Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,14,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.a (trivial) |
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: | yes |
Analytic conductor: | \(5.36154644760\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4466x - 18720 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.21238\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 56.4248 | 0.623411 | 0.311706 | − | 0.950179i | \(-0.399100\pi\) | ||||
0.311706 | + | 0.950179i | \(0.399100\pi\) | |||||||
\(3\) | 2114.98 | 1.67501 | 0.837506 | − | 0.546428i | \(-0.184013\pi\) | ||||
0.837506 | + | 0.546428i | \(0.184013\pi\) | |||||||
\(4\) | −5008.25 | −0.611358 | ||||||||
\(5\) | 15625.0 | 0.447214 | ||||||||
\(6\) | 119337. | 1.04422 | ||||||||
\(7\) | 325303. | 1.04508 | 0.522541 | − | 0.852614i | \(-0.324984\pi\) | ||||
0.522541 | + | 0.852614i | \(0.324984\pi\) | |||||||
\(8\) | −744821. | −1.00454 | ||||||||
\(9\) | 2.87881e6 | 1.80566 | ||||||||
\(10\) | 881637. | 0.278798 | ||||||||
\(11\) | −1.61316e6 | −0.274551 | −0.137276 | − | 0.990533i | \(-0.543835\pi\) | ||||
−0.137276 | + | 0.990533i | \(0.543835\pi\) | |||||||
\(12\) | −1.05923e7 | −1.02403 | ||||||||
\(13\) | −3.19654e7 | −1.83674 | −0.918371 | − | 0.395720i | \(-0.870495\pi\) | ||||
−0.918371 | + | 0.395720i | \(0.870495\pi\) | |||||||
\(14\) | 1.83551e7 | 0.651516 | ||||||||
\(15\) | 3.30465e7 | 0.749088 | ||||||||
\(16\) | −998777. | −0.0148829 | ||||||||
\(17\) | 3.82330e6 | 0.0384167 | 0.0192084 | − | 0.999816i | \(-0.493885\pi\) | ||||
0.0192084 | + | 0.999816i | \(0.493885\pi\) | |||||||
\(18\) | 1.62436e8 | 1.12567 | ||||||||
\(19\) | −1.98761e8 | −0.969245 | −0.484622 | − | 0.874723i | \(-0.661043\pi\) | ||||
−0.484622 | + | 0.874723i | \(0.661043\pi\) | |||||||
\(20\) | −7.82539e7 | −0.273408 | ||||||||
\(21\) | 6.88008e8 | 1.75052 | ||||||||
\(22\) | −9.10219e7 | −0.171159 | ||||||||
\(23\) | −1.86577e8 | −0.262801 | −0.131400 | − | 0.991329i | \(-0.541947\pi\) | ||||
−0.131400 | + | 0.991329i | \(0.541947\pi\) | |||||||
\(24\) | −1.57528e9 | −1.68261 | ||||||||
\(25\) | 2.44141e8 | 0.200000 | ||||||||
\(26\) | −1.80364e9 | −1.14505 | ||||||||
\(27\) | 2.71667e9 | 1.34950 | ||||||||
\(28\) | −1.62920e9 | −0.638919 | ||||||||
\(29\) | 2.45694e9 | 0.767022 | 0.383511 | − | 0.923536i | \(-0.374715\pi\) | ||||
0.383511 | + | 0.923536i | \(0.374715\pi\) | |||||||
\(30\) | 1.86464e9 | 0.466990 | ||||||||
\(31\) | −9.66435e8 | −0.195579 | −0.0977893 | − | 0.995207i | \(-0.531177\pi\) | ||||
−0.0977893 | + | 0.995207i | \(0.531177\pi\) | |||||||
\(32\) | 6.04522e9 | 0.995261 | ||||||||
\(33\) | −3.41179e9 | −0.459877 | ||||||||
\(34\) | 2.15729e8 | 0.0239494 | ||||||||
\(35\) | 5.08285e9 | 0.467375 | ||||||||
\(36\) | −1.44178e10 | −1.10391 | ||||||||
\(37\) | 2.20805e10 | 1.41481 | 0.707403 | − | 0.706810i | \(-0.249867\pi\) | ||||
0.707403 | + | 0.706810i | \(0.249867\pi\) | |||||||
\(38\) | −1.12151e10 | −0.604238 | ||||||||
\(39\) | −6.76061e10 | −3.07656 | ||||||||
\(40\) | −1.16378e10 | −0.449244 | ||||||||
\(41\) | 4.05651e10 | 1.33370 | 0.666850 | − | 0.745192i | \(-0.267642\pi\) | ||||
0.666850 | + | 0.745192i | \(0.267642\pi\) | |||||||
\(42\) | 3.88207e10 | 1.09130 | ||||||||
\(43\) | 2.28510e10 | 0.551264 | 0.275632 | − | 0.961263i | \(-0.411113\pi\) | ||||
0.275632 | + | 0.961263i | \(0.411113\pi\) | |||||||
\(44\) | 8.07908e9 | 0.167849 | ||||||||
\(45\) | 4.49814e10 | 0.807518 | ||||||||
\(46\) | −1.05275e10 | −0.163833 | ||||||||
\(47\) | −7.97391e10 | −1.07903 | −0.539517 | − | 0.841975i | \(-0.681393\pi\) | ||||
−0.539517 | + | 0.841975i | \(0.681393\pi\) | |||||||
\(48\) | −2.11239e9 | −0.0249291 | ||||||||
\(49\) | 8.93279e9 | 0.0921961 | ||||||||
\(50\) | 1.37756e10 | 0.124682 | ||||||||
\(51\) | 8.08620e9 | 0.0643485 | ||||||||
\(52\) | 1.60091e11 | 1.12291 | ||||||||
\(53\) | −2.25113e11 | −1.39511 | −0.697553 | − | 0.716534i | \(-0.745728\pi\) | ||||
−0.697553 | + | 0.716534i | \(0.745728\pi\) | |||||||
\(54\) | 1.53287e11 | 0.841292 | ||||||||
\(55\) | −2.52056e10 | −0.122783 | ||||||||
\(56\) | −2.42292e11 | −1.04983 | ||||||||
\(57\) | −4.20376e11 | −1.62350 | ||||||||
\(58\) | 1.38632e11 | 0.478170 | ||||||||
\(59\) | 7.96680e10 | 0.245893 | 0.122946 | − | 0.992413i | \(-0.460766\pi\) | ||||
0.122946 | + | 0.992413i | \(0.460766\pi\) | |||||||
\(60\) | −1.65505e11 | −0.457961 | ||||||||
\(61\) | 4.91133e11 | 1.22055 | 0.610275 | − | 0.792190i | \(-0.291059\pi\) | ||||
0.610275 | + | 0.792190i | \(0.291059\pi\) | |||||||
\(62\) | −5.45308e10 | −0.121926 | ||||||||
\(63\) | 9.36485e11 | 1.88707 | ||||||||
\(64\) | 3.49282e11 | 0.635340 | ||||||||
\(65\) | −4.99459e11 | −0.821416 | ||||||||
\(66\) | −1.92509e11 | −0.286693 | ||||||||
\(67\) | 2.25405e11 | 0.304423 | 0.152212 | − | 0.988348i | \(-0.451360\pi\) | ||||
0.152212 | + | 0.988348i | \(0.451360\pi\) | |||||||
\(68\) | −1.91480e10 | −0.0234864 | ||||||||
\(69\) | −3.94606e11 | −0.440194 | ||||||||
\(70\) | 2.86799e11 | 0.291367 | ||||||||
\(71\) | −6.50849e11 | −0.602978 | −0.301489 | − | 0.953470i | \(-0.597484\pi\) | ||||
−0.301489 | + | 0.953470i | \(0.597484\pi\) | |||||||
\(72\) | −2.14420e12 | −1.81386 | ||||||||
\(73\) | −1.03710e11 | −0.0802087 | −0.0401043 | − | 0.999195i | \(-0.512769\pi\) | ||||
−0.0401043 | + | 0.999195i | \(0.512769\pi\) | |||||||
\(74\) | 1.24588e12 | 0.882006 | ||||||||
\(75\) | 5.16352e11 | 0.335002 | ||||||||
\(76\) | 9.95446e11 | 0.592556 | ||||||||
\(77\) | −5.24764e11 | −0.286929 | ||||||||
\(78\) | −3.81466e12 | −1.91797 | ||||||||
\(79\) | 2.08051e12 | 0.962927 | 0.481464 | − | 0.876466i | \(-0.340105\pi\) | ||||
0.481464 | + | 0.876466i | \(0.340105\pi\) | |||||||
\(80\) | −1.56059e10 | −0.00665585 | ||||||||
\(81\) | 1.15594e12 | 0.454760 | ||||||||
\(82\) | 2.28888e12 | 0.831443 | ||||||||
\(83\) | 3.39017e12 | 1.13819 | 0.569094 | − | 0.822272i | \(-0.307294\pi\) | ||||
0.569094 | + | 0.822272i | \(0.307294\pi\) | |||||||
\(84\) | −3.44571e12 | −1.07020 | ||||||||
\(85\) | 5.97390e10 | 0.0171805 | ||||||||
\(86\) | 1.28936e12 | 0.343664 | ||||||||
\(87\) | 5.19638e12 | 1.28477 | ||||||||
\(88\) | 1.20151e12 | 0.275798 | ||||||||
\(89\) | −7.20835e12 | −1.53745 | −0.768724 | − | 0.639580i | \(-0.779108\pi\) | ||||
−0.768724 | + | 0.639580i | \(0.779108\pi\) | |||||||
\(90\) | 2.53807e12 | 0.503416 | ||||||||
\(91\) | −1.03984e13 | −1.91955 | ||||||||
\(92\) | 9.34422e11 | 0.160665 | ||||||||
\(93\) | −2.04399e12 | −0.327597 | ||||||||
\(94\) | −4.49926e12 | −0.672682 | ||||||||
\(95\) | −3.10565e12 | −0.433459 | ||||||||
\(96\) | 1.27855e13 | 1.66707 | ||||||||
\(97\) | 7.00185e12 | 0.853486 | 0.426743 | − | 0.904373i | \(-0.359661\pi\) | ||||
0.426743 | + | 0.904373i | \(0.359661\pi\) | |||||||
\(98\) | 5.04030e11 | 0.0574761 | ||||||||
\(99\) | −4.64397e12 | −0.495748 | ||||||||
\(100\) | −1.22272e12 | −0.122272 | ||||||||
\(101\) | −1.36319e13 | −1.27781 | −0.638907 | − | 0.769284i | \(-0.720613\pi\) | ||||
−0.638907 | + | 0.769284i | \(0.720613\pi\) | |||||||
\(102\) | 4.56262e11 | 0.0401156 | ||||||||
\(103\) | −6.72899e12 | −0.555275 | −0.277637 | − | 0.960686i | \(-0.589551\pi\) | ||||
−0.277637 | + | 0.960686i | \(0.589551\pi\) | |||||||
\(104\) | 2.38085e13 | 1.84508 | ||||||||
\(105\) | 1.07501e13 | 0.782858 | ||||||||
\(106\) | −1.27019e13 | −0.869724 | ||||||||
\(107\) | 5.49424e12 | 0.353927 | 0.176963 | − | 0.984217i | \(-0.443373\pi\) | ||||
0.176963 | + | 0.984217i | \(0.443373\pi\) | |||||||
\(108\) | −1.36057e13 | −0.825026 | ||||||||
\(109\) | 1.05471e13 | 0.602369 | 0.301184 | − | 0.953566i | \(-0.402618\pi\) | ||||
0.301184 | + | 0.953566i | \(0.402618\pi\) | |||||||
\(110\) | −1.42222e12 | −0.0765444 | ||||||||
\(111\) | 4.66997e13 | 2.36982 | ||||||||
\(112\) | −3.24905e11 | −0.0155539 | ||||||||
\(113\) | 1.30490e13 | 0.589612 | 0.294806 | − | 0.955557i | \(-0.404745\pi\) | ||||
0.294806 | + | 0.955557i | \(0.404745\pi\) | |||||||
\(114\) | −2.37196e13 | −1.01211 | ||||||||
\(115\) | −2.91526e12 | −0.117528 | ||||||||
\(116\) | −1.23050e13 | −0.468925 | ||||||||
\(117\) | −9.20224e13 | −3.31654 | ||||||||
\(118\) | 4.49525e12 | 0.153292 | ||||||||
\(119\) | 1.24373e12 | 0.0401486 | ||||||||
\(120\) | −2.46138e13 | −0.752488 | ||||||||
\(121\) | −3.19204e13 | −0.924622 | ||||||||
\(122\) | 2.77121e13 | 0.760905 | ||||||||
\(123\) | 8.57944e13 | 2.23396 | ||||||||
\(124\) | 4.84014e12 | 0.119569 | ||||||||
\(125\) | 3.81470e12 | 0.0894427 | ||||||||
\(126\) | 5.28410e13 | 1.17642 | ||||||||
\(127\) | −1.04514e13 | −0.221030 | −0.110515 | − | 0.993874i | \(-0.535250\pi\) | ||||
−0.110515 | + | 0.993874i | \(0.535250\pi\) | |||||||
\(128\) | −2.98143e13 | −0.599183 | ||||||||
\(129\) | 4.83293e13 | 0.923374 | ||||||||
\(130\) | −2.81819e13 | −0.512080 | ||||||||
\(131\) | 8.39814e12 | 0.145184 | 0.0725922 | − | 0.997362i | \(-0.476873\pi\) | ||||
0.0725922 | + | 0.997362i | \(0.476873\pi\) | |||||||
\(132\) | 1.70871e13 | 0.281150 | ||||||||
\(133\) | −6.46576e13 | −1.01294 | ||||||||
\(134\) | 1.27184e13 | 0.189781 | ||||||||
\(135\) | 4.24479e13 | 0.603514 | ||||||||
\(136\) | −2.84767e12 | −0.0385911 | ||||||||
\(137\) | 2.62849e13 | 0.339643 | 0.169822 | − | 0.985475i | \(-0.445681\pi\) | ||||
0.169822 | + | 0.985475i | \(0.445681\pi\) | |||||||
\(138\) | −2.22655e13 | −0.274422 | ||||||||
\(139\) | 6.83006e13 | 0.803209 | 0.401604 | − | 0.915813i | \(-0.368453\pi\) | ||||
0.401604 | + | 0.915813i | \(0.368453\pi\) | |||||||
\(140\) | −2.54562e13 | −0.285733 | ||||||||
\(141\) | −1.68646e14 | −1.80739 | ||||||||
\(142\) | −3.67240e13 | −0.375903 | ||||||||
\(143\) | 5.15651e13 | 0.504280 | ||||||||
\(144\) | −2.87529e12 | −0.0268736 | ||||||||
\(145\) | 3.83897e13 | 0.343023 | ||||||||
\(146\) | −5.85180e12 | −0.0500030 | ||||||||
\(147\) | 1.88927e13 | 0.154430 | ||||||||
\(148\) | −1.10584e14 | −0.864953 | ||||||||
\(149\) | −1.70193e14 | −1.27418 | −0.637089 | − | 0.770790i | \(-0.719862\pi\) | ||||
−0.637089 | + | 0.770790i | \(0.719862\pi\) | |||||||
\(150\) | 2.91351e13 | 0.208844 | ||||||||
\(151\) | 1.84944e13 | 0.126967 | 0.0634835 | − | 0.997983i | \(-0.479779\pi\) | ||||
0.0634835 | + | 0.997983i | \(0.479779\pi\) | |||||||
\(152\) | 1.48042e14 | 0.973644 | ||||||||
\(153\) | 1.10066e13 | 0.0693677 | ||||||||
\(154\) | −2.96097e13 | −0.178875 | ||||||||
\(155\) | −1.51005e13 | −0.0874654 | ||||||||
\(156\) | 3.38588e14 | 1.88088 | ||||||||
\(157\) | 1.72832e14 | 0.921035 | 0.460517 | − | 0.887651i | \(-0.347664\pi\) | ||||
0.460517 | + | 0.887651i | \(0.347664\pi\) | |||||||
\(158\) | 1.17392e14 | 0.600300 | ||||||||
\(159\) | −4.76109e14 | −2.33682 | ||||||||
\(160\) | 9.44565e13 | 0.445094 | ||||||||
\(161\) | −6.06939e13 | −0.274648 | ||||||||
\(162\) | 6.52235e13 | 0.283502 | ||||||||
\(163\) | 2.52994e14 | 1.05655 | 0.528275 | − | 0.849073i | \(-0.322839\pi\) | ||||
0.528275 | + | 0.849073i | \(0.322839\pi\) | |||||||
\(164\) | −2.03160e14 | −0.815368 | ||||||||
\(165\) | −5.33092e13 | −0.205663 | ||||||||
\(166\) | 1.91290e14 | 0.709559 | ||||||||
\(167\) | −1.37321e14 | −0.489870 | −0.244935 | − | 0.969539i | \(-0.578767\pi\) | ||||
−0.244935 | + | 0.969539i | \(0.578767\pi\) | |||||||
\(168\) | −5.12443e14 | −1.75847 | ||||||||
\(169\) | 7.18911e14 | 2.37362 | ||||||||
\(170\) | 3.37076e12 | 0.0107105 | ||||||||
\(171\) | −5.72197e14 | −1.75013 | ||||||||
\(172\) | −1.14443e14 | −0.337020 | ||||||||
\(173\) | −1.57684e14 | −0.447186 | −0.223593 | − | 0.974683i | \(-0.571779\pi\) | ||||
−0.223593 | + | 0.974683i | \(0.571779\pi\) | |||||||
\(174\) | 2.93204e14 | 0.800941 | ||||||||
\(175\) | 7.94196e13 | 0.209016 | ||||||||
\(176\) | 1.61118e12 | 0.00408613 | ||||||||
\(177\) | 1.68496e14 | 0.411873 | ||||||||
\(178\) | −4.06729e14 | −0.958463 | ||||||||
\(179\) | −2.76902e14 | −0.629189 | −0.314595 | − | 0.949226i | \(-0.601869\pi\) | ||||
−0.314595 | + | 0.949226i | \(0.601869\pi\) | |||||||
\(180\) | −2.25278e14 | −0.493683 | ||||||||
\(181\) | −1.39415e14 | −0.294712 | −0.147356 | − | 0.989084i | \(-0.547076\pi\) | ||||
−0.147356 | + | 0.989084i | \(0.547076\pi\) | |||||||
\(182\) | −5.86729e14 | −1.19667 | ||||||||
\(183\) | 1.03874e15 | 2.04444 | ||||||||
\(184\) | 1.38966e14 | 0.263994 | ||||||||
\(185\) | 3.45007e14 | 0.632720 | ||||||||
\(186\) | −1.15332e14 | −0.204227 | ||||||||
\(187\) | −6.16758e12 | −0.0105474 | ||||||||
\(188\) | 3.99353e14 | 0.659676 | ||||||||
\(189\) | 8.83739e14 | 1.41034 | ||||||||
\(190\) | −1.75235e14 | −0.270224 | ||||||||
\(191\) | 6.42718e14 | 0.957864 | 0.478932 | − | 0.877852i | \(-0.341024\pi\) | ||||
0.478932 | + | 0.877852i | \(0.341024\pi\) | |||||||
\(192\) | 7.38724e14 | 1.06420 | ||||||||
\(193\) | −1.22414e14 | −0.170494 | −0.0852470 | − | 0.996360i | \(-0.527168\pi\) | ||||
−0.0852470 | + | 0.996360i | \(0.527168\pi\) | |||||||
\(194\) | 3.95078e14 | 0.532073 | ||||||||
\(195\) | −1.05635e15 | −1.37588 | ||||||||
\(196\) | −4.47376e13 | −0.0563648 | ||||||||
\(197\) | −1.36916e15 | −1.66887 | −0.834435 | − | 0.551106i | \(-0.814206\pi\) | ||||
−0.834435 | + | 0.551106i | \(0.814206\pi\) | |||||||
\(198\) | −2.62035e14 | −0.309055 | ||||||||
\(199\) | −1.51380e15 | −1.72792 | −0.863961 | − | 0.503558i | \(-0.832024\pi\) | ||||
−0.863961 | + | 0.503558i | \(0.832024\pi\) | |||||||
\(200\) | −1.81841e14 | −0.200908 | ||||||||
\(201\) | 4.76727e14 | 0.509912 | ||||||||
\(202\) | −7.69177e14 | −0.796604 | ||||||||
\(203\) | 7.99250e14 | 0.801601 | ||||||||
\(204\) | −4.04977e13 | −0.0393400 | ||||||||
\(205\) | 6.33830e14 | 0.596448 | ||||||||
\(206\) | −3.79681e14 | −0.346164 | ||||||||
\(207\) | −5.37119e14 | −0.474530 | ||||||||
\(208\) | 3.19263e13 | 0.0273361 | ||||||||
\(209\) | 3.20633e14 | 0.266108 | ||||||||
\(210\) | 6.06573e14 | 0.488043 | ||||||||
\(211\) | 1.41808e15 | 1.10628 | 0.553141 | − | 0.833088i | \(-0.313429\pi\) | ||||
0.553141 | + | 0.833088i | \(0.313429\pi\) | |||||||
\(212\) | 1.12742e15 | 0.852909 | ||||||||
\(213\) | −1.37653e15 | −1.00999 | ||||||||
\(214\) | 3.10011e14 | 0.220642 | ||||||||
\(215\) | 3.57047e14 | 0.246533 | ||||||||
\(216\) | −2.02343e15 | −1.35562 | ||||||||
\(217\) | −3.14384e14 | −0.204396 | ||||||||
\(218\) | 5.95120e14 | 0.375523 | ||||||||
\(219\) | −2.19344e14 | −0.134350 | ||||||||
\(220\) | 1.26236e14 | 0.0750645 | ||||||||
\(221\) | −1.22213e14 | −0.0705616 | ||||||||
\(222\) | 2.63502e15 | 1.47737 | ||||||||
\(223\) | −3.48697e15 | −1.89874 | −0.949371 | − | 0.314157i | \(-0.898278\pi\) | ||||
−0.949371 | + | 0.314157i | \(0.898278\pi\) | |||||||
\(224\) | 1.96652e15 | 1.04013 | ||||||||
\(225\) | 7.02835e14 | 0.361133 | ||||||||
\(226\) | 7.36285e14 | 0.367571 | ||||||||
\(227\) | 1.43848e15 | 0.697808 | 0.348904 | − | 0.937158i | \(-0.386554\pi\) | ||||
0.348904 | + | 0.937158i | \(0.386554\pi\) | |||||||
\(228\) | 2.10535e15 | 0.992538 | ||||||||
\(229\) | 1.00326e14 | 0.0459709 | 0.0229855 | − | 0.999736i | \(-0.492683\pi\) | ||||
0.0229855 | + | 0.999736i | \(0.492683\pi\) | |||||||
\(230\) | −1.64493e14 | −0.0732683 | ||||||||
\(231\) | −1.10986e15 | −0.480609 | ||||||||
\(232\) | −1.82998e15 | −0.770504 | ||||||||
\(233\) | 1.04926e15 | 0.429607 | 0.214803 | − | 0.976657i | \(-0.431089\pi\) | ||||
0.214803 | + | 0.976657i | \(0.431089\pi\) | |||||||
\(234\) | −5.19234e15 | −2.06757 | ||||||||
\(235\) | −1.24592e15 | −0.482559 | ||||||||
\(236\) | −3.98997e14 | −0.150329 | ||||||||
\(237\) | 4.40023e15 | 1.61291 | ||||||||
\(238\) | 7.01771e13 | 0.0250291 | ||||||||
\(239\) | −4.68165e15 | −1.62485 | −0.812424 | − | 0.583067i | \(-0.801853\pi\) | ||||
−0.812424 | + | 0.583067i | \(0.801853\pi\) | |||||||
\(240\) | −3.30061e13 | −0.0111486 | ||||||||
\(241\) | −1.22689e15 | −0.403361 | −0.201680 | − | 0.979451i | \(-0.564640\pi\) | ||||
−0.201680 | + | 0.979451i | \(0.564640\pi\) | |||||||
\(242\) | −1.80110e15 | −0.576420 | ||||||||
\(243\) | −1.88646e15 | −0.587770 | ||||||||
\(244\) | −2.45972e15 | −0.746193 | ||||||||
\(245\) | 1.39575e14 | 0.0412313 | ||||||||
\(246\) | 4.84093e15 | 1.39268 | ||||||||
\(247\) | 6.35348e15 | 1.78025 | ||||||||
\(248\) | 7.19821e14 | 0.196466 | ||||||||
\(249\) | 7.17014e15 | 1.90648 | ||||||||
\(250\) | 2.15243e14 | 0.0557596 | ||||||||
\(251\) | −2.74250e15 | −0.692258 | −0.346129 | − | 0.938187i | \(-0.612504\pi\) | ||||
−0.346129 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(252\) | −4.69015e15 | −1.15367 | ||||||||
\(253\) | 3.00977e14 | 0.0721523 | ||||||||
\(254\) | −5.89720e14 | −0.137793 | ||||||||
\(255\) | 1.26347e14 | 0.0287775 | ||||||||
\(256\) | −4.54358e15 | −1.00888 | ||||||||
\(257\) | −3.96785e15 | −0.858994 | −0.429497 | − | 0.903068i | \(-0.641309\pi\) | ||||
−0.429497 | + | 0.903068i | \(0.641309\pi\) | |||||||
\(258\) | 2.72697e15 | 0.575642 | ||||||||
\(259\) | 7.18283e15 | 1.47859 | ||||||||
\(260\) | 2.50141e15 | 0.502179 | ||||||||
\(261\) | 7.07307e15 | 1.38498 | ||||||||
\(262\) | 4.73863e14 | 0.0905096 | ||||||||
\(263\) | 4.19100e15 | 0.780917 | 0.390459 | − | 0.920621i | \(-0.372316\pi\) | ||||
0.390459 | + | 0.920621i | \(0.372316\pi\) | |||||||
\(264\) | 2.54117e15 | 0.461964 | ||||||||
\(265\) | −3.51739e15 | −0.623910 | ||||||||
\(266\) | −3.64829e15 | −0.631478 | ||||||||
\(267\) | −1.52455e16 | −2.57524 | ||||||||
\(268\) | −1.12888e15 | −0.186112 | ||||||||
\(269\) | 1.20414e15 | 0.193771 | 0.0968854 | − | 0.995296i | \(-0.469112\pi\) | ||||
0.0968854 | + | 0.995296i | \(0.469112\pi\) | |||||||
\(270\) | 2.39511e15 | 0.376237 | ||||||||
\(271\) | 8.17556e15 | 1.25377 | 0.626884 | − | 0.779113i | \(-0.284330\pi\) | ||||
0.626884 | + | 0.779113i | \(0.284330\pi\) | |||||||
\(272\) | −3.81862e12 | −0.000571753 0 | ||||||||
\(273\) | −2.19924e16 | −3.21526 | ||||||||
\(274\) | 1.48312e15 | 0.211738 | ||||||||
\(275\) | −3.93837e14 | −0.0549103 | ||||||||
\(276\) | 1.97628e15 | 0.269116 | ||||||||
\(277\) | 5.65506e15 | 0.752175 | 0.376088 | − | 0.926584i | \(-0.377269\pi\) | ||||
0.376088 | + | 0.926584i | \(0.377269\pi\) | |||||||
\(278\) | 3.85385e15 | 0.500730 | ||||||||
\(279\) | −2.78218e15 | −0.353149 | ||||||||
\(280\) | −3.78581e15 | −0.469496 | ||||||||
\(281\) | −1.38960e16 | −1.68383 | −0.841917 | − | 0.539607i | \(-0.818573\pi\) | ||||
−0.841917 | + | 0.539607i | \(0.818573\pi\) | |||||||
\(282\) | −9.51584e15 | −1.12675 | ||||||||
\(283\) | 1.68555e16 | 1.95042 | 0.975212 | − | 0.221271i | \(-0.0710205\pi\) | ||||
0.975212 | + | 0.221271i | \(0.0710205\pi\) | |||||||
\(284\) | 3.25961e15 | 0.368635 | ||||||||
\(285\) | −6.56837e15 | −0.726050 | ||||||||
\(286\) | 2.90955e15 | 0.314374 | ||||||||
\(287\) | 1.31959e16 | 1.39383 | ||||||||
\(288\) | 1.74030e16 | 1.79711 | ||||||||
\(289\) | −9.88996e15 | −0.998524 | ||||||||
\(290\) | 2.16613e15 | 0.213844 | ||||||||
\(291\) | 1.48088e16 | 1.42960 | ||||||||
\(292\) | 5.19404e14 | 0.0490362 | ||||||||
\(293\) | 8.49847e15 | 0.784696 | 0.392348 | − | 0.919817i | \(-0.371663\pi\) | ||||
0.392348 | + | 0.919817i | \(0.371663\pi\) | |||||||
\(294\) | 1.06601e15 | 0.0962731 | ||||||||
\(295\) | 1.24481e15 | 0.109967 | ||||||||
\(296\) | −1.64460e16 | −1.42123 | ||||||||
\(297\) | −4.38241e15 | −0.370506 | ||||||||
\(298\) | −9.60308e15 | −0.794337 | ||||||||
\(299\) | 5.96400e15 | 0.482697 | ||||||||
\(300\) | −2.58602e15 | −0.204806 | ||||||||
\(301\) | 7.43348e15 | 0.576116 | ||||||||
\(302\) | 1.04354e15 | 0.0791527 | ||||||||
\(303\) | −2.88312e16 | −2.14035 | ||||||||
\(304\) | 1.98518e14 | 0.0144252 | ||||||||
\(305\) | 7.67396e15 | 0.545846 | ||||||||
\(306\) | 6.21043e14 | 0.0432446 | ||||||||
\(307\) | −2.68116e14 | −0.0182778 | −0.00913890 | − | 0.999958i | \(-0.502909\pi\) | ||||
−0.00913890 | + | 0.999958i | \(0.502909\pi\) | |||||||
\(308\) | 2.62815e15 | 0.175416 | ||||||||
\(309\) | −1.42317e16 | −0.930091 | ||||||||
\(310\) | −8.52044e14 | −0.0545269 | ||||||||
\(311\) | −2.25419e16 | −1.41270 | −0.706348 | − | 0.707865i | \(-0.749659\pi\) | ||||
−0.706348 | + | 0.707865i | \(0.749659\pi\) | |||||||
\(312\) | 5.03544e16 | 3.09053 | ||||||||
\(313\) | 2.91559e15 | 0.175262 | 0.0876312 | − | 0.996153i | \(-0.472070\pi\) | ||||
0.0876312 | + | 0.996153i | \(0.472070\pi\) | |||||||
\(314\) | 9.75200e15 | 0.574184 | ||||||||
\(315\) | 1.46326e16 | 0.843922 | ||||||||
\(316\) | −1.04197e16 | −0.588693 | ||||||||
\(317\) | −2.90121e16 | −1.60581 | −0.802903 | − | 0.596109i | \(-0.796713\pi\) | ||||
−0.802903 | + | 0.596109i | \(0.796713\pi\) | |||||||
\(318\) | −2.68643e16 | −1.45680 | ||||||||
\(319\) | −3.96343e15 | −0.210587 | ||||||||
\(320\) | 5.45753e15 | 0.284133 | ||||||||
\(321\) | 1.16202e16 | 0.592831 | ||||||||
\(322\) | −3.42464e15 | −0.171219 | ||||||||
\(323\) | −7.59924e14 | −0.0372352 | ||||||||
\(324\) | −5.78922e15 | −0.278021 | ||||||||
\(325\) | −7.80405e15 | −0.367348 | ||||||||
\(326\) | 1.42751e16 | 0.658665 | ||||||||
\(327\) | 2.23070e16 | 1.00897 | ||||||||
\(328\) | −3.02138e16 | −1.33975 | ||||||||
\(329\) | −2.59393e16 | −1.12768 | ||||||||
\(330\) | −3.00796e15 | −0.128213 | ||||||||
\(331\) | 3.67428e16 | 1.53564 | 0.767821 | − | 0.640665i | \(-0.221341\pi\) | ||||
0.767821 | + | 0.640665i | \(0.221341\pi\) | |||||||
\(332\) | −1.69788e16 | −0.695841 | ||||||||
\(333\) | 6.35655e16 | 2.55466 | ||||||||
\(334\) | −7.74833e15 | −0.305391 | ||||||||
\(335\) | 3.52196e15 | 0.136142 | ||||||||
\(336\) | −6.87166e14 | −0.0260529 | ||||||||
\(337\) | 2.62017e16 | 0.974395 | 0.487197 | − | 0.873292i | \(-0.338019\pi\) | ||||
0.487197 | + | 0.873292i | \(0.338019\pi\) | |||||||
\(338\) | 4.05644e16 | 1.47974 | ||||||||
\(339\) | 2.75983e16 | 0.987608 | ||||||||
\(340\) | −2.99188e14 | −0.0105034 | ||||||||
\(341\) | 1.55901e15 | 0.0536964 | ||||||||
\(342\) | −3.22861e16 | −1.09105 | ||||||||
\(343\) | −2.86124e16 | −0.948729 | ||||||||
\(344\) | −1.70199e16 | −0.553767 | ||||||||
\(345\) | −6.16572e15 | −0.196861 | ||||||||
\(346\) | −8.89729e15 | −0.278781 | ||||||||
\(347\) | 4.16211e15 | 0.127989 | 0.0639944 | − | 0.997950i | \(-0.479616\pi\) | ||||
0.0639944 | + | 0.997950i | \(0.479616\pi\) | |||||||
\(348\) | −2.60248e16 | −0.785455 | ||||||||
\(349\) | −3.79966e16 | −1.12559 | −0.562794 | − | 0.826597i | \(-0.690274\pi\) | ||||
−0.562794 | + | 0.826597i | \(0.690274\pi\) | |||||||
\(350\) | 4.48123e15 | 0.130303 | ||||||||
\(351\) | −8.68393e16 | −2.47868 | ||||||||
\(352\) | −9.75187e15 | −0.273250 | ||||||||
\(353\) | 6.24372e16 | 1.71754 | 0.858772 | − | 0.512358i | \(-0.171228\pi\) | ||||
0.858772 | + | 0.512358i | \(0.171228\pi\) | |||||||
\(354\) | 9.50735e15 | 0.256767 | ||||||||
\(355\) | −1.01695e16 | −0.269660 | ||||||||
\(356\) | 3.61012e16 | 0.939932 | ||||||||
\(357\) | 2.63046e15 | 0.0672494 | ||||||||
\(358\) | −1.56241e16 | −0.392244 | ||||||||
\(359\) | 4.66231e16 | 1.14944 | 0.574721 | − | 0.818349i | \(-0.305110\pi\) | ||||
0.574721 | + | 0.818349i | \(0.305110\pi\) | |||||||
\(360\) | −3.35031e16 | −0.811183 | ||||||||
\(361\) | −2.54692e15 | −0.0605646 | ||||||||
\(362\) | −7.86645e15 | −0.183727 | ||||||||
\(363\) | −6.75111e16 | −1.54875 | ||||||||
\(364\) | 5.20779e16 | 1.17353 | ||||||||
\(365\) | −1.62047e15 | −0.0358704 | ||||||||
\(366\) | 5.86105e16 | 1.27452 | ||||||||
\(367\) | −5.72445e16 | −1.22294 | −0.611469 | − | 0.791269i | \(-0.709421\pi\) | ||||
−0.611469 | + | 0.791269i | \(0.709421\pi\) | |||||||
\(368\) | 1.86348e14 | 0.00391124 | ||||||||
\(369\) | 1.16779e17 | 2.40821 | ||||||||
\(370\) | 1.94669e16 | 0.394445 | ||||||||
\(371\) | −7.32298e16 | −1.45800 | ||||||||
\(372\) | 1.02368e16 | 0.200279 | ||||||||
\(373\) | −2.68476e16 | −0.516176 | −0.258088 | − | 0.966121i | \(-0.583092\pi\) | ||||
−0.258088 | + | 0.966121i | \(0.583092\pi\) | |||||||
\(374\) | −3.48004e14 | −0.00657535 | ||||||||
\(375\) | 8.06800e15 | 0.149818 | ||||||||
\(376\) | 5.93913e16 | 1.08393 | ||||||||
\(377\) | −7.85371e16 | −1.40882 | ||||||||
\(378\) | 4.98648e16 | 0.879219 | ||||||||
\(379\) | 3.18194e16 | 0.551489 | 0.275744 | − | 0.961231i | \(-0.411076\pi\) | ||||
0.275744 | + | 0.961231i | \(0.411076\pi\) | |||||||
\(380\) | 1.55538e16 | 0.264999 | ||||||||
\(381\) | −2.21046e16 | −0.370228 | ||||||||
\(382\) | 3.62652e16 | 0.597143 | ||||||||
\(383\) | 1.08164e17 | 1.75101 | 0.875505 | − | 0.483208i | \(-0.160529\pi\) | ||||
0.875505 | + | 0.483208i | \(0.160529\pi\) | |||||||
\(384\) | −6.30565e16 | −1.00364 | ||||||||
\(385\) | −8.19943e15 | −0.128318 | ||||||||
\(386\) | −6.90719e15 | −0.106288 | ||||||||
\(387\) | 6.57837e16 | 0.995398 | ||||||||
\(388\) | −3.50670e16 | −0.521786 | ||||||||
\(389\) | −9.51462e16 | −1.39226 | −0.696128 | − | 0.717918i | \(-0.745095\pi\) | ||||
−0.696128 | + | 0.717918i | \(0.745095\pi\) | |||||||
\(390\) | −5.96040e16 | −0.857740 | ||||||||
\(391\) | −7.13339e14 | −0.0100959 | ||||||||
\(392\) | −6.65333e15 | −0.0926146 | ||||||||
\(393\) | 1.77619e16 | 0.243185 | ||||||||
\(394\) | −7.72543e16 | −1.04039 | ||||||||
\(395\) | 3.25079e16 | 0.430634 | ||||||||
\(396\) | 2.32582e16 | 0.303079 | ||||||||
\(397\) | −4.83241e16 | −0.619477 | −0.309739 | − | 0.950822i | \(-0.600242\pi\) | ||||
−0.309739 | + | 0.950822i | \(0.600242\pi\) | |||||||
\(398\) | −8.54160e16 | −1.07721 | ||||||||
\(399\) | −1.36749e17 | −1.69669 | ||||||||
\(400\) | −2.43842e14 | −0.00297659 | ||||||||
\(401\) | 4.29285e16 | 0.515593 | 0.257797 | − | 0.966199i | \(-0.417004\pi\) | ||||
0.257797 | + | 0.966199i | \(0.417004\pi\) | |||||||
\(402\) | 2.68992e16 | 0.317885 | ||||||||
\(403\) | 3.08925e16 | 0.359228 | ||||||||
\(404\) | 6.82719e16 | 0.781202 | ||||||||
\(405\) | 1.80615e16 | 0.203375 | ||||||||
\(406\) | 4.50975e16 | 0.499727 | ||||||||
\(407\) | −3.56192e16 | −0.388437 | ||||||||
\(408\) | −6.02277e15 | −0.0646405 | ||||||||
\(409\) | 8.36651e16 | 0.883777 | 0.441889 | − | 0.897070i | \(-0.354309\pi\) | ||||
0.441889 | + | 0.897070i | \(0.354309\pi\) | |||||||
\(410\) | 3.57637e16 | 0.371833 | ||||||||
\(411\) | 5.55921e16 | 0.568907 | ||||||||
\(412\) | 3.37004e16 | 0.339472 | ||||||||
\(413\) | 2.59162e16 | 0.256978 | ||||||||
\(414\) | −3.03068e16 | −0.295827 | ||||||||
\(415\) | 5.29714e16 | 0.509013 | ||||||||
\(416\) | −1.93238e17 | −1.82804 | ||||||||
\(417\) | 1.44454e17 | 1.34538 | ||||||||
\(418\) | 1.80916e16 | 0.165894 | ||||||||
\(419\) | −1.35543e17 | −1.22373 | −0.611865 | − | 0.790962i | \(-0.709580\pi\) | ||||
−0.611865 | + | 0.790962i | \(0.709580\pi\) | |||||||
\(420\) | −5.38393e16 | −0.478607 | ||||||||
\(421\) | 5.25025e16 | 0.459565 | 0.229782 | − | 0.973242i | \(-0.426199\pi\) | ||||
0.229782 | + | 0.973242i | \(0.426199\pi\) | |||||||
\(422\) | 8.00150e16 | 0.689669 | ||||||||
\(423\) | −2.29554e17 | −1.94837 | ||||||||
\(424\) | 1.67669e17 | 1.40144 | ||||||||
\(425\) | 9.33423e14 | 0.00768334 | ||||||||
\(426\) | −7.76705e16 | −0.629642 | ||||||||
\(427\) | 1.59767e17 | 1.27557 | ||||||||
\(428\) | −2.75165e16 | −0.216376 | ||||||||
\(429\) | 1.09059e17 | 0.844675 | ||||||||
\(430\) | 2.01463e16 | 0.153691 | ||||||||
\(431\) | 2.51192e15 | 0.0188757 | 0.00943785 | − | 0.999955i | \(-0.496996\pi\) | ||||
0.00943785 | + | 0.999955i | \(0.496996\pi\) | |||||||
\(432\) | −2.71334e15 | −0.0200845 | ||||||||
\(433\) | −7.31447e16 | −0.533349 | −0.266675 | − | 0.963787i | \(-0.585925\pi\) | ||||
−0.266675 | + | 0.963787i | \(0.585925\pi\) | |||||||
\(434\) | −1.77390e16 | −0.127423 | ||||||||
\(435\) | 8.11934e16 | 0.574567 | ||||||||
\(436\) | −5.28227e16 | −0.368263 | ||||||||
\(437\) | 3.70842e16 | 0.254718 | ||||||||
\(438\) | −1.23764e16 | −0.0837556 | ||||||||
\(439\) | −7.23430e16 | −0.482367 | −0.241183 | − | 0.970480i | \(-0.577536\pi\) | ||||
−0.241183 | + | 0.970480i | \(0.577536\pi\) | |||||||
\(440\) | 1.87736e16 | 0.123340 | ||||||||
\(441\) | 2.57158e16 | 0.166475 | ||||||||
\(442\) | −6.89585e15 | −0.0439889 | ||||||||
\(443\) | 2.25527e17 | 1.41767 | 0.708833 | − | 0.705377i | \(-0.249222\pi\) | ||||
0.708833 | + | 0.705377i | \(0.249222\pi\) | |||||||
\(444\) | −2.33884e17 | −1.44881 | ||||||||
\(445\) | −1.12630e17 | −0.687568 | ||||||||
\(446\) | −1.96751e17 | −1.18370 | ||||||||
\(447\) | −3.59954e17 | −2.13426 | ||||||||
\(448\) | 1.13622e17 | 0.663982 | ||||||||
\(449\) | 5.33358e16 | 0.307197 | 0.153599 | − | 0.988133i | \(-0.450914\pi\) | ||||
0.153599 | + | 0.988133i | \(0.450914\pi\) | |||||||
\(450\) | 3.96573e16 | 0.225134 | ||||||||
\(451\) | −6.54379e16 | −0.366169 | ||||||||
\(452\) | −6.53525e16 | −0.360464 | ||||||||
\(453\) | 3.91153e16 | 0.212671 | ||||||||
\(454\) | 8.11659e16 | 0.435022 | ||||||||
\(455\) | −1.62475e17 | −0.858447 | ||||||||
\(456\) | 3.13105e17 | 1.63087 | ||||||||
\(457\) | −9.83492e16 | −0.505028 | −0.252514 | − | 0.967593i | \(-0.581257\pi\) | ||||
−0.252514 | + | 0.967593i | \(0.581257\pi\) | |||||||
\(458\) | 5.66087e15 | 0.0286588 | ||||||||
\(459\) | 1.03866e16 | 0.0518433 | ||||||||
\(460\) | 1.46003e16 | 0.0718517 | ||||||||
\(461\) | 2.01882e17 | 0.979583 | 0.489791 | − | 0.871840i | \(-0.337073\pi\) | ||||
0.489791 | + | 0.871840i | \(0.337073\pi\) | |||||||
\(462\) | −6.26238e16 | −0.299617 | ||||||||
\(463\) | −1.21471e17 | −0.573057 | −0.286528 | − | 0.958072i | \(-0.592501\pi\) | ||||
−0.286528 | + | 0.958072i | \(0.592501\pi\) | |||||||
\(464\) | −2.45394e15 | −0.0114155 | ||||||||
\(465\) | −3.19373e16 | −0.146506 | ||||||||
\(466\) | 5.92045e16 | 0.267822 | ||||||||
\(467\) | 4.32550e17 | 1.92964 | 0.964820 | − | 0.262910i | \(-0.0846821\pi\) | ||||
0.964820 | + | 0.262910i | \(0.0846821\pi\) | |||||||
\(468\) | 4.60871e17 | 2.02759 | ||||||||
\(469\) | 7.33249e16 | 0.318147 | ||||||||
\(470\) | −7.03009e16 | −0.300833 | ||||||||
\(471\) | 3.65536e17 | 1.54274 | ||||||||
\(472\) | −5.93384e16 | −0.247009 | ||||||||
\(473\) | −3.68622e16 | −0.151350 | ||||||||
\(474\) | 2.48282e17 | 1.00551 | ||||||||
\(475\) | −4.85257e16 | −0.193849 | ||||||||
\(476\) | −6.22890e15 | −0.0245452 | ||||||||
\(477\) | −6.48057e17 | −2.51909 | ||||||||
\(478\) | −2.64161e17 | −1.01295 | ||||||||
\(479\) | −1.80742e17 | −0.683719 | −0.341860 | − | 0.939751i | \(-0.611057\pi\) | ||||
−0.341860 | + | 0.939751i | \(0.611057\pi\) | |||||||
\(480\) | 1.99773e17 | 0.745538 | ||||||||
\(481\) | −7.05810e17 | −2.59863 | ||||||||
\(482\) | −6.92268e16 | −0.251460 | ||||||||
\(483\) | −1.28366e17 | −0.460039 | ||||||||
\(484\) | 1.59865e17 | 0.565275 | ||||||||
\(485\) | 1.09404e17 | 0.381691 | ||||||||
\(486\) | −1.06443e17 | −0.366422 | ||||||||
\(487\) | 1.79248e17 | 0.608858 | 0.304429 | − | 0.952535i | \(-0.401534\pi\) | ||||
0.304429 | + | 0.952535i | \(0.401534\pi\) | |||||||
\(488\) | −3.65806e17 | −1.22609 | ||||||||
\(489\) | 5.35076e17 | 1.76973 | ||||||||
\(490\) | 7.87548e15 | 0.0257041 | ||||||||
\(491\) | 3.27397e17 | 1.05450 | 0.527248 | − | 0.849712i | \(-0.323224\pi\) | ||||
0.527248 | + | 0.849712i | \(0.323224\pi\) | |||||||
\(492\) | −4.29680e17 | −1.36575 | ||||||||
\(493\) | 9.39362e15 | 0.0294665 | ||||||||
\(494\) | 3.58494e17 | 1.10983 | ||||||||
\(495\) | −7.25621e16 | −0.221705 | ||||||||
\(496\) | 9.65252e14 | 0.00291078 | ||||||||
\(497\) | −2.11723e17 | −0.630161 | ||||||||
\(498\) | 4.04573e17 | 1.18852 | ||||||||
\(499\) | −4.14032e17 | −1.20055 | −0.600275 | − | 0.799794i | \(-0.704942\pi\) | ||||
−0.600275 | + | 0.799794i | \(0.704942\pi\) | |||||||
\(500\) | −1.91049e16 | −0.0546815 | ||||||||
\(501\) | −2.90432e17 | −0.820539 | ||||||||
\(502\) | −1.54745e17 | −0.431562 | ||||||||
\(503\) | 1.04795e17 | 0.288503 | 0.144251 | − | 0.989541i | \(-0.453923\pi\) | ||||
0.144251 | + | 0.989541i | \(0.453923\pi\) | |||||||
\(504\) | −6.97514e17 | −1.89563 | ||||||||
\(505\) | −2.12999e17 | −0.571456 | ||||||||
\(506\) | 1.69826e16 | 0.0449806 | ||||||||
\(507\) | 1.52048e18 | 3.97584 | ||||||||
\(508\) | 5.23434e16 | 0.135129 | ||||||||
\(509\) | 4.12726e17 | 1.05195 | 0.525976 | − | 0.850499i | \(-0.323700\pi\) | ||||
0.525976 | + | 0.850499i | \(0.323700\pi\) | |||||||
\(510\) | 7.12909e15 | 0.0179402 | ||||||||
\(511\) | −3.37371e16 | −0.0838246 | ||||||||
\(512\) | −1.21319e16 | −0.0297629 | ||||||||
\(513\) | −5.39968e17 | −1.30799 | ||||||||
\(514\) | −2.23885e17 | −0.535507 | ||||||||
\(515\) | −1.05140e17 | −0.248326 | ||||||||
\(516\) | −2.42045e17 | −0.564512 | ||||||||
\(517\) | 1.28632e17 | 0.296250 | ||||||||
\(518\) | 4.05290e17 | 0.921769 | ||||||||
\(519\) | −3.33499e17 | −0.749042 | ||||||||
\(520\) | 3.72008e17 | 0.825145 | ||||||||
\(521\) | 2.21835e17 | 0.485942 | 0.242971 | − | 0.970034i | \(-0.421878\pi\) | ||||
0.242971 | + | 0.970034i | \(0.421878\pi\) | |||||||
\(522\) | 3.99097e17 | 0.863415 | ||||||||
\(523\) | 7.40537e17 | 1.58229 | 0.791145 | − | 0.611629i | \(-0.209486\pi\) | ||||
0.791145 | + | 0.611629i | \(0.209486\pi\) | |||||||
\(524\) | −4.20600e16 | −0.0887596 | ||||||||
\(525\) | 1.67971e17 | 0.350105 | ||||||||
\(526\) | 2.36476e17 | 0.486833 | ||||||||
\(527\) | −3.69497e15 | −0.00751349 | ||||||||
\(528\) | 3.40762e15 | 0.00684432 | ||||||||
\(529\) | −4.69225e17 | −0.930936 | ||||||||
\(530\) | −1.98468e17 | −0.388953 | ||||||||
\(531\) | 2.29349e17 | 0.444000 | ||||||||
\(532\) | 3.23821e17 | 0.619269 | ||||||||
\(533\) | −1.29668e18 | −2.44966 | ||||||||
\(534\) | −8.60224e17 | −1.60544 | ||||||||
\(535\) | 8.58475e16 | 0.158281 | ||||||||
\(536\) | −1.67886e17 | −0.305805 | ||||||||
\(537\) | −5.85642e17 | −1.05390 | ||||||||
\(538\) | 6.79435e16 | 0.120799 | ||||||||
\(539\) | −1.44100e16 | −0.0253126 | ||||||||
\(540\) | −2.12590e17 | −0.368963 | ||||||||
\(541\) | 1.10461e18 | 1.89420 | 0.947101 | − | 0.320936i | \(-0.103997\pi\) | ||||
0.947101 | + | 0.320936i | \(0.103997\pi\) | |||||||
\(542\) | 4.61304e17 | 0.781613 | ||||||||
\(543\) | −2.94859e17 | −0.493646 | ||||||||
\(544\) | 2.31127e16 | 0.0382347 | ||||||||
\(545\) | 1.64799e17 | 0.269387 | ||||||||
\(546\) | −1.24092e18 | −2.00443 | ||||||||
\(547\) | −6.13521e17 | −0.979292 | −0.489646 | − | 0.871921i | \(-0.662874\pi\) | ||||
−0.489646 | + | 0.871921i | \(0.662874\pi\) | |||||||
\(548\) | −1.31641e17 | −0.207644 | ||||||||
\(549\) | 1.41388e18 | 2.20390 | ||||||||
\(550\) | −2.22221e16 | −0.0342317 | ||||||||
\(551\) | −4.88345e17 | −0.743432 | ||||||||
\(552\) | 2.93911e17 | 0.442192 | ||||||||
\(553\) | 6.76795e17 | 1.00634 | ||||||||
\(554\) | 3.19086e17 | 0.468915 | ||||||||
\(555\) | 7.29683e17 | 1.05981 | ||||||||
\(556\) | −3.42066e17 | −0.491048 | ||||||||
\(557\) | −2.17270e17 | −0.308276 | −0.154138 | − | 0.988049i | \(-0.549260\pi\) | ||||
−0.154138 | + | 0.988049i | \(0.549260\pi\) | |||||||
\(558\) | −1.56984e17 | −0.220157 | ||||||||
\(559\) | −7.30440e17 | −1.01253 | ||||||||
\(560\) | −5.07663e15 | −0.00695591 | ||||||||
\(561\) | −1.30443e16 | −0.0176670 | ||||||||
\(562\) | −7.84080e17 | −1.04972 | ||||||||
\(563\) | −1.16883e18 | −1.54684 | −0.773422 | − | 0.633892i | \(-0.781457\pi\) | ||||
−0.773422 | + | 0.633892i | \(0.781457\pi\) | |||||||
\(564\) | 8.44623e17 | 1.10497 | ||||||||
\(565\) | 2.03890e17 | 0.263683 | ||||||||
\(566\) | 9.51066e17 | 1.21592 | ||||||||
\(567\) | 3.76030e17 | 0.475261 | ||||||||
\(568\) | 4.84766e17 | 0.605715 | ||||||||
\(569\) | −4.86769e17 | −0.601302 | −0.300651 | − | 0.953734i | \(-0.597204\pi\) | ||||
−0.300651 | + | 0.953734i | \(0.597204\pi\) | |||||||
\(570\) | −3.70619e17 | −0.452628 | ||||||||
\(571\) | −3.75968e17 | −0.453958 | −0.226979 | − | 0.973900i | \(-0.572885\pi\) | ||||
−0.226979 | + | 0.973900i | \(0.572885\pi\) | |||||||
\(572\) | −2.58251e17 | −0.308296 | ||||||||
\(573\) | 1.35934e18 | 1.60443 | ||||||||
\(574\) | 7.44578e17 | 0.868926 | ||||||||
\(575\) | −4.55510e16 | −0.0525601 | ||||||||
\(576\) | 1.00552e18 | 1.14721 | ||||||||
\(577\) | 2.49769e17 | 0.281771 | 0.140885 | − | 0.990026i | \(-0.455005\pi\) | ||||
0.140885 | + | 0.990026i | \(0.455005\pi\) | |||||||
\(578\) | −5.58039e17 | −0.622491 | ||||||||
\(579\) | −2.58903e17 | −0.285579 | ||||||||
\(580\) | −1.92265e17 | −0.209710 | ||||||||
\(581\) | 1.10283e18 | 1.18950 | ||||||||
\(582\) | 8.35581e17 | 0.891228 | ||||||||
\(583\) | 3.63142e17 | 0.383028 | ||||||||
\(584\) | 7.72452e16 | 0.0805728 | ||||||||
\(585\) | −1.43785e18 | −1.48320 | ||||||||
\(586\) | 4.79524e17 | 0.489188 | ||||||||
\(587\) | −1.02718e18 | −1.03633 | −0.518165 | − | 0.855281i | \(-0.673385\pi\) | ||||
−0.518165 | + | 0.855281i | \(0.673385\pi\) | |||||||
\(588\) | −9.46191e16 | −0.0944118 | ||||||||
\(589\) | 1.92090e17 | 0.189564 | ||||||||
\(590\) | 7.02382e16 | 0.0685544 | ||||||||
\(591\) | −2.89574e18 | −2.79538 | ||||||||
\(592\) | −2.20534e16 | −0.0210565 | ||||||||
\(593\) | 1.25381e18 | 1.18406 | 0.592032 | − | 0.805914i | \(-0.298326\pi\) | ||||
0.592032 | + | 0.805914i | \(0.298326\pi\) | |||||||
\(594\) | −2.47276e17 | −0.230978 | ||||||||
\(595\) | 1.94333e16 | 0.0179550 | ||||||||
\(596\) | 8.52367e17 | 0.778979 | ||||||||
\(597\) | −3.20166e18 | −2.89429 | ||||||||
\(598\) | 3.36517e17 | 0.300919 | ||||||||
\(599\) | −5.76424e17 | −0.509879 | −0.254940 | − | 0.966957i | \(-0.582056\pi\) | ||||
−0.254940 | + | 0.966957i | \(0.582056\pi\) | |||||||
\(600\) | −3.84590e17 | −0.336523 | ||||||||
\(601\) | −1.23224e18 | −1.06663 | −0.533313 | − | 0.845918i | \(-0.679053\pi\) | ||||
−0.533313 | + | 0.845918i | \(0.679053\pi\) | |||||||
\(602\) | 4.19433e17 | 0.359158 | ||||||||
\(603\) | 6.48899e17 | 0.549686 | ||||||||
\(604\) | −9.26247e16 | −0.0776223 | ||||||||
\(605\) | −4.98757e17 | −0.413503 | ||||||||
\(606\) | −1.62679e18 | −1.33432 | ||||||||
\(607\) | 1.17936e18 | 0.957019 | 0.478510 | − | 0.878082i | \(-0.341177\pi\) | ||||
0.478510 | + | 0.878082i | \(0.341177\pi\) | |||||||
\(608\) | −1.20156e18 | −0.964651 | ||||||||
\(609\) | 1.69040e18 | 1.34269 | ||||||||
\(610\) | 4.33001e17 | 0.340287 | ||||||||
\(611\) | 2.54889e18 | 1.98191 | ||||||||
\(612\) | −5.51236e16 | −0.0424085 | ||||||||
\(613\) | 7.39177e17 | 0.562672 | 0.281336 | − | 0.959609i | \(-0.409222\pi\) | ||||
0.281336 | + | 0.959609i | \(0.409222\pi\) | |||||||
\(614\) | −1.51284e16 | −0.0113946 | ||||||||
\(615\) | 1.34054e18 | 0.999058 | ||||||||
\(616\) | 3.90855e17 | 0.288231 | ||||||||
\(617\) | 2.13054e18 | 1.55467 | 0.777333 | − | 0.629090i | \(-0.216572\pi\) | ||||
0.777333 | + | 0.629090i | \(0.216572\pi\) | |||||||
\(618\) | −8.03018e17 | −0.579830 | ||||||||
\(619\) | 1.66755e18 | 1.19149 | 0.595744 | − | 0.803175i | \(-0.296857\pi\) | ||||
0.595744 | + | 0.803175i | \(0.296857\pi\) | |||||||
\(620\) | 7.56272e16 | 0.0534727 | ||||||||
\(621\) | −5.06867e17 | −0.354649 | ||||||||
\(622\) | −1.27192e18 | −0.880691 | ||||||||
\(623\) | −2.34489e18 | −1.60676 | ||||||||
\(624\) | 6.75234e16 | 0.0457883 | ||||||||
\(625\) | 5.96046e16 | 0.0400000 | ||||||||
\(626\) | 1.64512e17 | 0.109261 | ||||||||
\(627\) | 6.78132e17 | 0.445733 | ||||||||
\(628\) | −8.65584e17 | −0.563082 | ||||||||
\(629\) | 8.44202e16 | 0.0543522 | ||||||||
\(630\) | 8.25640e17 | 0.526111 | ||||||||
\(631\) | −7.05851e16 | −0.0445166 | −0.0222583 | − | 0.999752i | \(-0.507086\pi\) | ||||
−0.0222583 | + | 0.999752i | \(0.507086\pi\) | |||||||
\(632\) | −1.54961e18 | −0.967298 | ||||||||
\(633\) | 2.99922e18 | 1.85304 | ||||||||
\(634\) | −1.63700e18 | −1.00108 | ||||||||
\(635\) | −1.63304e17 | −0.0988477 | ||||||||
\(636\) | 2.38447e18 | 1.42863 | ||||||||
\(637\) | −2.85540e17 | −0.169340 | ||||||||
\(638\) | −2.23636e17 | −0.131282 | ||||||||
\(639\) | −1.87367e18 | −1.08878 | ||||||||
\(640\) | −4.65848e17 | −0.267963 | ||||||||
\(641\) | −2.27477e18 | −1.29527 | −0.647635 | − | 0.761951i | \(-0.724242\pi\) | ||||
−0.647635 | + | 0.761951i | \(0.724242\pi\) | |||||||
\(642\) | 6.55667e17 | 0.369578 | ||||||||
\(643\) | −1.40077e18 | −0.781621 | −0.390810 | − | 0.920471i | \(-0.627805\pi\) | ||||
−0.390810 | + | 0.920471i | \(0.627805\pi\) | |||||||
\(644\) | 3.03970e17 | 0.167908 | ||||||||
\(645\) | 7.55146e17 | 0.412946 | ||||||||
\(646\) | −4.28785e16 | −0.0232129 | ||||||||
\(647\) | 3.49376e18 | 1.87247 | 0.936237 | − | 0.351369i | \(-0.114284\pi\) | ||||
0.936237 | + | 0.351369i | \(0.114284\pi\) | |||||||
\(648\) | −8.60967e17 | −0.456824 | ||||||||
\(649\) | −1.28517e17 | −0.0675102 | ||||||||
\(650\) | −4.40342e17 | −0.229009 | ||||||||
\(651\) | −6.64915e17 | −0.342365 | ||||||||
\(652\) | −1.26705e18 | −0.645930 | ||||||||
\(653\) | 4.17303e17 | 0.210628 | 0.105314 | − | 0.994439i | \(-0.466415\pi\) | ||||
0.105314 | + | 0.994439i | \(0.466415\pi\) | |||||||
\(654\) | 1.25867e18 | 0.629006 | ||||||||
\(655\) | 1.31221e17 | 0.0649284 | ||||||||
\(656\) | −4.05155e16 | −0.0198494 | ||||||||
\(657\) | −2.98561e17 | −0.144830 | ||||||||
\(658\) | −1.46362e18 | −0.703008 | ||||||||
\(659\) | −2.83630e18 | −1.34895 | −0.674477 | − | 0.738296i | \(-0.735631\pi\) | ||||
−0.674477 | + | 0.738296i | \(0.735631\pi\) | |||||||
\(660\) | 2.66986e17 | 0.125734 | ||||||||
\(661\) | 8.05065e17 | 0.375423 | 0.187712 | − | 0.982224i | \(-0.439893\pi\) | ||||
0.187712 | + | 0.982224i | \(0.439893\pi\) | |||||||
\(662\) | 2.07320e18 | 0.957336 | ||||||||
\(663\) | −2.58478e17 | −0.118192 | ||||||||
\(664\) | −2.52507e18 | −1.14335 | ||||||||
\(665\) | −1.01027e18 | −0.453001 | ||||||||
\(666\) | 3.58667e18 | 1.59261 | ||||||||
\(667\) | −4.58408e17 | −0.201574 | ||||||||
\(668\) | 6.87740e17 | 0.299486 | ||||||||
\(669\) | −7.37486e18 | −3.18042 | ||||||||
\(670\) | 1.98726e17 | 0.0848726 | ||||||||
\(671\) | −7.92274e17 | −0.335104 | ||||||||
\(672\) | 4.15916e18 | 1.74223 | ||||||||
\(673\) | 3.03151e18 | 1.25765 | 0.628827 | − | 0.777546i | \(-0.283535\pi\) | ||||
0.628827 | + | 0.777546i | \(0.283535\pi\) | |||||||
\(674\) | 1.47842e18 | 0.607449 | ||||||||
\(675\) | 6.63249e17 | 0.269900 | ||||||||
\(676\) | −3.60048e18 | −1.45113 | ||||||||
\(677\) | −1.58711e18 | −0.633551 | −0.316775 | − | 0.948501i | \(-0.602600\pi\) | ||||
−0.316775 | + | 0.948501i | \(0.602600\pi\) | |||||||
\(678\) | 1.55723e18 | 0.615686 | ||||||||
\(679\) | 2.27772e18 | 0.891963 | ||||||||
\(680\) | −4.44949e16 | −0.0172585 | ||||||||
\(681\) | 3.04236e18 | 1.16884 | ||||||||
\(682\) | 8.79667e16 | 0.0334749 | ||||||||
\(683\) | 9.37243e17 | 0.353279 | 0.176640 | − | 0.984276i | \(-0.443477\pi\) | ||||
0.176640 | + | 0.984276i | \(0.443477\pi\) | |||||||
\(684\) | 2.86570e18 | 1.06996 | ||||||||
\(685\) | 4.10702e17 | 0.151893 | ||||||||
\(686\) | −1.61445e18 | −0.591449 | ||||||||
\(687\) | 2.12187e17 | 0.0770018 | ||||||||
\(688\) | −2.28230e16 | −0.00820443 | ||||||||
\(689\) | 7.19582e18 | 2.56245 | ||||||||
\(690\) | −3.47899e17 | −0.122725 | ||||||||
\(691\) | −4.89005e18 | −1.70886 | −0.854428 | − | 0.519569i | \(-0.826093\pi\) | ||||
−0.854428 | + | 0.519569i | \(0.826093\pi\) | |||||||
\(692\) | 7.89721e17 | 0.273391 | ||||||||
\(693\) | −1.51070e18 | −0.518097 | ||||||||
\(694\) | 2.34846e17 | 0.0797897 | ||||||||
\(695\) | 1.06720e18 | 0.359206 | ||||||||
\(696\) | −3.87037e18 | −1.29060 | ||||||||
\(697\) | 1.55093e17 | 0.0512364 | ||||||||
\(698\) | −2.14395e18 | −0.701704 | ||||||||
\(699\) | 2.21917e18 | 0.719597 | ||||||||
\(700\) | −3.97753e17 | −0.127784 | ||||||||
\(701\) | 1.21554e18 | 0.386902 | 0.193451 | − | 0.981110i | \(-0.438032\pi\) | ||||
0.193451 | + | 0.981110i | \(0.438032\pi\) | |||||||
\(702\) | −4.89989e18 | −1.54524 | ||||||||
\(703\) | −4.38874e18 | −1.37129 | ||||||||
\(704\) | −5.63446e17 | −0.174433 | ||||||||
\(705\) | −2.63510e18 | −0.808292 | ||||||||
\(706\) | 3.52300e18 | 1.07074 | ||||||||
\(707\) | −4.43449e18 | −1.33542 | ||||||||
\(708\) | −8.43870e17 | −0.251802 | ||||||||
\(709\) | 2.62006e18 | 0.774658 | 0.387329 | − | 0.921942i | \(-0.373398\pi\) | ||||
0.387329 | + | 0.921942i | \(0.373398\pi\) | |||||||
\(710\) | −5.73813e17 | −0.168109 | ||||||||
\(711\) | 5.98939e18 | 1.73872 | ||||||||
\(712\) | 5.36893e18 | 1.54443 | ||||||||
\(713\) | 1.80314e17 | 0.0513982 | ||||||||
\(714\) | 1.48423e17 | 0.0419240 | ||||||||
\(715\) | 8.05705e17 | 0.225521 | ||||||||
\(716\) | 1.38679e18 | 0.384660 | ||||||||
\(717\) | −9.90160e18 | −2.72164 | ||||||||
\(718\) | 2.63070e18 | 0.716576 | ||||||||
\(719\) | −2.75759e18 | −0.744375 | −0.372187 | − | 0.928158i | \(-0.621392\pi\) | ||||
−0.372187 | + | 0.928158i | \(0.621392\pi\) | |||||||
\(720\) | −4.49264e16 | −0.0120182 | ||||||||
\(721\) | −2.18896e18 | −0.580307 | ||||||||
\(722\) | −1.43710e17 | −0.0377567 | ||||||||
\(723\) | −2.59484e18 | −0.675634 | ||||||||
\(724\) | 6.98224e17 | 0.180175 | ||||||||
\(725\) | 5.99839e17 | 0.153404 | ||||||||
\(726\) | −3.80930e18 | −0.965510 | ||||||||
\(727\) | 5.02204e18 | 1.26156 | 0.630778 | − | 0.775963i | \(-0.282736\pi\) | ||||
0.630778 | + | 0.775963i | \(0.282736\pi\) | |||||||
\(728\) | 7.74496e18 | 1.92826 | ||||||||
\(729\) | −5.83276e18 | −1.43928 | ||||||||
\(730\) | −9.14344e16 | −0.0223620 | ||||||||
\(731\) | 8.73661e16 | 0.0211778 | ||||||||
\(732\) | −5.20225e18 | −1.24988 | ||||||||
\(733\) | −4.44902e17 | −0.105947 | −0.0529734 | − | 0.998596i | \(-0.516870\pi\) | ||||
−0.0529734 | + | 0.998596i | \(0.516870\pi\) | |||||||
\(734\) | −3.23001e18 | −0.762393 | ||||||||
\(735\) | 2.95198e17 | 0.0690630 | ||||||||
\(736\) | −1.12790e18 | −0.261555 | ||||||||
\(737\) | −3.63614e17 | −0.0835798 | ||||||||
\(738\) | 6.58925e18 | 1.50131 | ||||||||
\(739\) | 7.66043e18 | 1.73007 | 0.865037 | − | 0.501709i | \(-0.167295\pi\) | ||||
0.865037 | + | 0.501709i | \(0.167295\pi\) | |||||||
\(740\) | −1.72788e18 | −0.386819 | ||||||||
\(741\) | 1.34375e19 | 2.98194 | ||||||||
\(742\) | −4.13197e18 | −0.908933 | ||||||||
\(743\) | 2.91989e18 | 0.636706 | 0.318353 | − | 0.947972i | \(-0.396870\pi\) | ||||
0.318353 | + | 0.947972i | \(0.396870\pi\) | |||||||
\(744\) | 1.52241e18 | 0.329084 | ||||||||
\(745\) | −2.65926e18 | −0.569830 | ||||||||
\(746\) | −1.51487e18 | −0.321790 | ||||||||
\(747\) | 9.75967e18 | 2.05519 | ||||||||
\(748\) | 3.08887e16 | 0.00644822 | ||||||||
\(749\) | 1.78729e18 | 0.369882 | ||||||||
\(750\) | 4.55235e17 | 0.0933980 | ||||||||
\(751\) | 1.98445e18 | 0.403628 | 0.201814 | − | 0.979424i | \(-0.435316\pi\) | ||||
0.201814 | + | 0.979424i | \(0.435316\pi\) | |||||||
\(752\) | 7.96415e16 | 0.0160592 | ||||||||
\(753\) | −5.80034e18 | −1.15954 | ||||||||
\(754\) | −4.43144e18 | −0.878276 | ||||||||
\(755\) | 2.88976e17 | 0.0567814 | ||||||||
\(756\) | −4.42598e18 | −0.862220 | ||||||||
\(757\) | −4.46722e18 | −0.862807 | −0.431404 | − | 0.902159i | \(-0.641982\pi\) | ||||
−0.431404 | + | 0.902159i | \(0.641982\pi\) | |||||||
\(758\) | 1.79540e18 | 0.343805 | ||||||||
\(759\) | 6.36560e17 | 0.120856 | ||||||||
\(760\) | 2.31315e18 | 0.435427 | ||||||||
\(761\) | −7.81343e18 | −1.45828 | −0.729141 | − | 0.684363i | \(-0.760080\pi\) | ||||
−0.729141 | + | 0.684363i | \(0.760080\pi\) | |||||||
\(762\) | −1.24724e18 | −0.230805 | ||||||||
\(763\) | 3.43101e18 | 0.629525 | ||||||||
\(764\) | −3.21889e18 | −0.585598 | ||||||||
\(765\) | 1.71978e17 | 0.0310222 | ||||||||
\(766\) | 6.10310e18 | 1.09160 | ||||||||
\(767\) | −2.54662e18 | −0.451642 | ||||||||
\(768\) | −9.60957e18 | −1.68988 | ||||||||
\(769\) | 2.15334e17 | 0.0375483 | 0.0187742 | − | 0.999824i | \(-0.494024\pi\) | ||||
0.0187742 | + | 0.999824i | \(0.494024\pi\) | |||||||
\(770\) | −4.62651e17 | −0.0799952 | ||||||||
\(771\) | −8.39193e18 | −1.43883 | ||||||||
\(772\) | 6.13080e17 | 0.104233 | ||||||||
\(773\) | −7.73551e18 | −1.30413 | −0.652067 | − | 0.758162i | \(-0.726098\pi\) | ||||
−0.652067 | + | 0.758162i | \(0.726098\pi\) | |||||||
\(774\) | 3.71183e18 | 0.620543 | ||||||||
\(775\) | −2.35946e17 | −0.0391157 | ||||||||
\(776\) | −5.21512e18 | −0.857360 | ||||||||
\(777\) | 1.51915e19 | 2.47665 | ||||||||
\(778\) | −5.36860e18 | −0.867948 | ||||||||
\(779\) | −8.06278e18 | −1.29268 | ||||||||
\(780\) | 5.29044e18 | 0.841157 | ||||||||
\(781\) | 1.04992e18 | 0.165548 | ||||||||
\(782\) | −4.02500e16 | −0.00629392 | ||||||||
\(783\) | 6.67469e18 | 1.03509 | ||||||||
\(784\) | −8.92186e15 | −0.00137215 | ||||||||
\(785\) | 2.70050e18 | 0.411899 | ||||||||
\(786\) | 1.00221e18 | 0.151605 | ||||||||
\(787\) | 7.07633e18 | 1.06163 | 0.530814 | − | 0.847488i | \(-0.321886\pi\) | ||||
0.530814 | + | 0.847488i | \(0.321886\pi\) | |||||||
\(788\) | 6.85707e18 | 1.02028 | ||||||||
\(789\) | 8.86387e18 | 1.30805 | ||||||||
\(790\) | 1.83425e18 | 0.268462 | ||||||||
\(791\) | 4.24487e18 | 0.616193 | ||||||||
\(792\) | 3.45893e18 | 0.497998 | ||||||||
\(793\) | −1.56993e19 | −2.24184 | ||||||||
\(794\) | −2.72668e18 | −0.386189 | ||||||||
\(795\) | −7.43920e18 | −1.04506 | ||||||||
\(796\) | 7.58150e18 | 1.05638 | ||||||||
\(797\) | 8.43425e17 | 0.116565 | 0.0582824 | − | 0.998300i | \(-0.481438\pi\) | ||||
0.0582824 | + | 0.998300i | \(0.481438\pi\) | |||||||
\(798\) | −7.71605e18 | −1.05773 | ||||||||
\(799\) | −3.04866e17 | −0.0414529 | ||||||||
\(800\) | 1.47588e18 | 0.199052 | ||||||||
\(801\) | −2.07515e19 | −2.77612 | ||||||||
\(802\) | 2.42223e18 | 0.321427 | ||||||||
\(803\) | 1.67300e17 | 0.0220214 | ||||||||
\(804\) | −2.38757e18 | −0.311739 | ||||||||
\(805\) | −9.48342e17 | −0.122826 | ||||||||
\(806\) | 1.74310e18 | 0.223947 | ||||||||
\(807\) | 2.54674e18 | 0.324568 | ||||||||
\(808\) | 1.01533e19 | 1.28361 | ||||||||
\(809\) | 5.80962e18 | 0.728588 | 0.364294 | − | 0.931284i | \(-0.381310\pi\) | ||||
0.364294 | + | 0.931284i | \(0.381310\pi\) | |||||||
\(810\) | 1.01912e18 | 0.126786 | ||||||||
\(811\) | 1.15747e19 | 1.42848 | 0.714240 | − | 0.699901i | \(-0.246773\pi\) | ||||
0.714240 | + | 0.699901i | \(0.246773\pi\) | |||||||
\(812\) | −4.00284e18 | −0.490065 | ||||||||
\(813\) | 1.72911e19 | 2.10008 | ||||||||
\(814\) | −2.00981e18 | −0.242156 | ||||||||
\(815\) | 3.95302e18 | 0.472503 | ||||||||
\(816\) | −8.07630e15 | −0.000957694 0 | ||||||||
\(817\) | −4.54189e18 | −0.534310 | ||||||||
\(818\) | 4.72078e18 | 0.550957 | ||||||||
\(819\) | −2.99351e19 | −3.46606 | ||||||||
\(820\) | −3.17438e18 | −0.364644 | ||||||||
\(821\) | 4.73256e18 | 0.539343 | 0.269672 | − | 0.962952i | \(-0.413085\pi\) | ||||
0.269672 | + | 0.962952i | \(0.413085\pi\) | |||||||
\(822\) | 3.13677e18 | 0.354663 | ||||||||
\(823\) | 5.39004e18 | 0.604634 | 0.302317 | − | 0.953207i | \(-0.402240\pi\) | ||||
0.302317 | + | 0.953207i | \(0.402240\pi\) | |||||||
\(824\) | 5.01189e18 | 0.557795 | ||||||||
\(825\) | −8.32956e17 | −0.0919754 | ||||||||
\(826\) | 1.46232e18 | 0.160203 | ||||||||
\(827\) | −4.87314e18 | −0.529692 | −0.264846 | − | 0.964291i | \(-0.585321\pi\) | ||||
−0.264846 | + | 0.964291i | \(0.585321\pi\) | |||||||
\(828\) | 2.69003e18 | 0.290108 | ||||||||
\(829\) | −1.10498e19 | −1.18236 | −0.591182 | − | 0.806538i | \(-0.701339\pi\) | ||||
−0.591182 | + | 0.806538i | \(0.701339\pi\) | |||||||
\(830\) | 2.98890e18 | 0.317325 | ||||||||
\(831\) | 1.19603e19 | 1.25990 | ||||||||
\(832\) | −1.11649e19 | −1.16696 | ||||||||
\(833\) | 3.41527e16 | 0.00354187 | ||||||||
\(834\) | 8.15080e18 | 0.838728 | ||||||||
\(835\) | −2.14565e18 | −0.219077 | ||||||||
\(836\) | −1.60581e18 | −0.162687 | ||||||||
\(837\) | −2.62548e18 | −0.263933 | ||||||||
\(838\) | −7.64797e18 | −0.762887 | ||||||||
\(839\) | 8.80967e17 | 0.0871981 | 0.0435990 | − | 0.999049i | \(-0.486118\pi\) | ||||
0.0435990 | + | 0.999049i | \(0.486118\pi\) | |||||||
\(840\) | −8.00692e18 | −0.786412 | ||||||||
\(841\) | −4.22407e18 | −0.411677 | ||||||||
\(842\) | 2.96244e18 | 0.286498 | ||||||||
\(843\) | −2.93898e19 | −2.82044 | ||||||||
\(844\) | −7.10211e18 | −0.676335 | ||||||||
\(845\) | 1.12330e19 | 1.06152 | ||||||||
\(846\) | −1.29525e19 | −1.21464 | ||||||||
\(847\) | −1.03838e19 | −0.966305 | ||||||||
\(848\) | 2.24837e17 | 0.0207633 | ||||||||
\(849\) | 3.56490e19 | 3.26698 | ||||||||
\(850\) | 5.26681e16 | 0.00478988 | ||||||||
\(851\) | −4.11970e18 | −0.371812 | ||||||||
\(852\) | 6.89401e18 | 0.617469 | ||||||||
\(853\) | −5.43444e18 | −0.483043 | −0.241522 | − | 0.970395i | \(-0.577646\pi\) | ||||
−0.241522 | + | 0.970395i | \(0.577646\pi\) | |||||||
\(854\) | 9.01481e18 | 0.795208 | ||||||||
\(855\) | −8.94057e18 | −0.782682 | ||||||||
\(856\) | −4.09223e18 | −0.355533 | ||||||||
\(857\) | 3.79499e18 | 0.327217 | 0.163608 | − | 0.986525i | \(-0.447687\pi\) | ||||
0.163608 | + | 0.986525i | \(0.447687\pi\) | |||||||
\(858\) | 6.15364e18 | 0.526580 | ||||||||
\(859\) | −1.65792e17 | −0.0140802 | −0.00704010 | − | 0.999975i | \(-0.502241\pi\) | ||||
−0.00704010 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(860\) | −1.78818e18 | −0.150720 | ||||||||
\(861\) | 2.79091e19 | 2.33467 | ||||||||
\(862\) | 1.41734e17 | 0.0117673 | ||||||||
\(863\) | 1.66111e19 | 1.36877 | 0.684383 | − | 0.729123i | \(-0.260072\pi\) | ||||
0.684383 | + | 0.729123i | \(0.260072\pi\) | |||||||
\(864\) | 1.64228e19 | 1.34310 | ||||||||
\(865\) | −2.46382e18 | −0.199988 | ||||||||
\(866\) | −4.12717e18 | −0.332496 | ||||||||
\(867\) | −2.09171e19 | −1.67254 | ||||||||
\(868\) | 1.57451e18 | 0.124959 | ||||||||
\(869\) | −3.35618e18 | −0.264373 | ||||||||
\(870\) | 4.58132e18 | 0.358192 | ||||||||
\(871\) | −7.20517e18 | −0.559147 | ||||||||
\(872\) | −7.85573e18 | −0.605103 | ||||||||
\(873\) | 2.01570e19 | 1.54111 | ||||||||
\(874\) | 2.09247e18 | 0.158794 | ||||||||
\(875\) | 1.24093e18 | 0.0934750 | ||||||||
\(876\) | 1.09853e18 | 0.0821363 | ||||||||
\(877\) | −2.03717e18 | −0.151192 | −0.0755960 | − | 0.997139i | \(-0.524086\pi\) | ||||
−0.0755960 | + | 0.997139i | \(0.524086\pi\) | |||||||
\(878\) | −4.08194e18 | −0.300713 | ||||||||
\(879\) | 1.79741e19 | 1.31437 | ||||||||
\(880\) | 2.51747e16 | 0.00182737 | ||||||||
\(881\) | −1.97226e19 | −1.42109 | −0.710545 | − | 0.703652i | \(-0.751551\pi\) | ||||
−0.710545 | + | 0.703652i | \(0.751551\pi\) | |||||||
\(882\) | 1.45101e18 | 0.103783 | ||||||||
\(883\) | 4.19713e18 | 0.297994 | 0.148997 | − | 0.988838i | \(-0.452396\pi\) | ||||
0.148997 | + | 0.988838i | \(0.452396\pi\) | |||||||
\(884\) | 6.12074e17 | 0.0431384 | ||||||||
\(885\) | 2.63275e18 | 0.184195 | ||||||||
\(886\) | 1.27253e19 | 0.883789 | ||||||||
\(887\) | −6.63464e18 | −0.457418 | −0.228709 | − | 0.973495i | \(-0.573450\pi\) | ||||
−0.228709 | + | 0.973495i | \(0.573450\pi\) | |||||||
\(888\) | −3.47829e19 | −2.38057 | ||||||||
\(889\) | −3.39988e18 | −0.230995 | ||||||||
\(890\) | −6.35514e18 | −0.428638 | ||||||||
\(891\) | −1.86471e18 | −0.124855 | ||||||||
\(892\) | 1.74636e19 | 1.16081 | ||||||||
\(893\) | 1.58490e19 | 1.04585 | ||||||||
\(894\) | −2.03103e19 | −1.33052 | ||||||||
\(895\) | −4.32659e18 | −0.281382 | ||||||||
\(896\) | −9.69866e18 | −0.626195 | ||||||||
\(897\) | 1.26137e19 | 0.808523 | ||||||||
\(898\) | 3.00946e18 | 0.191510 | ||||||||
\(899\) | −2.37447e18 | −0.150013 | ||||||||
\(900\) | −3.51997e18 | −0.220782 | ||||||||
\(901\) | −8.60673e17 | −0.0535954 | ||||||||
\(902\) | −3.69232e18 | −0.228274 | ||||||||
\(903\) | 1.57217e19 | 0.965002 | ||||||||
\(904\) | −9.71915e18 | −0.592289 | ||||||||
\(905\) | −2.17836e18 | −0.131799 | ||||||||
\(906\) | 2.20707e18 | 0.132582 | ||||||||
\(907\) | 5.59272e18 | 0.333561 | 0.166781 | − | 0.985994i | \(-0.446663\pi\) | ||||
0.166781 | + | 0.985994i | \(0.446663\pi\) | |||||||
\(908\) | −7.20427e18 | −0.426611 | ||||||||
\(909\) | −3.92437e19 | −2.30730 | ||||||||
\(910\) | −9.16763e18 | −0.535166 | ||||||||
\(911\) | 4.19586e18 | 0.243193 | 0.121597 | − | 0.992580i | \(-0.461199\pi\) | ||||
0.121597 | + | 0.992580i | \(0.461199\pi\) | |||||||
\(912\) | 4.19862e17 | 0.0241624 | ||||||||
\(913\) | −5.46887e18 | −0.312491 | ||||||||
\(914\) | −5.54933e18 | −0.314840 | ||||||||
\(915\) | 1.62303e19 | 0.914299 | ||||||||
\(916\) | −5.02458e17 | −0.0281047 | ||||||||
\(917\) | 2.73194e18 | 0.151730 | ||||||||
\(918\) | 5.86063e17 | 0.0323197 | ||||||||
\(919\) | 6.83436e18 | 0.374237 | 0.187119 | − | 0.982337i | \(-0.440085\pi\) | ||||
0.187119 | + | 0.982337i | \(0.440085\pi\) | |||||||
\(920\) | 2.17135e18 | 0.118062 | ||||||||
\(921\) | −5.67061e17 | −0.0306155 | ||||||||
\(922\) | 1.13911e19 | 0.610683 | ||||||||
\(923\) | 2.08047e19 | 1.10751 | ||||||||
\(924\) | 5.55847e18 | 0.293824 | ||||||||
\(925\) | 5.39074e18 | 0.282961 | ||||||||
\(926\) | −6.85399e18 | −0.357250 | ||||||||
\(927\) | −1.93715e19 | −1.00264 | ||||||||
\(928\) | 1.48527e19 | 0.763387 | ||||||||
\(929\) | −7.68529e18 | −0.392246 | −0.196123 | − | 0.980579i | \(-0.562835\pi\) | ||||
−0.196123 | + | 0.980579i | \(0.562835\pi\) | |||||||
\(930\) | −1.80206e18 | −0.0913333 | ||||||||
\(931\) | −1.77549e18 | −0.0893606 | ||||||||
\(932\) | −5.25497e18 | −0.262644 | ||||||||
\(933\) | −4.76757e19 | −2.36628 | ||||||||
\(934\) | 2.44065e19 | 1.20296 | ||||||||
\(935\) | −9.63684e16 | −0.00471693 | ||||||||
\(936\) | 6.85402e19 | 3.33159 | ||||||||
\(937\) | 1.82302e19 | 0.880004 | 0.440002 | − | 0.897997i | \(-0.354978\pi\) | ||||
0.440002 | + | 0.897997i | \(0.354978\pi\) | |||||||
\(938\) | 4.13734e18 | 0.198337 | ||||||||
\(939\) | 6.16641e18 | 0.293566 | ||||||||
\(940\) | 6.23989e18 | 0.295016 | ||||||||
\(941\) | 4.01498e18 | 0.188517 | 0.0942586 | − | 0.995548i | \(-0.469952\pi\) | ||||
0.0942586 | + | 0.995548i | \(0.469952\pi\) | |||||||
\(942\) | 2.06253e19 | 0.961764 | ||||||||
\(943\) | −7.56851e18 | −0.350497 | ||||||||
\(944\) | −7.95705e16 | −0.00365961 | ||||||||
\(945\) | 1.38084e19 | 0.630721 | ||||||||
\(946\) | −2.07994e18 | −0.0943536 | ||||||||
\(947\) | 2.28347e19 | 1.02877 | 0.514387 | − | 0.857558i | \(-0.328020\pi\) | ||||
0.514387 | + | 0.857558i | \(0.328020\pi\) | |||||||
\(948\) | −2.20374e19 | −0.986068 | ||||||||
\(949\) | 3.31513e18 | 0.147323 | ||||||||
\(950\) | −2.73805e18 | −0.120848 | ||||||||
\(951\) | −6.13599e19 | −2.68975 | ||||||||
\(952\) | −9.26355e17 | −0.0403309 | ||||||||
\(953\) | −3.72340e19 | −1.61004 | −0.805018 | − | 0.593250i | \(-0.797845\pi\) | ||||
−0.805018 | + | 0.593250i | \(0.797845\pi\) | |||||||
\(954\) | −3.65665e19 | −1.57043 | ||||||||
\(955\) | 1.00425e19 | 0.428370 | ||||||||
\(956\) | 2.34469e19 | 0.993364 | ||||||||
\(957\) | −8.38257e18 | −0.352736 | ||||||||
\(958\) | −1.01983e19 | −0.426238 | ||||||||
\(959\) | 8.55056e18 | 0.354955 | ||||||||
\(960\) | 1.15426e19 | 0.475926 | ||||||||
\(961\) | −2.34836e19 | −0.961749 | ||||||||
\(962\) | −3.98252e19 | −1.62002 | ||||||||
\(963\) | 1.58169e19 | 0.639073 | ||||||||
\(964\) | 6.14455e18 | 0.246598 | ||||||||
\(965\) | −1.91272e18 | −0.0762472 | ||||||||
\(966\) | −7.24304e18 | −0.286794 | ||||||||
\(967\) | 1.86235e19 | 0.732471 | 0.366235 | − | 0.930522i | \(-0.380647\pi\) | ||||
0.366235 | + | 0.930522i | \(0.380647\pi\) | |||||||
\(968\) | 2.37750e19 | 0.928818 | ||||||||
\(969\) | −1.60722e18 | −0.0623694 | ||||||||
\(970\) | 6.17309e18 | 0.237950 | ||||||||
\(971\) | −4.46491e19 | −1.70957 | −0.854787 | − | 0.518980i | \(-0.826312\pi\) | ||||
−0.854787 | + | 0.518980i | \(0.826312\pi\) | |||||||
\(972\) | 9.44786e18 | 0.359338 | ||||||||
\(973\) | 2.22184e19 | 0.839419 | ||||||||
\(974\) | 1.01140e19 | 0.379569 | ||||||||
\(975\) | −1.65054e19 | −0.615313 | ||||||||
\(976\) | −4.90533e17 | −0.0181654 | ||||||||
\(977\) | 3.67191e19 | 1.35076 | 0.675378 | − | 0.737471i | \(-0.263980\pi\) | ||||
0.675378 | + | 0.737471i | \(0.263980\pi\) | |||||||
\(978\) | 3.01915e19 | 1.10327 | ||||||||
\(979\) | 1.16282e19 | 0.422109 | ||||||||
\(980\) | −6.99025e17 | −0.0252071 | ||||||||
\(981\) | 3.03632e19 | 1.08768 | ||||||||
\(982\) | 1.84733e19 | 0.657384 | ||||||||
\(983\) | −1.84031e19 | −0.650570 | −0.325285 | − | 0.945616i | \(-0.605460\pi\) | ||||
−0.325285 | + | 0.945616i | \(0.605460\pi\) | |||||||
\(984\) | −6.39015e19 | −2.24410 | ||||||||
\(985\) | −2.13931e19 | −0.746341 | ||||||||
\(986\) | 5.30033e17 | 0.0183697 | ||||||||
\(987\) | −5.48611e19 | −1.88888 | ||||||||
\(988\) | −3.18198e19 | −1.08837 | ||||||||
\(989\) | −4.26346e18 | −0.144873 | ||||||||
\(990\) | −4.09430e18 | −0.138214 | ||||||||
\(991\) | 5.17113e19 | 1.73423 | 0.867115 | − | 0.498108i | \(-0.165972\pi\) | ||||
0.867115 | + | 0.498108i | \(0.165972\pi\) | |||||||
\(992\) | −5.84231e18 | −0.194652 | ||||||||
\(993\) | 7.77102e19 | 2.57222 | ||||||||
\(994\) | −1.19464e19 | −0.392850 | ||||||||
\(995\) | −2.36532e19 | −0.772751 | ||||||||
\(996\) | −3.59098e19 | −1.16554 | ||||||||
\(997\) | −4.39824e19 | −1.41827 | −0.709137 | − | 0.705071i | \(-0.750915\pi\) | ||||
−0.709137 | + | 0.705071i | \(0.750915\pi\) | |||||||
\(998\) | −2.33617e19 | −0.748437 | ||||||||
\(999\) | 5.99853e19 | 1.90928 |
(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 | 5.14.a.b.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 45.14.a.e.1.2 | 3 | |||
4.3 | odd | 2 | 80.14.a.g.1.1 | 3 | |||
5.2 | odd | 4 | 25.14.b.b.24.4 | 6 | |||
5.3 | odd | 4 | 25.14.b.b.24.3 | 6 | |||
5.4 | even | 2 | 25.14.a.b.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.14.a.b.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
25.14.a.b.1.2 | 3 | 5.4 | even | 2 | |||
25.14.b.b.24.3 | 6 | 5.3 | odd | 4 | |||
25.14.b.b.24.4 | 6 | 5.2 | odd | 4 | |||
45.14.a.e.1.2 | 3 | 3.2 | odd | 2 | |||
80.14.a.g.1.1 | 3 | 4.3 | odd | 2 |