Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,34,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.4914144405\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 26286285043 x^{14} + \cdots + 16\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{83}\cdot 3^{26}\cdot 5^{53}\cdot 7^{4}\cdot 11^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.14 | ||
Root | \(78034.2i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.34.b.a.4.3 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 156068.i | 1.68392i | 0.539544 | + | 0.841958i | \(0.318597\pi\) | ||||
−0.539544 | + | 0.841958i | \(0.681403\pi\) | |||||||
\(3\) | 6.96239e7i | 0.933808i | 0.884308 | + | 0.466904i | \(0.154631\pi\) | ||||
−0.884308 | + | 0.466904i | \(0.845369\pi\) | |||||||
\(4\) | −1.57674e10 | −1.83557 | ||||||||
\(5\) | −2.14154e11 | + | 2.65619e11i | −0.627654 | + | 0.778493i | ||||
\(6\) | −1.08661e13 | −1.57245 | ||||||||
\(7\) | − | 1.55193e14i | − | 1.76504i | −0.470275 | − | 0.882520i | \(-0.655845\pi\) | ||
0.470275 | − | 0.882520i | \(-0.344155\pi\) | |||||||
\(8\) | − | 1.12018e15i | − | 1.40703i | ||||||
\(9\) | 7.11573e14 | 0.128002 | ||||||||
\(10\) | −4.14548e16 | − | 3.34226e16i | −1.31092 | − | 1.05692i | ||||
\(11\) | 4.13199e16 | 0.271132 | 0.135566 | − | 0.990768i | \(-0.456715\pi\) | ||||
0.135566 | + | 0.990768i | \(0.456715\pi\) | |||||||
\(12\) | − | 1.09779e18i | − | 1.71407i | ||||||
\(13\) | 2.38246e18i | 0.993025i | 0.868029 | + | 0.496513i | \(0.165386\pi\) | ||||
−0.868029 | + | 0.496513i | \(0.834614\pi\) | |||||||
\(14\) | 2.42207e19 | 2.97218 | ||||||||
\(15\) | −1.84934e19 | − | 1.49102e19i | −0.726963 | − | 0.586108i | ||||
\(16\) | 3.93836e19 | 0.533747 | ||||||||
\(17\) | − | 2.91772e20i | − | 1.45424i | −0.686511 | − | 0.727120i | \(-0.740858\pi\) | ||
0.686511 | − | 0.727120i | \(-0.259142\pi\) | |||||||
\(18\) | 1.11054e20i | 0.215545i | ||||||||
\(19\) | 3.61361e20 | 0.287414 | 0.143707 | − | 0.989620i | \(-0.454098\pi\) | ||||
0.143707 | + | 0.989620i | \(0.454098\pi\) | |||||||
\(20\) | 3.37665e21 | − | 4.18813e21i | 1.15210 | − | 1.42898i | ||||
\(21\) | 1.08051e22 | 1.64821 | ||||||||
\(22\) | 6.44874e21i | 0.456563i | ||||||||
\(23\) | − | 3.81748e22i | − | 1.29798i | −0.760798 | − | 0.648989i | \(-0.775192\pi\) | ||
0.760798 | − | 0.648989i | \(-0.224808\pi\) | |||||||
\(24\) | 7.79913e22 | 1.31390 | ||||||||
\(25\) | −2.46919e22 | − | 1.13767e23i | −0.212102 | − | 0.977248i | ||||
\(26\) | −3.71827e23 | −1.67217 | ||||||||
\(27\) | 4.36586e23i | 1.05334i | ||||||||
\(28\) | 2.44699e24i | 3.23985i | ||||||||
\(29\) | −1.65188e24 | −1.22577 | −0.612887 | − | 0.790170i | \(-0.709992\pi\) | ||||
−0.612887 | + | 0.790170i | \(0.709992\pi\) | |||||||
\(30\) | 2.32701e24 | − | 2.88624e24i | 0.986956 | − | 1.22414i | ||||
\(31\) | −2.76253e24 | −0.682086 | −0.341043 | − | 0.940048i | \(-0.610780\pi\) | ||||
−0.341043 | + | 0.940048i | \(0.610780\pi\) | |||||||
\(32\) | − | 3.47573e24i | − | 0.508244i | ||||||
\(33\) | 2.87685e24i | 0.253185i | ||||||||
\(34\) | 4.55364e25 | 2.44882 | ||||||||
\(35\) | 4.12223e25 | + | 3.32351e25i | 1.37407 | + | 1.10783i | ||||
\(36\) | −1.12197e25 | −0.234957 | ||||||||
\(37\) | − | 8.70723e24i | − | 0.116025i | −0.998316 | − | 0.0580125i | \(-0.981524\pi\) | ||
0.998316 | − | 0.0580125i | \(-0.0184763\pi\) | |||||||
\(38\) | 5.63971e25i | 0.483980i | ||||||||
\(39\) | −1.65876e26 | −0.927295 | ||||||||
\(40\) | 2.97541e26 | + | 2.39891e26i | 1.09536 | + | 0.883127i | ||||
\(41\) | 2.69048e26 | 0.659015 | 0.329508 | − | 0.944153i | \(-0.393117\pi\) | ||||
0.329508 | + | 0.944153i | \(0.393117\pi\) | |||||||
\(42\) | 1.68634e27i | 2.77544i | ||||||||
\(43\) | 1.33984e26i | 0.149563i | 0.997200 | + | 0.0747815i | \(0.0238259\pi\) | ||||
−0.997200 | + | 0.0747815i | \(0.976174\pi\) | |||||||
\(44\) | −6.51509e26 | −0.497681 | ||||||||
\(45\) | −1.52386e26 | + | 1.89008e26i | −0.0803412 | + | 0.0996489i | ||||
\(46\) | 5.95788e27 | 2.18568 | ||||||||
\(47\) | − | 2.88434e27i | − | 0.742047i | −0.928623 | − | 0.371024i | \(-0.879007\pi\) | ||
0.928623 | − | 0.371024i | \(-0.120993\pi\) | |||||||
\(48\) | 2.74204e27i | 0.498418i | ||||||||
\(49\) | −1.63539e28 | −2.11537 | ||||||||
\(50\) | 1.77554e28 | − | 3.85362e27i | 1.64560 | − | 0.357161i | ||||
\(51\) | 2.03143e28 | 1.35798 | ||||||||
\(52\) | − | 3.75653e28i | − | 1.82277i | ||||||
\(53\) | 2.92563e28i | 1.03673i | 0.855158 | + | 0.518367i | \(0.173460\pi\) | ||||
−0.855158 | + | 0.518367i | \(0.826540\pi\) | |||||||
\(54\) | −6.81373e28 | −1.77373 | ||||||||
\(55\) | −8.84880e27 | + | 1.09754e28i | −0.170177 | + | 0.211074i | ||||
\(56\) | −1.73844e29 | −2.48346 | ||||||||
\(57\) | 2.51594e28i | 0.268389i | ||||||||
\(58\) | − | 2.57806e29i | − | 2.06410i | ||||||
\(59\) | −1.51134e29 | −0.912650 | −0.456325 | − | 0.889813i | \(-0.650834\pi\) | ||||
−0.456325 | + | 0.889813i | \(0.650834\pi\) | |||||||
\(60\) | 2.91594e29 | + | 2.35096e29i | 1.33439 | + | 1.07584i | ||||
\(61\) | 2.88604e29 | 1.00545 | 0.502725 | − | 0.864446i | \(-0.332331\pi\) | ||||
0.502725 | + | 0.864446i | \(0.332331\pi\) | |||||||
\(62\) | − | 4.31144e29i | − | 1.14857i | ||||||
\(63\) | − | 1.10431e29i | − | 0.225929i | ||||||
\(64\) | 8.80755e29 | 1.38959 | ||||||||
\(65\) | −6.32827e29 | − | 5.10212e29i | −0.773063 | − | 0.623276i | ||||
\(66\) | −4.48986e29 | −0.426342 | ||||||||
\(67\) | − | 8.72314e29i | − | 0.646307i | −0.946347 | − | 0.323153i | \(-0.895257\pi\) | ||
0.946347 | − | 0.323153i | \(-0.104743\pi\) | |||||||
\(68\) | 4.60049e30i | 2.66936i | ||||||||
\(69\) | 2.65788e30 | 1.21206 | ||||||||
\(70\) | −5.18696e30 | + | 6.43349e30i | −1.86550 | + | 2.31382i | ||||
\(71\) | 3.08526e30 | 0.878069 | 0.439034 | − | 0.898470i | \(-0.355321\pi\) | ||||
0.439034 | + | 0.898470i | \(0.355321\pi\) | |||||||
\(72\) | − | 7.97090e29i | − | 0.180103i | ||||||
\(73\) | − | 2.41300e30i | − | 0.434240i | −0.976145 | − | 0.217120i | \(-0.930334\pi\) | ||
0.976145 | − | 0.217120i | \(-0.0696662\pi\) | |||||||
\(74\) | 1.35892e30 | 0.195376 | ||||||||
\(75\) | 7.92087e30 | − | 1.71914e30i | 0.912562 | − | 0.198062i | ||||
\(76\) | −5.69774e30 | −0.527568 | ||||||||
\(77\) | − | 6.41256e30i | − | 0.478558i | ||||||
\(78\) | − | 2.58880e31i | − | 1.56149i | ||||||
\(79\) | 3.21352e31 | 1.57085 | 0.785423 | − | 0.618960i | \(-0.212446\pi\) | ||||
0.785423 | + | 0.618960i | \(0.212446\pi\) | |||||||
\(80\) | −8.43414e30 | + | 1.04610e31i | −0.335009 | + | 0.415518i | ||||
\(81\) | −2.64411e31 | −0.855613 | ||||||||
\(82\) | 4.19898e31i | 1.10973i | ||||||||
\(83\) | − | 7.79056e31i | − | 1.68570i | −0.538148 | − | 0.842850i | \(-0.680876\pi\) | ||
0.538148 | − | 0.842850i | \(-0.319124\pi\) | |||||||
\(84\) | −1.70369e32 | −3.02540 | ||||||||
\(85\) | 7.75002e31 | + | 6.24839e31i | 1.13211 | + | 0.912759i | ||||
\(86\) | −2.09107e31 | −0.251851 | ||||||||
\(87\) | − | 1.15010e32i | − | 1.14464i | ||||||
\(88\) | − | 4.62857e31i | − | 0.381490i | ||||||
\(89\) | −1.41115e32 | −0.965245 | −0.482623 | − | 0.875828i | \(-0.660316\pi\) | ||||
−0.482623 | + | 0.875828i | \(0.660316\pi\) | |||||||
\(90\) | −2.94981e31 | − | 2.37826e31i | −0.167800 | − | 0.135288i | ||||
\(91\) | 3.69741e32 | 1.75273 | ||||||||
\(92\) | 6.01918e32i | 2.38253i | ||||||||
\(93\) | − | 1.92338e32i | − | 0.636937i | ||||||
\(94\) | 4.50154e32 | 1.24954 | ||||||||
\(95\) | −7.73868e31 | + | 9.59845e31i | −0.180396 | + | 0.223749i | ||||
\(96\) | 2.41994e32 | 0.474602 | ||||||||
\(97\) | 7.13656e32i | 1.17966i | 0.807529 | + | 0.589828i | \(0.200804\pi\) | ||||
−0.807529 | + | 0.589828i | \(0.799196\pi\) | |||||||
\(98\) | − | 2.55232e33i | − | 3.56210i | ||||||
\(99\) | 2.94021e31 | 0.0347055 | ||||||||
\(100\) | 3.89327e32 | + | 1.79381e33i | 0.389327 | + | 1.79381i | ||||
\(101\) | −9.02530e32 | −0.765877 | −0.382939 | − | 0.923774i | \(-0.625088\pi\) | ||||
−0.382939 | + | 0.923774i | \(0.625088\pi\) | |||||||
\(102\) | 3.17042e33i | 2.28672i | ||||||||
\(103\) | − | 6.15871e32i | − | 0.378160i | −0.981962 | − | 0.189080i | \(-0.939449\pi\) | ||
0.981962 | − | 0.189080i | \(-0.0605505\pi\) | |||||||
\(104\) | 2.66878e33 | 1.39722 | ||||||||
\(105\) | −2.31396e33 | + | 2.87005e33i | −1.03450 | + | 1.28312i | ||||
\(106\) | −4.56598e33 | −1.74577 | ||||||||
\(107\) | − | 4.51029e33i | − | 1.47697i | −0.674270 | − | 0.738485i | \(-0.735541\pi\) | ||
0.674270 | − | 0.738485i | \(-0.264459\pi\) | |||||||
\(108\) | − | 6.88384e33i | − | 1.93348i | ||||||
\(109\) | 1.07835e33 | 0.260149 | 0.130074 | − | 0.991504i | \(-0.458478\pi\) | ||||
0.130074 | + | 0.991504i | \(0.458478\pi\) | |||||||
\(110\) | −1.71291e33 | − | 1.38102e33i | −0.355431 | − | 0.286563i | ||||
\(111\) | 6.06231e32 | 0.108345 | ||||||||
\(112\) | − | 6.11206e33i | − | 0.942085i | ||||||
\(113\) | − | 2.37121e31i | − | 0.00315629i | −0.999999 | − | 0.00157814i | \(-0.999498\pi\) | ||
0.999999 | − | 0.00157814i | \(-0.000502339\pi\) | |||||||
\(114\) | −3.92659e33 | −0.451944 | ||||||||
\(115\) | 1.01400e34 | + | 8.17526e33i | 1.01047 | + | 0.814681i | ||||
\(116\) | 2.60458e34 | 2.24999 | ||||||||
\(117\) | 1.69529e33i | 0.127110i | ||||||||
\(118\) | − | 2.35873e34i | − | 1.53682i | ||||||
\(119\) | −4.52809e34 | −2.56679 | ||||||||
\(120\) | −1.67021e34 | + | 2.07160e34i | −0.824671 | + | 1.02286i | ||||
\(121\) | −2.15178e34 | −0.926488 | ||||||||
\(122\) | 4.50420e34i | 1.69309i | ||||||||
\(123\) | 1.87321e34i | 0.615394i | ||||||||
\(124\) | 4.35580e34 | 1.25202 | ||||||||
\(125\) | 3.55065e34 | + | 1.78049e34i | 0.893906 | + | 0.448254i | ||||
\(126\) | 1.72348e34 | 0.380446 | ||||||||
\(127\) | − | 6.78580e34i | − | 1.31474i | −0.753568 | − | 0.657370i | \(-0.771669\pi\) | ||
0.753568 | − | 0.657370i | \(-0.228331\pi\) | |||||||
\(128\) | 1.07602e35i | 1.83170i | ||||||||
\(129\) | −9.32850e33 | −0.139663 | ||||||||
\(130\) | 7.96280e34 | − | 9.87644e34i | 1.04954 | − | 1.30177i | ||||
\(131\) | 7.18678e34 | 0.834753 | 0.417377 | − | 0.908734i | \(-0.362950\pi\) | ||||
0.417377 | + | 0.908734i | \(0.362950\pi\) | |||||||
\(132\) | − | 4.53606e34i | − | 0.464739i | ||||||
\(133\) | − | 5.60808e34i | − | 0.507296i | ||||||
\(134\) | 1.36141e35 | 1.08833 | ||||||||
\(135\) | −1.15966e35 | − | 9.34964e34i | −0.820016 | − | 0.661131i | ||||
\(136\) | −3.26837e35 | −2.04616 | ||||||||
\(137\) | − | 1.24185e34i | − | 0.0688940i | −0.999407 | − | 0.0344470i | \(-0.989033\pi\) | ||
0.999407 | − | 0.0344470i | \(-0.0109670\pi\) | |||||||
\(138\) | 4.14811e35i | 2.04101i | ||||||||
\(139\) | −3.36802e34 | −0.147106 | −0.0735531 | − | 0.997291i | \(-0.523434\pi\) | ||||
−0.0735531 | + | 0.997291i | \(0.523434\pi\) | |||||||
\(140\) | −6.49969e35 | − | 5.24032e35i | −2.52220 | − | 2.03351i | ||||
\(141\) | 2.00819e35 | 0.692930 | ||||||||
\(142\) | 4.81511e35i | 1.47859i | ||||||||
\(143\) | 9.84431e34i | 0.269241i | ||||||||
\(144\) | 2.80243e34 | 0.0683210 | ||||||||
\(145\) | 3.53755e35 | − | 4.38770e35i | 0.769362 | − | 0.954256i | ||||
\(146\) | 3.76593e35 | 0.731223 | ||||||||
\(147\) | − | 1.13862e36i | − | 1.97535i | ||||||
\(148\) | 1.37291e35i | 0.212972i | ||||||||
\(149\) | −7.60967e35 | −1.05631 | −0.528156 | − | 0.849147i | \(-0.677116\pi\) | ||||
−0.528156 | + | 0.849147i | \(0.677116\pi\) | |||||||
\(150\) | 2.68304e35 | + | 1.23620e36i | 0.333520 | + | 1.53668i | ||||
\(151\) | 3.06240e35 | 0.341147 | 0.170574 | − | 0.985345i | \(-0.445438\pi\) | ||||
0.170574 | + | 0.985345i | \(0.445438\pi\) | |||||||
\(152\) | − | 4.04790e35i | − | 0.404399i | ||||||
\(153\) | − | 2.07617e35i | − | 0.186146i | ||||||
\(154\) | 1.00080e36 | 0.805851 | ||||||||
\(155\) | 5.91605e35 | − | 7.33781e35i | 0.428114 | − | 0.530999i | ||||
\(156\) | 2.61544e36 | 1.70212 | ||||||||
\(157\) | 2.10956e36i | 1.23551i | 0.786370 | + | 0.617755i | \(0.211958\pi\) | ||||
−0.786370 | + | 0.617755i | \(0.788042\pi\) | |||||||
\(158\) | 5.01528e36i | 2.64517i | ||||||||
\(159\) | −2.03694e36 | −0.968110 | ||||||||
\(160\) | 9.23222e35 | + | 7.44341e35i | 0.395664 | + | 0.319001i | ||||
\(161\) | −5.92446e36 | −2.29098 | ||||||||
\(162\) | − | 4.12663e36i | − | 1.44078i | ||||||
\(163\) | − | 2.09987e36i | − | 0.662365i | −0.943567 | − | 0.331182i | \(-0.892552\pi\) | ||
0.943567 | − | 0.331182i | \(-0.107448\pi\) | |||||||
\(164\) | −4.24219e36 | −1.20967 | ||||||||
\(165\) | −7.64148e35 | − | 6.16088e35i | −0.197103 | − | 0.158912i | ||||
\(166\) | 1.21586e37 | 2.83858 | ||||||||
\(167\) | 4.97146e36i | 1.05114i | 0.850749 | + | 0.525572i | \(0.176149\pi\) | ||||
−0.850749 | + | 0.525572i | \(0.823851\pi\) | |||||||
\(168\) | − | 1.21037e37i | − | 2.31908i | ||||||
\(169\) | 8.00138e34 | 0.0139006 | ||||||||
\(170\) | −9.75177e36 | + | 1.20953e37i | −1.53701 | + | 1.90639i | ||||
\(171\) | 2.57135e35 | 0.0367896 | ||||||||
\(172\) | − | 2.11259e36i | − | 0.274533i | ||||||
\(173\) | − | 1.51427e37i | − | 1.78831i | −0.447753 | − | 0.894157i | \(-0.647776\pi\) | ||
0.447753 | − | 0.894157i | \(-0.352224\pi\) | |||||||
\(174\) | 1.79494e37 | 1.92747 | ||||||||
\(175\) | −1.76558e37 | + | 3.83201e36i | −1.72488 | + | 0.374368i | ||||
\(176\) | 1.62733e36 | 0.144716 | ||||||||
\(177\) | − | 1.05225e37i | − | 0.852240i | ||||||
\(178\) | − | 2.20236e37i | − | 1.62539i | ||||||
\(179\) | −9.15862e36 | −0.616247 | −0.308124 | − | 0.951346i | \(-0.599701\pi\) | ||||
−0.308124 | + | 0.951346i | \(0.599701\pi\) | |||||||
\(180\) | 2.40273e36 | − | 2.98016e36i | 0.147472 | − | 0.182913i | ||||
\(181\) | 1.09431e37 | 0.612975 | 0.306488 | − | 0.951875i | \(-0.400846\pi\) | ||||
0.306488 | + | 0.951875i | \(0.400846\pi\) | |||||||
\(182\) | 5.77049e37i | 2.95145i | ||||||||
\(183\) | 2.00938e37i | 0.938898i | ||||||||
\(184\) | −4.27626e37 | −1.82629 | ||||||||
\(185\) | 2.31281e36 | + | 1.86468e36i | 0.0903246 | + | 0.0728235i | ||||
\(186\) | 3.00179e37 | 1.07255 | ||||||||
\(187\) | − | 1.20560e37i | − | 0.394290i | ||||||
\(188\) | 4.54786e37i | 1.36208i | ||||||||
\(189\) | 6.77551e37 | 1.85918 | ||||||||
\(190\) | −1.49802e37 | − | 1.20776e37i | −0.376775 | − | 0.303772i | ||||
\(191\) | −2.18522e37 | −0.504016 | −0.252008 | − | 0.967725i | \(-0.581091\pi\) | ||||
−0.252008 | + | 0.967725i | \(0.581091\pi\) | |||||||
\(192\) | 6.13216e37i | 1.29761i | ||||||||
\(193\) | − | 7.41572e37i | − | 1.44032i | −0.693810 | − | 0.720158i | \(-0.744069\pi\) | ||
0.693810 | − | 0.720158i | \(-0.255931\pi\) | |||||||
\(194\) | −1.11379e38 | −1.98644 | ||||||||
\(195\) | 3.55230e37 | − | 4.40599e37i | 0.582020 | − | 0.721892i | ||||
\(196\) | 2.57859e38 | 3.88290 | ||||||||
\(197\) | − | 9.94695e37i | − | 1.37720i | −0.725141 | − | 0.688601i | \(-0.758225\pi\) | ||
0.725141 | − | 0.688601i | \(-0.241775\pi\) | |||||||
\(198\) | 4.58875e36i | 0.0584411i | ||||||||
\(199\) | −1.85341e37 | −0.217217 | −0.108609 | − | 0.994085i | \(-0.534640\pi\) | ||||
−0.108609 | + | 0.994085i | \(0.534640\pi\) | |||||||
\(200\) | −1.27439e38 | + | 2.76593e37i | −1.37502 | + | 0.298433i | ||||
\(201\) | 6.07339e37 | 0.603526 | ||||||||
\(202\) | − | 1.40857e38i | − | 1.28967i | ||||||
\(203\) | 2.56360e38i | 2.16354i | ||||||||
\(204\) | −3.20304e38 | −2.49267 | ||||||||
\(205\) | −5.76175e37 | + | 7.14642e37i | −0.413633 | + | 0.513038i | ||||
\(206\) | 9.61180e37 | 0.636789 | ||||||||
\(207\) | − | 2.71642e37i | − | 0.166144i | ||||||
\(208\) | 9.38299e37i | 0.530025i | ||||||||
\(209\) | 1.49314e37 | 0.0779269 | ||||||||
\(210\) | −4.47925e38 | − | 3.61136e38i | −2.16066 | − | 1.74202i | ||||
\(211\) | −2.61345e38 | −1.16561 | −0.582805 | − | 0.812612i | \(-0.698045\pi\) | ||||
−0.582805 | + | 0.812612i | \(0.698045\pi\) | |||||||
\(212\) | − | 4.61296e38i | − | 1.90300i | ||||||
\(213\) | 2.14808e38i | 0.819948i | ||||||||
\(214\) | 7.03914e38 | 2.48709 | ||||||||
\(215\) | −3.55888e37 | − | 2.86932e37i | −0.116434 | − | 0.0938738i | ||||
\(216\) | 4.89055e38 | 1.48208 | ||||||||
\(217\) | 4.28725e38i | 1.20391i | ||||||||
\(218\) | 1.68296e38i | 0.438068i | ||||||||
\(219\) | 1.68002e38 | 0.405496 | ||||||||
\(220\) | 1.39523e38 | − | 1.73053e38i | 0.312371 | − | 0.387441i | ||||
\(221\) | 6.95134e38 | 1.44410 | ||||||||
\(222\) | 9.46135e37i | 0.182444i | ||||||||
\(223\) | 2.67594e38i | 0.479122i | 0.970881 | + | 0.239561i | \(0.0770035\pi\) | ||||
−0.970881 | + | 0.239561i | \(0.922997\pi\) | |||||||
\(224\) | −5.39410e38 | −0.897070 | ||||||||
\(225\) | −1.75701e37 | − | 8.09533e37i | −0.0271495 | − | 0.125090i | ||||
\(226\) | 3.70072e36 | 0.00531492 | ||||||||
\(227\) | − | 3.53241e38i | − | 0.471677i | −0.971792 | − | 0.235838i | \(-0.924216\pi\) | ||
0.971792 | − | 0.235838i | \(-0.0757836\pi\) | |||||||
\(228\) | − | 3.96699e38i | − | 0.492647i | ||||||
\(229\) | −1.17673e39 | −1.35954 | −0.679769 | − | 0.733427i | \(-0.737920\pi\) | ||||
−0.679769 | + | 0.733427i | \(0.737920\pi\) | |||||||
\(230\) | −1.27590e39 | + | 1.58253e39i | −1.37185 | + | 1.70154i | ||||
\(231\) | 4.46468e38 | 0.446881 | ||||||||
\(232\) | 1.85040e39i | 1.72470i | ||||||||
\(233\) | − | 1.12975e38i | − | 0.0980870i | −0.998797 | − | 0.0490435i | \(-0.984383\pi\) | ||
0.998797 | − | 0.0490435i | \(-0.0156173\pi\) | |||||||
\(234\) | −2.64582e38 | −0.214042 | ||||||||
\(235\) | 7.66136e38 | + | 6.17691e38i | 0.577678 | + | 0.465749i | ||||
\(236\) | 2.38299e39 | 1.67523 | ||||||||
\(237\) | 2.23738e39i | 1.46687i | ||||||||
\(238\) | − | 7.06692e39i | − | 4.32226i | ||||||
\(239\) | −9.43852e38 | −0.538690 | −0.269345 | − | 0.963044i | \(-0.586807\pi\) | ||||
−0.269345 | + | 0.963044i | \(0.586807\pi\) | |||||||
\(240\) | −7.28339e38 | − | 5.87218e38i | −0.388015 | − | 0.312834i | ||||
\(241\) | 7.67029e38 | 0.381532 | 0.190766 | − | 0.981636i | \(-0.438903\pi\) | ||||
0.190766 | + | 0.981636i | \(0.438903\pi\) | |||||||
\(242\) | − | 3.35825e39i | − | 1.56013i | ||||||
\(243\) | 5.86073e38i | 0.254359i | ||||||||
\(244\) | −4.55055e39 | −1.84558 | ||||||||
\(245\) | 3.50224e39 | − | 4.34390e39i | 1.32772 | − | 1.64680i | ||||
\(246\) | −2.92350e39 | −1.03627 | ||||||||
\(247\) | 8.60929e38i | 0.285409i | ||||||||
\(248\) | 3.09453e39i | 0.959714i | ||||||||
\(249\) | 5.42409e39 | 1.57412 | ||||||||
\(250\) | −2.77878e39 | + | 5.54144e39i | −0.754821 | + | 1.50526i | ||||
\(251\) | −2.55001e39 | −0.648524 | −0.324262 | − | 0.945967i | \(-0.605116\pi\) | ||||
−0.324262 | + | 0.945967i | \(0.605116\pi\) | |||||||
\(252\) | 1.74122e39i | 0.414709i | ||||||||
\(253\) | − | 1.57738e39i | − | 0.351923i | ||||||
\(254\) | 1.05905e40 | 2.21391 | ||||||||
\(255\) | −4.35038e39 | + | 5.39587e39i | −0.852342 | + | 1.05718i | ||||
\(256\) | −9.22761e39 | −1.69484 | ||||||||
\(257\) | − | 7.67124e39i | − | 1.32120i | −0.750737 | − | 0.660601i | \(-0.770302\pi\) | ||
0.750737 | − | 0.660601i | \(-0.229698\pi\) | |||||||
\(258\) | − | 1.45588e39i | − | 0.235181i | ||||||
\(259\) | −1.35130e39 | −0.204789 | ||||||||
\(260\) | 9.97806e39 | + | 8.04473e39i | 1.41901 | + | 1.14407i | ||||
\(261\) | −1.17543e39 | −0.156902 | ||||||||
\(262\) | 1.12163e40i | 1.40565i | ||||||||
\(263\) | 1.76090e39i | 0.207236i | 0.994617 | + | 0.103618i | \(0.0330419\pi\) | ||||
−0.994617 | + | 0.103618i | \(0.966958\pi\) | |||||||
\(264\) | 3.22259e39 | 0.356238 | ||||||||
\(265\) | −7.77103e39 | − | 6.26533e39i | −0.807089 | − | 0.650710i | ||||
\(266\) | 8.75244e39 | 0.854244 | ||||||||
\(267\) | − | 9.82497e39i | − | 0.901354i | ||||||
\(268\) | 1.37541e40i | 1.18634i | ||||||||
\(269\) | −1.37145e38 | −0.0111241 | −0.00556206 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00556206 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(270\) | 1.45918e40 | − | 1.80986e40i | 1.11329 | − | 1.38084i | ||||
\(271\) | 1.20503e40 | 0.864978 | 0.432489 | − | 0.901639i | \(-0.357635\pi\) | ||||
0.432489 | + | 0.901639i | \(0.357635\pi\) | |||||||
\(272\) | − | 1.14910e40i | − | 0.776197i | ||||||
\(273\) | 2.57428e40i | 1.63671i | ||||||||
\(274\) | 1.93814e39 | 0.116012 | ||||||||
\(275\) | −1.02027e39 | − | 4.70083e39i | −0.0575074 | − | 0.264963i | ||||
\(276\) | −4.19079e40 | −2.22483 | ||||||||
\(277\) | − | 1.15971e40i | − | 0.580005i | −0.957026 | − | 0.290002i | \(-0.906344\pi\) | ||
0.957026 | − | 0.290002i | \(-0.0936561\pi\) | |||||||
\(278\) | − | 5.25642e39i | − | 0.247714i | ||||||
\(279\) | −1.96574e39 | −0.0873086 | ||||||||
\(280\) | 3.72293e40 | − | 4.61763e40i | 1.55875 | − | 1.93336i | ||||
\(281\) | −3.63872e40 | −1.43646 | −0.718232 | − | 0.695804i | \(-0.755048\pi\) | ||||
−0.718232 | + | 0.695804i | \(0.755048\pi\) | |||||||
\(282\) | 3.13415e40i | 1.16684i | ||||||||
\(283\) | 1.87432e40i | 0.658213i | 0.944293 | + | 0.329107i | \(0.106748\pi\) | ||||
−0.944293 | + | 0.329107i | \(0.893252\pi\) | |||||||
\(284\) | −4.86466e40 | −1.61176 | ||||||||
\(285\) | −6.68282e39 | − | 5.38797e39i | −0.208939 | − | 0.168455i | ||||
\(286\) | −1.53639e40 | −0.453378 | ||||||||
\(287\) | − | 4.17543e40i | − | 1.16319i | ||||||
\(288\) | − | 2.47324e39i | − | 0.0650564i | ||||||
\(289\) | −4.48762e40 | −1.11481 | ||||||||
\(290\) | 6.84782e40 | + | 5.52100e40i | 1.60689 | + | 1.29554i | ||||
\(291\) | −4.96875e40 | −1.10157 | ||||||||
\(292\) | 3.80467e40i | 0.797077i | ||||||||
\(293\) | 2.34908e40i | 0.465139i | 0.972580 | + | 0.232569i | \(0.0747132\pi\) | ||||
−0.972580 | + | 0.232569i | \(0.925287\pi\) | |||||||
\(294\) | 1.77703e41 | 3.32631 | ||||||||
\(295\) | 3.23659e40 | − | 4.01441e40i | 0.572828 | − | 0.710491i | ||||
\(296\) | −9.75366e39 | −0.163250 | ||||||||
\(297\) | 1.80397e40i | 0.285593i | ||||||||
\(298\) | − | 1.18763e41i | − | 1.77874i | ||||||
\(299\) | 9.09499e40 | 1.28893 | ||||||||
\(300\) | −1.24892e41 | + | 2.71065e40i | −1.67507 | + | 0.363557i | ||||
\(301\) | 2.07934e40 | 0.263985 | ||||||||
\(302\) | 4.77944e40i | 0.574463i | ||||||||
\(303\) | − | 6.28377e40i | − | 0.715182i | ||||||
\(304\) | 1.42317e40 | 0.153406 | ||||||||
\(305\) | −6.18057e40 | + | 7.66589e40i | −0.631075 | + | 0.782736i | ||||
\(306\) | 3.24024e40 | 0.313454 | ||||||||
\(307\) | − | 2.12921e40i | − | 0.195180i | −0.995227 | − | 0.0975901i | \(-0.968887\pi\) | ||
0.995227 | − | 0.0975901i | \(-0.0311134\pi\) | |||||||
\(308\) | 1.01110e41i | 0.878427i | ||||||||
\(309\) | 4.28793e40 | 0.353129 | ||||||||
\(310\) | 1.14520e41 | + | 9.23309e40i | 0.894157 | + | 0.720907i | ||||
\(311\) | 9.65601e40 | 0.714910 | 0.357455 | − | 0.933930i | \(-0.383645\pi\) | ||||
0.357455 | + | 0.933930i | \(0.383645\pi\) | |||||||
\(312\) | 1.85811e41i | 1.30473i | ||||||||
\(313\) | 2.25901e40i | 0.150465i | 0.997166 | + | 0.0752327i | \(0.0239700\pi\) | ||||
−0.997166 | + | 0.0752327i | \(0.976030\pi\) | |||||||
\(314\) | −3.29235e41 | −2.08050 | ||||||||
\(315\) | 2.93326e40 | + | 2.36492e40i | 0.175884 | + | 0.141805i | ||||
\(316\) | −5.06689e41 | −2.88340 | ||||||||
\(317\) | − | 1.90392e40i | − | 0.102842i | −0.998677 | − | 0.0514209i | \(-0.983625\pi\) | ||
0.998677 | − | 0.0514209i | \(-0.0163750\pi\) | |||||||
\(318\) | − | 3.17901e41i | − | 1.63021i | ||||||
\(319\) | −6.82554e40 | −0.332346 | ||||||||
\(320\) | −1.88617e41 | + | 2.33946e41i | −0.872179 | + | 1.08178i | ||||
\(321\) | 3.14024e41 | 1.37921 | ||||||||
\(322\) | − | 9.24621e41i | − | 3.85782i | ||||||
\(323\) | − | 1.05435e41i | − | 0.417968i | ||||||
\(324\) | 4.16909e41 | 1.57054 | ||||||||
\(325\) | 2.71044e41 | − | 5.88274e40i | 0.970432 | − | 0.210622i | ||||
\(326\) | 3.27724e41 | 1.11537 | ||||||||
\(327\) | 7.50788e40i | 0.242929i | ||||||||
\(328\) | − | 3.01382e41i | − | 0.927253i | ||||||
\(329\) | −4.47629e41 | −1.30974 | ||||||||
\(330\) | 9.61519e40 | − | 1.19259e41i | 0.267595 | − | 0.331904i | ||||
\(331\) | 8.34163e39 | 0.0220846 | 0.0110423 | − | 0.999939i | \(-0.496485\pi\) | ||||
0.0110423 | + | 0.999939i | \(0.496485\pi\) | |||||||
\(332\) | 1.22837e42i | 3.09422i | ||||||||
\(333\) | − | 6.19583e39i | − | 0.0148515i | ||||||
\(334\) | −7.75889e41 | −1.77004 | ||||||||
\(335\) | 2.31703e41 | + | 1.86809e41i | 0.503145 | + | 0.405657i | ||||
\(336\) | 4.25546e41 | 0.879727 | ||||||||
\(337\) | 1.27475e41i | 0.250918i | 0.992099 | + | 0.125459i | \(0.0400404\pi\) | ||||
−0.992099 | + | 0.125459i | \(0.959960\pi\) | |||||||
\(338\) | 1.24876e40i | 0.0234075i | ||||||||
\(339\) | 1.65093e39 | 0.00294737 | ||||||||
\(340\) | −1.22198e42 | − | 9.85211e41i | −2.07808 | − | 1.67543i | ||||
\(341\) | −1.14147e41 | −0.184935 | ||||||||
\(342\) | 4.01307e40i | 0.0619506i | ||||||||
\(343\) | 1.33821e42i | 1.96866i | ||||||||
\(344\) | 1.50086e41 | 0.210439 | ||||||||
\(345\) | −5.69194e41 | + | 7.05983e41i | −0.760756 | + | 0.943582i | ||||
\(346\) | 2.36330e42 | 3.01137 | ||||||||
\(347\) | − | 2.90496e41i | − | 0.352943i | −0.984306 | − | 0.176471i | \(-0.943532\pi\) | ||
0.984306 | − | 0.176471i | \(-0.0564683\pi\) | |||||||
\(348\) | 1.81341e42i | 2.10106i | ||||||||
\(349\) | 1.05476e42 | 1.16556 | 0.582779 | − | 0.812631i | \(-0.301965\pi\) | ||||
0.582779 | + | 0.812631i | \(0.301965\pi\) | |||||||
\(350\) | −5.98055e41 | − | 2.75551e42i | −0.630403 | − | 2.90455i | ||||
\(351\) | −1.04015e42 | −1.04599 | ||||||||
\(352\) | − | 1.43617e41i | − | 0.137801i | ||||||
\(353\) | 1.42033e42i | 1.30049i | 0.759724 | + | 0.650246i | \(0.225334\pi\) | ||||
−0.759724 | + | 0.650246i | \(0.774666\pi\) | |||||||
\(354\) | 1.64224e42 | 1.43510 | ||||||||
\(355\) | −6.60719e41 | + | 8.19504e41i | −0.551123 | + | 0.683570i | ||||
\(356\) | 2.22502e42 | 1.77177 | ||||||||
\(357\) | − | 3.15263e42i | − | 2.39689i | ||||||
\(358\) | − | 1.42937e42i | − | 1.03771i | ||||||
\(359\) | 3.15371e41 | 0.218657 | 0.109329 | − | 0.994006i | \(-0.465130\pi\) | ||||
0.109329 | + | 0.994006i | \(0.465130\pi\) | |||||||
\(360\) | 2.11722e41 | + | 1.70700e41i | 0.140209 | + | 0.113042i | ||||
\(361\) | −1.45019e42 | −0.917393 | ||||||||
\(362\) | 1.70787e42i | 1.03220i | ||||||||
\(363\) | − | 1.49815e42i | − | 0.865162i | ||||||
\(364\) | −5.82987e42 | −3.21726 | ||||||||
\(365\) | 6.40938e41 | + | 5.16752e41i | 0.338052 | + | 0.272552i | ||||
\(366\) | −3.13600e42 | −1.58102 | ||||||||
\(367\) | − | 3.83973e41i | − | 0.185059i | −0.995710 | − | 0.0925297i | \(-0.970505\pi\) | ||
0.995710 | − | 0.0925297i | \(-0.0294953\pi\) | |||||||
\(368\) | − | 1.50346e42i | − | 0.692792i | ||||||
\(369\) | 1.91447e41 | 0.0843555 | ||||||||
\(370\) | −2.91018e41 | + | 3.60956e41i | −0.122629 | + | 0.152099i | ||||
\(371\) | 4.54037e42 | 1.82988 | ||||||||
\(372\) | 3.03268e42i | 1.16914i | ||||||||
\(373\) | − | 2.58713e42i | − | 0.954164i | −0.878859 | − | 0.477082i | \(-0.841695\pi\) | ||
0.878859 | − | 0.477082i | \(-0.158305\pi\) | |||||||
\(374\) | 1.88156e42 | 0.663951 | ||||||||
\(375\) | −1.23965e42 | + | 2.47210e42i | −0.418583 | + | 0.834737i | ||||
\(376\) | −3.23098e42 | −1.04408 | ||||||||
\(377\) | − | 3.93553e42i | − | 1.21723i | ||||||
\(378\) | 1.05744e43i | 3.13071i | ||||||||
\(379\) | −1.90182e42 | −0.539042 | −0.269521 | − | 0.962994i | \(-0.586865\pi\) | ||||
−0.269521 | + | 0.962994i | \(0.586865\pi\) | |||||||
\(380\) | 1.22019e42 | − | 1.51343e42i | 0.331130 | − | 0.410708i | ||||
\(381\) | 4.72454e42 | 1.22771 | ||||||||
\(382\) | − | 3.41044e42i | − | 0.848720i | ||||||
\(383\) | − | 6.82259e42i | − | 1.62618i | −0.582135 | − | 0.813092i | \(-0.697783\pi\) | ||
0.582135 | − | 0.813092i | \(-0.302217\pi\) | |||||||
\(384\) | −7.49165e42 | −1.71046 | ||||||||
\(385\) | 1.70330e42 | + | 1.37327e42i | 0.372554 | + | 0.300369i | ||||
\(386\) | 1.15736e43 | 2.42537 | ||||||||
\(387\) | 9.53396e40i | 0.0191444i | ||||||||
\(388\) | − | 1.12525e43i | − | 2.16534i | ||||||
\(389\) | 2.03241e42 | 0.374837 | 0.187419 | − | 0.982280i | \(-0.439988\pi\) | ||||
0.187419 | + | 0.982280i | \(0.439988\pi\) | |||||||
\(390\) | 6.87636e42 | + | 5.54401e42i | 1.21561 | + | 0.980073i | ||||
\(391\) | −1.11383e43 | −1.88757 | ||||||||
\(392\) | 1.83193e43i | 2.97638i | ||||||||
\(393\) | 5.00372e42i | 0.779499i | ||||||||
\(394\) | 1.55241e43 | 2.31909 | ||||||||
\(395\) | −6.88186e42 | + | 8.53572e42i | −0.985947 | + | 1.22289i | ||||
\(396\) | −4.63596e41 | −0.0637044 | ||||||||
\(397\) | − | 7.63461e42i | − | 1.00634i | −0.864188 | − | 0.503168i | \(-0.832168\pi\) | ||
0.864188 | − | 0.503168i | \(-0.167832\pi\) | |||||||
\(398\) | − | 2.89258e42i | − | 0.365776i | ||||||
\(399\) | 3.90456e42 | 0.473717 | ||||||||
\(400\) | −9.72455e41 | − | 4.48054e42i | −0.113209 | − | 0.521603i | ||||
\(401\) | −1.09608e43 | −1.22450 | −0.612250 | − | 0.790664i | \(-0.709736\pi\) | ||||
−0.612250 | + | 0.790664i | \(0.709736\pi\) | |||||||
\(402\) | 9.47864e42i | 1.01629i | ||||||||
\(403\) | − | 6.58162e42i | − | 0.677328i | ||||||
\(404\) | 1.42306e43 | 1.40582 | ||||||||
\(405\) | 5.66246e42 | − | 7.02328e42i | 0.537029 | − | 0.666088i | ||||
\(406\) | −4.00097e43 | −3.64322 | ||||||||
\(407\) | − | 3.59782e41i | − | 0.0314580i | ||||||
\(408\) | − | 2.27557e43i | − | 1.91072i | ||||||
\(409\) | −1.27736e43 | −1.03010 | −0.515050 | − | 0.857160i | \(-0.672227\pi\) | ||||
−0.515050 | + | 0.857160i | \(0.672227\pi\) | |||||||
\(410\) | −1.11533e43 | − | 8.99227e42i | −0.863913 | − | 0.696523i | ||||
\(411\) | 8.64628e41 | 0.0643338 | ||||||||
\(412\) | 9.71070e42i | 0.694139i | ||||||||
\(413\) | 2.34549e43i | 1.61086i | ||||||||
\(414\) | 4.23947e42 | 0.279773 | ||||||||
\(415\) | 2.06932e43 | + | 1.66838e43i | 1.31231 | + | 1.05804i | ||||
\(416\) | 8.28080e42 | 0.504699 | ||||||||
\(417\) | − | 2.34495e42i | − | 0.137369i | ||||||
\(418\) | 2.33032e42i | 0.131222i | ||||||||
\(419\) | −1.81304e43 | −0.981467 | −0.490734 | − | 0.871310i | \(-0.663271\pi\) | ||||
−0.490734 | + | 0.871310i | \(0.663271\pi\) | |||||||
\(420\) | 3.64852e43 | − | 4.52534e43i | 1.89891 | − | 2.35525i | ||||
\(421\) | 1.35628e43 | 0.678724 | 0.339362 | − | 0.940656i | \(-0.389789\pi\) | ||||
0.339362 | + | 0.940656i | \(0.389789\pi\) | |||||||
\(422\) | − | 4.07877e43i | − | 1.96279i | ||||||
\(423\) | − | 2.05242e42i | − | 0.0949839i | ||||||
\(424\) | 3.27723e43 | 1.45871 | ||||||||
\(425\) | −3.31939e43 | + | 7.20439e42i | −1.42115 | + | 0.308446i | ||||
\(426\) | −3.35247e43 | −1.38072 | ||||||||
\(427\) | − | 4.47894e43i | − | 1.77466i | ||||||
\(428\) | 7.11156e43i | 2.71108i | ||||||||
\(429\) | −6.85399e42 | −0.251419 | ||||||||
\(430\) | 4.47810e42 | − | 5.55429e42i | 0.158075 | − | 0.196064i | ||||
\(431\) | 4.12465e43 | 1.40124 | 0.700620 | − | 0.713535i | \(-0.252907\pi\) | ||||
0.700620 | + | 0.713535i | \(0.252907\pi\) | |||||||
\(432\) | 1.71943e43i | 0.562216i | ||||||||
\(433\) | 5.05620e43i | 1.59138i | 0.605704 | + | 0.795690i | \(0.292892\pi\) | ||||
−0.605704 | + | 0.795690i | \(0.707108\pi\) | |||||||
\(434\) | −6.69105e43 | −2.02728 | ||||||||
\(435\) | 3.05489e43 | + | 2.46298e43i | 0.891092 | + | 0.718436i | ||||
\(436\) | −1.70028e43 | −0.477521 | ||||||||
\(437\) | − | 1.37949e43i | − | 0.373056i | ||||||
\(438\) | 2.62198e43i | 0.682822i | ||||||||
\(439\) | 2.66416e43 | 0.668182 | 0.334091 | − | 0.942541i | \(-0.391571\pi\) | ||||
0.334091 | + | 0.942541i | \(0.391571\pi\) | |||||||
\(440\) | 1.22944e43 | + | 9.91226e42i | 0.296987 | + | 0.239444i | ||||
\(441\) | −1.16370e43 | −0.270772 | ||||||||
\(442\) | 1.08489e44i | 2.43174i | ||||||||
\(443\) | 1.04497e43i | 0.225653i | 0.993615 | + | 0.112826i | \(0.0359904\pi\) | ||||
−0.993615 | + | 0.112826i | \(0.964010\pi\) | |||||||
\(444\) | −9.55870e42 | −0.198875 | ||||||||
\(445\) | 3.02202e43 | − | 3.74828e43i | 0.605840 | − | 0.751436i | ||||
\(446\) | −4.17630e43 | −0.806800 | ||||||||
\(447\) | − | 5.29815e43i | − | 0.986393i | ||||||
\(448\) | − | 1.36687e44i | − | 2.45268i | ||||||
\(449\) | 5.66906e43 | 0.980497 | 0.490248 | − | 0.871583i | \(-0.336906\pi\) | ||||
0.490248 | + | 0.871583i | \(0.336906\pi\) | |||||||
\(450\) | 1.26342e43 | − | 2.74213e42i | 0.210641 | − | 0.0457175i | ||||
\(451\) | 1.11170e43 | 0.178680 | ||||||||
\(452\) | 3.73879e41i | 0.00579358i | ||||||||
\(453\) | 2.13216e43i | 0.318566i | ||||||||
\(454\) | 5.51298e43 | 0.794264 | ||||||||
\(455\) | −7.91814e43 | + | 9.82104e43i | −1.10011 | + | 1.36449i | ||||
\(456\) | 2.81830e43 | 0.377631 | ||||||||
\(457\) | − | 1.11812e44i | − | 1.44501i | −0.691366 | − | 0.722505i | \(-0.742991\pi\) | ||
0.691366 | − | 0.722505i | \(-0.257009\pi\) | |||||||
\(458\) | − | 1.83650e44i | − | 2.28935i | ||||||
\(459\) | 1.27383e44 | 1.53181 | ||||||||
\(460\) | −1.59881e44 | − | 1.28903e44i | −1.85478 | − | 1.49540i | ||||
\(461\) | −2.91705e43 | −0.326496 | −0.163248 | − | 0.986585i | \(-0.552197\pi\) | ||||
−0.163248 | + | 0.986585i | \(0.552197\pi\) | |||||||
\(462\) | 6.96795e43i | 0.752510i | ||||||||
\(463\) | 1.20018e44i | 1.25072i | 0.780335 | + | 0.625362i | \(0.215048\pi\) | ||||
−0.780335 | + | 0.625362i | \(0.784952\pi\) | |||||||
\(464\) | −6.50569e43 | −0.654254 | ||||||||
\(465\) | 5.10887e43 | + | 4.11899e43i | 0.495851 | + | 0.399776i | ||||
\(466\) | 1.76319e43 | 0.165170 | ||||||||
\(467\) | 2.20756e43i | 0.199611i | 0.995007 | + | 0.0998054i | \(0.0318220\pi\) | ||||
−0.995007 | + | 0.0998054i | \(0.968178\pi\) | |||||||
\(468\) | − | 2.67304e43i | − | 0.233319i | ||||||
\(469\) | −1.35377e44 | −1.14076 | ||||||||
\(470\) | −9.64021e43 | + | 1.19570e44i | −0.784281 | + | 0.972761i | ||||
\(471\) | −1.46875e44 | −1.15373 | ||||||||
\(472\) | 1.69297e44i | 1.28412i | ||||||||
\(473\) | 5.53622e42i | 0.0405512i | ||||||||
\(474\) | −3.49184e44 | −2.47008 | ||||||||
\(475\) | −8.92269e42 | − | 4.11108e43i | −0.0609609 | − | 0.280874i | ||||
\(476\) | 7.13964e44 | 4.71152 | ||||||||
\(477\) | 2.08180e43i | 0.132704i | ||||||||
\(478\) | − | 1.47306e44i | − | 0.907108i | ||||||
\(479\) | −7.80915e43 | −0.464588 | −0.232294 | − | 0.972646i | \(-0.574623\pi\) | ||||
−0.232294 | + | 0.972646i | \(0.574623\pi\) | |||||||
\(480\) | −5.18239e43 | + | 6.42783e43i | −0.297886 | + | 0.369474i | ||||
\(481\) | 2.07446e43 | 0.115216 | ||||||||
\(482\) | 1.19709e44i | 0.642467i | ||||||||
\(483\) | − | 4.12484e44i | − | 2.13934i | ||||||
\(484\) | 3.39281e44 | 1.70063 | ||||||||
\(485\) | −1.89561e44 | − | 1.52832e44i | −0.918353 | − | 0.740415i | ||||
\(486\) | −9.14674e43 | −0.428320 | ||||||||
\(487\) | 4.19385e44i | 1.89839i | 0.314693 | + | 0.949194i | \(0.398099\pi\) | ||||
−0.314693 | + | 0.949194i | \(0.601901\pi\) | |||||||
\(488\) | − | 3.23289e44i | − | 1.41470i | ||||||
\(489\) | 1.46201e44 | 0.618522 | ||||||||
\(490\) | 6.77947e44 | + | 5.46589e44i | 2.77307 | + | 2.23576i | ||||
\(491\) | 4.24412e44 | 1.67859 | 0.839293 | − | 0.543680i | \(-0.182969\pi\) | ||||
0.839293 | + | 0.543680i | \(0.182969\pi\) | |||||||
\(492\) | − | 2.95358e44i | − | 1.12960i | ||||||
\(493\) | 4.81971e44i | 1.78257i | ||||||||
\(494\) | −1.34364e44 | −0.480604 | ||||||||
\(495\) | −6.29657e42 | + | 7.80978e42i | −0.0217830 | + | 0.0270180i | ||||
\(496\) | −1.08798e44 | −0.364061 | ||||||||
\(497\) | − | 4.78810e44i | − | 1.54983i | ||||||
\(498\) | 8.46530e44i | 2.65069i | ||||||||
\(499\) | −6.09953e44 | −1.84772 | −0.923862 | − | 0.382726i | \(-0.874985\pi\) | ||||
−0.923862 | + | 0.382726i | \(0.874985\pi\) | |||||||
\(500\) | −5.59845e44 | − | 2.80737e44i | −1.64083 | − | 0.822801i | ||||
\(501\) | −3.46133e44 | −0.981567 | ||||||||
\(502\) | − | 3.97976e44i | − | 1.09206i | ||||||
\(503\) | − | 3.00762e44i | − | 0.798639i | −0.916812 | − | 0.399320i | \(-0.869246\pi\) | ||
0.916812 | − | 0.399320i | \(-0.130754\pi\) | |||||||
\(504\) | −1.23703e44 | −0.317889 | ||||||||
\(505\) | 1.93280e44 | − | 2.39729e44i | 0.480706 | − | 0.596230i | ||||
\(506\) | 2.46179e44 | 0.592608 | ||||||||
\(507\) | 5.57087e42i | 0.0129805i | ||||||||
\(508\) | 1.06995e45i | 2.41330i | ||||||||
\(509\) | −1.45444e44 | −0.317578 | −0.158789 | − | 0.987313i | \(-0.550759\pi\) | ||||
−0.158789 | + | 0.987313i | \(0.550759\pi\) | |||||||
\(510\) | −8.42124e44 | − | 6.78956e44i | −1.78020 | − | 1.43527i | ||||
\(511\) | −3.74480e44 | −0.766450 | ||||||||
\(512\) | − | 5.15847e44i | − | 1.02227i | ||||||
\(513\) | 1.57765e44i | 0.302744i | ||||||||
\(514\) | 1.19724e45 | 2.22479 | ||||||||
\(515\) | 1.63587e44 | + | 1.31891e44i | 0.294395 | + | 0.237353i | ||||
\(516\) | 1.47086e44 | 0.256361 | ||||||||
\(517\) | − | 1.19181e44i | − | 0.201192i | ||||||
\(518\) | − | 2.10895e44i | − | 0.344847i | ||||||
\(519\) | 1.05430e45 | 1.66994 | ||||||||
\(520\) | −5.71530e44 | + | 7.08881e44i | −0.876968 | + | 1.08772i | ||||
\(521\) | 3.35096e44 | 0.498135 | 0.249067 | − | 0.968486i | \(-0.419876\pi\) | ||||
0.249067 | + | 0.968486i | \(0.419876\pi\) | |||||||
\(522\) | − | 1.83448e44i | − | 0.264210i | ||||||
\(523\) | − | 7.95243e44i | − | 1.10974i | −0.831937 | − | 0.554871i | \(-0.812768\pi\) | ||
0.831937 | − | 0.554871i | \(-0.187232\pi\) | |||||||
\(524\) | −1.13317e45 | −1.53225 | ||||||||
\(525\) | −2.66799e44 | − | 1.22926e45i | −0.349588 | − | 1.61071i | ||||
\(526\) | −2.74821e44 | −0.348967 | ||||||||
\(527\) | 8.06028e44i | 0.991916i | ||||||||
\(528\) | 1.13301e44i | 0.135137i | ||||||||
\(529\) | −5.92309e44 | −0.684747 | ||||||||
\(530\) | 9.77821e44 | − | 1.21281e45i | 1.09574 | − | 1.35907i | ||||
\(531\) | −1.07543e44 | −0.116821 | ||||||||
\(532\) | 8.84249e44i | 0.931178i | ||||||||
\(533\) | 6.40995e44i | 0.654419i | ||||||||
\(534\) | 1.53337e45 | 1.51780 | ||||||||
\(535\) | 1.19802e45 | + | 9.65894e44i | 1.14981 | + | 0.927026i | ||||
\(536\) | −9.77149e44 | −0.909372 | ||||||||
\(537\) | − | 6.37659e44i | − | 0.575457i | ||||||
\(538\) | − | 2.14039e43i | − | 0.0187321i | ||||||
\(539\) | −6.75741e44 | −0.573542 | ||||||||
\(540\) | 1.82848e45 | + | 1.47420e45i | 1.50520 | + | 1.21355i | ||||
\(541\) | 1.21161e45 | 0.967402 | 0.483701 | − | 0.875233i | \(-0.339292\pi\) | ||||
0.483701 | + | 0.875233i | \(0.339292\pi\) | |||||||
\(542\) | 1.88067e45i | 1.45655i | ||||||||
\(543\) | 7.61900e44i | 0.572401i | ||||||||
\(544\) | −1.01412e45 | −0.739108 | ||||||||
\(545\) | −2.30932e44 | + | 2.86430e44i | −0.163283 | + | 0.202524i | ||||
\(546\) | −4.01764e45 | −2.75609 | ||||||||
\(547\) | 1.99236e45i | 1.32610i | 0.748573 | + | 0.663052i | \(0.230739\pi\) | ||||
−0.748573 | + | 0.663052i | \(0.769261\pi\) | |||||||
\(548\) | 1.95808e44i | 0.126460i | ||||||||
\(549\) | 2.05363e44 | 0.128700 | ||||||||
\(550\) | 7.33651e44 | − | 1.59231e44i | 0.446175 | − | 0.0968376i | ||||
\(551\) | −5.96924e44 | −0.352304 | ||||||||
\(552\) | − | 2.97730e45i | − | 1.70541i | ||||||
\(553\) | − | 4.98715e45i | − | 2.77260i | ||||||
\(554\) | 1.80993e45 | 0.976679 | ||||||||
\(555\) | −1.29827e44 | + | 1.61027e44i | −0.0680032 | + | 0.0843458i | ||||
\(556\) | 5.31051e44 | 0.270024 | ||||||||
\(557\) | 1.74444e45i | 0.861082i | 0.902571 | + | 0.430541i | \(0.141677\pi\) | ||||
−0.902571 | + | 0.430541i | \(0.858323\pi\) | |||||||
\(558\) | − | 3.06790e44i | − | 0.147020i | ||||||
\(559\) | −3.19212e44 | −0.148520 | ||||||||
\(560\) | 1.62348e45 | + | 1.30892e45i | 0.733407 | + | 0.591303i | ||||
\(561\) | 8.39384e44 | 0.368191 | ||||||||
\(562\) | − | 5.67890e45i | − | 2.41888i | ||||||
\(563\) | 1.30371e45i | 0.539251i | 0.962965 | + | 0.269626i | \(0.0868999\pi\) | ||||
−0.962965 | + | 0.269626i | \(0.913100\pi\) | |||||||
\(564\) | −3.16640e45 | −1.27192 | ||||||||
\(565\) | 6.29840e42 | + | 5.07804e42i | 0.00245715 | + | 0.00198105i | ||||
\(566\) | −2.92522e45 | −1.10838 | ||||||||
\(567\) | 4.10348e45i | 1.51019i | ||||||||
\(568\) | − | 3.45604e45i | − | 1.23547i | ||||||
\(569\) | −8.99757e43 | −0.0312445 | −0.0156222 | − | 0.999878i | \(-0.504973\pi\) | ||||
−0.0156222 | + | 0.999878i | \(0.504973\pi\) | |||||||
\(570\) | 8.40892e44 | − | 1.04298e45i | 0.283665 | − | 0.351835i | ||||
\(571\) | 2.85011e45 | 0.934039 | 0.467020 | − | 0.884247i | \(-0.345328\pi\) | ||||
0.467020 | + | 0.884247i | \(0.345328\pi\) | |||||||
\(572\) | − | 1.55219e45i | − | 0.494210i | ||||||
\(573\) | − | 1.52143e45i | − | 0.470654i | ||||||
\(574\) | 6.51653e45 | 1.95871 | ||||||||
\(575\) | −4.34302e45 | + | 9.42607e44i | −1.26845 | + | 0.275303i | ||||
\(576\) | 6.26722e44 | 0.177870 | ||||||||
\(577\) | 6.49472e45i | 1.79126i | 0.444797 | + | 0.895632i | \(0.353276\pi\) | ||||
−0.444797 | + | 0.895632i | \(0.646724\pi\) | |||||||
\(578\) | − | 7.00376e45i | − | 1.87725i | ||||||
\(579\) | 5.16312e45 | 1.34498 | ||||||||
\(580\) | −5.57781e45 | + | 6.91828e45i | −1.41222 | + | 1.75160i | ||||
\(581\) | −1.20904e46 | −2.97533 | ||||||||
\(582\) | − | 7.75465e45i | − | 1.85495i | ||||||
\(583\) | 1.20887e45i | 0.281091i | ||||||||
\(584\) | −2.70299e45 | −0.610988 | ||||||||
\(585\) | −4.50303e44 | − | 3.63053e44i | −0.0989539 | − | 0.0797808i | ||||
\(586\) | −3.66618e45 | −0.783254 | ||||||||
\(587\) | − | 5.04614e44i | − | 0.104817i | −0.998626 | − | 0.0524084i | \(-0.983310\pi\) | ||
0.998626 | − | 0.0524084i | \(-0.0166898\pi\) | |||||||
\(588\) | 1.79531e46i | 3.62588i | ||||||||
\(589\) | −9.98271e44 | −0.196041 | ||||||||
\(590\) | 6.26523e45 | + | 5.05129e45i | 1.19641 | + | 0.964594i | ||||
\(591\) | 6.92546e45 | 1.28604 | ||||||||
\(592\) | − | 3.42922e44i | − | 0.0619280i | ||||||
\(593\) | − | 1.38106e45i | − | 0.242555i | −0.992619 | − | 0.121277i | \(-0.961301\pi\) | ||
0.992619 | − | 0.121277i | \(-0.0386990\pi\) | |||||||
\(594\) | −2.81543e45 | −0.480915 | ||||||||
\(595\) | 9.69707e45 | − | 1.20275e46i | 1.61106 | − | 1.99823i | ||||
\(596\) | 1.19985e46 | 1.93894 | ||||||||
\(597\) | − | 1.29041e45i | − | 0.202839i | ||||||
\(598\) | 1.41944e46i | 2.17044i | ||||||||
\(599\) | 7.75620e45 | 1.15374 | 0.576868 | − | 0.816837i | \(-0.304275\pi\) | ||||
0.576868 | + | 0.816837i | \(0.304275\pi\) | |||||||
\(600\) | −1.92575e45 | − | 8.87281e45i | −0.278679 | − | 1.28400i | ||||
\(601\) | −1.97032e45 | −0.277400 | −0.138700 | − | 0.990334i | \(-0.544292\pi\) | ||||
−0.138700 | + | 0.990334i | \(0.544292\pi\) | |||||||
\(602\) | 3.24520e45i | 0.444528i | ||||||||
\(603\) | − | 6.20715e44i | − | 0.0827288i | ||||||
\(604\) | −4.82861e45 | −0.626200 | ||||||||
\(605\) | 4.60812e45 | − | 5.71555e45i | 0.581513 | − | 0.721264i | ||||
\(606\) | 9.80698e45 | 1.20431 | ||||||||
\(607\) | − | 3.36784e45i | − | 0.402474i | −0.979543 | − | 0.201237i | \(-0.935504\pi\) | ||
0.979543 | − | 0.201237i | \(-0.0644962\pi\) | |||||||
\(608\) | − | 1.25600e45i | − | 0.146076i | ||||||
\(609\) | −1.78488e46 | −2.02033 | ||||||||
\(610\) | −1.19640e46 | − | 9.64591e45i | −1.31806 | − | 1.06268i | ||||
\(611\) | 6.87182e45 | 0.736872 | ||||||||
\(612\) | 3.27358e45i | 0.341684i | ||||||||
\(613\) | − | 9.87239e45i | − | 1.00305i | −0.865142 | − | 0.501527i | \(-0.832772\pi\) | ||
0.865142 | − | 0.501527i | \(-0.167228\pi\) | |||||||
\(614\) | 3.32303e45 | 0.328667 | ||||||||
\(615\) | −4.97562e45 | − | 4.01155e45i | −0.479079 | − | 0.386254i | ||||
\(616\) | −7.18322e45 | −0.673345 | ||||||||
\(617\) | 3.29814e45i | 0.300998i | 0.988610 | + | 0.150499i | \(0.0480880\pi\) | ||||
−0.988610 | + | 0.150499i | \(0.951912\pi\) | |||||||
\(618\) | 6.69211e45i | 0.594639i | ||||||||
\(619\) | −1.65886e46 | −1.43521 | −0.717604 | − | 0.696451i | \(-0.754761\pi\) | ||||
−0.717604 | + | 0.696451i | \(0.754761\pi\) | |||||||
\(620\) | −9.32809e45 | + | 1.15698e46i | −0.785832 | + | 0.974685i | ||||
\(621\) | 1.66666e46 | 1.36721 | ||||||||
\(622\) | 1.50700e46i | 1.20385i | ||||||||
\(623\) | 2.19000e46i | 1.70370i | ||||||||
\(624\) | −6.53280e45 | −0.494941 | ||||||||
\(625\) | −1.23332e46 | + | 5.61822e45i | −0.910026 | + | 0.414551i | ||||
\(626\) | −3.52560e45 | −0.253371 | ||||||||
\(627\) | 1.03958e45i | 0.0727688i | ||||||||
\(628\) | − | 3.32623e46i | − | 2.26787i | ||||||
\(629\) | −2.54052e45 | −0.168728 | ||||||||
\(630\) | −3.69090e45 | + | 4.57790e45i | −0.238788 | + | 0.296174i | ||||
\(631\) | 5.39111e45 | 0.339777 | 0.169888 | − | 0.985463i | \(-0.445659\pi\) | ||||
0.169888 | + | 0.985463i | \(0.445659\pi\) | |||||||
\(632\) | − | 3.59972e46i | − | 2.21023i | ||||||
\(633\) | − | 1.81958e46i | − | 1.08846i | ||||||
\(634\) | 2.97141e45 | 0.173177 | ||||||||
\(635\) | 1.80244e46 | + | 1.45320e46i | 1.02352 | + | 0.825201i | ||||
\(636\) | 3.21172e46 | 1.77703 | ||||||||
\(637\) | − | 3.89625e46i | − | 2.10061i | ||||||
\(638\) | − | 1.06525e46i | − | 0.559643i | ||||||
\(639\) | 2.19539e45 | 0.112395 | ||||||||
\(640\) | −2.85811e46 | − | 2.30433e46i | −1.42597 | − | 1.14967i | ||||
\(641\) | −3.59612e46 | −1.74854 | −0.874271 | − | 0.485438i | \(-0.838660\pi\) | ||||
−0.874271 | + | 0.485438i | \(0.838660\pi\) | |||||||
\(642\) | 4.90092e46i | 2.32247i | ||||||||
\(643\) | 3.23556e46i | 1.49441i | 0.664596 | + | 0.747203i | \(0.268604\pi\) | ||||
−0.664596 | + | 0.747203i | \(0.731396\pi\) | |||||||
\(644\) | 9.34135e46 | 4.20526 | ||||||||
\(645\) | 1.99773e45 | − | 2.47783e45i | 0.0876601 | − | 0.108727i | ||||
\(646\) | 1.64551e46 | 0.703823 | ||||||||
\(647\) | − | 5.30852e45i | − | 0.221336i | −0.993857 | − | 0.110668i | \(-0.964701\pi\) | ||
0.993857 | − | 0.110668i | \(-0.0352991\pi\) | |||||||
\(648\) | 2.96188e46i | 1.20387i | ||||||||
\(649\) | −6.24485e45 | −0.247448 | ||||||||
\(650\) | 9.18110e45 | + | 4.23015e46i | 0.354670 | + | 1.63412i | ||||
\(651\) | −2.98495e46 | −1.12422 | ||||||||
\(652\) | 3.31096e46i | 1.21582i | ||||||||
\(653\) | − | 2.38611e46i | − | 0.854326i | −0.904175 | − | 0.427163i | \(-0.859513\pi\) | ||
0.904175 | − | 0.427163i | \(-0.140487\pi\) | |||||||
\(654\) | −1.17174e46 | −0.409072 | ||||||||
\(655\) | −1.53907e46 | + | 1.90895e46i | −0.523936 | + | 0.649849i | ||||
\(656\) | 1.05961e46 | 0.351748 | ||||||||
\(657\) | − | 1.71702e45i | − | 0.0555837i | ||||||
\(658\) | − | 6.98608e46i | − | 2.20550i | ||||||
\(659\) | −2.81962e46 | −0.868122 | −0.434061 | − | 0.900883i | \(-0.642920\pi\) | ||||
−0.434061 | + | 0.900883i | \(0.642920\pi\) | |||||||
\(660\) | 1.20486e46 | + | 9.71413e45i | 0.361796 | + | 0.291695i | ||||
\(661\) | 3.38643e46 | 0.991786 | 0.495893 | − | 0.868384i | \(-0.334841\pi\) | ||||
0.495893 | + | 0.868384i | \(0.334841\pi\) | |||||||
\(662\) | 1.30187e45i | 0.0371886i | ||||||||
\(663\) | 4.83980e46i | 1.34851i | ||||||||
\(664\) | −8.72683e46 | −2.37183 | ||||||||
\(665\) | 1.48961e46 | + | 1.20099e46i | 0.394926 | + | 0.318406i | ||||
\(666\) | 9.66973e44 | 0.0250086 | ||||||||
\(667\) | 6.30600e46i | 1.59103i | ||||||||
\(668\) | − | 7.83872e46i | − | 1.92945i | ||||||
\(669\) | −1.86309e46 | −0.447408 | ||||||||
\(670\) | −2.91550e46 | + | 3.61616e46i | −0.683091 | + | 0.847253i | ||||
\(671\) | 1.19251e46 | 0.272609 | ||||||||
\(672\) | − | 3.75558e46i | − | 0.837692i | ||||||
\(673\) | − | 3.57808e46i | − | 0.778756i | −0.921078 | − | 0.389378i | \(-0.872690\pi\) | ||
0.921078 | − | 0.389378i | \(-0.127310\pi\) | |||||||
\(674\) | −1.98949e46 | −0.422525 | ||||||||
\(675\) | 4.96689e46 | − | 1.07801e46i | 1.02937 | − | 0.223415i | ||||
\(676\) | −1.26161e45 | −0.0255156 | ||||||||
\(677\) | − | 6.06906e46i | − | 1.19787i | −0.800799 | − | 0.598933i | \(-0.795591\pi\) | ||
0.800799 | − | 0.598933i | \(-0.204409\pi\) | |||||||
\(678\) | 2.57658e44i | 0.00496311i | ||||||||
\(679\) | 1.10754e47 | 2.08214 | ||||||||
\(680\) | 6.99933e46 | − | 8.68142e46i | 1.28428 | − | 1.59292i | ||||
\(681\) | 2.45940e46 | 0.440456 | ||||||||
\(682\) | − | 1.78148e46i | − | 0.311415i | ||||||
\(683\) | 6.22121e46i | 1.06153i | 0.847518 | + | 0.530766i | \(0.178096\pi\) | ||||
−0.847518 | + | 0.530766i | \(0.821904\pi\) | |||||||
\(684\) | −4.05436e45 | −0.0675299 | ||||||||
\(685\) | 3.29860e45 | + | 2.65947e45i | 0.0536335 | + | 0.0432416i | ||||
\(686\) | −2.08853e47 | −3.31506 | ||||||||
\(687\) | − | 8.19285e46i | − | 1.26955i | ||||||
\(688\) | 5.27678e45i | 0.0798289i | ||||||||
\(689\) | −6.97019e46 | −1.02950 | ||||||||
\(690\) | −1.10182e47 | − | 8.88332e46i | −1.58891 | − | 1.28105i | ||||
\(691\) | 1.23978e47 | 1.74565 | 0.872825 | − | 0.488033i | \(-0.162285\pi\) | ||||
0.872825 | + | 0.488033i | \(0.162285\pi\) | |||||||
\(692\) | 2.38762e47i | 3.28258i | ||||||||
\(693\) | − | 4.56301e45i | − | 0.0612566i | ||||||
\(694\) | 4.53373e46 | 0.594326 | ||||||||
\(695\) | 7.21274e45 | − | 8.94612e45i | 0.0923317 | − | 0.114521i | ||||
\(696\) | −1.28832e47 | −1.61054 | ||||||||
\(697\) | − | 7.85005e46i | − | 0.958366i | ||||||
\(698\) | 1.64615e47i | 1.96270i | ||||||||
\(699\) | 7.86579e45 | 0.0915944 | ||||||||
\(700\) | 2.78386e47 | − | 6.04209e46i | 3.16614 | − | 0.687178i | ||||
\(701\) | −7.57725e46 | −0.841713 | −0.420857 | − | 0.907127i | \(-0.638270\pi\) | ||||
−0.420857 | + | 0.907127i | \(0.638270\pi\) | |||||||
\(702\) | − | 1.62334e47i | − | 1.76136i | ||||||
\(703\) | − | 3.14645e45i | − | 0.0333471i | ||||||
\(704\) | 3.63927e46 | 0.376761 | ||||||||
\(705\) | −4.30061e46 | + | 5.33414e46i | −0.434920 | + | 0.539441i | ||||
\(706\) | −2.21669e47 | −2.18992 | ||||||||
\(707\) | 1.40066e47i | 1.35180i | ||||||||
\(708\) | 1.65913e47i | 1.56435i | ||||||||
\(709\) | 9.15900e46 | 0.843694 | 0.421847 | − | 0.906667i | \(-0.361382\pi\) | ||||
0.421847 | + | 0.906667i | \(0.361382\pi\) | |||||||
\(710\) | −1.27899e47 | − | 1.03117e47i | −1.15107 | − | 0.928045i | ||||
\(711\) | 2.28665e46 | 0.201072 | ||||||||
\(712\) | 1.58074e47i | 1.35813i | ||||||||
\(713\) | 1.05459e47i | 0.885332i | ||||||||
\(714\) | 4.92027e47 | 4.03616 | ||||||||
\(715\) | −2.61484e46 | − | 2.10819e46i | −0.209602 | − | 0.168990i | ||||
\(716\) | 1.44408e47 | 1.13117 | ||||||||
\(717\) | − | 6.57147e46i | − | 0.503033i | ||||||
\(718\) | 4.92195e46i | 0.368200i | ||||||||
\(719\) | −1.43667e47 | −1.05034 | −0.525169 | − | 0.850998i | \(-0.675998\pi\) | ||||
−0.525169 | + | 0.850998i | \(0.675998\pi\) | |||||||
\(720\) | −6.00151e45 | + | 7.44380e45i | −0.0428819 | + | 0.0531874i | ||||
\(721\) | −9.55788e46 | −0.667467 | ||||||||
\(722\) | − | 2.26329e47i | − | 1.54481i | ||||||
\(723\) | 5.34036e46i | 0.356277i | ||||||||
\(724\) | −1.72544e47 | −1.12516 | ||||||||
\(725\) | 4.07879e46 | + | 1.87928e47i | 0.259989 | + | 1.19789i | ||||
\(726\) | 2.33815e47 | 1.45686 | ||||||||
\(727\) | − | 9.62263e46i | − | 0.586106i | −0.956096 | − | 0.293053i | \(-0.905329\pi\) | ||
0.956096 | − | 0.293053i | \(-0.0946712\pi\) | |||||||
\(728\) | − | 4.14177e47i | − | 2.46614i | ||||||
\(729\) | −1.87793e47 | −1.09314 | ||||||||
\(730\) | −8.06486e46 | + | 1.00030e47i | −0.458955 | + | 0.569251i | ||||
\(731\) | 3.90928e46 | 0.217500 | ||||||||
\(732\) | − | 3.16827e47i | − | 1.72341i | ||||||
\(733\) | − | 1.83322e47i | − | 0.974988i | −0.873126 | − | 0.487494i | \(-0.837911\pi\) | ||
0.873126 | − | 0.487494i | \(-0.162089\pi\) | |||||||
\(734\) | 5.99261e46 | 0.311624 | ||||||||
\(735\) | 3.02440e47 | + | 2.43840e47i | 1.53779 | + | 1.23983i | ||||
\(736\) | −1.32685e47 | −0.659689 | ||||||||
\(737\) | − | 3.60439e46i | − | 0.175234i | ||||||
\(738\) | 2.98788e46i | 0.142048i | ||||||||
\(739\) | −2.28000e47 | −1.05999 | −0.529996 | − | 0.848000i | \(-0.677806\pi\) | ||||
−0.529996 | + | 0.848000i | \(0.677806\pi\) | |||||||
\(740\) | −3.64670e46 | − | 2.94013e46i | −0.165797 | − | 0.133673i | ||||
\(741\) | −5.99412e46 | −0.266517 | ||||||||
\(742\) | 7.08608e47i | 3.08135i | ||||||||
\(743\) | − | 4.61345e46i | − | 0.196205i | −0.995176 | − | 0.0981026i | \(-0.968723\pi\) | ||
0.995176 | − | 0.0981026i | \(-0.0312773\pi\) | |||||||
\(744\) | −2.15453e47 | −0.896189 | ||||||||
\(745\) | 1.62964e47 | − | 2.02128e47i | 0.662999 | − | 0.822332i | ||||
\(746\) | 4.03770e47 | 1.60673 | ||||||||
\(747\) | − | 5.54356e46i | − | 0.215774i | ||||||
\(748\) | 1.90092e47i | 0.723747i | ||||||||
\(749\) | −6.99965e47 | −2.60691 | ||||||||
\(750\) | −3.85816e47 | − | 1.93470e47i | −1.40563 | − | 0.704858i | ||||
\(751\) | −3.50719e46 | −0.124997 | −0.0624986 | − | 0.998045i | \(-0.519907\pi\) | ||||
−0.0624986 | + | 0.998045i | \(0.519907\pi\) | |||||||
\(752\) | − | 1.13596e47i | − | 0.396066i | ||||||
\(753\) | − | 1.77542e47i | − | 0.605597i | ||||||
\(754\) | 6.14212e47 | 2.04970 | ||||||||
\(755\) | −6.55823e46 | + | 8.13432e46i | −0.214122 | + | 0.265581i | ||||
\(756\) | −1.06832e48 | −3.41266 | ||||||||
\(757\) | − | 1.87145e47i | − | 0.584921i | −0.956278 | − | 0.292460i | \(-0.905526\pi\) | ||
0.956278 | − | 0.292460i | \(-0.0944739\pi\) | |||||||
\(758\) | − | 2.96814e47i | − | 0.907701i | ||||||
\(759\) | 1.09823e47 | 0.328628 | ||||||||
\(760\) | 1.07520e47 | + | 8.66872e46i | 0.314822 | + | 0.253823i | ||||
\(761\) | 2.20228e47 | 0.630994 | 0.315497 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315497 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(762\) | 7.37352e47i | 2.06737i | ||||||||
\(763\) | − | 1.67352e47i | − | 0.459173i | ||||||
\(764\) | 3.44553e47 | 0.925157 | ||||||||
\(765\) | 5.51470e46 | + | 4.44619e46i | 0.144913 | + | 0.116835i | ||||
\(766\) | 1.06479e48 | 2.73836 | ||||||||
\(767\) | − | 3.60071e47i | − | 0.906284i | ||||||
\(768\) | − | 6.42462e47i | − | 1.58266i | ||||||
\(769\) | 2.66239e47 | 0.641928 | 0.320964 | − | 0.947091i | \(-0.395993\pi\) | ||||
0.320964 | + | 0.947091i | \(0.395993\pi\) | |||||||
\(770\) | −2.14325e47 | + | 2.65831e47i | −0.505795 | + | 0.627349i | ||||
\(771\) | 5.34102e47 | 1.23375 | ||||||||
\(772\) | 1.16927e48i | 2.64380i | ||||||||
\(773\) | − | 5.04292e45i | − | 0.0111614i | −0.999984 | − | 0.00558072i | \(-0.998224\pi\) | ||
0.999984 | − | 0.00558072i | \(-0.00177641\pi\) | |||||||
\(774\) | −1.48795e46 | −0.0322376 | ||||||||
\(775\) | 6.82120e46 | + | 3.14284e47i | 0.144671 | + | 0.666567i | ||||
\(776\) | 7.99423e47 | 1.65981 | ||||||||
\(777\) | − | 9.40828e46i | − | 0.191233i | ||||||
\(778\) | 3.17195e47i | 0.631194i | ||||||||
\(779\) | 9.72234e46 | 0.189410 | ||||||||
\(780\) | −5.60106e47 | + | 6.94711e47i | −1.06834 | + | 1.32508i | ||||
\(781\) | 1.27483e47 | 0.238072 | ||||||||
\(782\) | − | 1.73834e48i | − | 3.17851i | ||||||
\(783\) | − | 7.21186e47i | − | 1.29115i | ||||||
\(784\) | −6.44075e47 | −1.12907 | ||||||||
\(785\) | −5.60338e47 | − | 4.51769e47i | −0.961836 | − | 0.775473i | ||||
\(786\) | −7.80922e47 | −1.31261 | ||||||||
\(787\) | 1.14740e48i | 1.88857i | 0.329133 | + | 0.944283i | \(0.393243\pi\) | ||||
−0.329133 | + | 0.944283i | \(0.606757\pi\) | |||||||
\(788\) | 1.56838e48i | 2.52795i | ||||||||
\(789\) | −1.22601e47 | −0.193518 | ||||||||
\(790\) | −1.33216e48 | − | 1.07404e48i | −2.05925 | − | 1.66025i | ||||
\(791\) | −3.67996e45 | −0.00557097 | ||||||||
\(792\) | − | 3.29357e46i | − | 0.0488316i | ||||||
\(793\) | 6.87589e47i | 0.998438i | ||||||||
\(794\) | 1.19152e48 | 1.69459 | ||||||||
\(795\) | 4.36217e47 | − | 5.41049e47i | 0.607638 | − | 0.753666i | ||||
\(796\) | 2.92234e47 | 0.398718 | ||||||||
\(797\) | 1.04385e48i | 1.39501i | 0.716582 | + | 0.697503i | \(0.245706\pi\) | ||||
−0.716582 | + | 0.697503i | \(0.754294\pi\) | |||||||
\(798\) | 6.09379e47i | 0.797700i | ||||||||
\(799\) | −8.41568e47 | −1.07911 | ||||||||
\(800\) | −3.95423e47 | + | 8.58224e46i | −0.496680 | + | 0.107799i | ||||
\(801\) | −1.00414e47 | −0.123554 | ||||||||
\(802\) | − | 1.71063e48i | − | 2.06196i | ||||||
\(803\) | − | 9.97048e46i | − | 0.117736i | ||||||
\(804\) | −9.57617e47 | −1.10781 | ||||||||
\(805\) | 1.26874e48 | − | 1.57365e48i | 1.43794 | − | 1.78351i | ||||
\(806\) | 1.02718e48 | 1.14056 | ||||||||
\(807\) | − | 9.54854e45i | − | 0.0103878i | ||||||
\(808\) | 1.01100e48i | 1.07761i | ||||||||
\(809\) | −1.19411e48 | −1.24707 | −0.623537 | − | 0.781794i | \(-0.714305\pi\) | ||||
−0.623537 | + | 0.781794i | \(0.714305\pi\) | |||||||
\(810\) | 1.09611e48 | + | 8.83732e47i | 1.12164 | + | 0.904311i | ||||
\(811\) | −1.04748e48 | −1.05027 | −0.525134 | − | 0.851019i | \(-0.675985\pi\) | ||||
−0.525134 | + | 0.851019i | \(0.675985\pi\) | |||||||
\(812\) | − | 4.04213e48i | − | 3.97133i | ||||||
\(813\) | 8.38990e47i | 0.807723i | ||||||||
\(814\) | 5.61506e46 | 0.0529727 | ||||||||
\(815\) | 5.57766e47 | + | 4.49695e47i | 0.515646 | + | 0.415736i | ||||
\(816\) | 8.00050e47 | 0.724819 | ||||||||
\(817\) | 4.84167e46i | 0.0429864i | ||||||||
\(818\) | − | 1.99356e48i | − | 1.73460i | ||||||
\(819\) | 2.63098e47 | 0.224354 | ||||||||
\(820\) | 9.08479e47 | − | 1.12681e48i | 0.759253 | − | 0.941718i | ||||
\(821\) | 8.56741e47 | 0.701758 | 0.350879 | − | 0.936421i | \(-0.385883\pi\) | ||||
0.350879 | + | 0.936421i | \(0.385883\pi\) | |||||||
\(822\) | 1.34941e47i | 0.108333i | ||||||||
\(823\) | − | 4.60629e47i | − | 0.362455i | −0.983441 | − | 0.181228i | \(-0.941993\pi\) | ||
0.983441 | − | 0.181228i | \(-0.0580070\pi\) | |||||||
\(824\) | −6.89886e47 | −0.532082 | ||||||||
\(825\) | 3.27290e47 | − | 7.10349e46i | 0.247424 | − | 0.0537009i | ||||
\(826\) | −3.66058e48 | −2.71256 | ||||||||
\(827\) | 2.09756e48i | 1.52361i | 0.647808 | + | 0.761803i | \(0.275686\pi\) | ||||
−0.647808 | + | 0.761803i | \(0.724314\pi\) | |||||||
\(828\) | 4.28309e47i | 0.304970i | ||||||||
\(829\) | 2.34867e48 | 1.63935 | 0.819675 | − | 0.572828i | \(-0.194154\pi\) | ||||
0.819675 | + | 0.572828i | \(0.194154\pi\) | |||||||
\(830\) | −2.60381e48 | + | 3.22956e48i | −1.78164 | + | 2.20981i | ||||
\(831\) | 8.07432e47 | 0.541613 | ||||||||
\(832\) | 2.09836e48i | 1.37989i | ||||||||
\(833\) | 4.77160e48i | 3.07625i | ||||||||
\(834\) | 3.65973e47 | 0.231318 | ||||||||
\(835\) | −1.32052e48 | − | 1.06466e48i | −0.818308 | − | 0.659755i | ||||
\(836\) | −2.35430e47 | −0.143040 | ||||||||
\(837\) | − | 1.20608e48i | − | 0.718467i | ||||||
\(838\) | − | 2.82958e48i | − | 1.65271i | ||||||
\(839\) | −3.05667e48 | −1.75056 | −0.875279 | − | 0.483618i | \(-0.839322\pi\) | ||||
−0.875279 | + | 0.483618i | \(0.839322\pi\) | |||||||
\(840\) | 3.21498e48 | + | 2.59205e48i | 1.80538 | + | 1.45558i | ||||
\(841\) | 9.12620e47 | 0.502523 | ||||||||
\(842\) | 2.11672e48i | 1.14291i | ||||||||
\(843\) | − | 2.53342e48i | − | 1.34138i | ||||||
\(844\) | 4.12074e48 | 2.13956 | ||||||||
\(845\) | −1.71352e46 | + | 2.12532e46i | −0.00872478 | + | 0.0108215i | ||||
\(846\) | 3.20318e47 | 0.159945 | ||||||||
\(847\) | 3.33942e48i | 1.63529i | ||||||||
\(848\) | 1.15222e48i | 0.553354i | ||||||||
\(849\) | −1.30497e48 | −0.614645 | ||||||||
\(850\) | −1.12438e48 | − | 5.18052e48i | −0.519398 | − | 2.39310i | ||||
\(851\) | −3.32397e47 | −0.150598 | ||||||||
\(852\) | − | 3.38696e48i | − | 1.50507i | ||||||
\(853\) | − | 3.72611e48i | − | 1.62404i | −0.583629 | − | 0.812021i | \(-0.698368\pi\) | ||
0.583629 | − | 0.812021i | \(-0.301632\pi\) | |||||||
\(854\) | 6.99021e48 | 2.98838 | ||||||||
\(855\) | −5.50664e46 | + | 6.83000e46i | −0.0230911 | + | 0.0286405i | ||||
\(856\) | −5.05233e48 | −2.07814 | ||||||||
\(857\) | − | 6.05125e47i | − | 0.244153i | −0.992521 | − | 0.122076i | \(-0.961045\pi\) | ||
0.992521 | − | 0.122076i | \(-0.0389553\pi\) | |||||||
\(858\) | − | 1.06969e48i | − | 0.423368i | ||||||
\(859\) | −2.95430e48 | −1.14701 | −0.573505 | − | 0.819202i | \(-0.694417\pi\) | ||||
−0.573505 | + | 0.819202i | \(0.694417\pi\) | |||||||
\(860\) | 5.61144e47 | + | 4.52418e47i | 0.213722 | + | 0.172312i | ||||
\(861\) | 2.90710e48 | 1.08619 | ||||||||
\(862\) | 6.43728e48i | 2.35957i | ||||||||
\(863\) | − | 5.76096e47i | − | 0.207165i | −0.994621 | − | 0.103583i | \(-0.966969\pi\) | ||
0.994621 | − | 0.103583i | \(-0.0330306\pi\) | |||||||
\(864\) | 1.51746e48 | 0.535352 | ||||||||
\(865\) | 4.02221e48 | + | 3.24287e48i | 1.39219 | + | 1.12244i | ||||
\(866\) | −7.89113e48 | −2.67975 | ||||||||
\(867\) | − | 3.12446e48i | − | 1.04102i | ||||||
\(868\) | − | 6.75989e48i | − | 2.20986i | ||||||
\(869\) | 1.32782e48 | 0.425906 | ||||||||
\(870\) | −3.84394e48 | + | 4.76772e48i | −1.20979 | + | 1.50052i | ||||
\(871\) | 2.07825e48 | 0.641799 | ||||||||
\(872\) | − | 1.20794e48i | − | 0.366037i | ||||||
\(873\) | 5.07818e47i | 0.150999i | ||||||||
\(874\) | 2.15295e48 | 0.628195 | ||||||||
\(875\) | 2.76319e48 | − | 5.51035e48i | 0.791186 | − | 1.57778i | ||||
\(876\) | −2.64896e48 | −0.744317 | ||||||||
\(877\) | 1.47230e48i | 0.405980i | 0.979181 | + | 0.202990i | \(0.0650658\pi\) | ||||
−0.979181 | + | 0.202990i | \(0.934934\pi\) | |||||||
\(878\) | 4.15791e48i | 1.12516i | ||||||||
\(879\) | −1.63552e48 | −0.434350 | ||||||||
\(880\) | −3.48498e47 | + | 4.32250e47i | −0.0908314 | + | 0.112660i | ||||
\(881\) | −6.01645e48 | −1.53900 | −0.769499 | − | 0.638648i | \(-0.779494\pi\) | ||||
−0.769499 | + | 0.638648i | \(0.779494\pi\) | |||||||
\(882\) | − | 1.81617e48i | − | 0.455957i | ||||||
\(883\) | − | 1.72340e48i | − | 0.424654i | −0.977199 | − | 0.212327i | \(-0.931896\pi\) | ||
0.977199 | − | 0.212327i | \(-0.0681041\pi\) | |||||||
\(884\) | −1.09605e49 | −2.65074 | ||||||||
\(885\) | 2.79499e48 | + | 2.25344e48i | 0.663462 | + | 0.534911i | ||||
\(886\) | −1.63086e48 | −0.379980 | ||||||||
\(887\) | − | 4.24957e48i | − | 0.971863i | −0.873997 | − | 0.485931i | \(-0.838480\pi\) | ||
0.873997 | − | 0.485931i | \(-0.161520\pi\) | |||||||
\(888\) | − | 6.79088e47i | − | 0.152445i | ||||||
\(889\) | −1.05311e49 | −2.32057 | ||||||||
\(890\) | 5.84989e48 | + | 4.71643e48i | 1.26535 | + | 1.02018i | ||||
\(891\) | −1.09255e48 | −0.231984 | ||||||||
\(892\) | − | 4.21927e48i | − | 0.879462i | ||||||
\(893\) | − | 1.04229e48i | − | 0.213274i | ||||||
\(894\) | 8.26874e48 | 1.66100 | ||||||||
\(895\) | 1.96135e48 | − | 2.43271e48i | 0.386790 | − | 0.479744i | ||||
\(896\) | 1.66990e49 | 3.23303 | ||||||||
\(897\) | 6.33229e48i | 1.20361i | ||||||||
\(898\) | 8.84761e48i | 1.65107i | ||||||||
\(899\) | 4.56336e48 | 0.836083 | ||||||||
\(900\) | 2.77035e47 | + | 1.27642e48i | 0.0498348 | + | 0.229612i | ||||
\(901\) | 8.53615e48 | 1.50766 | ||||||||
\(902\) | 1.73502e48i | 0.300882i | ||||||||
\(903\) | 1.44772e48i | 0.246511i | ||||||||
\(904\) | −2.65619e46 | −0.00444099 | ||||||||
\(905\) | −2.34350e48 | + | 2.90669e48i | −0.384736 | + | 0.477197i | ||||
\(906\) | −3.32763e48 | −0.536438 | ||||||||
\(907\) | − | 1.37448e48i | − | 0.217579i | −0.994065 | − | 0.108789i | \(-0.965303\pi\) | ||
0.994065 | − | 0.108789i | \(-0.0346974\pi\) | |||||||
\(908\) | 5.56970e48i | 0.865796i | ||||||||
\(909\) | −6.42216e47 | −0.0980341 | ||||||||
\(910\) | −1.53275e49 | − | 1.23577e49i | −2.29768 | − | 1.85249i | ||||
\(911\) | −6.36073e48 | −0.936383 | −0.468192 | − | 0.883627i | \(-0.655094\pi\) | ||||
−0.468192 | + | 0.883627i | \(0.655094\pi\) | |||||||
\(912\) | 9.90867e47i | 0.143252i | ||||||||
\(913\) | − | 3.21905e48i | − | 0.457047i | ||||||
\(914\) | 1.74503e49 | 2.43327 | ||||||||
\(915\) | −5.33729e48 | − | 4.30315e48i | −0.730925 | − | 0.589303i | ||||
\(916\) | 1.85540e49 | 2.49553 | ||||||||
\(917\) | − | 1.11534e49i | − | 1.47337i | ||||||
\(918\) | 1.98805e49i | 2.57943i | ||||||||
\(919\) | −1.02620e49 | −1.30775 | −0.653876 | − | 0.756601i | \(-0.726858\pi\) | ||||
−0.653876 | + | 0.756601i | \(0.726858\pi\) | |||||||
\(920\) | 9.15777e48 | − | 1.13586e49i | 1.14628 | − | 1.42176i | ||||
\(921\) | 1.48244e48 | 0.182261 | ||||||||
\(922\) | − | 4.55259e48i | − | 0.549792i | ||||||
\(923\) | 7.35050e48i | 0.871945i | ||||||||
\(924\) | −7.03965e48 | −0.820282 | ||||||||
\(925\) | −9.90592e47 | + | 2.14998e47i | −0.113385 | + | 0.0246091i | ||||
\(926\) | −1.87311e49 | −2.10611 | ||||||||
\(927\) | − | 4.38237e47i | − | 0.0484054i | ||||||
\(928\) | 5.74148e48i | 0.622992i | ||||||||
\(929\) | 8.18502e48 | 0.872490 | 0.436245 | − | 0.899828i | \(-0.356308\pi\) | ||||
0.436245 | + | 0.899828i | \(0.356308\pi\) | |||||||
\(930\) | −6.42844e48 | + | 7.97333e48i | −0.673189 | + | 0.834971i | ||||
\(931\) | −5.90966e48 | −0.607985 | ||||||||
\(932\) | 1.78133e48i | 0.180046i | ||||||||
\(933\) | 6.72289e48i | 0.667589i | ||||||||
\(934\) | −3.44530e48 | −0.336128 | ||||||||
\(935\) | 3.20230e48 | + | 2.58183e48i | 0.306952 | + | 0.247478i | ||||
\(936\) | 1.89904e48 | 0.178847 | ||||||||
\(937\) | 2.10406e49i | 1.94695i | 0.228800 | + | 0.973474i | \(0.426520\pi\) | ||||
−0.228800 | + | 0.973474i | \(0.573480\pi\) | |||||||
\(938\) | − | 2.11281e49i | − | 1.92094i | ||||||
\(939\) | −1.57281e48 | −0.140506 | ||||||||
\(940\) | −1.20800e49 | − | 9.73940e48i | −1.06037 | − | 0.854915i | ||||
\(941\) | 1.12511e49 | 0.970434 | 0.485217 | − | 0.874394i | \(-0.338741\pi\) | ||||
0.485217 | + | 0.874394i | \(0.338741\pi\) | |||||||
\(942\) | − | 2.29226e49i | − | 1.94278i | ||||||
\(943\) | − | 1.02708e49i | − | 0.855387i | ||||||
\(944\) | −5.95220e48 | −0.487124 | ||||||||
\(945\) | −1.45100e49 | + | 1.79971e49i | −1.16692 | + | 1.44736i | ||||
\(946\) | −8.64029e47 | −0.0682849 | ||||||||
\(947\) | − | 1.47061e49i | − | 1.14215i | −0.820898 | − | 0.571075i | \(-0.806526\pi\) | ||
0.820898 | − | 0.571075i | \(-0.193474\pi\) | |||||||
\(948\) | − | 3.52777e49i | − | 2.69254i | ||||||
\(949\) | 5.74887e48 | 0.431211 | ||||||||
\(950\) | 6.41611e48 | − | 1.39255e48i | 0.472968 | − | 0.102653i | ||||
\(951\) | 1.32558e48 | 0.0960346 | ||||||||
\(952\) | 5.07228e49i | 3.61155i | ||||||||
\(953\) | − | 6.20681e47i | − | 0.0434346i | −0.999764 | − | 0.0217173i | \(-0.993087\pi\) | ||
0.999764 | − | 0.0217173i | \(-0.00691338\pi\) | |||||||
\(954\) | −3.24903e48 | −0.223463 | ||||||||
\(955\) | 4.67972e48 | − | 5.80436e48i | 0.316348 | − | 0.392373i | ||||
\(956\) | 1.48821e49 | 0.988803 | ||||||||
\(957\) | − | 4.75221e48i | − | 0.310348i | ||||||
\(958\) | − | 1.21876e49i | − | 0.782327i | ||||||
\(959\) | −1.92727e48 | −0.121601 | ||||||||
\(960\) | −1.62882e49 | − | 1.31322e49i | −1.01018 | − | 0.814448i | ||||
\(961\) | −8.77191e48 | −0.534759 | ||||||||
\(962\) | 3.23758e48i | 0.194013i | ||||||||
\(963\) | − | 3.20940e48i | − | 0.189056i | ||||||
\(964\) | −1.20941e49 | −0.700328 | ||||||||
\(965\) | 1.96976e49 | + | 1.58810e49i | 1.12128 | + | 0.904020i | ||||
\(966\) | 6.43757e49 | 3.60246 | ||||||||
\(967\) | 1.22644e49i | 0.674699i | 0.941379 | + | 0.337350i | \(0.109530\pi\) | ||||
−0.941379 | + | 0.337350i | \(0.890470\pi\) | |||||||
\(968\) | 2.41038e49i | 1.30360i | ||||||||
\(969\) | 7.34080e48 | 0.390302 | ||||||||
\(970\) | 2.38522e49 | − | 2.95845e49i | 1.24680 | − | 1.54643i | ||||
\(971\) | 1.12879e49 | 0.580090 | 0.290045 | − | 0.957013i | \(-0.406330\pi\) | ||||
0.290045 | + | 0.957013i | \(0.406330\pi\) | |||||||
\(972\) | − | 9.24086e48i | − | 0.466895i | ||||||
\(973\) | 5.22694e48i | 0.259648i | ||||||||
\(974\) | −6.54527e49 | −3.19672 | ||||||||
\(975\) | 4.09579e48 | + | 1.88712e49i | 0.196681 | + | 0.906197i | ||||
\(976\) | 1.13663e49 | 0.536657 | ||||||||
\(977\) | − | 4.11771e49i | − | 1.91159i | −0.294029 | − | 0.955796i | \(-0.594996\pi\) | ||
0.294029 | − | 0.955796i | \(-0.405004\pi\) | |||||||
\(978\) | 2.28174e49i | 1.04154i | ||||||||
\(979\) | −5.83085e48 | −0.261708 | ||||||||
\(980\) | −5.52213e49 | + | 6.84922e49i | −2.43712 | + | 3.02281i | ||||
\(981\) | 7.67323e47 | 0.0332996 | ||||||||
\(982\) | 6.62374e49i | 2.82660i | ||||||||
\(983\) | − | 1.02350e49i | − | 0.429494i | −0.976670 | − | 0.214747i | \(-0.931107\pi\) | ||
0.976670 | − | 0.214747i | \(-0.0688926\pi\) | |||||||
\(984\) | 2.09834e49 | 0.865877 | ||||||||
\(985\) | 2.64210e49 | + | 2.13018e49i | 1.07214 | + | 0.864405i | ||||
\(986\) | −7.52204e49 | −3.00170 | ||||||||
\(987\) | − | 3.11657e49i | − | 1.22305i | ||||||
\(988\) | − | 1.35746e49i | − | 0.523888i | ||||||
\(989\) | 5.11482e48 | 0.194129 | ||||||||
\(990\) | −1.21886e48 | − | 9.82696e47i | −0.0454960 | − | 0.0366808i | ||||
\(991\) | 1.68749e49 | 0.619478 | 0.309739 | − | 0.950822i | \(-0.399758\pi\) | ||||
0.309739 | + | 0.950822i | \(0.399758\pi\) | |||||||
\(992\) | 9.60182e48i | 0.346666i | ||||||||
\(993\) | 5.80777e47i | 0.0206228i | ||||||||
\(994\) | 7.47272e49 | 2.60978 | ||||||||
\(995\) | 3.96913e48 | − | 4.92300e48i | 0.136337 | − | 0.169102i | ||||
\(996\) | −8.55240e49 | −2.88941 | ||||||||
\(997\) | − | 1.90551e49i | − | 0.633200i | −0.948559 | − | 0.316600i | \(-0.897459\pi\) | ||
0.948559 | − | 0.316600i | \(-0.102541\pi\) | |||||||
\(998\) | − | 9.51944e49i | − | 3.11141i | ||||||
\(999\) | 3.80145e48 | 0.122213 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5.34.b.a.4.14 | yes | 16 | |
5.2 | odd | 4 | 25.34.a.f.1.3 | 16 | |||
5.3 | odd | 4 | 25.34.a.f.1.14 | 16 | |||
5.4 | even | 2 | inner | 5.34.b.a.4.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.b.a.4.3 | ✓ | 16 | 5.4 | even | 2 | inner | |
5.34.b.a.4.14 | yes | 16 | 1.1 | even | 1 | trivial | |
25.34.a.f.1.3 | 16 | 5.2 | odd | 4 | |||
25.34.a.f.1.14 | 16 | 5.3 | odd | 4 |