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: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 17386x^{8} + 91191193x^{6} + 169741365808x^{4} + 89987894131456x^{2} + 6183051813523456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{52}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.3 | ||
Root | \(49.7838i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.10.d.d.193.8 |
$q$-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 | ||||||||
\(5\) | 309.546i | 0.221493i | 0.993849 | + | 0.110747i | \(0.0353242\pi\) | ||||
−0.993849 | + | 0.110747i | \(0.964676\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5272.51 | −0.829997 | −0.414998 | − | 0.909822i | \(-0.636218\pi\) | ||||
−0.414998 | + | 0.909822i | \(0.636218\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 67092.3i | − 1.38167i | −0.723010 | − | 0.690837i | \(-0.757242\pi\) | ||||
0.723010 | − | 0.690837i | \(-0.242758\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 145625.i | 1.41414i | 0.707146 | + | 0.707068i | \(0.249983\pi\) | ||||
−0.707146 | + | 0.707068i | \(0.750017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25073.2 | 0.127879 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 280963. | 0.815886 | 0.407943 | − | 0.913007i | \(-0.366246\pi\) | ||||
0.407943 | + | 0.913007i | \(0.366246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 561917.i | − 0.989194i | −0.869123 | − | 0.494597i | \(-0.835316\pi\) | ||||
0.869123 | − | 0.494597i | \(-0.164684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 427073.i | 0.479199i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.25321e6 | −0.933790 | −0.466895 | − | 0.884313i | \(-0.654627\pi\) | ||||
−0.466895 | + | 0.884313i | \(0.654627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.85731e6 | 0.950941 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.22372e6i | 0.846382i | 0.906040 | + | 0.423191i | \(0.139090\pi\) | ||||
−0.906040 | + | 0.423191i | \(0.860910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.89612e6 | −0.952192 | −0.476096 | − | 0.879393i | \(-0.657948\pi\) | ||||
−0.476096 | + | 0.879393i | \(0.657948\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.43448e6 | −0.797710 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.63208e6i | − 0.183838i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.02493e7i | 0.899058i | 0.893266 | + | 0.449529i | \(0.148408\pi\) | ||||
−0.893266 | + | 0.449529i | \(0.851592\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.17956e7 | 0.816452 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.07376e6 | −0.225148 | −0.112574 | − | 0.993643i | \(-0.535910\pi\) | ||||
−0.112574 | + | 0.993643i | \(0.535910\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.29943e7i | 1.02568i | 0.858484 | + | 0.512840i | \(0.171406\pi\) | ||||
−0.858484 | + | 0.512840i | \(0.828594\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2.03093e6i | − 0.0738310i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.57099e6 | −0.286099 | −0.143050 | − | 0.989716i | \(-0.545691\pi\) | ||||
−0.143050 | + | 0.989716i | \(0.545691\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.25542e7 | −0.311105 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 2.27580e7i | − 0.471052i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.95368e7i | 1.03644i | 0.855247 | + | 0.518220i | \(0.173405\pi\) | ||||
−0.855247 | + | 0.518220i | \(0.826595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.07681e7 | 0.306031 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.55153e7 | −0.571111 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.97217e6i | 0.0963969i | 0.998838 | + | 0.0481985i | \(0.0153480\pi\) | ||||
−0.998838 | + | 0.0481985i | \(0.984652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.82954e8i | − 1.69183i | −0.533319 | − | 0.845914i | \(-0.679055\pi\) | ||||
0.533319 | − | 0.845914i | \(-0.320945\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.45930e7 | 0.276666 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.50777e7 | −0.313221 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.19427e8i | − 1.33031i | −0.746704 | − | 0.665156i | \(-0.768365\pi\) | ||||
0.746704 | − | 0.665156i | \(-0.231635\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.01510e8i | 0.539124i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.11168e8 | −0.986203 | −0.493101 | − | 0.869972i | \(-0.664137\pi\) | ||||
−0.493101 | + | 0.869972i | \(0.664137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.05164e8 | 1.66985 | 0.834927 | − | 0.550361i | \(-0.185510\pi\) | ||||
0.834927 | + | 0.550361i | \(0.185510\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.50442e8i | − 0.549026i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.53745e8i | 1.14679i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.72184e8 | −0.497359 | −0.248680 | − | 0.968586i | \(-0.579997\pi\) | ||||
−0.248680 | + | 0.968586i | \(0.579997\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.57672e8i | 1.75239i | 0.481960 | + | 0.876193i | \(0.339925\pi\) | ||||
−0.481960 | + | 0.876193i | \(0.660075\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.69710e7i | 0.180713i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.61121e8 | 0.488659 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.23467e8 | 1.56015 | 0.780075 | − | 0.625686i | \(-0.215181\pi\) | ||||
0.780075 | + | 0.625686i | \(0.215181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 7.67810e8i | − 1.17373i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.96586e8i | 0.549748i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.73939e8 | 0.219099 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.91926e8 | 0.908264 | 0.454132 | − | 0.890935i | \(-0.349950\pi\) | ||||
0.454132 | + | 0.890935i | \(0.349950\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.40193e8i | 0.460558i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.08355e9i | − 1.03611i | −0.855349 | − | 0.518053i | \(-0.826657\pi\) | ||||
0.855349 | − | 0.518053i | \(-0.173343\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.17446e9 | 1.02819 | 0.514093 | − | 0.857735i | \(-0.328129\pi\) | ||||
0.514093 | + | 0.857735i | \(0.328129\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.32199e8 | −0.106139 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.23598e8i | 0.607419i | 0.952765 | + | 0.303710i | \(0.0982252\pi\) | ||||
−0.952765 | + | 0.303710i | \(0.901775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.44977e9i | 0.983736i | 0.870670 | + | 0.491868i | \(0.163686\pi\) | ||||
−0.870670 | + | 0.491868i | \(0.836314\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.30196e8 | 0.519071 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.16643e9 | −1.24995 | −0.624974 | − | 0.780646i | \(-0.714890\pi\) | ||||
−0.624974 | + | 0.780646i | \(0.714890\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.87927e8i | − 0.206828i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 9.55446e8i | − 0.471379i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.48138e9 | −0.677182 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.14343e9 | −0.909023 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.29975e8i | 0.129989i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.17950e9i | 0.432120i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.66249e9 | −1.24928 | −0.624640 | − | 0.780912i | \(-0.714754\pi\) | ||||
−0.624640 | + | 0.780912i | \(0.714754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.86254e9 | 0.592176 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 3.73034e9i | − 1.10669i | −0.832951 | − | 0.553346i | \(-0.813351\pi\) | ||||
0.832951 | − | 0.553346i | \(-0.186649\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.96272e9i | 0.821027i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.64505e8 | −0.0426264 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.65957e9 | 1.13006 | 0.565032 | − | 0.825069i | \(-0.308864\pi\) | ||||
0.565032 | + | 0.825069i | \(0.308864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.13924e9i | − 0.486064i | −0.970018 | − | 0.243032i | \(-0.921858\pi\) | ||||
0.970018 | − | 0.243032i | \(-0.0781420\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.75251e8i | 0.165179i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.77032e9 | 1.95388 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.97890e8 | −0.187468 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.01689e9i | 0.179617i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.49237e9i | 0.414261i | 0.978313 | + | 0.207130i | \(0.0664124\pi\) | ||||
−0.978313 | + | 0.207130i | \(0.933588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.88631e8 | −0.139099 | −0.0695497 | − | 0.997578i | \(-0.522156\pi\) | ||||
−0.0695497 | + | 0.997578i | \(0.522156\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.84340e9 | −0.271962 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.51557e9i | − 0.210904i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.27297e9i | 0.298569i | 0.988794 | + | 0.149285i | \(0.0476971\pi\) | ||||
−0.988794 | + | 0.149285i | \(0.952303\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.82248e9 | 0.598389 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.60757e9 | 0.775043 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.57075e7i | − 0.00950987i | −0.999989 | − | 0.00475494i | \(-0.998486\pi\) | ||||
0.999989 | − | 0.00475494i | \(-0.00151355\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1.68222e9i | − 0.176687i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.54333e10 | 1.53545 | 0.767724 | − | 0.640781i | \(-0.221389\pi\) | ||||
0.767724 | + | 0.640781i | \(0.221389\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.06022e10 | −0.999781 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.68674e9i | 0.329731i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 8.71262e9i | − 0.739505i | −0.929130 | − | 0.369753i | \(-0.879442\pi\) | ||||
0.929130 | − | 0.369753i | \(-0.120558\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.79267e9 | −0.789278 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.26745e8 | 0.0556548 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 7.50026e9i | − 0.546056i | −0.962006 | − | 0.273028i | \(-0.911975\pi\) | ||||
0.962006 | − | 0.273028i | \(-0.0880252\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.92534e10i | − 1.33338i | −0.745336 | − | 0.666689i | \(-0.767711\pi\) | ||||
0.745336 | − | 0.666689i | \(-0.232289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.48192e10 | −0.976778 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.17264e9 | −0.199135 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.88505e10i | − 1.12729i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2.80203e9i | − 0.159733i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.84333e9 | −0.426433 | −0.213216 | − | 0.977005i | \(-0.568394\pi\) | ||||
−0.213216 | + | 0.977005i | \(0.568394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.46224e10 | 0.758595 | 0.379297 | − | 0.925275i | \(-0.376166\pi\) | ||||
0.379297 | + | 0.925275i | \(0.376166\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.65129e9i | 0.180838i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2.90067e10i | − 1.37215i | −0.727532 | − | 0.686074i | \(-0.759333\pi\) | ||||
0.727532 | − | 0.686074i | \(-0.240667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.70653e10 | 1.67544 | 0.837720 | − | 0.546100i | \(-0.183888\pi\) | ||||
0.837720 | + | 0.546100i | \(0.183888\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.77736e10 | −0.768056 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.69971e10i | − 0.702495i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.26102e9i | − 0.0498688i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.22232e9 | 0.311263 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.77003e10 | −1.36674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.06794e10i | − 0.370917i | −0.982652 | − | 0.185459i | \(-0.940623\pi\) | ||||
0.982652 | − | 0.185459i | \(-0.0593770\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.71046e10i | 0.569384i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.11778e9 | −0.227181 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.58148e10 | 0.790316 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 3.28183e10i | − 0.964090i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.09153e10i | 1.15377i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.10565e10 | 1.11176 | 0.555879 | − | 0.831263i | \(-0.312382\pi\) | ||||
0.555879 | + | 0.831263i | \(0.312382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.21858e10 | −0.316980 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5.35803e10i | − 1.33933i | −0.742662 | − | 0.669666i | \(-0.766437\pi\) | ||||
0.742662 | − | 0.669666i | \(-0.233563\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2.94863e10i | − 0.708534i | −0.935144 | − | 0.354267i | \(-0.884730\pi\) | ||||
0.935144 | − | 0.354267i | \(-0.115270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.86533e10 | 0.662097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.35264e10 | −0.522941 | −0.261471 | − | 0.965211i | \(-0.584207\pi\) | ||||
−0.261471 | + | 0.965211i | \(0.584207\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2.96266e9i | − 0.0633690i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.39469e10i | 0.287150i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.57950e10 | 0.709629 | 0.354815 | − | 0.934937i | \(-0.384544\pi\) | ||||
0.354815 | + | 0.934937i | \(0.384544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.63821e10 | −0.694722 | −0.347361 | − | 0.937731i | \(-0.612922\pi\) | ||||
−0.347361 | + | 0.937731i | \(0.612922\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3.48678e9i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.88611e9i | − 0.0689077i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.18293e10 | 1.39885 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.13714e10 | 1.01174 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.59465e10i | 1.20775i | 0.797080 | + | 0.603873i | \(0.206377\pi\) | ||||
−0.797080 | + | 0.603873i | \(0.793623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.40809e10i | 1.29019i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.04465e9 | 0.104335 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.54224e10 | 1.22144 | 0.610721 | − | 0.791846i | \(-0.290880\pi\) | ||||
0.610721 | + | 0.791846i | \(0.290880\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 5.40397e10i | − 0.746215i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2.11508e10i | − 0.282127i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.34744e10 | 0.560316 | 0.280158 | − | 0.959954i | \(-0.409613\pi\) | ||||
0.280158 | + | 0.959954i | \(0.409613\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.84294e10 | −0.229564 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 7.48009e10i | − 0.900753i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 2.19478e10i | − 0.255568i | −0.991802 | − | 0.127784i | \(-0.959214\pi\) | ||||
0.991802 | − | 0.127784i | \(-0.0407864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.41640e10 | 0.947904 | 0.473952 | − | 0.880551i | \(-0.342827\pi\) | ||||
0.473952 | + | 0.880551i | \(0.342827\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.21926e10 | −0.677652 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.24611e11i | − 1.31389i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.30614e10i | 0.439470i | 0.975560 | + | 0.219735i | \(0.0705193\pi\) | ||||
−0.975560 | + | 0.219735i | \(0.929481\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.21234e10 | 0.317397 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.94411e10 | 0.186012 | 0.0930062 | − | 0.995666i | \(-0.470352\pi\) | ||||
0.0930062 | + | 0.995666i | \(0.470352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 7.38936e10i | − 0.684807i | −0.939553 | − | 0.342403i | \(-0.888759\pi\) | ||||
0.939553 | − | 0.342403i | \(-0.111241\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.40891e10i | − 0.126497i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.14790e10 | 0.186872 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.96476e10 | −0.334331 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 6.41460e10i | − 0.524386i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.07308e9i | 0.0243595i | 0.999926 | + | 0.0121798i | \(0.00387704\pi\) | ||||
−0.999926 | + | 0.0121798i | \(0.996123\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.77730e9 | −0.0213513 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.56556e10 | 0.265903 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.82499e11i | − 1.32051i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.21238e11i | − 0.851311i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.77678e10 | −0.598196 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.66325e10 | 0.374728 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.68581e9i | 0.0493818i | 0.999695 | + | 0.0246909i | \(0.00786016\pi\) | ||||
−0.999695 | + | 0.0246909i | \(0.992140\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 9.51315e10i | − 0.593623i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.31483e11 | 1.40313 | 0.701564 | − | 0.712607i | \(-0.252486\pi\) | ||||
0.701564 | + | 0.712607i | \(0.252486\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.14841e10 | 0.420979 | 0.210489 | − | 0.977596i | \(-0.432494\pi\) | ||||
0.210489 | + | 0.977596i | \(0.432494\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.07081e10i | 0.0612795i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6.96471e10i | − 0.387380i | −0.981063 | − | 0.193690i | \(-0.937954\pi\) | ||||
0.981063 | − | 0.193690i | \(-0.0620455\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.16287e11 | 1.16942 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.67115e10 | 0.350694 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.57878e11i | − 0.807069i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.70470e11i | 1.34476i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.17431e11 | 0.567960 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.04632e10 | 0.237461 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 3.26115e11i | − 1.49329i | −0.665221 | − | 0.746646i | \(-0.731663\pi\) | ||||
0.665221 | − | 0.746646i | \(-0.268337\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.72458e10i | − 0.299686i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.79228e10 | 0.294655 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.97450e11 | 1.25626 | 0.628130 | − | 0.778108i | \(-0.283821\pi\) | ||||
0.628130 | + | 0.778108i | \(0.283821\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.75481e11i | 0.721657i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.28492e11i | 1.31562i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.78957e11 | 1.08821 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.14221e10 | −0.119412 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.03340e11i | − 0.752905i | −0.926436 | − | 0.376452i | \(-0.877144\pi\) | ||||
0.926436 | − | 0.376452i | \(-0.122856\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.09580e11i | 0.395384i | 0.980264 | + | 0.197692i | \(0.0633445\pi\) | ||||
−0.980264 | + | 0.197692i | \(0.936655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.73912e10 | −0.272151 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.46299e10 | −0.255815 | −0.127908 | − | 0.991786i | \(-0.540826\pi\) | ||||
−0.127908 | + | 0.991786i | \(0.540826\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 6.53663e10i | − 0.218437i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.19992e11i | 0.390971i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.98306e11 | 1.58333 | 0.791664 | − | 0.610957i | \(-0.209215\pi\) | ||||
0.791664 | + | 0.610957i | \(0.209215\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.93654e9 | 0.0214961 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.73618e11i | 0.524825i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.25417e11i | 0.369861i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.00929e11 | −0.578158 | −0.289079 | − | 0.957305i | \(-0.593349\pi\) | ||||
−0.289079 | + | 0.957305i | \(0.593349\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.67280e10 | 0.0750494 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.13909e11i | − 0.860242i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2.20541e11i | − 0.589930i | −0.955508 | − | 0.294965i | \(-0.904692\pi\) | ||||
0.955508 | − | 0.294965i | \(-0.0953079\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.55398e10 | 0.249484 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.69455e11 | −1.19690 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3.61774e11i | − 0.900660i | −0.892862 | − | 0.450330i | \(-0.851306\pi\) | ||||
0.892862 | − | 0.450330i | \(-0.148694\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.96662e11i | 0.721273i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.73049e10 | 0.231068 | 0.115534 | − | 0.993304i | \(-0.463142\pi\) | ||||
0.115534 | + | 0.993304i | \(0.463142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.09500e11 | −0.254005 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.50865e11i | − 0.341893i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6.77438e11i | − 1.50002i | −0.661428 | − | 0.750009i | \(-0.730049\pi\) | ||||
0.661428 | − | 0.750009i | \(-0.269951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.52106e11 | −0.761866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.02157e11 | −0.638949 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 5.32988e10i | − 0.110162i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.50301e11i | − 0.909799i | −0.890543 | − | 0.454899i | \(-0.849675\pi\) | ||||
0.890543 | − | 0.454899i | \(-0.150325\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.39980e11 | 0.474020 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.04222e11 | −1.16694 | −0.583468 | − | 0.812136i | \(-0.698305\pi\) | ||||
−0.583468 | + | 0.812136i | \(0.698305\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 7.12998e11i | − 1.34653i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.33249e10i | 0.0246103i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.87651e11 | 1.24220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.46829e11 | −0.789563 | −0.394782 | − | 0.918775i | \(-0.629180\pi\) | ||||
−0.394782 | + | 0.918775i | \(0.629180\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 3.77425e11i | − 0.652443i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.73059e10i | − 0.0800092i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.34534e11 | −0.388141 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.73279e11 | −0.280629 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.15985e11i | 0.342342i | 0.985241 | + | 0.171171i | \(0.0547551\pi\) | ||||
−0.985241 | + | 0.171171i | \(0.945245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 2.01623e11i | − 0.312803i | −0.987694 | − | 0.156402i | \(-0.950011\pi\) | ||||
0.987694 | − | 0.156402i | \(-0.0499894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.27953e10 | 0.0953664 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.21835e11 | 0.775859 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.64625e11i | 1.40421i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 7.91396e11i | − 1.12807i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.02060e12 | −1.42466 | −0.712328 | − | 0.701847i | \(-0.752359\pi\) | ||||
−0.712328 | + | 0.701847i | \(0.752359\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.31704e12 | 1.80054 | 0.900269 | − | 0.435335i | \(-0.143370\pi\) | ||||
0.900269 | + | 0.435335i | \(0.143370\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.08291e10i | 0.108235i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.04201e11i | 0.923699i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.17939e12 | 1.51554 | 0.757769 | − | 0.652523i | \(-0.226289\pi\) | ||||
0.757769 | + | 0.652523i | \(0.226289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.23683e10 | 0.103702 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.50044e11i | 0.925273i | 0.886548 | + | 0.462636i | \(0.153096\pi\) | ||||
−0.886548 | + | 0.462636i | \(0.846904\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.85856e11i | 0.345563i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.01882e11 | 0.239174 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.15176e11 | −0.946548 | −0.473274 | − | 0.880915i | \(-0.656928\pi\) | ||||
−0.473274 | + | 0.880915i | \(0.656928\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.73318e11i | 0.311082i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.19791e10i | 0.0803091i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.37672e11 | 0.259973 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.63242e11 | 0.389559 | 0.194779 | − | 0.980847i | \(-0.437601\pi\) | ||||
0.194779 | + | 0.980847i | \(0.437601\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.49315e11i | 0.157017i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.30313e12i | − 1.34380i | −0.740643 | − | 0.671899i | \(-0.765479\pi\) | ||||
0.740643 | − | 0.671899i | \(-0.234521\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.12709e12 | −1.13984 | −0.569920 | − | 0.821700i | \(-0.693026\pi\) | ||||
−0.569920 | + | 0.821700i | \(0.693026\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.22761e11 | −0.121765 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.62119e12i | 1.57727i | 0.614859 | + | 0.788637i | \(0.289213\pi\) | ||||
−0.614859 | + | 0.788637i | \(0.710787\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.15693e12i | 1.10416i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.84111e11 | 0.172379 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.54274e12 | 1.41715 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.04365e12i | − 0.940665i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.90621e11i | − 0.345480i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.14450e11 | −0.533306 | −0.266653 | − | 0.963793i | \(-0.585918\pi\) | ||||
−0.266653 | + | 0.963793i | \(0.585918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.49256e12 | −1.27139 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 5.35213e11i | − 0.447471i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.45138e11i | 0.201174i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.12192e12 | 1.70942 | 0.854709 | − | 0.519107i | \(-0.173735\pi\) | ||||
0.854709 | + | 0.519107i | \(0.173735\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.94231e9 | −0.00549053 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 1.80606e12i | − 1.40238i | −0.712974 | − | 0.701191i | \(-0.752652\pi\) | ||||
0.712974 | − | 0.701191i | \(-0.247348\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.05747e11i | 0.690551i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.36260e11 | −0.102010 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.11339e12 | 0.818545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 5.53469e11i | − 0.399614i | −0.979835 | − | 0.199807i | \(-0.935968\pi\) | ||||
0.979835 | − | 0.199807i | \(-0.0640315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 1.25010e12i | − 0.886491i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.40841e12 | −1.67754 | −0.838772 | − | 0.544482i | \(-0.816726\pi\) | ||||
−0.838772 | + | 0.544482i | \(0.816726\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.35409e11 | 0.229490 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.58776e11i | 0.577224i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.01973e12i | − 0.673375i | −0.941616 | − | 0.336687i | \(-0.890693\pi\) | ||||
0.941616 | − | 0.336687i | \(-0.109307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.13623e12 | −1.38597 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.98626e11 | 0.190370 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.63550e11i | 0.227736i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.42140e11i | 0.395296i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.05722e11 | −0.426954 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.56824e12 | −1.52709 | −0.763547 | − | 0.645753i | \(-0.776544\pi\) | ||||
−0.763547 | + | 0.645753i | \(0.776544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.89472e12i | 1.10736i | 0.832731 | + | 0.553678i | \(0.186776\pi\) | ||||
−0.832731 | + | 0.553678i | \(0.813224\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.93206e11i | 0.455690i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.37563e12 | −0.776879 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.30613e11 | −0.128036 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5.88664e10i | − 0.0321323i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5.93242e11i | − 0.318390i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.54941e11 | −0.134539 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.07521e11 | −0.315266 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.42292e11i | 0.429846i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.87444e12i | 0.940772i | 0.882461 | + | 0.470386i | \(0.155885\pi\) | ||||
−0.882461 | + | 0.470386i | \(0.844115\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.55952e12 | −0.769826 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.48769e11 | −0.217891 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.54576e12i | 1.69343i | 0.532049 | + | 0.846713i | \(0.321422\pi\) | ||||
−0.532049 | + | 0.846713i | \(0.678578\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.20036e12i | 0.563943i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.81147e12 | 0.837236 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.07841e11 | 0.412807 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.56984e11i | 0.114971i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.10406e12i | 1.36641i | 0.730226 | + | 0.683206i | \(0.239415\pi\) | ||||
−0.730226 | + | 0.683206i | \(0.760585\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.34854e12 | −1.45045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.52689e12 | −0.650840 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.85117e11i | 0.245445i | 0.992441 | + | 0.122723i | \(0.0391625\pi\) | ||||
−0.992441 | + | 0.122723i | \(0.960837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 6.70610e11i | − 0.276855i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.26964e11 | −0.0922219 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.06739e11 | 0.282653 | 0.141327 | − | 0.989963i | \(-0.454863\pi\) | ||||
0.141327 | + | 0.989963i | \(0.454863\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.79486e12i | 1.88762i | 0.330495 | + | 0.943808i | \(0.392784\pi\) | ||||
−0.330495 | + | 0.943808i | \(0.607216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.35310e11i | 0.246201i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.32760e12 | −0.887979 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.75415e12 | 1.41000 | 0.705001 | − | 0.709206i | \(-0.250946\pi\) | ||||
0.705001 | + | 0.709206i | \(0.250946\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.18441e12i | − 0.437975i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 3.99483e12i | − 1.45447i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.99446e12 | 1.43202 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.95755e11 | 0.104407 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.48518e12i | 0.863946i | 0.901887 | + | 0.431973i | \(0.142182\pi\) | ||||
−0.901887 | + | 0.431973i | \(0.857818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.75121e12i | 0.941902i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.34955e12 | −0.792210 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.26542e12 | 0.420230 | 0.210115 | − | 0.977677i | \(-0.432616\pi\) | ||||
0.210115 | + | 0.977677i | \(0.432616\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.58556e11i | − 0.149991i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.00229e12i | − 0.967315i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.21302e12 | 1.01975 | 0.509873 | − | 0.860249i | \(-0.329692\pi\) | ||||
0.509873 | + | 0.860249i | \(0.329692\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.89466e12 | 1.84299 | 0.921496 | − | 0.388387i | \(-0.126968\pi\) | ||||
0.921496 | + | 0.388387i | \(0.126968\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.43966e12i | 0.443438i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 6.63490e11i | − 0.201342i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.40258e12 | −1.91428 | −0.957141 | − | 0.289622i | \(-0.906470\pi\) | ||||
−0.957141 | + | 0.289622i | \(0.906470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.37677e12 | −0.405585 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.39378e12i | − 0.404583i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.04612e12i | 1.15735i | 0.815557 | + | 0.578677i | \(0.196431\pi\) | ||||
−0.815557 | + | 0.578677i | \(0.803569\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.02142e11 | −0.0287917 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.75659e12 | −1.87691 | −0.938456 | − | 0.345398i | \(-0.887744\pi\) | ||||
−0.938456 | + | 0.345398i | \(0.887744\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 2.17914e10i | − 0.00596592i | −0.999996 | − | 0.00298296i | \(-0.999050\pi\) | ||||
0.999996 | − | 0.00298296i | \(-0.000949507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 6.66008e11i | − 0.179708i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.86899e12 | −1.29492 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.26244e12 | 0.855229 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.05373e12i | 0.789089i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.87968e12i | 0.733528i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.02427e12 | −1.26166 | −0.630828 | − | 0.775922i | \(-0.717285\pi\) | ||||
−0.630828 | + | 0.775922i | \(0.717285\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.65033e11 | −0.214149 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.13371e12i | − 0.276707i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.82821e12i | − 0.439945i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.38548e12 | 0.328734 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.91095e12 | 1.14896 | 0.574479 | − | 0.818519i | \(-0.305205\pi\) | ||||
0.574479 | + | 0.818519i | \(0.305205\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.32211e12i | 1.68922i | 0.535381 | + | 0.844611i | \(0.320168\pi\) | ||||
−0.535381 | + | 0.844611i | \(0.679832\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.76540e11i | 0.131163i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.54218e12 | 0.794697 | 0.397349 | − | 0.917668i | \(-0.369930\pi\) | ||||
0.397349 | + | 0.917668i | \(0.369930\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.01963e11 | 0.133189 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2.09100e12i | − 0.456289i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.23728e11i | 0.177286i | 0.996063 | + | 0.0886430i | \(0.0282530\pi\) | ||||
−0.996063 | + | 0.0886430i | \(0.971747\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.15471e12 | 0.245125 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.65828e12 | −0.556618 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.70546e12i | 1.17844i | 0.807974 | + | 0.589218i | \(0.200564\pi\) | ||||
−0.807974 | + | 0.589218i | \(0.799436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 4.16492e12i | − 0.848593i | −0.905523 | − | 0.424297i | \(-0.860521\pi\) | ||||
0.905523 | − | 0.424297i | \(-0.139479\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.31414e12 | 0.666131 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.17097e11 | −0.181852 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.04001e12i | − 0.790343i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 3.32558e12i | − 0.641873i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.22748e13 | −2.33756 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.31368e11 | 0.0810551 | 0.0405276 | − | 0.999178i | \(-0.487096\pi\) | ||||
0.0405276 | + | 0.999178i | \(0.487096\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.87049e11i | 0.183009i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 8.06501e12i | − 1.47556i | −0.675043 | − | 0.737778i | \(-0.735875\pi\) | ||||
0.675043 | − | 0.737778i | \(-0.264125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.17544e12 | −0.753856 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.34000e12 | −0.773264 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.19549e12i | 0.561882i | 0.959725 | + | 0.280941i | \(0.0906465\pi\) | ||||
−0.959725 | + | 0.280941i | \(0.909354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.44235e12i | 0.250301i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.38839e12 | −0.409072 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.67006e12 | −1.46567 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 8.23728e12i | − 1.37446i | −0.726439 | − | 0.687231i | \(-0.758826\pi\) | ||||
0.726439 | − | 0.687231i | \(-0.241174\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.32092e12i | − 0.382262i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.62194e11 | 0.107660 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.14458e12 | −0.183695 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.90564e12i | 0.301920i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 9.25378e12i | − 1.44740i | −0.690116 | − | 0.723699i | \(-0.742440\pi\) | ||||
0.690116 | − | 0.723699i | \(-0.257560\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.75928e12 | 0.889342 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.39976e11 | −0.0365861 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.71305e12i | 0.859964i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.53630e12i | 1.26871i | 0.773043 | + | 0.634354i | \(0.218734\pi\) | ||||
−0.773043 | + | 0.634354i | \(0.781266\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.12970e12 | 0.165786 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.13587e12 | 0.889147 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.02436e12i | 0.432770i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.89939e12i | − 0.409705i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.29268e11 | −0.0599031 | −0.0299515 | − | 0.999551i | \(-0.509535\pi\) | ||||
−0.0299515 | + | 0.999551i | \(0.509535\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.19237e12 | −0.853391 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.94695e12i | 0.401098i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.98744e12i | 0.804859i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.30507e13 | 1.73272 | 0.866360 | − | 0.499420i | \(-0.166454\pi\) | ||||
0.866360 | + | 0.499420i | \(0.166454\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.46055e12i | 0.836837i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.38098e13i | 1.76693i | 0.468500 | + | 0.883463i | \(0.344794\pi\) | ||||
−0.468500 | + | 0.883463i | \(0.655206\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.14775e11 | −0.0397839 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.47219e13 | −1.83806 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.03935e12i | − 0.251532i | −0.992060 | − | 0.125766i | \(-0.959861\pi\) | ||||
0.992060 | − | 0.125766i | \(-0.0401388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 6.62817e12i | − 0.807629i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.47512e11 | 0.102023 | 0.0510113 | − | 0.998698i | \(-0.483756\pi\) | ||||
0.0510113 | + | 0.998698i | \(0.483756\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.71502e11 | −0.0917558 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.97109e12i | − 0.584129i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 4.34243e12i | − 0.504156i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.58689e13 | −1.82040 | −0.910198 | − | 0.414173i | \(-0.864071\pi\) | ||||
−0.910198 | + | 0.414173i | \(0.864071\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.15166e12 | 0.697293 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2.75072e11i | − 0.0308095i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.67467e12i | 0.628072i | 0.949411 | + | 0.314036i | \(0.101681\pi\) | ||||
−0.949411 | + | 0.314036i | \(0.898319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.81055e12 | 0.744893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.49613e11 | 0.0918312 | 0.0459156 | − | 0.998945i | \(-0.485379\pi\) | ||||
0.0459156 | + | 0.998945i | \(0.485379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.64390e12i | − 0.816497i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 5.70617e11i | − 0.0602377i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.30657e12 | −0.136318 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.44948e13 | 1.49467 | 0.747333 | − | 0.664450i | \(-0.231334\pi\) | ||||
0.747333 | + | 0.664450i | \(0.231334\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 6.91921e12i | − 0.705200i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.06395e12i | 0.711607i | 0.934561 | + | 0.355803i | \(0.115793\pi\) | ||||
−0.934561 | + | 0.355803i | \(0.884207\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.09359e12 | −0.905478 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.37722e12 | −0.430827 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.28912e12i | 0.222715i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.41678e13i | 1.36261i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.71322e12 | −0.162886 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.03589e11 | −0.0661310 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 4.72071e11i | − 0.0438653i | −0.999759 | − | 0.0219326i | \(-0.993018\pi\) | ||||
0.999759 | − | 0.0219326i | \(-0.00698193\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 3.52143e12i | − 0.323499i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.14225e13 | 1.03745 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.66426e13 | 2.39248 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.49278e12i | 0.132539i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.16384e13i | − 1.02171i | −0.859666 | − | 0.510857i | \(-0.829328\pi\) | ||||
0.859666 | − | 0.510857i | \(-0.170672\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.68910e12 | −0.233424 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.05887e12 | −0.520050 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.71834e13i | − 2.30719i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.04535e12i | 0.171667i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.77777e12 | −0.147552 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.50266e13 | −1.23337 | −0.616684 | − | 0.787210i | \(-0.711525\pi\) | ||||
−0.616684 | + | 0.787210i | \(0.711525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 7.77282e12i | − 0.630935i | −0.948936 | − | 0.315468i | \(-0.897839\pi\) | ||||
0.948936 | − | 0.315468i | \(-0.102161\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.81728e12i | − 0.547273i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.65304e10 | 0.00210637 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.29209e13 | 1.01460 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.03760e12i | 0.391243i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.88473e13i | − 1.44779i | −0.689911 | − | 0.723894i | \(-0.742351\pi\) | ||||
0.689911 | − | 0.723894i | \(-0.257649\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.03328e13 | 0.785089 | 0.392545 | − | 0.919733i | \(-0.371595\pi\) | ||||
0.392545 | + | 0.919733i | \(0.371595\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.00935e13 | −0.758575 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 4.38883e12i | − 0.326268i | −0.986604 | − | 0.163134i | \(-0.947840\pi\) | ||||
0.986604 | − | 0.163134i | \(-0.0521603\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 2.55336e12i | − 0.187766i | −0.995583 | − | 0.0938828i | \(-0.970072\pi\) | ||||
0.995583 | − | 0.0938828i | \(-0.0299279\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.48798e12 | 0.253728 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.52728e12 | −0.253826 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.77732e12i | 0.340091i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2.60200e12i | − 0.183249i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.82154e13 | 1.26914 | 0.634570 | − | 0.772866i | \(-0.281177\pi\) | ||||
0.634570 | + | 0.772866i | \(0.281177\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.11476e12 | 0.283637 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.57473e12i | − 0.107394i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 3.28186e12i | − 0.221444i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.13013e13 | 0.754486 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.98538e12 | −0.395373 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.28446e13i | − 0.839531i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.23877e12i | 0.468160i | 0.972217 | + | 0.234080i | \(0.0752077\pi\) | ||||
−0.972217 | + | 0.234080i | \(0.924792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.14122e12 | −0.0730332 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.12329e11 | −0.0387768 | −0.0193884 | − | 0.999812i | \(-0.506172\pi\) | ||||
−0.0193884 | + | 0.999812i | \(0.506172\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.23751e12i | 0.328213i | 0.986443 | + | 0.164106i | \(0.0524741\pi\) | ||||
−0.986443 | + | 0.164106i | \(0.947526\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.73980e12i | − 0.107891i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.53764e13 | 1.55733 | 0.778667 | − | 0.627437i | \(-0.215896\pi\) | ||||
0.778667 | + | 0.627437i | \(0.215896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.69696e12 | 0.163795 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.21145e12i | 0.193026i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.15522e13i | 0.687188i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.19541e13 | 1.88124 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.19583e12 | −0.302755 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6.21895e12i | − 0.358658i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.79628e12i | − 0.216701i | −0.994113 | − | 0.108350i | \(-0.965443\pi\) | ||||
0.994113 | − | 0.108350i | \(-0.0345568\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.48919e11 | 0.0140640 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.09066e13 | 0.609955 | 0.304977 | − | 0.952360i | \(-0.401351\pi\) | ||||
0.304977 | + | 0.952360i | \(0.401351\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.44991e12i | 0.135621i | 0.997698 | + | 0.0678105i | \(0.0216013\pi\) | ||||
−0.997698 | + | 0.0678105i | \(0.978399\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.24961e11i | 0.0123272i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.15847e13 | −1.17082 | −0.585410 | − | 0.810737i | \(-0.699067\pi\) | ||||
−0.585410 | + | 0.810737i | \(0.699067\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.93105e13 | 1.03690 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2.88810e12i | − 0.153519i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.37811e12i | 0.283008i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.32167e12 | 0.120948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.47824e13 | −0.762394 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.57837e13i | − 0.805918i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.67277e13i | 0.845617i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.82024e12 | −0.491504 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.95980e12 | 0.295334 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.44358e13i | − 0.708287i | −0.935191 | − | 0.354144i | \(-0.884772\pi\) | ||||
0.935191 | − | 0.354144i | \(-0.115228\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.10919e12i | 0.345368i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.86787e13 | 1.37952 | 0.689759 | − | 0.724039i | \(-0.257716\pi\) | ||||
0.689759 | + | 0.724039i | \(0.257716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.08340e13 | 2.42123 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 4.58723e12i | − 0.216349i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.96682e13i | 0.918551i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.98333e13 | 1.37969 | 0.689845 | − | 0.723957i | \(-0.257678\pi\) | ||||
0.689845 | + | 0.723957i | \(0.257678\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.22551e11 | 0.0285106 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.07514e13i | − 1.39462i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.90361e13i | 0.854951i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.70565e12 | −0.342729 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.98679e13 | −0.875148 | −0.437574 | − | 0.899182i | \(-0.644162\pi\) | ||||
−0.437574 | + | 0.899182i | \(0.644162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.05444e12i | 0.307743i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.87501e13i | − 0.810096i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.83509e12 | 0.249686 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.96309e12 | −0.422246 | −0.211123 | − | 0.977459i | \(-0.567712\pi\) | ||||
−0.211123 | + | 0.977459i | \(0.567712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 5.79021e12i | − 0.243052i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.05934e13i | − 0.856197i | −0.903732 | − | 0.428099i | \(-0.859184\pi\) | ||||
0.903732 | − | 0.428099i | \(-0.140816\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.10529e12 | 0.210241 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.67357e11 | 0.0353797 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.73914e13i | 0.702681i | 0.936248 | + | 0.351341i | \(0.114274\pi\) | ||||
−0.936248 | + | 0.351341i | \(0.885726\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.90021e13i | 2.36140i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.64142e12 | −0.223654 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.85939e13 | −0.730219 | −0.365109 | − | 0.930965i | \(-0.618968\pi\) | ||||
−0.365109 | + | 0.930965i | \(0.618968\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2.42787e12i | − 0.0944518i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.75192e13i | − 0.675168i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.45676e13 | −0.937949 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.46764e12 | −0.0933312 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 5.40363e12i | − 0.202473i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.52629e12i | 0.168023i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.68504e13 | −0.987489 | −0.493744 | − | 0.869607i | \(-0.664372\pi\) | ||||
−0.493744 | + | 0.869607i | \(0.664372\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.27881e13 | −0.465961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.06066e13i | − 0.743908i | −0.928251 | − | 0.371954i | \(-0.878688\pi\) | ||||
0.928251 | − | 0.371954i | \(-0.121312\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.12792e13i | 0.403432i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.19081e13 | 0.776397 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.31007e13 | 0.811146 | 0.405573 | − | 0.914063i | \(-0.367072\pi\) | ||||
0.405573 | + | 0.914063i | \(0.367072\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 6.19576e13i | − 2.15562i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 9.51191e12i | − 0.327912i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.68661e12 | −0.296729 | −0.148364 | − | 0.988933i | \(-0.547401\pi\) | ||||
−0.148364 | + | 0.988933i | \(0.547401\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.97892e12 | 0.303921 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 4.08752e12i | − 0.137098i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2.88167e13i | − 0.957769i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.74347e13 | 0.903585 | 0.451793 | − | 0.892123i | \(-0.350785\pi\) | ||||
0.451793 | + | 0.892123i | \(0.350785\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.64153e13 | −0.862153 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.14734e13i | 0.371098i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 6.62173e12i | − 0.212248i | −0.994353 | − | 0.106124i | \(-0.966156\pi\) | ||||
0.994353 | − | 0.106124i | \(-0.0338440\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.44691e12 | −0.173024 |
(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.d.193.3 | yes | 10 | |
4.3 | odd | 2 | 384.10.d.c.193.8 | yes | 10 | ||
8.3 | odd | 2 | 384.10.d.c.193.3 | ✓ | 10 | ||
8.5 | even | 2 | inner | 384.10.d.d.193.8 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.d.c.193.3 | ✓ | 10 | 8.3 | odd | 2 | ||
384.10.d.c.193.8 | yes | 10 | 4.3 | odd | 2 | ||
384.10.d.d.193.3 | yes | 10 | 1.1 | even | 1 | trivial | |
384.10.d.d.193.8 | yes | 10 | 8.5 | even | 2 | inner |