Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,21,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(20.2811012082\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.7 | ||
Root | \(22670.7 - 1.21630e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.21.d.b.3.8 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −340.525 | − | 965.722i | −0.332544 | − | 0.943088i | ||||
\(3\) | 84336.7 | 1.42825 | 0.714125 | − | 0.700018i | \(-0.246825\pi\) | ||||
0.714125 | + | 0.700018i | \(0.246825\pi\) | |||||||
\(4\) | −816662. | + | 657705.i | −0.778829 | + | 0.627236i | ||||
\(5\) | 4.86521e6i | 0.498198i | 0.968478 | + | 0.249099i | \(0.0801344\pi\) | ||||
−0.968478 | + | 0.249099i | \(0.919866\pi\) | |||||||
\(6\) | −2.87188e7 | − | 8.14458e7i | −0.474956 | − | 1.34697i | ||||
\(7\) | − | 1.26224e8i | − | 0.446849i | −0.974721 | − | 0.223424i | \(-0.928276\pi\) | ||
0.974721 | − | 0.223424i | \(-0.0717236\pi\) | |||||||
\(8\) | 9.13253e8 | + | 5.64703e8i | 0.850533 | + | 0.525921i | ||||
\(9\) | 3.62590e9 | 1.03990 | ||||||||
\(10\) | 4.69844e9 | − | 1.65673e9i | 0.469844 | − | 0.165673i | ||||
\(11\) | 1.51387e10 | 0.583664 | 0.291832 | − | 0.956470i | \(-0.405735\pi\) | ||||
0.291832 | + | 0.956470i | \(0.405735\pi\) | |||||||
\(12\) | −6.88746e10 | + | 5.54687e10i | −1.11236 | + | 0.895850i | ||||
\(13\) | 1.95170e11i | 1.41573i | 0.706348 | + | 0.707865i | \(0.250341\pi\) | ||||
−0.706348 | + | 0.707865i | \(0.749659\pi\) | |||||||
\(14\) | −1.21897e11 | + | 4.29823e10i | −0.421418 | + | 0.148597i | ||||
\(15\) | 4.10316e11i | 0.711551i | ||||||||
\(16\) | 2.34361e11 | − | 1.07424e12i | 0.213150 | − | 0.977019i | ||||
\(17\) | 3.56201e12 | 1.76688 | 0.883439 | − | 0.468546i | \(-0.155222\pi\) | ||||
0.883439 | + | 0.468546i | \(0.155222\pi\) | |||||||
\(18\) | −1.23471e12 | − | 3.50161e12i | −0.345812 | − | 0.980715i | ||||
\(19\) | 3.48807e12 | 0.568918 | 0.284459 | − | 0.958688i | \(-0.408186\pi\) | ||||
0.284459 | + | 0.958688i | \(0.408186\pi\) | |||||||
\(20\) | −3.19987e12 | − | 3.97323e12i | −0.312488 | − | 0.388011i | ||||
\(21\) | − | 1.06453e13i | − | 0.638212i | ||||||
\(22\) | −5.15512e12 | − | 1.46198e13i | −0.194094 | − | 0.550446i | ||||
\(23\) | − | 1.17677e13i | − | 0.284063i | −0.989862 | − | 0.142031i | \(-0.954637\pi\) | ||
0.989862 | − | 0.142031i | \(-0.0453634\pi\) | |||||||
\(24\) | 7.70208e13 | + | 4.76252e13i | 1.21477 | + | 0.751147i | ||||
\(25\) | 7.16971e13 | 0.751799 | ||||||||
\(26\) | 1.88480e14 | − | 6.64604e13i | 1.33516 | − | 0.470792i | ||||
\(27\) | 1.17326e13 | 0.0569844 | ||||||||
\(28\) | 8.30179e13 | + | 1.03082e14i | 0.280280 | + | 0.348019i | ||||
\(29\) | − | 7.56048e14i | − | 1.79709i | −0.438882 | − | 0.898545i | \(-0.644625\pi\) | ||
0.438882 | − | 0.898545i | \(-0.355375\pi\) | |||||||
\(30\) | 3.96251e14 | − | 1.39723e14i | 0.671055 | − | 0.236622i | ||||
\(31\) | 1.11233e15i | 1.35711i | 0.734548 | + | 0.678557i | \(0.237394\pi\) | ||||
−0.734548 | + | 0.678557i | \(0.762606\pi\) | |||||||
\(32\) | −1.11723e15 | + | 1.39479e14i | −0.992297 | + | 0.123883i | ||||
\(33\) | 1.27675e15 | 0.833618 | ||||||||
\(34\) | −1.21295e15 | − | 3.43992e15i | −0.587564 | − | 1.66632i | ||||
\(35\) | 6.14105e14 | 0.222619 | ||||||||
\(36\) | −2.96113e15 | + | 2.38477e15i | −0.809903 | + | 0.652261i | ||||
\(37\) | − | 7.17444e14i | − | 0.149201i | −0.997214 | − | 0.0746003i | \(-0.976232\pi\) | ||
0.997214 | − | 0.0746003i | \(-0.0237681\pi\) | |||||||
\(38\) | −1.18778e15 | − | 3.36851e15i | −0.189190 | − | 0.536540i | ||||
\(39\) | 1.64600e16i | 2.02202i | ||||||||
\(40\) | −2.74740e15 | + | 4.44317e15i | −0.262013 | + | 0.423734i | ||||
\(41\) | 3.23458e15 | 0.240979 | 0.120490 | − | 0.992715i | \(-0.461554\pi\) | ||||
0.120490 | + | 0.992715i | \(0.461554\pi\) | |||||||
\(42\) | −1.02804e16 | + | 3.62499e15i | −0.601890 | + | 0.212233i | ||||
\(43\) | −1.36789e16 | −0.632946 | −0.316473 | − | 0.948602i | \(-0.602499\pi\) | ||||
−0.316473 | + | 0.948602i | \(0.602499\pi\) | |||||||
\(44\) | −1.23632e16 | + | 9.95682e15i | −0.454574 | + | 0.366095i | ||||
\(45\) | 1.76408e16i | 0.518075i | ||||||||
\(46\) | −1.13644e16 | + | 4.00720e15i | −0.267896 | + | 0.0944633i | ||||
\(47\) | − | 4.28694e16i | − | 0.815021i | −0.913201 | − | 0.407510i | \(-0.866397\pi\) | ||
0.913201 | − | 0.407510i | \(-0.133603\pi\) | |||||||
\(48\) | 1.97652e16 | − | 9.05983e16i | 0.304431 | − | 1.39543i | ||||
\(49\) | 6.38598e16 | 0.800326 | ||||||||
\(50\) | −2.44147e16 | − | 6.92395e16i | −0.250006 | − | 0.709013i | ||||
\(51\) | 3.00409e17 | 2.52354 | ||||||||
\(52\) | −1.28364e17 | − | 1.59388e17i | −0.887997 | − | 1.10261i | ||||
\(53\) | 3.34779e17i | 1.91425i | 0.289671 | + | 0.957126i | \(0.406454\pi\) | ||||
−0.289671 | + | 0.957126i | \(0.593546\pi\) | |||||||
\(54\) | −3.99524e15 | − | 1.13304e16i | −0.0189498 | − | 0.0537413i | ||||
\(55\) | 7.36531e16i | 0.290780i | ||||||||
\(56\) | 7.12790e16 | − | 1.15274e17i | 0.235007 | − | 0.380060i | ||||
\(57\) | 2.94173e17 | 0.812557 | ||||||||
\(58\) | −7.30133e17 | + | 2.57453e17i | −1.69481 | + | 0.597611i | ||||
\(59\) | 2.74237e17 | 0.536545 | 0.268272 | − | 0.963343i | \(-0.413547\pi\) | ||||
0.268272 | + | 0.963343i | \(0.413547\pi\) | |||||||
\(60\) | −2.69867e17 | − | 3.35089e17i | −0.446310 | − | 0.554177i | ||||
\(61\) | 1.49210e17i | 0.209170i | 0.994516 | + | 0.104585i | \(0.0333515\pi\) | ||||
−0.994516 | + | 0.104585i | \(0.966648\pi\) | |||||||
\(62\) | 1.07420e18 | − | 3.78775e17i | 1.27988 | − | 0.451300i | ||||
\(63\) | − | 4.57675e17i | − | 0.464677i | ||||||
\(64\) | 5.15142e17 | + | 1.03143e18i | 0.446814 | + | 0.894627i | ||||
\(65\) | −9.49545e17 | −0.705313 | ||||||||
\(66\) | −4.34766e17 | − | 1.23299e18i | −0.277214 | − | 0.786175i | ||||
\(67\) | −2.92321e18 | −1.60366 | −0.801828 | − | 0.597555i | \(-0.796139\pi\) | ||||
−0.801828 | + | 0.597555i | \(0.796139\pi\) | |||||||
\(68\) | −2.90896e18 | + | 2.34275e18i | −1.37610 | + | 1.10825i | ||||
\(69\) | − | 9.92452e17i | − | 0.405712i | ||||||
\(70\) | −2.09118e17 | − | 5.93055e17i | −0.0740306 | − | 0.209949i | ||||
\(71\) | 3.51233e18i | 1.07898i | 0.841993 | + | 0.539489i | \(0.181382\pi\) | ||||
−0.841993 | + | 0.539489i | \(0.818618\pi\) | |||||||
\(72\) | 3.31137e18 | + | 2.04756e18i | 0.884468 | + | 0.546904i | ||||
\(73\) | 5.45402e17 | 0.126908 | 0.0634539 | − | 0.997985i | \(-0.479788\pi\) | ||||
0.0634539 | + | 0.997985i | \(0.479788\pi\) | |||||||
\(74\) | −6.92851e17 | + | 2.44307e17i | −0.140709 | + | 0.0496157i | ||||
\(75\) | 6.04670e18 | 1.07376 | ||||||||
\(76\) | −2.84858e18 | + | 2.29412e18i | −0.443090 | + | 0.356846i | ||||
\(77\) | − | 1.91087e18i | − | 0.260809i | ||||||
\(78\) | 1.58958e19 | − | 5.60505e18i | 1.90694 | − | 0.672409i | ||||
\(79\) | − | 1.64097e19i | − | 1.73312i | −0.499070 | − | 0.866562i | \(-0.666325\pi\) | ||
0.499070 | − | 0.866562i | \(-0.333675\pi\) | |||||||
\(80\) | 5.22643e18 | + | 1.14022e18i | 0.486749 | + | 0.106191i | ||||
\(81\) | −1.16532e19 | −0.958510 | ||||||||
\(82\) | −1.10145e18 | − | 3.12370e18i | −0.0801361 | − | 0.227264i | ||||
\(83\) | −1.30232e19 | −0.839335 | −0.419668 | − | 0.907678i | \(-0.637853\pi\) | ||||
−0.419668 | + | 0.907678i | \(0.637853\pi\) | |||||||
\(84\) | 7.00146e18 | + | 8.69361e18i | 0.400309 | + | 0.497058i | ||||
\(85\) | 1.73300e19i | 0.880254i | ||||||||
\(86\) | 4.65801e18 | + | 1.32100e19i | 0.210482 | + | 0.596924i | ||||
\(87\) | − | 6.37627e19i | − | 2.56669i | ||||||
\(88\) | 1.38255e19 | + | 8.54889e18i | 0.496426 | + | 0.306961i | ||||
\(89\) | −2.43956e19 | −0.782368 | −0.391184 | − | 0.920313i | \(-0.627934\pi\) | ||||
−0.391184 | + | 0.920313i | \(0.627934\pi\) | |||||||
\(90\) | 1.70361e19 | − | 6.00712e18i | 0.488590 | − | 0.172283i | ||||
\(91\) | 2.46351e19 | 0.632617 | ||||||||
\(92\) | 7.73969e18 | + | 9.61025e18i | 0.178174 | + | 0.221236i | ||||
\(93\) | 9.38101e19i | 1.93830i | ||||||||
\(94\) | −4.13999e19 | + | 1.45981e19i | −0.768636 | + | 0.271030i | ||||
\(95\) | 1.69702e19i | 0.283434i | ||||||||
\(96\) | −9.42233e19 | + | 1.17632e19i | −1.41725 | + | 0.176935i | ||||
\(97\) | −7.85794e18 | −0.106559 | −0.0532796 | − | 0.998580i | \(-0.516967\pi\) | ||||
−0.0532796 | + | 0.998580i | \(0.516967\pi\) | |||||||
\(98\) | −2.17459e19 | − | 6.16708e19i | −0.266143 | − | 0.754778i | ||||
\(99\) | 5.48915e19 | 0.606951 | ||||||||
\(100\) | −5.85523e19 | + | 4.71555e19i | −0.585523 | + | 0.471555i | ||||
\(101\) | 1.53362e20i | 1.38837i | 0.719799 | + | 0.694183i | \(0.244234\pi\) | ||||
−0.719799 | + | 0.694183i | \(0.755766\pi\) | |||||||
\(102\) | −1.02297e20 | − | 2.90111e20i | −0.839189 | − | 2.37992i | ||||
\(103\) | − | 7.06517e19i | − | 0.525715i | −0.964835 | − | 0.262857i | \(-0.915335\pi\) | ||
0.964835 | − | 0.262857i | \(-0.0846649\pi\) | |||||||
\(104\) | −1.10213e20 | + | 1.78240e20i | −0.744562 | + | 1.20413i | ||||
\(105\) | 5.17916e19 | 0.317956 | ||||||||
\(106\) | 3.23303e20 | − | 1.14001e20i | 1.80531 | − | 0.636573i | ||||
\(107\) | 1.69073e20 | 0.859483 | 0.429742 | − | 0.902952i | \(-0.358605\pi\) | ||||
0.429742 | + | 0.902952i | \(0.358605\pi\) | |||||||
\(108\) | −9.58155e18 | + | 7.71657e18i | −0.0443811 | + | 0.0357427i | ||||
\(109\) | − | 1.46975e20i | − | 0.620838i | −0.950600 | − | 0.310419i | \(-0.899531\pi\) | ||
0.950600 | − | 0.310419i | \(-0.100469\pi\) | |||||||
\(110\) | 7.11285e19 | − | 2.50807e19i | 0.274231 | − | 0.0966971i | ||||
\(111\) | − | 6.05069e19i | − | 0.213096i | ||||||
\(112\) | −1.35595e20 | − | 2.95819e19i | −0.436580 | − | 0.0952458i | ||||
\(113\) | 1.92152e20 | 0.566059 | 0.283029 | − | 0.959111i | \(-0.408661\pi\) | ||||
0.283029 | + | 0.959111i | \(0.408661\pi\) | |||||||
\(114\) | −1.00173e20 | − | 2.84089e20i | −0.270211 | − | 0.766313i | ||||
\(115\) | 5.72525e19 | 0.141519 | ||||||||
\(116\) | 4.97257e20 | + | 6.17436e20i | 1.12720 | + | 1.39963i | ||||
\(117\) | 7.07668e20i | 1.47221i | ||||||||
\(118\) | −9.33845e19 | − | 2.64837e20i | −0.178425 | − | 0.506009i | ||||
\(119\) | − | 4.49611e20i | − | 0.789527i | ||||||
\(120\) | −2.31707e20 | + | 3.74723e20i | −0.374219 | + | 0.605198i | ||||
\(121\) | −4.43569e20 | −0.659337 | ||||||||
\(122\) | 1.44096e20 | − | 5.08098e19i | 0.197266 | − | 0.0695583i | ||||
\(123\) | 2.72794e20 | 0.344178 | ||||||||
\(124\) | −7.31584e20 | − | 9.08396e20i | −0.851230 | − | 1.05696i | ||||
\(125\) | 8.12805e20i | 0.872742i | ||||||||
\(126\) | −4.41986e20 | + | 1.55850e20i | −0.438231 | + | 0.154526i | ||||
\(127\) | − | 1.52243e21i | − | 1.39476i | −0.716702 | − | 0.697379i | \(-0.754349\pi\) | ||
0.716702 | − | 0.697379i | \(-0.245651\pi\) | |||||||
\(128\) | 8.20660e20 | − | 8.48713e20i | 0.695126 | − | 0.718888i | ||||
\(129\) | −1.15363e21 | −0.904005 | ||||||||
\(130\) | 3.23344e20 | + | 9.16996e20i | 0.234548 | + | 0.665172i | ||||
\(131\) | −8.13929e20 | −0.546857 | −0.273428 | − | 0.961892i | \(-0.588158\pi\) | ||||
−0.273428 | + | 0.961892i | \(0.588158\pi\) | |||||||
\(132\) | −1.04267e21 | + | 8.39725e20i | −0.649246 | + | 0.522875i | ||||
\(133\) | − | 4.40278e20i | − | 0.254220i | ||||||
\(134\) | 9.95424e20 | + | 2.82300e21i | 0.533286 | + | 1.51239i | ||||
\(135\) | 5.70815e19i | 0.0283895i | ||||||||
\(136\) | 3.25302e21 | + | 2.01148e21i | 1.50279 | + | 0.929238i | ||||
\(137\) | −1.95796e21 | −0.840615 | −0.420308 | − | 0.907382i | \(-0.638078\pi\) | ||||
−0.420308 | + | 0.907382i | \(0.638078\pi\) | |||||||
\(138\) | −9.58432e20 | + | 3.37954e20i | −0.382623 | + | 0.134917i | ||||
\(139\) | −3.33138e21 | −1.23731 | −0.618653 | − | 0.785665i | \(-0.712321\pi\) | ||||
−0.618653 | + | 0.785665i | \(0.712321\pi\) | |||||||
\(140\) | −5.01516e20 | + | 4.03900e20i | −0.173382 | + | 0.139635i | ||||
\(141\) | − | 3.61546e21i | − | 1.16405i | ||||||
\(142\) | 3.39194e21 | − | 1.19604e21i | 1.01757 | − | 0.358807i | ||||
\(143\) | 2.95463e21i | 0.826310i | ||||||||
\(144\) | 8.49769e20 | − | 3.89510e21i | 0.221654 | − | 1.01600i | ||||
\(145\) | 3.67834e21 | 0.895306 | ||||||||
\(146\) | −1.85723e20 | − | 5.26707e20i | −0.0422024 | − | 0.119685i | ||||
\(147\) | 5.38573e21 | 1.14307 | ||||||||
\(148\) | 4.71866e20 | + | 5.85909e20i | 0.0935840 | + | 0.116202i | ||||
\(149\) | − | 7.16621e21i | − | 1.32870i | −0.747422 | − | 0.664350i | \(-0.768709\pi\) | ||
0.747422 | − | 0.664350i | \(-0.231291\pi\) | |||||||
\(150\) | −2.05905e21 | − | 5.83943e21i | −0.357071 | − | 1.01265i | ||||
\(151\) | 4.35389e21i | 0.706493i | 0.935530 | + | 0.353246i | \(0.114922\pi\) | ||||
−0.935530 | + | 0.353246i | \(0.885078\pi\) | |||||||
\(152\) | 3.18550e21 | + | 1.96973e21i | 0.483884 | + | 0.299206i | ||||
\(153\) | 1.29155e22 | 1.83737 | ||||||||
\(154\) | −1.84537e21 | + | 6.50698e20i | −0.245966 | + | 0.0867306i | ||||
\(155\) | −5.41171e21 | −0.676111 | ||||||||
\(156\) | −1.08258e22 | − | 1.34423e22i | −1.26828 | − | 1.57481i | ||||
\(157\) | − | 3.66999e21i | − | 0.403338i | −0.979454 | − | 0.201669i | \(-0.935364\pi\) | ||
0.979454 | − | 0.201669i | \(-0.0646365\pi\) | |||||||
\(158\) | −1.58472e22 | + | 5.58791e21i | −1.63449 | + | 0.576339i | ||||
\(159\) | 2.82342e22i | 2.73403i | ||||||||
\(160\) | −6.78597e20 | − | 5.43555e21i | −0.0617180 | − | 0.494360i | ||||
\(161\) | −1.48537e21 | −0.126933 | ||||||||
\(162\) | 3.96822e21 | + | 1.12538e22i | 0.318747 | + | 0.903959i | ||||
\(163\) | 3.23237e20 | 0.0244144 | 0.0122072 | − | 0.999925i | \(-0.496114\pi\) | ||||
0.0122072 | + | 0.999925i | \(0.496114\pi\) | |||||||
\(164\) | −2.64156e21 | + | 2.12740e21i | −0.187682 | + | 0.151151i | ||||
\(165\) | 6.21167e21i | 0.415306i | ||||||||
\(166\) | 4.43471e21 | + | 1.25768e22i | 0.279116 | + | 0.791567i | ||||
\(167\) | − | 1.38936e22i | − | 0.823474i | −0.911303 | − | 0.411737i | \(-0.864922\pi\) | ||
0.911303 | − | 0.411737i | \(-0.135078\pi\) | |||||||
\(168\) | 6.01143e21 | − | 9.72185e21i | 0.335649 | − | 0.542821i | ||||
\(169\) | −1.90865e22 | −1.00429 | ||||||||
\(170\) | 1.67359e22 | − | 5.90128e21i | 0.830157 | − | 0.292723i | ||||
\(171\) | 1.26474e22 | 0.591617 | ||||||||
\(172\) | 1.11710e22 | − | 8.99668e21i | 0.492957 | − | 0.397006i | ||||
\(173\) | 4.49412e21i | 0.187147i | 0.995612 | + | 0.0935737i | \(0.0298291\pi\) | ||||
−0.995612 | + | 0.0935737i | \(0.970171\pi\) | |||||||
\(174\) | −6.15770e22 | + | 2.17128e22i | −2.42062 | + | 0.853538i | ||||
\(175\) | − | 9.04988e21i | − | 0.335941i | ||||||
\(176\) | 3.54793e21 | − | 1.62627e22i | 0.124408 | − | 0.570251i | ||||
\(177\) | 2.31283e22 | 0.766320 | ||||||||
\(178\) | 8.30730e21 | + | 2.35593e22i | 0.260172 | + | 0.737842i | ||||
\(179\) | −3.47973e22 | −1.03042 | −0.515211 | − | 0.857063i | \(-0.672286\pi\) | ||||
−0.515211 | + | 0.857063i | \(0.672286\pi\) | |||||||
\(180\) | −1.16024e22 | − | 1.44065e22i | −0.324955 | − | 0.403492i | ||||
\(181\) | − | 2.34167e22i | − | 0.620497i | −0.950655 | − | 0.310248i | \(-0.899588\pi\) | ||
0.950655 | − | 0.310248i | \(-0.100412\pi\) | |||||||
\(182\) | −8.38887e21 | − | 2.37907e22i | −0.210373 | − | 0.596613i | ||||
\(183\) | 1.25839e22i | 0.298748i | ||||||||
\(184\) | 6.64527e21 | − | 1.07469e22i | 0.149395 | − | 0.241605i | ||||
\(185\) | 3.49052e21 | 0.0743314 | ||||||||
\(186\) | 9.05945e22 | − | 3.19447e22i | 1.82798 | − | 0.644569i | ||||
\(187\) | 5.39244e22 | 1.03126 | ||||||||
\(188\) | 2.81954e22 | + | 3.50098e22i | 0.511210 | + | 0.634762i | ||||
\(189\) | − | 1.48093e21i | − | 0.0254634i | ||||||
\(190\) | 1.63885e22 | − | 5.77878e21i | 0.267303 | − | 0.0942541i | ||||
\(191\) | − | 2.58648e22i | − | 0.400291i | −0.979766 | − | 0.200145i | \(-0.935859\pi\) | ||
0.979766 | − | 0.200145i | \(-0.0641415\pi\) | |||||||
\(192\) | 4.34454e22 | + | 8.69878e22i | 0.638163 | + | 1.27775i | ||||
\(193\) | 2.68246e22 | 0.374076 | 0.187038 | − | 0.982353i | \(-0.440111\pi\) | ||||
0.187038 | + | 0.982353i | \(0.440111\pi\) | |||||||
\(194\) | 2.67582e21 | + | 7.58858e21i | 0.0354356 | + | 0.100495i | ||||
\(195\) | −8.00815e22 | −1.00736 | ||||||||
\(196\) | −5.21519e22 | + | 4.20009e22i | −0.623317 | + | 0.501993i | ||||
\(197\) | − | 4.69360e22i | − | 0.533143i | −0.963815 | − | 0.266572i | \(-0.914109\pi\) | ||
0.963815 | − | 0.266572i | \(-0.0858909\pi\) | |||||||
\(198\) | −1.86919e22 | − | 5.30100e22i | −0.201838 | − | 0.572408i | ||||
\(199\) | − | 6.01397e22i | − | 0.617491i | −0.951145 | − | 0.308746i | \(-0.900091\pi\) | ||
0.951145 | − | 0.308746i | \(-0.0999092\pi\) | |||||||
\(200\) | 6.54777e22 | + | 4.04876e22i | 0.639430 | + | 0.395387i | ||||
\(201\) | −2.46534e23 | −2.29042 | ||||||||
\(202\) | 1.48105e23 | − | 5.22235e22i | 1.30935 | − | 0.461692i | ||||
\(203\) | −9.54313e22 | −0.803027 | ||||||||
\(204\) | −2.45332e23 | + | 1.97580e23i | −1.96541 | + | 1.58286i | ||||
\(205\) | 1.57369e22i | 0.120055i | ||||||||
\(206\) | −6.82299e22 | + | 2.40587e22i | −0.495795 | + | 0.174823i | ||||
\(207\) | − | 4.26686e22i | − | 0.295396i | ||||||
\(208\) | 2.09661e23 | + | 4.57403e22i | 1.38320 | + | 0.301763i | ||||
\(209\) | 5.28050e22 | 0.332057 | ||||||||
\(210\) | −1.76363e22 | − | 5.00163e22i | −0.105734 | − | 0.299860i | ||||
\(211\) | 2.54766e23 | 1.45652 | 0.728262 | − | 0.685299i | \(-0.240329\pi\) | ||||
0.728262 | + | 0.685299i | \(0.240329\pi\) | |||||||
\(212\) | −2.20186e23 | − | 2.73401e23i | −1.20069 | − | 1.49088i | ||||
\(213\) | 2.96219e23i | 1.54105i | ||||||||
\(214\) | −5.75737e22 | − | 1.63278e23i | −0.285816 | − | 0.810568i | ||||
\(215\) | − | 6.65507e22i | − | 0.315332i | ||||||
\(216\) | 1.07148e22 | + | 6.62543e21i | 0.0484671 | + | 0.0299693i | ||||
\(217\) | 1.40402e23 | 0.606424 | ||||||||
\(218\) | −1.41937e23 | + | 5.00486e22i | −0.585505 | + | 0.206456i | ||||
\(219\) | 4.59974e22 | 0.181256 | ||||||||
\(220\) | −4.84420e22 | − | 6.01497e22i | −0.182388 | − | 0.226468i | ||||
\(221\) | 6.95200e23i | 2.50142i | ||||||||
\(222\) | −5.84328e22 | + | 2.06041e22i | −0.200968 | + | 0.0708637i | ||||
\(223\) | − | 3.52305e23i | − | 1.15843i | −0.815174 | − | 0.579216i | \(-0.803359\pi\) | ||
0.815174 | − | 0.579216i | \(-0.196641\pi\) | |||||||
\(224\) | 1.76056e22 | + | 1.41021e23i | 0.0553568 | + | 0.443407i | ||||
\(225\) | 2.59967e23 | 0.781794 | ||||||||
\(226\) | −6.54327e22 | − | 1.85566e23i | −0.188239 | − | 0.533843i | ||||
\(227\) | 4.23328e23 | 1.16525 | 0.582624 | − | 0.812742i | \(-0.302026\pi\) | ||||
0.582624 | + | 0.812742i | \(0.302026\pi\) | |||||||
\(228\) | −2.40240e23 | + | 1.93479e23i | −0.632843 | + | 0.509665i | ||||
\(229\) | 9.70854e22i | 0.244793i | 0.992481 | + | 0.122396i | \(0.0390580\pi\) | ||||
−0.992481 | + | 0.122396i | \(0.960942\pi\) | |||||||
\(230\) | −1.94959e22 | − | 5.52900e22i | −0.0470614 | − | 0.133465i | ||||
\(231\) | − | 1.61156e23i | − | 0.372501i | ||||||
\(232\) | 4.26943e23 | − | 6.90464e23i | 0.945127 | − | 1.52848i | ||||
\(233\) | −4.99591e23 | −1.05939 | −0.529694 | − | 0.848189i | \(-0.677693\pi\) | ||||
−0.529694 | + | 0.848189i | \(0.677693\pi\) | |||||||
\(234\) | 6.83411e23 | − | 2.40979e23i | 1.38843 | − | 0.489576i | ||||
\(235\) | 2.08569e23 | 0.406042 | ||||||||
\(236\) | −2.23959e23 | + | 1.80367e23i | −0.417877 | + | 0.336540i | ||||
\(237\) | − | 1.38394e24i | − | 2.47533i | ||||||
\(238\) | −4.34199e23 | + | 1.53104e23i | −0.744594 | + | 0.262552i | ||||
\(239\) | 4.59439e23i | 0.755525i | 0.925902 | + | 0.377763i | \(0.123306\pi\) | ||||
−0.925902 | + | 0.377763i | \(0.876694\pi\) | |||||||
\(240\) | 4.40780e23 | + | 9.61620e22i | 0.695199 | + | 0.151667i | ||||
\(241\) | 6.71339e23 | 1.01571 | 0.507857 | − | 0.861441i | \(-0.330438\pi\) | ||||
0.507857 | + | 0.861441i | \(0.330438\pi\) | |||||||
\(242\) | 1.51046e23 | + | 4.28364e23i | 0.219258 | + | 0.621812i | ||||
\(243\) | −1.02371e24 | −1.42598 | ||||||||
\(244\) | −9.81363e22 | − | 1.21854e23i | −0.131199 | − | 0.162908i | ||||
\(245\) | 3.10692e23i | 0.398721i | ||||||||
\(246\) | −9.28931e22 | − | 2.63443e23i | −0.114454 | − | 0.324590i | ||||
\(247\) | 6.80769e23i | 0.805434i | ||||||||
\(248\) | −6.28136e23 | + | 1.01584e24i | −0.713734 | + | 1.15427i | ||||
\(249\) | −1.09833e24 | −1.19878 | ||||||||
\(250\) | 7.84943e23 | − | 2.76780e23i | 0.823073 | − | 0.290225i | ||||
\(251\) | −5.67208e23 | −0.571486 | −0.285743 | − | 0.958306i | \(-0.592240\pi\) | ||||
−0.285743 | + | 0.958306i | \(0.592240\pi\) | |||||||
\(252\) | 3.01015e23 | + | 3.73765e23i | 0.291462 | + | 0.361904i | ||||
\(253\) | − | 1.78148e23i | − | 0.165797i | ||||||
\(254\) | −1.47024e24 | + | 5.18424e23i | −1.31538 | + | 0.463818i | ||||
\(255\) | 1.46155e24i | 1.25722i | ||||||||
\(256\) | −1.09908e24 | − | 5.03522e23i | −0.909134 | − | 0.416503i | ||||
\(257\) | 1.43742e24 | 1.14354 | 0.571770 | − | 0.820414i | \(-0.306257\pi\) | ||||
0.571770 | + | 0.820414i | \(0.306257\pi\) | |||||||
\(258\) | 3.92841e23 | + | 1.11409e24i | 0.300621 | + | 0.852556i | ||||
\(259\) | −9.05584e22 | −0.0666701 | ||||||||
\(260\) | 7.75457e23 | − | 6.24520e23i | 0.549319 | − | 0.442398i | ||||
\(261\) | − | 2.74136e24i | − | 1.86879i | ||||||
\(262\) | 2.77163e23 | + | 7.86029e23i | 0.181854 | + | 0.515734i | ||||
\(263\) | 4.04959e23i | 0.255773i | 0.991789 | + | 0.127886i | \(0.0408193\pi\) | ||||
−0.991789 | + | 0.127886i | \(0.959181\pi\) | |||||||
\(264\) | 1.16600e24 | + | 7.20986e23i | 0.709020 | + | 0.438417i | ||||
\(265\) | −1.62877e24 | −0.953676 | ||||||||
\(266\) | −4.25186e23 | + | 1.49926e23i | −0.239752 | + | 0.0845394i | ||||
\(267\) | −2.05744e24 | −1.11742 | ||||||||
\(268\) | 2.38727e24 | − | 1.92261e24i | 1.24897 | − | 1.00587i | ||||
\(269\) | − | 7.34903e23i | − | 0.370431i | −0.982698 | − | 0.185215i | \(-0.940702\pi\) | ||
0.982698 | − | 0.185215i | \(-0.0592983\pi\) | |||||||
\(270\) | 5.51248e22 | − | 1.94377e22i | 0.0267738 | − | 0.00944075i | ||||
\(271\) | − | 4.11047e24i | − | 1.92397i | −0.273100 | − | 0.961986i | \(-0.588049\pi\) | ||
0.273100 | − | 0.961986i | \(-0.411951\pi\) | |||||||
\(272\) | 8.34797e23 | − | 3.82647e24i | 0.376610 | − | 1.72627i | ||||
\(273\) | 2.07765e24 | 0.903535 | ||||||||
\(274\) | 6.66733e23 | + | 1.89084e24i | 0.279541 | + | 0.792774i | ||||
\(275\) | 1.08540e24 | 0.438798 | ||||||||
\(276\) | 6.52740e23 | + | 8.10497e23i | 0.254477 | + | 0.315981i | ||||
\(277\) | 6.38513e23i | 0.240089i | 0.992769 | + | 0.120044i | \(0.0383037\pi\) | ||||
−0.992769 | + | 0.120044i | \(0.961696\pi\) | |||||||
\(278\) | 1.13442e24 | + | 3.21719e24i | 0.411458 | + | 1.16689i | ||||
\(279\) | 4.03319e24i | 1.41126i | ||||||||
\(280\) | 5.60834e23 | + | 3.46787e23i | 0.189345 | + | 0.117080i | ||||
\(281\) | −4.28449e24 | −1.39584 | −0.697921 | − | 0.716175i | \(-0.745891\pi\) | ||||
−0.697921 | + | 0.716175i | \(0.745891\pi\) | |||||||
\(282\) | −3.49153e24 | + | 1.23116e24i | −1.09780 | + | 0.387099i | ||||
\(283\) | 4.08346e24 | 1.23927 | 0.619633 | − | 0.784892i | \(-0.287282\pi\) | ||||
0.619633 | + | 0.784892i | \(0.287282\pi\) | |||||||
\(284\) | −2.31008e24 | − | 2.86839e24i | −0.676773 | − | 0.840339i | ||||
\(285\) | 1.43121e24i | 0.404814i | ||||||||
\(286\) | 2.85335e24 | − | 1.00613e24i | 0.779283 | − | 0.274784i | ||||
\(287\) | − | 4.08281e23i | − | 0.107681i | ||||||
\(288\) | −4.05095e24 | + | 5.05738e23i | −1.03189 | + | 0.128825i | ||||
\(289\) | 8.62372e24 | 2.12186 | ||||||||
\(290\) | −1.25256e24 | − | 3.55225e24i | −0.297728 | − | 0.844352i | ||||
\(291\) | −6.62713e23 | −0.152193 | ||||||||
\(292\) | −4.45409e23 | + | 3.58713e23i | −0.0988394 | + | 0.0796011i | ||||
\(293\) | 2.47467e24i | 0.530690i | 0.964154 | + | 0.265345i | \(0.0854858\pi\) | ||||
−0.964154 | + | 0.265345i | \(0.914514\pi\) | |||||||
\(294\) | −1.83397e24 | − | 5.20112e24i | −0.380119 | − | 1.07801i | ||||
\(295\) | 1.33422e24i | 0.267305i | ||||||||
\(296\) | 4.05143e23 | − | 6.55208e23i | 0.0784677 | − | 0.126900i | ||||
\(297\) | 1.77616e23 | 0.0332597 | ||||||||
\(298\) | −6.92056e24 | + | 2.44027e24i | −1.25308 | + | 0.441851i | ||||
\(299\) | 2.29671e24 | 0.402156 | ||||||||
\(300\) | −4.93811e24 | + | 3.97694e24i | −0.836273 | + | 0.673499i | ||||
\(301\) | 1.72660e24i | 0.282831i | ||||||||
\(302\) | 4.20464e24 | − | 1.48261e24i | 0.666285 | − | 0.234940i | ||||
\(303\) | 1.29340e25i | 1.98293i | ||||||||
\(304\) | 8.17468e23 | − | 3.74704e24i | 0.121265 | − | 0.555844i | ||||
\(305\) | −7.25940e23 | −0.104208 | ||||||||
\(306\) | −4.39805e24 | − | 1.24728e25i | −0.611007 | − | 1.73280i | ||||
\(307\) | −8.40302e24 | −1.12993 | −0.564965 | − | 0.825115i | \(-0.691110\pi\) | ||||
−0.564965 | + | 0.825115i | \(0.691110\pi\) | |||||||
\(308\) | 1.25679e24 | + | 1.56053e24i | 0.163589 | + | 0.203126i | ||||
\(309\) | − | 5.95853e24i | − | 0.750852i | ||||||
\(310\) | 1.84282e24 | + | 5.22621e24i | 0.224836 | + | 0.637632i | ||||
\(311\) | − | 1.49760e25i | − | 1.76926i | −0.466292 | − | 0.884631i | \(-0.654410\pi\) | ||
0.466292 | − | 0.884631i | \(-0.345590\pi\) | |||||||
\(312\) | −9.29503e24 | + | 1.50322e25i | −1.06342 | + | 1.71979i | ||||
\(313\) | −1.48295e25 | −1.64318 | −0.821588 | − | 0.570081i | \(-0.806912\pi\) | ||||
−0.821588 | + | 0.570081i | \(0.806912\pi\) | |||||||
\(314\) | −3.54419e24 | + | 1.24972e24i | −0.380383 | + | 0.134127i | ||||
\(315\) | 2.22668e24 | 0.231501 | ||||||||
\(316\) | 1.07927e25 | + | 1.34012e25i | 1.08708 | + | 1.34981i | ||||
\(317\) | 6.07588e24i | 0.592948i | 0.955041 | + | 0.296474i | \(0.0958108\pi\) | ||||
−0.955041 | + | 0.296474i | \(0.904189\pi\) | |||||||
\(318\) | 2.72663e25 | − | 9.61443e24i | 2.57843 | − | 0.909185i | ||||
\(319\) | − | 1.14456e25i | − | 1.04890i | ||||||
\(320\) | −5.01815e24 | + | 2.50627e24i | −0.445701 | + | 0.222602i | ||||
\(321\) | 1.42591e25 | 1.22756 | ||||||||
\(322\) | 5.05804e23 | + | 1.43445e24i | 0.0422108 | + | 0.119709i | ||||
\(323\) | 1.24246e25 | 1.00521 | ||||||||
\(324\) | 9.51676e24 | − | 7.66439e24i | 0.746516 | − | 0.601212i | ||||
\(325\) | 1.39932e25i | 1.06434i | ||||||||
\(326\) | −1.10070e23 | − | 3.12157e23i | −0.00811885 | − | 0.0230249i | ||||
\(327\) | − | 1.23954e25i | − | 0.886712i | ||||||
\(328\) | 2.95399e24 | + | 1.82658e24i | 0.204961 | + | 0.126736i | ||||
\(329\) | −5.41114e24 | −0.364191 | ||||||||
\(330\) | 5.99874e24 | − | 2.11523e24i | 0.391670 | − | 0.138108i | ||||
\(331\) | −8.24033e24 | −0.521993 | −0.260996 | − | 0.965340i | \(-0.584051\pi\) | ||||
−0.260996 | + | 0.965340i | \(0.584051\pi\) | |||||||
\(332\) | 1.06355e25 | − | 8.56539e24i | 0.653699 | − | 0.526461i | ||||
\(333\) | − | 2.60138e24i | − | 0.155153i | ||||||
\(334\) | −1.34173e25 | + | 4.73111e24i | −0.776608 | + | 0.273841i | ||||
\(335\) | − | 1.42220e25i | − | 0.798938i | ||||||
\(336\) | −1.14357e25 | − | 2.49484e24i | −0.623545 | − | 0.136035i | ||||
\(337\) | −3.21488e25 | −1.70163 | −0.850815 | − | 0.525465i | \(-0.823891\pi\) | ||||
−0.850815 | + | 0.525465i | \(0.823891\pi\) | |||||||
\(338\) | 6.49943e24 | + | 1.84323e25i | 0.333970 | + | 0.947134i | ||||
\(339\) | 1.62055e25 | 0.808473 | ||||||||
\(340\) | −1.13980e25 | − | 1.41527e25i | −0.552127 | − | 0.685568i | ||||
\(341\) | 1.68392e25i | 0.792098i | ||||||||
\(342\) | −4.30676e24 | − | 1.22139e25i | −0.196738 | − | 0.557947i | ||||
\(343\) | − | 1.81323e25i | − | 0.804474i | ||||||
\(344\) | −1.24923e25 | − | 7.72452e24i | −0.538342 | − | 0.332880i | ||||
\(345\) | 4.82849e24 | 0.202125 | ||||||||
\(346\) | 4.34007e24 | − | 1.53036e24i | 0.176496 | − | 0.0622347i | ||||
\(347\) | −1.27479e25 | −0.503667 | −0.251834 | − | 0.967771i | \(-0.581034\pi\) | ||||
−0.251834 | + | 0.967771i | \(0.581034\pi\) | |||||||
\(348\) | 4.19370e25 | + | 5.20725e25i | 1.60992 | + | 1.99902i | ||||
\(349\) | 1.13915e25i | 0.424940i | 0.977168 | + | 0.212470i | \(0.0681508\pi\) | ||||
−0.977168 | + | 0.212470i | \(0.931849\pi\) | |||||||
\(350\) | −8.73967e24 | + | 3.08171e24i | −0.316821 | + | 0.111715i | ||||
\(351\) | 2.28985e24i | 0.0806745i | ||||||||
\(352\) | −1.69134e25 | + | 2.11154e24i | −0.579168 | + | 0.0723058i | ||||
\(353\) | 2.47620e25 | 0.824211 | 0.412106 | − | 0.911136i | \(-0.364793\pi\) | ||||
0.412106 | + | 0.911136i | \(0.364793\pi\) | |||||||
\(354\) | −7.87575e24 | − | 2.23355e25i | −0.254835 | − | 0.722707i | ||||
\(355\) | −1.70882e25 | −0.537544 | ||||||||
\(356\) | 1.99229e25 | − | 1.60451e25i | 0.609331 | − | 0.490729i | ||||
\(357\) | − | 3.79187e25i | − | 1.12764i | ||||||
\(358\) | 1.18493e25 | + | 3.36045e25i | 0.342660 | + | 0.971778i | ||||
\(359\) | 4.85328e25i | 1.36487i | 0.730947 | + | 0.682434i | \(0.239078\pi\) | ||||
−0.730947 | + | 0.682434i | \(0.760922\pi\) | |||||||
\(360\) | −9.96180e24 | + | 1.61105e25i | −0.272466 | + | 0.440640i | ||||
\(361\) | −2.54233e25 | −0.676332 | ||||||||
\(362\) | −2.26140e25 | + | 7.97396e24i | −0.585183 | + | 0.206342i | ||||
\(363\) | −3.74091e25 | −0.941698 | ||||||||
\(364\) | −2.01186e25 | + | 1.62026e25i | −0.492701 | + | 0.396800i | ||||
\(365\) | 2.65350e24i | 0.0632251i | ||||||||
\(366\) | 1.21526e25 | − | 4.28513e24i | 0.281745 | − | 0.0993467i | ||||
\(367\) | 5.19588e25i | 1.17219i | 0.810242 | + | 0.586096i | \(0.199336\pi\) | ||||
−0.810242 | + | 0.586096i | \(0.800664\pi\) | |||||||
\(368\) | −1.26414e25 | − | 2.75789e24i | −0.277535 | − | 0.0605480i | ||||
\(369\) | 1.17283e25 | 0.250594 | ||||||||
\(370\) | −1.18861e24 | − | 3.37087e24i | −0.0247184 | − | 0.0701010i | ||||
\(371\) | 4.22570e25 | 0.855382 | ||||||||
\(372\) | −6.16994e25 | − | 7.66111e25i | −1.21577 | − | 1.50960i | ||||
\(373\) | − | 3.44797e25i | − | 0.661417i | −0.943733 | − | 0.330708i | \(-0.892712\pi\) | ||
0.943733 | − | 0.330708i | \(-0.107288\pi\) | |||||||
\(374\) | −1.83626e25 | − | 5.20760e25i | −0.342940 | − | 0.972571i | ||||
\(375\) | 6.85493e25i | 1.24649i | ||||||||
\(376\) | 2.42085e25 | − | 3.91506e25i | 0.428637 | − | 0.693203i | ||||
\(377\) | 1.47558e26 | 2.54419 | ||||||||
\(378\) | −1.43017e24 | + | 5.04294e23i | −0.0240142 | + | 0.00846770i | ||||
\(379\) | 7.98002e25 | 1.30500 | 0.652502 | − | 0.757787i | \(-0.273719\pi\) | ||||
0.652502 | + | 0.757787i | \(0.273719\pi\) | |||||||
\(380\) | −1.11614e25 | − | 1.38589e25i | −0.177780 | − | 0.220746i | ||||
\(381\) | − | 1.28396e26i | − | 1.99206i | ||||||
\(382\) | −2.49782e25 | + | 8.80761e24i | −0.377509 | + | 0.133114i | ||||
\(383\) | 3.01797e25i | 0.444352i | 0.975007 | + | 0.222176i | \(0.0713160\pi\) | ||||
−0.975007 | + | 0.222176i | \(0.928684\pi\) | |||||||
\(384\) | 6.92118e25 | − | 7.15777e25i | 0.992814 | − | 1.02675i | ||||
\(385\) | 9.29678e24 | 0.129935 | ||||||||
\(386\) | −9.13445e24 | − | 2.59051e25i | −0.124397 | − | 0.352787i | ||||
\(387\) | −4.95983e25 | −0.658199 | ||||||||
\(388\) | 6.41728e24 | − | 5.16820e24i | 0.0829915 | − | 0.0668378i | ||||
\(389\) | 9.38588e25i | 1.18298i | 0.806311 | + | 0.591492i | \(0.201461\pi\) | ||||
−0.806311 | + | 0.591492i | \(0.798539\pi\) | |||||||
\(390\) | 2.72697e25 | + | 7.73365e25i | 0.334992 | + | 0.950032i | ||||
\(391\) | − | 4.19168e25i | − | 0.501904i | ||||||
\(392\) | 5.83202e25 | + | 3.60619e25i | 0.680704 | + | 0.420908i | ||||
\(393\) | −6.86441e25 | −0.781048 | ||||||||
\(394\) | −4.53271e25 | + | 1.59829e25i | −0.502801 | + | 0.177293i | ||||
\(395\) | 7.98366e25 | 0.863438 | ||||||||
\(396\) | −4.48278e25 | + | 3.61024e25i | −0.472711 | + | 0.380701i | ||||
\(397\) | 4.72991e25i | 0.486349i | 0.969983 | + | 0.243174i | \(0.0781887\pi\) | ||||
−0.969983 | + | 0.243174i | \(0.921811\pi\) | |||||||
\(398\) | −5.80783e25 | + | 2.04791e25i | −0.582348 | + | 0.205343i | ||||
\(399\) | − | 3.71316e25i | − | 0.363090i | ||||||
\(400\) | 1.68030e25 | − | 7.70203e25i | 0.160246 | − | 0.734522i | ||||
\(401\) | −1.29001e26 | −1.19991 | −0.599957 | − | 0.800032i | \(-0.704816\pi\) | ||||
−0.599957 | + | 0.800032i | \(0.704816\pi\) | |||||||
\(402\) | 8.39508e25 | + | 2.38083e26i | 0.761666 | + | 2.16007i | ||||
\(403\) | −2.17094e26 | −1.92131 | ||||||||
\(404\) | −1.00867e26 | − | 1.25245e26i | −0.870833 | − | 1.08130i | ||||
\(405\) | − | 5.66955e25i | − | 0.477527i | ||||||
\(406\) | 3.24967e25 | + | 9.21601e25i | 0.267042 | + | 0.757325i | ||||
\(407\) | − | 1.08612e25i | − | 0.0870830i | ||||||
\(408\) | 2.74349e26 | + | 1.69642e26i | 2.14636 | + | 1.32718i | ||||
\(409\) | 9.77077e25 | 0.745926 | 0.372963 | − | 0.927846i | \(-0.378342\pi\) | ||||
0.372963 | + | 0.927846i | \(0.378342\pi\) | |||||||
\(410\) | 1.51975e25 | − | 5.35881e24i | 0.113223 | − | 0.0399236i | ||||
\(411\) | −1.65128e26 | −1.20061 | ||||||||
\(412\) | 4.64679e25 | + | 5.76985e25i | 0.329747 | + | 0.409442i | ||||
\(413\) | − | 3.46152e25i | − | 0.239754i | ||||||
\(414\) | −4.12060e25 | + | 1.45297e25i | −0.278585 | + | 0.0982322i | ||||
\(415\) | − | 6.33604e25i | − | 0.418155i | ||||||
\(416\) | −2.72222e25 | − | 2.18050e26i | −0.175384 | − | 1.40482i | ||||
\(417\) | −2.80958e26 | −1.76718 | ||||||||
\(418\) | −1.79814e25 | − | 5.09950e25i | −0.110423 | − | 0.313159i | ||||
\(419\) | 1.45698e26 | 0.873603 | 0.436801 | − | 0.899558i | \(-0.356111\pi\) | ||||
0.436801 | + | 0.899558i | \(0.356111\pi\) | |||||||
\(420\) | −4.22962e25 | + | 3.40636e25i | −0.247633 | + | 0.199433i | ||||
\(421\) | − | 1.12181e26i | − | 0.641354i | −0.947189 | − | 0.320677i | \(-0.896090\pi\) | ||
0.947189 | − | 0.320677i | \(-0.103910\pi\) | |||||||
\(422\) | −8.67543e25 | − | 2.46033e26i | −0.484358 | − | 1.37363i | ||||
\(423\) | − | 1.55440e26i | − | 0.847539i | ||||||
\(424\) | −1.89051e26 | + | 3.05738e26i | −1.00675 | + | 1.62814i | ||||
\(425\) | 2.55386e26 | 1.32834 | ||||||||
\(426\) | 2.86065e26 | − | 1.00870e26i | 1.45334 | − | 0.512466i | ||||
\(427\) | 1.88339e25 | 0.0934676 | ||||||||
\(428\) | −1.38076e26 | + | 1.11200e26i | −0.669391 | + | 0.539099i | ||||
\(429\) | 2.49184e26i | 1.18018i | ||||||||
\(430\) | −6.42695e25 | + | 2.26622e25i | −0.297386 | + | 0.104862i | ||||
\(431\) | 1.82538e26i | 0.825240i | 0.910903 | + | 0.412620i | \(0.135386\pi\) | ||||
−0.910903 | + | 0.412620i | \(0.864614\pi\) | |||||||
\(432\) | 2.74966e24 | − | 1.26037e25i | 0.0121462 | − | 0.0556749i | ||||
\(433\) | −2.27223e26 | −0.980785 | −0.490392 | − | 0.871502i | \(-0.663147\pi\) | ||||
−0.490392 | + | 0.871502i | \(0.663147\pi\) | |||||||
\(434\) | −4.78105e25 | − | 1.35590e26i | −0.201663 | − | 0.571912i | ||||
\(435\) | 3.10219e26 | 1.27872 | ||||||||
\(436\) | 9.66661e25 | + | 1.20029e26i | 0.389412 | + | 0.483527i | ||||
\(437\) | − | 4.10467e25i | − | 0.161608i | ||||||
\(438\) | −1.56633e25 | − | 4.44207e25i | −0.0602755 | − | 0.170940i | ||||
\(439\) | 2.33052e26i | 0.876614i | 0.898825 | + | 0.438307i | \(0.144422\pi\) | ||||
−0.898825 | + | 0.438307i | \(0.855578\pi\) | |||||||
\(440\) | −4.15922e25 | + | 6.72640e25i | −0.152927 | + | 0.247318i | ||||
\(441\) | 2.31549e26 | 0.832258 | ||||||||
\(442\) | 6.71370e26 | − | 2.36733e26i | 2.35906 | − | 0.831832i | ||||
\(443\) | −1.40927e26 | −0.484124 | −0.242062 | − | 0.970261i | \(-0.577824\pi\) | ||||
−0.242062 | + | 0.970261i | \(0.577824\pi\) | |||||||
\(444\) | 3.97956e25 | + | 4.94136e25i | 0.133661 | + | 0.165965i | ||||
\(445\) | − | 1.18690e26i | − | 0.389774i | ||||||
\(446\) | −3.40229e26 | + | 1.19969e26i | −1.09250 | + | 0.385230i | ||||
\(447\) | − | 6.04374e26i | − | 1.89771i | ||||||
\(448\) | 1.30191e26 | − | 6.50231e25i | 0.399763 | − | 0.199658i | ||||
\(449\) | 1.40666e26 | 0.422400 | 0.211200 | − | 0.977443i | \(-0.432263\pi\) | ||||
0.211200 | + | 0.977443i | \(0.432263\pi\) | |||||||
\(450\) | −8.85251e25 | − | 2.51056e26i | −0.259981 | − | 0.737301i | ||||
\(451\) | 4.89674e25 | 0.140651 | ||||||||
\(452\) | −1.56924e26 | + | 1.26380e26i | −0.440863 | + | 0.355052i | ||||
\(453\) | 3.67193e26i | 1.00905i | ||||||||
\(454\) | −1.44154e26 | − | 4.08817e26i | −0.387496 | − | 1.09893i | ||||
\(455\) | 1.19855e26i | 0.315168i | ||||||||
\(456\) | 2.68654e26 | + | 1.66120e26i | 0.691107 | + | 0.427341i | ||||
\(457\) | 1.27721e26 | 0.321441 | 0.160720 | − | 0.987000i | \(-0.448618\pi\) | ||||
0.160720 | + | 0.987000i | \(0.448618\pi\) | |||||||
\(458\) | 9.37575e25 | − | 3.30600e25i | 0.230861 | − | 0.0814044i | ||||
\(459\) | 4.17916e25 | 0.100684 | ||||||||
\(460\) | −4.67559e25 | + | 3.76552e25i | −0.110219 | + | 0.0887660i | ||||
\(461\) | 3.61599e26i | 0.834100i | 0.908883 | + | 0.417050i | \(0.136936\pi\) | ||||
−0.908883 | + | 0.417050i | \(0.863064\pi\) | |||||||
\(462\) | −1.55632e26 | + | 5.48777e25i | −0.351301 | + | 0.123873i | ||||
\(463\) | − | 4.74287e26i | − | 1.04769i | −0.851815 | − | 0.523843i | \(-0.824498\pi\) | ||
0.851815 | − | 0.523843i | \(-0.175502\pi\) | |||||||
\(464\) | −8.12181e26 | − | 1.77188e26i | −1.75579 | − | 0.383050i | ||||
\(465\) | −4.56406e26 | −0.965655 | ||||||||
\(466\) | 1.70123e26 | + | 4.82466e26i | 0.352293 | + | 0.999096i | ||||
\(467\) | 3.26188e26 | 0.661150 | 0.330575 | − | 0.943780i | \(-0.392757\pi\) | ||||
0.330575 | + | 0.943780i | \(0.392757\pi\) | |||||||
\(468\) | −4.65437e26 | − | 5.77925e26i | −0.923426 | − | 1.14660i | ||||
\(469\) | 3.68978e26i | 0.716592i | ||||||||
\(470\) | −7.10228e25 | − | 2.01419e26i | −0.135027 | − | 0.382933i | ||||
\(471\) | − | 3.09515e26i | − | 0.576067i | ||||||
\(472\) | 2.50448e26 | + | 1.54863e26i | 0.456349 | + | 0.282180i | ||||
\(473\) | −2.07081e26 | −0.369428 | ||||||||
\(474\) | −1.33650e27 | + | 4.71266e26i | −2.33446 | + | 0.823157i | ||||
\(475\) | 2.50085e26 | 0.427712 | ||||||||
\(476\) | 2.95711e26 | + | 3.67180e26i | 0.495220 | + | 0.614907i | ||||
\(477\) | 1.21387e27i | 1.99063i | ||||||||
\(478\) | 4.43690e26 | − | 1.56450e26i | 0.712527 | − | 0.251245i | ||||
\(479\) | 9.19723e26i | 1.44644i | 0.690615 | + | 0.723222i | \(0.257340\pi\) | ||||
−0.690615 | + | 0.723222i | \(0.742660\pi\) | |||||||
\(480\) | −5.72306e25 | − | 4.58416e26i | −0.0881488 | − | 0.706070i | ||||
\(481\) | 1.40024e26 | 0.211228 | ||||||||
\(482\) | −2.28608e26 | − | 6.48327e26i | −0.337769 | − | 0.957907i | ||||
\(483\) | −1.25271e26 | −0.181292 | ||||||||
\(484\) | 3.62246e26 | − | 2.91737e26i | 0.513511 | − | 0.413560i | ||||
\(485\) | − | 3.82305e25i | − | 0.0530876i | ||||||
\(486\) | 3.48597e26 | + | 9.88615e26i | 0.474200 | + | 1.34482i | ||||
\(487\) | − | 3.19780e26i | − | 0.426149i | −0.977036 | − | 0.213074i | \(-0.931652\pi\) | ||
0.977036 | − | 0.213074i | \(-0.0683477\pi\) | |||||||
\(488\) | −8.42595e25 | + | 1.36267e26i | −0.110007 | + | 0.177906i | ||||
\(489\) | 2.72608e25 | 0.0348698 | ||||||||
\(490\) | 3.00042e26 | − | 1.05798e26i | 0.376029 | − | 0.132592i | ||||
\(491\) | 7.81706e25 | 0.0959905 | 0.0479953 | − | 0.998848i | \(-0.484717\pi\) | ||||
0.0479953 | + | 0.998848i | \(0.484717\pi\) | |||||||
\(492\) | −2.22780e26 | + | 1.79418e26i | −0.268056 | + | 0.215881i | ||||
\(493\) | − | 2.69306e27i | − | 3.17524i | ||||||
\(494\) | 6.57433e26 | − | 2.31819e26i | 0.759595 | − | 0.267842i | ||||
\(495\) | 2.67059e26i | 0.302381i | ||||||||
\(496\) | 1.19491e27 | + | 2.60686e26i | 1.32593 | + | 0.289269i | ||||
\(497\) | 4.43340e26 | 0.482140 | ||||||||
\(498\) | 3.74009e26 | + | 1.06068e27i | 0.398647 | + | 1.13056i | ||||
\(499\) | −9.10365e26 | −0.951064 | −0.475532 | − | 0.879698i | \(-0.657744\pi\) | ||||
−0.475532 | + | 0.879698i | \(0.657744\pi\) | |||||||
\(500\) | −5.34585e26 | − | 6.63786e26i | −0.547415 | − | 0.679717i | ||||
\(501\) | − | 1.17174e27i | − | 1.17613i | ||||||
\(502\) | 1.93149e26 | + | 5.47766e26i | 0.190044 | + | 0.538961i | ||||
\(503\) | 1.52189e26i | 0.146792i | 0.997303 | + | 0.0733959i | \(0.0233837\pi\) | ||||
−0.997303 | + | 0.0733959i | \(0.976616\pi\) | |||||||
\(504\) | 2.58450e26 | − | 4.17973e26i | 0.244383 | − | 0.395224i | ||||
\(505\) | −7.46138e26 | −0.691680 | ||||||||
\(506\) | −1.72042e26 | + | 6.06640e25i | −0.156361 | + | 0.0551348i | ||||
\(507\) | −1.60969e27 | −1.43438 | ||||||||
\(508\) | 1.00131e27 | + | 1.24331e27i | 0.874843 | + | 1.08628i | ||||
\(509\) | − | 6.41114e26i | − | 0.549234i | −0.961554 | − | 0.274617i | \(-0.911449\pi\) | ||
0.961554 | − | 0.274617i | \(-0.0885510\pi\) | |||||||
\(510\) | 1.41145e27 | − | 4.97695e26i | 1.18567 | − | 0.418082i | ||||
\(511\) | − | 6.88427e25i | − | 0.0567086i | ||||||
\(512\) | −1.11999e26 | + | 1.23286e27i | −0.0904724 | + | 0.995899i | ||||
\(513\) | 4.09241e25 | 0.0324194 | ||||||||
\(514\) | −4.89476e26 | − | 1.38814e27i | −0.380277 | − | 1.07846i | ||||
\(515\) | 3.43735e26 | 0.261910 | ||||||||
\(516\) | 9.42128e26 | − | 7.58750e26i | 0.704066 | − | 0.567024i | ||||
\(517\) | − | 6.48988e26i | − | 0.475698i | ||||||
\(518\) | 3.08374e25 | + | 8.74543e25i | 0.0221707 | + | 0.0628758i | ||||
\(519\) | 3.79020e26i | 0.267293i | ||||||||
\(520\) | −8.67175e26 | − | 5.36211e26i | −0.599892 | − | 0.370939i | ||||
\(521\) | 1.33712e27 | 0.907388 | 0.453694 | − | 0.891157i | \(-0.350106\pi\) | ||||
0.453694 | + | 0.891157i | \(0.350106\pi\) | |||||||
\(522\) | −2.64739e27 | + | 9.33500e26i | −1.76243 | + | 0.621454i | ||||
\(523\) | −4.93173e26 | −0.322094 | −0.161047 | − | 0.986947i | \(-0.551487\pi\) | ||||
−0.161047 | + | 0.986947i | \(0.551487\pi\) | |||||||
\(524\) | 6.64705e26 | − | 5.35325e26i | 0.425908 | − | 0.343008i | ||||
\(525\) | − | 7.63237e26i | − | 0.479807i | ||||||
\(526\) | 3.91078e26 | − | 1.37899e26i | 0.241216 | − | 0.0850556i | ||||
\(527\) | 3.96213e27i | 2.39785i | ||||||||
\(528\) | 2.99221e26 | − | 1.37154e27i | 0.177686 | − | 0.814461i | ||||
\(529\) | 1.57768e27 | 0.919308 | ||||||||
\(530\) | 5.54637e26 | + | 1.57294e27i | 0.317139 | + | 0.899400i | ||||
\(531\) | 9.94356e26 | 0.557952 | ||||||||
\(532\) | 2.89573e26 | + | 3.59558e26i | 0.159456 | + | 0.197994i | ||||
\(533\) | 6.31294e26i | 0.341161i | ||||||||
\(534\) | 7.00610e26 | + | 1.98692e27i | 0.371590 | + | 1.05382i | ||||
\(535\) | 8.22578e26i | 0.428192i | ||||||||
\(536\) | −2.66963e27 | − | 1.65074e27i | −1.36396 | − | 0.843396i | ||||
\(537\) | −2.93469e27 | −1.47170 | ||||||||
\(538\) | −7.09712e26 | + | 2.50253e26i | −0.349349 | + | 0.123184i | ||||
\(539\) | 9.66757e26 | 0.467121 | ||||||||
\(540\) | −3.75428e25 | − | 4.66163e25i | −0.0178069 | − | 0.0221106i | ||||
\(541\) | 2.72131e27i | 1.26708i | 0.773709 | + | 0.633541i | \(0.218399\pi\) | ||||
−0.773709 | + | 0.633541i | \(0.781601\pi\) | |||||||
\(542\) | −3.96957e27 | + | 1.39972e27i | −1.81447 | + | 0.639805i | ||||
\(543\) | − | 1.97489e27i | − | 0.886225i | ||||||
\(544\) | −3.97958e27 | + | 4.96828e26i | −1.75327 | + | 0.218885i | ||||
\(545\) | 7.15064e26 | 0.309300 | ||||||||
\(546\) | −7.07490e26 | − | 2.00643e27i | −0.300465 | − | 0.852113i | ||||
\(547\) | −3.35783e26 | −0.140019 | −0.0700093 | − | 0.997546i | \(-0.522303\pi\) | ||||
−0.0700093 | + | 0.997546i | \(0.522303\pi\) | |||||||
\(548\) | 1.59899e27 | − | 1.28776e27i | 0.654696 | − | 0.527264i | ||||
\(549\) | 5.41022e26i | 0.217516i | ||||||||
\(550\) | −3.69607e26 | − | 1.04820e27i | −0.145920 | − | 0.413825i | ||||
\(551\) | − | 2.63715e27i | − | 1.02240i | ||||||
\(552\) | 5.60441e26 | − | 9.06360e26i | 0.213373 | − | 0.345072i | ||||
\(553\) | −2.07129e27 | −0.774444 | ||||||||
\(554\) | 6.16626e26 | − | 2.17430e26i | 0.226425 | − | 0.0798401i | ||||
\(555\) | 2.94379e26 | 0.106164 | ||||||||
\(556\) | 2.72061e27 | − | 2.19107e27i | 0.963649 | − | 0.776082i | ||||
\(557\) | 1.68401e27i | 0.585859i | 0.956134 | + | 0.292929i | \(0.0946301\pi\) | ||||
−0.956134 | + | 0.292929i | \(0.905370\pi\) | |||||||
\(558\) | 3.89494e27 | − | 1.37340e27i | 1.33094 | − | 0.469306i | ||||
\(559\) | − | 2.66972e27i | − | 0.896080i | ||||||
\(560\) | 1.43922e26 | − | 6.59699e26i | 0.0474512 | − | 0.217503i | ||||
\(561\) | 4.54781e27 | 1.47290 | ||||||||
\(562\) | 1.45898e27 | + | 4.13763e27i | 0.464179 | + | 1.31640i | ||||
\(563\) | 1.64929e27 | 0.515481 | 0.257741 | − | 0.966214i | \(-0.417022\pi\) | ||||
0.257741 | + | 0.966214i | \(0.417022\pi\) | |||||||
\(564\) | 2.37791e27 | + | 2.95261e27i | 0.730136 | + | 0.906599i | ||||
\(565\) | 9.34862e26i | 0.282009i | ||||||||
\(566\) | −1.39052e27 | − | 3.94349e27i | −0.412110 | − | 1.16874i | ||||
\(567\) | 1.47092e27i | 0.428309i | ||||||||
\(568\) | −1.98343e27 | + | 3.20765e27i | −0.567457 | + | 0.917706i | ||||
\(569\) | 4.44042e26 | 0.124825 | 0.0624125 | − | 0.998050i | \(-0.480121\pi\) | ||||
0.0624125 | + | 0.998050i | \(0.480121\pi\) | |||||||
\(570\) | 1.38215e27 | − | 4.87363e26i | 0.381775 | − | 0.134618i | ||||
\(571\) | 1.78241e27 | 0.483777 | 0.241889 | − | 0.970304i | \(-0.422233\pi\) | ||||
0.241889 | + | 0.970304i | \(0.422233\pi\) | |||||||
\(572\) | −1.94328e27 | − | 2.41293e27i | −0.518291 | − | 0.643554i | ||||
\(573\) | − | 2.18135e27i | − | 0.571715i | ||||||
\(574\) | −3.94286e26 | + | 1.39030e26i | −0.101553 | + | 0.0358087i | ||||
\(575\) | − | 8.43712e26i | − | 0.213558i | ||||||
\(576\) | 1.86785e27 | + | 3.73988e27i | 0.464641 | + | 0.930321i | ||||
\(577\) | −5.12768e26 | −0.125361 | −0.0626805 | − | 0.998034i | \(-0.519965\pi\) | ||||
−0.0626805 | + | 0.998034i | \(0.519965\pi\) | |||||||
\(578\) | −2.93659e27 | − | 8.32811e27i | −0.705610 | − | 2.00110i | ||||
\(579\) | 2.26230e27 | 0.534275 | ||||||||
\(580\) | −3.00396e27 | + | 2.41926e27i | −0.697290 | + | 0.561568i | ||||
\(581\) | 1.64383e27i | 0.375056i | ||||||||
\(582\) | 2.25670e26 | + | 6.39996e26i | 0.0506109 | + | 0.143532i | ||||
\(583\) | 5.06813e27i | 1.11728i | ||||||||
\(584\) | 4.98090e26 | + | 3.07990e26i | 0.107939 | + | 0.0667434i | ||||
\(585\) | −3.44296e27 | −0.733454 | ||||||||
\(586\) | 2.38984e27 | − | 8.42686e26i | 0.500487 | − | 0.176478i | ||||
\(587\) | −4.59426e27 | −0.945878 | −0.472939 | − | 0.881095i | \(-0.656807\pi\) | ||||
−0.472939 | + | 0.881095i | \(0.656807\pi\) | |||||||
\(588\) | −4.39832e27 | + | 3.54222e27i | −0.890253 | + | 0.716972i | ||||
\(589\) | 3.87988e27i | 0.772086i | ||||||||
\(590\) | 1.28849e27 | − | 4.54336e26i | 0.252092 | − | 0.0888908i | ||||
\(591\) | − | 3.95843e27i | − | 0.761462i | ||||||
\(592\) | −7.70710e26 | − | 1.68141e26i | −0.145772 | − | 0.0318021i | ||||
\(593\) | 5.91413e27 | 1.09988 | 0.549939 | − | 0.835205i | \(-0.314651\pi\) | ||||
0.549939 | + | 0.835205i | \(0.314651\pi\) | |||||||
\(594\) | −6.04828e25 | − | 1.71528e26i | −0.0110603 | − | 0.0313668i | ||||
\(595\) | 2.18745e27 | 0.393341 | ||||||||
\(596\) | 4.71325e27 | + | 5.85237e27i | 0.833408 | + | 1.03483i | ||||
\(597\) | − | 5.07199e27i | − | 0.881932i | ||||||
\(598\) | −7.82087e26 | − | 2.21798e27i | −0.133734 | − | 0.379268i | ||||
\(599\) | − | 8.24036e27i | − | 1.38573i | −0.721068 | − | 0.692864i | \(-0.756349\pi\) | ||
0.721068 | − | 0.692864i | \(-0.243651\pi\) | |||||||
\(600\) | 5.52217e27 | + | 3.41459e27i | 0.913266 | + | 0.564711i | ||||
\(601\) | −8.63115e27 | −1.40386 | −0.701930 | − | 0.712246i | \(-0.747678\pi\) | ||||
−0.701930 | + | 0.712246i | \(0.747678\pi\) | |||||||
\(602\) | 1.66742e27 | − | 5.87951e26i | 0.266735 | − | 0.0940537i | ||||
\(603\) | −1.05993e28 | −1.66764 | ||||||||
\(604\) | −2.86357e27 | − | 3.55565e27i | −0.443138 | − | 0.550237i | ||||
\(605\) | − | 2.15806e27i | − | 0.328480i | ||||||
\(606\) | 1.24907e28 | − | 4.40436e27i | 1.87008 | − | 0.659412i | ||||
\(607\) | − | 3.90613e27i | − | 0.575254i | −0.957742 | − | 0.287627i | \(-0.907134\pi\) | ||
0.957742 | − | 0.287627i | \(-0.0928664\pi\) | |||||||
\(608\) | −3.89697e27 | + | 4.86514e26i | −0.564536 | + | 0.0704790i | ||||
\(609\) | −8.04836e27 | −1.14692 | ||||||||
\(610\) | 2.47200e26 | + | 7.01056e26i | 0.0346538 | + | 0.0982775i | ||||
\(611\) | 8.36683e27 | 1.15385 | ||||||||
\(612\) | −1.05476e28 | + | 8.49459e27i | −1.43100 | + | 1.15247i | ||||
\(613\) | 8.78457e27i | 1.17251i | 0.810127 | + | 0.586254i | \(0.199398\pi\) | ||||
−0.810127 | + | 0.586254i | \(0.800602\pi\) | |||||||
\(614\) | 2.86144e27 | + | 8.11498e27i | 0.375751 | + | 1.06562i | ||||
\(615\) | 1.32720e27i | 0.171469i | ||||||||
\(616\) | 1.07907e27 | − | 1.74511e27i | 0.137165 | − | 0.221827i | ||||
\(617\) | −9.93663e27 | −1.24276 | −0.621381 | − | 0.783509i | \(-0.713428\pi\) | ||||
−0.621381 | + | 0.783509i | \(0.713428\pi\) | |||||||
\(618\) | −5.75429e27 | + | 2.02903e27i | −0.708120 | + | 0.249691i | ||||
\(619\) | −1.10877e28 | −1.34256 | −0.671281 | − | 0.741203i | \(-0.734256\pi\) | ||||
−0.671281 | + | 0.741203i | \(0.734256\pi\) | |||||||
\(620\) | 4.41954e27 | − | 3.55931e27i | 0.526575 | − | 0.424081i | ||||
\(621\) | − | 1.38066e26i | − | 0.0161871i | ||||||
\(622\) | −1.44627e28 | + | 5.09970e27i | −1.66857 | + | 0.588357i | ||||
\(623\) | 3.07930e27i | 0.349600i | ||||||||
\(624\) | 1.76821e28 | + | 3.85759e27i | 1.97555 | + | 0.430993i | ||||
\(625\) | 2.88311e27 | 0.317001 | ||||||||
\(626\) | 5.04983e27 | + | 1.43212e28i | 0.546428 | + | 1.54966i | ||||
\(627\) | 4.45340e27 | 0.474260 | ||||||||
\(628\) | 2.41377e27 | + | 2.99714e27i | 0.252988 | + | 0.314131i | ||||
\(629\) | − | 2.55554e27i | − | 0.263619i | ||||||
\(630\) | −7.58241e26 | − | 2.15036e27i | −0.0769843 | − | 0.218326i | ||||
\(631\) | − | 1.33853e28i | − | 1.33763i | −0.743429 | − | 0.668815i | \(-0.766802\pi\) | ||
0.743429 | − | 0.668815i | \(-0.233198\pi\) | |||||||
\(632\) | 9.26661e27 | − | 1.49862e28i | 0.911486 | − | 1.47408i | ||||
\(633\) | 2.14862e28 | 2.08028 | ||||||||
\(634\) | 5.86761e27 | − | 2.06899e27i | 0.559202 | − | 0.197181i | ||||
\(635\) | 7.40692e27 | 0.694865 | ||||||||
\(636\) | −1.85697e28 | − | 2.30578e28i | −1.71488 | − | 2.12934i | ||||
\(637\) | 1.24635e28i | 1.13305i | ||||||||
\(638\) | −1.10533e28 | + | 3.89752e27i | −0.989201 | + | 0.348804i | ||||
\(639\) | 1.27354e28i | 1.12203i | ||||||||
\(640\) | 4.12917e27 | + | 3.99269e27i | 0.358148 | + | 0.346310i | ||||
\(641\) | 6.17579e27 | 0.527366 | 0.263683 | − | 0.964609i | \(-0.415063\pi\) | ||||
0.263683 | + | 0.964609i | \(0.415063\pi\) | |||||||
\(642\) | −4.85558e27 | − | 1.37703e28i | −0.408216 | − | 1.15769i | ||||
\(643\) | 1.45988e28 | 1.20839 | 0.604195 | − | 0.796837i | \(-0.293495\pi\) | ||||
0.604195 | + | 0.796837i | \(0.293495\pi\) | |||||||
\(644\) | 1.21304e27 | − | 9.76932e26i | 0.0988592 | − | 0.0796170i | ||||
\(645\) | − | 5.61267e27i | − | 0.450373i | ||||||
\(646\) | −4.23088e27 | − | 1.19987e28i | −0.334276 | − | 0.948000i | ||||
\(647\) | 1.88186e27i | 0.146401i | 0.997317 | + | 0.0732004i | \(0.0233213\pi\) | ||||
−0.997317 | + | 0.0732004i | \(0.976679\pi\) | |||||||
\(648\) | −1.06424e28 | − | 6.58063e27i | −0.815245 | − | 0.504101i | ||||
\(649\) | 4.15160e27 | 0.313162 | ||||||||
\(650\) | 1.35135e28 | − | 4.76502e27i | 1.00377 | − | 0.353941i | ||||
\(651\) | 1.18411e28 | 0.866126 | ||||||||
\(652\) | −2.63976e26 | + | 2.12595e26i | −0.0190146 | + | 0.0153136i | ||||
\(653\) | − | 7.52706e27i | − | 0.533941i | −0.963705 | − | 0.266971i | \(-0.913977\pi\) | ||
0.963705 | − | 0.266971i | \(-0.0860227\pi\) | |||||||
\(654\) | −1.19705e28 | + | 4.22094e27i | −0.836247 | + | 0.294870i | ||||
\(655\) | − | 3.95994e27i | − | 0.272443i | ||||||
\(656\) | 7.58059e26 | − | 3.47473e27i | 0.0513647 | − | 0.235441i | ||||
\(657\) | 1.97757e27 | 0.131971 | ||||||||
\(658\) | 1.84263e27 | + | 5.22565e27i | 0.121110 | + | 0.343464i | ||||
\(659\) | −2.74243e28 | −1.77534 | −0.887669 | − | 0.460482i | \(-0.847677\pi\) | ||||
−0.887669 | + | 0.460482i | \(0.847677\pi\) | |||||||
\(660\) | −4.08544e27 | − | 5.07283e27i | −0.260495 | − | 0.323453i | ||||
\(661\) | − | 1.11450e28i | − | 0.699950i | −0.936759 | − | 0.349975i | \(-0.886190\pi\) | ||
0.936759 | − | 0.349975i | \(-0.113810\pi\) | |||||||
\(662\) | 2.80604e27 | + | 7.95786e27i | 0.173585 | + | 0.492285i | ||||
\(663\) | 5.86309e28i | 3.57265i | ||||||||
\(664\) | −1.18934e28 | − | 7.35422e27i | −0.713883 | − | 0.441424i | ||||
\(665\) | 2.14204e27 | 0.126652 | ||||||||
\(666\) | −2.51221e27 | + | 8.85834e26i | −0.146323 | + | 0.0515953i | ||||
\(667\) | −8.89697e27 | −0.510486 | ||||||||
\(668\) | 9.13788e27 | + | 1.13464e28i | 0.516512 | + | 0.641345i | ||||
\(669\) | − | 2.97123e28i | − | 1.65453i | ||||||
\(670\) | −1.37345e28 | + | 4.84295e27i | −0.753469 | + | 0.265682i | ||||
\(671\) | 2.25885e27i | 0.122085i | ||||||||
\(672\) | 1.48480e27 | + | 1.18932e28i | 0.0790633 | + | 0.633296i | ||||
\(673\) | −8.66157e27 | −0.454408 | −0.227204 | − | 0.973847i | \(-0.572958\pi\) | ||||
−0.227204 | + | 0.973847i | \(0.572958\pi\) | |||||||
\(674\) | 1.09475e28 | + | 3.10468e28i | 0.565867 | + | 1.60479i | ||||
\(675\) | 8.41193e26 | 0.0428408 | ||||||||
\(676\) | 1.55872e28 | − | 1.25533e28i | 0.782171 | − | 0.629927i | ||||
\(677\) | 6.27182e27i | 0.310104i | 0.987906 | + | 0.155052i | \(0.0495545\pi\) | ||||
−0.987906 | + | 0.155052i | \(0.950446\pi\) | |||||||
\(678\) | −5.51838e27 | − | 1.56500e28i | −0.268853 | − | 0.762461i | ||||
\(679\) | 9.91858e26i | 0.0476159i | ||||||||
\(680\) | −9.78628e27 | + | 1.58266e28i | −0.462944 | + | 0.748686i | ||||
\(681\) | 3.57021e28 | 1.66426 | ||||||||
\(682\) | 1.62620e28 | − | 5.73418e27i | 0.747018 | − | 0.263407i | ||||
\(683\) | −2.46439e28 | −1.11559 | −0.557793 | − | 0.829980i | \(-0.688352\pi\) | ||||
−0.557793 | + | 0.829980i | \(0.688352\pi\) | |||||||
\(684\) | −1.03287e28 | + | 8.31826e27i | −0.460768 | + | 0.371083i | ||||
\(685\) | − | 9.52587e27i | − | 0.418792i | ||||||
\(686\) | −1.75108e28 | + | 6.17450e27i | −0.758689 | + | 0.267523i | ||||
\(687\) | 8.18786e27i | 0.349626i | ||||||||
\(688\) | −3.20580e27 | + | 1.46945e28i | −0.134912 | + | 0.618401i | ||||
\(689\) | −6.53389e28 | −2.71006 | ||||||||
\(690\) | −1.64422e27 | − | 4.66298e27i | −0.0672154 | − | 0.190622i | ||||
\(691\) | 3.79505e28 | 1.52910 | 0.764552 | − | 0.644562i | \(-0.222960\pi\) | ||||
0.764552 | + | 0.644562i | \(0.222960\pi\) | |||||||
\(692\) | −2.95580e27 | − | 3.67018e27i | −0.117386 | − | 0.145756i | ||||
\(693\) | − | 6.92862e27i | − | 0.271215i | ||||||
\(694\) | 4.34097e27 | + | 1.23109e28i | 0.167491 | + | 0.475002i | ||||
\(695\) | − | 1.62079e28i | − | 0.616422i | ||||||
\(696\) | 3.60070e28 | − | 5.82315e28i | 1.34988 | − | 2.18306i | ||||
\(697\) | 1.15216e28 | 0.425780 | ||||||||
\(698\) | 1.10010e28 | − | 3.87910e27i | 0.400756 | − | 0.141311i | ||||
\(699\) | −4.21338e28 | −1.51307 | ||||||||
\(700\) | 5.95215e27 | + | 7.39069e27i | 0.210714 | + | 0.261640i | ||||
\(701\) | − | 2.03325e27i | − | 0.0709596i | −0.999370 | − | 0.0354798i | \(-0.988704\pi\) | ||
0.999370 | − | 0.0354798i | \(-0.0112959\pi\) | |||||||
\(702\) | 2.21136e27 | − | 7.79751e26i | 0.0760831 | − | 0.0268278i | ||||
\(703\) | − | 2.50250e27i | − | 0.0848829i | ||||||
\(704\) | 7.79860e27 | + | 1.56146e28i | 0.260789 | + | 0.522161i | ||||
\(705\) | 1.75900e28 | 0.579929 | ||||||||
\(706\) | −8.43208e27 | − | 2.39132e28i | −0.274086 | − | 0.777304i | ||||
\(707\) | 1.93579e28 | 0.620389 | ||||||||
\(708\) | −1.88880e28 | + | 1.52116e28i | −0.596833 | + | 0.480664i | ||||
\(709\) | 3.94725e28i | 1.22979i | 0.788608 | + | 0.614896i | \(0.210802\pi\) | ||||
−0.788608 | + | 0.614896i | \(0.789198\pi\) | |||||||
\(710\) | 5.81897e27 | + | 1.65025e28i | 0.178757 | + | 0.506951i | ||||
\(711\) | − | 5.94999e28i | − | 1.80227i | ||||||
\(712\) | −2.22793e28 | − | 1.37763e28i | −0.665430 | − | 0.411464i | ||||
\(713\) | 1.30896e28 | 0.385505 | ||||||||
\(714\) | −3.66189e28 | + | 1.29123e28i | −1.06347 | + | 0.374990i | ||||
\(715\) | −1.43749e28 | −0.411666 | ||||||||
\(716\) | 2.84176e28 | − | 2.28863e28i | 0.802523 | − | 0.646318i | ||||
\(717\) | 3.87476e28i | 1.07908i | ||||||||
\(718\) | 4.68692e28 | − | 1.65266e28i | 1.28719 | − | 0.453878i | ||||
\(719\) | − | 2.52527e28i | − | 0.683942i | −0.939710 | − | 0.341971i | \(-0.888905\pi\) | ||
0.939710 | − | 0.341971i | \(-0.111095\pi\) | |||||||
\(720\) | 1.89505e28 | + | 4.13431e27i | 0.506169 | + | 0.110428i | ||||
\(721\) | −8.91792e27 | −0.234915 | ||||||||
\(722\) | 8.65727e27 | + | 2.45519e28i | 0.224910 | + | 0.637841i | ||||
\(723\) | 5.66185e28 | 1.45069 | ||||||||
\(724\) | 1.54013e28 | + | 1.91235e28i | 0.389198 | + | 0.483261i | ||||
\(725\) | − | 5.42065e28i | − | 1.35105i | ||||||
\(726\) | 1.27387e28 | + | 3.61268e28i | 0.313156 | + | 0.888103i | ||||
\(727\) | − | 6.02907e28i | − | 1.46186i | −0.682452 | − | 0.730931i | \(-0.739086\pi\) | ||
0.682452 | − | 0.730931i | \(-0.260914\pi\) | |||||||
\(728\) | 2.24981e28 | + | 1.39115e28i | 0.538062 | + | 0.332707i | ||||
\(729\) | −4.57036e28 | −1.07814 | ||||||||
\(730\) | 2.56254e27 | − | 9.03581e26i | 0.0596268 | − | 0.0210251i | ||||
\(731\) | −4.87244e28 | −1.11834 | ||||||||
\(732\) | −8.27649e27 | − | 1.02768e28i | −0.187385 | − | 0.232673i | ||||
\(733\) | 2.73732e28i | 0.611345i | 0.952137 | + | 0.305673i | \(0.0988813\pi\) | ||||
−0.952137 | + | 0.305673i | \(0.901119\pi\) | |||||||
\(734\) | 5.01778e28 | − | 1.76933e28i | 1.10548 | − | 0.389805i | ||||
\(735\) | 2.62027e28i | 0.569473i | ||||||||
\(736\) | 1.64136e27 | + | 1.31472e28i | 0.0351904 | + | 0.281874i | ||||
\(737\) | −4.42536e28 | −0.935996 | ||||||||
\(738\) | −3.99376e27 | − | 1.13262e28i | −0.0833334 | − | 0.236332i | ||||
\(739\) | 8.14966e28 | 1.67763 | 0.838813 | − | 0.544419i | \(-0.183250\pi\) | ||||
0.838813 | + | 0.544419i | \(0.183250\pi\) | |||||||
\(740\) | −2.85057e27 | + | 2.29573e27i | −0.0578915 | + | 0.0466233i | ||||
\(741\) | 5.74138e28i | 1.15036i | ||||||||
\(742\) | −1.43896e28 | − | 4.08085e28i | −0.284452 | − | 0.806700i | ||||
\(743\) | 4.08224e28i | 0.796178i | 0.917347 | + | 0.398089i | \(0.130326\pi\) | ||||
−0.917347 | + | 0.398089i | \(0.869674\pi\) | |||||||
\(744\) | −5.29749e28 | + | 8.56724e28i | −1.01939 | + | 1.64859i | ||||
\(745\) | 3.48651e28 | 0.661955 | ||||||||
\(746\) | −3.32978e28 | + | 1.17412e28i | −0.623774 | + | 0.219950i | ||||
\(747\) | −4.72207e28 | −0.872823 | ||||||||
\(748\) | −4.40380e28 | + | 3.54663e28i | −0.803177 | + | 0.646845i | ||||
\(749\) | − | 2.13411e28i | − | 0.384059i | ||||||
\(750\) | 6.61995e28 | − | 2.33427e28i | 1.17555 | − | 0.414514i | ||||
\(751\) | − | 1.72660e28i | − | 0.302547i | −0.988492 | − | 0.151273i | \(-0.951663\pi\) | ||
0.988492 | − | 0.151273i | \(-0.0483374\pi\) | |||||||
\(752\) | −4.60522e28 | − | 1.00469e28i | −0.796291 | − | 0.173722i | ||||
\(753\) | −4.78365e28 | −0.816225 | ||||||||
\(754\) | −5.02472e28 | − | 1.42500e29i | −0.846055 | − | 2.39940i | ||||
\(755\) | −2.11826e28 | −0.351973 | ||||||||
\(756\) | 9.74015e26 | + | 1.20942e27i | 0.0159716 | + | 0.0198316i | ||||
\(757\) | 6.18361e28i | 1.00065i | 0.865837 | + | 0.500326i | \(0.166787\pi\) | ||||
−0.865837 | + | 0.500326i | \(0.833213\pi\) | |||||||
\(758\) | −2.71739e28 | − | 7.70648e28i | −0.433971 | − | 1.23073i | ||||
\(759\) | − | 1.50245e28i | − | 0.236800i | ||||||
\(760\) | −9.58314e27 | + | 1.54981e28i | −0.149064 | + | 0.241070i | ||||
\(761\) | 6.86927e28 | 1.05454 | 0.527271 | − | 0.849697i | \(-0.323215\pi\) | ||||
0.527271 | + | 0.849697i | \(0.323215\pi\) | |||||||
\(762\) | −1.23995e29 | + | 4.37222e28i | −1.87869 | + | 0.662448i | ||||
\(763\) | −1.85517e28 | −0.277421 | ||||||||
\(764\) | 1.70114e28 | + | 2.11228e28i | 0.251077 | + | 0.311758i | ||||
\(765\) | 6.28367e28i | 0.915375i | ||||||||
\(766\) | 2.91452e28 | − | 1.02769e28i | 0.419063 | − | 0.147767i | ||||
\(767\) | 5.35230e28i | 0.759603i | ||||||||
\(768\) | −9.26925e28 | − | 4.24654e28i | −1.29847 | − | 0.594871i | ||||
\(769\) | 1.05970e29 | 1.46528 | 0.732638 | − | 0.680619i | \(-0.238289\pi\) | ||||
0.732638 | + | 0.680619i | \(0.238289\pi\) | |||||||
\(770\) | −3.16578e27 | − | 8.97810e27i | −0.0432090 | − | 0.122540i | ||||
\(771\) | 1.21227e29 | 1.63326 | ||||||||
\(772\) | −2.19066e28 | + | 1.76427e28i | −0.291342 | + | 0.234634i | ||||
\(773\) | − | 1.36439e29i | − | 1.79120i | −0.444857 | − | 0.895601i | \(-0.646746\pi\) | ||
0.444857 | − | 0.895601i | \(-0.353254\pi\) | |||||||
\(774\) | 1.68895e28 | + | 4.78982e28i | 0.218880 | + | 0.620740i | ||||
\(775\) | 7.97508e28i | 1.02028i | ||||||||
\(776\) | −7.17629e27 | − | 4.43740e27i | −0.0906322 | − | 0.0560417i | ||||
\(777\) | −7.63740e27 | −0.0952216 | ||||||||
\(778\) | 9.06415e28 | − | 3.19613e28i | 1.11566 | − | 0.393394i | ||||
\(779\) | 1.12825e28 | 0.137097 | ||||||||
\(780\) | 6.53995e28 | − | 5.26700e28i | 0.784564 | − | 0.631855i | ||||
\(781\) | 5.31723e28i | 0.629760i | ||||||||
\(782\) | −4.04800e28 | + | 1.42737e28i | −0.473340 | + | 0.166905i | ||||
\(783\) | − | 8.87040e27i | − | 0.102406i | ||||||
\(784\) | 1.49662e28 | − | 6.86011e28i | 0.170590 | − | 0.781934i | ||||
\(785\) | 1.78553e28 | 0.200942 | ||||||||
\(786\) | 2.33750e28 | + | 6.62911e28i | 0.259733 | + | 0.736597i | ||||
\(787\) | 2.50792e28 | 0.275148 | 0.137574 | − | 0.990492i | \(-0.456070\pi\) | ||||
0.137574 | + | 0.990492i | \(0.456070\pi\) | |||||||
\(788\) | 3.08700e28 | + | 3.83308e28i | 0.334407 | + | 0.415228i | ||||
\(789\) | 3.41530e28i | 0.365307i | ||||||||
\(790\) | −2.71863e28 | − | 7.71000e28i | −0.287131 | − | 0.814298i | ||||
\(791\) | − | 2.42542e28i | − | 0.252943i | ||||||
\(792\) | 5.01299e28 | + | 3.09974e28i | 0.516232 | + | 0.319208i | ||||
\(793\) | −2.91214e28 | −0.296129 | ||||||||
\(794\) | 4.56778e28 | − | 1.61065e28i | 0.458670 | − | 0.161732i | ||||
\(795\) | −1.37365e29 | −1.36209 | ||||||||
\(796\) | 3.95542e28 | + | 4.91138e28i | 0.387313 | + | 0.480920i | ||||
\(797\) | 3.02327e28i | 0.292343i | 0.989259 | + | 0.146172i | \(0.0466952\pi\) | ||||
−0.989259 | + | 0.146172i | \(0.953305\pi\) | |||||||
\(798\) | −3.58588e28 | + | 1.26442e28i | −0.342426 | + | 0.120743i | ||||
\(799\) | − | 1.52701e29i | − | 1.44004i | ||||||
\(800\) | −8.01020e28 | + | 1.00003e28i | −0.746008 | + | 0.0931348i | ||||
\(801\) | −8.84559e28 | −0.813583 | ||||||||
\(802\) | 4.39281e28 | + | 1.24579e29i | 0.399024 | + | 1.13162i | ||||
\(803\) | 8.25669e27 | 0.0740714 | ||||||||
\(804\) | 2.01335e29 | − | 1.62146e29i | 1.78385 | − | 1.43664i | ||||
\(805\) | − | 7.22662e27i | − | 0.0632378i | ||||||
\(806\) | 7.39257e28 | + | 2.09652e29i | 0.638918 | + | 1.81196i | ||||
\(807\) | − | 6.19793e28i | − | 0.529068i | ||||||
\(808\) | −8.66040e28 | + | 1.40058e29i | −0.730170 | + | 1.18085i | ||||
\(809\) | −8.70610e28 | −0.725001 | −0.362500 | − | 0.931984i | \(-0.618077\pi\) | ||||
−0.362500 | + | 0.931984i | \(0.618077\pi\) | |||||||
\(810\) | −5.47521e28 | + | 1.93062e28i | −0.450350 | + | 0.158799i | ||||
\(811\) | 3.36143e28 | 0.273096 | 0.136548 | − | 0.990633i | \(-0.456399\pi\) | ||||
0.136548 | + | 0.990633i | \(0.456399\pi\) | |||||||
\(812\) | 7.79350e28 | − | 6.27656e28i | 0.625421 | − | 0.503688i | ||||
\(813\) | − | 3.46664e29i | − | 2.74791i | ||||||
\(814\) | −1.04889e28 | + | 3.69851e27i | −0.0821269 | + | 0.0289589i | ||||
\(815\) | 1.57262e27i | 0.0121632i | ||||||||
\(816\) | 7.04041e28 | − | 3.22712e29i | 0.537893 | − | 2.46555i | ||||
\(817\) | −4.77130e28 | −0.360094 | ||||||||
\(818\) | −3.32719e28 | − | 9.43585e28i | −0.248053 | − | 0.703474i | ||||
\(819\) | 8.93245e28 | 0.657857 | ||||||||
\(820\) | −1.03502e28 | − | 1.28517e28i | −0.0753029 | − | 0.0935025i | ||||
\(821\) | 4.64099e28i | 0.333564i | 0.985994 | + | 0.166782i | \(0.0533376\pi\) | ||||
−0.985994 | + | 0.166782i | \(0.946662\pi\) | |||||||
\(822\) | 5.62300e28 | + | 1.59467e29i | 0.399255 | + | 1.13228i | ||||
\(823\) | 1.17639e29i | 0.825186i | 0.910915 | + | 0.412593i | \(0.135377\pi\) | ||||
−0.910915 | + | 0.412593i | \(0.864623\pi\) | |||||||
\(824\) | 3.98972e28 | − | 6.45229e28i | 0.276484 | − | 0.447138i | ||||
\(825\) | 9.15394e28 | 0.626713 | ||||||||
\(826\) | −3.34287e28 | + | 1.17873e28i | −0.226110 | + | 0.0797289i | ||||
\(827\) | −2.44978e29 | −1.63709 | −0.818545 | − | 0.574442i | \(-0.805219\pi\) | ||||
−0.818545 | + | 0.574442i | \(0.805219\pi\) | |||||||
\(828\) | 2.80633e28 | + | 3.48458e28i | 0.185283 | + | 0.230063i | ||||
\(829\) | 5.12749e28i | 0.334472i | 0.985917 | + | 0.167236i | \(0.0534841\pi\) | ||||
−0.985917 | + | 0.167236i | \(0.946516\pi\) | |||||||
\(830\) | −6.11886e28 | + | 2.15758e28i | −0.394357 | + | 0.139055i | ||||
\(831\) | 5.38501e28i | 0.342907i | ||||||||
\(832\) | −2.01305e29 | + | 1.00540e29i | −1.26655 | + | 0.632568i | ||||
\(833\) | 2.27470e29 | 1.41408 | ||||||||
\(834\) | 9.56732e28 | + | 2.71327e29i | 0.587665 | + | 1.66661i | ||||
\(835\) | 6.75952e28 | 0.410253 | ||||||||
\(836\) | −4.31238e28 | + | 3.47301e28i | −0.258616 | + | 0.208278i | ||||
\(837\) | 1.30505e28i | 0.0773343i | ||||||||
\(838\) | −4.96139e28 | − | 1.40704e29i | −0.290511 | − | 0.823884i | ||||
\(839\) | 3.38731e29i | 1.95991i | 0.199228 | + | 0.979953i | \(0.436157\pi\) | ||||
−0.199228 | + | 0.979953i | \(0.563843\pi\) | |||||||
\(840\) | 4.72989e28 | + | 2.92469e28i | 0.270432 | + | 0.167220i | ||||
\(841\) | −3.94615e29 | −2.22953 | ||||||||
\(842\) | −1.08336e29 | + | 3.82004e28i | −0.604853 | + | 0.213278i | ||||
\(843\) | −3.61340e29 | −1.99361 | ||||||||
\(844\) | −2.08058e29 | + | 1.67561e29i | −1.13438 | + | 0.913584i | ||||
\(845\) | − | 9.28599e28i | − | 0.500335i | ||||||
\(846\) | −1.50112e29 | + | 5.29312e28i | −0.799303 | + | 0.281844i | ||||
\(847\) | 5.59889e28i | 0.294624i | ||||||||
\(848\) | 3.59634e29 | + | 7.84591e28i | 1.87026 | + | 0.408023i | ||||
\(849\) | 3.44386e29 | 1.76998 | ||||||||
\(850\) | −8.69654e28 | − | 2.46632e29i | −0.441730 | − | 1.25274i | ||||
\(851\) | −8.44268e27 | −0.0423823 | ||||||||
\(852\) | −1.94824e29 | − | 2.41910e29i | −0.966601 | − | 1.20021i | ||||
\(853\) | − | 2.20403e29i | − | 1.08076i | −0.841423 | − | 0.540378i | \(-0.818281\pi\) | ||
0.841423 | − | 0.540378i | \(-0.181719\pi\) | |||||||
\(854\) | −6.41340e27 | − | 1.81883e28i | −0.0310821 | − | 0.0881481i | ||||
\(855\) | 6.15323e28i | 0.294742i | ||||||||
\(856\) | 1.54407e29 | + | 9.54763e28i | 0.731019 | + | 0.452020i | ||||
\(857\) | −3.05396e27 | −0.0142908 | −0.00714539 | − | 0.999974i | \(-0.502274\pi\) | ||||
−0.00714539 | + | 0.999974i | \(0.502274\pi\) | |||||||
\(858\) | 2.40642e29 | − | 8.48533e28i | 1.11301 | − | 0.392461i | ||||
\(859\) | −1.31353e29 | −0.600494 | −0.300247 | − | 0.953861i | \(-0.597069\pi\) | ||||
−0.300247 | + | 0.953861i | \(0.597069\pi\) | |||||||
\(860\) | 4.37707e28 | + | 5.43494e28i | 0.197788 | + | 0.245590i | ||||
\(861\) | − | 3.44331e28i | − | 0.153796i | ||||||
\(862\) | 1.76281e29 | − | 6.21587e28i | 0.778274 | − | 0.274428i | ||||
\(863\) | 1.63710e29i | 0.714441i | 0.934020 | + | 0.357221i | \(0.116276\pi\) | ||||
−0.934020 | + | 0.357221i | \(0.883724\pi\) | |||||||
\(864\) | −1.31080e28 | + | 1.63645e27i | −0.0565454 | + | 0.00705937i | ||||
\(865\) | −2.18649e28 | −0.0932364 | ||||||||
\(866\) | 7.73751e28 | + | 2.19434e29i | 0.326154 | + | 0.924966i | ||||
\(867\) | 7.27296e29 | 3.03054 | ||||||||
\(868\) | −1.14661e29 | + | 9.23432e28i | −0.472301 | + | 0.380371i | ||||
\(869\) | − | 2.48422e29i | − | 1.01156i | ||||||
\(870\) | −1.05637e29 | − | 2.99585e29i | −0.425230 | − | 1.20595i | ||||
\(871\) | − | 5.70523e29i | − | 2.27034i | ||||||
\(872\) | 8.29972e28 | − | 1.34225e29i | 0.326512 | − | 0.528043i | ||||
\(873\) | −2.84921e28 | −0.110811 | ||||||||
\(874\) | −3.96397e28 | + | 1.39774e28i | −0.152411 | + | 0.0537419i | ||||
\(875\) | 1.02595e29 | 0.389984 | ||||||||
\(876\) | −3.75643e28 | + | 3.02527e28i | −0.141167 | + | 0.113690i | ||||
\(877\) | 3.08590e29i | 1.14653i | 0.819370 | + | 0.573265i | \(0.194323\pi\) | ||||
−0.819370 | + | 0.573265i | \(0.805677\pi\) | |||||||
\(878\) | 2.25064e29 | − | 7.93602e28i | 0.826724 | − | 0.291513i | ||||
\(879\) | 2.08705e29i | 0.757957i | ||||||||
\(880\) | 7.91215e28 | + | 1.72614e28i | 0.284098 | + | 0.0619797i | ||||
\(881\) | 2.88421e29 | 1.02392 | 0.511962 | − | 0.859008i | \(-0.328919\pi\) | ||||
0.511962 | + | 0.859008i | \(0.328919\pi\) | |||||||
\(882\) | −7.88483e28 | − | 2.23612e29i | −0.276762 | − | 0.784892i | ||||
\(883\) | −2.99132e29 | −1.03814 | −0.519069 | − | 0.854732i | \(-0.673721\pi\) | ||||
−0.519069 | + | 0.854732i | \(0.673721\pi\) | |||||||
\(884\) | −4.57236e29 | − | 5.67743e29i | −1.56898 | − | 1.94818i | ||||
\(885\) | 1.12524e29i | 0.381779i | ||||||||
\(886\) | 4.79891e28 | + | 1.36096e29i | 0.160993 | + | 0.456572i | ||||
\(887\) | 5.86956e28i | 0.194701i | 0.995250 | + | 0.0973507i | \(0.0310368\pi\) | ||||
−0.995250 | + | 0.0973507i | \(0.968963\pi\) | |||||||
\(888\) | 3.41684e28 | − | 5.52581e28i | 0.112072 | − | 0.181245i | ||||
\(889\) | −1.92166e29 | −0.623246 | ||||||||
\(890\) | −1.14621e29 | + | 4.04168e28i | −0.367591 | + | 0.129617i | ||||
\(891\) | −1.76415e29 | −0.559448 | ||||||||
\(892\) | 2.31713e29 | + | 2.87714e29i | 0.726611 | + | 0.902221i | ||||
\(893\) | − | 1.49532e29i | − | 0.463680i | ||||||
\(894\) | −5.83658e29 | + | 2.05805e29i | −1.78971 | + | 0.631073i | ||||
\(895\) | − | 1.69296e29i | − | 0.513354i | ||||||
\(896\) | −1.07128e29 | − | 1.03587e29i | −0.321234 | − | 0.310616i | ||||
\(897\) | 1.93697e29 | 0.574379 | ||||||||
\(898\) | −4.79001e28 | − | 1.35844e29i | −0.140467 | − | 0.398361i | ||||
\(899\) | 8.40974e29 | 2.43885 | ||||||||
\(900\) | −2.12305e29 | + | 1.70981e29i | −0.608884 | + | 0.490370i | ||||
\(901\) | 1.19249e30i | 3.38225i | ||||||||
\(902\) | −1.66746e28 | − | 4.72889e28i | −0.0467725 | − | 0.132646i | ||||
\(903\) | 1.45616e29i | 0.403954i | ||||||||
\(904\) | 1.75484e29 | + | 1.08509e29i | 0.481452 | + | 0.297702i | ||||
\(905\) | 1.13927e29 | 0.309130 | ||||||||
\(906\) | 3.54606e29 | − | 1.25038e29i | 0.951621 | − | 0.335553i | ||||
\(907\) | 1.72537e29 | 0.457942 | 0.228971 | − | 0.973433i | \(-0.426464\pi\) | ||||
0.228971 | + | 0.973433i | \(0.426464\pi\) | |||||||
\(908\) | −3.45715e29 | + | 2.78425e29i | −0.907529 | + | 0.730885i | ||||
\(909\) | 5.56075e29i | 1.44376i | ||||||||
\(910\) | 1.15747e29 | − | 4.08136e28i | 0.297231 | − | 0.104807i | ||||
\(911\) | − | 5.22848e29i | − | 1.32798i | −0.747741 | − | 0.663990i | \(-0.768862\pi\) | ||
0.747741 | − | 0.663990i | \(-0.231138\pi\) | |||||||
\(912\) | 6.89426e28 | − | 3.16013e29i | 0.173197 | − | 0.793884i | ||||
\(913\) | −1.97154e29 | −0.489890 | ||||||||
\(914\) | −4.34922e28 | − | 1.23343e29i | −0.106893 | − | 0.303147i | ||||
\(915\) | −6.12234e28 | −0.148835 | ||||||||
\(916\) | −6.38535e28 | − | 7.92859e28i | −0.153543 | − | 0.190652i | ||||
\(917\) | 1.02737e29i | 0.244362i | ||||||||
\(918\) | −1.42311e28 | − | 4.03591e28i | −0.0334820 | − | 0.0949543i | ||||
\(919\) | − | 7.80290e29i | − | 1.81594i | −0.419038 | − | 0.907969i | \(-0.637632\pi\) | ||
0.419038 | − | 0.907969i | \(-0.362368\pi\) | |||||||
\(920\) | 5.22860e28 | + | 3.23307e28i | 0.120367 | + | 0.0744280i | ||||
\(921\) | −7.08684e29 | −1.61382 | ||||||||
\(922\) | 3.49204e29 | − | 1.23134e29i | 0.786630 | − | 0.277375i | ||||
\(923\) | −6.85503e29 | −1.52754 | ||||||||
\(924\) | 1.05993e29 | + | 1.31610e29i | 0.233646 | + | 0.290115i | ||||
\(925\) | − | 5.14387e28i | − | 0.112169i | ||||||
\(926\) | −4.58029e29 | + | 1.61506e29i | −0.988060 | + | 0.348401i | ||||
\(927\) | − | 2.56176e29i | − | 0.546690i | ||||||
\(928\) | 1.05453e29 | + | 8.44678e29i | 0.222628 | + | 1.78325i | ||||
\(929\) | −4.97570e29 | −1.03920 | −0.519598 | − | 0.854411i | \(-0.673918\pi\) | ||||
−0.519598 | + | 0.854411i | \(0.673918\pi\) | |||||||
\(930\) | 1.55418e29 | + | 4.40761e29i | 0.321123 | + | 0.910697i | ||||
\(931\) | 2.22748e29 | 0.455320 | ||||||||
\(932\) | 4.07997e29 | − | 3.28583e29i | 0.825083 | − | 0.664486i | ||||
\(933\) | − | 1.26303e30i | − | 2.52695i | ||||||
\(934\) | −1.11075e29 | − | 3.15007e29i | −0.219861 | − | 0.623522i | ||||
\(935\) | 2.62354e29i | 0.513773i | ||||||||
\(936\) | −3.99623e29 | + | 6.46280e29i | −0.774268 | + | 1.25217i | ||||
\(937\) | 2.52525e29 | 0.484070 | 0.242035 | − | 0.970268i | \(-0.422185\pi\) | ||||
0.242035 | + | 0.970268i | \(0.422185\pi\) | |||||||
\(938\) | 3.56330e29 | − | 1.25646e29i | 0.675809 | − | 0.238298i | ||||
\(939\) | −1.25067e30 | −2.34687 | ||||||||
\(940\) | −1.70330e29 | + | 1.37177e29i | −0.316237 | + | 0.254684i | ||||
\(941\) | 2.37447e29i | 0.436185i | 0.975928 | + | 0.218093i | \(0.0699835\pi\) | ||||
−0.975928 | + | 0.218093i | \(0.930017\pi\) | |||||||
\(942\) | −2.98906e29 | + | 1.05398e29i | −0.543282 | + | 0.191568i | ||||
\(943\) | − | 3.80636e28i | − | 0.0684531i | ||||||
\(944\) | 6.42705e28 | − | 2.94598e29i | 0.114365 | − | 0.524215i | ||||
\(945\) | 7.20504e27 | 0.0126858 | ||||||||
\(946\) | 7.05163e28 | + | 1.99983e29i | 0.122851 | + | 0.348403i | ||||
\(947\) | 3.70419e29 | 0.638548 | 0.319274 | − | 0.947662i | \(-0.396561\pi\) | ||||
0.319274 | + | 0.947662i | \(0.396561\pi\) | |||||||
\(948\) | 9.10223e29 | + | 1.13021e30i | 1.55262 | + | 1.92786i | ||||
\(949\) | 1.06446e29i | 0.179667i | ||||||||
\(950\) | −8.51601e28 | − | 2.41513e29i | −0.142233 | − | 0.403370i | ||||
\(951\) | 5.12420e29i | 0.846878i | ||||||||
\(952\) | 2.53897e29 | − | 4.10609e29i | 0.415229 | − | 0.671519i | ||||
\(953\) | 1.08040e29 | 0.174846 | 0.0874232 | − | 0.996171i | \(-0.472137\pi\) | ||||
0.0874232 | + | 0.996171i | \(0.472137\pi\) | |||||||
\(954\) | 1.17227e30 | − | 4.13354e29i | 1.87734 | − | 0.661971i | ||||
\(955\) | 1.25838e29 | 0.199424 | ||||||||
\(956\) | −3.02175e29 | − | 3.75206e29i | −0.473893 | − | 0.588425i | ||||
\(957\) | − | 9.65286e29i | − | 1.49809i | ||||||
\(958\) | 8.88196e29 | − | 3.13188e29i | 1.36412 | − | 0.481006i | ||||
\(959\) | 2.47140e29i | 0.375628i | ||||||||
\(960\) | −4.23214e29 | + | 2.11371e29i | −0.636572 | + | 0.317931i | ||||
\(961\) | −5.65484e29 | −0.841756 | ||||||||
\(962\) | −4.76816e28 | − | 1.35224e29i | −0.0702425 | − | 0.199206i | ||||
\(963\) | 6.13043e29 | 0.893775 | ||||||||
\(964\) | −5.48257e29 | + | 4.41543e29i | −0.791068 | + | 0.637092i | ||||
\(965\) | 1.30507e29i | 0.186364i | ||||||||
\(966\) | 4.26579e28 | + | 1.20977e29i | 0.0602876 | + | 0.170974i | ||||
\(967\) | − | 9.56100e29i | − | 1.33733i | −0.743564 | − | 0.668665i | \(-0.766866\pi\) | ||
0.743564 | − | 0.668665i | \(-0.233134\pi\) | |||||||
\(968\) | −4.05091e29 | − | 2.50485e29i | −0.560788 | − | 0.346759i | ||||
\(969\) | 1.04785e30 | 1.43569 | ||||||||
\(970\) | −3.69201e28 | + | 1.30184e28i | −0.0500662 | + | 0.0176539i | ||||
\(971\) | 4.95486e29 | 0.665026 | 0.332513 | − | 0.943099i | \(-0.392103\pi\) | ||||
0.332513 | + | 0.943099i | \(0.392103\pi\) | |||||||
\(972\) | 8.36021e29 | − | 6.73296e29i | 1.11059 | − | 0.894424i | ||||
\(973\) | 4.20500e29i | 0.552888i | ||||||||
\(974\) | −3.08818e29 | + | 1.08893e29i | −0.401896 | + | 0.141713i | ||||
\(975\) | 1.18014e30i | 1.52015i | ||||||||
\(976\) | 1.60288e29 | + | 3.49691e28i | 0.204364 | + | 0.0445847i | ||||
\(977\) | 8.15060e29 | 1.02859 | 0.514297 | − | 0.857612i | \(-0.328053\pi\) | ||||
0.514297 | + | 0.857612i | \(0.328053\pi\) | |||||||
\(978\) | −9.28297e27 | − | 2.63263e28i | −0.0115957 | − | 0.0328853i | ||||
\(979\) | −3.69318e29 | −0.456640 | ||||||||
\(980\) | −2.04343e29 | − | 2.53730e29i | −0.250092 | − | 0.310535i | ||||
\(981\) | − | 5.32916e29i | − | 0.645608i | ||||||
\(982\) | −2.66190e28 | − | 7.54910e28i | −0.0319210 | − | 0.0905275i | ||||
\(983\) | 1.10181e30i | 1.30789i | 0.756542 | + | 0.653945i | \(0.226887\pi\) | ||||
−0.756542 | + | 0.653945i | \(0.773113\pi\) | |||||||
\(984\) | 2.49130e29 | + | 1.54048e29i | 0.292735 | + | 0.181011i | ||||
\(985\) | 2.28354e29 | 0.265611 | ||||||||
\(986\) | −2.60074e30 | + | 9.17052e29i | −2.99453 | + | 1.05591i | ||||
\(987\) | −4.56357e29 | −0.520156 | ||||||||
\(988\) | −4.47745e29 | − | 5.55958e29i | −0.505197 | − | 0.627296i | ||||
\(989\) | 1.60970e29i | 0.179796i | ||||||||
\(990\) | 2.57905e29 | − | 9.09402e28i | 0.285172 | − | 0.100555i | ||||
\(991\) | − | 1.03685e30i | − | 1.13496i | −0.823388 | − | 0.567478i | \(-0.807919\pi\) | ||
0.823388 | − | 0.567478i | \(-0.192081\pi\) | |||||||
\(992\) | −1.55147e29 | − | 1.24272e30i | −0.168123 | − | 1.34666i | ||||
\(993\) | −6.94962e29 | −0.745536 | ||||||||
\(994\) | −1.50968e29 | − | 4.28143e29i | −0.160333 | − | 0.454700i | ||||
\(995\) | 2.92593e29 | 0.307633 | ||||||||
\(996\) | 8.96965e29 | − | 7.22377e29i | 0.933646 | − | 0.751918i | ||||
\(997\) | 3.50619e29i | 0.361313i | 0.983546 | + | 0.180657i | \(0.0578223\pi\) | ||||
−0.983546 | + | 0.180657i | \(0.942178\pi\) | |||||||
\(998\) | 3.10002e29 | + | 8.79159e29i | 0.316271 | + | 0.896937i | ||||
\(999\) | − | 8.41747e27i | − | 0.00850211i |
(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 | 8.21.d.b.3.7 | ✓ | 18 | |
3.2 | odd | 2 | 72.21.b.b.19.12 | 18 | |||
4.3 | odd | 2 | 32.21.d.b.15.2 | 18 | |||
8.3 | odd | 2 | inner | 8.21.d.b.3.8 | yes | 18 | |
8.5 | even | 2 | 32.21.d.b.15.1 | 18 | |||
24.11 | even | 2 | 72.21.b.b.19.11 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.21.d.b.3.7 | ✓ | 18 | 1.1 | even | 1 | trivial | |
8.21.d.b.3.8 | yes | 18 | 8.3 | odd | 2 | inner | |
32.21.d.b.15.1 | 18 | 8.5 | even | 2 | |||
32.21.d.b.15.2 | 18 | 4.3 | odd | 2 | |||
72.21.b.b.19.11 | 18 | 24.11 | even | 2 | |||
72.21.b.b.19.12 | 18 | 3.2 | odd | 2 |