Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,15,Mod(65,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("176.65");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.h (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: | \(218.818983947\) |
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: | \( 2^{64}\cdot 3^{10}\cdot 11^{7} \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.4 | ||
Root | \(-2599.55 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 176.65 |
Dual form | 176.15.h.e.65.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/176\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(133\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2913.55 | −1.33221 | −0.666106 | − | 0.745857i | \(-0.732040\pi\) | ||||
−0.666106 | + | 0.745857i | \(0.732040\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −75323.6 | −0.964141 | −0.482071 | − | 0.876132i | \(-0.660115\pi\) | ||||
−0.482071 | + | 0.876132i | \(0.660115\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 867659.i | 1.05357i | 0.849999 | + | 0.526784i | \(0.176603\pi\) | ||||
−0.849999 | + | 0.526784i | \(0.823397\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.70579e6 | 0.774788 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.56983e7 | − | 1.15461e7i | 0.805572 | − | 0.592497i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.47214e7i | 0.553343i | 0.960965 | + | 0.276671i | \(0.0892314\pi\) | ||||
−0.960965 | + | 0.276671i | \(0.910769\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.19459e8 | 1.28444 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.76380e8i | 0.673542i | 0.941587 | + | 0.336771i | \(0.109335\pi\) | ||||
−0.941587 | + | 0.336771i | \(0.890665\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.30217e8i | 0.928787i | 0.885629 | + | 0.464394i | \(0.153728\pi\) | ||||
−0.885629 | + | 0.464394i | \(0.846272\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.52797e9i | − | 1.40358i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.71780e9 | 1.67932 | 0.839661 | − | 0.543111i | \(-0.182754\pi\) | ||||
0.839661 | + | 0.543111i | \(0.182754\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.29878e8 | −0.0704312 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.13842e9 | 0.300030 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.61317e10i | 1.51489i | 0.652898 | + | 0.757446i | \(0.273553\pi\) | ||||
−0.652898 | + | 0.757446i | \(0.726447\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.69092e10 | 0.614597 | 0.307298 | − | 0.951613i | \(-0.400575\pi\) | ||||
0.307298 | + | 0.951613i | \(0.400575\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.57378e10 | + | 3.36401e10i | −1.07319 | + | 0.789332i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 6.53552e10i | − | 1.01579i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.99862e10 | 0.842564 | 0.421282 | − | 0.906930i | \(-0.361580\pi\) | ||||
0.421282 | + | 0.906930i | \(0.361580\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.01163e11i | − | 0.737170i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.95749e11i | − | 1.00511i | −0.864546 | − | 0.502553i | \(-0.832394\pi\) | ||
0.864546 | − | 0.502553i | \(-0.167606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.34553e11i | − | 0.862904i | −0.902136 | − | 0.431452i | \(-0.858002\pi\) | ||
0.902136 | − | 0.431452i | \(-0.141998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.79133e11 | −0.747005 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.41052e11 | 1.26534 | 0.632671 | − | 0.774421i | \(-0.281959\pi\) | ||||
0.632671 | + | 0.774421i | \(0.281959\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.46096e10 | −0.110008 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 8.05247e11i | − | 0.897301i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.06181e12 | −0.903891 | −0.451946 | − | 0.892046i | \(-0.649270\pi\) | ||||
−0.451946 | + | 0.892046i | \(0.649270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18245e12 | + | 8.69693e11i | −0.776686 | + | 0.571251i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.41888e12i | − | 1.23734i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.40545e12 | −1.36839 | −0.684195 | − | 0.729299i | \(-0.739846\pi\) | ||||
−0.684195 | + | 0.729299i | \(0.739846\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.58361e12i | − | 1.14028i | −0.821547 | − | 0.570140i | \(-0.806889\pi\) | ||
0.821547 | − | 0.570140i | \(-0.193111\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.21536e12i | 0.816292i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.61534e12i | − | 0.533501i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.80232e11 | −0.0792370 | −0.0396185 | − | 0.999215i | \(-0.512614\pi\) | ||||
−0.0396185 | + | 0.999215i | \(0.512614\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.66591e13 | −2.23721 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.31225e11 | −0.0474128 | −0.0237064 | − | 0.999719i | \(-0.507547\pi\) | ||||
−0.0237064 | + | 0.999719i | \(0.507547\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.05979e12i | − | 0.367488i | −0.982974 | − | 0.183744i | \(-0.941178\pi\) | ||
0.982974 | − | 0.183744i | \(-0.0588218\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.25247e12 | 0.0938293 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00181e13 | + | 1.36208e13i | 0.624237 | + | 0.848726i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.11530e13i | 1.10149i | 0.834672 | + | 0.550747i | \(0.185657\pi\) | ||||
−0.834672 | + | 0.550747i | \(0.814343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.68686e13 | −1.17449 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.92388e12i | 0.181452i | 0.995876 | + | 0.0907258i | \(0.0289187\pi\) | ||||
−0.995876 | + | 0.0907258i | \(0.971081\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.08180e13i | − | 0.649390i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.61359e13i | − | 2.01816i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.53865e12 | −0.170437 | −0.0852185 | − | 0.996362i | \(-0.527159\pi\) | ||||
−0.0852185 | + | 0.996362i | \(0.527159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.01264e13 | −0.582985 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.92656e13 | −0.818773 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.25349e13i | − | 0.895482i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.89366e13 | −0.605664 | −0.302832 | − | 0.953044i | \(-0.597932\pi\) | ||||
−0.302832 | + | 0.953044i | \(0.597932\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.81746e13 | − | 4.27874e13i | 0.624148 | − | 0.459060i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.98660e14i | − | 1.85294i | −0.376373 | − | 0.926468i | \(-0.622829\pi\) | ||
0.376373 | − | 0.926468i | \(-0.377171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.35157e14 | 1.09895 | 0.549477 | − | 0.835509i | \(-0.314827\pi\) | ||||
0.549477 | + | 0.835509i | \(0.314827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.90415e14i | 1.35325i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.67405e14i | 1.04251i | 0.853400 | + | 0.521256i | \(0.174536\pi\) | ||||
−0.853400 | + | 0.521256i | \(0.825464\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.43567e14i | − | 0.785362i | −0.919675 | − | 0.392681i | \(-0.871548\pi\) | ||
0.919675 | − | 0.392681i | \(-0.128452\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.33044e14 | −1.12247 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.01260e14 | 0.430416 | 0.215208 | − | 0.976568i | \(-0.430957\pi\) | ||||
0.215208 | + | 0.976568i | \(0.430957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.30685e14 | −1.61910 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.28670e14i | 0.428723i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.39804e14 | −0.709623 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.13125e14 | − | 3.62509e14i | 0.297893 | − | 0.954599i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.70323e14i | 1.33901i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.92118e14 | 1.03205 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.04866e15i | − | 1.96792i | −0.178381 | − | 0.983962i | \(-0.557086\pi\) | ||
0.178381 | − | 0.983962i | \(-0.442914\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.83382e14i | 1.14957i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.08808e15i | − | 1.64347i | −0.569867 | − | 0.821737i | \(-0.693005\pi\) | ||
0.569867 | − | 0.821737i | \(-0.306995\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.20345e14 | −0.978541 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.36397e14 | −0.289272 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.50193e14 | 1.04898 | 0.524491 | − | 0.851416i | \(-0.324256\pi\) | ||||
0.524491 | + | 0.851416i | \(0.324256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.42444e15i | 1.42082i | 0.703788 | + | 0.710410i | \(0.251491\pi\) | ||||
−0.703788 | + | 0.710410i | \(0.748509\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.86773e15 | −1.68570 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00897e14 | + | 5.45069e14i | 0.327854 | + | 0.445758i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.96833e15i | − | 1.46057i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.17379e14 | 0.146553 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.48573e15i | 1.52458i | 0.647238 | + | 0.762288i | \(0.275924\pi\) | ||||
−0.647238 | + | 0.762288i | \(0.724076\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.33993e14i | − | 0.465933i | −0.972485 | − | 0.232967i | \(-0.925157\pi\) | ||
0.972485 | − | 0.232967i | \(-0.0748433\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.02421e15i | 0.521852i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.27366e15 | −0.592558 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.83439e14 | −0.120549 | −0.0602744 | − | 0.998182i | \(-0.519198\pi\) | ||||
−0.0602744 | + | 0.998182i | \(0.519198\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.09364e15 | 1.20417 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.96110e15i | 1.76928i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.94421e15 | 1.61727 | 0.808636 | − | 0.588309i | \(-0.200206\pi\) | ||||
0.808636 | + | 0.588309i | \(0.200206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.44513e15 | − | 2.53389e15i | 1.03471 | − | 0.761028i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.57889e13i | − | 0.0126399i | −0.999980 | − | 0.00631997i | \(-0.997988\pi\) | ||
0.999980 | − | 0.00631997i | \(-0.00201172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.73180e15 | 0.693812 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.07661e15i | 0.719613i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.39265e15i | − | 1.37835i | −0.724597 | − | 0.689173i | \(-0.757974\pi\) | ||
0.724597 | − | 0.689173i | \(-0.242026\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.72988e14i | − | 0.0742042i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.92192e15 | 1.82298 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.80106e15 | −0.475719 | −0.237860 | − | 0.971300i | \(-0.576446\pi\) | ||||
−0.237860 | + | 0.971300i | \(0.576446\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.02858e14 | 0.0947251 | 0.0473626 | − | 0.998878i | \(-0.484918\pi\) | ||||
0.0473626 | + | 0.998878i | \(0.484918\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.04410e16i | 1.51909i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.02484e15 | −0.812351 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.19112e15 | + | 4.33871e15i | 0.399072 | + | 0.542587i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.72308e15i | 0.316103i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.61123e16 | 1.73749 | 0.868747 | − | 0.495257i | \(-0.164926\pi\) | ||||
0.868747 | + | 0.495257i | \(0.164926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.93899e15i | − | 0.394897i | −0.980313 | − | 0.197449i | \(-0.936734\pi\) | ||
0.980313 | − | 0.197449i | \(-0.0632656\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.61992e15i | 0.710736i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.74963e15i | 0.412474i | 0.978502 | + | 0.206237i | \(0.0661218\pi\) | ||||
−0.978502 | + | 0.206237i | \(0.933878\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.59379e16 | 1.28962 | 0.644808 | − | 0.764345i | \(-0.276937\pi\) | ||||
0.644808 | + | 0.764345i | \(0.276937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.39918e15 | 0.105560 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.26734e16 | −1.59604 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.47445e16i | 0.969065i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.11889e16 | 1.30112 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.58576e15 | + | 1.30330e16i | 0.550304 | + | 0.748205i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.73324e16i | − | 0.930854i | −0.885086 | − | 0.465427i | \(-0.845901\pi\) | ||
0.885086 | − | 0.465427i | \(-0.154099\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.25639e15 | 0.0631639 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.76674e16i | 0.831961i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.46714e16i | 0.647520i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.18284e16i | 0.489572i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.59633e15 | −0.372700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.42689e16 | −1.24959 | −0.624794 | − | 0.780790i | \(-0.714817\pi\) | ||||
−0.624794 | + | 0.780790i | \(0.714817\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.59304e15 | −0.0545693 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 3.10536e16i | − | 0.999840i | −0.866072 | − | 0.499920i | \(-0.833363\pi\) | ||
0.866072 | − | 0.499920i | \(-0.166637\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.49288e16 | −0.452039 | −0.226019 | − | 0.974123i | \(-0.572571\pi\) | ||||
−0.226019 | + | 0.974123i | \(0.572571\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.91881e16 | − | 3.96848e16i | −0.831616 | − | 1.13068i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.44002e16i | 1.19095i | 0.803374 | + | 0.595475i | \(0.203036\pi\) | ||||
−0.803374 | + | 0.595475i | \(0.796964\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.82863e16 | −1.21997 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.16302e16i | − | 1.46742i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.76683e16i | − | 1.29465i | −0.762214 | − | 0.647325i | \(-0.775888\pi\) | ||
0.762214 | − | 0.647325i | \(-0.224112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.57373e16i | − | 0.968614i | −0.874898 | − | 0.484307i | \(-0.839072\pi\) | ||
0.874898 | − | 0.484307i | \(-0.160928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.32720e16 | 1.26464 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.61986e15 | 0.106063 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.88263e16 | −0.513938 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.43459e16i | − | 0.241732i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.06905e16 | 1.12628 | 0.563138 | − | 0.826363i | \(-0.309594\pi\) | ||||
0.563138 | + | 0.826363i | \(0.309594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.97599e16 | − | 6.60183e16i | 1.35282 | − | 0.994994i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.06541e16i | 0.865125i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.76880e16 | 0.508946 | 0.254473 | − | 0.967080i | \(-0.418098\pi\) | ||||
0.254473 | + | 0.967080i | \(0.418098\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.94008e16i | 0.887699i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.68385e16i | 1.17372i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.52822e17i | 1.75588i | 0.478769 | + | 0.877941i | \(0.341083\pi\) | ||||
−0.478769 | + | 0.877941i | \(0.658917\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.99794e16 | 0.871479 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.19642e16 | 0.227058 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.05450e17 | −1.03462 | −0.517311 | − | 0.855797i | \(-0.673067\pi\) | ||||
−0.517311 | + | 0.855797i | \(0.673067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.33967e16i | − | 0.404270i | −0.979358 | − | 0.202135i | \(-0.935212\pi\) | ||
0.979358 | − | 0.202135i | \(-0.0647880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.77746e16 | 0.776659 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.74837e15 | + | 4.96342e15i | −0.0567375 | + | 0.0417303i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.21949e16i | − | 0.177376i | −0.996059 | − | 0.0886879i | \(-0.971733\pi\) | ||
0.996059 | − | 0.0886879i | \(-0.0282674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.26617e16 | 0.476182 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.54163e17i | 1.83725i | 0.395132 | + | 0.918624i | \(0.370699\pi\) | ||||
−0.395132 | + | 0.918624i | \(0.629301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.93577e16i | 0.270723i | 0.990796 | + | 0.135361i | \(0.0432196\pi\) | ||||
−0.990796 | + | 0.135361i | \(0.956780\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.82198e17i | 1.19297i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.69843e17 | 1.05895 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.19917e16 | 0.546341 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.42579e17 | 0.806873 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.46259e16i | 0.402547i | 0.979535 | + | 0.201273i | \(0.0645079\pi\) | ||||
−0.979535 | + | 0.201273i | \(0.935492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.56510e17 | 1.31932 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.92680e16 | − | 3.62365e16i | 0.241696 | − | 0.177767i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.98530e17i | 0.929241i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.03512e17 | 0.909128 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.78805e17i | 2.46850i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.69930e17i | 1.09939i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.23515e17i | − | 1.64778i | −0.566747 | − | 0.823892i | \(-0.691798\pi\) | ||
0.566747 | − | 0.823892i | \(-0.308202\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.93787e17 | −1.46404 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.34000e17 | 1.89766 | 0.948831 | − | 0.315785i | \(-0.102268\pi\) | ||||
0.948831 | + | 0.315785i | \(0.102268\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.33634e17 | 1.13360 | 0.566801 | − | 0.823855i | \(-0.308181\pi\) | ||||
0.566801 | + | 0.823855i | \(0.308181\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 2.42192e17i | − | 0.787021i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.20010e17 | 0.994829 | 0.497414 | − | 0.867513i | \(-0.334283\pi\) | ||||
0.497414 | + | 0.867513i | \(0.334283\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.01719e17 | + | 4.10224e17i | 0.897569 | + | 1.22035i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 4.87741e17i | − | 1.38885i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.29456e17 | −0.625577 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.49260e16i | − | 0.0389726i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.18290e17i | 1.04627i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.56214e17i | 1.33313i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.12757e17 | 0.488751 | 0.244375 | − | 0.969681i | \(-0.421417\pi\) | ||||
0.244375 | + | 0.969681i | \(0.421417\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.96412e17 | 0.652808 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.61728e16 | 0.0763956 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.14484e17i | 0.637074i | 0.947910 | + | 0.318537i | \(0.103191\pi\) | ||||
−0.947910 | + | 0.318537i | \(0.896809\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.95025e17 | −0.573405 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.65446e17 | − | 1.95235e17i | 0.495102 | − | 0.364147i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.23731e17i | 0.937668i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.25482e18 | 2.15699 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.11559e17i | − | 0.514321i | −0.966369 | − | 0.257161i | \(-0.917213\pi\) | ||
0.966369 | − | 0.257161i | \(-0.0827870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.05194e16i | − | 0.0166807i | −0.999965 | − | 0.00834036i | \(-0.997345\pi\) | ||
0.999965 | − | 0.00834036i | \(-0.00265485\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.08971e17i | 0.166020i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.03740e17 | −1.17677 | −0.588386 | − | 0.808580i | \(-0.700237\pi\) | ||||
−0.588386 | + | 0.808580i | \(0.700237\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.24814e16 | 0.0457126 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.98680e17 | 0.945368 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1.25415e18i | − | 1.63189i | −0.578133 | − | 0.815943i | \(-0.696218\pi\) | ||
0.578133 | − | 0.815943i | \(-0.303782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.09747e17 | 0.137354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.29595e17 | + | 1.05619e18i | −0.396857 | + | 1.27173i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.05798e17i | 0.354311i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.57611e17 | 1.06789 | 0.533945 | − | 0.845519i | \(-0.320709\pi\) | ||||
0.533945 | + | 0.845519i | \(0.320709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 7.25403e17i | − | 0.778744i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.21290e17i | − | 0.952312i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.80613e17i | − | 0.876644i | −0.898818 | − | 0.438322i | \(-0.855573\pi\) | ||
0.898818 | − | 0.438322i | \(-0.144427\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.43381e18 | −1.37491 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.07330e17 | −0.838254 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.16292e18 | −1.03532 | −0.517661 | − | 0.855586i | \(-0.673197\pi\) | ||||
−0.517661 | + | 0.855586i | \(0.673197\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.05532e18i | 2.62169i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.81244e17 | 0.398083 | 0.199042 | − | 0.979991i | \(-0.436217\pi\) | ||||
0.199042 | + | 0.979991i | \(0.436217\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.54597e17 | − | 1.02597e18i | −0.601853 | − | 0.818292i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 8.69204e17i | − | 0.668567i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.53981e18 | −1.14240 | −0.571202 | − | 0.820810i | \(-0.693523\pi\) | ||||
−0.571202 | + | 0.820810i | \(0.693523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.58029e18i | 1.13109i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.17018e18i | 2.18945i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.59332e18i | − | 1.06200i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.44294e17 | 0.607538 | 0.303769 | − | 0.952746i | \(-0.401755\pi\) | ||||
0.303769 | + | 0.952746i | \(0.401755\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.09876e18 | 1.30362 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.13296e18 | −1.27930 | −0.639651 | − | 0.768666i | \(-0.720921\pi\) | ||||
−0.639651 | + | 0.768666i | \(0.720921\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.87111e17i | 0.340083i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.02384e18 | 1.13238 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.25565e18 | − | 9.23529e17i | 0.678746 | − | 0.499217i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.40285e18i | − | 0.732739i | −0.930469 | − | 0.366369i | \(-0.880601\pi\) | ||
0.930469 | − | 0.366369i | \(-0.119399\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.76843e18 | −1.39747 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.95477e18i | − | 1.44169i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3.70884e17i | − | 0.174945i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.15016e18i | − | 1.89283i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.90588e18 | −1.72275 | −0.861373 | − | 0.507974i | \(-0.830395\pi\) | ||||
−0.861373 | + | 0.507974i | \(0.830395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.25755e17 | 0.0963080 | 0.0481540 | − | 0.998840i | \(-0.484666\pi\) | ||||
0.0481540 | + | 0.998840i | \(0.484666\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.37560e18 | 0.980372 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.18810e17i | − | 0.0474384i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.10935e18 | 1.20136 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.16803e18 | − | 1.58808e18i | −0.436771 | − | 0.593844i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.76525e18i | 1.00091i | 0.865763 | + | 0.500454i | \(0.166833\pi\) | ||||
−0.865763 | + | 0.500454i | \(0.833167\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.73403e18 | −0.607633 | −0.303817 | − | 0.952731i | \(-0.598261\pi\) | ||||
−0.303817 | + | 0.952731i | \(0.598261\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.73483e18i | 1.94579i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.74701e18i | 1.55973i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.38152e18i | 0.439648i | 0.975540 | + | 0.219824i | \(0.0705484\pi\) | ||||
−0.975540 | + | 0.219824i | \(0.929452\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.76487e17 | −0.0852325 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.78840e18 | −0.534121 | −0.267060 | − | 0.963680i | \(-0.586052\pi\) | ||||
−0.267060 | + | 0.963680i | \(0.586052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.67838e17 | 0.164325 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 7.24228e18i | − | 2.03106i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.40865e18 | 0.654710 | 0.327355 | − | 0.944901i | \(-0.393843\pi\) | ||||
0.327355 | + | 0.944901i | \(0.393843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.26014e18 | − | 3.07293e18i | −0.595523 | − | 0.809686i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.42988e18i | 0.620722i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.26923e18 | 0.562080 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.07586e18i | − | 0.979051i | −0.871989 | − | 0.489526i | \(-0.837170\pi\) | ||
0.871989 | − | 0.489526i | \(-0.162830\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.67398e17i | 0.202083i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.96254e18i | − | 0.669511i | −0.942305 | − | 0.334755i | \(-0.891346\pi\) | ||
0.942305 | − | 0.334755i | \(-0.108654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.04238e18 | 0.886278 | 0.443139 | − | 0.896453i | \(-0.353865\pi\) | ||||
0.443139 | + | 0.896453i | \(0.353865\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.71086e18 | 0.789413 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.69967e18 | −1.17661 | −0.588304 | − | 0.808640i | \(-0.700204\pi\) | ||||
−0.588304 | + | 0.808640i | \(0.700204\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.16678e17i | − | 0.0834816i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.25814e17 | 0.160596 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.70818e18 | − | 3.68209e18i | −0.511268 | − | 0.695131i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.56892e17i | − | 0.0654156i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.93484e18 | −0.700324 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.40327e18i | 1.27960i | 0.768541 | + | 0.639801i | \(0.220983\pi\) | ||||
−0.768541 | + | 0.639801i | \(0.779017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.77724e18i | 0.466227i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.44544e19i | − | 2.35706i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.68608e18 | 0.583946 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.76288e18 | −1.50271 | −0.751355 | − | 0.659898i | \(-0.770599\pi\) | ||||
−0.751355 | + | 0.659898i | \(0.770599\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.44052e19 | −2.15455 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.09802e18i | − | 0.886378i | −0.896428 | − | 0.443189i | \(-0.853847\pi\) | ||
0.896428 | − | 0.443189i | \(-0.146153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.22229e18 | −1.02034 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.38192e18 | + | 3.22290e18i | −0.601767 | + | 0.442599i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.74156e17i | − | 0.0499527i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.40351e19 | 1.82185 | 0.910924 | − | 0.412574i | \(-0.135370\pi\) | ||||
0.910924 | + | 0.412574i | \(0.135370\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.33408e17i | 0.0168391i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.18305e18i | − | 0.636223i | −0.948053 | − | 0.318111i | \(-0.896951\pi\) | ||
0.948053 | − | 0.318111i | \(-0.103049\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.49638e19i | 1.78649i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.95922e18 | −0.924304 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.31946e19 | −1.49064 | −0.745319 | − | 0.666708i | \(-0.767703\pi\) | ||||
−0.745319 | + | 0.666708i | \(0.767703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.52251e18 | 0.387174 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.60557e18i | 0.278664i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.01805e19 | −1.05955 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.00634e19 | − | 7.40165e18i | 1.01932 | − | 0.749712i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.86253e19i | 1.83625i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.02649e19 | 0.985124 | 0.492562 | − | 0.870277i | \(-0.336060\pi\) | ||||
0.492562 | + | 0.870277i | \(0.336060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.64600e18i | − | 0.807799i | −0.914803 | − | 0.403900i | \(-0.867655\pi\) | ||
0.914803 | − | 0.403900i | \(-0.132345\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.08672e18i | 0.0988557i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.67336e18i | 0.413957i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.11004e19 | 1.82012 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.26199e19 | −1.06021 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.79668e18 | 0.556169 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.26095e19i | − | 1.00513i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.16101e18 | 0.633759 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.17125e18 | + | 8.61450e17i | −0.0886190 | + | 0.0651792i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.19057e19i | − | 0.877757i | −0.898546 | − | 0.438879i | \(-0.855376\pi\) | ||
0.898546 | − | 0.438879i | \(-0.144624\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.75646e18 | −0.126194 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.08140e19i | 0.757200i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.01805e19i | 0.694799i | 0.937717 | + | 0.347400i | \(0.112935\pi\) | ||||
−0.937717 | + | 0.347400i | \(0.887065\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 1.32801e19i | − | 0.883475i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.16950e19 | −1.40701 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.83536e19 | −1.16050 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.75537e19 | 1.08222 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 2.05299e19i | − | 1.23424i | −0.786867 | − | 0.617122i | \(-0.788298\pi\) | ||
0.786867 | − | 0.617122i | \(-0.211702\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.14403e18 | 0.477482 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.29746e18 | − | 1.26410e19i | −0.531648 | − | 0.722840i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.56873e19i | − | 1.43272i | −0.697733 | − | 0.716358i | \(-0.745808\pi\) | ||
0.697733 | − | 0.716358i | \(-0.254192\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.62726e18 | −0.414982 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.33128e19i | − | 1.23741i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.26575e19i | − | 0.655485i | −0.944767 | − | 0.327742i | \(-0.893712\pi\) | ||
0.944767 | − | 0.327742i | \(-0.106288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.03372e18i | 0.153293i | 0.997058 | + | 0.0766466i | \(0.0244213\pi\) | ||||
−0.997058 | + | 0.0766466i | \(0.975579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.69439e19 | −2.31471 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.45796e18 | −0.118277 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.75043e19 | −0.822082 | −0.411041 | − | 0.911617i | \(-0.634835\pi\) | ||||
−0.411041 | + | 0.911617i | \(0.634835\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.14764e19i | 0.526087i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.27225e18 | −0.191172 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.66687e19 | + | 1.22598e19i | −0.728150 | + | 0.535553i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 9.69190e18i | − | 0.413350i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.01981e17 | −0.00841092 | −0.00420546 | − | 0.999991i | \(-0.501339\pi\) | ||||
−0.00420546 | + | 0.999991i | \(0.501339\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.40383e19i | 0.570830i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1.38383e19i | − | 0.549503i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.53501e19i | − | 1.37091i | −0.728116 | − | 0.685454i | \(-0.759604\pi\) | ||
0.728116 | − | 0.685454i | \(-0.240396\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.80629e19 | 0.684177 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.64359e19 | −1.71804 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.03003e19 | −1.09511 | −0.547557 | − | 0.836768i | \(-0.684442\pi\) | ||||
−0.547557 | + | 0.836768i | \(0.684442\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.23510e19i | 0.789181i | 0.918857 | + | 0.394590i | \(0.129113\pi\) | ||||
−0.918857 | + | 0.394590i | \(0.870887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.77964e18 | −0.0613918 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.52098e18 | + | 2.73055e19i | −0.287211 | + | 0.920369i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.83948e18i | − | 0.225269i | −0.993636 | − | 0.112635i | \(-0.964071\pi\) | ||
0.993636 | − | 0.112635i | \(-0.0359290\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.60600e19 | 2.12627 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.22582e19i | 0.700168i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 7.18627e18i | − | 0.220943i | −0.993879 | − | 0.110471i | \(-0.964764\pi\) | ||
0.993879 | − | 0.110471i | \(-0.0352361\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 4.29588e19i | − | 1.29100i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.06287e18 | −0.236861 | −0.118431 | − | 0.992962i | \(-0.537786\pi\) | ||||
−0.118431 | + | 0.992962i | \(0.537786\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.95921e19 | 0.849849 | 0.424924 | − | 0.905229i | \(-0.360301\pi\) | ||||
0.424924 | + | 0.905229i | \(0.360301\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.79449e19 | 0.503847 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6.54098e18i | − | 0.179567i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.44443e19 | −0.924608 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.79286e19 | − | 3.79723e19i | −0.733122 | − | 0.996768i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.21066e19i | 0.567502i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.84818e18 | −0.146830 | −0.0734151 | − | 0.997301i | \(-0.523390\pi\) | ||||
−0.0734151 | + | 0.997301i | \(0.523390\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.04988e19i | 1.24009i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.89887e19i | 1.89736i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.59055e18i | − | 0.0608719i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.59803e18 | −0.0367349 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.07064e19 | 0.690594 | 0.345297 | − | 0.938493i | \(-0.387778\pi\) | ||||
0.345297 | + | 0.938493i | \(0.387778\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.34635e19 | 0.736366 | 0.368183 | − | 0.929753i | \(-0.379980\pi\) | ||||
0.368183 | + | 0.929753i | \(0.379980\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 5.14747e19i | − | 1.10835i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.22302e19 | 0.679098 | 0.339549 | − | 0.940588i | \(-0.389725\pi\) | ||||
0.339549 | + | 0.940588i | \(0.389725\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.34598e19 | + | 3.93196e19i | −1.10234 | + | 0.810767i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 4.27458e19i | − | 0.862634i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.05170e19 | 1.59036 | 0.795179 | − | 0.606374i | \(-0.207377\pi\) | ||||
0.795179 | + | 0.606374i | \(0.207377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.19582e19i | 1.58454i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.50447e19i | − | 0.284726i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.02662e19i | 1.48708i | 0.668690 | + | 0.743541i | \(0.266855\pi\) | ||||
−0.668690 | + | 0.743541i | \(0.733145\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.55001e19 | 0.825282 | 0.412641 | − | 0.910894i | \(-0.364606\pi\) | ||||
0.412641 | + | 0.910894i | \(0.364606\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.79593e19 | 0.496515 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.42590e19 | 0.943452 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.49416e20i | 2.54399i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.98441e19 | 1.66471 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.13767e19 | − | 5.62567e19i | −0.675613 | − | 0.918578i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.46349e19i | − | 0.234038i | −0.993130 | − | 0.117019i | \(-0.962666\pi\) | ||
0.993130 | − | 0.117019i | \(-0.0373338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.34914e18 | −0.0211315 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 6.09622e19i | − | 0.935276i | −0.883920 | − | 0.467638i | \(-0.845105\pi\) | ||
0.883920 | − | 0.467638i | \(-0.154895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.24603e19i | − | 0.638109i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.04760e19i | 1.33200i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.87414e17 | −0.00847226 | −0.00423613 | − | 0.999991i | \(-0.501348\pi\) | ||||
−0.00423613 | + | 0.999991i | \(0.501348\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.15719e19 | −1.01137 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.34957e19 | 0.602211 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 3.68676e19i | − | 0.500162i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.07427e20 | 1.42812 | 0.714062 | − | 0.700083i | \(-0.246853\pi\) | ||||
0.714062 | + | 0.700083i | \(0.246853\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.71249e19 | + | 5.04758e19i | 0.483651 | + | 0.657583i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.07294e20i | − | 1.36987i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.41011e19 | 0.676982 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.29362e20i | − | 1.58660i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.14615e20i | 1.37789i | 0.724812 | + | 0.688947i | \(0.241927\pi\) | ||||
−0.724812 | + | 0.688947i | \(0.758073\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.64059e19i | 0.782563i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.40684e20 | 1.62526 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.72369e20 | 1.95220 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.19675e19 | 0.466003 | 0.233002 | − | 0.972476i | \(-0.425145\pi\) | ||||
0.233002 | + | 0.972476i | \(0.425145\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.83885e19i | 0.853424i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.66832e19 | 1.03211 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.01970e19 | − | 4.10565e19i | −0.316098 | − | 0.429773i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.68019e20i | 1.72475i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.88410e18 | 0.0189671 | 0.00948356 | − | 0.999955i | \(-0.496981\pi\) | ||||
0.00948356 | + | 0.999955i | \(0.496981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.17271e20i | 1.15782i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.33258e20i | 1.29040i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.12334e19i | − | 0.106696i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.64591e19 | 0.246510 | 0.123255 | − | 0.992375i | \(-0.460667\pi\) | ||||
0.123255 | + | 0.992375i | \(0.460667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.58341e19 | −0.510278 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.48259e19 | 0.581202 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.62616e19i | 0.230990i | 0.993308 | + | 0.115495i | \(0.0368454\pi\) | ||||
−0.993308 | + | 0.115495i | \(0.963155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.63737e19 | −0.141298 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.53884e18 | + | 5.54481e18i | −0.0638311 | + | 0.0469477i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.35064e20i | 1.95288i | 0.215800 | + | 0.976438i | \(0.430764\pi\) | ||||
−0.215800 | + | 0.976438i | \(0.569236\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.39868e19 | 0.684674 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.17854e20i | − | 1.74279i | −0.490584 | − | 0.871394i | \(-0.663217\pi\) | ||
0.490584 | − | 0.871394i | \(-0.336783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.87234e20i | − | 1.46991i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.82468e19i | 0.140586i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.45250e20 | −1.09836 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.99894e19 | 0.593680 | 0.296840 | − | 0.954927i | \(-0.404067\pi\) | ||||
0.296840 | + | 0.954927i | \(0.404067\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.05960e20 | −1.50044 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.28193e19i | 0.449226i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.22053e20 | −0.856794 | −0.428397 | − | 0.903591i | \(-0.640922\pi\) | ||||
−0.428397 | + | 0.903591i | \(0.640922\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.61520e20 | + | 1.92347e20i | −1.80224 | + | 1.32554i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.68403e20i | 1.13935i | 0.821871 | + | 0.569674i | \(0.192930\pi\) | ||||
−0.821871 | + | 0.569674i | \(0.807070\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.24567e20 | 0.827433 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 7.71469e19i | − | 0.503139i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.18242e20i | − | 0.757189i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.56302e19i | 0.286925i | 0.989656 | + | 0.143462i | \(0.0458236\pi\) | ||||
−0.989656 | + | 0.143462i | \(0.954176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.09806e20 | −0.678024 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.35365e19 | 0.203358 | 0.101679 | − | 0.994817i | \(-0.467579\pi\) | ||||
0.101679 | + | 0.994817i | \(0.467579\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.26888e18 | −0.0432868 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.02202e20i | − | 1.18260i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.62514e20 | 0.933530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.76951e18 | + | 4.97897e18i | −0.0381944 | + | 0.0280920i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.20123e19i | 0.454513i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.13497e19 | 0.116226 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.81672e20i | − | 1.50633i | −0.657831 | − | 0.753165i | \(-0.728526\pi\) | ||
0.657831 | − | 0.753165i | \(-0.271474\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 4.45254e20i | − | 2.33921i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.78591e19i | 0.453473i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.24428e20 | 0.630966 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.33024e20 | −1.16099 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.50971e20 | −1.22861 | −0.614307 | − | 0.789067i | \(-0.710564\pi\) | ||||
−0.614307 | + | 0.789067i | \(0.710564\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.77174e20i | 0.852261i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.79366e19 | −0.132052 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.68747e19 | − | 6.37319e19i | −0.217736 | − | 0.296038i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 3.73688e20i | − | 1.70584i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.07234e20 | 1.37834 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.67113e20i | 0.736834i | 0.929661 | + | 0.368417i | \(0.120100\pi\) | ||||
−0.929661 | + | 0.368417i | \(0.879900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.31549e19i | − | 0.360364i | −0.983633 | − | 0.180182i | \(-0.942331\pi\) | ||
0.983633 | − | 0.180182i | \(-0.0576687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.26438e20i | 0.538573i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.72415e20 | −1.55928 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.94730e20 | 0.801454 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.11642e20 | −0.451690 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.86972e20i | 0.743660i | 0.928301 | + | 0.371830i | \(0.121270\pi\) | ||||
−0.928301 | + | 0.371830i | \(0.878730\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.33342e20 | −0.521397 | −0.260698 | − | 0.965420i | \(-0.583953\pi\) | ||||
−0.260698 | + | 0.965420i | \(0.583953\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.96617e19 | − | 1.44611e19i | 0.0755863 | − | 0.0555936i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.37762e19i | − | 0.203260i | −0.994822 | − | 0.101630i | \(-0.967594\pi\) | ||
0.994822 | − | 0.101630i | \(-0.0324057\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.94236e20 | 1.46512 | 0.732562 | − | 0.680700i | \(-0.238324\pi\) | ||||
0.732562 | + | 0.680700i | \(0.238324\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.46658e19i | 0.236302i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.06206e19i | − | 0.0740947i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.44898e18i | 0.0121867i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.30681e19 | 0.184398 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.55689e19 | −0.0532015 | −0.0266007 | − | 0.999646i | \(-0.508468\pi\) | ||||
−0.0266007 | + | 0.999646i | \(0.508468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.85307e20 | −1.29490 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 7.40515e20i | − | 2.44760i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.05769e20 | −0.668933 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.14534e20 | + | 9.81540e19i | 1.00574 | + | 0.313851i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.14671e20i | − | 0.360660i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.57345e20 | 1.41494 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.69284e19i | 0.173255i | 0.996241 | + | 0.0866274i | \(0.0276090\pi\) | ||||
−0.996241 | + | 0.0866274i | \(0.972391\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.31741e20i | − | 0.693809i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.82987e20i | 0.538958i | 0.963006 | + | 0.269479i | \(0.0868515\pi\) | ||||
−0.963006 | + | 0.269479i | \(0.913148\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.81449e20 | −1.10531 | −0.552655 | − | 0.833410i | \(-0.686385\pi\) | ||||
−0.552655 | + | 0.833410i | \(0.686385\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.94846e20 | −1.41074 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.41862e20 | 0.397916 | 0.198958 | − | 0.980008i | \(-0.436244\pi\) | ||||
0.198958 | + | 0.980008i | \(0.436244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.81517e20i | 1.32892i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.68022e20 | −0.727842 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.44235e20 | + | 3.32066e20i | 0.652632 | + | 0.887333i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.66744e19i | − | 0.0438452i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.81349e20 | −0.469261 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.26991e20i | 1.08733i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 4.00254e19i | − | 0.100309i | −0.998741 | − | 0.0501544i | \(-0.984029\pi\) | ||
0.998741 | − | 0.0501544i | \(-0.0159713\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2.17426e20i | − | 0.536277i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.93534e20 | 1.92634 | 0.963172 | − | 0.268885i | \(-0.0866552\pi\) | ||||
0.963172 | + | 0.268885i | \(0.0866552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.32658e20 | 1.51162 | 0.755812 | − | 0.654788i | \(-0.227242\pi\) | ||||
0.755812 | + | 0.654788i | \(0.227242\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.47355e20 | −1.75762 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.94341e20i | 0.681373i | 0.940177 | + | 0.340686i | \(0.110659\pi\) | ||||
−0.940177 | + | 0.340686i | \(0.889341\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.09878e20 | 2.07334 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.21792e20 | + | 3.10228e20i | −0.946138 | + | 0.695883i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.32212e20i | 1.17523i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.10986e20 | 0.458661 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.78427e20i | − | 1.23795i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.41865e20i | 0.931047i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.93464e20i | − | 0.608809i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.92943e20 | −1.21115 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.54094e19 | −0.0913284 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.43443e20 | −1.07623 | −0.538113 | − | 0.842873i | \(-0.680862\pi\) | ||||
−0.538113 | + | 0.842873i | \(0.680862\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 7.36191e20i | − | 1.43563i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.55809e20 | 0.875294 | 0.437647 | − | 0.899147i | \(-0.355812\pi\) | ||||
0.437647 | + | 0.899147i | \(0.355812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.68516e19 | + | 7.72966e19i | 0.107510 | + | 0.146172i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 7.86454e20i | − | 1.46462i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.44085e20 | 1.73151 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.46063e20i | 0.986356i | 0.869928 | + | 0.493178i | \(0.164165\pi\) | ||||
−0.869928 | + | 0.493178i | \(0.835835\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.23393e21i | 2.19520i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.49728e19i | − | 0.0262355i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.43843e19 | −0.0593428 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.00865e20 | 0.851456 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.23731e20 | −0.374641 | −0.187321 | − | 0.982299i | \(-0.559980\pi\) | ||||
−0.187321 | + | 0.982299i | \(0.559980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6.19422e19i | − | 0.102174i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.55583e21 | −2.52809 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.40366e20 | − | 3.26807e20i | −0.384762 | − | 0.523130i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.55067e20i | − | 1.34841i | −0.738543 | − | 0.674206i | \(-0.764486\pi\) | ||
0.738543 | − | 0.674206i | \(-0.235514\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.72059e20 | −1.51020 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 9.05540e20i | − | 1.38605i | −0.720911 | − | 0.693027i | \(-0.756277\pi\) | ||
0.720911 | − | 0.693027i | \(-0.243723\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.11925e21i | − | 1.68790i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 2.05112e20i | − | 0.304768i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.85540e20 | 1.00365 | 0.501826 | − | 0.864969i | \(-0.332662\pi\) | ||||
0.501826 | + | 0.864969i | \(0.332662\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.40962e20 | 0.203347 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.32363e20 | −1.32532 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.24466e20i | 0.874698i | 0.899292 | + | 0.437349i | \(0.144083\pi\) | ||||
−0.899292 | + | 0.437349i | \(0.855917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.21363e21 | −1.67519 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.79073e20 | − | 1.19521e21i | −1.19575 | − | 1.62577i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.24444e20i | 1.10517i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.71024e20 | −0.622271 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.20366e20i | 0.807726i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.96699e20i | 0.380737i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.81318e20i | 0.229327i | 0.993404 | + | 0.114664i | \(0.0365790\pi\) | ||||
−0.993404 | + | 0.114664i | \(0.963421\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.68530e20 | 0.833401 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.19816e20 | 0.638726 | 0.319363 | − | 0.947632i | \(-0.396531\pi\) | ||||
0.319363 | + | 0.947632i | \(0.396531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.23593e21 | −1.49693 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.34876e19i | 0.0519198i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.78331e20 | 0.445257 | 0.222628 | − | 0.974903i | \(-0.428536\pi\) | ||||
0.222628 | + | 0.974903i | \(0.428536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.18344e20 | + | 8.70420e19i | −0.137299 | + | 0.100983i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 5.32030e20i | − | 0.608489i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.85688e20 | 0.885881 | 0.442941 | − | 0.896551i | \(-0.353935\pi\) | ||||
0.442941 | + | 0.896551i | \(0.353935\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 3.57759e20i | − | 0.397683i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.62056e21i | − | 1.77600i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.34113e21i | − | 1.44909i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.09370e21 | 1.16515 | 0.582574 | − | 0.812778i | \(-0.302046\pi\) | ||||
0.582574 | + | 0.812778i | \(0.302046\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.19877e20 | −0.651120 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.20050e21 | −1.24337 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.11125e21i | 1.13487i | 0.823418 | + | 0.567435i | \(0.192064\pi\) | ||||
−0.823418 | + | 0.567435i | \(0.807936\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 176.15.h.e.65.4 | 14 | ||
4.3 | odd | 2 | 22.15.b.a.21.6 | ✓ | 14 | ||
11.10 | odd | 2 | inner | 176.15.h.e.65.3 | 14 | ||
44.43 | even | 2 | 22.15.b.a.21.13 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.15.b.a.21.6 | ✓ | 14 | 4.3 | odd | 2 | ||
22.15.b.a.21.13 | yes | 14 | 44.43 | even | 2 | ||
176.15.h.e.65.3 | 14 | 11.10 | odd | 2 | inner | ||
176.15.h.e.65.4 | 14 | 1.1 | even | 1 | trivial |