Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,18,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.16110436723\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 203459x^{6} + 12362849196x^{4} + 237701205446144x^{2} + 1320400799499206656 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.2 | ||
Root | \(-256.320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.18.b.a.4.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 512.640i | − | 1.41598i | −0.706221 | − | 0.707991i | \(-0.749602\pi\) | ||
0.706221 | − | 0.707991i | \(-0.250398\pi\) | |||||||
\(3\) | 18245.5i | 1.60555i | 0.596280 | + | 0.802777i | \(0.296645\pi\) | ||||
−0.596280 | + | 0.802777i | \(0.703355\pi\) | |||||||
\(4\) | −131728. | −1.00501 | ||||||||
\(5\) | 346646. | − | 801733.i | 0.396863 | − | 0.917878i | ||||
\(6\) | 9.35337e6 | 2.27343 | ||||||||
\(7\) | − | 1.34806e7i | − | 0.883841i | −0.897054 | − | 0.441921i | \(-0.854297\pi\) | ||
0.897054 | − | 0.441921i | \(-0.145703\pi\) | |||||||
\(8\) | 336370.i | 0.00708846i | ||||||||
\(9\) | −2.03757e8 | −1.57780 | ||||||||
\(10\) | −4.11001e8 | − | 1.77705e8i | −1.29970 | − | 0.561951i | ||||
\(11\) | 8.20239e8 | 1.15373 | 0.576863 | − | 0.816841i | \(-0.304277\pi\) | ||||
0.576863 | + | 0.816841i | \(0.304277\pi\) | |||||||
\(12\) | − | 2.40344e9i | − | 1.61359i | ||||||
\(13\) | − | 2.92679e9i | − | 0.995114i | −0.867431 | − | 0.497557i | \(-0.834231\pi\) | ||
0.867431 | − | 0.497557i | \(-0.165769\pi\) | |||||||
\(14\) | −6.91067e9 | −1.25150 | ||||||||
\(15\) | 1.46280e10 | + | 6.32472e9i | 1.47370 | + | 0.637185i | ||||
\(16\) | −1.70934e10 | −0.994969 | ||||||||
\(17\) | − | 3.73919e10i | − | 1.30005i | −0.759911 | − | 0.650027i | \(-0.774758\pi\) | ||
0.759911 | − | 0.650027i | \(-0.225242\pi\) | |||||||
\(18\) | 1.04454e11i | 2.23414i | ||||||||
\(19\) | 3.00949e10 | 0.406525 | 0.203262 | − | 0.979124i | \(-0.434846\pi\) | ||||
0.203262 | + | 0.979124i | \(0.434846\pi\) | |||||||
\(20\) | −4.56630e10 | + | 1.05611e11i | −0.398850 | + | 0.922473i | ||||
\(21\) | 2.45959e11 | 1.41905 | ||||||||
\(22\) | − | 4.20488e11i | − | 1.63365i | ||||||
\(23\) | 4.40887e11i | 1.17393i | 0.809614 | + | 0.586963i | \(0.199677\pi\) | ||||
−0.809614 | + | 0.586963i | \(0.800323\pi\) | |||||||
\(24\) | −6.13723e9 | −0.0113809 | ||||||||
\(25\) | −5.22613e11 | − | 5.55835e11i | −0.684999 | − | 0.728544i | ||||
\(26\) | −1.50039e12 | −1.40906 | ||||||||
\(27\) | − | 1.36143e12i | − | 0.927690i | ||||||
\(28\) | 1.77577e12i | 0.888266i | ||||||||
\(29\) | 1.80846e12 | 0.671314 | 0.335657 | − | 0.941984i | \(-0.391042\pi\) | ||||
0.335657 | + | 0.941984i | \(0.391042\pi\) | |||||||
\(30\) | 3.24231e12 | − | 7.49891e12i | 0.902242 | − | 2.08674i | ||||
\(31\) | 2.90970e12 | 0.612736 | 0.306368 | − | 0.951913i | \(-0.400886\pi\) | ||||
0.306368 | + | 0.951913i | \(0.400886\pi\) | |||||||
\(32\) | 8.80687e12i | 1.41595i | ||||||||
\(33\) | 1.49657e13i | 1.85237i | ||||||||
\(34\) | −1.91686e13 | −1.84085 | ||||||||
\(35\) | −1.08078e13 | − | 4.67297e12i | −0.811258 | − | 0.350764i | ||||
\(36\) | 2.68406e13 | 1.58570 | ||||||||
\(37\) | 3.31096e12i | 0.154967i | 0.996994 | + | 0.0774834i | \(0.0246885\pi\) | ||||
−0.996994 | + | 0.0774834i | \(0.975312\pi\) | |||||||
\(38\) | − | 1.54279e13i | − | 0.575632i | ||||||
\(39\) | 5.34006e13 | 1.59771 | ||||||||
\(40\) | 2.69679e11 | + | 1.16601e11i | 0.00650634 | + | 0.00281315i | ||||
\(41\) | −7.87183e13 | −1.53962 | −0.769809 | − | 0.638275i | \(-0.779648\pi\) | ||||
−0.769809 | + | 0.638275i | \(0.779648\pi\) | |||||||
\(42\) | − | 1.26089e14i | − | 2.00936i | ||||||
\(43\) | 4.61355e12i | 0.0601940i | 0.999547 | + | 0.0300970i | \(0.00958162\pi\) | ||||
−0.999547 | + | 0.0300970i | \(0.990418\pi\) | |||||||
\(44\) | −1.08049e14 | −1.15950 | ||||||||
\(45\) | −7.06316e13 | + | 1.63359e14i | −0.626171 | + | 1.44823i | ||||
\(46\) | 2.26016e14 | 1.66226 | ||||||||
\(47\) | 1.39204e14i | 0.852746i | 0.904547 | + | 0.426373i | \(0.140209\pi\) | ||||
−0.904547 | + | 0.426373i | \(0.859791\pi\) | |||||||
\(48\) | − | 3.11878e14i | − | 1.59748i | ||||||
\(49\) | 5.09053e13 | 0.218824 | ||||||||
\(50\) | −2.84943e14 | + | 2.67913e14i | −1.03160 | + | 0.969947i | ||||
\(51\) | 6.82233e14 | 2.08731 | ||||||||
\(52\) | 3.85540e14i | 1.00010i | ||||||||
\(53\) | 4.39747e13i | 0.0970194i | 0.998823 | + | 0.0485097i | \(0.0154472\pi\) | ||||
−0.998823 | + | 0.0485097i | \(0.984553\pi\) | |||||||
\(54\) | −6.97923e14 | −1.31359 | ||||||||
\(55\) | 2.84332e14 | − | 6.57613e14i | 0.457871 | − | 1.05898i | ||||
\(56\) | 4.53445e12 | 0.00626508 | ||||||||
\(57\) | 5.49096e14i | 0.652697i | ||||||||
\(58\) | − | 9.27089e14i | − | 0.950569i | ||||||
\(59\) | −3.18887e14 | −0.282745 | −0.141372 | − | 0.989957i | \(-0.545151\pi\) | ||||
−0.141372 | + | 0.989957i | \(0.545151\pi\) | |||||||
\(60\) | −1.92692e15 | − | 8.33143e14i | −1.48108 | − | 0.640375i | ||||
\(61\) | 7.17560e14 | 0.479242 | 0.239621 | − | 0.970867i | \(-0.422977\pi\) | ||||
0.239621 | + | 0.970867i | \(0.422977\pi\) | |||||||
\(62\) | − | 1.49163e15i | − | 0.867623i | ||||||
\(63\) | 2.74676e15i | 1.39453i | ||||||||
\(64\) | 2.27429e15 | 1.00999 | ||||||||
\(65\) | −2.34650e15 | − | 1.01456e15i | −0.913393 | − | 0.394924i | ||||
\(66\) | 7.67200e15 | 2.62292 | ||||||||
\(67\) | − | 2.87655e15i | − | 0.865438i | −0.901529 | − | 0.432719i | \(-0.857554\pi\) | ||
0.901529 | − | 0.432719i | \(-0.142446\pi\) | |||||||
\(68\) | 4.92556e15i | 1.30656i | ||||||||
\(69\) | −8.04420e15 | −1.88480 | ||||||||
\(70\) | −2.39556e15 | + | 5.54052e15i | −0.496676 | + | 1.14873i | ||||
\(71\) | −3.39253e14 | −0.0623488 | −0.0311744 | − | 0.999514i | \(-0.509925\pi\) | ||||
−0.0311744 | + | 0.999514i | \(0.509925\pi\) | |||||||
\(72\) | − | 6.85378e13i | − | 0.0111842i | ||||||
\(73\) | 8.49295e15i | 1.23258i | 0.787520 | + | 0.616289i | \(0.211365\pi\) | ||||
−0.787520 | + | 0.616289i | \(0.788635\pi\) | |||||||
\(74\) | 1.69733e15 | 0.219430 | ||||||||
\(75\) | 1.01415e16 | − | 9.53533e15i | 1.16972 | − | 1.09980i | ||||
\(76\) | −3.96434e15 | −0.408560 | ||||||||
\(77\) | − | 1.10573e16i | − | 1.01971i | ||||||
\(78\) | − | 2.73753e16i | − | 2.26233i | ||||||
\(79\) | 1.05825e16 | 0.784800 | 0.392400 | − | 0.919795i | \(-0.371645\pi\) | ||||
0.392400 | + | 0.919795i | \(0.371645\pi\) | |||||||
\(80\) | −5.92536e15 | + | 1.37044e16i | −0.394866 | + | 0.913260i | ||||
\(81\) | −1.47335e15 | −0.0883454 | ||||||||
\(82\) | 4.03542e16i | 2.18007i | ||||||||
\(83\) | − | 2.86866e16i | − | 1.39803i | −0.715108 | − | 0.699014i | \(-0.753623\pi\) | ||
0.715108 | − | 0.699014i | \(-0.246377\pi\) | |||||||
\(84\) | −3.23997e16 | −1.42616 | ||||||||
\(85\) | −2.99783e16 | − | 1.29617e16i | −1.19329 | − | 0.515943i | ||||
\(86\) | 2.36509e15 | 0.0852337 | ||||||||
\(87\) | 3.29962e16i | 1.07783i | ||||||||
\(88\) | 2.75904e14i | 0.00817814i | ||||||||
\(89\) | 6.62578e16 | 1.78411 | 0.892055 | − | 0.451926i | \(-0.149263\pi\) | ||||
0.892055 | + | 0.451926i | \(0.149263\pi\) | |||||||
\(90\) | 8.37445e16 | + | 3.62086e16i | 2.05067 | + | 0.886647i | ||||
\(91\) | −3.94547e16 | −0.879523 | ||||||||
\(92\) | − | 5.80772e16i | − | 1.17980i | ||||||
\(93\) | 5.30888e16i | 0.983780i | ||||||||
\(94\) | 7.13616e16 | 1.20747 | ||||||||
\(95\) | 1.04323e16 | − | 2.41281e16i | 0.161335 | − | 0.373140i | ||||
\(96\) | −1.60686e17 | −2.27338 | ||||||||
\(97\) | 2.94405e16i | 0.381405i | 0.981648 | + | 0.190702i | \(0.0610765\pi\) | ||||
−0.981648 | + | 0.190702i | \(0.938923\pi\) | |||||||
\(98\) | − | 2.60961e16i | − | 0.309852i | ||||||
\(99\) | −1.67130e17 | −1.82035 | ||||||||
\(100\) | 6.88429e16 | + | 7.32191e16i | 0.688429 | + | 0.732191i | ||||
\(101\) | 3.97485e16 | 0.365249 | 0.182625 | − | 0.983183i | \(-0.441541\pi\) | ||||
0.182625 | + | 0.983183i | \(0.441541\pi\) | |||||||
\(102\) | − | 3.49740e17i | − | 2.95559i | ||||||
\(103\) | 1.45599e17i | 1.13251i | 0.824229 | + | 0.566256i | \(0.191609\pi\) | ||||
−0.824229 | + | 0.566256i | \(0.808391\pi\) | |||||||
\(104\) | 9.84483e14 | 0.00705383 | ||||||||
\(105\) | 8.52607e16 | − | 1.97194e17i | 0.563170 | − | 1.30252i | ||||
\(106\) | 2.25432e16 | 0.137378 | ||||||||
\(107\) | 1.76418e17i | 0.992612i | 0.868148 | + | 0.496306i | \(0.165311\pi\) | ||||
−0.868148 | + | 0.496306i | \(0.834689\pi\) | |||||||
\(108\) | 1.79338e17i | 0.932334i | ||||||||
\(109\) | 2.43800e17 | 1.17195 | 0.585974 | − | 0.810330i | \(-0.300712\pi\) | ||||
0.585974 | + | 0.810330i | \(0.300712\pi\) | |||||||
\(110\) | −3.37119e17 | − | 1.45760e17i | −1.49950 | − | 0.648337i | ||||
\(111\) | −6.04100e16 | −0.248808 | ||||||||
\(112\) | 2.30429e17i | 0.879395i | ||||||||
\(113\) | − | 1.83084e17i | − | 0.647864i | −0.946080 | − | 0.323932i | \(-0.894995\pi\) | ||
0.946080 | − | 0.323932i | \(-0.105005\pi\) | |||||||
\(114\) | 2.81489e17 | 0.924208 | ||||||||
\(115\) | 3.53474e17 | + | 1.52832e17i | 1.07752 | + | 0.465888i | ||||
\(116\) | −2.38225e17 | −0.674675 | ||||||||
\(117\) | 5.96355e17i | 1.57009i | ||||||||
\(118\) | 1.63474e17i | 0.400361i | ||||||||
\(119\) | −5.04063e17 | −1.14904 | ||||||||
\(120\) | −2.12744e15 | + | 4.92042e15i | −0.00451666 | + | 0.0104463i | ||||
\(121\) | 1.67345e17 | 0.331082 | ||||||||
\(122\) | − | 3.67850e17i | − | 0.678598i | ||||||
\(123\) | − | 1.43625e18i | − | 2.47194i | ||||||
\(124\) | −3.83289e17 | −0.615803 | ||||||||
\(125\) | −6.26793e17 | + | 2.26319e17i | −0.940565 | + | 0.339614i | ||||
\(126\) | 1.40810e18 | 1.97462 | ||||||||
\(127\) | − | 2.96492e16i | − | 0.0388760i | −0.999811 | − | 0.0194380i | \(-0.993812\pi\) | ||
0.999811 | − | 0.0194380i | \(-0.00618770\pi\) | |||||||
\(128\) | − | 1.15574e16i | − | 0.0141767i | ||||||
\(129\) | −8.41764e16 | −0.0966447 | ||||||||
\(130\) | −5.20103e17 | + | 1.20291e18i | −0.559205 | + | 1.29335i | ||||
\(131\) | 1.21062e18 | 1.21956 | 0.609779 | − | 0.792572i | \(-0.291258\pi\) | ||||
0.609779 | + | 0.792572i | \(0.291258\pi\) | |||||||
\(132\) | − | 1.97140e18i | − | 1.86164i | ||||||
\(133\) | − | 4.05696e17i | − | 0.359304i | ||||||
\(134\) | −1.47464e18 | −1.22544 | ||||||||
\(135\) | −1.09150e18 | − | 4.71933e17i | −0.851506 | − | 0.368166i | ||||
\(136\) | 1.25775e16 | 0.00921538 | ||||||||
\(137\) | 1.52381e18i | 1.04907i | 0.851388 | + | 0.524537i | \(0.175762\pi\) | ||||
−0.851388 | + | 0.524537i | \(0.824238\pi\) | |||||||
\(138\) | 4.12378e18i | 2.66884i | ||||||||
\(139\) | 1.00912e18 | 0.614208 | 0.307104 | − | 0.951676i | \(-0.400640\pi\) | ||||
0.307104 | + | 0.951676i | \(0.400640\pi\) | |||||||
\(140\) | 1.42369e18 | + | 6.15562e17i | 0.815320 | + | 0.352520i | ||||
\(141\) | −2.53984e18 | −1.36913 | ||||||||
\(142\) | 1.73915e17i | 0.0882848i | ||||||||
\(143\) | − | 2.40066e18i | − | 1.14809i | ||||||
\(144\) | 3.48291e18 | 1.56986 | ||||||||
\(145\) | 6.26895e17 | − | 1.44990e18i | 0.266420 | − | 0.616184i | ||||
\(146\) | 4.35383e18 | 1.74531 | ||||||||
\(147\) | 9.28791e17i | 0.351334i | ||||||||
\(148\) | − | 4.36146e17i | − | 0.155743i | ||||||
\(149\) | −1.64103e18 | −0.553393 | −0.276696 | − | 0.960957i | \(-0.589240\pi\) | ||||
−0.276696 | + | 0.960957i | \(0.589240\pi\) | |||||||
\(150\) | −4.88819e18 | − | 5.19893e18i | −1.55730 | − | 1.65630i | ||||
\(151\) | 2.07485e16 | 0.00624716 | 0.00312358 | − | 0.999995i | \(-0.499006\pi\) | ||||
0.00312358 | + | 0.999995i | \(0.499006\pi\) | |||||||
\(152\) | 1.01230e16i | 0.00288164i | ||||||||
\(153\) | 7.61887e18i | 2.05123i | ||||||||
\(154\) | −5.66840e18 | −1.44389 | ||||||||
\(155\) | 1.00863e18 | − | 2.33280e18i | 0.243172 | − | 0.562417i | ||||
\(156\) | −7.03437e18 | −1.60571 | ||||||||
\(157\) | − | 1.83892e18i | − | 0.397572i | −0.980043 | − | 0.198786i | \(-0.936300\pi\) | ||
0.980043 | − | 0.198786i | \(-0.0636999\pi\) | |||||||
\(158\) | − | 5.42503e18i | − | 1.11126i | ||||||
\(159\) | −8.02340e17 | −0.155770 | ||||||||
\(160\) | 7.06076e18 | + | 3.05286e18i | 1.29967 | + | 0.561937i | ||||
\(161\) | 5.94340e18 | 1.03756 | ||||||||
\(162\) | 7.55300e17i | 0.125095i | ||||||||
\(163\) | − | 5.45886e18i | − | 0.858039i | −0.903295 | − | 0.429020i | \(-0.858859\pi\) | ||
0.903295 | − | 0.429020i | \(-0.141141\pi\) | |||||||
\(164\) | 1.03694e19 | 1.54732 | ||||||||
\(165\) | 1.19985e19 | + | 5.18778e18i | 1.70025 | + | 0.735136i | ||||
\(166\) | −1.47059e19 | −1.97958 | ||||||||
\(167\) | − | 5.91125e17i | − | 0.0756118i | −0.999285 | − | 0.0378059i | \(-0.987963\pi\) | ||
0.999285 | − | 0.0378059i | \(-0.0120369\pi\) | |||||||
\(168\) | 8.27332e16i | 0.0100589i | ||||||||
\(169\) | 8.43308e16 | 0.00974876 | ||||||||
\(170\) | −6.64471e18 | + | 1.53681e19i | −0.730567 | + | 1.68968i | ||||
\(171\) | −6.13206e18 | −0.641415 | ||||||||
\(172\) | − | 6.07734e17i | − | 0.0604953i | ||||||
\(173\) | 1.31685e19i | 1.24780i | 0.781506 | + | 0.623898i | \(0.214452\pi\) | ||||
−0.781506 | + | 0.623898i | \(0.785548\pi\) | |||||||
\(174\) | 1.69152e19 | 1.52619 | ||||||||
\(175\) | −7.49296e18 | + | 7.04511e18i | −0.643917 | + | 0.605431i | ||||
\(176\) | −1.40207e19 | −1.14792 | ||||||||
\(177\) | − | 5.81824e18i | − | 0.453961i | ||||||
\(178\) | − | 3.39664e19i | − | 2.52627i | ||||||
\(179\) | −1.56562e19 | −1.11029 | −0.555145 | − | 0.831754i | \(-0.687337\pi\) | ||||
−0.555145 | + | 0.831754i | \(0.687337\pi\) | |||||||
\(180\) | 9.30417e18 | − | 2.15190e19i | 0.629306 | − | 1.45548i | ||||
\(181\) | 1.63176e19 | 1.05290 | 0.526450 | − | 0.850206i | \(-0.323523\pi\) | ||||
0.526450 | + | 0.850206i | \(0.323523\pi\) | |||||||
\(182\) | 2.02261e19i | 1.24539i | ||||||||
\(183\) | 1.30922e19i | 0.769448i | ||||||||
\(184\) | −1.48301e17 | −0.00832133 | ||||||||
\(185\) | 2.65450e18 | + | 1.14773e18i | 0.142241 | + | 0.0615006i | ||||
\(186\) | 2.72155e19 | 1.39301 | ||||||||
\(187\) | − | 3.06703e19i | − | 1.49991i | ||||||
\(188\) | − | 1.83371e19i | − | 0.857015i | ||||||
\(189\) | −1.83528e19 | −0.819931 | ||||||||
\(190\) | −1.23690e19 | − | 5.34800e18i | −0.528360 | − | 0.228447i | ||||
\(191\) | −4.29371e19 | −1.75408 | −0.877040 | − | 0.480417i | \(-0.840485\pi\) | ||||
−0.877040 | + | 0.480417i | \(0.840485\pi\) | |||||||
\(192\) | 4.14955e19i | 1.62159i | ||||||||
\(193\) | 1.05930e19i | 0.396080i | 0.980194 | + | 0.198040i | \(0.0634576\pi\) | ||||
−0.980194 | + | 0.198040i | \(0.936542\pi\) | |||||||
\(194\) | 1.50924e19 | 0.540062 | ||||||||
\(195\) | 1.85111e19 | − | 4.28131e19i | 0.634071 | − | 1.46650i | ||||
\(196\) | −6.70565e18 | −0.219920 | ||||||||
\(197\) | 2.04072e19i | 0.640945i | 0.947258 | + | 0.320473i | \(0.103842\pi\) | ||||
−0.947258 | + | 0.320473i | \(0.896158\pi\) | |||||||
\(198\) | 8.56775e19i | 2.57758i | ||||||||
\(199\) | 2.52073e19 | 0.726566 | 0.363283 | − | 0.931679i | \(-0.381656\pi\) | ||||
0.363283 | + | 0.931679i | \(0.381656\pi\) | |||||||
\(200\) | 1.86966e17 | − | 1.75791e17i | 0.00516425 | − | 0.00485559i | ||||
\(201\) | 5.24840e19 | 1.38951 | ||||||||
\(202\) | − | 2.03767e19i | − | 0.517187i | ||||||
\(203\) | − | 2.43790e19i | − | 0.593335i | ||||||
\(204\) | −8.98693e19 | −2.09775 | ||||||||
\(205\) | −2.72873e19 | + | 6.31111e19i | −0.611017 | + | 1.41318i | ||||
\(206\) | 7.46401e19 | 1.60362 | ||||||||
\(207\) | − | 8.98340e19i | − | 1.85222i | ||||||
\(208\) | 5.00289e19i | 0.990107i | ||||||||
\(209\) | 2.46850e19 | 0.469018 | ||||||||
\(210\) | −1.01089e20 | − | 4.37081e19i | −1.84434 | − | 0.797439i | ||||
\(211\) | 5.82521e19 | 1.02073 | 0.510365 | − | 0.859958i | \(-0.329510\pi\) | ||||
0.510365 | + | 0.859958i | \(0.329510\pi\) | |||||||
\(212\) | − | 5.79271e18i | − | 0.0975051i | ||||||
\(213\) | − | 6.18984e18i | − | 0.100104i | ||||||
\(214\) | 9.04387e19 | 1.40552 | ||||||||
\(215\) | 3.69884e18 | + | 1.59927e18i | 0.0552507 | + | 0.0238888i | ||||
\(216\) | 4.57943e17 | 0.00657590 | ||||||||
\(217\) | − | 3.92243e19i | − | 0.541561i | ||||||
\(218\) | − | 1.24982e20i | − | 1.65946i | ||||||
\(219\) | −1.54958e20 | −1.97897 | ||||||||
\(220\) | −3.74546e19 | + | 8.66261e19i | −0.460163 | + | 1.06428i | ||||
\(221\) | −1.09438e20 | −1.29370 | ||||||||
\(222\) | 3.09686e19i | 0.352307i | ||||||||
\(223\) | − | 7.59414e19i | − | 0.831548i | −0.909468 | − | 0.415774i | \(-0.863511\pi\) | ||
0.909468 | − | 0.415774i | \(-0.136489\pi\) | |||||||
\(224\) | 1.18722e20 | 1.25147 | ||||||||
\(225\) | 1.06486e20 | + | 1.13255e20i | 1.08079 | + | 1.14950i | ||||
\(226\) | −9.38564e19 | −0.917365 | ||||||||
\(227\) | 2.04064e20i | 1.92109i | 0.278125 | + | 0.960545i | \(0.410287\pi\) | ||||
−0.278125 | + | 0.960545i | \(0.589713\pi\) | |||||||
\(228\) | − | 7.23314e19i | − | 0.655965i | ||||||
\(229\) | −2.06891e20 | −1.80775 | −0.903877 | − | 0.427792i | \(-0.859292\pi\) | ||||
−0.903877 | + | 0.427792i | \(0.859292\pi\) | |||||||
\(230\) | 7.83476e19 | − | 1.81205e20i | 0.659689 | − | 1.52575i | ||||
\(231\) | 2.01745e20 | 1.63720 | ||||||||
\(232\) | 6.08311e17i | 0.00475859i | ||||||||
\(233\) | − | 1.17415e19i | − | 0.0885519i | −0.999019 | − | 0.0442759i | \(-0.985902\pi\) | ||
0.999019 | − | 0.0442759i | \(-0.0140981\pi\) | |||||||
\(234\) | 3.05716e20 | 2.22322 | ||||||||
\(235\) | 1.11604e20 | + | 4.82544e19i | 0.782717 | + | 0.338423i | ||||
\(236\) | 4.20063e19 | 0.284160 | ||||||||
\(237\) | 1.93083e20i | 1.26004i | ||||||||
\(238\) | 2.58403e20i | 1.62702i | ||||||||
\(239\) | −2.08822e20 | −1.26880 | −0.634402 | − | 0.773003i | \(-0.718754\pi\) | ||||
−0.634402 | + | 0.773003i | \(0.718754\pi\) | |||||||
\(240\) | −2.50043e20 | − | 1.08111e20i | −1.46629 | − | 0.633979i | ||||
\(241\) | 1.13616e20 | 0.643123 | 0.321562 | − | 0.946889i | \(-0.395792\pi\) | ||||
0.321562 | + | 0.946889i | \(0.395792\pi\) | |||||||
\(242\) | − | 8.57876e19i | − | 0.468807i | ||||||
\(243\) | − | 2.02697e20i | − | 1.06953i | ||||||
\(244\) | −9.45229e19 | −0.481641 | ||||||||
\(245\) | 1.76461e19 | − | 4.08124e19i | 0.0868434 | − | 0.200854i | ||||
\(246\) | −7.36281e20 | −3.50022 | ||||||||
\(247\) | − | 8.80814e19i | − | 0.404539i | ||||||
\(248\) | 9.78734e17i | 0.00434335i | ||||||||
\(249\) | 5.23401e20 | 2.24461 | ||||||||
\(250\) | 1.16020e20 | + | 3.21319e20i | 0.480887 | + | 1.33182i | ||||
\(251\) | −1.87124e20 | −0.749725 | −0.374862 | − | 0.927080i | \(-0.622310\pi\) | ||||
−0.374862 | + | 0.927080i | \(0.622310\pi\) | |||||||
\(252\) | − | 3.61826e20i | − | 1.40151i | ||||||
\(253\) | 3.61633e20i | 1.35439i | ||||||||
\(254\) | −1.51994e19 | −0.0550477 | ||||||||
\(255\) | 2.36493e20 | − | 5.46969e20i | 0.828374 | − | 1.91589i | ||||
\(256\) | 2.92171e20 | 0.989913 | ||||||||
\(257\) | − | 3.72191e20i | − | 1.21993i | −0.792429 | − | 0.609964i | \(-0.791184\pi\) | ||
0.792429 | − | 0.609964i | \(-0.208816\pi\) | |||||||
\(258\) | 4.31522e19i | 0.136847i | ||||||||
\(259\) | 4.46335e19 | 0.136966 | ||||||||
\(260\) | 3.09100e20 | + | 1.33646e20i | 0.917965 | + | 0.396901i | ||||
\(261\) | −3.68487e20 | −1.05920 | ||||||||
\(262\) | − | 6.20614e20i | − | 1.72687i | ||||||
\(263\) | 4.29984e20i | 1.15832i | 0.815214 | + | 0.579160i | \(0.196619\pi\) | ||||
−0.815214 | + | 0.579160i | \(0.803381\pi\) | |||||||
\(264\) | −5.03399e18 | −0.0131304 | ||||||||
\(265\) | 3.52560e19 | + | 1.52437e19i | 0.0890519 | + | 0.0385034i | ||||
\(266\) | −2.07976e20 | −0.508768 | ||||||||
\(267\) | 1.20890e21i | 2.86448i | ||||||||
\(268\) | 3.78922e20i | 0.869770i | ||||||||
\(269\) | −7.19281e20 | −1.59957 | −0.799787 | − | 0.600285i | \(-0.795054\pi\) | ||||
−0.799787 | + | 0.600285i | \(0.795054\pi\) | |||||||
\(270\) | −2.41932e20 | + | 5.59548e20i | −0.521316 | + | 1.20572i | ||||
\(271\) | 3.85312e19 | 0.0804588 | 0.0402294 | − | 0.999190i | \(-0.487191\pi\) | ||||
0.0402294 | + | 0.999190i | \(0.487191\pi\) | |||||||
\(272\) | 6.39156e20i | 1.29351i | ||||||||
\(273\) | − | 7.19870e20i | − | 1.41212i | ||||||
\(274\) | 7.81167e20 | 1.48547 | ||||||||
\(275\) | −4.28668e20 | − | 4.55917e20i | −0.790301 | − | 0.840539i | ||||
\(276\) | 1.05965e21 | 1.89424 | ||||||||
\(277\) | − | 1.09040e21i | − | 1.89019i | −0.326792 | − | 0.945096i | \(-0.605968\pi\) | ||
0.326792 | − | 0.945096i | \(-0.394032\pi\) | |||||||
\(278\) | − | 5.17314e20i | − | 0.869707i | ||||||
\(279\) | −5.92872e20 | −0.966775 | ||||||||
\(280\) | 1.57185e18 | − | 3.63542e18i | 0.00248638 | − | 0.00575057i | ||||
\(281\) | 1.21849e21 | 1.86989 | 0.934947 | − | 0.354786i | \(-0.115446\pi\) | ||||
0.934947 | + | 0.354786i | \(0.115446\pi\) | |||||||
\(282\) | 1.30203e21i | 1.93866i | ||||||||
\(283\) | − | 5.78122e20i | − | 0.835285i | −0.908611 | − | 0.417643i | \(-0.862856\pi\) | ||
0.908611 | − | 0.417643i | \(-0.137144\pi\) | |||||||
\(284\) | 4.46892e19 | 0.0626610 | ||||||||
\(285\) | 4.40228e20 | + | 1.90342e20i | 0.599097 | + | 0.259032i | ||||
\(286\) | −1.23068e21 | −1.62567 | ||||||||
\(287\) | 1.06117e21i | 1.36078i | ||||||||
\(288\) | − | 1.79447e21i | − | 2.23408i | ||||||
\(289\) | −5.70912e20 | −0.690140 | ||||||||
\(290\) | −7.43278e20 | − | 3.21371e20i | −0.872506 | − | 0.377246i | ||||
\(291\) | −5.37157e20 | −0.612365 | ||||||||
\(292\) | − | 1.11876e21i | − | 1.23875i | ||||||
\(293\) | 6.74703e20i | 0.725668i | 0.931854 | + | 0.362834i | \(0.118191\pi\) | ||||
−0.931854 | + | 0.362834i | \(0.881809\pi\) | |||||||
\(294\) | 4.76136e20 | 0.497483 | ||||||||
\(295\) | −1.10541e20 | + | 2.55662e20i | −0.112211 | + | 0.259525i | ||||
\(296\) | −1.11371e18 | −0.00109848 | ||||||||
\(297\) | − | 1.11670e21i | − | 1.07030i | ||||||
\(298\) | 8.41258e20i | 0.783594i | ||||||||
\(299\) | 1.29038e21 | 1.16819 | ||||||||
\(300\) | −1.33592e21 | + | 1.25607e21i | −1.17557 | + | 1.10531i | ||||
\(301\) | 6.21932e19 | 0.0532020 | ||||||||
\(302\) | − | 1.06365e19i | − | 0.00884587i | ||||||
\(303\) | 7.25231e20i | 0.586427i | ||||||||
\(304\) | −5.14425e20 | −0.404480 | ||||||||
\(305\) | 2.48739e20 | − | 5.75292e20i | 0.190193 | − | 0.439886i | ||||
\(306\) | 3.90574e21 | 2.90450 | ||||||||
\(307\) | − | 1.91771e20i | − | 0.138710i | −0.997592 | − | 0.0693548i | \(-0.977906\pi\) | ||
0.997592 | − | 0.0693548i | \(-0.0220941\pi\) | |||||||
\(308\) | 1.45655e21i | 1.02481i | ||||||||
\(309\) | −2.65653e21 | −1.81831 | ||||||||
\(310\) | −1.19589e21 | − | 5.17066e20i | −0.796372 | − | 0.344328i | ||||
\(311\) | 2.70588e21 | 1.75325 | 0.876627 | − | 0.481171i | \(-0.159788\pi\) | ||||
0.876627 | + | 0.481171i | \(0.159788\pi\) | |||||||
\(312\) | 1.79624e19i | 0.0113253i | ||||||||
\(313\) | 1.59470e21i | 0.978477i | 0.872150 | + | 0.489239i | \(0.162725\pi\) | ||||
−0.872150 | + | 0.489239i | \(0.837275\pi\) | |||||||
\(314\) | −9.42705e20 | −0.562955 | ||||||||
\(315\) | 2.20217e21 | + | 9.52153e20i | 1.28000 | + | 0.553436i | ||||
\(316\) | −1.39402e21 | −0.788729 | ||||||||
\(317\) | − | 1.14239e21i | − | 0.629234i | −0.949219 | − | 0.314617i | \(-0.898124\pi\) | ||
0.949219 | − | 0.314617i | \(-0.101876\pi\) | |||||||
\(318\) | 4.11312e20i | 0.220567i | ||||||||
\(319\) | 1.48337e21 | 0.774512 | ||||||||
\(320\) | 7.88372e20 | − | 1.82337e21i | 0.400826 | − | 0.927045i | ||||
\(321\) | −3.21882e21 | −1.59369 | ||||||||
\(322\) | − | 3.04683e21i | − | 1.46917i | ||||||
\(323\) | − | 1.12530e21i | − | 0.528504i | ||||||
\(324\) | 1.94082e20 | 0.0887876 | ||||||||
\(325\) | −1.62681e21 | + | 1.52958e21i | −0.724984 | + | 0.681652i | ||||
\(326\) | −2.79843e21 | −1.21497 | ||||||||
\(327\) | 4.44825e21i | 1.88162i | ||||||||
\(328\) | − | 2.64785e19i | − | 0.0109135i | ||||||
\(329\) | 1.87655e21 | 0.753692 | ||||||||
\(330\) | 2.65946e21 | − | 6.15090e21i | 1.04094 | − | 2.40752i | ||||
\(331\) | −1.23995e21 | −0.473006 | −0.236503 | − | 0.971631i | \(-0.576001\pi\) | ||||
−0.236503 | + | 0.971631i | \(0.576001\pi\) | |||||||
\(332\) | 3.77884e21i | 1.40503i | ||||||||
\(333\) | − | 6.74632e20i | − | 0.244507i | ||||||
\(334\) | −3.03035e20 | −0.107065 | ||||||||
\(335\) | −2.30623e21 | − | 9.97143e20i | −0.794366 | − | 0.343460i | ||||
\(336\) | −4.20429e21 | −1.41191 | ||||||||
\(337\) | − | 5.46590e21i | − | 1.78981i | −0.446255 | − | 0.894906i | \(-0.647243\pi\) | ||
0.446255 | − | 0.894906i | \(-0.352757\pi\) | |||||||
\(338\) | − | 4.32314e19i | − | 0.0138041i | ||||||
\(339\) | 3.34046e21 | 1.04018 | ||||||||
\(340\) | 3.94899e21 | + | 1.70742e21i | 1.19926 | + | 0.518526i | ||||
\(341\) | 2.38665e21 | 0.706929 | ||||||||
\(342\) | 3.14354e21i | 0.908233i | ||||||||
\(343\) | − | 3.82222e21i | − | 1.07725i | ||||||
\(344\) | −1.55186e18 | −0.000426683 | ||||||||
\(345\) | −2.78849e21 | + | 6.44930e21i | −0.748008 | + | 1.73002i | ||||
\(346\) | 6.75069e21 | 1.76686 | ||||||||
\(347\) | 3.32900e21i | 0.850185i | 0.905150 | + | 0.425093i | \(0.139759\pi\) | ||||
−0.905150 | + | 0.425093i | \(0.860241\pi\) | |||||||
\(348\) | − | 4.34653e21i | − | 1.08323i | ||||||
\(349\) | 1.29318e21 | 0.314517 | 0.157258 | − | 0.987558i | \(-0.449734\pi\) | ||||
0.157258 | + | 0.987558i | \(0.449734\pi\) | |||||||
\(350\) | 3.61161e21 | + | 3.84119e21i | 0.857279 | + | 0.911775i | ||||
\(351\) | −3.98461e21 | −0.923157 | ||||||||
\(352\) | 7.22374e21i | 1.63361i | ||||||||
\(353\) | − | 1.41320e21i | − | 0.311974i | −0.987759 | − | 0.155987i | \(-0.950144\pi\) | ||
0.987759 | − | 0.155987i | \(-0.0498558\pi\) | |||||||
\(354\) | −2.98266e21 | −0.642801 | ||||||||
\(355\) | −1.17601e20 | + | 2.71991e20i | −0.0247439 | + | 0.0572286i | ||||
\(356\) | −8.72801e21 | −1.79304 | ||||||||
\(357\) | − | 9.19687e21i | − | 1.84485i | ||||||
\(358\) | 8.02601e21i | 1.57215i | ||||||||
\(359\) | −6.70882e21 | −1.28334 | −0.641672 | − | 0.766979i | \(-0.721759\pi\) | ||||
−0.641672 | + | 0.766979i | \(0.721759\pi\) | |||||||
\(360\) | −5.49491e19 | − | 2.37583e19i | −0.0102657 | − | 0.00443859i | ||||
\(361\) | −4.57468e21 | −0.834737 | ||||||||
\(362\) | − | 8.36504e21i | − | 1.49089i | ||||||
\(363\) | 3.05328e21i | 0.531570i | ||||||||
\(364\) | 5.19730e21 | 0.883926 | ||||||||
\(365\) | 6.80908e21 | + | 2.94404e21i | 1.13136 | + | 0.489164i | ||||
\(366\) | 6.71161e21 | 1.08953 | ||||||||
\(367\) | 1.37823e21i | 0.218606i | 0.994009 | + | 0.109303i | \(0.0348618\pi\) | ||||
−0.994009 | + | 0.109303i | \(0.965138\pi\) | |||||||
\(368\) | − | 7.53627e21i | − | 1.16802i | ||||||
\(369\) | 1.60394e22 | 2.42921 | ||||||||
\(370\) | 5.88372e20 | − | 1.36081e21i | 0.0870838 | − | 0.201410i | ||||
\(371\) | 5.92804e20 | 0.0857497 | ||||||||
\(372\) | − | 6.99329e21i | − | 0.988705i | ||||||
\(373\) | − | 5.63938e21i | − | 0.779303i | −0.920962 | − | 0.389652i | \(-0.872595\pi\) | ||
0.920962 | − | 0.389652i | \(-0.127405\pi\) | |||||||
\(374\) | −1.57228e22 | −2.12384 | ||||||||
\(375\) | −4.12929e21 | − | 1.14361e22i | −0.545268 | − | 1.51013i | ||||
\(376\) | −4.68240e19 | −0.00604466 | ||||||||
\(377\) | − | 5.29298e21i | − | 0.668034i | ||||||
\(378\) | 9.40839e21i | 1.16101i | ||||||||
\(379\) | −7.95543e21 | −0.959910 | −0.479955 | − | 0.877293i | \(-0.659347\pi\) | ||||
−0.479955 | + | 0.877293i | \(0.659347\pi\) | |||||||
\(380\) | −1.37422e21 | + | 3.17835e21i | −0.162142 | + | 0.375008i | ||||
\(381\) | 5.40964e20 | 0.0624175 | ||||||||
\(382\) | 2.20113e22i | 2.48375i | ||||||||
\(383\) | 9.82389e21i | 1.08416i | 0.840326 | + | 0.542081i | \(0.182363\pi\) | ||||
−0.840326 | + | 0.542081i | \(0.817637\pi\) | |||||||
\(384\) | 2.10871e20 | 0.0227615 | ||||||||
\(385\) | −8.86498e21 | − | 3.83295e21i | −0.935969 | − | 0.404685i | ||||
\(386\) | 5.43042e21 | 0.560843 | ||||||||
\(387\) | − | 9.40045e20i | − | 0.0949742i | ||||||
\(388\) | − | 3.87815e21i | − | 0.383314i | ||||||
\(389\) | 1.88950e21 | 0.182716 | 0.0913579 | − | 0.995818i | \(-0.470879\pi\) | ||||
0.0913579 | + | 0.995818i | \(0.470879\pi\) | |||||||
\(390\) | −2.19477e22 | − | 9.48954e21i | −2.07654 | − | 0.897834i | ||||
\(391\) | 1.64856e22 | 1.52617 | ||||||||
\(392\) | 1.71230e19i | 0.00155113i | ||||||||
\(393\) | 2.20884e22i | 1.95807i | ||||||||
\(394\) | 1.04616e22 | 0.907567 | ||||||||
\(395\) | 3.66839e21 | − | 8.48436e21i | 0.311458 | − | 0.720351i | ||||
\(396\) | 2.20157e22 | 1.82946 | ||||||||
\(397\) | 2.38867e22i | 1.94284i | 0.237364 | + | 0.971421i | \(0.423716\pi\) | ||||
−0.237364 | + | 0.971421i | \(0.576284\pi\) | |||||||
\(398\) | − | 1.29223e22i | − | 1.02881i | ||||||
\(399\) | 7.40212e21 | 0.576881 | ||||||||
\(400\) | 8.93325e21 | + | 9.50112e21i | 0.681553 | + | 0.724878i | ||||
\(401\) | −5.01330e21 | −0.374452 | −0.187226 | − | 0.982317i | \(-0.559950\pi\) | ||||
−0.187226 | + | 0.982317i | \(0.559950\pi\) | |||||||
\(402\) | − | 2.69054e22i | − | 1.96752i | ||||||
\(403\) | − | 8.51606e21i | − | 0.609742i | ||||||
\(404\) | −5.23600e21 | −0.367078 | ||||||||
\(405\) | −5.10731e20 | + | 1.18124e21i | −0.0350610 | + | 0.0810903i | ||||
\(406\) | −1.24977e22 | −0.840152 | ||||||||
\(407\) | 2.71578e21i | 0.178789i | ||||||||
\(408\) | 2.29482e20i | 0.0147958i | ||||||||
\(409\) | −1.79789e22 | −1.13531 | −0.567657 | − | 0.823265i | \(-0.692150\pi\) | ||||
−0.567657 | + | 0.823265i | \(0.692150\pi\) | |||||||
\(410\) | 3.23533e22 | + | 1.39886e22i | 2.00104 | + | 0.865190i | ||||
\(411\) | −2.78027e22 | −1.68434 | ||||||||
\(412\) | − | 1.91795e22i | − | 1.13818i | ||||||
\(413\) | 4.29877e21i | 0.249901i | ||||||||
\(414\) | −4.60525e22 | −2.62271 | ||||||||
\(415\) | −2.29990e22 | − | 9.94409e21i | −1.28322 | − | 0.554825i | ||||
\(416\) | 2.57758e22 | 1.40903 | ||||||||
\(417\) | 1.84118e22i | 0.986143i | ||||||||
\(418\) | − | 1.26545e22i | − | 0.664122i | ||||||
\(419\) | 3.00683e22 | 1.54628 | 0.773142 | − | 0.634233i | \(-0.218684\pi\) | ||||
0.773142 | + | 0.634233i | \(0.218684\pi\) | |||||||
\(420\) | −1.12312e22 | + | 2.59760e22i | −0.565989 | + | 1.30904i | ||||
\(421\) | 1.89938e22 | 0.938026 | 0.469013 | − | 0.883191i | \(-0.344610\pi\) | ||||
0.469013 | + | 0.883191i | \(0.344610\pi\) | |||||||
\(422\) | − | 2.98624e22i | − | 1.44534i | ||||||
\(423\) | − | 2.83638e22i | − | 1.34546i | ||||||
\(424\) | −1.47918e19 | −0.000687718 | ||||||||
\(425\) | −2.07837e22 | + | 1.95415e22i | −0.947146 | + | 0.890536i | ||||
\(426\) | −3.17316e21 | −0.141746 | ||||||||
\(427\) | − | 9.67311e21i | − | 0.423574i | ||||||
\(428\) | − | 2.32392e22i | − | 0.997581i | ||||||
\(429\) | 4.38013e22 | 1.84332 | ||||||||
\(430\) | 8.19849e20 | − | 1.89617e21i | 0.0338261 | − | 0.0782341i | ||||
\(431\) | 1.12764e22 | 0.456155 | 0.228077 | − | 0.973643i | \(-0.426756\pi\) | ||||
0.228077 | + | 0.973643i | \(0.426756\pi\) | |||||||
\(432\) | 2.32715e22i | 0.923023i | ||||||||
\(433\) | − | 8.94358e21i | − | 0.347828i | −0.984761 | − | 0.173914i | \(-0.944359\pi\) | ||
0.984761 | − | 0.173914i | \(-0.0556414\pi\) | |||||||
\(434\) | −2.01080e22 | −0.766841 | ||||||||
\(435\) | 2.64542e22 | + | 1.14380e22i | 0.989317 | + | 0.427751i | ||||
\(436\) | −3.21153e22 | −1.17781 | ||||||||
\(437\) | 1.32684e22i | 0.477230i | ||||||||
\(438\) | 7.94377e22i | 2.80218i | ||||||||
\(439\) | 3.08777e22 | 1.06831 | 0.534154 | − | 0.845387i | \(-0.320630\pi\) | ||||
0.534154 | + | 0.845387i | \(0.320630\pi\) | |||||||
\(440\) | 2.21201e20 | + | 9.56407e19i | 0.00750653 | + | 0.00324560i | ||||
\(441\) | −1.03723e22 | −0.345261 | ||||||||
\(442\) | 5.61024e22i | 1.83186i | ||||||||
\(443\) | − | 3.82645e21i | − | 0.122564i | −0.998120 | − | 0.0612822i | \(-0.980481\pi\) | ||
0.998120 | − | 0.0612822i | \(-0.0195190\pi\) | |||||||
\(444\) | 7.95770e21 | 0.250053 | ||||||||
\(445\) | 2.29680e22 | − | 5.31211e22i | 0.708048 | − | 1.63760i | ||||
\(446\) | −3.89306e22 | −1.17746 | ||||||||
\(447\) | − | 2.99414e22i | − | 0.888501i | ||||||
\(448\) | − | 3.06587e22i | − | 0.892668i | ||||||
\(449\) | −5.61218e22 | −1.60339 | −0.801693 | − | 0.597736i | \(-0.796067\pi\) | ||||
−0.801693 | + | 0.597736i | \(0.796067\pi\) | |||||||
\(450\) | 5.80593e22 | − | 5.45892e22i | 1.62767 | − | 1.53038i | ||||
\(451\) | −6.45678e22 | −1.77630 | ||||||||
\(452\) | 2.41173e22i | 0.651108i | ||||||||
\(453\) | 3.78566e20i | 0.0100301i | ||||||||
\(454\) | 1.04612e23 | 2.72023 | ||||||||
\(455\) | −1.36768e22 | + | 3.16322e22i | −0.349050 | + | 0.807294i | ||||
\(456\) | −1.84699e20 | −0.00462662 | ||||||||
\(457\) | 1.57770e22i | 0.387915i | 0.981010 | + | 0.193957i | \(0.0621324\pi\) | ||||
−0.981010 | + | 0.193957i | \(0.937868\pi\) | |||||||
\(458\) | 1.06061e23i | 2.55975i | ||||||||
\(459\) | −5.09064e22 | −1.20605 | ||||||||
\(460\) | −4.65624e22 | − | 2.01322e22i | −1.08291 | − | 0.468220i | ||||
\(461\) | 1.26163e22 | 0.288055 | 0.144027 | − | 0.989574i | \(-0.453995\pi\) | ||||
0.144027 | + | 0.989574i | \(0.453995\pi\) | |||||||
\(462\) | − | 1.03423e23i | − | 2.31824i | ||||||
\(463\) | − | 5.01130e22i | − | 1.10284i | −0.834228 | − | 0.551420i | \(-0.814086\pi\) | ||
0.834228 | − | 0.551420i | \(-0.185914\pi\) | |||||||
\(464\) | −3.09128e22 | −0.667937 | ||||||||
\(465\) | 4.25631e22 | + | 1.84030e22i | 0.902990 | + | 0.390426i | ||||
\(466\) | −6.01916e21 | −0.125388 | ||||||||
\(467\) | 1.34110e22i | 0.274326i | 0.990548 | + | 0.137163i | \(0.0437985\pi\) | ||||
−0.990548 | + | 0.137163i | \(0.956202\pi\) | |||||||
\(468\) | − | 7.85567e22i | − | 1.57795i | ||||||
\(469\) | −3.87775e22 | −0.764910 | ||||||||
\(470\) | 2.47372e22 | − | 5.72129e22i | 0.479202 | − | 1.10831i | ||||
\(471\) | 3.35520e22 | 0.638323 | ||||||||
\(472\) | − | 1.07264e20i | − | 0.00200422i | ||||||
\(473\) | 3.78421e21i | 0.0694474i | ||||||||
\(474\) | 9.89823e22 | 1.78419 | ||||||||
\(475\) | −1.57280e22 | − | 1.67278e22i | −0.278469 | − | 0.296171i | ||||
\(476\) | 6.63993e22 | 1.15479 | ||||||||
\(477\) | − | 8.96018e21i | − | 0.153077i | ||||||
\(478\) | 1.07051e23i | 1.79660i | ||||||||
\(479\) | −9.41455e22 | −1.55220 | −0.776100 | − | 0.630609i | \(-0.782805\pi\) | ||||
−0.776100 | + | 0.630609i | \(0.782805\pi\) | |||||||
\(480\) | −5.57010e22 | + | 1.28827e23i | −0.902220 | + | 2.08668i | ||||
\(481\) | 9.69047e21 | 0.154210 | ||||||||
\(482\) | − | 5.82441e22i | − | 0.910651i | ||||||
\(483\) | 1.08440e23i | 1.66586i | ||||||||
\(484\) | −2.20440e22 | −0.332740 | ||||||||
\(485\) | 2.36035e22 | + | 1.02054e22i | 0.350083 | + | 0.151365i | ||||
\(486\) | −1.03911e23 | −1.51444 | ||||||||
\(487\) | − | 9.22452e22i | − | 1.32114i | −0.750766 | − | 0.660568i | \(-0.770316\pi\) | ||
0.750766 | − | 0.660568i | \(-0.229684\pi\) | |||||||
\(488\) | 2.41366e20i | 0.00339709i | ||||||||
\(489\) | 9.95995e22 | 1.37763 | ||||||||
\(490\) | −2.09221e22 | − | 9.04609e21i | −0.284406 | − | 0.122969i | ||||
\(491\) | 5.46994e22 | 0.730786 | 0.365393 | − | 0.930853i | \(-0.380935\pi\) | ||||
0.365393 | + | 0.930853i | \(0.380935\pi\) | |||||||
\(492\) | 1.89195e23i | 2.48431i | ||||||||
\(493\) | − | 6.76217e22i | − | 0.872745i | ||||||
\(494\) | −4.51541e22 | −0.572819 | ||||||||
\(495\) | −5.79348e22 | + | 1.33993e23i | −0.722429 | + | 1.67086i | ||||
\(496\) | −4.97367e22 | −0.609653 | ||||||||
\(497\) | 4.57332e21i | 0.0551065i | ||||||||
\(498\) | − | 2.68317e23i | − | 3.17832i | ||||||
\(499\) | 1.31366e23 | 1.52978 | 0.764889 | − | 0.644162i | \(-0.222794\pi\) | ||||
0.764889 | + | 0.644162i | \(0.222794\pi\) | |||||||
\(500\) | 8.25662e22 | − | 2.98125e22i | 0.945274 | − | 0.341314i | ||||
\(501\) | 1.07854e22 | 0.121399 | ||||||||
\(502\) | 9.59271e22i | 1.06160i | ||||||||
\(503\) | − | 2.61038e22i | − | 0.284038i | −0.989864 | − | 0.142019i | \(-0.954641\pi\) | ||
0.989864 | − | 0.142019i | \(-0.0453594\pi\) | |||||||
\(504\) | −9.23928e20 | −0.00988504 | ||||||||
\(505\) | 1.37787e22 | − | 3.18677e22i | 0.144954 | − | 0.335254i | ||||
\(506\) | 1.85387e23 | 1.91779 | ||||||||
\(507\) | 1.53866e21i | 0.0156521i | ||||||||
\(508\) | 3.90564e21i | 0.0390706i | ||||||||
\(509\) | −1.64322e22 | −0.161657 | −0.0808285 | − | 0.996728i | \(-0.525757\pi\) | ||||
−0.0808285 | + | 0.996728i | \(0.525757\pi\) | |||||||
\(510\) | −2.80398e23 | − | 1.21236e23i | −2.71287 | − | 1.17296i | ||||
\(511\) | 1.14490e23 | 1.08940 | ||||||||
\(512\) | − | 1.51293e23i | − | 1.41588i | ||||||
\(513\) | − | 4.09720e22i | − | 0.377129i | ||||||
\(514\) | −1.90800e23 | −1.72740 | ||||||||
\(515\) | 1.16732e23 | + | 5.04714e22i | 1.03951 | + | 0.449452i | ||||
\(516\) | 1.10884e22 | 0.0971285 | ||||||||
\(517\) | 1.14180e23i | 0.983835i | ||||||||
\(518\) | − | 2.28809e22i | − | 0.193942i | ||||||
\(519\) | −2.40265e23 | −2.00340 | ||||||||
\(520\) | 3.41267e20 | − | 7.89293e20i | 0.00279940 | − | 0.00647455i | ||||
\(521\) | −8.34710e22 | −0.673620 | −0.336810 | − | 0.941573i | \(-0.609348\pi\) | ||||
−0.336810 | + | 0.941573i | \(0.609348\pi\) | |||||||
\(522\) | 1.88901e23i | 1.49981i | ||||||||
\(523\) | 1.83965e23i | 1.43704i | 0.695505 | + | 0.718522i | \(0.255181\pi\) | ||||
−0.695505 | + | 0.718522i | \(0.744819\pi\) | |||||||
\(524\) | −1.59473e23 | −1.22566 | ||||||||
\(525\) | −1.28541e23 | − | 1.36713e23i | −0.972051 | − | 1.03384i | ||||
\(526\) | 2.20427e23 | 1.64016 | ||||||||
\(527\) | − | 1.08799e23i | − | 0.796590i | ||||||
\(528\) | − | 2.55814e23i | − | 1.84305i | ||||||
\(529\) | −5.33313e22 | −0.378102 | ||||||||
\(530\) | 7.81451e21 | − | 1.80737e22i | 0.0545201 | − | 0.126096i | ||||
\(531\) | 6.49755e22 | 0.446115 | ||||||||
\(532\) | 5.34416e22i | 0.361102i | ||||||||
\(533\) | 2.30392e23i | 1.53209i | ||||||||
\(534\) | 6.19733e23 | 4.05606 | ||||||||
\(535\) | 1.41440e23 | + | 6.11544e22i | 0.911097 | + | 0.393931i | ||||
\(536\) | 9.67584e20 | 0.00613463 | ||||||||
\(537\) | − | 2.85655e23i | − | 1.78263i | ||||||
\(538\) | 3.68732e23i | 2.26497i | ||||||||
\(539\) | 4.17545e22 | 0.252463 | ||||||||
\(540\) | 1.43782e23 | + | 6.21669e22i | 0.855769 | + | 0.370009i | ||||
\(541\) | −3.23384e23 | −1.89471 | −0.947353 | − | 0.320192i | \(-0.896253\pi\) | ||||
−0.947353 | + | 0.320192i | \(0.896253\pi\) | |||||||
\(542\) | − | 1.97527e22i | − | 0.113928i | ||||||
\(543\) | 2.97722e23i | 1.69049i | ||||||||
\(544\) | 3.29305e23 | 1.84081 | ||||||||
\(545\) | 8.45122e22 | − | 1.95462e23i | 0.465103 | − | 1.07570i | ||||
\(546\) | −3.69035e23 | −1.99954 | ||||||||
\(547\) | − | 1.81693e23i | − | 0.969272i | −0.874716 | − | 0.484636i | \(-0.838952\pi\) | ||
0.874716 | − | 0.484636i | \(-0.161048\pi\) | |||||||
\(548\) | − | 2.00729e23i | − | 1.05433i | ||||||
\(549\) | −1.46208e23 | −0.756148 | ||||||||
\(550\) | −2.33722e23 | + | 2.19752e23i | −1.19019 | + | 1.11905i | ||||
\(551\) | 5.44254e22 | 0.272906 | ||||||||
\(552\) | − | 2.70582e21i | − | 0.0133603i | ||||||
\(553\) | − | 1.42658e23i | − | 0.693639i | ||||||
\(554\) | −5.58981e23 | −2.67648 | ||||||||
\(555\) | −2.09409e22 | + | 4.84327e22i | −0.0987425 | + | 0.228375i | ||||
\(556\) | −1.32929e23 | −0.617283 | ||||||||
\(557\) | 3.53126e23i | 1.61496i | 0.589898 | + | 0.807478i | \(0.299168\pi\) | ||||
−0.589898 | + | 0.807478i | \(0.700832\pi\) | |||||||
\(558\) | 3.03930e23i | 1.36894i | ||||||||
\(559\) | 1.35029e22 | 0.0598999 | ||||||||
\(560\) | 1.84743e23 | + | 7.98772e22i | 0.807177 | + | 0.348999i | ||||
\(561\) | 5.59594e23 | 2.40818 | ||||||||
\(562\) | − | 6.24646e23i | − | 2.64774i | ||||||
\(563\) | − | 2.98124e23i | − | 1.24473i | −0.782727 | − | 0.622365i | \(-0.786172\pi\) | ||
0.782727 | − | 0.622365i | \(-0.213828\pi\) | |||||||
\(564\) | 3.34569e23 | 1.37598 | ||||||||
\(565\) | −1.46785e23 | − | 6.34653e22i | −0.594660 | − | 0.257113i | ||||
\(566\) | −2.96369e23 | −1.18275 | ||||||||
\(567\) | 1.98616e22i | 0.0780833i | ||||||||
\(568\) | − | 1.14115e20i | − | 0.000441957i | ||||||
\(569\) | −2.50456e23 | −0.955602 | −0.477801 | − | 0.878468i | \(-0.658566\pi\) | ||||
−0.477801 | + | 0.878468i | \(0.658566\pi\) | |||||||
\(570\) | 9.75768e22 | − | 2.25679e23i | 0.366784 | − | 0.848310i | ||||
\(571\) | 6.51987e22 | 0.241453 | 0.120726 | − | 0.992686i | \(-0.461478\pi\) | ||||
0.120726 | + | 0.992686i | \(0.461478\pi\) | |||||||
\(572\) | 3.16235e23i | 1.15384i | ||||||||
\(573\) | − | 7.83409e23i | − | 2.81627i | ||||||
\(574\) | 5.43996e23 | 1.92684 | ||||||||
\(575\) | 2.45060e23 | − | 2.30413e23i | 0.855256 | − | 0.804139i | ||||
\(576\) | −4.63403e23 | −1.59356 | ||||||||
\(577\) | 2.02985e23i | 0.687811i | 0.939004 | + | 0.343905i | \(0.111750\pi\) | ||||
−0.939004 | + | 0.343905i | \(0.888250\pi\) | |||||||
\(578\) | 2.92672e23i | 0.977226i | ||||||||
\(579\) | −1.93275e23 | −0.635928 | ||||||||
\(580\) | −8.25797e22 | + | 1.90993e23i | −0.267753 | + | 0.619269i | ||||
\(581\) | −3.86711e23 | −1.23563 | ||||||||
\(582\) | 2.75368e23i | 0.867099i | ||||||||
\(583\) | 3.60698e22i | 0.111934i | ||||||||
\(584\) | −2.85677e21 | −0.00873708 | ||||||||
\(585\) | 4.78117e23 | + | 2.06724e23i | 1.44115 | + | 0.623111i | ||||
\(586\) | 3.45880e23 | 1.02753 | ||||||||
\(587\) | 4.32091e23i | 1.26518i | 0.774488 | + | 0.632589i | \(0.218008\pi\) | ||||
−0.774488 | + | 0.632589i | \(0.781992\pi\) | |||||||
\(588\) | − | 1.22348e23i | − | 0.353093i | ||||||
\(589\) | 8.75670e22 | 0.249092 | ||||||||
\(590\) | 1.31063e23 | + | 5.66676e22i | 0.367483 | + | 0.158889i | ||||
\(591\) | −3.72339e23 | −1.02907 | ||||||||
\(592\) | − | 5.65956e22i | − | 0.154187i | ||||||
\(593\) | − | 2.09720e23i | − | 0.563215i | −0.959530 | − | 0.281608i | \(-0.909132\pi\) | ||
0.959530 | − | 0.281608i | \(-0.0908676\pi\) | |||||||
\(594\) | −5.72464e23 | −1.51553 | ||||||||
\(595\) | −1.74731e23 | + | 4.04124e23i | −0.456012 | + | 1.05468i | ||||
\(596\) | 2.16170e23 | 0.556163 | ||||||||
\(597\) | 4.59919e23i | 1.16654i | ||||||||
\(598\) | − | 6.61502e23i | − | 1.65414i | ||||||
\(599\) | 4.27137e23 | 1.05303 | 0.526514 | − | 0.850167i | \(-0.323499\pi\) | ||||
0.526514 | + | 0.850167i | \(0.323499\pi\) | |||||||
\(600\) | 3.20740e21 | + | 3.41128e21i | 0.00779591 | + | 0.00829148i | ||||
\(601\) | −2.36643e23 | −0.567102 | −0.283551 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283551 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(602\) | − | 3.18827e22i | − | 0.0753330i | ||||||
\(603\) | 5.86118e23i | 1.36549i | ||||||||
\(604\) | −2.73316e21 | −0.00627843 | ||||||||
\(605\) | 5.80093e22 | − | 1.34166e23i | 0.131394 | − | 0.303893i | ||||
\(606\) | 3.71783e23 | 0.830371 | ||||||||
\(607\) | − | 2.71884e23i | − | 0.598798i | −0.954128 | − | 0.299399i | \(-0.903214\pi\) | ||
0.954128 | − | 0.299399i | \(-0.0967861\pi\) | |||||||
\(608\) | 2.65042e23i | 0.575618i | ||||||||
\(609\) | 4.44807e23 | 0.952631 | ||||||||
\(610\) | −2.94918e23 | − | 1.27514e23i | −0.622870 | − | 0.269311i | ||||
\(611\) | 4.07420e23 | 0.848579 | ||||||||
\(612\) | − | 1.00362e24i | − | 2.06149i | ||||||
\(613\) | 4.19323e22i | 0.0849444i | 0.999098 | + | 0.0424722i | \(0.0135234\pi\) | ||||
−0.999098 | + | 0.0424722i | \(0.986477\pi\) | |||||||
\(614\) | −9.83095e22 | −0.196410 | ||||||||
\(615\) | −1.15149e24 | − | 4.97871e23i | −2.26894 | − | 0.981021i | ||||
\(616\) | 3.71933e21 | 0.00722818 | ||||||||
\(617\) | − | 2.53421e23i | − | 0.485757i | −0.970057 | − | 0.242879i | \(-0.921908\pi\) | ||
0.970057 | − | 0.242879i | \(-0.0780917\pi\) | |||||||
\(618\) | 1.36184e24i | 2.57469i | ||||||||
\(619\) | 1.42452e23 | 0.265642 | 0.132821 | − | 0.991140i | \(-0.457596\pi\) | ||||
0.132821 | + | 0.991140i | \(0.457596\pi\) | |||||||
\(620\) | −1.32865e23 | + | 3.07295e23i | −0.244390 | + | 0.565232i | ||||
\(621\) | 6.00236e23 | 1.08904 | ||||||||
\(622\) | − | 1.38714e24i | − | 2.48258i | ||||||
\(623\) | − | 8.93191e23i | − | 1.57687i | ||||||
\(624\) | −9.12801e23 | −1.58967 | ||||||||
\(625\) | −3.58277e22 | + | 5.80973e23i | −0.0615516 | + | 0.998104i | ||||
\(626\) | 8.17505e23 | 1.38551 | ||||||||
\(627\) | 4.50390e23i | 0.753034i | ||||||||
\(628\) | 2.42238e23i | 0.399562i | ||||||||
\(629\) | 1.23803e23 | 0.201465 | ||||||||
\(630\) | 4.88112e23 | − | 1.12892e24i | 0.783655 | − | 1.81246i | ||||
\(631\) | −7.06224e23 | −1.11865 | −0.559323 | − | 0.828950i | \(-0.688939\pi\) | ||||
−0.559323 | + | 0.828950i | \(0.688939\pi\) | |||||||
\(632\) | 3.55964e21i | 0.00556303i | ||||||||
\(633\) | 1.06284e24i | 1.63884i | ||||||||
\(634\) | −5.85638e23 | −0.890985 | ||||||||
\(635\) | −2.37708e22 | − | 1.02778e22i | −0.0356834 | − | 0.0154284i | ||||
\(636\) | 1.05691e23 | 0.156550 | ||||||||
\(637\) | − | 1.48989e23i | − | 0.217755i | ||||||
\(638\) | − | 7.60435e23i | − | 1.09670i | ||||||
\(639\) | 6.91254e22 | 0.0983740 | ||||||||
\(640\) | −9.26598e21 | − | 4.00633e21i | −0.0130125 | − | 0.00562623i | ||||
\(641\) | 1.55017e23 | 0.214826 | 0.107413 | − | 0.994214i | \(-0.465743\pi\) | ||||
0.107413 | + | 0.994214i | \(0.465743\pi\) | |||||||
\(642\) | 1.65010e24i | 2.25664i | ||||||||
\(643\) | 1.13817e23i | 0.153608i | 0.997046 | + | 0.0768041i | \(0.0244716\pi\) | ||||
−0.997046 | + | 0.0768041i | \(0.975528\pi\) | |||||||
\(644\) | −7.82913e23 | −1.04276 | ||||||||
\(645\) | −2.91794e22 | + | 6.74870e22i | −0.0383547 | + | 0.0887080i | ||||
\(646\) | −5.76876e23 | −0.748353 | ||||||||
\(647\) | 5.81112e23i | 0.744001i | 0.928233 | + | 0.372000i | \(0.121328\pi\) | ||||
−0.928233 | + | 0.372000i | \(0.878672\pi\) | |||||||
\(648\) | − | 4.95591e20i | − | 0.000626233i | ||||||
\(649\) | −2.61563e23 | −0.326210 | ||||||||
\(650\) | 7.84123e23 | + | 8.33968e23i | 0.965208 | + | 1.02656i | ||||
\(651\) | 7.15666e23 | 0.869505 | ||||||||
\(652\) | 7.19085e23i | 0.862335i | ||||||||
\(653\) | 1.22090e24i | 1.44517i | 0.691282 | + | 0.722585i | \(0.257046\pi\) | ||||
−0.691282 | + | 0.722585i | \(0.742954\pi\) | |||||||
\(654\) | 2.28035e24 | 2.66435 | ||||||||
\(655\) | 4.19657e23 | − | 9.70596e23i | 0.483997 | − | 1.11941i | ||||
\(656\) | 1.34557e24 | 1.53187 | ||||||||
\(657\) | − | 1.73050e24i | − | 1.94476i | ||||||
\(658\) | − | 9.61993e23i | − | 1.06721i | ||||||
\(659\) | −8.05650e23 | −0.882308 | −0.441154 | − | 0.897431i | \(-0.645431\pi\) | ||||
−0.441154 | + | 0.897431i | \(0.645431\pi\) | |||||||
\(660\) | −1.58054e24 | − | 6.83376e23i | −1.70876 | − | 0.738816i | ||||
\(661\) | 1.62925e22 | 0.0173891 | 0.00869453 | − | 0.999962i | \(-0.497232\pi\) | ||||
0.00869453 | + | 0.999962i | \(0.497232\pi\) | |||||||
\(662\) | 6.35649e23i | 0.669768i | ||||||||
\(663\) | − | 1.99675e24i | − | 2.07711i | ||||||
\(664\) | 9.64931e21 | 0.00990986 | ||||||||
\(665\) | −3.25260e23 | − | 1.40633e23i | −0.329797 | − | 0.142594i | ||||
\(666\) | −3.45844e23 | −0.346217 | ||||||||
\(667\) | 7.97326e23i | 0.788073i | ||||||||
\(668\) | 7.78679e22i | 0.0759903i | ||||||||
\(669\) | 1.38559e24 | 1.33509 | ||||||||
\(670\) | −5.11176e23 | + | 1.18226e24i | −0.486334 | + | 1.12481i | ||||
\(671\) | 5.88571e23 | 0.552914 | ||||||||
\(672\) | 2.16613e24i | 2.00931i | ||||||||
\(673\) | − | 9.71208e22i | − | 0.0889578i | −0.999010 | − | 0.0444789i | \(-0.985837\pi\) | ||
0.999010 | − | 0.0444789i | \(-0.0141628\pi\) | |||||||
\(674\) | −2.80204e24 | −2.53434 | ||||||||
\(675\) | −7.56729e23 | + | 7.11500e23i | −0.675863 | + | 0.635467i | ||||
\(676\) | −1.11087e22 | −0.00979756 | ||||||||
\(677\) | − | 6.85083e23i | − | 0.596677i | −0.954460 | − | 0.298339i | \(-0.903568\pi\) | ||
0.954460 | − | 0.298339i | \(-0.0964325\pi\) | |||||||
\(678\) | − | 1.71245e24i | − | 1.47288i | ||||||
\(679\) | 3.96875e23 | 0.337101 | ||||||||
\(680\) | 4.35993e21 | − | 1.00838e22i | 0.00365725 | − | 0.00845860i | ||||
\(681\) | −3.72325e24 | −3.08441 | ||||||||
\(682\) | − | 1.22349e24i | − | 1.00100i | ||||||
\(683\) | − | 2.54919e23i | − | 0.205981i | −0.994682 | − | 0.102990i | \(-0.967159\pi\) | ||
0.994682 | − | 0.102990i | \(-0.0328410\pi\) | |||||||
\(684\) | 8.07765e23 | 0.644626 | ||||||||
\(685\) | 1.22169e24 | + | 5.28222e23i | 0.962922 | + | 0.416339i | ||||
\(686\) | −1.95942e24 | −1.52536 | ||||||||
\(687\) | − | 3.77482e24i | − | 2.90245i | ||||||
\(688\) | − | 7.88614e22i | − | 0.0598912i | ||||||
\(689\) | 1.28705e23 | 0.0965453 | ||||||||
\(690\) | 3.30617e24 | + | 1.42949e24i | 2.44967 | + | 1.05917i | ||||
\(691\) | 2.08545e24 | 1.52628 | 0.763142 | − | 0.646231i | \(-0.223656\pi\) | ||||
0.763142 | + | 0.646231i | \(0.223656\pi\) | |||||||
\(692\) | − | 1.73466e24i | − | 1.25404i | ||||||
\(693\) | 2.25300e24i | 1.60890i | ||||||||
\(694\) | 1.70658e24 | 1.20385 | ||||||||
\(695\) | 3.49806e23 | − | 8.09042e23i | 0.243756 | − | 0.563768i | ||||
\(696\) | −1.10989e22 | −0.00764016 | ||||||||
\(697\) | 2.94342e24i | 2.00159i | ||||||||
\(698\) | − | 6.62938e23i | − | 0.445350i | ||||||
\(699\) | 2.14229e23 | 0.142175 | ||||||||
\(700\) | 9.87033e23 | − | 9.28040e23i | 0.647140 | − | 0.608462i | ||||
\(701\) | −1.58460e24 | −1.02640 | −0.513201 | − | 0.858268i | \(-0.671541\pi\) | ||||
−0.513201 | + | 0.858268i | \(0.671541\pi\) | |||||||
\(702\) | 2.04267e24i | 1.30717i | ||||||||
\(703\) | 9.96429e22i | 0.0629979i | ||||||||
\(704\) | 1.86546e24 | 1.16525 | ||||||||
\(705\) | −8.80425e23 | + | 2.03628e24i | −0.543357 | + | 1.25669i | ||||
\(706\) | −7.24463e23 | −0.441750 | ||||||||
\(707\) | − | 5.35832e23i | − | 0.322823i | ||||||
\(708\) | 7.66426e23i | 0.456234i | ||||||||
\(709\) | 6.54139e23 | 0.384749 | 0.192374 | − | 0.981322i | \(-0.438381\pi\) | ||||
0.192374 | + | 0.981322i | \(0.438381\pi\) | |||||||
\(710\) | 1.39433e23 | + | 6.02869e22i | 0.0810347 | + | 0.0350370i | ||||
\(711\) | −2.15627e24 | −1.23826 | ||||||||
\(712\) | 2.22871e22i | 0.0126466i | ||||||||
\(713\) | 1.28285e24i | 0.719306i | ||||||||
\(714\) | −4.71469e24 | −2.61227 | ||||||||
\(715\) | −1.92469e24 | − | 8.32180e23i | −1.05380 | − | 0.455634i | ||||
\(716\) | 2.06237e24 | 1.11585 | ||||||||
\(717\) | − | 3.81006e24i | − | 2.03713i | ||||||
\(718\) | 3.43921e24i | 1.81719i | ||||||||
\(719\) | −9.39757e23 | −0.490704 | −0.245352 | − | 0.969434i | \(-0.578904\pi\) | ||||
−0.245352 | + | 0.969434i | \(0.578904\pi\) | |||||||
\(720\) | 1.20734e24 | − | 2.79237e24i | 0.623021 | − | 1.44094i | ||||
\(721\) | 1.96276e24 | 1.00096 | ||||||||
\(722\) | 2.34517e24i | 1.18197i | ||||||||
\(723\) | 2.07298e24i | 1.03257i | ||||||||
\(724\) | −2.14948e24 | −1.05817 | ||||||||
\(725\) | −9.45125e23 | − | 1.00520e24i | −0.459850 | − | 0.489082i | ||||
\(726\) | 1.56524e24 | 0.752694 | ||||||||
\(727\) | 3.68851e24i | 1.75311i | 0.481303 | + | 0.876555i | \(0.340164\pi\) | ||||
−0.481303 | + | 0.876555i | \(0.659836\pi\) | |||||||
\(728\) | − | 1.32714e22i | − | 0.00623446i | ||||||
\(729\) | 3.50804e24 | 1.62885 | ||||||||
\(730\) | 1.50924e24 | − | 3.49061e24i | 0.692648 | − | 1.60198i | ||||
\(731\) | 1.72509e23 | 0.0782555 | ||||||||
\(732\) | − | 1.72462e24i | − | 0.773300i | ||||||
\(733\) | − | 1.51915e24i | − | 0.673314i | −0.941627 | − | 0.336657i | \(-0.890704\pi\) | ||
0.941627 | − | 0.336657i | \(-0.109296\pi\) | |||||||
\(734\) | 7.06538e23 | 0.309542 | ||||||||
\(735\) | 7.44643e23 | + | 3.21961e23i | 0.322482 | + | 0.139432i | ||||
\(736\) | −3.88284e24 | −1.66222 | ||||||||
\(737\) | − | 2.35946e24i | − | 0.998478i | ||||||
\(738\) | − | 8.22246e24i | − | 3.43972i | ||||||
\(739\) | 2.81865e24 | 1.16564 | 0.582819 | − | 0.812602i | \(-0.301950\pi\) | ||||
0.582819 | + | 0.812602i | \(0.301950\pi\) | |||||||
\(740\) | −3.49673e23 | − | 1.51188e23i | −0.142953 | − | 0.0618085i | ||||
\(741\) | 1.60709e24 | 0.649508 | ||||||||
\(742\) | − | 3.03895e23i | − | 0.121420i | ||||||
\(743\) | 2.00449e23i | 0.0791769i | 0.999216 | + | 0.0395884i | \(0.0126047\pi\) | ||||
−0.999216 | + | 0.0395884i | \(0.987395\pi\) | |||||||
\(744\) | −1.78575e22 | −0.00697349 | ||||||||
\(745\) | −5.68856e23 | + | 1.31567e24i | −0.219621 | + | 0.507947i | ||||
\(746\) | −2.89098e24 | −1.10348 | ||||||||
\(747\) | 5.84511e24i | 2.20581i | ||||||||
\(748\) | 4.04014e24i | 1.50741i | ||||||||
\(749\) | 2.37821e24 | 0.877312 | ||||||||
\(750\) | −5.86262e24 | + | 2.11684e24i | −2.13831 | + | 0.772090i | ||||
\(751\) | −1.04857e24 | −0.378146 | −0.189073 | − | 0.981963i | \(-0.560548\pi\) | ||||
−0.189073 | + | 0.981963i | \(0.560548\pi\) | |||||||
\(752\) | − | 2.37947e24i | − | 0.848456i | ||||||
\(753\) | − | 3.41416e24i | − | 1.20372i | ||||||
\(754\) | −2.71339e24 | −0.945924 | ||||||||
\(755\) | 7.19238e21 | − | 1.66348e22i | 0.00247927 | − | 0.00573413i | ||||
\(756\) | 2.41758e24 | 0.824035 | ||||||||
\(757\) | − | 9.69171e23i | − | 0.326652i | −0.986572 | − | 0.163326i | \(-0.947778\pi\) | ||
0.986572 | − | 0.163326i | \(-0.0522222\pi\) | |||||||
\(758\) | 4.07827e24i | 1.35922i | ||||||||
\(759\) | −6.59816e24 | −2.17454 | ||||||||
\(760\) | 8.11596e21 | + | 3.50910e21i | 0.00264499 | + | 0.00114362i | ||||
\(761\) | 5.85969e23 | 0.188845 | 0.0944224 | − | 0.995532i | \(-0.469900\pi\) | ||||
0.0944224 | + | 0.995532i | \(0.469900\pi\) | |||||||
\(762\) | − | 2.77320e23i | − | 0.0883821i | ||||||
\(763\) | − | 3.28656e24i | − | 1.03582i | ||||||
\(764\) | 5.65603e24 | 1.76286 | ||||||||
\(765\) | 6.10830e24 | + | 2.64105e24i | 1.88277 | + | 0.814056i | ||||
\(766\) | 5.03612e24 | 1.53515 | ||||||||
\(767\) | 9.33313e23i | 0.281363i | ||||||||
\(768\) | 5.33080e24i | 1.58936i | ||||||||
\(769\) | −4.42159e24 | −1.30378 | −0.651891 | − | 0.758313i | \(-0.726024\pi\) | ||||
−0.651891 | + | 0.758313i | \(0.726024\pi\) | |||||||
\(770\) | −1.96493e24 | + | 4.54455e24i | −0.573027 | + | 1.32532i | ||||
\(771\) | 6.79080e24 | 1.95866 | ||||||||
\(772\) | − | 1.39540e24i | − | 0.398063i | ||||||
\(773\) | − | 2.69572e24i | − | 0.760587i | −0.924866 | − | 0.380293i | \(-0.875823\pi\) | ||
0.924866 | − | 0.380293i | \(-0.124177\pi\) | |||||||
\(774\) | −4.81905e23 | −0.134482 | ||||||||
\(775\) | −1.52065e24 | − | 1.61731e24i | −0.419724 | − | 0.446405i | ||||
\(776\) | −9.90291e21 | −0.00270357 | ||||||||
\(777\) | 8.14360e23i | 0.219906i | ||||||||
\(778\) | − | 9.68636e23i | − | 0.258722i | ||||||
\(779\) | −2.36902e24 | −0.625893 | ||||||||
\(780\) | −2.43843e24 | + | 5.63969e24i | −0.637245 | + | 1.47384i | ||||
\(781\) | −2.78269e23 | −0.0719334 | ||||||||
\(782\) | − | 8.45118e24i | − | 2.16103i | ||||||
\(783\) | − | 2.46209e24i | − | 0.622771i | ||||||
\(784\) | −8.70146e23 | −0.217724 | ||||||||
\(785\) | −1.47432e24 | − | 6.37454e23i | −0.364923 | − | 0.157782i | ||||
\(786\) | 1.13234e25 | 2.77259 | ||||||||
\(787\) | 7.00740e24i | 1.69735i | 0.528914 | + | 0.848675i | \(0.322599\pi\) | ||||
−0.528914 | + | 0.848675i | \(0.677401\pi\) | |||||||
\(788\) | − | 2.68820e24i | − | 0.644154i | ||||||
\(789\) | −7.84527e24 | −1.85974 | ||||||||
\(790\) | −4.34943e24 | − | 1.88056e24i | −1.02000 | − | 0.441019i | ||||
\(791\) | −2.46808e24 | −0.572609 | ||||||||
\(792\) | − | 5.62174e22i | − | 0.0129035i | ||||||
\(793\) | − | 2.10015e24i | − | 0.476900i | ||||||
\(794\) | 1.22453e25 | 2.75103 | ||||||||
\(795\) | −2.78128e23 | + | 6.43263e23i | −0.0618193 | + | 0.142978i | ||||
\(796\) | −3.32051e24 | −0.730204 | ||||||||
\(797\) | 3.76526e24i | 0.819217i | 0.912261 | + | 0.409609i | \(0.134335\pi\) | ||||
−0.912261 | + | 0.409609i | \(0.865665\pi\) | |||||||
\(798\) | − | 3.79462e24i | − | 0.816853i | ||||||
\(799\) | 5.20510e24 | 1.10862 | ||||||||
\(800\) | 4.89517e24 | − | 4.60259e24i | 1.03158 | − | 0.969923i | ||||
\(801\) | −1.35005e25 | −2.81497 | ||||||||
\(802\) | 2.57002e24i | 0.530218i | ||||||||
\(803\) | 6.96625e24i | 1.42206i | ||||||||
\(804\) | −6.91362e24 | −1.39646 | ||||||||
\(805\) | 2.06025e24 | − | 4.76502e24i | 0.411771 | − | 0.952357i | ||||
\(806\) | −4.36568e24 | −0.863384 | ||||||||
\(807\) | − | 1.31236e25i | − | 2.56820i | ||||||
\(808\) | 1.33702e22i | 0.00258906i | ||||||||
\(809\) | −9.26474e23 | −0.177530 | −0.0887648 | − | 0.996053i | \(-0.528292\pi\) | ||||
−0.0887648 | + | 0.996053i | \(0.528292\pi\) | |||||||
\(810\) | 6.05549e23 | + | 2.61821e23i | 0.114822 | + | 0.0496458i | ||||
\(811\) | 6.94634e24 | 1.30340 | 0.651702 | − | 0.758475i | \(-0.274055\pi\) | ||||
0.651702 | + | 0.758475i | \(0.274055\pi\) | |||||||
\(812\) | 3.21140e24i | 0.596305i | ||||||||
\(813\) | 7.03021e23i | 0.129181i | ||||||||
\(814\) | 1.39222e24 | 0.253162 | ||||||||
\(815\) | −4.37655e24 | − | 1.89229e24i | −0.787575 | − | 0.340524i | ||||
\(816\) | −1.16617e25 | −2.07680 | ||||||||
\(817\) | 1.38844e23i | 0.0244704i | ||||||||
\(818\) | 9.21673e24i | 1.60758i | ||||||||
\(819\) | 8.03919e24 | 1.38771 | ||||||||
\(820\) | 3.59451e24 | − | 8.31350e24i | 0.614076 | − | 1.42026i | ||||
\(821\) | −1.86509e23 | −0.0315343 | −0.0157671 | − | 0.999876i | \(-0.505019\pi\) | ||||
−0.0157671 | + | 0.999876i | \(0.505019\pi\) | |||||||
\(822\) | 1.42528e25i | 2.38500i | ||||||||
\(823\) | − | 3.26650e24i | − | 0.540984i | −0.962722 | − | 0.270492i | \(-0.912814\pi\) | ||
0.962722 | − | 0.270492i | \(-0.0871863\pi\) | |||||||
\(824\) | −4.89752e22 | −0.00802777 | ||||||||
\(825\) | 8.31843e24 | − | 7.82125e24i | 1.34953 | − | 1.26887i | ||||
\(826\) | 2.20372e24 | 0.353856 | ||||||||
\(827\) | 4.98019e24i | 0.791496i | 0.918359 | + | 0.395748i | \(0.129515\pi\) | ||||
−0.918359 | + | 0.395748i | \(0.870485\pi\) | |||||||
\(828\) | 1.18337e25i | 1.86149i | ||||||||
\(829\) | −5.35813e24 | −0.834256 | −0.417128 | − | 0.908848i | \(-0.636963\pi\) | ||||
−0.417128 | + | 0.908848i | \(0.636963\pi\) | |||||||
\(830\) | −5.09774e24 | + | 1.17902e25i | −0.785623 | + | 1.81701i | ||||
\(831\) | 1.98948e25 | 3.03480 | ||||||||
\(832\) | − | 6.65636e24i | − | 1.00505i | ||||||
\(833\) | − | 1.90344e24i | − | 0.284484i | ||||||
\(834\) | 9.43864e24 | 1.39636 | ||||||||
\(835\) | −4.73925e23 | − | 2.04911e23i | −0.0694024 | − | 0.0300075i | ||||
\(836\) | −3.25171e24 | −0.471366 | ||||||||
\(837\) | − | 3.96134e24i | − | 0.568429i | ||||||
\(838\) | − | 1.54142e25i | − | 2.18951i | ||||||
\(839\) | −4.84743e24 | −0.681608 | −0.340804 | − | 0.940134i | \(-0.610699\pi\) | ||||
−0.340804 | + | 0.940134i | \(0.610699\pi\) | |||||||
\(840\) | 6.63300e22 | + | 2.86791e22i | 0.00923285 | + | 0.00399201i | ||||
\(841\) | −3.98662e24 | −0.549337 | ||||||||
\(842\) | − | 9.73701e24i | − | 1.32823i | ||||||
\(843\) | 2.22319e25i | 3.00222i | ||||||||
\(844\) | −7.67345e24 | −1.02584 | ||||||||
\(845\) | 2.92329e22 | − | 6.76108e22i | 0.00386892 | − | 0.00894817i | ||||
\(846\) | −1.45404e25 | −1.90515 | ||||||||
\(847\) | − | 2.25590e24i | − | 0.292624i | ||||||
\(848\) | − | 7.51680e23i | − | 0.0965313i | ||||||
\(849\) | 1.05481e25 | 1.34109 | ||||||||
\(850\) | 1.00178e25 | + | 1.06546e25i | 1.26098 | + | 1.34114i | ||||
\(851\) | −1.45976e24 | −0.181920 | ||||||||
\(852\) | 8.15377e23i | 0.100605i | ||||||||
\(853\) | 5.61088e24i | 0.685432i | 0.939439 | + | 0.342716i | \(0.111347\pi\) | ||||
−0.939439 | + | 0.342716i | \(0.888653\pi\) | |||||||
\(854\) | −4.95883e24 | −0.599773 | ||||||||
\(855\) | −2.12565e24 | + | 4.91628e24i | −0.254554 | + | 0.588741i | ||||
\(856\) | −5.93415e22 | −0.00703609 | ||||||||
\(857\) | 6.10091e24i | 0.716238i | 0.933676 | + | 0.358119i | \(0.116582\pi\) | ||||
−0.933676 | + | 0.358119i | \(0.883418\pi\) | |||||||
\(858\) | − | 2.24543e25i | − | 2.61010i | ||||||
\(859\) | −1.47049e25 | −1.69247 | −0.846236 | − | 0.532808i | \(-0.821137\pi\) | ||||
−0.846236 | + | 0.532808i | \(0.821137\pi\) | |||||||
\(860\) | −4.87241e23 | − | 2.10668e23i | −0.0555273 | − | 0.0240084i | ||||
\(861\) | −1.93615e25 | −2.18480 | ||||||||
\(862\) | − | 5.78072e24i | − | 0.645907i | ||||||
\(863\) | − | 1.08713e25i | − | 1.20279i | −0.798952 | − | 0.601394i | \(-0.794612\pi\) | ||
0.798952 | − | 0.601394i | \(-0.205388\pi\) | |||||||
\(864\) | 1.19899e25 | 1.31356 | ||||||||
\(865\) | 1.05576e25 | + | 4.56480e24i | 1.14532 | + | 0.495204i | ||||
\(866\) | −4.58484e24 | −0.492518 | ||||||||
\(867\) | − | 1.04166e25i | − | 1.10806i | ||||||
\(868\) | 5.16695e24i | 0.544272i | ||||||||
\(869\) | 8.68020e24 | 0.905444 | ||||||||
\(870\) | 5.86358e24 | − | 1.35615e25i | 0.605688 | − | 1.40085i | ||||
\(871\) | −8.41905e24 | −0.861209 | ||||||||
\(872\) | 8.20069e22i | 0.00830731i | ||||||||
\(873\) | − | 5.99873e24i | − | 0.601781i | ||||||
\(874\) | 6.80194e24 | 0.675750 | ||||||||
\(875\) | 3.05090e24 | + | 8.44951e24i | 0.300165 | + | 0.831310i | ||||
\(876\) | 2.04123e25 | 1.98888 | ||||||||
\(877\) | 3.28692e24i | 0.317170i | 0.987345 | + | 0.158585i | \(0.0506932\pi\) | ||||
−0.987345 | + | 0.158585i | \(0.949307\pi\) | |||||||
\(878\) | − | 1.58292e25i | − | 1.51271i | ||||||
\(879\) | −1.23103e25 | −1.16510 | ||||||||
\(880\) | −4.86021e24 | + | 1.12409e25i | −0.455567 | + | 1.05365i | ||||
\(881\) | 1.61469e25 | 1.49897 | 0.749487 | − | 0.662019i | \(-0.230300\pi\) | ||||
0.749487 | + | 0.662019i | \(0.230300\pi\) | |||||||
\(882\) | 5.31727e24i | 0.488884i | ||||||||
\(883\) | 2.87856e24i | 0.262126i | 0.991374 | + | 0.131063i | \(0.0418390\pi\) | ||||
−0.991374 | + | 0.131063i | \(0.958161\pi\) | |||||||
\(884\) | 1.44161e25 | 1.30018 | ||||||||
\(885\) | −4.66468e24 | − | 2.01687e24i | −0.416681 | − | 0.180160i | ||||
\(886\) | −1.96159e24 | −0.173549 | ||||||||
\(887\) | − | 7.90457e23i | − | 0.0692672i | −0.999400 | − | 0.0346336i | \(-0.988974\pi\) | ||
0.999400 | − | 0.0346336i | \(-0.0110264\pi\) | |||||||
\(888\) | − | 2.03201e22i | − | 0.00176366i | ||||||
\(889\) | −3.99688e23 | −0.0343602 | ||||||||
\(890\) | −2.72320e25 | − | 1.17743e25i | −2.31881 | − | 1.00258i | ||||
\(891\) | −1.20850e24 | −0.101926 | ||||||||
\(892\) | 1.00036e25i | 0.835711i | ||||||||
\(893\) | 4.18933e24i | 0.346663i | ||||||||
\(894\) | −1.53492e25 | −1.25810 | ||||||||
\(895\) | −5.42716e24 | + | 1.25521e25i | −0.440633 | + | 1.01911i | ||||
\(896\) | −1.55801e23 | −0.0125300 | ||||||||
\(897\) | 2.35437e25i | 1.87559i | ||||||||
\(898\) | 2.87703e25i | 2.27037i | ||||||||
\(899\) | 5.26207e24 | 0.411338 | ||||||||
\(900\) | −1.40272e25 | − | 1.49189e25i | −1.08620 | − | 1.15525i | ||||
\(901\) | 1.64430e24 | 0.126130 | ||||||||
\(902\) | 3.31001e25i | 2.51520i | ||||||||
\(903\) | 1.13474e24i | 0.0854186i | ||||||||
\(904\) | 6.15840e22 | 0.00459236 | ||||||||
\(905\) | 5.65641e24 | − | 1.30823e25i | 0.417857 | − | 0.966434i | ||||
\(906\) | 1.94068e23 | 0.0142025 | ||||||||
\(907\) | − | 1.50080e25i | − | 1.08808i | −0.839060 | − | 0.544039i | \(-0.816894\pi\) | ||
0.839060 | − | 0.544039i | \(-0.183106\pi\) | |||||||
\(908\) | − | 2.68810e25i | − | 1.93071i | ||||||
\(909\) | −8.09906e24 | −0.576291 | ||||||||
\(910\) | 1.62159e25 | + | 7.01128e24i | 1.14311 | + | 0.494249i | ||||
\(911\) | 2.71017e25 | 1.89274 | 0.946369 | − | 0.323089i | \(-0.104721\pi\) | ||||
0.946369 | + | 0.323089i | \(0.104721\pi\) | |||||||
\(912\) | − | 9.38594e24i | − | 0.649414i | ||||||
\(913\) | − | 2.35299e25i | − | 1.61294i | ||||||
\(914\) | 8.08792e24 | 0.549281 | ||||||||
\(915\) | 1.04965e25 | + | 4.53837e24i | 0.706260 | + | 0.305366i | ||||
\(916\) | 2.72533e25 | 1.81680 | ||||||||
\(917\) | − | 1.63198e25i | − | 1.07790i | ||||||
\(918\) | 2.60967e25i | 1.70774i | ||||||||
\(919\) | −1.69557e25 | −1.09934 | −0.549672 | − | 0.835381i | \(-0.685247\pi\) | ||||
−0.549672 | + | 0.835381i | \(0.685247\pi\) | |||||||
\(920\) | −5.14079e22 | + | 1.18898e23i | −0.00330243 | + | 0.00763796i | ||||
\(921\) | 3.49895e24 | 0.222706 | ||||||||
\(922\) | − | 6.46764e24i | − | 0.407881i | ||||||
\(923\) | 9.92923e23i | 0.0620442i | ||||||||
\(924\) | −2.65755e25 | −1.64539 | ||||||||
\(925\) | 1.84034e24 | − | 1.73035e24i | 0.112900 | − | 0.106152i | ||||
\(926\) | −2.56900e25 | −1.56160 | ||||||||
\(927\) | − | 2.96670e25i | − | 1.78688i | ||||||
\(928\) | 1.59269e25i | 0.950545i | ||||||||
\(929\) | 2.04480e25 | 1.20925 | 0.604627 | − | 0.796508i | \(-0.293322\pi\) | ||||
0.604627 | + | 0.796508i | \(0.293322\pi\) | |||||||
\(930\) | 9.43412e24 | − | 2.18195e25i | 0.552836 | − | 1.27862i | ||||
\(931\) | 1.53199e24 | 0.0889576 | ||||||||
\(932\) | 1.54668e24i | 0.0889952i | ||||||||
\(933\) | 4.93700e25i | 2.81494i | ||||||||
\(934\) | 6.87502e24 | 0.388441 | ||||||||
\(935\) | −2.45894e25 | − | 1.06317e25i | −1.37673 | − | 0.595257i | ||||
\(936\) | −2.00596e23 | −0.0111295 | ||||||||
\(937\) | − | 8.19968e24i | − | 0.450828i | −0.974263 | − | 0.225414i | \(-0.927627\pi\) | ||
0.974263 | − | 0.225414i | \(-0.0723734\pi\) | |||||||
\(938\) | 1.98789e25i | 1.08310i | ||||||||
\(939\) | −2.90960e25 | −1.57100 | ||||||||
\(940\) | −1.47014e25 | − | 6.35647e24i | −0.786635 | − | 0.340118i | ||||
\(941\) | −2.83403e25 | −1.50277 | −0.751385 | − | 0.659864i | \(-0.770614\pi\) | ||||
−0.751385 | + | 0.659864i | \(0.770614\pi\) | |||||||
\(942\) | − | 1.72001e25i | − | 0.903854i | ||||||
\(943\) | − | 3.47059e25i | − | 1.80740i | ||||||
\(944\) | 5.45087e24 | 0.281322 | ||||||||
\(945\) | −6.36192e24 | + | 1.47141e25i | −0.325400 | + | 0.752596i | ||||
\(946\) | 1.93994e24 | 0.0983362 | ||||||||
\(947\) | − | 9.30935e24i | − | 0.467676i | −0.972276 | − | 0.233838i | \(-0.924872\pi\) | ||
0.972276 | − | 0.233838i | \(-0.0751285\pi\) | |||||||
\(948\) | − | 2.54345e25i | − | 1.26635i | ||||||
\(949\) | 2.48571e25 | 1.22655 | ||||||||
\(950\) | −8.57534e24 | + | 8.06280e24i | −0.419373 | + | 0.394308i | ||||
\(951\) | 2.08435e25 | 1.01027 | ||||||||
\(952\) | − | 1.69552e23i | − | 0.00814494i | ||||||
\(953\) | − | 5.32214e24i | − | 0.253394i | −0.991941 | − | 0.126697i | \(-0.959562\pi\) | ||
0.991941 | − | 0.126697i | \(-0.0404376\pi\) | |||||||
\(954\) | −4.59335e24 | −0.216755 | ||||||||
\(955\) | −1.48840e25 | + | 3.44241e25i | −0.696130 | + | 1.61003i | ||||
\(956\) | 2.75078e25 | 1.27516 | ||||||||
\(957\) | 2.70648e25i | 1.24352i | ||||||||
\(958\) | 4.82628e25i | 2.19789i | ||||||||
\(959\) | 2.05418e25 | 0.927215 | ||||||||
\(960\) | 3.32683e25 | + | 1.43842e25i | 1.48842 | + | 0.643548i | ||||
\(961\) | −1.40838e25 | −0.624555 | ||||||||
\(962\) | − | 4.96773e24i | − | 0.218358i | ||||||
\(963\) | − | 3.59464e25i | − | 1.56614i | ||||||
\(964\) | −1.49664e25 | −0.646343 | ||||||||
\(965\) | 8.49279e24 | + | 3.67203e24i | 0.363553 | + | 0.157190i | ||||
\(966\) | 5.55908e25 | 2.35883 | ||||||||
\(967\) | 6.06321e24i | 0.255022i | 0.991837 | + | 0.127511i | \(0.0406988\pi\) | ||||
−0.991837 | + | 0.127511i | \(0.959301\pi\) | |||||||
\(968\) | 5.62897e22i | 0.00234687i | ||||||||
\(969\) | 2.05317e25 | 0.848542 | ||||||||
\(970\) | 5.23172e24 | − | 1.21001e25i | 0.214331 | − | 0.495711i | ||||
\(971\) | −2.02360e25 | −0.821791 | −0.410895 | − | 0.911682i | \(-0.634784\pi\) | ||||
−0.410895 | + | 0.911682i | \(0.634784\pi\) | |||||||
\(972\) | 2.67009e25i | 1.07489i | ||||||||
\(973\) | − | 1.36034e25i | − | 0.542862i | ||||||
\(974\) | −4.72886e25 | −1.87070 | ||||||||
\(975\) | −2.79079e25 | − | 2.96819e25i | −1.09443 | − | 1.16400i | ||||
\(976\) | −1.22656e25 | −0.476831 | ||||||||
\(977\) | 4.01733e25i | 1.54822i | 0.633049 | + | 0.774112i | \(0.281803\pi\) | ||||
−0.633049 | + | 0.774112i | \(0.718197\pi\) | |||||||
\(978\) | − | 5.10587e25i | − | 1.95070i | ||||||
\(979\) | 5.43472e25 | 2.05837 | ||||||||
\(980\) | −2.32449e24 | + | 5.37615e24i | −0.0872781 | + | 0.201860i | ||||
\(981\) | −4.96760e25 | −1.84910 | ||||||||
\(982\) | − | 2.80411e25i | − | 1.03478i | ||||||
\(983\) | 3.08058e25i | 1.12701i | 0.826113 | + | 0.563504i | \(0.190547\pi\) | ||||
−0.826113 | + | 0.563504i | \(0.809453\pi\) | |||||||
\(984\) | 4.83112e23 | 0.0175222 | ||||||||
\(985\) | 1.63611e25 | + | 7.07407e24i | 0.588309 | + | 0.254367i | ||||
\(986\) | −3.46656e25 | −1.23579 | ||||||||
\(987\) | 3.42385e25i | 1.21009i | ||||||||
\(988\) | 1.16028e25i | 0.406564i | ||||||||
\(989\) | −2.03405e24 | −0.0706633 | ||||||||
\(990\) | 6.86905e25 | + | 2.96997e25i | 2.36591 | + | 1.02295i | ||||
\(991\) | −4.65791e24 | −0.159061 | −0.0795307 | − | 0.996832i | \(-0.525342\pi\) | ||||
−0.0795307 | + | 0.996832i | \(0.525342\pi\) | |||||||
\(992\) | 2.56253e25i | 0.867601i | ||||||||
\(993\) | − | 2.26235e25i | − | 0.759436i | ||||||
\(994\) | 2.34447e24 | 0.0780298 | ||||||||
\(995\) | 8.73800e24 | − | 2.02095e25i | 0.288347 | − | 0.666899i | ||||
\(996\) | −6.89467e25 | −2.25584 | ||||||||
\(997\) | − | 1.57451e25i | − | 0.510782i | −0.966838 | − | 0.255391i | \(-0.917796\pi\) | ||
0.966838 | − | 0.255391i | \(-0.0822041\pi\) | |||||||
\(998\) | − | 6.73435e25i | − | 2.16614i | ||||||
\(999\) | 4.50763e24 | 0.143761 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5.18.b.a.4.2 | ✓ | 8 | |
3.2 | odd | 2 | 45.18.b.b.19.7 | 8 | |||
4.3 | odd | 2 | 80.18.c.b.49.1 | 8 | |||
5.2 | odd | 4 | 25.18.a.f.1.7 | 8 | |||
5.3 | odd | 4 | 25.18.a.f.1.2 | 8 | |||
5.4 | even | 2 | inner | 5.18.b.a.4.7 | yes | 8 | |
15.14 | odd | 2 | 45.18.b.b.19.2 | 8 | |||
20.19 | odd | 2 | 80.18.c.b.49.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.18.b.a.4.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5.18.b.a.4.7 | yes | 8 | 5.4 | even | 2 | inner | |
25.18.a.f.1.2 | 8 | 5.3 | odd | 4 | |||
25.18.a.f.1.7 | 8 | 5.2 | odd | 4 | |||
45.18.b.b.19.2 | 8 | 15.14 | odd | 2 | |||
45.18.b.b.19.7 | 8 | 3.2 | odd | 2 | |||
80.18.c.b.49.1 | 8 | 4.3 | odd | 2 | |||
80.18.c.b.49.8 | 8 | 20.19 | odd | 2 |