) | −2.95302e10 | −0.0359517 | ||||||||
\(953\) | − | 4.62488e10i | − | 0.0560698i | −0.999607 | − | 0.0280349i | \(-0.991075\pi\) | ||
0.999607 | − | 0.0280349i | \(-0.00892495\pi\) | |||||||
\(954\) | 5.18482e10 | − | 7.09758e10i | 0.0625950 | − | 0.0856874i | ||||
\(955\) | −9.50336e10 | −0.114252 | ||||||||
\(956\) | 1.13820e12i | 1.36266i | ||||||||
\(957\) | 1.69717e11 | + | 3.34158e11i | 0.202339 | + | 0.398386i | ||||
\(958\) | −6.06841e11 | −0.720465 | ||||||||
\(959\) | − | 2.78847e9i | − | 0.00329679i | ||||||
\(960\) | 1.96397e11 | − | 9.97492e10i | 0.231233 | − | 0.117442i | ||||
\(961\) | 3.97473e11 | 0.466030 | ||||||||
\(962\) | − | 3.18109e11i | − | 0.371429i | ||||||
\(963\) | 6.11276e11 | + | 4.46540e11i | 0.710775 | + | 0.519225i | ||||
\(964\) | 1.71727e12 | 1.98852 | ||||||||
\(965\) | − | 5.98662e10i | − | 0.0690355i | ||||||
\(966\) | 9.08397e8 | + | 1.78855e9i | 0.00104320 | + | 0.00205396i | ||||
\(967\) | −2.00768e11 | −0.229609 | −0.114804 | − | 0.993388i | \(-0.536624\pi\) | ||||
−0.114804 | + | 0.993388i | \(0.536624\pi\) | |||||||
\(968\) | − | 1.24192e11i | − | 0.141447i | ||||||
\(969\) | 6.28173e11 | − | 3.19047e11i | 0.712499 | − | 0.361875i | ||||
\(970\) | −4.80268e11 | −0.542496 | ||||||||
\(971\) | 1.55116e12i | 1.74493i | 0.488675 | + | 0.872466i | \(0.337480\pi\) | ||||
−0.488675 | + | 0.872466i | \(0.662520\pi\) | |||||||
\(972\) | 1.21447e12 | − | 1.19885e12i | 1.36057 | − | 1.34308i | ||||
\(973\) | 2.06872e10 | 0.0230808 | ||||||||
\(974\) | 2.94634e12i | 3.27376i | ||||||||
\(975\) | 8.98931e10 | + | 1.76991e11i | 0.0994736 | + | 0.195854i | ||||
\(976\) | −8.14869e11 | −0.898025 | ||||||||
\(977\) | 1.59766e12i | 1.75350i | 0.480947 | + | 0.876750i | \(0.340293\pi\) | ||||
−0.480947 | + | 0.876750i | \(0.659707\pi\) | |||||||
\(978\) | −8.90316e11 | + | 4.52188e11i | −0.973171 | + | 0.494270i | ||||
\(979\) | 4.30558e11 | 0.468707 | ||||||||
\(980\) | 3.70441e11i | 0.401620i | ||||||||
\(981\) | 6.33914e11 | − | 8.67776e11i | 0.684470 | − | 0.936983i | ||||
\(982\) | 1.05769e12 | 1.13740 | ||||||||
\(983\) | − | 4.00959e11i | − | 0.429423i | −0.976677 | − | 0.214712i | \(-0.931119\pi\) | ||
0.976677 | − | 0.214712i | \(-0.0688812\pi\) | |||||||
\(984\) | 9.71136e11 | + | 1.91208e12i | 1.03586 | + | 2.03951i | ||||
\(985\) | 3.35237e11 | 0.356129 | ||||||||
\(986\) | − | 3.01255e12i | − | 3.18732i | ||||||
\(987\) | 2.48282e10 | − | 1.26101e10i | 0.0261623 | − | 0.0132877i | ||||
\(988\) | −2.65436e11 | −0.278568 | ||||||||
\(989\) | 1.24931e10i | 0.0130582i | ||||||||
\(990\) | −8.38650e10 | − | 6.12638e10i | −0.0873052 | − | 0.0637769i | ||||
\(991\) | −4.91421e11 | −0.509517 | −0.254759 | − | 0.967005i | \(-0.581996\pi\) | ||||
−0.254759 | + | 0.967005i | \(0.581996\pi\) | |||||||
\(992\) | − | 3.37337e11i | − | 0.348351i | ||||||
\(993\) | −5.87370e11 | − | 1.15648e12i | −0.604108 | − | 1.18943i | ||||
\(994\) | 2.04963e10 | 0.0209957 | ||||||||
\(995\) | 2.76404e10i | 0.0282002i | ||||||||
\(996\) | 1.55467e12 | − | 7.89611e11i | 1.57980 | − | 0.802373i | ||||
\(997\) | −1.19748e12 | −1.21195 | −0.605977 | − | 0.795482i | \(-0.707218\pi\) | ||||
−0.605977 | + | 0.795482i | \(0.707218\pi\) | |||||||
\(998\) | 9.22475e11i | 0.929892i | ||||||||
\(999\) | −9.31161e11 | − | 1.51190e11i | −0.934895 | − | 0.151796i |
(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.23.3 | ✓ | 26 | |
3.2 | odd | 2 | inner | 33.9.b.a.23.24 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.9.b.a.23.3 | ✓ | 26 | 1.1 | even | 1 | trivial | |
33.9.b.a.23.24 | yes | 26 | 3.2 | odd | 2 | inner |