Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,11,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.d (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: | \(7.62428703208\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} + 198 x^{8} - 1066 x^{7} + 30608 x^{6} - 147714 x^{5} + 2092829 x^{4} - 9587938 x^{3} + 101463432 x^{2} - 344403128 x + 1648684816 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.10 | ||
Root | \(3.29676 + 5.71016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.11.d.a.7.9 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 31.4354 | + | 5.98464i | 0.982356 | + | 0.187020i | ||||
\(3\) | 140.296i | 0.577350i | ||||||||
\(4\) | 952.368 | + | 376.259i | 0.930047 | + | 0.367440i | ||||
\(5\) | 581.119 | 0.185958 | 0.0929791 | − | 0.995668i | \(-0.470361\pi\) | ||||
0.0929791 | + | 0.995668i | \(0.470361\pi\) | |||||||
\(6\) | −839.621 | + | 4410.26i | −0.107976 | + | 0.567164i | ||||
\(7\) | 18141.8i | 1.07942i | 0.841851 | + | 0.539710i | \(0.181466\pi\) | ||||
−0.841851 | + | 0.539710i | \(0.818534\pi\) | |||||||
\(8\) | 27686.3 | + | 17527.4i | 0.844919 | + | 0.534895i | ||||
\(9\) | −19683.0 | −0.333333 | ||||||||
\(10\) | 18267.7 | + | 3477.79i | 0.182677 | + | 0.0347779i | ||||
\(11\) | 3142.03i | 0.0195095i | 0.999952 | + | 0.00975477i | \(0.00310509\pi\) | ||||
−0.999952 | + | 0.00975477i | \(0.996895\pi\) | |||||||
\(12\) | −52787.7 | + | 133614.i | −0.212142 | + | 0.536963i | ||||
\(13\) | 277162. | 0.746477 | 0.373239 | − | 0.927735i | \(-0.378247\pi\) | ||||
0.373239 | + | 0.927735i | \(0.378247\pi\) | |||||||
\(14\) | −108572. | + | 570295.i | −0.201873 | + | 1.06037i | ||||
\(15\) | 81528.8i | 0.107363i | ||||||||
\(16\) | 765434. | + | 716674.i | 0.729975 | + | 0.683474i | ||||
\(17\) | −405267. | −0.285428 | −0.142714 | − | 0.989764i | \(-0.545583\pi\) | ||||
−0.142714 | + | 0.989764i | \(0.545583\pi\) | |||||||
\(18\) | −618743. | − | 117796.i | −0.327452 | − | 0.0623400i | ||||
\(19\) | − | 4.64051e6i | − | 1.87412i | −0.349169 | − | 0.937060i | \(-0.613536\pi\) | ||
0.349169 | − | 0.937060i | \(-0.386464\pi\) | |||||||
\(20\) | 553440. | + | 218651.i | 0.172950 | + | 0.0683285i | ||||
\(21\) | −2.54522e6 | −0.623203 | ||||||||
\(22\) | −18803.9 | + | 98771.0i | −0.00364867 | + | 0.0191653i | ||||
\(23\) | − | 1.16775e7i | − | 1.81430i | −0.420806 | − | 0.907151i | \(-0.638253\pi\) | ||
0.420806 | − | 0.907151i | \(-0.361747\pi\) | |||||||
\(24\) | −2.45903e6 | + | 3.88428e6i | −0.308822 | + | 0.487814i | ||||
\(25\) | −9.42793e6 | −0.965420 | ||||||||
\(26\) | 8.71269e6 | + | 1.65871e6i | 0.733306 | + | 0.139606i | ||||
\(27\) | − | 2.76145e6i | − | 0.192450i | ||||||
\(28\) | −6.82602e6 | + | 1.72777e7i | −0.396622 | + | 1.00391i | ||||
\(29\) | 3.05985e7 | 1.49180 | 0.745900 | − | 0.666058i | \(-0.232020\pi\) | ||||
0.745900 | + | 0.666058i | \(0.232020\pi\) | |||||||
\(30\) | −487920. | + | 2.56289e6i | −0.0200790 | + | 0.105469i | ||||
\(31\) | 2.15851e7i | 0.753955i | 0.926223 | + | 0.376977i | \(0.123037\pi\) | ||||
−0.926223 | + | 0.376977i | \(0.876963\pi\) | |||||||
\(32\) | 1.97727e7 | + | 2.71098e7i | 0.589272 | + | 0.807934i | ||||
\(33\) | −440815. | −0.0112638 | ||||||||
\(34\) | −1.27397e7 | − | 2.42538e6i | −0.280392 | − | 0.0533807i | ||||
\(35\) | 1.05426e7i | 0.200727i | ||||||||
\(36\) | −1.87455e7 | − | 7.40590e6i | −0.310016 | − | 0.122480i | ||||
\(37\) | −8.42940e7 | −1.21559 | −0.607796 | − | 0.794093i | \(-0.707946\pi\) | ||||
−0.607796 | + | 0.794093i | \(0.707946\pi\) | |||||||
\(38\) | 2.77717e7 | − | 1.45876e8i | 0.350498 | − | 1.84105i | ||||
\(39\) | 3.88847e7i | 0.430979i | ||||||||
\(40\) | 1.60890e7 | + | 1.01855e7i | 0.157120 | + | 0.0994680i | ||||
\(41\) | 1.25396e8 | 1.08234 | 0.541170 | − | 0.840913i | \(-0.317981\pi\) | ||||
0.541170 | + | 0.840913i | \(0.317981\pi\) | |||||||
\(42\) | −8.00101e7 | − | 1.52322e7i | −0.612207 | − | 0.116551i | ||||
\(43\) | 9.50638e7i | 0.646655i | 0.946287 | + | 0.323328i | \(0.104802\pi\) | ||||
−0.946287 | + | 0.323328i | \(0.895198\pi\) | |||||||
\(44\) | −1.18222e6 | + | 2.99237e6i | −0.00716859 | + | 0.0181448i | ||||
\(45\) | −1.14382e7 | −0.0619861 | ||||||||
\(46\) | 6.98854e7 | − | 3.67086e8i | 0.339311 | − | 1.78229i | ||||
\(47\) | 4.66101e7i | 0.203232i | 0.994824 | + | 0.101616i | \(0.0324012\pi\) | ||||
−0.994824 | + | 0.101616i | \(0.967599\pi\) | |||||||
\(48\) | −1.00547e8 | + | 1.07387e8i | −0.394604 | + | 0.421451i | ||||
\(49\) | −4.66498e7 | −0.165147 | ||||||||
\(50\) | −2.96371e8 | − | 5.64227e7i | −0.948386 | − | 0.180553i | ||||
\(51\) | − | 5.68574e7i | − | 0.164792i | ||||||
\(52\) | 2.63960e8 | + | 1.04285e8i | 0.694259 | + | 0.274286i | ||||
\(53\) | −6.20248e7 | −0.148315 | −0.0741577 | − | 0.997247i | \(-0.523627\pi\) | ||||
−0.0741577 | + | 0.997247i | \(0.523627\pi\) | |||||||
\(54\) | 1.65263e7 | − | 8.68072e7i | 0.0359920 | − | 0.189055i | ||||
\(55\) | 1.82590e6i | 0.00362796i | ||||||||
\(56\) | −3.17979e8 | + | 5.02279e8i | −0.577376 | + | 0.912022i | ||||
\(57\) | 6.51045e8 | 1.08202 | ||||||||
\(58\) | 9.61877e8 | + | 1.83121e8i | 1.46548 | + | 0.278996i | ||||
\(59\) | 9.07127e7i | 0.126884i | 0.997986 | + | 0.0634422i | \(0.0202079\pi\) | ||||
−0.997986 | + | 0.0634422i | \(0.979792\pi\) | |||||||
\(60\) | −3.06759e7 | + | 7.76454e7i | −0.0394495 | + | 0.0998526i | ||||
\(61\) | −1.27440e9 | −1.50889 | −0.754446 | − | 0.656362i | \(-0.772094\pi\) | ||||
−0.754446 | + | 0.656362i | \(0.772094\pi\) | |||||||
\(62\) | −1.29179e8 | + | 6.78535e8i | −0.141005 | + | 0.740652i | ||||
\(63\) | − | 3.57085e8i | − | 0.359807i | ||||||
\(64\) | 4.59320e8 | + | 9.70539e8i | 0.427775 | + | 0.903885i | ||||
\(65\) | 1.61064e8 | 0.138814 | ||||||||
\(66\) | −1.38572e7 | − | 2.63812e6i | −0.0110651 | − | 0.00210656i | ||||
\(67\) | − | 9.02217e8i | − | 0.668247i | −0.942529 | − | 0.334124i | \(-0.891560\pi\) | ||
0.942529 | − | 0.334124i | \(-0.108440\pi\) | |||||||
\(68\) | −3.85963e8 | − | 1.52485e8i | −0.265461 | − | 0.104878i | ||||
\(69\) | 1.63830e9 | 1.04749 | ||||||||
\(70\) | −6.30934e7 | + | 3.31409e8i | −0.0375399 | + | 0.197185i | ||||
\(71\) | − | 2.49217e9i | − | 1.38129i | −0.723192 | − | 0.690647i | \(-0.757326\pi\) | ||
0.723192 | − | 0.690647i | \(-0.242674\pi\) | |||||||
\(72\) | −5.44949e8 | − | 3.44992e8i | −0.281640 | − | 0.178298i | ||||
\(73\) | −2.26517e9 | −1.09267 | −0.546333 | − | 0.837568i | \(-0.683977\pi\) | ||||
−0.546333 | + | 0.837568i | \(0.683977\pi\) | |||||||
\(74\) | −2.64981e9 | − | 5.04469e8i | −1.19414 | − | 0.227340i | ||||
\(75\) | − | 1.32270e9i | − | 0.557385i | ||||||
\(76\) | 1.74603e9 | − | 4.41947e9i | 0.688627 | − | 1.74302i | ||||
\(77\) | −5.70021e7 | −0.0210590 | ||||||||
\(78\) | −2.32711e8 | + | 1.22236e9i | −0.0806016 | + | 0.423375i | ||||
\(79\) | 2.04203e9i | 0.663631i | 0.943344 | + | 0.331815i | \(0.107661\pi\) | ||||
−0.943344 | + | 0.331815i | \(0.892339\pi\) | |||||||
\(80\) | 4.44809e8 | + | 4.16473e8i | 0.135745 | + | 0.127098i | ||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | 3.94187e9 | + | 7.50449e8i | 1.06324 | + | 0.202419i | ||||
\(83\) | 6.44397e9i | 1.63592i | 0.575273 | + | 0.817962i | \(0.304896\pi\) | ||||
−0.575273 | + | 0.817962i | \(0.695104\pi\) | |||||||
\(84\) | −2.42399e9 | − | 9.57664e8i | −0.579608 | − | 0.228990i | ||||
\(85\) | −2.35508e8 | −0.0530777 | ||||||||
\(86\) | −5.68922e8 | + | 2.98837e9i | −0.120937 | + | 0.635246i | ||||
\(87\) | 4.29286e9i | 0.861291i | ||||||||
\(88\) | −5.50717e7 | + | 8.69912e7i | −0.0104356 | + | 0.0164840i | ||||
\(89\) | 7.08476e9 | 1.26875 | 0.634374 | − | 0.773026i | \(-0.281258\pi\) | ||||
0.634374 | + | 0.773026i | \(0.281258\pi\) | |||||||
\(90\) | −3.59563e8 | − | 6.84533e7i | −0.0608924 | − | 0.0115926i | ||||
\(91\) | 5.02821e9i | 0.805762i | ||||||||
\(92\) | 4.39375e9 | − | 1.11212e10i | 0.666648 | − | 1.68739i | ||||
\(93\) | −3.02830e9 | −0.435296 | ||||||||
\(94\) | −2.78945e8 | + | 1.46521e9i | −0.0380084 | + | 0.199646i | ||||
\(95\) | − | 2.69669e9i | − | 0.348508i | ||||||
\(96\) | −3.80340e9 | + | 2.77403e9i | −0.466461 | + | 0.340217i | ||||
\(97\) | −4.17526e9 | −0.486211 | −0.243106 | − | 0.970000i | \(-0.578166\pi\) | ||||
−0.243106 | + | 0.970000i | \(0.578166\pi\) | |||||||
\(98\) | −1.46646e9 | − | 2.79182e8i | −0.162233 | − | 0.0308857i | ||||
\(99\) | − | 6.18446e7i | − | 0.00650318i | ||||||
\(100\) | −8.97886e9 | − | 3.54734e9i | −0.897886 | − | 0.354734i | ||||
\(101\) | 5.10423e9 | 0.485650 | 0.242825 | − | 0.970070i | \(-0.421926\pi\) | ||||
0.242825 | + | 0.970070i | \(0.421926\pi\) | |||||||
\(102\) | 3.40271e8 | − | 1.78733e9i | 0.0308194 | − | 0.161884i | ||||
\(103\) | − | 5.36716e9i | − | 0.462976i | −0.972838 | − | 0.231488i | \(-0.925641\pi\) | ||
0.972838 | − | 0.231488i | \(-0.0743594\pi\) | |||||||
\(104\) | 7.67358e9 | + | 4.85793e9i | 0.630713 | + | 0.399287i | ||||
\(105\) | −1.47908e9 | −0.115890 | ||||||||
\(106\) | −1.94977e9 | − | 3.71196e8i | −0.145698 | − | 0.0277379i | ||||
\(107\) | − | 1.25180e10i | − | 0.892517i | −0.894904 | − | 0.446259i | \(-0.852756\pi\) | ||
0.894904 | − | 0.446259i | \(-0.147244\pi\) | |||||||
\(108\) | 1.03902e9 | − | 2.62992e9i | 0.0707139 | − | 0.178988i | ||||
\(109\) | 1.78943e9 | 0.116301 | 0.0581503 | − | 0.998308i | \(-0.481480\pi\) | ||||
0.0581503 | + | 0.998308i | \(0.481480\pi\) | |||||||
\(110\) | −1.09273e7 | + | 5.73977e7i | −0.000678501 | + | 0.00356395i | ||||
\(111\) | − | 1.18261e10i | − | 0.701822i | ||||||
\(112\) | −1.30018e10 | + | 1.38864e10i | −0.737755 | + | 0.787949i | ||||
\(113\) | −2.08033e10 | −1.12912 | −0.564559 | − | 0.825393i | \(-0.690954\pi\) | ||||
−0.564559 | + | 0.825393i | \(0.690954\pi\) | |||||||
\(114\) | 2.04659e10 | + | 3.89627e9i | 1.06293 | + | 0.202360i | ||||
\(115\) | − | 6.78600e9i | − | 0.337384i | ||||||
\(116\) | 2.91411e10 | + | 1.15130e10i | 1.38744 | + | 0.548148i | ||||
\(117\) | −5.45537e9 | −0.248826 | ||||||||
\(118\) | −5.42883e8 | + | 2.85159e9i | −0.0237299 | + | 0.124646i | ||||
\(119\) | − | 7.35227e9i | − | 0.308097i | ||||||
\(120\) | −1.42899e9 | + | 2.25723e9i | −0.0574279 | + | 0.0907130i | ||||
\(121\) | 2.59276e10 | 0.999619 | ||||||||
\(122\) | −4.00614e10 | − | 7.62685e9i | −1.48227 | − | 0.282193i | ||||
\(123\) | 1.75926e10i | 0.624890i | ||||||||
\(124\) | −8.12158e9 | + | 2.05569e10i | −0.277033 | + | 0.701213i | ||||
\(125\) | −1.11537e10 | −0.365486 | ||||||||
\(126\) | 2.13703e9 | − | 1.12251e10i | 0.0672910 | − | 0.353458i | ||||
\(127\) | − | 3.45877e10i | − | 1.04689i | −0.852058 | − | 0.523447i | \(-0.824646\pi\) | ||
0.852058 | − | 0.523447i | \(-0.175354\pi\) | |||||||
\(128\) | 8.63059e9 | + | 3.32581e10i | 0.251183 | + | 0.967940i | ||||
\(129\) | −1.33371e10 | −0.373346 | ||||||||
\(130\) | 5.06311e9 | + | 9.63910e8i | 0.136364 | + | 0.0259609i | ||||
\(131\) | 5.54439e10i | 1.43713i | 0.695457 | + | 0.718567i | \(0.255202\pi\) | ||||
−0.695457 | + | 0.718567i | \(0.744798\pi\) | |||||||
\(132\) | −4.19818e8 | − | 1.65861e8i | −0.0104759 | − | 0.00413879i | ||||
\(133\) | 8.41871e10 | 2.02296 | ||||||||
\(134\) | 5.39944e9 | − | 2.83616e10i | 0.124976 | − | 0.656457i | ||||
\(135\) | − | 1.60473e9i | − | 0.0357877i | ||||||
\(136\) | −1.12203e10 | − | 7.10329e9i | −0.241163 | − | 0.152674i | ||||
\(137\) | −5.51790e10 | −1.14333 | −0.571664 | − | 0.820488i | \(-0.693702\pi\) | ||||
−0.571664 | + | 0.820488i | \(0.693702\pi\) | |||||||
\(138\) | 5.15007e10 | + | 9.80465e9i | 1.02901 | + | 0.195901i | ||||
\(139\) | 5.84773e10i | 1.12697i | 0.826125 | + | 0.563487i | \(0.190540\pi\) | ||||
−0.826125 | + | 0.563487i | \(0.809460\pi\) | |||||||
\(140\) | −3.96673e9 | + | 1.00404e10i | −0.0737552 | + | 0.186685i | ||||
\(141\) | −6.53922e9 | −0.117336 | ||||||||
\(142\) | 1.49147e10 | − | 7.83424e10i | 0.258330 | − | 1.35692i | ||||
\(143\) | 8.70851e8i | 0.0145634i | ||||||||
\(144\) | −1.50660e10 | − | 1.41063e10i | −0.243325 | − | 0.227825i | ||||
\(145\) | 1.77814e10 | 0.277412 | ||||||||
\(146\) | −7.12066e10 | − | 1.35562e10i | −1.07339 | − | 0.204350i | ||||
\(147\) | − | 6.54479e9i | − | 0.0953474i | ||||||
\(148\) | −8.02789e10 | − | 3.17164e10i | −1.13056 | − | 0.446658i | ||||
\(149\) | −5.65933e10 | −0.770608 | −0.385304 | − | 0.922790i | \(-0.625903\pi\) | ||||
−0.385304 | + | 0.922790i | \(0.625903\pi\) | |||||||
\(150\) | 7.91589e9 | − | 4.15796e10i | 0.104242 | − | 0.547551i | ||||
\(151\) | − | 4.52959e10i | − | 0.576998i | −0.957480 | − | 0.288499i | \(-0.906844\pi\) | ||
0.957480 | − | 0.288499i | \(-0.0931562\pi\) | |||||||
\(152\) | 8.13361e10 | − | 1.28478e11i | 1.00246 | − | 1.58348i | ||||
\(153\) | 7.97687e9 | 0.0951427 | ||||||||
\(154\) | −1.79188e9 | − | 3.41137e8i | −0.0206874 | − | 0.00393845i | ||||
\(155\) | 1.25435e10i | 0.140204i | ||||||||
\(156\) | −1.46307e10 | + | 3.70326e10i | −0.158359 | + | 0.400831i | ||||
\(157\) | −8.52098e10 | −0.893288 | −0.446644 | − | 0.894712i | \(-0.647381\pi\) | ||||
−0.446644 | + | 0.894712i | \(0.647381\pi\) | |||||||
\(158\) | −1.22208e10 | + | 6.41920e10i | −0.124112 | + | 0.651922i | ||||
\(159\) | − | 8.70184e9i | − | 0.0856299i | ||||||
\(160\) | 1.14903e10 | + | 1.57540e10i | 0.109580 | + | 0.150242i | ||||
\(161\) | 2.11850e11 | 1.95839 | ||||||||
\(162\) | 1.21787e10 | + | 2.31857e9i | 0.109151 | + | 0.0207800i | ||||
\(163\) | 1.31501e11i | 1.14285i | 0.820653 | + | 0.571426i | \(0.193610\pi\) | ||||
−0.820653 | + | 0.571426i | \(0.806390\pi\) | |||||||
\(164\) | 1.19423e11 | + | 4.71813e10i | 1.00663 | + | 0.397696i | ||||
\(165\) | −2.56166e8 | −0.00209460 | ||||||||
\(166\) | −3.85648e10 | + | 2.02569e11i | −0.305950 | + | 1.60706i | ||||
\(167\) | − | 8.75191e10i | − | 0.673784i | −0.941543 | − | 0.336892i | \(-0.890624\pi\) | ||
0.941543 | − | 0.336892i | \(-0.109376\pi\) | |||||||
\(168\) | −7.04679e10 | − | 4.46112e10i | −0.526556 | − | 0.333348i | ||||
\(169\) | −6.10399e10 | −0.442772 | ||||||||
\(170\) | −7.40330e9 | − | 1.40943e9i | −0.0521412 | − | 0.00992658i | ||||
\(171\) | 9.13391e10i | 0.624706i | ||||||||
\(172\) | −3.57686e10 | + | 9.05357e10i | −0.237607 | + | 0.601420i | ||||
\(173\) | 7.79794e10 | 0.503210 | 0.251605 | − | 0.967830i | \(-0.419042\pi\) | ||||
0.251605 | + | 0.967830i | \(0.419042\pi\) | |||||||
\(174\) | −2.56912e10 | + | 1.34948e11i | −0.161079 | + | 0.846095i | ||||
\(175\) | − | 1.71040e11i | − | 1.04209i | ||||||
\(176\) | −2.25181e9 | + | 2.40502e9i | −0.0133343 | + | 0.0142415i | ||||
\(177\) | −1.27266e10 | −0.0732567 | ||||||||
\(178\) | 2.22712e11 | + | 4.23997e10i | 1.24636 | + | 0.237281i | ||||
\(179\) | − | 4.15281e10i | − | 0.225984i | −0.993596 | − | 0.112992i | \(-0.963957\pi\) | ||
0.993596 | − | 0.112992i | \(-0.0360434\pi\) | |||||||
\(180\) | −1.08934e10 | − | 4.30371e9i | −0.0576500 | − | 0.0227762i | ||||
\(181\) | −2.42696e11 | −1.24931 | −0.624654 | − | 0.780901i | \(-0.714760\pi\) | ||||
−0.624654 | + | 0.780901i | \(0.714760\pi\) | |||||||
\(182\) | −3.00920e10 | + | 1.58064e11i | −0.150694 | + | 0.791545i | ||||
\(183\) | − | 1.78794e11i | − | 0.871159i | ||||||
\(184\) | 2.04676e11 | − | 3.23306e11i | 0.970460 | − | 1.53294i | ||||
\(185\) | −4.89848e10 | −0.226049 | ||||||||
\(186\) | −9.51959e10 | − | 1.81233e10i | −0.427616 | − | 0.0814090i | ||||
\(187\) | − | 1.27336e9i | − | 0.00556857i | ||||||
\(188\) | −1.75375e10 | + | 4.43900e10i | −0.0746755 | + | 0.189015i | ||||
\(189\) | 5.00977e10 | 0.207734 | ||||||||
\(190\) | 1.61387e10 | − | 8.47714e10i | 0.0651779 | − | 0.342359i | ||||
\(191\) | − | 3.31770e11i | − | 1.30518i | −0.757711 | − | 0.652590i | \(-0.773682\pi\) | ||
0.757711 | − | 0.652590i | \(-0.226318\pi\) | |||||||
\(192\) | −1.36163e11 | + | 6.44409e10i | −0.521858 | + | 0.246976i | ||||
\(193\) | −8.15179e10 | −0.304415 | −0.152208 | − | 0.988349i | \(-0.548638\pi\) | ||||
−0.152208 | + | 0.988349i | \(0.548638\pi\) | |||||||
\(194\) | −1.31251e11 | − | 2.49874e10i | −0.477633 | − | 0.0909312i | ||||
\(195\) | 2.25967e10i | 0.0801440i | ||||||||
\(196\) | −4.44278e10 | − | 1.75524e10i | −0.153594 | − | 0.0606815i | ||||
\(197\) | 1.09584e11 | 0.369333 | 0.184666 | − | 0.982801i | \(-0.440880\pi\) | ||||
0.184666 | + | 0.982801i | \(0.440880\pi\) | |||||||
\(198\) | 3.70118e8 | − | 1.94411e9i | 0.00121622 | − | 0.00638844i | ||||
\(199\) | − | 5.96022e10i | − | 0.190984i | −0.995430 | − | 0.0954920i | \(-0.969558\pi\) | ||
0.995430 | − | 0.0954920i | \(-0.0304424\pi\) | |||||||
\(200\) | −2.61024e11 | − | 1.65247e11i | −0.815701 | − | 0.516398i | ||||
\(201\) | 1.26578e11 | 0.385813 | ||||||||
\(202\) | 1.60454e11 | + | 3.05470e10i | 0.477082 | + | 0.0908263i | ||||
\(203\) | 5.55113e11i | 1.61028i | ||||||||
\(204\) | 2.13931e10 | − | 5.41492e10i | 0.0605512 | − | 0.153264i | ||||
\(205\) | 7.28699e10 | 0.201270 | ||||||||
\(206\) | 3.21205e10 | − | 1.68719e11i | 0.0865857 | − | 0.454807i | ||||
\(207\) | 2.29848e11i | 0.604767i | ||||||||
\(208\) | 2.12149e11 | + | 1.98635e11i | 0.544910 | + | 0.510197i | ||||
\(209\) | 1.45806e10 | 0.0365632 | ||||||||
\(210\) | −4.64954e10 | − | 8.85175e9i | −0.113845 | − | 0.0216737i | ||||
\(211\) | 4.78144e11i | 1.14326i | 0.820510 | + | 0.571632i | \(0.193689\pi\) | ||||
−0.820510 | + | 0.571632i | \(0.806311\pi\) | |||||||
\(212\) | −5.90705e10 | − | 2.33374e10i | −0.137940 | − | 0.0544970i | ||||
\(213\) | 3.49642e11 | 0.797491 | ||||||||
\(214\) | 7.49158e10 | − | 3.93509e11i | 0.166919 | − | 0.876770i | ||||
\(215\) | 5.52434e10i | 0.120251i | ||||||||
\(216\) | 4.84011e10 | − | 7.64543e10i | 0.102941 | − | 0.162605i | ||||
\(217\) | −3.91592e11 | −0.813833 | ||||||||
\(218\) | 5.62514e10 | + | 1.07091e10i | 0.114249 | + | 0.0217505i | ||||
\(219\) | − | 3.17795e11i | − | 0.630851i | ||||||
\(220\) | −6.87009e8 | + | 1.73892e9i | −0.00133306 | + | 0.00337417i | ||||
\(221\) | −1.12324e11 | −0.213065 | ||||||||
\(222\) | 7.07750e10 | − | 3.71759e11i | 0.131255 | − | 0.689440i | ||||
\(223\) | 1.98948e11i | 0.360758i | 0.983597 | + | 0.180379i | \(0.0577324\pi\) | ||||
−0.983597 | + | 0.180379i | \(0.942268\pi\) | |||||||
\(224\) | −4.91820e11 | + | 3.58712e11i | −0.872100 | + | 0.636072i | ||||
\(225\) | 1.85570e11 | 0.321807 | ||||||||
\(226\) | −6.53959e11 | − | 1.24500e11i | −1.10920 | − | 0.211168i | ||||
\(227\) | 7.86470e11i | 1.30483i | 0.757863 | + | 0.652413i | \(0.226243\pi\) | ||||
−0.757863 | + | 0.652413i | \(0.773757\pi\) | |||||||
\(228\) | 6.20034e11 | + | 2.44961e11i | 1.00633 | + | 0.397579i | ||||
\(229\) | 2.14353e11 | 0.340370 | 0.170185 | − | 0.985412i | \(-0.445563\pi\) | ||||
0.170185 | + | 0.985412i | \(0.445563\pi\) | |||||||
\(230\) | 4.06118e10 | − | 2.13321e11i | 0.0630976 | − | 0.331431i | ||||
\(231\) | − | 7.99718e9i | − | 0.0121584i | ||||||
\(232\) | 8.47160e11 | + | 5.36314e11i | 1.26045 | + | 0.797956i | ||||
\(233\) | −4.85585e11 | −0.707107 | −0.353554 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353554 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(234\) | −1.71492e11 | − | 3.26484e10i | −0.244435 | − | 0.0465354i | ||||
\(235\) | 2.70861e10i | 0.0377926i | ||||||||
\(236\) | −3.41315e10 | + | 8.63919e10i | −0.0466225 | + | 0.118008i | ||||
\(237\) | −2.86489e11 | −0.383147 | ||||||||
\(238\) | 4.40007e10 | − | 2.31122e11i | 0.0576202 | − | 0.302661i | ||||
\(239\) | − | 1.23745e12i | − | 1.58685i | −0.608666 | − | 0.793426i | \(-0.708295\pi\) | ||
0.608666 | − | 0.793426i | \(-0.291705\pi\) | |||||||
\(240\) | −5.84296e10 | + | 6.24049e10i | −0.0733798 | + | 0.0783723i | ||||
\(241\) | 1.00244e12 | 1.23303 | 0.616516 | − | 0.787342i | \(-0.288543\pi\) | ||||
0.616516 | + | 0.787342i | \(0.288543\pi\) | |||||||
\(242\) | 8.15043e11 | + | 1.55167e11i | 0.981982 | + | 0.186949i | ||||
\(243\) | 5.43536e10i | 0.0641500i | ||||||||
\(244\) | −1.21370e12 | − | 4.79506e11i | −1.40334 | − | 0.554428i | ||||
\(245\) | −2.71091e10 | −0.0307104 | ||||||||
\(246\) | −1.05285e11 | + | 5.53029e11i | −0.116867 | + | 0.613864i | ||||
\(247\) | − | 1.28617e12i | − | 1.39899i | ||||||
\(248\) | −3.78331e11 | + | 5.97611e11i | −0.403286 | + | 0.637030i | ||||
\(249\) | −9.04064e11 | −0.944501 | ||||||||
\(250\) | −3.50622e11 | − | 6.67511e10i | −0.359037 | − | 0.0683531i | ||||
\(251\) | − | 9.10834e11i | − | 0.914262i | −0.889399 | − | 0.457131i | \(-0.848877\pi\) | ||
0.889399 | − | 0.457131i | \(-0.151123\pi\) | |||||||
\(252\) | 1.34356e11 | − | 3.40077e11i | 0.132207 | − | 0.334637i | ||||
\(253\) | 3.66910e10 | 0.0353962 | ||||||||
\(254\) | 2.06995e11 | − | 1.08728e12i | 0.195790 | − | 1.02842i | ||||
\(255\) | − | 3.30409e10i | − | 0.0306444i | ||||||
\(256\) | 7.22682e10 | + | 1.09713e12i | 0.0657275 | + | 0.997838i | ||||
\(257\) | 3.40622e11 | 0.303814 | 0.151907 | − | 0.988395i | \(-0.451459\pi\) | ||||
0.151907 | + | 0.988395i | \(0.451459\pi\) | |||||||
\(258\) | −4.19256e11 | − | 7.98176e10i | −0.366759 | − | 0.0698232i | ||||
\(259\) | − | 1.52924e12i | − | 1.31213i | ||||||
\(260\) | 1.53392e11 | + | 6.06018e10i | 0.129103 | + | 0.0510057i | ||||
\(261\) | −6.02271e11 | −0.497267 | ||||||||
\(262\) | −3.31812e11 | + | 1.74290e12i | −0.268773 | + | 1.41178i | ||||
\(263\) | 8.19806e11i | 0.651527i | 0.945451 | + | 0.325764i | \(0.105621\pi\) | ||||
−0.945451 | + | 0.325764i | \(0.894379\pi\) | |||||||
\(264\) | −1.22045e10 | − | 7.72635e9i | −0.00951703 | − | 0.00602497i | ||||
\(265\) | −3.60438e10 | −0.0275805 | ||||||||
\(266\) | 2.64646e12 | + | 5.03830e11i | 1.98727 | + | 0.378334i | ||||
\(267\) | 9.93965e11i | 0.732512i | ||||||||
\(268\) | 3.39467e11 | − | 8.59243e11i | 0.245541 | − | 0.621501i | ||||
\(269\) | −1.13267e12 | −0.804156 | −0.402078 | − | 0.915605i | \(-0.631712\pi\) | ||||
−0.402078 | + | 0.915605i | \(0.631712\pi\) | |||||||
\(270\) | 9.60373e9 | − | 5.04454e10i | 0.00669301 | − | 0.0351562i | ||||
\(271\) | 1.56800e12i | 1.07275i | 0.843980 | + | 0.536375i | \(0.180207\pi\) | ||||
−0.843980 | + | 0.536375i | \(0.819793\pi\) | |||||||
\(272\) | −3.10205e11 | − | 2.90444e11i | −0.208355 | − | 0.195082i | ||||
\(273\) | −7.05439e11 | −0.465207 | ||||||||
\(274\) | −1.73457e12 | − | 3.30226e11i | −1.12316 | − | 0.213825i | ||||
\(275\) | − | 2.96228e10i | − | 0.0188349i | ||||||
\(276\) | 1.56027e12 | + | 6.16426e11i | 0.974213 | + | 0.384889i | ||||
\(277\) | 2.90739e12 | 1.78281 | 0.891405 | − | 0.453208i | \(-0.149720\pi\) | ||||
0.891405 | + | 0.453208i | \(0.149720\pi\) | |||||||
\(278\) | −3.49966e11 | + | 1.83826e12i | −0.210766 | + | 1.10709i | ||||
\(279\) | − | 4.24859e11i | − | 0.251318i | ||||||
\(280\) | −1.84784e11 | + | 2.91884e11i | −0.107368 | + | 0.169598i | ||||
\(281\) | 1.81823e12 | 1.03781 | 0.518905 | − | 0.854832i | \(-0.326340\pi\) | ||||
0.518905 | + | 0.854832i | \(0.326340\pi\) | |||||||
\(282\) | −2.05563e11 | − | 3.91349e10i | −0.115266 | − | 0.0219441i | ||||
\(283\) | 2.28784e12i | 1.26036i | 0.776450 | + | 0.630179i | \(0.217019\pi\) | ||||
−0.776450 | + | 0.630179i | \(0.782981\pi\) | |||||||
\(284\) | 9.37702e11 | − | 2.37347e12i | 0.507543 | − | 1.28467i | ||||
\(285\) | 3.78335e11 | 0.201211 | ||||||||
\(286\) | −5.21173e9 | + | 2.73755e10i | −0.00272365 | + | 0.0143065i | ||||
\(287\) | 2.27491e12i | 1.16830i | ||||||||
\(288\) | −3.89186e11 | − | 5.33602e11i | −0.196424 | − | 0.269311i | ||||
\(289\) | −1.85175e12 | −0.918531 | ||||||||
\(290\) | 5.58965e11 | + | 1.06415e11i | 0.272518 | + | 0.0518817i | ||||
\(291\) | − | 5.85773e11i | − | 0.280714i | ||||||
\(292\) | −2.15728e12 | − | 8.52292e11i | −1.01623 | − | 0.401489i | ||||
\(293\) | −3.64665e10 | −0.0168871 | −0.00844357 | − | 0.999964i | \(-0.502688\pi\) | ||||
−0.00844357 | + | 0.999964i | \(0.502688\pi\) | |||||||
\(294\) | 3.91682e10 | − | 2.05738e11i | 0.0178319 | − | 0.0936651i | ||||
\(295\) | 5.27149e10i | 0.0235952i | ||||||||
\(296\) | −2.33379e12 | − | 1.47746e12i | −1.02708 | − | 0.650214i | ||||
\(297\) | 8.67656e9 | 0.00375461 | ||||||||
\(298\) | −1.77903e12 | − | 3.38690e11i | −0.757011 | − | 0.144119i | ||||
\(299\) | − | 3.23655e12i | − | 1.35433i | ||||||
\(300\) | 4.97678e11 | − | 1.25970e12i | 0.204806 | − | 0.518395i | ||||
\(301\) | −1.72463e12 | −0.698012 | ||||||||
\(302\) | 2.71080e11 | − | 1.42390e12i | 0.107910 | − | 0.566818i | ||||
\(303\) | 7.16104e11i | 0.280390i | ||||||||
\(304\) | 3.32573e12 | − | 3.55200e12i | 1.28091 | − | 1.36806i | ||||
\(305\) | −7.40581e11 | −0.280591 | ||||||||
\(306\) | 2.50756e11 | + | 4.77387e10i | 0.0934640 | + | 0.0177936i | ||||
\(307\) | − | 1.45894e12i | − | 0.534992i | −0.963559 | − | 0.267496i | \(-0.913804\pi\) | ||
0.963559 | − | 0.267496i | \(-0.0861961\pi\) | |||||||
\(308\) | −5.42870e10 | − | 2.14476e10i | −0.0195858 | − | 0.00773792i | ||||
\(309\) | 7.52991e11 | 0.267299 | ||||||||
\(310\) | −7.50683e10 | + | 3.94310e11i | −0.0262209 | + | 0.137730i | ||||
\(311\) | 2.53238e12i | 0.870415i | 0.900330 | + | 0.435207i | \(0.143325\pi\) | ||||
−0.900330 | + | 0.435207i | \(0.856675\pi\) | |||||||
\(312\) | −6.81549e11 | + | 1.07657e12i | −0.230528 | + | 0.364142i | ||||
\(313\) | 3.44067e12 | 1.14531 | 0.572653 | − | 0.819798i | \(-0.305914\pi\) | ||||
0.572653 | + | 0.819798i | \(0.305914\pi\) | |||||||
\(314\) | −2.67860e12 | − | 5.09950e11i | −0.877527 | − | 0.167063i | ||||
\(315\) | − | 2.07509e11i | − | 0.0669090i | ||||||
\(316\) | −7.68331e11 | + | 1.94476e12i | −0.243845 | + | 0.617208i | ||||
\(317\) | −2.61867e12 | −0.818060 | −0.409030 | − | 0.912521i | \(-0.634133\pi\) | ||||
−0.409030 | + | 0.912521i | \(0.634133\pi\) | |||||||
\(318\) | 5.20774e10 | − | 2.73546e11i | 0.0160145 | − | 0.0841191i | ||||
\(319\) | 9.61416e10i | 0.0291043i | ||||||||
\(320\) | 2.66920e11 | + | 5.63999e11i | 0.0795484 | + | 0.168085i | ||||
\(321\) | 1.75623e12 | 0.515295 | ||||||||
\(322\) | 6.65960e12 | + | 1.26785e12i | 1.92384 | + | 0.366258i | ||||
\(323\) | 1.88064e12i | 0.534926i | ||||||||
\(324\) | 3.68967e11 | + | 1.45770e11i | 0.103339 | + | 0.0408267i | ||||
\(325\) | −2.61306e12 | −0.720664 | ||||||||
\(326\) | −7.86985e11 | + | 4.13378e12i | −0.213736 | + | 1.12269i | ||||
\(327\) | 2.51050e11i | 0.0671461i | ||||||||
\(328\) | 3.47175e12 | + | 2.19787e12i | 0.914490 | + | 0.578938i | ||||
\(329\) | −8.45592e11 | −0.219372 | ||||||||
\(330\) | −8.05268e9 | − | 1.53306e9i | −0.00205765 | − | 0.000391733i | ||||
\(331\) | − | 4.64858e12i | − | 1.16999i | −0.811038 | − | 0.584993i | \(-0.801097\pi\) | ||
0.811038 | − | 0.584993i | \(-0.198903\pi\) | |||||||
\(332\) | −2.42460e12 | + | 6.13703e12i | −0.601104 | + | 1.52149i | ||||
\(333\) | 1.65916e12 | 0.405197 | ||||||||
\(334\) | 5.23770e11 | − | 2.75120e12i | 0.126011 | − | 0.661896i | ||||
\(335\) | − | 5.24296e11i | − | 0.124266i | ||||||
\(336\) | −1.94820e12 | − | 1.82410e12i | −0.454923 | − | 0.425943i | ||||
\(337\) | −1.43141e12 | −0.329316 | −0.164658 | − | 0.986351i | \(-0.552652\pi\) | ||||
−0.164658 | + | 0.986351i | \(0.552652\pi\) | |||||||
\(338\) | −1.91881e12 | − | 3.65301e11i | −0.434960 | − | 0.0828072i | ||||
\(339\) | − | 2.91862e12i | − | 0.651897i | ||||||
\(340\) | −2.24291e11 | − | 8.86121e10i | −0.0493647 | − | 0.0195029i | ||||
\(341\) | −6.78210e10 | −0.0147093 | ||||||||
\(342\) | −5.46631e11 | + | 2.87128e12i | −0.116833 | + | 0.613684i | ||||
\(343\) | 4.27830e12i | 0.901157i | ||||||||
\(344\) | −1.66622e12 | + | 2.63196e12i | −0.345892 | + | 0.546371i | ||||
\(345\) | 9.52050e11 | 0.194789 | ||||||||
\(346\) | 2.45131e12 | + | 4.66679e11i | 0.494332 | + | 0.0941104i | ||||
\(347\) | − | 6.99656e12i | − | 1.39071i | −0.718666 | − | 0.695356i | \(-0.755247\pi\) | ||
0.718666 | − | 0.695356i | \(-0.244753\pi\) | |||||||
\(348\) | −1.61523e12 | + | 4.08838e12i | −0.316473 | + | 0.801041i | ||||
\(349\) | 8.06897e11 | 0.155844 | 0.0779222 | − | 0.996959i | \(-0.475171\pi\) | ||||
0.0779222 | + | 0.996959i | \(0.475171\pi\) | |||||||
\(350\) | 1.02361e12 | − | 5.37670e12i | 0.194892 | − | 1.02371i | ||||
\(351\) | − | 7.65368e11i | − | 0.143660i | ||||||
\(352\) | −8.51798e10 | + | 6.21265e10i | −0.0157624 | + | 0.0114964i | ||||
\(353\) | 8.82163e12 | 1.60944 | 0.804721 | − | 0.593653i | \(-0.202315\pi\) | ||||
0.804721 | + | 0.593653i | \(0.202315\pi\) | |||||||
\(354\) | −4.00067e11 | − | 7.61644e10i | −0.0719642 | − | 0.0137005i | ||||
\(355\) | − | 1.44825e12i | − | 0.256863i | ||||||
\(356\) | 6.74730e12 | + | 2.66570e12i | 1.17999 | + | 0.466189i | ||||
\(357\) | 1.03150e12 | 0.177880 | ||||||||
\(358\) | 2.48531e11 | − | 1.30545e12i | 0.0422635 | − | 0.221997i | ||||
\(359\) | − | 9.24360e11i | − | 0.155013i | −0.996992 | − | 0.0775066i | \(-0.975304\pi\) | ||
0.996992 | − | 0.0775066i | \(-0.0246959\pi\) | |||||||
\(360\) | −3.16681e11 | − | 2.00482e11i | −0.0523732 | − | 0.0331560i | ||||
\(361\) | −1.54032e13 | −2.51232 | ||||||||
\(362\) | −7.62924e12 | − | 1.45245e12i | −1.22727 | − | 0.233646i | ||||
\(363\) | 3.63753e12i | 0.577131i | ||||||||
\(364\) | −1.89191e12 | + | 4.78871e12i | −0.296069 | + | 0.749397i | ||||
\(365\) | −1.31634e12 | −0.203190 | ||||||||
\(366\) | 1.07002e12 | − | 5.62046e12i | 0.162924 | − | 0.855788i | ||||
\(367\) | 3.72669e12i | 0.559748i | 0.960037 | + | 0.279874i | \(0.0902927\pi\) | ||||
−0.960037 | + | 0.279874i | \(0.909707\pi\) | |||||||
\(368\) | 8.36894e12 | − | 8.93834e12i | 1.24003 | − | 1.32440i | ||||
\(369\) | −2.46817e12 | −0.360780 | ||||||||
\(370\) | −1.53986e12 | − | 2.93157e11i | −0.222061 | − | 0.0422757i | ||||
\(371\) | − | 1.12524e12i | − | 0.160094i | ||||||
\(372\) | −2.88406e12 | − | 1.13943e12i | −0.404846 | − | 0.159945i | ||||
\(373\) | −1.67319e12 | −0.231740 | −0.115870 | − | 0.993264i | \(-0.536966\pi\) | ||||
−0.115870 | + | 0.993264i | \(0.536966\pi\) | |||||||
\(374\) | 7.62061e9 | − | 4.00286e10i | 0.00104143 | − | 0.00547032i | ||||
\(375\) | − | 1.56483e12i | − | 0.211013i | ||||||
\(376\) | −8.16956e11 | + | 1.29046e12i | −0.108707 | + | 0.171714i | ||||
\(377\) | 8.48074e12 | 1.11359 | ||||||||
\(378\) | 1.57484e12 | + | 2.99816e11i | 0.204069 | + | 0.0388505i | ||||
\(379\) | − | 4.67608e11i | − | 0.0597979i | −0.999553 | − | 0.0298989i | \(-0.990481\pi\) | ||
0.999553 | − | 0.0298989i | \(-0.00951855\pi\) | |||||||
\(380\) | 1.01465e12 | − | 2.56824e12i | 0.128056 | − | 0.324129i | ||||
\(381\) | 4.85252e12 | 0.604425 | ||||||||
\(382\) | 1.98552e12 | − | 1.04293e13i | 0.244095 | − | 1.28215i | ||||
\(383\) | 9.26004e12i | 1.12362i | 0.827267 | + | 0.561810i | \(0.189895\pi\) | ||||
−0.827267 | + | 0.561810i | \(0.810105\pi\) | |||||||
\(384\) | −4.66599e12 | + | 1.21084e12i | −0.558840 | + | 0.145021i | ||||
\(385\) | −3.31250e10 | −0.00391609 | ||||||||
\(386\) | −2.56255e12 | − | 4.87855e11i | −0.299044 | − | 0.0569317i | ||||
\(387\) | − | 1.87114e12i | − | 0.215552i | ||||||
\(388\) | −3.97639e12 | − | 1.57098e12i | −0.452199 | − | 0.178654i | ||||
\(389\) | 2.57559e12 | 0.289153 | 0.144577 | − | 0.989494i | \(-0.453818\pi\) | ||||
0.144577 | + | 0.989494i | \(0.453818\pi\) | |||||||
\(390\) | −1.35233e11 | + | 7.10335e11i | −0.0149885 | + | 0.0787300i | ||||
\(391\) | 4.73249e12i | 0.517852i | ||||||||
\(392\) | −1.29156e12 | − | 8.17651e11i | −0.139535 | − | 0.0883360i | ||||
\(393\) | −7.77857e12 | −0.829730 | ||||||||
\(394\) | 3.44483e12 | + | 6.55823e11i | 0.362816 | + | 0.0690726i | ||||
\(395\) | 1.18666e12i | 0.123408i | ||||||||
\(396\) | 2.32696e10 | − | 5.88988e10i | 0.00238953 | − | 0.00604827i | ||||
\(397\) | 1.20101e13 | 1.21785 | 0.608923 | − | 0.793229i | \(-0.291602\pi\) | ||||
0.608923 | + | 0.793229i | \(0.291602\pi\) | |||||||
\(398\) | 3.56697e11 | − | 1.87362e12i | 0.0357178 | − | 0.187614i | ||||
\(399\) | 1.18111e13i | 1.16796i | ||||||||
\(400\) | −7.21646e12 | − | 6.75675e12i | −0.704732 | − | 0.659839i | ||||
\(401\) | −8.93905e12 | −0.862124 | −0.431062 | − | 0.902322i | \(-0.641861\pi\) | ||||
−0.431062 | + | 0.902322i | \(0.641861\pi\) | |||||||
\(402\) | 3.97902e12 | + | 7.57521e11i | 0.379005 | + | 0.0721547i | ||||
\(403\) | 5.98256e12i | 0.562810i | ||||||||
\(404\) | 4.86111e12 | + | 1.92051e12i | 0.451678 | + | 0.178448i | ||||
\(405\) | 2.25138e11 | 0.0206620 | ||||||||
\(406\) | −3.32215e12 | + | 1.74502e13i | −0.301154 | + | 1.58187i | ||||
\(407\) | − | 2.64854e11i | − | 0.0237157i | ||||||
\(408\) | 9.96563e11 | − | 1.57417e12i | 0.0881463 | − | 0.139236i | ||||
\(409\) | 1.11240e13 | 0.971955 | 0.485978 | − | 0.873971i | \(-0.338464\pi\) | ||||
0.485978 | + | 0.873971i | \(0.338464\pi\) | |||||||
\(410\) | 2.29070e12 | + | 4.36100e11i | 0.197719 | + | 0.0376415i | ||||
\(411\) | − | 7.74140e12i | − | 0.660101i | ||||||
\(412\) | 2.01944e12 | − | 5.11151e12i | 0.170116 | − | 0.430589i | ||||
\(413\) | −1.64569e12 | −0.136962 | ||||||||
\(414\) | −1.37555e12 | + | 7.22535e12i | −0.113104 | + | 0.594097i | ||||
\(415\) | 3.74472e12i | 0.304213i | ||||||||
\(416\) | 5.48024e12 | + | 7.51379e12i | 0.439878 | + | 0.603105i | ||||
\(417\) | −8.20414e12 | −0.650658 | ||||||||
\(418\) | 4.58347e11 | + | 8.72597e10i | 0.0359181 | + | 0.00683805i | ||||
\(419\) | 9.31086e12i | 0.720974i | 0.932764 | + | 0.360487i | \(0.117390\pi\) | ||||
−0.932764 | + | 0.360487i | \(0.882610\pi\) | |||||||
\(420\) | −1.40863e12 | − | 5.56517e11i | −0.107783 | − | 0.0425826i | ||||
\(421\) | 8.00485e12 | 0.605261 | 0.302630 | − | 0.953108i | \(-0.402135\pi\) | ||||
0.302630 | + | 0.953108i | \(0.402135\pi\) | |||||||
\(422\) | −2.86152e12 | + | 1.50306e13i | −0.213813 | + | 1.12309i | ||||
\(423\) | − | 9.17427e11i | − | 0.0677439i | ||||||
\(424\) | −1.71724e12 | − | 1.08714e12i | −0.125314 | − | 0.0793331i | ||||
\(425\) | 3.82083e12 | 0.275558 | ||||||||
\(426\) | 1.09911e13 | + | 2.09248e12i | 0.783420 | + | 0.149147i | ||||
\(427\) | − | 2.31200e13i | − | 1.62873i | ||||||
\(428\) | 4.71002e12 | − | 1.19218e13i | 0.327947 | − | 0.830083i | ||||
\(429\) | −1.22177e11 | −0.00840820 | ||||||||
\(430\) | −3.30612e11 | + | 1.73660e12i | −0.0224893 | + | 0.118129i | ||||
\(431\) | − | 2.49720e13i | − | 1.67906i | −0.543313 | − | 0.839530i | \(-0.682830\pi\) | ||
0.543313 | − | 0.839530i | \(-0.317170\pi\) | |||||||
\(432\) | 1.97906e12 | − | 2.11371e12i | 0.131535 | − | 0.140484i | ||||
\(433\) | 2.14688e12 | 0.141049 | 0.0705243 | − | 0.997510i | \(-0.477533\pi\) | ||||
0.0705243 | + | 0.997510i | \(0.477533\pi\) | |||||||
\(434\) | −1.23099e13 | − | 2.34354e12i | −0.799474 | − | 0.152203i | ||||
\(435\) | 2.49466e12i | 0.160164i | ||||||||
\(436\) | 1.70419e12 | + | 6.73288e11i | 0.108165 | + | 0.0427335i | ||||
\(437\) | −5.41893e13 | −3.40022 | ||||||||
\(438\) | 1.90189e12 | − | 9.99002e12i | 0.117982 | − | 0.619720i | ||||
\(439\) | − | 2.89742e13i | − | 1.77700i | −0.458872 | − | 0.888502i | \(-0.651746\pi\) | ||
0.458872 | − | 0.888502i | \(-0.348254\pi\) | |||||||
\(440\) | −3.20032e10 | + | 5.05523e10i | −0.00194058 | + | 0.00306533i | ||||
\(441\) | 9.18209e11 | 0.0550489 | ||||||||
\(442\) | −3.53096e12 | − | 6.72221e11i | −0.209306 | − | 0.0398475i | ||||
\(443\) | 3.44524e12i | 0.201930i | 0.994890 | + | 0.100965i | \(0.0321930\pi\) | ||||
−0.994890 | + | 0.100965i | \(0.967807\pi\) | |||||||
\(444\) | 4.44968e12 | − | 1.12628e13i | 0.257878 | − | 0.652728i | ||||
\(445\) | 4.11709e12 | 0.235934 | ||||||||
\(446\) | −1.19063e12 | + | 6.25402e12i | −0.0674689 | + | 0.354393i | ||||
\(447\) | − | 7.93982e12i | − | 0.444911i | ||||||
\(448\) | −1.76073e13 | + | 8.33290e12i | −0.975671 | + | 0.461749i | ||||
\(449\) | 1.60801e13 | 0.881163 | 0.440582 | − | 0.897713i | \(-0.354772\pi\) | ||||
0.440582 | + | 0.897713i | \(0.354772\pi\) | |||||||
\(450\) | 5.83346e12 | + | 1.11057e12i | 0.316129 | + | 0.0601842i | ||||
\(451\) | 3.93998e11i | 0.0211160i | ||||||||
\(452\) | −1.98124e13 | − | 7.82742e12i | −1.05013 | − | 0.414884i | ||||
\(453\) | 6.35484e12 | 0.333130 | ||||||||
\(454\) | −4.70674e12 | + | 2.47230e13i | −0.244029 | + | 1.28180i | ||||
\(455\) | 2.92199e12i | 0.149838i | ||||||||
\(456\) | 1.80250e13 | + | 1.14111e13i | 0.914222 | + | 0.578768i | ||||
\(457\) | 1.01711e13 | 0.510256 | 0.255128 | − | 0.966907i | \(-0.417882\pi\) | ||||
0.255128 | + | 0.966907i | \(0.417882\pi\) | |||||||
\(458\) | 6.73826e12 | + | 1.28282e12i | 0.334365 | + | 0.0636560i | ||||
\(459\) | 1.11912e12i | 0.0549306i | ||||||||
\(460\) | 2.55329e12 | − | 6.46277e12i | 0.123969 | − | 0.313783i | ||||
\(461\) | 9.47340e12 | 0.454989 | 0.227495 | − | 0.973779i | \(-0.426947\pi\) | ||||
0.227495 | + | 0.973779i | \(0.426947\pi\) | |||||||
\(462\) | 4.78602e10 | − | 2.51394e11i | 0.00227387 | − | 0.0119439i | ||||
\(463\) | 2.15026e13i | 1.01062i | 0.862939 | + | 0.505308i | \(0.168621\pi\) | ||||
−0.862939 | + | 0.505308i | \(0.831379\pi\) | |||||||
\(464\) | 2.34212e13 | + | 2.19292e13i | 1.08898 | + | 1.01961i | ||||
\(465\) | −1.75981e12 | −0.0809468 | ||||||||
\(466\) | −1.52645e13 | − | 2.90605e12i | −0.694631 | − | 0.132243i | ||||
\(467\) | 3.94717e12i | 0.177706i | 0.996045 | + | 0.0888529i | \(0.0283201\pi\) | ||||
−0.996045 | + | 0.0888529i | \(0.971680\pi\) | |||||||
\(468\) | −5.19553e12 | − | 2.05263e12i | −0.231420 | − | 0.0914286i | ||||
\(469\) | 1.63679e13 | 0.721319 | ||||||||
\(470\) | −1.62100e11 | + | 8.51461e11i | −0.00706796 | + | 0.0371258i | ||||
\(471\) | − | 1.19546e13i | − | 0.515740i | ||||||
\(472\) | −1.58996e12 | + | 2.51150e12i | −0.0678698 | + | 0.107207i | ||||
\(473\) | −2.98693e11 | −0.0126159 | ||||||||
\(474\) | −9.00589e12 | − | 1.71453e12i | −0.376387 | − | 0.0716562i | ||||
\(475\) | 4.37503e13i | 1.80931i | ||||||||
\(476\) | 2.76636e12 | − | 7.00207e12i | 0.113207 | − | 0.286544i | ||||
\(477\) | 1.22083e12 | 0.0494384 | ||||||||
\(478\) | 7.40566e12 | − | 3.88996e13i | 0.296773 | − | 1.55885i | ||||
\(479\) | 2.30004e13i | 0.912132i | 0.889946 | + | 0.456066i | \(0.150742\pi\) | ||||
−0.889946 | + | 0.456066i | \(0.849258\pi\) | |||||||
\(480\) | −2.21023e12 | + | 1.61204e12i | −0.0867423 | + | 0.0632661i | ||||
\(481\) | −2.33631e13 | −0.907412 | ||||||||
\(482\) | 3.15122e13 | + | 5.99926e12i | 1.21128 | + | 0.230602i | ||||
\(483\) | 2.97218e13i | 1.13068i | ||||||||
\(484\) | 2.46926e13 | + | 9.75547e12i | 0.929693 | + | 0.367300i | ||||
\(485\) | −2.42633e12 | −0.0904150 | ||||||||
\(486\) | −3.25287e11 | + | 1.70863e12i | −0.0119973 | + | 0.0630182i | ||||
\(487\) | − | 2.30674e13i | − | 0.842081i | −0.907042 | − | 0.421041i | \(-0.861665\pi\) | ||
0.907042 | − | 0.421041i | \(-0.138335\pi\) | |||||||
\(488\) | −3.52835e13 | − | 2.23370e13i | −1.27489 | − | 0.807098i | ||||
\(489\) | −1.84490e13 | −0.659826 | ||||||||
\(490\) | −8.52186e11 | − | 1.62238e11i | −0.0301685 | − | 0.00574345i | ||||
\(491\) | − | 2.98502e12i | − | 0.104602i | −0.998631 | − | 0.0523010i | \(-0.983344\pi\) | ||
0.998631 | − | 0.0523010i | \(-0.0166555\pi\) | |||||||
\(492\) | −6.61935e12 | + | 1.67546e13i | −0.229610 | + | 0.581177i | ||||
\(493\) | −1.24006e13 | −0.425801 | ||||||||
\(494\) | 7.69726e12 | − | 4.04313e13i | 0.261639 | − | 1.37430i | ||||
\(495\) | − | 3.59391e10i | − | 0.00120932i | ||||||
\(496\) | −1.54695e13 | + | 1.65220e13i | −0.515308 | + | 0.550368i | ||||
\(497\) | 4.52125e13 | 1.49100 | ||||||||
\(498\) | −2.84196e13 | − | 5.41049e12i | −0.927836 | − | 0.176640i | ||||
\(499\) | 3.07334e13i | 0.993364i | 0.867933 | + | 0.496682i | \(0.165448\pi\) | ||||
−0.867933 | + | 0.496682i | \(0.834552\pi\) | |||||||
\(500\) | −1.06225e13 | − | 4.19670e12i | −0.339919 | − | 0.134294i | ||||
\(501\) | 1.22786e13 | 0.389009 | ||||||||
\(502\) | 5.45101e12 | − | 2.86324e13i | 0.170985 | − | 0.898130i | ||||
\(503\) | − | 4.69700e12i | − | 0.145875i | −0.997337 | − | 0.0729375i | \(-0.976763\pi\) | ||
0.997337 | − | 0.0729375i | \(-0.0232374\pi\) | |||||||
\(504\) | 6.25878e12 | − | 9.88637e12i | 0.192459 | − | 0.304007i | ||||
\(505\) | 2.96617e12 | 0.0903106 | ||||||||
\(506\) | 1.15340e12 | + | 2.19582e11i | 0.0347717 | + | 0.00661980i | ||||
\(507\) | − | 8.56366e12i | − | 0.255634i | ||||||
\(508\) | 1.30139e13 | − | 3.29402e13i | 0.384671 | − | 0.973662i | ||||
\(509\) | −3.25728e13 | −0.953379 | −0.476690 | − | 0.879072i | \(-0.658163\pi\) | ||||
−0.476690 | + | 0.879072i | \(0.658163\pi\) | |||||||
\(510\) | 1.97738e11 | − | 1.03865e12i | 0.00573111 | − | 0.0301037i | ||||
\(511\) | − | 4.10943e13i | − | 1.17944i | ||||||
\(512\) | −4.29417e12 | + | 3.49213e13i | −0.122048 | + | 0.992524i | ||||
\(513\) | −1.28145e13 | −0.360674 | ||||||||
\(514\) | 1.07076e13 | + | 2.03850e12i | 0.298453 | + | 0.0568192i | ||||
\(515\) | − | 3.11896e12i | − | 0.0860941i | ||||||
\(516\) | −1.27018e13 | − | 5.01819e12i | −0.347230 | − | 0.137183i | ||||
\(517\) | −1.46451e11 | −0.00396496 | ||||||||
\(518\) | 9.15197e12 | − | 4.80724e13i | 0.245395 | − | 1.28898i | ||||
\(519\) | 1.09402e13i | 0.290529i | ||||||||
\(520\) | 4.45927e12 | + | 2.82304e12i | 0.117286 | + | 0.0742506i | ||||
\(521\) | 5.30729e13 | 1.38256 | 0.691281 | − | 0.722586i | \(-0.257047\pi\) | ||||
0.691281 | + | 0.722586i | \(0.257047\pi\) | |||||||
\(522\) | −1.89326e13 | − | 3.60437e12i | −0.488493 | − | 0.0929988i | ||||
\(523\) | − | 1.20881e13i | − | 0.308924i | −0.987999 | − | 0.154462i | \(-0.950636\pi\) | ||
0.987999 | − | 0.154462i | \(-0.0493644\pi\) | |||||||
\(524\) | −2.08613e13 | + | 5.28030e13i | −0.528061 | + | 1.33660i | ||||
\(525\) | 2.39962e13 | 0.601653 | ||||||||
\(526\) | −4.90624e12 | + | 2.57709e13i | −0.121849 | + | 0.640032i | ||||
\(527\) | − | 8.74772e12i | − | 0.215200i | ||||||
\(528\) | −3.37415e11 | − | 3.15921e11i | −0.00822233 | − | 0.00769854i | ||||
\(529\) | −9.49367e13 | −2.29169 | ||||||||
\(530\) | −1.13305e12 | − | 2.15709e11i | −0.0270938 | − | 0.00515809i | ||||
\(531\) | − | 1.78550e12i | − | 0.0422948i | ||||||
\(532\) | 8.01772e13 | + | 3.16762e13i | 1.88145 | + | 0.743318i | ||||
\(533\) | 3.47549e13 | 0.807942 | ||||||||
\(534\) | −5.94852e12 | + | 3.12457e13i | −0.136994 | + | 0.719587i | ||||
\(535\) | − | 7.27446e12i | − | 0.165971i | ||||||
\(536\) | 1.58135e13 | − | 2.49791e13i | 0.357442 | − | 0.564615i | ||||
\(537\) | 5.82624e12 | 0.130472 | ||||||||
\(538\) | −3.56058e13 | − | 6.77859e12i | −0.789968 | − | 0.150393i | ||||
\(539\) | − | 1.46575e11i | − | 0.00322194i | ||||||
\(540\) | 6.03794e11 | − | 1.52829e12i | 0.0131498 | − | 0.0332842i | ||||
\(541\) | −1.20532e12 | −0.0260085 | −0.0130042 | − | 0.999915i | \(-0.504139\pi\) | ||||
−0.0130042 | + | 0.999915i | \(0.504139\pi\) | |||||||
\(542\) | −9.38388e12 | + | 4.92905e13i | −0.200626 | + | 1.05382i | ||||
\(543\) | − | 3.40493e13i | − | 0.721289i | ||||||
\(544\) | −8.01322e12 | − | 1.09867e13i | −0.168195 | − | 0.230607i | ||||
\(545\) | 1.03987e12 | 0.0216270 | ||||||||
\(546\) | −2.21758e13 | − | 4.22180e12i | −0.456999 | − | 0.0870030i | ||||
\(547\) | 6.28676e13i | 1.28378i | 0.766797 | + | 0.641890i | \(0.221849\pi\) | ||||
−0.766797 | + | 0.641890i | \(0.778151\pi\) | |||||||
\(548\) | −5.25508e13 | − | 2.07616e13i | −1.06335 | − | 0.420105i | ||||
\(549\) | 2.50841e13 | 0.502964 | ||||||||
\(550\) | 1.77282e11 | − | 9.31206e11i | 0.00352250 | − | 0.0185026i | ||||
\(551\) | − | 1.41993e14i | − | 2.79581i | ||||||
\(552\) | 4.53586e13 | + | 2.87152e13i | 0.885042 | + | 0.560295i | ||||
\(553\) | −3.70461e13 | −0.716336 | ||||||||
\(554\) | 9.13951e13 | + | 1.73997e13i | 1.75135 | + | 0.333421i | ||||
\(555\) | − | 6.87238e12i | − | 0.130510i | ||||||
\(556\) | −2.20026e13 | + | 5.56919e13i | −0.414095 | + | 1.04814i | ||||
\(557\) | −7.32140e13 | −1.36558 | −0.682791 | − | 0.730614i | \(-0.739234\pi\) | ||||
−0.682791 | + | 0.730614i | \(0.739234\pi\) | |||||||
\(558\) | 2.54263e12 | − | 1.33556e13i | 0.0470015 | − | 0.246884i | ||||
\(559\) | 2.63480e13i | 0.482713i | ||||||||
\(560\) | −7.55557e12 | + | 8.06963e12i | −0.137192 | + | 0.146526i | ||||
\(561\) | 1.78648e11 | 0.00321502 | ||||||||
\(562\) | 5.71569e13 | + | 1.08815e13i | 1.01950 | + | 0.194091i | ||||
\(563\) | 7.76911e13i | 1.37350i | 0.726893 | + | 0.686751i | \(0.240964\pi\) | ||||
−0.726893 | + | 0.686751i | \(0.759036\pi\) | |||||||
\(564\) | −6.22775e12 | − | 2.46044e12i | −0.109128 | − | 0.0431139i | ||||
\(565\) | −1.20892e13 | −0.209969 | ||||||||
\(566\) | −1.36919e13 | + | 7.19193e13i | −0.235712 | + | 1.23812i | ||||
\(567\) | 7.02851e12i | 0.119936i | ||||||||
\(568\) | 4.36814e13 | − | 6.89990e13i | 0.738847 | − | 1.16708i | ||||
\(569\) | 8.43027e13 | 1.41345 | 0.706725 | − | 0.707489i | \(-0.250172\pi\) | ||||
0.706725 | + | 0.707489i | \(0.250172\pi\) | |||||||
\(570\) | 1.18931e13 | + | 2.26420e12i | 0.197661 | + | 0.0376305i | ||||
\(571\) | − | 9.41889e13i | − | 1.55174i | −0.630892 | − | 0.775870i | \(-0.717311\pi\) | ||
0.630892 | − | 0.775870i | \(-0.282689\pi\) | |||||||
\(572\) | −3.27665e11 | + | 8.29371e11i | −0.00535119 | + | 0.0135447i | ||||
\(573\) | 4.65461e13 | 0.753546 | ||||||||
\(574\) | −1.36145e13 | + | 7.15126e13i | −0.218495 | + | 1.14769i | ||||
\(575\) | 1.10094e14i | 1.75156i | ||||||||
\(576\) | −9.04080e12 | − | 1.91031e13i | −0.142592 | − | 0.301295i | ||||
\(577\) | 5.21382e13 | 0.815224 | 0.407612 | − | 0.913155i | \(-0.366362\pi\) | ||||
0.407612 | + | 0.913155i | \(0.366362\pi\) | |||||||
\(578\) | −5.82106e13 | − | 1.10821e13i | −0.902324 | − | 0.171784i | ||||
\(579\) | − | 1.14366e13i | − | 0.175754i | ||||||
\(580\) | 1.69344e13 | + | 6.69041e12i | 0.258007 | + | 0.101933i | ||||
\(581\) | −1.16905e14 | −1.76585 | ||||||||
\(582\) | 3.50564e12 | − | 1.84140e13i | 0.0524992 | − | 0.275761i | ||||
\(583\) | − | 1.94884e11i | − | 0.00289357i | ||||||
\(584\) | −6.27143e13 | − | 3.97027e13i | −0.923214 | − | 0.584461i | ||||
\(585\) | −3.17022e12 | −0.0462712 | ||||||||
\(586\) | −1.14634e12 | − | 2.18239e11i | −0.0165892 | − | 0.00315823i | ||||
\(587\) | 6.27357e12i | 0.0900169i | 0.998987 | + | 0.0450084i | \(0.0143315\pi\) | ||||
−0.998987 | + | 0.0450084i | \(0.985669\pi\) | |||||||
\(588\) | 2.46254e12 | − | 6.23305e12i | 0.0350345 | − | 0.0886776i | ||||
\(589\) | 1.00166e14 | 1.41300 | ||||||||
\(590\) | −3.15480e11 | + | 1.65711e12i | −0.00441277 | + | 0.0231789i | ||||
\(591\) | 1.53743e13i | 0.213234i | ||||||||
\(592\) | −6.45215e13 | − | 6.04113e13i | −0.887352 | − | 0.830825i | ||||
\(593\) | −2.50022e13 | −0.340961 | −0.170480 | − | 0.985361i | \(-0.554532\pi\) | ||||
−0.170480 | + | 0.985361i | \(0.554532\pi\) | |||||||
\(594\) | 2.72751e11 | + | 5.19261e10i | 0.00368837 | + | 0.000702188i | ||||
\(595\) | − | 4.27255e12i | − | 0.0572931i | ||||||
\(596\) | −5.38976e13 | − | 2.12937e13i | −0.716702 | − | 0.283152i | ||||
\(597\) | 8.36195e12 | 0.110265 | ||||||||
\(598\) | 1.93696e13 | − | 1.01742e14i | 0.253288 | − | 1.33044i | ||||
\(599\) | − | 6.23083e13i | − | 0.808001i | −0.914759 | − | 0.404000i | \(-0.867619\pi\) | ||
0.914759 | − | 0.404000i | \(-0.132381\pi\) | |||||||
\(600\) | 2.31836e13 | − | 3.66207e13i | 0.298142 | − | 0.470945i | ||||
\(601\) | −6.66674e13 | −0.850239 | −0.425120 | − | 0.905137i | \(-0.639768\pi\) | ||||
−0.425120 | + | 0.905137i | \(0.639768\pi\) | |||||||
\(602\) | −5.42144e13 | − | 1.03213e13i | −0.685696 | − | 0.130542i | ||||
\(603\) | 1.77583e13i | 0.222749i | ||||||||
\(604\) | 1.70430e13 | − | 4.31384e13i | 0.212012 | − | 0.536635i | ||||
\(605\) | 1.50670e13 | 0.185887 | ||||||||
\(606\) | −4.28562e12 | + | 2.25110e13i | −0.0524386 | + | 0.275443i | ||||
\(607\) | − | 5.40578e11i | − | 0.00656016i | −0.999995 | − | 0.00328008i | \(-0.998956\pi\) | ||
0.999995 | − | 0.00328008i | \(-0.00104408\pi\) | |||||||
\(608\) | 1.25803e14 | − | 9.17553e13i | 1.51417 | − | 1.10437i | ||||
\(609\) | −7.78801e13 | −0.929695 | ||||||||
\(610\) | −2.32805e13 | − | 4.43211e12i | −0.275640 | − | 0.0524761i | ||||
\(611\) | 1.29185e13i | 0.151708i | ||||||||
\(612\) | 7.59692e12 | + | 3.00137e12i | 0.0884872 | + | 0.0349593i | ||||
\(613\) | 1.04416e14 | 1.20633 | 0.603163 | − | 0.797618i | \(-0.293907\pi\) | ||||
0.603163 | + | 0.797618i | \(0.293907\pi\) | |||||||
\(614\) | 8.73125e12 | − | 4.58625e13i | 0.100054 | − | 0.525552i | ||||
\(615\) | 1.02234e13i | 0.116203i | ||||||||
\(616\) | −1.57818e12 | − | 9.99101e11i | −0.0177931 | − | 0.0112643i | ||||
\(617\) | −8.83409e13 | −0.987952 | −0.493976 | − | 0.869476i | \(-0.664457\pi\) | ||||
−0.493976 | + | 0.869476i | \(0.664457\pi\) | |||||||
\(618\) | 2.36706e13 | + | 4.50638e12i | 0.262583 | + | 0.0499903i | ||||
\(619\) | 5.36101e13i | 0.589921i | 0.955509 | + | 0.294960i | \(0.0953065\pi\) | ||||
−0.955509 | + | 0.294960i | \(0.904694\pi\) | |||||||
\(620\) | −4.71961e12 | + | 1.19460e13i | −0.0515166 | + | 0.130396i | ||||
\(621\) | −3.22467e13 | −0.349162 | ||||||||
\(622\) | −1.51554e13 | + | 7.96063e13i | −0.162785 | + | 0.855057i | ||||
\(623\) | 1.28530e14i | 1.36951i | ||||||||
\(624\) | −2.78677e13 | + | 2.97637e13i | −0.294563 | + | 0.314604i | ||||
\(625\) | 8.55879e13 | 0.897454 | ||||||||
\(626\) | 1.08159e14 | + | 2.05912e13i | 1.12510 | + | 0.214195i | ||||
\(627\) | 2.04560e12i | 0.0211098i | ||||||||
\(628\) | −8.11511e13 | − | 3.20610e13i | −0.830800 | − | 0.328230i | ||||
\(629\) | 3.41616e13 | 0.346964 | ||||||||
\(630\) | 1.24187e12 | − | 6.52313e12i | 0.0125133 | − | 0.0657284i | ||||
\(631\) | 1.20585e13i | 0.120544i | 0.998182 | + | 0.0602720i | \(0.0191968\pi\) | ||||
−0.998182 | + | 0.0602720i | \(0.980803\pi\) | |||||||
\(632\) | −3.57915e13 | + | 5.65362e13i | −0.354972 | + | 0.560714i | ||||
\(633\) | −6.70817e13 | −0.660063 | ||||||||
\(634\) | −8.23191e13 | − | 1.56718e13i | −0.803626 | − | 0.152994i | ||||
\(635\) | − | 2.00996e13i | − | 0.194679i | ||||||
\(636\) | 3.27414e12 | − | 8.28736e12i | 0.0314639 | − | 0.0796398i | ||||
\(637\) | −1.29295e13 | −0.123278 | ||||||||
\(638\) | −5.75373e11 | + | 3.02225e12i | −0.00544309 | + | 0.0285908i | ||||
\(639\) | 4.90534e13i | 0.460432i | ||||||||
\(640\) | 5.01540e12 | + | 1.93270e13i | 0.0467096 | + | 0.179996i | ||||
\(641\) | 1.89650e14 | 1.75252 | 0.876261 | − | 0.481837i | \(-0.160030\pi\) | ||||
0.876261 | + | 0.481837i | \(0.160030\pi\) | |||||||
\(642\) | 5.52078e13 | + | 1.05104e13i | 0.506203 | + | 0.0963705i | ||||
\(643\) | 1.11907e14i | 1.01813i | 0.860729 | + | 0.509064i | \(0.170008\pi\) | ||||
−0.860729 | + | 0.509064i | \(0.829992\pi\) | |||||||
\(644\) | 2.01760e14 | + | 7.97106e13i | 1.82140 | + | 0.719592i | ||||
\(645\) | −7.75043e12 | −0.0694268 | ||||||||
\(646\) | −1.12550e13 | + | 5.91188e13i | −0.100042 | + | 0.525488i | ||||
\(647\) | − | 7.82465e13i | − | 0.690150i | −0.938575 | − | 0.345075i | \(-0.887854\pi\) | ||
0.938575 | − | 0.345075i | \(-0.112146\pi\) | |||||||
\(648\) | 1.07262e13 | + | 6.79048e12i | 0.0938799 | + | 0.0594327i | ||||
\(649\) | −2.85022e11 | −0.00247546 | ||||||||
\(650\) | −8.21426e13 | − | 1.56382e13i | −0.707948 | − | 0.134778i | ||||
\(651\) | − | 5.49389e13i | − | 0.469867i | ||||||
\(652\) | −4.94783e13 | + | 1.25237e14i | −0.419930 | + | 1.06291i | ||||
\(653\) | −1.20791e14 | −1.01735 | −0.508674 | − | 0.860959i | \(-0.669864\pi\) | ||||
−0.508674 | + | 0.860959i | \(0.669864\pi\) | |||||||
\(654\) | −1.50244e12 | + | 7.89185e12i | −0.0125577 | + | 0.0659614i | ||||
\(655\) | 3.22195e13i | 0.267247i | ||||||||
\(656\) | 9.59823e13 | + | 8.98680e13i | 0.790082 | + | 0.739751i | ||||
\(657\) | 4.45854e13 | 0.364222 | ||||||||
\(658\) | −2.65815e13 | − | 5.06056e12i | −0.215502 | − | 0.0410270i | ||||
\(659\) | − | 7.03328e13i | − | 0.565889i | −0.959136 | − | 0.282944i | \(-0.908689\pi\) | ||
0.959136 | − | 0.282944i | \(-0.0913112\pi\) | |||||||
\(660\) | −2.43964e11 | − | 9.63848e10i | −0.00194808 | − | 0.000769642i | ||||
\(661\) | −1.51959e13 | −0.120425 | −0.0602127 | − | 0.998186i | \(-0.519178\pi\) | ||||
−0.0602127 | + | 0.998186i | \(0.519178\pi\) | |||||||
\(662\) | 2.78201e13 | − | 1.46130e14i | 0.218811 | − | 1.14934i | ||||
\(663\) | − | 1.57587e13i | − | 0.123013i | ||||||
\(664\) | −1.12946e14 | + | 1.78410e14i | −0.875047 | + | 1.38222i | ||||
\(665\) | 4.89228e13 | 0.376186 | ||||||||
\(666\) | 5.21563e13 | + | 9.92946e12i | 0.398048 | + | 0.0757800i | ||||
\(667\) | − | 3.57313e14i | − | 2.70658i | ||||||
\(668\) | 3.29298e13 | − | 8.33504e13i | 0.247575 | − | 0.626651i | ||||
\(669\) | −2.79117e13 | −0.208284 | ||||||||
\(670\) | 3.13772e12 | − | 1.64815e13i | 0.0232402 | − | 0.122074i | ||||
\(671\) | − | 4.00422e12i | − | 0.0294378i | ||||||
\(672\) | −5.03260e13 | − | 6.90005e13i | −0.367236 | − | 0.503507i | ||||
\(673\) | −3.29058e11 | −0.00238340 | −0.00119170 | − | 0.999999i | \(-0.500379\pi\) | ||||
−0.00119170 | + | 0.999999i | \(0.500379\pi\) | |||||||
\(674\) | −4.49968e13 | − | 8.56645e12i | −0.323506 | − | 0.0615887i | ||||
\(675\) | 2.60347e13i | 0.185795i | ||||||||
\(676\) | −5.81324e13 | − | 2.29668e13i | −0.411799 | − | 0.162692i | ||||
\(677\) | −4.89695e13 | −0.344336 | −0.172168 | − | 0.985068i | \(-0.555077\pi\) | ||||
−0.172168 | + | 0.985068i | \(0.555077\pi\) | |||||||
\(678\) | 1.74669e13 | − | 9.17479e13i | 0.121918 | − | 0.640395i | ||||
\(679\) | − | 7.57468e13i | − | 0.524826i | ||||||
\(680\) | −6.52036e12 | − | 4.12786e12i | −0.0448463 | − | 0.0283910i | ||||
\(681\) | −1.10339e14 | −0.753342 | ||||||||
\(682\) | −2.13198e12 | − | 4.05884e11i | −0.0144498 | − | 0.00275093i | ||||
\(683\) | − | 2.08049e14i | − | 1.39979i | −0.714247 | − | 0.699893i | \(-0.753231\pi\) | ||
0.714247 | − | 0.699893i | \(-0.246769\pi\) | |||||||
\(684\) | −3.43671e13 | + | 8.69884e13i | −0.229542 | + | 0.581006i | ||||
\(685\) | −3.20656e13 | −0.212611 | ||||||||
\(686\) | −2.56041e13 | + | 1.34490e14i | −0.168534 | + | 0.885257i | ||||
\(687\) | 3.00729e13i | 0.196513i | ||||||||
\(688\) | −6.81297e13 | + | 7.27651e13i | −0.441972 | + | 0.472042i | ||||
\(689\) | −1.71909e13 | −0.110714 | ||||||||
\(690\) | 2.99281e13 | + | 5.69767e12i | 0.191352 | + | 0.0364294i | ||||
\(691\) | − | 7.10583e13i | − | 0.451050i | −0.974237 | − | 0.225525i | \(-0.927590\pi\) | ||
0.974237 | − | 0.225525i | \(-0.0724097\pi\) | |||||||
\(692\) | 7.42651e13 | + | 2.93405e13i | 0.468009 | + | 0.184900i | ||||
\(693\) | 1.12197e12 | 0.00701966 | ||||||||
\(694\) | 4.18719e13 | − | 2.19939e14i | 0.260091 | − | 1.36617i | ||||
\(695\) | 3.39823e13i | 0.209570i | ||||||||
\(696\) | −7.52427e13 | + | 1.18853e14i | −0.460700 | + | 0.727721i | ||||
\(697\) | −5.08188e13 | −0.308930 | ||||||||
\(698\) | 2.53651e13 | + | 4.82899e12i | 0.153095 | + | 0.0291460i | ||||
\(699\) | − | 6.81256e13i | − | 0.408249i | ||||||
\(700\) | 6.43552e13 | − | 1.62893e14i | 0.382907 | − | 0.969195i | ||||
\(701\) | −8.56643e13 | −0.506069 | −0.253034 | − | 0.967457i | \(-0.581429\pi\) | ||||
−0.253034 | + | 0.967457i | \(0.581429\pi\) | |||||||
\(702\) | 4.58045e12 | − | 2.40596e13i | 0.0268672 | − | 0.141125i | ||||
\(703\) | 3.91167e14i | 2.27816i | ||||||||
\(704\) | −3.04947e12 | + | 1.44320e12i | −0.0176344 | + | 0.00834571i | ||||
\(705\) | −3.80007e12 | −0.0218196 | ||||||||
\(706\) | 2.77312e14 | + | 5.27943e13i | 1.58105 | + | 0.300998i | ||||
\(707\) | 9.26000e13i | 0.524220i | ||||||||
\(708\) | −1.21205e13 | − | 4.78851e12i | −0.0681322 | − | 0.0269175i | ||||
\(709\) | 7.70651e13 | 0.430156 | 0.215078 | − | 0.976597i | \(-0.430999\pi\) | ||||
0.215078 | + | 0.976597i | \(0.430999\pi\) | |||||||
\(710\) | 8.66725e12 | − | 4.55263e13i | 0.0480385 | − | 0.252331i | ||||
\(711\) | − | 4.01932e13i | − | 0.221210i | ||||||
\(712\) | 1.96151e14 | + | 1.24178e14i | 1.07199 | + | 0.678646i | ||||
\(713\) | 2.52059e14 | 1.36790 | ||||||||
\(714\) | 3.24255e13 | + | 6.17313e12i | 0.174741 | + | 0.0332670i | ||||
\(715\) | 5.06068e11i | 0.00270819i | ||||||||
\(716\) | 1.56253e13 | − | 3.95501e13i | 0.0830356 | − | 0.210176i | ||||
\(717\) | 1.73609e14 | 0.916170 | ||||||||
\(718\) | 5.53196e12 | − | 2.90576e13i | 0.0289906 | − | 0.152278i | ||||
\(719\) | 1.84786e14i | 0.961664i | 0.876813 | + | 0.480832i | \(0.159665\pi\) | ||||
−0.876813 | + | 0.480832i | \(0.840335\pi\) | |||||||
\(720\) | −8.75517e12 | − | 8.19744e12i | −0.0452483 | − | 0.0423658i | ||||
\(721\) | 9.73699e13 | 0.499745 | ||||||||
\(722\) | −4.84206e14 | − | 9.21827e13i | −2.46800 | − | 0.469855i | ||||
\(723\) | 1.40639e14i | 0.711892i | ||||||||
\(724\) | −2.31136e14 | − | 9.13165e13i | −1.16192 | − | 0.459046i | ||||
\(725\) | −2.88481e14 | −1.44021 | ||||||||
\(726\) | −2.17693e13 | + | 1.14347e14i | −0.107935 | + | 0.566948i | ||||
\(727\) | − | 1.03169e14i | − | 0.508015i | −0.967202 | − | 0.254008i | \(-0.918251\pi\) | ||
0.967202 | − | 0.254008i | \(-0.0817489\pi\) | |||||||
\(728\) | −8.81317e13 | + | 1.39213e14i | −0.430998 | + | 0.680803i | ||||
\(729\) | −7.62560e12 | −0.0370370 | ||||||||
\(730\) | −4.13796e13 | − | 7.87780e12i | −0.199605 | − | 0.0380006i | ||||
\(731\) | − | 3.85262e13i | − | 0.184573i | ||||||
\(732\) | 6.72728e13 | − | 1.70278e14i | 0.320099 | − | 0.810219i | ||||
\(733\) | −4.49715e13 | −0.212528 | −0.106264 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106264 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(734\) | −2.23029e13 | + | 1.17150e14i | −0.104684 | + | 0.549872i | ||||
\(735\) | − | 3.80330e12i | − | 0.0177306i | ||||||
\(736\) | 3.16574e14 | − | 2.30895e14i | 1.46584 | − | 1.06912i | ||||
\(737\) | 2.83480e12 | 0.0130372 | ||||||||
\(738\) | −7.75878e13 | − | 1.47711e13i | −0.354415 | − | 0.0674731i | ||||
\(739\) | 1.52473e14i | 0.691782i | 0.938275 | + | 0.345891i | \(0.112423\pi\) | ||||
−0.938275 | + | 0.345891i | \(0.887577\pi\) | |||||||
\(740\) | −4.66516e13 | − | 1.84310e13i | −0.210236 | − | 0.0830596i | ||||
\(741\) | 1.80445e14 | 0.807706 | ||||||||
\(742\) | 6.73417e12 | − | 3.53724e13i | 0.0299409 | − | 0.157270i | ||||
\(743\) | 4.33975e14i | 1.91655i | 0.285844 | + | 0.958276i | \(0.407726\pi\) | ||||
−0.285844 | + | 0.958276i | \(0.592274\pi\) | |||||||
\(744\) | −8.38425e13 | − | 5.30784e13i | −0.367790 | − | 0.232837i | ||||
\(745\) | −3.28874e13 | −0.143301 | ||||||||
\(746\) | −5.25973e13 | − | 1.00134e13i | −0.227651 | − | 0.0433400i | ||||
\(747\) | − | 1.26837e14i | − | 0.545308i | ||||||
\(748\) | 4.79114e11 | − | 1.21271e12i | 0.00204612 | − | 0.00517903i | ||||
\(749\) | 2.27099e14 | 0.963401 | ||||||||
\(750\) | 9.36492e12 | − | 4.91909e13i | 0.0394637 | − | 0.207290i | ||||
\(751\) | 9.28346e13i | 0.388607i | 0.980942 | + | 0.194303i | \(0.0622446\pi\) | ||||
−0.980942 | + | 0.194303i | \(0.937755\pi\) | |||||||
\(752\) | −3.34043e13 | + | 3.56770e13i | −0.138903 | + | 0.148354i | ||||
\(753\) | 1.27786e14 | 0.527849 | ||||||||
\(754\) | 2.66596e14 | + | 5.07542e13i | 1.09395 | + | 0.208264i | ||||
\(755\) | − | 2.63223e13i | − | 0.107298i | ||||||
\(756\) | 4.77114e13 | + | 1.88497e13i | 0.193203 | + | 0.0763300i | ||||
\(757\) | −1.57105e14 | −0.631990 | −0.315995 | − | 0.948761i | \(-0.602338\pi\) | ||||
−0.315995 | + | 0.948761i | \(0.602338\pi\) | |||||||
\(758\) | 2.79846e12 | − | 1.46994e13i | 0.0111834 | − | 0.0587428i | ||||
\(759\) | 5.14760e12i | 0.0204360i | ||||||||
\(760\) | 4.72660e13 | − | 7.46613e13i | 0.186415 | − | 0.294461i | ||||
\(761\) | −3.45476e14 | −1.35361 | −0.676806 | − | 0.736161i | \(-0.736636\pi\) | ||||
−0.676806 | + | 0.736161i | \(0.736636\pi\) | |||||||
\(762\) | 1.52541e14 | + | 2.90406e13i | 0.593761 | + | 0.113040i | ||||
\(763\) | 3.24634e13i | 0.125537i | ||||||||
\(764\) | 1.24831e14 | − | 3.15967e14i | 0.479576 | − | 1.21388i | ||||
\(765\) | 4.63551e12 | 0.0176926 | ||||||||
\(766\) | −5.54180e13 | + | 2.91093e14i | −0.210139 | + | 1.10379i | ||||
\(767\) | 2.51421e13i | 0.0947163i | ||||||||
\(768\) | −1.53924e14 | + | 1.01389e13i | −0.576102 | + | 0.0379478i | ||||
\(769\) | −4.95927e14 | −1.84411 | −0.922053 | − | 0.387064i | \(-0.873489\pi\) | ||||
−0.922053 | + | 0.387064i | \(0.873489\pi\) | |||||||
\(770\) | −1.04130e12 | − | 1.98241e11i | −0.00384700 | − | 0.000732387i | ||||
\(771\) | 4.77880e13i | 0.175407i | ||||||||
\(772\) | −7.76351e13 | − | 3.06718e13i | −0.283121 | − | 0.111854i | ||||
\(773\) | 5.38678e14 | 1.95179 | 0.975893 | − | 0.218251i | \(-0.0700352\pi\) | ||||
0.975893 | + | 0.218251i | \(0.0700352\pi\) | |||||||
\(774\) | 1.11981e13 | − | 5.88200e13i | 0.0403125 | − | 0.211749i | ||||
\(775\) | − | 2.03503e14i | − | 0.727882i | ||||||
\(776\) | −1.15598e14 | − | 7.31816e13i | −0.410809 | − | 0.260072i | ||||
\(777\) | 2.14547e14 | 0.757561 | ||||||||
\(778\) | 8.09645e13 | + | 1.54139e13i | 0.284051 | + | 0.0540774i | ||||
\(779\) | − | 5.81900e14i | − | 2.02844i | ||||||
\(780\) | −8.50219e12 | + | 2.15203e13i | −0.0294481 | + | 0.0745377i | ||||
\(781\) | 7.83048e12 | 0.0269484 | ||||||||
\(782\) | −2.83222e13 | + | 1.48768e14i | −0.0968487 | + | 0.508715i | ||||
\(783\) | − | 8.44963e13i | − | 0.287097i | ||||||
\(784\) | −3.57074e13 | − | 3.34327e13i | −0.120553 | − | 0.112873i | ||||
\(785\) | −4.95171e13 | −0.166114 | ||||||||
\(786\) | −2.44522e14 | − | 4.65519e13i | −0.815091 | − | 0.155176i | ||||
\(787\) | 9.70514e13i | 0.321461i | 0.986998 | + | 0.160730i | \(0.0513850\pi\) | ||||
−0.986998 | + | 0.160730i | \(0.948615\pi\) | |||||||
\(788\) | 1.04365e14 | + | 4.12321e13i | 0.343497 | + | 0.135708i | ||||
\(789\) | −1.15016e14 | −0.376159 | ||||||||
\(790\) | −7.10174e12 | + | 3.73032e13i | −0.0230797 | + | 0.121230i | ||||
\(791\) | − | 3.77409e14i | − | 1.21879i | ||||||
\(792\) | 1.08398e12 | − | 1.71225e12i | 0.00347852 | − | 0.00549466i | ||||
\(793\) | −3.53216e14 | −1.12635 | ||||||||
\(794\) | 3.77541e14 | + | 7.18758e13i | 1.19636 | + | 0.227762i | ||||
\(795\) | − | 5.05681e12i | − | 0.0159236i | ||||||
\(796\) | 2.24259e13 | − | 5.67632e13i | 0.0701752 | − | 0.177624i | ||||
\(797\) | −1.94845e14 | −0.605896 | −0.302948 | − | 0.953007i | \(-0.597971\pi\) | ||||
−0.302948 | + | 0.953007i | \(0.597971\pi\) | |||||||
\(798\) | −7.06853e13 | + | 3.71288e14i | −0.218431 | + | 1.14735i | ||||
\(799\) | − | 1.88895e13i | − | 0.0580080i | ||||||
\(800\) | −1.86416e14 | − | 2.55589e14i | −0.568895 | − | 0.779996i | ||||
\(801\) | −1.39449e14 | −0.422916 | ||||||||
\(802\) | −2.81003e14 | − | 5.34970e13i | −0.846913 | − | 0.161234i | ||||
\(803\) | − | 7.11725e12i | − | 0.0213174i | ||||||
\(804\) | 1.20548e14 | + | 4.76259e13i | 0.358824 | + | 0.141763i | ||||
\(805\) | 1.23110e14 | 0.364179 | ||||||||
\(806\) | −3.58034e13 | + | 1.88064e14i | −0.105257 | + | 0.552880i | ||||
\(807\) | − | 1.58909e14i | − | 0.464280i | ||||||
\(808\) | 1.41317e14 | + | 8.94641e13i | 0.410335 | + | 0.259772i | ||||
\(809\) | 3.48567e14 | 1.00587 | 0.502937 | − | 0.864323i | \(-0.332253\pi\) | ||||
0.502937 | + | 0.864323i | \(0.332253\pi\) | |||||||
\(810\) | 7.07729e12 | + | 1.34737e12i | 0.0202975 | + | 0.00386421i | ||||
\(811\) | − | 2.49629e14i | − | 0.711527i | −0.934576 | − | 0.355764i | \(-0.884221\pi\) | ||
0.934576 | − | 0.355764i | \(-0.115779\pi\) | |||||||
\(812\) | −2.08866e14 | + | 5.28672e14i | −0.591681 | + | 1.49763i | ||||
\(813\) | −2.19984e14 | −0.619352 | ||||||||
\(814\) | 1.58506e12 | − | 8.32580e12i | 0.00443530 | − | 0.0232972i | ||||
\(815\) | 7.64176e13i | 0.212523i | ||||||||
\(816\) | 4.07482e13 | − | 4.35206e13i | 0.112631 | − | 0.120294i | ||||
\(817\) | 4.41144e14 | 1.21191 | ||||||||
\(818\) | 3.49689e14 | + | 6.65734e13i | 0.954806 | + | 0.181775i | ||||
\(819\) | − | 9.89703e13i | − | 0.268587i | ||||||
\(820\) | 6.93990e13 | + | 2.74180e13i | 0.187191 | + | 0.0739547i | ||||
\(821\) | 1.10644e14 | 0.296628 | 0.148314 | − | 0.988940i | \(-0.452615\pi\) | ||||
0.148314 | + | 0.988940i | \(0.452615\pi\) | |||||||
\(822\) | 4.63295e13 | − | 2.43354e14i | 0.123452 | − | 0.648455i | ||||
\(823\) | − | 7.95142e13i | − | 0.210594i | −0.994441 | − | 0.105297i | \(-0.966421\pi\) | ||
0.994441 | − | 0.105297i | \(-0.0335793\pi\) | |||||||
\(824\) | 9.40725e13 | − | 1.48597e14i | 0.247643 | − | 0.391177i | ||||
\(825\) | 4.15597e12 | 0.0108743 | ||||||||
\(826\) | −5.17330e13 | − | 9.84888e12i | −0.134545 | − | 0.0256145i | ||||
\(827\) | 4.26755e14i | 1.10319i | 0.834112 | + | 0.551595i | \(0.185981\pi\) | ||||
−0.834112 | + | 0.551595i | \(0.814019\pi\) | |||||||
\(828\) | −8.64822e13 | + | 2.18900e14i | −0.222216 | + | 0.562462i | ||||
\(829\) | −2.10345e14 | −0.537230 | −0.268615 | − | 0.963248i | \(-0.586566\pi\) | ||||
−0.268615 | + | 0.963248i | \(0.586566\pi\) | |||||||
\(830\) | −2.24108e13 | + | 1.17717e14i | −0.0568940 | + | 0.298846i | ||||
\(831\) | 4.07896e14i | 1.02931i | ||||||||
\(832\) | 1.27306e14 | + | 2.68996e14i | 0.319325 | + | 0.674729i | ||||
\(833\) | 1.89056e13 | 0.0471375 | ||||||||
\(834\) | −2.57900e14 | − | 4.90988e13i | −0.639178 | − | 0.121686i | ||||
\(835\) | − | 5.08590e13i | − | 0.125296i | ||||||
\(836\) | 1.38861e13 | + | 5.48609e12i | 0.0340055 | + | 0.0134348i | ||||
\(837\) | 5.96061e13 | 0.145099 | ||||||||
\(838\) | −5.57221e13 | + | 2.92691e14i | −0.134837 | + | 0.708253i | ||||
\(839\) | − | 5.23755e14i | − | 1.25985i | −0.776657 | − | 0.629924i | \(-0.783086\pi\) | ||
0.776657 | − | 0.629924i | \(-0.216914\pi\) | |||||||
\(840\) | −4.09502e13 | − | 2.59245e13i | −0.0979174 | − | 0.0619888i | ||||
\(841\) | 5.15563e14 | 1.22547 | ||||||||
\(842\) | 2.51636e14 | + | 4.79061e13i | 0.594582 | + | 0.113196i | ||||
\(843\) | 2.55091e14i | 0.599180i | ||||||||
\(844\) | −1.79906e14 | + | 4.55369e14i | −0.420081 | + | 1.06329i | ||||
\(845\) | −3.54714e13 | −0.0823371 | ||||||||
\(846\) | 5.49047e12 | − | 2.88397e13i | 0.0126695 | − | 0.0665486i | ||||
\(847\) | 4.70373e14i | 1.07901i | ||||||||
\(848\) | −4.74759e13 | − | 4.44516e13i | −0.108267 | − | 0.101370i | ||||
\(849\) | −3.20976e14 | −0.727668 | ||||||||
\(850\) | 1.20109e14 | + | 2.28663e13i | 0.270696 | + | 0.0515348i | ||||
\(851\) | 9.84340e14i | 2.20545i | ||||||||
\(852\) | 3.32988e14 | + | 1.31556e14i | 0.741704 | + | 0.293030i | ||||
\(853\) | −2.01871e13 | −0.0447022 | −0.0223511 | − | 0.999750i | \(-0.507115\pi\) | ||||
−0.0223511 | + | 0.999750i | \(0.507115\pi\) | |||||||
\(854\) | 1.38365e14 | − | 7.26786e14i | 0.304604 | − | 1.59999i | ||||
\(855\) | 5.30789e13i | 0.116169i | ||||||||
\(856\) | 2.19409e14 | − | 3.46578e14i | 0.477403 | − | 0.754105i | ||||
\(857\) | −3.39453e14 | −0.734304 | −0.367152 | − | 0.930161i | \(-0.619667\pi\) | ||||
−0.367152 | + | 0.930161i | \(0.619667\pi\) | |||||||
\(858\) | −3.84068e12 | − | 7.31185e11i | −0.00825985 | − | 0.00157250i | ||||
\(859\) | − | 2.59695e14i | − | 0.555262i | −0.960688 | − | 0.277631i | \(-0.910451\pi\) | ||
0.960688 | − | 0.277631i | \(-0.0895493\pi\) | |||||||
\(860\) | −2.07858e13 | + | 5.26120e13i | −0.0441850 | + | 0.111839i | ||||
\(861\) | −3.19161e14 | −0.674518 | ||||||||
\(862\) | 1.49448e14 | − | 7.85003e14i | 0.314018 | − | 1.64943i | ||||
\(863\) | − | 3.06623e14i | − | 0.640547i | −0.947325 | − | 0.320274i | \(-0.896225\pi\) | ||
0.947325 | − | 0.320274i | \(-0.103775\pi\) | |||||||
\(864\) | 7.48623e13 | − | 5.46013e13i | 0.155487 | − | 0.113406i | ||||
\(865\) | 4.53154e13 | 0.0935761 | ||||||||
\(866\) | 6.74881e13 | + | 1.28483e13i | 0.138560 | + | 0.0263789i | ||||
\(867\) | − | 2.59794e14i | − | 0.530314i | ||||||
\(868\) | −3.72940e14 | − | 1.47340e14i | −0.756903 | − | 0.299035i | ||||
\(869\) | −6.41612e12 | −0.0129471 | ||||||||
\(870\) | −1.49296e13 | + | 7.84207e13i | −0.0299539 | + | 0.157338i | ||||
\(871\) | − | 2.50060e14i | − | 0.498831i | ||||||
\(872\) | 4.95426e13 | + | 3.13641e13i | 0.0982645 | + | 0.0622085i | ||||
\(873\) | 8.21817e13 | 0.162070 | ||||||||
\(874\) | −1.70346e15 | − | 3.24304e14i | −3.34022 | − | 0.635908i | ||||
\(875\) | − | 2.02349e14i | − | 0.394513i | ||||||
\(876\) | 1.19573e14 | − | 3.02658e14i | 0.231800 | − | 0.586721i | ||||
\(877\) | 2.51052e14 | 0.483912 | 0.241956 | − | 0.970287i | \(-0.422211\pi\) | ||||
0.241956 | + | 0.970287i | \(0.422211\pi\) | |||||||
\(878\) | 1.73400e14 | − | 9.10815e14i | 0.332335 | − | 1.74565i | ||||
\(879\) | − | 5.11611e12i | − | 0.00974980i | ||||||
\(880\) | −1.30857e12 | + | 1.39760e12i | −0.00247961 | + | 0.00264832i | ||||
\(881\) | −4.49257e14 | −0.846478 | −0.423239 | − | 0.906018i | \(-0.639107\pi\) | ||||
−0.423239 | + | 0.906018i | \(0.639107\pi\) | |||||||
\(882\) | 2.88642e13 | + | 5.49515e12i | 0.0540776 | + | 0.0102952i | ||||
\(883\) | 5.14061e14i | 0.957660i | 0.877908 | + | 0.478830i | \(0.158939\pi\) | ||||
−0.877908 | + | 0.478830i | \(0.841061\pi\) | |||||||
\(884\) | −1.06974e14 | − | 4.22631e13i | −0.198161 | − | 0.0782888i | ||||
\(885\) | −7.39570e12 | −0.0136227 | ||||||||
\(886\) | −2.06185e13 | + | 1.08302e14i | −0.0377649 | + | 0.198367i | ||||
\(887\) | − | 2.84864e14i | − | 0.518824i | −0.965767 | − | 0.259412i | \(-0.916471\pi\) | ||
0.965767 | − | 0.259412i | \(-0.0835287\pi\) | |||||||
\(888\) | 2.07281e14 | − | 3.27421e14i | 0.375401 | − | 0.592983i | ||||
\(889\) | 6.27483e14 | 1.13004 | ||||||||
\(890\) | 1.29422e14 | + | 2.46393e13i | 0.231771 | + | 0.0441244i | ||||
\(891\) | 1.21729e12i | 0.00216773i | ||||||||
\(892\) | −7.48561e13 | + | 1.89472e14i | −0.132557 | + | 0.335522i | ||||
\(893\) | 2.16295e14 | 0.380880 | ||||||||
\(894\) | 4.75169e13 | − | 2.49591e14i | 0.0832072 | − | 0.437061i | ||||
\(895\) | − | 2.41328e13i | − | 0.0420235i | ||||||
\(896\) | −6.03363e14 | + | 1.56575e14i | −1.04481 | + | 0.271132i | ||||
\(897\) | 4.54075e14 | 0.781925 | ||||||||
\(898\) | 5.05483e14 | + | 9.62334e13i | 0.865616 | + | 0.164795i | ||||
\(899\) | 6.60472e14i | 1.12475i | ||||||||
\(900\) | 1.76731e14 | + | 6.98223e13i | 0.299295 | + | 0.118245i | ||||
\(901\) | 2.51366e13 | 0.0423333 | ||||||||
\(902\) | −2.35793e12 | + | 1.23855e13i | −0.00394911 | + | 0.0207434i | ||||
\(903\) | − | 2.41959e14i | − | 0.402997i | ||||||
\(904\) | −5.75966e14 | − | 3.64628e14i | −0.954013 | − | 0.603959i | ||||
\(905\) | −1.41035e14 | −0.232319 | ||||||||
\(906\) | 1.99767e14 | + | 3.80314e13i | 0.327252 | + | 0.0623020i | ||||
\(907\) | 6.52723e14i | 1.06339i | 0.846936 | + | 0.531695i | \(0.178445\pi\) | ||||
−0.846936 | + | 0.531695i | \(0.821555\pi\) | |||||||
\(908\) | −2.95916e14 | + | 7.49009e14i | −0.479446 | + | 1.21355i | ||||
\(909\) | −1.00467e14 | −0.161883 | ||||||||
\(910\) | −1.74871e13 | + | 9.18540e13i | −0.0280227 | + | 0.147194i | ||||
\(911\) | 7.55207e14i | 1.20358i | 0.798655 | + | 0.601789i | \(0.205545\pi\) | ||||
−0.798655 | + | 0.601789i | \(0.794455\pi\) | |||||||
\(912\) | 4.98332e14 | + | 4.66587e14i | 0.789850 | + | 0.739534i | ||||
\(913\) | −2.02472e13 | −0.0319161 | ||||||||
\(914\) | 3.19734e14 | + | 6.08706e13i | 0.501253 | + | 0.0954281i | ||||
\(915\) | − | 1.03901e14i | − | 0.161999i | ||||||
\(916\) | 2.04143e14 | + | 8.06521e13i | 0.316560 | + | 0.125066i | ||||
\(917\) | −1.00585e15 | −1.55127 | ||||||||
\(918\) | −6.69755e12 | + | 3.51801e13i | −0.0102731 | + | 0.0539614i | ||||
\(919\) | − | 6.42521e14i | − | 0.980189i | −0.871669 | − | 0.490094i | \(-0.836962\pi\) | ||
0.871669 | − | 0.490094i | \(-0.163038\pi\) | |||||||
\(920\) | 1.18941e14 | − | 1.87879e14i | 0.180465 | − | 0.285062i | ||||
\(921\) | 2.04684e14 | 0.308878 | ||||||||
\(922\) | 2.97800e14 | + | 5.66948e13i | 0.446961 | + | 0.0850921i | ||||
\(923\) | − | 6.90735e14i | − | 1.03110i | ||||||
\(924\) | 3.00901e12 | − | 7.61626e12i | 0.00446749 | − | 0.0113079i | ||||
\(925\) | 7.94717e14 | 1.17356 | ||||||||
\(926\) | −1.28685e14 | + | 6.75943e14i | −0.189005 | + | 0.992784i | ||||
\(927\) | 1.05642e14i | 0.154325i | ||||||||
\(928\) | 6.05016e14 | + | 8.29520e14i | 0.879077 | + | 1.20528i | ||||
\(929\) | −5.50071e14 | −0.794951 | −0.397476 | − | 0.917613i | \(-0.630114\pi\) | ||||
−0.397476 | + | 0.917613i | \(0.630114\pi\) | |||||||
\(930\) | −5.53202e13 | − | 1.05318e13i | −0.0795186 | − | 0.0151387i | ||||
\(931\) | 2.16479e14i | 0.309504i | ||||||||
\(932\) | −4.62455e14 | − | 1.82706e14i | −0.657643 | − | 0.259820i | ||||
\(933\) | −3.55283e14 | −0.502534 | ||||||||
\(934\) | −2.36224e13 | + | 1.24081e14i | −0.0332345 | + | 0.174570i | ||||
\(935\) | − | 7.39975e11i | − | 0.00103552i | ||||||
\(936\) | −1.51039e14 | − | 9.56187e13i | −0.210238 | − | 0.133096i | ||||
\(937\) | −1.18951e14 | −0.164691 | −0.0823456 | − | 0.996604i | \(-0.526241\pi\) | ||||
−0.0823456 | + | 0.996604i | \(0.526241\pi\) | |||||||
\(938\) | 5.14530e14 | + | 9.79557e13i | 0.708592 | + | 0.134901i | ||||
\(939\) | 4.82713e14i | 0.661243i | ||||||||
\(940\) | −1.01914e13 | + | 2.57959e13i | −0.0138865 | + | 0.0351489i | ||||
\(941\) | 1.25811e15 | 1.70518 | 0.852588 | − | 0.522584i | \(-0.175032\pi\) | ||||
0.852588 | + | 0.522584i | \(0.175032\pi\) | |||||||
\(942\) | 7.15440e13 | − | 3.75798e14i | 0.0964536 | − | 0.506640i | ||||
\(943\) | − | 1.46431e15i | − | 1.96369i | ||||||
\(944\) | −6.50115e13 | + | 6.94347e13i | −0.0867222 | + | 0.0926225i | ||||
\(945\) | 2.91127e13 | 0.0386299 | ||||||||
\(946\) | −9.38954e12 | − | 1.78757e12i | −0.0123934 | − | 0.00235943i | ||||
\(947\) | 5.61155e14i | 0.736772i | 0.929673 | + | 0.368386i | \(0.120089\pi\) | ||||
−0.929673 | + | 0.368386i | \(0.879911\pi\) | |||||||
\(948\) | −2.72843e14 | − | 1.07794e14i | −0.356345 | − | 0.140784i | ||||
\(949\) | −6.27820e14 | −0.815650 | ||||||||
\(950\) | −2.61830e14 | + | 1.37531e15i | −0.338377 | + | 1.77739i | ||||
\(951\) | − | 3.67390e14i | − | 0.472307i | ||||||
\(952\) | 1.28866e14 | − | 2.03557e14i | 0.164799 | − | 0.260317i | ||||
\(953\) | −4.49938e14 | −0.572385 | −0.286192 | − | 0.958172i | \(-0.592390\pi\) | ||||
−0.286192 | + | 0.958172i | \(0.592390\pi\) | |||||||
\(954\) | 3.83774e13 | + | 7.30625e12i | 0.0485662 | + | 0.00924598i | ||||
\(955\) | − | 1.92798e14i | − | 0.242709i | ||||||
\(956\) | 4.65600e14 | − | 1.17850e15i | 0.583074 | − | 1.47585i | ||||
\(957\) | −1.34883e13 | −0.0168034 | ||||||||
\(958\) | −1.37649e14 | + | 7.23026e14i | −0.170587 | + | 0.896038i | ||||
\(959\) | − | 1.00105e15i | − | 1.23413i | ||||||
\(960\) | −7.91269e13 | + | 3.74478e13i | −0.0970438 | + | 0.0459273i | ||||
\(961\) | 3.53713e14 | 0.431553 | ||||||||
\(962\) | −7.34427e14 | − | 1.39819e14i | −0.891401 | − | 0.169704i | ||||
\(963\) | 2.46392e14i | 0.297506i | ||||||||
\(964\) | 9.54695e14 | + | 3.77178e14i | 1.14678 | + | 0.453066i | ||||
\(965\) | −4.73716e13 | −0.0566085 | ||||||||
\(966\) | −1.77874e14 | + | 9.34316e14i | −0.211459 | + | 1.11073i | ||||
\(967\) | 2.27748e13i | 0.0269353i | 0.999909 | + | 0.0134677i | \(0.00428702\pi\) | ||||
−0.999909 | + | 0.0134677i | \(0.995713\pi\) | |||||||
\(968\) | 7.17838e14 | + | 4.54443e14i | 0.844597 | + | 0.534691i | ||||
\(969\) | −2.63847e14 | −0.308840 | ||||||||
\(970\) | −7.62725e13 | − | 1.45207e13i | −0.0888197 | − | 0.0169094i | ||||
\(971\) | − | 5.54217e14i | − | 0.642072i | −0.947067 | − | 0.321036i | \(-0.895969\pi\) | ||
0.947067 | − | 0.321036i | \(-0.104031\pi\) | |||||||
\(972\) | −2.04510e13 | + | 5.17646e13i | −0.0235713 | + | 0.0596625i | ||||
\(973\) | −1.06088e15 | −1.21648 | ||||||||
\(974\) | 1.38050e14 | − | 7.25133e14i | 0.157486 | − | 0.827224i | ||||
\(975\) | − | 3.66602e14i | − | 0.416075i | ||||||
\(976\) | −9.75473e14 | − | 9.13332e14i | −1.10145 | − | 1.03129i | ||||
\(977\) | 2.31981e14 | 0.260604 | 0.130302 | − | 0.991474i | \(-0.458405\pi\) | ||||
0.130302 | + | 0.991474i | \(0.458405\pi\) | |||||||
\(978\) | −5.79953e14 | − | 1.10411e14i | −0.648184 | − | 0.123401i | ||||
\(979\) | 2.22605e13i | 0.0247527i | ||||||||
\(980\) | −2.58179e13 | − | 1.02000e13i | −0.0285621 | − | 0.0112842i | ||||
\(981\) | −3.52213e13 | −0.0387668 | ||||||||
\(982\) | 1.78643e13 | − | 9.38353e13i | 0.0195627 | − | 0.102756i | ||||
\(983\) | − | 6.70127e14i | − | 0.730112i | −0.930986 | − | 0.365056i | \(-0.881050\pi\) | ||
0.930986 | − | 0.365056i | \(-0.118950\pi\) | |||||||
\(984\) | −3.08352e14 | + | 4.87073e14i | −0.334250 | + | 0.527981i | ||||
\(985\) | 6.36817e13 | 0.0686805 | ||||||||
\(986\) | −3.89817e14 | − | 7.42129e13i | −0.418289 | − | 0.0796334i | ||||
\(987\) | − | 1.18633e14i | − | 0.126655i | ||||||
\(988\) | 4.83933e14 | − | 1.22491e15i | 0.514044 | − | 1.30112i | ||||
\(989\) | 1.11010e15 | 1.17323 | ||||||||
\(990\) | 2.15083e11 | − | 1.12976e12i | 0.000226167 | − | 0.00118798i | ||||
\(991\) | 1.09249e15i | 1.14300i | 0.820601 | + | 0.571501i | \(0.193639\pi\) | ||||
−0.820601 | + | 0.571501i | \(0.806361\pi\) | |||||||
\(992\) | −5.85167e14 | + | 4.26795e14i | −0.609146 | + | 0.444285i | ||||
\(993\) | 6.52178e14 | 0.675492 | ||||||||
\(994\) | 1.42127e15 | + | 2.70580e14i | 1.46469 | + | 0.278846i | ||||
\(995\) | − | 3.46360e13i | − | 0.0355150i | ||||||
\(996\) | −8.61002e14 | − | 3.40162e14i | −0.878430 | − | 0.347048i | ||||
\(997\) | −6.70174e14 | −0.680317 | −0.340159 | − | 0.940368i | \(-0.610481\pi\) | ||||
−0.340159 | + | 0.940368i | \(0.610481\pi\) | |||||||
\(998\) | −1.83928e14 | + | 9.66118e14i | −0.185779 | + | 0.975837i | ||||
\(999\) | 2.32773e14i | 0.233941i |
(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 | 12.11.d.a.7.10 | yes | 10 | |
3.2 | odd | 2 | 36.11.d.e.19.1 | 10 | |||
4.3 | odd | 2 | inner | 12.11.d.a.7.9 | ✓ | 10 | |
8.3 | odd | 2 | 192.11.g.e.127.8 | 10 | |||
8.5 | even | 2 | 192.11.g.e.127.3 | 10 | |||
12.11 | even | 2 | 36.11.d.e.19.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.11.d.a.7.9 | ✓ | 10 | 4.3 | odd | 2 | inner | |
12.11.d.a.7.10 | yes | 10 | 1.1 | even | 1 | trivial | |
36.11.d.e.19.1 | 10 | 3.2 | odd | 2 | |||
36.11.d.e.19.2 | 10 | 12.11 | even | 2 | |||
192.11.g.e.127.3 | 10 | 8.5 | even | 2 | |||
192.11.g.e.127.8 | 10 | 8.3 | odd | 2 |