Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,15,Mod(21,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.21");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.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: | \(27.3523729934\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 38299509 x^{12} + 1255603312 x^{11} + 548839279225666 x^{10} + \cdots + 61\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{56}\cdot 3^{6}\cdot 11^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.13 | ||
Root | \(-2599.55 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.21 |
Dual form | 22.15.b.a.21.6 |
$q$-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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 90.5097i | 0.707107i | ||||||||
\(3\) | 2913.55 | 1.33221 | 0.666106 | − | 0.745857i | \(-0.267960\pi\) | ||||
0.666106 | + | 0.745857i | \(0.267960\pi\) | |||||||
\(4\) | −8192.00 | −0.500000 | ||||||||
\(5\) | −75323.6 | −0.964141 | −0.482071 | − | 0.876132i | \(-0.660115\pi\) | ||||
−0.482071 | + | 0.876132i | \(0.660115\pi\) | |||||||
\(6\) | 263704.i | 0.942016i | ||||||||
\(7\) | 867659.i | 1.05357i | 0.849999 | + | 0.526784i | \(0.176603\pi\) | ||||
−0.849999 | + | 0.526784i | \(0.823397\pi\) | |||||||
\(8\) | − | 741455.i | − | 0.353553i | ||||||
\(9\) | 3.70579e6 | 0.774788 | ||||||||
\(10\) | − | 6.81751e6i | − | 0.681751i | ||||||
\(11\) | −1.56983e7 | − | 1.15461e7i | −0.805572 | − | 0.592497i | ||||
\(12\) | −2.38678e7 | −0.666106 | ||||||||
\(13\) | − | 3.47214e7i | − | 0.553343i | −0.960965 | − | 0.276671i | \(-0.910769\pi\) | ||
0.960965 | − | 0.276671i | \(-0.0892314\pi\) | |||||||
\(14\) | −7.85316e7 | −0.744986 | ||||||||
\(15\) | −2.19459e8 | −1.28444 | ||||||||
\(16\) | 6.71089e7 | 0.250000 | ||||||||
\(17\) | − | 2.76380e8i | − | 0.673542i | −0.941587 | − | 0.336771i | \(-0.890665\pi\) | ||
0.941587 | − | 0.336771i | \(-0.109335\pi\) | |||||||
\(18\) | 3.35409e8i | 0.547858i | ||||||||
\(19\) | 8.30217e8i | 0.928787i | 0.885629 | + | 0.464394i | \(0.153728\pi\) | ||||
−0.885629 | + | 0.464394i | \(0.846272\pi\) | |||||||
\(20\) | 6.17051e8 | 0.482071 | ||||||||
\(21\) | 2.52797e9i | 1.40358i | ||||||||
\(22\) | 1.04503e9 | − | 1.42085e9i | 0.418959 | − | 0.569626i | ||||
\(23\) | −5.71780e9 | −1.67932 | −0.839661 | − | 0.543111i | \(-0.817246\pi\) | ||||
−0.839661 | + | 0.543111i | \(0.817246\pi\) | |||||||
\(24\) | − | 2.16026e9i | − | 0.471008i | ||||||
\(25\) | −4.29878e8 | −0.0704312 | ||||||||
\(26\) | 3.14263e9 | 0.391273 | ||||||||
\(27\) | −3.13842e9 | −0.300030 | ||||||||
\(28\) | − | 7.10787e9i | − | 0.526784i | ||||||
\(29\) | − | 2.61317e10i | − | 1.51489i | −0.652898 | − | 0.757446i | \(-0.726447\pi\) | ||
0.652898 | − | 0.757446i | \(-0.273553\pi\) | |||||||
\(30\) | − | 1.98631e10i | − | 0.908237i | ||||||
\(31\) | −1.69092e10 | −0.614597 | −0.307298 | − | 0.951613i | \(-0.599425\pi\) | ||||
−0.307298 | + | 0.951613i | \(0.599425\pi\) | |||||||
\(32\) | 6.07400e9i | 0.176777i | ||||||||
\(33\) | −4.57378e10 | − | 3.36401e10i | −1.07319 | − | 0.789332i | ||||
\(34\) | 2.50151e10 | 0.476266 | ||||||||
\(35\) | − | 6.53552e10i | − | 1.01579i | ||||||
\(36\) | −3.03578e10 | −0.387394 | ||||||||
\(37\) | 7.99862e10 | 0.842564 | 0.421282 | − | 0.906930i | \(-0.361580\pi\) | ||||
0.421282 | + | 0.906930i | \(0.361580\pi\) | |||||||
\(38\) | −7.51426e10 | −0.656752 | ||||||||
\(39\) | − | 1.01163e11i | − | 0.737170i | ||||||
\(40\) | 5.58490e10i | 0.340875i | ||||||||
\(41\) | 1.95749e11i | 1.00511i | 0.864546 | + | 0.502553i | \(0.167606\pi\) | ||||
−0.864546 | + | 0.502553i | \(0.832394\pi\) | |||||||
\(42\) | −2.28805e11 | −0.992479 | ||||||||
\(43\) | − | 2.34553e11i | − | 0.862904i | −0.902136 | − | 0.431452i | \(-0.858002\pi\) | ||
0.902136 | − | 0.431452i | \(-0.141998\pi\) | |||||||
\(44\) | 1.28601e11 | + | 9.45856e10i | 0.402786 | + | 0.296249i | ||||
\(45\) | −2.79133e11 | −0.747005 | ||||||||
\(46\) | − | 5.17516e11i | − | 1.18746i | ||||||
\(47\) | −6.41052e11 | −1.26534 | −0.632671 | − | 0.774421i | \(-0.718041\pi\) | ||||
−0.632671 | + | 0.774421i | \(0.718041\pi\) | |||||||
\(48\) | 1.95525e11 | 0.333053 | ||||||||
\(49\) | −7.46096e10 | −0.110008 | ||||||||
\(50\) | − | 3.89081e10i | − | 0.0498024i | ||||||
\(51\) | − | 8.05247e11i | − | 0.897301i | ||||||
\(52\) | 2.84438e11i | 0.276671i | ||||||||
\(53\) | −1.06181e12 | −0.903891 | −0.451946 | − | 0.892046i | \(-0.649270\pi\) | ||||
−0.451946 | + | 0.892046i | \(0.649270\pi\) | |||||||
\(54\) | − | 2.84058e11i | − | 0.212153i | ||||||
\(55\) | 1.18245e12 | + | 8.69693e11i | 0.776686 | + | 0.571251i | ||||
\(56\) | 6.43331e11 | 0.372493 | ||||||||
\(57\) | 2.41888e12i | 1.23734i | ||||||||
\(58\) | 2.36517e12 | 1.07119 | ||||||||
\(59\) | 3.40545e12 | 1.36839 | 0.684195 | − | 0.729299i | \(-0.260154\pi\) | ||||
0.684195 | + | 0.729299i | \(0.260154\pi\) | |||||||
\(60\) | 1.79781e12 | 0.642220 | ||||||||
\(61\) | 3.58361e12i | 1.14028i | 0.821547 | + | 0.570140i | \(0.193111\pi\) | ||||
−0.821547 | + | 0.570140i | \(0.806889\pi\) | |||||||
\(62\) | − | 1.53044e12i | − | 0.434586i | ||||||
\(63\) | 3.21536e12i | 0.816292i | ||||||||
\(64\) | −5.49756e11 | −0.125000 | ||||||||
\(65\) | 2.61534e12i | 0.533501i | ||||||||
\(66\) | 3.04475e12 | − | 4.13971e12i | 0.558142 | − | 0.758862i | ||||
\(67\) | 4.80232e11 | 0.0792370 | 0.0396185 | − | 0.999215i | \(-0.487386\pi\) | ||||
0.0396185 | + | 0.999215i | \(0.487386\pi\) | |||||||
\(68\) | 2.26411e12i | 0.336771i | ||||||||
\(69\) | −1.66591e13 | −2.23721 | ||||||||
\(70\) | 5.91528e12 | 0.718272 | ||||||||
\(71\) | 4.31225e11 | 0.0474128 | 0.0237064 | − | 0.999719i | \(-0.492453\pi\) | ||||
0.0237064 | + | 0.999719i | \(0.492453\pi\) | |||||||
\(72\) | − | 2.74767e12i | − | 0.273929i | ||||||
\(73\) | 4.05979e12i | 0.367488i | 0.982974 | + | 0.183744i | \(0.0588218\pi\) | ||||
−0.982974 | + | 0.183744i | \(0.941178\pi\) | |||||||
\(74\) | 7.23952e12i | 0.595783i | ||||||||
\(75\) | −1.25247e12 | −0.0938293 | ||||||||
\(76\) | − | 6.80113e12i | − | 0.464394i | ||||||
\(77\) | 1.00181e13 | − | 1.36208e13i | 0.624237 | − | 0.848726i | ||||
\(78\) | 9.15619e12 | 0.521258 | ||||||||
\(79\) | 2.11530e13i | 1.10149i | 0.834672 | + | 0.550747i | \(0.185657\pi\) | ||||
−0.834672 | + | 0.550747i | \(0.814343\pi\) | |||||||
\(80\) | −5.05488e12 | −0.241035 | ||||||||
\(81\) | −2.68686e13 | −1.17449 | ||||||||
\(82\) | −1.77172e13 | −0.710718 | ||||||||
\(83\) | 4.92388e12i | 0.181452i | 0.995876 | + | 0.0907258i | \(0.0289187\pi\) | ||||
−0.995876 | + | 0.0907258i | \(0.971081\pi\) | |||||||
\(84\) | − | 2.07091e13i | − | 0.701788i | ||||||
\(85\) | 2.08180e13i | 0.649390i | ||||||||
\(86\) | 2.12293e13 | 0.610165 | ||||||||
\(87\) | − | 7.61359e13i | − | 2.01816i | ||||||
\(88\) | −8.56092e12 | + | 1.16396e13i | −0.209479 | + | 0.284813i | ||||
\(89\) | −7.53865e12 | −0.170437 | −0.0852185 | − | 0.996362i | \(-0.527159\pi\) | ||||
−0.0852185 | + | 0.996362i | \(0.527159\pi\) | |||||||
\(90\) | − | 2.52642e13i | − | 0.528212i | ||||||
\(91\) | 3.01264e13 | 0.582985 | ||||||||
\(92\) | 4.68402e13 | 0.839661 | ||||||||
\(93\) | −4.92656e13 | −0.818773 | ||||||||
\(94\) | − | 5.80214e13i | − | 0.894732i | ||||||
\(95\) | − | 6.25349e13i | − | 0.895482i | ||||||
\(96\) | 1.76969e13i | 0.235504i | ||||||||
\(97\) | −4.89366e13 | −0.605664 | −0.302832 | − | 0.953044i | \(-0.597932\pi\) | ||||
−0.302832 | + | 0.953044i | \(0.597932\pi\) | |||||||
\(98\) | − | 6.75289e12i | − | 0.0777871i | ||||||
\(99\) | −5.81746e13 | − | 4.27874e13i | −0.624148 | − | 0.459060i | ||||
\(100\) | 3.52156e12 | 0.0352156 | ||||||||
\(101\) | 1.98660e14i | 1.85294i | 0.376373 | + | 0.926468i | \(0.377171\pi\) | ||||
−0.376373 | + | 0.926468i | \(0.622829\pi\) | |||||||
\(102\) | 7.28826e13 | 0.634487 | ||||||||
\(103\) | −1.35157e14 | −1.09895 | −0.549477 | − | 0.835509i | \(-0.685173\pi\) | ||||
−0.549477 | + | 0.835509i | \(0.685173\pi\) | |||||||
\(104\) | −2.57444e13 | −0.195636 | ||||||||
\(105\) | − | 1.90415e14i | − | 1.35325i | ||||||
\(106\) | − | 9.61042e13i | − | 0.639148i | ||||||
\(107\) | 1.67405e14i | 1.04251i | 0.853400 | + | 0.521256i | \(0.174536\pi\) | ||||
−0.853400 | + | 0.521256i | \(0.825464\pi\) | |||||||
\(108\) | 2.57100e13 | 0.150015 | ||||||||
\(109\) | 1.43567e14i | 0.785362i | 0.919675 | + | 0.392681i | \(0.128452\pi\) | ||||
−0.919675 | + | 0.392681i | \(0.871548\pi\) | |||||||
\(110\) | −7.87156e13 | + | 1.07023e14i | −0.403936 | + | 0.549200i | ||||
\(111\) | 2.33044e14 | 1.12247 | ||||||||
\(112\) | 5.82276e13i | 0.263392i | ||||||||
\(113\) | 1.01260e14 | 0.430416 | 0.215208 | − | 0.976568i | \(-0.430957\pi\) | ||||
0.215208 | + | 0.976568i | \(0.430957\pi\) | |||||||
\(114\) | −2.18932e14 | −0.874932 | ||||||||
\(115\) | 4.30685e14 | 1.61910 | ||||||||
\(116\) | 2.14071e14i | 0.757446i | ||||||||
\(117\) | − | 1.28670e14i | − | 0.428723i | ||||||
\(118\) | 3.08226e14i | 0.967598i | ||||||||
\(119\) | 2.39804e14 | 0.709623 | ||||||||
\(120\) | 1.62719e14i | 0.454118i | ||||||||
\(121\) | 1.13125e14 | + | 3.62509e14i | 0.297893 | + | 0.954599i | ||||
\(122\) | −3.24351e14 | −0.806300 | ||||||||
\(123\) | 5.70323e14i | 1.33901i | ||||||||
\(124\) | 1.38520e14 | 0.307298 | ||||||||
\(125\) | 4.92118e14 | 1.03205 | ||||||||
\(126\) | −2.91021e14 | −0.577206 | ||||||||
\(127\) | − | 1.04866e15i | − | 1.96792i | −0.178381 | − | 0.983962i | \(-0.557086\pi\) | ||
0.178381 | − | 0.983962i | \(-0.442914\pi\) | |||||||
\(128\) | − | 4.97582e13i | − | 0.0883883i | ||||||
\(129\) | − | 6.83382e14i | − | 1.14957i | ||||||
\(130\) | −2.36714e14 | −0.377242 | ||||||||
\(131\) | − | 1.08808e15i | − | 1.64347i | −0.569867 | − | 0.821737i | \(-0.693005\pi\) | ||
0.569867 | − | 0.821737i | \(-0.306995\pi\) | |||||||
\(132\) | 3.74684e14 | + | 2.75580e14i | 0.536596 | + | 0.394666i | ||||
\(133\) | −7.20345e14 | −0.978541 | ||||||||
\(134\) | 4.34657e13i | 0.0560290i | ||||||||
\(135\) | 2.36397e14 | 0.289272 | ||||||||
\(136\) | −2.04924e14 | −0.238133 | ||||||||
\(137\) | 9.50193e14 | 1.04898 | 0.524491 | − | 0.851416i | \(-0.324256\pi\) | ||||
0.524491 | + | 0.851416i | \(0.324256\pi\) | |||||||
\(138\) | − | 1.50781e15i | − | 1.58195i | ||||||
\(139\) | 1.42444e15i | 1.42082i | 0.703788 | + | 0.710410i | \(0.251491\pi\) | ||||
−0.703788 | + | 0.710410i | \(0.748509\pi\) | |||||||
\(140\) | 5.35390e14i | 0.507895i | ||||||||
\(141\) | −1.86773e15 | −1.68570 | ||||||||
\(142\) | 3.90300e13i | 0.0335259i | ||||||||
\(143\) | −4.00897e14 | + | 5.45069e14i | −0.327854 | + | 0.445758i | ||||
\(144\) | 2.48691e14 | 0.193697 | ||||||||
\(145\) | 1.96833e15i | 1.46057i | ||||||||
\(146\) | −3.67450e14 | −0.259854 | ||||||||
\(147\) | −2.17379e14 | −0.146553 | ||||||||
\(148\) | −6.55247e14 | −0.421282 | ||||||||
\(149\) | − | 2.48573e15i | − | 1.52458i | −0.647238 | − | 0.762288i | \(-0.724076\pi\) | ||
0.647238 | − | 0.762288i | \(-0.275924\pi\) | |||||||
\(150\) | − | 1.13361e14i | − | 0.0663474i | ||||||
\(151\) | − | 8.33993e14i | − | 0.465933i | −0.972485 | − | 0.232967i | \(-0.925157\pi\) | ||
0.972485 | − | 0.232967i | \(-0.0748433\pi\) | |||||||
\(152\) | 6.15568e14 | 0.328376 | ||||||||
\(153\) | − | 1.02421e15i | − | 0.521852i | ||||||
\(154\) | 1.23281e15 | + | 9.06733e14i | 0.600140 | + | 0.441402i | ||||
\(155\) | 1.27366e15 | 0.592558 | ||||||||
\(156\) | 8.28724e14i | 0.368585i | ||||||||
\(157\) | −2.83439e14 | −0.120549 | −0.0602744 | − | 0.998182i | \(-0.519198\pi\) | ||||
−0.0602744 | + | 0.998182i | \(0.519198\pi\) | |||||||
\(158\) | −1.91455e15 | −0.778874 | ||||||||
\(159\) | −3.09364e15 | −1.20417 | ||||||||
\(160\) | − | 4.57515e14i | − | 0.170438i | ||||||
\(161\) | − | 4.96110e15i | − | 1.76928i | ||||||
\(162\) | − | 2.43187e15i | − | 0.830491i | ||||||
\(163\) | −4.94421e15 | −1.61727 | −0.808636 | − | 0.588309i | \(-0.799794\pi\) | ||||
−0.808636 | + | 0.588309i | \(0.799794\pi\) | |||||||
\(164\) | − | 1.60357e15i | − | 0.502553i | ||||||
\(165\) | 3.44513e15 | + | 2.53389e15i | 1.03471 | + | 0.761028i | ||||
\(166\) | −4.45659e14 | −0.128306 | ||||||||
\(167\) | − | 4.57889e13i | − | 0.0126399i | −0.999980 | − | 0.00631997i | \(-0.997988\pi\) | ||
0.999980 | − | 0.00631997i | \(-0.00201172\pi\) | |||||||
\(168\) | 1.87437e15 | 0.496239 | ||||||||
\(169\) | 2.73180e15 | 0.693812 | ||||||||
\(170\) | −1.88423e15 | −0.459188 | ||||||||
\(171\) | 3.07661e15i | 0.719613i | ||||||||
\(172\) | 1.92146e15i | 0.431452i | ||||||||
\(173\) | 6.39265e15i | 1.37835i | 0.724597 | + | 0.689173i | \(0.242026\pi\) | ||||
−0.724597 | + | 0.689173i | \(0.757974\pi\) | |||||||
\(174\) | 6.89104e15 | 1.42705 | ||||||||
\(175\) | − | 3.72988e14i | − | 0.0742042i | ||||||
\(176\) | −1.05350e15 | − | 7.74846e14i | −0.201393 | − | 0.148124i | ||||
\(177\) | 9.92192e15 | 1.82298 | ||||||||
\(178\) | − | 6.82321e14i | − | 0.120517i | ||||||
\(179\) | 2.80106e15 | 0.475719 | 0.237860 | − | 0.971300i | \(-0.423554\pi\) | ||||
0.237860 | + | 0.971300i | \(0.423554\pi\) | |||||||
\(180\) | 2.28666e15 | 0.373503 | ||||||||
\(181\) | 6.02858e14 | 0.0947251 | 0.0473626 | − | 0.998878i | \(-0.484918\pi\) | ||||
0.0473626 | + | 0.998878i | \(0.484918\pi\) | |||||||
\(182\) | 2.72673e15i | 0.412233i | ||||||||
\(183\) | 1.04410e16i | 1.51909i | ||||||||
\(184\) | 4.23949e15i | 0.593730i | ||||||||
\(185\) | −6.02484e15 | −0.812351 | ||||||||
\(186\) | − | 4.45902e15i | − | 0.578960i | ||||||
\(187\) | −3.19112e15 | + | 4.33871e15i | −0.399072 | + | 0.542587i | ||||
\(188\) | 5.25149e15 | 0.632671 | ||||||||
\(189\) | − | 2.72308e15i | − | 0.316103i | ||||||
\(190\) | 5.66001e15 | 0.633202 | ||||||||
\(191\) | −1.61123e16 | −1.73749 | −0.868747 | − | 0.495257i | \(-0.835074\pi\) | ||||
−0.868747 | + | 0.495257i | \(0.835074\pi\) | |||||||
\(192\) | −1.60174e15 | −0.166526 | ||||||||
\(193\) | 3.93899e15i | 0.394897i | 0.980313 | + | 0.197449i | \(0.0632656\pi\) | ||||
−0.980313 | + | 0.197449i | \(0.936734\pi\) | |||||||
\(194\) | − | 4.42924e15i | − | 0.428269i | ||||||
\(195\) | 7.61992e15i | 0.710736i | ||||||||
\(196\) | 6.11202e14 | 0.0550038 | ||||||||
\(197\) | − | 4.74963e15i | − | 0.412474i | −0.978502 | − | 0.206237i | \(-0.933878\pi\) | ||
0.978502 | − | 0.206237i | \(-0.0661218\pi\) | |||||||
\(198\) | 3.87267e15 | − | 5.26537e15i | 0.324604 | − | 0.441339i | ||||
\(199\) | −1.59379e16 | −1.28962 | −0.644808 | − | 0.764345i | \(-0.723063\pi\) | ||||
−0.644808 | + | 0.764345i | \(0.723063\pi\) | |||||||
\(200\) | 3.18735e14i | 0.0249012i | ||||||||
\(201\) | 1.39918e15 | 0.105560 | ||||||||
\(202\) | −1.79806e16 | −1.31022 | ||||||||
\(203\) | 2.26734e16 | 1.59604 | ||||||||
\(204\) | 6.59658e15i | 0.448650i | ||||||||
\(205\) | − | 1.47445e16i | − | 0.969065i | ||||||
\(206\) | − | 1.22331e16i | − | 0.777077i | ||||||
\(207\) | −2.11889e16 | −1.30112 | ||||||||
\(208\) | − | 2.33012e15i | − | 0.138336i | ||||||
\(209\) | 9.58576e15 | − | 1.30330e16i | 0.550304 | − | 0.748205i | ||||
\(210\) | 1.72344e16 | 0.956890 | ||||||||
\(211\) | − | 1.73324e16i | − | 0.930854i | −0.885086 | − | 0.465427i | \(-0.845901\pi\) | ||
0.885086 | − | 0.465427i | \(-0.154099\pi\) | |||||||
\(212\) | 8.69836e15 | 0.451946 | ||||||||
\(213\) | 1.25639e15 | 0.0631639 | ||||||||
\(214\) | −1.51517e16 | −0.737167 | ||||||||
\(215\) | 1.76674e16i | 0.831961i | ||||||||
\(216\) | 2.32700e15i | 0.106077i | ||||||||
\(217\) | − | 1.46714e16i | − | 0.647520i | ||||||
\(218\) | −1.29942e16 | −0.555335 | ||||||||
\(219\) | 1.18284e16i | 0.489572i | ||||||||
\(220\) | −9.68666e15 | − | 7.12453e15i | −0.388343 | − | 0.285626i | ||||
\(221\) | −9.59633e15 | −0.372700 | ||||||||
\(222\) | 2.10927e16i | 0.793709i | ||||||||
\(223\) | 3.42689e16 | 1.24959 | 0.624794 | − | 0.780790i | \(-0.285183\pi\) | ||||
0.624794 | + | 0.780790i | \(0.285183\pi\) | |||||||
\(224\) | −5.27016e15 | −0.186246 | ||||||||
\(225\) | −1.59304e15 | −0.0545693 | ||||||||
\(226\) | 9.16500e15i | 0.304350i | ||||||||
\(227\) | − | 3.10536e16i | − | 0.999840i | −0.866072 | − | 0.499920i | \(-0.833363\pi\) | ||
0.866072 | − | 0.499920i | \(-0.166637\pi\) | |||||||
\(228\) | − | 1.98154e16i | − | 0.618671i | ||||||
\(229\) | −1.49288e16 | −0.452039 | −0.226019 | − | 0.974123i | \(-0.572571\pi\) | ||||
−0.226019 | + | 0.974123i | \(0.572571\pi\) | |||||||
\(230\) | 3.89812e16i | 1.14488i | ||||||||
\(231\) | 2.91881e16 | − | 3.96848e16i | 0.831616 | − | 1.13068i | ||||
\(232\) | −1.93755e16 | −0.535595 | ||||||||
\(233\) | − | 4.44002e16i | − | 1.19095i | −0.803374 | − | 0.595475i | \(-0.796964\pi\) | ||
0.803374 | − | 0.595475i | \(-0.203036\pi\) | |||||||
\(234\) | 1.16459e16 | 0.303153 | ||||||||
\(235\) | 4.82863e16 | 1.21997 | ||||||||
\(236\) | −2.78974e16 | −0.684195 | ||||||||
\(237\) | 6.16302e16i | 1.46742i | ||||||||
\(238\) | 2.17046e16i | 0.501779i | ||||||||
\(239\) | − | 5.76683e16i | − | 1.29465i | −0.762214 | − | 0.647325i | \(-0.775888\pi\) | ||
0.762214 | − | 0.647325i | \(-0.224112\pi\) | |||||||
\(240\) | −1.47276e16 | −0.321110 | ||||||||
\(241\) | 4.57373e16i | 0.968614i | 0.874898 | + | 0.484307i | \(0.160928\pi\) | ||||
−0.874898 | + | 0.484307i | \(0.839072\pi\) | |||||||
\(242\) | −3.28106e16 | + | 1.02389e16i | −0.675004 | + | 0.210642i | ||||
\(243\) | −6.32720e16 | −1.26464 | ||||||||
\(244\) | − | 2.93569e16i | − | 0.570140i | ||||||
\(245\) | 5.61986e15 | 0.106063 | ||||||||
\(246\) | −5.16198e16 | −0.946826 | ||||||||
\(247\) | 2.88263e16 | 0.513938 | ||||||||
\(248\) | 1.25374e16i | 0.217293i | ||||||||
\(249\) | 1.43459e16i | 0.241732i | ||||||||
\(250\) | 4.45415e16i | 0.729768i | ||||||||
\(251\) | −7.06905e16 | −1.12628 | −0.563138 | − | 0.826363i | \(-0.690406\pi\) | ||||
−0.563138 | + | 0.826363i | \(0.690406\pi\) | |||||||
\(252\) | − | 2.63402e16i | − | 0.408146i | ||||||
\(253\) | 8.97599e16 | + | 6.60183e16i | 1.35282 | + | 0.994994i | ||||
\(254\) | 9.49138e16 | 1.39153 | ||||||||
\(255\) | 6.06541e16i | 0.865125i | ||||||||
\(256\) | 4.50360e15 | 0.0625000 | ||||||||
\(257\) | 3.76880e16 | 0.508946 | 0.254473 | − | 0.967080i | \(-0.418098\pi\) | ||||
0.254473 | + | 0.967080i | \(0.418098\pi\) | |||||||
\(258\) | 6.18527e16 | 0.812869 | ||||||||
\(259\) | 6.94008e16i | 0.887699i | ||||||||
\(260\) | − | 2.14249e16i | − | 0.266750i | ||||||
\(261\) | − | 9.68385e16i | − | 1.17372i | ||||||
\(262\) | 9.84820e16 | 1.16211 | ||||||||
\(263\) | 1.52822e17i | 1.75588i | 0.478769 | + | 0.877941i | \(0.341083\pi\) | ||||
−0.478769 | + | 0.877941i | \(0.658917\pi\) | |||||||
\(264\) | −2.49426e16 | + | 3.39125e16i | −0.279071 | + | 0.379431i | ||||
\(265\) | 7.99794e16 | 0.871479 | ||||||||
\(266\) | − | 6.51982e16i | − | 0.691933i | ||||||
\(267\) | −2.19642e16 | −0.227058 | ||||||||
\(268\) | −3.93406e15 | −0.0396185 | ||||||||
\(269\) | −1.05450e17 | −1.03462 | −0.517311 | − | 0.855797i | \(-0.673067\pi\) | ||||
−0.517311 | + | 0.855797i | \(0.673067\pi\) | |||||||
\(270\) | 2.13962e16i | 0.204546i | ||||||||
\(271\) | − | 4.33967e16i | − | 0.404270i | −0.979358 | − | 0.202135i | \(-0.935212\pi\) | ||
0.979358 | − | 0.202135i | \(-0.0647880\pi\) | |||||||
\(272\) | − | 1.85476e16i | − | 0.168386i | ||||||
\(273\) | 8.77746e16 | 0.776659 | ||||||||
\(274\) | 8.60017e16i | 0.741742i | ||||||||
\(275\) | 6.74837e15 | + | 4.96342e15i | 0.0567375 | + | 0.0417303i | ||||
\(276\) | 1.36471e17 | 1.11861 | ||||||||
\(277\) | 2.21949e16i | 0.177376i | 0.996059 | + | 0.0886879i | \(0.0282674\pi\) | ||||
−0.996059 | + | 0.0886879i | \(0.971733\pi\) | |||||||
\(278\) | −1.28925e17 | −1.00467 | ||||||||
\(279\) | −6.26617e16 | −0.476182 | ||||||||
\(280\) | −4.84579e16 | −0.359136 | ||||||||
\(281\) | − | 2.54163e17i | − | 1.83725i | −0.395132 | − | 0.918624i | \(-0.629301\pi\) | ||
0.395132 | − | 0.918624i | \(-0.370699\pi\) | |||||||
\(282\) | − | 1.69048e17i | − | 1.19197i | ||||||
\(283\) | 3.93577e16i | 0.270723i | 0.990796 | + | 0.135361i | \(0.0432196\pi\) | ||||
−0.990796 | + | 0.135361i | \(0.956780\pi\) | |||||||
\(284\) | −3.53260e15 | −0.0237064 | ||||||||
\(285\) | − | 1.82198e17i | − | 1.19297i | ||||||
\(286\) | −4.93340e16 | − | 3.62851e16i | −0.315198 | − | 0.231828i | ||||
\(287\) | −1.69843e17 | −1.05895 | ||||||||
\(288\) | 2.25089e16i | 0.136964i | ||||||||
\(289\) | 9.19917e16 | 0.546341 | ||||||||
\(290\) | −1.78153e17 | −1.03278 | ||||||||
\(291\) | −1.42579e17 | −0.806873 | ||||||||
\(292\) | − | 3.32578e16i | − | 0.183744i | ||||||
\(293\) | − | 7.46259e16i | − | 0.402547i | −0.979535 | − | 0.201273i | \(-0.935492\pi\) | ||
0.979535 | − | 0.201273i | \(-0.0645079\pi\) | |||||||
\(294\) | − | 1.96749e16i | − | 0.103629i | ||||||
\(295\) | −2.56510e17 | −1.31932 | ||||||||
\(296\) | − | 5.93062e16i | − | 0.297891i | ||||||
\(297\) | 4.92680e16 | + | 3.62365e16i | 0.241696 | + | 0.177767i | ||||
\(298\) | 2.24982e17 | 1.07804 | ||||||||
\(299\) | 1.98530e17i | 0.929241i | ||||||||
\(300\) | 1.02602e16 | 0.0469147 | ||||||||
\(301\) | 2.03512e17 | 0.909128 | ||||||||
\(302\) | 7.54844e16 | 0.329465 | ||||||||
\(303\) | 5.78805e17i | 2.46850i | ||||||||
\(304\) | 5.57149e16i | 0.232197i | ||||||||
\(305\) | − | 2.69930e17i | − | 1.09939i | ||||||
\(306\) | 9.27006e16 | 0.369005 | ||||||||
\(307\) | − | 4.23515e17i | − | 1.64778i | −0.566747 | − | 0.823892i | \(-0.691798\pi\) | ||
0.566747 | − | 0.823892i | \(-0.308202\pi\) | |||||||
\(308\) | −8.20681e16 | + | 1.11582e17i | −0.312118 | + | 0.424363i | ||||
\(309\) | −3.93787e17 | −1.46404 | ||||||||
\(310\) | 1.15278e17i | 0.419002i | ||||||||
\(311\) | −5.34000e17 | −1.89766 | −0.948831 | − | 0.315785i | \(-0.897732\pi\) | ||||
−0.948831 | + | 0.315785i | \(0.897732\pi\) | |||||||
\(312\) | −7.50075e16 | −0.260629 | ||||||||
\(313\) | 3.33634e17 | 1.13360 | 0.566801 | − | 0.823855i | \(-0.308181\pi\) | ||||
0.566801 | + | 0.823855i | \(0.308181\pi\) | |||||||
\(314\) | − | 2.56540e16i | − | 0.0852408i | ||||||
\(315\) | − | 2.42192e17i | − | 0.787021i | ||||||
\(316\) | − | 1.73285e17i | − | 0.550747i | ||||||
\(317\) | 3.20010e17 | 0.994829 | 0.497414 | − | 0.867513i | \(-0.334283\pi\) | ||||
0.497414 | + | 0.867513i | \(0.334283\pi\) | |||||||
\(318\) | − | 2.80004e17i | − | 0.851480i | ||||||
\(319\) | −3.01719e17 | + | 4.10224e17i | −0.897569 | + | 1.22035i | ||||
\(320\) | 4.14096e16 | 0.120518 | ||||||||
\(321\) | 4.87741e17i | 1.38885i | ||||||||
\(322\) | 4.49028e17 | 1.25107 | ||||||||
\(323\) | 2.29456e17 | 0.625577 | ||||||||
\(324\) | 2.20108e17 | 0.587246 | ||||||||
\(325\) | 1.49260e16i | 0.0389726i | ||||||||
\(326\) | − | 4.47498e17i | − | 1.14358i | ||||||
\(327\) | 4.18290e17i | 1.04627i | ||||||||
\(328\) | 1.45139e17 | 0.355359 | ||||||||
\(329\) | − | 5.56214e17i | − | 1.33313i | ||||||
\(330\) | −2.29342e17 | + | 3.11818e17i | −0.538128 | + | 0.731650i | ||||
\(331\) | −2.12757e17 | −0.488751 | −0.244375 | − | 0.969681i | \(-0.578583\pi\) | ||||
−0.244375 | + | 0.969681i | \(0.578583\pi\) | |||||||
\(332\) | − | 4.03364e16i | − | 0.0907258i | ||||||
\(333\) | 2.96412e17 | 0.652808 | ||||||||
\(334\) | 4.14434e15 | 0.00893778 | ||||||||
\(335\) | −3.61728e16 | −0.0763956 | ||||||||
\(336\) | 1.69649e17i | 0.350894i | ||||||||
\(337\) | − | 3.14484e17i | − | 0.637074i | −0.947910 | − | 0.318537i | \(-0.896809\pi\) | ||
0.947910 | − | 0.318537i | \(-0.103191\pi\) | |||||||
\(338\) | 2.47254e17i | 0.490599i | ||||||||
\(339\) | 2.95025e17 | 0.573405 | ||||||||
\(340\) | − | 1.70541e17i | − | 0.324695i | ||||||
\(341\) | 2.65446e17 | + | 1.95235e17i | 0.495102 | + | 0.364147i | ||||
\(342\) | −2.78463e17 | −0.508843 | ||||||||
\(343\) | 5.23731e17i | 0.937668i | ||||||||
\(344\) | −1.73911e17 | −0.305082 | ||||||||
\(345\) | 1.25482e18 | 2.15699 | ||||||||
\(346\) | −5.78596e17 | −0.974637 | ||||||||
\(347\) | − | 3.11559e17i | − | 0.514321i | −0.966369 | − | 0.257161i | \(-0.917213\pi\) | ||
0.966369 | − | 0.257161i | \(-0.0827870\pi\) | |||||||
\(348\) | 6.23705e17i | 1.00908i | ||||||||
\(349\) | 1.05194e16i | 0.0166807i | 0.999965 | + | 0.00834036i | \(0.00265485\pi\) | ||||
−0.999965 | + | 0.00834036i | \(0.997345\pi\) | |||||||
\(350\) | 3.37590e16 | 0.0524703 | ||||||||
\(351\) | 1.08971e17i | 0.166020i | ||||||||
\(352\) | 7.01310e16 | − | 9.53516e16i | 0.104740 | − | 0.142406i | ||||
\(353\) | −8.03740e17 | −1.17677 | −0.588386 | − | 0.808580i | \(-0.700237\pi\) | ||||
−0.588386 | + | 0.808580i | \(0.700237\pi\) | |||||||
\(354\) | 8.98030e17i | 1.28904i | ||||||||
\(355\) | −3.24814e16 | −0.0457126 | ||||||||
\(356\) | 6.17566e16 | 0.0852185 | ||||||||
\(357\) | 6.98680e17 | 0.945368 | ||||||||
\(358\) | 2.53523e17i | 0.336384i | ||||||||
\(359\) | − | 1.25415e18i | − | 1.63189i | −0.578133 | − | 0.815943i | \(-0.696218\pi\) | ||
0.578133 | − | 0.815943i | \(-0.303782\pi\) | |||||||
\(360\) | 2.06965e17i | 0.264106i | ||||||||
\(361\) | 1.09747e17 | 0.137354 | ||||||||
\(362\) | 5.45645e16i | 0.0669808i | ||||||||
\(363\) | 3.29595e17 | + | 1.05619e18i | 0.396857 | + | 1.27173i | ||||
\(364\) | −2.46795e17 | −0.291492 | ||||||||
\(365\) | − | 3.05798e17i | − | 0.354311i | ||||||
\(366\) | −9.45012e17 | −1.07416 | ||||||||
\(367\) | −9.57611e17 | −1.06789 | −0.533945 | − | 0.845519i | \(-0.679291\pi\) | ||||
−0.533945 | + | 0.845519i | \(0.679291\pi\) | |||||||
\(368\) | −3.83715e17 | −0.419831 | ||||||||
\(369\) | 7.25403e17i | 0.778744i | ||||||||
\(370\) | − | 5.45307e17i | − | 0.574419i | ||||||
\(371\) | − | 9.21290e17i | − | 0.952312i | ||||||
\(372\) | 4.03584e17 | 0.409386 | ||||||||
\(373\) | 8.80613e17i | 0.876644i | 0.898818 | + | 0.438322i | \(0.144427\pi\) | ||||
−0.898818 | + | 0.438322i | \(0.855573\pi\) | |||||||
\(374\) | −3.92695e17 | − | 2.88827e17i | −0.383667 | − | 0.282187i | ||||
\(375\) | 1.43381e18 | 1.37491 | ||||||||
\(376\) | 4.75311e17i | 0.447366i | ||||||||
\(377\) | −9.07330e17 | −0.838254 | ||||||||
\(378\) | 2.46465e17 | 0.223518 | ||||||||
\(379\) | 1.16292e18 | 1.03532 | 0.517661 | − | 0.855586i | \(-0.326803\pi\) | ||||
0.517661 | + | 0.855586i | \(0.326803\pi\) | |||||||
\(380\) | 5.12286e17i | 0.447741i | ||||||||
\(381\) | − | 3.05532e18i | − | 2.62169i | ||||||
\(382\) | − | 1.45832e18i | − | 1.22859i | ||||||
\(383\) | −4.81244e17 | −0.398083 | −0.199042 | − | 0.979991i | \(-0.563783\pi\) | ||||
−0.199042 | + | 0.979991i | \(0.563783\pi\) | |||||||
\(384\) | − | 1.44973e17i | − | 0.117752i | ||||||
\(385\) | −7.54597e17 | + | 1.02597e18i | −0.601853 | + | 0.818292i | ||||
\(386\) | −3.56517e17 | −0.279235 | ||||||||
\(387\) | − | 8.69204e17i | − | 0.668567i | ||||||
\(388\) | 4.00889e17 | 0.302832 | ||||||||
\(389\) | −1.53981e18 | −1.14240 | −0.571202 | − | 0.820810i | \(-0.693523\pi\) | ||||
−0.571202 | + | 0.820810i | \(0.693523\pi\) | |||||||
\(390\) | −6.89677e17 | −0.502566 | ||||||||
\(391\) | 1.58029e18i | 1.13109i | ||||||||
\(392\) | 5.53197e16i | 0.0388935i | ||||||||
\(393\) | − | 3.17018e18i | − | 2.18945i | ||||||
\(394\) | 4.29888e17 | 0.291663 | ||||||||
\(395\) | − | 1.59332e18i | − | 1.06200i | ||||||
\(396\) | 4.76567e17 | + | 3.50514e17i | 0.312074 | + | 0.229530i | ||||
\(397\) | 9.44294e17 | 0.607538 | 0.303769 | − | 0.952746i | \(-0.401755\pi\) | ||||
0.303769 | + | 0.952746i | \(0.401755\pi\) | |||||||
\(398\) | − | 1.44254e18i | − | 0.911896i | ||||||
\(399\) | −2.09876e18 | −1.30362 | ||||||||
\(400\) | −2.88486e16 | −0.0176078 | ||||||||
\(401\) | −2.13296e18 | −1.27930 | −0.639651 | − | 0.768666i | \(-0.720921\pi\) | ||||
−0.639651 | + | 0.768666i | \(0.720921\pi\) | |||||||
\(402\) | 1.26639e17i | 0.0746425i | ||||||||
\(403\) | 5.87111e17i | 0.340083i | ||||||||
\(404\) | − | 1.62742e18i | − | 0.926468i | ||||||
\(405\) | 2.02384e18 | 1.13238 | ||||||||
\(406\) | 2.05216e18i | 1.12857i | ||||||||
\(407\) | −1.25565e18 | − | 9.23529e17i | −0.678746 | − | 0.499217i | ||||
\(408\) | −5.97055e17 | −0.317244 | ||||||||
\(409\) | 1.40285e18i | 0.732739i | 0.930469 | + | 0.366369i | \(0.119399\pi\) | ||||
−0.930469 | + | 0.366369i | \(0.880601\pi\) | |||||||
\(410\) | 1.33452e18 | 0.685232 | ||||||||
\(411\) | 2.76843e18 | 1.39747 | ||||||||
\(412\) | 1.10721e18 | 0.549477 | ||||||||
\(413\) | 2.95477e18i | 1.44169i | ||||||||
\(414\) | − | 1.91780e18i | − | 0.920030i | ||||||
\(415\) | − | 3.70884e17i | − | 0.174945i | ||||||
\(416\) | 2.10898e17 | 0.0978181 | ||||||||
\(417\) | 4.15016e18i | 1.89283i | ||||||||
\(418\) | 1.17961e18 | + | 8.67604e17i | 0.529061 | + | 0.389124i | ||||
\(419\) | 3.90588e18 | 1.72275 | 0.861373 | − | 0.507974i | \(-0.169605\pi\) | ||||
0.861373 | + | 0.507974i | \(0.169605\pi\) | |||||||
\(420\) | 1.55988e18i | 0.676623i | ||||||||
\(421\) | 2.25755e17 | 0.0963080 | 0.0481540 | − | 0.998840i | \(-0.484666\pi\) | ||||
0.0481540 | + | 0.998840i | \(0.484666\pi\) | |||||||
\(422\) | 1.56875e18 | 0.658213 | ||||||||
\(423\) | −2.37560e18 | −0.980372 | ||||||||
\(424\) | 7.87285e17i | 0.319574i | ||||||||
\(425\) | 1.18810e17i | 0.0474384i | ||||||||
\(426\) | 1.13716e17i | 0.0446636i | ||||||||
\(427\) | −3.10935e18 | −1.20136 | ||||||||
\(428\) | − | 1.37138e18i | − | 0.521256i | ||||||
\(429\) | −1.16803e18 | + | 1.58808e18i | −0.436771 | + | 0.593844i | ||||
\(430\) | −1.59907e18 | −0.588285 | ||||||||
\(431\) | 2.76525e18i | 1.00091i | 0.865763 | + | 0.500454i | \(0.166833\pi\) | ||||
−0.865763 | + | 0.500454i | \(0.833167\pi\) | |||||||
\(432\) | −2.10616e17 | −0.0750076 | ||||||||
\(433\) | −1.73403e18 | −0.607633 | −0.303817 | − | 0.952731i | \(-0.598261\pi\) | ||||
−0.303817 | + | 0.952731i | \(0.598261\pi\) | |||||||
\(434\) | 1.32790e18 | 0.457866 | ||||||||
\(435\) | 5.73483e18i | 1.94579i | ||||||||
\(436\) | − | 1.17610e18i | − | 0.392681i | ||||||
\(437\) | − | 4.74701e18i | − | 1.55973i | ||||||
\(438\) | −1.07058e18 | −0.346180 | ||||||||
\(439\) | 1.38152e18i | 0.439648i | 0.975540 | + | 0.219824i | \(0.0705484\pi\) | ||||
−0.975540 | + | 0.219824i | \(0.929452\pi\) | |||||||
\(440\) | 6.44839e17 | − | 8.76736e17i | 0.201968 | − | 0.274600i | ||||
\(441\) | −2.76487e17 | −0.0852325 | ||||||||
\(442\) | − | 8.68560e17i | − | 0.263538i | ||||||
\(443\) | 1.78840e18 | 0.534121 | 0.267060 | − | 0.963680i | \(-0.413948\pi\) | ||||
0.267060 | + | 0.963680i | \(0.413948\pi\) | |||||||
\(444\) | −1.90909e18 | −0.561237 | ||||||||
\(445\) | 5.67838e17 | 0.164325 | ||||||||
\(446\) | 3.10167e18i | 0.883592i | ||||||||
\(447\) | − | 7.24228e18i | − | 2.03106i | ||||||
\(448\) | − | 4.77001e17i | − | 0.131696i | ||||||
\(449\) | 2.40865e18 | 0.654710 | 0.327355 | − | 0.944901i | \(-0.393843\pi\) | ||||
0.327355 | + | 0.944901i | \(0.393843\pi\) | |||||||
\(450\) | − | 1.44185e17i | − | 0.0385863i | ||||||
\(451\) | 2.26014e18 | − | 3.07293e18i | 0.595523 | − | 0.809686i | ||||
\(452\) | −8.29521e17 | −0.215208 | ||||||||
\(453\) | − | 2.42988e18i | − | 0.620722i | ||||||
\(454\) | 2.81065e18 | 0.706993 | ||||||||
\(455\) | −2.26923e18 | −0.562080 | ||||||||
\(456\) | 1.79349e18 | 0.437466 | ||||||||
\(457\) | 4.07586e18i | 0.979051i | 0.871989 | + | 0.489526i | \(0.162830\pi\) | ||||
−0.871989 | + | 0.489526i | \(0.837170\pi\) | |||||||
\(458\) | − | 1.35120e18i | − | 0.319640i | ||||||
\(459\) | 8.67398e17i | 0.202083i | ||||||||
\(460\) | −3.52817e18 | −0.809552 | ||||||||
\(461\) | 2.96254e18i | 0.669511i | 0.942305 | + | 0.334755i | \(0.108654\pi\) | ||||
−0.942305 | + | 0.334755i | \(0.891346\pi\) | |||||||
\(462\) | 3.59186e18 | + | 2.64181e18i | 0.799513 | + | 0.588041i | ||||
\(463\) | −4.04238e18 | −0.886278 | −0.443139 | − | 0.896453i | \(-0.646135\pi\) | ||||
−0.443139 | + | 0.896453i | \(0.646135\pi\) | |||||||
\(464\) | − | 1.75367e18i | − | 0.378723i | ||||||
\(465\) | 3.71086e18 | 0.789413 | ||||||||
\(466\) | 4.01865e18 | 0.842129 | ||||||||
\(467\) | 5.69967e18 | 1.17661 | 0.588304 | − | 0.808640i | \(-0.299796\pi\) | ||||
0.588304 | + | 0.808640i | \(0.299796\pi\) | |||||||
\(468\) | 1.05407e18i | 0.214362i | ||||||||
\(469\) | 4.16678e17i | 0.0834816i | ||||||||
\(470\) | 4.37038e18i | 0.862648i | ||||||||
\(471\) | −8.25814e17 | −0.160596 | ||||||||
\(472\) | − | 2.52499e18i | − | 0.483799i | ||||||
\(473\) | −2.70818e18 | + | 3.68209e18i | −0.511268 | + | 0.695131i | ||||
\(474\) | −5.57813e18 | −1.03762 | ||||||||
\(475\) | − | 3.56892e17i | − | 0.0654156i | ||||||
\(476\) | −1.96447e18 | −0.354811 | ||||||||
\(477\) | −3.93484e18 | −0.700324 | ||||||||
\(478\) | 5.21954e18 | 0.915455 | ||||||||
\(479\) | 7.40327e18i | 1.27960i | 0.768541 | + | 0.639801i | \(0.220983\pi\) | ||||
−0.768541 | + | 0.639801i | \(0.779017\pi\) | |||||||
\(480\) | − | 1.33299e18i | − | 0.227059i | ||||||
\(481\) | − | 2.77724e18i | − | 0.466227i | ||||||
\(482\) | −4.13966e18 | −0.684914 | ||||||||
\(483\) | − | 1.44544e19i | − | 2.35706i | ||||||
\(484\) | −9.26720e17 | − | 2.96967e18i | −0.148947 | − | 0.477300i | ||||
\(485\) | 3.68608e18 | 0.583946 | ||||||||
\(486\) | − | 5.72672e18i | − | 0.894236i | ||||||
\(487\) | 9.76288e18 | 1.50271 | 0.751355 | − | 0.659898i | \(-0.229401\pi\) | ||||
0.751355 | + | 0.659898i | \(0.229401\pi\) | |||||||
\(488\) | 2.65709e18 | 0.403150 | ||||||||
\(489\) | −1.44052e19 | −2.15455 | ||||||||
\(490\) | 5.08652e17i | 0.0749977i | ||||||||
\(491\) | − | 6.09802e18i | − | 0.886378i | −0.896428 | − | 0.443189i | \(-0.853847\pi\) | ||
0.896428 | − | 0.443189i | \(-0.146153\pi\) | |||||||
\(492\) | − | 4.67209e18i | − | 0.669507i | ||||||
\(493\) | −7.22229e18 | −1.02034 | ||||||||
\(494\) | 2.60906e18i | 0.363409i | ||||||||
\(495\) | 4.38192e18 | + | 3.22290e18i | 0.601767 | + | 0.442599i | ||||
\(496\) | −1.13475e18 | −0.153649 | ||||||||
\(497\) | 3.74156e17i | 0.0499527i | ||||||||
\(498\) | −1.29845e18 | −0.170930 | ||||||||
\(499\) | −1.40351e19 | −1.82185 | −0.910924 | − | 0.412574i | \(-0.864630\pi\) | ||||
−0.910924 | + | 0.412574i | \(0.864630\pi\) | |||||||
\(500\) | −4.03143e18 | −0.516024 | ||||||||
\(501\) | − | 1.33408e17i | − | 0.0168391i | ||||||
\(502\) | − | 6.39818e18i | − | 0.796398i | ||||||
\(503\) | − | 5.18305e18i | − | 0.636223i | −0.948053 | − | 0.318111i | \(-0.896951\pi\) | ||
0.948053 | − | 0.318111i | \(-0.103049\pi\) | |||||||
\(504\) | 2.38405e18 | 0.288603 | ||||||||
\(505\) | − | 1.49638e19i | − | 1.78649i | ||||||
\(506\) | −5.97529e18 | + | 8.12414e18i | −0.703567 | + | 0.956585i | ||||
\(507\) | 7.95922e18 | 0.924304 | ||||||||
\(508\) | 8.59061e18i | 0.983962i | ||||||||
\(509\) | −1.31946e19 | −1.49064 | −0.745319 | − | 0.666708i | \(-0.767703\pi\) | ||||
−0.745319 | + | 0.666708i | \(0.767703\pi\) | |||||||
\(510\) | −5.48978e18 | −0.611736 | ||||||||
\(511\) | −3.52251e18 | −0.387174 | ||||||||
\(512\) | 4.07619e17i | 0.0441942i | ||||||||
\(513\) | − | 2.60557e18i | − | 0.278664i | ||||||
\(514\) | 3.41113e18i | 0.359879i | ||||||||
\(515\) | 1.01805e19 | 1.05955 | ||||||||
\(516\) | 5.59826e18i | 0.574785i | ||||||||
\(517\) | 1.00634e19 | + | 7.40165e18i | 1.01932 | + | 0.749712i | ||||
\(518\) | −6.28144e18 | −0.627698 | ||||||||
\(519\) | 1.86253e19i | 1.83625i | ||||||||
\(520\) | 1.93916e18 | 0.188621 | ||||||||
\(521\) | 1.02649e19 | 0.985124 | 0.492562 | − | 0.870277i | \(-0.336060\pi\) | ||||
0.492562 | + | 0.870277i | \(0.336060\pi\) | |||||||
\(522\) | 8.76482e18 | 0.829945 | ||||||||
\(523\) | − | 8.64600e18i | − | 0.807799i | −0.914803 | − | 0.403900i | \(-0.867655\pi\) | ||
0.914803 | − | 0.403900i | \(-0.132345\pi\) | |||||||
\(524\) | 8.91357e18i | 0.821737i | ||||||||
\(525\) | − | 1.08672e18i | − | 0.0988557i | ||||||
\(526\) | −1.38319e19 | −1.24160 | ||||||||
\(527\) | 4.67336e18i | 0.413957i | ||||||||
\(528\) | −3.06941e18 | − | 2.25755e18i | −0.268298 | − | 0.197333i | ||||
\(529\) | 2.11004e19 | 1.82012 | ||||||||
\(530\) | 7.23891e18i | 0.616229i | ||||||||
\(531\) | 1.26199e19 | 1.06021 | ||||||||
\(532\) | 5.90107e18 | 0.489271 | ||||||||
\(533\) | 6.79668e18 | 0.556169 | ||||||||
\(534\) | − | 1.98797e18i | − | 0.160554i | ||||||
\(535\) | − | 1.26095e19i | − | 1.00513i | ||||||
\(536\) | − | 3.56071e17i | − | 0.0280145i | ||||||
\(537\) | 8.16101e18 | 0.633759 | ||||||||
\(538\) | − | 9.54427e18i | − | 0.731588i | ||||||
\(539\) | 1.17125e18 | + | 8.61450e17i | 0.0886190 | + | 0.0651792i | ||||
\(540\) | −1.93657e18 | −0.144636 | ||||||||
\(541\) | 1.19057e19i | 0.877757i | 0.898546 | + | 0.438879i | \(0.144624\pi\) | ||||
−0.898546 | + | 0.438879i | \(0.855376\pi\) | |||||||
\(542\) | 3.92782e18 | 0.285862 | ||||||||
\(543\) | 1.75646e18 | 0.126194 | ||||||||
\(544\) | 1.67873e18 | 0.119067 | ||||||||
\(545\) | − | 1.08140e19i | − | 0.757200i | ||||||
\(546\) | 7.94445e18i | 0.549181i | ||||||||
\(547\) | 1.01805e19i | 0.694799i | 0.937717 | + | 0.347400i | \(0.112935\pi\) | ||||
−0.937717 | + | 0.347400i | \(0.887065\pi\) | |||||||
\(548\) | −7.78398e18 | −0.524491 | ||||||||
\(549\) | 1.32801e19i | 0.883475i | ||||||||
\(550\) | −4.49237e17 | + | 6.10793e17i | −0.0295078 | + | 0.0401194i | ||||
\(551\) | 2.16950e19 | 1.40701 | ||||||||
\(552\) | 1.23520e19i | 0.790974i | ||||||||
\(553\) | −1.83536e19 | −1.16050 | ||||||||
\(554\) | −2.00885e18 | −0.125424 | ||||||||
\(555\) | −1.75537e19 | −1.08222 | ||||||||
\(556\) | − | 1.16690e19i | − | 0.710410i | ||||||
\(557\) | 2.05299e19i | 1.23424i | 0.786867 | + | 0.617122i | \(0.211702\pi\) | ||||
−0.786867 | + | 0.617122i | \(0.788298\pi\) | |||||||
\(558\) | − | 5.67149e18i | − | 0.336712i | ||||||
\(559\) | −8.14403e18 | −0.477482 | ||||||||
\(560\) | − | 4.38591e18i | − | 0.253947i | ||||||
\(561\) | −9.29746e18 | + | 1.26410e19i | −0.531648 | + | 0.722840i | ||||
\(562\) | 2.30042e19 | 1.29913 | ||||||||
\(563\) | − | 2.56873e19i | − | 1.43272i | −0.697733 | − | 0.716358i | \(-0.745808\pi\) | ||
0.697733 | − | 0.716358i | \(-0.254192\pi\) | |||||||
\(564\) | 1.53005e19 | 0.842852 | ||||||||
\(565\) | −7.62726e18 | −0.414982 | ||||||||
\(566\) | −3.56226e18 | −0.191430 | ||||||||
\(567\) | − | 2.33128e19i | − | 1.23741i | ||||||
\(568\) | − | 3.19734e17i | − | 0.0167630i | ||||||
\(569\) | 1.26575e19i | 0.655485i | 0.944767 | + | 0.327742i | \(0.106288\pi\) | ||||
−0.944767 | + | 0.327742i | \(0.893712\pi\) | |||||||
\(570\) | 1.64907e19 | 0.843559 | ||||||||
\(571\) | 3.03372e18i | 0.153293i | 0.997058 | + | 0.0766466i | \(0.0244213\pi\) | ||||
−0.997058 | + | 0.0766466i | \(0.975579\pi\) | |||||||
\(572\) | 3.28415e18 | − | 4.46520e18i | 0.163927 | − | 0.222879i | ||||
\(573\) | −4.69439e19 | −2.31471 | ||||||||
\(574\) | − | 1.53725e19i | − | 0.748790i | ||||||
\(575\) | 2.45796e18 | 0.118277 | ||||||||
\(576\) | −2.03728e18 | −0.0968485 | ||||||||
\(577\) | −1.75043e19 | −0.822082 | −0.411041 | − | 0.911617i | \(-0.634835\pi\) | ||||
−0.411041 | + | 0.911617i | \(0.634835\pi\) | |||||||
\(578\) | 8.32614e18i | 0.386321i | ||||||||
\(579\) | 1.14764e19i | 0.526087i | ||||||||
\(580\) | − | 1.61246e19i | − | 0.730285i | ||||||
\(581\) | −4.27225e18 | −0.191172 | ||||||||
\(582\) | − | 1.29048e19i | − | 0.570545i | ||||||
\(583\) | 1.66687e19 | + | 1.22598e19i | 0.728150 | + | 0.535553i | ||||
\(584\) | 3.01015e18 | 0.129927 | ||||||||
\(585\) | 9.69190e18i | 0.413350i | ||||||||
\(586\) | 6.75436e18 | 0.284643 | ||||||||
\(587\) | 2.01981e17 | 0.00841092 | 0.00420546 | − | 0.999991i | \(-0.498661\pi\) | ||||
0.00420546 | + | 0.999991i | \(0.498661\pi\) | |||||||
\(588\) | 1.78077e18 | 0.0732766 | ||||||||
\(589\) | − | 1.40383e19i | − | 0.570830i | ||||||
\(590\) | − | 2.32167e19i | − | 0.932901i | ||||||
\(591\) | − | 1.38383e19i | − | 0.549503i | ||||||
\(592\) | 5.36778e18 | 0.210641 | ||||||||
\(593\) | 3.53501e19i | 1.37091i | 0.728116 | + | 0.685454i | \(0.240396\pi\) | ||||
−0.728116 | + | 0.685454i | \(0.759604\pi\) | |||||||
\(594\) | −3.27976e18 | + | 4.45923e18i | −0.125700 | + | 0.170905i | ||||
\(595\) | −1.80629e19 | −0.684177 | ||||||||
\(596\) | 2.03631e19i | 0.762288i | ||||||||
\(597\) | −4.64359e19 | −1.71804 | ||||||||
\(598\) | −1.79689e19 | −0.657073 | ||||||||
\(599\) | 3.03003e19 | 1.09511 | 0.547557 | − | 0.836768i | \(-0.315558\pi\) | ||||
0.547557 | + | 0.836768i | \(0.315558\pi\) | |||||||
\(600\) | 9.28651e17i | 0.0331737i | ||||||||
\(601\) | − | 2.23510e19i | − | 0.789181i | −0.918857 | − | 0.394590i | \(-0.870887\pi\) | ||
0.918857 | − | 0.394590i | \(-0.129113\pi\) | |||||||
\(602\) | 1.84198e19i | 0.642851i | ||||||||
\(603\) | 1.77964e18 | 0.0613918 | ||||||||
\(604\) | 6.83207e18i | 0.232967i | ||||||||
\(605\) | −8.52098e18 | − | 2.73055e19i | −0.287211 | − | 0.920369i | ||||
\(606\) | −5.23874e19 | −1.74550 | ||||||||
\(607\) | − | 6.83948e18i | − | 0.225269i | −0.993636 | − | 0.112635i | \(-0.964071\pi\) | ||
0.993636 | − | 0.112635i | \(-0.0359290\pi\) | |||||||
\(608\) | −5.04274e18 | −0.164188 | ||||||||
\(609\) | 6.60600e19 | 2.12627 | ||||||||
\(610\) | 2.44313e19 | 0.777387 | ||||||||
\(611\) | 2.22582e19i | 0.700168i | ||||||||
\(612\) | 8.39030e18i | 0.260926i | ||||||||
\(613\) | 7.18627e18i | 0.220943i | 0.993879 | + | 0.110471i | \(0.0352361\pi\) | ||||
−0.993879 | + | 0.110471i | \(0.964764\pi\) | |||||||
\(614\) | 3.83322e19 | 1.16516 | ||||||||
\(615\) | − | 4.29588e19i | − | 1.29100i | ||||||
\(616\) | −1.00992e19 | − | 7.42796e18i | −0.300070 | − | 0.220701i | ||||
\(617\) | −8.06287e18 | −0.236861 | −0.118431 | − | 0.992962i | \(-0.537786\pi\) | ||||
−0.118431 | + | 0.992962i | \(0.537786\pi\) | |||||||
\(618\) | − | 3.56416e19i | − | 1.03523i | ||||||
\(619\) | −2.95921e19 | −0.849849 | −0.424924 | − | 0.905229i | \(-0.639699\pi\) | ||||
−0.424924 | + | 0.905229i | \(0.639699\pi\) | |||||||
\(620\) | −1.04338e19 | −0.296279 | ||||||||
\(621\) | 1.79449e19 | 0.503847 | ||||||||
\(622\) | − | 4.83322e19i | − | 1.34185i | ||||||
\(623\) | − | 6.54098e18i | − | 0.179567i | ||||||
\(624\) | − | 6.78890e18i | − | 0.184292i | ||||||
\(625\) | −3.44443e19 | −0.924608 | ||||||||
\(626\) | 3.01971e19i | 0.801577i | ||||||||
\(627\) | 2.79286e19 | − | 3.79723e19i | 0.733122 | − | 0.996768i | ||||
\(628\) | 2.32194e18 | 0.0602744 | ||||||||
\(629\) | − | 2.21066e19i | − | 0.567502i | ||||||
\(630\) | 2.19207e19 | 0.556508 | ||||||||
\(631\) | 5.84818e18 | 0.146830 | 0.0734151 | − | 0.997301i | \(-0.476610\pi\) | ||||
0.0734151 | + | 0.997301i | \(0.476610\pi\) | |||||||
\(632\) | 1.56840e19 | 0.389437 | ||||||||
\(633\) | − | 5.04988e19i | − | 1.24009i | ||||||
\(634\) | 2.89640e19i | 0.703450i | ||||||||
\(635\) | 7.89887e19i | 1.89736i | ||||||||
\(636\) | 2.53431e19 | 0.602087 | ||||||||
\(637\) | 2.59055e18i | 0.0608719i | ||||||||
\(638\) | −3.71292e19 | − | 2.73085e19i | −0.862921 | − | 0.634677i | ||||
\(639\) | 1.59803e18 | 0.0367349 | ||||||||
\(640\) | 3.74797e18i | 0.0852189i | ||||||||
\(641\) | 3.07064e19 | 0.690594 | 0.345297 | − | 0.938493i | \(-0.387778\pi\) | ||||
0.345297 | + | 0.938493i | \(0.387778\pi\) | |||||||
\(642\) | −4.41453e19 | −0.982063 | ||||||||
\(643\) | −3.34635e19 | −0.736366 | −0.368183 | − | 0.929753i | \(-0.620020\pi\) | ||||
−0.368183 | + | 0.929753i | \(0.620020\pi\) | |||||||
\(644\) | 4.06413e19i | 0.884641i | ||||||||
\(645\) | 5.14747e19i | 1.10835i | ||||||||
\(646\) | 2.07679e19i | 0.442350i | ||||||||
\(647\) | −3.22302e19 | −0.679098 | −0.339549 | − | 0.940588i | \(-0.610275\pi\) | ||||
−0.339549 | + | 0.940588i | \(0.610275\pi\) | |||||||
\(648\) | 1.99219e19i | 0.415246i | ||||||||
\(649\) | −5.34598e19 | − | 3.93196e19i | −1.10234 | − | 0.810767i | ||||
\(650\) | −1.35095e18 | −0.0275578 | ||||||||
\(651\) | − | 4.27458e19i | − | 0.862634i | ||||||
\(652\) | 4.05029e19 | 0.808636 | ||||||||
\(653\) | 8.05170e19 | 1.59036 | 0.795179 | − | 0.606374i | \(-0.207377\pi\) | ||||
0.795179 | + | 0.606374i | \(0.207377\pi\) | |||||||
\(654\) | −3.78593e19 | −0.739824 | ||||||||
\(655\) | 8.19582e19i | 1.58454i | ||||||||
\(656\) | 1.31365e19i | 0.251277i | ||||||||
\(657\) | 1.50447e19i | 0.284726i | ||||||||
\(658\) | 5.03428e19 | 0.942662 | ||||||||
\(659\) | 8.02662e19i | 1.48708i | 0.668690 | + | 0.743541i | \(0.266855\pi\) | ||||
−0.668690 | + | 0.743541i | \(0.733145\pi\) | |||||||
\(660\) | −2.82225e19 | − | 2.07576e19i | −0.517355 | − | 0.380514i | ||||
\(661\) | 4.55001e19 | 0.825282 | 0.412641 | − | 0.910894i | \(-0.364606\pi\) | ||||
0.412641 | + | 0.910894i | \(0.364606\pi\) | |||||||
\(662\) | − | 1.92566e19i | − | 0.345599i | ||||||
\(663\) | −2.79593e19 | −0.496515 | ||||||||
\(664\) | 3.65083e18 | 0.0641528 | ||||||||
\(665\) | 5.42590e19 | 0.943452 | ||||||||
\(666\) | 2.68281e19i | 0.461605i | ||||||||
\(667\) | 1.49416e20i | 2.54399i | ||||||||
\(668\) | 3.75103e17i | 0.00631997i | ||||||||
\(669\) | 9.98441e19 | 1.66471 | ||||||||
\(670\) | − | 3.27399e18i | − | 0.0540199i | ||||||
\(671\) | 4.13767e19 | − | 5.62567e19i | 0.675613 | − | 0.918578i | ||||
\(672\) | −1.53549e19 | −0.248120 | ||||||||
\(673\) | 1.46349e19i | 0.234038i | 0.993130 | + | 0.117019i | \(0.0373338\pi\) | ||||
−0.993130 | + | 0.117019i | \(0.962666\pi\) | |||||||
\(674\) | 2.84639e19 | 0.450479 | ||||||||
\(675\) | 1.34914e18 | 0.0211315 | ||||||||
\(676\) | −2.23789e19 | −0.346906 | ||||||||
\(677\) | 6.09622e19i | 0.935276i | 0.883920 | + | 0.467638i | \(0.154895\pi\) | ||||
−0.883920 | + | 0.467638i | \(0.845105\pi\) | |||||||
\(678\) | 2.67027e19i | 0.405459i | ||||||||
\(679\) | − | 4.24603e19i | − | 0.638109i | ||||||
\(680\) | 1.54356e19 | 0.229594 | ||||||||
\(681\) | − | 9.04760e19i | − | 1.33200i | ||||||
\(682\) | −1.76706e19 | + | 2.40254e19i | −0.257491 | + | 0.350090i | ||||
\(683\) | 5.87414e17 | 0.00847226 | 0.00423613 | − | 0.999991i | \(-0.498652\pi\) | ||||
0.00423613 | + | 0.999991i | \(0.498652\pi\) | |||||||
\(684\) | − | 2.52036e19i | − | 0.359807i | ||||||
\(685\) | −7.15719e19 | −1.01137 | ||||||||
\(686\) | −4.74027e19 | −0.663032 | ||||||||
\(687\) | −4.34957e19 | −0.602211 | ||||||||
\(688\) | − | 1.57406e19i | − | 0.215726i | ||||||
\(689\) | 3.68676e19i | 0.500162i | ||||||||
\(690\) | 1.13573e20i | 1.52522i | ||||||||
\(691\) | −1.07427e20 | −1.42812 | −0.714062 | − | 0.700083i | \(-0.753147\pi\) | ||||
−0.714062 | + | 0.700083i | \(0.753147\pi\) | |||||||
\(692\) | − | 5.23686e19i | − | 0.689173i | ||||||
\(693\) | 3.71249e19 | − | 5.04758e19i | 0.483651 | − | 0.657583i | ||||
\(694\) | 2.81991e19 | 0.363680 | ||||||||
\(695\) | − | 1.07294e20i | − | 1.36987i | ||||||
\(696\) | −5.64514e19 | −0.713526 | ||||||||
\(697\) | 5.41011e19 | 0.676982 | ||||||||
\(698\) | −9.52112e17 | −0.0117951 | ||||||||
\(699\) | − | 1.29362e20i | − | 1.58660i | ||||||
\(700\) | 3.05552e18i | 0.0371021i | ||||||||
\(701\) | − | 1.14615e20i | − | 1.37789i | −0.724812 | − | 0.688947i | \(-0.758073\pi\) | ||
0.724812 | − | 0.688947i | \(-0.241927\pi\) | |||||||
\(702\) | −9.86289e18 | −0.117394 | ||||||||
\(703\) | 6.64059e19i | 0.782563i | ||||||||
\(704\) | 8.63025e18 | + | 6.34754e18i | 0.100697 | + | 0.0740622i | ||||
\(705\) | 1.40684e20 | 1.62526 | ||||||||
\(706\) | − | 7.27462e19i | − | 0.832104i | ||||||
\(707\) | −1.72369e20 | −1.95220 | ||||||||
\(708\) | −8.12804e19 | −0.911492 | ||||||||
\(709\) | 4.19675e19 | 0.466003 | 0.233002 | − | 0.972476i | \(-0.425145\pi\) | ||||
0.233002 | + | 0.972476i | \(0.425145\pi\) | |||||||
\(710\) | − | 2.93988e18i | − | 0.0323237i | ||||||
\(711\) | 7.83885e19i | 0.853424i | ||||||||
\(712\) | 5.58957e18i | 0.0602585i | ||||||||
\(713\) | 9.66832e19 | 1.03211 | ||||||||
\(714\) | 6.32373e19i | 0.668476i | ||||||||
\(715\) | 3.01970e19 | − | 4.10565e19i | 0.316098 | − | 0.429773i | ||||
\(716\) | −2.29463e19 | −0.237860 | ||||||||
\(717\) | − | 1.68019e20i | − | 1.72475i | ||||||
\(718\) | 1.13513e20 | 1.15392 | ||||||||
\(719\) | −1.88410e18 | −0.0189671 | −0.00948356 | − | 0.999955i | \(-0.503019\pi\) | ||||
−0.00948356 | + | 0.999955i | \(0.503019\pi\) | |||||||
\(720\) | −1.87323e19 | −0.186751 | ||||||||
\(721\) | − | 1.17271e20i | − | 1.15782i | ||||||
\(722\) | 9.93316e18i | 0.0971241i | ||||||||
\(723\) | 1.33258e20i | 1.29040i | ||||||||
\(724\) | −4.93861e18 | −0.0473626 | ||||||||
\(725\) | 1.12334e19i | 0.106696i | ||||||||
\(726\) | −9.55951e19 | + | 2.98315e19i | −0.899248 | + | 0.280620i | ||||
\(727\) | −2.64591e19 | −0.246510 | −0.123255 | − | 0.992375i | \(-0.539333\pi\) | ||||
−0.123255 | + | 0.992375i | \(0.539333\pi\) | |||||||
\(728\) | − | 2.23374e19i | − | 0.206116i | ||||||
\(729\) | −5.58341e19 | −0.510278 | ||||||||
\(730\) | 2.76777e19 | 0.250536 | ||||||||
\(731\) | −6.48259e19 | −0.581202 | ||||||||
\(732\) | − | 8.55328e19i | − | 0.759547i | ||||||
\(733\) | − | 2.62616e19i | − | 0.230990i | −0.993308 | − | 0.115495i | \(-0.963155\pi\) | ||
0.993308 | − | 0.115495i | \(-0.0368454\pi\) | |||||||
\(734\) | − | 8.66730e19i | − | 0.755112i | ||||||
\(735\) | 1.63737e19 | 0.141298 | ||||||||
\(736\) | − | 3.47299e19i | − | 0.296865i | ||||||
\(737\) | −7.53884e18 | − | 5.54481e18i | −0.0638311 | − | 0.0469477i | ||||
\(738\) | −6.56560e19 | −0.550655 | ||||||||
\(739\) | 2.35064e20i | 1.95288i | 0.215800 | + | 0.976438i | \(0.430764\pi\) | ||||
−0.215800 | + | 0.976438i | \(0.569236\pi\) | |||||||
\(740\) | 4.93555e19 | 0.406175 | ||||||||
\(741\) | 8.39868e19 | 0.684674 | ||||||||
\(742\) | 8.33857e19 | 0.673386 | ||||||||
\(743\) | − | 2.17854e20i | − | 1.74279i | −0.490584 | − | 0.871394i | \(-0.663217\pi\) | ||
0.490584 | − | 0.871394i | \(-0.336783\pi\) | |||||||
\(744\) | 3.65283e19i | 0.289480i | ||||||||
\(745\) | 1.87234e20i | 1.46991i | ||||||||
\(746\) | −7.97040e19 | −0.619881 | ||||||||
\(747\) | 1.82468e19i | 0.140586i | ||||||||
\(748\) | 2.61416e19 | − | 3.55427e19i | 0.199536 | − | 0.271293i | ||||
\(749\) | −1.45250e20 | −1.09836 | ||||||||
\(750\) | 1.29774e20i | 0.972205i | ||||||||
\(751\) | −7.99894e19 | −0.593680 | −0.296840 | − | 0.954927i | \(-0.595933\pi\) | ||||
−0.296840 | + | 0.954927i | \(0.595933\pi\) | |||||||
\(752\) | −4.30202e19 | −0.316336 | ||||||||
\(753\) | −2.05960e20 | −1.50044 | ||||||||
\(754\) | − | 8.21221e19i | − | 0.592735i | ||||||
\(755\) | 6.28193e19i | 0.449226i | ||||||||
\(756\) | 2.23075e19i | 0.158051i | ||||||||
\(757\) | −1.22053e20 | −0.856794 | −0.428397 | − | 0.903591i | \(-0.640922\pi\) | ||||
−0.428397 | + | 0.903591i | \(0.640922\pi\) | |||||||
\(758\) | 1.05256e20i | 0.732083i | ||||||||
\(759\) | 2.61520e20 | + | 1.92347e20i | 1.80224 | + | 1.32554i | ||||
\(760\) | −4.63668e19 | −0.316601 | ||||||||
\(761\) | − | 1.68403e20i | − | 1.13935i | −0.821871 | − | 0.569674i | \(-0.807070\pi\) | ||
0.821871 | − | 0.569674i | \(-0.192930\pi\) | |||||||
\(762\) | 2.76536e20 | 1.85381 | ||||||||
\(763\) | −1.24567e20 | −0.827433 | ||||||||
\(764\) | 1.31992e20 | 0.868747 | ||||||||
\(765\) | 7.71469e19i | 0.503139i | ||||||||
\(766\) | − | 4.35572e19i | − | 0.281487i | ||||||
\(767\) | − | 1.18242e20i | − | 0.757189i | ||||||
\(768\) | 1.31214e19 | 0.0832632 | ||||||||
\(769\) | − | 4.56302e19i | − | 0.286925i | −0.989656 | − | 0.143462i | \(-0.954176\pi\) | ||
0.989656 | − | 0.143462i | \(-0.0458236\pi\) | |||||||
\(770\) | −9.28599e19 | − | 6.82984e19i | −0.578620 | − | 0.425574i | ||||
\(771\) | 1.09806e20 | 0.678024 | ||||||||
\(772\) | − | 3.22682e19i | − | 0.197449i | ||||||
\(773\) | 3.35365e19 | 0.203358 | 0.101679 | − | 0.994817i | \(-0.467579\pi\) | ||||
0.101679 | + | 0.994817i | \(0.467579\pi\) | |||||||
\(774\) | 7.86714e19 | 0.472748 | ||||||||
\(775\) | 7.26888e18 | 0.0432868 | ||||||||
\(776\) | 3.62843e19i | 0.214135i | ||||||||
\(777\) | 2.02202e20i | 1.18260i | ||||||||
\(778\) | − | 1.39368e20i | − | 0.807801i | ||||||
\(779\) | −1.62514e20 | −0.933530 | ||||||||
\(780\) | − | 6.24224e19i | − | 0.355368i | ||||||
\(781\) | −6.76951e18 | − | 4.97897e18i | −0.0381944 | − | 0.0280920i | ||||
\(782\) | −1.43031e20 | −0.799804 | ||||||||
\(783\) | 8.20123e19i | 0.454513i | ||||||||
\(784\) | −5.00697e18 | −0.0275019 | ||||||||
\(785\) | 2.13497e19 | 0.116226 | ||||||||
\(786\) | 2.86932e20 | 1.54818 | ||||||||
\(787\) | − | 2.81672e20i | − | 1.50633i | −0.657831 | − | 0.753165i | \(-0.728526\pi\) | ||
0.657831 | − | 0.753165i | \(-0.271474\pi\) | |||||||
\(788\) | 3.89090e19i | 0.206237i | ||||||||
\(789\) | 4.45254e20i | 2.33921i | ||||||||
\(790\) | 1.44211e20 | 0.750944 | ||||||||
\(791\) | 8.78591e19i | 0.453473i | ||||||||
\(792\) | −3.17249e19 | + | 4.31339e19i | −0.162302 | + | 0.220670i | ||||
\(793\) | 1.24428e20 | 0.630966 | ||||||||
\(794\) | 8.54677e19i | 0.429594i | ||||||||
\(795\) | 2.33024e20 | 1.16099 | ||||||||
\(796\) | 1.30563e20 | 0.644808 | ||||||||
\(797\) | −2.50971e20 | −1.22861 | −0.614307 | − | 0.789067i | \(-0.710564\pi\) | ||||
−0.614307 | + | 0.789067i | \(0.710564\pi\) | |||||||
\(798\) | − | 1.89958e20i | − | 0.921802i | ||||||
\(799\) | 1.77174e20i | 0.852261i | ||||||||
\(800\) | − | 2.61108e18i | − | 0.0124506i | ||||||
\(801\) | −2.79366e19 | −0.132052 | ||||||||
\(802\) | − | 1.93054e20i | − | 0.904602i | ||||||
\(803\) | 4.68747e19 | − | 6.37319e19i | 0.217736 | − | 0.296038i | ||||
\(804\) | −1.14621e19 | −0.0527802 | ||||||||
\(805\) | 3.73688e20i | 1.70584i | ||||||||
\(806\) | −5.31392e19 | −0.240475 | ||||||||
\(807\) | −3.07234e20 | −1.37834 | ||||||||
\(808\) | 1.47297e20 | 0.655112 | ||||||||
\(809\) | − | 1.67113e20i | − | 0.736834i | −0.929661 | − | 0.368417i | \(-0.879900\pi\) | ||
0.929661 | − | 0.368417i | \(-0.120100\pi\) | |||||||
\(810\) | 1.83177e20i | 0.800711i | ||||||||
\(811\) | − | 8.31549e19i | − | 0.360364i | −0.983633 | − | 0.180182i | \(-0.942331\pi\) | ||
0.983633 | − | 0.180182i | \(-0.0576687\pi\) | |||||||
\(812\) | −1.85741e20 | −0.798021 | ||||||||
\(813\) | − | 1.26438e20i | − | 0.538573i | ||||||
\(814\) | 8.35883e19 | − | 1.13648e20i | 0.353000 | − | 0.479946i | ||||
\(815\) | 3.72415e20 | 1.55928 | ||||||||
\(816\) | − | 5.40392e19i | − | 0.224325i | ||||||
\(817\) | 1.94730e20 | 0.801454 | ||||||||
\(818\) | −1.26972e20 | −0.518125 | ||||||||
\(819\) | 1.11642e20 | 0.451690 | ||||||||
\(820\) | 1.20787e20i | 0.484532i | ||||||||
\(821\) | − | 1.86972e20i | − | 0.743660i | −0.928301 | − | 0.371830i | \(-0.878730\pi\) | ||
0.928301 | − | 0.371830i | \(-0.121270\pi\) | |||||||
\(822\) | 2.50570e20i | 0.988158i | ||||||||
\(823\) | 1.33342e20 | 0.521397 | 0.260698 | − | 0.965420i | \(-0.416047\pi\) | ||||
0.260698 | + | 0.965420i | \(0.416047\pi\) | |||||||
\(824\) | 1.00213e20i | 0.388539i | ||||||||
\(825\) | 1.96617e19 | + | 1.44611e19i | 0.0755863 | + | 0.0555936i | ||||
\(826\) | −2.67435e20 | −1.01943 | ||||||||
\(827\) | − | 5.37762e19i | − | 0.203260i | −0.994822 | − | 0.101630i | \(-0.967594\pi\) | ||
0.994822 | − | 0.101630i | \(-0.0324057\pi\) | |||||||
\(828\) | 1.73580e20 | 0.650559 | ||||||||
\(829\) | 3.94236e20 | 1.46512 | 0.732562 | − | 0.680700i | \(-0.238324\pi\) | ||||
0.732562 | + | 0.680700i | \(0.238324\pi\) | |||||||
\(830\) | 3.35686e19 | 0.123705 | ||||||||
\(831\) | 6.46658e19i | 0.236302i | ||||||||
\(832\) | 1.90883e19i | 0.0691679i | ||||||||
\(833\) | 2.06206e19i | 0.0740947i | ||||||||
\(834\) | −3.75630e20 | −1.33844 | ||||||||
\(835\) | 3.44898e18i | 0.0121867i | ||||||||
\(836\) | −7.85266e19 | + | 1.06766e20i | −0.275152 | + | 0.374103i | ||||
\(837\) | 5.30681e19 | 0.184398 | ||||||||
\(838\) | 3.53520e20i | 1.21816i | ||||||||
\(839\) | 1.55689e19 | 0.0532015 | 0.0266007 | − | 0.999646i | \(-0.491532\pi\) | ||||
0.0266007 | + | 0.999646i | \(0.491532\pi\) | |||||||
\(840\) | −1.41184e20 | −0.478445 | ||||||||
\(841\) | −3.85307e20 | −1.29490 | ||||||||
\(842\) | 2.04330e19i | 0.0681000i | ||||||||
\(843\) | − | 7.40515e20i | − | 2.44760i | ||||||
\(844\) | 1.41987e20i | 0.465427i | ||||||||
\(845\) | −2.05769e20 | −0.668933 | ||||||||
\(846\) | − | 2.15015e20i | − | 0.693228i | ||||||
\(847\) | −3.14534e20 | + | 9.81540e19i | −1.00574 | + | 0.313851i | ||||
\(848\) | −7.12569e19 | −0.225973 | ||||||||
\(849\) | 1.14671e20i | 0.360660i | ||||||||
\(850\) | −1.07534e19 | −0.0335440 | ||||||||
\(851\) | −4.57345e20 | −1.41494 | ||||||||
\(852\) | −1.02924e19 | −0.0315819 | ||||||||
\(853\) | − | 5.69284e19i | − | 0.173255i | −0.996241 | − | 0.0866274i | \(-0.972391\pi\) | ||
0.996241 | − | 0.0866274i | \(-0.0276090\pi\) | |||||||
\(854\) | − | 2.81426e20i | − | 0.849493i | ||||||
\(855\) | − | 2.31741e20i | − | 0.693809i | ||||||
\(856\) | 1.24123e20 | 0.368584 | ||||||||
\(857\) | − | 1.82987e20i | − | 0.538958i | −0.963006 | − | 0.269479i | \(-0.913148\pi\) | ||
0.963006 | − | 0.269479i | \(-0.0868515\pi\) | |||||||
\(858\) | −1.43737e20 | − | 1.05718e20i | −0.419911 | − | 0.308844i | ||||
\(859\) | 3.81449e20 | 1.10531 | 0.552655 | − | 0.833410i | \(-0.313615\pi\) | ||||
0.552655 | + | 0.833410i | \(0.313615\pi\) | |||||||
\(860\) | − | 1.44731e20i | − | 0.415981i | ||||||
\(861\) | −4.94846e20 | −1.41074 | ||||||||
\(862\) | −2.50282e20 | −0.707748 | ||||||||
\(863\) | −1.41862e20 | −0.397916 | −0.198958 | − | 0.980008i | \(-0.563756\pi\) | ||||
−0.198958 | + | 0.980008i | \(0.563756\pi\) | |||||||
\(864\) | − | 1.90628e19i | − | 0.0530384i | ||||||
\(865\) | − | 4.81517e20i | − | 1.32892i | ||||||
\(866\) | − | 1.56947e20i | − | 0.429662i | ||||||
\(867\) | 2.68022e20 | 0.727842 | ||||||||
\(868\) | 1.20188e20i | 0.323760i | ||||||||
\(869\) | 2.44235e20 | − | 3.32066e20i | 0.652632 | − | 0.887333i | ||||
\(870\) | −5.19057e20 | −1.37588 | ||||||||
\(871\) | − | 1.66744e19i | − | 0.0438452i | ||||||
\(872\) | 1.06449e20 | 0.277667 | ||||||||
\(873\) | −1.81349e20 | −0.469261 | ||||||||
\(874\) | 4.29650e20 | 1.10290 | ||||||||
\(875\) | 4.26991e20i | 1.08733i | ||||||||
\(876\) | − | 9.68982e19i | − | 0.244786i | ||||||
\(877\) | 4.00254e19i | 0.100309i | 0.998741 | + | 0.0501544i | \(0.0159713\pi\) | ||||
−0.998741 | + | 0.0501544i | \(0.984029\pi\) | |||||||
\(878\) | −1.25041e20 | −0.310878 | ||||||||
\(879\) | − | 2.17426e20i | − | 0.536277i | ||||||
\(880\) | 7.93531e19 | + | 5.83641e19i | 0.194171 | + | 0.142813i | ||||
\(881\) | 7.93534e20 | 1.92634 | 0.963172 | − | 0.268885i | \(-0.0866552\pi\) | ||||
0.963172 | + | 0.268885i | \(0.0866552\pi\) | |||||||
\(882\) | − | 2.50248e19i | − | 0.0602685i | ||||||
\(883\) | −6.32658e20 | −1.51162 | −0.755812 | − | 0.654788i | \(-0.772758\pi\) | ||||
−0.755812 | + | 0.654788i | \(0.772758\pi\) | |||||||
\(884\) | 7.86131e19 | 0.186350 | ||||||||
\(885\) | −7.47355e20 | −1.75762 | ||||||||
\(886\) | 1.61868e20i | 0.377680i | ||||||||
\(887\) | 2.94341e20i | 0.681373i | 0.940177 | + | 0.340686i | \(0.110659\pi\) | ||||
−0.940177 | + | 0.340686i | \(0.889341\pi\) | |||||||
\(888\) | − | 1.72791e20i | − | 0.396854i | ||||||
\(889\) | 9.09878e20 | 2.07334 | ||||||||
\(890\) | 5.13948e19i | 0.116196i | ||||||||
\(891\) | 4.21792e20 | + | 3.10228e20i | 0.946138 | + | 0.695883i | ||||
\(892\) | −2.80731e20 | −0.624794 | ||||||||
\(893\) | − | 5.32212e20i | − | 1.17523i | ||||||
\(894\) | 6.55496e20 | 1.43618 | ||||||||
\(895\) | −2.10986e20 | −0.458661 | ||||||||
\(896\) | 4.31732e19 | 0.0931232 | ||||||||
\(897\) | 5.78427e20i | 1.23795i | ||||||||
\(898\) | 2.18006e20i | 0.462950i | ||||||||
\(899\) | 4.41865e20i | 0.931047i | ||||||||
\(900\) | 1.30502e19 | 0.0272846 | ||||||||
\(901\) | 2.93464e20i | 0.608809i | ||||||||
\(902\) | 2.78130e20 | + | 2.04564e20i | 0.572534 | + | 0.421098i | ||||
\(903\) | 5.92943e20 | 1.21115 | ||||||||
\(904\) | − | 7.50797e19i | − | 0.152175i | ||||||
\(905\) | −4.54094e19 | −0.0913284 | ||||||||
\(906\) | 2.19927e20 | 0.438917 | ||||||||
\(907\) | 5.43443e20 | 1.07623 | 0.538113 | − | 0.842873i | \(-0.319138\pi\) | ||||
0.538113 | + | 0.842873i | \(0.319138\pi\) | |||||||
\(908\) | 2.54391e20i | 0.499920i | ||||||||
\(909\) | 7.36191e20i | 1.43563i | ||||||||
\(910\) | − | 2.05387e20i | − | 0.397451i | ||||||
\(911\) | −4.55809e20 | −0.875294 | −0.437647 | − | 0.899147i | \(-0.644188\pi\) | ||||
−0.437647 | + | 0.899147i | \(0.644188\pi\) | |||||||
\(912\) | 1.62328e20i | 0.309335i | ||||||||
\(913\) | 5.68516e19 | − | 7.72966e19i | 0.107510 | − | 0.146172i | ||||
\(914\) | −3.68904e20 | −0.692294 | ||||||||
\(915\) | − | 7.86454e20i | − | 1.46462i | ||||||
\(916\) | 1.22296e20 | 0.226019 | ||||||||
\(917\) | 9.44085e20 | 1.73151 | ||||||||
\(918\) | −7.85079e19 | −0.142894 | ||||||||
\(919\) | 5.46063e20i | 0.986356i | 0.869928 | + | 0.493178i | \(0.164165\pi\) | ||||
−0.869928 | + | 0.493178i | \(0.835835\pi\) | |||||||
\(920\) | − | 3.19334e20i | − | 0.572440i | ||||||
\(921\) | − | 1.23393e21i | − | 2.19520i | ||||||
\(922\) | −2.68138e20 | −0.473416 | ||||||||
\(923\) | − | 1.49728e19i | − | 0.0262355i | ||||||
\(924\) | −2.39109e20 | + | 3.25098e20i | −0.415808 | + | 0.565341i | ||||
\(925\) | −3.43843e19 | −0.0593428 | ||||||||
\(926\) | − | 3.65874e20i | − | 0.626693i | ||||||
\(927\) | −5.00865e20 | −0.851456 | ||||||||
\(928\) | 1.58724e20 | 0.267798 | ||||||||
\(929\) | −2.23731e20 | −0.374641 | −0.187321 | − | 0.982299i | \(-0.559980\pi\) | ||||
−0.187321 | + | 0.982299i | \(0.559980\pi\) | |||||||
\(930\) | 3.35869e20i | 0.558199i | ||||||||
\(931\) | − | 6.19422e19i | − | 0.102174i | ||||||
\(932\) | 3.63727e20i | 0.595475i | ||||||||
\(933\) | −1.55583e21 | −2.52809 | ||||||||
\(934\) | 5.15875e20i | 0.831987i | ||||||||
\(935\) | 2.40366e20 | − | 3.26807e20i | 0.384762 | − | 0.523130i | ||||
\(936\) | −9.54032e19 | −0.151577 | ||||||||
\(937\) | 8.55067e20i | 1.34841i | 0.738543 | + | 0.674206i | \(0.235514\pi\) | ||||
−0.738543 | + | 0.674206i | \(0.764486\pi\) | |||||||
\(938\) | −3.77134e19 | −0.0590304 | ||||||||
\(939\) | 9.72059e20 | 1.51020 | ||||||||
\(940\) | −3.95561e20 | −0.609984 | ||||||||
\(941\) | 9.05540e20i | 1.38605i | 0.720911 | + | 0.693027i | \(0.243723\pi\) | ||||
−0.720911 | + | 0.693027i | \(0.756277\pi\) | |||||||
\(942\) | − | 7.47442e19i | − | 0.113559i | ||||||
\(943\) | − | 1.11925e21i | − | 1.68790i | ||||||
\(944\) | 2.28536e20 | 0.342097 | ||||||||
\(945\) | 2.05112e20i | 0.304768i | ||||||||
\(946\) | −3.33265e20 | − | 2.45116e20i | −0.491532 | − | 0.361521i | ||||
\(947\) | −6.85540e20 | −1.00365 | −0.501826 | − | 0.864969i | \(-0.667338\pi\) | ||||
−0.501826 | + | 0.864969i | \(0.667338\pi\) | |||||||
\(948\) | − | 5.04875e20i | − | 0.733711i | ||||||
\(949\) | 1.40962e20 | 0.203347 | ||||||||
\(950\) | 3.23022e19 | 0.0462558 | ||||||||
\(951\) | 9.32363e20 | 1.32532 | ||||||||
\(952\) | − | 1.77804e20i | − | 0.250890i | ||||||
\(953\) | − | 6.24466e20i | − | 0.874698i | −0.899292 | − | 0.437349i | \(-0.855917\pi\) | ||
0.899292 | − | 0.437349i | \(-0.144083\pi\) | |||||||
\(954\) | − | 3.56141e20i | − | 0.495204i | ||||||
\(955\) | 1.21363e21 | 1.67519 | ||||||||
\(956\) | 4.72419e20i | 0.647325i | ||||||||
\(957\) | −8.79073e20 | + | 1.19521e21i | −1.19575 | + | 1.62577i | ||||
\(958\) | −6.70067e20 | −0.904815 | ||||||||
\(959\) | 8.24444e20i | 1.10517i | ||||||||
\(960\) | 1.20649e20 | 0.160555 | ||||||||
\(961\) | −4.71024e20 | −0.622271 | ||||||||
\(962\) | 2.51367e20 | 0.329672 | ||||||||
\(963\) | 6.20366e20i | 0.807726i | ||||||||
\(964\) | − | 3.74680e20i | − | 0.484307i | ||||||
\(965\) | − | 2.96699e20i | − | 0.380737i | ||||||
\(966\) | 1.30826e21 | 1.66669 | ||||||||
\(967\) | 1.81318e20i | 0.229327i | 0.993404 | + | 0.114664i | \(0.0365790\pi\) | ||||
−0.993404 | + | 0.114664i | \(0.963421\pi\) | |||||||
\(968\) | 2.68784e20 | − | 8.38771e19i | 0.337502 | − | 0.105321i | ||||
\(969\) | 6.68530e20 | 0.833401 | ||||||||
\(970\) | 3.33626e20i | 0.412912i | ||||||||
\(971\) | −5.19816e20 | −0.638726 | −0.319363 | − | 0.947632i | \(-0.603469\pi\) | ||||
−0.319363 | + | 0.947632i | \(0.603469\pi\) | |||||||
\(972\) | 5.18324e20 | 0.632321 | ||||||||
\(973\) | −1.23593e21 | −1.49693 | ||||||||
\(974\) | 8.83635e20i | 1.06258i | ||||||||
\(975\) | 4.34876e19i | 0.0519198i | ||||||||
\(976\) | 2.40492e20i | 0.285070i | ||||||||
\(977\) | 3.78331e20 | 0.445257 | 0.222628 | − | 0.974903i | \(-0.428536\pi\) | ||||
0.222628 | + | 0.974903i | \(0.428536\pi\) | |||||||
\(978\) | − | 1.30381e21i | − | 1.52350i | ||||||
\(979\) | 1.18344e20 | + | 8.70420e19i | 0.137299 | + | 0.100983i | ||||
\(980\) | −4.60379e19 | −0.0530314 | ||||||||
\(981\) | 5.32030e20i | 0.608489i | ||||||||
\(982\) | 5.51930e20 | 0.626764 | ||||||||
\(983\) | −7.85688e20 | −0.885881 | −0.442941 | − | 0.896551i | \(-0.646065\pi\) | ||||
−0.442941 | + | 0.896551i | \(0.646065\pi\) | |||||||
\(984\) | 4.22869e20 | 0.473413 | ||||||||
\(985\) | 3.57759e20i | 0.397683i | ||||||||
\(986\) | − | 6.53687e20i | − | 0.721492i | ||||||
\(987\) | − | 1.62056e21i | − | 1.77600i | ||||||
\(988\) | −2.36145e20 | −0.256969 | ||||||||
\(989\) | 1.34113e21i | 1.44909i | ||||||||
\(990\) | −2.91703e20 | + | 3.96606e20i | −0.312964 | + | 0.425513i | ||||
\(991\) | −1.09370e21 | −1.16515 | −0.582574 | − | 0.812778i | \(-0.697954\pi\) | ||||
−0.582574 | + | 0.812778i | \(0.697954\pi\) | |||||||
\(992\) | − | 1.02706e20i | − | 0.108646i | ||||||
\(993\) | −6.19877e20 | −0.651120 | ||||||||
\(994\) | −3.38648e19 | −0.0353219 | ||||||||
\(995\) | 1.20050e21 | 1.24337 | ||||||||
\(996\) | − | 1.17522e20i | − | 0.120866i | ||||||
\(997\) | − | 1.11125e21i | − | 1.13487i | −0.823418 | − | 0.567435i | \(-0.807936\pi\) | ||
0.823418 | − | 0.567435i | \(-0.192064\pi\) | |||||||
\(998\) | − | 1.27031e21i | − | 1.28824i | ||||||
\(999\) | −2.51030e20 | −0.252795 |
(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 | 22.15.b.a.21.13 | yes | 14 | |
4.3 | odd | 2 | 176.15.h.e.65.3 | 14 | |||
11.10 | odd | 2 | inner | 22.15.b.a.21.6 | ✓ | 14 | |
44.43 | even | 2 | 176.15.h.e.65.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.15.b.a.21.6 | ✓ | 14 | 11.10 | odd | 2 | inner | |
22.15.b.a.21.13 | yes | 14 | 1.1 | even | 1 | trivial | |
176.15.h.e.65.3 | 14 | 4.3 | odd | 2 | |||
176.15.h.e.65.4 | 14 | 44.43 | even | 2 |