Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,20,Mod(49,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.49");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.b (of order \(2\), degree \(1\), 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: | \(171.612522417\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 43741x^{2} + 478296900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(148.386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.49 |
Dual form | 75.20.b.b.49.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1238.32i | 1.71020i | 0.518465 | + | 0.855099i | \(0.326504\pi\) | ||||
−0.518465 | + | 0.855099i | \(0.673496\pi\) | |||||||
\(3\) | 19683.0i | 0.577350i | ||||||||
\(4\) | −1.00914e6 | −1.92478 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.43738e7 | −0.987383 | ||||||||
\(7\) | 214621.i | 0.00201021i | 0.999999 | + | 0.00100510i | \(0.000319934\pi\) | ||||
−0.999999 | + | 0.00100510i | \(0.999680\pi\) | |||||||
\(8\) | − 6.00397e8i | − 1.58155i | ||||||||
\(9\) | −3.87420e8 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.30816e10 | −1.67275 | −0.836373 | − | 0.548161i | \(-0.815328\pi\) | ||||
−0.836373 | + | 0.548161i | \(0.815328\pi\) | |||||||
\(12\) | − 1.98629e10i | − 1.11127i | ||||||||
\(13\) | − 1.34409e10i | − 0.351533i | −0.984432 | − | 0.175766i | \(-0.943760\pi\) | ||||
0.984432 | − | 0.175766i | \(-0.0562404\pi\) | |||||||
\(14\) | −2.65768e8 | −0.00343785 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.14402e11 | 0.779990 | ||||||||
\(17\) | − 3.48802e11i | − 0.713368i | −0.934225 | − | 0.356684i | \(-0.883907\pi\) | ||||
0.934225 | − | 0.356684i | \(-0.116093\pi\) | |||||||
\(18\) | − 4.79749e11i | − 0.570066i | ||||||||
\(19\) | 6.20630e11 | 0.441238 | 0.220619 | − | 0.975360i | \(-0.429192\pi\) | ||||
0.220619 | + | 0.975360i | \(0.429192\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.22438e9 | −0.00116059 | ||||||||
\(22\) | − 1.61991e13i | − 2.86073i | ||||||||
\(23\) | 2.65405e12i | 0.307252i | 0.988129 | + | 0.153626i | \(0.0490951\pi\) | ||||
−0.988129 | + | 0.153626i | \(0.950905\pi\) | |||||||
\(24\) | 1.18176e13 | 0.913109 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.66441e13 | 0.601191 | ||||||||
\(27\) | − 7.62560e12i | − 0.192450i | ||||||||
\(28\) | − 2.16582e11i | − 0.00386920i | ||||||||
\(29\) | −1.27229e14 | −1.62857 | −0.814286 | − | 0.580464i | \(-0.802871\pi\) | ||||
−0.814286 | + | 0.580464i | \(0.802871\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32290e12 | 0.0157795 | 0.00788977 | − | 0.999969i | \(-0.497489\pi\) | ||||
0.00788977 | + | 0.999969i | \(0.497489\pi\) | |||||||
\(32\) | − 4.92835e13i | − 0.247615i | ||||||||
\(33\) | − 2.57485e14i | − 0.965760i | ||||||||
\(34\) | 4.31927e14 | 1.22000 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.90961e14 | 0.641592 | ||||||||
\(37\) | − 7.19096e14i | − 0.909642i | −0.890583 | − | 0.454821i | \(-0.849703\pi\) | ||||
0.890583 | − | 0.454821i | \(-0.150297\pi\) | |||||||
\(38\) | 7.68535e14i | 0.754605i | ||||||||
\(39\) | 2.64557e14 | 0.202958 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.72545e15 | 0.823105 | 0.411553 | − | 0.911386i | \(-0.364987\pi\) | ||||
0.411553 | + | 0.911386i | \(0.364987\pi\) | |||||||
\(42\) | − 5.23112e12i | − 0.00198484i | ||||||||
\(43\) | − 2.48385e15i | − 0.753660i | −0.926282 | − | 0.376830i | \(-0.877014\pi\) | ||||
0.926282 | − | 0.376830i | \(-0.122986\pi\) | |||||||
\(44\) | 1.32011e16 | 3.21966 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.28655e15 | −0.525462 | ||||||||
\(47\) | 1.39689e15i | 0.182067i | 0.995848 | + | 0.0910336i | \(0.0290171\pi\) | ||||
−0.995848 | + | 0.0910336i | \(0.970983\pi\) | |||||||
\(48\) | 4.22007e15i | 0.450327i | ||||||||
\(49\) | 1.13988e16 | 0.999996 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.86546e15 | 0.411863 | ||||||||
\(52\) | 1.35637e16i | 0.676623i | ||||||||
\(53\) | − 1.05483e16i | − 0.439099i | −0.975601 | − | 0.219550i | \(-0.929541\pi\) | ||||
0.975601 | − | 0.219550i | \(-0.0704588\pi\) | |||||||
\(54\) | 9.44290e15 | 0.329128 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.28858e14 | 0.00317925 | ||||||||
\(57\) | 1.22159e16i | 0.254749i | ||||||||
\(58\) | − 1.57550e17i | − 2.78518i | ||||||||
\(59\) | 2.80846e16 | 0.422060 | 0.211030 | − | 0.977480i | \(-0.432318\pi\) | ||||
0.211030 | + | 0.977480i | \(0.432318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.60392e16 | −0.394586 | −0.197293 | − | 0.980345i | \(-0.563215\pi\) | ||||
−0.197293 | + | 0.980345i | \(0.563215\pi\) | |||||||
\(62\) | 2.87648e15i | 0.0269861i | ||||||||
\(63\) | − 8.31485e13i | 0 0.000670069i | ||||||||
\(64\) | 1.73437e17 | 1.20346 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.18848e17 | 1.65164 | ||||||||
\(67\) | 2.91862e17i | 1.31059i | 0.755373 | + | 0.655296i | \(0.227456\pi\) | ||||
−0.755373 | + | 0.655296i | \(0.772544\pi\) | |||||||
\(68\) | 3.51989e17i | 1.37308i | ||||||||
\(69\) | −5.22397e16 | −0.177392 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.20038e17 | 0.828414 | 0.414207 | − | 0.910183i | \(-0.364059\pi\) | ||||
0.414207 | + | 0.910183i | \(0.364059\pi\) | |||||||
\(72\) | 2.32606e17i | 0.527184i | ||||||||
\(73\) | 3.15819e17i | 0.627873i | 0.949444 | + | 0.313936i | \(0.101648\pi\) | ||||
−0.949444 | + | 0.313936i | \(0.898352\pi\) | |||||||
\(74\) | 8.90467e17 | 1.55567 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.26301e17 | −0.849286 | ||||||||
\(77\) | − 2.80758e15i | − 0.00336256i | ||||||||
\(78\) | 3.27605e17i | 0.347098i | ||||||||
\(79\) | −1.83029e18 | −1.71815 | −0.859077 | − | 0.511846i | \(-0.828962\pi\) | ||||
−0.859077 | + | 0.511846i | \(0.828962\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.50095e17 | 0.111111 | ||||||||
\(82\) | 2.13665e18i | 1.40767i | ||||||||
\(83\) | 1.64758e18i | 0.967397i | 0.875235 | + | 0.483698i | \(0.160707\pi\) | ||||
−0.875235 | + | 0.483698i | \(0.839293\pi\) | |||||||
\(84\) | 4.26298e15 | 0.00223388 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.07579e18 | 1.28891 | ||||||||
\(87\) | − 2.50426e18i | − 0.940256i | ||||||||
\(88\) | 7.85414e18i | 2.64553i | ||||||||
\(89\) | −5.75855e18 | −1.74224 | −0.871120 | − | 0.491069i | \(-0.836606\pi\) | ||||
−0.871120 | + | 0.491069i | \(0.836606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.88469e15 | 0.000706654 0 | ||||||||
\(92\) | − 2.67830e18i | − 0.591392i | ||||||||
\(93\) | 4.57216e16i | 0.00911032i | ||||||||
\(94\) | −1.72979e18 | −0.311371 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.70047e17 | 0.142960 | ||||||||
\(97\) | 6.23309e18i | 0.832477i | 0.909256 | + | 0.416238i | \(0.136652\pi\) | ||||
−0.909256 | + | 0.416238i | \(0.863348\pi\) | |||||||
\(98\) | 1.41154e19i | 1.71019i | ||||||||
\(99\) | 5.06808e18 | 0.557582 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.80411e17 | 0.0801000 | 0.0400500 | − | 0.999198i | \(-0.487248\pi\) | ||||
0.0400500 | + | 0.999198i | \(0.487248\pi\) | |||||||
\(102\) | 8.50161e18i | 0.704368i | ||||||||
\(103\) | 1.96998e19i | 1.48767i | 0.668361 | + | 0.743837i | \(0.266996\pi\) | ||||
−0.668361 | + | 0.743837i | \(0.733004\pi\) | |||||||
\(104\) | −8.06987e18 | −0.555968 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.30622e19 | 0.750946 | ||||||||
\(107\) | 2.58893e19i | 1.36136i | 0.732579 | + | 0.680682i | \(0.238316\pi\) | ||||
−0.732579 | + | 0.680682i | \(0.761684\pi\) | |||||||
\(108\) | 7.69528e18i | 0.370424i | ||||||||
\(109\) | 3.42533e19 | 1.51060 | 0.755302 | − | 0.655377i | \(-0.227490\pi\) | ||||
0.755302 | + | 0.655377i | \(0.227490\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.41540e19 | 0.525182 | ||||||||
\(112\) | 4.60151e16i | 0.00156794i | ||||||||
\(113\) | − 5.49844e19i | − 1.72185i | −0.508735 | − | 0.860923i | \(-0.669887\pi\) | ||||
0.508735 | − | 0.860923i | \(-0.330113\pi\) | |||||||
\(114\) | −1.51271e19 | −0.435671 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.28392e20 | 3.13464 | ||||||||
\(117\) | 5.20727e18i | 0.117178i | ||||||||
\(118\) | 3.47776e19i | 0.721806i | ||||||||
\(119\) | 7.48601e16 | 0.00143402 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.09969e20 | 1.79808 | ||||||||
\(122\) | − 4.46279e19i | − 0.674821i | ||||||||
\(123\) | 3.39620e19i | 0.475220i | ||||||||
\(124\) | −2.34412e18 | −0.0303721 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.02964e17 | 0.00114595 | ||||||||
\(127\) | − 8.76640e19i | − 0.905078i | −0.891745 | − | 0.452539i | \(-0.850518\pi\) | ||||
0.891745 | − | 0.452539i | \(-0.149482\pi\) | |||||||
\(128\) | 1.88931e20i | 1.81054i | ||||||||
\(129\) | 4.88897e19 | 0.435126 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.23083e20 | −0.946497 | −0.473249 | − | 0.880929i | \(-0.656919\pi\) | ||||
−0.473249 | + | 0.880929i | \(0.656919\pi\) | |||||||
\(132\) | 2.59838e20i | 1.85887i | ||||||||
\(133\) | 1.33200e17i | 0 0.000886980i | ||||||||
\(134\) | −3.61418e20 | −2.24137 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.09419e20 | −1.12823 | ||||||||
\(137\) | − 1.10729e20i | − 0.556435i | −0.960518 | − | 0.278218i | \(-0.910256\pi\) | ||||
0.960518 | − | 0.278218i | \(-0.0897437\pi\) | |||||||
\(138\) | − 6.46892e19i | − 0.303376i | ||||||||
\(139\) | 2.36141e20 | 1.03402 | 0.517012 | − | 0.855978i | \(-0.327044\pi\) | ||||
0.517012 | + | 0.855978i | \(0.327044\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.74949e19 | −0.105117 | ||||||||
\(142\) | 3.96308e20i | 1.41675i | ||||||||
\(143\) | 1.75828e20i | 0.588025i | ||||||||
\(144\) | −8.30637e19 | −0.259997 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.91084e20 | −1.07379 | ||||||||
\(147\) | 2.24364e20i | 0.577348i | ||||||||
\(148\) | 7.25666e20i | 1.75086i | ||||||||
\(149\) | −2.05810e20 | −0.465796 | −0.232898 | − | 0.972501i | \(-0.574821\pi\) | ||||
−0.232898 | + | 0.972501i | \(0.574821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.24449e20 | −0.447546 | −0.223773 | − | 0.974641i | \(-0.571837\pi\) | ||||
−0.223773 | + | 0.974641i | \(0.571837\pi\) | |||||||
\(152\) | − 3.72624e20i | − 0.697842i | ||||||||
\(153\) | 1.35133e20i | 0.237789i | ||||||||
\(154\) | 3.47667e18 | 0.00575065 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.66974e20 | −0.390648 | ||||||||
\(157\) | 3.13212e20i | 0.431312i | 0.976469 | + | 0.215656i | \(0.0691889\pi\) | ||||
−0.976469 | + | 0.215656i | \(0.930811\pi\) | |||||||
\(158\) | − 2.26647e21i | − 2.93838i | ||||||||
\(159\) | 2.07623e20 | 0.253514 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.69615e17 | −0.000617640 0 | ||||||||
\(162\) | 1.85865e20i | 0.190022i | ||||||||
\(163\) | − 2.00591e20i | − 0.193432i | −0.995312 | − | 0.0967160i | \(-0.969166\pi\) | ||||
0.995312 | − | 0.0967160i | \(-0.0308339\pi\) | |||||||
\(164\) | −1.74122e21 | −1.58429 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.04022e21 | −1.65444 | ||||||||
\(167\) | − 2.56060e21i | − 1.96126i | −0.195860 | − | 0.980632i | \(-0.562750\pi\) | ||||
0.195860 | − | 0.980632i | \(-0.437250\pi\) | |||||||
\(168\) | 2.53631e18i | 0.00183554i | ||||||||
\(169\) | 1.28126e21 | 0.876425 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.40445e20 | −0.147079 | ||||||||
\(172\) | 2.50655e21i | 1.45063i | ||||||||
\(173\) | − 2.86308e21i | − 1.56818i | −0.620649 | − | 0.784089i | \(-0.713131\pi\) | ||||
0.620649 | − | 0.784089i | \(-0.286869\pi\) | |||||||
\(174\) | 3.10106e21 | 1.60802 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.80472e21 | −1.30472 | ||||||||
\(177\) | 5.52789e20i | 0.243676i | ||||||||
\(178\) | − 7.13090e21i | − 2.97958i | ||||||||
\(179\) | −3.79065e20 | −0.150179 | −0.0750896 | − | 0.997177i | \(-0.523924\pi\) | ||||
−0.0750896 | + | 0.997177i | \(0.523924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.15578e21 | −1.12502 | −0.562510 | − | 0.826790i | \(-0.690164\pi\) | ||||
−0.562510 | + | 0.826790i | \(0.690164\pi\) | |||||||
\(182\) | 3.57216e18i | 0.00120852i | ||||||||
\(183\) | − 7.09360e20i | − 0.227814i | ||||||||
\(184\) | 1.59348e21 | 0.485935 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.66178e19 | −0.0155805 | ||||||||
\(187\) | 4.56288e21i | 1.19328i | ||||||||
\(188\) | − 1.40965e21i | − 0.350439i | ||||||||
\(189\) | 1.63661e18 | 0.000386864 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.79667e21 | 0.598170 | 0.299085 | − | 0.954226i | \(-0.403319\pi\) | ||||
0.299085 | + | 0.954226i | \(0.403319\pi\) | |||||||
\(192\) | 3.41376e21i | 0.694818i | ||||||||
\(193\) | 7.34293e20i | 0.142257i | 0.997467 | + | 0.0711287i | \(0.0226601\pi\) | ||||
−0.997467 | + | 0.0711287i | \(0.977340\pi\) | |||||||
\(194\) | −7.71854e21 | −1.42370 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.15030e22 | −1.92477 | ||||||||
\(197\) | − 5.32518e21i | − 0.848995i | −0.905429 | − | 0.424498i | \(-0.860451\pi\) | ||||
0.905429 | − | 0.424498i | \(-0.139549\pi\) | |||||||
\(198\) | 6.27588e21i | 0.953576i | ||||||||
\(199\) | 2.54553e21 | 0.368701 | 0.184350 | − | 0.982861i | \(-0.440982\pi\) | ||||
0.184350 | + | 0.982861i | \(0.440982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.74472e21 | −0.756670 | ||||||||
\(202\) | 1.09023e21i | 0.136987i | ||||||||
\(203\) | − 2.73061e19i | − 0.00327376i | ||||||||
\(204\) | −6.92820e21 | −0.792745 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.43945e22 | −2.54422 | ||||||||
\(207\) | − 1.02823e21i | − 0.102417i | ||||||||
\(208\) | − 2.88175e21i | − 0.274192i | ||||||||
\(209\) | −8.11882e21 | −0.738080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.77610e21 | 0.645771 | 0.322886 | − | 0.946438i | \(-0.395347\pi\) | ||||
0.322886 | + | 0.946438i | \(0.395347\pi\) | |||||||
\(212\) | 1.06447e22i | 0.845168i | ||||||||
\(213\) | 6.29931e21i | 0.478285i | ||||||||
\(214\) | −3.20591e22 | −2.32820 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.57838e21 | −0.304370 | ||||||||
\(217\) | 4.98543e17i | 0 3.17201e-5i | ||||||||
\(218\) | 4.24164e22i | 2.58343i | ||||||||
\(219\) | −6.21627e21 | −0.362503 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.68820e21 | −0.250772 | ||||||||
\(222\) | 1.75271e22i | 0.898165i | ||||||||
\(223\) | 1.89249e22i | 0.929259i | 0.885505 | + | 0.464629i | \(0.153812\pi\) | ||||
−0.885505 | + | 0.464629i | \(0.846188\pi\) | |||||||
\(224\) | 1.05773e19 | 0.000497757 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.80881e22 | 2.94470 | ||||||||
\(227\) | 2.42145e22i | 1.00422i | 0.864803 | + | 0.502111i | \(0.167443\pi\) | ||||
−0.864803 | + | 0.502111i | \(0.832557\pi\) | |||||||
\(228\) | − 1.23275e22i | − 0.490335i | ||||||||
\(229\) | 3.29966e22 | 1.25902 | 0.629510 | − | 0.776992i | \(-0.283256\pi\) | ||||
0.629510 | + | 0.776992i | \(0.283256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.52616e19 | 0.00194138 | ||||||||
\(232\) | 7.63882e22i | 2.57567i | ||||||||
\(233\) | 8.99479e21i | 0.291145i | 0.989348 | + | 0.145573i | \(0.0465025\pi\) | ||||
−0.989348 | + | 0.145573i | \(0.953498\pi\) | |||||||
\(234\) | −6.44825e21 | −0.200397 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.83412e22 | −0.812371 | ||||||||
\(237\) | − 3.60256e22i | − 0.991977i | ||||||||
\(238\) | 9.27005e19i | 0.00245245i | ||||||||
\(239\) | −1.22851e22 | −0.312319 | −0.156159 | − | 0.987732i | \(-0.549911\pi\) | ||||
−0.156159 | + | 0.987732i | \(0.549911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.48313e22 | −1.05298 | −0.526489 | − | 0.850182i | \(-0.676492\pi\) | ||||
−0.526489 | + | 0.850182i | \(0.676492\pi\) | |||||||
\(242\) | 1.36176e23i | 3.07507i | ||||||||
\(243\) | 2.95431e21i | 0.0641500i | ||||||||
\(244\) | 3.63685e22 | 0.759491 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.20557e22 | −0.812720 | ||||||||
\(247\) | − 8.34181e21i | − 0.155110i | ||||||||
\(248\) | − 1.39466e21i | − 0.0249562i | ||||||||
\(249\) | −3.24293e22 | −0.558527 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.85123e22 | 0.614750 | 0.307375 | − | 0.951588i | \(-0.400549\pi\) | ||||
0.307375 | + | 0.951588i | \(0.400549\pi\) | |||||||
\(252\) | 8.39083e19i | 0.00128973i | ||||||||
\(253\) | − 3.47192e22i | − 0.513955i | ||||||||
\(254\) | 1.08556e23 | 1.54786 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.43025e23 | −1.89292 | ||||||||
\(257\) | 9.07321e22i | 1.15717i | 0.815623 | + | 0.578584i | \(0.196394\pi\) | ||||
−0.815623 | + | 0.578584i | \(0.803606\pi\) | |||||||
\(258\) | 6.05408e22i | 0.744151i | ||||||||
\(259\) | 1.54333e20 | 0.00182857 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.92913e22 | 0.542857 | ||||||||
\(262\) | − 1.52415e23i | − 1.61870i | ||||||||
\(263\) | 2.56086e21i | 0.0262305i | 0.999914 | + | 0.0131152i | \(0.00417483\pi\) | ||||
−0.999914 | + | 0.0131152i | \(0.995825\pi\) | |||||||
\(264\) | −1.54593e23 | −1.52740 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.64944e20 | −0.00151691 | ||||||||
\(267\) | − 1.13346e23i | − 1.00588i | ||||||||
\(268\) | − 2.94529e23i | − 2.52260i | ||||||||
\(269\) | −3.82577e22 | −0.316281 | −0.158140 | − | 0.987417i | \(-0.550550\pi\) | ||||
−0.158140 | + | 0.987417i | \(0.550550\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.64857e22 | 0.281135 | 0.140567 | − | 0.990071i | \(-0.455107\pi\) | ||||
0.140567 | + | 0.990071i | \(0.455107\pi\) | |||||||
\(272\) | − 7.47838e22i | − 0.556420i | ||||||||
\(273\) | 5.67794e19i | 0 0.000407987i | ||||||||
\(274\) | 1.37117e23 | 0.951615 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.27170e22 | 0.341440 | ||||||||
\(277\) | 1.78571e23i | 1.11752i | 0.829331 | + | 0.558758i | \(0.188722\pi\) | ||||
−0.829331 | + | 0.558758i | \(0.811278\pi\) | |||||||
\(278\) | 2.92417e23i | 1.76839i | ||||||||
\(279\) | −8.99939e20 | −0.00525985 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.28261e23 | −1.24659 | −0.623293 | − | 0.781989i | \(-0.714205\pi\) | ||||
−0.623293 | + | 0.781989i | \(0.714205\pi\) | |||||||
\(282\) | − 3.40474e22i | − 0.179770i | ||||||||
\(283\) | − 1.87538e23i | − 0.957453i | −0.877964 | − | 0.478727i | \(-0.841098\pi\) | ||||
0.877964 | − | 0.478727i | \(-0.158902\pi\) | |||||||
\(284\) | −3.22962e23 | −1.59451 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.17731e23 | −1.00564 | ||||||||
\(287\) | 3.70317e20i | 0.00165461i | ||||||||
\(288\) | 1.90934e22i | 0.0825383i | ||||||||
\(289\) | 1.17410e23 | 0.491106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.22686e23 | −0.480631 | ||||||||
\(292\) | − 3.18705e23i | − 1.20852i | ||||||||
\(293\) | − 2.82617e23i | − 1.03742i | −0.854950 | − | 0.518711i | \(-0.826412\pi\) | ||||
0.854950 | − | 0.518711i | \(-0.173588\pi\) | |||||||
\(294\) | −2.77833e23 | −0.987379 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.31743e23 | −1.43865 | ||||||||
\(297\) | 9.97549e22i | 0.321920i | ||||||||
\(298\) | − 2.54857e23i | − 0.796604i | ||||||||
\(299\) | 3.56728e22 | 0.108009 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.33087e20 | 0.00151501 | ||||||||
\(302\) | − 2.77939e23i | − 0.765392i | ||||||||
\(303\) | 1.73291e22i | 0.0462457i | ||||||||
\(304\) | 1.33064e23 | 0.344162 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.67337e23 | −0.406667 | ||||||||
\(307\) | − 2.47019e23i | − 0.581991i | −0.956724 | − | 0.290996i | \(-0.906014\pi\) | ||||
0.956724 | − | 0.290996i | \(-0.0939865\pi\) | |||||||
\(308\) | 2.83324e21i | 0.00647219i | ||||||||
\(309\) | −3.87751e23 | −0.858909 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.27126e23 | 0.681539 | 0.340770 | − | 0.940147i | \(-0.389312\pi\) | ||||
0.340770 | + | 0.940147i | \(0.389312\pi\) | |||||||
\(312\) | − 1.58839e23i | − 0.320988i | ||||||||
\(313\) | − 3.73412e23i | − 0.732011i | −0.930613 | − | 0.366005i | \(-0.880725\pi\) | ||||
0.930613 | − | 0.366005i | \(-0.119275\pi\) | |||||||
\(314\) | −3.87855e23 | −0.737628 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.84701e24 | 3.30706 | ||||||||
\(317\) | − 5.83518e22i | − 0.101389i | −0.998714 | − | 0.0506945i | \(-0.983857\pi\) | ||||
0.998714 | − | 0.0506945i | \(-0.0161435\pi\) | |||||||
\(318\) | 2.57102e23i | 0.433559i | ||||||||
\(319\) | 1.66436e24 | 2.72419 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.09579e23 | −0.785984 | ||||||||
\(322\) | − 7.05363e20i | − 0.00105629i | ||||||||
\(323\) | − 2.16477e23i | − 0.314766i | ||||||||
\(324\) | −1.51466e23 | −0.213864 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.48394e23 | 0.330807 | ||||||||
\(327\) | 6.74208e23i | 0.872148i | ||||||||
\(328\) | − 1.03595e24i | − 1.30178i | ||||||||
\(329\) | −2.99801e20 | −0.000365993 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.84253e23 | 0.442845 | 0.221422 | − | 0.975178i | \(-0.428930\pi\) | ||||
0.221422 | + | 0.975178i | \(0.428930\pi\) | |||||||
\(332\) | − 1.66263e24i | − 1.86202i | ||||||||
\(333\) | 2.78592e23i | 0.303214i | ||||||||
\(334\) | 3.17084e24 | 3.35415 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −9.05716e20 | −0.000905251 0 | ||||||||
\(337\) | 1.30128e24i | 1.26440i | 0.774803 | + | 0.632202i | \(0.217849\pi\) | ||||
−0.774803 | + | 0.632202i | \(0.782151\pi\) | |||||||
\(338\) | 1.58661e24i | 1.49886i | ||||||||
\(339\) | 1.08226e24 | 0.994109 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.03872e22 | −0.0263952 | ||||||||
\(342\) | − 2.97746e23i | − 0.251535i | ||||||||
\(343\) | 4.89287e21i | 0.00402040i | ||||||||
\(344\) | −1.49130e24 | −1.19195 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.54539e24 | 2.68189 | ||||||||
\(347\) | − 8.56826e22i | − 0.0630613i | −0.999503 | − | 0.0315306i | \(-0.989962\pi\) | ||||
0.999503 | − | 0.0315306i | \(-0.0100382\pi\) | |||||||
\(348\) | 2.52714e24i | 1.80978i | ||||||||
\(349\) | 1.11294e24 | 0.775586 | 0.387793 | − | 0.921746i | \(-0.373237\pi\) | ||||
0.387793 | + | 0.921746i | \(0.373237\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.02495e23 | −0.0676526 | ||||||||
\(352\) | 6.44706e23i | 0.414197i | ||||||||
\(353\) | 2.23748e24i | 1.39926i | 0.714505 | + | 0.699631i | \(0.246652\pi\) | ||||
−0.714505 | + | 0.699631i | \(0.753348\pi\) | |||||||
\(354\) | −6.84527e23 | −0.416735 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.81117e24 | 3.35343 | ||||||||
\(357\) | 1.47347e21i | 0 0.000827930i | ||||||||
\(358\) | − 4.69402e23i | − 0.256836i | ||||||||
\(359\) | −2.02884e24 | −1.08106 | −0.540531 | − | 0.841324i | \(-0.681777\pi\) | ||||
−0.540531 | + | 0.841324i | \(0.681777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.59324e24 | −0.805309 | ||||||||
\(362\) | − 3.90785e24i | − 1.92401i | ||||||||
\(363\) | 2.16452e24i | 1.03812i | ||||||||
\(364\) | −2.91105e21 | −0.00136015 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.78412e23 | 0.389608 | ||||||||
\(367\) | − 2.03395e24i | − 0.879049i | −0.898230 | − | 0.439525i | \(-0.855147\pi\) | ||||
0.898230 | − | 0.439525i | \(-0.144853\pi\) | |||||||
\(368\) | 5.69034e23i | 0.239654i | ||||||||
\(369\) | −6.68474e23 | −0.274368 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.26389e21 | 0.000882680 0 | ||||||||
\(372\) | − 4.61394e22i | − 0.0175353i | ||||||||
\(373\) | 7.78333e23i | 0.288358i | 0.989552 | + | 0.144179i | \(0.0460540\pi\) | ||||
−0.989552 | + | 0.144179i | \(0.953946\pi\) | |||||||
\(374\) | −5.65029e24 | −2.04075 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.38687e23 | 0.287949 | ||||||||
\(377\) | 1.71008e24i | 0.572497i | ||||||||
\(378\) | 2.02664e21i | 0 0.000661615i | ||||||||
\(379\) | −3.15677e24 | −1.00501 | −0.502505 | − | 0.864575i | \(-0.667588\pi\) | ||||
−0.502505 | + | 0.864575i | \(0.667588\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.72549e24 | 0.522547 | ||||||||
\(382\) | 3.46316e24i | 1.02299i | ||||||||
\(383\) | 3.09305e24i | 0.891249i | 0.895220 | + | 0.445625i | \(0.147018\pi\) | ||||
−0.895220 | + | 0.445625i | \(0.852982\pi\) | |||||||
\(384\) | −3.71873e24 | −1.04532 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.09286e23 | −0.243288 | ||||||||
\(387\) | 9.62295e23i | 0.251220i | ||||||||
\(388\) | − 6.29005e24i | − 1.60233i | ||||||||
\(389\) | 4.58505e24 | 1.13978 | 0.569892 | − | 0.821719i | \(-0.306985\pi\) | ||||
0.569892 | + | 0.821719i | \(0.306985\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.25738e23 | 0.219184 | ||||||||
\(392\) | − 6.84383e24i | − 1.58155i | ||||||||
\(393\) | − 2.42263e24i | − 0.546460i | ||||||||
\(394\) | 6.59426e24 | 1.45195 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.11439e24 | −1.07322 | ||||||||
\(397\) | 5.62169e24i | 1.15175i | 0.817539 | + | 0.575873i | \(0.195338\pi\) | ||||
−0.817539 | + | 0.575873i | \(0.804662\pi\) | |||||||
\(398\) | 3.15217e24i | 0.630551i | ||||||||
\(399\) | −2.62178e21 | −0.000512098 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.34521e24 | −1.55441 | −0.777206 | − | 0.629247i | \(-0.783364\pi\) | ||||
−0.777206 | + | 0.629247i | \(0.783364\pi\) | |||||||
\(402\) | − 7.11378e24i | − 1.29406i | ||||||||
\(403\) | − 3.12218e22i | − 0.00554703i | ||||||||
\(404\) | −8.88456e23 | −0.154175 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.38136e22 | 0.00559878 | ||||||||
\(407\) | 9.40691e24i | 1.52160i | ||||||||
\(408\) | − 4.12200e24i | − 0.651383i | ||||||||
\(409\) | 1.09120e25 | 1.68474 | 0.842370 | − | 0.538900i | \(-0.181160\pi\) | ||||
0.842370 | + | 0.538900i | \(0.181160\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.17947e24 | 0.321258 | ||||||||
\(412\) | − 1.98798e25i | − 2.86344i | ||||||||
\(413\) | 6.02754e21i | 0 0.000848427i | ||||||||
\(414\) | 1.27328e24 | 0.175154 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.62414e23 | −0.0870448 | ||||||||
\(417\) | 4.64796e24i | 0.596994i | ||||||||
\(418\) | − 1.00537e25i | − 1.26226i | ||||||||
\(419\) | 1.35175e25 | 1.65906 | 0.829529 | − | 0.558463i | \(-0.188609\pi\) | ||||
0.829529 | + | 0.558463i | \(0.188609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.91185e24 | 1.16272 | 0.581360 | − | 0.813647i | \(-0.302521\pi\) | ||||
0.581360 | + | 0.813647i | \(0.302521\pi\) | |||||||
\(422\) | 9.62927e24i | 1.10440i | ||||||||
\(423\) | − 5.41183e23i | − 0.0606891i | ||||||||
\(424\) | −6.33318e24 | −0.694458 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.80053e24 | −0.817962 | ||||||||
\(427\) | − 7.73477e21i | 0 0.000793200i | ||||||||
\(428\) | − 2.61259e25i | − 2.62032i | ||||||||
\(429\) | −3.46083e24 | −0.339497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.91272e24 | 0.179522 | 0.0897610 | − | 0.995963i | \(-0.471390\pi\) | ||||
0.0897610 | + | 0.995963i | \(0.471390\pi\) | |||||||
\(432\) | − 1.63494e24i | − 0.150109i | ||||||||
\(433\) | − 5.77174e24i | − 0.518408i | −0.965823 | − | 0.259204i | \(-0.916540\pi\) | ||||
0.965823 | − | 0.259204i | \(-0.0834602\pi\) | |||||||
\(434\) | −6.17353e20 | −5.42477e−5 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.45663e25 | −2.90758 | ||||||||
\(437\) | 1.64718e24i | 0.135571i | ||||||||
\(438\) | − 7.69771e24i | − 0.619951i | ||||||||
\(439\) | −8.11473e21 | −0.000639530 0 | −0.000319765 | − | 1.00000i | \(-0.500102\pi\) | ||||
−0.000319765 | 1.00000i | \(0.500102\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.41615e24 | −0.333332 | ||||||||
\(442\) | − 5.80548e24i | − 0.428871i | ||||||||
\(443\) | − 2.51728e24i | − 0.182010i | −0.995850 | − | 0.0910051i | \(-0.970992\pi\) | ||||
0.995850 | − | 0.0910051i | \(-0.0290079\pi\) | |||||||
\(444\) | −1.42833e25 | −1.01086 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.34350e25 | −1.58922 | ||||||||
\(447\) | − 4.05095e24i | − 0.268928i | ||||||||
\(448\) | 3.72232e22i | 0.00241920i | ||||||||
\(449\) | 1.07451e25 | 0.683706 | 0.341853 | − | 0.939753i | \(-0.388945\pi\) | ||||
0.341853 | + | 0.939753i | \(0.388945\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.25716e25 | −1.37685 | ||||||||
\(452\) | 5.54869e25i | 3.31417i | ||||||||
\(453\) | − 4.41784e24i | − 0.258391i | ||||||||
\(454\) | −2.99852e25 | −1.71742 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.33436e24 | 0.402899 | ||||||||
\(457\) | 8.09140e24i | 0.435331i | 0.976023 | + | 0.217665i | \(0.0698442\pi\) | ||||
−0.976023 | + | 0.217665i | \(0.930156\pi\) | |||||||
\(458\) | 4.08603e25i | 2.15317i | ||||||||
\(459\) | −2.65982e24 | −0.137288 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.48075e25 | 0.733368 | 0.366684 | − | 0.930346i | \(-0.380493\pi\) | ||||
0.366684 | + | 0.930346i | \(0.380493\pi\) | |||||||
\(462\) | 6.84313e22i | 0.00332014i | ||||||||
\(463\) | 2.65292e25i | 1.26097i | 0.776202 | + | 0.630485i | \(0.217144\pi\) | ||||
−0.776202 | + | 0.630485i | \(0.782856\pi\) | |||||||
\(464\) | −2.72783e25 | −1.27027 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.11384e25 | −0.497916 | ||||||||
\(467\) | 3.57468e25i | 1.56576i | 0.622170 | + | 0.782882i | \(0.286251\pi\) | ||||
−0.622170 | + | 0.782882i | \(0.713749\pi\) | |||||||
\(468\) | − 5.25486e24i | − 0.225541i | ||||||||
\(469\) | −6.26397e22 | −0.00263456 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.16494e24 | −0.249018 | ||||||||
\(472\) | − 1.68619e25i | − 0.667510i | ||||||||
\(473\) | 3.24927e25i | 1.26068i | ||||||||
\(474\) | 4.46110e25 | 1.69648 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.55442e22 | −0.00276016 | ||||||||
\(477\) | 4.08664e24i | 0.146366i | ||||||||
\(478\) | − 1.52128e25i | − 0.534127i | ||||||||
\(479\) | 2.88220e24 | 0.0992056 | 0.0496028 | − | 0.998769i | \(-0.484204\pi\) | ||||
0.0496028 | + | 0.998769i | \(0.484204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.66528e24 | −0.319769 | ||||||||
\(482\) | − 5.55152e25i | − 1.80080i | ||||||||
\(483\) | − 1.12117e22i | 0 0.000356595i | ||||||||
\(484\) | −1.10974e26 | −3.46090 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.65837e24 | −0.109709 | ||||||||
\(487\) | 6.03233e25i | 1.77403i | 0.461743 | + | 0.887014i | \(0.347224\pi\) | ||||
−0.461743 | + | 0.887014i | \(0.652776\pi\) | |||||||
\(488\) | 2.16378e25i | 0.624059i | ||||||||
\(489\) | 3.94822e24 | 0.111678 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.20599e25 | 1.14444 | 0.572222 | − | 0.820099i | \(-0.306082\pi\) | ||||
0.572222 | + | 0.820099i | \(0.306082\pi\) | |||||||
\(492\) | − 3.42723e25i | − 0.914693i | ||||||||
\(493\) | 4.43779e25i | 1.16177i | ||||||||
\(494\) | 1.03298e25 | 0.265269 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.98034e23 | 0.0123079 | ||||||||
\(497\) | 6.86869e22i | 0.00166528i | ||||||||
\(498\) | − 4.01577e25i | − 0.955191i | ||||||||
\(499\) | 3.96358e25 | 0.924979 | 0.462490 | − | 0.886625i | \(-0.346956\pi\) | ||||
0.462490 | + | 0.886625i | \(0.346956\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.04004e25 | 1.13234 | ||||||||
\(502\) | 4.76904e25i | 1.05134i | ||||||||
\(503\) | − 5.09940e25i | − 1.10312i | −0.834135 | − | 0.551561i | \(-0.814032\pi\) | ||||
0.834135 | − | 0.551561i | \(-0.185968\pi\) | |||||||
\(504\) | −4.99221e22 | −0.00105975 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.29933e25 | 0.878965 | ||||||||
\(507\) | 2.52191e25i | 0.506004i | ||||||||
\(508\) | 8.84651e25i | 1.74207i | ||||||||
\(509\) | 4.45056e25 | 0.860193 | 0.430096 | − | 0.902783i | \(-0.358480\pi\) | ||||
0.430096 | + | 0.902783i | \(0.358480\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.77814e22 | −0.00126215 | ||||||||
\(512\) | − 7.80561e25i | − 1.42673i | ||||||||
\(513\) | − 4.73267e24i | − 0.0849164i | ||||||||
\(514\) | −1.12355e26 | −1.97899 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.93364e25 | −0.837520 | ||||||||
\(517\) | − 1.82735e25i | − 0.304552i | ||||||||
\(518\) | 1.91113e23i | 0.00312721i | ||||||||
\(519\) | 5.63540e25 | 0.905388 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.65819e24 | −0.0256847 | −0.0128424 | − | 0.999918i | \(-0.504088\pi\) | ||||
−0.0128424 | + | 0.999918i | \(0.504088\pi\) | |||||||
\(522\) | 6.10382e25i | 0.928393i | ||||||||
\(523\) | 4.69898e25i | 0.701839i | 0.936406 | + | 0.350920i | \(0.114131\pi\) | ||||
−0.936406 | + | 0.350920i | \(0.885869\pi\) | |||||||
\(524\) | 1.24207e26 | 1.82180 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.17115e24 | −0.0448593 | ||||||||
\(527\) | − 8.10231e23i | − 0.0112566i | ||||||||
\(528\) | − 5.52053e25i | − 0.753283i | ||||||||
\(529\) | 6.75715e25 | 0.905596 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.08805e25 | −0.140687 | ||||||||
\(532\) | − 1.34417e23i | − 0.00170724i | ||||||||
\(533\) | − 2.31916e25i | − 0.289349i | ||||||||
\(534\) | 1.40358e26 | 1.72026 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.75233e26 | 2.07277 | ||||||||
\(537\) | − 7.46114e24i | − 0.0867060i | ||||||||
\(538\) | − 4.73752e25i | − 0.540903i | ||||||||
\(539\) | −1.49115e26 | −1.67274 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.20242e25 | 0.671718 | 0.335859 | − | 0.941912i | \(-0.390973\pi\) | ||||
0.335859 | + | 0.941912i | \(0.390973\pi\) | |||||||
\(542\) | 4.51808e25i | 0.480796i | ||||||||
\(543\) | − 6.21152e25i | − 0.649531i | ||||||||
\(544\) | −1.71902e25 | −0.176641 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.03109e22 | −0.000697738 0 | ||||||||
\(547\) | 7.76624e25i | 0.757410i | 0.925517 | + | 0.378705i | \(0.123630\pi\) | ||||
−0.925517 | + | 0.378705i | \(0.876370\pi\) | |||||||
\(548\) | 1.11740e26i | 1.07101i | ||||||||
\(549\) | 1.39623e25 | 0.131529 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.89624e25 | −0.718588 | ||||||||
\(552\) | 3.13646e25i | 0.280555i | ||||||||
\(553\) | − 3.92818e23i | − 0.00345384i | ||||||||
\(554\) | −2.21128e26 | −1.91117 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.38299e26 | −1.99027 | ||||||||
\(557\) | 3.67420e25i | 0.301675i | 0.988559 | + | 0.150837i | \(0.0481969\pi\) | ||||
−0.988559 | + | 0.150837i | \(0.951803\pi\) | |||||||
\(558\) | − 1.11441e24i | − 0.00899538i | ||||||||
\(559\) | −3.33852e25 | −0.264936 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.98112e25 | −0.688943 | ||||||||
\(562\) | − 2.82659e26i | − 2.13191i | ||||||||
\(563\) | − 1.24531e26i | − 0.923526i | −0.887003 | − | 0.461763i | \(-0.847217\pi\) | ||||
0.887003 | − | 0.461763i | \(-0.152783\pi\) | |||||||
\(564\) | 2.77462e25 | 0.202326 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.32231e26 | 1.63743 | ||||||||
\(567\) | 3.22134e22i | 0 0.000223356i | ||||||||
\(568\) | − 1.92150e26i | − 1.31018i | ||||||||
\(569\) | 5.63513e25 | 0.377866 | 0.188933 | − | 0.981990i | \(-0.439497\pi\) | ||||
0.188933 | + | 0.981990i | \(0.439497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.23813e26 | −0.803012 | −0.401506 | − | 0.915856i | \(-0.631513\pi\) | ||||
−0.401506 | + | 0.915856i | \(0.631513\pi\) | |||||||
\(572\) | − 1.77435e26i | − 1.13182i | ||||||||
\(573\) | 5.50469e25i | 0.345354i | ||||||||
\(574\) | −4.58570e23 | −0.00282971 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.71930e25 | −0.401153 | ||||||||
\(577\) | − 3.01722e26i | − 1.77189i | −0.463790 | − | 0.885945i | \(-0.653511\pi\) | ||||
0.463790 | − | 0.885945i | \(-0.346489\pi\) | |||||||
\(578\) | 1.45390e26i | 0.839888i | ||||||||
\(579\) | −1.44531e25 | −0.0821323 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.53605e23 | −0.00194467 | ||||||||
\(582\) | − 1.51924e26i | − 0.821974i | ||||||||
\(583\) | 1.37989e26i | 0.734501i | ||||||||
\(584\) | 1.89617e26 | 0.993014 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.49968e26 | 1.77420 | ||||||||
\(587\) | − 6.00743e25i | − 0.299659i | −0.988712 | − | 0.149829i | \(-0.952128\pi\) | ||||
0.988712 | − | 0.149829i | \(-0.0478724\pi\) | |||||||
\(588\) | − 2.26414e26i | − 1.11127i | ||||||||
\(589\) | 1.44166e24 | 0.00696254 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.04816e26 | 0.490168 | ||||||||
\(592\) | − 1.54176e26i | − 0.709511i | ||||||||
\(593\) | 9.94196e25i | 0.450248i | 0.974330 | + | 0.225124i | \(0.0722788\pi\) | ||||
−0.974330 | + | 0.225124i | \(0.927721\pi\) | |||||||
\(594\) | −1.23528e26 | −0.550547 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.07690e26 | 0.896554 | ||||||||
\(597\) | 5.01037e25i | 0.212869i | ||||||||
\(598\) | 4.41742e25i | 0.184717i | ||||||||
\(599\) | 1.95677e26 | 0.805350 | 0.402675 | − | 0.915343i | \(-0.368080\pi\) | ||||
0.402675 | + | 0.915343i | \(0.368080\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.73445e26 | −1.88782 | −0.943912 | − | 0.330197i | \(-0.892885\pi\) | ||||
−0.943912 | + | 0.330197i | \(0.892885\pi\) | |||||||
\(602\) | 6.60129e23i | 0.00259097i | ||||||||
\(603\) | − 1.13073e26i | − 0.436864i | ||||||||
\(604\) | 2.26500e26 | 0.861426 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.14589e25 | −0.0790894 | ||||||||
\(607\) | − 1.22707e26i | − 0.445222i | −0.974907 | − | 0.222611i | \(-0.928542\pi\) | ||||
0.974907 | − | 0.222611i | \(-0.0714580\pi\) | |||||||
\(608\) | − 3.05868e25i | − 0.109257i | ||||||||
\(609\) | 5.37466e23 | 0.00189011 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.87754e25 | 0.0640026 | ||||||||
\(612\) | − 1.36368e26i | − 0.457692i | ||||||||
\(613\) | − 3.20354e26i | − 1.05866i | −0.848417 | − | 0.529329i | \(-0.822444\pi\) | ||||
0.848417 | − | 0.529329i | \(-0.177556\pi\) | |||||||
\(614\) | 3.05888e26 | 0.995320 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.68566e24 | −0.00531807 | ||||||||
\(617\) | 9.79781e25i | 0.304383i | 0.988351 | + | 0.152191i | \(0.0486330\pi\) | ||||
−0.988351 | + | 0.152191i | \(0.951367\pi\) | |||||||
\(618\) | − 4.80158e26i | − 1.46890i | ||||||||
\(619\) | 1.22713e25 | 0.0369682 | 0.0184841 | − | 0.999829i | \(-0.494116\pi\) | ||||
0.0184841 | + | 0.999829i | \(0.494116\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.02387e25 | 0.0591307 | ||||||||
\(622\) | 4.05085e26i | 1.16557i | ||||||||
\(623\) | − 1.23591e24i | − 0.00350226i | ||||||||
\(624\) | 5.67215e25 | 0.158305 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.62402e26 | 1.25188 | ||||||||
\(627\) | − 1.59803e26i | − 0.426131i | ||||||||
\(628\) | − 3.16074e26i | − 0.830179i | ||||||||
\(629\) | −2.50822e26 | −0.648909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.30803e26 | 1.08143 | 0.540716 | − | 0.841205i | \(-0.318153\pi\) | ||||
0.540716 | + | 0.841205i | \(0.318153\pi\) | |||||||
\(632\) | 1.09890e27i | 2.71735i | ||||||||
\(633\) | 1.53057e26i | 0.372836i | ||||||||
\(634\) | 7.22579e25 | 0.173395 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.09520e26 | −0.487958 | ||||||||
\(637\) | − 1.53211e26i | − 0.351532i | ||||||||
\(638\) | 2.06101e27i | 4.65890i | ||||||||
\(639\) | −1.23989e26 | −0.276138 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.54923e26 | 1.19972 | 0.599862 | − | 0.800104i | \(-0.295222\pi\) | ||||
0.599862 | + | 0.800104i | \(0.295222\pi\) | |||||||
\(642\) | − 6.31020e26i | − 1.34419i | ||||||||
\(643\) | − 6.72911e26i | − 1.41239i | −0.708019 | − | 0.706193i | \(-0.750411\pi\) | ||||
0.708019 | − | 0.706193i | \(-0.249589\pi\) | |||||||
\(644\) | 5.74820e23 | 0.00118882 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.68066e26 | 0.538311 | ||||||||
\(647\) | − 3.57860e26i | − 0.708146i | −0.935218 | − | 0.354073i | \(-0.884796\pi\) | ||||
0.935218 | − | 0.354073i | \(-0.115204\pi\) | |||||||
\(648\) | − 9.01163e25i | − 0.175728i | ||||||||
\(649\) | −3.67391e26 | −0.705999 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.81282e21 | −1.83136e−5 0 | ||||||||
\(652\) | 2.02423e26i | 0.372313i | ||||||||
\(653\) | − 5.10990e26i | − 0.926269i | −0.886288 | − | 0.463135i | \(-0.846725\pi\) | ||||
0.886288 | − | 0.463135i | \(-0.153275\pi\) | |||||||
\(654\) | −8.34882e26 | −1.49155 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.69940e26 | 0.642014 | ||||||||
\(657\) | − 1.22355e26i | − 0.209291i | ||||||||
\(658\) | − 3.71249e23i | 0 0.000625920i | ||||||||
\(659\) | 6.67000e26 | 1.10844 | 0.554222 | − | 0.832369i | \(-0.313016\pi\) | ||||
0.554222 | + | 0.832369i | \(0.313016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.27178e26 | 0.366819 | 0.183410 | − | 0.983037i | \(-0.441287\pi\) | ||||
0.183410 | + | 0.983037i | \(0.441287\pi\) | |||||||
\(662\) | 4.75827e26i | 0.757352i | ||||||||
\(663\) | − 9.22779e25i | − 0.144784i | ||||||||
\(664\) | 9.89202e26 | 1.52999 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.44985e26 | −0.518556 | ||||||||
\(667\) | − 3.37674e26i | − 0.500382i | ||||||||
\(668\) | 2.58400e27i | 3.77500i | ||||||||
\(669\) | −3.72498e26 | −0.536508 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.71450e26 | 0.660043 | ||||||||
\(672\) | 2.08192e23i | 0 0.000287380i | ||||||||
\(673\) | − 2.72017e26i | − 0.370214i | −0.982718 | − | 0.185107i | \(-0.940737\pi\) | ||||
0.982718 | − | 0.185107i | \(-0.0592632\pi\) | |||||||
\(674\) | −1.61139e27 | −2.16238 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.29297e27 | −1.68692 | ||||||||
\(677\) | 4.27674e26i | 0.550200i | 0.961416 | + | 0.275100i | \(0.0887110\pi\) | ||||
−0.961416 | + | 0.275100i | \(0.911289\pi\) | |||||||
\(678\) | 1.34018e27i | 1.70012i | ||||||||
\(679\) | −1.33775e24 | −0.00167345 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.76614e26 | −0.579788 | ||||||||
\(682\) | − 3.76290e25i | − 0.0451409i | ||||||||
\(683\) | 1.11866e26i | 0.132344i | 0.997808 | + | 0.0661719i | \(0.0210786\pi\) | ||||
−0.997808 | + | 0.0661719i | \(0.978921\pi\) | |||||||
\(684\) | 2.42642e26 | 0.283095 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.05892e24 | −0.00687569 | ||||||||
\(687\) | 6.49473e26i | 0.726896i | ||||||||
\(688\) | − 5.32543e26i | − 0.587847i | ||||||||
\(689\) | −1.41779e26 | −0.154358 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.82536e27 | 1.93333 | 0.966667 | − | 0.256037i | \(-0.0824171\pi\) | ||||
0.966667 | + | 0.256037i | \(0.0824171\pi\) | |||||||
\(692\) | 2.88924e27i | 3.01839i | ||||||||
\(693\) | 1.08771e24i | 0.00112085i | ||||||||
\(694\) | 1.06102e26 | 0.107847 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.50355e27 | −1.48706 | ||||||||
\(697\) | − 6.01839e26i | − 0.587177i | ||||||||
\(698\) | 1.37817e27i | 1.32641i | ||||||||
\(699\) | −1.77045e26 | −0.168093 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.03227e27 | −1.87785 | −0.938924 | − | 0.344125i | \(-0.888176\pi\) | ||||
−0.938924 | + | 0.344125i | \(0.888176\pi\) | |||||||
\(702\) | − 1.26921e26i | − 0.115699i | ||||||||
\(703\) | − 4.46292e26i | − 0.401369i | ||||||||
\(704\) | −2.26883e27 | −2.01308 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.77070e27 | −2.39301 | ||||||||
\(707\) | 1.88955e23i | 0 0.000161017i | ||||||||
\(708\) | − 5.57840e26i | − 0.469023i | ||||||||
\(709\) | 1.86039e27 | 1.54335 | 0.771675 | − | 0.636017i | \(-0.219419\pi\) | ||||
0.771675 | + | 0.636017i | \(0.219419\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.09091e26 | 0.572718 | ||||||||
\(712\) | 3.45742e27i | 2.75544i | ||||||||
\(713\) | 6.16510e24i | 0.00484830i | ||||||||
\(714\) | −1.82462e24 | −0.00141592 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.82529e26 | 0.289062 | ||||||||
\(717\) | − 2.41807e26i | − 0.180317i | ||||||||
\(718\) | − 2.51234e27i | − 1.84883i | ||||||||
\(719\) | −1.92780e27 | −1.40003 | −0.700014 | − | 0.714129i | \(-0.746823\pi\) | ||||
−0.700014 | + | 0.714129i | \(0.746823\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.22798e24 | −0.00299053 | ||||||||
\(722\) | − 1.97293e27i | − 1.37724i | ||||||||
\(723\) | − 8.82414e26i | − 0.607937i | ||||||||
\(724\) | 3.18462e27 | 2.16541 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.68036e27 | −1.77539 | ||||||||
\(727\) | − 1.11559e27i | − 0.729339i | −0.931137 | − | 0.364670i | \(-0.881182\pi\) | ||||
0.931137 | − | 0.364670i | \(-0.118818\pi\) | |||||||
\(728\) | − 1.73196e24i | − 0.00111761i | ||||||||
\(729\) | −5.81497e25 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.66372e26 | −0.537637 | ||||||||
\(732\) | 7.15842e26i | 0.438492i | ||||||||
\(733\) | − 2.04762e27i | − 1.23812i | −0.785344 | − | 0.619059i | \(-0.787514\pi\) | ||||
0.785344 | − | 0.619059i | \(-0.212486\pi\) | |||||||
\(734\) | 2.51868e27 | 1.50335 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.30801e26 | 0.0760802 | ||||||||
\(737\) | − 3.81802e27i | − 2.19229i | ||||||||
\(738\) | − 8.27782e26i | − 0.469224i | ||||||||
\(739\) | −1.50373e27 | −0.841486 | −0.420743 | − | 0.907180i | \(-0.638231\pi\) | ||||
−0.420743 | + | 0.907180i | \(0.638231\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.64192e26 | 0.0895527 | ||||||||
\(742\) | 2.80341e24i | 0.00150956i | ||||||||
\(743\) | − 1.88836e27i | − 1.00390i | −0.864897 | − | 0.501950i | \(-0.832616\pi\) | ||||
0.864897 | − | 0.501950i | \(-0.167384\pi\) | |||||||
\(744\) | 2.74511e25 | 0.0144084 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.63821e26 | −0.493149 | ||||||||
\(747\) | − 6.38306e26i | − 0.322466i | ||||||||
\(748\) | − 4.60457e27i | − 2.29681i | ||||||||
\(749\) | −5.55638e24 | −0.00273662 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.19244e26 | 0.393400 | 0.196700 | − | 0.980464i | \(-0.436978\pi\) | ||||
0.196700 | + | 0.980464i | \(0.436978\pi\) | |||||||
\(752\) | 2.99495e26i | 0.142011i | ||||||||
\(753\) | 7.58037e26i | 0.354926i | ||||||||
\(754\) | −2.11762e27 | −0.979082 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.65157e24 | −0.000744628 0 | ||||||||
\(757\) | 1.94096e27i | 0.864184i | 0.901829 | + | 0.432092i | \(0.142224\pi\) | ||||
−0.901829 | + | 0.432092i | \(0.857776\pi\) | |||||||
\(758\) | − 3.90907e27i | − 1.71876i | ||||||||
\(759\) | 6.83378e26 | 0.296732 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.40135e27 | 1.01695 | 0.508477 | − | 0.861076i | \(-0.330209\pi\) | ||||
0.508477 | + | 0.861076i | \(0.330209\pi\) | |||||||
\(762\) | 2.13670e27i | 0.893659i | ||||||||
\(763\) | 7.35147e24i | 0.00303663i | ||||||||
\(764\) | −2.82223e27 | −1.15134 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.83018e27 | −1.52421 | ||||||||
\(767\) | − 3.77482e26i | − 0.148368i | ||||||||
\(768\) | − 2.81516e27i | − 1.09288i | ||||||||
\(769\) | 3.49979e27 | 1.34197 | 0.670984 | − | 0.741472i | \(-0.265872\pi\) | ||||
0.670984 | + | 0.741472i | \(0.265872\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.78588e27 | −0.668091 | ||||||||
\(772\) | − 7.41002e26i | − 0.273814i | ||||||||
\(773\) | 3.84483e27i | 1.40337i | 0.712487 | + | 0.701685i | \(0.247569\pi\) | ||||
−0.712487 | + | 0.701685i | \(0.752431\pi\) | |||||||
\(774\) | −1.19163e27 | −0.429636 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.74233e27 | 1.31661 | ||||||||
\(777\) | 3.03774e24i | 0.00105572i | ||||||||
\(778\) | 5.67774e27i | 1.94926i | ||||||||
\(779\) | 1.07086e27 | 0.363186 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.18661e27 | −1.38573 | ||||||||
\(782\) | 1.14636e27i | 0.374848i | ||||||||
\(783\) | 9.70201e26i | 0.313419i | ||||||||
\(784\) | 2.44394e27 | 0.779987 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.99999e27 | 0.934556 | ||||||||
\(787\) | 4.22212e27i | 1.29948i | 0.760155 | + | 0.649741i | \(0.225123\pi\) | ||||
−0.760155 | + | 0.649741i | \(0.774877\pi\) | |||||||
\(788\) | 5.37384e27i | 1.63413i | ||||||||
\(789\) | −5.04054e25 | −0.0151442 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.18008e25 | 0.00346127 | ||||||||
\(792\) | − 3.04286e27i | − 0.881845i | ||||||||
\(793\) | 4.84399e26i | 0.138710i | ||||||||
\(794\) | −6.96142e27 | −1.96971 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.56879e27 | −0.709667 | ||||||||
\(797\) | − 2.10706e27i | − 0.575205i | −0.957750 | − | 0.287602i | \(-0.907142\pi\) | ||||
0.957750 | − | 0.287602i | \(-0.0928582\pi\) | |||||||
\(798\) | − 3.24659e24i | 0 0.000875789i | ||||||||
\(799\) | 4.87237e26 | 0.129881 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.23098e27 | 0.580747 | ||||||||
\(802\) | − 1.03340e28i | − 2.65835i | ||||||||
\(803\) | − 4.13142e27i | − 1.05027i | ||||||||
\(804\) | 5.79722e27 | 1.45642 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.86625e25 | 0.00948652 | ||||||||
\(807\) | − 7.53027e26i | − 0.182605i | ||||||||
\(808\) | − 5.28596e26i | − 0.126682i | ||||||||
\(809\) | −2.31386e27 | −0.548056 | −0.274028 | − | 0.961722i | \(-0.588356\pi\) | ||||
−0.274028 | + | 0.961722i | \(0.588356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.32427e27 | 0.537760 | 0.268880 | − | 0.963174i | \(-0.413347\pi\) | ||||
0.268880 | + | 0.963174i | \(0.413347\pi\) | |||||||
\(812\) | 2.75556e25i | 0.00630127i | ||||||||
\(813\) | 7.18148e26i | 0.162313i | ||||||||
\(814\) | −1.16487e28 | −2.60224 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.47197e27 | 0.321249 | ||||||||
\(817\) | − 1.54155e27i | − 0.332544i | ||||||||
\(818\) | 1.35125e28i | 2.88124i | ||||||||
\(819\) | −1.11759e24 | −0.000235551 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.08231e27 | 1.25259 | 0.626295 | − | 0.779587i | \(-0.284571\pi\) | ||||
0.626295 | + | 0.779587i | \(0.284571\pi\) | |||||||
\(822\) | 2.69888e27i | 0.549415i | ||||||||
\(823\) | 3.84390e27i | 0.773523i | 0.922180 | + | 0.386762i | \(0.126406\pi\) | ||||
−0.922180 | + | 0.386762i | \(0.873594\pi\) | |||||||
\(824\) | 1.18277e28 | 2.35283 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.46400e24 | −0.00145098 | ||||||||
\(827\) | 5.47093e27i | 1.05138i | 0.850677 | + | 0.525689i | \(0.176193\pi\) | ||||
−0.850677 | + | 0.525689i | \(0.823807\pi\) | |||||||
\(828\) | 1.03763e27i | 0.197131i | ||||||||
\(829\) | −8.53655e26 | −0.160330 | −0.0801649 | − | 0.996782i | \(-0.525545\pi\) | ||||
−0.0801649 | + | 0.996782i | \(0.525545\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.51482e27 | −0.645198 | ||||||||
\(832\) | − 2.33115e27i | − 0.423056i | ||||||||
\(833\) | − 3.97594e27i | − 0.713365i | ||||||||
\(834\) | −5.75564e27 | −1.02098 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.19301e27 | 1.42064 | ||||||||
\(837\) | − 1.77135e25i | − 0.00303677i | ||||||||
\(838\) | 1.67389e28i | 2.83732i | ||||||||
\(839\) | 8.76504e27 | 1.46898 | 0.734489 | − | 0.678621i | \(-0.237422\pi\) | ||||
0.734489 | + | 0.678621i | \(0.237422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00841e28 | 1.65224 | ||||||||
\(842\) | 1.22740e28i | 1.98848i | ||||||||
\(843\) | − 4.49287e27i | − 0.719716i | ||||||||
\(844\) | −7.84716e27 | −1.24297 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.70155e26 | 0.103790 | ||||||||
\(847\) | 2.36016e25i | 0.00361451i | ||||||||
\(848\) | − 2.26158e27i | − 0.342493i | ||||||||
\(849\) | 3.69131e27 | 0.552786 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.90852e27 | 0.279489 | ||||||||
\(852\) | − 6.35687e27i | − 0.920592i | ||||||||
\(853\) | − 4.55754e27i | − 0.652702i | −0.945249 | − | 0.326351i | \(-0.894181\pi\) | ||||
0.945249 | − | 0.326351i | \(-0.105819\pi\) | |||||||
\(854\) | 9.57809e24 | 0.00135653 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.55438e28 | 2.15307 | ||||||||
\(857\) | 8.72531e27i | 1.19526i | 0.801771 | + | 0.597631i | \(0.203891\pi\) | ||||
−0.801771 | + | 0.597631i | \(0.796109\pi\) | |||||||
\(858\) | − 4.28559e27i | − 0.580606i | ||||||||
\(859\) | 6.82608e27 | 0.914610 | 0.457305 | − | 0.889310i | \(-0.348815\pi\) | ||||
0.457305 | + | 0.889310i | \(0.348815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.28895e24 | −0.000955290 0 | ||||||||
\(862\) | 2.36855e27i | 0.307018i | ||||||||
\(863\) | − 1.70088e27i | − 0.218058i | −0.994039 | − | 0.109029i | \(-0.965226\pi\) | ||||
0.994039 | − | 0.109029i | \(-0.0347741\pi\) | |||||||
\(864\) | −3.75816e26 | −0.0476535 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.14723e27 | 0.886580 | ||||||||
\(867\) | 2.31098e27i | 0.283540i | ||||||||
\(868\) | − 5.03098e23i | 0 6.10542e-5i | ||||||||
\(869\) | 2.39431e28 | 2.87404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.92289e27 | 0.460716 | ||||||||
\(872\) | − 2.05656e28i | − 2.38910i | ||||||||
\(873\) | − 2.41483e27i | − 0.277492i | ||||||||
\(874\) | −2.03973e27 | −0.231854 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.27308e27 | 0.697737 | ||||||||
\(877\) | − 9.69466e27i | − 1.06669i | −0.845899 | − | 0.533343i | \(-0.820936\pi\) | ||||
0.845899 | − | 0.533343i | \(-0.179064\pi\) | |||||||
\(878\) | − 1.00486e25i | − 0.00109372i | ||||||||
\(879\) | 5.56274e27 | 0.598955 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.20901e27 | −0.232769 | −0.116385 | − | 0.993204i | \(-0.537131\pi\) | ||||
−0.116385 | + | 0.993204i | \(0.537131\pi\) | |||||||
\(882\) | − 5.46858e27i | − 0.570064i | ||||||||
\(883\) | 5.45945e27i | 0.563018i | 0.959559 | + | 0.281509i | \(0.0908349\pi\) | ||||
−0.959559 | + | 0.281509i | \(0.909165\pi\) | |||||||
\(884\) | 4.73104e27 | 0.482681 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.11718e27 | 0.311273 | ||||||||
\(887\) | 1.69664e28i | 1.67616i | 0.545546 | + | 0.838081i | \(0.316322\pi\) | ||||
−0.545546 | + | 0.838081i | \(0.683678\pi\) | |||||||
\(888\) | − 8.49799e27i | − 0.830602i | ||||||||
\(889\) | 1.88145e25 | 0.00181939 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.96348e27 | −0.185861 | ||||||||
\(892\) | − 1.90978e28i | − 1.78862i | ||||||||
\(893\) | 8.66950e26i | 0.0803351i | ||||||||
\(894\) | 5.01636e27 | 0.459920 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.05485e25 | −0.00363956 | ||||||||
\(897\) | 7.02148e26i | 0.0623592i | ||||||||
\(898\) | 1.33058e28i | 1.16927i | ||||||||
\(899\) | −2.95541e26 | −0.0256981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.67927e27 | −0.313239 | ||||||||
\(902\) | − 2.79508e28i | − 2.35468i | ||||||||
\(903\) | 1.04927e25i | 0 0.000874692i | ||||||||
\(904\) | −3.30125e28 | −2.72319 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.47068e27 | 0.441899 | ||||||||
\(907\) | 1.06963e28i | 0.854996i | 0.904016 | + | 0.427498i | \(0.140605\pi\) | ||||
−0.904016 | + | 0.427498i | \(0.859395\pi\) | |||||||
\(908\) | − 2.44357e28i | − 1.93290i | ||||||||
\(909\) | −3.41089e26 | −0.0267000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.36272e28 | −1.81129 | −0.905645 | − | 0.424036i | \(-0.860613\pi\) | ||||
−0.905645 | + | 0.424036i | \(0.860613\pi\) | |||||||
\(912\) | 2.61910e27i | 0.198702i | ||||||||
\(913\) | − 2.15530e28i | − 1.61821i | ||||||||
\(914\) | −1.00197e28 | −0.744502 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.32982e28 | −2.42333 | ||||||||
\(917\) | − 2.64161e25i | − 0.00190265i | ||||||||
\(918\) | − 3.29370e27i | − 0.234789i | ||||||||
\(919\) | −4.79736e27 | −0.338458 | −0.169229 | − | 0.985577i | \(-0.554128\pi\) | ||||
−0.169229 | + | 0.985577i | \(0.554128\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.86208e27 | 0.336013 | ||||||||
\(922\) | 1.83363e28i | 1.25420i | ||||||||
\(923\) | − 4.30160e27i | − 0.291215i | ||||||||
\(924\) | −5.57666e25 | −0.00373672 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.28515e28 | −2.15651 | ||||||||
\(927\) | − 7.63210e27i | − 0.495891i | ||||||||
\(928\) | 6.27031e27i | 0.403258i | ||||||||
\(929\) | 4.77499e27 | 0.303965 | 0.151982 | − | 0.988383i | \(-0.451434\pi\) | ||||
0.151982 | + | 0.988383i | \(0.451434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.07446e27 | 0.441237 | ||||||||
\(932\) | − 9.07699e27i | − 0.560390i | ||||||||
\(933\) | 6.43881e27i | 0.393487i | ||||||||
\(934\) | −4.42658e28 | −2.67777 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.12643e27 | 0.185323 | ||||||||
\(937\) | − 3.08658e27i | − 0.181114i | −0.995891 | − | 0.0905568i | \(-0.971135\pi\) | ||||
0.995891 | − | 0.0905568i | \(-0.0288647\pi\) | |||||||
\(938\) | − 7.75677e25i | − 0.00450562i | ||||||||
\(939\) | 7.34987e27 | 0.422627 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.51804e27 | 0.141893 | 0.0709466 | − | 0.997480i | \(-0.477398\pi\) | ||||
0.0709466 | + | 0.997480i | \(0.477398\pi\) | |||||||
\(942\) | − 7.63414e27i | − 0.425870i | ||||||||
\(943\) | 4.57943e27i | 0.252901i | ||||||||
\(944\) | 6.02139e27 | 0.329202 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.02363e28 | −2.15602 | ||||||||
\(947\) | 8.85552e27i | 0.469774i | 0.972023 | + | 0.234887i | \(0.0754720\pi\) | ||||
−0.972023 | + | 0.234887i | \(0.924528\pi\) | |||||||
\(948\) | 3.63547e28i | 1.90933i | ||||||||
\(949\) | 4.24489e27 | 0.220718 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.14854e27 | 0.0585370 | ||||||||
\(952\) | − 4.49458e25i | − 0.00226797i | ||||||||
\(953\) | − 1.35516e28i | − 0.677030i | −0.940961 | − | 0.338515i | \(-0.890075\pi\) | ||||
0.940961 | − | 0.338515i | \(-0.109925\pi\) | |||||||
\(954\) | −5.06055e27 | −0.250315 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.23973e28 | 0.601144 | ||||||||
\(957\) | 3.27597e28i | 1.57281i | ||||||||
\(958\) | 3.56907e27i | 0.169661i | ||||||||
\(959\) | 2.37647e25 | 0.00111855 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.16653e28 | −0.999751 | ||||||||
\(962\) | − 1.19687e28i | − 0.546868i | ||||||||
\(963\) | − 1.00300e28i | − 0.453788i | ||||||||
\(964\) | 4.52409e28 | 2.02675 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.38837e25 | 0.000609848 0 | ||||||||
\(967\) | 5.51108e27i | 0.239710i | 0.992791 | + | 0.119855i | \(0.0382429\pi\) | ||||
−0.992791 | + | 0.119855i | \(0.961757\pi\) | |||||||
\(968\) | − 6.60250e28i | − 2.84376i | ||||||||
\(969\) | 4.26091e27 | 0.181730 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.37023e28 | 0.991308 | 0.495654 | − | 0.868520i | \(-0.334928\pi\) | ||||
0.495654 | + | 0.868520i | \(0.334928\pi\) | |||||||
\(972\) | − 2.98131e27i | − 0.123475i | ||||||||
\(973\) | 5.06808e25i | 0.00207860i | ||||||||
\(974\) | −7.46993e28 | −3.03394 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.72688e27 | −0.307773 | ||||||||
\(977\) | − 6.97540e27i | − 0.275151i | −0.990491 | − | 0.137575i | \(-0.956069\pi\) | ||||
0.990491 | − | 0.137575i | \(-0.0439309\pi\) | |||||||
\(978\) | 4.88915e27i | 0.190992i | ||||||||
\(979\) | 7.53310e28 | 2.91433 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.32704e28 | −0.503535 | ||||||||
\(982\) | 5.20835e28i | 1.95722i | ||||||||
\(983\) | − 1.96330e28i | − 0.730683i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) | ||||
0.930874 | − | 0.365341i | \(-0.119048\pi\) | |||||||
\(984\) | 2.03907e28 | 0.751585 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.49538e28 | −1.98686 | ||||||||
\(987\) | − 5.90099e24i | 0 0.000211306i | ||||||||
\(988\) | 8.41804e27i | 0.298552i | ||||||||
\(989\) | 6.59227e27 | 0.231564 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.20556e28 | 1.44918 | 0.724592 | − | 0.689178i | \(-0.242028\pi\) | ||||
0.724592 | + | 0.689178i | \(0.242028\pi\) | |||||||
\(992\) | − 1.14481e26i | − 0.00390725i | ||||||||
\(993\) | 7.56325e27i | 0.255676i | ||||||||
\(994\) | −8.50560e25 | −0.00284796 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.27256e28 | 1.07504 | ||||||||
\(997\) | − 1.15418e28i | − 0.375551i | −0.982212 | − | 0.187776i | \(-0.939872\pi\) | ||||
0.982212 | − | 0.187776i | \(-0.0601278\pi\) | |||||||
\(998\) | 4.90816e28i | 1.58190i | ||||||||
\(999\) | −5.48353e27 | −0.175061 |
(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 | 75.20.b.b.49.4 | 4 | ||
5.2 | odd | 4 | 75.20.a.b.1.1 | 2 | |||
5.3 | odd | 4 | 3.20.a.b.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 75.20.b.b.49.1 | 4 | ||
15.8 | even | 4 | 9.20.a.c.1.1 | 2 | |||
20.3 | even | 4 | 48.20.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.20.a.b.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
9.20.a.c.1.1 | 2 | 15.8 | even | 4 | |||
48.20.a.j.1.2 | 2 | 20.3 | even | 4 | |||
75.20.a.b.1.1 | 2 | 5.2 | odd | 4 | |||
75.20.b.b.49.1 | 4 | 5.4 | even | 2 | inner | ||
75.20.b.b.49.4 | 4 | 1.1 | even | 1 | trivial |