Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,12,Mod(33,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.33");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.e (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(98.3479271116\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 33.6 | ||
Character | \(\chi\) | \(=\) | 128.33 |
Dual form | 128.12.e.b.97.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −255.917 | − | 255.917i | −0.608040 | − | 0.608040i | 0.334394 | − | 0.942433i | \(-0.391468\pi\) |
−0.942433 | + | 0.334394i | \(0.891468\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4214.49 | − | 4214.49i | 0.603128 | − | 0.603128i | −0.338013 | − | 0.941141i | \(-0.609755\pi\) |
0.941141 | + | 0.338013i | \(0.109755\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 80345.3i | − | 1.80685i | −0.428751 | − | 0.903423i | \(-0.641046\pi\) | ||
0.428751 | − | 0.903423i | \(-0.358954\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 46160.2i | − | 0.260576i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −611105. | + | 611105.i | −1.14408 | + | 1.14408i | −0.156382 | + | 0.987697i | \(0.549983\pi\) |
−0.987697 | + | 0.156382i | \(0.950017\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −370364. | − | 370364.i | −0.276656 | − | 0.276656i | 0.555116 | − | 0.831773i | \(-0.312674\pi\) |
−0.831773 | + | 0.555116i | \(0.812674\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.15712e6 | −0.733452 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −725142. | −0.123867 | −0.0619333 | − | 0.998080i | \(-0.519727\pi\) | ||||
−0.0619333 | + | 0.998080i | \(0.519727\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.13100e7 | + | 1.13100e7i | 1.04789 | + | 1.04789i | 0.998794 | + | 0.0490973i | \(0.0156345\pi\) |
0.0490973 | + | 0.998794i | \(0.484366\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.05617e7 | + | 2.05617e7i | −1.09863 | + | 1.09863i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.89011e7i | 1.58422i | 0.610378 | + | 0.792110i | \(0.291018\pi\) | ||||
−0.610378 | + | 0.792110i | \(0.708982\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.33043e7i | 0.272472i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.71481e7 | + | 5.71481e7i | −0.766480 | + | 0.766480i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.98291e7 | − | 4.98291e7i | −0.451122 | − | 0.451122i | 0.444605 | − | 0.895727i | \(-0.353344\pi\) |
−0.895727 | + | 0.444605i | \(0.853344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.20747e7 | 0.263956 | 0.131978 | − | 0.991253i | \(-0.457867\pi\) | ||||
0.131978 | + | 0.991253i | \(0.457867\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.12784e8 | 1.39129 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.38614e8 | − | 3.38614e8i | −1.08976 | − | 1.08976i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.05666e8 | − | 1.05666e8i | 0.250510 | − | 0.250510i | −0.570670 | − | 0.821180i | \(-0.693316\pi\) |
0.821180 | + | 0.570670i | \(0.193316\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.89565e8i | 0.336436i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.49063e8i | − | 0.605335i | −0.953096 | − | 0.302668i | \(-0.902123\pi\) | ||
0.953096 | − | 0.302668i | \(-0.0978772\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.89791e8 | + | 7.89791e8i | −0.819286 | + | 0.819286i | −0.986005 | − | 0.166718i | \(-0.946683\pi\) |
0.166718 | + | 0.986005i | \(0.446683\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.94542e8 | − | 1.94542e8i | −0.157161 | − | 0.157161i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.32368e9 | 0.841870 | 0.420935 | − | 0.907091i | \(-0.361702\pi\) | ||||
0.420935 | + | 0.907091i | \(0.361702\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.47803e9 | −2.26469 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.85576e8 | + | 1.85576e8i | 0.0753158 | + | 0.0753158i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.74345e9 | + | 1.74345e9i | −0.572655 | + | 0.572655i | −0.932870 | − | 0.360214i | \(-0.882704\pi\) |
0.360214 | + | 0.932870i | \(0.382704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.15099e9i | 1.38005i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.78882e9i | − | 1.27432i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.71604e8 | − | 6.71604e8i | 0.122300 | − | 0.122300i | −0.643308 | − | 0.765608i | \(-0.722438\pi\) |
0.765608 | + | 0.643308i | \(0.222438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.30682e8 | + | 8.30682e8i | 0.125928 | + | 0.125928i | 0.767262 | − | 0.641334i | \(-0.221619\pi\) |
−0.641334 | + | 0.767262i | \(0.721619\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.70875e9 | −0.470820 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.12179e9 | −0.333718 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.88275e9 | − | 3.88275e9i | −0.351340 | − | 0.351340i | 0.509268 | − | 0.860608i | \(-0.329916\pi\) |
−0.860608 | + | 0.509268i | \(0.829916\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.25146e10 | − | 1.25146e10i | 0.963269 | − | 0.963269i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.14233e9i | 0.338251i | 0.985595 | + | 0.169125i | \(0.0540943\pi\) | ||||
−0.985595 | + | 0.169125i | \(0.945906\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.42543e9i | 0.249850i | 0.992166 | + | 0.124925i | \(0.0398690\pi\) | ||||
−0.992166 | + | 0.124925i | \(0.960131\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.40480e9 | − | 3.40480e9i | 0.165674 | − | 0.165674i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.90994e10 | + | 4.90994e10i | 2.06717 | + | 2.06717i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.71827e10 | 0.993902 | 0.496951 | − | 0.867779i | \(-0.334453\pi\) | ||||
0.496951 | + | 0.867779i | \(0.334453\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.10732e10 | 0.671525 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.81378e10 | − | 1.81378e10i | −0.505423 | − | 0.505423i | 0.407695 | − | 0.913118i | \(-0.366333\pi\) |
−0.913118 | + | 0.407695i | \(0.866333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.05610e9 | + | 3.05610e9i | −0.0747075 | + | 0.0747075i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.55042e10i | 0.548600i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.56593e10i | − | 1.05656i | −0.849071 | − | 0.528278i | \(-0.822838\pi\) | ||
0.849071 | − | 0.528278i | \(-0.177162\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.97570e10 | + | 2.97570e10i | −0.499875 | + | 0.499875i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.07676e10 | − | 1.07676e10i | −0.160496 | − | 0.160496i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.53314e10 | 1.26403 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.61297e10 | 0.308951 | 0.154476 | − | 0.987997i | \(-0.450631\pi\) | ||||
0.154476 | + | 0.987997i | \(0.450631\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.82087e10 | + | 2.82087e10i | 0.298119 | + | 0.298119i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.83525e10 | − | 4.83525e10i | 0.457774 | − | 0.457774i | −0.440150 | − | 0.897924i | \(-0.645075\pi\) |
0.897924 | + | 0.440150i | \(0.145075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.13751e10i | 0.691651i | 0.938299 | + | 0.345825i | \(0.112401\pi\) | ||||
−0.938299 | + | 0.345825i | \(0.887599\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.73314e11i | 1.32523i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.97606e10 | − | 1.97606e10i | 0.136204 | − | 0.136204i | −0.635718 | − | 0.771922i | \(-0.719296\pi\) |
0.771922 | + | 0.635718i | \(0.219296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.02515e11 | − | 1.02515e11i | −0.638175 | − | 0.638175i | 0.311930 | − | 0.950105i | \(-0.399025\pi\) |
−0.950105 | + | 0.311930i | \(0.899025\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.40834e10 | −0.304640 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.99733e11 | 1.53039 | 0.765196 | − | 0.643798i | \(-0.222642\pi\) | ||||
0.765196 | + | 0.643798i | \(0.222642\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.06093e11 | + | 2.06093e11i | 0.955488 | + | 0.955488i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.70961e10 | + | 1.70961e10i | −0.0720899 | + | 0.0720899i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.82617e10i | 0.223808i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 4.61586e11i | − | 1.61783i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.14923e11 | + | 1.14923e11i | −0.368068 | + | 0.368068i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.61856e11 | + | 2.61856e11i | 0.767464 | + | 0.767464i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.80100e11 | −1.82664 | −0.913319 | − | 0.407245i | \(-0.866490\pi\) | ||||
−0.913319 | + | 0.407245i | \(0.866490\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.04242e11 | 0.996317 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.89403e11 | + | 4.89403e11i | 1.10834 | + | 1.10834i | 0.993368 | + | 0.114976i | \(0.0366790\pi\) |
0.114976 | + | 0.993368i | \(0.463321\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.08702e11 | − | 9.08702e11i | 1.89338 | − | 1.89338i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.81700e11i | 0.924572i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.45344e11i | 1.14243i | 0.820802 | + | 0.571213i | \(0.193527\pi\) | ||||
−0.820802 | + | 0.571213i | \(0.806473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.22257e11 | + | 7.22257e11i | −1.18062 | + | 1.18062i | −0.201036 | + | 0.979584i | \(0.564431\pi\) |
−0.979584 | + | 0.201036i | \(0.935569\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.38752e11 | − | 3.38752e11i | −0.511890 | − | 0.511890i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.52662e11 | 0.633033 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.20008e11 | −0.544169 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.14600e12 | + | 1.14600e12i | 1.37702 | + | 1.37702i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.59849e11 | + | 7.59849e11i | −0.847623 | + | 0.847623i | −0.989836 | − | 0.142213i | \(-0.954578\pi\) |
0.142213 | + | 0.989836i | \(0.454578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.60628e12i | 1.66513i | 0.553925 | + | 0.832566i | \(0.313129\pi\) | ||||
−0.553925 | + | 0.832566i | \(0.686871\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.34727e10i | 0.0322766i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.77323e11 | − | 1.77323e11i | 0.159200 | − | 0.159200i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.80944e11 | + | 4.80944e11i | 0.402389 | + | 0.402389i | 0.879074 | − | 0.476685i | \(-0.158162\pi\) |
−0.476685 | + | 0.879074i | \(0.658162\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.92358e11 | 0.696394 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.92897e12 | 2.86244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.15153e12 | − | 1.15153e12i | −0.783872 | − | 0.783872i | 0.196610 | − | 0.980482i | \(-0.437007\pi\) |
−0.980482 | + | 0.196610i | \(0.937007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.31822e12 | − | 1.31822e12i | 0.839127 | − | 0.839127i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.12515e12i | − | 0.670301i | −0.942165 | − | 0.335150i | \(-0.891213\pi\) | ||
0.942165 | − | 0.335150i | \(-0.108787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.51782e12i | − | 0.846923i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.22070e11 | − | 5.22070e11i | 0.273055 | − | 0.273055i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.94285e11 | + | 3.94285e11i | 0.193445 | + | 0.193445i | 0.797183 | − | 0.603738i | \(-0.206323\pi\) |
−0.603738 | + | 0.797183i | \(0.706323\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.06894e12 | 0.492315 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.43750e11 | −0.148727 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.94035e11 | − | 4.94035e11i | −0.200940 | − | 0.200940i | 0.599463 | − | 0.800403i | \(-0.295381\pi\) |
−0.800403 | + | 0.599463i | \(0.795381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.41767e12 | − | 1.41767e12i | 0.542430 | − | 0.542430i | −0.381811 | − | 0.924240i | \(-0.624699\pi\) |
0.924240 | + | 0.381811i | \(0.124699\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.25171e11i | − | 0.153138i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 8.90656e11i | − | 0.302180i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.43138e11 | − | 4.43138e11i | 0.141713 | − | 0.141713i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.59158e12 | + | 4.59158e12i | 1.38491 | + | 1.38491i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.48907e12 | 0.423868 | 0.211934 | − | 0.977284i | \(-0.432024\pi\) | ||||
0.211934 | + | 0.977284i | \(0.432024\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.59604e11 | 0.123543 | 0.0617716 | − | 0.998090i | \(-0.480325\pi\) | ||||
0.0617716 | + | 0.998090i | \(0.480325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.98918e11 | + | 7.98918e11i | 0.202914 | + | 0.202914i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.16767e12 | + | 2.16767e12i | −0.520509 | + | 0.520509i | −0.917725 | − | 0.397216i | \(-0.869976\pi\) |
0.397216 | + | 0.917725i | \(0.369976\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.81559e12i | 1.54814i | 0.633097 | + | 0.774072i | \(0.281783\pi\) | ||||
−0.633097 | + | 0.774072i | \(0.718217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.98732e12i | 0.427257i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.00353e12 | + | 4.00353e12i | −0.815108 | + | 0.815108i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.89257e12 | − | 1.89257e12i | −0.365095 | − | 0.365095i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.25728e12 | 0.412809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.38231e13 | −2.39774 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.06969e11 | − | 9.06969e11i | −0.149293 | − | 0.149293i | 0.628509 | − | 0.777802i | \(-0.283665\pi\) |
−0.777802 | + | 0.628509i | \(0.783665\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.31601e12 | − | 1.31601e12i | 0.205670 | − | 0.205670i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.65713e12i | 0.988270i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.38051e12i | − | 0.476928i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.13254e12 | − | 1.13254e12i | 0.151919 | − | 0.151919i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.68567e11 | + | 2.68567e11i | 0.0342685 | + | 0.0342685i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.21567e13 | −1.47618 | −0.738090 | − | 0.674702i | \(-0.764272\pi\) | ||||
−0.738090 | + | 0.674702i | \(0.764272\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.14129e11 | 0.0709996 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.41697e12 | − | 5.41697e12i | −0.596506 | − | 0.596506i | 0.342875 | − | 0.939381i | \(-0.388599\pi\) |
−0.939381 | + | 0.342875i | \(0.888599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.76215e11 | − | 6.76215e11i | 0.0709561 | − | 0.0709561i | −0.670738 | − | 0.741694i | \(-0.734023\pi\) |
0.741694 | + | 0.670738i | \(0.234023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.51307e13i | − | 2.51385i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2.89696e12i | − | 0.276366i | −0.990407 | − | 0.138183i | \(-0.955874\pi\) | ||
0.990407 | − | 0.138183i | \(-0.0441262\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.57864e12 | − | 5.57864e12i | 0.507756 | − | 0.507756i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.95651e12 | − | 6.95651e12i | −0.604332 | − | 0.604332i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.40938e12 | −0.199856 | −0.0999278 | − | 0.994995i | \(-0.531861\pi\) | ||||
−0.0999278 | + | 0.994995i | \(0.531861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.75923e12 | 0.535555 | 0.267777 | − | 0.963481i | \(-0.413711\pi\) | ||||
0.267777 | + | 0.963481i | \(0.413711\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.73063e12 | + | 4.73063e12i | 0.358166 | + | 0.358166i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.88726e13 | + | 1.88726e13i | −1.36590 | + | 1.36590i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.37761e12i | − | 0.579811i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.28353e12i | 0.614634i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.02005e13 | − | 1.02005e13i | 0.646273 | − | 0.646273i | −0.305817 | − | 0.952090i | \(-0.598930\pi\) |
0.952090 | + | 0.305817i | \(0.0989297\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.98837e13 | − | 2.98837e13i | −1.81247 | − | 1.81247i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.56422e12 | 0.0908502 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.59010e13 | −0.884695 | −0.442347 | − | 0.896844i | \(-0.645854\pi\) | ||||
−0.442347 | + | 0.896844i | \(0.645854\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.48976e12 | − | 8.48976e12i | −0.452633 | − | 0.452633i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.30012e12 | + | 2.30012e12i | −0.117551 | + | 0.117551i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.14522e13i | − | 1.05127i | −0.850710 | − | 0.525636i | \(-0.823827\pi\) | ||
0.850710 | − | 0.525636i | \(-0.176173\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.46955e13i | 0.690769i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.42441e13 | + | 1.42441e13i | −0.642428 | + | 0.642428i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.79297e13 | + | 1.79297e13i | 0.776130 | + | 0.776130i | 0.979170 | − | 0.203040i | \(-0.0650823\pi\) |
−0.203040 | + | 0.979170i | \(0.565082\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.69476e13 | 0.704330 | 0.352165 | − | 0.935938i | \(-0.385446\pi\) | ||||
0.352165 | + | 0.935938i | \(0.385446\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.52306e13 | 0.607888 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.13033e12 | − | 8.13033e12i | −0.311730 | − | 0.311730i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.82782e12 | + | 6.82782e12i | −0.251561 | + | 0.251561i | −0.821610 | − | 0.570050i | \(-0.806924\pi\) |
0.570050 | + | 0.821610i | \(0.306924\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.94218e12i | − | 0.0687806i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.34594e13i | 1.47979i | 0.672724 | + | 0.739893i | \(0.265124\pi\) | ||||
−0.672724 | + | 0.739893i | \(0.734876\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.07572e13 | − | 2.07572e13i | 0.679739 | − | 0.679739i | −0.280202 | − | 0.959941i | \(-0.590401\pi\) |
0.959941 | + | 0.280202i | \(0.0904013\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.43969e13 | − | 2.43969e13i | −0.768578 | − | 0.768578i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.60801e13 | −1.09375 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.37461e13 | −0.984657 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.68703e12 | − | 6.68703e12i | −0.187855 | − | 0.187855i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.66490e12 | + | 4.66490e12i | −0.126203 | + | 0.126203i | −0.767387 | − | 0.641184i | \(-0.778444\pi\) |
0.641184 | + | 0.767387i | \(0.278444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.66093e12i | − | 0.147525i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 6.98469e13i | − | 1.75383i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.81112e13 | − | 1.81112e13i | 0.438284 | − | 0.438284i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.34560e13 | + | 6.34560e13i | 1.48032 | + | 1.48032i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.47484e13 | −0.556690 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.00180e12 | 0.151901 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.07573e13 | + | 2.07573e13i | 0.434421 | + | 0.434421i | 0.890129 | − | 0.455708i | \(-0.150614\pi\) |
−0.455708 | + | 0.890129i | \(0.650614\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.08253e13 | − | 2.08253e13i | 0.420551 | − | 0.420551i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.82615e13i | − | 1.33043i | −0.746650 | − | 0.665217i | \(-0.768339\pi\) | ||
0.746650 | − | 0.665217i | \(-0.231661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.58243e13i | 1.23849i | 0.785198 | + | 0.619245i | \(0.212561\pi\) | ||||
−0.785198 | + | 0.619245i | \(0.787439\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.56305e13 | + | 1.56305e13i | −0.283965 | + | 0.283965i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.67518e13 | − | 1.67518e13i | −0.293924 | − | 0.293924i | 0.544704 | − | 0.838628i | \(-0.316642\pi\) |
−0.838628 | + | 0.544704i | \(0.816642\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.09016e13 | 1.03224 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.01141e13 | −0.165635 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.20133e12 | − | 8.20133e12i | −0.129799 | − | 0.129799i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.92744e12 | − | 4.92744e12i | 0.0753811 | − | 0.0753811i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.24704e13i | 0.776071i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.06351e14i | − | 1.52113i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.92920e13 | − | 2.92920e13i | 0.405224 | − | 0.405224i | −0.474845 | − | 0.880069i | \(-0.657496\pi\) |
0.880069 | + | 0.474845i | \(0.157496\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.87756e12 | − | 4.87756e12i | −0.0652769 | − | 0.0652769i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.27276e13 | −0.423806 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.08695e13 | −1.01349 | −0.506746 | − | 0.862095i | \(-0.669152\pi\) | ||||
−0.506746 | + | 0.862095i | \(0.669152\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.67066e13 | − | 7.67066e13i | −0.930539 | − | 0.930539i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.57121e13 | + | 2.57121e13i | −0.301987 | + | 0.301987i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.00920e14i | 2.28510i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 1.05485e14i | − | 1.16195i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.33385e13 | + | 7.33385e13i | −0.782564 | + | 0.782564i | −0.980263 | − | 0.197698i | \(-0.936653\pi\) |
0.197698 | + | 0.980263i | \(0.436653\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.93654e13 | − | 2.93654e13i | −0.303596 | − | 0.303596i | 0.538823 | − | 0.842419i | \(-0.318869\pi\) |
−0.842419 | + | 0.538823i | \(0.818869\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.23312e13 | 0.424103 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.76163e13 | 0.559480 | 0.279740 | − | 0.960076i | \(-0.409752\pi\) | ||||
0.279740 | + | 0.960076i | \(0.409752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.16723e13 | + | 2.16723e13i | 0.204009 | + | 0.204009i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.49102e13 | − | 1.49102e13i | 0.136084 | − | 0.136084i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.50109e14i | 1.32858i | 0.747475 | + | 0.664290i | \(0.231266\pi\) | ||||
−0.747475 | + | 0.664290i | \(0.768734\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.39340e14i | 1.19615i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.18128e14 | + | 1.18128e14i | −0.983706 | + | 0.983706i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.86509e13 | + | 1.86509e13i | 0.150692 | + | 0.150692i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.30917e14 | 1.81047 | 0.905237 | − | 0.424908i | \(-0.139693\pi\) | ||||
0.905237 | + | 0.424908i | \(0.139693\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.07288e13 | −0.157736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.40078e14 | + | 1.40078e14i | 1.03470 | + | 1.03470i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.43352e13 | − | 7.43352e13i | 0.533084 | − | 0.533084i | −0.388405 | − | 0.921489i | \(-0.626974\pi\) |
0.921489 | + | 0.388405i | \(0.126974\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.34027e14i | − | 0.933297i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.69098e13i | 0.249611i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.39364e13 | + | 5.39364e13i | −0.354296 | + | 0.354296i | −0.861705 | − | 0.507409i | \(-0.830603\pi\) |
0.507409 | + | 0.861705i | \(0.330603\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.74049e14 | + | 1.74049e14i | 1.11067 | + | 1.11067i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.62840e13 | 0.100965 | 0.0504823 | − | 0.998725i | \(-0.483924\pi\) | ||||
0.0504823 | + | 0.998725i | \(0.483924\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.13857e14 | 2.49354 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.64569e13 | + | 3.64569e13i | 0.213486 | + | 0.213486i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00553e14 | − | 1.00553e14i | 0.572361 | − | 0.572361i | −0.360426 | − | 0.932788i | \(-0.617369\pi\) |
0.932788 | + | 0.360426i | \(0.117369\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.54603e13i | − | 0.196232i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.50493e14i | − | 1.34783i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.14561e14 | − | 1.14561e14i | 0.599451 | − | 0.599451i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.36644e13 | + | 5.36644e13i | 0.273110 | + | 0.273110i | 0.830351 | − | 0.557241i | \(-0.188140\pi\) |
−0.557241 | + | 0.830351i | \(0.688140\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.65104e14 | −2.30250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.33118e14 | 0.641127 | 0.320563 | − | 0.947227i | \(-0.396128\pi\) | ||||
0.320563 | + | 0.947227i | \(0.396128\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.55830e13 | − | 1.55830e13i | −0.0730252 | − | 0.0730252i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.88126e13 | − | 8.88126e13i | 0.405016 | − | 0.405016i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.29146e14i | 0.573207i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.22329e14i | 1.39259i | 0.717758 | + | 0.696293i | \(0.245168\pi\) | ||||
−0.717758 | + | 0.696293i | \(0.754832\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.65154e14 | − | 1.65154e14i | 0.694640 | − | 0.694640i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.39602e13 | − | 5.39602e13i | −0.220978 | − | 0.220978i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.52883e14 | −0.609669 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.69675e14 | 1.43573 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.82378e14 | + | 2.82378e14i | 1.06820 | + | 1.06820i | 0.997497 | + | 0.0707064i | \(0.0225254\pi\) |
0.0707064 | + | 0.997497i | \(0.477475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.97312e14 | − | 1.97312e14i | 0.727112 | − | 0.727112i | −0.242931 | − | 0.970044i | \(-0.578109\pi\) |
0.970044 | + | 0.242931i | \(0.0781089\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.11014e13i | − | 0.219371i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 9.64752e12i | − | 0.0337502i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.67414e13 | − | 6.67414e13i | 0.227532 | − | 0.227532i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.15844e14 | − | 1.15844e14i | −0.384909 | − | 0.384909i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.78445e14 | 1.22568 | 0.612840 | − | 0.790207i | \(-0.290027\pi\) | ||||
0.612840 | + | 0.790207i | \(0.290027\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.87357e14 | −1.85447 | −0.927233 | − | 0.374485i | \(-0.877820\pi\) | ||||
−0.927233 | + | 0.374485i | \(0.877820\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.07487e14 | + | 1.07487e14i | 0.330876 | + | 0.330876i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.53070e14 | + | 5.53070e14i | −1.66009 | + | 1.66009i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.95351e14i | − | 0.571821i | −0.958256 | − | 0.285910i | \(-0.907704\pi\) | ||
0.958256 | − | 0.285910i | \(-0.0922960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.06707e14i | 0.590123i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.24637e14 | + | 3.24637e14i | −0.904018 | + | 0.904018i | −0.995781 | − | 0.0917627i | \(-0.970750\pi\) |
0.0917627 | + | 0.995781i | \(0.470750\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.34575e14 | − | 2.34575e14i | −0.637239 | − | 0.637239i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.88916e14 | 1.03078 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.80220e13 | −0.124190 | −0.0620949 | − | 0.998070i | \(-0.519778\pi\) | ||||
−0.0620949 | + | 0.998070i | \(0.519778\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.74425e14 | + | 2.74425e14i | 0.692551 | + | 0.692551i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.11075e14 | − | 4.11075e14i | 1.01247 | − | 1.01247i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.50821e14i | 0.602978i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.54781e13i | 0.130192i | 0.997879 | + | 0.0650958i | \(0.0207353\pi\) | ||||
−0.997879 | + | 0.0650958i | \(0.979265\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.14405e13 | − | 4.14405e13i | 0.0949413 | − | 0.0949413i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.39250e13 | + | 2.39250e13i | 0.0535177 | + | 0.0535177i | 0.733359 | − | 0.679841i | \(-0.237951\pi\) |
−0.679841 | + | 0.733359i | \(0.737951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.76509e14 | −1.69610 | −0.848049 | − | 0.529918i | \(-0.822223\pi\) | ||||
−0.848049 | + | 0.529918i | \(0.822223\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.07601e13 | −0.193599 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.52807e14 | − | 4.52807e14i | −0.943344 | − | 0.943344i | 0.0551351 | − | 0.998479i | \(-0.482441\pi\) |
−0.998479 | + | 0.0551351i | \(0.982441\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.11960e14 | + | 3.11960e14i | −0.634817 | + | 0.634817i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2.46163e14i | − | 0.489337i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.65290e14i | − | 1.87466i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.50471e14 | + | 1.50471e14i | −0.285521 | + | 0.285521i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.04782e13 | + | 8.04782e13i | 0.149220 | + | 0.149220i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.36724e14 | 0.247742 | 0.123871 | − | 0.992298i | \(-0.460469\pi\) | ||||
0.123871 | + | 0.992298i | \(0.460469\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.82697e13 | −0.138610 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00549e15 | − | 1.00549e15i | −1.74048 | − | 1.74048i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.10123e14 | − | 1.10123e14i | 0.186337 | − | 0.186337i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.79388e14i | − | 0.296746i | −0.988931 | − | 0.148373i | \(-0.952596\pi\) | ||
0.988931 | − | 0.148373i | \(-0.0474037\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.89394e14i | 0.953250i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.42827e14 | − | 3.42827e14i | 0.542159 | − | 0.542159i | −0.382002 | − | 0.924161i | \(-0.624765\pi\) |
0.924161 | + | 0.382002i | \(0.124765\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.61332e13 | + | 3.61332e13i | 0.0558790 | + | 0.0558790i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.37771e14 | 0.359608 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.13162e14 | 0.611167 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.85485e14 | − | 1.85485e14i | −0.268383 | − | 0.268383i | 0.560065 | − | 0.828448i | \(-0.310776\pi\) |
−0.828448 | + | 0.560065i | \(0.810776\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.87945e14 | + | 2.87945e14i | −0.407569 | + | 0.407569i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.66232e14i | 0.507145i | 0.967316 | + | 0.253572i | \(0.0816056\pi\) | ||||
−0.967316 | + | 0.253572i | \(0.918394\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 4.07562e14i | − | 0.552193i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.88436e14 | + | 3.88436e14i | −0.514963 | + | 0.514963i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.50462e13 | − | 7.50462e13i | −0.0973600 | − | 0.0973600i | 0.656749 | − | 0.754109i | \(-0.271931\pi\) |
−0.754109 | + | 0.656749i | \(0.771931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.55562e14 | 0.451441 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.29268e15 | −1.60638 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.42954e14 | + | 3.42954e14i | 0.417154 | + | 0.417154i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.08908e14 | + | 8.08908e14i | −0.963166 | + | 0.963166i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.01809e14i | − | 0.235244i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.52126e14i | 0.972516i | 0.873815 | + | 0.486258i | \(0.161638\pi\) | ||||
−0.873815 | + | 0.486258i | \(0.838362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.84070e14 | + | 3.84070e14i | −0.429192 | + | 0.429192i | −0.888353 | − | 0.459161i | \(-0.848150\pi\) |
0.459161 | + | 0.888353i | \(0.348150\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.73559e14 | − | 2.73559e14i | −0.299347 | − | 0.299347i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.05102e13 | −0.0326954 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.43851e15 | −1.50975 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.10014e13 | − | 3.10014e13i | −0.0318685 | − | 0.0318685i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.66317e14 | + | 1.66317e14i | −0.167470 | + | 0.167470i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.66562e14i | − | 0.164297i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.52864e14i | 0.244359i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.73655e15 | − | 2.73655e15i | 2.59098 | − | 2.59098i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.73890e13 | − | 1.73890e13i | −0.0161320 | − | 0.0161320i | 0.698995 | − | 0.715127i | \(-0.253631\pi\) |
−0.715127 | + | 0.698995i | \(0.753631\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.25612e14 | −0.659637 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.64092e14 | −0.769803 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.23494e15 | − | 1.23494e15i | −1.07824 | − | 1.07824i | −0.996667 | − | 0.0815740i | \(-0.974005\pi\) |
−0.0815740 | − | 0.996667i | \(-0.525995\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.83445e13 | − | 3.83445e13i | 0.0328137 | − | 0.0328137i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.12713e15i | − | 0.945454i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.18400e15i | − | 1.79583i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.27934e14 | + | 2.27934e14i | −0.183737 | + | 0.183737i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.19349e15 | + | 1.19349e15i | 0.943223 | + | 0.943223i | 0.998473 | − | 0.0552494i | \(-0.0175954\pi\) |
−0.0552494 | + | 0.998473i | \(0.517595\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.85021e14 | 0.453321 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.26813e14 | −0.172334 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.15004e14 | + | 5.15004e14i | 0.383720 | + | 0.383720i | 0.872440 | − | 0.488720i | \(-0.162536\pi\) |
−0.488720 | + | 0.872440i | \(0.662536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.26322e15 | − | 1.26322e15i | 0.923023 | − | 0.923023i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.69313e15i | − | 1.21334i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.36483e15i | 0.959315i | 0.877456 | + | 0.479657i | \(0.159239\pi\) | ||||
−0.877456 | + | 0.479657i | \(0.840761\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.77410e15 | + | 1.77410e15i | −1.22315 | + | 1.22315i | −0.256639 | + | 0.966507i | \(0.582615\pi\) |
−0.966507 | + | 0.256639i | \(0.917385\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.81077e14 | − | 3.81077e14i | −0.257729 | − | 0.257729i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.50596e14 | −0.431656 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.65991e14 | 0.238234 | 0.119117 | − | 0.992880i | \(-0.461994\pi\) | ||||
0.119117 | + | 0.992880i | \(0.461994\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.17620e14 | − | 1.17620e14i | −0.0751191 | − | 0.0751191i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.45728e15 | + | 1.45728e15i | −0.913220 | + | 0.913220i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.13087e15i | − | 1.31032i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.44102e14i | 0.0869589i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.82609e15 | − | 1.82609e15i | 1.08146 | − | 1.08146i | 0.0850900 | − | 0.996373i | \(-0.472882\pi\) |
0.996373 | − | 0.0850900i | \(-0.0271178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.75864e14 | + | 4.75864e14i | 0.276598 | + | 0.276598i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.10949e15 | 0.632981 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.34557e15 | 1.87357 | 0.936784 | − | 0.349909i | \(-0.113787\pi\) | ||||
0.936784 | + | 0.349909i | \(0.113787\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.45543e14 | + | 2.45543e14i | 0.134985 | + | 0.134985i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.74422e15 | − | 1.74422e15i | 0.941333 | − | 0.941333i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.39597e15i | 1.79935i | 0.436556 | + | 0.899677i | \(0.356198\pi\) | ||||
−0.436556 | + | 0.899677i | \(0.643802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.43538e15i | 1.78717i | 0.448898 | + | 0.893583i | \(0.351817\pi\) | ||||
−0.448898 | + | 0.893583i | \(0.648183\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.79228e14 | + | 1.79228e14i | −0.0915507 | + | 0.0915507i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.94535e15 | − | 1.94535e15i | −0.975760 | − | 0.975760i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.96296e14 | 0.0966884 | 0.0483442 | − | 0.998831i | \(-0.484606\pi\) | ||||
0.0483442 | + | 0.998831i | \(0.484606\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.04914e15 | 0.991236 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.90244e14 | − | 4.90244e14i | −0.232909 | − | 0.232909i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.99692e15 | + | 1.99692e15i | −0.931813 | + | 0.931813i | −0.997819 | − | 0.0660064i | \(-0.978974\pi\) |
0.0660064 | + | 0.997819i | \(0.478974\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.68681e14i | 0.443984i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.13465e15i | − | 0.961079i | −0.876973 | − | 0.480539i | \(-0.840441\pi\) | ||
0.876973 | − | 0.480539i | \(-0.159559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.66182e15 | + | 1.66182e15i | −0.734998 | + | 0.734998i | −0.971605 | − | 0.236608i | \(-0.923964\pi\) |
0.236608 | + | 0.971605i | \(0.423964\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.79460e15 | − | 2.79460e15i | −1.21427 | − | 1.21427i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.47196e15 | −1.90903 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.55756e15 | 0.653287 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.53757e15 | + | 3.53757e15i | 1.45792 | + | 1.45792i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.66229e13 | + | 7.66229e13i | −0.0310299 | + | 0.0310299i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.28852e15i | 0.512778i | 0.966574 | + | 0.256389i | \(0.0825328\pi\) | ||||
−0.966574 | + | 0.256389i | \(0.917467\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.64217e14i | 0.181552i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.86627e15 | + | 2.86627e15i | −1.10170 | + | 1.10170i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.65850e15 | + | 1.65850e15i | 0.626541 | + | 0.626541i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.37371e14 | 0.0881399 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.37556e15 | −0.867055 | −0.433528 | − | 0.901140i | \(-0.642731\pi\) | ||||
−0.433528 | + | 0.901140i | \(0.642731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.12329e15 | + | 3.12329e15i | 1.12060 | + | 1.12060i | 0.991651 | + | 0.128951i | \(0.0411611\pi\) |
0.128951 | + | 0.991651i | \(0.458839\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.70367e15 | − | 1.70367e15i | 0.600907 | − | 0.600907i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.99929e15i | 1.04003i | 0.854158 | + | 0.520014i | \(0.174073\pi\) | ||||
−0.854158 | + | 0.520014i | \(0.825927\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.20841e14i | 0.279842i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.65128e14 | + | 8.65128e14i | −0.289991 | + | 0.289991i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.19197e15 | − | 1.19197e15i | −0.392866 | − | 0.392866i | 0.482842 | − | 0.875708i | \(-0.339605\pi\) |
−0.875708 | + | 0.482842i | \(0.839605\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.12517e15 | 1.33695 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.04279e14 | 0.0651049 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.22810e15 | − | 2.22810e15i | −0.698337 | − | 0.698337i | 0.265715 | − | 0.964052i | \(-0.414392\pi\) |
−0.964052 | + | 0.265715i | \(0.914392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.31704e15 | − | 1.31704e15i | 0.405967 | − | 0.405967i | −0.474362 | − | 0.880330i | \(-0.657321\pi\) |
0.880330 | + | 0.474362i | \(0.157321\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.37461e14i | − | 0.0416732i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 7.65942e15i | − | 2.28390i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.43670e15 | − | 2.43670e15i | 0.714677 | − | 0.714677i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.11111e15 | + | 3.11111e15i | 0.897576 | + | 0.897576i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.01527e15 | −0.288142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.44297e14 | 0.0402879 | 0.0201439 | − | 0.999797i | \(-0.493588\pi\) | ||||
0.0201439 | + | 0.999797i | \(0.493588\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.60315e14 | − | 7.60315e14i | −0.208845 | − | 0.208845i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.26299e14 | − | 1.26299e14i | 0.0341320 | − | 0.0341320i | −0.689835 | − | 0.723967i | \(-0.742317\pi\) |
0.723967 | + | 0.689835i | \(0.242317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.09940e15i | − | 0.558227i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.77259e15i | 0.725398i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.21846e14 | − | 2.21846e14i | 0.0571133 | − | 0.0571133i | −0.677973 | − | 0.735087i | \(-0.737141\pi\) |
0.735087 | + | 0.677973i | \(0.237141\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.71979e15 | + | 2.71979e15i | 0.689029 | + | 0.689029i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.46109e14 | −0.0862882 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.29143e15 | 0.316857 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.10228e15 | + | 4.10228e15i | 0.990596 | + | 0.990596i | 0.999956 | − | 0.00936034i | \(-0.00297953\pi\) |
−0.00936034 | + | 0.999956i | \(0.502980\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.26644e15 | − | 2.26644e15i | 0.538655 | − | 0.538655i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.08788e15i | 1.42413i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.25635e14i | 0.0749808i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.41381e14 | + | 7.41381e14i | −0.168042 | + | 0.168042i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.04410e15 | + | 3.04410e15i | 0.679218 | + | 0.679218i | 0.959823 | − | 0.280605i | \(-0.0905351\pi\) |
−0.280605 | + | 0.959823i | \(0.590535\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.39016e15 | 0.525015 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.85533e15 | −0.617471 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.88489e15 | − | 3.88489e15i | −0.827127 | − | 0.827127i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.62095e15 | − | 4.62095e15i | 0.968672 | − | 0.968672i | −0.0308521 | − | 0.999524i | \(-0.509822\pi\) |
0.999524 | + | 0.0308521i | \(0.00982209\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.25476e15i | − | 0.258987i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.05750e15i | 0.418165i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.90774e15 | − | 1.90774e15i | 0.381800 | − | 0.381800i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.16600e14 | + | 6.16600e14i | 0.121520 | + | 0.121520i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.71684e12 | −0.000333212 | −0.000166606 | − | 1.00000i | \(-0.500053\pi\) | ||||
−0.000166606 | 1.00000i | \(0.500053\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.53810e15 | 1.24971 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.72980e15 | − | 1.72980e15i | −0.325638 | − | 0.325638i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.62942e14 | − | 6.62942e14i | 0.122918 | − | 0.122918i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.86270e14i | − | 0.107068i | −0.998566 | − | 0.0535339i | \(-0.982951\pi\) | ||
0.998566 | − | 0.0535339i | \(-0.0170485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 6.15434e15i | − | 1.10708i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.72711e14 | − | 5.72711e14i | 0.101482 | − | 0.101482i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.03937e15 | + | 3.03937e15i | 0.530531 | + | 0.530531i | 0.920731 | − | 0.390199i | \(-0.127594\pi\) |
−0.390199 | + | 0.920731i | \(0.627594\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.65964e15 | 1.66104 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.74553e15 | 0.803921 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.93959e15 | − | 3.93959e15i | −0.657516 | − | 0.657516i | 0.297276 | − | 0.954792i | \(-0.403922\pi\) |
−0.954792 | + | 0.297276i | \(0.903922\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.14397e15 | + | 2.14397e15i | −0.352548 | + | 0.352548i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.16532e15i | − | 0.188803i | −0.995534 | − | 0.0944013i | \(-0.969906\pi\) | ||
0.995534 | − | 0.0944013i | \(-0.0300937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.40475e15i | 1.02245i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.37243e14 | + | 8.37243e14i | −0.131701 | + | 0.131701i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.58767e15 | − | 1.58767e15i | −0.246099 | − | 0.246099i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.91358e15 | −1.20880 | −0.604399 | − | 0.796682i | \(-0.706587\pi\) | ||||
−0.604399 | + | 0.796682i | \(0.706587\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.22096e15 | −0.785919 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.76966e15 | + | 6.76966e15i | 1.00429 | + | 1.00429i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.02992e15 | + | 4.02992e15i | −0.589209 | + | 0.589209i | −0.937417 | − | 0.348208i | \(-0.886790\pi\) |
0.348208 | + | 0.937417i | \(0.386790\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.52955e16i | 2.20411i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7.01563e15i | − | 0.996440i | −0.867051 | − | 0.498220i | \(-0.833987\pi\) | ||
0.867051 | − | 0.498220i | \(-0.166013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.23656e15 | + | 8.23656e15i | −1.15308 | + | 1.15308i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.41070e14 | + | 1.41070e14i | 0.0194669 | + | 0.0194669i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.97476e14 | −0.0676702 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.74998e15 | −0.502845 | −0.251422 | − | 0.967877i | \(-0.580898\pi\) | ||||
−0.251422 | + | 0.967877i | \(0.580898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.06935e15 | + | 4.06935e15i | 0.537930 | + | 0.537930i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.30098e15 | + | 9.30098e15i | −1.21211 | + | 1.21211i | −0.241777 | + | 0.970332i | \(0.577730\pi\) |
−0.970332 | + | 0.241777i | \(0.922270\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.59775e14i | 0.0719208i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.34534e15i | 0.550438i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.07888e15 | − | 5.07888e15i | 0.634326 | − | 0.634326i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.14250e15 | − | 3.14250e15i | −0.386985 | − | 0.386985i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.69527e15 | 0.691552 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.05386e15 | 0.485385 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.11730e16 | − | 1.11730e16i | −1.31919 | − | 1.31919i | −0.914417 | − | 0.404774i | \(-0.867350\pi\) |
−0.404774 | − | 0.914417i | \(-0.632650\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.48998e15 | + | 5.48998e15i | −0.639215 | + | 0.639215i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.40821e16i | − | 2.76518i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.15310e14i | − | 0.0696773i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.76083e15 | − | 3.76083e15i | 0.420015 | − | 0.420015i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.36170e15 | − | 4.36170e15i | −0.480435 | − | 0.480435i | 0.424836 | − | 0.905271i | \(-0.360332\pi\) |
−0.905271 | + | 0.424836i | \(0.860332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.59857e14 | −0.104280 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.56924e15 | −0.275313 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.70440e15 | − | 2.70440e15i | −0.285848 | − | 0.285848i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.65586e16 | − | 1.65586e16i | 1.72642 | − | 1.72642i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.17700e15i | − | 0.943836i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.84145e15i | 0.897029i | 0.893775 | + | 0.448515i | \(0.148047\pi\) | ||||
−0.893775 | + | 0.448515i | \(0.851953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.54171e14 | − | 8.54171e14i | 0.0854929 | − | 0.0854929i | −0.663067 | − | 0.748560i | \(-0.730746\pi\) |
0.748560 | + | 0.663067i | \(0.230746\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.33716e15 | − | 4.33716e15i | −0.428260 | − | 0.428260i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.70625e15 | −0.945550 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.78650e16 | −1.71705 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.37359e15 | + | 1.37359e15i | 0.130255 | + | 0.130255i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.55379e15 | − | 2.55379e15i | 0.238945 | − | 0.238945i | −0.577468 | − | 0.816413i | \(-0.695959\pi\) |
0.816413 | + | 0.577468i | \(0.195959\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.46679e15i | − | 0.135415i | −0.997705 | − | 0.0677076i | \(-0.978431\pi\) | ||
0.997705 | − | 0.0677076i | \(-0.0215685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.16137e15i | 0.379088i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.01585e15 | + | 3.01585e15i | −0.271100 | + | 0.271100i | −0.829543 | − | 0.558443i | \(-0.811399\pi\) |
0.558443 | + | 0.829543i | \(0.311399\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.28217e16 | − | 1.28217e16i | −1.13736 | − | 1.13736i | −0.988922 | − | 0.148433i | \(-0.952577\pi\) |
−0.148433 | − | 0.988922i | \(-0.547423\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.49471e15 | 0.305918 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.24721e15 | 0.280519 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.74193e15 | − | 4.74193e15i | −0.404277 | − | 0.404277i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.40449e15 | + | 2.40449e15i | −0.202317 | + | 0.202317i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.46711e15i | − | 0.370967i | −0.982647 | − | 0.185484i | \(-0.940615\pi\) | ||
0.982647 | − | 0.185484i | \(-0.0593852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.23463e15i | − | 0.592978i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.11220e16 | − | 1.11220e16i | 0.899769 | − | 0.899769i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.39684e15 | − | 6.39684e15i | −0.510803 | − | 0.510803i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.70863e16 | −2.92317 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.06242e16 | −0.826617 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.16718e15 | + | 5.16718e15i | 0.396864 | + | 0.396864i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.63160e16 | + | 1.63160e16i | −1.23707 | + | 1.23707i | −0.275876 | + | 0.961193i | \(0.588968\pi\) |
−0.961193 | + | 0.275876i | \(0.911032\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4.40051e15i | − | 0.329374i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.20290e16i | − | 0.888861i | −0.895813 | − | 0.444430i | \(-0.853406\pi\) | ||
0.895813 | − | 0.444430i | \(-0.146594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.64963e15 | + | 7.64963e15i | −0.558057 | + | 0.558057i | −0.928754 | − | 0.370697i | \(-0.879119\pi\) |
0.370697 | + | 0.928754i | \(0.379119\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.23350e15 | + | 9.23350e15i | 0.665042 | + | 0.665042i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.49922e16 | 1.06612 | 0.533061 | − | 0.846077i | \(-0.321041\pi\) | ||||
0.533061 | + | 0.846077i | \(0.321041\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.32342e15 | 0.233344 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.63618e15 | + | 8.63618e15i | 0.598711 | + | 0.598711i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.66115e16 | + | 1.66115e16i | −1.13710 | + | 1.13710i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.87606e15i | 0.194401i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.20615e15i | − | 0.0805051i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.10389e16 | − | 2.10389e16i | 1.38669 | − | 1.38669i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.04625e15 | − | 7.04625e15i | −0.458628 | − | 0.458628i | 0.439577 | − | 0.898205i | \(-0.355128\pi\) |
−0.898205 | + | 0.439577i | \(0.855128\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.38765e15 | 0.153473 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.40033e15 | −0.596727 | −0.298363 | − | 0.954452i | \(-0.596441\pi\) | ||||
−0.298363 | + | 0.954452i | \(0.596441\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.11010e15 | + | 7.11010e15i | 0.445751 | + | 0.445751i | 0.893939 | − | 0.448189i | \(-0.147931\pi\) |
−0.448189 | + | 0.893939i | \(0.647931\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.44873e15 | + | 1.44873e15i | −0.0897013 | + | 0.0897013i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.85237e15i | 0.602505i | 0.953544 | + | 0.301253i | \(0.0974047\pi\) | ||||
−0.953544 | + | 0.301253i | \(0.902595\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.46428e16i | 3.30045i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.28779e16 | + | 1.28779e16i | −0.768277 | + | 0.768277i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.49708e16 | + | 1.49708e16i | 0.882188 | + | 0.882188i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.16421e15 | −0.242385 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.26993e15 | −0.532989 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.09655e15 | − | 2.09655e15i | −0.119077 | − | 0.119077i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26425e15 | − | 1.26425e15i | 0.0709328 | − | 0.0709328i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 3.24789e16i | − | 1.80019i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.19495e16i | − | 0.654309i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.16098e16 | + | 1.16098e16i | −0.628038 | + | 0.628038i | −0.947574 | − | 0.319536i | \(-0.896473\pi\) |
0.319536 | + | 0.947574i | \(0.396473\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.23196e15 | − | 2.23196e15i | −0.119285 | − | 0.119285i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.25287e15 | 0.382965 | 0.191482 | − | 0.981496i | \(-0.438671\pi\) | ||||
0.191482 | + | 0.981496i | \(0.438671\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.21682e16 | 1.15649 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.79188e15 | − | 1.79188e15i | −0.0923618 | − | 0.0923618i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.93212e16 | − | 3.93212e16i | 2.00261 | − | 2.00261i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.55963e16i | 0.784849i | 0.919784 | + | 0.392425i | \(0.128364\pi\) | ||||
−0.919784 | + | 0.392425i | \(0.871636\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1.06243e16i | − | 0.528290i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.90453e15 | − | 1.90453e15i | 0.0935792 | − | 0.0935792i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.40581e15 | + | 1.40581e15i | 0.0682571 | + | 0.0682571i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.75629e15 | 0.180227 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.27007e16 | 0.602201 | 0.301101 | − | 0.953592i | \(-0.402646\pi\) | ||||
0.301101 | + | 0.953592i | \(0.402646\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.06464e16 | − | 5.06464e16i | −2.37315 | − | 2.37315i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.74693e16 | + | 1.74693e16i | −0.808957 | + | 0.808957i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.73520e15i | − | 0.170942i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.55502e16i | − | 1.60796i | −0.594657 | − | 0.803979i | \(-0.702712\pi\) | ||
0.594657 | − | 0.803979i | \(-0.297288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.68455e16 | − | 1.68455e16i | 0.753050 | − | 0.753050i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.37174e16 | + | 1.37174e16i | 0.606078 | + | 0.606078i | 0.941919 | − | 0.335841i | \(-0.109021\pi\) |
−0.335841 | + | 0.941919i | \(0.609021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.19597e16 | 0.958985 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.87023e16 | 1.67056 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.05720e16 | − | 1.05720e16i | −0.451058 | − | 0.451058i | 0.444648 | − | 0.895706i | \(-0.353329\pi\) |
−0.895706 | + | 0.444648i | \(0.853329\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.63902e15 | − | 1.63902e15i | 0.0691226 | − | 0.0691226i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.57413e15i | 0.357435i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.45464e15i | − | 0.0599440i | −0.999551 | − | 0.0299720i | \(-0.990458\pi\) | ||
0.999551 | − | 0.0299720i | \(-0.00954181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.27566e15 | − | 6.27566e15i | 0.255647 | − | 0.255647i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.55857e16 | − | 1.55857e16i | −0.627642 | − | 0.627642i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.18503e16 | 2.06419 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.36382e16 | −0.930327 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.12154e14 | − | 9.12154e14i | −0.0354914 | − | 0.0354914i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.93700e15 | − | 1.93700e15i | 0.0745124 | − | 0.0745124i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.07005e15i | 0.0406967i | 0.999793 | + | 0.0203484i | \(0.00647753\pi\) | ||||
−0.999793 | + | 0.0203484i | \(0.993522\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.19772e15i | 0.157846i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.63799e15 | + | 7.63799e15i | −0.283971 | + | 0.283971i | −0.834690 | − | 0.550720i | \(-0.814353\pi\) |
0.550720 | + | 0.834690i | \(0.314353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.80299e16 | + | 5.80299e16i | 2.13320 | + | 2.13320i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.52203e15 | −0.0916694 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.17074e16 | −1.13957 | −0.569784 | − | 0.821794i | \(-0.692973\pi\) | ||||
−0.569784 | + | 0.821794i | \(0.692973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.40137e16 | + | 3.40137e16i | 1.20878 | + | 1.20878i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.73209e15 | + | 4.73209e15i | −0.166293 | + | 0.166293i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.52427e16i | 1.57219i | 0.618107 | + | 0.786094i | \(0.287900\pi\) | ||||
−0.618107 | + | 0.786094i | \(0.712100\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.82712e16i | 0.627868i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.72171e16 | + | 2.72171e16i | −0.924907 | + | 0.924907i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.86217e16 | − | 3.86217e16i | −1.29793 | − | 1.29793i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.90319e16 | −0.632523 | −0.316261 | − | 0.948672i | \(-0.602428\pi\) | ||||
−0.316261 | + | 0.948672i | \(0.602428\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.49926e16 | −0.492785 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.87242e16 | + | 2.87242e16i | 0.933730 | + | 0.933730i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.23350e16 | − | 1.23350e16i | 0.396568 | − | 0.396568i | −0.480453 | − | 0.877021i | \(-0.659528\pi\) |
0.877021 | + | 0.480453i | \(0.159528\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.20772e16i | 0.384022i |
(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 | 128.12.e.b.33.6 | 42 | ||
4.3 | odd | 2 | 128.12.e.a.33.16 | 42 | |||
8.3 | odd | 2 | 64.12.e.a.17.6 | 42 | |||
8.5 | even | 2 | 16.12.e.a.13.15 | yes | 42 | ||
16.3 | odd | 4 | 64.12.e.a.49.6 | 42 | |||
16.5 | even | 4 | inner | 128.12.e.b.97.6 | 42 | ||
16.11 | odd | 4 | 128.12.e.a.97.16 | 42 | |||
16.13 | even | 4 | 16.12.e.a.5.15 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.12.e.a.5.15 | ✓ | 42 | 16.13 | even | 4 | ||
16.12.e.a.13.15 | yes | 42 | 8.5 | even | 2 | ||
64.12.e.a.17.6 | 42 | 8.3 | odd | 2 | |||
64.12.e.a.49.6 | 42 | 16.3 | odd | 4 | |||
128.12.e.a.33.16 | 42 | 4.3 | odd | 2 | |||
128.12.e.a.97.16 | 42 | 16.11 | odd | 4 | |||
128.12.e.b.33.6 | 42 | 1.1 | even | 1 | trivial | ||
128.12.e.b.97.6 | 42 | 16.5 | even | 4 | inner |