Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,12,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not 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: | \(37.6488158474\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 30.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.30 |
Dual form | 49.12.c.c.18.1 |
$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 12.0000 | − | 20.7846i | 0.265165 | − | 0.459279i | −0.702442 | − | 0.711741i | \(-0.747907\pi\) |
0.967607 | + | 0.252462i | \(0.0812402\pi\) | |||||||
\(3\) | 126.000 | + | 218.238i | 0.299367 | + | 0.518519i | 0.975991 | − | 0.217810i | \(-0.0698912\pi\) |
−0.676624 | + | 0.736328i | \(0.736558\pi\) | |||||||
\(4\) | 736.000 | + | 1274.79i | 0.359375 | + | 0.622456i | ||||
\(5\) | 2415.00 | − | 4182.90i | 0.345607 | − | 0.598608i | −0.639857 | − | 0.768494i | \(-0.721006\pi\) |
0.985464 | + | 0.169886i | \(0.0543398\pi\) | |||||||
\(6\) | 6048.00 | 0.317526 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 84480.0 | 0.911505 | ||||||||
\(9\) | 56821.5 | − | 98417.7i | 0.320759 | − | 0.555571i | ||||
\(10\) | −57960.0 | − | 100390.i | −0.183286 | − | 0.317460i | ||||
\(11\) | −267306. | − | 462988.i | −0.500436 | − | 0.866781i | −1.00000 | 0.000504048i | \(-0.999840\pi\) | |
0.499563 | − | 0.866277i | \(-0.333494\pi\) | |||||||
\(12\) | −185472. | + | 321247.i | −0.215170 | + | 0.372685i | ||||
\(13\) | 577738. | 0.431561 | 0.215781 | − | 0.976442i | \(-0.430770\pi\) | ||||
0.215781 | + | 0.976442i | \(0.430770\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.21716e6 | 0.413853 | ||||||||
\(16\) | −493568. | + | 854885.i | −0.117676 | + | 0.203820i | ||||
\(17\) | −3.45297e6 | − | 5.98071e6i | −0.589825 | − | 1.02161i | −0.994255 | − | 0.107038i | \(-0.965863\pi\) |
0.404430 | − | 0.914569i | \(-0.367470\pi\) | |||||||
\(18\) | −1.36372e6 | − | 2.36203e6i | −0.170108 | − | 0.294636i | ||||
\(19\) | 5.33071e6 | − | 9.23306e6i | 0.493901 | − | 0.855462i | −0.506074 | − | 0.862490i | \(-0.668904\pi\) |
0.999975 | + | 0.00702781i | \(0.00223704\pi\) | |||||||
\(20\) | 7.10976e6 | 0.496810 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.28307e7 | −0.530793 | ||||||||
\(23\) | −9.32164e6 | + | 1.61455e7i | −0.301988 | + | 0.523058i | −0.976586 | − | 0.215127i | \(-0.930983\pi\) |
0.674599 | + | 0.738185i | \(0.264317\pi\) | |||||||
\(24\) | 1.06445e7 | + | 1.84368e7i | 0.272874 | + | 0.472632i | ||||
\(25\) | 1.27496e7 | + | 2.20830e7i | 0.261112 | + | 0.452259i | ||||
\(26\) | 6.93286e6 | − | 1.20081e7i | 0.114435 | − | 0.198207i | ||||
\(27\) | 7.32791e7 | 0.982832 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.28407e8 | 1.16251 | 0.581257 | − | 0.813720i | \(-0.302561\pi\) | ||||
0.581257 | + | 0.813720i | \(0.302561\pi\) | |||||||
\(30\) | 1.46059e7 | − | 2.52982e7i | 0.109739 | − | 0.190074i | ||||
\(31\) | −2.64216e7 | − | 4.57635e7i | −0.165756 | − | 0.287098i | 0.771167 | − | 0.636632i | \(-0.219673\pi\) |
−0.936924 | + | 0.349534i | \(0.886340\pi\) | |||||||
\(32\) | 9.83532e7 | + | 1.70353e8i | 0.518159 | + | 0.897478i | ||||
\(33\) | 6.73611e7 | − | 1.16673e8i | 0.299628 | − | 0.518971i | ||||
\(34\) | −1.65742e8 | −0.625604 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.67282e8 | 0.461091 | ||||||||
\(37\) | 9.11067e7 | − | 1.57801e8i | 0.215993 | − | 0.374112i | −0.737586 | − | 0.675253i | \(-0.764034\pi\) |
0.953579 | + | 0.301142i | \(0.0973677\pi\) | |||||||
\(38\) | −1.27937e8 | − | 2.21593e8i | −0.261931 | − | 0.453677i | ||||
\(39\) | 7.27950e7 | + | 1.26085e8i | 0.129195 | + | 0.223773i | ||||
\(40\) | 2.04019e8 | − | 3.53372e8i | 0.315022 | − | 0.545634i | ||||
\(41\) | −3.08120e8 | −0.415345 | −0.207673 | − | 0.978198i | \(-0.566589\pi\) | ||||
−0.207673 | + | 0.978198i | \(0.566589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.71257e7 | −0.0177653 | −0.00888264 | − | 0.999961i | \(-0.502827\pi\) | ||||
−0.00888264 | + | 0.999961i | \(0.502827\pi\) | |||||||
\(44\) | 3.93474e8 | − | 6.81518e8i | 0.359689 | − | 0.622999i | ||||
\(45\) | −2.74448e8 | − | 4.75358e8i | −0.221713 | − | 0.384018i | ||||
\(46\) | 2.23719e8 | + | 3.87493e8i | 0.160153 | + | 0.277393i | ||||
\(47\) | 1.34367e9 | − | 2.32731e9i | 0.854586 | − | 1.48019i | −0.0224426 | − | 0.999748i | \(-0.507144\pi\) |
0.877029 | − | 0.480438i | \(-0.159522\pi\) | |||||||
\(48\) | −2.48758e8 | −0.140913 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.11981e8 | 0.276951 | ||||||||
\(51\) | 8.70148e8 | − | 1.50714e9i | 0.353148 | − | 0.611671i | ||||
\(52\) | 4.25215e8 | + | 7.36494e8i | 0.155092 | + | 0.268628i | ||||
\(53\) | 7.98028e8 | + | 1.38222e9i | 0.262120 | + | 0.454006i | 0.966805 | − | 0.255515i | \(-0.0822449\pi\) |
−0.704685 | + | 0.709520i | \(0.748912\pi\) | |||||||
\(54\) | 8.79349e8 | − | 1.52308e9i | 0.260613 | − | 0.451394i | ||||
\(55\) | −2.58218e9 | −0.691817 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.68668e9 | 0.591431 | ||||||||
\(58\) | 1.54088e9 | − | 2.66888e9i | 0.308258 | − | 0.533919i | ||||
\(59\) | −2.59460e9 | − | 4.49398e9i | −0.472481 | − | 0.818362i | 0.527023 | − | 0.849851i | \(-0.323308\pi\) |
−0.999504 | + | 0.0314895i | \(0.989975\pi\) | |||||||
\(60\) | 8.95830e8 | + | 1.55162e9i | 0.148728 | + | 0.257605i | ||||
\(61\) | 3.47824e9 | − | 6.02449e9i | 0.527285 | − | 0.913284i | −0.472209 | − | 0.881486i | \(-0.656543\pi\) |
0.999494 | − | 0.0317979i | \(-0.0101233\pi\) | |||||||
\(62\) | −1.26824e9 | −0.175811 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.69930e9 | 0.314240 | ||||||||
\(65\) | 1.39524e9 | − | 2.41662e9i | 0.149150 | − | 0.258336i | ||||
\(66\) | −1.61667e9 | − | 2.80015e9i | −0.158902 | − | 0.275226i | ||||
\(67\) | 7.74091e9 | + | 1.34077e10i | 0.700456 | + | 1.21323i | 0.968307 | + | 0.249765i | \(0.0803533\pi\) |
−0.267851 | + | 0.963460i | \(0.586313\pi\) | |||||||
\(68\) | 5.08277e9 | − | 8.80361e9i | 0.423937 | − | 0.734280i | ||||
\(69\) | −4.69810e9 | −0.361620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.79149e9 | 0.644062 | 0.322031 | − | 0.946729i | \(-0.395634\pi\) | ||||
0.322031 | + | 0.946729i | \(0.395634\pi\) | |||||||
\(72\) | 4.80028e9 | − | 8.31433e9i | 0.292373 | − | 0.506406i | ||||
\(73\) | 7.31896e8 | + | 1.26768e9i | 0.0413212 | + | 0.0715705i | 0.885946 | − | 0.463788i | \(-0.153510\pi\) |
−0.844625 | + | 0.535358i | \(0.820177\pi\) | |||||||
\(74\) | −2.18656e9 | − | 3.78723e9i | −0.114548 | − | 0.198403i | ||||
\(75\) | −3.21290e9 | + | 5.56491e9i | −0.156337 | + | 0.270783i | ||||
\(76\) | 1.56936e10 | 0.709983 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.49416e9 | 0.137032 | ||||||||
\(79\) | −1.90584e10 | + | 3.30102e10i | −0.696848 | + | 1.20698i | 0.272706 | + | 0.962097i | \(0.412081\pi\) |
−0.969554 | + | 0.244878i | \(0.921252\pi\) | |||||||
\(80\) | 2.38393e9 | + | 4.12909e9i | 0.0813391 | + | 0.140883i | ||||
\(81\) | −8.32594e8 | − | 1.44210e9i | −0.0265317 | − | 0.0459543i | ||||
\(82\) | −3.69745e9 | + | 6.40416e9i | −0.110135 | + | 0.190760i | ||||
\(83\) | 2.93351e10 | 0.817444 | 0.408722 | − | 0.912659i | \(-0.365975\pi\) | ||||
0.408722 | + | 0.912659i | \(0.365975\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.33557e10 | −0.815390 | ||||||||
\(86\) | −2.05508e8 | + | 3.55951e8i | −0.00471073 | + | 0.00815923i | ||||
\(87\) | 1.61792e10 | + | 2.80233e10i | 0.348018 | + | 0.602785i | ||||
\(88\) | −2.25820e10 | − | 3.91132e10i | −0.456150 | − | 0.790075i | ||||
\(89\) | −1.24965e10 | + | 2.16445e10i | −0.237215 | + | 0.410868i | −0.959914 | − | 0.280294i | \(-0.909568\pi\) |
0.722699 | + | 0.691163i | \(0.242901\pi\) | |||||||
\(90\) | −1.31735e10 | −0.235162 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.74429e10 | −0.434107 | ||||||||
\(93\) | 6.65824e9 | − | 1.15324e10i | 0.0992438 | − | 0.171895i | ||||
\(94\) | −3.22482e10 | − | 5.58555e10i | −0.453213 | − | 0.784987i | ||||
\(95\) | −2.57473e10 | − | 4.45957e10i | −0.341391 | − | 0.591307i | ||||
\(96\) | −2.47850e10 | + | 4.29289e10i | −0.310239 | + | 0.537351i | ||||
\(97\) | −7.50136e10 | −0.886942 | −0.443471 | − | 0.896289i | \(-0.646253\pi\) | ||||
−0.443471 | + | 0.896289i | \(0.646253\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.07549e10 | −0.642078 | ||||||||
\(100\) | −1.87674e10 | + | 3.25061e10i | −0.187674 | + | 0.325061i | ||||
\(101\) | 4.08715e10 | + | 7.07915e10i | 0.386948 | + | 0.670214i | 0.992037 | − | 0.125944i | \(-0.0401959\pi\) |
−0.605089 | + | 0.796158i | \(0.706863\pi\) | |||||||
\(102\) | −2.08835e10 | − | 3.61714e10i | −0.187285 | − | 0.324387i | ||||
\(103\) | −1.12878e11 | + | 1.95510e11i | −0.959407 | + | 1.66174i | −0.235463 | + | 0.971883i | \(0.575661\pi\) |
−0.723944 | + | 0.689858i | \(0.757673\pi\) | |||||||
\(104\) | 4.88073e10 | 0.393370 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.83053e10 | 0.278021 | ||||||||
\(107\) | −4.51206e10 | + | 7.81512e10i | −0.311003 | + | 0.538673i | −0.978580 | − | 0.205868i | \(-0.933998\pi\) |
0.667577 | + | 0.744541i | \(0.267332\pi\) | |||||||
\(108\) | 5.39334e10 | + | 9.34154e10i | 0.353205 | + | 0.611769i | ||||
\(109\) | −3.67413e10 | − | 6.36379e10i | −0.228723 | − | 0.396159i | 0.728707 | − | 0.684825i | \(-0.240122\pi\) |
−0.957430 | + | 0.288666i | \(0.906788\pi\) | |||||||
\(110\) | −3.09861e10 | + | 5.36695e10i | −0.183446 | + | 0.317737i | ||||
\(111\) | 4.59178e10 | 0.258645 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.51469e10 | −0.434748 | −0.217374 | − | 0.976088i | \(-0.569749\pi\) | ||||
−0.217374 | + | 0.976088i | \(0.569749\pi\) | |||||||
\(114\) | 3.22401e10 | − | 5.58416e10i | 0.156827 | − | 0.271632i | ||||
\(115\) | 4.50235e10 | + | 7.79830e10i | 0.208738 | + | 0.361545i | ||||
\(116\) | 9.45073e10 | + | 1.63691e11i | 0.417779 | + | 0.723614i | ||||
\(117\) | 3.28279e10 | − | 5.68597e10i | 0.138427 | − | 0.239763i | ||||
\(118\) | −1.24541e11 | −0.501142 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.02826e11 | 0.377229 | ||||||||
\(121\) | −2.49160e8 | + | 4.31558e8i | −0.000873290 | + | 0.00151258i | ||||
\(122\) | −8.34777e10 | − | 1.44588e11i | −0.279635 | − | 0.484342i | ||||
\(123\) | −3.88232e10 | − | 6.72437e10i | −0.124341 | − | 0.215364i | ||||
\(124\) | 3.88926e10 | − | 6.73639e10i | 0.119137 | − | 0.206352i | ||||
\(125\) | 3.59001e11 | 1.05218 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.62717e11 | −0.705615 | −0.352808 | − | 0.935696i | \(-0.614773\pi\) | ||||
−0.352808 | + | 0.935696i | \(0.614773\pi\) | |||||||
\(128\) | −1.69036e11 | + | 2.92778e11i | −0.434834 | + | 0.753155i | ||||
\(129\) | −2.15784e9 | − | 3.73749e9i | −0.00531833 | − | 0.00921163i | ||||
\(130\) | −3.34857e10 | − | 5.79989e10i | −0.0790990 | − | 0.137003i | ||||
\(131\) | 3.15764e11 | − | 5.46920e11i | 0.715107 | − | 1.23860i | −0.247811 | − | 0.968808i | \(-0.579711\pi\) |
0.962918 | − | 0.269793i | \(-0.0869554\pi\) | |||||||
\(132\) | 1.98311e11 | 0.430715 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.71564e11 | 0.742946 | ||||||||
\(135\) | 1.76969e11 | − | 3.06519e11i | 0.339673 | − | 0.588331i | ||||
\(136\) | −2.91707e11 | − | 5.05251e11i | −0.537629 | − | 0.931200i | ||||
\(137\) | 1.48599e11 | + | 2.57382e11i | 0.263059 | + | 0.455632i | 0.967053 | − | 0.254574i | \(-0.0819351\pi\) |
−0.703994 | + | 0.710206i | \(0.748602\pi\) | |||||||
\(138\) | −5.63773e10 | + | 9.76483e10i | −0.0958890 | + | 0.166085i | ||||
\(139\) | −5.96794e11 | −0.975535 | −0.487767 | − | 0.872974i | \(-0.662189\pi\) | ||||
−0.487767 | + | 0.872974i | \(0.662189\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.77212e11 | 1.02334 | ||||||||
\(142\) | 1.17498e11 | − | 2.03512e11i | 0.170783 | − | 0.295804i | ||||
\(143\) | −1.54433e11 | − | 2.67486e11i | −0.215969 | − | 0.374069i | ||||
\(144\) | 5.60905e10 | + | 9.71517e10i | 0.0754911 | + | 0.130754i | ||||
\(145\) | 3.10102e11 | − | 5.37112e11i | 0.401773 | − | 0.695891i | ||||
\(146\) | 3.51310e10 | 0.0438278 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.68218e11 | 0.310491 | ||||||||
\(149\) | 5.57717e11 | − | 9.65994e11i | 0.622142 | − | 1.07758i | −0.366945 | − | 0.930243i | \(-0.619596\pi\) |
0.989086 | − | 0.147338i | \(-0.0470705\pi\) | |||||||
\(150\) | 7.71097e10 | + | 1.33558e11i | 0.0829100 | + | 0.143604i | ||||
\(151\) | 4.12224e11 | + | 7.13992e11i | 0.427326 | + | 0.740151i | 0.996635 | − | 0.0819732i | \(-0.0261222\pi\) |
−0.569308 | + | 0.822124i | \(0.692789\pi\) | |||||||
\(152\) | 4.50338e11 | − | 7.80009e11i | 0.450194 | − | 0.779758i | ||||
\(153\) | −7.84811e11 | −0.756767 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.55233e11 | −0.229146 | ||||||||
\(156\) | −1.07154e11 | + | 1.85597e11i | −0.0928590 | + | 0.160837i | ||||
\(157\) | 6.57558e11 | + | 1.13892e12i | 0.550156 | + | 0.952899i | 0.998263 | + | 0.0589187i | \(0.0187653\pi\) |
−0.448106 | + | 0.893980i | \(0.647901\pi\) | |||||||
\(158\) | 4.57402e11 | + | 7.92244e11i | 0.369559 | + | 0.640096i | ||||
\(159\) | −2.01103e11 | + | 3.48321e11i | −0.156940 | + | 0.271829i | ||||
\(160\) | 9.50091e11 | 0.716317 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.99645e10 | −0.0281412 | ||||||||
\(163\) | 1.78916e11 | − | 3.09892e11i | 0.121792 | − | 0.210950i | −0.798682 | − | 0.601753i | \(-0.794469\pi\) |
0.920474 | + | 0.390803i | \(0.127803\pi\) | |||||||
\(164\) | −2.26777e11 | − | 3.92789e11i | −0.149265 | − | 0.258534i | ||||
\(165\) | −3.25354e11 | − | 5.63530e11i | −0.207107 | − | 0.358720i | ||||
\(166\) | 3.52021e11 | − | 6.09719e11i | 0.216758 | − | 0.375435i | ||||
\(167\) | −2.75483e12 | −1.64117 | −0.820587 | − | 0.571521i | \(-0.806354\pi\) | ||||
−0.820587 | + | 0.571521i | \(0.806354\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.45838e12 | −0.813755 | ||||||||
\(170\) | −4.00268e11 | + | 6.93284e11i | −0.216213 | + | 0.374492i | ||||
\(171\) | −6.05798e11 | − | 1.04927e12i | −0.316847 | − | 0.548795i | ||||
\(172\) | −1.26045e10 | − | 2.18317e10i | −0.00638440 | − | 0.0110581i | ||||
\(173\) | −4.75194e11 | + | 8.23060e11i | −0.233140 | + | 0.403811i | −0.958731 | − | 0.284316i | \(-0.908233\pi\) |
0.725590 | + | 0.688127i | \(0.241567\pi\) | |||||||
\(174\) | 7.76603e11 | 0.369129 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.27735e11 | 0.235557 | ||||||||
\(177\) | 6.53840e11 | − | 1.13248e12i | 0.282890 | − | 0.489981i | ||||
\(178\) | 2.99915e11 | + | 5.19468e11i | 0.125802 | + | 0.217896i | ||||
\(179\) | −8.40692e11 | − | 1.45612e12i | −0.341936 | − | 0.592251i | 0.642856 | − | 0.765987i | \(-0.277749\pi\) |
−0.984792 | + | 0.173736i | \(0.944416\pi\) | |||||||
\(180\) | 4.03987e11 | − | 6.99726e11i | 0.159356 | − | 0.276013i | ||||
\(181\) | 9.96774e11 | 0.381386 | 0.190693 | − | 0.981650i | \(-0.438927\pi\) | ||||
0.190693 | + | 0.981650i | \(0.438927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.75303e12 | 0.631406 | ||||||||
\(184\) | −7.87492e11 | + | 1.36398e12i | −0.275263 | + | 0.476770i | ||||
\(185\) | −4.40045e11 | − | 7.62181e11i | −0.149298 | − | 0.258591i | ||||
\(186\) | −1.59798e11 | − | 2.76778e11i | −0.0526319 | − | 0.0911612i | ||||
\(187\) | −1.84600e12 | + | 3.19736e12i | −0.590340 | + | 1.02250i | ||||
\(188\) | 3.95578e12 | 1.22847 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.23587e12 | −0.362100 | ||||||||
\(191\) | −1.38120e12 | + | 2.39231e12i | −0.393164 | + | 0.680980i | −0.992865 | − | 0.119244i | \(-0.961953\pi\) |
0.599701 | + | 0.800224i | \(0.295286\pi\) | |||||||
\(192\) | 3.40111e11 | + | 5.89090e11i | 0.0940729 | + | 0.162939i | ||||
\(193\) | −2.72119e12 | − | 4.71325e12i | −0.731466 | − | 1.26694i | −0.956256 | − | 0.292530i | \(-0.905503\pi\) |
0.224790 | − | 0.974407i | \(-0.427830\pi\) | |||||||
\(194\) | −9.00163e11 | + | 1.55913e12i | −0.235186 | + | 0.407354i | ||||
\(195\) | 7.03200e11 | 0.178603 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.87609e12 | −0.690619 | −0.345309 | − | 0.938489i | \(-0.612226\pi\) | ||||
−0.345309 | + | 0.938489i | \(0.612226\pi\) | |||||||
\(198\) | −7.29059e11 | + | 1.26277e12i | −0.170257 | + | 0.294893i | ||||
\(199\) | 3.64196e11 | + | 6.30805e11i | 0.0827262 | + | 0.143286i | 0.904420 | − | 0.426643i | \(-0.140304\pi\) |
−0.821694 | + | 0.569929i | \(0.806971\pi\) | |||||||
\(200\) | 1.07709e12 | + | 1.86557e12i | 0.238005 | + | 0.412237i | ||||
\(201\) | −1.95071e12 | + | 3.37873e12i | −0.419386 | + | 0.726399i | ||||
\(202\) | 1.96183e12 | 0.410421 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.56171e12 | 0.507651 | ||||||||
\(205\) | −7.44111e11 | + | 1.28884e12i | −0.143546 | + | 0.248629i | ||||
\(206\) | 2.70906e12 | + | 4.69223e12i | 0.508802 | + | 0.881272i | ||||
\(207\) | 1.05934e12 | + | 1.83483e12i | 0.193730 | + | 0.335551i | ||||
\(208\) | −2.85153e11 | + | 4.93899e11i | −0.0507843 | + | 0.0879610i | ||||
\(209\) | −5.69972e12 | −0.988665 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.79317e12 | −1.11820 | −0.559099 | − | 0.829101i | \(-0.688853\pi\) | ||||
−0.559099 | + | 0.829101i | \(0.688853\pi\) | |||||||
\(212\) | −1.17470e12 | + | 2.03463e12i | −0.188399 | + | 0.326317i | ||||
\(213\) | 1.23373e12 | + | 2.13688e12i | 0.192811 | + | 0.333958i | ||||
\(214\) | 1.08290e12 | + | 1.87563e12i | 0.164934 | + | 0.285674i | ||||
\(215\) | −4.13586e10 | + | 7.16352e10i | −0.00613980 | + | 0.0106344i | ||||
\(216\) | 6.19062e12 | 0.895856 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.76358e12 | −0.242597 | ||||||||
\(219\) | −1.84438e11 | + | 3.19455e11i | −0.0247404 | + | 0.0428517i | ||||
\(220\) | −1.90048e12 | − | 3.29173e12i | −0.248622 | − | 0.430625i | ||||
\(221\) | −1.99491e12 | − | 3.45529e12i | −0.254546 | − | 0.440886i | ||||
\(222\) | 5.51013e11 | − | 9.54383e11i | 0.0685836 | − | 0.118790i | ||||
\(223\) | −7.33486e12 | −0.890667 | −0.445333 | − | 0.895365i | \(-0.646915\pi\) | ||||
−0.445333 | + | 0.895365i | \(0.646915\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.89781e12 | 0.335016 | ||||||||
\(226\) | −1.02176e12 | + | 1.76974e12i | −0.115280 | + | 0.199671i | ||||
\(227\) | −6.79920e11 | − | 1.17766e12i | −0.0748713 | − | 0.129681i | 0.826159 | − | 0.563437i | \(-0.190521\pi\) |
−0.901030 | + | 0.433756i | \(0.857188\pi\) | |||||||
\(228\) | 1.97739e12 | + | 3.42495e12i | 0.212545 | + | 0.368139i | ||||
\(229\) | −5.91221e12 | + | 1.02402e13i | −0.620375 | + | 1.07452i | 0.369041 | + | 0.929413i | \(0.379686\pi\) |
−0.989416 | + | 0.145108i | \(0.953647\pi\) | |||||||
\(230\) | 2.16113e12 | 0.221400 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.08478e13 | 1.05964 | ||||||||
\(233\) | 8.78168e12 | − | 1.52103e13i | 0.837761 | − | 1.45104i | −0.0540024 | − | 0.998541i | \(-0.517198\pi\) |
0.891763 | − | 0.452503i | \(-0.149469\pi\) | |||||||
\(234\) | −7.87871e11 | − | 1.36463e12i | −0.0734121 | − | 0.127153i | ||||
\(235\) | −6.48995e12 | − | 1.12409e13i | −0.590701 | − | 1.02312i | ||||
\(236\) | 3.81925e12 | − | 6.61514e12i | 0.339596 | − | 0.588197i | ||||
\(237\) | −9.60545e12 | −0.834452 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.13958e12 | −0.592221 | −0.296111 | − | 0.955154i | \(-0.595690\pi\) | ||||
−0.296111 | + | 0.955154i | \(0.595690\pi\) | |||||||
\(240\) | −6.00751e11 | + | 1.04053e12i | −0.0487004 | + | 0.0843516i | ||||
\(241\) | −1.15653e11 | − | 2.00318e11i | −0.00916357 | − | 0.0158718i | 0.861407 | − | 0.507915i | \(-0.169584\pi\) |
−0.870571 | + | 0.492043i | \(0.836250\pi\) | |||||||
\(242\) | 5.97984e9 | + | 1.03574e10i | 0.000463132 | + | 0.000802169i | ||||
\(243\) | 6.70040e12 | − | 1.16054e13i | 0.507301 | − | 0.878672i | ||||
\(244\) | 1.02399e13 | 0.757972 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.86351e12 | −0.131883 | ||||||||
\(247\) | 3.07975e12 | − | 5.33429e12i | 0.213149 | − | 0.369184i | ||||
\(248\) | −2.23210e12 | − | 3.86610e12i | −0.151087 | − | 0.261691i | ||||
\(249\) | 3.69622e12 | + | 6.40205e12i | 0.244716 | + | 0.423860i | ||||
\(250\) | 4.30801e12 | − | 7.46170e12i | 0.279002 | − | 0.483245i | ||||
\(251\) | −1.29831e13 | −0.822567 | −0.411284 | − | 0.911507i | \(-0.634919\pi\) | ||||
−0.411284 | + | 0.911507i | \(0.634919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.96692e12 | 0.604502 | ||||||||
\(254\) | −3.15261e12 | + | 5.46047e12i | −0.187105 | + | 0.324075i | ||||
\(255\) | −4.20281e12 | − | 7.27949e12i | −0.244101 | − | 0.422795i | ||||
\(256\) | 6.82094e12 | + | 1.18142e13i | 0.387725 | + | 0.671560i | ||||
\(257\) | 1.19806e13 | − | 2.07510e13i | 0.666571 | − | 1.15453i | −0.312286 | − | 0.949988i | \(-0.601095\pi\) |
0.978857 | − | 0.204546i | \(-0.0655719\pi\) | |||||||
\(258\) | −1.03576e11 | −0.00564095 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.10758e12 | 0.214404 | ||||||||
\(261\) | 7.29626e12 | − | 1.26375e13i | 0.372887 | − | 0.645859i | ||||
\(262\) | −7.57835e12 | − | 1.31261e13i | −0.379243 | − | 0.656868i | ||||
\(263\) | 1.21369e13 | + | 2.10217e13i | 0.594771 | + | 1.03017i | 0.993579 | + | 0.113139i | \(0.0360907\pi\) |
−0.398808 | + | 0.917034i | \(0.630576\pi\) | |||||||
\(264\) | 5.69067e12 | − | 9.85652e12i | 0.273112 | − | 0.473045i | ||||
\(265\) | 7.70895e12 | 0.362362 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.29822e12 | −0.284057 | ||||||||
\(268\) | −1.13946e13 | + | 1.97361e13i | −0.503453 | + | 0.872006i | ||||
\(269\) | 1.29189e13 | + | 2.23761e13i | 0.559225 | + | 0.968606i | 0.997561 | + | 0.0697949i | \(0.0222345\pi\) |
−0.438337 | + | 0.898811i | \(0.644432\pi\) | |||||||
\(270\) | −4.24726e12 | − | 7.35646e12i | −0.180139 | − | 0.312010i | ||||
\(271\) | −1.88397e12 | + | 3.26313e12i | −0.0782964 | + | 0.135613i | −0.902515 | − | 0.430658i | \(-0.858281\pi\) |
0.824219 | + | 0.566272i | \(0.191615\pi\) | |||||||
\(272\) | 6.81710e12 | 0.277633 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.13277e12 | 0.279017 | ||||||||
\(275\) | 6.81610e12 | − | 1.18058e13i | 0.261340 | − | 0.452654i | ||||
\(276\) | −3.45780e12 | − | 5.98909e12i | −0.129957 | − | 0.225093i | ||||
\(277\) | 8.20947e12 | + | 1.42192e13i | 0.302466 | + | 0.523886i | 0.976694 | − | 0.214637i | \(-0.0688569\pi\) |
−0.674228 | + | 0.738523i | \(0.735524\pi\) | |||||||
\(278\) | −7.16152e12 | + | 1.24041e13i | −0.258678 | + | 0.448043i | ||||
\(279\) | −6.00526e12 | −0.212671 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.10357e13 | 0.716263 | 0.358132 | − | 0.933671i | \(-0.383414\pi\) | ||||
0.358132 | + | 0.933671i | \(0.383414\pi\) | |||||||
\(282\) | 8.12654e12 | − | 1.40756e13i | 0.271354 | − | 0.469998i | ||||
\(283\) | 8.35659e12 | + | 1.44740e13i | 0.273655 | + | 0.473985i | 0.969795 | − | 0.243922i | \(-0.0784340\pi\) |
−0.696140 | + | 0.717906i | \(0.745101\pi\) | |||||||
\(284\) | 7.20653e12 | + | 1.24821e13i | 0.231460 | + | 0.400900i | ||||
\(285\) | 6.48833e12 | − | 1.12381e13i | 0.204402 | − | 0.354035i | ||||
\(286\) | −7.41278e12 | −0.229070 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.23543e13 | 0.664817 | ||||||||
\(289\) | −6.71001e12 | + | 1.16221e13i | −0.195788 | + | 0.339114i | ||||
\(290\) | −7.44245e12 | − | 1.28907e13i | −0.213072 | − | 0.369052i | ||||
\(291\) | −9.45171e12 | − | 1.63708e13i | −0.265521 | − | 0.459896i | ||||
\(292\) | −1.07735e12 | + | 1.86603e12i | −0.0296996 | + | 0.0514413i | ||||
\(293\) | 2.39269e13 | 0.647312 | 0.323656 | − | 0.946175i | \(-0.395088\pi\) | ||||
0.323656 | + | 0.946175i | \(0.395088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.50639e13 | −0.653171 | ||||||||
\(296\) | 7.69669e12 | − | 1.33311e13i | 0.196879 | − | 0.341005i | ||||
\(297\) | −1.95879e13 | − | 3.39273e13i | −0.491845 | − | 0.851900i | ||||
\(298\) | −1.33852e13 | − | 2.31839e13i | −0.329940 | − | 0.571474i | ||||
\(299\) | −5.38546e12 | + | 9.32790e12i | −0.130326 | + | 0.225731i | ||||
\(300\) | −9.45878e12 | −0.224734 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.97867e13 | 0.453248 | ||||||||
\(303\) | −1.02996e13 | + | 1.78395e13i | −0.231679 | + | 0.401280i | ||||
\(304\) | 5.26214e12 | + | 9.11429e12i | 0.116240 | + | 0.201334i | ||||
\(305\) | −1.67999e13 | − | 2.90983e13i | −0.364466 | − | 0.631274i | ||||
\(306\) | −9.41773e12 | + | 1.63120e13i | −0.200668 | + | 0.347567i | ||||
\(307\) | −1.53111e13 | −0.320439 | −0.160219 | − | 0.987081i | \(-0.551220\pi\) | ||||
−0.160219 | + | 0.987081i | \(0.551220\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.68903e13 | −1.14886 | ||||||||
\(310\) | −3.06279e12 | + | 5.30491e12i | −0.0607614 | + | 0.105242i | ||||
\(311\) | 2.49376e13 | + | 4.31932e13i | 0.486040 | + | 0.841846i | 0.999871 | − | 0.0160451i | \(-0.00510753\pi\) |
−0.513831 | + | 0.857891i | \(0.671774\pi\) | |||||||
\(312\) | 6.14972e12 | + | 1.06516e13i | 0.117762 | + | 0.203970i | ||||
\(313\) | −4.97404e13 | + | 8.61529e13i | −0.935870 | + | 1.62097i | −0.162795 | + | 0.986660i | \(0.552051\pi\) |
−0.773075 | + | 0.634315i | \(0.781282\pi\) | |||||||
\(314\) | 3.15628e13 | 0.583529 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.61080e13 | −1.00172 | ||||||||
\(317\) | −4.16846e13 | + | 7.21999e13i | −0.731392 | + | 1.26681i | 0.224897 | + | 0.974383i | \(0.427795\pi\) |
−0.956289 | + | 0.292425i | \(0.905538\pi\) | |||||||
\(318\) | 4.82647e12 | + | 8.35970e12i | 0.0832301 | + | 0.144159i | ||||
\(319\) | −3.43239e13 | − | 5.94507e13i | −0.581765 | − | 1.00765i | ||||
\(320\) | 6.51880e12 | − | 1.12909e13i | 0.108603 | − | 0.188106i | ||||
\(321\) | −2.27408e13 | −0.372416 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.36271e13 | −1.16526 | ||||||||
\(324\) | 1.22558e12 | − | 2.12276e12i | 0.0190697 | − | 0.0330297i | ||||
\(325\) | 7.36594e12 | + | 1.27582e13i | 0.112686 | + | 0.195178i | ||||
\(326\) | −4.29399e12 | − | 7.43741e12i | −0.0645899 | − | 0.111873i | ||||
\(327\) | 9.25882e12 | − | 1.60367e13i | 0.136944 | − | 0.237194i | ||||
\(328\) | −2.60300e13 | −0.378589 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.56170e13 | −0.219670 | ||||||||
\(331\) | 3.17920e13 | − | 5.50654e13i | 0.439809 | − | 0.761771i | −0.557865 | − | 0.829931i | \(-0.688379\pi\) |
0.997674 | + | 0.0681600i | \(0.0217128\pi\) | |||||||
\(332\) | 2.15906e13 | + | 3.73961e13i | 0.293769 | + | 0.508823i | ||||
\(333\) | −1.03536e13 | − | 1.79330e13i | −0.138564 | − | 0.239999i | ||||
\(334\) | −3.30580e13 | + | 5.72581e13i | −0.435182 | + | 0.753758i | ||||
\(335\) | 7.47772e13 | 0.968329 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.21001e14 | 1.51644 | 0.758221 | − | 0.651997i | \(-0.226069\pi\) | ||||
0.758221 | + | 0.651997i | \(0.226069\pi\) | |||||||
\(338\) | −1.75006e13 | + | 3.03118e13i | −0.215779 | + | 0.373741i | ||||
\(339\) | −1.07285e13 | − | 1.85823e13i | −0.130149 | − | 0.225425i | ||||
\(340\) | −2.45498e13 | − | 4.25214e13i | −0.293031 | − | 0.507544i | ||||
\(341\) | −1.41253e13 | + | 2.44657e13i | −0.165901 | + | 0.287349i | ||||
\(342\) | −2.90783e13 | −0.336067 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.44678e12 | −0.0161931 | ||||||||
\(345\) | −1.13459e13 | + | 1.96517e13i | −0.124978 | + | 0.216469i | ||||
\(346\) | 1.14046e13 | + | 1.97534e13i | 0.123641 | + | 0.214153i | ||||
\(347\) | 7.78308e13 | + | 1.34807e14i | 0.830499 | + | 1.43847i | 0.897643 | + | 0.440724i | \(0.145278\pi\) |
−0.0671435 | + | 0.997743i | \(0.521389\pi\) | |||||||
\(348\) | −2.38158e13 | + | 4.12502e13i | −0.250138 | + | 0.433252i | ||||
\(349\) | 2.56430e13 | 0.265112 | 0.132556 | − | 0.991176i | \(-0.457682\pi\) | ||||
0.132556 | + | 0.991176i | \(0.457682\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.23361e13 | 0.424152 | ||||||||
\(352\) | 5.25808e13 | − | 9.10726e13i | 0.518612 | − | 0.898262i | ||||
\(353\) | 1.24549e13 | + | 2.15725e13i | 0.120943 | + | 0.209479i | 0.920140 | − | 0.391590i | \(-0.128075\pi\) |
−0.799197 | + | 0.601069i | \(0.794742\pi\) | |||||||
\(354\) | −1.56922e13 | − | 2.71796e13i | −0.150025 | − | 0.259851i | ||||
\(355\) | 2.36464e13 | − | 4.09568e13i | 0.222592 | − | 0.385541i | ||||
\(356\) | −3.67896e13 | −0.340996 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.03532e13 | −0.362678 | ||||||||
\(359\) | −7.87921e13 | + | 1.36472e14i | −0.697370 | + | 1.20788i | 0.272006 | + | 0.962296i | \(0.412313\pi\) |
−0.969375 | + | 0.245584i | \(0.921020\pi\) | |||||||
\(360\) | −2.31854e13 | − | 4.01582e13i | −0.202092 | − | 0.350034i | ||||
\(361\) | 1.41219e12 | + | 2.44599e12i | 0.0121228 | + | 0.0209974i | ||||
\(362\) | 1.19613e13 | − | 2.07176e13i | 0.101130 | − | 0.175163i | ||||
\(363\) | −1.25577e11 | −0.00104574 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.07011e12 | 0.0571236 | ||||||||
\(366\) | 2.10364e13 | − | 3.64361e13i | 0.167427 | − | 0.289992i | ||||
\(367\) | −8.89506e13 | − | 1.54067e14i | −0.697406 | − | 1.20794i | −0.969363 | − | 0.245633i | \(-0.921004\pi\) |
0.271957 | − | 0.962309i | \(-0.412329\pi\) | |||||||
\(368\) | −9.20172e12 | − | 1.59379e13i | −0.0710732 | − | 0.123102i | ||||
\(369\) | −1.75079e13 | + | 3.03245e13i | −0.133226 | + | 0.230754i | ||||
\(370\) | −2.11222e13 | −0.158354 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.96019e13 | 0.142663 | ||||||||
\(373\) | 2.75809e13 | − | 4.77715e13i | 0.197792 | − | 0.342586i | −0.750020 | − | 0.661415i | \(-0.769956\pi\) |
0.947812 | + | 0.318829i | \(0.103290\pi\) | |||||||
\(374\) | 4.43039e13 | + | 7.67367e13i | 0.313075 | + | 0.542262i | ||||
\(375\) | 4.52341e13 | + | 7.83478e13i | 0.314988 | + | 0.545576i | ||||
\(376\) | 1.13514e14 | − | 1.96611e14i | 0.778959 | − | 1.34920i | ||||
\(377\) | 7.41854e13 | 0.501696 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.46463e14 | 0.962083 | 0.481042 | − | 0.876698i | \(-0.340259\pi\) | ||||
0.481042 | + | 0.876698i | \(0.340259\pi\) | |||||||
\(380\) | 3.79001e13 | − | 6.56448e13i | 0.245375 | − | 0.425002i | ||||
\(381\) | −3.31024e13 | − | 5.73350e13i | −0.211238 | − | 0.365875i | ||||
\(382\) | 3.31488e13 | + | 5.74155e13i | 0.208507 | + | 0.361144i | ||||
\(383\) | 1.15725e14 | − | 2.00441e14i | 0.717519 | − | 1.24278i | −0.244462 | − | 0.969659i | \(-0.578611\pi\) |
0.961980 | − | 0.273120i | \(-0.0880555\pi\) | |||||||
\(384\) | −8.51940e13 | −0.520700 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.30617e14 | −0.775837 | ||||||||
\(387\) | −9.73108e11 | + | 1.68547e12i | −0.00569837 | + | 0.00986987i | ||||
\(388\) | −5.52100e13 | − | 9.56265e13i | −0.318745 | − | 0.552082i | ||||
\(389\) | 7.49358e13 | + | 1.29793e14i | 0.426547 | + | 0.738800i | 0.996563 | − | 0.0828326i | \(-0.0263967\pi\) |
−0.570017 | + | 0.821633i | \(0.693063\pi\) | |||||||
\(390\) | 8.43840e12 | − | 1.46157e13i | 0.0473592 | − | 0.0820286i | ||||
\(391\) | 1.28749e14 | 0.712480 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.59145e14 | 0.856317 | ||||||||
\(394\) | −3.45131e13 | + | 5.97784e13i | −0.183128 | + | 0.317187i | ||||
\(395\) | 9.20522e13 | + | 1.59439e14i | 0.481671 | + | 0.834278i | ||||
\(396\) | −4.47156e13 | − | 7.74497e13i | −0.230747 | − | 0.399665i | ||||
\(397\) | 1.04055e14 | − | 1.80229e14i | 0.529562 | − | 0.917228i | −0.469844 | − | 0.882750i | \(-0.655690\pi\) |
0.999405 | − | 0.0344782i | \(-0.0109769\pi\) | |||||||
\(398\) | 1.74814e13 | 0.0877443 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.51712e13 | −0.122906 | ||||||||
\(401\) | 6.67040e13 | − | 1.15535e14i | 0.321261 | − | 0.556440i | −0.659488 | − | 0.751715i | \(-0.729227\pi\) |
0.980748 | + | 0.195275i | \(0.0625601\pi\) | |||||||
\(402\) | 4.68170e13 | + | 8.10895e13i | 0.222413 | + | 0.385231i | ||||
\(403\) | −1.52648e13 | − | 2.64393e13i | −0.0715339 | − | 0.123900i | ||||
\(404\) | −6.01628e13 | + | 1.04205e14i | −0.278119 | + | 0.481716i | ||||
\(405\) | −8.04286e12 | −0.0366782 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.74134e13 | −0.432364 | ||||||||
\(408\) | 7.35101e13 | − | 1.27323e14i | 0.321896 | − | 0.557541i | ||||
\(409\) | −1.03084e14 | − | 1.78546e14i | −0.445361 | − | 0.771388i | 0.552716 | − | 0.833369i | \(-0.313591\pi\) |
−0.998077 | + | 0.0619816i | \(0.980258\pi\) | |||||||
\(410\) | 1.78587e13 | + | 3.09321e13i | 0.0761268 | + | 0.131856i | ||||
\(411\) | −3.74470e13 | + | 6.48602e13i | −0.157503 | + | 0.272802i | ||||
\(412\) | −3.32312e14 | −1.37915 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.08483e13 | 0.205482 | ||||||||
\(415\) | 7.08443e13 | − | 1.22706e14i | 0.282514 | − | 0.489329i | ||||
\(416\) | 5.68224e13 | + | 9.84192e13i | 0.223618 | + | 0.387317i | ||||
\(417\) | −7.51960e13 | − | 1.30243e14i | −0.292043 | − | 0.505833i | ||||
\(418\) | −6.83967e13 | + | 1.18467e14i | −0.262159 | + | 0.454073i | ||||
\(419\) | −7.34035e13 | −0.277677 | −0.138838 | − | 0.990315i | \(-0.544337\pi\) | ||||
−0.138838 | + | 0.990315i | \(0.544337\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.71112e14 | 0.630563 | 0.315282 | − | 0.948998i | \(-0.397901\pi\) | ||||
0.315282 | + | 0.948998i | \(0.397901\pi\) | |||||||
\(422\) | −8.15180e13 | + | 1.41193e14i | −0.296507 | + | 0.513565i | ||||
\(423\) | −1.52699e14 | − | 2.64483e14i | −0.548232 | − | 0.949566i | ||||
\(424\) | 6.74174e13 | + | 1.16770e14i | 0.238924 | + | 0.413828i | ||||
\(425\) | 8.80480e13 | − | 1.52504e14i | 0.308021 | − | 0.533508i | ||||
\(426\) | 5.92189e13 | 0.204507 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.32835e14 | −0.447067 | ||||||||
\(429\) | 3.89171e13 | − | 6.74063e13i | 0.129308 | − | 0.223968i | ||||
\(430\) | 9.92606e11 | + | 1.71924e12i | 0.00325612 | + | 0.00563977i | ||||
\(431\) | 3.58879e13 | + | 6.21597e13i | 0.116231 | + | 0.201319i | 0.918271 | − | 0.395952i | \(-0.129585\pi\) |
−0.802040 | + | 0.597270i | \(0.796252\pi\) | |||||||
\(432\) | −3.61682e13 | + | 6.26452e13i | −0.115656 | + | 0.200321i | ||||
\(433\) | −9.98812e13 | −0.315356 | −0.157678 | − | 0.987491i | \(-0.550401\pi\) | ||||
−0.157678 | + | 0.987491i | \(0.550401\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.56291e14 | 0.481110 | ||||||||
\(436\) | 5.40832e13 | − | 9.36749e13i | 0.164394 | − | 0.284739i | ||||
\(437\) | 9.93819e13 | + | 1.72134e14i | 0.298304 | + | 0.516678i | ||||
\(438\) | 4.42650e12 | + | 7.66693e12i | 0.0131206 | + | 0.0227255i | ||||
\(439\) | −1.45156e13 | + | 2.51418e13i | −0.0424894 | + | 0.0735938i | −0.886488 | − | 0.462752i | \(-0.846862\pi\) |
0.843999 | + | 0.536345i | \(0.180196\pi\) | |||||||
\(440\) | −2.18142e14 | −0.630594 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.57557e13 | −0.269987 | ||||||||
\(443\) | −1.64185e14 | + | 2.84377e14i | −0.457207 | + | 0.791906i | −0.998812 | − | 0.0487274i | \(-0.984483\pi\) |
0.541605 | + | 0.840633i | \(0.317817\pi\) | |||||||
\(444\) | 3.37955e13 | + | 5.85355e13i | 0.0929506 | + | 0.160995i | ||||
\(445\) | 6.03579e13 | + | 1.04543e14i | 0.163966 | + | 0.283998i | ||||
\(446\) | −8.80184e13 | + | 1.52452e14i | −0.236174 | + | 0.409065i | ||||
\(447\) | 2.81089e14 | 0.744994 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.12368e14 | −1.58364 | −0.791822 | − | 0.610752i | \(-0.790867\pi\) | ||||
−0.791822 | + | 0.610752i | \(0.790867\pi\) | |||||||
\(450\) | 3.47737e13 | − | 6.02298e13i | 0.0888346 | − | 0.153866i | ||||
\(451\) | 8.23624e13 | + | 1.42656e14i | 0.207854 | + | 0.360014i | ||||
\(452\) | −6.26681e13 | − | 1.08544e14i | −0.156237 | − | 0.270611i | ||||
\(453\) | −1.03880e14 | + | 1.79926e14i | −0.255855 | + | 0.443153i | ||||
\(454\) | −3.26361e13 | −0.0794130 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.26971e14 | 0.539092 | ||||||||
\(457\) | −1.51742e14 | + | 2.62824e14i | −0.356095 | + | 0.616774i | −0.987305 | − | 0.158838i | \(-0.949225\pi\) |
0.631210 | + | 0.775612i | \(0.282559\pi\) | |||||||
\(458\) | 1.41893e14 | + | 2.45766e14i | 0.329004 | + | 0.569851i | ||||
\(459\) | −2.53030e14 | − | 4.38261e14i | −0.579699 | − | 1.00407i | ||||
\(460\) | −6.62746e13 | + | 1.14791e14i | −0.150030 | + | 0.259860i | ||||
\(461\) | 7.29308e14 | 1.63138 | 0.815691 | − | 0.578487i | \(-0.196357\pi\) | ||||
0.815691 | + | 0.578487i | \(0.196357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.22188e14 | 0.266891 | 0.133445 | − | 0.991056i | \(-0.457396\pi\) | ||||
0.133445 | + | 0.991056i | \(0.457396\pi\) | |||||||
\(464\) | −6.33774e13 | + | 1.09773e14i | −0.136800 | + | 0.236944i | ||||
\(465\) | −3.21593e13 | − | 5.57015e13i | −0.0685986 | − | 0.118816i | ||||
\(466\) | −2.10760e14 | − | 3.65047e14i | −0.444290 | − | 0.769532i | ||||
\(467\) | −3.08690e14 | + | 5.34667e14i | −0.643103 | + | 1.11389i | 0.341634 | + | 0.939833i | \(0.389020\pi\) |
−0.984736 | + | 0.174053i | \(0.944314\pi\) | |||||||
\(468\) | 9.66455e13 | 0.198989 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.11517e14 | −0.626533 | ||||||||
\(471\) | −1.65705e14 | + | 2.87009e14i | −0.329397 | + | 0.570533i | ||||
\(472\) | −2.19192e14 | − | 3.79652e14i | −0.430669 | − | 0.745941i | ||||
\(473\) | 4.57780e12 | + | 7.92899e12i | 0.00889039 | + | 0.0153986i | ||||
\(474\) | −1.15265e14 | + | 1.99645e14i | −0.221268 | + | 0.383247i | ||||
\(475\) | 2.71858e14 | 0.515854 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.81381e14 | 0.336310 | ||||||||
\(478\) | −8.56749e13 | + | 1.48393e14i | −0.157036 | + | 0.271995i | ||||
\(479\) | 5.25419e14 | + | 9.10052e14i | 0.952052 | + | 1.64900i | 0.740976 | + | 0.671532i | \(0.234363\pi\) |
0.211076 | + | 0.977470i | \(0.432303\pi\) | |||||||
\(480\) | 1.19712e14 | + | 2.07346e14i | 0.214442 | + | 0.371424i | ||||
\(481\) | 5.26358e13 | − | 9.11678e13i | 0.0932144 | − | 0.161452i | ||||
\(482\) | −5.55137e12 | −0.00971944 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.33527e11 | −0.00125536 | ||||||||
\(485\) | −1.81158e14 | + | 3.13774e14i | −0.306533 | + | 0.530931i | ||||
\(486\) | −1.60810e14 | − | 2.78530e14i | −0.269037 | − | 0.465986i | ||||
\(487\) | 1.09955e14 | + | 1.90448e14i | 0.181889 | + | 0.315040i | 0.942524 | − | 0.334139i | \(-0.108446\pi\) |
−0.760635 | + | 0.649180i | \(0.775112\pi\) | |||||||
\(488\) | 2.93842e14 | − | 5.08949e14i | 0.480623 | − | 0.832463i | ||||
\(489\) | 9.01739e13 | 0.145842 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.83863e14 | −0.765199 | −0.382599 | − | 0.923914i | \(-0.624971\pi\) | ||||
−0.382599 | + | 0.923914i | \(0.624971\pi\) | |||||||
\(492\) | 5.71477e13 | − | 9.89827e13i | 0.0893698 | − | 0.154793i | ||||
\(493\) | −4.43384e14 | − | 7.67963e14i | −0.685681 | − | 1.18763i | ||||
\(494\) | −7.39141e13 | − | 1.28023e14i | −0.113039 | − | 0.195790i | ||||
\(495\) | −1.46723e14 | + | 2.54132e14i | −0.221906 | + | 0.384353i | ||||
\(496\) | 5.21634e13 | 0.0780219 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.77419e14 | 0.259560 | ||||||||
\(499\) | 5.44389e13 | − | 9.42909e13i | 0.0787691 | − | 0.136432i | −0.823950 | − | 0.566663i | \(-0.808234\pi\) |
0.902719 | + | 0.430230i | \(0.141568\pi\) | |||||||
\(500\) | 2.64225e14 | + | 4.57651e14i | 0.378128 | + | 0.654937i | ||||
\(501\) | −3.47109e14 | − | 6.01211e14i | −0.491313 | − | 0.850979i | ||||
\(502\) | −1.55797e14 | + | 2.69848e14i | −0.218116 | + | 0.377788i | ||||
\(503\) | −5.06588e14 | −0.701506 | −0.350753 | − | 0.936468i | \(-0.614074\pi\) | ||||
−0.350753 | + | 0.936468i | \(0.614074\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.94818e14 | 0.534927 | ||||||||
\(506\) | 1.19603e14 | − | 2.07158e14i | 0.160293 | − | 0.277635i | ||||
\(507\) | −1.83756e14 | − | 3.18274e14i | −0.243611 | − | 0.421947i | ||||
\(508\) | −1.93360e14 | − | 3.34909e14i | −0.253581 | − | 0.439214i | ||||
\(509\) | 4.28767e13 | − | 7.42646e13i | 0.0556254 | − | 0.0963461i | −0.836872 | − | 0.547399i | \(-0.815618\pi\) |
0.892497 | + | 0.451053i | \(0.148951\pi\) | |||||||
\(510\) | −2.01735e14 | −0.258908 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.64965e14 | −0.458423 | ||||||||
\(513\) | 3.90630e14 | − | 6.76590e14i | 0.485422 | − | 0.840776i | ||||
\(514\) | −2.87534e14 | − | 4.98024e14i | −0.353503 | − | 0.612284i | ||||
\(515\) | 5.45199e14 | + | 9.44312e14i | 0.663155 | + | 1.14862i | ||||
\(516\) | 3.17634e12 | − | 5.50158e12i | 0.00382255 | − | 0.00662086i | ||||
\(517\) | −1.43669e15 | −1.71066 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.39498e14 | −0.279178 | ||||||||
\(520\) | 1.17870e14 | − | 2.04156e14i | 0.135951 | − | 0.235475i | ||||
\(521\) | 4.63787e14 | + | 8.03303e14i | 0.529312 | + | 0.916795i | 0.999416 | + | 0.0341835i | \(0.0108831\pi\) |
−0.470104 | + | 0.882611i | \(0.655784\pi\) | |||||||
\(522\) | −1.75110e14 | − | 3.03300e14i | −0.197753 | − | 0.342519i | ||||
\(523\) | −1.09093e13 | + | 1.88955e13i | −0.0121910 | + | 0.0211154i | −0.872057 | − | 0.489405i | \(-0.837214\pi\) |
0.859866 | + | 0.510521i | \(0.170547\pi\) | |||||||
\(524\) | 9.29610e14 | 1.02797 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.82569e14 | 0.630850 | ||||||||
\(527\) | −1.82466e14 | + | 3.16040e14i | −0.195534 | + | 0.338675i | ||||
\(528\) | 6.64946e13 | + | 1.15172e14i | 0.0705179 | + | 0.122141i | ||||
\(529\) | 3.02619e14 | + | 5.24152e14i | 0.317607 | + | 0.550112i | ||||
\(530\) | 9.25074e13 | − | 1.60227e14i | 0.0960858 | − | 0.166425i | ||||
\(531\) | −5.89717e14 | −0.606211 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.78013e14 | −0.179247 | ||||||||
\(534\) | −7.55786e13 | + | 1.30906e14i | −0.0753220 | + | 0.130462i | ||||
\(535\) | 2.17933e14 | + | 3.77470e14i | 0.214969 | + | 0.372338i | ||||
\(536\) | 6.53952e14 | + | 1.13268e15i | 0.638469 | + | 1.10586i | ||||
\(537\) | 2.11854e14 | − | 3.66943e14i | 0.204729 | − | 0.354601i | ||||
\(538\) | 6.20105e14 | 0.593147 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.20997e14 | 0.488280 | ||||||||
\(541\) | 8.47633e14 | − | 1.46814e15i | 0.786363 | − | 1.36202i | −0.141819 | − | 0.989893i | \(-0.545295\pi\) |
0.928181 | − | 0.372128i | \(-0.121372\pi\) | |||||||
\(542\) | 4.52152e13 | + | 7.83150e13i | 0.0415230 | + | 0.0719199i | ||||
\(543\) | 1.25594e14 | + | 2.17534e14i | 0.114174 | + | 0.197756i | ||||
\(544\) | 6.79220e14 | − | 1.17644e15i | 0.611247 | − | 1.05871i | ||||
\(545\) | −3.54921e14 | −0.316192 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.52145e14 | 0.656706 | 0.328353 | − | 0.944555i | \(-0.393506\pi\) | ||||
0.328353 | + | 0.944555i | \(0.393506\pi\) | |||||||
\(548\) | −2.18738e14 | + | 3.78866e14i | −0.189074 | + | 0.327486i | ||||
\(549\) | −3.95278e14 | − | 6.84641e14i | −0.338263 | − | 0.585888i | ||||
\(550\) | −1.63586e14 | − | 2.83340e14i | −0.138596 | − | 0.240056i | ||||
\(551\) | 6.84499e14 | − | 1.18559e15i | 0.574168 | − | 0.994488i | ||||
\(552\) | −3.96896e14 | −0.329619 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.94054e14 | 0.320813 | ||||||||
\(555\) | 1.10891e14 | − | 1.92070e14i | 0.0893895 | − | 0.154827i | ||||
\(556\) | −4.39240e14 | − | 7.60786e14i | −0.350583 | − | 0.607227i | ||||
\(557\) | −9.37445e13 | − | 1.62370e14i | −0.0740870 | − | 0.128323i | 0.826602 | − | 0.562787i | \(-0.190271\pi\) |
−0.900689 | + | 0.434465i | \(0.856938\pi\) | |||||||
\(558\) | −7.20631e13 | + | 1.24817e14i | −0.0563929 | + | 0.0976754i | ||||
\(559\) | −9.89417e12 | −0.00766681 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.30383e14 | −0.706913 | ||||||||
\(562\) | 2.52429e14 | − | 4.37219e14i | 0.189928 | − | 0.328965i | ||||
\(563\) | 1.22486e14 | + | 2.12151e14i | 0.0912618 | + | 0.158070i | 0.908042 | − | 0.418878i | \(-0.137577\pi\) |
−0.816781 | + | 0.576949i | \(0.804243\pi\) | |||||||
\(564\) | 4.98428e14 | + | 8.63302e14i | 0.367762 | + | 0.636983i | ||||
\(565\) | −2.05630e14 | + | 3.56161e14i | −0.150252 | + | 0.260244i | ||||
\(566\) | 4.01116e14 | 0.290255 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.27185e14 | 0.587066 | ||||||||
\(569\) | −6.76213e14 | + | 1.17124e15i | −0.475298 | + | 0.823240i | −0.999600 | − | 0.0282923i | \(-0.990993\pi\) |
0.524302 | + | 0.851533i | \(0.324326\pi\) | |||||||
\(570\) | −1.55720e14 | − | 2.69715e14i | −0.108401 | − | 0.187756i | ||||
\(571\) | −7.16114e14 | − | 1.24035e15i | −0.493723 | − | 0.855154i | 0.506250 | − | 0.862387i | \(-0.331031\pi\) |
−0.999974 | + | 0.00723249i | \(0.997698\pi\) | |||||||
\(572\) | 2.27325e14 | − | 3.93739e14i | 0.155228 | − | 0.268862i | ||||
\(573\) | −6.96126e14 | −0.470801 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.75389e14 | −0.315410 | ||||||||
\(576\) | 1.53378e14 | − | 2.65659e14i | 0.100795 | − | 0.174582i | ||||
\(577\) | −4.38830e14 | − | 7.60075e14i | −0.285647 | − | 0.494754i | 0.687119 | − | 0.726545i | \(-0.258875\pi\) |
−0.972766 | + | 0.231790i | \(0.925542\pi\) | |||||||
\(578\) | 1.61040e14 | + | 2.78930e14i | 0.103832 | + | 0.179842i | ||||
\(579\) | 6.85741e14 | − | 1.18774e15i | 0.437953 | − | 0.758558i | ||||
\(580\) | 9.12940e14 | 0.577548 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.53682e14 | −0.281628 | ||||||||
\(583\) | 4.26635e14 | − | 7.38954e14i | 0.262349 | − | 0.454402i | ||||
\(584\) | 6.18305e13 | + | 1.07094e14i | 0.0376645 | + | 0.0652369i | ||||
\(585\) | −1.58559e14 | − | 2.74632e14i | −0.0956827 | − | 0.165727i | ||||
\(586\) | 2.87122e14 | − | 4.97310e14i | 0.171645 | − | 0.297297i | ||||
\(587\) | 2.43425e15 | 1.44164 | 0.720818 | − | 0.693124i | \(-0.243766\pi\) | ||||
0.720818 | + | 0.693124i | \(0.243766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.63383e14 | −0.327469 | ||||||||
\(590\) | −3.00766e14 | + | 5.20942e14i | −0.173198 | + | 0.299988i | ||||
\(591\) | −3.62388e14 | − | 6.27674e14i | −0.206748 | − | 0.358099i | ||||
\(592\) | 8.99347e13 | + | 1.55771e14i | 0.0508344 | + | 0.0880478i | ||||
\(593\) | −1.51659e14 | + | 2.62681e14i | −0.0849313 | + | 0.147105i | −0.905362 | − | 0.424641i | \(-0.860400\pi\) |
0.820431 | + | 0.571746i | \(0.193734\pi\) | |||||||
\(594\) | −9.40221e14 | −0.521680 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.64192e15 | 0.894329 | ||||||||
\(597\) | −9.17773e13 | + | 1.58963e14i | −0.0495309 | + | 0.0857901i | ||||
\(598\) | 1.29251e14 | + | 2.23870e14i | 0.0691159 | + | 0.119712i | ||||
\(599\) | 8.50992e14 | + | 1.47396e15i | 0.450898 | + | 0.780978i | 0.998442 | − | 0.0557990i | \(-0.0177706\pi\) |
−0.547544 | + | 0.836777i | \(0.684437\pi\) | |||||||
\(600\) | −2.71426e14 | + | 4.70124e14i | −0.142502 | + | 0.246820i | ||||
\(601\) | −2.33922e15 | −1.21692 | −0.608458 | − | 0.793586i | \(-0.708212\pi\) | ||||
−0.608458 | + | 0.793586i | \(0.708212\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.75940e15 | 0.898710 | ||||||||
\(604\) | −6.06793e14 | + | 1.05100e15i | −0.307141 | + | 0.531984i | ||||
\(605\) | 1.20344e12 | + | 2.08442e12i | 0.000603630 | + | 0.00104552i | ||||
\(606\) | 2.47191e14 | + | 4.28147e14i | 0.122866 | + | 0.212811i | ||||
\(607\) | −1.24804e15 | + | 2.16166e15i | −0.614737 | + | 1.06476i | 0.375694 | + | 0.926744i | \(0.377405\pi\) |
−0.990431 | + | 0.138012i | \(0.955929\pi\) | |||||||
\(608\) | 2.09717e15 | 1.02368 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.06395e14 | −0.386575 | ||||||||
\(611\) | 7.76292e14 | − | 1.34458e15i | 0.368806 | − | 0.638791i | ||||
\(612\) | −5.77621e14 | − | 1.00047e15i | −0.271963 | − | 0.471054i | ||||
\(613\) | −1.23650e15 | − | 2.14169e15i | −0.576983 | − | 0.999364i | −0.995823 | − | 0.0913040i | \(-0.970897\pi\) |
0.418840 | − | 0.908060i | \(-0.362437\pi\) | |||||||
\(614\) | −1.83733e14 | + | 3.18235e14i | −0.0849692 | + | 0.147171i | ||||
\(615\) | −3.75032e14 | −0.171892 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.43368e13 | 0.0109571 | 0.00547854 | − | 0.999985i | \(-0.498256\pi\) | ||||
0.00547854 | + | 0.999985i | \(0.498256\pi\) | |||||||
\(618\) | −6.82684e14 | + | 1.18244e15i | −0.304637 | + | 0.527647i | ||||
\(619\) | 2.11273e15 | + | 3.65935e15i | 0.934425 | + | 1.61847i | 0.775656 | + | 0.631156i | \(0.217419\pi\) |
0.158769 | + | 0.987316i | \(0.449247\pi\) | |||||||
\(620\) | −1.87851e14 | − | 3.25368e14i | −0.0823492 | − | 0.142633i | ||||
\(621\) | −6.83081e14 | + | 1.18313e15i | −0.296803 | + | 0.514078i | ||||
\(622\) | 1.19700e15 | 0.515523 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.43717e14 | −0.0608126 | ||||||||
\(625\) | 2.44448e14 | − | 4.23396e14i | 0.102529 | − | 0.177585i | ||||
\(626\) | 1.19377e15 | + | 2.06767e15i | 0.496320 | + | 0.859652i | ||||
\(627\) | −7.18165e14 | − | 1.24390e15i | −0.295973 | − | 0.512641i | ||||
\(628\) | −9.67926e14 | + | 1.67650e15i | −0.395425 | + | 0.684896i | ||||
\(629\) | −1.25835e15 | −0.509594 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.26326e15 | −1.69660 | −0.848302 | − | 0.529513i | \(-0.822375\pi\) | ||||
−0.848302 | + | 0.529513i | \(0.822375\pi\) | |||||||
\(632\) | −1.61006e15 | + | 2.78870e15i | −0.635180 | + | 1.10016i | ||||
\(633\) | −8.55939e14 | − | 1.48253e15i | −0.334751 | − | 0.579807i | ||||
\(634\) | 1.00043e15 | + | 1.73280e15i | 0.387879 | + | 0.671826i | ||||
\(635\) | −6.34462e14 | + | 1.09892e15i | −0.243865 | + | 0.422387i | ||||
\(636\) | −5.92047e14 | −0.225602 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.64755e15 | −0.617055 | ||||||||
\(639\) | 5.56367e14 | − | 9.63656e14i | 0.206589 | − | 0.357822i | ||||
\(640\) | 8.16442e14 | + | 1.41412e15i | 0.300563 | + | 0.520591i | ||||
\(641\) | −5.04148e14 | − | 8.73210e14i | −0.184009 | − | 0.318713i | 0.759233 | − | 0.650819i | \(-0.225574\pi\) |
−0.943242 | + | 0.332106i | \(0.892241\pi\) | |||||||
\(642\) | −2.72890e14 | + | 4.72659e14i | −0.0987516 | + | 0.171043i | ||||
\(643\) | −3.03982e14 | −0.109066 | −0.0545328 | − | 0.998512i | \(-0.517367\pi\) | ||||
−0.0545328 | + | 0.998512i | \(0.517367\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.08447e13 | −0.00735221 | ||||||||
\(646\) | −8.83525e14 | + | 1.53031e15i | −0.308987 | + | 0.535181i | ||||
\(647\) | 1.71791e15 | + | 2.97551e15i | 0.595700 | + | 1.03178i | 0.993448 | + | 0.114288i | \(0.0364588\pi\) |
−0.397747 | + | 0.917495i | \(0.630208\pi\) | |||||||
\(648\) | −7.03376e13 | − | 1.21828e14i | −0.0241838 | − | 0.0418876i | ||||
\(649\) | −1.38711e15 | + | 2.40254e15i | −0.472894 | + | 0.819076i | ||||
\(650\) | 3.53565e14 | 0.119521 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.26730e14 | 0.175076 | ||||||||
\(653\) | 5.92694e14 | − | 1.02658e15i | 0.195347 | − | 0.338352i | −0.751667 | − | 0.659543i | \(-0.770750\pi\) |
0.947014 | + | 0.321191i | \(0.104083\pi\) | |||||||
\(654\) | −2.22212e14 | − | 3.84882e14i | −0.0726255 | − | 0.125791i | ||||
\(655\) | −1.52514e15 | − | 2.64162e15i | −0.494291 | − | 0.856138i | ||||
\(656\) | 1.52078e14 | − | 2.63407e14i | 0.0488761 | − | 0.0846559i | ||||
\(657\) | 1.66350e14 | 0.0530167 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.26510e15 | −0.709934 | −0.354967 | − | 0.934879i | \(-0.615508\pi\) | ||||
−0.354967 | + | 0.934879i | \(0.615508\pi\) | |||||||
\(660\) | 4.78921e14 | − | 8.29516e14i | 0.148858 | − | 0.257830i | ||||
\(661\) | −2.66506e15 | − | 4.61602e15i | −0.821484 | − | 1.42285i | −0.904577 | − | 0.426310i | \(-0.859813\pi\) |
0.0830931 | − | 0.996542i | \(-0.473520\pi\) | |||||||
\(662\) | −7.63008e14 | − | 1.32157e15i | −0.233244 | − | 0.403990i | ||||
\(663\) | 5.02717e14 | − | 8.70732e14i | 0.152405 | − | 0.263973i | ||||
\(664\) | 2.47823e15 | 0.745104 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.96974e14 | −0.146969 | ||||||||
\(667\) | −1.19696e15 | + | 2.07320e15i | −0.351065 | + | 0.608062i | ||||
\(668\) | −2.02756e15 | − | 3.51183e15i | −0.589797 | − | 1.02156i | ||||
\(669\) | −9.24193e14 | − | 1.60075e15i | −0.266636 | − | 0.461827i | ||||
\(670\) | 8.97327e14 | − | 1.55422e15i | 0.256767 | − | 0.444733i | ||||
\(671\) | −3.71902e15 | −1.05549 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.74120e15 | 1.32375 | 0.661874 | − | 0.749615i | \(-0.269761\pi\) | ||||
0.661874 | + | 0.749615i | \(0.269761\pi\) | |||||||
\(674\) | 1.45202e15 | − | 2.51497e15i | 0.402108 | − | 0.696471i | ||||
\(675\) | 9.34280e14 | + | 1.61822e15i | 0.256629 | + | 0.444495i | ||||
\(676\) | −1.07337e15 | − | 1.85913e15i | −0.292443 | − | 0.506526i | ||||
\(677\) | −7.06536e14 | + | 1.22376e15i | −0.190940 | + | 0.330717i | −0.945562 | − | 0.325442i | \(-0.894487\pi\) |
0.754622 | + | 0.656160i | \(0.227820\pi\) | |||||||
\(678\) | −5.14968e14 | −0.138044 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.81789e15 | −0.743232 | ||||||||
\(681\) | 1.71340e14 | − | 2.96769e14i | 0.0448280 | − | 0.0776443i | ||||
\(682\) | 3.39007e14 | + | 5.87178e14i | 0.0879822 | + | 0.152390i | ||||
\(683\) | 1.51558e15 | + | 2.62506e15i | 0.390180 | + | 0.675811i | 0.992473 | − | 0.122464i | \(-0.0390796\pi\) |
−0.602293 | + | 0.798275i | \(0.705746\pi\) | |||||||
\(684\) | 8.91734e14 | − | 1.54453e15i | 0.227734 | − | 0.394446i | ||||
\(685\) | 1.43547e15 | 0.363660 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.97975e15 | −0.742879 | ||||||||
\(688\) | 8.45270e12 | − | 1.46405e13i | 0.00209054 | − | 0.00362093i | ||||
\(689\) | 4.61051e14 | + | 7.98564e14i | 0.113121 | + | 0.195931i | ||||
\(690\) | 2.72302e14 | + | 4.71641e14i | 0.0662798 | + | 0.114800i | ||||
\(691\) | −1.37366e15 | + | 2.37924e15i | −0.331703 | + | 0.574526i | −0.982846 | − | 0.184429i | \(-0.940956\pi\) |
0.651143 | + | 0.758955i | \(0.274290\pi\) | |||||||
\(692\) | −1.39897e15 | −0.335139 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.73588e15 | 0.880878 | ||||||||
\(695\) | −1.44126e15 | + | 2.49633e15i | −0.337151 | + | 0.583963i | ||||
\(696\) | 1.36682e15 | + | 2.36740e15i | 0.317220 | + | 0.549442i | ||||
\(697\) | 1.06393e15 | + | 1.84278e15i | 0.244981 | + | 0.424320i | ||||
\(698\) | 3.07716e14 | − | 5.32980e14i | 0.0702984 | − | 0.121760i | ||||
\(699\) | 4.42597e15 | 1.00319 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.72747e15 | 1.27795 | 0.638974 | − | 0.769228i | \(-0.279359\pi\) | ||||
0.638974 | + | 0.769228i | \(0.279359\pi\) | |||||||
\(702\) | 5.08033e14 | − | 8.79940e14i | 0.112470 | − | 0.194804i | ||||
\(703\) | −9.71326e14 | − | 1.68239e15i | −0.213359 | − | 0.369549i | ||||
\(704\) | −7.21538e14 | − | 1.24974e15i | −0.157257 | − | 0.272377i | ||||
\(705\) | 1.63547e15 | − | 2.83271e15i | 0.353673 | − | 0.612579i | ||||
\(706\) | 5.97836e14 | 0.128279 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.92490e15 | 0.406655 | ||||||||
\(709\) | −3.49163e14 | + | 6.04768e14i | −0.0731938 | + | 0.126775i | −0.900299 | − | 0.435271i | \(-0.856652\pi\) |
0.827106 | + | 0.562047i | \(0.189986\pi\) | |||||||
\(710\) | −5.67514e14 | − | 9.82964e14i | −0.118047 | − | 0.204464i | ||||
\(711\) | 2.16586e15 | + | 3.75137e15i | 0.447040 | + | 0.774297i | ||||
\(712\) | −1.05570e15 | + | 1.82853e15i | −0.216223 | + | 0.374508i | ||||
\(713\) | 9.85170e14 | 0.200225 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.49182e15 | −0.298561 | ||||||||
\(716\) | 1.23750e15 | − | 2.14341e15i | 0.245767 | − | 0.425681i | ||||
\(717\) | −8.99587e14 | − | 1.55813e15i | −0.177291 | − | 0.307078i | ||||
\(718\) | 1.89101e15 | + | 3.27533e15i | 0.369836 | + | 0.640575i | ||||
\(719\) | 4.85489e15 | − | 8.40892e15i | 0.942260 | − | 1.63204i | 0.181114 | − | 0.983462i | \(-0.442030\pi\) |
0.761146 | − | 0.648580i | \(-0.224637\pi\) | |||||||
\(720\) | 5.41835e14 | 0.104361 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.77852e13 | 0.0128582 | ||||||||
\(723\) | 2.91447e13 | − | 5.04801e13i | 0.00548654 | − | 0.00950297i | ||||
\(724\) | 7.33626e14 | + | 1.27068e15i | 0.137061 | + | 0.237396i | ||||
\(725\) | 1.63713e15 | + | 2.83560e15i | 0.303547 | + | 0.525758i | ||||
\(726\) | −1.50692e12 | + | 2.61006e12i | −0.000277293 | + | 0.000480285i | ||||
\(727\) | −2.46469e15 | −0.450114 | −0.225057 | − | 0.974346i | \(-0.572257\pi\) | ||||
−0.225057 | + | 0.974346i | \(0.572257\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.08202e15 | 0.554413 | ||||||||
\(730\) | 8.48413e13 | − | 1.46950e14i | 0.0151472 | − | 0.0262357i | ||||
\(731\) | 5.91345e13 | + | 1.02424e14i | 0.0104784 | + | 0.0181491i | ||||
\(732\) | 1.29023e15 | + | 2.23475e15i | 0.226912 | + | 0.393023i | ||||
\(733\) | 3.95643e15 | − | 6.85273e15i | 0.690607 | − | 1.19617i | −0.281032 | − | 0.959698i | \(-0.590677\pi\) |
0.971639 | − | 0.236469i | \(-0.0759900\pi\) | |||||||
\(734\) | −4.26963e15 | −0.739711 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.66725e15 | −0.625911 | ||||||||
\(737\) | 4.13839e15 | − | 7.16789e15i | 0.701067 | − | 1.21428i | ||||
\(738\) | 4.20189e14 | + | 7.27788e14i | 0.0706536 | + | 0.122376i | ||||
\(739\) | 4.20347e15 | + | 7.28062e15i | 0.701558 | + | 1.21513i | 0.967920 | + | 0.251260i | \(0.0808450\pi\) |
−0.266362 | + | 0.963873i | \(0.585822\pi\) | |||||||
\(740\) | 6.47746e14 | − | 1.12193e15i | 0.107308 | − | 0.185862i | ||||
\(741\) | 1.55220e15 | 0.255239 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.36287e15 | 0.220809 | 0.110404 | − | 0.993887i | \(-0.464785\pi\) | ||||
0.110404 | + | 0.993887i | \(0.464785\pi\) | |||||||
\(744\) | 5.62488e14 | − | 9.74258e14i | 0.0904612 | − | 0.156683i | ||||
\(745\) | −2.69377e15 | − | 4.66575e15i | −0.430033 | − | 0.744838i | ||||
\(746\) | −6.61941e14 | − | 1.14652e15i | −0.104895 | − | 0.181684i | ||||
\(747\) | 1.66686e15 | − | 2.88709e15i | 0.262203 | − | 0.454148i | ||||
\(748\) | −5.43462e15 | −0.848614 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.17124e15 | 0.334095 | ||||||||
\(751\) | −3.40861e15 | + | 5.90389e15i | −0.520664 | + | 0.901817i | 0.479047 | + | 0.877789i | \(0.340982\pi\) |
−0.999711 | + | 0.0240276i | \(0.992351\pi\) | |||||||
\(752\) | 1.32639e15 | + | 2.29737e15i | 0.201128 | + | 0.348364i | ||||
\(753\) | −1.63586e15 | − | 2.83340e15i | −0.246249 | − | 0.426516i | ||||
\(754\) | 8.90225e14 | − | 1.54191e15i | 0.133032 | − | 0.230419i | ||||
\(755\) | 3.98208e15 | 0.590747 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.67049e14 | −0.0975282 | −0.0487641 | − | 0.998810i | \(-0.515528\pi\) | ||||
−0.0487641 | + | 0.998810i | \(0.515528\pi\) | |||||||
\(758\) | 1.75756e15 | − | 3.04418e15i | 0.255111 | − | 0.441865i | ||||
\(759\) | 1.25583e15 | + | 2.17516e15i | 0.180968 | + | 0.313446i | ||||
\(760\) | −2.17513e15 | − | 3.76744e15i | −0.311180 | − | 0.538979i | ||||
\(761\) | −3.87204e15 | + | 6.70657e15i | −0.549951 | + | 0.952544i | 0.448326 | + | 0.893870i | \(0.352020\pi\) |
−0.998277 | + | 0.0586734i | \(0.981313\pi\) | |||||||
\(762\) | −1.58891e15 | −0.224052 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.06626e15 | −0.565173 | ||||||||
\(765\) | −1.89532e15 | + | 3.28279e15i | −0.261544 | + | 0.453007i | ||||
\(766\) | −2.77739e15 | − | 4.81059e15i | −0.380522 | − | 0.659083i | ||||
\(767\) | −1.49900e15 | − | 2.59634e15i | −0.203905 | − | 0.353173i | ||||
\(768\) | −1.71888e15 | + | 2.97718e15i | −0.232144 | + | 0.402086i | ||||
\(769\) | −2.52411e15 | −0.338465 | −0.169232 | − | 0.985576i | \(-0.554129\pi\) | ||||
−0.169232 | + | 0.985576i | \(0.554129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.03822e15 | 0.798197 | ||||||||
\(772\) | 4.00560e15 | − | 6.93790e15i | 0.525741 | − | 0.910611i | ||||
\(773\) | −5.57263e15 | − | 9.65209e15i | −0.726229 | − | 1.25786i | −0.958466 | − | 0.285206i | \(-0.907938\pi\) |
0.232238 | − | 0.972659i | \(-0.425395\pi\) | |||||||
\(774\) | 2.33546e13 | + | 4.04514e13i | 0.00302202 | + | 0.00523429i | ||||
\(775\) | 6.73730e14 | − | 1.16693e15i | 0.0865618 | − | 0.149930i | ||||
\(776\) | −6.33715e15 | −0.808452 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.59692e15 | 0.452421 | ||||||||
\(779\) | −1.64250e15 | + | 2.84489e15i | −0.205140 | + | 0.355312i | ||||
\(780\) | 5.17555e14 | + | 8.96431e14i | 0.0641854 | + | 0.111172i | ||||
\(781\) | −2.61732e15 | − | 4.53334e15i | −0.322312 | − | 0.558261i | ||||
\(782\) | 1.54499e15 | − | 2.67600e15i | 0.188925 | − | 0.327227i | ||||
\(783\) | 9.40952e15 | 1.14256 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.35201e15 | 0.760551 | ||||||||
\(786\) | 1.90974e15 | − | 3.30777e15i | 0.227065 | − | 0.393289i | ||||
\(787\) | 6.61355e15 | + | 1.14550e16i | 0.780861 | + | 1.35249i | 0.931441 | + | 0.363893i | \(0.118553\pi\) |
−0.150580 | + | 0.988598i | \(0.548114\pi\) | |||||||
\(788\) | −2.11680e15 | − | 3.66641e15i | −0.248191 | − | 0.429880i | ||||
\(789\) | −3.05849e15 | + | 5.29746e15i | −0.356109 | + | 0.616800i | ||||
\(790\) | 4.41850e15 | 0.510889 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.13257e15 | −0.585257 | ||||||||
\(793\) | 2.00951e15 | − | 3.48058e15i | 0.227556 | − | 0.394138i | ||||
\(794\) | −2.49733e15 | − | 4.32550e15i | −0.280843 | − | 0.486434i | ||||
\(795\) | 9.71328e14 | + | 1.68239e15i | 0.108479 | + | 0.187892i | ||||
\(796\) | −5.36096e14 | + | 9.28546e14i | −0.0594594 | + | 0.102987i | ||||
\(797\) | −2.30248e15 | −0.253615 | −0.126807 | − | 0.991927i | \(-0.540473\pi\) | ||||
−0.126807 | + | 0.991927i | \(0.540473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.85587e16 | −2.01623 | ||||||||
\(800\) | −2.50793e15 | + | 4.34386e15i | −0.270595 | + | 0.468685i | ||||
\(801\) | 1.42014e15 | + | 2.45975e15i | 0.152178 | + | 0.263579i | ||||
\(802\) | −1.60090e15 | − | 2.77283e15i | −0.170374 | − | 0.295097i | ||||
\(803\) | 3.91280e14 | − | 6.77717e14i | 0.0413573 | − | 0.0716330i | ||||
\(804\) | −5.74289e15 | −0.602868 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.32708e14 | −0.0758732 | ||||||||
\(807\) | −3.25555e15 | + | 5.63878e15i | −0.334827 | + | 0.579937i | ||||
\(808\) | 3.45282e15 | + | 5.98046e15i | 0.352705 | + | 0.610903i | ||||
\(809\) | −2.80236e15 | − | 4.85383e15i | −0.284320 | − | 0.492456i | 0.688124 | − | 0.725593i | \(-0.258434\pi\) |
−0.972444 | + | 0.233137i | \(0.925101\pi\) | |||||||
\(810\) | −9.65143e13 | + | 1.67168e14i | −0.00972577 | + | 0.0168455i | ||||
\(811\) | 5.08516e15 | 0.508968 | 0.254484 | − | 0.967077i | \(-0.418094\pi\) | ||||
0.254484 | + | 0.967077i | \(0.418094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.49519e14 | −0.0937574 | ||||||||
\(814\) | −1.16896e15 | + | 2.02470e15i | −0.114648 | + | 0.198576i | ||||
\(815\) | −8.64166e14 | − | 1.49678e15i | −0.0841842 | − | 0.145811i | ||||
\(816\) | 8.58954e14 | + | 1.48775e15i | 0.0831140 | + | 0.143958i | ||||
\(817\) | −9.12922e13 | + | 1.58123e14i | −0.00877430 | + | 0.0151975i | ||||
\(818\) | −4.94802e15 | −0.472377 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.19066e15 | −0.206348 | ||||||||
\(821\) | −1.39555e14 | + | 2.41717e14i | −0.0130575 | + | 0.0226162i | −0.872480 | − | 0.488649i | \(-0.837490\pi\) |
0.859423 | + | 0.511265i | \(0.170823\pi\) | |||||||
\(822\) | 8.98729e14 | + | 1.55664e15i | 0.0835283 | + | 0.144675i | ||||
\(823\) | 6.76326e15 | + | 1.17143e16i | 0.624391 | + | 1.08148i | 0.988658 | + | 0.150183i | \(0.0479863\pi\) |
−0.364267 | + | 0.931295i | \(0.618680\pi\) | |||||||
\(824\) | −9.53590e15 | + | 1.65167e16i | −0.874504 | + | 1.51469i | ||||
\(825\) | 3.43531e15 | 0.312946 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.72544e14 | 0.0244994 | 0.0122497 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122497 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(828\) | −1.55935e15 | + | 2.70087e15i | −0.139244 | + | 0.241177i | ||||
\(829\) | 9.02296e15 | + | 1.56282e16i | 0.800385 | + | 1.38631i | 0.919363 | + | 0.393411i | \(0.128705\pi\) |
−0.118978 | + | 0.992897i | \(0.537962\pi\) | |||||||
\(830\) | −1.70026e15 | − | 2.94494e15i | −0.149826 | − | 0.259506i | ||||
\(831\) | −2.06879e15 | + | 3.58324e15i | −0.181096 | + | 0.313668i | ||||
\(832\) | 1.55949e15 | 0.135614 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.60941e15 | −0.309758 | ||||||||
\(835\) | −6.65292e15 | + | 1.15232e16i | −0.567201 | + | 0.982421i | ||||
\(836\) | −4.19500e15 | − | 7.26595e15i | −0.355302 | − | 0.615400i | ||||
\(837\) | −1.93615e15 | − | 3.35351e15i | −0.162910 | − | 0.282169i | ||||
\(838\) | −8.80842e14 | + | 1.52566e15i | −0.0736302 | + | 0.127531i | ||||
\(839\) | 7.96183e15 | 0.661184 | 0.330592 | − | 0.943774i | \(-0.392752\pi\) | ||||
0.330592 | + | 0.943774i | \(0.392752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.28775e15 | 0.351440 | ||||||||
\(842\) | 2.05334e15 | − | 3.55649e15i | 0.167203 | − | 0.289605i | ||||
\(843\) | 2.65050e15 | + | 4.59080e15i | 0.214425 | + | 0.371396i | ||||
\(844\) | −4.99977e15 | − | 8.65986e15i | −0.401853 | − | 0.696029i | ||||
\(845\) | −3.52199e15 | + | 6.10026e15i | −0.281239 | + | 0.487120i | ||||
\(846\) | −7.32956e15 | −0.581488 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.57552e15 | −0.123381 | ||||||||
\(849\) | −2.10586e15 | + | 3.64746e15i | −0.163847 | + | 0.283791i | ||||
\(850\) | −2.11315e15 | − | 3.66009e15i | −0.163353 | − | 0.282935i | ||||
\(851\) | 1.69853e15 | + | 2.94193e15i | 0.130455 | + | 0.225954i | ||||
\(852\) | −1.81605e15 | + | 3.14548e15i | −0.138583 | + | 0.240032i | ||||
\(853\) | 1.49826e16 | 1.13598 | 0.567988 | − | 0.823037i | \(-0.307722\pi\) | ||||
0.567988 | + | 0.823037i | \(0.307722\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.85201e15 | −0.438017 | ||||||||
\(856\) | −3.81179e15 | + | 6.60222e15i | −0.283481 | + | 0.491003i | ||||
\(857\) | −1.11281e16 | − | 1.92744e16i | −0.822290 | − | 1.42425i | −0.903973 | − | 0.427590i | \(-0.859363\pi\) |
0.0816825 | − | 0.996658i | \(-0.473971\pi\) | |||||||
\(858\) | −9.34010e14 | − | 1.61775e15i | −0.0685759 | − | 0.118777i | ||||
\(859\) | 2.72118e15 | − | 4.71323e15i | 0.198516 | − | 0.343840i | −0.749532 | − | 0.661969i | \(-0.769721\pi\) |
0.948047 | + | 0.318129i | \(0.103055\pi\) | |||||||
\(860\) | −1.21760e14 | −0.00882596 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.72262e15 | 0.123282 | ||||||||
\(863\) | −5.40549e15 | + | 9.36259e15i | −0.384393 | + | 0.665789i | −0.991685 | − | 0.128690i | \(-0.958923\pi\) |
0.607291 | + | 0.794479i | \(0.292256\pi\) | |||||||
\(864\) | 7.20723e15 | + | 1.24833e16i | 0.509264 | + | 0.882071i | ||||
\(865\) | 2.29519e15 | + | 3.97538e15i | 0.161150 | + | 0.279119i | ||||
\(866\) | −1.19857e15 | + | 2.07599e15i | −0.0836213 | + | 0.144836i | ||||
\(867\) | −3.38185e15 | −0.234449 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.03777e16 | 1.39491 | ||||||||
\(870\) | 1.87550e15 | − | 3.24846e15i | 0.127574 | − | 0.220964i | ||||
\(871\) | 4.47222e15 | + | 7.74611e15i | 0.302290 | + | 0.523581i | ||||
\(872\) | −3.10391e15 | − | 5.37613e15i | −0.208482 | − | 0.361101i | ||||
\(873\) | −4.26238e15 | + | 7.38266e15i | −0.284495 | + | 0.492759i | ||||
\(874\) | 4.77033e15 | 0.316399 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.42985e14 | −0.0355644 | ||||||||
\(877\) | 1.40512e16 | − | 2.43374e16i | 0.914568 | − | 1.58408i | 0.107037 | − | 0.994255i | \(-0.465864\pi\) |
0.807532 | − | 0.589824i | \(-0.200803\pi\) | |||||||
\(878\) | 3.48375e14 | + | 6.03403e14i | 0.0225334 | + | 0.0390290i | ||||
\(879\) | 3.01478e15 | + | 5.22176e15i | 0.193784 | + | 0.335643i | ||||
\(880\) | 1.27448e15 | − | 2.20746e15i | 0.0814101 | − | 0.141006i | ||||
\(881\) | −4.22209e15 | −0.268016 | −0.134008 | − | 0.990980i | \(-0.542785\pi\) | ||||
−0.134008 | + | 0.990980i | \(0.542785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.16092e14 | 0.0323551 | 0.0161776 | − | 0.999869i | \(-0.494850\pi\) | ||||
0.0161776 | + | 0.999869i | \(0.494850\pi\) | |||||||
\(884\) | 2.93651e15 | − | 5.08618e15i | 0.182955 | − | 0.316887i | ||||
\(885\) | −3.15805e15 | − | 5.46990e15i | −0.195538 | − | 0.338681i | ||||
\(886\) | 3.94044e15 | + | 6.82504e15i | 0.242471 | + | 0.419971i | ||||
\(887\) | 2.85953e15 | − | 4.95285e15i | 0.174870 | − | 0.302883i | −0.765246 | − | 0.643737i | \(-0.777383\pi\) |
0.940116 | + | 0.340854i | \(0.110716\pi\) | |||||||
\(888\) | 3.87913e15 | 0.235756 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.89718e15 | 0.173912 | ||||||||
\(891\) | −4.45115e14 | + | 7.70962e14i | −0.0265549 | + | 0.0459944i | ||||
\(892\) | −5.39846e15 | − | 9.35041e15i | −0.320083 | − | 0.554401i | ||||
\(893\) | −1.43255e16 | − | 2.48125e16i | −0.844162 | − | 1.46213i | ||||
\(894\) | 3.37307e15 | − | 5.84233e15i | 0.197546 | − | 0.342160i | ||||
\(895\) | −8.12109e15 | −0.472702 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.71427e15 | −0.156061 | ||||||||
\(898\) | −7.34842e15 | + | 1.27278e16i | −0.419927 | + | 0.727335i | ||||
\(899\) | −3.39271e15 | − | 5.87634e15i | −0.192694 | − | 0.333756i | ||||
\(900\) | 2.13279e15 | + | 3.69410e15i | 0.120396 | + | 0.208533i | ||||
\(901\) | 5.51113e15 | − | 9.54555e15i | 0.309210 | − | 0.535568i | ||||
\(902\) | 3.95340e15 | 0.220462 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.19321e15 | −0.396275 | ||||||||
\(905\) | 2.40721e15 | − | 4.16941e15i | 0.131810 | − | 0.228301i | ||||
\(906\) | 2.49313e15 | + | 4.31823e15i | 0.135687 | + | 0.235018i | ||||
\(907\) | 4.21889e13 | + | 7.30733e13i | 0.00228222 | + | 0.00395293i | 0.867164 | − | 0.498022i | \(-0.165940\pi\) |
−0.864882 | + | 0.501975i | \(0.832607\pi\) | |||||||
\(908\) | 1.00084e15 | − | 1.73351e15i | 0.0538138 | − | 0.0932082i | ||||
\(909\) | 9.28952e15 | 0.496468 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.10091e16 | −0.581298 | −0.290649 | − | 0.956830i | \(-0.593871\pi\) | ||||
−0.290649 | + | 0.956830i | \(0.593871\pi\) | |||||||
\(912\) | −1.32606e15 | + | 2.29680e15i | −0.0695971 | + | 0.120546i | ||||
\(913\) | −7.84145e15 | − | 1.35818e16i | −0.409079 | − | 0.708545i | ||||
\(914\) | 3.64180e15 | + | 6.30778e15i | 0.188848 | + | 0.327094i | ||||
\(915\) | 4.23357e15 | − | 7.33276e15i | 0.218218 | − | 0.377965i | ||||
\(916\) | −1.74055e16 | −0.891789 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.21455e16 | −0.614864 | ||||||||
\(919\) | 2.43176e15 | − | 4.21193e15i | 0.122373 | − | 0.211956i | −0.798330 | − | 0.602220i | \(-0.794283\pi\) |
0.920703 | + | 0.390264i | \(0.127616\pi\) | |||||||
\(920\) | 3.80359e15 | + | 6.58800e15i | 0.190266 | + | 0.329550i | ||||
\(921\) | −1.92920e15 | − | 3.34147e15i | −0.0959287 | − | 0.166153i | ||||
\(922\) | 8.75170e15 | − | 1.51584e16i | 0.432586 | − | 0.749260i | ||||
\(923\) | 5.65691e15 | 0.277952 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.64630e15 | 0.225594 | ||||||||
\(926\) | 1.46626e15 | − | 2.53963e15i | 0.0707701 | − | 0.122577i | ||||
\(927\) | 1.28277e16 | + | 2.22183e16i | 0.615477 | + | 1.06604i | ||||
\(928\) | 1.26292e16 | + | 2.18744e16i | 0.602368 | + | 1.04333i | ||||
\(929\) | 1.78767e15 | − | 3.09634e15i | 0.0847620 | − | 0.146812i | −0.820528 | − | 0.571607i | \(-0.806320\pi\) |
0.905290 | + | 0.424795i | \(0.139654\pi\) | |||||||
\(930\) | −1.54365e15 | −0.0727598 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.58533e16 | 1.20428 | ||||||||
\(933\) | −6.28427e15 | + | 1.08847e16i | −0.291009 | + | 0.504042i | ||||
\(934\) | 7.40857e15 | + | 1.28320e16i | 0.341057 | + | 0.590727i | ||||
\(935\) | 8.91617e15 | + | 1.54433e16i | 0.408051 | + | 0.706765i | ||||
\(936\) | 2.77330e15 | − | 4.80350e15i | 0.126177 | − | 0.218545i | ||||
\(937\) | −3.86373e16 | −1.74759 | −0.873795 | − | 0.486295i | \(-0.838348\pi\) | ||||
−0.873795 | + | 0.486295i | \(0.838348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.50692e16 | −1.12067 | ||||||||
\(940\) | 9.55320e15 | − | 1.65466e16i | 0.424567 | − | 0.735371i | ||||
\(941\) | −1.74499e16 | − | 3.02241e16i | −0.770991 | − | 1.33539i | −0.937021 | − | 0.349274i | \(-0.886428\pi\) |
0.166030 | − | 0.986121i | \(-0.446905\pi\) | |||||||
\(942\) | 3.97691e15 | + | 6.88822e15i | 0.174689 | + | 0.302571i | ||||
\(943\) | 2.87219e15 | − | 4.97477e15i | 0.125429 | − | 0.217250i | ||||
\(944\) | 5.12245e15 | 0.222398 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.19735e14 | 0.00942969 | ||||||||
\(947\) | 1.42561e16 | − | 2.46924e16i | 0.608243 | − | 1.05351i | −0.383287 | − | 0.923629i | \(-0.625208\pi\) |
0.991530 | − | 0.129879i | \(-0.0414588\pi\) | |||||||
\(948\) | −7.06961e15 | − | 1.22449e16i | −0.299881 | − | 0.519410i | ||||
\(949\) | 4.22844e14 | + | 7.32387e14i | 0.0178327 | + | 0.0308871i | ||||
\(950\) | 3.26230e15 | − | 5.65046e15i | 0.136787 | − | 0.236921i | ||||
\(951\) | −2.10091e16 | −0.875817 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.00334e16 | 1.64973 | 0.824863 | − | 0.565332i | \(-0.191252\pi\) | ||||
0.824863 | + | 0.565332i | \(0.191252\pi\) | |||||||
\(954\) | 2.17657e15 | − | 3.76992e15i | 0.0891776 | − | 0.154460i | ||||
\(955\) | 6.67120e15 | + | 1.15549e16i | 0.271760 | + | 0.470702i | ||||
\(956\) | −5.25473e15 | − | 9.10146e15i | −0.212830 | − | 0.368632i | ||||
\(957\) | 8.64961e15 | − | 1.49816e16i | 0.348322 | − | 0.603312i | ||||
\(958\) | 2.52201e16 | 1.00980 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.28548e15 | 0.130049 | ||||||||
\(961\) | 1.13080e16 | − | 1.95861e16i | 0.445050 | − | 0.770849i | ||||
\(962\) | −1.26326e15 | − | 2.18803e15i | −0.0494344 | − | 0.0856229i | ||||
\(963\) | 5.12764e15 | + | 8.88134e15i | 0.199514 | + | 0.345568i | ||||
\(964\) | 1.70242e14 | − | 2.94868e14i | 0.00658632 | − | 0.0114078i | ||||
\(965\) | −2.62867e16 | −1.01120 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.84953e16 | 0.703422 | 0.351711 | − | 0.936109i | \(-0.385600\pi\) | ||||
0.351711 | + | 0.936109i | \(0.385600\pi\) | |||||||
\(968\) | −2.10490e13 | + | 3.64580e13i | −0.000796008 | + | 0.00137873i | ||||
\(969\) | −9.27701e15 | − | 1.60683e16i | −0.348841 | − | 0.604210i | ||||
\(970\) | 4.34779e15 | + | 7.53059e15i | 0.162564 | + | 0.281569i | ||||
\(971\) | −1.07438e16 | + | 1.86089e16i | −0.399442 | + | 0.691853i | −0.993657 | − | 0.112453i | \(-0.964129\pi\) |
0.594215 | + | 0.804306i | \(0.297463\pi\) | |||||||
\(972\) | 1.97260e16 | 0.729246 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.27784e15 | 0.192922 | ||||||||
\(975\) | −1.85622e15 | + | 3.21506e15i | −0.0674688 | + | 0.116859i | ||||
\(976\) | 3.43350e15 | + | 5.94699e15i | 0.124097 | + | 0.214943i | ||||
\(977\) | 4.36940e15 | + | 7.56802e15i | 0.157037 | + | 0.271996i | 0.933799 | − | 0.357798i | \(-0.116473\pi\) |
−0.776762 | + | 0.629794i | \(0.783139\pi\) | |||||||
\(978\) | 1.08209e15 | − | 1.87423e15i | 0.0386721 | − | 0.0669821i | ||||
\(979\) | 1.33615e16 | 0.474844 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.35079e15 | −0.293459 | ||||||||
\(982\) | −5.80636e15 | + | 1.00569e16i | −0.202904 | + | 0.351440i | ||||
\(983\) | 5.94621e15 | + | 1.02991e16i | 0.206631 | + | 0.357896i | 0.950651 | − | 0.310261i | \(-0.100417\pi\) |
−0.744020 | + | 0.668157i | \(0.767083\pi\) | |||||||
\(984\) | −3.27978e15 | − | 5.68075e15i | −0.113337 | − | 0.196306i | ||||
\(985\) | −6.94576e15 | + | 1.20304e16i | −0.238682 | + | 0.413410i | ||||
\(986\) | −2.12824e16 | −0.727274 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.06679e15 | 0.306401 | ||||||||
\(989\) | 1.59640e14 | − | 2.76504e14i | 0.00536489 | − | 0.00929227i | ||||
\(990\) | 3.52135e15 | + | 6.09917e15i | 0.117684 | + | 0.203834i | ||||
\(991\) | −1.17204e16 | − | 2.03004e16i | −0.389528 | − | 0.674682i | 0.602858 | − | 0.797848i | \(-0.294028\pi\) |
−0.992386 | + | 0.123166i | \(0.960695\pi\) | |||||||
\(992\) | 5.19729e15 | − | 9.00197e15i | 0.171776 | − | 0.297525i | ||||
\(993\) | 1.60232e16 | 0.526657 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.51813e15 | 0.114363 | ||||||||
\(996\) | −5.44084e15 | + | 9.42381e15i | −0.175889 | + | 0.304649i | ||||
\(997\) | −1.07002e16 | − | 1.85333e16i | −0.344008 | − | 0.595840i | 0.641165 | − | 0.767403i | \(-0.278451\pi\) |
−0.985173 | + | 0.171563i | \(0.945118\pi\) | |||||||
\(998\) | −1.30653e15 | − | 2.26298e15i | −0.0417736 | − | 0.0723541i | ||||
\(999\) | 6.67621e15 | − | 1.15635e16i | 0.212285 | − | 0.367689i |
(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 | 49.12.c.c.30.1 | 2 | ||
7.2 | even | 3 | 49.12.a.a.1.1 | 1 | |||
7.3 | odd | 6 | 49.12.c.b.18.1 | 2 | |||
7.4 | even | 3 | inner | 49.12.c.c.18.1 | 2 | ||
7.5 | odd | 6 | 1.12.a.a.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 49.12.c.b.30.1 | 2 | |||
21.5 | even | 6 | 9.12.a.b.1.1 | 1 | |||
28.19 | even | 6 | 16.12.a.a.1.1 | 1 | |||
35.12 | even | 12 | 25.12.b.b.24.1 | 2 | |||
35.19 | odd | 6 | 25.12.a.b.1.1 | 1 | |||
35.33 | even | 12 | 25.12.b.b.24.2 | 2 | |||
56.5 | odd | 6 | 64.12.a.b.1.1 | 1 | |||
56.19 | even | 6 | 64.12.a.f.1.1 | 1 | |||
63.5 | even | 6 | 81.12.c.b.55.1 | 2 | |||
63.40 | odd | 6 | 81.12.c.d.55.1 | 2 | |||
63.47 | even | 6 | 81.12.c.b.28.1 | 2 | |||
63.61 | odd | 6 | 81.12.c.d.28.1 | 2 | |||
77.54 | even | 6 | 121.12.a.b.1.1 | 1 | |||
84.47 | odd | 6 | 144.12.a.d.1.1 | 1 | |||
91.12 | odd | 6 | 169.12.a.a.1.1 | 1 | |||
105.47 | odd | 12 | 225.12.b.d.199.2 | 2 | |||
105.68 | odd | 12 | 225.12.b.d.199.1 | 2 | |||
105.89 | even | 6 | 225.12.a.b.1.1 | 1 | |||
112.5 | odd | 12 | 256.12.b.e.129.1 | 2 | |||
112.19 | even | 12 | 256.12.b.c.129.1 | 2 | |||
112.61 | odd | 12 | 256.12.b.e.129.2 | 2 | |||
112.75 | even | 12 | 256.12.b.c.129.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.12.a.a.1.1 | ✓ | 1 | 7.5 | odd | 6 | ||
9.12.a.b.1.1 | 1 | 21.5 | even | 6 | |||
16.12.a.a.1.1 | 1 | 28.19 | even | 6 | |||
25.12.a.b.1.1 | 1 | 35.19 | odd | 6 | |||
25.12.b.b.24.1 | 2 | 35.12 | even | 12 | |||
25.12.b.b.24.2 | 2 | 35.33 | even | 12 | |||
49.12.a.a.1.1 | 1 | 7.2 | even | 3 | |||
49.12.c.b.18.1 | 2 | 7.3 | odd | 6 | |||
49.12.c.b.30.1 | 2 | 7.6 | odd | 2 | |||
49.12.c.c.18.1 | 2 | 7.4 | even | 3 | inner | ||
49.12.c.c.30.1 | 2 | 1.1 | even | 1 | trivial | ||
64.12.a.b.1.1 | 1 | 56.5 | odd | 6 | |||
64.12.a.f.1.1 | 1 | 56.19 | even | 6 | |||
81.12.c.b.28.1 | 2 | 63.47 | even | 6 | |||
81.12.c.b.55.1 | 2 | 63.5 | even | 6 | |||
81.12.c.d.28.1 | 2 | 63.61 | odd | 6 | |||
81.12.c.d.55.1 | 2 | 63.40 | odd | 6 | |||
121.12.a.b.1.1 | 1 | 77.54 | even | 6 | |||
144.12.a.d.1.1 | 1 | 84.47 | odd | 6 | |||
169.12.a.a.1.1 | 1 | 91.12 | odd | 6 | |||
225.12.a.b.1.1 | 1 | 105.89 | even | 6 | |||
225.12.b.d.199.1 | 2 | 105.68 | odd | 12 | |||
225.12.b.d.199.2 | 2 | 105.47 | odd | 12 | |||
256.12.b.c.129.1 | 2 | 112.19 | even | 12 | |||
256.12.b.c.129.2 | 2 | 112.75 | even | 12 | |||
256.12.b.e.129.1 | 2 | 112.5 | odd | 12 | |||
256.12.b.e.129.2 | 2 | 112.61 | odd | 12 |