Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,9,Mod(13,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.13");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.f (of order \(4\), degree \(2\), 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: | \(8.14757220122\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4 x^{7} + 8 x^{6} + 22254 x^{5} + 4820745 x^{4} + 50131374 x^{3} + 307615702 x^{2} + \cdots + 2405464244 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{13}\cdot 5^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(-29.1758 + 30.1758i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.17 |
Dual form | 20.9.f.a.13.3 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 18.1203 | − | 18.1203i | 0.223708 | − | 0.223708i | −0.586350 | − | 0.810058i | \(-0.699436\pi\) |
0.810058 | + | 0.586350i | \(0.199436\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −577.254 | + | 239.589i | −0.923607 | + | 0.383342i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −190.873 | − | 190.873i | −0.0794971 | − | 0.0794971i | 0.666240 | − | 0.745737i | \(-0.267903\pi\) |
−0.745737 | + | 0.666240i | \(0.767903\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5904.31i | 0.899910i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19026.8 | −1.29955 | −0.649776 | − | 0.760125i | \(-0.725137\pi\) | ||||
−0.649776 | + | 0.760125i | \(0.725137\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −27902.1 | + | 27902.1i | −0.976930 | + | 0.976930i | −0.999740 | − | 0.0228094i | \(-0.992739\pi\) |
0.0228094 | + | 0.999740i | \(0.492739\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6118.61 | + | 14801.5i | −0.120861 | + | 0.292374i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22518.5 | − | 22518.5i | −0.269615 | − | 0.269615i | 0.559330 | − | 0.828945i | \(-0.311058\pi\) |
−0.828945 | + | 0.559330i | \(0.811058\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 63405.3i | 0.486532i | 0.969960 | + | 0.243266i | \(0.0782188\pi\) | ||||
−0.969960 | + | 0.243266i | \(0.921781\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6917.35 | −0.0355682 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 196829. | − | 196829.i | 0.703360 | − | 0.703360i | −0.261770 | − | 0.965130i | \(-0.584306\pi\) |
0.965130 | + | 0.261770i | \(0.0843063\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 275820. | − | 276607.i | 0.706098 | − | 0.708114i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 225875. | + | 225875.i | 0.425024 | + | 0.425024i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 595585.i | − | 0.842077i | −0.907043 | − | 0.421039i | \(-0.861666\pi\) | ||
0.907043 | − | 0.421039i | \(-0.138334\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 249340. | 0.269988 | 0.134994 | − | 0.990846i | \(-0.456898\pi\) | ||||
0.134994 | + | 0.990846i | \(0.456898\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −344771. | + | 344771.i | −0.290720 | + | 0.290720i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 155913. | + | 64451.1i | 0.103899 | + | 0.0429495i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 229540. | + | 229540.i | 0.122476 | + | 0.122476i | 0.765688 | − | 0.643212i | \(-0.222399\pi\) |
−0.643212 | + | 0.765688i | \(0.722399\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.01119e6i | 0.437094i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.30046e6 | −1.52188 | −0.760938 | − | 0.648824i | \(-0.775261\pi\) | ||||
−0.760938 | + | 0.648824i | \(0.775261\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.59483e6 | + | 3.59483e6i | −1.05149 | + | 1.05149i | −0.0528880 | + | 0.998600i | \(0.516843\pi\) |
−0.998600 | + | 0.0528880i | \(0.983157\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.41460e6 | − | 3.40829e6i | −0.344973 | − | 0.831163i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.19225e6 | + | 6.19225e6i | 1.26899 | + | 1.26899i | 0.946612 | + | 0.322375i | \(0.104481\pi\) |
0.322375 | + | 0.946612i | \(0.395519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.69194e6i | − | 0.987360i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −816086. | −0.120630 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −253926. | + | 253926.i | −0.0321813 | + | 0.0321813i | −0.723014 | − | 0.690833i | \(-0.757244\pi\) |
0.690833 | + | 0.723014i | \(0.257244\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.09833e7 | − | 4.55859e6i | 1.20028 | − | 0.498173i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.14893e6 | + | 1.14893e6i | 0.108841 | + | 0.108841i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 7.27642e6i | − | 0.600496i | −0.953861 | − | 0.300248i | \(-0.902931\pi\) | ||
0.953861 | − | 0.300248i | \(-0.0970694\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.24983e6 | −0.234715 | −0.117358 | − | 0.993090i | \(-0.537442\pi\) | ||||
−0.117358 | + | 0.993090i | \(0.537442\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.12697e6 | − | 1.12697e6i | 0.0715402 | − | 0.0715402i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.42158e6 | − | 2.27916e7i | 0.527801 | − | 1.27680i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.68654e7 | + | 2.68654e7i | 1.33320 | + | 1.33320i | 0.902493 | + | 0.430705i | \(0.141735\pi\) |
0.430705 | + | 0.902493i | \(0.358265\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 7.13321e6i | − | 0.314694i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.70958e7 | −1.45979 | −0.729896 | − | 0.683559i | \(-0.760431\pi\) | ||||
−0.729896 | + | 0.683559i | \(0.760431\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.76665e7 | + | 2.76665e7i | −0.974234 | + | 0.974234i | −0.999676 | − | 0.0254420i | \(-0.991901\pi\) |
0.0254420 | + | 0.999676i | \(0.491901\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14267.5 | − | 1.00102e7i | −0.000450922 | − | 0.316370i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.63169e6 | + | 3.63169e6i | 0.103311 | + | 0.103311i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.03584e7i | 0.522681i | 0.965247 | + | 0.261340i | \(0.0841645\pi\) | ||||
−0.965247 | + | 0.261340i | \(0.915836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.05523e7 | −0.709747 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.23434e7 | + | 2.23434e7i | −0.470800 | + | 0.470800i | −0.902173 | − | 0.431374i | \(-0.858029\pi\) |
0.431374 | + | 0.902173i | \(0.358029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.83941e7 | + | 7.60373e6i | 0.352373 | + | 0.145663i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.07922e7 | − | 1.07922e7i | −0.188379 | − | 0.188379i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.64461e7i | − | 0.421504i | −0.977540 | − | 0.210752i | \(-0.932409\pi\) | ||
0.977540 | − | 0.210752i | \(-0.0675912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.06515e7 | 0.155326 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.51812e6 | − | 4.51812e6i | 0.0603984 | − | 0.0603984i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.51912e7 | − | 3.66010e7i | −0.186508 | − | 0.449364i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.78714e7 | + | 9.78714e7i | 1.10553 | + | 1.10553i | 0.993731 | + | 0.111795i | \(0.0356600\pi\) |
0.111795 | + | 0.993731i | \(0.464340\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.12340e8i | − | 1.16948i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.04946e8 | 1.00851 | 0.504257 | − | 0.863553i | \(-0.331766\pi\) | ||||
0.504257 | + | 0.863553i | \(0.331766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.04986e8 | − | 1.04986e8i | 0.932789 | − | 0.932789i | −0.0650901 | − | 0.997879i | \(-0.520733\pi\) |
0.997879 | + | 0.0650901i | \(0.0207335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.99307e6 | − | 1.65732e6i | 0.0328511 | − | 0.0136348i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.19346e8 | − | 1.19346e8i | −0.910485 | − | 0.910485i | 0.0858251 | − | 0.996310i | \(-0.472647\pi\) |
−0.996310 | + | 0.0858251i | \(0.972647\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.74582e8i | 1.23678i | 0.785871 | + | 0.618390i | \(0.212215\pi\) | ||||
−0.785871 | + | 0.618390i | \(0.787785\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.31868e6 | 0.0547977 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.45939e6 | − | 5.45939e6i | 0.0334835 | − | 0.0334835i | −0.690167 | − | 0.723650i | \(-0.742463\pi\) |
0.723650 | + | 0.690167i | \(0.242463\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.64623e7 | + | 1.60778e8i | −0.380001 | + | 0.919255i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.64743e8 | − | 1.64743e8i | −0.879149 | − | 0.879149i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.59633e6i | 0.0428672i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.47658e8 | 0.688838 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.79257e7 | + | 7.79257e7i | −0.340456 | + | 0.340456i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.29461e7 | + | 2.25756e8i | −0.380707 | + | 0.924696i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.35128e6 | + | 6.35128e6i | 0.0244144 | + | 0.0244144i | 0.719209 | − | 0.694794i | \(-0.244505\pi\) |
−0.694794 | + | 0.719209i | \(0.744505\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.30279e8i | 0.470452i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.24615e8 | −0.762699 | −0.381350 | − | 0.924431i | \(-0.624541\pi\) | ||||
−0.381350 | + | 0.924431i | \(0.624541\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.21023e7 | − | 1.21023e7i | 0.0386779 | − | 0.0386779i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.84505e8 | − | 7.62703e7i | −0.555485 | − | 0.229626i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.38143e8 | − | 3.38143e8i | −0.959882 | − | 0.959882i | 0.0393439 | − | 0.999226i | \(-0.487473\pi\) |
−0.999226 | + | 0.0393439i | \(0.987473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.48983e8i | 1.47062i | 0.677732 | + | 0.735309i | \(0.262963\pi\) | ||||
−0.677732 | + | 0.735309i | \(0.737037\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.24411e8 | 0.567764 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.30887e8 | − | 5.30887e8i | 1.26957 | − | 1.26957i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.42695e8 | + | 3.43804e8i | 0.322803 | + | 0.777748i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.03140e8 | − | 1.03140e8i | −0.220880 | − | 0.220880i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 5.66486e8i | − | 1.14933i | −0.818389 | − | 0.574665i | \(-0.805133\pi\) | ||
0.818389 | − | 0.574665i | \(-0.194867\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.43633e8 | 1.81508 | 0.907539 | − | 0.419968i | \(-0.137959\pi\) | ||||
0.907539 | + | 0.419968i | \(0.137959\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.32956e8 | − | 1.32956e8i | 0.242629 | − | 0.242629i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.43932e8 | + | 5.97389e7i | −0.249363 | + | 0.103498i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.37850e8 | − | 1.37850e8i | −0.226886 | − | 0.226886i | 0.584505 | − | 0.811390i | \(-0.301289\pi\) |
−0.811390 | + | 0.584505i | \(0.801289\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.20244e6i | 0.0143984i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.51385e7 | −0.111830 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.86924e8 | + | 1.86924e8i | −0.264798 | + | 0.264798i | −0.827000 | − | 0.562202i | \(-0.809954\pi\) |
0.562202 | + | 0.827000i | \(0.309954\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.16417e8 | − | 2.81624e8i | 0.157066 | − | 0.379956i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.37971e8 | + | 5.37971e8i | 0.691661 | + | 0.691661i | 0.962597 | − | 0.270936i | \(-0.0873332\pi\) |
−0.270936 | + | 0.962597i | \(0.587333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.41325e8i | − | 0.908786i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.74365e8 | −0.437835 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.79607e8 | + | 4.79607e8i | −0.535428 | + | 0.535428i | −0.922183 | − | 0.386754i | \(-0.873596\pi\) |
0.386754 | + | 0.922183i | \(0.373596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.05443e8 | + | 150288.i | −0.112426 | + | 0.000160240i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.31851e8 | − | 1.31851e8i | −0.134335 | − | 0.134335i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.39076e9i | 1.35469i | 0.735665 | + | 0.677346i | \(0.236870\pi\) | ||||
−0.735665 | + | 0.677346i | \(0.763130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.45715e9 | −1.35766 | −0.678830 | − | 0.734296i | \(-0.737512\pi\) | ||||
−0.678830 | + | 0.734296i | \(0.737512\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.88880e7 | + | 5.88880e7i | −0.0525076 | + | 0.0525076i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.87498e8 | − | 7.75078e7i | −0.160070 | − | 0.0661696i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.28454e8 | + | 4.28454e8i | 0.350379 | + | 0.350379i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 8.62269e7i | − | 0.0675765i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.33136e8 | −0.325455 | −0.162727 | − | 0.986671i | \(-0.552029\pi\) | ||||
−0.162727 | + | 0.986671i | \(0.552029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.36884e8 | + | 9.36884e8i | −0.675237 | + | 0.675237i | −0.958919 | − | 0.283681i | \(-0.908444\pi\) |
0.283681 | + | 0.958919i | \(0.408444\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.42270e8 | − | 5.83714e8i | −0.167556 | − | 0.403703i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.12789e8 | + | 7.12789e8i | 0.473256 | + | 0.473256i | 0.902967 | − | 0.429711i | \(-0.141384\pi\) |
−0.429711 | + | 0.902967i | \(0.641384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.63094e9i | − | 1.03998i | −0.854173 | − | 0.519989i | \(-0.825936\pi\) | ||
0.854173 | − | 0.519989i | \(-0.174064\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.73621e8 | 0.596493 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.13681e8 | + | 1.13681e8i | −0.0669427 | + | 0.0669427i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.48246e9 | − | 1.03034e9i | 1.40562 | − | 0.583399i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.16214e9 | + | 1.16214e9i | 0.632960 | + | 0.632960i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.20640e9i | − | 0.632274i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.87914e9 | −1.45255 | −0.726277 | − | 0.687402i | \(-0.758751\pi\) | ||||
−0.726277 | + | 0.687402i | \(0.758751\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.72187e8 | + | 6.72187e8i | −0.326567 | + | 0.326567i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.21385e9 | − | 2.93641e9i | 0.568082 | − | 1.37424i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.75921e7 | − | 4.75921e7i | −0.0214633 | − | 0.0214633i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.00265e9i | 0.435887i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.25663e9 | 0.526790 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.77849e9 | − | 2.77849e9i | 1.12354 | − | 1.12354i | 0.132337 | − | 0.991205i | \(-0.457752\pi\) |
0.991205 | − | 0.132337i | \(-0.0422480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.63317e9 | + | 1.62852e9i | 0.637239 | + | 0.635425i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.66218e9 | + | 1.66218e9i | 0.626001 | + | 0.626001i | 0.947059 | − | 0.321059i | \(-0.104039\pi\) |
−0.321059 | + | 0.947059i | \(0.604039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.39534e9i | − | 0.507384i | −0.967285 | − | 0.253692i | \(-0.918355\pi\) | ||
0.967285 | − | 0.253692i | \(-0.0816450\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.31615e8 | 0.0462228 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.53597e9 | + | 1.53597e9i | −0.521146 | + | 0.521146i | −0.917918 | − | 0.396771i | \(-0.870131\pi\) |
0.396771 | + | 0.917918i | \(0.370131\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.05809e9 | − | 2.09091e9i | −1.65850 | − | 0.685589i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.68902e8 | + | 3.68902e8i | 0.116928 | + | 0.116928i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.45417e8i | 0.167162i | 0.996501 | + | 0.0835809i | \(0.0266357\pi\) | ||||
−0.996501 | + | 0.0835809i | \(0.973364\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.46365e8 | −0.280537 | −0.140269 | − | 0.990113i | \(-0.544797\pi\) | ||||
−0.140269 | + | 0.990113i | \(0.544797\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.03559e9 | + | 2.03559e9i | −0.583800 | + | 0.583800i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.36372e9 | + | 3.28569e9i | 0.378496 | + | 0.911933i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.76914e9 | − | 1.76914e9i | −0.475308 | − | 0.475308i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.09738e8i | 0.210643i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.66712e9 | −1.17585 | −0.587927 | − | 0.808914i | \(-0.700056\pi\) | ||||
−0.587927 | + | 0.808914i | \(0.700056\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.74502e9 | + | 3.74502e9i | −0.914053 | + | 0.914053i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.71089e8 | − | 1.95525e8i | 0.111415 | − | 0.0462425i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.22158e8 | + | 4.22158e8i | 0.0967705 | + | 0.0967705i | 0.753835 | − | 0.657064i | \(-0.228202\pi\) |
−0.657064 | + | 0.753835i | \(0.728202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.76258e7i | − | 0.0194730i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.51652e9 | 0.757793 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.92697e9 | − | 3.92697e9i | 0.820794 | − | 0.820794i | −0.165428 | − | 0.986222i | \(-0.552900\pi\) |
0.986222 | + | 0.165428i | \(0.0529004\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.57420e7 | − | 2.07418e8i | 0.0173864 | − | 0.0420593i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.79212e8 | − | 4.79212e8i | −0.0942936 | − | 0.0942936i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.88692e9i | 0.360366i | 0.983633 | + | 0.180183i | \(0.0576691\pi\) | ||||
−0.983633 | + | 0.180183i | \(0.942331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.82459e9 | 0.709100 | 0.354550 | − | 0.935037i | \(-0.384634\pi\) | ||||
0.354550 | + | 0.935037i | \(0.384634\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.93009e8 | − | 1.93009e8i | 0.0347477 | − | 0.0347477i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.24795e9 | + | 5.26293e9i | −0.917612 | + | 0.920231i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.08916e9 | − | 6.08916e9i | −1.03428 | − | 1.03428i | −0.999391 | − | 0.0348898i | \(-0.988892\pi\) |
−0.0348898 | − | 0.999391i | \(-0.511108\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.47218e9i | 0.242965i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.36217e9 | 1.18081 | 0.590406 | − | 0.807107i | \(-0.298968\pi\) | ||||
0.590406 | + | 0.807107i | \(0.298968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.50823e9 | − | 7.50823e9i | 1.17055 | − | 1.17055i | 0.188477 | − | 0.982078i | \(-0.439645\pi\) |
0.982078 | − | 0.188477i | \(-0.0603550\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.38491e8 | − | 3.87952e8i | −0.142250 | − | 0.0588029i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.20840e8 | + | 8.20840e8i | 0.120985 | + | 0.120985i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 5.96159e9i | − | 0.854616i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.54692e9 | 0.494630 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.53947e9 | − | 5.53947e9i | 0.751619 | − | 0.751619i | −0.223163 | − | 0.974781i | \(-0.571638\pi\) |
0.974781 | + | 0.223163i | \(0.0716381\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.74335e9 | + | 4.20034e9i | 0.230195 | + | 0.554622i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.29768e9 | − | 4.29768e9i | −0.552342 | − | 0.552342i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.09839e10i | 1.37427i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.37231e9 | 0.167181 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.90166e9 | − | 1.90166e9i | 0.225613 | − | 0.225613i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.87598e9 | − | 7.78623e8i | 0.216785 | − | 0.0899762i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.64460e8 | − | 5.64460e8i | −0.0635448 | − | 0.0635448i | 0.674620 | − | 0.738165i | \(-0.264307\pi\) |
−0.738165 | + | 0.674620i | \(0.764307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 3.80477e9i | − | 0.417344i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.47892e9 | −0.264984 | −0.132492 | − | 0.991184i | \(-0.542298\pi\) | ||||
−0.132492 | + | 0.991184i | \(0.542298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.72227e9 | + | 9.72227e9i | −1.01296 | + | 1.01296i | −0.0130407 | + | 0.999915i | \(0.504151\pi\) |
−0.999915 | + | 0.0130407i | \(0.995849\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.80539e8 | + | 9.20558e8i | −0.0386507 | + | 0.0934994i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.03089e10 | − | 1.03089e10i | −1.02088 | − | 1.02088i | −0.999777 | − | 0.0211068i | \(-0.993281\pi\) |
−0.0211068 | − | 0.999777i | \(-0.506719\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.13321e10i | 1.09432i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.32518e9 | −0.407365 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.42779e9 | − | 1.42779e9i | 0.131176 | − | 0.131176i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.19694e7 | + | 1.54139e10i | 0.00196917 | + | 1.38159i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.16348e9 | + | 3.16348e9i | 0.276677 | + | 0.276677i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.36386e9i | − | 0.201762i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.62056e9 | 0.634855 | 0.317428 | − | 0.948282i | \(-0.397181\pi\) | ||||
0.317428 | + | 0.948282i | \(0.397181\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.35527e9 | + | 1.35527e9i | −0.110217 | + | 0.110217i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.19448e10 | − | 9.07153e9i | −1.74242 | − | 0.720280i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.43147e9 | − | 1.43147e9i | −0.110985 | − | 0.110985i | 0.649433 | − | 0.760418i | \(-0.275006\pi\) |
−0.760418 | + | 0.649433i | \(0.775006\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 1.97852e8i | − | 0.0149810i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.74412e9 | −0.350864 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.18678e9 | + | 2.18678e9i | −0.157989 | + | 0.157989i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.70904e9 | + | 4.11767e9i | 0.120635 | + | 0.290654i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.72187e9 | + | 7.72187e9i | 0.532604 | + | 0.532604i | 0.921346 | − | 0.388742i | \(-0.127090\pi\) |
−0.388742 | + | 0.921346i | \(0.627090\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.20836e9i | 0.216263i | 0.994137 | + | 0.108131i | \(0.0344867\pi\) | ||||
−0.994137 | + | 0.108131i | \(0.965513\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.26048e10 | −0.830439 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.06371e9 | − | 5.06371e9i | 0.326115 | − | 0.326115i | −0.524992 | − | 0.851107i | \(-0.675932\pi\) |
0.851107 | + | 0.524992i | \(0.175932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.14137e10 | − | 8.88772e9i | 1.34827 | − | 0.559599i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.55768e8 | + | 1.55768e8i | 0.00958973 | + | 0.00958973i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.18165e9i | − | 0.372157i | −0.982535 | − | 0.186079i | \(-0.940422\pi\) | ||
0.982535 | − | 0.186079i | \(-0.0595779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.29633e10 | 0.763287 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.67562e9 | − | 2.67562e9i | 0.154098 | − | 0.154098i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.34204e9 | − | 2.25992e10i | 0.526345 | − | 1.27327i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.55537e10 | + | 1.55537e10i | 0.857371 | + | 0.857371i | 0.991028 | − | 0.133657i | \(-0.0426720\pi\) |
−0.133657 | + | 0.991028i | \(0.542672\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.53912e10i | − | 1.36955i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.69350e7 | 0.00511664 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.05344e9 | + | 8.05344e9i | −0.416051 | + | 0.416051i | −0.883840 | − | 0.467789i | \(-0.845051\pi\) |
0.467789 | + | 0.883840i | \(0.345051\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.40655e9 | + | 5.77498e9i | 0.121694 | + | 0.292029i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.66181e10 | + | 1.66181e10i | 0.822651 | + | 0.822651i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.11955e10i | − | 1.02727i | −0.858007 | − | 0.513637i | \(-0.828298\pi\) | ||
0.858007 | − | 0.513637i | \(-0.171702\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.30175e8 | 0.0109234 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.49717e9 | + | 4.49717e9i | −0.208999 | + | 0.208999i | −0.803842 | − | 0.594843i | \(-0.797214\pi\) |
0.594843 | + | 0.803842i | \(0.297214\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.96652e9 | − | 1.22630e9i | −0.135022 | − | 0.0558152i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.12250e10 | − | 2.12250e10i | −0.946245 | − | 0.946245i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.17946e10i | 0.515093i | 0.966266 | + | 0.257547i | \(0.0829141\pi\) | ||||
−0.966266 | + | 0.257547i | \(0.917086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.86459e9 | −0.379273 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.07010e9 | + | 4.07010e9i | −0.170622 | + | 0.170622i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.87765e9 | − | 1.17520e10i | −0.200365 | − | 0.482751i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.96839e10 | + | 2.96839e10i | 1.19498 | + | 1.19498i | 0.975652 | + | 0.219324i | \(0.0703853\pi\) |
0.219324 | + | 0.975652i | \(0.429615\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 4.38597e8i | − | 0.0173051i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.98937e10 | −1.15612 | −0.578059 | − | 0.815995i | \(-0.696190\pi\) | ||||
−0.578059 | + | 0.815995i | \(0.696190\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.95710e9 | + | 6.95710e9i | −0.263760 | + | 0.263760i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.76364e10 | − | 7.31998e9i | 0.655527 | − | 0.272076i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.36740e9 | − | 4.36740e9i | −0.159164 | − | 0.159164i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.06334e10i | 1.45208i | 0.687654 | + | 0.726039i | \(0.258641\pi\) | ||||
−0.687654 | + | 0.726039i | \(0.741359\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.22545e10 | −0.429466 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.38887e9 | + | 1.38887e9i | −0.0477377 | + | 0.0477377i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.54458e9 | − | 1.82510e10i | 0.254356 | − | 0.615311i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.94775e9 | + | 9.94775e9i | 0.328988 | + | 0.328988i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5.67792e9i | − | 0.184218i | −0.995749 | − | 0.0921092i | \(-0.970639\pi\) | ||
0.995749 | − | 0.0921092i | \(-0.0293609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.08470e10 | −0.981938 | −0.490969 | − | 0.871177i | \(-0.663357\pi\) | ||||
−0.490969 | + | 0.871177i | \(0.663357\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.65610e10 | + | 3.65610e10i | −1.14197 | + | 1.14197i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.24398e10 | + | 1.77305e7i | −0.381293 | + | 0.000543456i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.20304e8 | + | 6.20304e8i | 0.0186592 | + | 0.0186592i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 1.92397e10i | − | 0.568026i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.27768e10 | −0.949856 | −0.474928 | − | 0.880025i | \(-0.657526\pi\) | ||||
−0.474928 | + | 0.880025i | \(0.657526\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.60012e9 | + | 7.60012e9i | −0.216206 | + | 0.216206i | −0.806898 | − | 0.590691i | \(-0.798855\pi\) |
0.590691 | + | 0.806898i | \(0.298855\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.81553e9 | + | 3.64415e9i | 0.246202 | + | 0.101775i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.24800e10 | + | 1.24800e10i | 0.342207 | + | 0.342207i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.35066e10i | − | 0.363654i | −0.983330 | − | 0.181827i | \(-0.941799\pi\) | ||
0.983330 | − | 0.181827i | \(-0.0582012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.36069e10 | 0.888535 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.65065e10 | − | 3.65065e10i | 0.947883 | − | 0.947883i | −0.0508241 | − | 0.998708i | \(-0.516185\pi\) |
0.998708 | + | 0.0508241i | \(0.0161848\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.33618e9 | + | 1.52661e10i | 0.161580 | + | 0.389303i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.02649e10 | − | 1.02649e10i | −0.257114 | − | 0.257114i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.93648e9i | − | 0.0722507i | −0.999347 | − | 0.0361253i | \(-0.988498\pi\) | ||
0.999347 | − | 0.0361253i | \(-0.0115016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.18238e10 | 1.97776 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.70989e10 | − | 1.70989e10i | 0.406047 | − | 0.406047i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.14862e9 | + | 2.55198e9i | −0.143460 | + | 0.0595431i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.06216e10 | − | 4.06216e10i | −0.931305 | − | 0.931305i | 0.0664829 | − | 0.997788i | \(-0.478822\pi\) |
−0.997788 | + | 0.0664829i | \(0.978822\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1.01728e10i | − | 0.229186i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.69744e10 | 0.375830 | 0.187915 | − | 0.982185i | \(-0.439827\pi\) | ||||
0.187915 | + | 0.982185i | \(0.439827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.02630e10 | + | 1.02630e10i | −0.223332 | + | 0.223332i | −0.809900 | − | 0.586568i | \(-0.800479\pi\) |
0.586568 | + | 0.809900i | \(0.300479\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.52561e9 | + | 3.69059e9i | −0.0326311 | + | 0.0789376i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.93031e10 | + | 1.93031e10i | 0.405845 | + | 0.405845i | 0.880287 | − | 0.474442i | \(-0.157350\pi\) |
−0.474442 | + | 0.880287i | \(0.657350\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.02557e10i | − | 0.211971i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.99576e9 | −0.101512 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.83979e10 | − | 6.83979e10i | 1.36646 | − | 1.36646i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.75384e10 | + | 1.74884e10i | 0.344520 | + | 0.343539i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.49926e9 | − | 1.49926e9i | −0.0289603 | − | 0.0289603i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.47760e10i | 1.23047i | 0.788343 | + | 0.615236i | \(0.210939\pi\) | ||||
−0.788343 | + | 0.615236i | \(0.789061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.28093e10 | −0.239301 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.36153e9 | + | 1.36153e9i | −0.0250173 | + | 0.0250173i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.99456e10 | − | 3.30478e10i | −1.44487 | − | 0.597277i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.13580e10 | − | 3.13580e10i | −0.557483 | − | 0.557483i | 0.371107 | − | 0.928590i | \(-0.378978\pi\) |
−0.928590 | + | 0.371107i | \(0.878978\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.77426e9i | 0.118475i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.72949e10 | 0.469630 | 0.234815 | − | 0.972040i | \(-0.424552\pi\) | ||||
0.234815 | + | 0.972040i | \(0.424552\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.34117e10 | + | 1.34117e10i | −0.227037 | + | 0.227037i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.69153e10 | + | 6.48486e10i | 0.448311 | + | 1.08014i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.08056e9 | + | 7.08056e9i | 0.116049 | + | 0.116049i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.55600e10i | − | 1.37997i | −0.723825 | − | 0.689984i | \(-0.757618\pi\) | ||
0.723825 | − | 0.689984i | \(-0.242382\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.94964e10 | 0.309460 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.20771e10 | + | 4.20771e10i | −0.657315 | + | 0.657315i | −0.954744 | − | 0.297429i | \(-0.903871\pi\) |
0.297429 | + | 0.954744i | \(0.403871\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.05808e10 | + | 2.51440e10i | −0.931471 | + | 0.386606i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.34330e10 | − | 1.34330e10i | −0.203302 | − | 0.203302i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.19496e11i | 1.78025i | 0.455714 | + | 0.890126i | \(0.349384\pi\) | ||||
−0.455714 | + | 0.890126i | \(0.650616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.05616e10 | 0.154898 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.43217e10 | + | 1.43217e10i | −0.206788 | + | 0.206788i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.54502e10 | + | 8.57573e10i | −0.503953 | + | 1.21911i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.17818e11 | − | 1.17818e11i | −1.64912 | − | 1.64912i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.73813e10i | 0.239559i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.31604e9 | −0.126439 | −0.0632194 | − | 0.998000i | \(-0.520137\pi\) | ||||
−0.0632194 | + | 0.998000i | \(0.520137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.01748e9 | + | 4.01748e9i | −0.0536967 | + | 0.0536967i | −0.733445 | − | 0.679749i | \(-0.762089\pi\) |
0.679749 | + | 0.733445i | \(0.262089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.90794e9 | + | 1.91339e9i | −0.0251147 | + | 0.0251864i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.61476e9 | − | 5.61476e9i | −0.0727928 | − | 0.0727928i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.27726e8i | 0.0105697i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.29622e10 | 0.540392 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.19992e11 | − | 1.19992e11i | 1.48677 | − | 1.48677i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.74869e10 | + | 4.02990e10i | 1.18996 | + | 0.491903i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.52010e10 | + | 2.52010e10i | 0.303055 | + | 0.303055i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.08299e11i | 1.28313i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.43998e10 | −0.635050 | −0.317525 | − | 0.948250i | \(-0.602852\pi\) | ||||
−0.317525 | + | 0.948250i | \(0.602852\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.64041e10 | + | 2.64041e10i | −0.303719 | + | 0.303719i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.18278e10 | − | 1.00778e11i | −0.474110 | − | 1.14230i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.69974e10 | − | 6.69974e10i | −0.748357 | − | 0.748357i | 0.225814 | − | 0.974171i | \(-0.427496\pi\) |
−0.974171 | + | 0.225814i | \(0.927496\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 1.91880e10i | − | 0.211223i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.77633e10 | 0.409697 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.88587e9 | − | 3.88587e9i | 0.0415516 | − | 0.0415516i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.80199e9 | + | 1.99306e9i | −0.0506115 | + | 0.0210063i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.16300e11 | + | 1.16300e11i | 1.20825 | + | 1.20825i | 0.971593 | + | 0.236660i | \(0.0760527\pi\) |
0.236660 | + | 0.971593i | \(0.423947\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.00607e11i | − | 2.05446i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.55275e10 | 0.156765 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.63107e10 | − | 4.63107e10i | 0.460944 | − | 0.460944i | −0.438021 | − | 0.898965i | \(-0.644320\pi\) |
0.898965 | + | 0.438021i | \(0.144320\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.84345e9 | + | 4.45947e9i | −0.0180899 | + | 0.0437612i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.83160e9 | + | 5.83160e9i | 0.0564229 | + | 0.0564229i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00951e10i | 0.287109i | 0.989642 | + | 0.143555i | \(0.0458532\pi\) | ||||
−0.989642 | + | 0.143555i | \(0.954147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.41650e10 | 0.509536 | 0.254768 | − | 0.967002i | \(-0.418001\pi\) | ||||
0.254768 | + | 0.967002i | \(0.418001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.84856e9 | + | 7.84856e9i | −0.0728067 | + | 0.0728067i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.54978e8 | − | 1.08734e11i | −0.00141774 | − | 0.994700i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.83913e10 | + | 4.83913e10i | 0.436581 | + | 0.436581i | 0.890859 | − | 0.454279i | \(-0.150103\pi\) |
−0.454279 | + | 0.890859i | \(0.650103\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.39533e10i | 0.302112i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.52947e9 | 0.0748544 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.83139e9 | − | 4.83139e9i | 0.0418213 | − | 0.0418213i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.34569e11 | + | 5.56279e10i | 1.14900 | + | 0.474973i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.35625e10 | − | 5.35625e10i | −0.451137 | − | 0.451137i | 0.444595 | − | 0.895732i | \(-0.353348\pi\) |
−0.895732 | + | 0.444595i | \(0.853348\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.58095e10i | 0.131358i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.58319e10 | 0.211742 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.01477e10 | − | 2.01477e10i | 0.162932 | − | 0.162932i | −0.620932 | − | 0.783864i | \(-0.713246\pi\) |
0.783864 | + | 0.620932i | \(0.213246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.05958e9 | − | 4.96227e9i | −0.0164328 | − | 0.0395925i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.95531e10 | − | 2.95531e10i | −0.232651 | − | 0.232651i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.82597e10i | − | 0.607898i | −0.952688 | − | 0.303949i | \(-0.901695\pi\) | ||
0.952688 | − | 0.303949i | \(-0.0983053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00940e11 | −0.773686 | −0.386843 | − | 0.922146i | \(-0.626434\pi\) | ||||
−0.386843 | + | 0.922146i | \(0.626434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.58622e11 | + | 1.58622e11i | −1.19976 | + | 1.19976i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.52364e10 | + | 3.53773e10i | −0.636215 | + | 0.264060i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.85629e10 | + | 6.85629e10i | 0.505050 | + | 0.505050i | 0.913003 | − | 0.407953i | \(-0.133757\pi\) |
−0.407953 | + | 0.913003i | \(0.633757\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.11987e9i | 0.0299512i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.45554e11 | −2.47942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.41547e11 | + | 1.41547e11i | −1.00244 | + | 1.00244i | −0.00244188 | + | 0.999997i | \(0.500777\pi\) |
−0.999997 | + | 0.00244188i | \(0.999223\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.63128e10 | − | 6.36531e10i | 0.183936 | − | 0.444958i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.48653e11 | + | 1.48653e11i | 1.02573 | + | 1.02573i | 0.999660 | + | 0.0260699i | \(0.00829924\pi\) |
0.0260699 | + | 0.999660i | \(0.491701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.85869e10i | 0.126603i | 0.997994 | + | 0.0633016i | \(0.0201630\pi\) | ||||
−0.997994 | + | 0.0633016i | \(0.979837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.89176e10 | 0.597890 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.04783e9 | + | 5.04783e9i | −0.0335083 | + | 0.0335083i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.34966e8 | − | 1.52587e11i | −0.00285059 | − | 0.999996i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.18603e10 | − | 2.18603e10i | −0.141445 | − | 0.141445i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.03378e10i | − | 0.0660428i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.57215e10 | −0.288405 | −0.144203 | − | 0.989548i | \(-0.546062\pi\) | ||||
−0.144203 | + | 0.989548i | \(0.546062\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.21709e10 | + | 5.21709e10i | −0.324948 | + | 0.324948i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.18800e9 | − | 2.14461e9i | −0.0319084 | − | 0.0131903i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.58817e11 | + | 1.58817e11i | 0.964582 | + | 0.964582i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 2.19025e11i | − | 1.31368i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.01366e11 | −0.600426 | −0.300213 | − | 0.953872i | \(-0.597058\pi\) | ||||
−0.300213 | + | 0.953872i | \(0.597058\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.00290e10 | + | 7.00290e10i | −0.409670 | + | 0.409670i | −0.881623 | − | 0.471953i | \(-0.843549\pi\) |
0.471953 | + | 0.881623i | \(0.343549\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.12134e10 | − | 7.52041e10i | −0.180344 | − | 0.434513i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.02119e11 | + | 2.02119e11i | 1.15343 | + | 1.15343i | 0.985861 | + | 0.167567i | \(0.0535912\pi\) |
0.167567 | + | 0.985861i | \(0.446409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.38447e11i | 0.780376i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.72477e9 | −0.00960300 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.44565e11 | − | 1.44565e11i | 0.795078 | − | 0.795078i | −0.187237 | − | 0.982315i | \(-0.559953\pi\) |
0.982315 | + | 0.187237i | \(0.0599531\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.29660e11 | − | 5.38152e10i | 0.704434 | − | 0.292374i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.63352e11 | − | 1.63352e11i | −0.876723 | − | 0.876723i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.86847e9i | 0.0364182i | 0.999834 | + | 0.0182091i | \(0.00579645\pi\) | ||||
−0.999834 | + | 0.0182091i | \(0.994204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.42797e10 | 0.179569 | 0.0897844 | − | 0.995961i | \(-0.471382\pi\) | ||||
0.0897844 | + | 0.995961i | \(0.471382\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.27705e10 | − | 2.27705e10i | 0.117847 | − | 0.117847i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.08654e9 | + | 9.88571e9i | −0.0208963 | + | 0.0505500i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.17228e11 | − | 1.17228e11i | −0.592283 | − | 0.592283i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.00694e11i | − | 0.502690i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.18337e10 | 0.305025 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.18977e10 | − | 5.18977e10i | 0.252981 | − | 0.252981i | −0.569211 | − | 0.822192i | \(-0.692751\pi\) |
0.822192 | + | 0.569211i | \(0.192751\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.24780e11 | − | 1.77848e8i | 0.601075 | − | 0.000856711i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.02064e9 | + | 5.02064e9i | 0.0239004 | + | 0.0239004i | 0.718956 | − | 0.695056i | \(-0.244620\pi\) |
−0.695056 | + | 0.718956i | \(0.744620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.73620e10i | − | 0.175772i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.02385e10 | 0.280082 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.82161e10 | − | 3.82161e10i | 0.175616 | − | 0.175616i | −0.613826 | − | 0.789441i | \(-0.710370\pi\) |
0.789441 | + | 0.613826i | \(0.210370\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.76209e11 | + | 1.14179e11i | 1.25452 | + | 0.518590i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.52839e10 | − | 2.52839e10i | −0.113506 | − | 0.113506i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.41701e10i | − | 0.0628778i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.21018e11 | 1.40805 | 0.704023 | − | 0.710177i | \(-0.251385\pi\) | ||||
0.704023 | + | 0.710177i | \(0.251385\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.14426e10 | + | 2.14426e10i | −0.0929703 | + | 0.0929703i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.31530e11 | − | 3.16903e11i | −0.563749 | − | 1.35827i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.68399e10 | + | 9.68399e10i | 0.410321 | + | 0.410321i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.56646e10i | 0.233169i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.92163e11 | −1.20991 | −0.604956 | − | 0.796259i | \(-0.706809\pi\) | ||||
−0.604956 | + | 0.796259i | \(0.706809\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.45541e10 | + | 1.45541e10i | −0.0595886 | + | 0.0595886i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.29542e11 | + | 5.37664e10i | −0.524391 | + | 0.217648i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.00314e10 | − | 2.00314e10i | −0.0801740 | − | 0.0801740i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.84412e11i | − | 0.729801i | −0.931047 | − | 0.364900i | \(-0.881103\pi\) | ||
0.931047 | − | 0.364900i | \(-0.118897\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.20203e11 | −0.470365 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.90773e10 | − | 4.90773e10i | 0.189899 | − | 0.189899i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.79262e11 | + | 4.33651e11i | −0.685905 | + | 1.65927i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.88314e9 | + | 9.88314e9i | 0.0373954 | + | 0.0373954i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.86759e11i | 1.44719i | 0.690226 | + | 0.723594i | \(0.257511\pi\) | ||||
−0.690226 | + | 0.723594i | \(0.742489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00780e10 | −0.148308 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.71484e10 | + | 1.71484e10i | −0.0627583 | + | 0.0627583i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.64743e11 | − | 1.64274e11i | −0.596286 | − | 0.594589i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.08489e11 | + | 1.08489e11i | 0.388373 | + | 0.388373i | 0.874107 | − | 0.485734i | \(-0.161448\pi\) |
−0.485734 | + | 0.874107i | \(0.661448\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.26683e11i | − | 0.448546i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.61900e11 | 0.566994 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.81338e11 | + | 1.81338e11i | −0.628165 | + | 0.628165i | −0.947606 | − | 0.319441i | \(-0.896505\pi\) |
0.319441 | + | 0.947606i | \(0.396505\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.42489e10 | + | 3.48267e10i | 0.288679 | + | 0.119334i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.11162e11 | − | 5.11162e11i | −1.73256 | − | 1.73256i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.46351e11i | 1.83187i | 0.401330 | + | 0.915933i | \(0.368548\pi\) | ||||
−0.401330 | + | 0.915933i | \(0.631452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.41149e10 | −0.212660 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.08189e11 | − | 3.08189e11i | 1.01126 | − | 1.01126i | 0.0113233 | − | 0.999936i | \(-0.496396\pi\) |
0.999936 | − | 0.0113233i | \(-0.00360441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.35724e11 | + | 3.27007e11i | 0.440586 | + | 1.06153i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.31922e11 | − | 1.31922e11i | −0.423677 | − | 0.423677i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.55598e10i | 0.144762i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.35575e9 | 0.00426205 | 0.00213103 | − | 0.999998i | \(-0.499322\pi\) | ||||
0.00213103 | + | 0.999998i | \(0.499322\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.45697e10 | + | 8.45697e10i | −0.263048 | + | 0.263048i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.44716e11 | + | 2.26084e11i | −1.67642 | + | 0.695795i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.95475e11 | − | 2.95475e11i | −0.899781 | − | 0.899781i | 0.0956356 | − | 0.995416i | \(-0.469512\pi\) |
−0.995416 | + | 0.0956356i | \(0.969512\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.35722e11i | 0.408962i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.50018e11 | 1.04364 | 0.521822 | − | 0.853055i | \(-0.325253\pi\) | ||||
0.521822 | + | 0.853055i | \(0.325253\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.33229e10 | − | 3.33229e10i | 0.0983205 | − | 0.0983205i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.48947e10 | + | 1.08604e11i | −0.131084 | + | 0.317104i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.03028e11 | + | 2.03028e11i | 0.586642 | + | 0.586642i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.37337e11i | − | 0.964624i | −0.875999 | − | 0.482312i | \(-0.839797\pi\) | ||
0.875999 | − | 0.482312i | \(-0.160203\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.52993e10 | 0.0432966 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.80219e10 | + | 5.80219e10i | −0.162508 | + | 0.162508i | −0.783677 | − | 0.621169i | \(-0.786658\pi\) |
0.621169 | + | 0.783677i | \(0.286658\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.87728e10 | − | 6.89691e10i | 0.190638 | − | 0.191182i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.58781e9 | − | 1.58781e9i | −0.00435626 | − | 0.00435626i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 2.72672e11i | − | 0.740442i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.05812e11 | 1.89708 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.34528e11 | − | 1.34528e11i | 0.357903 | − | 0.357903i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.12601e11 | + | 4.65470e10i | 0.296528 | + | 0.122578i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.28984e10 | + | 1.28984e10i | 0.0336231 | + | 0.0336231i | 0.723718 | − | 0.690095i | \(-0.242431\pi\) |
−0.690095 | + | 0.723718i | \(0.742431\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1.42316e11i | − | 0.367236i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.08410e9 | −0.00532368 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.06772e10 | − | 9.06772e10i | 0.229301 | − | 0.229301i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.20480e9 | − | 5.31215e9i | −0.00551951 | − | 0.0132985i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.41350e10 | + | 1.41350e10i | 0.0350318 | + | 0.0350318i | 0.724406 | − | 0.689374i | \(-0.242114\pi\) |
−0.689374 | + | 0.724406i | \(0.742114\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.78881e11i | − | 0.684276i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.56146e11 | 0.379315 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.26404e11 | − | 5.26404e11i | 1.26607 | − | 1.26607i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.33740e10 | − | 1.80023e10i | 0.103287 | − | 0.0428692i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.41916e10 | + | 3.41916e10i | 0.0806167 | + | 0.0806167i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.90397e11i | 1.61178i | 0.592067 | + | 0.805889i | \(0.298312\pi\) | ||||
−0.592067 | + | 0.805889i | \(0.701688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.75326e10 | −0.202342 | −0.101171 | − | 0.994869i | \(-0.532259\pi\) | ||||
−0.101171 | + | 0.994869i | \(0.532259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.93027e10 | − | 6.93027e10i | 0.158631 | − | 0.158631i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.31179e10 | − | 1.52688e11i | 0.143061 | − | 0.346078i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.27931e11 | − | 2.27931e11i | −0.511583 | − | 0.511583i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.28897e10i | 0.139780i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.30471e11 | −0.507275 | −0.253638 | − | 0.967299i | \(-0.581627\pi\) | ||||
−0.253638 | + | 0.967299i | \(0.581627\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.64879e10 | + | 8.64879e10i | −0.188519 | + | 0.188519i | −0.795056 | − | 0.606536i | \(-0.792558\pi\) |
0.606536 | + | 0.795056i | \(0.292558\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.71463e8 | + | 1.90461e11i | 0.000585997 | + | 0.411140i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.31886e11 | − | 2.31886e11i | −0.495739 | − | 0.495739i | 0.414370 | − | 0.910109i | \(-0.364002\pi\) |
−0.910109 | + | 0.414370i | \(0.864002\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.24583e11i | 0.263779i | 0.991264 | + | 0.131890i | \(0.0421044\pi\) | ||||
−0.991264 | + | 0.131890i | \(0.957896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.20675e11 | −0.462753 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.28174e11 | + | 1.28174e11i | −0.266207 | + | 0.266207i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.39438e11 | − | 1.81654e11i | −0.903965 | − | 0.373680i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.63197e10 | + | 5.63197e10i | 0.114752 | + | 0.114752i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.32482e11i | 0.267367i | 0.991024 | + | 0.133684i | \(0.0426806\pi\) | ||||
−0.991024 | + | 0.133684i | \(0.957319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.45525e11 | 0.290906 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.33405e11 | − | 1.33405e11i | 0.264157 | − | 0.264157i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.77613e11 | + | 4.27933e11i | 0.348376 | + | 0.839361i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.81840e10 | − | 2.81840e10i | −0.0547606 | − | 0.0547606i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 2.72103e11i | − | 0.523724i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.03602e10 | 0.172290 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.92442e11 | + | 1.92442e11i | −0.363499 | + | 0.363499i | −0.865099 | − | 0.501600i | \(-0.832745\pi\) |
0.501600 | + | 0.865099i | \(0.332745\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.16103e11 | − | 8.96935e10i | 0.404387 | − | 0.167840i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.33628e11 | + | 5.33628e11i | 0.989272 | + | 0.989272i | 0.999943 | − | 0.0106713i | \(-0.00339685\pi\) |
−0.0106713 | + | 0.999943i | \(0.503397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.48989e11i | 0.640972i | 0.947253 | + | 0.320486i | \(0.103846\pi\) | ||||
−0.947253 | + | 0.320486i | \(0.896154\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.97478e10 | 0.0541305 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.36194e11 | + | 7.36194e11i | −1.32724 | + | 1.32724i | −0.419470 | + | 0.907769i | \(0.637784\pi\) |
−0.907769 | + | 0.419470i | \(0.862216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.61947e11 | − | 3.91764e11i | 0.289273 | − | 0.699777i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.08026e11 | − | 1.08026e11i | −0.191184 | − | 0.191184i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 3.87355e11i | − | 0.679251i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.49920e12 | −2.60488 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.77863e11 | + | 5.77863e11i | −0.994874 | + | 0.994874i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.08315e10 | − | 2.53497e10i | 0.103776 | − | 0.0432455i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.69351e10 | − | 5.69351e10i | −0.0962458 | − | 0.0962458i | 0.657344 | − | 0.753590i | \(-0.271680\pi\) |
−0.753590 | + | 0.657344i | \(0.771680\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2.00754e11i | − | 0.336286i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.10972e11 | −0.682196 | −0.341098 | − | 0.940028i | \(-0.610799\pi\) | ||||
−0.341098 | + | 0.940028i | \(0.610799\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.49612e11 | − | 3.49612e11i | 0.575100 | − | 0.575100i | −0.358449 | − | 0.933549i | \(-0.616694\pi\) |
0.933549 | + | 0.358449i | \(0.116694\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.07702e11 | + | 4.45216e10i | 0.175570 | + | 0.0725767i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.64244e11 | + | 5.64244e11i | 0.911533 | + | 0.911533i | 0.996393 | − | 0.0848602i | \(-0.0270444\pi\) |
−0.0848602 | + | 0.996393i | \(0.527044\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.42457e9i | − | 0.00388175i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.81311e11 | 0.922354 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.92622e11 | + | 3.92622e11i | −0.617403 | + | 0.617403i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.33210e11 | − | 8.02822e11i | −0.519310 | − | 1.25120i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.99032e11 | + | 1.99032e11i | 0.307434 | + | 0.307434i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.48503e11i | − | 0.227351i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14361e10 | 0.0173531 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.48667e10 | − | 2.48667e10i | 0.0373996 | − | 0.0373996i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.41147e11 | − | 3.49117e11i | 1.25394 | − | 0.520447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.44245e8 | − | 9.44245e8i | −0.00139526 | − | 0.00139526i | 0.706409 | − | 0.707804i | \(-0.250314\pi\) |
−0.707804 | + | 0.706409i | \(0.750314\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.19636e11i | 0.907572i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.02795e11 | −0.584804 | −0.292402 | − | 0.956295i | \(-0.594455\pi\) | ||||
−0.292402 | + | 0.956295i | \(0.594455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.25122e11 | − | 4.25122e11i | 0.611829 | − | 0.611829i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.98845e10 | − | 4.81022e10i | 0.0283680 | − | 0.0686248i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.28728e10 | + | 4.28728e10i | 0.0606324 | + | 0.0606324i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.71953e11i | − | 0.801860i | −0.916109 | − | 0.400930i | \(-0.868687\pi\) | ||
0.916109 | − | 0.400930i | \(-0.131313\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.04564e10 | −0.0284309 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.03505e12 | − | 1.03505e12i | 1.42611 | − | 1.42611i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.26804e11 | − | 1.80734e8i | 0.173207 | − | 0.000246872i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.19871e11 | + | 6.19871e11i | 0.839426 | + | 0.839426i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 9.36530e11i | − | 1.25736i | −0.777665 | − | 0.628679i | \(-0.783596\pi\) | ||
0.777665 | − | 0.628679i | \(-0.216404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.60899e11 | 0.480382 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.49188e10 | + | 4.49188e10i | −0.0592791 | + | 0.0592791i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.49980e11 | − | 1.44674e11i | −0.457927 | − | 0.189297i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.93070e11 | + | 2.93070e11i | 0.380200 | + | 0.380200i | 0.871174 | − | 0.490974i | \(-0.163359\pi\) |
−0.490974 | + | 0.871174i | \(0.663359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.52342e11i | 0.453212i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.88370e11 | 1.13301 | 0.566507 | − | 0.824057i | \(-0.308294\pi\) | ||||
0.566507 | + | 0.824057i | \(0.308294\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.46455e11 | + | 8.46455e11i | −1.07043 | + | 1.07043i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.06590e10 | + | 4.97748e10i | 0.0259049 | + | 0.0624141i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.47904e10 | − | 5.47904e10i | −0.0681247 | − | 0.0681247i | 0.672224 | − | 0.740348i | \(-0.265339\pi\) |
−0.740348 | + | 0.672224i | \(0.765339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.54391e12i | − | 1.90352i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.73602e11 | −0.456759 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.59818e11 | + | 9.59818e11i | −1.16364 | + | 1.16364i | −0.179963 | + | 0.983673i | \(0.557598\pi\) |
−0.983673 | + | 0.179963i | \(0.942402\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.50029e11 | − | 1.03774e11i | 0.300592 | − | 0.124760i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.05340e11 | + | 2.05340e11i | 0.244809 | + | 0.244809i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.29084e11i | 0.152616i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.90721e11 | −0.927106 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.04656e11 | − | 7.04656e11i | 0.819354 | − | 0.819354i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.16353e11 | − | 7.65287e11i | 0.364807 | − | 0.882500i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.73546e11 | + | 5.73546e11i | 0.655938 | + | 0.655938i | 0.954416 | − | 0.298479i | \(-0.0964792\pi\) |
−0.298479 | + | 0.954416i | \(0.596479\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.17442e10i | − | 0.0586903i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.59341e11 | 0.741708 | 0.370854 | − | 0.928691i | \(-0.379065\pi\) | ||||
0.370854 | + | 0.928691i | \(0.379065\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.04786e11 | − | 1.04786e11i | 0.116910 | − | 0.116910i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.79702e11 | + | 2.78906e11i | 0.309512 | + | 0.308631i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.80295e11 | − | 4.80295e11i | −0.527144 | − | 0.527144i | 0.392576 | − | 0.919720i | \(-0.371584\pi\) |
−0.919720 | + | 0.392576i | \(0.871584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.03183e11i | 0.547766i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.03078e12 | −1.11299 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.05351e12 | + | 1.05351e12i | −1.12830 | + | 1.12830i | −0.137852 | + | 0.990453i | \(0.544020\pi\) |
−0.990453 | + | 0.137852i | \(0.955980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.82236e11 | − | 2.40684e11i | −0.618521 | − | 0.255684i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.28340e10 | − | 4.28340e10i | −0.0451356 | − | 0.0451356i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.41513e12i | 1.47915i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.86106e11 | −0.711372 | −0.355686 | − | 0.934606i | \(-0.615753\pi\) | ||||
−0.355686 | + | 0.934606i | \(0.615753\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.38087e11 | − | 1.38087e11i | 0.142022 | − | 0.142022i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.90754e11 | + | 9.41464e11i | 0.398667 | + | 0.960531i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.70841e11 | − | 9.70841e11i | −0.982579 | − | 0.982579i | 0.0172719 | − | 0.999851i | \(-0.494502\pi\) |
−0.999851 | + | 0.0172719i | \(0.994502\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.03695e11i | 0.104111i |
(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 | 20.9.f.a.17.3 | yes | 8 | |
3.2 | odd | 2 | 180.9.l.a.37.4 | 8 | |||
4.3 | odd | 2 | 80.9.p.d.17.2 | 8 | |||
5.2 | odd | 4 | 100.9.f.b.93.2 | 8 | |||
5.3 | odd | 4 | inner | 20.9.f.a.13.3 | ✓ | 8 | |
5.4 | even | 2 | 100.9.f.b.57.2 | 8 | |||
15.8 | even | 4 | 180.9.l.a.73.4 | 8 | |||
20.3 | even | 4 | 80.9.p.d.33.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.9.f.a.13.3 | ✓ | 8 | 5.3 | odd | 4 | inner | |
20.9.f.a.17.3 | yes | 8 | 1.1 | even | 1 | trivial | |
80.9.p.d.17.2 | 8 | 4.3 | odd | 2 | |||
80.9.p.d.33.2 | 8 | 20.3 | even | 4 | |||
100.9.f.b.57.2 | 8 | 5.4 | even | 2 | |||
100.9.f.b.93.2 | 8 | 5.2 | odd | 4 | |||
180.9.l.a.37.4 | 8 | 3.2 | odd | 2 | |||
180.9.l.a.73.4 | 8 | 15.8 | even | 4 |