Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (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: | \(197.773761087\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 300700 x^{18} + 6140664 x^{17} + 35387063979 x^{16} - 1130222504088 x^{15} + \cdots + 12\!\cdots\!52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{175}\cdot 3^{32} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.8 | ||
Root | \(4.28001 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.10.d.f.193.13 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 81.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1655.59i | 1.18465i | 0.805701 | + | 0.592323i | \(0.201789\pi\) | ||||
−0.805701 | + | 0.592323i | \(0.798211\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11370.0 | 1.78986 | 0.894929 | − | 0.446208i | \(-0.147226\pi\) | ||||
0.894929 | + | 0.446208i | \(0.147226\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 94507.4i | 1.94625i | 0.230276 | + | 0.973125i | \(0.426037\pi\) | ||||
−0.230276 | + | 0.973125i | \(0.573963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 140234.i | − 1.36178i | −0.732385 | − | 0.680891i | \(-0.761593\pi\) | ||||
0.732385 | − | 0.680891i | \(-0.238407\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 134103. | 0.683956 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −531000. | −1.54196 | −0.770982 | − | 0.636857i | \(-0.780234\pi\) | ||||
−0.770982 | + | 0.636857i | \(0.780234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 387485.i | 0.682124i | 0.940041 | + | 0.341062i | \(0.110787\pi\) | ||||
−0.940041 | + | 0.341062i | \(0.889213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 920969.i | − 1.03338i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.36100e6 | 1.75922 | 0.879610 | − | 0.475695i | \(-0.157803\pi\) | ||||
0.879610 | + | 0.475695i | \(0.157803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −787863. | −0.403386 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.70715e6i | 0.710756i | 0.934723 | + | 0.355378i | \(0.115648\pi\) | ||||
−0.934723 | + | 0.355378i | \(0.884352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.18531e6 | 1.00843 | 0.504216 | − | 0.863577i | \(-0.331781\pi\) | ||||
0.504216 | + | 0.863577i | \(0.331781\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.65510e6 | 1.12367 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.88241e7i | 2.12035i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 142841.i | − 0.0125298i | −0.999980 | − | 0.00626492i | \(-0.998006\pi\) | ||||
0.999980 | − | 0.00626492i | \(-0.00199420\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.13589e7 | −0.786225 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92825e6 | 0.106570 | 0.0532851 | − | 0.998579i | \(-0.483031\pi\) | ||||
0.0532851 | + | 0.998579i | \(0.483031\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65243e7i | 0.737080i | 0.929612 | + | 0.368540i | \(0.120142\pi\) | ||||
−0.929612 | + | 0.368540i | \(0.879858\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.08623e7i | − 0.394882i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.78851e7 | 0.534627 | 0.267314 | − | 0.963610i | \(-0.413864\pi\) | ||||
0.267314 | + | 0.963610i | \(0.413864\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.89229e7 | 2.20359 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.30110e7i | 0.890253i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.01018e6i | − 0.0349940i | −0.999847 | − | 0.0174970i | \(-0.994430\pi\) | ||||
0.999847 | − | 0.0174970i | \(-0.00556975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.56466e8 | −2.30562 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.13863e7 | 0.393825 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.71099e7i | 1.04335i | 0.853145 | + | 0.521674i | \(0.174692\pi\) | ||||
−0.853145 | + | 0.521674i | \(0.825308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23555e6i | 0.0669094i | 0.999440 | + | 0.0334547i | \(0.0106509\pi\) | ||||
−0.999440 | + | 0.0334547i | \(0.989349\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.45985e7 | −0.596619 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.32170e8 | 1.61323 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.34701e8i | − 1.42291i | −0.702730 | − | 0.711457i | \(-0.748036\pi\) | ||||
0.702730 | − | 0.711457i | \(-0.251964\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 1.91241e8i | − 1.01569i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.62515e7 | 0.122600 | 0.0613002 | − | 0.998119i | \(-0.480475\pi\) | ||||
0.0613002 | + | 0.998119i | \(0.480475\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.59965e8 | −1.48357 | −0.741785 | − | 0.670638i | \(-0.766020\pi\) | ||||
−0.741785 | + | 0.670638i | \(0.766020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.38169e7i | 0.232895i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.07455e9i | 3.48351i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.01072e8 | 0.869658 | 0.434829 | − | 0.900513i | \(-0.356809\pi\) | ||||
0.434829 | + | 0.900513i | \(0.356809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.48363e8i | − 0.805714i | −0.915263 | − | 0.402857i | \(-0.868017\pi\) | ||||
0.915263 | − | 0.402857i | \(-0.131983\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 8.79119e8i | − 1.82668i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.19279e8 | 0.410355 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.32242e8 | 1.57497 | 0.787487 | − | 0.616331i | \(-0.211382\pi\) | ||||
0.787487 | + | 0.616331i | \(0.211382\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.59446e9i | − 2.43740i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.20010e8i | − 0.582219i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.41517e8 | −0.808075 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.09752e8 | −1.04340 | −0.521699 | − | 0.853129i | \(-0.674702\pi\) | ||||
−0.521699 | + | 0.853129i | \(0.674702\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 6.20063e8i | − 0.648750i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 3.56743e8i | − 0.341121i | −0.985347 | − | 0.170561i | \(-0.945442\pi\) | ||||
0.985347 | − | 0.170561i | \(-0.0545579\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.27419e9 | −1.11550 | −0.557748 | − | 0.830010i | \(-0.688334\pi\) | ||||
−0.557748 | + | 0.830010i | \(0.688334\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.52475e9 | 1.22418 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.90069e9i | 1.40179i | 0.713264 | + | 0.700896i | \(0.247216\pi\) | ||||
−0.713264 | + | 0.700896i | \(0.752784\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.92409e8i | 0.130559i | 0.997867 | + | 0.0652793i | \(0.0207938\pi\) | ||||
−0.997867 | + | 0.0652793i | \(0.979206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.15701e7 | −0.00723411 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.29060e9 | −1.32159 | −0.660793 | − | 0.750568i | \(-0.729780\pi\) | ||||
−0.660793 | + | 0.750568i | \(0.729780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.90885e9i | 2.08405i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.20074e8i | 0.453927i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.03746e9 | −2.75990 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.57370e9 | −2.78789 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.56188e8i | − 0.0615283i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.92920e9i | 0.706776i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.60539e7 | 0.0327641 | 0.0163821 | − | 0.999866i | \(-0.494785\pi\) | ||||
0.0163821 | + | 0.999866i | \(0.494785\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.33847e9 | 0.425554 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.10259e9i | 0.623783i | 0.950118 | + | 0.311892i | \(0.100963\pi\) | ||||
−0.950118 | + | 0.311892i | \(0.899037\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.40569e9i | 1.22091i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.79850e8 | −0.227985 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.18137e8 | −0.198419 | −0.0992095 | − | 0.995067i | \(-0.531631\pi\) | ||||
−0.0992095 | + | 0.995067i | \(0.531631\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.00619e8i | 0.159190i | 0.996827 | + | 0.0795950i | \(0.0253627\pi\) | ||||
−0.996827 | + | 0.0795950i | \(0.974637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 1.44869e9i | − 0.308667i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.32531e10 | 2.65037 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.48193e9 | −0.841994 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 7.20276e9i | − 1.27224i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 4.80548e9i | − 0.798728i | −0.916792 | − | 0.399364i | \(-0.869231\pi\) | ||||
0.916792 | − | 0.399364i | \(-0.130769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.05075e9 | 0.164477 | 0.0822383 | − | 0.996613i | \(-0.473793\pi\) | ||||
0.0822383 | + | 0.996613i | \(0.473793\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.48389e9 | 0.513988 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.58476e9i | 1.19464i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.84280e9i | 0.373421i | 0.982415 | + | 0.186710i | \(0.0597826\pi\) | ||||
−0.982415 | + | 0.186710i | \(0.940217\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.62825e8 | −0.0202038 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.68445e10 | 3.14876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1.36183e9i | − 0.151105i | −0.997142 | − | 0.0755527i | \(-0.975928\pi\) | ||||
0.997142 | − | 0.0755527i | \(-0.0240721\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.26737e10i | 1.33115i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.81425e9 | 0.379477 | 0.189738 | − | 0.981835i | \(-0.439236\pi\) | ||||
0.189738 | + | 0.981835i | \(0.439236\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.06101e9 | −0.854450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.54229e9i | − 0.227375i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.35181e10i | − 1.14738i | −0.819071 | − | 0.573692i | \(-0.805511\pi\) | ||||
0.819071 | − | 0.573692i | \(-0.194489\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.95799e9 | −0.722004 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.86590e9 | 0.602378 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.34665e9i | 0.170848i | 0.996345 | + | 0.0854240i | \(0.0272245\pi\) | ||||
−0.996345 | + | 0.0854240i | \(0.972776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.69581e10i | 1.86696i | 0.358627 | + | 0.933481i | \(0.383245\pi\) | ||||
−0.358627 | + | 0.933481i | \(0.616755\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.86079e8 | 0.0386302 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.36487e8 | 0.0148434 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.01834e10i | − 3.00105i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.04248e9i | 0.344458i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.44999e9 | −0.187572 | −0.0937859 | − | 0.995592i | \(-0.529897\pi\) | ||||
−0.0937859 | + | 0.995592i | \(0.529897\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.93617e10 | 1.00447 | 0.502234 | − | 0.864732i | \(-0.332512\pi\) | ||||
0.502234 | + | 0.864732i | \(0.332512\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1.88058e10i | − 0.931398i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.11248e10i | 0.999298i | 0.866228 | + | 0.499649i | \(0.166538\pi\) | ||||
−0.866228 | + | 0.499649i | \(0.833462\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.06345e10 | 1.38475 | 0.692376 | − | 0.721536i | \(-0.256564\pi\) | ||||
0.692376 | + | 0.721536i | \(0.256564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.90108e10 | −0.821519 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.07802e10i | 1.27215i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.19239e9i | 0.126248i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.54905e10 | −0.586407 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.66202e10 | −1.32758 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.75426e9i | − 0.130393i | −0.997872 | − | 0.0651964i | \(-0.979233\pi\) | ||||
0.997872 | − | 0.0651964i | \(-0.0207674\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2.12637e9i | − 0.0707834i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.73575e10 | −0.873179 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.89569e10 | 1.80495 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.91572e10i | 0.856539i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.44641e10i | 2.09982i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.80461e9 | −0.157181 | −0.0785907 | − | 0.996907i | \(-0.525042\pi\) | ||||
−0.0785907 | + | 0.996907i | \(0.525042\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.16917e9 | 0.134462 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.37575e10i | 1.09379i | 0.837200 | + | 0.546897i | \(0.184191\pi\) | ||||
−0.837200 | + | 0.546897i | \(0.815809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5.00629e10i | − 1.20298i | −0.798882 | − | 0.601488i | \(-0.794575\pi\) | ||||
0.798882 | − | 0.601488i | \(-0.205425\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.70384e10 | 2.01121 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.78995e10 | −1.28698 | −0.643492 | − | 0.765453i | \(-0.722515\pi\) | ||||
−0.643492 | + | 0.765453i | \(0.722515\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.96104e10i | 0.633344i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2.43868e10i | − 0.502097i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.59252e10 | 1.30696 | 0.653478 | − | 0.756945i | \(-0.273309\pi\) | ||||
0.653478 | + | 0.756945i | \(0.273309\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.03616e10 | −0.197857 | −0.0989284 | − | 0.995095i | \(-0.531541\pi\) | ||||
−0.0989284 | + | 0.995095i | \(0.531541\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3.48678e9i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.47220e11i | 2.61048i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.43384e10 | 0.928904 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.82174e10 | −0.465179 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.88299e10i | 1.25360i | 0.779180 | + | 0.626800i | \(0.215636\pi\) | ||||
−0.779180 | + | 0.626800i | \(0.784364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.23132e11i | 3.42388i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.12087e10 | −1.05463 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.14179e9 | 0.0592228 | 0.0296114 | − | 0.999561i | \(-0.490573\pi\) | ||||
0.0296114 | + | 0.999561i | \(0.490573\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.62410e9i | − 0.0224267i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1.77616e10i | − 0.236919i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.51316e10 | −0.839442 | −0.419721 | − | 0.907653i | \(-0.637872\pi\) | ||||
−0.419721 | + | 0.907653i | \(0.637872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.32804e9 | 0.0414555 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 7.55116e10i | − 0.909312i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.43073e10i | 0.515930i | 0.966154 | + | 0.257965i | \(0.0830519\pi\) | ||||
−0.966154 | + | 0.257965i | \(0.916948\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.19147e10 | −1.03520 | −0.517598 | − | 0.855624i | \(-0.673174\pi\) | ||||
−0.517598 | + | 0.855624i | \(0.673174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.29151e11 | −1.40723 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 7.44589e10i | − 0.785090i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.23505e10i | − 0.330158i | −0.986280 | − | 0.165079i | \(-0.947212\pi\) | ||||
0.986280 | − | 0.165079i | \(-0.0527880\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.40208e10 | −0.336144 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.98617e10 | −0.572757 | −0.286379 | − | 0.958117i | \(-0.592451\pi\) | ||||
−0.286379 | + | 0.958117i | \(0.592451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.24438e11i | 1.15323i | 0.817017 | + | 0.576614i | \(0.195626\pi\) | ||||
−0.817017 | + | 0.576614i | \(0.804374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.19629e10i | 0.466543i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.19241e10 | 0.190745 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.63373e11 | 1.37765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.36899e10i | 0.602407i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.22003e10i | 0.730850i | 0.930841 | + | 0.365425i | \(0.119076\pi\) | ||||
−0.930841 | + | 0.365425i | \(0.880924\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.60774e11 | −1.23600 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.02251e10 | −0.374556 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3.31092e11i | − 2.39567i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.87881e11i | 1.31927i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.88961e10 | −0.196946 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.19791e10 | −0.0792639 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.08578e11i | − 1.34013i | −0.742303 | − | 0.670064i | \(-0.766267\pi\) | ||||
0.742303 | − | 0.670064i | \(-0.233733\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.03210e11i | 0.644032i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.15604e11 | −0.700728 | −0.350364 | − | 0.936614i | \(-0.613942\pi\) | ||||
−0.350364 | + | 0.936614i | \(0.613942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.38691e11 | −0.816769 | −0.408384 | − | 0.912810i | \(-0.633908\pi\) | ||||
−0.408384 | + | 0.912810i | \(0.633908\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.23505e11i | − 0.706783i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.75006e10i | 0.319820i | 0.987132 | + | 0.159910i | \(0.0511204\pi\) | ||||
−0.987132 | + | 0.159910i | \(0.948880\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.55845e11 | −1.38331 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.53956e11 | 0.809325 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.05754e11i | − 1.05181i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.10485e11i | 0.549324i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.55851e10 | 0.0753780 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.03353e11 | 0.956907 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.43458e11i | 1.57271i | 0.617776 | + | 0.786354i | \(0.288034\pi\) | ||||
−0.617776 | + | 0.786354i | \(0.711966\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.37181e8i | 0.00417662i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.88569e11 | 1.68565 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.16926e11 | 1.33851 | 0.669257 | − | 0.743031i | \(-0.266612\pi\) | ||||
0.669257 | + | 0.743031i | \(0.266612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.85538e11i | 0.763019i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.90050e11i | 1.96266i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.52232e11 | 2.15426 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.16617e11 | 1.20323 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.34668e10i | 0.234998i | 0.993073 | + | 0.117499i | \(0.0374877\pi\) | ||||
−0.993073 | + | 0.117499i | \(0.962512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.80264e11i | 1.73287i | 0.499291 | + | 0.866434i | \(0.333594\pi\) | ||||
−0.499291 | + | 0.866434i | \(0.666406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.45260e10 | 0.262075 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.25576e10 | 0.180156 | 0.0900781 | − | 0.995935i | \(-0.471288\pi\) | ||||
0.0900781 | + | 0.995935i | \(0.471288\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.34618e10i | 0.145238i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.89034e11i | 1.59343i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.68799e11 | −1.17183 | −0.585916 | − | 0.810372i | \(-0.699265\pi\) | ||||
−0.585916 | + | 0.810372i | \(0.699265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.72543e11 | 0.534707 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.32470e11i | 1.60959i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.95956e11i | − 1.75750i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.50239e11 | 0.720043 | 0.360022 | − | 0.932944i | \(-0.382769\pi\) | ||||
0.360022 | + | 0.932944i | \(0.382769\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.26512e10 | −0.0355234 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.28557e10i | − 0.0626343i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.47052e11i | 1.73081i | 0.501073 | + | 0.865405i | \(0.332939\pi\) | ||||
−0.501073 | + | 0.865405i | \(0.667061\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.56265e11 | 0.408058 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.79633e11 | 0.967895 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.44133e11i | 0.856742i | 0.903603 | + | 0.428371i | \(0.140912\pi\) | ||||
−0.903603 | + | 0.428371i | \(0.859088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 7.78037e9i | − 0.0189164i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.36072e11 | −0.560595 | −0.280298 | − | 0.959913i | \(-0.590433\pi\) | ||||
−0.280298 | + | 0.959913i | \(0.590433\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.77901e12 | −4.12673 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.08416e11i | − 0.245693i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2.69565e11i | − 0.596885i | −0.954428 | − | 0.298442i | \(-0.903533\pi\) | ||||
0.954428 | − | 0.298442i | \(-0.0964671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.25369e12 | −2.71265 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.70310e11 | 0.360141 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.98453e11i | 1.03024i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.24972e11i | − 0.454540i | −0.973832 | − | 0.227270i | \(-0.927020\pi\) | ||||
0.973832 | − | 0.227270i | \(-0.0729800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.56861e11 | 0.704890 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.94935e11 | −0.569609 | −0.284805 | − | 0.958586i | \(-0.591929\pi\) | ||||
−0.284805 | + | 0.958586i | \(0.591929\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 7.27155e11i | − 1.37327i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.12678e10i | 0.131627i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.34996e10 | 0.0243862 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.05914e11 | −1.24737 | −0.623687 | − | 0.781674i | \(-0.714366\pi\) | ||||
−0.623687 | + | 0.781674i | \(0.714366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.62691e10i | 0.114557i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.10414e12i | 1.86745i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.76748e11 | 0.954486 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.67502e10 | 0.0919083 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 6.73207e11i | − 1.06705i | −0.845784 | − | 0.533526i | \(-0.820867\pi\) | ||||
0.845784 | − | 0.533526i | \(-0.179133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 7.27739e11i | − 1.12903i | −0.825422 | − | 0.564516i | \(-0.809063\pi\) | ||||
0.825422 | − | 0.564516i | \(-0.190937\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.17344e11 | −0.178209 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.18355e11 | 0.622006 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.22680e10i | 0.119758i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1.07350e12i | − 1.53019i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.32994e11 | 0.744003 | 0.372001 | − | 0.928232i | \(-0.378672\pi\) | ||||
0.372001 | + | 0.928232i | \(0.378672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.23588e11 | 0.305670 | 0.152835 | − | 0.988252i | \(-0.451160\pi\) | ||||
0.152835 | + | 0.988252i | \(0.451160\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.63036e11i | 0.486126i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.14851e11i | 1.20001i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.15099e10 | 0.117592 | 0.0587960 | − | 0.998270i | \(-0.481274\pi\) | ||||
0.0587960 | + | 0.998270i | \(0.481274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.83423e11 | −0.734531 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.99027e11i | − 0.862337i | −0.902271 | − | 0.431169i | \(-0.858101\pi\) | ||||
0.902271 | − | 0.431169i | \(-0.141899\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.54341e12i | 1.86579i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.89244e11 | −0.461146 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.69460e11 | 0.312886 | 0.156443 | − | 0.987687i | \(-0.449997\pi\) | ||||
0.156443 | + | 0.987687i | \(0.449997\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.82234e11i | 0.207412i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 8.51109e10i | − 0.0949606i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.63977e12 | 2.88745 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.28944e11 | 0.781756 | 0.390878 | − | 0.920443i | \(-0.372171\pi\) | ||||
0.390878 | + | 0.920443i | \(0.372171\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.82195e11i | − 0.296751i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.09764e12i | 1.13190i | 0.824440 | + | 0.565949i | \(0.191490\pi\) | ||||
−0.824440 | + | 0.565949i | \(0.808510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.32754e11 | 0.235387 | 0.117693 | − | 0.993050i | \(-0.462450\pi\) | ||||
0.117693 | + | 0.993050i | \(0.462450\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.95365e11 | 0.689723 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 6.68871e11i | − 0.650754i | −0.945584 | − | 0.325377i | \(-0.894509\pi\) | ||||
0.945584 | − | 0.325377i | \(-0.105491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2.66855e12i | − 2.54681i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.30267e11 | 0.215595 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.56167e12 | −1.43454 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 3.05285e11i | − 0.275159i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.31888e10i | 0.0116647i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.61992e12 | −1.40599 | −0.702996 | − | 0.711194i | \(-0.748155\pi\) | ||||
−0.702996 | + | 0.711194i | \(0.748155\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00312e10 | −0.0170629 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.17441e12i | − 1.81794i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.50618e12i | − 1.23606i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.49759e11 | 0.201206 | 0.100603 | − | 0.994927i | \(-0.467923\pi\) | ||||
0.100603 | + | 0.994927i | \(0.467923\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.10309e11 | −0.0872407 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.89367e12i | 1.47040i | 0.677848 | + | 0.735202i | \(0.262913\pi\) | ||||
−0.677848 | + | 0.735202i | \(0.737087\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.43749e12i | − 1.09596i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.02657e12 | 0.768539 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.98479e11 | 0.219437 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.18338e11i | − 0.302047i | −0.988530 | − | 0.151024i | \(-0.951743\pi\) | ||||
0.988530 | − | 0.151024i | \(-0.0482569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 3.08954e11i | − 0.219091i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.09661e12 | 1.46036 | 0.730182 | − | 0.683253i | \(-0.239435\pi\) | ||||
0.730182 | + | 0.683253i | \(0.239435\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.90620e11 | 0.404108 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.33942e11i | 0.493317i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.81715e12i | − 1.19994i | −0.800022 | − | 0.599970i | \(-0.795179\pi\) | ||||
0.800022 | − | 0.599970i | \(-0.204821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.09280e12 | −2.65538 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.05925e11 | −0.131275 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.10955e12i | − 1.32147i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.69027e12i | 1.04052i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.09497e12 | −0.662443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.17238e11 | −0.485936 | −0.242968 | − | 0.970034i | \(-0.578121\pi\) | ||||
−0.242968 | + | 0.970034i | \(0.578121\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.36193e12i | 0.795969i | 0.917392 | + | 0.397984i | \(0.130290\pi\) | ||||
−0.917392 | + | 0.397984i | \(0.869710\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.25597e11i | 0.416849i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.75340e12 | −1.55497 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.77316e12 | 2.09486 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 6.37138e11i | − 0.347783i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2.70406e11i | − 0.145125i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.14676e12 | −1.66063 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.90079e11 | 0.0986392 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.40387e12i | 4.28874i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 2.08586e12i | − 1.04688i | −0.852063 | − | 0.523440i | \(-0.824649\pi\) | ||||
0.852063 | − | 0.523440i | \(-0.175351\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.18360e12 | 1.07789 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.18550e11 | −0.154666 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.54074e12i | 1.21344i | 0.794917 | + | 0.606719i | \(0.207515\pi\) | ||||
−0.794917 | + | 0.606719i | \(0.792485\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4.74724e10i | − 0.0223031i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.04898e12 | −0.484824 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.42319e12 | 1.55657 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1.91554e10i | − 0.00856986i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 2.62379e12i | − 1.15500i | −0.816391 | − | 0.577499i | \(-0.804029\pi\) | ||||
0.816391 | − | 0.577499i | \(-0.195971\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.31726e12 | 1.00374 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.06485e12 | −1.73266 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.67317e12i | 0.701863i | 0.936401 | + | 0.350932i | \(0.114135\pi\) | ||||
−0.936401 | + | 0.350932i | \(0.885865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.79230e12i | − 1.56561i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.89441e11 | 0.198873 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.63787e12 | 1.45493 | 0.727466 | − | 0.686144i | \(-0.240698\pi\) | ||||
0.727466 | + | 0.686144i | \(0.240698\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.12669e12i | − 0.837223i | −0.908165 | − | 0.418612i | \(-0.862517\pi\) | ||||
0.908165 | − | 0.418612i | \(-0.137483\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.79449e11i | 0.108295i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.86014e12 | −0.709645 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.52863e12 | 0.949716 | 0.474858 | − | 0.880062i | \(-0.342499\pi\) | ||||
0.474858 | + | 0.880062i | \(0.342499\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.56830e12i | − 0.579930i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 3.96088e12i | − 1.44211i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.89977e11 | 0.0681071 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.52327e12 | −0.537743 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.94162e12i | − 0.674981i | −0.941329 | − | 0.337491i | \(-0.890422\pi\) | ||||
0.941329 | − | 0.337491i | \(-0.109578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00923e12i | 0.687876i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.71111e12 | 0.576945 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.39070e12 | −0.793926 | −0.396963 | − | 0.917835i | \(-0.629936\pi\) | ||||
−0.396963 | + | 0.917835i | \(0.629936\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 9.99557e12i | − 3.26950i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 2.48140e12i | − 0.799488i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.02268e11 | 0.0324576 | 0.0162288 | − | 0.999868i | \(-0.494834\pi\) | ||||
0.0162288 | + | 0.999868i | \(0.494834\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.63671e12 | −1.13704 | −0.568518 | − | 0.822671i | \(-0.692483\pi\) | ||||
−0.568518 | + | 0.822671i | \(0.692483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.53987e12i | 0.474304i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1.08834e13i | − 3.30266i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.46914e12 | −1.03723 | −0.518613 | − | 0.855009i | \(-0.673551\pi\) | ||||
−0.518613 | + | 0.855009i | \(0.673551\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.49320e12 | 0.734478 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.50810e12i | − 0.728046i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.39770e12i | 0.971881i | 0.873992 | + | 0.485941i | \(0.161523\pi\) | ||||
−0.873992 | + | 0.485941i | \(0.838477\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.58584e11 | 0.0728893 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.17197e12 | −0.603351 | −0.301676 | − | 0.953411i | \(-0.597546\pi\) | ||||
−0.301676 | + | 0.953411i | \(0.597546\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.30312e12i | 1.17808i | 0.808103 | + | 0.589041i | \(0.200494\pi\) | ||||
−0.808103 | + | 0.589041i | \(0.799506\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.25473e12i | 0.338562i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.05996e13 | 2.81898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.73276e12 | −1.24067 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.96623e12i | 0.766481i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.58486e10i | 0.0193206i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.20938e12 | −1.05703 | −0.528513 | − | 0.848925i | \(-0.677250\pi\) | ||||
−0.528513 | + | 0.848925i | \(0.677250\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.04095e11 | −0.0752823 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.59026e11i | 0.0388139i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.24700e13i | − 3.00081i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.72236e11 | −0.0408668 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.60479e11 | −0.177920 | −0.0889602 | − | 0.996035i | \(-0.528354\pi\) | ||||
−0.0889602 | + | 0.996035i | \(0.528354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7.42913e12i | − 1.71391i | −0.515389 | − | 0.856957i | \(-0.672352\pi\) | ||||
0.515389 | − | 0.856957i | \(-0.327648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.21596e12i | 0.504130i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.60122e12 | 0.583590 | 0.291795 | − | 0.956481i | \(-0.405748\pi\) | ||||
0.291795 | + | 0.956481i | \(0.405748\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.17760e12 | −2.03062 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 4.77551e12i | − 1.04209i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.06819e12i | 0.660348i | 0.943920 | + | 0.330174i | \(0.107107\pi\) | ||||
−0.943920 | + | 0.330174i | \(0.892893\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.48103e12 | −0.738962 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.36173e12 | 0.494523 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 2.46719e12i | − 0.509586i | −0.966996 | − | 0.254793i | \(-0.917993\pi\) | ||||
0.966996 | − | 0.254793i | \(-0.0820073\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.01622e12i | 0.818297i | 0.912468 | + | 0.409148i | \(0.134174\pi\) | ||||
−0.912468 | + | 0.409148i | \(0.865826\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.03159e12 | 1.21233 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.29404e12 | −1.44634 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.39157e12i | 1.25038i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.70173e11i | 0.0907487i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.83813e11 | −0.130222 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.90823e12 | 1.48598 | 0.742988 | − | 0.669305i | \(-0.233408\pi\) | ||||
0.742988 | + | 0.669305i | \(0.233408\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 4.18703e11i | − 0.0776316i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.08763e11i | 0.0381949i | 0.999818 | + | 0.0190974i | \(0.00607927\pi\) | ||||
−0.999818 | + | 0.0190974i | \(0.993921\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.03439e13 | −1.86754 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.54435e12 | 0.631503 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.71560e12i | 0.653335i | 0.945139 | + | 0.326667i | \(0.105926\pi\) | ||||
−0.945139 | + | 0.326667i | \(0.894074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.35450e12i | − 0.235056i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.05510e12 | −0.694538 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.81895e11 | −0.0476542 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 6.47722e12i | − 1.08078i | −0.841415 | − | 0.540390i | \(-0.818277\pi\) | ||||
0.841415 | − | 0.540390i | \(-0.181723\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 7.05011e12i | − 1.16117i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.15994e12 | −0.188584 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.02390e12 | −0.164327 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.68986e12i | 0.743040i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.68628e12i | 1.20222i | 0.799165 | + | 0.601112i | \(0.205275\pi\) | ||||
−0.799165 | + | 0.601112i | \(0.794725\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.53488e10 | 0.00854691 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.39845e12 | 0.365661 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.05616e12i | − 0.610559i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.27745e13i | − 1.89861i | −0.314358 | − | 0.949304i | \(-0.601789\pi\) | ||||
0.314358 | − | 0.949304i | \(-0.398211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.97533e12 | −0.289886 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.22425e13 | 1.77406 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.19418e13i | 3.13975i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 5.33994e12i | − 0.754571i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.64154e12 | 1.34545 | 0.672723 | − | 0.739894i | \(-0.265124\pi\) | ||||
0.672723 | + | 0.739894i | \(0.265124\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.44876e13 | −1.99658 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.39292e11i | 0.114233i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.13286e12i | − 0.286709i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.93455e12 | −0.256848 | −0.128424 | − | 0.991719i | \(-0.540992\pi\) | ||||
−0.128424 | + | 0.991719i | \(0.540992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 8.77439e12i | − 1.13655i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4.64764e12i | − 0.594654i | −0.954776 | − | 0.297327i | \(-0.903905\pi\) | ||||
0.954776 | − | 0.297327i | \(-0.0960951\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.19248e13 | 1.50716 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.21810e13 | 2.76935 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.50955e13i | 1.86186i | 0.365194 | + | 0.930932i | \(0.381003\pi\) | ||||
−0.365194 | + | 0.930932i | \(0.618997\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 4.40141e12i | − 0.536303i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.13339e13 | 1.36437 | 0.682183 | − | 0.731182i | \(-0.261031\pi\) | ||||
0.682183 | + | 0.731182i | \(0.261031\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.95593e12 | 0.946210 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.28561e12i | 0.268571i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.16108e13i | 2.50901i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.43395e12 | −0.738071 | −0.369035 | − | 0.929415i | \(-0.620312\pi\) | ||||
−0.369035 | + | 0.929415i | \(0.620312\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.38522e12 | 0.723766 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.73962e12i | 0.194847i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.59289e11i | 0.0176301i | 0.999961 | + | 0.00881507i | \(0.00280596\pi\) | ||||
−0.999961 | + | 0.00881507i | \(0.997194\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.80737e13 | 1.97678 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.38855e12 | −0.150083 | −0.0750413 | − | 0.997180i | \(-0.523909\pi\) | ||||
−0.0750413 | + | 0.997180i | \(0.523909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.18768e12i | 0.233681i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.76790e12i | 0.608894i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.36181e13 | 1.42081 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.69105e12 | −0.793080 | −0.396540 | − | 0.918017i | \(-0.629789\pi\) | ||||
−0.396540 | + | 0.918017i | \(0.629789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 3.35485e11i | − 0.0341923i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.48855e13i | − 1.49954i | −0.661701 | − | 0.749768i | \(-0.730165\pi\) | ||||
0.661701 | − | 0.749768i | \(-0.269835\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.08531e12 | −0.406787 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.31552e11 | −0.0129480 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.47167e11i | 0.0726941i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.48096e12i | 0.238611i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.43869e12 | −0.136785 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.70653e12 | −0.442372 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 8.96061e12i | − 0.832629i | −0.909221 | − | 0.416314i | \(-0.863322\pi\) | ||||
0.909221 | − | 0.416314i | \(-0.136678\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.27566e12i | 0.484652i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.60441e13 | −2.36545 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.01467e12 | 0.0911160 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 2.69571e11i | − 0.0239343i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.13567e12i | 0.538641i | 0.963051 | + | 0.269320i | \(0.0867991\pi\) | ||||
−0.963051 | + | 0.269320i | \(0.913201\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.49698e12 | −0.824375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.11644e12 | −0.524992 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.40194e13i | − 2.88740i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.44436e13i | 3.73016i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.58890e12 | 0.297872 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.68903e13 | 1.38634 | 0.693170 | − | 0.720774i | \(-0.256214\pi\) | ||||
0.693170 | + | 0.720774i | \(0.256214\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.31863e13i | − 1.07036i | −0.844739 | − | 0.535179i | \(-0.820244\pi\) | ||||
0.844739 | − | 0.535179i | \(-0.179756\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.44509e12i | 0.597671i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.25464e12 | 0.179006 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.40291e12 | −0.502780 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.04612e13i | 0.812466i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 6.47323e12i | − 0.497252i | −0.968600 | − | 0.248626i | \(-0.920021\pi\) | ||||
0.968600 | − | 0.248626i | \(-0.0799790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.72880e13 | 1.31355 | 0.656773 | − | 0.754088i | \(-0.271921\pi\) | ||||
0.656773 | + | 0.754088i | \(0.271921\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.03117e12 | −0.453272 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.84398e12i | 0.137082i | 0.997648 | + | 0.0685410i | \(0.0218344\pi\) | ||||
−0.997648 | + | 0.0685410i | \(0.978166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.85743e12i | 0.136589i | 0.997665 | + | 0.0682947i | \(0.0217558\pi\) | ||||
−0.997665 | + | 0.0682947i | \(0.978244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.62039e12 | −0.190617 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.72180e13 | −3.39786 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.31485e12i | 0.449546i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.75568e12i | 0.194073i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.04502e12 | −0.0728106 | −0.0364053 | − | 0.999337i | \(-0.511591\pi\) | ||||
−0.0364053 | + | 0.999337i | \(0.511591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.17851e12 | 0.494826 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.84880e12i | 0.330681i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.50013e13i | − 1.01222i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.47429e13 | −4.98993 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.00795e13 | 0.665816 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 3.37248e11i | − 0.0220428i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4.28041e12i | − 0.276831i | −0.990374 | − | 0.138415i | \(-0.955799\pi\) | ||||
0.990374 | − | 0.138415i | \(-0.0442009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.20899e12 | 0.269358 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.25941e12 | 0.586367 | 0.293184 | − | 0.956056i | \(-0.405285\pi\) | ||||
0.293184 | + | 0.956056i | \(0.405285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 9.57537e12i | − 0.600049i | −0.953932 | − | 0.300024i | \(-0.903005\pi\) | ||||
0.953932 | − | 0.300024i | \(-0.0969948\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.77586e12i | − 0.110127i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.56057e13 | 0.957713 | 0.478856 | − | 0.877893i | \(-0.341051\pi\) | ||||
0.478856 | + | 0.877893i | \(0.341051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.23805e13 | 1.35924 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.32332e13i | − 0.795387i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.84535e13i | 1.69257i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.29130e13 | −1.93770 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.96888e12 | 0.347800 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.19350e13i | 1.26503i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.51400e13i | 1.43505i | 0.696532 | + | 0.717526i | \(0.254726\pi\) | ||||
−0.696532 | + | 0.717526i | \(0.745274\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.46822e12 | 0.421956 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.06427e12 | 0.0595198 | 0.0297599 | − | 0.999557i | \(-0.490526\pi\) | ||||
0.0297599 | + | 0.999557i | \(0.490526\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.43027e13i | − 1.89891i | −0.313902 | − | 0.949455i | \(-0.601636\pi\) | ||||
0.313902 | − | 0.949455i | \(-0.398364\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.30227e13i | 0.713604i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.38759e13 | 0.752670 | 0.376335 | − | 0.926484i | \(-0.377184\pi\) | ||||
0.376335 | + | 0.926484i | \(0.377184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.09213e12 | 0.0586431 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.06823e12i | 0.216250i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.93020e12i | 0.364682i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.88510e12 | −0.202394 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.68184e13 | −1.38314 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.40374e13i | 0.716750i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.06740e12i | 0.0539595i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.52184e13 | 0.761681 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.46316e13 | −2.21169 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 7.19852e12i | − 0.353192i | −0.984283 | − | 0.176596i | \(-0.943491\pi\) | ||||
0.984283 | − | 0.176596i | \(-0.0565086\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.34059e12i | 0.113707i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.48977e12 | 0.119764 | 0.0598820 | − | 0.998205i | \(-0.480928\pi\) | ||||
0.0598820 | + | 0.998205i | \(0.480928\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.29229e13 | 1.56812 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.70309e11i | 0.0457631i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.39064e13i | 1.11648i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.73700e13 | −0.803303 | −0.401652 | − | 0.915793i | \(-0.631564\pi\) | ||||
−0.401652 | + | 0.915793i | \(0.631564\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.68948e13 | −0.773723 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.68135e12i | − 0.166955i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12539e11i | 0.00505436i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.35999e12 | 0.371832 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.98860e12 | −0.219739 | −0.109870 | − | 0.993946i | \(-0.535043\pi\) | ||||
−0.109870 | + | 0.993946i | \(0.535043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.44563e13i | 1.50312i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.36389e12i | 0.404565i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.30833e13 | 3.55518 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.01453e12 | 0.0853781 | 0.0426890 | − | 0.999088i | \(-0.486408\pi\) | ||||
0.0426890 | + | 0.999088i | \(0.486408\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.12340e13i | 0.471562i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.75127e13i | − 1.14388i | −0.820296 | − | 0.571939i | \(-0.806191\pi\) | ||||
0.820296 | − | 0.571939i | \(-0.193809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.55259e12 | 0.187480 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.00039e13 | −0.408061 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.57827e13i | 1.04173i | 0.853640 | + | 0.520863i | \(0.174390\pi\) | ||||
−0.853640 | + | 0.520863i | \(0.825610\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.04793e13i | 2.02030i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.65755e12 | 0.184648 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.06001e13 | −0.809004 | −0.404502 | − | 0.914537i | \(-0.632555\pi\) | ||||
−0.404502 | + | 0.914537i | \(0.632555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 5.71178e12i | − 0.222206i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.07235e13i | 0.798654i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.30220e12 | −0.355142 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.47786e11 | 0.0169362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.24704e13i | − 0.467264i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.20551e13i | 1.18994i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.94563e13 | −1.45110 | −0.725550 | − | 0.688170i | \(-0.758414\pi\) | ||||
−0.725550 | + | 0.688170i | \(0.758414\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.66661e13 | −0.607263 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.55423e12i | 0.308812i | 0.988007 | + | 0.154406i | \(0.0493464\pi\) | ||||
−0.988007 | + | 0.154406i | \(0.950654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.96603e12i | 0.284927i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.94929e12 | 0.317152 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.68374e12 | −0.0591221 | −0.0295611 | − | 0.999563i | \(-0.509411\pi\) | ||||
−0.0295611 | + | 0.999563i | \(0.509411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.81038e13i | 3.06530i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.26239e12i | − 0.0435195i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.66001e13 | −1.93342 | −0.966711 | − | 0.255872i | \(-0.917637\pi\) | ||||
−0.966711 | + | 0.255872i | \(0.917637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.49741e13 | −1.18381 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.64716e13i | − 0.552470i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.90138e13i | 1.29669i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.49565e12 | 0.246875 | 0.123438 | − | 0.992352i | \(-0.460608\pi\) | ||||
0.123438 | + | 0.992352i | \(0.460608\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.78201e13 | 0.908003 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.07183e13i | 1.64044i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5.52784e13i | − 1.77185i | −0.463828 | − | 0.885925i | \(-0.653524\pi\) | ||||
0.463828 | − | 0.885925i | \(-0.346476\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.59117e10 | 0.00241137 |
(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 | 384.10.d.f.193.8 | yes | 20 | |
4.3 | odd | 2 | inner | 384.10.d.f.193.18 | yes | 20 | |
8.3 | odd | 2 | inner | 384.10.d.f.193.3 | ✓ | 20 | |
8.5 | even | 2 | inner | 384.10.d.f.193.13 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.d.f.193.3 | ✓ | 20 | 8.3 | odd | 2 | inner | |
384.10.d.f.193.8 | yes | 20 | 1.1 | even | 1 | trivial | |
384.10.d.f.193.13 | yes | 20 | 8.5 | even | 2 | inner | |
384.10.d.f.193.18 | yes | 20 | 4.3 | odd | 2 | inner |