Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(45,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.45");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.e (of order \(3\), degree \(2\), 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: | \(23.7412619368\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.9 | ||
Character | \(\chi\) | \(=\) | 76.49 |
Dual form | 76.8.e.a.45.9 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 20.3841 | − | 35.3063i | 0.435881 | − | 0.754967i | −0.561486 | − | 0.827486i | \(-0.689770\pi\) |
0.997367 | + | 0.0725186i | \(0.0231037\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 172.055 | − | 298.008i | 0.615562 | − | 1.06618i | −0.374724 | − | 0.927137i | \(-0.622262\pi\) |
0.990286 | − | 0.139048i | \(-0.0444043\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 763.824 | 0.841686 | 0.420843 | − | 0.907134i | \(-0.361734\pi\) | ||||
0.420843 | + | 0.907134i | \(0.361734\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 262.475 | + | 454.621i | 0.120016 | + | 0.207874i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7897.42 | 1.78900 | 0.894501 | − | 0.447066i | \(-0.147531\pi\) | ||||
0.894501 | + | 0.447066i | \(0.147531\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2125.23 | − | 3681.00i | −0.268289 | − | 0.464691i | 0.700131 | − | 0.714014i | \(-0.253125\pi\) |
−0.968420 | + | 0.249324i | \(0.919792\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7014.37 | − | 12149.2i | −0.536623 | − | 0.929458i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −9333.93 | + | 16166.8i | −0.460780 | + | 0.798094i | −0.999000 | − | 0.0447103i | \(-0.985764\pi\) |
0.538220 | + | 0.842804i | \(0.319097\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26381.1 | + | 14068.1i | 0.882378 | + | 0.470541i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15569.9 | − | 26967.8i | 0.366874 | − | 0.635445i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −52061.5 | − | 90173.2i | −0.892215 | − | 1.54536i | −0.837214 | − | 0.546875i | \(-0.815817\pi\) |
−0.0550002 | − | 0.998486i | \(-0.517516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20143.2 | − | 34889.1i | −0.257833 | − | 0.446580i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 110561. | 1.08101 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 57126.3 | + | 98945.6i | 0.434954 | + | 0.753362i | 0.997292 | − | 0.0735454i | \(-0.0234314\pi\) |
−0.562338 | + | 0.826907i | \(0.690098\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −254738. | −1.53578 | −0.767889 | − | 0.640583i | \(-0.778693\pi\) | ||||
−0.767889 | + | 0.640583i | \(0.778693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 160982. | − | 278829.i | 0.779791 | − | 1.35064i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 131420. | − | 227625.i | 0.518110 | − | 0.897392i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −269808. | −0.875686 | −0.437843 | − | 0.899051i | \(-0.644257\pi\) | ||||
−0.437843 | + | 0.899051i | \(0.644257\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −173283. | −0.467768 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 355506. | − | 615754.i | 0.805570 | − | 1.39529i | −0.110336 | − | 0.993894i | \(-0.535193\pi\) |
0.915906 | − | 0.401394i | \(-0.131474\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 377944. | − | 654618.i | 0.724916 | − | 1.25559i | −0.234092 | − | 0.972214i | \(-0.575212\pi\) |
0.959008 | − | 0.283378i | \(-0.0914550\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 180641. | 0.295510 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 142495. | + | 246809.i | 0.200197 | + | 0.346752i | 0.948592 | − | 0.316502i | \(-0.102508\pi\) |
−0.748394 | + | 0.663254i | \(0.769175\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −240116. | −0.291565 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 380528. | + | 659094.i | 0.401690 | + | 0.695747i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −111042. | − | 192331.i | −0.102453 | − | 0.177453i | 0.810242 | − | 0.586096i | \(-0.199336\pi\) |
−0.912695 | + | 0.408642i | \(0.866002\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.35879e6 | − | 2.35349e6i | 1.10124 | − | 1.90741i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.03445e6 | − | 644653.i | 0.739855 | − | 0.461067i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.18510e6 | + | 2.05264e6i | −0.751227 | + | 1.30116i | 0.196001 | + | 0.980604i | \(0.437204\pi\) |
−0.947228 | + | 0.320560i | \(0.896129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00808e6 | − | 1.74604e6i | −0.568643 | − | 0.984918i | −0.996701 | − | 0.0811670i | \(-0.974135\pi\) |
0.428058 | − | 0.903751i | \(-0.359198\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 200485. | + | 347250.i | 0.101016 | + | 0.174965i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.46262e6 | −0.660595 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.18150e6 | + | 2.04642e6i | 0.479923 | + | 0.831251i | 0.999735 | − | 0.0230300i | \(-0.00733131\pi\) |
−0.519812 | + | 0.854281i | \(0.673998\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.24491e6 | −1.55560 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.86418e6 | + | 4.96090e6i | −0.949720 | + | 1.64496i | −0.203707 | + | 0.979032i | \(0.565299\pi\) |
−0.746013 | + | 0.665931i | \(0.768034\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.26377e6 | + | 2.18891e6i | −0.380222 | + | 0.658563i | −0.991094 | − | 0.133166i | \(-0.957486\pi\) |
0.610872 | + | 0.791729i | \(0.290819\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.64241e6 | −0.449538 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.03224e6 | 1.50578 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.01818e6 | + | 1.76354e6i | −0.232343 | + | 0.402430i | −0.958497 | − | 0.285102i | \(-0.907973\pi\) |
0.726154 | + | 0.687532i | \(0.241306\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.67966e6 | − | 2.90926e6i | 0.351176 | − | 0.608255i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.00053e6 | −0.192069 | −0.0960345 | − | 0.995378i | \(-0.530616\pi\) | ||||
−0.0960345 | + | 0.995378i | \(0.530616\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.21190e6 | + | 5.56317e6i | 0.567277 | + | 0.982553i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.65788e6 | 0.758352 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.55510e6 | + | 2.69352e6i | 0.233827 | + | 0.405000i | 0.958931 | − | 0.283639i | \(-0.0915418\pi\) |
−0.725104 | + | 0.688639i | \(0.758208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.62330e6 | − | 2.81163e6i | −0.225815 | − | 0.391123i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.19262e6 | + | 8.99387e6i | −0.669416 | + | 1.15946i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.73139e6 | − | 5.44128e6i | 1.04484 | − | 0.651131i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −278642. | + | 482622.i | −0.0309989 | + | 0.0536916i | −0.881109 | − | 0.472914i | \(-0.843202\pi\) |
0.850110 | + | 0.526606i | \(0.176535\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.07288e6 | + | 3.59033e6i | 0.214709 | + | 0.371887i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.20859e6 | + | 9.02155e6i | 0.503032 | + | 0.871277i | 0.999994 | + | 0.00350465i | \(0.00111557\pi\) |
−0.496962 | + | 0.867772i | \(0.665551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.42567e7 | −1.28555 | −0.642776 | − | 0.766054i | \(-0.722217\pi\) | ||||
−0.642776 | + | 0.766054i | \(0.722217\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.35774e6 | − | 9.27988e6i | −0.451668 | − | 0.782312i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.55135e7 | −1.22424 | −0.612121 | − | 0.790764i | \(-0.709683\pi\) | ||||
−0.612121 | + | 0.790764i | \(0.709683\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.13010e6 | − | 3.68944e6i | 0.157546 | − | 0.272877i | −0.776437 | − | 0.630195i | \(-0.782975\pi\) |
0.933983 | + | 0.357317i | \(0.116308\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.49979e6 | + | 9.52592e6i | −0.381695 | + | 0.661114i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.30464e7 | 1.50255 | 0.751273 | − | 0.659991i | \(-0.229440\pi\) | ||||
0.751273 | + | 0.659991i | \(0.229440\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.58297e7 | −2.19685 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.11564e6 | − | 1.93234e6i | 0.0643981 | − | 0.111541i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.12948e6 | + | 1.23486e7i | −0.387832 | + | 0.671744i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.28821e7 | 2.20053 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.44933e7 | − | 2.51032e7i | −0.702265 | − | 1.21636i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.30206e7 | 0.596275 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.43040e6 | − | 2.47753e6i | −0.0619647 | − | 0.107326i | 0.833379 | − | 0.552702i | \(-0.186403\pi\) |
−0.895344 | + | 0.445376i | \(0.853070\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.54081e7 | − | 2.66876e7i | −0.631954 | − | 1.09458i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.66732e7 | − | 2.88789e7i | 0.647992 | − | 1.12236i | −0.335609 | − | 0.942001i | \(-0.608942\pi\) |
0.983602 | − | 0.180354i | \(-0.0577244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.01505e7 | + | 1.07455e7i | 0.742685 | + | 0.396048i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.90226e7 | − | 3.29482e7i | 0.665430 | − | 1.15256i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.75793e7 | − | 3.04482e7i | −0.584089 | − | 1.01167i | −0.994988 | − | 0.0999912i | \(-0.968119\pi\) |
0.410899 | − | 0.911681i | \(-0.365215\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.11587e7 | + | 1.93274e7i | 0.352421 | + | 0.610411i | 0.986673 | − | 0.162715i | \(-0.0520252\pi\) |
−0.634252 | + | 0.773126i | \(0.718692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.16186e7 | 0.349049 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.67838e7 | − | 2.90704e7i | −0.479970 | − | 0.831332i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.93154e7 | 1.07096 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.89456e6 | + | 8.47763e6i | −0.127088 | + | 0.220122i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.07619e7 | + | 1.86402e7i | −0.266525 | + | 0.461635i | −0.967962 | − | 0.251097i | \(-0.919209\pi\) |
0.701437 | + | 0.712731i | \(0.252542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.11138e7 | 0.499054 | 0.249527 | − | 0.968368i | \(-0.419725\pi\) | ||||
0.249527 | + | 0.968368i | \(0.419725\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.79971e6 | −0.221204 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.38289e7 | + | 7.59140e7i | −0.945366 | + | 1.63742i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.37055e6 | − | 1.62303e7i | 0.193249 | − | 0.334716i | −0.753076 | − | 0.657933i | \(-0.771431\pi\) |
0.946325 | + | 0.323217i | \(0.104764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.05401e6 | −0.178629 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.97658e7 | − | 6.88764e7i | −0.750964 | − | 1.30071i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.64707e7 | 1.02133 | 0.510665 | − | 0.859780i | \(-0.329399\pi\) | ||||
0.510665 | + | 0.859780i | \(0.329399\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.53954e7 | − | 9.59477e7i | −0.960020 | − | 1.66280i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.96978e7 | + | 3.41175e7i | 0.327272 | + | 0.566852i | 0.981970 | − | 0.189039i | \(-0.0605372\pi\) |
−0.654697 | + | 0.755891i | \(0.727204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.23411e7 | − | 3.86959e7i | 0.356042 | − | 0.616682i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 528732. | + | 1.56859e7i | 0.00808628 | + | 0.239896i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.18329e6 | + | 1.59059e7i | −0.134846 | + | 0.233560i | −0.925538 | − | 0.378654i | \(-0.876387\pi\) |
0.790693 | + | 0.612213i | \(0.209721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.53859e7 | − | 2.66491e7i | −0.217014 | − | 0.375880i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.83142e7 | + | 8.36827e7i | 0.654891 | + | 1.13430i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.85565e7 | 0.372151 | 0.186076 | − | 0.982535i | \(-0.440423\pi\) | ||||
0.186076 | + | 0.982535i | \(0.440423\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.54109e7 | + | 1.13295e8i | 0.819927 | + | 1.42015i | 0.905736 | + | 0.423843i | \(0.139319\pi\) |
−0.0858088 | + | 0.996312i | \(0.527347\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.21951e7 | −0.991442 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.64217e7 | + | 8.04048e7i | −0.539039 | + | 0.933643i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.37140e7 | + | 1.27676e8i | −0.824336 | + | 1.42779i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.44495e7 | 0.909872 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.80507e8 | −1.87447 | −0.937235 | − | 0.348699i | \(-0.886623\pi\) | ||||
−0.937235 | + | 0.348699i | \(0.886623\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.89076e7 | − | 6.73900e7i | 0.389569 | − | 0.674753i | −0.602823 | − | 0.797875i | \(-0.705957\pi\) |
0.992392 | + | 0.123122i | \(0.0392907\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.98142e7 | + | 5.16398e7i | −0.287940 | + | 0.498727i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.00103e8 | −0.932862 | −0.466431 | − | 0.884558i | \(-0.654460\pi\) | ||||
−0.466431 | + | 0.884558i | \(0.654460\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.11667e7 | + | 7.13028e7i | 0.370305 | + | 0.641388i | 0.989612 | − | 0.143761i | \(-0.0459197\pi\) |
−0.619307 | + | 0.785149i | \(0.712586\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.63352e7 | 0.836756 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.36344e7 | + | 7.55770e7i | 0.366094 | + | 0.634094i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.22333e8 | − | 2.11887e8i | −0.991756 | − | 1.71777i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.73297e7 | − | 4.73365e7i | 0.214160 | − | 0.370937i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.08342e8 | + | 1.11102e8i | 1.57858 | + | 0.841799i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.52366e7 | + | 1.47634e8i | −0.624651 | + | 1.08193i | 0.363957 | + | 0.931416i | \(0.381425\pi\) |
−0.988608 | + | 0.150512i | \(0.951908\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.16767e8 | + | 2.02247e8i | 0.827929 | + | 1.43402i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.30054e8 | − | 2.25260e8i | −0.892462 | − | 1.54579i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.94575e8 | −1.29264 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.15215e7 | + | 8.92379e7i | 0.331462 | + | 0.574110i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.93468e7 | 0.494489 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.26304e7 | − | 3.91969e7i | 0.136655 | − | 0.236693i | −0.789574 | − | 0.613656i | \(-0.789698\pi\) |
0.926228 | + | 0.376963i | \(0.123032\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.05742e7 | − | 1.83150e7i | 0.0618883 | − | 0.107194i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.05766e7 | −0.286985 | −0.143492 | − | 0.989651i | \(-0.545833\pi\) | ||||
−0.143492 | + | 0.989651i | \(0.545833\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.90300e8 | 1.04716 | 0.523582 | − | 0.851975i | \(-0.324595\pi\) | ||||
0.523582 | + | 0.851975i | \(0.324595\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.22962e8 | − | 2.12976e8i | 0.656339 | − | 1.13681i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.73168e7 | + | 1.16596e8i | −0.348641 | + | 0.603863i | −0.986008 | − | 0.166697i | \(-0.946690\pi\) |
0.637368 | + | 0.770560i | \(0.280023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.80681e7 | 0.492936 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.15094e7 | + | 7.18964e7i | 0.202548 | + | 0.350823i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.54361e7 | −0.0731382 | −0.0365691 | − | 0.999331i | \(-0.511643\pi\) | ||||
−0.0365691 | + | 0.999331i | \(0.511643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.15573e6 | + | 1.41261e7i | 0.0375321 | + | 0.0650075i | 0.884181 | − | 0.467144i | \(-0.154717\pi\) |
−0.846649 | + | 0.532151i | \(0.821384\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.24220e7 | + | 9.07976e7i | 0.234364 | + | 0.405931i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.13132e7 | + | 7.15565e7i | −0.179476 | + | 0.310862i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.28106e6 | − | 1.27007e8i | −0.0180764 | − | 0.536274i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.03949e7 | + | 3.53251e7i | −0.0837191 | + | 0.145006i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.43578e8 | − | 2.48684e8i | −0.573100 | − | 0.992638i | −0.996245 | − | 0.0865759i | \(-0.972407\pi\) |
0.423146 | − | 0.906062i | \(-0.360926\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.11152e8 | − | 7.12136e8i | −1.59617 | − | 2.76465i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.61887e8 | 0.989060 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.40727e7 | + | 4.16952e7i | 0.0884626 | + | 0.153222i | 0.906861 | − | 0.421429i | \(-0.138471\pi\) |
−0.818399 | + | 0.574651i | \(0.805138\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.06086e8 | −0.737052 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.99885e7 | + | 5.19416e7i | −0.104403 | + | 0.180831i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.11604e8 | + | 1.93303e8i | −0.378298 | + | 0.655231i | −0.990815 | − | 0.135227i | \(-0.956824\pi\) |
0.612517 | + | 0.790457i | \(0.290157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.64216e7 | −0.252264 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.26798e8 | 0.407682 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.87382e7 | + | 4.97759e7i | −0.0900173 | + | 0.155914i | −0.907518 | − | 0.420013i | \(-0.862026\pi\) |
0.817501 | + | 0.575927i | \(0.195359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 344314. | − | 596369.i | 0.00105090 | − | 0.00182022i | −0.865499 | − | 0.500910i | \(-0.832999\pi\) |
0.866550 | + | 0.499090i | \(0.166332\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.32358e8 | −0.393714 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.59079e8 | − | 2.75534e8i | −0.461264 | − | 0.798933i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.27655e8 | 1.20897 | 0.604483 | − | 0.796618i | \(-0.293380\pi\) | ||||
0.604483 | + | 0.796618i | \(0.293380\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.68625e7 | − | 1.15809e8i | −0.184318 | − | 0.319248i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.75581e7 | + | 1.34335e8i | 0.208523 | + | 0.361173i | 0.951250 | − | 0.308422i | \(-0.0998009\pi\) |
−0.742726 | + | 0.669595i | \(0.766468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.37217e8 | − | 4.10871e8i | 0.622147 | − | 1.07759i | −0.366939 | − | 0.930245i | \(-0.619594\pi\) |
0.989085 | − | 0.147344i | \(-0.0470725\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.41298e7 | − | 4.19189e8i | −0.0361558 | − | 1.07264i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.71544e8 | − | 4.70328e8i | 0.678037 | − | 1.17439i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.09248e7 | + | 5.35633e7i | 0.0753640 | + | 0.130534i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.13598e7 | + | 1.96757e7i | 0.0270236 | + | 0.0468063i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.69999e8 | −0.859338 | −0.429669 | − | 0.902986i | \(-0.641370\pi\) | ||||
−0.429669 | + | 0.902986i | \(0.641370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.07803e8 | + | 7.06335e8i | 0.924853 | + | 1.60189i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.73150e8 | 1.93393 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.21285e8 | + | 3.83277e8i | −0.478743 | + | 0.829207i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.88683e8 | − | 5.00013e8i | 0.610152 | − | 1.05681i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.24690e8 | 0.877048 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.93779e8 | −1.40014 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.93752e8 | − | 6.81998e8i | 0.776673 | − | 1.34524i | −0.157176 | − | 0.987571i | \(-0.550239\pi\) |
0.933849 | − | 0.357666i | \(-0.116428\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.90611e8 | + | 5.03353e8i | −0.560347 | + | 0.970550i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.56302e8 | −0.671672 | −0.335836 | − | 0.941920i | \(-0.609019\pi\) | ||||
−0.335836 | + | 0.941920i | \(0.609019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.79419e7 | − | 6.57172e7i | −0.0699380 | − | 0.121136i | 0.828936 | − | 0.559344i | \(-0.188947\pi\) |
−0.898874 | + | 0.438208i | \(0.855613\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.37978e8 | 0.248726 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.64310e8 | − | 2.84594e8i | −0.289706 | − | 0.501786i | 0.684033 | − | 0.729451i | \(-0.260224\pi\) |
−0.973740 | + | 0.227665i | \(0.926891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.51150e8 | + | 7.81415e8i | 0.778133 | + | 1.34777i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.16229e8 | + | 5.47725e8i | −0.533623 | + | 0.924262i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.73676e8 | + | 2.95188e8i | −0.782118 | + | 0.487405i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.56177e7 | + | 1.48294e8i | −0.138348 | + | 0.239625i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.68404e7 | − | 1.50412e8i | −0.137342 | − | 0.237884i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.08841e8 | + | 1.88519e8i | 0.168503 | + | 0.291856i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.39307e8 | −0.362709 | −0.181354 | − | 0.983418i | \(-0.558048\pi\) | ||||
−0.181354 | + | 0.983418i | \(0.558048\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.08179e7 | − | 1.22660e8i | −0.105096 | − | 0.182032i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.13130e8 | 1.18169 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.21762e8 | + | 2.10899e8i | −0.173304 | + | 0.300171i | −0.939573 | − | 0.342349i | \(-0.888778\pi\) |
0.766269 | + | 0.642520i | \(0.222111\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.69780e8 | − | 8.13683e8i | 0.654931 | − | 1.13437i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.01178e9 | −2.74751 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.12448e8 | −1.08709 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.30358e8 | + | 1.26502e9i | −0.957566 | + | 1.65855i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.83780e8 | + | 1.01114e9i | −0.750061 | + | 1.29914i | 0.197732 | + | 0.980256i | \(0.436642\pi\) |
−0.947793 | + | 0.318887i | \(0.896691\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.42418e8 | 0.305264 | 0.152632 | − | 0.988283i | \(-0.451225\pi\) | ||||
0.152632 | + | 0.988283i | \(0.451225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.34968e8 | − | 4.06976e8i | −0.290024 | − | 0.502336i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.36964e8 | −0.649731 | −0.324865 | − | 0.945760i | \(-0.605319\pi\) | ||||
−0.324865 | + | 0.945760i | \(0.605319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.85591e8 | + | 1.70709e9i | 1.16922 | + | 2.02515i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.90656e8 | + | 5.03431e8i | 0.338097 | + | 0.585601i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.13560e8 | + | 3.69896e8i | −0.243606 | + | 0.421938i | −0.961739 | − | 0.273968i | \(-0.911664\pi\) |
0.718133 | + | 0.695906i | \(0.244997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.98049e8 | + | 7.42263e8i | 0.557182 | + | 0.830391i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.74113e8 | − | 1.51401e9i | 0.959168 | − | 1.66133i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.34874e8 | + | 7.53224e8i | 0.468100 | + | 0.810773i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.14235e8 | + | 1.97861e8i | 0.120634 | + | 0.208943i | 0.920018 | − | 0.391877i | \(-0.128174\pi\) |
−0.799384 | + | 0.600820i | \(0.794841\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.73246e8 | 0.386726 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.48169e7 | − | 1.46907e8i | −0.0862330 | − | 0.149360i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.22173e8 | −0.221672 | −0.110836 | − | 0.993839i | \(-0.535353\pi\) | ||||
−0.110836 | + | 0.993839i | \(0.535353\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.65414e8 | − | 4.59710e8i | 0.259905 | − | 0.450168i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.42812e8 | − | 4.20564e8i | 0.233387 | − | 0.404238i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.44798e8 | −0.419687 | −0.209843 | − | 0.977735i | \(-0.567295\pi\) | ||||
−0.209843 | + | 0.977735i | \(0.567295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.16630e8 | −0.108037 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.31050e7 | + | 5.73395e7i | −0.0301091 | + | 0.0521504i | −0.880687 | − | 0.473698i | \(-0.842919\pi\) |
0.850578 | + | 0.525849i | \(0.176252\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.03788e9 | − | 1.79765e9i | 0.926899 | − | 1.60544i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.96804e8 | 0.348007 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.39474e8 | − | 9.34397e8i | −0.464673 | − | 0.804836i | 0.534514 | − | 0.845160i | \(-0.320495\pi\) |
−0.999187 | + | 0.0403231i | \(0.987161\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.94375e9 | 1.64446 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.79738e8 | − | 1.17734e9i | −0.564895 | − | 0.978426i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.50366e8 | + | 6.06851e8i | 0.286043 | + | 0.495441i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.36185e8 | + | 7.55495e8i | −0.349868 | + | 0.605989i | −0.986226 | − | 0.165405i | \(-0.947107\pi\) |
0.636358 | + | 0.771394i | \(0.280440\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.90136e8 | − | 4.92401e8i | 0.622725 | − | 0.388073i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.83386e8 | + | 1.01045e9i | −0.451805 | + | 0.782549i | −0.998498 | − | 0.0547842i | \(-0.982553\pi\) |
0.546694 | + | 0.837333i | \(0.315886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.41376e8 | + | 9.37691e8i | 0.412033 | + | 0.713661i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.77989e8 | − | 1.00111e9i | −0.432341 | − | 0.748837i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.13078e9 | −1.56660 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.26686e7 | + | 2.19427e7i | 0.00915583 | + | 0.0158584i | 0.870567 | − | 0.492050i | \(-0.163752\pi\) |
−0.861411 | + | 0.507908i | \(0.830419\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.43335e9 | −1.01837 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.05204e8 | + | 1.56786e9i | −0.632297 | + | 1.09517i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.72146e8 | + | 2.98166e8i | −0.118230 | + | 0.204781i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.09841e8 | 0.614454 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.27777e9 | 1.51273 | 0.756364 | − | 0.654151i | \(-0.226974\pi\) | ||||
0.756364 | + | 0.654151i | \(0.226974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.34147e8 | − | 1.09838e9i | 0.414193 | − | 0.717403i | −0.581150 | − | 0.813796i | \(-0.697397\pi\) |
0.995343 | + | 0.0963929i | \(0.0307305\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.48031e7 | + | 1.29563e8i | −0.0480539 | + | 0.0832317i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.52061e8 | 0.475217 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.69994e8 | − | 1.33367e9i | −0.478619 | − | 0.828992i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.36849e9 | −0.836838 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.45935e8 | − | 1.29200e9i | −0.448777 | − | 0.777305i | 0.549530 | − | 0.835474i | \(-0.314807\pi\) |
−0.998307 | + | 0.0581694i | \(0.981474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.28240e8 | − | 3.95324e8i | −0.135109 | − | 0.234016i | 0.790530 | − | 0.612423i | \(-0.209805\pi\) |
−0.925639 | + | 0.378407i | \(0.876472\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.01410e8 | − | 1.38808e9i | 0.466812 | − | 0.808543i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.04873e8 | − | 3.11127e9i | −0.0601144 | − | 1.78342i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.05633e8 | + | 1.82961e8i | −0.0595898 | + | 0.103213i | −0.894281 | − | 0.447505i | \(-0.852313\pi\) |
0.834692 | + | 0.550718i | \(0.185646\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.30246e7 | − | 1.09162e8i | −0.0349925 | − | 0.0606088i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.72858e8 | + | 8.19014e8i | 0.258415 | + | 0.447588i | 0.965818 | − | 0.259223i | \(-0.0834665\pi\) |
−0.707402 | + | 0.706811i | \(0.750133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.07025e9 | 0.575740 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.38745e8 | + | 7.59928e8i | 0.232346 | + | 0.402435i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.59343e9 | −0.830753 | −0.415376 | − | 0.909650i | \(-0.636350\pi\) | ||||
−0.415376 | + | 0.909650i | \(0.636350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.80758e9 | − | 4.86287e9i | 1.44117 | − | 2.49617i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.30387e8 | − | 7.45451e8i | 0.217528 | − | 0.376769i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.11718e9 | −0.556013 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.49871e9 | 0.734533 | 0.367266 | − | 0.930116i | \(-0.380294\pi\) | ||||
0.367266 | + | 0.930116i | \(0.380294\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.03197e9 | + | 1.78743e9i | −0.498109 | + | 0.862749i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.40723e8 | + | 1.45618e9i | −0.399668 | + | 0.692246i | −0.993685 | − | 0.112207i | \(-0.964208\pi\) |
0.594016 | + | 0.804453i | \(0.297541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.39074e9 | −1.11943 | −0.559717 | − | 0.828684i | \(-0.689090\pi\) | ||||
−0.559717 | + | 0.828684i | \(0.689090\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.78683e9 | + | 3.09488e9i | 0.824134 | + | 1.42744i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.94773e8 | −0.179365 | −0.0896827 | − | 0.995970i | \(-0.528585\pi\) | ||||
−0.0896827 | + | 0.995970i | \(0.528585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.02457e8 | + | 1.56310e9i | 0.403944 | + | 0.699652i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.82021e8 | − | 6.61679e8i | −0.168467 | − | 0.291793i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.98478e9 | − | 5.16980e9i | 1.29688 | − | 2.24626i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.05766e7 | − | 1.20379e9i | −0.0173719 | − | 0.515374i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.82918e7 | − | 1.00964e8i | 0.0245920 | − | 0.0425945i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.31983e9 | + | 2.28602e9i | 0.548713 | + | 0.950398i | 0.998363 | + | 0.0571936i | \(0.0182152\pi\) |
−0.449650 | + | 0.893205i | \(0.648451\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.73402e8 | + | 9.93162e8i | 0.234937 | + | 0.406923i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.24236e9 | −1.30932 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.58835e7 | + | 1.66075e8i | 0.0381634 | + | 0.0661010i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.67689e9 | −1.83487 | −0.917436 | − | 0.397884i | \(-0.869745\pi\) | ||||
−0.917436 | + | 0.397884i | \(0.869745\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.15110e9 | − | 1.99377e9i | 0.445178 | − | 0.771071i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.40204e8 | + | 7.62455e8i | −0.167830 | + | 0.290689i | −0.937657 | − | 0.347563i | \(-0.887009\pi\) |
0.769827 | + | 0.638253i | \(0.220342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.13285e9 | −0.801672 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.42659e9 | 0.528667 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.18773e9 | + | 3.78925e9i | −0.799366 | + | 1.38454i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.18972e9 | − | 2.06065e9i | 0.428639 | − | 0.742425i | −0.568113 | − | 0.822950i | \(-0.692326\pi\) |
0.996753 | + | 0.0805254i | \(0.0256598\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.60609e9 | 0.570607 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.37727e9 | + | 2.38550e9i | 0.482537 | + | 0.835779i | 0.999799 | − | 0.0200484i | \(-0.00638203\pi\) |
−0.517262 | + | 0.855827i | \(0.673049\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.58465e9 | 1.23859 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.10807e8 | − | 1.57756e9i | −0.310383 | − | 0.537600i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.97659e8 | − | 1.03518e9i | −0.200882 | − | 0.347938i | 0.747931 | − | 0.663777i | \(-0.231048\pi\) |
−0.948813 | + | 0.315839i | \(0.897714\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.65295e8 | + | 1.67194e9i | −0.320027 | + | 0.554303i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.91673e9 | + | 1.55539e9i | 0.953861 | + | 0.508661i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.45294e9 | + | 4.24861e9i | −0.791337 | + | 1.37064i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.12535e9 | + | 1.94916e9i | 0.358154 | + | 0.620340i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.74387e8 | + | 6.48457e8i | 0.117553 | + | 0.203608i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.77984e9 | 1.79054 | 0.895269 | − | 0.445526i | \(-0.146983\pi\) | ||||
0.895269 | + | 0.445526i | \(0.146983\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.15665e9 | − | 3.73543e9i | −0.659211 | − | 1.14179i | −0.980820 | − | 0.194914i | \(-0.937557\pi\) |
0.321609 | − | 0.946872i | \(-0.395776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.25451e9 | −0.378370 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.37771e9 | − | 4.11831e9i | 0.707655 | − | 1.22569i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.71839e9 | + | 6.44044e9i | −1.09209 | + | 1.89156i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.24423e9 | −0.360637 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.02212e9 | −0.864503 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.66917e9 | + | 4.62315e9i | −0.753596 | + | 1.30527i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.82099e8 | − | 1.00823e9i | 0.162214 | − | 0.280962i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.89630e9 | −0.521611 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.58977e9 | − | 4.48560e9i | −0.703186 | − | 1.21795i | −0.967342 | − | 0.253473i | \(-0.918427\pi\) |
0.264157 | − | 0.964480i | \(-0.414906\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.33337e9 | 1.42956 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.32987e8 | − | 1.26957e9i | −0.193958 | − | 0.335946i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.30165e9 | + | 3.98657e9i | 0.601289 | + | 1.04146i | 0.992626 | + | 0.121215i | \(0.0386791\pi\) |
−0.391338 | + | 0.920247i | \(0.627988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.29191e8 | − | 9.16586e8i | 0.136493 | − | 0.236412i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.15075e8 | + | 3.41395e9i | 0.0293057 | + | 0.869414i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.77710e8 | + | 1.34703e9i | −0.195560 | + | 0.338720i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.89253e9 | + | 3.27796e9i | 0.469913 | + | 0.813914i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.39358e8 | + | 1.28061e9i | 0.181285 | + | 0.313995i | 0.942318 | − | 0.334718i | \(-0.108641\pi\) |
−0.761033 | + | 0.648713i | \(0.775308\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.21286e9 | −0.777949 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00519e9 | + | 5.20514e9i | 0.718624 | + | 1.24469i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.10479e9 | −0.497084 | −0.248542 | − | 0.968621i | \(-0.579951\pi\) | ||||
−0.248542 | + | 0.968621i | \(0.579951\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.96524e9 | − | 6.86799e9i | 0.924911 | − | 1.60199i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.28297e9 | − | 2.22216e9i | 0.295580 | − | 0.511959i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.07912e9 | −1.83853 | −0.919266 | − | 0.393637i | \(-0.871217\pi\) | ||||
−0.919266 | + | 0.393637i | \(0.871217\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.56191e9 | −1.25025 | −0.625126 | − | 0.780524i | \(-0.714952\pi\) | ||||
−0.625126 | + | 0.780524i | \(0.714952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.67949e9 | + | 6.37306e9i | −0.817045 | + | 1.41516i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.09737e9 | + | 3.63276e9i | −0.460085 | + | 0.796891i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.65106e9 | 1.00795 | 0.503973 | − | 0.863720i | \(-0.331871\pi\) | ||||
0.503973 | + | 0.863720i | \(0.331871\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.58620e9 | − | 2.74737e9i | −0.339611 | − | 0.588223i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.64229e8 | −0.161662 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.76949e8 | − | 1.51892e9i | −0.183288 | − | 0.317464i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.83902e8 | − | 6.64938e8i | −0.0792820 | − | 0.137320i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.12889e9 | + | 1.95529e9i | −0.230365 | + | 0.399004i | −0.957916 | − | 0.287050i | \(-0.907325\pi\) |
0.727550 | + | 0.686054i | \(0.240659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.72027e9 | − | 3.58368e9i | −1.35514 | − | 0.722647i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.04052e9 | + | 3.53429e9i | −0.406616 | + | 0.704280i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.83822e9 | + | 6.64799e9i | 0.755855 | + | 1.30918i | 0.944948 | + | 0.327220i | \(0.106112\pi\) |
−0.189093 | + | 0.981959i | \(0.560555\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.45332e9 | + | 4.24928e9i | 0.477469 | + | 0.827000i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.35658e9 | 0.645636 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.77718e9 | − | 8.27432e9i | −0.908192 | − | 1.57303i | −0.816574 | − | 0.577240i | \(-0.804130\pi\) |
−0.0916174 | − | 0.995794i | \(-0.529204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.21987e9 | 0.980841 | 0.490421 | − | 0.871486i | \(-0.336843\pi\) | ||||
0.490421 | + | 0.871486i | \(0.336843\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.20229e8 | + | 1.07427e9i | −0.115197 | + | 0.199527i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.37807e9 | − | 1.27792e10i | 1.35456 | − | 2.34617i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.03564e10 | 1.87953 | 0.939766 | − | 0.341818i | \(-0.111043\pi\) | ||||
0.939766 | + | 0.341818i | \(0.111043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.55780e9 | 0.638294 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.05670e8 | − | 1.04905e9i | 0.107422 | − | 0.186060i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.26571e9 | − | 3.92433e9i | 0.397277 | − | 0.688103i | −0.596112 | − | 0.802901i | \(-0.703289\pi\) |
0.993389 | + | 0.114798i | \(0.0366220\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.97460e9 | −1.72915 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.40556e9 | − | 5.89860e9i | −0.583701 | − | 1.01100i | −0.995036 | − | 0.0995151i | \(-0.968271\pi\) |
0.411335 | − | 0.911484i | \(-0.365062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.17695e9 | 0.707852 | 0.353926 | − | 0.935273i | \(-0.384847\pi\) | ||||
0.353926 | + | 0.935273i | \(0.384847\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.75600e9 | − | 9.96968e9i | −0.964495 | − | 1.67055i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.18782e9 | + | 2.05737e9i | 0.196809 | + | 0.340883i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.81395e9 | − | 6.60595e9i | 0.624877 | − | 1.08232i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.16947e9 | − | 5.09109e9i | 1.32360 | − | 0.824849i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.51837e9 | − | 4.36194e9i | 0.403498 | − | 0.698880i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.09597e9 | + | 8.82648e9i | 0.807466 | + | 1.39857i | 0.914614 | + | 0.404328i | \(0.132495\pi\) |
−0.107148 | + | 0.994243i | \(0.534172\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.47495e9 | + | 6.01878e9i | 0.544547 | + | 0.943182i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.84429e8 | −0.152572 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.10301e8 | + | 8.83868e8i | 0.0782238 | + | 0.135488i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00710e9 | −0.455927 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.70675e9 | − | 8.15234e9i | 0.705860 | − | 1.22258i | −0.260521 | − | 0.965468i | \(-0.583894\pi\) |
0.966380 | − | 0.257117i | \(-0.0827724\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.72052e9 | − | 2.98003e9i | 0.255224 | − | 0.442061i | −0.709732 | − | 0.704471i | \(-0.751184\pi\) |
0.964956 | + | 0.262411i | \(0.0845175\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.06042e10 | −1.55603 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.18237e10 | 1.71628 | 0.858140 | − | 0.513416i | \(-0.171620\pi\) | ||||
0.858140 | + | 0.513416i | \(0.171620\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.35919e9 | + | 1.62106e10i | −1.34395 | + | 2.32778i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.96624e9 | + | 6.86973e9i | −0.563438 | + | 0.975903i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.26605e9 | 0.318473 | 0.159237 | − | 0.987240i | \(-0.449097\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.73741e9 | − | 9.93749e9i | −0.797759 | − | 1.38176i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.32683e9 | −0.182531 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.34562e9 | + | 4.06273e9i | 0.319270 | + | 0.552992i | 0.980336 | − | 0.197336i | \(-0.0632290\pi\) |
−0.661066 | + | 0.750328i | \(0.729896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.10580e9 | + | 7.11145e9i | 0.552958 | + | 0.957752i | 0.998059 | + | 0.0622714i | \(0.0198344\pi\) |
−0.445101 | + | 0.895480i | \(0.646832\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.61742e9 | − | 2.80145e9i | 0.215538 | − | 0.373323i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.66924e9 | − | 4.15617e9i | 0.879429 | − | 0.548047i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.94816e9 | − | 1.03025e10i | 0.776144 | − | 1.34432i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.22600e8 | − | 1.59799e9i | −0.119130 | − | 0.206340i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.96121e9 | − | 1.37892e10i | −1.01730 | − | 1.76202i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.29691e10 | −1.64005 | −0.820024 | − | 0.572329i | \(-0.806040\pi\) | ||||
−0.820024 | + | 0.572329i | \(0.806040\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.22706e9 | − | 3.85739e9i | −0.278721 | − | 0.482758i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.30963e9 | −0.286076 | −0.143038 | − | 0.989717i | \(-0.545687\pi\) | ||||
−0.143038 | + | 0.989717i | \(0.545687\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.12834e8 | + | 3.68638e8i | −0.0260913 | + | 0.0451915i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.03096e9 | + | 1.78567e9i | −0.125091 | + | 0.216664i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.30069e9 | −1.11697 | −0.558487 | − | 0.829514i | \(-0.688618\pi\) | ||||
−0.558487 | + | 0.829514i | \(0.688618\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.20984e10 | −1.43817 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.87910e9 | − | 6.71880e9i | 0.456439 | − | 0.790575i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.71981e8 | + | 8.17494e8i | −0.0549739 | + | 0.0952176i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.16697e9 | −0.480449 | −0.240224 | − | 0.970717i | \(-0.577221\pi\) | ||||
−0.240224 | + | 0.970717i | \(0.577221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.58331e9 | + | 2.74238e9i | 0.180718 | + | 0.313012i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.67963e9 | 0.867748 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.63653e9 | + | 1.14948e10i | 0.742381 | + | 1.28584i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.74439e9 | + | 4.75342e9i | 0.303931 | + | 0.526425i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.34218e9 | − | 2.32472e9i | 0.147162 | − | 0.254893i | −0.783015 | − | 0.622002i | \(-0.786319\pi\) |
0.930178 | + | 0.367110i | \(0.119653\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.11781e9 | − | 3.79568e9i | −0.772686 | − | 0.412046i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.99903e9 | − | 3.46243e9i | 0.214861 | − | 0.372150i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.97845e9 | + | 6.89087e9i | 0.423395 | + | 0.733341i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.40028e9 | − | 1.10856e10i | −0.674431 | − | 1.16815i | −0.976635 | − | 0.214905i | \(-0.931056\pi\) |
0.302204 | − | 0.953243i | \(-0.402278\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.06899e9 | −0.111540 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.32621e10 | + | 2.29706e10i | 1.37024 | + | 2.37333i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.15509e10 | −1.18181 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.14651e8 | + | 5.44992e8i | −0.0318795 | + | 0.0552170i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.87954e7 | + | 6.71956e7i | −0.00389250 | + | 0.00674201i | −0.867965 | − | 0.496625i | \(-0.834572\pi\) |
0.864073 | + | 0.503367i | \(0.167906\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.08896e10 | −1.08203 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.64989e8 | 0.0654381 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.30141e9 | − | 3.98617e9i | 0.224291 | − | 0.388483i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.07271e9 | + | 1.85799e9i | −0.103541 | + | 0.179338i | −0.913141 | − | 0.407644i | \(-0.866351\pi\) |
0.809600 | + | 0.586982i | \(0.199684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.16212e10 | 1.11097 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.05541e9 | + | 1.22203e10i | 0.668054 | + | 1.15710i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.44935e10 | 1.35928 | 0.679641 | − | 0.733545i | \(-0.262136\pi\) | ||||
0.679641 | + | 0.733545i | \(0.262136\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.68427e9 | + | 2.91723e9i | 0.156461 | + | 0.270998i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.33079e9 | + | 1.61614e10i | 0.858583 | + | 1.48711i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.36673e9 | + | 5.83134e9i | −0.306869 | + | 0.531512i | −0.977676 | − | 0.210120i | \(-0.932615\pi\) |
0.670807 | + | 0.741632i | \(0.265948\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.57140e9 | − | 2.43777e9i | −0.412748 | − | 0.220104i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.89679e9 | − | 1.36776e10i | 0.706301 | − | 1.22335i | −0.259919 | − | 0.965630i | \(-0.583696\pi\) |
0.966220 | − | 0.257719i | \(-0.0829708\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.70328e9 | + | 6.41427e9i | 0.328125 | + | 0.568330i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.62615e8 | − | 4.54862e8i | −0.0230514 | − | 0.0399261i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.18496e10 | −1.03043 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.28316e9 | + | 1.08827e10i | 0.541300 | + | 0.937559i | 0.998830 | + | 0.0483648i | \(0.0154010\pi\) |
−0.457530 | + | 0.889194i | \(0.651266\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.17068e10 | −0.999212 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.63273e9 | − | 6.29208e9i | 0.307199 | − | 0.532083i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.66258e9 | − | 1.67361e10i | 0.809576 | − | 1.40223i | −0.103582 | − | 0.994621i | \(-0.533030\pi\) |
0.913158 | − | 0.407606i | \(-0.133636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.35239e10 | −2.78297 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.32887e10 | 1.09304 | 0.546520 | − | 0.837446i | \(-0.315952\pi\) | ||||
0.546520 | + | 0.837446i | \(0.315952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.62702e9 | − | 2.81808e9i | 0.132604 | − | 0.229677i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.68609e9 | + | 2.92039e9i | −0.136165 | + | 0.235844i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.00744e10 | 0.806184 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.41494e9 | − | 1.45751e10i | −0.667281 | − | 1.15577i | −0.978661 | − | 0.205480i | \(-0.934125\pi\) |
0.311380 | − | 0.950285i | \(-0.399209\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.96281e9 | 0.154236 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.09688e9 | + | 3.63191e9i | 0.163285 | + | 0.282818i | 0.936045 | − | 0.351880i | \(-0.114458\pi\) |
−0.772760 | + | 0.634698i | \(0.781124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.13125e9 | + | 8.88758e9i | 0.395974 | + | 0.685848i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.20087e9 | + | 7.27612e9i | −0.321267 | + | 0.556450i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.80411e10 | − | 1.12430e10i | 1.36736 | − | 0.852117i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.26196e10 | + | 3.91783e10i | −1.69905 | + | 2.94284i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.31597e9 | + | 1.09396e10i | 0.470190 | + | 0.814393i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.22450e9 | − | 5.58499e9i | −0.237913 | − | 0.412077i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.29627e10 | −0.947949 | −0.473974 | − | 0.880539i | \(-0.657181\pi\) | ||||
−0.473974 | + | 0.880539i | \(0.657181\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.54989e9 | + | 7.88064e9i | 0.329785 | + | 0.571205i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.76034e10 | 1.26467 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.28478e9 | + | 7.42146e9i | −0.305122 | + | 0.528486i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.55779e9 | + | 2.69817e9i | −0.109957 | + | 0.190451i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.05545e10 | −1.43814 | −0.719072 | − | 0.694935i | \(-0.755433\pi\) | ||||
−0.719072 | + | 0.694935i | \(0.755433\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.32017e9 | −0.368988 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.16353e8 | + | 1.41396e9i | −0.0561260 | + | 0.0972131i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.98049e9 | + | 1.72867e10i | −0.680217 | + | 1.17817i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.73676e10 | −1.84906 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.17160e9 | + | 2.02928e9i | 0.0784736 | + | 0.135920i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.55722e9 | −0.568215 | −0.284108 | − | 0.958792i | \(-0.591697\pi\) | ||||
−0.284108 | + | 0.958792i | \(0.591697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.06340e9 | − | 5.30596e9i | −0.201665 | − | 0.349294i | 0.747400 | − | 0.664374i | \(-0.231302\pi\) |
−0.949065 | + | 0.315080i | \(0.897969\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.40371e7 | − | 2.43129e7i | −0.000916136 | − | 0.00158679i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.71605e9 | − | 1.68287e10i | 0.628692 | − | 1.08893i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.91798e10 | − | 1.19526e10i | 1.23046 | − | 0.766804i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.52151e8 | − | 1.47597e9i | 0.0542029 | − | 0.0938823i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.45124e9 | − | 2.51363e9i | −0.0915248 | − | 0.158526i | 0.816628 | − | 0.577164i | \(-0.195841\pi\) |
−0.908153 | + | 0.418639i | \(0.862507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.53722e9 | − | 2.66254e9i | −0.0961251 | − | 0.166494i | 0.813953 | − | 0.580931i | \(-0.197312\pi\) |
−0.910078 | + | 0.414438i | \(0.863978\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.29708e10 | −0.804224 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.13705e9 | + | 1.58258e10i | 0.561742 | + | 0.972965i | 0.997345 | + | 0.0728262i | \(0.0232018\pi\) |
−0.435603 | + | 0.900139i | \(0.643465\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.01460e9 | 0.549548 | 0.274774 | − | 0.961509i | \(-0.411397\pi\) | ||||
0.274774 | + | 0.961509i | \(0.411397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.71737e9 | − | 1.50989e10i | 0.526965 | − | 0.912730i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.24123e9 | − | 3.88193e9i | 0.134347 | − | 0.232696i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.35564e10 | 0.805826 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.81642e10 | −1.66019 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.54610e9 | + | 1.30702e10i | −0.441119 | + | 0.764041i | −0.997773 | − | 0.0667039i | \(-0.978752\pi\) |
0.556654 | + | 0.830745i | \(0.312085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.09811e9 | − | 3.63403e9i | 0.121630 | − | 0.210670i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.32381e9 | 0.363565 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.68779e9 | − | 1.33156e10i | −0.438332 | − | 0.759213i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.27543e10 | 1.85215 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.67091e9 | − | 1.67505e10i | −0.542363 | − | 0.939401i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.40466e10 | + | 2.43294e10i | 0.781300 | + | 1.35325i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.67500e9 | − | 9.82938e9i | 0.313072 | − | 0.542256i | −0.665954 | − | 0.745993i | \(-0.731975\pi\) |
0.979026 | + | 0.203736i | \(0.0653086\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.76549e9 | + | 2.54127e9i | 0.260751 | + | 0.139049i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.66231e10 | − | 2.87920e10i | 0.902150 | − | 1.56257i | 0.0774512 | − | 0.996996i | \(-0.475322\pi\) |
0.824698 | − | 0.565573i | \(-0.191345\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.50363e9 | − | 2.60437e9i | −0.0809404 | − | 0.140193i | 0.822714 | − | 0.568456i | \(-0.192459\pi\) |
−0.903654 | + | 0.428263i | \(0.859126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.10704e10 | − | 1.91744e10i | −0.591086 | − | 1.02379i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.49472e9 | 0.238048 | 0.119024 | − | 0.992891i | \(-0.462023\pi\) | ||||
0.119024 | + | 0.992891i | \(0.462023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.16006e9 | + | 5.47338e9i | 0.166012 | + | 0.287541i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.52150e9 | 0.131399 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.04100e9 | + | 1.39274e10i | −0.415662 | + | 0.719948i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.02190e9 | − | 8.69819e9i | 0.257516 | − | 0.446031i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.92547e8 | −0.0148815 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.94546e9 | 0.501876 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.18672e8 | + | 7.25162e8i | −0.0209593 | + | 0.0363025i | −0.876315 | − | 0.481739i | \(-0.840005\pi\) |
0.855356 | + | 0.518041i | \(0.173339\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.54211e9 | + | 1.30633e10i | −0.374569 | + | 0.648772i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.15343e10 | −1.55370 | −0.776850 | − | 0.629686i | \(-0.783183\pi\) | ||||
−0.776850 | + | 0.629686i | \(0.783183\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.55490e10 | − | 2.69317e10i | −0.760046 | − | 1.31644i | −0.942826 | − | 0.333285i | \(-0.891843\pi\) |
0.182780 | − | 0.983154i | \(-0.441490\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.32508e10 | 1.61250 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.04311e10 | − | 1.80672e10i | −0.501878 | − | 0.869278i | −0.999998 | − | 0.00216966i | \(-0.999309\pi\) |
0.498120 | − | 0.867108i | \(-0.334024\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.09257e9 | − | 1.89239e9i | −0.0521548 | − | 0.0903348i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.32650e10 | − | 2.29757e10i | 0.628255 | − | 1.08817i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.87044e8 | + | 8.51574e9i | 0.0134886 | + | 0.400168i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.91328e9 | − | 8.51006e9i | 0.229082 | − | 0.396782i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.02139e9 | + | 1.56255e10i | 0.417350 | + | 0.722871i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.45523e10 | − | 2.52052e10i | −0.667992 | − | 1.15700i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.14585e9 | 0.188833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.17691e10 | − | 2.03846e10i | −0.531907 | − | 0.921289i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.50170e10 | 2.01886 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.03278e9 | − | 5.25293e9i | 0.134963 | − | 0.233763i | −0.790620 | − | 0.612307i | \(-0.790242\pi\) |
0.925583 | + | 0.378544i | \(0.123575\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.73425e9 | + | 4.73587e9i | −0.120744 | + | 0.209135i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.13646e9 | 0.181265 | 0.0906326 | − | 0.995884i | \(-0.471111\pi\) | ||||
0.0906326 | + | 0.995884i | \(0.471111\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.90161e9 | −0.343612 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.41421e10 | + | 2.44948e10i | −0.610294 | + | 1.05706i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.27354e10 | − | 2.20584e10i | 0.545406 | − | 0.944671i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.44886e8 | 0.0146579 | 0.00732895 | − | 0.999973i | \(-0.497667\pi\) | ||||
0.00732895 | + | 0.999973i | \(0.497667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.60526e10 | − | 2.78039e10i | −0.677073 | − | 1.17273i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.43481e10 | 1.01920 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.43479e9 | + | 9.41334e9i | 0.225781 | + | 0.391064i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.74204e9 | − | 6.48140e9i | −0.154287 | − | 0.267233i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.47597e10 | + | 2.55645e10i | −0.603978 | + | 1.04612i | 0.388234 | + | 0.921561i | \(0.373085\pi\) |
−0.992212 | + | 0.124560i | \(0.960248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.33453e9 | − | 3.37798e9i | −0.257271 | − | 0.137193i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.26291e9 | + | 1.25797e10i | −0.292769 | + | 0.507090i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.53657e10 | + | 4.39347e10i | 1.01486 | + | 1.75779i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.46858e9 | + | 6.00776e9i | 0.137741 | + | 0.238574i | 0.926641 | − | 0.375947i | \(-0.122683\pi\) |
−0.788900 | + | 0.614521i | \(0.789349\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.09365e9 | −0.121939 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.66311e9 | − | 6.34469e9i | −0.143313 | − | 0.248226i | 0.785429 | − | 0.618951i | \(-0.212442\pi\) |
−0.928742 | + | 0.370726i | \(0.879109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.40327e10 | −2.87496 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.45299e10 | − | 2.51666e10i | 0.560083 | − | 0.970092i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.03267e10 | − | 1.78864e10i | 0.395128 | − | 0.684382i | −0.597990 | − | 0.801504i | \(-0.704034\pi\) |
0.993118 | + | 0.117122i | \(0.0373669\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.07432e10 | 0.408037 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.33973e10 | −0.505109 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.69049e9 | − | 8.12417e9i | 0.175547 | − | 0.304056i | −0.764803 | − | 0.644264i | \(-0.777164\pi\) |
0.940350 | + | 0.340207i | \(0.110497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.10572e10 | + | 5.37926e10i | −1.15385 | + | 1.99853i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.67852e10 | 1.35669 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.34275e10 | − | 2.32571e10i | −0.491619 | − | 0.851510i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.73790e10 | 1.35861 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.07192e9 | − | 7.05276e9i | −0.146929 | − | 0.254488i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.33885e10 | − | 2.31895e10i | −0.479607 | − | 0.830704i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.57077e10 | − | 2.72065e10i | 0.558624 | − | 0.967566i | −0.438987 | − | 0.898493i | \(-0.644663\pi\) |
0.997612 | − | 0.0690723i | \(-0.0220039\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.66537e8 | + | 2.27409e10i | 0.0270645 | + | 0.802924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.31990e10 | − | 2.28613e10i | 0.462672 | − | 0.801372i | −0.536421 | − | 0.843951i | \(-0.680224\pi\) |
0.999093 | + | 0.0425786i | \(0.0135573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.52328e9 | + | 1.47627e10i | 0.296628 | + | 0.513774i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.49048e9 | + | 6.04570e9i | 0.120606 | + | 0.208896i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.07059e10 | 0.367276 | 0.183638 | − | 0.982994i | \(-0.441213\pi\) | ||||
0.183638 | + | 0.982994i | \(0.441213\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.22813e10 | + | 2.12718e10i | 0.418317 | + | 0.724546i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.23639e9 | 0.0756322 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.30088e9 | − | 9.18139e9i | 0.177996 | − | 0.308298i | −0.763198 | − | 0.646165i | \(-0.776372\pi\) |
0.941194 | + | 0.337866i | \(0.109705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.72233e10 | + | 2.98316e10i | −0.574234 | + | 0.994603i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.87455e9 | 0.293789 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.87054e10 | −2.58712 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.42320e10 | + | 4.19711e10i | −0.790919 | + | 1.36991i | 0.134479 | + | 0.990916i | \(0.457064\pi\) |
−0.925398 | + | 0.378996i | \(0.876269\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.87807e9 | + | 8.44907e9i | −0.158098 | + | 0.273833i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.83317e10 | 0.911783 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.47652e10 | + | 4.28946e10i | 0.791423 | + | 1.37078i | 0.925086 | + | 0.379758i | \(0.123993\pi\) |
−0.133663 | + | 0.991027i | \(0.542674\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.98303e10 | −0.946627 |
(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 | 76.8.e.a.49.9 | yes | 22 | |
19.7 | even | 3 | inner | 76.8.e.a.45.9 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.e.a.45.9 | ✓ | 22 | 19.7 | even | 3 | inner | |
76.8.e.a.49.9 | yes | 22 | 1.1 | even | 1 | trivial |