Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,8,Mod(13,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.13");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.49724061162\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 52 x^{12} + 300 x^{11} - 1005 x^{10} - 23250 x^{9} + 349930 x^{8} + \cdots + 3813237677250 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{37}\cdot 3^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.6 | ||
Root | \(2.71713 + 7.81354i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.13 |
Dual form | 24.8.d.a.13.5 |
$q$-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 \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(13\) | \(17\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.09641 | + | 9.53067i | −0.538852 | + | 0.842401i | ||||
\(3\) | − | 27.0000i | − | 0.577350i | ||||||
\(4\) | −53.6675 | − | 116.206i | −0.419277 | − | 0.907858i | ||||
\(5\) | 137.155i | 0.490701i | 0.969434 | + | 0.245351i | \(0.0789031\pi\) | ||||
−0.969434 | + | 0.245351i | \(0.921097\pi\) | |||||||
\(6\) | 257.328 | + | 164.603i | 0.486360 | + | 0.311106i | ||||
\(7\) | 808.153 | 0.890534 | 0.445267 | − | 0.895398i | \(-0.353109\pi\) | ||||
0.445267 | + | 0.895398i | \(0.353109\pi\) | |||||||
\(8\) | 1434.70 | + | 196.951i | 0.990709 | + | 0.136002i | ||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | −1307.18 | − | 836.155i | −0.413367 | − | 0.264415i | ||||
\(11\) | 8242.25i | 1.86712i | 0.358426 | + | 0.933558i | \(0.383314\pi\) | ||||
−0.358426 | + | 0.933558i | \(0.616686\pi\) | |||||||
\(12\) | −3137.56 | + | 1449.02i | −0.524152 | + | 0.242070i | ||||
\(13\) | 3408.20i | 0.430253i | 0.976586 | + | 0.215127i | \(0.0690164\pi\) | ||||
−0.976586 | + | 0.215127i | \(0.930984\pi\) | |||||||
\(14\) | −4926.84 | + | 7702.25i | −0.479866 | + | 0.750187i | ||||
\(15\) | 3703.19 | 0.283307 | ||||||||
\(16\) | −10623.6 | + | 12473.0i | −0.648413 | + | 0.761289i | ||||
\(17\) | 20783.8 | 1.02602 | 0.513008 | − | 0.858384i | \(-0.328531\pi\) | ||||
0.513008 | + | 0.858384i | \(0.328531\pi\) | |||||||
\(18\) | 4444.29 | − | 6947.86i | 0.179617 | − | 0.280800i | ||||
\(19\) | 6307.04i | 0.210954i | 0.994422 | + | 0.105477i | \(0.0336370\pi\) | ||||
−0.994422 | + | 0.105477i | \(0.966363\pi\) | |||||||
\(20\) | 15938.2 | − | 7360.78i | 0.445487 | − | 0.205740i | ||||
\(21\) | − | 21820.1i | − | 0.514150i | ||||||
\(22\) | −78554.2 | − | 50248.2i | −1.57286 | − | 1.00610i | ||||
\(23\) | 68891.6 | 1.18064 | 0.590322 | − | 0.807168i | \(-0.299001\pi\) | ||||
0.590322 | + | 0.807168i | \(0.299001\pi\) | |||||||
\(24\) | 5317.69 | − | 38736.9i | 0.0785206 | − | 0.571986i | ||||
\(25\) | 59313.5 | 0.759212 | ||||||||
\(26\) | −32482.5 | − | 20777.8i | −0.362445 | − | 0.231843i | ||||
\(27\) | 19683.0i | 0.192450i | ||||||||
\(28\) | −43371.6 | − | 93912.2i | −0.373381 | − | 0.808479i | ||||
\(29\) | 42047.6i | 0.320146i | 0.987105 | + | 0.160073i | \(0.0511730\pi\) | ||||
−0.987105 | + | 0.160073i | \(0.948827\pi\) | |||||||
\(30\) | −22576.2 | + | 35293.9i | −0.152660 | + | 0.238658i | ||||
\(31\) | −214737. | −1.29462 | −0.647309 | − | 0.762228i | \(-0.724106\pi\) | ||||
−0.647309 | + | 0.762228i | \(0.724106\pi\) | |||||||
\(32\) | −54109.8 | − | 177290.i | −0.291911 | − | 0.956445i | ||||
\(33\) | 222541. | 1.07798 | ||||||||
\(34\) | −126707. | + | 198084.i | −0.552871 | + | 0.864317i | ||||
\(35\) | 110842.i | 0.436986i | ||||||||
\(36\) | 39123.6 | + | 84714.1i | 0.139759 | + | 0.302619i | ||||
\(37\) | − | 182746.i | − | 0.593118i | −0.955015 | − | 0.296559i | \(-0.904161\pi\) | ||
0.955015 | − | 0.296559i | \(-0.0958391\pi\) | |||||||
\(38\) | −60110.3 | − | 38450.3i | −0.177708 | − | 0.113673i | ||||
\(39\) | 92021.5 | 0.248407 | ||||||||
\(40\) | −27012.9 | + | 196776.i | −0.0667362 | + | 0.486142i | ||||
\(41\) | 395877. | 0.897051 | 0.448525 | − | 0.893770i | \(-0.351949\pi\) | ||||
0.448525 | + | 0.893770i | \(0.351949\pi\) | |||||||
\(42\) | 207961. | + | 133025.i | 0.433120 | + | 0.277051i | ||||
\(43\) | 433527.i | 0.831527i | 0.909473 | + | 0.415763i | \(0.136486\pi\) | ||||
−0.909473 | + | 0.415763i | \(0.863514\pi\) | |||||||
\(44\) | 957798. | − | 442341.i | 1.69508 | − | 0.782840i | ||||
\(45\) | − | 99986.1i | − | 0.163567i | ||||||
\(46\) | −419992. | + | 656584.i | −0.636192 | + | 0.994575i | ||||
\(47\) | −1.32987e6 | −1.86839 | −0.934194 | − | 0.356766i | \(-0.883880\pi\) | ||||
−0.934194 | + | 0.356766i | \(0.883880\pi\) | |||||||
\(48\) | 336770. | + | 286837.i | 0.439530 | + | 0.374361i | ||||
\(49\) | −170431. | −0.206949 | ||||||||
\(50\) | −361599. | + | 565297.i | −0.409103 | + | 0.639561i | ||||
\(51\) | − | 561163.i | − | 0.592371i | ||||||
\(52\) | 396053. | − | 182910.i | 0.390609 | − | 0.180395i | ||||
\(53\) | − | 225062.i | − | 0.207652i | −0.994595 | − | 0.103826i | \(-0.966891\pi\) | ||
0.994595 | − | 0.103826i | \(-0.0331085\pi\) | |||||||
\(54\) | −187592. | − | 119996.i | −0.162120 | − | 0.103702i | ||||
\(55\) | −1.13047e6 | −0.916197 | ||||||||
\(56\) | 1.15946e6 | + | 159167.i | 0.882260 | + | 0.121114i | ||||
\(57\) | 170290. | 0.121794 | ||||||||
\(58\) | −400742. | − | 256340.i | −0.269691 | − | 0.172511i | ||||
\(59\) | 2.06725e6i | 1.31042i | 0.755445 | + | 0.655212i | \(0.227421\pi\) | ||||
−0.755445 | + | 0.655212i | \(0.772579\pi\) | |||||||
\(60\) | −198741. | − | 430332.i | −0.118784 | − | 0.257202i | ||||
\(61\) | − | 3.11174e6i | − | 1.75529i | −0.479310 | − | 0.877646i | \(-0.659113\pi\) | ||
0.479310 | − | 0.877646i | \(-0.340887\pi\) | |||||||
\(62\) | 1.30913e6 | − | 2.04659e6i | 0.697607 | − | 1.09059i | ||||
\(63\) | −589144. | −0.296845 | ||||||||
\(64\) | 2.01957e6 | + | 565132.i | 0.963007 | + | 0.269476i | ||||
\(65\) | −467453. | −0.211126 | ||||||||
\(66\) | −1.35670e6 | + | 2.12096e6i | −0.580872 | + | 0.908091i | ||||
\(67\) | − | 1.22034e6i | − | 0.495699i | −0.968798 | − | 0.247850i | \(-0.920276\pi\) | ||
0.968798 | − | 0.247850i | \(-0.0797239\pi\) | |||||||
\(68\) | −1.11542e6 | − | 2.41520e6i | −0.430185 | − | 0.931478i | ||||
\(69\) | − | 1.86007e6i | − | 0.681645i | ||||||
\(70\) | −1.05640e6 | − | 675741.i | −0.368118 | − | 0.235471i | ||||
\(71\) | −1.63667e6 | −0.542695 | −0.271348 | − | 0.962481i | \(-0.587469\pi\) | ||||
−0.271348 | + | 0.962481i | \(0.587469\pi\) | |||||||
\(72\) | −1.04590e6 | − | 143578.i | −0.330236 | − | 0.0453339i | ||||
\(73\) | 3.43311e6 | 1.03290 | 0.516450 | − | 0.856318i | \(-0.327253\pi\) | ||||
0.516450 | + | 0.856318i | \(0.327253\pi\) | |||||||
\(74\) | 1.74169e6 | + | 1.11409e6i | 0.499643 | + | 0.319603i | ||||
\(75\) | − | 1.60146e6i | − | 0.438331i | ||||||
\(76\) | 732915. | − | 338483.i | 0.191516 | − | 0.0884483i | ||||
\(77\) | 6.66100e6i | 1.66273i | ||||||||
\(78\) | −561001. | + | 877027.i | −0.133854 | + | 0.209258i | ||||
\(79\) | 6.60063e6 | 1.50623 | 0.753113 | − | 0.657891i | \(-0.228551\pi\) | ||||
0.753113 | + | 0.657891i | \(0.228551\pi\) | |||||||
\(80\) | −1.71073e6 | − | 1.45708e6i | −0.373565 | − | 0.318177i | ||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −2.41343e6 | + | 3.77298e6i | −0.483377 | + | 0.755676i | ||||
\(83\) | 3.38713e6i | 0.650217i | 0.945677 | + | 0.325108i | \(0.105401\pi\) | ||||
−0.945677 | + | 0.325108i | \(0.894599\pi\) | |||||||
\(84\) | −2.53563e6 | + | 1.17103e6i | −0.466776 | + | 0.215572i | ||||
\(85\) | 2.85061e6i | 0.503468i | ||||||||
\(86\) | −4.13180e6 | − | 2.64296e6i | −0.700478 | − | 0.448070i | ||||
\(87\) | 1.13529e6 | 0.184836 | ||||||||
\(88\) | −1.62332e6 | + | 1.18252e7i | −0.253931 | + | 1.84977i | ||||
\(89\) | −688852. | −0.103576 | −0.0517882 | − | 0.998658i | \(-0.516492\pi\) | ||||
−0.0517882 | + | 0.998658i | \(0.516492\pi\) | |||||||
\(90\) | 952935. | + | 609557.i | 0.137789 | + | 0.0881384i | ||||
\(91\) | 2.75435e6i | 0.383155i | ||||||||
\(92\) | −3.69724e6 | − | 8.00561e6i | −0.495017 | − | 1.07186i | ||||
\(93\) | 5.79791e6i | 0.747448i | ||||||||
\(94\) | 8.10744e6 | − | 1.26746e7i | 1.00678 | − | 1.57393i | ||||
\(95\) | −865043. | −0.103515 | ||||||||
\(96\) | −4.78684e6 | + | 1.46096e6i | −0.552204 | + | 0.168535i | ||||
\(97\) | −3.48055e6 | −0.387210 | −0.193605 | − | 0.981080i | \(-0.562018\pi\) | ||||
−0.193605 | + | 0.981080i | \(0.562018\pi\) | |||||||
\(98\) | 1.03902e6 | − | 1.62432e6i | 0.111515 | − | 0.174334i | ||||
\(99\) | − | 6.00860e6i | − | 0.622372i | ||||||
\(100\) | −3.18320e6 | − | 6.89257e6i | −0.318320 | − | 0.689257i | ||||
\(101\) | 6.80385e6i | 0.657098i | 0.944487 | + | 0.328549i | \(0.106560\pi\) | ||||
−0.944487 | + | 0.328549i | \(0.893440\pi\) | |||||||
\(102\) | 5.34827e6 | + | 3.42108e6i | 0.499014 | + | 0.319200i | ||||
\(103\) | 1.85092e7 | 1.66900 | 0.834502 | − | 0.551005i | \(-0.185756\pi\) | ||||
0.834502 | + | 0.551005i | \(0.185756\pi\) | |||||||
\(104\) | −671251. | + | 4.88975e6i | −0.0585151 | + | 0.426255i | ||||
\(105\) | 2.99275e6 | 0.252294 | ||||||||
\(106\) | 2.14499e6 | + | 1.37207e6i | 0.174926 | + | 0.111894i | ||||
\(107\) | − | 1.69583e7i | − | 1.33826i | −0.743146 | − | 0.669129i | \(-0.766667\pi\) | ||
0.743146 | − | 0.669129i | \(-0.233333\pi\) | |||||||
\(108\) | 2.28728e6 | − | 1.05634e6i | 0.174717 | − | 0.0806900i | ||||
\(109\) | − | 2.40588e7i | − | 1.77943i | −0.456512 | − | 0.889717i | \(-0.650901\pi\) | ||
0.456512 | − | 0.889717i | \(-0.349099\pi\) | |||||||
\(110\) | 6.89180e6 | − | 1.07741e7i | 0.493694 | − | 0.771804i | ||||
\(111\) | −4.93413e6 | −0.342437 | ||||||||
\(112\) | −8.58550e6 | + | 1.00801e7i | −0.577434 | + | 0.677954i | ||||
\(113\) | −1.97853e7 | −1.28993 | −0.644967 | − | 0.764211i | \(-0.723129\pi\) | ||||
−0.644967 | + | 0.764211i | \(0.723129\pi\) | |||||||
\(114\) | −1.03816e6 | + | 1.62298e6i | −0.0656291 | + | 0.102600i | ||||
\(115\) | 9.44885e6i | 0.579344i | ||||||||
\(116\) | 4.88618e6 | − | 2.25659e6i | 0.290647 | − | 0.134230i | ||||
\(117\) | − | 2.48458e6i | − | 0.143418i | ||||||
\(118\) | −1.97023e7 | − | 1.26028e7i | −1.10390 | − | 0.706125i | ||||
\(119\) | 1.67965e7 | 0.913703 | ||||||||
\(120\) | 5.31296e6 | + | 729349.i | 0.280674 | + | 0.0385302i | ||||
\(121\) | −4.84475e7 | −2.48612 | ||||||||
\(122\) | 2.96570e7 | + | 1.89705e7i | 1.47866 | + | 0.945842i | ||||
\(123\) | − | 1.06887e7i | − | 0.517912i | ||||||
\(124\) | 1.15244e7 | + | 2.49537e7i | 0.542804 | + | 1.17533i | ||||
\(125\) | 1.88504e7i | 0.863248i | ||||||||
\(126\) | 3.59166e6 | − | 5.61494e6i | 0.159955 | − | 0.250062i | ||||
\(127\) | −2.74201e7 | −1.18783 | −0.593917 | − | 0.804526i | \(-0.702419\pi\) | ||||
−0.593917 | + | 0.804526i | \(0.702419\pi\) | |||||||
\(128\) | −1.76982e7 | + | 1.58026e7i | −0.745925 | + | 0.666030i | ||||
\(129\) | 1.17052e7 | 0.480082 | ||||||||
\(130\) | 2.84979e6 | − | 4.45514e6i | 0.113766 | − | 0.177852i | ||||
\(131\) | − | 1.22444e7i | − | 0.475868i | −0.971281 | − | 0.237934i | \(-0.923530\pi\) | ||
0.971281 | − | 0.237934i | \(-0.0764703\pi\) | |||||||
\(132\) | −1.19432e7 | − | 2.58605e7i | −0.451973 | − | 0.978653i | ||||
\(133\) | 5.09705e6i | 0.187862i | ||||||||
\(134\) | 1.16306e7 | + | 7.43969e6i | 0.417577 | + | 0.267109i | ||||
\(135\) | −2.69963e6 | −0.0944355 | ||||||||
\(136\) | 2.98185e7 | + | 4.09341e6i | 1.01648 | + | 0.139540i | ||||
\(137\) | 4.83466e7 | 1.60636 | 0.803182 | − | 0.595733i | \(-0.203138\pi\) | ||||
0.803182 | + | 0.595733i | \(0.203138\pi\) | |||||||
\(138\) | 1.77278e7 | + | 1.13398e7i | 0.574218 | + | 0.367306i | ||||
\(139\) | 2.54730e7i | 0.804503i | 0.915529 | + | 0.402252i | \(0.131772\pi\) | ||||
−0.915529 | + | 0.402252i | \(0.868228\pi\) | |||||||
\(140\) | 1.28805e7 | − | 5.94864e6i | 0.396722 | − | 0.183218i | ||||
\(141\) | 3.59065e7i | 1.07871i | ||||||||
\(142\) | 9.97779e6 | − | 1.55985e7i | 0.292432 | − | 0.457167i | ||||
\(143\) | −2.80913e7 | −0.803333 | ||||||||
\(144\) | 7.74460e6 | − | 9.09278e6i | 0.216138 | − | 0.253763i | ||||
\(145\) | −5.76705e6 | −0.157096 | ||||||||
\(146\) | −2.09297e7 | + | 3.27199e7i | −0.556580 | + | 0.870115i | ||||
\(147\) | 4.60164e6i | 0.119482i | ||||||||
\(148\) | −2.12361e7 | + | 9.80750e6i | −0.538467 | + | 0.248681i | ||||
\(149\) | − | 5.26513e7i | − | 1.30394i | −0.758245 | − | 0.651969i | \(-0.773943\pi\) | ||
0.758245 | − | 0.651969i | \(-0.226057\pi\) | |||||||
\(150\) | 1.52630e7 | + | 9.76318e6i | 0.369251 | + | 0.236196i | ||||
\(151\) | 2.75769e7 | 0.651817 | 0.325909 | − | 0.945401i | \(-0.394330\pi\) | ||||
0.325909 | + | 0.945401i | \(0.394330\pi\) | |||||||
\(152\) | −1.24218e6 | + | 9.04870e6i | −0.0286901 | + | 0.208994i | ||||
\(153\) | −1.51514e7 | −0.342006 | ||||||||
\(154\) | −6.34838e7 | − | 4.06082e7i | −1.40069 | − | 0.895966i | ||||
\(155\) | − | 2.94523e7i | − | 0.635271i | ||||||
\(156\) | −4.93857e6 | − | 1.06934e7i | −0.104151 | − | 0.225518i | ||||
\(157\) | − | 1.50946e7i | − | 0.311296i | −0.987813 | − | 0.155648i | \(-0.950253\pi\) | ||
0.987813 | − | 0.155648i | \(-0.0497466\pi\) | |||||||
\(158\) | −4.02401e7 | + | 6.29084e7i | −0.811633 | + | 1.26885i | ||||
\(159\) | −6.07667e6 | −0.119888 | ||||||||
\(160\) | 2.43163e7 | − | 7.42144e6i | 0.469329 | − | 0.143241i | ||||
\(161\) | 5.56750e7 | 1.05140 | ||||||||
\(162\) | −3.23988e6 | + | 5.06499e6i | −0.0598724 | + | 0.0936001i | ||||
\(163\) | 7.23758e7i | 1.30899i | 0.756066 | + | 0.654496i | \(0.227119\pi\) | ||||
−0.756066 | + | 0.654496i | \(0.772881\pi\) | |||||||
\(164\) | −2.12457e7 | − | 4.60032e7i | −0.376113 | − | 0.814395i | ||||
\(165\) | 3.05226e7i | 0.528966i | ||||||||
\(166\) | −3.22816e7 | − | 2.06493e7i | −0.547743 | − | 0.350370i | ||||
\(167\) | −2.87007e7 | −0.476854 | −0.238427 | − | 0.971160i | \(-0.576632\pi\) | ||||
−0.238427 | + | 0.971160i | \(0.576632\pi\) | |||||||
\(168\) | 4.29751e6 | − | 3.13053e7i | 0.0699253 | − | 0.509373i | ||||
\(169\) | 5.11327e7 | 0.814882 | ||||||||
\(170\) | −2.71682e7 | − | 1.73785e7i | −0.424121 | − | 0.271295i | ||||
\(171\) | − | 4.59783e6i | − | 0.0703180i | ||||||
\(172\) | 5.03783e7 | − | 2.32663e7i | 0.754908 | − | 0.348640i | ||||
\(173\) | − | 1.61003e7i | − | 0.236414i | −0.992989 | − | 0.118207i | \(-0.962285\pi\) | ||
0.992989 | − | 0.118207i | \(-0.0377146\pi\) | |||||||
\(174\) | −6.92117e6 | + | 1.08200e7i | −0.0995995 | + | 0.155706i | ||||
\(175\) | 4.79344e7 | 0.676104 | ||||||||
\(176\) | −1.02805e8 | − | 8.75624e7i | −1.42141 | − | 1.21066i | ||||
\(177\) | 5.58159e7 | 0.756574 | ||||||||
\(178\) | 4.19953e6 | − | 6.56522e6i | 0.0558124 | − | 0.0872528i | ||||
\(179\) | − | 5.41747e7i | − | 0.706010i | −0.935622 | − | 0.353005i | \(-0.885160\pi\) | ||
0.935622 | − | 0.353005i | \(-0.114840\pi\) | |||||||
\(180\) | −1.16190e7 | + | 5.36601e6i | −0.148496 | + | 0.0685800i | ||||
\(181\) | − | 1.36783e8i | − | 1.71458i | −0.514836 | − | 0.857288i | \(-0.672147\pi\) | ||
0.514836 | − | 0.857288i | \(-0.327853\pi\) | |||||||
\(182\) | −2.62508e7 | − | 1.67917e7i | −0.322770 | − | 0.206464i | ||||
\(183\) | −8.40171e7 | −1.01342 | ||||||||
\(184\) | 9.88388e7 | + | 1.35683e7i | 1.16967 | + | 0.160570i | ||||
\(185\) | 2.50645e7 | 0.291044 | ||||||||
\(186\) | −5.52580e7 | − | 3.53464e7i | −0.629651 | − | 0.402764i | ||||
\(187\) | 1.71306e8i | 1.91569i | ||||||||
\(188\) | 7.13709e7 | + | 1.54539e8i | 0.783373 | + | 1.69623i | ||||
\(189\) | 1.59069e7i | 0.171383i | ||||||||
\(190\) | 5.27366e6 | − | 8.24444e6i | 0.0557795 | − | 0.0872015i | ||||
\(191\) | 9.18294e6 | 0.0953597 | 0.0476799 | − | 0.998863i | \(-0.484817\pi\) | ||||
0.0476799 | + | 0.998863i | \(0.484817\pi\) | |||||||
\(192\) | 1.52586e7 | − | 5.45285e7i | 0.155582 | − | 0.555992i | ||||
\(193\) | 3.02678e7 | 0.303062 | 0.151531 | − | 0.988453i | \(-0.451580\pi\) | ||||
0.151531 | + | 0.988453i | \(0.451580\pi\) | |||||||
\(194\) | 2.12189e7 | − | 3.31720e7i | 0.208649 | − | 0.326186i | ||||
\(195\) | 1.26212e7i | 0.121894i | ||||||||
\(196\) | 9.14661e6 | + | 1.98051e7i | 0.0867689 | + | 0.187880i | ||||
\(197\) | 5.72982e7i | 0.533960i | 0.963702 | + | 0.266980i | \(0.0860258\pi\) | ||||
−0.963702 | + | 0.266980i | \(0.913974\pi\) | |||||||
\(198\) | 5.72660e7 | + | 3.66309e7i | 0.524287 | + | 0.335366i | ||||
\(199\) | −2.41023e6 | −0.0216807 | −0.0108403 | − | 0.999941i | \(-0.503451\pi\) | ||||
−0.0108403 | + | 0.999941i | \(0.503451\pi\) | |||||||
\(200\) | 8.50970e7 | + | 1.16819e7i | 0.752158 | + | 0.103254i | ||||
\(201\) | −3.29491e7 | −0.286192 | ||||||||
\(202\) | −6.48453e7 | − | 4.14791e7i | −0.553540 | − | 0.354078i | ||||
\(203\) | 3.39809e7i | 0.285101i | ||||||||
\(204\) | −6.52105e7 | + | 3.01162e7i | −0.537789 | + | 0.248368i | ||||
\(205\) | 5.42966e7i | 0.440184i | ||||||||
\(206\) | −1.12840e8 | + | 1.76405e8i | −0.899346 | + | 1.40597i | ||||
\(207\) | −5.02220e7 | −0.393548 | ||||||||
\(208\) | −4.25104e7 | − | 3.62074e7i | −0.327547 | − | 0.278982i | ||||
\(209\) | −5.19842e7 | −0.393876 | ||||||||
\(210\) | −1.82450e7 | + | 2.85229e7i | −0.135949 | + | 0.212533i | ||||
\(211\) | − | 1.41783e8i | − | 1.03905i | −0.854457 | − | 0.519523i | \(-0.826110\pi\) | ||
0.854457 | − | 0.519523i | \(-0.173890\pi\) | |||||||
\(212\) | −2.61535e7 | + | 1.20785e7i | −0.188519 | + | 0.0870638i | ||||
\(213\) | 4.41900e7i | 0.313325i | ||||||||
\(214\) | 1.61624e8 | + | 1.03385e8i | 1.12735 | + | 0.721123i | ||||
\(215\) | −5.94604e7 | −0.408031 | ||||||||
\(216\) | −3.87660e6 | + | 2.82392e7i | −0.0261735 | + | 0.190662i | ||||
\(217\) | −1.73541e8 | −1.15290 | ||||||||
\(218\) | 2.29297e8 | + | 1.46673e8i | 1.49900 | + | 0.958852i | ||||
\(219\) | − | 9.26940e7i | − | 0.596345i | ||||||
\(220\) | 6.06694e7 | + | 1.31367e8i | 0.384140 | + | 0.831777i | ||||
\(221\) | 7.08356e7i | 0.441447i | ||||||||
\(222\) | 3.00805e7 | − | 4.70256e7i | 0.184523 | − | 0.288469i | ||||
\(223\) | −2.72134e7 | −0.164330 | −0.0821649 | − | 0.996619i | \(-0.526183\pi\) | ||||
−0.0821649 | + | 0.996619i | \(0.526183\pi\) | |||||||
\(224\) | −4.37290e7 | − | 1.43278e8i | −0.259957 | − | 0.851747i | ||||
\(225\) | −4.32395e7 | −0.253071 | ||||||||
\(226\) | 1.20619e8 | − | 1.88567e8i | 0.695083 | − | 1.08664i | ||||
\(227\) | 4.60299e6i | 0.0261186i | 0.999915 | + | 0.0130593i | \(0.00415702\pi\) | ||||
−0.999915 | + | 0.0130593i | \(0.995843\pi\) | |||||||
\(228\) | −9.13904e6 | − | 1.97887e7i | −0.0510656 | − | 0.110572i | ||||
\(229\) | − | 1.66323e8i | − | 0.915224i | −0.889152 | − | 0.457612i | \(-0.848705\pi\) | ||
0.889152 | − | 0.457612i | \(-0.151295\pi\) | |||||||
\(230\) | −9.00539e7 | − | 5.76041e7i | −0.488039 | − | 0.312180i | ||||
\(231\) | 1.79847e8 | 0.959978 | ||||||||
\(232\) | −8.28134e6 | + | 6.03257e7i | −0.0435404 | + | 0.317172i | ||||
\(233\) | −5.18994e7 | −0.268792 | −0.134396 | − | 0.990928i | \(-0.542909\pi\) | ||||
−0.134396 | + | 0.990928i | \(0.542909\pi\) | |||||||
\(234\) | 2.36797e7 | + | 1.51470e7i | 0.120815 | + | 0.0772809i | ||||
\(235\) | − | 1.82399e8i | − | 0.916820i | ||||||
\(236\) | 2.40227e8 | − | 1.10944e8i | 1.18968 | − | 0.549431i | ||||
\(237\) | − | 1.78217e8i | − | 0.869620i | ||||||
\(238\) | −1.02399e8 | + | 1.60082e8i | −0.492351 | + | 0.769704i | ||||
\(239\) | −2.02994e7 | −0.0961811 | −0.0480906 | − | 0.998843i | \(-0.515314\pi\) | ||||
−0.0480906 | + | 0.998843i | \(0.515314\pi\) | |||||||
\(240\) | −3.93412e7 | + | 4.61897e7i | −0.183700 | + | 0.215678i | ||||
\(241\) | −3.40237e7 | −0.156575 | −0.0782875 | − | 0.996931i | \(-0.524945\pi\) | ||||
−0.0782875 | + | 0.996931i | \(0.524945\pi\) | |||||||
\(242\) | 2.95356e8 | − | 4.61738e8i | 1.33965 | − | 2.09431i | ||||
\(243\) | − | 1.43489e7i | − | 0.0641500i | ||||||
\(244\) | −3.61603e8 | + | 1.66999e8i | −1.59356 | + | 0.735954i | ||||
\(245\) | − | 2.33755e7i | − | 0.101550i | ||||||
\(246\) | 1.01870e8 | + | 6.51626e7i | 0.436290 | + | 0.279078i | ||||
\(247\) | −2.14957e7 | −0.0907636 | ||||||||
\(248\) | −3.08083e8 | − | 4.22928e7i | −1.28259 | − | 0.176070i | ||||
\(249\) | 9.14524e7 | 0.375403 | ||||||||
\(250\) | −1.79657e8 | − | 1.14920e8i | −0.727200 | − | 0.465163i | ||||
\(251\) | − | 5.06937e7i | − | 0.202347i | −0.994869 | − | 0.101173i | \(-0.967740\pi\) | ||
0.994869 | − | 0.101173i | \(-0.0322596\pi\) | |||||||
\(252\) | 3.16179e7 | + | 6.84620e7i | 0.124460 | + | 0.269493i | ||||
\(253\) | 5.67822e8i | 2.20440i | ||||||||
\(254\) | 1.67164e8 | − | 2.61332e8i | 0.640067 | − | 1.00063i | ||||
\(255\) | 7.69665e7 | 0.290677 | ||||||||
\(256\) | −4.27137e7 | − | 2.65015e8i | −0.159121 | − | 0.987259i | ||||
\(257\) | −4.16956e8 | −1.53223 | −0.766116 | − | 0.642702i | \(-0.777813\pi\) | ||||
−0.766116 | + | 0.642702i | \(0.777813\pi\) | |||||||
\(258\) | −7.13598e7 | + | 1.11559e8i | −0.258693 | + | 0.404421i | ||||
\(259\) | − | 1.47687e8i | − | 0.528192i | ||||||
\(260\) | 2.50870e7 | + | 5.43208e7i | 0.0885202 | + | 0.191672i | ||||
\(261\) | − | 3.06527e7i | − | 0.106715i | ||||||
\(262\) | 1.16697e8 | + | 7.46467e7i | 0.400872 | + | 0.256423i | ||||
\(263\) | 3.30240e8 | 1.11940 | 0.559699 | − | 0.828696i | \(-0.310917\pi\) | ||||
0.559699 | + | 0.828696i | \(0.310917\pi\) | |||||||
\(264\) | 3.19279e8 | + | 4.38297e7i | 1.06796 | + | 0.146607i | ||||
\(265\) | 3.08684e7 | 0.101895 | ||||||||
\(266\) | −4.85784e7 | − | 3.10738e7i | −0.158255 | − | 0.101230i | ||||
\(267\) | 1.85990e7i | 0.0597999i | ||||||||
\(268\) | −1.41810e8 | + | 6.54925e7i | −0.450025 | + | 0.207835i | ||||
\(269\) | 3.55998e8i | 1.11510i | 0.830143 | + | 0.557551i | \(0.188259\pi\) | ||||
−0.830143 | + | 0.557551i | \(0.811741\pi\) | |||||||
\(270\) | 1.64580e7 | − | 2.57293e7i | 0.0508868 | − | 0.0795525i | ||||
\(271\) | 2.92692e8 | 0.893343 | 0.446671 | − | 0.894698i | \(-0.352609\pi\) | ||||
0.446671 | + | 0.894698i | \(0.352609\pi\) | |||||||
\(272\) | −2.20799e8 | + | 2.59236e8i | −0.665283 | + | 0.781095i | ||||
\(273\) | 7.43675e7 | 0.221215 | ||||||||
\(274\) | −2.94741e8 | + | 4.60776e8i | −0.865593 | + | 1.35320i | ||||
\(275\) | 4.88876e8i | 1.41754i | ||||||||
\(276\) | −2.16152e8 | + | 9.98255e7i | −0.618837 | + | 0.285798i | ||||
\(277\) | − | 3.30724e8i | − | 0.934947i | −0.884007 | − | 0.467473i | \(-0.845164\pi\) | ||
0.884007 | − | 0.467473i | \(-0.154836\pi\) | |||||||
\(278\) | −2.42775e8 | − | 1.55294e8i | −0.677714 | − | 0.433508i | ||||
\(279\) | 1.56543e8 | 0.431539 | ||||||||
\(280\) | −2.18306e7 | + | 1.59026e8i | −0.0594309 | + | 0.432926i | ||||
\(281\) | 2.85026e8 | 0.766325 | 0.383163 | − | 0.923681i | \(-0.374835\pi\) | ||||
0.383163 | + | 0.923681i | \(0.374835\pi\) | |||||||
\(282\) | −3.42213e8 | − | 2.18901e8i | −0.908709 | − | 0.581267i | ||||
\(283\) | − | 4.02132e7i | − | 0.105467i | −0.998609 | − | 0.0527334i | \(-0.983207\pi\) | ||
0.998609 | − | 0.0527334i | \(-0.0167934\pi\) | |||||||
\(284\) | 8.78358e7 | + | 1.90190e8i | 0.227540 | + | 0.492690i | ||||
\(285\) | 2.33562e7i | 0.0597647i | ||||||||
\(286\) | 1.71256e8 | − | 2.67729e8i | 0.432877 | − | 0.676728i | ||||
\(287\) | 3.19929e8 | 0.798854 | ||||||||
\(288\) | 3.94460e7 | + | 1.29245e8i | 0.0973038 | + | 0.318815i | ||||
\(289\) | 2.16289e7 | 0.0527100 | ||||||||
\(290\) | 3.51583e7 | − | 5.49639e7i | 0.0846516 | − | 0.132338i | ||||
\(291\) | 9.39749e7i | 0.223556i | ||||||||
\(292\) | −1.84247e8 | − | 3.98948e8i | −0.433071 | − | 0.937726i | ||||
\(293\) | − | 1.53923e8i | − | 0.357493i | −0.983895 | − | 0.178747i | \(-0.942796\pi\) | ||
0.983895 | − | 0.178747i | \(-0.0572043\pi\) | |||||||
\(294\) | −4.38567e7 | − | 2.80535e7i | −0.100652 | − | 0.0643830i | ||||
\(295\) | −2.83535e8 | −0.643027 | ||||||||
\(296\) | 3.59920e7 | − | 2.62185e8i | 0.0806650 | − | 0.587607i | ||||
\(297\) | −1.62232e8 | −0.359327 | ||||||||
\(298\) | 5.01802e8 | + | 3.20984e8i | 1.09844 | + | 0.702630i | ||||
\(299\) | 2.34797e8i | 0.507976i | ||||||||
\(300\) | −1.86099e8 | + | 8.59465e7i | −0.397943 | + | 0.183782i | ||||
\(301\) | 3.50356e8i | 0.740503i | ||||||||
\(302\) | −1.68120e8 | + | 2.62826e8i | −0.351233 | + | 0.549091i | ||||
\(303\) | 1.83704e8 | 0.379376 | ||||||||
\(304\) | −7.86674e7 | − | 6.70035e7i | −0.160597 | − | 0.136785i | ||||
\(305\) | 4.26792e8 | 0.861324 | ||||||||
\(306\) | 9.23693e7 | − | 1.44403e8i | 0.184290 | − | 0.288106i | ||||
\(307\) | − | 2.93832e8i | − | 0.579583i | −0.957090 | − | 0.289791i | \(-0.906414\pi\) | ||
0.957090 | − | 0.289791i | \(-0.0935859\pi\) | |||||||
\(308\) | 7.74047e8 | − | 3.57479e8i | 1.50952 | − | 0.697145i | ||||
\(309\) | − | 4.99748e8i | − | 0.963600i | ||||||
\(310\) | 2.80701e8 | + | 1.79554e8i | 0.535152 | + | 0.342317i | ||||
\(311\) | −9.52586e8 | −1.79574 | −0.897869 | − | 0.440263i | \(-0.854885\pi\) | ||||
−0.897869 | + | 0.440263i | \(0.854885\pi\) | |||||||
\(312\) | 1.32023e8 | + | 1.81238e7i | 0.246099 | + | 0.0337837i | ||||
\(313\) | 7.11814e8 | 1.31208 | 0.656041 | − | 0.754725i | \(-0.272230\pi\) | ||||
0.656041 | + | 0.754725i | \(0.272230\pi\) | |||||||
\(314\) | 1.43862e8 | + | 9.20231e7i | 0.262236 | + | 0.167742i | ||||
\(315\) | − | 8.08041e7i | − | 0.145662i | ||||||
\(316\) | −3.54239e8 | − | 7.67031e8i | −0.631527 | − | 1.36744i | ||||
\(317\) | 1.92856e7i | 0.0340037i | 0.999855 | + | 0.0170018i | \(0.00541212\pi\) | ||||
−0.999855 | + | 0.0170018i | \(0.994588\pi\) | |||||||
\(318\) | 3.70459e7 | − | 5.79147e7i | 0.0646018 | − | 0.100994i | ||||
\(319\) | −3.46567e8 | −0.597750 | ||||||||
\(320\) | −7.75108e7 | + | 2.76995e8i | −0.132232 | + | 0.472549i | ||||
\(321\) | −4.57875e8 | −0.772643 | ||||||||
\(322\) | −3.39418e8 | + | 5.30620e8i | −0.566551 | + | 0.885703i | ||||
\(323\) | 1.31084e8i | 0.216442i | ||||||||
\(324\) | −2.85211e7 | − | 6.17566e7i | −0.0465864 | − | 0.100873i | ||||
\(325\) | 2.02152e8i | 0.326653i | ||||||||
\(326\) | −6.89790e8 | − | 4.41233e8i | −1.10270 | − | 0.705353i | ||||
\(327\) | −6.49589e8 | −1.02736 | ||||||||
\(328\) | 5.67965e8 | + | 7.79686e7i | 0.888716 | + | 0.122000i | ||||
\(329\) | −1.07474e9 | −1.66386 | ||||||||
\(330\) | −2.90901e8 | − | 1.86079e8i | −0.445602 | − | 0.285035i | ||||
\(331\) | − | 6.26075e8i | − | 0.948918i | −0.880278 | − | 0.474459i | \(-0.842644\pi\) | ||
0.880278 | − | 0.474459i | \(-0.157356\pi\) | |||||||
\(332\) | 3.93604e8 | − | 1.81779e8i | 0.590304 | − | 0.272621i | ||||
\(333\) | 1.33222e8i | 0.197706i | ||||||||
\(334\) | 1.74971e8 | − | 2.73537e8i | 0.256953 | − | 0.401702i | ||||
\(335\) | 1.67376e8 | 0.243240 | ||||||||
\(336\) | 2.72162e8 | + | 2.31808e8i | 0.391417 | + | 0.333382i | ||||
\(337\) | 6.06096e8 | 0.862655 | 0.431327 | − | 0.902196i | \(-0.358045\pi\) | ||||
0.431327 | + | 0.902196i | \(0.358045\pi\) | |||||||
\(338\) | −3.11726e8 | + | 4.87329e8i | −0.439101 | + | 0.686457i | ||||
\(339\) | 5.34202e8i | 0.744743i | ||||||||
\(340\) | 3.31258e8 | − | 1.52985e8i | 0.457077 | − | 0.211093i | ||||
\(341\) | − | 1.76992e9i | − | 2.41720i | ||||||
\(342\) | 4.38204e7 | + | 2.80303e7i | 0.0592359 | + | 0.0378910i | ||||
\(343\) | −8.03284e8 | −1.07483 | ||||||||
\(344\) | −8.53837e7 | + | 6.21980e8i | −0.113089 | + | 0.823801i | ||||
\(345\) | 2.55119e8 | 0.334484 | ||||||||
\(346\) | 1.53447e8 | + | 9.81542e7i | 0.199155 | + | 0.127392i | ||||
\(347\) | − | 5.46595e8i | − | 0.702283i | −0.936322 | − | 0.351142i | \(-0.885794\pi\) | ||
0.936322 | − | 0.351142i | \(-0.114206\pi\) | |||||||
\(348\) | −6.09279e7 | − | 1.31927e8i | −0.0774977 | − | 0.167805i | ||||
\(349\) | 2.67022e8i | 0.336246i | 0.985766 | + | 0.168123i | \(0.0537706\pi\) | ||||
−0.985766 | + | 0.168123i | \(0.946229\pi\) | |||||||
\(350\) | −2.92228e8 | + | 4.56847e8i | −0.364320 | + | 0.569551i | ||||
\(351\) | −6.70837e7 | −0.0828022 | ||||||||
\(352\) | 1.46127e9 | − | 4.45987e8i | 1.78579 | − | 0.545033i | ||||
\(353\) | 4.23784e8 | 0.512783 | 0.256391 | − | 0.966573i | \(-0.417466\pi\) | ||||
0.256391 | + | 0.966573i | \(0.417466\pi\) | |||||||
\(354\) | −3.40277e8 | + | 5.31963e8i | −0.407681 | + | 0.637338i | ||||
\(355\) | − | 2.24477e8i | − | 0.266301i | ||||||
\(356\) | 3.69690e7 | + | 8.00486e7i | 0.0434272 | + | 0.0940327i | ||||
\(357\) | − | 4.53506e8i | − | 0.527527i | ||||||
\(358\) | 5.16321e8 | + | 3.30271e8i | 0.594743 | + | 0.380435i | ||||
\(359\) | 2.46440e8 | 0.281113 | 0.140557 | − | 0.990073i | \(-0.455111\pi\) | ||||
0.140557 | + | 0.990073i | \(0.455111\pi\) | |||||||
\(360\) | 1.96924e7 | − | 1.43450e8i | 0.0222454 | − | 0.162047i | ||||
\(361\) | 8.54093e8 | 0.955498 | ||||||||
\(362\) | 1.30363e9 | + | 8.33885e8i | 1.44436 | + | 0.923903i | ||||
\(363\) | 1.30808e9i | 1.43536i | ||||||||
\(364\) | 3.20072e8 | − | 1.47819e8i | 0.347851 | − | 0.160648i | ||||
\(365\) | 4.70869e8i | 0.506845i | ||||||||
\(366\) | 5.12203e8 | − | 8.00739e8i | 0.546082 | − | 0.853704i | ||||
\(367\) | −9.48483e8 | −1.00161 | −0.500805 | − | 0.865560i | \(-0.666963\pi\) | ||||
−0.500805 | + | 0.865560i | \(0.666963\pi\) | |||||||
\(368\) | −7.31877e8 | + | 8.59282e8i | −0.765545 | + | 0.898811i | ||||
\(369\) | −2.88594e8 | −0.299017 | ||||||||
\(370\) | −1.52804e8 | + | 2.38882e8i | −0.156829 | + | 0.245175i | ||||
\(371\) | − | 1.81884e8i | − | 0.184921i | ||||||
\(372\) | 6.73751e8 | − | 3.11159e8i | 0.678577 | − | 0.313388i | ||||
\(373\) | 4.22758e8i | 0.421804i | 0.977507 | + | 0.210902i | \(0.0676401\pi\) | ||||
−0.977507 | + | 0.210902i | \(0.932360\pi\) | |||||||
\(374\) | −1.63266e9 | − | 1.04435e9i | −1.61378 | − | 1.03227i | ||||
\(375\) | 5.08961e8 | 0.498396 | ||||||||
\(376\) | −1.90797e9 | − | 2.61920e8i | −1.85103 | − | 0.254104i | ||||
\(377\) | −1.43307e8 | −0.137744 | ||||||||
\(378\) | −1.51603e8 | − | 9.69749e7i | −0.144373 | − | 0.0923503i | ||||
\(379\) | 1.90673e9i | 1.79909i | 0.436828 | + | 0.899545i | \(0.356102\pi\) | ||||
−0.436828 | + | 0.899545i | \(0.643898\pi\) | |||||||
\(380\) | 4.64247e7 | + | 1.00523e8i | 0.0434017 | + | 0.0939773i | ||||
\(381\) | 7.40343e8i | 0.685797i | ||||||||
\(382\) | −5.59830e7 | + | 8.75196e7i | −0.0513848 | + | 0.0803311i | ||||
\(383\) | −4.96320e7 | −0.0451405 | −0.0225702 | − | 0.999745i | \(-0.507185\pi\) | ||||
−0.0225702 | + | 0.999745i | \(0.507185\pi\) | |||||||
\(384\) | 4.26670e8 | + | 4.77852e8i | 0.384533 | + | 0.430660i | ||||
\(385\) | −9.13591e8 | −0.815904 | ||||||||
\(386\) | −1.84525e8 | + | 2.88473e8i | −0.163305 | + | 0.255299i | ||||
\(387\) | − | 3.16041e8i | − | 0.277176i | ||||||
\(388\) | 1.86792e8 | + | 4.04460e8i | 0.162348 | + | 0.351532i | ||||
\(389\) | − | 1.83253e9i | − | 1.57844i | −0.614112 | − | 0.789219i | \(-0.710486\pi\) | ||
0.614112 | − | 0.789219i | \(-0.289514\pi\) | |||||||
\(390\) | −1.20289e8 | − | 7.69442e7i | −0.102683 | − | 0.0656825i | ||||
\(391\) | 1.43183e9 | 1.21136 | ||||||||
\(392\) | −2.44517e8 | − | 3.35667e7i | −0.205026 | − | 0.0281454i | ||||
\(393\) | −3.30598e8 | −0.274743 | ||||||||
\(394\) | −5.46090e8 | − | 3.49313e8i | −0.449808 | − | 0.287726i | ||||
\(395\) | 9.05310e8i | 0.739107i | ||||||||
\(396\) | −6.98235e8 | + | 3.22467e8i | −0.565026 | + | 0.260947i | ||||
\(397\) | 1.24041e9i | 0.994942i | 0.867481 | + | 0.497471i | \(0.165738\pi\) | ||||
−0.867481 | + | 0.497471i | \(0.834262\pi\) | |||||||
\(398\) | 1.46938e7 | − | 2.29711e7i | 0.0116827 | − | 0.0182638i | ||||
\(399\) | 1.37620e8 | 0.108462 | ||||||||
\(400\) | −6.30122e8 | + | 7.39814e8i | −0.492283 | + | 0.577980i | ||||
\(401\) | 1.72908e9 | 1.33909 | 0.669544 | − | 0.742772i | \(-0.266489\pi\) | ||||
0.669544 | + | 0.742772i | \(0.266489\pi\) | |||||||
\(402\) | 2.00872e8 | − | 3.14027e8i | 0.154215 | − | 0.241088i | ||||
\(403\) | − | 7.31869e8i | − | 0.557013i | ||||||
\(404\) | 7.90648e8 | − | 3.65146e8i | 0.596552 | − | 0.275506i | ||||
\(405\) | 7.28899e7i | 0.0545224i | ||||||||
\(406\) | −3.23861e8 | − | 2.07162e8i | −0.240169 | − | 0.153627i | ||||
\(407\) | 1.50624e9 | 1.10742 | ||||||||
\(408\) | 1.10522e8 | − | 8.05101e8i | 0.0805634 | − | 0.586867i | ||||
\(409\) | −1.59861e9 | −1.15534 | −0.577670 | − | 0.816271i | \(-0.696038\pi\) | ||||
−0.577670 | + | 0.816271i | \(0.696038\pi\) | |||||||
\(410\) | −5.17483e8 | − | 3.31015e8i | −0.370811 | − | 0.237194i | ||||
\(411\) | − | 1.30536e9i | − | 0.927435i | ||||||
\(412\) | −9.93342e8 | − | 2.15088e9i | −0.699775 | − | 1.51522i | ||||
\(413\) | 1.67066e9i | 1.16698i | ||||||||
\(414\) | 3.06174e8 | − | 4.78650e8i | 0.212064 | − | 0.331525i | ||||
\(415\) | −4.64562e8 | −0.319062 | ||||||||
\(416\) | 6.04242e8 | − | 1.84417e8i | 0.411514 | − | 0.125596i | ||||
\(417\) | 6.87770e8 | 0.464480 | ||||||||
\(418\) | 3.16917e8 | − | 4.95444e8i | 0.212241 | − | 0.331801i | ||||
\(419\) | − | 1.44325e9i | − | 0.958501i | −0.877678 | − | 0.479250i | \(-0.840909\pi\) | ||
0.877678 | − | 0.479250i | \(-0.159091\pi\) | |||||||
\(420\) | −1.60613e8 | − | 3.47775e8i | −0.105781 | − | 0.229047i | ||||
\(421\) | − | 8.96348e8i | − | 0.585450i | −0.956197 | − | 0.292725i | \(-0.905438\pi\) | ||
0.956197 | − | 0.292725i | \(-0.0945620\pi\) | |||||||
\(422\) | 1.35128e9 | + | 8.64366e8i | 0.875292 | + | 0.559892i | ||||
\(423\) | 9.69476e8 | 0.622796 | ||||||||
\(424\) | 4.43262e7 | − | 3.22896e8i | 0.0282410 | − | 0.205723i | ||||
\(425\) | 1.23276e9 | 0.778964 | ||||||||
\(426\) | −4.21160e8 | − | 2.69400e8i | −0.263945 | − | 0.168836i | ||||
\(427\) | − | 2.51477e9i | − | 1.56315i | ||||||
\(428\) | −1.97066e9 | + | 9.10111e8i | −1.21495 | + | 0.561101i | ||||
\(429\) | 7.58465e8i | 0.463804i | ||||||||
\(430\) | 3.62495e8 | − | 5.66698e8i | 0.219868 | − | 0.343726i | ||||
\(431\) | 7.07247e8 | 0.425501 | 0.212751 | − | 0.977107i | \(-0.431758\pi\) | ||||
0.212751 | + | 0.977107i | \(0.431758\pi\) | |||||||
\(432\) | −2.45505e8 | − | 2.09104e8i | −0.146510 | − | 0.124787i | ||||
\(433\) | −4.90457e8 | −0.290331 | −0.145166 | − | 0.989407i | \(-0.546371\pi\) | ||||
−0.145166 | + | 0.989407i | \(0.546371\pi\) | |||||||
\(434\) | 1.05798e9 | − | 1.65396e9i | 0.621243 | − | 0.971205i | ||||
\(435\) | 1.55710e8i | 0.0906995i | ||||||||
\(436\) | −2.79578e9 | + | 1.29118e9i | −1.61547 | + | 0.746077i | ||||
\(437\) | 4.34502e8i | 0.249062i | ||||||||
\(438\) | 8.83437e8 | + | 5.65101e8i | 0.502361 | + | 0.321342i | ||||
\(439\) | 1.06892e9 | 0.603002 | 0.301501 | − | 0.953466i | \(-0.402512\pi\) | ||||
0.301501 | + | 0.953466i | \(0.402512\pi\) | |||||||
\(440\) | −1.62188e9 | − | 2.22647e8i | −0.907684 | − | 0.124604i | ||||
\(441\) | 1.24244e8 | 0.0689829 | ||||||||
\(442\) | −6.75111e8 | − | 4.31843e8i | −0.371875 | − | 0.237874i | ||||
\(443\) | − | 1.01920e9i | − | 0.556989i | −0.960438 | − | 0.278495i | \(-0.910165\pi\) | ||
0.960438 | − | 0.278495i | \(-0.0898355\pi\) | |||||||
\(444\) | 2.64803e8 | + | 5.73375e8i | 0.143576 | + | 0.310884i | ||||
\(445\) | − | 9.44796e7i | − | 0.0508251i | ||||||
\(446\) | 1.65904e8 | − | 2.59362e8i | 0.0885494 | − | 0.138432i | ||||
\(447\) | −1.42158e9 | −0.752829 | ||||||||
\(448\) | 1.63212e9 | + | 4.56714e8i | 0.857591 | + | 0.239978i | ||||
\(449\) | −2.46756e9 | −1.28649 | −0.643244 | − | 0.765661i | \(-0.722412\pi\) | ||||
−0.643244 | + | 0.765661i | \(0.722412\pi\) | |||||||
\(450\) | 2.63606e8 | − | 4.12102e8i | 0.136368 | − | 0.213187i | ||||
\(451\) | 3.26292e9i | 1.67490i | ||||||||
\(452\) | 1.06183e9 | + | 2.29916e9i | 0.540840 | + | 1.17108i | ||||
\(453\) | − | 7.44576e8i | − | 0.376327i | ||||||
\(454\) | −4.38696e7 | − | 2.80617e7i | −0.0220023 | − | 0.0140740i | ||||
\(455\) | −3.77774e8 | −0.188015 | ||||||||
\(456\) | 2.44315e8 | + | 3.35389e7i | 0.120663 | + | 0.0165642i | ||||
\(457\) | −1.08845e9 | −0.533460 | −0.266730 | − | 0.963771i | \(-0.585943\pi\) | ||||
−0.266730 | + | 0.963771i | \(0.585943\pi\) | |||||||
\(458\) | 1.58517e9 | + | 1.01397e9i | 0.770985 | + | 0.493170i | ||||
\(459\) | 4.09088e8i | 0.197457i | ||||||||
\(460\) | 1.09801e9 | − | 5.07096e8i | 0.525962 | − | 0.242906i | ||||
\(461\) | 2.65805e9i | 1.26360i | 0.775131 | + | 0.631801i | \(0.217684\pi\) | ||||
−0.775131 | + | 0.631801i | \(0.782316\pi\) | |||||||
\(462\) | −1.09642e9 | + | 1.71406e9i | −0.517286 | + | 0.808686i | ||||
\(463\) | 1.27045e9 | 0.594871 | 0.297435 | − | 0.954742i | \(-0.403869\pi\) | ||||
0.297435 | + | 0.954742i | \(0.403869\pi\) | |||||||
\(464\) | −5.24458e8 | − | 4.46697e8i | −0.243724 | − | 0.207587i | ||||
\(465\) | −7.95213e8 | −0.366774 | ||||||||
\(466\) | 3.16400e8 | − | 4.94637e8i | 0.144839 | − | 0.226431i | ||||
\(467\) | − | 6.33304e8i | − | 0.287742i | −0.989596 | − | 0.143871i | \(-0.954045\pi\) | ||
0.989596 | − | 0.143871i | \(-0.0459550\pi\) | |||||||
\(468\) | −2.88723e8 | + | 1.33341e8i | −0.130203 | + | 0.0601318i | ||||
\(469\) | − | 9.86220e8i | − | 0.441437i | ||||||
\(470\) | 1.73838e9 | + | 1.11198e9i | 0.772330 | + | 0.494030i | ||||
\(471\) | −4.07555e8 | −0.179727 | ||||||||
\(472\) | −4.07149e8 | + | 2.96589e9i | −0.178220 | + | 1.29825i | ||||
\(473\) | −3.57323e9 | −1.55256 | ||||||||
\(474\) | 1.69853e9 | + | 1.08648e9i | 0.732569 | + | 0.468596i | ||||
\(475\) | 3.74092e8i | 0.160159i | ||||||||
\(476\) | −9.01427e8 | − | 1.95185e9i | −0.383095 | − | 0.829513i | ||||
\(477\) | 1.64070e8i | 0.0692173i | ||||||||
\(478\) | 1.23753e8 | − | 1.93467e8i | 0.0518274 | − | 0.0810230i | ||||
\(479\) | −2.97478e6 | −0.00123674 | −0.000618372 | − | 1.00000i | \(-0.500197\pi\) | ||||
−0.000618372 | 1.00000i | \(0.500197\pi\) | ||||||||
\(480\) | −2.00379e8 | − | 6.56540e8i | −0.0827004 | − | 0.270967i | ||||
\(481\) | 6.22835e8 | 0.255191 | ||||||||
\(482\) | 2.07423e8 | − | 3.24269e8i | 0.0843707 | − | 0.131899i | ||||
\(483\) | − | 1.50323e9i | − | 0.607029i | ||||||
\(484\) | 2.60006e9 | + | 5.62989e9i | 1.04238 | + | 2.25705i | ||||
\(485\) | − | 4.77376e8i | − | 0.190005i | ||||||
\(486\) | 1.36755e8 | + | 8.74769e7i | 0.0540400 | + | 0.0345674i | ||||
\(487\) | −7.68410e8 | −0.301468 | −0.150734 | − | 0.988574i | \(-0.548164\pi\) | ||||
−0.150734 | + | 0.988574i | \(0.548164\pi\) | |||||||
\(488\) | 6.12862e8 | − | 4.46442e9i | 0.238723 | − | 1.73898i | ||||
\(489\) | 1.95415e9 | 0.755747 | ||||||||
\(490\) | 2.22784e8 | + | 1.42507e8i | 0.0855458 | + | 0.0547204i | ||||
\(491\) | 1.44626e9i | 0.551391i | 0.961245 | + | 0.275696i | \(0.0889081\pi\) | ||||
−0.961245 | + | 0.275696i | \(0.911092\pi\) | |||||||
\(492\) | −1.24209e9 | + | 5.73635e8i | −0.470191 | + | 0.217149i | ||||
\(493\) | 8.73910e8i | 0.328475i | ||||||||
\(494\) | 1.31047e8 | − | 2.04868e8i | 0.0489082 | − | 0.0764593i | ||||
\(495\) | 8.24111e8 | 0.305399 | ||||||||
\(496\) | 2.28128e9 | − | 2.67841e9i | 0.839447 | − | 0.985578i | ||||
\(497\) | −1.32268e9 | −0.483289 | ||||||||
\(498\) | −5.57532e8 | + | 8.71603e8i | −0.202286 | + | 0.316239i | ||||
\(499\) | − | 9.02518e8i | − | 0.325165i | −0.986695 | − | 0.162583i | \(-0.948018\pi\) | ||
0.986695 | − | 0.162583i | \(-0.0519824\pi\) | |||||||
\(500\) | 2.19053e9 | − | 1.01165e9i | 0.783707 | − | 0.361940i | ||||
\(501\) | 7.74919e8i | 0.275312i | ||||||||
\(502\) | 4.83145e8 | + | 3.09050e8i | 0.170457 | + | 0.109035i | ||||
\(503\) | −3.71023e9 | −1.29991 | −0.649954 | − | 0.759974i | \(-0.725212\pi\) | ||||
−0.649954 | + | 0.759974i | \(0.725212\pi\) | |||||||
\(504\) | −8.45244e8 | − | 1.16033e8i | −0.294087 | − | 0.0403714i | ||||
\(505\) | −9.33184e8 | −0.322439 | ||||||||
\(506\) | −5.41173e9 | − | 3.46168e9i | −1.85699 | − | 1.18785i | ||||
\(507\) | − | 1.38058e9i | − | 0.470473i | ||||||
\(508\) | 1.47157e9 | + | 3.18638e9i | 0.498032 | + | 1.07839i | ||||
\(509\) | 7.61723e8i | 0.256027i | 0.991772 | + | 0.128013i | \(0.0408600\pi\) | ||||
−0.991772 | + | 0.128013i | \(0.959140\pi\) | |||||||
\(510\) | −4.69219e8 | + | 7.33542e8i | −0.156632 | + | 0.244867i | ||||
\(511\) | 2.77448e9 | 0.919832 | ||||||||
\(512\) | 2.78618e9 | + | 1.20855e9i | 0.917410 | + | 0.397943i | ||||
\(513\) | −1.24141e8 | −0.0405981 | ||||||||
\(514\) | 2.54194e9 | − | 3.97387e9i | 0.825646 | − | 1.29075i | ||||
\(515\) | 2.53863e9i | 0.818982i | ||||||||
\(516\) | −6.28190e8 | − | 1.36021e9i | −0.201288 | − | 0.435846i | ||||
\(517\) | − | 1.09611e10i | − | 3.48850i | ||||||
\(518\) | 1.40755e9 | + | 9.00358e8i | 0.444949 | + | 0.284617i | ||||
\(519\) | −4.34708e8 | −0.136494 | ||||||||
\(520\) | −6.70655e8 | − | 9.20656e7i | −0.209164 | − | 0.0287135i | ||||
\(521\) | 4.48514e9 | 1.38945 | 0.694726 | − | 0.719274i | \(-0.255525\pi\) | ||||
0.694726 | + | 0.719274i | \(0.255525\pi\) | |||||||
\(522\) | 2.92141e8 | + | 1.86872e8i | 0.0898971 | + | 0.0575038i | ||||
\(523\) | − | 3.54373e8i | − | 0.108319i | −0.998532 | − | 0.0541595i | \(-0.982752\pi\) | ||
0.998532 | − | 0.0541595i | \(-0.0172479\pi\) | |||||||
\(524\) | −1.42287e9 | + | 6.57125e8i | −0.432021 | + | 0.199521i | ||||
\(525\) | − | 1.29423e9i | − | 0.390349i | ||||||
\(526\) | −2.01328e9 | + | 3.14741e9i | −0.603190 | + | 0.942981i | ||||
\(527\) | −4.46306e9 | −1.32830 | ||||||||
\(528\) | −2.36418e9 | + | 2.77574e9i | −0.698976 | + | 0.820654i | ||||
\(529\) | 1.34123e9 | 0.393921 | ||||||||
\(530\) | −1.88186e8 | + | 2.94197e8i | −0.0549064 | + | 0.0858365i | ||||
\(531\) | − | 1.50703e9i | − | 0.436808i | ||||||
\(532\) | 5.92308e8 | − | 2.73546e8i | 0.170552 | − | 0.0787662i | ||||
\(533\) | 1.34923e9i | 0.385959i | ||||||||
\(534\) | −1.77261e8 | − | 1.13387e8i | −0.0503755 | − | 0.0322233i | ||||
\(535\) | 2.32592e9 | 0.656685 | ||||||||
\(536\) | 2.40347e8 | − | 1.75082e9i | 0.0674160 | − | 0.491094i | ||||
\(537\) | −1.46272e9 | −0.407615 | ||||||||
\(538\) | −3.39290e9 | − | 2.17031e9i | −0.939362 | − | 0.600875i | ||||
\(539\) | − | 1.40474e9i | − | 0.386397i | ||||||
\(540\) | 1.44882e8 | + | 3.13712e8i | 0.0395947 | + | 0.0857341i | ||||
\(541\) | 2.98685e9i | 0.811005i | 0.914094 | + | 0.405502i | \(0.132903\pi\) | ||||
−0.914094 | + | 0.405502i | \(0.867097\pi\) | |||||||
\(542\) | −1.78437e9 | + | 2.78955e9i | −0.481379 | + | 0.752552i | ||||
\(543\) | −3.69314e9 | −0.989911 | ||||||||
\(544\) | −1.12461e9 | − | 3.68477e9i | −0.299506 | − | 0.981329i | ||||
\(545\) | 3.29980e9 | 0.873171 | ||||||||
\(546\) | −4.53375e8 | + | 7.08773e8i | −0.119202 | + | 0.186351i | ||||
\(547\) | 5.14992e9i | 1.34538i | 0.739925 | + | 0.672690i | \(0.234861\pi\) | ||||
−0.739925 | + | 0.672690i | \(0.765139\pi\) | |||||||
\(548\) | −2.59464e9 | − | 5.61816e9i | −0.673512 | − | 1.45835i | ||||
\(549\) | 2.26846e9i | 0.585097i | ||||||||
\(550\) | −4.65932e9 | − | 2.98039e9i | −1.19413 | − | 0.763843i | ||||
\(551\) | −2.65196e8 | −0.0675361 | ||||||||
\(552\) | 3.66344e8 | − | 2.66865e9i | 0.0927049 | − | 0.675312i | ||||
\(553\) | 5.33432e9 | 1.34135 | ||||||||
\(554\) | 3.15202e9 | + | 2.01623e9i | 0.787600 | + | 0.503798i | ||||
\(555\) | − | 6.76742e8i | − | 0.168034i | ||||||
\(556\) | 2.96011e9 | − | 1.36707e9i | 0.730375 | − | 0.337310i | ||||
\(557\) | 3.21644e9i | 0.788647i | 0.918972 | + | 0.394323i | \(0.129021\pi\) | ||||
−0.918972 | + | 0.394323i | \(0.870979\pi\) | |||||||
\(558\) | −9.54354e8 | + | 1.49197e9i | −0.232536 | + | 0.363529i | ||||
\(559\) | −1.47755e9 | −0.357767 | ||||||||
\(560\) | −1.38253e9 | − | 1.17755e9i | −0.332673 | − | 0.283348i | ||||
\(561\) | 4.62525e9 | 1.10603 | ||||||||
\(562\) | −1.73764e9 | + | 2.71649e9i | −0.412936 | + | 0.645553i | ||||
\(563\) | 6.23693e8i | 0.147296i | 0.997284 | + | 0.0736481i | \(0.0234642\pi\) | ||||
−0.997284 | + | 0.0736481i | \(0.976536\pi\) | |||||||
\(564\) | 4.17255e9 | − | 1.92701e9i | 0.979320 | − | 0.452280i | ||||
\(565\) | − | 2.71365e9i | − | 0.632972i | ||||||
\(566\) | 3.83259e8 | + | 2.45156e8i | 0.0888453 | + | 0.0568310i | ||||
\(567\) | 4.29486e8 | 0.0989483 | ||||||||
\(568\) | −2.34812e9 | − | 3.22344e8i | −0.537653 | − | 0.0738074i | ||||
\(569\) | 2.58144e9 | 0.587449 | 0.293724 | − | 0.955890i | \(-0.405105\pi\) | ||||
0.293724 | + | 0.955890i | \(0.405105\pi\) | |||||||
\(570\) | −2.22600e8 | − | 1.42389e8i | −0.0503458 | − | 0.0322043i | ||||
\(571\) | 4.51863e9i | 1.01573i | 0.861436 | + | 0.507867i | \(0.169566\pi\) | ||||
−0.861436 | + | 0.507867i | \(0.830434\pi\) | |||||||
\(572\) | 1.50759e9 | + | 3.26437e9i | 0.336819 | + | 0.729312i | ||||
\(573\) | − | 2.47939e8i | − | 0.0550560i | ||||||
\(574\) | −1.95042e9 | + | 3.04914e9i | −0.430464 | + | 0.672955i | ||||
\(575\) | 4.08620e9 | 0.896360 | ||||||||
\(576\) | −1.47227e9 | − | 4.11981e8i | −0.321002 | − | 0.0898254i | ||||
\(577\) | −5.58211e9 | −1.20972 | −0.604858 | − | 0.796334i | \(-0.706770\pi\) | ||||
−0.604858 | + | 0.796334i | \(0.706770\pi\) | |||||||
\(578\) | −1.31859e8 | + | 2.06138e8i | −0.0284029 | + | 0.0444029i | ||||
\(579\) | − | 8.17232e8i | − | 0.174973i | ||||||
\(580\) | 3.09503e8 | + | 6.70165e8i | 0.0658669 | + | 0.142621i | ||||
\(581\) | 2.73732e9i | 0.579040i | ||||||||
\(582\) | −8.95644e8 | − | 5.72910e8i | −0.188324 | − | 0.120464i | ||||
\(583\) | 1.85502e9 | 0.387710 | ||||||||
\(584\) | 4.92548e9 | + | 6.76157e8i | 1.02330 | + | 0.140476i | ||||
\(585\) | 3.40773e8 | 0.0703753 | ||||||||
\(586\) | 1.46699e9 | + | 9.38381e8i | 0.301153 | + | 0.192636i | ||||
\(587\) | 3.49384e9i | 0.712967i | 0.934302 | + | 0.356484i | \(0.116024\pi\) | ||||
−0.934302 | + | 0.356484i | \(0.883976\pi\) | |||||||
\(588\) | 5.34738e8 | − | 2.46958e8i | 0.108473 | − | 0.0500960i | ||||
\(589\) | − | 1.35436e9i | − | 0.273105i | ||||||
\(590\) | 1.72854e9 | − | 2.70228e9i | 0.346496 | − | 0.541686i | ||||
\(591\) | 1.54705e9 | 0.308282 | ||||||||
\(592\) | 2.27938e9 | + | 1.94142e9i | 0.451534 | + | 0.384585i | ||||
\(593\) | 6.78437e8 | 0.133604 | 0.0668018 | − | 0.997766i | \(-0.478720\pi\) | ||||
0.0668018 | + | 0.997766i | \(0.478720\pi\) | |||||||
\(594\) | 9.89035e8 | − | 1.54618e9i | 0.193624 | − | 0.302697i | ||||
\(595\) | 2.30373e9i | 0.448355i | ||||||||
\(596\) | −6.11839e9 | + | 2.82566e9i | −1.18379 | + | 0.546712i | ||||
\(597\) | 6.50762e7i | 0.0125173i | ||||||||
\(598\) | −2.23777e9 | − | 1.43142e9i | −0.427919 | − | 0.273724i | ||||
\(599\) | 2.98442e8 | 0.0567370 | 0.0283685 | − | 0.999598i | \(-0.490969\pi\) | ||||
0.0283685 | + | 0.999598i | \(0.490969\pi\) | |||||||
\(600\) | 3.15411e8 | − | 2.29762e9i | 0.0596138 | − | 0.434259i | ||||
\(601\) | −4.58275e8 | −0.0861123 | −0.0430561 | − | 0.999073i | \(-0.513709\pi\) | ||||
−0.0430561 | + | 0.999073i | \(0.513709\pi\) | |||||||
\(602\) | −3.33913e9 | − | 2.13591e9i | −0.623800 | − | 0.399021i | ||||
\(603\) | 8.89627e8i | 0.165233i | ||||||||
\(604\) | −1.47998e9 | − | 3.20459e9i | −0.273292 | − | 0.591758i | ||||
\(605\) | − | 6.64483e9i | − | 1.21994i | ||||||
\(606\) | −1.11994e9 | + | 1.75082e9i | −0.204427 | + | 0.319586i | ||||
\(607\) | −8.38542e9 | −1.52182 | −0.760912 | − | 0.648855i | \(-0.775248\pi\) | ||||
−0.760912 | + | 0.648855i | \(0.775248\pi\) | |||||||
\(608\) | 1.11818e9 | − | 3.41273e8i | 0.201766 | − | 0.0615799i | ||||
\(609\) | 9.17485e8 | 0.164603 | ||||||||
\(610\) | −2.60190e9 | + | 4.06761e9i | −0.464126 | + | 0.725580i | ||||
\(611\) | − | 4.53247e9i | − | 0.803880i | ||||||
\(612\) | 8.13138e8 | + | 1.76068e9i | 0.143395 | + | 0.310493i | ||||
\(613\) | 5.53124e9i | 0.969865i | 0.874552 | + | 0.484932i | \(0.161156\pi\) | ||||
−0.874552 | + | 0.484932i | \(0.838844\pi\) | |||||||
\(614\) | 2.80042e9 | + | 1.79132e9i | 0.488241 | + | 0.312309i | ||||
\(615\) | 1.46601e9 | 0.254140 | ||||||||
\(616\) | −1.31189e9 | + | 9.55654e9i | −0.226134 | + | 1.64728i | ||||
\(617\) | 4.15289e9 | 0.711791 | 0.355896 | − | 0.934526i | \(-0.384176\pi\) | ||||
0.355896 | + | 0.934526i | \(0.384176\pi\) | |||||||
\(618\) | 4.76294e9 | + | 3.04667e9i | 0.811737 | + | 0.519237i | ||||
\(619\) | − | 2.84793e9i | − | 0.482627i | −0.970447 | − | 0.241314i | \(-0.922422\pi\) | ||
0.970447 | − | 0.241314i | \(-0.0775782\pi\) | |||||||
\(620\) | −3.42253e9 | + | 1.58063e9i | −0.576736 | + | 0.266355i | ||||
\(621\) | 1.35599e9i | 0.227215i | ||||||||
\(622\) | 5.80736e9 | − | 9.07879e9i | 0.967637 | − | 1.51273i | ||||
\(623\) | −5.56698e8 | −0.0922384 | ||||||||
\(624\) | −9.77600e8 | + | 1.14778e9i | −0.161070 | + | 0.189109i | ||||
\(625\) | 2.04843e9 | 0.335615 | ||||||||
\(626\) | −4.33951e9 | + | 6.78406e9i | −0.707018 | + | 1.10530i | ||||
\(627\) | 1.40357e9i | 0.227404i | ||||||||
\(628\) | −1.75408e9 | + | 8.10091e8i | −0.282613 | + | 0.130519i | ||||
\(629\) | − | 3.79815e9i | − | 0.608549i | ||||||
\(630\) | 7.70118e8 | + | 4.92615e8i | 0.122706 | + | 0.0784903i | ||||
\(631\) | 8.88293e8 | 0.140752 | 0.0703758 | − | 0.997521i | \(-0.477580\pi\) | ||||
0.0703758 | + | 0.997521i | \(0.477580\pi\) | |||||||
\(632\) | 9.46991e9 | + | 1.30000e9i | 1.49223 | + | 0.204849i | ||||
\(633\) | −3.82813e9 | −0.599893 | ||||||||
\(634\) | −1.83805e8 | − | 1.17573e8i | −0.0286447 | − | 0.0183230i | ||||
\(635\) | − | 3.76081e9i | − | 0.582872i | ||||||
\(636\) | 3.26119e8 | + | 7.06144e8i | 0.0502663 | + | 0.108841i | ||||
\(637\) | − | 5.80864e8i | − | 0.0890403i | ||||||
\(638\) | 2.11282e9 | − | 3.30302e9i | 0.322099 | − | 0.503545i | ||||
\(639\) | 1.19313e9 | 0.180898 | ||||||||
\(640\) | −2.16741e9 | − | 2.42741e9i | −0.326822 | − | 0.366026i | ||||
\(641\) | −1.13079e10 | −1.69582 | −0.847910 | − | 0.530139i | \(-0.822140\pi\) | ||||
−0.847910 | + | 0.530139i | \(0.822140\pi\) | |||||||
\(642\) | 2.79139e9 | − | 4.36385e9i | 0.416340 | − | 0.650875i | ||||
\(643\) | − | 8.67974e9i | − | 1.28756i | −0.765209 | − | 0.643781i | \(-0.777365\pi\) | ||
0.765209 | − | 0.643781i | \(-0.222635\pi\) | |||||||
\(644\) | −2.98794e9 | − | 6.46976e9i | −0.440830 | − | 0.954526i | ||||
\(645\) | 1.60543e9i | 0.235577i | ||||||||
\(646\) | −1.24932e9 | − | 7.99145e8i | −0.182331 | − | 0.116630i | ||||
\(647\) | −9.12604e9 | −1.32470 | −0.662350 | − | 0.749195i | \(-0.730441\pi\) | ||||
−0.662350 | + | 0.749195i | \(0.730441\pi\) | |||||||
\(648\) | 7.62458e8 | + | 1.04668e8i | 0.110079 | + | 0.0151113i | ||||
\(649\) | −1.70388e10 | −2.44671 | ||||||||
\(650\) | −1.92665e9 | − | 1.23240e9i | −0.275173 | − | 0.176018i | ||||
\(651\) | 4.68560e9i | 0.665628i | ||||||||
\(652\) | 8.41049e9 | − | 3.88423e9i | 1.18838 | − | 0.548831i | ||||
\(653\) | − | 9.07309e9i | − | 1.27514i | −0.770391 | − | 0.637572i | \(-0.779939\pi\) | ||
0.770391 | − | 0.637572i | \(-0.220061\pi\) | |||||||
\(654\) | 3.96016e9 | − | 6.19102e9i | 0.553593 | − | 0.865446i | ||||
\(655\) | 1.67938e9 | 0.233509 | ||||||||
\(656\) | −4.20564e9 | + | 4.93776e9i | −0.581659 | + | 0.682915i | ||||
\(657\) | −2.50274e9 | −0.344300 | ||||||||
\(658\) | 6.55206e9 | − | 1.02430e10i | 0.896576 | − | 1.40164i | ||||
\(659\) | − | 5.93620e9i | − | 0.807996i | −0.914760 | − | 0.403998i | \(-0.867620\pi\) | ||
0.914760 | − | 0.403998i | \(-0.132380\pi\) | |||||||
\(660\) | 3.54691e9 | − | 1.63807e9i | 0.480226 | − | 0.221784i | ||||
\(661\) | 4.99352e9i | 0.672515i | 0.941770 | + | 0.336257i | \(0.109161\pi\) | ||||
−0.941770 | + | 0.336257i | \(0.890839\pi\) | |||||||
\(662\) | 5.96692e9 | + | 3.81681e9i | 0.799369 | + | 0.511326i | ||||
\(663\) | 1.91256e9 | 0.254869 | ||||||||
\(664\) | −6.67099e8 | + | 4.85951e9i | −0.0884305 | + | 0.644175i | ||||
\(665\) | −6.99088e8 | −0.0921841 | ||||||||
\(666\) | −1.26969e9 | − | 8.12174e8i | −0.166548 | − | 0.106534i | ||||
\(667\) | 2.89673e9i | 0.377979i | ||||||||
\(668\) | 1.54030e9 | + | 3.33519e9i | 0.199934 | + | 0.432915i | ||||
\(669\) | 7.34763e8i | 0.0948759i | ||||||||
\(670\) | −1.02039e9 | + | 1.59520e9i | −0.131071 | + | 0.204906i | ||||
\(671\) | 2.56478e10 | 3.27733 | ||||||||
\(672\) | −3.86850e9 | + | 1.18068e9i | −0.491757 | + | 0.150086i | ||||
\(673\) | 2.02208e9 | 0.255708 | 0.127854 | − | 0.991793i | \(-0.459191\pi\) | ||||
0.127854 | + | 0.991793i | \(0.459191\pi\) | |||||||
\(674\) | −3.69501e9 | + | 5.77651e9i | −0.464843 | + | 0.726701i | ||||
\(675\) | 1.16747e9i | 0.146110i | ||||||||
\(676\) | −2.74416e9 | − | 5.94191e9i | −0.341662 | − | 0.739798i | ||||
\(677\) | − | 2.99982e9i | − | 0.371565i | −0.982591 | − | 0.185783i | \(-0.940518\pi\) | ||
0.982591 | − | 0.185783i | \(-0.0594820\pi\) | |||||||
\(678\) | −5.09131e9 | − | 3.25672e9i | −0.627372 | − | 0.401306i | ||||
\(679\) | −2.81282e9 | −0.344824 | ||||||||
\(680\) | −5.61432e8 | + | 4.08977e9i | −0.0684725 | + | 0.498790i | ||||
\(681\) | 1.24281e8 | 0.0150796 | ||||||||
\(682\) | 1.68685e10 | + | 1.07902e10i | 2.03625 | + | 1.30251i | ||||
\(683\) | − | 7.77019e9i | − | 0.933166i | −0.884477 | − | 0.466583i | \(-0.845485\pi\) | ||
0.884477 | − | 0.466583i | \(-0.154515\pi\) | |||||||
\(684\) | −5.34295e8 | + | 2.46754e8i | −0.0638388 | + | 0.0294828i | ||||
\(685\) | 6.63099e9i | 0.788245i | ||||||||
\(686\) | 4.89715e9 | − | 7.65583e9i | 0.579174 | − | 0.905437i | ||||
\(687\) | −4.49071e9 | −0.528405 | ||||||||
\(688\) | −5.40736e9 | − | 4.60561e9i | −0.633032 | − | 0.539173i | ||||
\(689\) | 7.67056e8 | 0.0893429 | ||||||||
\(690\) | −1.55531e9 | + | 2.43145e9i | −0.180237 | + | 0.281770i | ||||
\(691\) | − | 4.29400e9i | − | 0.495095i | −0.968876 | − | 0.247547i | \(-0.920375\pi\) | ||
0.968876 | − | 0.247547i | \(-0.0796246\pi\) | |||||||
\(692\) | −1.87095e9 | + | 8.64063e8i | −0.214630 | + | 0.0991230i | ||||
\(693\) | − | 4.85587e9i | − | 0.554244i | ||||||
\(694\) | 5.20942e9 | + | 3.33227e9i | 0.591604 | + | 0.378427i | ||||
\(695\) | −3.49375e9 | −0.394771 | ||||||||
\(696\) | 1.62879e9 | + | 2.23596e8i | 0.183119 | + | 0.0251381i | ||||
\(697\) | 8.22784e9 | 0.920389 | ||||||||
\(698\) | −2.54489e9 | − | 1.62787e9i | −0.283254 | − | 0.181187i | ||||
\(699\) | 1.40129e9i | 0.155187i | ||||||||
\(700\) | −2.57252e9 | − | 5.57025e9i | −0.283475 | − | 0.613807i | ||||
\(701\) | 1.78556e10i | 1.95777i | 0.204420 | + | 0.978883i | \(0.434469\pi\) | ||||
−0.204420 | + | 0.978883i | \(0.565531\pi\) | |||||||
\(702\) | 4.08970e8 | − | 6.39353e8i | 0.0446181 | − | 0.0697527i | ||||
\(703\) | 1.15258e9 | 0.125121 | ||||||||
\(704\) | −4.65796e9 | + | 1.66458e10i | −0.503143 | + | 1.79805i | ||||
\(705\) | −4.92477e9 | −0.529327 | ||||||||
\(706\) | −2.58356e9 | + | 4.03895e9i | −0.276314 | + | 0.431968i | ||||
\(707\) | 5.49856e9i | 0.585168i | ||||||||
\(708\) | −2.99550e9 | − | 6.48613e9i | −0.317214 | − | 0.686862i | ||||
\(709\) | 1.41108e10i | 1.48693i | 0.668775 | + | 0.743465i | \(0.266819\pi\) | ||||
−0.668775 | + | 0.743465i | \(0.733181\pi\) | |||||||
\(710\) | 2.13942e9 | + | 1.36851e9i | 0.224332 | + | 0.143497i | ||||
\(711\) | −4.81186e9 | −0.502075 | ||||||||
\(712\) | −9.88296e8 | − | 1.35670e8i | −0.102614 | − | 0.0140866i | ||||
\(713\) | −1.47936e10 | −1.52848 | ||||||||
\(714\) | 4.32222e9 | + | 2.76476e9i | 0.444389 | + | 0.284259i | ||||
\(715\) | − | 3.85286e9i | − | 0.394196i | ||||||
\(716\) | −6.29541e9 | + | 2.90742e9i | −0.640957 | + | 0.296014i | ||||
\(717\) | 5.48083e8i | 0.0555302i | ||||||||
\(718\) | −1.50240e9 | + | 2.34874e9i | −0.151478 | + | 0.236810i | ||||
\(719\) | 3.78839e9 | 0.380105 | 0.190052 | − | 0.981774i | \(-0.439134\pi\) | ||||
0.190052 | + | 0.981774i | \(0.439134\pi\) | |||||||
\(720\) | 1.24712e9 | + | 1.06221e9i | 0.124522 | + | 0.106059i | ||||
\(721\) | 1.49583e10 | 1.48630 | ||||||||
\(722\) | −5.20690e9 | + | 8.14008e9i | −0.514872 | + | 0.804912i | ||||
\(723\) | 9.18641e8i | 0.0903986i | ||||||||
\(724\) | −1.58950e10 | + | 7.34080e9i | −1.55659 | + | 0.718883i | ||||
\(725\) | 2.49399e9i | 0.243059i | ||||||||
\(726\) | −1.24669e10 | − | 7.97461e9i | −1.20915 | − | 0.773449i | ||||
\(727\) | 3.16436e9 | 0.305433 | 0.152716 | − | 0.988270i | \(-0.451198\pi\) | ||||
0.152716 | + | 0.988270i | \(0.451198\pi\) | |||||||
\(728\) | −5.42474e8 | + | 3.95167e9i | −0.0521097 | + | 0.379595i | ||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | −4.48770e9 | − | 2.87061e9i | −0.426967 | − | 0.273114i | ||||
\(731\) | 9.01034e9i | 0.853160i | ||||||||
\(732\) | 4.50898e9 | + | 9.76327e9i | 0.424903 | + | 0.920040i | ||||
\(733\) | − | 1.63026e10i | − | 1.52895i | −0.644654 | − | 0.764474i | \(-0.722999\pi\) | ||
0.644654 | − | 0.764474i | \(-0.277001\pi\) | |||||||
\(734\) | 5.78235e9 | − | 9.03968e9i | 0.539719 | − | 0.843756i | ||||
\(735\) | −6.31139e8 | −0.0586299 | ||||||||
\(736\) | −3.72771e9 | − | 1.22138e10i | −0.344644 | − | 1.12922i | ||||
\(737\) | 1.00583e10 | 0.925528 | ||||||||
\(738\) | 1.75939e9 | − | 2.75050e9i | 0.161126 | − | 0.251892i | ||||
\(739\) | 6.96883e9i | 0.635191i | 0.948226 | + | 0.317595i | \(0.102875\pi\) | ||||
−0.948226 | + | 0.317595i | \(0.897125\pi\) | |||||||
\(740\) | −1.34515e9 | − | 2.91264e9i | −0.122028 | − | 0.264226i | ||||
\(741\) | 5.80383e8i | 0.0524024i | ||||||||
\(742\) | 1.73348e9 | + | 1.10884e9i | 0.155778 | + | 0.0996451i | ||||
\(743\) | 2.95248e9 | 0.264074 | 0.132037 | − | 0.991245i | \(-0.457848\pi\) | ||||
0.132037 | + | 0.991245i | \(0.457848\pi\) | |||||||
\(744\) | −1.14191e9 | + | 8.31825e9i | −0.101654 | + | 0.740503i | ||||
\(745\) | 7.22140e9 | 0.639844 | ||||||||
\(746\) | −4.02917e9 | − | 2.57731e9i | −0.355328 | − | 0.227290i | ||||
\(747\) | − | 2.46921e9i | − | 0.216739i | ||||||
\(748\) | 1.99067e10 | − | 9.19354e9i | 1.73918 | − | 0.803206i | ||||
\(749\) | − | 1.37049e10i | − | 1.19176i | ||||||
\(750\) | −3.10283e9 | + | 4.85074e9i | −0.268562 | + | 0.419849i | ||||
\(751\) | 1.61693e10 | 1.39300 | 0.696502 | − | 0.717555i | \(-0.254739\pi\) | ||||
0.696502 | + | 0.717555i | \(0.254739\pi\) | |||||||
\(752\) | 1.41280e10 | − | 1.65874e10i | 1.21149 | − | 1.42238i | ||||
\(753\) | −1.36873e9 | −0.116825 | ||||||||
\(754\) | 8.73658e8 | − | 1.36581e9i | 0.0742235 | − | 0.116036i | ||||
\(755\) | 3.78231e9i | 0.319848i | ||||||||
\(756\) | 1.84847e9 | − | 8.53683e8i | 0.155592 | − | 0.0718572i | ||||
\(757\) | 2.26203e10i | 1.89523i | 0.319412 | + | 0.947616i | \(0.396515\pi\) | ||||
−0.319412 | + | 0.947616i | \(0.603485\pi\) | |||||||
\(758\) | −1.81725e10 | − | 1.16242e10i | −1.51555 | − | 0.969443i | ||||
\(759\) | 1.53312e10 | 1.27271 | ||||||||
\(760\) | −1.24108e9 | − | 1.70372e8i | −0.102554 | − | 0.0140783i | ||||
\(761\) | 8.62411e9 | 0.709362 | 0.354681 | − | 0.934987i | \(-0.384589\pi\) | ||||
0.354681 | + | 0.934987i | \(0.384589\pi\) | |||||||
\(762\) | −7.05596e9 | − | 4.51343e9i | −0.577715 | − | 0.369543i | ||||
\(763\) | − | 1.94432e10i | − | 1.58465i | ||||||
\(764\) | −4.92826e8 | − | 1.06711e9i | −0.0399822 | − | 0.0865731i | ||||
\(765\) | − | 2.07809e9i | − | 0.167823i | ||||||
\(766\) | 3.02577e8 | − | 4.73026e8i | 0.0243240 | − | 0.0380263i | ||||
\(767\) | −7.04563e9 | −0.563814 | ||||||||
\(768\) | −7.15541e9 | + | 1.15327e9i | −0.569994 | + | 0.0918685i | ||||
\(769\) | −7.71654e9 | −0.611900 | −0.305950 | − | 0.952048i | \(-0.598974\pi\) | ||||
−0.305950 | + | 0.952048i | \(0.598974\pi\) | |||||||
\(770\) | 5.56963e9 | − | 8.70714e9i | 0.439652 | − | 0.687318i | ||||
\(771\) | 1.12578e10i | 0.884635i | ||||||||
\(772\) | −1.62440e9 | − | 3.51730e9i | −0.127067 | − | 0.275137i | ||||
\(773\) | 6.35693e8i | 0.0495016i | 0.999694 | + | 0.0247508i | \(0.00787923\pi\) | ||||
−0.999694 | + | 0.0247508i | \(0.992121\pi\) | |||||||
\(774\) | 3.01208e9 | + | 1.92672e9i | 0.233493 | + | 0.149357i | ||||
\(775\) | −1.27368e10 | −0.982890 | ||||||||
\(776\) | −4.99354e9 | − | 6.85499e8i | −0.383613 | − | 0.0526612i | ||||
\(777\) | −3.98754e9 | −0.304952 | ||||||||
\(778\) | 1.74652e10 | + | 1.11719e10i | 1.32968 | + | 0.850544i | ||||
\(779\) | 2.49681e9i | 0.189236i | ||||||||
\(780\) | 1.46666e9 | − | 6.77350e8i | 0.110662 | − | 0.0511072i | ||||
\(781\) | − | 1.34898e10i | − | 1.01327i | ||||||
\(782\) | −8.72904e9 | + | 1.36463e10i | −0.652744 | + | 1.02045i | ||||
\(783\) | −8.27623e8 | −0.0616122 | ||||||||
\(784\) | 1.81059e9 | − | 2.12578e9i | 0.134188 | − | 0.157548i | ||||
\(785\) | 2.07031e9 | 0.152753 | ||||||||
\(786\) | 2.01546e9 | − | 3.15082e9i | 0.148046 | − | 0.231443i | ||||
\(787\) | − | 1.72173e10i | − | 1.25908i | −0.776968 | − | 0.629540i | \(-0.783243\pi\) | ||
0.776968 | − | 0.629540i | \(-0.216757\pi\) | |||||||
\(788\) | 6.65838e9 | − | 3.07505e9i | 0.484760 | − | 0.223877i | ||||
\(789\) | − | 8.91648e9i | − | 0.646285i | ||||||
\(790\) | −8.62821e9 | − | 5.51914e9i | −0.622624 | − | 0.398269i | ||||
\(791\) | −1.59895e10 | −1.14873 | ||||||||
\(792\) | 1.18340e9 | − | 8.62054e9i | 0.0846437 | − | 0.616589i | ||||
\(793\) | 1.06055e10 | 0.755220 | ||||||||
\(794\) | −1.18219e10 | − | 7.56204e9i | −0.838139 | − | 0.536126i | ||||
\(795\) | − | 8.33446e8i | − | 0.0588292i | ||||||
\(796\) | 1.29351e8 | + | 2.80083e8i | 0.00909021 | + | 0.0196830i | ||||
\(797\) | − | 2.34758e10i | − | 1.64254i | −0.570537 | − | 0.821272i | \(-0.693265\pi\) | ||
0.570537 | − | 0.821272i | \(-0.306735\pi\) | |||||||
\(798\) | −8.38991e8 | + | 1.31162e9i | −0.0584450 | + | 0.0913685i | ||||
\(799\) | −2.76398e10 | −1.91700 | ||||||||
\(800\) | −3.20944e9 | − | 1.05157e10i | −0.221623 | − | 0.726145i | ||||
\(801\) | 5.02173e8 | 0.0345255 | ||||||||
\(802\) | −1.05412e10 | + | 1.64793e10i | −0.721571 | + | 1.12805i | ||||
\(803\) | 2.82966e10i | 1.92854i | ||||||||
\(804\) | 1.76830e9 | + | 3.82888e9i | 0.119994 | + | 0.259822i | ||||
\(805\) | 7.63612e9i | 0.515925i | ||||||||
\(806\) | 6.97520e9 | + | 4.46177e9i | 0.469228 | + | 0.300148i | ||||
\(807\) | 9.61194e9 | 0.643804 | ||||||||
\(808\) | −1.34003e9 | + | 9.76148e9i | −0.0893664 | + | 0.650993i | ||||
\(809\) | −7.71245e9 | −0.512121 | −0.256060 | − | 0.966661i | \(-0.582425\pi\) | ||||
−0.256060 | + | 0.966661i | \(0.582425\pi\) | |||||||
\(810\) | −6.94690e8 | − | 4.44367e8i | −0.0459297 | − | 0.0293795i | ||||
\(811\) | 2.49188e10i | 1.64041i | 0.572067 | + | 0.820207i | \(0.306142\pi\) | ||||
−0.572067 | + | 0.820207i | \(0.693858\pi\) | |||||||
\(812\) | 3.94878e9 | − | 1.82367e9i | 0.258831 | − | 0.119536i | ||||
\(813\) | − | 7.90268e9i | − | 0.515772i | ||||||
\(814\) | −9.18263e9 | + | 1.43554e10i | −0.596735 | + | 0.932891i | ||||
\(815\) | −9.92672e9 | −0.642324 | ||||||||
\(816\) | 6.99937e9 | + | 5.96158e9i | 0.450965 | + | 0.384101i | ||||
\(817\) | −2.73427e9 | −0.175414 | ||||||||
\(818\) | 9.74576e9 | − | 1.52358e10i | 0.622557 | − | 0.973259i | ||||
\(819\) | − | 2.00792e9i | − | 0.127718i | ||||||
\(820\) | 6.30958e9 | − | 2.91396e9i | 0.399625 | − | 0.184559i | ||||
\(821\) | 1.20840e9i | 0.0762098i | 0.999274 | + | 0.0381049i | \(0.0121321\pi\) | ||||
−0.999274 | + | 0.0381049i | \(0.987868\pi\) | |||||||
\(822\) | 1.24410e10 | + | 7.95801e9i | 0.781272 | + | 0.499750i | ||||
\(823\) | 8.05412e9 | 0.503638 | 0.251819 | − | 0.967774i | \(-0.418971\pi\) | ||||
0.251819 | + | 0.967774i | \(0.418971\pi\) | |||||||
\(824\) | 2.65551e10 | + | 3.64541e9i | 1.65350 | + | 0.226987i | ||||
\(825\) | 1.31997e10 | 0.818416 | ||||||||
\(826\) | −1.59225e10 | − | 1.01850e10i | −0.983063 | − | 0.628828i | ||||
\(827\) | 2.99837e9i | 0.184338i | 0.995743 | + | 0.0921692i | \(0.0293801\pi\) | ||||
−0.995743 | + | 0.0921692i | \(0.970620\pi\) | |||||||
\(828\) | 2.69529e9 | + | 5.83609e9i | 0.165006 | + | 0.357286i | ||||
\(829\) | − | 7.99710e8i | − | 0.0487519i | −0.999703 | − | 0.0243760i | \(-0.992240\pi\) | ||
0.999703 | − | 0.0243760i | \(-0.00775987\pi\) | |||||||
\(830\) | 2.83216e9 | − | 4.42759e9i | 0.171927 | − | 0.268778i | ||||
\(831\) | −8.92955e9 | −0.539792 | ||||||||
\(832\) | −1.92609e9 | + | 6.88312e9i | −0.115943 | + | 0.414337i | ||||
\(833\) | −3.54221e9 | −0.212333 | ||||||||
\(834\) | −4.19293e9 | + | 6.55491e9i | −0.250286 | + | 0.391278i | ||||
\(835\) | − | 3.93645e9i | − | 0.233993i | ||||||
\(836\) | 2.78986e9 | + | 6.04087e9i | 0.165143 | + | 0.357583i | ||||
\(837\) | − | 4.22667e9i | − | 0.249149i | ||||||
\(838\) | 1.37551e10 | + | 8.79865e9i | 0.807442 | + | 0.516490i | ||||
\(839\) | 7.15014e9 | 0.417972 | 0.208986 | − | 0.977919i | \(-0.432984\pi\) | ||||
0.208986 | + | 0.977919i | \(0.432984\pi\) | |||||||
\(840\) | 4.29369e9 | + | 5.89426e8i | 0.249950 | + | 0.0343124i | ||||
\(841\) | 1.54819e10 | 0.897506 | ||||||||
\(842\) | 8.54280e9 | + | 5.46451e9i | 0.493183 | + | 0.315471i | ||||
\(843\) | − | 7.69571e9i | − | 0.442438i | ||||||
\(844\) | −1.64760e10 | + | 7.60912e9i | −0.943306 | + | 0.435648i | ||||
\(845\) | 7.01311e9i | 0.399864i | ||||||||
\(846\) | −5.91033e9 | + | 9.23976e9i | −0.335595 | + | 0.524644i | ||||
\(847\) | −3.91530e10 | −2.21398 | ||||||||
\(848\) | 2.80718e9 | + | 2.39097e9i | 0.158083 | + | 0.134644i | ||||
\(849\) | −1.08576e9 | −0.0608913 | ||||||||
\(850\) | −7.51542e9 | + | 1.17490e10i | −0.419746 | + | 0.656200i | ||||
\(851\) | − | 1.25896e10i | − | 0.700261i | ||||||
\(852\) | 5.13513e9 | − | 2.37157e9i | 0.284455 | − | 0.131370i | ||||
\(853\) | − | 5.59947e9i | − | 0.308905i | −0.988000 | − | 0.154453i | \(-0.950639\pi\) | ||
0.988000 | − | 0.154453i | \(-0.0493614\pi\) | |||||||
\(854\) | 2.39674e10 | + | 1.53310e10i | 1.31680 | + | 0.842305i | ||||
\(855\) | 6.30616e8 | 0.0345051 | ||||||||
\(856\) | 3.33997e9 | − | 2.43301e10i | 0.182005 | − | 1.32582i | ||||
\(857\) | −1.20730e10 | −0.655213 | −0.327606 | − | 0.944814i | \(-0.606242\pi\) | ||||
−0.327606 | + | 0.944814i | \(0.606242\pi\) | |||||||
\(858\) | −7.22868e9 | − | 4.62391e9i | −0.390709 | − | 0.249922i | ||||
\(859\) | − | 2.95709e10i | − | 1.59180i | −0.605427 | − | 0.795901i | \(-0.706998\pi\) | ||
0.605427 | − | 0.795901i | \(-0.293002\pi\) | |||||||
\(860\) | 3.19109e9 | + | 6.90965e9i | 0.171078 | + | 0.370434i | ||||
\(861\) | − | 8.63810e9i | − | 0.461219i | ||||||
\(862\) | −4.31167e9 | + | 6.74054e9i | −0.229282 | + | 0.358442i | ||||
\(863\) | 1.10938e10 | 0.587546 | 0.293773 | − | 0.955875i | \(-0.405089\pi\) | ||||
0.293773 | + | 0.955875i | \(0.405089\pi\) | |||||||
\(864\) | 3.48961e9 | − | 1.06504e9i | 0.184068 | − | 0.0561784i | ||||
\(865\) | 2.20824e9 | 0.116009 | ||||||||
\(866\) | 2.99003e9 | − | 4.67439e9i | 0.156445 | − | 0.244575i | ||||
\(867\) | − | 5.83982e8i | − | 0.0304321i | ||||||
\(868\) | 9.31349e9 | + | 2.01664e10i | 0.483385 | + | 1.04667i | ||||
\(869\) | 5.44040e10i | 2.81230i | ||||||||
\(870\) | −1.48402e9 | − | 9.49274e8i | −0.0764053 | − | 0.0488736i | ||||
\(871\) | 4.15916e9 | 0.213276 | ||||||||
\(872\) | 4.73843e9 | − | 3.45172e10i | 0.242006 | − | 1.76290i | ||||
\(873\) | 2.53732e9 | 0.129070 | ||||||||
\(874\) | −4.14110e9 | − | 2.64891e9i | −0.209810 | − | 0.134207i | ||||
\(875\) | 1.52340e10i | 0.768752i | ||||||||
\(876\) | −1.07716e10 | + | 4.97466e9i | −0.541397 | + | 0.250034i | ||||
\(877\) | − | 1.31675e10i | − | 0.659179i | −0.944124 | − | 0.329589i | \(-0.893090\pi\) | ||
0.944124 | − | 0.329589i | \(-0.106910\pi\) | |||||||
\(878\) | −6.51657e9 | + | 1.01875e10i | −0.324929 | + | 0.507969i | ||||
\(879\) | −4.15593e9 | −0.206399 | ||||||||
\(880\) | 1.20096e10 | − | 1.41003e10i | 0.594074 | − | 0.697490i | ||||
\(881\) | 6.99376e9 | 0.344584 | 0.172292 | − | 0.985046i | \(-0.444883\pi\) | ||||
0.172292 | + | 0.985046i | \(0.444883\pi\) | |||||||
\(882\) | −7.57444e8 | + | 1.18413e9i | −0.0371716 | + | 0.0581112i | ||||
\(883\) | 4.62869e9i | 0.226254i | 0.993581 | + | 0.113127i | \(0.0360866\pi\) | ||||
−0.993581 | + | 0.113127i | \(0.963913\pi\) | |||||||
\(884\) | 8.23151e9 | − | 3.80157e9i | 0.400771 | − | 0.185089i | ||||
\(885\) | 7.65544e9i | 0.371252i | ||||||||
\(886\) | 9.71368e9 | + | 6.21347e9i | 0.469208 | + | 0.300135i | ||||
\(887\) | −2.71747e10 | −1.30747 | −0.653735 | − | 0.756724i | \(-0.726799\pi\) | ||||
−0.653735 | + | 0.756724i | \(0.726799\pi\) | |||||||
\(888\) | −7.07900e9 | − | 9.71785e8i | −0.339255 | − | 0.0465720i | ||||
\(889\) | −2.21596e10 | −1.05781 | ||||||||
\(890\) | 9.00455e8 | + | 5.75987e8i | 0.0428151 | + | 0.0273872i | ||||
\(891\) | 4.38027e9i | 0.207457i | ||||||||
\(892\) | 1.46048e9 | + | 3.16236e9i | 0.0688998 | + | 0.149188i | ||||
\(893\) | − | 8.38755e9i | − | 0.394144i | ||||||
\(894\) | 8.66657e9 | − | 1.35487e10i | 0.405663 | − | 0.634184i | ||||
\(895\) | 7.43034e9 | 0.346440 | ||||||||
\(896\) | −1.43029e10 | + | 1.27709e10i | −0.664272 | + | 0.593123i | ||||
\(897\) | 6.33951e9 | 0.293280 | ||||||||
\(898\) | 1.50433e10 | − | 2.35175e10i | 0.693227 | − | 1.08374i | ||||
\(899\) | − | 9.02919e9i | − | 0.414467i | ||||||
\(900\) | 2.32056e9 | + | 5.02468e9i | 0.106107 | + | 0.229752i | ||||
\(901\) | − | 4.67764e9i | − | 0.213054i | ||||||
\(902\) | −3.10978e10 | − | 1.98921e10i | −1.41093 | − | 0.902522i | ||||
\(903\) | 9.45961e9 | 0.427530 | ||||||||
\(904\) | −2.83859e10 | − | 3.89674e9i | −1.27795 | − | 0.175433i | ||||
\(905\) | 1.87605e10 | 0.841345 | ||||||||
\(906\) | 7.09631e9 | + | 4.53924e9i | 0.317018 | + | 0.202784i | ||||
\(907\) | 3.63626e10i | 1.61819i | 0.587679 | + | 0.809095i | \(0.300042\pi\) | ||||
−0.587679 | + | 0.809095i | \(0.699958\pi\) | |||||||
\(908\) | 5.34894e8 | − | 2.47031e8i | 0.0237120 | − | 0.0109509i | ||||
\(909\) | − | 4.96001e9i | − | 0.219033i | ||||||
\(910\) | 2.30306e9 | − | 3.60044e9i | 0.101312 | − | 0.158384i | ||||
\(911\) | 3.56701e10 | 1.56311 | 0.781556 | − | 0.623834i | \(-0.214426\pi\) | ||||
0.781556 | + | 0.623834i | \(0.214426\pi\) | |||||||
\(912\) | −1.80909e9 | + | 2.12402e9i | −0.0789731 | + | 0.0927207i | ||||
\(913\) | −2.79175e10 | −1.21403 | ||||||||
\(914\) | 6.63564e9 | − | 1.03737e10i | 0.287456 | − | 0.449387i | ||||
\(915\) | − | 1.15234e10i | − | 0.497286i | ||||||
\(916\) | −1.93277e10 | + | 8.92612e9i | −0.830894 | + | 0.383733i | ||||
\(917\) | − | 9.89533e9i | − | 0.423777i | ||||||
\(918\) | −3.89889e9 | − | 2.49397e9i | −0.166338 | − | 0.106400i | ||||
\(919\) | 3.65009e10 | 1.55131 | 0.775657 | − | 0.631155i | \(-0.217419\pi\) | ||||
0.775657 | + | 0.631155i | \(0.217419\pi\) | |||||||
\(920\) | −1.86096e9 | + | 1.35563e10i | −0.0787917 | + | 0.573961i | ||||
\(921\) | −7.93347e9 | −0.334622 | ||||||||
\(922\) | −2.53330e10 | − | 1.62046e10i | −1.06446 | − | 0.680894i | ||||
\(923\) | − | 5.57809e9i | − | 0.233496i | ||||||
\(924\) | −9.65194e9 | − | 2.08993e10i | −0.402497 | − | 0.871524i | ||||
\(925\) | − | 1.08393e10i | − | 0.450302i | ||||||
\(926\) | −7.74516e9 | + | 1.21082e10i | −0.320547 | + | 0.501119i | ||||
\(927\) | −1.34932e10 | −0.556334 | ||||||||
\(928\) | 7.45464e9 | − | 2.27519e9i | 0.306202 | − | 0.0934543i | ||||
\(929\) | 6.38374e8 | 0.0261228 | 0.0130614 | − | 0.999915i | \(-0.495842\pi\) | ||||
0.0130614 | + | 0.999915i | \(0.495842\pi\) | |||||||
\(930\) | 4.84795e9 | − | 7.57892e9i | 0.197637 | − | 0.308970i | ||||
\(931\) | − | 1.07492e9i | − | 0.0436567i | ||||||
\(932\) | 2.78531e9 | + | 6.03102e9i | 0.112699 | + | 0.244025i | ||||
\(933\) | 2.57198e10i | 1.03677i | ||||||||
\(934\) | 6.03582e9 | + | 3.86088e9i | 0.242394 | + | 0.155050i | ||||
\(935\) | −2.34954e10 | −0.940033 | ||||||||
\(936\) | 4.89342e8 | − | 3.56463e9i | 0.0195050 | − | 0.142085i | ||||
\(937\) | 1.01827e10 | 0.404367 | 0.202183 | − | 0.979348i | \(-0.435196\pi\) | ||||
0.202183 | + | 0.979348i | \(0.435196\pi\) | |||||||
\(938\) | 9.39935e9 | + | 6.01241e9i | 0.371867 | + | 0.237869i | ||||
\(939\) | − | 1.92190e10i | − | 0.757531i | ||||||
\(940\) | −2.11958e10 | + | 9.78888e9i | −0.832343 | + | 0.384402i | ||||
\(941\) | − | 3.07639e10i | − | 1.20359i | −0.798652 | − | 0.601793i | \(-0.794453\pi\) | ||
0.798652 | − | 0.601793i | \(-0.205547\pi\) | |||||||
\(942\) | 2.48462e9 | − | 3.88427e9i | 0.0968462 | − | 0.151402i | ||||
\(943\) | 2.72726e10 | 1.05910 | ||||||||
\(944\) | −2.57848e10 | − | 2.19617e10i | −0.997611 | − | 0.849696i | ||||
\(945\) | −2.18171e9 | −0.0840981 | ||||||||
\(946\) | 2.17839e10 | − | 3.40553e10i | 0.836598 | − | 1.30787i | ||||
\(947\) | − | 1.28317e10i | − | 0.490974i | −0.969400 | − | 0.245487i | \(-0.921052\pi\) | ||
0.969400 | − | 0.245487i | \(-0.0789479\pi\) | |||||||
\(948\) | −2.07098e10 | + | 9.56445e9i | −0.789492 | + | 0.364612i | ||||
\(949\) | 1.17008e10i | 0.444408i | ||||||||
\(950\) | −3.56535e9 | − | 2.28062e9i | −0.134918 | − | 0.0863019i | ||||
\(951\) | 5.20712e8 | 0.0196320 | ||||||||
\(952\) | 2.40980e10 | + | 3.30810e9i | 0.905213 | + | 0.124265i | ||||
\(953\) | −1.24916e10 | −0.467511 | −0.233756 | − | 0.972295i | \(-0.575102\pi\) | ||||
−0.233756 | + | 0.972295i | \(0.575102\pi\) | |||||||
\(954\) | −1.56370e9 | − | 1.00024e9i | −0.0583087 | − | 0.0372979i | ||||
\(955\) | 1.25949e9i | 0.0467932i | ||||||||
\(956\) | 1.08942e9 | + | 2.35891e9i | 0.0403266 | + | 0.0873188i | ||||
\(957\) | 9.35731e9i | 0.345111i | ||||||||
\(958\) | 1.81355e7 | − | 2.83516e7i | 0.000666422 | − | 0.00104183i | ||||
\(959\) | 3.90715e10 | 1.43052 | ||||||||
\(960\) | 7.47886e9 | + | 2.09279e9i | 0.272826 | + | 0.0763443i | ||||
\(961\) | 1.85995e10 | 0.676035 | ||||||||
\(962\) | −3.79706e9 | + | 5.93603e9i | −0.137510 | + | 0.214973i | ||||
\(963\) | 1.23626e10i | 0.446086i | ||||||||
\(964\) | 1.82597e9 | + | 3.95376e9i | 0.0656483 | + | 0.142148i | ||||
\(965\) | 4.15139e9i | 0.148713i | ||||||||
\(966\) | 1.43267e10 | + | 9.16428e9i | 0.511361 | + | 0.327098i | ||||
\(967\) | 4.23912e10 | 1.50759 | 0.753795 | − | 0.657110i | \(-0.228221\pi\) | ||||
0.753795 | + | 0.657110i | \(0.228221\pi\) | |||||||
\(968\) | −6.95076e10 | − | 9.54181e9i | −2.46302 | − | 0.338117i | ||||
\(969\) | 3.53928e9 | 0.124963 | ||||||||
\(970\) | 4.54971e9 | + | 2.91028e9i | 0.160060 | + | 0.102384i | ||||
\(971\) | − | 3.64229e10i | − | 1.27676i | −0.769723 | − | 0.638378i | \(-0.779606\pi\) | ||
0.769723 | − | 0.638378i | \(-0.220394\pi\) | |||||||
\(972\) | −1.66743e9 | + | 7.70070e8i | −0.0582391 | + | 0.0268967i | ||||
\(973\) | 2.05861e10i | 0.716438i | ||||||||
\(974\) | 4.68454e9 | − | 7.32346e9i | 0.162447 | − | 0.253957i | ||||
\(975\) | 5.45811e9 | 0.188593 | ||||||||
\(976\) | 3.88126e10 | + | 3.30579e10i | 1.33628 | + | 1.13815i | ||||
\(977\) | −9.15850e9 | −0.314191 | −0.157095 | − | 0.987583i | \(-0.550213\pi\) | ||||
−0.157095 | + | 0.987583i | \(0.550213\pi\) | |||||||
\(978\) | −1.19133e10 | + | 1.86243e10i | −0.407236 | + | 0.636641i | ||||
\(979\) | − | 5.67769e9i | − | 0.193389i | ||||||
\(980\) | −2.71637e9 | + | 1.25451e9i | −0.0921930 | + | 0.0425776i | ||||
\(981\) | 1.75389e10i | 0.593145i | ||||||||
\(982\) | −1.37838e10 | − | 8.81697e9i | −0.464492 | − | 0.297118i | ||||
\(983\) | 1.91841e9 | 0.0644176 | 0.0322088 | − | 0.999481i | \(-0.489746\pi\) | ||||
0.0322088 | + | 0.999481i | \(0.489746\pi\) | |||||||
\(984\) | 2.10515e9 | − | 1.53350e10i | 0.0704370 | − | 0.513100i | ||||
\(985\) | −7.85874e9 | −0.262015 | ||||||||
\(986\) | −8.32896e9 | − | 5.32772e9i | −0.276708 | − | 0.177000i | ||||
\(987\) | 2.90180e10i | 0.960632i | ||||||||
\(988\) | 1.15362e9 | + | 2.49792e9i | 0.0380551 | + | 0.0824005i | ||||
\(989\) | 2.98664e10i | 0.981737i | ||||||||
\(990\) | −5.02412e9 | + | 7.85433e9i | −0.164565 | + | 0.257268i | ||||
\(991\) | 4.46181e9 | 0.145631 | 0.0728154 | − | 0.997345i | \(-0.476802\pi\) | ||||
0.0728154 | + | 0.997345i | \(0.476802\pi\) | |||||||
\(992\) | 1.16194e10 | + | 3.80709e10i | 0.377914 | + | 1.23823i | ||||
\(993\) | −1.69040e10 | −0.547858 | ||||||||
\(994\) | 8.06359e9 | − | 1.26060e10i | 0.260421 | − | 0.407123i | ||||
\(995\) | − | 3.30576e8i | − | 0.0106387i | ||||||
\(996\) | −4.90802e9 | − | 1.06273e10i | −0.157398 | − | 0.340812i | ||||
\(997\) | − | 2.09203e10i | − | 0.668552i | −0.942475 | − | 0.334276i | \(-0.891508\pi\) | ||
0.942475 | − | 0.334276i | \(-0.108492\pi\) | |||||||
\(998\) | 8.60161e9 | + | 5.50212e9i | 0.273919 | + | 0.175216i | ||||
\(999\) | 3.59698e9 | 0.114146 |
(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 | 24.8.d.a.13.6 | yes | 14 | |
3.2 | odd | 2 | 72.8.d.d.37.9 | 14 | |||
4.3 | odd | 2 | 96.8.d.a.49.13 | 14 | |||
8.3 | odd | 2 | 96.8.d.a.49.2 | 14 | |||
8.5 | even | 2 | inner | 24.8.d.a.13.5 | ✓ | 14 | |
12.11 | even | 2 | 288.8.d.d.145.4 | 14 | |||
24.5 | odd | 2 | 72.8.d.d.37.10 | 14 | |||
24.11 | even | 2 | 288.8.d.d.145.11 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.8.d.a.13.5 | ✓ | 14 | 8.5 | even | 2 | inner | |
24.8.d.a.13.6 | yes | 14 | 1.1 | even | 1 | trivial | |
72.8.d.d.37.9 | 14 | 3.2 | odd | 2 | |||
72.8.d.d.37.10 | 14 | 24.5 | odd | 2 | |||
96.8.d.a.49.2 | 14 | 8.3 | odd | 2 | |||
96.8.d.a.49.13 | 14 | 4.3 | odd | 2 | |||
288.8.d.d.145.4 | 14 | 12.11 | even | 2 | |||
288.8.d.d.145.11 | 14 | 24.11 | even | 2 |