Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,10,Mod(28,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.9360392488\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 28.10 | ||
Character | \(\chi\) | \(=\) | 29.28 |
Dual form | 29.10.b.a.28.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 9.11441i | − | 0.402804i | −0.979509 | − | 0.201402i | \(-0.935450\pi\) | ||
0.979509 | − | 0.201402i | \(-0.0645498\pi\) | |||||||
\(3\) | 171.314i | 1.22109i | 0.791982 | + | 0.610544i | \(0.209049\pi\) | ||||
−0.791982 | + | 0.610544i | \(0.790951\pi\) | |||||||
\(4\) | 428.927 | 0.837749 | ||||||||
\(5\) | 2218.10 | 1.58714 | 0.793571 | − | 0.608477i | \(-0.208219\pi\) | ||||
0.793571 | + | 0.608477i | \(0.208219\pi\) | |||||||
\(6\) | 1561.43 | 0.491859 | ||||||||
\(7\) | −1871.46 | −0.294604 | −0.147302 | − | 0.989092i | \(-0.547059\pi\) | ||||
−0.147302 | + | 0.989092i | \(0.547059\pi\) | |||||||
\(8\) | − | 8576.00i | − | 0.740253i | ||||||
\(9\) | −9665.49 | −0.491058 | ||||||||
\(10\) | − | 20216.7i | − | 0.639307i | ||||||
\(11\) | 7045.14i | 0.145085i | 0.997365 | + | 0.0725425i | \(0.0231113\pi\) | ||||
−0.997365 | + | 0.0725425i | \(0.976889\pi\) | |||||||
\(12\) | 73481.3i | 1.02297i | ||||||||
\(13\) | 42558.5 | 0.413277 | 0.206639 | − | 0.978417i | \(-0.433748\pi\) | ||||
0.206639 | + | 0.978417i | \(0.433748\pi\) | |||||||
\(14\) | 17057.2i | 0.118668i | ||||||||
\(15\) | 379992.i | 1.93804i | ||||||||
\(16\) | 141446. | 0.539572 | ||||||||
\(17\) | − | 88283.5i | − | 0.256366i | −0.991751 | − | 0.128183i | \(-0.959086\pi\) | ||
0.991751 | − | 0.128183i | \(-0.0409144\pi\) | |||||||
\(18\) | 88095.2i | 0.197800i | ||||||||
\(19\) | − | 8133.60i | − | 0.0143183i | −0.999974 | − | 0.00715915i | \(-0.997721\pi\) | ||
0.999974 | − | 0.00715915i | \(-0.00227885\pi\) | |||||||
\(20\) | 951404. | 1.32963 | ||||||||
\(21\) | − | 320607.i | − | 0.359738i | ||||||
\(22\) | 64212.3 | 0.0584408 | ||||||||
\(23\) | 117858. | 0.0878180 | 0.0439090 | − | 0.999036i | \(-0.486019\pi\) | ||||
0.0439090 | + | 0.999036i | \(0.486019\pi\) | |||||||
\(24\) | 1.46919e6 | 0.903914 | ||||||||
\(25\) | 2.96684e6 | 1.51902 | ||||||||
\(26\) | − | 387896.i | − | 0.166470i | ||||||
\(27\) | 1.71614e6i | 0.621464i | ||||||||
\(28\) | −802720. | −0.246804 | ||||||||
\(29\) | −3.17798e6 | + | 2.09943e6i | −0.834373 | + | 0.551200i | ||||
\(30\) | 3.46340e6 | 0.780651 | ||||||||
\(31\) | 7.39306e6i | 1.43779i | 0.695116 | + | 0.718897i | \(0.255353\pi\) | ||||
−0.695116 | + | 0.718897i | \(0.744647\pi\) | |||||||
\(32\) | − | 5.68011e6i | − | 0.957594i | ||||||
\(33\) | −1.20693e6 | −0.177162 | ||||||||
\(34\) | −804653. | −0.103265 | ||||||||
\(35\) | −4.15108e6 | −0.467579 | ||||||||
\(36\) | −4.14579e6 | −0.411383 | ||||||||
\(37\) | 1.28436e7i | 1.12662i | 0.826246 | + | 0.563310i | \(0.190472\pi\) | ||||
−0.826246 | + | 0.563310i | \(0.809528\pi\) | |||||||
\(38\) | −74133.0 | −0.00576747 | ||||||||
\(39\) | 7.29087e6i | 0.504648i | ||||||||
\(40\) | − | 1.90224e7i | − | 1.17489i | ||||||
\(41\) | − | 2.51109e7i | − | 1.38782i | −0.720060 | − | 0.693912i | \(-0.755886\pi\) | ||
0.720060 | − | 0.693912i | \(-0.244114\pi\) | |||||||
\(42\) | −2.92214e6 | −0.144904 | ||||||||
\(43\) | − | 3.64484e7i | − | 1.62581i | −0.582393 | − | 0.812907i | \(-0.697884\pi\) | ||
0.582393 | − | 0.812907i | \(-0.302116\pi\) | |||||||
\(44\) | 3.02186e6i | 0.121545i | ||||||||
\(45\) | −2.14390e7 | −0.779378 | ||||||||
\(46\) | − | 1.07421e6i | − | 0.0353734i | ||||||
\(47\) | 5.99932e6i | 0.179334i | 0.995972 | + | 0.0896668i | \(0.0285802\pi\) | ||||
−0.995972 | + | 0.0896668i | \(0.971420\pi\) | |||||||
\(48\) | 2.42316e7i | 0.658866i | ||||||||
\(49\) | −3.68513e7 | −0.913208 | ||||||||
\(50\) | − | 2.70410e7i | − | 0.611868i | ||||||
\(51\) | 1.51242e7 | 0.313045 | ||||||||
\(52\) | 1.82545e7 | 0.346223 | ||||||||
\(53\) | −5.45801e7 | −0.950152 | −0.475076 | − | 0.879945i | \(-0.657579\pi\) | ||||
−0.475076 | + | 0.879945i | \(0.657579\pi\) | |||||||
\(54\) | 1.56416e7 | 0.250328 | ||||||||
\(55\) | 1.56268e7i | 0.230271i | ||||||||
\(56\) | 1.60496e7i | 0.218082i | ||||||||
\(57\) | 1.39340e6 | 0.0174839 | ||||||||
\(58\) | 1.91350e7 | + | 2.89654e7i | 0.222026 | + | 0.336089i | ||||
\(59\) | −2.16595e7 | −0.232710 | −0.116355 | − | 0.993208i | \(-0.537121\pi\) | ||||
−0.116355 | + | 0.993208i | \(0.537121\pi\) | |||||||
\(60\) | 1.62989e8i | 1.62359i | ||||||||
\(61\) | − | 1.42627e8i | − | 1.31892i | −0.751739 | − | 0.659460i | \(-0.770785\pi\) | ||
0.751739 | − | 0.659460i | \(-0.229215\pi\) | |||||||
\(62\) | 6.73834e7 | 0.579149 | ||||||||
\(63\) | 1.80886e7 | 0.144668 | ||||||||
\(64\) | 2.06493e7 | 0.153849 | ||||||||
\(65\) | 9.43990e7 | 0.655930 | ||||||||
\(66\) | 1.10005e7i | 0.0713614i | ||||||||
\(67\) | −7.07911e7 | −0.429183 | −0.214591 | − | 0.976704i | \(-0.568842\pi\) | ||||
−0.214591 | + | 0.976704i | \(0.568842\pi\) | |||||||
\(68\) | − | 3.78672e7i | − | 0.214770i | ||||||
\(69\) | 2.01907e7i | 0.107234i | ||||||||
\(70\) | 3.78347e7i | 0.188343i | ||||||||
\(71\) | 3.47332e8 | 1.62212 | 0.811058 | − | 0.584966i | \(-0.198892\pi\) | ||||
0.811058 | + | 0.584966i | \(0.198892\pi\) | |||||||
\(72\) | 8.28912e7i | 0.363507i | ||||||||
\(73\) | − | 2.96925e8i | − | 1.22375i | −0.790953 | − | 0.611877i | \(-0.790415\pi\) | ||
0.790953 | − | 0.611877i | \(-0.209585\pi\) | |||||||
\(74\) | 1.17061e8 | 0.453807 | ||||||||
\(75\) | 5.08261e8i | 1.85486i | ||||||||
\(76\) | − | 3.48872e6i | − | 0.0119951i | ||||||
\(77\) | − | 1.31847e7i | − | 0.0427427i | ||||||
\(78\) | 6.64520e7 | 0.203274 | ||||||||
\(79\) | 3.79683e8i | 1.09673i | 0.836240 | + | 0.548364i | \(0.184749\pi\) | ||||
−0.836240 | + | 0.548364i | \(0.815251\pi\) | |||||||
\(80\) | 3.13741e8 | 0.856378 | ||||||||
\(81\) | −4.84245e8 | −1.24992 | ||||||||
\(82\) | −2.28871e8 | −0.559021 | ||||||||
\(83\) | 1.33956e8 | 0.309822 | 0.154911 | − | 0.987928i | \(-0.450491\pi\) | ||||
0.154911 | + | 0.987928i | \(0.450491\pi\) | |||||||
\(84\) | − | 1.37517e8i | − | 0.301370i | ||||||
\(85\) | − | 1.95822e8i | − | 0.406889i | ||||||
\(86\) | −3.32206e8 | −0.654885 | ||||||||
\(87\) | −3.59661e8 | − | 5.44432e8i | −0.673065 | − | 1.01884i | ||||
\(88\) | 6.04192e7 | 0.107400 | ||||||||
\(89\) | − | 8.73876e8i | − | 1.47637i | −0.674599 | − | 0.738185i | \(-0.735683\pi\) | ||
0.674599 | − | 0.738185i | \(-0.264317\pi\) | |||||||
\(90\) | 1.95404e8i | 0.313937i | ||||||||
\(91\) | −7.96465e7 | −0.121753 | ||||||||
\(92\) | 5.05525e7 | 0.0735695 | ||||||||
\(93\) | −1.26654e9 | −1.75567 | ||||||||
\(94\) | 5.46803e7 | 0.0722363 | ||||||||
\(95\) | − | 1.80411e7i | − | 0.0227252i | ||||||
\(96\) | 9.73082e8 | 1.16931 | ||||||||
\(97\) | − | 2.02736e8i | − | 0.232519i | −0.993219 | − | 0.116259i | \(-0.962910\pi\) | ||
0.993219 | − | 0.116259i | \(-0.0370904\pi\) | |||||||
\(98\) | 3.35878e8i | 0.367844i | ||||||||
\(99\) | − | 6.80947e7i | − | 0.0712451i | ||||||
\(100\) | 1.27256e9 | 1.27256 | ||||||||
\(101\) | 5.18428e8i | 0.495726i | 0.968795 | + | 0.247863i | \(0.0797283\pi\) | ||||
−0.968795 | + | 0.247863i | \(0.920272\pi\) | |||||||
\(102\) | − | 1.37848e8i | − | 0.126096i | ||||||
\(103\) | −2.00795e9 | −1.75786 | −0.878931 | − | 0.476949i | \(-0.841743\pi\) | ||||
−0.878931 | + | 0.476949i | \(0.841743\pi\) | |||||||
\(104\) | − | 3.64982e8i | − | 0.305930i | ||||||
\(105\) | − | 7.11138e8i | − | 0.570955i | ||||||
\(106\) | 4.97466e8i | 0.382725i | ||||||||
\(107\) | −2.74837e8 | −0.202697 | −0.101349 | − | 0.994851i | \(-0.532316\pi\) | ||||
−0.101349 | + | 0.994851i | \(0.532316\pi\) | |||||||
\(108\) | 7.36100e8i | 0.520631i | ||||||||
\(109\) | 3.29796e8 | 0.223783 | 0.111891 | − | 0.993720i | \(-0.464309\pi\) | ||||
0.111891 | + | 0.993720i | \(0.464309\pi\) | |||||||
\(110\) | 1.42429e8 | 0.0927540 | ||||||||
\(111\) | −2.20028e9 | −1.37570 | ||||||||
\(112\) | −2.64710e8 | −0.158960 | ||||||||
\(113\) | − | 8.04680e8i | − | 0.464270i | −0.972684 | − | 0.232135i | \(-0.925429\pi\) | ||
0.972684 | − | 0.232135i | \(-0.0745711\pi\) | |||||||
\(114\) | − | 1.27000e7i | − | 0.00704259i | ||||||
\(115\) | 2.61421e8 | 0.139380 | ||||||||
\(116\) | −1.36312e9 | + | 9.00501e8i | −0.698995 | + | 0.461768i | ||||
\(117\) | −4.11349e8 | −0.202943 | ||||||||
\(118\) | 1.97414e8i | 0.0937363i | ||||||||
\(119\) | 1.65219e8i | 0.0755264i | ||||||||
\(120\) | 3.25881e9 | 1.43464 | ||||||||
\(121\) | 2.30831e9 | 0.978950 | ||||||||
\(122\) | −1.29996e9 | −0.531266 | ||||||||
\(123\) | 4.30185e9 | 1.69466 | ||||||||
\(124\) | 3.17109e9i | 1.20451i | ||||||||
\(125\) | 2.24852e9 | 0.823763 | ||||||||
\(126\) | − | 1.64867e8i | − | 0.0582727i | ||||||
\(127\) | − | 1.60518e9i | − | 0.547530i | −0.961797 | − | 0.273765i | \(-0.911731\pi\) | ||
0.961797 | − | 0.273765i | \(-0.0882691\pi\) | |||||||
\(128\) | − | 3.09642e9i | − | 1.01957i | ||||||
\(129\) | 6.24413e9 | 1.98526 | ||||||||
\(130\) | − | 8.60392e8i | − | 0.264211i | ||||||
\(131\) | 4.65180e9i | 1.38007i | 0.723777 | + | 0.690034i | \(0.242404\pi\) | ||||
−0.723777 | + | 0.690034i | \(0.757596\pi\) | |||||||
\(132\) | −5.17686e8 | −0.148417 | ||||||||
\(133\) | 1.52217e7i | 0.00421823i | ||||||||
\(134\) | 6.45220e8i | 0.172877i | ||||||||
\(135\) | 3.80657e9i | 0.986352i | ||||||||
\(136\) | −7.57120e8 | −0.189775 | ||||||||
\(137\) | − | 4.52630e9i | − | 1.09774i | −0.835906 | − | 0.548872i | \(-0.815057\pi\) | ||
0.835906 | − | 0.548872i | \(-0.184943\pi\) | |||||||
\(138\) | 1.84027e8 | 0.0431941 | ||||||||
\(139\) | −7.21815e9 | −1.64006 | −0.820029 | − | 0.572323i | \(-0.806043\pi\) | ||||
−0.820029 | + | 0.572323i | \(0.806043\pi\) | |||||||
\(140\) | −1.78051e9 | −0.391714 | ||||||||
\(141\) | −1.02777e9 | −0.218982 | ||||||||
\(142\) | − | 3.16572e9i | − | 0.653395i | ||||||
\(143\) | 2.99831e8i | 0.0599604i | ||||||||
\(144\) | −1.36714e9 | −0.264961 | ||||||||
\(145\) | −7.04908e9 | + | 4.65674e9i | −1.32427 | + | 0.874834i | ||||
\(146\) | −2.70630e9 | −0.492933 | ||||||||
\(147\) | − | 6.31314e9i | − | 1.11511i | ||||||
\(148\) | 5.50895e9i | 0.943825i | ||||||||
\(149\) | 1.01411e10 | 1.68557 | 0.842783 | − | 0.538254i | \(-0.180916\pi\) | ||||
0.842783 | + | 0.538254i | \(0.180916\pi\) | |||||||
\(150\) | 4.63250e9 | 0.747145 | ||||||||
\(151\) | −8.28140e9 | −1.29631 | −0.648153 | − | 0.761510i | \(-0.724458\pi\) | ||||
−0.648153 | + | 0.761510i | \(0.724458\pi\) | |||||||
\(152\) | −6.97538e7 | −0.0105992 | ||||||||
\(153\) | 8.53303e8i | 0.125890i | ||||||||
\(154\) | −1.20171e8 | −0.0172169 | ||||||||
\(155\) | 1.63986e10i | 2.28199i | ||||||||
\(156\) | 3.12725e9i | 0.422768i | ||||||||
\(157\) | − | 4.78086e9i | − | 0.627997i | −0.949423 | − | 0.313999i | \(-0.898331\pi\) | ||
0.949423 | − | 0.313999i | \(-0.101669\pi\) | |||||||
\(158\) | 3.46059e9 | 0.441767 | ||||||||
\(159\) | − | 9.35033e9i | − | 1.16022i | ||||||
\(160\) | − | 1.25990e10i | − | 1.51984i | ||||||
\(161\) | −2.20566e8 | −0.0258716 | ||||||||
\(162\) | 4.41361e9i | 0.503473i | ||||||||
\(163\) | − | 7.68815e9i | − | 0.853056i | −0.904474 | − | 0.426528i | \(-0.859737\pi\) | ||
0.904474 | − | 0.426528i | \(-0.140263\pi\) | |||||||
\(164\) | − | 1.07707e10i | − | 1.16265i | ||||||
\(165\) | −2.67709e9 | −0.281181 | ||||||||
\(166\) | − | 1.22093e9i | − | 0.124797i | ||||||
\(167\) | 9.12487e8 | 0.0907826 | 0.0453913 | − | 0.998969i | \(-0.485547\pi\) | ||||
0.0453913 | + | 0.998969i | \(0.485547\pi\) | |||||||
\(168\) | −2.74953e9 | −0.266297 | ||||||||
\(169\) | −8.79327e9 | −0.829202 | ||||||||
\(170\) | −1.78480e9 | −0.163896 | ||||||||
\(171\) | 7.86152e7i | 0.00703111i | ||||||||
\(172\) | − | 1.56337e10i | − | 1.36202i | ||||||
\(173\) | −4.69144e9 | −0.398197 | −0.199099 | − | 0.979979i | \(-0.563801\pi\) | ||||
−0.199099 | + | 0.979979i | \(0.563801\pi\) | |||||||
\(174\) | −4.96218e9 | + | 3.27810e9i | −0.410394 | + | 0.271113i | ||||
\(175\) | −5.55232e9 | −0.447510 | ||||||||
\(176\) | 9.96505e8i | 0.0782839i | ||||||||
\(177\) | − | 3.71057e9i | − | 0.284159i | ||||||
\(178\) | −7.96487e9 | −0.594687 | ||||||||
\(179\) | 2.28637e10 | 1.66459 | 0.832297 | − | 0.554330i | \(-0.187026\pi\) | ||||
0.832297 | + | 0.554330i | \(0.187026\pi\) | |||||||
\(180\) | −9.19578e9 | −0.652923 | ||||||||
\(181\) | 2.88439e9 | 0.199756 | 0.0998780 | − | 0.995000i | \(-0.468155\pi\) | ||||
0.0998780 | + | 0.995000i | \(0.468155\pi\) | |||||||
\(182\) | 7.25931e8i | 0.0490427i | ||||||||
\(183\) | 2.44341e10 | 1.61052 | ||||||||
\(184\) | − | 1.01075e9i | − | 0.0650075i | ||||||
\(185\) | 2.84883e10i | 1.78811i | ||||||||
\(186\) | 1.15437e10i | 0.707193i | ||||||||
\(187\) | 6.21970e8 | 0.0371948 | ||||||||
\(188\) | 2.57327e9i | 0.150237i | ||||||||
\(189\) | − | 3.21169e9i | − | 0.183086i | ||||||
\(190\) | −1.64434e8 | −0.00915380 | ||||||||
\(191\) | 3.49991e10i | 1.90286i | 0.307866 | + | 0.951430i | \(0.400385\pi\) | ||||
−0.307866 | + | 0.951430i | \(0.599615\pi\) | |||||||
\(192\) | 3.53752e9i | 0.187864i | ||||||||
\(193\) | 9.82019e9i | 0.509462i | 0.967012 | + | 0.254731i | \(0.0819870\pi\) | ||||
−0.967012 | + | 0.254731i | \(0.918013\pi\) | |||||||
\(194\) | −1.84782e9 | −0.0936595 | ||||||||
\(195\) | 1.61719e10i | 0.800949i | ||||||||
\(196\) | −1.58065e10 | −0.765039 | ||||||||
\(197\) | 2.87802e10 | 1.36143 | 0.680715 | − | 0.732548i | \(-0.261669\pi\) | ||||
0.680715 | + | 0.732548i | \(0.261669\pi\) | |||||||
\(198\) | −6.20643e8 | −0.0286978 | ||||||||
\(199\) | 1.15729e10 | 0.523122 | 0.261561 | − | 0.965187i | \(-0.415763\pi\) | ||||
0.261561 | + | 0.965187i | \(0.415763\pi\) | |||||||
\(200\) | − | 2.54436e10i | − | 1.12446i | ||||||
\(201\) | − | 1.21275e10i | − | 0.524070i | ||||||
\(202\) | 4.72516e9 | 0.199680 | ||||||||
\(203\) | 5.94746e9 | − | 3.92899e9i | 0.245810 | − | 0.162386i | ||||
\(204\) | 6.48719e9 | 0.262253 | ||||||||
\(205\) | − | 5.56984e10i | − | 2.20268i | ||||||
\(206\) | 1.83013e10i | 0.708074i | ||||||||
\(207\) | −1.13915e9 | −0.0431237 | ||||||||
\(208\) | 6.01972e9 | 0.222993 | ||||||||
\(209\) | 5.73024e7 | 0.00207737 | ||||||||
\(210\) | −6.48161e9 | −0.229983 | ||||||||
\(211\) | 2.26337e10i | 0.786113i | 0.919514 | + | 0.393057i | \(0.128582\pi\) | ||||
−0.919514 | + | 0.393057i | \(0.871418\pi\) | |||||||
\(212\) | −2.34109e10 | −0.795989 | ||||||||
\(213\) | 5.95028e10i | 1.98075i | ||||||||
\(214\) | 2.50498e9i | 0.0816473i | ||||||||
\(215\) | − | 8.08463e10i | − | 2.58040i | ||||||
\(216\) | 1.47176e10 | 0.460040 | ||||||||
\(217\) | − | 1.38358e10i | − | 0.423580i | ||||||
\(218\) | − | 3.00590e9i | − | 0.0901406i | ||||||
\(219\) | 5.08674e10 | 1.49431 | ||||||||
\(220\) | 6.70278e9i | 0.192909i | ||||||||
\(221\) | − | 3.75722e9i | − | 0.105950i | ||||||
\(222\) | 2.00543e10i | 0.554139i | ||||||||
\(223\) | −3.15612e10 | −0.854636 | −0.427318 | − | 0.904101i | \(-0.640542\pi\) | ||||
−0.427318 | + | 0.904101i | \(0.640542\pi\) | |||||||
\(224\) | 1.06301e10i | 0.282111i | ||||||||
\(225\) | −2.86760e10 | −0.745927 | ||||||||
\(226\) | −7.33419e9 | −0.187010 | ||||||||
\(227\) | 5.42144e10 | 1.35518 | 0.677592 | − | 0.735438i | \(-0.263024\pi\) | ||||
0.677592 | + | 0.735438i | \(0.263024\pi\) | |||||||
\(228\) | 5.97667e8 | 0.0146471 | ||||||||
\(229\) | − | 3.97970e10i | − | 0.956292i | −0.878280 | − | 0.478146i | \(-0.841309\pi\) | ||
0.878280 | − | 0.478146i | \(-0.158691\pi\) | |||||||
\(230\) | − | 2.38270e9i | − | 0.0561427i | ||||||
\(231\) | 2.25872e9 | 0.0521926 | ||||||||
\(232\) | 1.80047e10 | + | 2.72544e10i | 0.408028 | + | 0.617647i | ||||
\(233\) | −5.97296e10 | −1.32766 | −0.663832 | − | 0.747882i | \(-0.731071\pi\) | ||||
−0.663832 | + | 0.747882i | \(0.731071\pi\) | |||||||
\(234\) | 3.74920e9i | 0.0817462i | ||||||||
\(235\) | 1.33071e10i | 0.284628i | ||||||||
\(236\) | −9.29035e9 | −0.194952 | ||||||||
\(237\) | −6.50450e10 | −1.33920 | ||||||||
\(238\) | 1.50587e9 | 0.0304223 | ||||||||
\(239\) | −4.96650e10 | −0.984601 | −0.492300 | − | 0.870425i | \(-0.663844\pi\) | ||||
−0.492300 | + | 0.870425i | \(0.663844\pi\) | |||||||
\(240\) | 5.37481e10i | 1.04571i | ||||||||
\(241\) | −4.65043e10 | −0.888007 | −0.444004 | − | 0.896025i | \(-0.646442\pi\) | ||||
−0.444004 | + | 0.896025i | \(0.646442\pi\) | |||||||
\(242\) | − | 2.10389e10i | − | 0.394325i | ||||||
\(243\) | − | 4.91791e10i | − | 0.904799i | ||||||
\(244\) | − | 6.11768e10i | − | 1.10492i | ||||||
\(245\) | −8.17397e10 | −1.44939 | ||||||||
\(246\) | − | 3.92088e10i | − | 0.682614i | ||||||
\(247\) | − | 3.46154e8i | − | 0.00591743i | ||||||
\(248\) | 6.34029e10 | 1.06433 | ||||||||
\(249\) | 2.29486e10i | 0.378320i | ||||||||
\(250\) | − | 2.04940e10i | − | 0.331815i | ||||||
\(251\) | 8.66926e10i | 1.37864i | 0.724458 | + | 0.689319i | \(0.242090\pi\) | ||||
−0.724458 | + | 0.689319i | \(0.757910\pi\) | |||||||
\(252\) | 7.75868e9 | 0.121195 | ||||||||
\(253\) | 8.30326e8i | 0.0127411i | ||||||||
\(254\) | −1.46303e10 | −0.220547 | ||||||||
\(255\) | 3.35470e10 | 0.496847 | ||||||||
\(256\) | −1.76496e10 | −0.256836 | ||||||||
\(257\) | 4.62355e10 | 0.661115 | 0.330557 | − | 0.943786i | \(-0.392763\pi\) | ||||
0.330557 | + | 0.943786i | \(0.392763\pi\) | |||||||
\(258\) | − | 5.69116e10i | − | 0.799672i | ||||||
\(259\) | − | 2.40362e10i | − | 0.331907i | ||||||
\(260\) | 4.04903e10 | 0.549505 | ||||||||
\(261\) | 3.07167e10 | − | 2.02920e10i | 0.409725 | − | 0.270671i | ||||
\(262\) | 4.23984e10 | 0.555897 | ||||||||
\(263\) | − | 5.98443e10i | − | 0.771297i | −0.922646 | − | 0.385649i | \(-0.873978\pi\) | ||
0.922646 | − | 0.385649i | \(-0.126022\pi\) | |||||||
\(264\) | 1.03506e10i | 0.131144i | ||||||||
\(265\) | −1.21064e11 | −1.50803 | ||||||||
\(266\) | 1.38737e8 | 0.00169912 | ||||||||
\(267\) | 1.49707e11 | 1.80278 | ||||||||
\(268\) | −3.03643e10 | −0.359547 | ||||||||
\(269\) | 1.19242e11i | 1.38849i | 0.719740 | + | 0.694244i | \(0.244261\pi\) | ||||
−0.719740 | + | 0.694244i | \(0.755739\pi\) | |||||||
\(270\) | 3.46947e10 | 0.397306 | ||||||||
\(271\) | 5.02511e10i | 0.565958i | 0.959126 | + | 0.282979i | \(0.0913226\pi\) | ||||
−0.959126 | + | 0.282979i | \(0.908677\pi\) | |||||||
\(272\) | − | 1.24873e10i | − | 0.138328i | ||||||
\(273\) | − | 1.36446e10i | − | 0.148671i | ||||||
\(274\) | −4.12546e10 | −0.442176 | ||||||||
\(275\) | 2.09018e10i | 0.220387i | ||||||||
\(276\) | 8.66035e9i | 0.0898348i | ||||||||
\(277\) | −6.86412e10 | −0.700529 | −0.350264 | − | 0.936651i | \(-0.613908\pi\) | ||||
−0.350264 | + | 0.936651i | \(0.613908\pi\) | |||||||
\(278\) | 6.57892e10i | 0.660622i | ||||||||
\(279\) | − | 7.14575e10i | − | 0.706040i | ||||||
\(280\) | 3.55997e10i | 0.346127i | ||||||||
\(281\) | 6.20906e10 | 0.594084 | 0.297042 | − | 0.954864i | \(-0.404000\pi\) | ||||
0.297042 | + | 0.954864i | \(0.404000\pi\) | |||||||
\(282\) | 9.36750e9i | 0.0882069i | ||||||||
\(283\) | −5.62239e10 | −0.521053 | −0.260527 | − | 0.965467i | \(-0.583896\pi\) | ||||
−0.260527 | + | 0.965467i | \(0.583896\pi\) | |||||||
\(284\) | 1.48980e11 | 1.35893 | ||||||||
\(285\) | 3.09070e9 | 0.0277495 | ||||||||
\(286\) | 2.73278e9 | 0.0241523 | ||||||||
\(287\) | 4.69940e10i | 0.408859i | ||||||||
\(288\) | 5.49010e10i | 0.470234i | ||||||||
\(289\) | 1.10794e11 | 0.934277 | ||||||||
\(290\) | 4.24434e10 | + | 6.42482e10i | 0.352387 | + | 0.533421i | ||||
\(291\) | 3.47315e10 | 0.283926 | ||||||||
\(292\) | − | 1.27359e11i | − | 1.02520i | ||||||
\(293\) | 1.00010e11i | 0.792756i | 0.918087 | + | 0.396378i | \(0.129733\pi\) | ||||
−0.918087 | + | 0.396378i | \(0.870267\pi\) | |||||||
\(294\) | −5.75405e10 | −0.449170 | ||||||||
\(295\) | −4.80429e10 | −0.369343 | ||||||||
\(296\) | 1.10146e11 | 0.833983 | ||||||||
\(297\) | −1.20905e10 | −0.0901651 | ||||||||
\(298\) | − | 9.24299e10i | − | 0.678953i | ||||||
\(299\) | 5.01586e9 | 0.0362932 | ||||||||
\(300\) | 2.18007e11i | 1.55391i | ||||||||
\(301\) | 6.82117e10i | 0.478972i | ||||||||
\(302\) | 7.54801e10i | 0.522157i | ||||||||
\(303\) | −8.88139e10 | −0.605326 | ||||||||
\(304\) | − | 1.15046e9i | − | 0.00772576i | ||||||
\(305\) | − | 3.16362e11i | − | 2.09332i | ||||||
\(306\) | 7.77736e9 | 0.0507091 | ||||||||
\(307\) | 1.37949e11i | 0.886330i | 0.896440 | + | 0.443165i | \(0.146144\pi\) | ||||
−0.896440 | + | 0.443165i | \(0.853856\pi\) | |||||||
\(308\) | − | 5.65528e9i | − | 0.0358076i | ||||||
\(309\) | − | 3.43990e11i | − | 2.14651i | ||||||
\(310\) | 1.49463e11 | 0.919193 | ||||||||
\(311\) | − | 8.54107e9i | − | 0.0517714i | −0.999665 | − | 0.0258857i | \(-0.991759\pi\) | ||
0.999665 | − | 0.0258857i | \(-0.00824060\pi\) | |||||||
\(312\) | 6.25265e10 | 0.373567 | ||||||||
\(313\) | −2.38313e11 | −1.40346 | −0.701728 | − | 0.712445i | \(-0.747588\pi\) | ||||
−0.701728 | + | 0.712445i | \(0.747588\pi\) | |||||||
\(314\) | −4.35748e10 | −0.252960 | ||||||||
\(315\) | 4.01222e10 | 0.229608 | ||||||||
\(316\) | 1.62856e11i | 0.918783i | ||||||||
\(317\) | − | 1.22497e11i | − | 0.681334i | −0.940184 | − | 0.340667i | \(-0.889347\pi\) | ||
0.940184 | − | 0.340667i | \(-0.110653\pi\) | |||||||
\(318\) | −8.52228e10 | −0.467341 | ||||||||
\(319\) | −1.47908e10 | − | 2.23893e10i | −0.0799709 | − | 0.121055i | ||||
\(320\) | 4.58023e10 | 0.244181 | ||||||||
\(321\) | − | 4.70834e10i | − | 0.247511i | ||||||
\(322\) | 2.01033e9i | 0.0104212i | ||||||||
\(323\) | −7.18063e8 | −0.00367072 | ||||||||
\(324\) | −2.07706e11 | −1.04712 | ||||||||
\(325\) | 1.26264e11 | 0.627777 | ||||||||
\(326\) | −7.00730e10 | −0.343614 | ||||||||
\(327\) | 5.64987e10i | 0.273259i | ||||||||
\(328\) | −2.15351e11 | −1.02734 | ||||||||
\(329\) | − | 1.12275e10i | − | 0.0528324i | ||||||
\(330\) | 2.44001e10i | 0.113261i | ||||||||
\(331\) | − | 1.53413e11i | − | 0.702484i | −0.936285 | − | 0.351242i | \(-0.885759\pi\) | ||
0.936285 | − | 0.351242i | \(-0.114241\pi\) | |||||||
\(332\) | 5.74576e10 | 0.259553 | ||||||||
\(333\) | − | 1.24139e11i | − | 0.553235i | ||||||
\(334\) | − | 8.31678e9i | − | 0.0365676i | ||||||
\(335\) | −1.57022e11 | −0.681174 | ||||||||
\(336\) | − | 4.53485e10i | − | 0.194105i | ||||||
\(337\) | 4.13594e11i | 1.74678i | 0.487018 | + | 0.873392i | \(0.338085\pi\) | ||||
−0.487018 | + | 0.873392i | \(0.661915\pi\) | |||||||
\(338\) | 8.01455e10i | 0.334006i | ||||||||
\(339\) | 1.37853e11 | 0.566915 | ||||||||
\(340\) | − | 8.39933e10i | − | 0.340871i | ||||||
\(341\) | −5.20852e10 | −0.208603 | ||||||||
\(342\) | 7.16531e8 | 0.00283216 | ||||||||
\(343\) | 1.44486e11 | 0.563639 | ||||||||
\(344\) | −3.12582e11 | −1.20351 | ||||||||
\(345\) | 4.47850e10i | 0.170195i | ||||||||
\(346\) | 4.27597e10i | 0.160395i | ||||||||
\(347\) | −2.73280e11 | −1.01187 | −0.505936 | − | 0.862571i | \(-0.668853\pi\) | ||||
−0.505936 | + | 0.862571i | \(0.668853\pi\) | |||||||
\(348\) | −1.54268e11 | − | 2.33522e11i | −0.563859 | − | 0.853535i | ||||
\(349\) | −1.35603e11 | −0.489278 | −0.244639 | − | 0.969614i | \(-0.578669\pi\) | ||||
−0.244639 | + | 0.969614i | \(0.578669\pi\) | |||||||
\(350\) | 5.06061e10i | 0.180259i | ||||||||
\(351\) | 7.30364e10i | 0.256837i | ||||||||
\(352\) | 4.00172e10 | 0.138933 | ||||||||
\(353\) | −2.37707e11 | −0.814808 | −0.407404 | − | 0.913248i | \(-0.633566\pi\) | ||||
−0.407404 | + | 0.913248i | \(0.633566\pi\) | |||||||
\(354\) | −3.38197e10 | −0.114460 | ||||||||
\(355\) | 7.70416e11 | 2.57453 | ||||||||
\(356\) | − | 3.74830e11i | − | 1.23683i | ||||||
\(357\) | −2.83043e10 | −0.0922244 | ||||||||
\(358\) | − | 2.08389e11i | − | 0.670505i | ||||||
\(359\) | − | 2.06080e11i | − | 0.654803i | −0.944885 | − | 0.327402i | \(-0.893827\pi\) | ||
0.944885 | − | 0.327402i | \(-0.106173\pi\) | |||||||
\(360\) | 1.83861e11i | 0.576937i | ||||||||
\(361\) | 3.22622e11 | 0.999795 | ||||||||
\(362\) | − | 2.62895e10i | − | 0.0804625i | ||||||
\(363\) | 3.95446e11i | 1.19539i | ||||||||
\(364\) | −3.41626e10 | −0.101999 | ||||||||
\(365\) | − | 6.58610e11i | − | 1.94227i | ||||||
\(366\) | − | 2.22702e11i | − | 0.648723i | ||||||
\(367\) | 9.73391e10i | 0.280085i | 0.990145 | + | 0.140043i | \(0.0447240\pi\) | ||||
−0.990145 | + | 0.140043i | \(0.955276\pi\) | |||||||
\(368\) | 1.66705e10 | 0.0473842 | ||||||||
\(369\) | 2.42709e11i | 0.681502i | ||||||||
\(370\) | 2.59654e11 | 0.720257 | ||||||||
\(371\) | 1.02144e11 | 0.279919 | ||||||||
\(372\) | −5.43252e11 | −1.47081 | ||||||||
\(373\) | 3.24735e11 | 0.868639 | 0.434319 | − | 0.900759i | \(-0.356989\pi\) | ||||
0.434319 | + | 0.900759i | \(0.356989\pi\) | |||||||
\(374\) | − | 5.66889e9i | − | 0.0149822i | ||||||
\(375\) | 3.85203e11i | 1.00589i | ||||||||
\(376\) | 5.14502e10 | 0.132752 | ||||||||
\(377\) | −1.35250e11 | + | 8.93485e10i | −0.344827 | + | 0.227799i | ||||
\(378\) | −2.92726e10 | −0.0737477 | ||||||||
\(379\) | 6.54191e11i | 1.62865i | 0.580408 | + | 0.814326i | \(0.302893\pi\) | ||||
−0.580408 | + | 0.814326i | \(0.697107\pi\) | |||||||
\(380\) | − | 7.73834e9i | − | 0.0190380i | ||||||
\(381\) | 2.74990e11 | 0.668583 | ||||||||
\(382\) | 3.18996e11 | 0.766479 | ||||||||
\(383\) | 2.53312e11 | 0.601536 | 0.300768 | − | 0.953697i | \(-0.402757\pi\) | ||||
0.300768 | + | 0.953697i | \(0.402757\pi\) | |||||||
\(384\) | 5.30460e11 | 1.24498 | ||||||||
\(385\) | − | 2.92450e10i | − | 0.0678387i | ||||||
\(386\) | 8.95053e10 | 0.205213 | ||||||||
\(387\) | 3.52292e11i | 0.798368i | ||||||||
\(388\) | − | 8.69590e10i | − | 0.194792i | ||||||
\(389\) | − | 3.46642e11i | − | 0.767551i | −0.923426 | − | 0.383776i | \(-0.874624\pi\) | ||
0.923426 | − | 0.383776i | \(-0.125376\pi\) | |||||||
\(390\) | 1.47397e11 | 0.322625 | ||||||||
\(391\) | − | 1.04049e10i | − | 0.0225135i | ||||||
\(392\) | 3.16036e11i | 0.676005i | ||||||||
\(393\) | −7.96919e11 | −1.68518 | ||||||||
\(394\) | − | 2.62314e11i | − | 0.548389i | ||||||
\(395\) | 8.42174e11i | 1.74066i | ||||||||
\(396\) | − | 2.92077e10i | − | 0.0596855i | ||||||
\(397\) | 4.37391e11 | 0.883717 | 0.441858 | − | 0.897085i | \(-0.354319\pi\) | ||||
0.441858 | + | 0.897085i | \(0.354319\pi\) | |||||||
\(398\) | − | 1.05480e11i | − | 0.210715i | ||||||
\(399\) | −2.60769e9 | −0.00515084 | ||||||||
\(400\) | 4.19647e11 | 0.819622 | ||||||||
\(401\) | −2.62577e11 | −0.507115 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(402\) | −1.10535e11 | −0.211098 | ||||||||
\(403\) | 3.14638e11i | 0.594208i | ||||||||
\(404\) | 2.22368e11i | 0.415294i | ||||||||
\(405\) | −1.07410e12 | −1.98380 | ||||||||
\(406\) | −3.58104e10 | − | 5.42076e10i | −0.0654097 | − | 0.0990131i | ||||
\(407\) | −9.04847e10 | −0.163456 | ||||||||
\(408\) | − | 1.29705e11i | − | 0.231732i | ||||||
\(409\) | 4.14934e11i | 0.733203i | 0.930378 | + | 0.366601i | \(0.119479\pi\) | ||||
−0.930378 | + | 0.366601i | \(0.880521\pi\) | |||||||
\(410\) | −5.07659e11 | −0.887247 | ||||||||
\(411\) | 7.75419e11 | 1.34044 | ||||||||
\(412\) | −8.61264e11 | −1.47265 | ||||||||
\(413\) | 4.05348e10 | 0.0685572 | ||||||||
\(414\) | 1.03827e10i | 0.0173704i | ||||||||
\(415\) | 2.97129e11 | 0.491732 | ||||||||
\(416\) | − | 2.41737e11i | − | 0.395752i | ||||||
\(417\) | − | 1.23657e12i | − | 2.00266i | ||||||
\(418\) | − | 5.22277e8i | − | 0.000836774i | ||||||
\(419\) | 5.99533e11 | 0.950277 | 0.475138 | − | 0.879911i | \(-0.342398\pi\) | ||||
0.475138 | + | 0.879911i | \(0.342398\pi\) | |||||||
\(420\) | − | 3.05027e11i | − | 0.478317i | ||||||
\(421\) | − | 8.07295e11i | − | 1.25246i | −0.779639 | − | 0.626229i | \(-0.784598\pi\) | ||
0.779639 | − | 0.626229i | \(-0.215402\pi\) | |||||||
\(422\) | 2.06293e11 | 0.316650 | ||||||||
\(423\) | − | 5.79863e10i | − | 0.0880631i | ||||||
\(424\) | 4.68079e11i | 0.703352i | ||||||||
\(425\) | − | 2.61923e11i | − | 0.389425i | ||||||
\(426\) | 5.42333e11 | 0.797853 | ||||||||
\(427\) | 2.66921e11i | 0.388559i | ||||||||
\(428\) | −1.17885e11 | −0.169810 | ||||||||
\(429\) | −5.13652e10 | −0.0732169 | ||||||||
\(430\) | −7.36866e11 | −1.03940 | ||||||||
\(431\) | 4.29919e11 | 0.600121 | 0.300060 | − | 0.953920i | \(-0.402993\pi\) | ||||
0.300060 | + | 0.953920i | \(0.402993\pi\) | |||||||
\(432\) | 2.42741e11i | 0.335325i | ||||||||
\(433\) | 7.16813e11i | 0.979965i | 0.871732 | + | 0.489983i | \(0.162997\pi\) | ||||
−0.871732 | + | 0.489983i | \(0.837003\pi\) | |||||||
\(434\) | −1.26105e11 | −0.170620 | ||||||||
\(435\) | −7.97764e11 | − | 1.20761e12i | −1.06825 | − | 1.61705i | ||||
\(436\) | 1.41459e11 | 0.187474 | ||||||||
\(437\) | − | 9.58609e8i | − | 0.00125740i | ||||||
\(438\) | − | 4.63627e11i | − | 0.601915i | ||||||
\(439\) | 6.17798e11 | 0.793882 | 0.396941 | − | 0.917844i | \(-0.370072\pi\) | ||||
0.396941 | + | 0.917844i | \(0.370072\pi\) | |||||||
\(440\) | 1.34016e11 | 0.170459 | ||||||||
\(441\) | 3.56185e11 | 0.448438 | ||||||||
\(442\) | −3.42448e10 | −0.0426771 | ||||||||
\(443\) | − | 8.50599e11i | − | 1.04932i | −0.851312 | − | 0.524660i | \(-0.824192\pi\) | ||
0.851312 | − | 0.524660i | \(-0.175808\pi\) | |||||||
\(444\) | −9.43761e11 | −1.15249 | ||||||||
\(445\) | − | 1.93834e12i | − | 2.34321i | ||||||
\(446\) | 2.87662e11i | 0.344251i | ||||||||
\(447\) | 1.73731e12i | 2.05823i | ||||||||
\(448\) | −3.86444e10 | −0.0453247 | ||||||||
\(449\) | 1.61972e12i | 1.88075i | 0.340145 | + | 0.940373i | \(0.389524\pi\) | ||||
−0.340145 | + | 0.940373i | \(0.610476\pi\) | |||||||
\(450\) | 2.61365e11i | 0.300463i | ||||||||
\(451\) | 1.76910e11 | 0.201353 | ||||||||
\(452\) | − | 3.45150e11i | − | 0.388942i | ||||||
\(453\) | − | 1.41872e12i | − | 1.58290i | ||||||
\(454\) | − | 4.94132e11i | − | 0.545873i | ||||||
\(455\) | −1.76664e11 | −0.193240 | ||||||||
\(456\) | − | 1.19498e10i | − | 0.0129425i | ||||||
\(457\) | −1.04762e12 | −1.12352 | −0.561761 | − | 0.827300i | \(-0.689876\pi\) | ||||
−0.561761 | + | 0.827300i | \(0.689876\pi\) | |||||||
\(458\) | −3.62726e11 | −0.385198 | ||||||||
\(459\) | 1.51507e11 | 0.159322 | ||||||||
\(460\) | 1.12131e11 | 0.116765 | ||||||||
\(461\) | 1.90900e12i | 1.96857i | 0.176582 | + | 0.984286i | \(0.443496\pi\) | ||||
−0.176582 | + | 0.984286i | \(0.556504\pi\) | |||||||
\(462\) | − | 2.05869e10i | − | 0.0210234i | ||||||
\(463\) | −1.01902e12 | −1.03055 | −0.515273 | − | 0.857026i | \(-0.672309\pi\) | ||||
−0.515273 | + | 0.857026i | \(0.672309\pi\) | |||||||
\(464\) | −4.49511e11 | + | 2.96955e11i | −0.450205 | + | 0.297412i | ||||
\(465\) | −2.80930e12 | −2.78651 | ||||||||
\(466\) | 5.44401e11i | 0.534788i | ||||||||
\(467\) | − | 1.04209e12i | − | 1.01386i | −0.861987 | − | 0.506931i | \(-0.830780\pi\) | ||
0.861987 | − | 0.506931i | \(-0.169220\pi\) | |||||||
\(468\) | −1.76439e11 | −0.170015 | ||||||||
\(469\) | 1.32483e11 | 0.126439 | ||||||||
\(470\) | 1.21286e11 | 0.114649 | ||||||||
\(471\) | 8.19029e11 | 0.766840 | ||||||||
\(472\) | 1.85752e11i | 0.172264i | ||||||||
\(473\) | 2.56785e11 | 0.235881 | ||||||||
\(474\) | 5.92847e11i | 0.539436i | ||||||||
\(475\) | − | 2.41311e10i | − | 0.0217498i | ||||||
\(476\) | 7.08670e10i | 0.0632721i | ||||||||
\(477\) | 5.27543e11 | 0.466579 | ||||||||
\(478\) | 4.52668e11i | 0.396601i | ||||||||
\(479\) | − | 1.23856e12i | − | 1.07500i | −0.843264 | − | 0.537500i | \(-0.819369\pi\) | ||
0.843264 | − | 0.537500i | \(-0.180631\pi\) | |||||||
\(480\) | 2.15839e12 | 1.85586 | ||||||||
\(481\) | 5.46603e11i | 0.465606i | ||||||||
\(482\) | 4.23859e11i | 0.357693i | ||||||||
\(483\) | − | 3.77861e10i | − | 0.0315915i | ||||||
\(484\) | 9.90099e11 | 0.820115 | ||||||||
\(485\) | − | 4.49688e11i | − | 0.369040i | ||||||
\(486\) | −4.48239e11 | −0.364457 | ||||||||
\(487\) | 1.23184e12 | 0.992375 | 0.496187 | − | 0.868215i | \(-0.334733\pi\) | ||||
0.496187 | + | 0.868215i | \(0.334733\pi\) | |||||||
\(488\) | −1.22317e12 | −0.976334 | ||||||||
\(489\) | 1.31709e12 | 1.04166 | ||||||||
\(490\) | 7.45010e11i | 0.583821i | ||||||||
\(491\) | 3.64942e11i | 0.283372i | 0.989912 | + | 0.141686i | \(0.0452524\pi\) | ||||
−0.989912 | + | 0.141686i | \(0.954748\pi\) | |||||||
\(492\) | 1.84518e12 | 1.41970 | ||||||||
\(493\) | 1.85345e11 | + | 2.80563e11i | 0.141309 | + | 0.213904i | ||||
\(494\) | −3.15499e9 | −0.00238356 | ||||||||
\(495\) | − | 1.51041e11i | − | 0.113076i | ||||||
\(496\) | 1.04572e12i | 0.775794i | ||||||||
\(497\) | −6.50017e11 | −0.477882 | ||||||||
\(498\) | 2.09163e11 | 0.152389 | ||||||||
\(499\) | 2.07329e12 | 1.49695 | 0.748474 | − | 0.663164i | \(-0.230787\pi\) | ||||
0.748474 | + | 0.663164i | \(0.230787\pi\) | |||||||
\(500\) | 9.64453e11 | 0.690106 | ||||||||
\(501\) | 1.56322e11i | 0.110854i | ||||||||
\(502\) | 7.90152e11 | 0.555321 | ||||||||
\(503\) | − | 1.35056e11i | − | 0.0940714i | −0.998893 | − | 0.0470357i | \(-0.985023\pi\) | ||
0.998893 | − | 0.0470357i | \(-0.0149774\pi\) | |||||||
\(504\) | − | 1.55127e11i | − | 0.107091i | ||||||
\(505\) | 1.14992e12i | 0.786788i | ||||||||
\(506\) | 7.56794e9 | 0.00513216 | ||||||||
\(507\) | − | 1.50641e12i | − | 1.01253i | ||||||
\(508\) | − | 6.88507e11i | − | 0.458693i | ||||||
\(509\) | −3.38159e11 | −0.223301 | −0.111650 | − | 0.993748i | \(-0.535614\pi\) | ||||
−0.111650 | + | 0.993748i | \(0.535614\pi\) | |||||||
\(510\) | − | 3.05761e11i | − | 0.200132i | ||||||
\(511\) | 5.55683e11i | 0.360523i | ||||||||
\(512\) | − | 1.42450e12i | − | 0.916111i | ||||||
\(513\) | 1.39584e10 | 0.00889831 | ||||||||
\(514\) | − | 4.21410e11i | − | 0.266300i | ||||||
\(515\) | −4.45383e12 | −2.78998 | ||||||||
\(516\) | 2.67828e12 | 1.66315 | ||||||||
\(517\) | −4.22661e10 | −0.0260186 | ||||||||
\(518\) | −2.19076e11 | −0.133693 | ||||||||
\(519\) | − | 8.03709e11i | − | 0.486234i | ||||||
\(520\) | − | 8.09566e11i | − | 0.485554i | ||||||
\(521\) | 1.36366e12 | 0.810841 | 0.405421 | − | 0.914130i | \(-0.367125\pi\) | ||||
0.405421 | + | 0.914130i | \(0.367125\pi\) | |||||||
\(522\) | −1.84949e11 | − | 2.79965e11i | −0.109027 | − | 0.165039i | ||||
\(523\) | −2.72495e12 | −1.59258 | −0.796289 | − | 0.604917i | \(-0.793206\pi\) | ||||
−0.796289 | + | 0.604917i | \(0.793206\pi\) | |||||||
\(524\) | 1.99528e12i | 1.15615i | ||||||||
\(525\) | − | 9.51190e11i | − | 0.546450i | ||||||
\(526\) | −5.45446e11 | −0.310682 | ||||||||
\(527\) | 6.52686e11 | 0.368601 | ||||||||
\(528\) | −1.70715e11 | −0.0955916 | ||||||||
\(529\) | −1.78726e12 | −0.992288 | ||||||||
\(530\) | 1.10343e12i | 0.607439i | ||||||||
\(531\) | 2.09350e11 | 0.114274 | ||||||||
\(532\) | 6.52900e9i | 0.00353382i | ||||||||
\(533\) | − | 1.06868e12i | − | 0.573556i | ||||||
\(534\) | − | 1.36449e12i | − | 0.726166i | ||||||
\(535\) | −6.09616e11 | −0.321710 | ||||||||
\(536\) | 6.07105e11i | 0.317704i | ||||||||
\(537\) | 3.91687e12i | 2.03262i | ||||||||
\(538\) | 1.08682e12 | 0.559289 | ||||||||
\(539\) | − | 2.59622e11i | − | 0.132493i | ||||||
\(540\) | 1.63274e12i | 0.826315i | ||||||||
\(541\) | 2.67959e12i | 1.34487i | 0.740155 | + | 0.672436i | \(0.234752\pi\) | ||||
−0.740155 | + | 0.672436i | \(0.765248\pi\) | |||||||
\(542\) | 4.58009e11 | 0.227970 | ||||||||
\(543\) | 4.94136e11i | 0.243920i | ||||||||
\(544\) | −5.01460e11 | −0.245494 | ||||||||
\(545\) | 7.31521e11 | 0.355175 | ||||||||
\(546\) | −1.24362e11 | −0.0598855 | ||||||||
\(547\) | 2.42147e12 | 1.15647 | 0.578237 | − | 0.815869i | \(-0.303741\pi\) | ||||
0.578237 | + | 0.815869i | \(0.303741\pi\) | |||||||
\(548\) | − | 1.94146e12i | − | 0.919634i | ||||||
\(549\) | 1.37856e12i | 0.647666i | ||||||||
\(550\) | 1.90508e11 | 0.0887730 | ||||||||
\(551\) | 1.70759e10 | + | 2.58484e10i | 0.00789225 | + | 0.0119468i | ||||
\(552\) | 1.73156e11 | 0.0793799 | ||||||||
\(553\) | − | 7.10561e11i | − | 0.323101i | ||||||
\(554\) | 6.25625e11i | 0.282176i | ||||||||
\(555\) | −4.88044e12 | −2.18344 | ||||||||
\(556\) | −3.09606e12 | −1.37396 | ||||||||
\(557\) | 3.83260e12 | 1.68712 | 0.843558 | − | 0.537038i | \(-0.180457\pi\) | ||||
0.843558 | + | 0.537038i | \(0.180457\pi\) | |||||||
\(558\) | −6.51294e11 | −0.284396 | ||||||||
\(559\) | − | 1.55119e12i | − | 0.671912i | ||||||
\(560\) | −5.87152e11 | −0.252293 | ||||||||
\(561\) | 1.06552e11i | 0.0454182i | ||||||||
\(562\) | − | 5.65920e11i | − | 0.239299i | ||||||
\(563\) | − | 3.03957e12i | − | 1.27504i | −0.770434 | − | 0.637520i | \(-0.779960\pi\) | ||
0.770434 | − | 0.637520i | \(-0.220040\pi\) | |||||||
\(564\) | −4.40838e11 | −0.183452 | ||||||||
\(565\) | − | 1.78486e12i | − | 0.736863i | ||||||
\(566\) | 5.12448e11i | 0.209882i | ||||||||
\(567\) | 9.06244e11 | 0.368232 | ||||||||
\(568\) | − | 2.97872e12i | − | 1.20078i | ||||||
\(569\) | − | 2.64705e12i | − | 1.05866i | −0.848416 | − | 0.529330i | \(-0.822443\pi\) | ||
0.848416 | − | 0.529330i | \(-0.177557\pi\) | |||||||
\(570\) | − | 2.81699e10i | − | 0.0111776i | ||||||
\(571\) | 1.38445e12 | 0.545021 | 0.272511 | − | 0.962153i | \(-0.412146\pi\) | ||||
0.272511 | + | 0.962153i | \(0.412146\pi\) | |||||||
\(572\) | 1.28606e11i | 0.0502317i | ||||||||
\(573\) | −5.99584e12 | −2.32356 | ||||||||
\(574\) | 4.28322e11 | 0.164690 | ||||||||
\(575\) | 3.49666e11 | 0.133398 | ||||||||
\(576\) | −1.99586e11 | −0.0755489 | ||||||||
\(577\) | − | 3.30623e12i | − | 1.24177i | −0.783900 | − | 0.620887i | \(-0.786773\pi\) | ||
0.783900 | − | 0.620887i | \(-0.213227\pi\) | |||||||
\(578\) | − | 1.00982e12i | − | 0.376330i | ||||||
\(579\) | −1.68234e12 | −0.622099 | ||||||||
\(580\) | −3.02354e12 | + | 1.99740e12i | −1.10940 | + | 0.732891i | ||||
\(581\) | −2.50694e11 | −0.0912748 | ||||||||
\(582\) | − | 3.16557e11i | − | 0.114366i | ||||||
\(583\) | − | 3.84525e11i | − | 0.137853i | ||||||
\(584\) | −2.54643e12 | −0.905887 | ||||||||
\(585\) | −9.12413e11 | −0.322099 | ||||||||
\(586\) | 9.11534e11 | 0.319325 | ||||||||
\(587\) | 1.19393e12 | 0.415055 | 0.207528 | − | 0.978229i | \(-0.433458\pi\) | ||||
0.207528 | + | 0.978229i | \(0.433458\pi\) | |||||||
\(588\) | − | 2.70788e12i | − | 0.934181i | ||||||
\(589\) | 6.01322e10 | 0.0205868 | ||||||||
\(590\) | 4.37883e11i | 0.148773i | ||||||||
\(591\) | 4.93045e12i | 1.66243i | ||||||||
\(592\) | 1.81666e12i | 0.607893i | ||||||||
\(593\) | 2.01482e12 | 0.669100 | 0.334550 | − | 0.942378i | \(-0.391416\pi\) | ||||
0.334550 | + | 0.942378i | \(0.391416\pi\) | |||||||
\(594\) | 1.10197e11i | 0.0363189i | ||||||||
\(595\) | 3.66472e11i | 0.119871i | ||||||||
\(596\) | 4.34978e12 | 1.41208 | ||||||||
\(597\) | 1.98260e12i | 0.638778i | ||||||||
\(598\) | − | 4.57166e10i | − | 0.0146190i | ||||||
\(599\) | 1.27106e12i | 0.403410i | 0.979446 | + | 0.201705i | \(0.0646482\pi\) | ||||
−0.979446 | + | 0.201705i | \(0.935352\pi\) | |||||||
\(600\) | 4.35885e12 | 1.37307 | ||||||||
\(601\) | − | 8.21053e11i | − | 0.256706i | −0.991729 | − | 0.128353i | \(-0.959031\pi\) | ||
0.991729 | − | 0.128353i | \(-0.0409691\pi\) | |||||||
\(602\) | 6.21710e11 | 0.192932 | ||||||||
\(603\) | 6.84231e11 | 0.210753 | ||||||||
\(604\) | −3.55212e12 | −1.08598 | ||||||||
\(605\) | 5.12007e12 | 1.55373 | ||||||||
\(606\) | 8.09486e11i | 0.243828i | ||||||||
\(607\) | − | 3.90308e12i | − | 1.16697i | −0.812125 | − | 0.583484i | \(-0.801689\pi\) | ||
0.812125 | − | 0.583484i | \(-0.198311\pi\) | |||||||
\(608\) | −4.61997e10 | −0.0137111 | ||||||||
\(609\) | 6.73091e11 | + | 1.01888e12i | 0.198288 | + | 0.300156i | ||||
\(610\) | −2.88345e12 | −0.843196 | ||||||||
\(611\) | 2.55322e11i | 0.0741145i | ||||||||
\(612\) | 3.66005e11i | 0.105464i | ||||||||
\(613\) | −3.39594e12 | −0.971376 | −0.485688 | − | 0.874132i | \(-0.661431\pi\) | ||||
−0.485688 | + | 0.874132i | \(0.661431\pi\) | |||||||
\(614\) | 1.25732e12 | 0.357017 | ||||||||
\(615\) | 9.54192e12 | 2.68966 | ||||||||
\(616\) | −1.13072e11 | −0.0316404 | ||||||||
\(617\) | 4.07289e12i | 1.13141i | 0.824609 | + | 0.565704i | \(0.191395\pi\) | ||||
−0.824609 | + | 0.565704i | \(0.808605\pi\) | |||||||
\(618\) | −3.13526e12 | −0.864621 | ||||||||
\(619\) | 7.71794e11i | 0.211297i | 0.994404 | + | 0.105649i | \(0.0336919\pi\) | ||||
−0.994404 | + | 0.105649i | \(0.966308\pi\) | |||||||
\(620\) | 7.03379e12i | 1.91173i | ||||||||
\(621\) | 2.02261e11i | 0.0545757i | ||||||||
\(622\) | −7.78468e10 | −0.0208537 | ||||||||
\(623\) | 1.63542e12i | 0.434945i | ||||||||
\(624\) | 1.03126e12i | 0.272294i | ||||||||
\(625\) | −8.07164e11 | −0.211593 | ||||||||
\(626\) | 2.17208e12i | 0.565317i | ||||||||
\(627\) | 9.81670e9i | 0.00253666i | ||||||||
\(628\) | − | 2.05064e12i | − | 0.526104i | ||||||
\(629\) | 1.13387e12 | 0.288827 | ||||||||
\(630\) | − | 3.65690e11i | − | 0.0924871i | ||||||
\(631\) | 5.11916e11 | 0.128548 | 0.0642742 | − | 0.997932i | \(-0.479527\pi\) | ||||
0.0642742 | + | 0.997932i | \(0.479527\pi\) | |||||||
\(632\) | 3.25616e12 | 0.811856 | ||||||||
\(633\) | −3.87747e12 | −0.959914 | ||||||||
\(634\) | −1.11649e12 | −0.274444 | ||||||||
\(635\) | − | 3.56046e12i | − | 0.869009i | ||||||
\(636\) | − | 4.01062e12i | − | 0.971973i | ||||||
\(637\) | −1.56833e12 | −0.377408 | ||||||||
\(638\) | −2.04066e11 | + | 1.34809e11i | −0.0487615 | + | 0.0322126i | ||||
\(639\) | −3.35713e12 | −0.796552 | ||||||||
\(640\) | − | 6.86817e12i | − | 1.61820i | ||||||
\(641\) | 8.56776e11i | 0.200450i | 0.994965 | + | 0.100225i | \(0.0319563\pi\) | ||||
−0.994965 | + | 0.100225i | \(0.968044\pi\) | |||||||
\(642\) | −4.29138e11 | −0.0996986 | ||||||||
\(643\) | −2.78211e12 | −0.641837 | −0.320919 | − | 0.947107i | \(-0.603992\pi\) | ||||
−0.320919 | + | 0.947107i | \(0.603992\pi\) | |||||||
\(644\) | −9.46069e10 | −0.0216739 | ||||||||
\(645\) | 1.38501e13 | 3.15090 | ||||||||
\(646\) | 6.54472e9i | 0.00147858i | ||||||||
\(647\) | −1.48557e12 | −0.333292 | −0.166646 | − | 0.986017i | \(-0.553294\pi\) | ||||
−0.166646 | + | 0.986017i | \(0.553294\pi\) | |||||||
\(648\) | 4.15288e12i | 0.925257i | ||||||||
\(649\) | − | 1.52594e11i | − | 0.0337627i | ||||||
\(650\) | − | 1.15083e12i | − | 0.252871i | ||||||
\(651\) | 2.37027e12 | 0.517229 | ||||||||
\(652\) | − | 3.29766e12i | − | 0.714647i | ||||||
\(653\) | − | 5.01554e12i | − | 1.07946i | −0.841837 | − | 0.539732i | \(-0.818525\pi\) | ||
0.841837 | − | 0.539732i | \(-0.181475\pi\) | |||||||
\(654\) | 5.14953e11 | 0.110070 | ||||||||
\(655\) | 1.03182e13i | 2.19036i | ||||||||
\(656\) | − | 3.55182e12i | − | 0.748832i | ||||||
\(657\) | 2.86993e12i | 0.600934i | ||||||||
\(658\) | −1.02332e11 | −0.0212811 | ||||||||
\(659\) | 5.38425e12i | 1.11209i | 0.831151 | + | 0.556046i | \(0.187682\pi\) | ||||
−0.831151 | + | 0.556046i | \(0.812318\pi\) | |||||||
\(660\) | −1.14828e12 | −0.235559 | ||||||||
\(661\) | 3.49051e12 | 0.711184 | 0.355592 | − | 0.934641i | \(-0.384279\pi\) | ||||
0.355592 | + | 0.934641i | \(0.384279\pi\) | |||||||
\(662\) | −1.39827e12 | −0.282963 | ||||||||
\(663\) | 6.43664e11 | 0.129374 | ||||||||
\(664\) | − | 1.14881e12i | − | 0.229346i | ||||||
\(665\) | 3.37632e10i | 0.00669494i | ||||||||
\(666\) | −1.13146e12 | −0.222845 | ||||||||
\(667\) | −3.74550e11 | + | 2.47434e11i | −0.0732730 | + | 0.0484053i | ||||
\(668\) | 3.91391e11 | 0.0760530 | ||||||||
\(669\) | − | 5.40687e12i | − | 1.04359i | ||||||
\(670\) | 1.43116e12i | 0.274380i | ||||||||
\(671\) | 1.00483e12 | 0.191356 | ||||||||
\(672\) | −1.82108e12 | −0.344483 | ||||||||
\(673\) | 5.18202e12 | 0.973714 | 0.486857 | − | 0.873482i | \(-0.338143\pi\) | ||||
0.486857 | + | 0.873482i | \(0.338143\pi\) | |||||||
\(674\) | 3.76966e12 | 0.703611 | ||||||||
\(675\) | 5.09152e12i | 0.944018i | ||||||||
\(676\) | −3.77168e12 | −0.694663 | ||||||||
\(677\) | 1.97020e11i | 0.0360463i | 0.999838 | + | 0.0180232i | \(0.00573726\pi\) | ||||
−0.999838 | + | 0.0180232i | \(0.994263\pi\) | |||||||
\(678\) | − | 1.25645e12i | − | 0.228355i | ||||||
\(679\) | 3.79412e11i | 0.0685010i | ||||||||
\(680\) | −1.67937e12 | −0.301200 | ||||||||
\(681\) | 9.28768e12i | 1.65480i | ||||||||
\(682\) | 4.74726e11i | 0.0840259i | ||||||||
\(683\) | −9.85344e12 | −1.73259 | −0.866293 | − | 0.499536i | \(-0.833504\pi\) | ||||
−0.866293 | + | 0.499536i | \(0.833504\pi\) | |||||||
\(684\) | 3.37202e10i | 0.00589031i | ||||||||
\(685\) | − | 1.00398e13i | − | 1.74228i | ||||||
\(686\) | − | 1.31690e12i | − | 0.227036i | ||||||
\(687\) | 6.81778e12 | 1.16772 | ||||||||
\(688\) | − | 5.15547e12i | − | 0.877245i | ||||||
\(689\) | −2.32285e12 | −0.392676 | ||||||||
\(690\) | 4.08189e11 | 0.0685552 | ||||||||
\(691\) | −6.94442e12 | −1.15874 | −0.579369 | − | 0.815066i | \(-0.696701\pi\) | ||||
−0.579369 | + | 0.815066i | \(0.696701\pi\) | |||||||
\(692\) | −2.01229e12 | −0.333589 | ||||||||
\(693\) | 1.27436e11i | 0.0209891i | ||||||||
\(694\) | 2.49079e12i | 0.407586i | ||||||||
\(695\) | −1.60106e13 | −2.60301 | ||||||||
\(696\) | −4.66905e12 | + | 3.08445e12i | −0.754201 | + | 0.498238i | ||||
\(697\) | −2.21688e12 | −0.355790 | ||||||||
\(698\) | 1.23594e12i | 0.197083i | ||||||||
\(699\) | − | 1.02325e13i | − | 1.62120i | ||||||
\(700\) | −2.38154e12 | −0.374901 | ||||||||
\(701\) | 5.73691e12 | 0.897319 | 0.448660 | − | 0.893703i | \(-0.351902\pi\) | ||||
0.448660 | + | 0.893703i | \(0.351902\pi\) | |||||||
\(702\) | 6.65684e11 | 0.103455 | ||||||||
\(703\) | 1.04464e11 | 0.0161313 | ||||||||
\(704\) | 1.45477e11i | 0.0223213i | ||||||||
\(705\) | −2.27969e12 | −0.347556 | ||||||||
\(706\) | 2.16656e12i | 0.328208i | ||||||||
\(707\) | − | 9.70215e11i | − | 0.146043i | ||||||
\(708\) | − | 1.59157e12i | − | 0.238054i | ||||||
\(709\) | 8.11851e12 | 1.20661 | 0.603307 | − | 0.797509i | \(-0.293849\pi\) | ||||
0.603307 | + | 0.797509i | \(0.293849\pi\) | |||||||
\(710\) | − | 7.02189e12i | − | 1.03703i | ||||||
\(711\) | − | 3.66982e12i | − | 0.538557i | ||||||
\(712\) | −7.49437e12 | −1.09289 | ||||||||
\(713\) | 8.71331e11i | 0.126264i | ||||||||
\(714\) | 2.57977e11i | 0.0371483i | ||||||||
\(715\) | 6.65055e11i | 0.0951657i | ||||||||
\(716\) | 9.80688e12 | 1.39451 | ||||||||
\(717\) | − | 8.50831e12i | − | 1.20228i | ||||||
\(718\) | −1.87830e12 | −0.263757 | ||||||||
\(719\) | 3.82838e12 | 0.534238 | 0.267119 | − | 0.963663i | \(-0.413928\pi\) | ||||
0.267119 | + | 0.963663i | \(0.413928\pi\) | |||||||
\(720\) | −3.03245e12 | −0.420531 | ||||||||
\(721\) | 3.75779e12 | 0.517874 | ||||||||
\(722\) | − | 2.94051e12i | − | 0.402721i | ||||||
\(723\) | − | 7.96684e12i | − | 1.08434i | ||||||
\(724\) | 1.23719e12 | 0.167345 | ||||||||
\(725\) | −9.42856e12 | + | 6.22866e12i | −1.26743 | + | 0.837286i | ||||
\(726\) | 3.60426e12 | 0.481506 | ||||||||
\(727\) | 1.18895e13i | 1.57855i | 0.614040 | + | 0.789275i | \(0.289543\pi\) | ||||
−0.614040 | + | 0.789275i | \(0.710457\pi\) | |||||||
\(728\) | 6.83049e11i | 0.0901281i | ||||||||
\(729\) | −1.10632e12 | −0.145080 | ||||||||
\(730\) | −6.00284e12 | −0.782355 | ||||||||
\(731\) | −3.21780e12 | −0.416803 | ||||||||
\(732\) | 1.04804e13 | 1.34921 | ||||||||
\(733\) | 1.35618e13i | 1.73520i | 0.497264 | + | 0.867599i | \(0.334338\pi\) | ||||
−0.497264 | + | 0.867599i | \(0.665662\pi\) | |||||||
\(734\) | 8.87189e11 | 0.112819 | ||||||||
\(735\) | − | 1.40032e13i | − | 1.76984i | ||||||
\(736\) | − | 6.69446e11i | − | 0.0840940i | ||||||
\(737\) | − | 4.98734e11i | − | 0.0622680i | ||||||
\(738\) | 2.21215e12 | 0.274512 | ||||||||
\(739\) | − | 5.92021e12i | − | 0.730192i | −0.930970 | − | 0.365096i | \(-0.881036\pi\) | ||
0.930970 | − | 0.365096i | \(-0.118964\pi\) | |||||||
\(740\) | 1.22194e13i | 1.49798i | ||||||||
\(741\) | 5.93010e10 | 0.00722570 | ||||||||
\(742\) | − | 9.30986e11i | − | 0.112752i | ||||||
\(743\) | − | 1.83434e12i | − | 0.220816i | −0.993886 | − | 0.110408i | \(-0.964784\pi\) | ||
0.993886 | − | 0.110408i | \(-0.0352158\pi\) | |||||||
\(744\) | 1.08618e13i | 1.29964i | ||||||||
\(745\) | 2.24939e13 | 2.67523 | ||||||||
\(746\) | − | 2.95977e12i | − | 0.349891i | ||||||
\(747\) | −1.29475e12 | −0.152140 | ||||||||
\(748\) | 2.66780e11 | 0.0311599 | ||||||||
\(749\) | 5.14346e11 | 0.0597155 | ||||||||
\(750\) | 3.51090e12 | 0.405175 | ||||||||
\(751\) | − | 1.39891e13i | − | 1.60476i | −0.596816 | − | 0.802378i | \(-0.703568\pi\) | ||
0.596816 | − | 0.802378i | \(-0.296432\pi\) | |||||||
\(752\) | 8.48577e11i | 0.0967634i | ||||||||
\(753\) | −1.48516e13 | −1.68344 | ||||||||
\(754\) | 8.14359e11 | + | 1.23273e12i | 0.0917582 | + | 0.138898i | ||||
\(755\) | −1.83690e13 | −2.05742 | ||||||||
\(756\) | − | 1.37758e12i | − | 0.153380i | ||||||
\(757\) | 5.92603e12i | 0.655892i | 0.944696 | + | 0.327946i | \(0.106356\pi\) | ||||
−0.944696 | + | 0.327946i | \(0.893644\pi\) | |||||||
\(758\) | 5.96257e12 | 0.656028 | ||||||||
\(759\) | −1.42246e11 | −0.0155580 | ||||||||
\(760\) | −1.54721e11 | −0.0168224 | ||||||||
\(761\) | 1.26129e13 | 1.36327 | 0.681637 | − | 0.731690i | \(-0.261268\pi\) | ||||
0.681637 | + | 0.731690i | \(0.261268\pi\) | |||||||
\(762\) | − | 2.50638e12i | − | 0.269308i | ||||||
\(763\) | −6.17200e11 | −0.0659273 | ||||||||
\(764\) | 1.50121e13i | 1.59412i | ||||||||
\(765\) | 1.89271e12i | 0.199806i | ||||||||
\(766\) | − | 2.30879e12i | − | 0.242301i | ||||||
\(767\) | −9.21796e11 | −0.0961736 | ||||||||
\(768\) | − | 3.02362e12i | − | 0.313619i | ||||||
\(769\) | − | 2.22074e12i | − | 0.228997i | −0.993423 | − | 0.114498i | \(-0.963474\pi\) | ||
0.993423 | − | 0.114498i | \(-0.0365261\pi\) | |||||||
\(770\) | −2.66551e11 | −0.0273257 | ||||||||
\(771\) | 7.92080e12i | 0.807280i | ||||||||
\(772\) | 4.21215e12i | 0.426802i | ||||||||
\(773\) | 4.19155e12i | 0.422247i | 0.977459 | + | 0.211124i | \(0.0677123\pi\) | ||||
−0.977459 | + | 0.211124i | \(0.932288\pi\) | |||||||
\(774\) | 3.21093e12 | 0.321586 | ||||||||
\(775\) | 2.19340e13i | 2.18404i | ||||||||
\(776\) | −1.73866e12 | −0.172123 | ||||||||
\(777\) | 4.11773e12 | 0.405288 | ||||||||
\(778\) | −3.15943e12 | −0.309173 | ||||||||
\(779\) | −2.04242e11 | −0.0198713 | ||||||||
\(780\) | 6.93656e12i | 0.670994i | ||||||||
\(781\) | 2.44700e12i | 0.235345i | ||||||||
\(782\) | −9.48347e10 | −0.00906853 | ||||||||
\(783\) | −3.60291e12 | − | 5.45386e12i | −0.342551 | − | 0.518533i | ||||
\(784\) | −5.21245e12 | −0.492742 | ||||||||
\(785\) | − | 1.06044e13i | − | 0.996722i | ||||||
\(786\) | 7.26344e12i | 0.678799i | ||||||||
\(787\) | 3.47697e12 | 0.323083 | 0.161542 | − | 0.986866i | \(-0.448353\pi\) | ||||
0.161542 | + | 0.986866i | \(0.448353\pi\) | |||||||
\(788\) | 1.23446e13 | 1.14054 | ||||||||
\(789\) | 1.02522e13 | 0.941822 | ||||||||
\(790\) | 7.67593e12 | 0.701147 | ||||||||
\(791\) | 1.50593e12i | 0.136776i | ||||||||
\(792\) | −5.83980e11 | −0.0527394 | ||||||||
\(793\) | − | 6.07001e12i | − | 0.545080i | ||||||
\(794\) | − | 3.98657e12i | − | 0.355965i | ||||||
\(795\) | − | 2.07400e13i | − | 1.84143i | ||||||
\(796\) | 4.96393e12 | 0.438245 | ||||||||
\(797\) | 1.52083e13i | 1.33512i | 0.744558 | + | 0.667558i | \(0.232660\pi\) | ||||
−0.744558 | + | 0.667558i | \(0.767340\pi\) | |||||||
\(798\) | 2.37675e10i | 0.00207478i | ||||||||
\(799\) | 5.29641e11 | 0.0459749 | ||||||||
\(800\) | − | 1.68520e13i | − | 1.45461i | ||||||
\(801\) | 8.44644e12i | 0.724982i | ||||||||
\(802\) | 2.39323e12i | 0.204268i | ||||||||
\(803\) | 2.09188e12 | 0.177548 | ||||||||
\(804\) | − | 5.20182e12i | − | 0.439039i | ||||||
\(805\) | −4.89238e11 | −0.0410619 | ||||||||
\(806\) | 2.86774e12 | 0.239349 | ||||||||
\(807\) | −2.04277e13 | −1.69547 | ||||||||
\(808\) | 4.44604e12 | 0.366963 | ||||||||
\(809\) | 6.02802e12i | 0.494773i | 0.968917 | + | 0.247387i | \(0.0795718\pi\) | ||||
−0.968917 | + | 0.247387i | \(0.920428\pi\) | |||||||
\(810\) | 9.78982e12i | 0.799083i | ||||||||
\(811\) | 1.28327e13 | 1.04166 | 0.520830 | − | 0.853661i | \(-0.325623\pi\) | ||||
0.520830 | + | 0.853661i | \(0.325623\pi\) | |||||||
\(812\) | 2.55103e12 | − | 1.68525e12i | 0.205927 | − | 0.136039i | ||||
\(813\) | −8.60872e12 | −0.691085 | ||||||||
\(814\) | 8.24715e11i | 0.0658406i | ||||||||
\(815\) | − | 1.70531e13i | − | 1.35392i | ||||||
\(816\) | 2.13925e12 | 0.168910 | ||||||||
\(817\) | −2.96457e11 | −0.0232789 | ||||||||
\(818\) | 3.78188e12 | 0.295337 | ||||||||
\(819\) | 7.69822e11 | 0.0597878 | ||||||||
\(820\) | − | 2.38906e13i | − | 1.84529i | ||||||
\(821\) | 7.11839e11 | 0.0546812 | 0.0273406 | − | 0.999626i | \(-0.491296\pi\) | ||||
0.0273406 | + | 0.999626i | \(0.491296\pi\) | |||||||
\(822\) | − | 7.06749e12i | − | 0.539936i | ||||||
\(823\) | − | 1.13470e12i | − | 0.0862146i | −0.999070 | − | 0.0431073i | \(-0.986274\pi\) | ||
0.999070 | − | 0.0431073i | \(-0.0137257\pi\) | |||||||
\(824\) | 1.72202e13i | 1.30126i | ||||||||
\(825\) | −3.58077e12 | −0.269113 | ||||||||
\(826\) | − | 3.69451e11i | − | 0.0276151i | ||||||
\(827\) | − | 2.22368e12i | − | 0.165310i | −0.996578 | − | 0.0826548i | \(-0.973660\pi\) | ||
0.996578 | − | 0.0826548i | \(-0.0263399\pi\) | |||||||
\(828\) | −4.88615e11 | −0.0361268 | ||||||||
\(829\) | − | 1.53409e12i | − | 0.112812i | −0.998408 | − | 0.0564062i | \(-0.982036\pi\) | ||
0.998408 | − | 0.0564062i | \(-0.0179642\pi\) | |||||||
\(830\) | − | 2.70815e12i | − | 0.198071i | ||||||
\(831\) | − | 1.17592e13i | − | 0.855408i | ||||||
\(832\) | 8.78805e11 | 0.0635825 | ||||||||
\(833\) | 3.25336e12i | 0.234115i | ||||||||
\(834\) | −1.12706e13 | −0.806677 | ||||||||
\(835\) | 2.02399e12 | 0.144085 | ||||||||
\(836\) | 2.45786e10 | 0.00174032 | ||||||||
\(837\) | −1.26875e13 | −0.893537 | ||||||||
\(838\) | − | 5.46439e12i | − | 0.382775i | ||||||
\(839\) | − | 4.49145e12i | − | 0.312938i | −0.987683 | − | 0.156469i | \(-0.949989\pi\) | ||
0.987683 | − | 0.156469i | \(-0.0500111\pi\) | |||||||
\(840\) | −6.09872e12 | −0.422651 | ||||||||
\(841\) | 5.69197e12 | − | 1.33439e13i | 0.392356 | − | 0.919813i | ||||
\(842\) | −7.35802e12 | −0.504495 | ||||||||
\(843\) | 1.06370e13i | 0.725429i | ||||||||
\(844\) | 9.70823e12i | 0.658566i | ||||||||
\(845\) | −1.95044e13 | −1.31606 | ||||||||
\(846\) | −5.28511e11 | −0.0354722 | ||||||||
\(847\) | −4.31991e12 | −0.288403 | ||||||||
\(848\) | −7.72012e12 | −0.512675 | ||||||||
\(849\) | − | 9.63194e12i | − | 0.636252i | ||||||
\(850\) | −2.38728e12 | −0.156862 | ||||||||
\(851\) | 1.51372e12i | 0.0989375i | ||||||||
\(852\) | 2.55224e13i | 1.65937i | ||||||||
\(853\) | 3.03833e13i | 1.96501i | 0.186248 | + | 0.982503i | \(0.440367\pi\) | ||||
−0.186248 | + | 0.982503i | \(0.559633\pi\) | |||||||
\(854\) | 2.43283e12 | 0.156513 | ||||||||
\(855\) | 1.74376e11i | 0.0111594i | ||||||||
\(856\) | 2.35700e12i | 0.150047i | ||||||||
\(857\) | 1.70562e13 | 1.08011 | 0.540055 | − | 0.841630i | \(-0.318403\pi\) | ||||
0.540055 | + | 0.841630i | \(0.318403\pi\) | |||||||
\(858\) | 4.68164e11i | 0.0294921i | ||||||||
\(859\) | 6.48723e12i | 0.406528i | 0.979124 | + | 0.203264i | \(0.0651549\pi\) | ||||
−0.979124 | + | 0.203264i | \(0.934845\pi\) | |||||||
\(860\) | − | 3.46772e13i | − | 2.16173i | ||||||
\(861\) | −8.05072e12 | −0.499253 | ||||||||
\(862\) | − | 3.91846e12i | − | 0.241731i | ||||||
\(863\) | −1.74624e13 | −1.07166 | −0.535828 | − | 0.844327i | \(-0.680001\pi\) | ||||
−0.535828 | + | 0.844327i | \(0.680001\pi\) | |||||||
\(864\) | 9.74786e12 | 0.595110 | ||||||||
\(865\) | −1.04061e13 | −0.631996 | ||||||||
\(866\) | 6.53333e12 | 0.394734 | ||||||||
\(867\) | 1.89805e13i | 1.14083i | ||||||||
\(868\) | − | 5.93456e12i | − | 0.354854i | ||||||
\(869\) | −2.67492e12 | −0.159119 | ||||||||
\(870\) | −1.10066e13 | + | 7.27115e12i | −0.651354 | + | 0.430295i | ||||
\(871\) | −3.01277e12 | −0.177371 | ||||||||
\(872\) | − | 2.82833e12i | − | 0.165656i | ||||||
\(873\) | 1.95954e12i | 0.114180i | ||||||||
\(874\) | −8.73716e9 | −0.000506488 | ||||||||
\(875\) | −4.20802e12 | −0.242684 | ||||||||
\(876\) | 2.18184e13 | 1.25186 | ||||||||
\(877\) | −1.33654e13 | −0.762931 | −0.381466 | − | 0.924383i | \(-0.624581\pi\) | ||||
−0.381466 | + | 0.924383i | \(0.624581\pi\) | |||||||
\(878\) | − | 5.63086e12i | − | 0.319779i | ||||||
\(879\) | −1.71331e13 | −0.968026 | ||||||||
\(880\) | 2.21035e12i | 0.124248i | ||||||||
\(881\) | − | 1.79363e13i | − | 1.00310i | −0.865130 | − | 0.501548i | \(-0.832764\pi\) | ||
0.865130 | − | 0.501548i | \(-0.167236\pi\) | |||||||
\(882\) | − | 3.24642e12i | − | 0.180633i | ||||||
\(883\) | 8.77653e12 | 0.485847 | 0.242924 | − | 0.970045i | \(-0.421894\pi\) | ||||
0.242924 | + | 0.970045i | \(0.421894\pi\) | |||||||
\(884\) | − | 1.61157e12i | − | 0.0887595i | ||||||
\(885\) | − | 8.23042e12i | − | 0.451001i | ||||||
\(886\) | −7.75271e12 | −0.422670 | ||||||||
\(887\) | − | 8.66694e12i | − | 0.470121i | −0.971981 | − | 0.235060i | \(-0.924471\pi\) | ||
0.971981 | − | 0.235060i | \(-0.0755288\pi\) | |||||||
\(888\) | 1.88696e13i | 1.01837i | ||||||||
\(889\) | 3.00403e12i | 0.161305i | ||||||||
\(890\) | −1.76669e13 | −0.943854 | ||||||||
\(891\) | − | 3.41157e12i | − | 0.181345i | ||||||
\(892\) | −1.35375e13 | −0.715970 | ||||||||
\(893\) | 4.87960e10 | 0.00256775 | ||||||||
\(894\) | 1.58345e13 | 0.829061 | ||||||||
\(895\) | 5.07140e13 | 2.64195 | ||||||||
\(896\) | 5.79482e12i | 0.300368i | ||||||||
\(897\) | 8.59287e11i | 0.0443172i | ||||||||
\(898\) | 1.47628e13 | 0.757572 | ||||||||
\(899\) | −1.55212e13 | − | 2.34950e13i | −0.792513 | − | 1.19966i | ||||
\(900\) | −1.22999e13 | −0.624900 | ||||||||
\(901\) | 4.81852e12i | 0.243586i | ||||||||
\(902\) | − | 1.61243e12i | − | 0.0811056i | ||||||
\(903\) | −1.16856e13 | −0.584867 | ||||||||
\(904\) | −6.90094e12 | −0.343677 | ||||||||
\(905\) | 6.39786e12 | 0.317041 | ||||||||
\(906\) | −1.29308e13 | −0.637600 | ||||||||
\(907\) | − | 1.23089e13i | − | 0.603928i | −0.953319 | − | 0.301964i | \(-0.902358\pi\) | ||
0.953319 | − | 0.301964i | \(-0.0976423\pi\) | |||||||
\(908\) | 2.32540e13 | 1.13530 | ||||||||
\(909\) | − | 5.01085e12i | − | 0.243430i | ||||||
\(910\) | 1.61019e12i | 0.0778377i | ||||||||
\(911\) | 1.40935e12i | 0.0677932i | 0.999425 | + | 0.0338966i | \(0.0107917\pi\) | ||||
−0.999425 | + | 0.0338966i | \(0.989208\pi\) | |||||||
\(912\) | 1.97090e11 | 0.00943384 | ||||||||
\(913\) | 9.43742e11i | 0.0449505i | ||||||||
\(914\) | 9.54845e12i | 0.452559i | ||||||||
\(915\) | 5.41972e13 | 2.55612 | ||||||||
\(916\) | − | 1.70700e13i | − | 0.801133i | ||||||
\(917\) | − | 8.70565e12i | − | 0.406574i | ||||||
\(918\) | − | 1.38090e12i | − | 0.0641755i | ||||||
\(919\) | 2.93611e13 | 1.35785 | 0.678926 | − | 0.734206i | \(-0.262446\pi\) | ||||
0.678926 | + | 0.734206i | \(0.262446\pi\) | |||||||
\(920\) | − | 2.24194e12i | − | 0.103176i | ||||||
\(921\) | −2.36326e13 | −1.08229 | ||||||||
\(922\) | 1.73994e13 | 0.792949 | ||||||||
\(923\) | 1.47819e13 | 0.670383 | ||||||||
\(924\) | 9.68828e11 | 0.0437243 | ||||||||
\(925\) | 3.81048e13i | 1.71136i | ||||||||
\(926\) | 9.28775e12i | 0.415108i | ||||||||
\(927\) | 1.94078e13 | 0.863211 | ||||||||
\(928\) | 1.19250e13 | + | 1.80513e13i | 0.527826 | + | 0.798991i | ||||
\(929\) | 3.19310e13 | 1.40651 | 0.703253 | − | 0.710940i | \(-0.251730\pi\) | ||||
0.703253 | + | 0.710940i | \(0.251730\pi\) | |||||||
\(930\) | 2.56051e13i | 1.12242i | ||||||||
\(931\) | 2.99733e11i | 0.0130756i | ||||||||
\(932\) | −2.56197e13 | −1.11225 | ||||||||
\(933\) | 1.46320e12 | 0.0632175 | ||||||||
\(934\) | −9.49802e12 | −0.408387 | ||||||||
\(935\) | 1.37959e12 | 0.0590335 | ||||||||
\(936\) | 3.52773e12i | 0.150229i | ||||||||
\(937\) | 8.05622e12 | 0.341431 | 0.170716 | − | 0.985320i | \(-0.445392\pi\) | ||||
0.170716 | + | 0.985320i | \(0.445392\pi\) | |||||||
\(938\) | − | 1.20750e12i | − | 0.0509301i | ||||||
\(939\) | − | 4.08264e13i | − | 1.71374i | ||||||
\(940\) | 5.70777e12i | 0.238447i | ||||||||
\(941\) | −6.01825e12 | −0.250217 | −0.125109 | − | 0.992143i | \(-0.539928\pi\) | ||||
−0.125109 | + | 0.992143i | \(0.539928\pi\) | |||||||
\(942\) | − | 7.46497e12i | − | 0.308886i | ||||||
\(943\) | − | 2.95952e12i | − | 0.121876i | ||||||
\(944\) | −3.06364e12 | −0.125564 | ||||||||
\(945\) | − | 7.12384e12i | − | 0.290583i | ||||||
\(946\) | − | 2.34044e12i | − | 0.0950140i | ||||||
\(947\) | 3.33563e13i | 1.34773i | 0.738855 | + | 0.673865i | \(0.235367\pi\) | ||||
−0.738855 | + | 0.673865i | \(0.764633\pi\) | |||||||
\(948\) | −2.78996e13 | −1.12192 | ||||||||
\(949\) | − | 1.26367e13i | − | 0.505750i | ||||||
\(950\) | −2.19941e11 | −0.00876091 | ||||||||
\(951\) | 2.09855e13 | 0.831969 | ||||||||
\(952\) | 1.41692e12 | 0.0559086 | ||||||||
\(953\) | −2.09184e12 | −0.0821505 | −0.0410753 | − | 0.999156i | \(-0.513078\pi\) | ||||
−0.0410753 | + | 0.999156i | \(0.513078\pi\) | |||||||
\(954\) | − | 4.80825e12i | − | 0.187940i | ||||||
\(955\) | 7.76315e13i | 3.02011i | ||||||||
\(956\) | −2.13027e13 | −0.824848 | ||||||||
\(957\) | 3.83560e12 | − | 2.53386e12i | 0.147819 | − | 0.0976516i | ||||
\(958\) | −1.12888e13 | −0.433014 | ||||||||
\(959\) | 8.47079e12i | 0.323400i | ||||||||
\(960\) | 7.84657e12i | 0.298167i | ||||||||
\(961\) | −2.82178e13 | −1.06725 | ||||||||
\(962\) | 4.98196e12 | 0.187548 | ||||||||
\(963\) | 2.65643e12 | 0.0995361 | ||||||||
\(964\) | −1.99470e13 | −0.743927 | ||||||||
\(965\) | 2.17822e13i | 0.808590i | ||||||||
\(966\) | −3.44398e11 | −0.0127252 | ||||||||
\(967\) | − | 2.03974e11i | − | 0.00750164i | −0.999993 | − | 0.00375082i | \(-0.998806\pi\) | ||
0.999993 | − | 0.00375082i | \(-0.00119393\pi\) | |||||||
\(968\) | − | 1.97961e13i | − | 0.724670i | ||||||
\(969\) | − | 1.23014e11i | − | 0.00448227i | ||||||
\(970\) | −4.09865e12 | −0.148651 | ||||||||
\(971\) | 1.90929e12i | 0.0689264i | 0.999406 | + | 0.0344632i | \(0.0109721\pi\) | ||||
−0.999406 | + | 0.0344632i | \(0.989028\pi\) | |||||||
\(972\) | − | 2.10943e13i | − | 0.757995i | ||||||
\(973\) | 1.35085e13 | 0.483168 | ||||||||
\(974\) | − | 1.12275e13i | − | 0.399732i | ||||||
\(975\) | 2.16309e13i | 0.766572i | ||||||||
\(976\) | − | 2.01740e13i | − | 0.711653i | ||||||
\(977\) | −4.87823e13 | −1.71292 | −0.856460 | − | 0.516213i | \(-0.827341\pi\) | ||||
−0.856460 | + | 0.516213i | \(0.827341\pi\) | |||||||
\(978\) | − | 1.20045e13i | − | 0.419584i | ||||||
\(979\) | 6.15658e12 | 0.214199 | ||||||||
\(980\) | −3.50604e13 | −1.21423 | ||||||||
\(981\) | −3.18764e12 | −0.109890 | ||||||||
\(982\) | 3.32623e12 | 0.114143 | ||||||||
\(983\) | 3.61858e13i | 1.23608i | 0.786146 | + | 0.618041i | \(0.212073\pi\) | ||||
−0.786146 | + | 0.618041i | \(0.787927\pi\) | |||||||
\(984\) | − | 3.68926e13i | − | 1.25447i | ||||||
\(985\) | 6.38373e13 | 2.16078 | ||||||||
\(986\) | 2.55717e12 | − | 1.68931e12i | 0.0861616 | − | 0.0569197i | ||||
\(987\) | 1.92342e12 | 0.0645131 | ||||||||
\(988\) | − | 1.48475e11i | − | 0.00495732i | ||||||
\(989\) | − | 4.29574e12i | − | 0.142776i | ||||||
\(990\) | −1.37665e12 | −0.0455475 | ||||||||
\(991\) | −1.83077e13 | −0.602979 | −0.301489 | − | 0.953470i | \(-0.597484\pi\) | ||||
−0.301489 | + | 0.953470i | \(0.597484\pi\) | |||||||
\(992\) | 4.19934e13 | 1.37682 | ||||||||
\(993\) | 2.62818e13 | 0.857795 | ||||||||
\(994\) | 5.92452e12i | 0.192493i | ||||||||
\(995\) | 2.56698e13 | 0.830269 | ||||||||
\(996\) | 9.84329e12i | 0.316937i | ||||||||
\(997\) | − | 5.07766e13i | − | 1.62755i | −0.581178 | − | 0.813777i | \(-0.697408\pi\) | ||
0.581178 | − | 0.813777i | \(-0.302592\pi\) | |||||||
\(998\) | − | 1.88968e13i | − | 0.602977i | ||||||
\(999\) | −2.20413e13 | −0.700154 |
(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 | 29.10.b.a.28.10 | ✓ | 22 | |
29.28 | even | 2 | inner | 29.10.b.a.28.13 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.10.b.a.28.10 | ✓ | 22 | 1.1 | even | 1 | trivial | |
29.10.b.a.28.13 | yes | 22 | 29.28 | even | 2 | inner |