Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,8,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.49908020387\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Root | \(-4.85268 - 2.90715i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.8.b.a.5.1 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.70536 | + | 5.81430i | −0.857840 | + | 0.513916i | ||||
\(3\) | − | 40.2163i | − | 0.859959i | −0.902839 | − | 0.429979i | \(-0.858521\pi\) | ||
0.902839 | − | 0.429979i | \(-0.141479\pi\) | |||||||
\(4\) | 60.3879 | − | 112.860i | 0.471781 | − | 0.881716i | ||||
\(5\) | − | 324.492i | − | 1.16094i | −0.814283 | − | 0.580468i | \(-0.802870\pi\) | ||
0.814283 | − | 0.580468i | \(-0.197130\pi\) | |||||||
\(6\) | 233.829 | + | 390.313i | 0.441947 | + | 0.737707i | ||||
\(7\) | −956.960 | −1.05451 | −0.527255 | − | 0.849707i | \(-0.676779\pi\) | ||||
−0.527255 | + | 0.849707i | \(0.676779\pi\) | |||||||
\(8\) | 70.1132 | + | 1446.46i | 0.0484155 | + | 0.998827i | ||||
\(9\) | 569.651 | 0.260471 | ||||||||
\(10\) | 1886.69 | + | 3149.31i | 0.596624 | + | 0.995898i | ||||
\(11\) | − | 5452.20i | − | 1.23509i | −0.786537 | − | 0.617544i | \(-0.788128\pi\) | ||
0.786537 | − | 0.617544i | \(-0.211872\pi\) | |||||||
\(12\) | −4538.80 | − | 2428.58i | −0.758239 | − | 0.405712i | ||||
\(13\) | 6289.38i | 0.793973i | 0.917824 | + | 0.396987i | \(0.129944\pi\) | ||||
−0.917824 | + | 0.396987i | \(0.870056\pi\) | |||||||
\(14\) | 9287.64 | − | 5564.05i | 0.904602 | − | 0.541930i | ||||
\(15\) | −13049.8 | −0.998357 | ||||||||
\(16\) | −9090.60 | − | 13630.7i | −0.554846 | − | 0.831953i | ||||
\(17\) | 34587.3 | 1.70744 | 0.853720 | − | 0.520733i | \(-0.174341\pi\) | ||||
0.853720 | + | 0.520733i | \(0.174341\pi\) | |||||||
\(18\) | −5528.66 | + | 3312.12i | −0.223443 | + | 0.133860i | ||||
\(19\) | 14595.6i | 0.488186i | 0.969752 | + | 0.244093i | \(0.0784903\pi\) | ||||
−0.969752 | + | 0.244093i | \(0.921510\pi\) | |||||||
\(20\) | −36622.0 | − | 19595.4i | −1.02362 | − | 0.547707i | ||||
\(21\) | 38485.4i | 0.906835i | ||||||||
\(22\) | 31700.7 | + | 52915.6i | 0.634731 | + | 1.05951i | ||||
\(23\) | −24667.5 | −0.422743 | −0.211372 | − | 0.977406i | \(-0.567793\pi\) | ||||
−0.211372 | + | 0.977406i | \(0.567793\pi\) | |||||||
\(24\) | 58171.1 | − | 2819.69i | 0.858950 | − | 0.0416354i | ||||
\(25\) | −27169.8 | −0.347774 | ||||||||
\(26\) | −36568.3 | − | 61040.6i | −0.408036 | − | 0.681102i | ||||
\(27\) | − | 110862.i | − | 1.08395i | ||||||
\(28\) | −57788.8 | + | 108002.i | −0.497497 | + | 0.929779i | ||||
\(29\) | − | 171116.i | − | 1.30286i | −0.758710 | − | 0.651429i | \(-0.774170\pi\) | ||
0.758710 | − | 0.651429i | \(-0.225830\pi\) | |||||||
\(30\) | 126653. | − | 75875.7i | 0.856431 | − | 0.513072i | ||||
\(31\) | 111688. | 0.673352 | 0.336676 | − | 0.941620i | \(-0.390697\pi\) | ||||
0.336676 | + | 0.941620i | \(0.390697\pi\) | |||||||
\(32\) | 167481. | + | 79435.5i | 0.903524 | + | 0.428539i | ||||
\(33\) | −219267. | −1.06212 | ||||||||
\(34\) | −335682. | + | 201101.i | −1.46471 | + | 0.877480i | ||||
\(35\) | 310526.i | 1.22422i | ||||||||
\(36\) | 34400.0 | − | 64290.6i | 0.122885 | − | 0.229662i | ||||
\(37\) | 103636.i | 0.336360i | 0.985756 | + | 0.168180i | \(0.0537890\pi\) | ||||
−0.985756 | + | 0.168180i | \(0.946211\pi\) | |||||||
\(38\) | −84863.4 | − | 141656.i | −0.250887 | − | 0.418786i | ||||
\(39\) | 252935. | 0.682784 | ||||||||
\(40\) | 469363. | − | 22751.1i | 1.15958 | − | 0.0562074i | ||||
\(41\) | 71691.3 | 0.162451 | 0.0812256 | − | 0.996696i | \(-0.474117\pi\) | ||||
0.0812256 | + | 0.996696i | \(0.474117\pi\) | |||||||
\(42\) | −223765. | − | 373514.i | −0.466037 | − | 0.777920i | ||||
\(43\) | 328419.i | 0.629925i | 0.949104 | + | 0.314962i | \(0.101992\pi\) | ||||
−0.949104 | + | 0.314962i | \(0.898008\pi\) | |||||||
\(44\) | −615334. | − | 329247.i | −1.08900 | − | 0.582690i | ||||
\(45\) | − | 184847.i | − | 0.302391i | ||||||
\(46\) | 239406. | − | 143424.i | 0.362646 | − | 0.217255i | ||||
\(47\) | 119043. | 0.167248 | 0.0836241 | − | 0.996497i | \(-0.473350\pi\) | ||||
0.0836241 | + | 0.996497i | \(0.473350\pi\) | |||||||
\(48\) | −548177. | + | 365590.i | −0.715445 | + | 0.477145i | ||||
\(49\) | 92230.3 | 0.111992 | ||||||||
\(50\) | 263693. | − | 157973.i | 0.298334 | − | 0.178727i | ||||
\(51\) | − | 1.39097e6i | − | 1.46833i | ||||||
\(52\) | 709817. | + | 379802.i | 0.700059 | + | 0.374581i | ||||
\(53\) | 1.04011e6i | 0.959648i | 0.877365 | + | 0.479824i | \(0.159300\pi\) | ||||
−0.877365 | + | 0.479824i | \(0.840700\pi\) | |||||||
\(54\) | 644586. | + | 1.07596e6i | 0.557061 | + | 0.929859i | ||||
\(55\) | −1.76919e6 | −1.43386 | ||||||||
\(56\) | −67095.6 | − | 1.38420e6i | −0.0510547 | − | 1.05327i | ||||
\(57\) | 586982. | 0.419820 | ||||||||
\(58\) | 994918. | + | 1.66074e6i | 0.669559 | + | 1.11764i | ||||
\(59\) | 225984.i | 0.143250i | 0.997432 | + | 0.0716250i | \(0.0228185\pi\) | ||||
−0.997432 | + | 0.0716250i | \(0.977182\pi\) | |||||||
\(60\) | −788053. | + | 1.47280e6i | −0.471006 | + | 0.880268i | ||||
\(61\) | − | 1.55268e6i | − | 0.875843i | −0.899013 | − | 0.437922i | \(-0.855715\pi\) | ||
0.899013 | − | 0.437922i | \(-0.144285\pi\) | |||||||
\(62\) | −1.08398e6 | + | 649390.i | −0.577629 | + | 0.346047i | ||||
\(63\) | −545133. | −0.274670 | ||||||||
\(64\) | −2.08732e6 | + | 202831.i | −0.995312 | + | 0.0967175i | ||||
\(65\) | 2.04085e6 | 0.921753 | ||||||||
\(66\) | 2.12807e6 | − | 1.27489e6i | 0.911133 | − | 0.545843i | ||||
\(67\) | − | 316375.i | − | 0.128511i | −0.997933 | − | 0.0642555i | \(-0.979533\pi\) | ||
0.997933 | − | 0.0642555i | \(-0.0204673\pi\) | |||||||
\(68\) | 2.08865e6 | − | 3.90351e6i | 0.805537 | − | 1.50548i | ||||
\(69\) | 992033.i | 0.363542i | ||||||||
\(70\) | −1.80549e6 | − | 3.01376e6i | −0.629146 | − | 1.05019i | ||||
\(71\) | 538965. | 0.178713 | 0.0893566 | − | 0.996000i | \(-0.471519\pi\) | ||||
0.0893566 | + | 0.996000i | \(0.471519\pi\) | |||||||
\(72\) | 39940.0 | + | 823975.i | 0.0126109 | + | 0.260166i | ||||
\(73\) | −2.68512e6 | −0.807856 | −0.403928 | − | 0.914791i | \(-0.632355\pi\) | ||||
−0.403928 | + | 0.914791i | \(0.632355\pi\) | |||||||
\(74\) | −602570. | − | 1.00582e6i | −0.172861 | − | 0.288543i | ||||
\(75\) | 1.09267e6i | 0.299071i | ||||||||
\(76\) | 1.64726e6 | + | 881400.i | 0.430442 | + | 0.230317i | ||||
\(77\) | 5.21754e6i | 1.30241i | ||||||||
\(78\) | −2.45483e6 | + | 1.47064e6i | −0.585720 | + | 0.350894i | ||||
\(79\) | 8.22632e6 | 1.87720 | 0.938600 | − | 0.345007i | \(-0.112123\pi\) | ||||
0.938600 | + | 0.345007i | \(0.112123\pi\) | |||||||
\(80\) | −4.42305e6 | + | 2.94982e6i | −0.965845 | + | 0.644141i | ||||
\(81\) | −3.21264e6 | −0.671684 | ||||||||
\(82\) | −695790. | + | 416834.i | −0.139357 | + | 0.0834863i | ||||
\(83\) | 5.89510e6i | 1.13167i | 0.824520 | + | 0.565833i | \(0.191445\pi\) | ||||
−0.824520 | + | 0.565833i | \(0.808555\pi\) | |||||||
\(84\) | 4.34345e6 | + | 2.32405e6i | 0.799571 | + | 0.427827i | ||||
\(85\) | − | 1.12233e7i | − | 1.98223i | ||||||
\(86\) | −1.90952e6 | − | 3.18742e6i | −0.323728 | − | 0.540375i | ||||
\(87\) | −6.88164e6 | −1.12040 | ||||||||
\(88\) | 7.88638e6 | − | 382271.i | 1.23364 | − | 0.0597974i | ||||
\(89\) | 437005. | 0.0657085 | 0.0328542 | − | 0.999460i | \(-0.489540\pi\) | ||||
0.0328542 | + | 0.999460i | \(0.489540\pi\) | |||||||
\(90\) | 1.07475e6 | + | 1.79400e6i | 0.155403 | + | 0.259403i | ||||
\(91\) | − | 6.01868e6i | − | 0.837253i | ||||||
\(92\) | −1.48962e6 | + | 2.78396e6i | −0.199442 | + | 0.372740i | ||||
\(93\) | − | 4.49169e6i | − | 0.579055i | ||||||
\(94\) | −1.15536e6 | + | 692152.i | −0.143472 | + | 0.0859516i | ||||
\(95\) | 4.73616e6 | 0.566753 | ||||||||
\(96\) | 3.19460e6 | − | 6.73545e6i | 0.368525 | − | 0.776993i | ||||
\(97\) | −7.84322e6 | −0.872556 | −0.436278 | − | 0.899812i | \(-0.643704\pi\) | ||||
−0.436278 | + | 0.899812i | \(0.643704\pi\) | |||||||
\(98\) | −895128. | + | 536254.i | −0.0960713 | + | 0.0575545i | ||||
\(99\) | − | 3.10585e6i | − | 0.321705i | ||||||
\(100\) | −1.64073e6 | + | 3.06638e6i | −0.164073 | + | 0.306638i | ||||
\(101\) | 6.19757e6i | 0.598545i | 0.954168 | + | 0.299272i | \(0.0967439\pi\) | ||||
−0.954168 | + | 0.299272i | \(0.903256\pi\) | |||||||
\(102\) | 8.08752e6 | + | 1.34999e7i | 0.754597 | + | 1.25959i | ||||
\(103\) | −6.59816e6 | −0.594966 | −0.297483 | − | 0.954727i | \(-0.596147\pi\) | ||||
−0.297483 | + | 0.954727i | \(0.596147\pi\) | |||||||
\(104\) | −9.09731e6 | + | 440968.i | −0.793042 | + | 0.0384406i | ||||
\(105\) | 1.24882e7 | 1.05278 | ||||||||
\(106\) | −6.04748e6 | − | 1.00946e7i | −0.493179 | − | 0.823225i | ||||
\(107\) | − | 512845.i | − | 0.0404709i | −0.999795 | − | 0.0202354i | \(-0.993558\pi\) | ||
0.999795 | − | 0.0202354i | \(-0.00644158\pi\) | |||||||
\(108\) | −1.25119e7 | − | 6.69474e6i | −0.955739 | − | 0.511388i | ||||
\(109\) | 1.95882e7i | 1.44878i | 0.689393 | + | 0.724388i | \(0.257877\pi\) | ||||
−0.689393 | + | 0.724388i | \(0.742123\pi\) | |||||||
\(110\) | 1.71707e7 | − | 1.02866e7i | 1.23002 | − | 0.736883i | ||||
\(111\) | 4.16785e6 | 0.289256 | ||||||||
\(112\) | 8.69934e6 | + | 1.30441e7i | 0.585091 | + | 0.877303i | ||||
\(113\) | 1.88876e7 | 1.23141 | 0.615705 | − | 0.787977i | \(-0.288871\pi\) | ||||
0.615705 | + | 0.787977i | \(0.288871\pi\) | |||||||
\(114\) | −5.69687e6 | + | 3.41289e6i | −0.360139 | + | 0.215752i | ||||
\(115\) | 8.00438e6i | 0.490778i | ||||||||
\(116\) | −1.93121e7 | − | 1.03333e7i | −1.14875 | − | 0.614663i | ||||
\(117\) | 3.58275e6i | 0.206807i | ||||||||
\(118\) | −1.31394e6 | − | 2.19325e6i | −0.0736185 | − | 0.122886i | ||||
\(119\) | −3.30987e7 | −1.80051 | ||||||||
\(120\) | −914967. | − | 1.88760e7i | −0.0483360 | − | 0.997187i | ||||
\(121\) | −1.02394e7 | −0.525441 | ||||||||
\(122\) | 9.02772e6 | + | 1.50693e7i | 0.450110 | + | 0.751334i | ||||
\(123\) | − | 2.88316e6i | − | 0.139701i | ||||||
\(124\) | 6.74463e6 | − | 1.26051e7i | 0.317675 | − | 0.593706i | ||||
\(125\) | − | 1.65345e7i | − | 0.757193i | ||||||
\(126\) | 5.29071e6 | − | 3.16957e6i | 0.235623 | − | 0.141157i | ||||
\(127\) | 3.96314e7 | 1.71683 | 0.858413 | − | 0.512959i | \(-0.171451\pi\) | ||||
0.858413 | + | 0.512959i | \(0.171451\pi\) | |||||||
\(128\) | 1.90789e7 | − | 1.41048e7i | 0.804114 | − | 0.594475i | ||||
\(129\) | 1.32078e7 | 0.541709 | ||||||||
\(130\) | −1.98072e7 | + | 1.18661e7i | −0.790717 | + | 0.473703i | ||||
\(131\) | − | 3.65337e7i | − | 1.41986i | −0.704274 | − | 0.709928i | \(-0.748727\pi\) | ||
0.704274 | − | 0.709928i | \(-0.251273\pi\) | |||||||
\(132\) | −1.32411e7 | + | 2.47464e7i | −0.501090 | + | 0.936492i | ||||
\(133\) | − | 1.39675e7i | − | 0.514797i | ||||||
\(134\) | 1.83950e6 | + | 3.07053e6i | 0.0660439 | + | 0.110242i | ||||
\(135\) | −3.59739e7 | −1.25840 | ||||||||
\(136\) | 2.42503e6 | + | 5.00290e7i | 0.0826666 | + | 1.70544i | ||||
\(137\) | −2.56967e7 | −0.853799 | −0.426899 | − | 0.904299i | \(-0.640394\pi\) | ||||
−0.426899 | + | 0.904299i | \(0.640394\pi\) | |||||||
\(138\) | −5.76798e6 | − | 9.62804e6i | −0.186830 | − | 0.311861i | ||||
\(139\) | 5.23001e7i | 1.65177i | 0.563836 | + | 0.825886i | \(0.309325\pi\) | ||||
−0.563836 | + | 0.825886i | \(0.690675\pi\) | |||||||
\(140\) | 3.50458e7 | + | 1.87520e7i | 1.07941 | + | 0.577563i | ||||
\(141\) | − | 4.78747e6i | − | 0.143827i | ||||||
\(142\) | −5.23085e6 | + | 3.13370e6i | −0.153307 | + | 0.0918436i | ||||
\(143\) | 3.42910e7 | 0.980626 | ||||||||
\(144\) | −5.17847e6 | − | 7.76475e6i | −0.144521 | − | 0.216700i | ||||
\(145\) | −5.55256e7 | −1.51254 | ||||||||
\(146\) | 2.60601e7 | − | 1.56121e7i | 0.693011 | − | 0.415170i | ||||
\(147\) | − | 3.70916e6i | − | 0.0963085i | ||||||
\(148\) | 1.16963e7 | + | 6.25836e6i | 0.296574 | + | 0.158688i | ||||
\(149\) | 1.80406e7i | 0.446785i | 0.974729 | + | 0.223392i | \(0.0717131\pi\) | ||||
−0.974729 | + | 0.223392i | \(0.928287\pi\) | |||||||
\(150\) | −6.35311e6 | − | 1.06047e7i | −0.153697 | − | 0.256555i | ||||
\(151\) | 3.87385e7 | 0.915637 | 0.457818 | − | 0.889046i | \(-0.348631\pi\) | ||||
0.457818 | + | 0.889046i | \(0.348631\pi\) | |||||||
\(152\) | −2.11120e7 | + | 1.02335e6i | −0.487614 | + | 0.0236358i | ||||
\(153\) | 1.97027e7 | 0.444739 | ||||||||
\(154\) | −3.03363e7 | − | 5.06381e7i | −0.669331 | − | 1.11726i | ||||
\(155\) | − | 3.62420e7i | − | 0.781719i | ||||||
\(156\) | 1.52742e7 | − | 2.85462e7i | 0.322124 | − | 0.602022i | ||||
\(157\) | − | 5.12341e7i | − | 1.05660i | −0.849058 | − | 0.528300i | \(-0.822830\pi\) | ||
0.849058 | − | 0.528300i | \(-0.177170\pi\) | |||||||
\(158\) | −7.98393e7 | + | 4.78302e7i | −1.61034 | + | 0.964723i | ||||
\(159\) | 4.18292e7 | 0.825258 | ||||||||
\(160\) | 2.57762e7 | − | 5.43460e7i | 0.497506 | − | 1.04893i | ||||
\(161\) | 2.36058e7 | 0.445787 | ||||||||
\(162\) | 3.11798e7 | − | 1.86793e7i | 0.576197 | − | 0.345189i | ||||
\(163\) | 8.57572e7i | 1.55101i | 0.631343 | + | 0.775504i | \(0.282504\pi\) | ||||
−0.631343 | + | 0.775504i | \(0.717496\pi\) | |||||||
\(164\) | 4.32929e6 | − | 8.09105e6i | 0.0766413 | − | 0.143236i | ||||
\(165\) | 7.11504e7i | 1.23306i | ||||||||
\(166\) | −3.42759e7 | − | 5.72141e7i | −0.581581 | − | 0.970789i | ||||
\(167\) | −1.05871e8 | −1.75901 | −0.879503 | − | 0.475893i | \(-0.842125\pi\) | ||||
−0.879503 | + | 0.475893i | \(0.842125\pi\) | |||||||
\(168\) | −5.56674e7 | + | 2.69833e6i | −0.905772 | + | 0.0439049i | ||||
\(169\) | 2.31923e7 | 0.369606 | ||||||||
\(170\) | 6.52555e7 | + | 1.08926e8i | 1.01870 | + | 1.70044i | ||||
\(171\) | 8.31441e6i | 0.127158i | ||||||||
\(172\) | 3.70652e7 | + | 1.98325e7i | 0.555415 | + | 0.297186i | ||||
\(173\) | − | 1.98148e7i | − | 0.290956i | −0.989361 | − | 0.145478i | \(-0.953528\pi\) | ||
0.989361 | − | 0.145478i | \(-0.0464720\pi\) | |||||||
\(174\) | 6.67888e7 | − | 4.00119e7i | 0.961128 | − | 0.575793i | ||||
\(175\) | 2.60005e7 | 0.366731 | ||||||||
\(176\) | −7.43175e7 | + | 4.95638e7i | −1.02753 | + | 0.685284i | ||||
\(177\) | 9.08822e6 | 0.123189 | ||||||||
\(178\) | −4.24129e6 | + | 2.54088e6i | −0.0563674 | + | 0.0337686i | ||||
\(179\) | − | 2.97800e7i | − | 0.388096i | −0.980992 | − | 0.194048i | \(-0.937838\pi\) | ||
0.980992 | − | 0.194048i | \(-0.0621618\pi\) | |||||||
\(180\) | −2.08617e7 | − | 1.11625e7i | −0.266623 | − | 0.142662i | ||||
\(181\) | − | 3.96227e6i | − | 0.0496671i | −0.999692 | − | 0.0248335i | \(-0.992094\pi\) | ||
0.999692 | − | 0.0248335i | \(-0.00790558\pi\) | |||||||
\(182\) | 3.49944e7 | + | 5.84135e7i | 0.430278 | + | 0.718230i | ||||
\(183\) | −6.24429e7 | −0.753189 | ||||||||
\(184\) | −1.72951e6 | − | 3.56804e7i | −0.0204674 | − | 0.422248i | ||||
\(185\) | 3.36290e7 | 0.390493 | ||||||||
\(186\) | 2.61160e7 | + | 4.35935e7i | 0.297586 | + | 0.496737i | ||||
\(187\) | − | 1.88577e8i | − | 2.10884i | ||||||
\(188\) | 7.18876e6 | − | 1.34352e7i | 0.0789045 | − | 0.147465i | ||||
\(189\) | 1.06091e8i | 1.14304i | ||||||||
\(190\) | −4.59662e7 | + | 2.75375e7i | −0.486184 | + | 0.291264i | ||||
\(191\) | −4.80105e7 | −0.498562 | −0.249281 | − | 0.968431i | \(-0.580194\pi\) | ||||
−0.249281 | + | 0.968431i | \(0.580194\pi\) | |||||||
\(192\) | 8.15712e6 | + | 8.39443e7i | 0.0831731 | + | 0.855927i | ||||
\(193\) | −4.72502e6 | −0.0473100 | −0.0236550 | − | 0.999720i | \(-0.507530\pi\) | ||||
−0.0236550 | + | 0.999720i | \(0.507530\pi\) | |||||||
\(194\) | 7.61212e7 | − | 4.56028e7i | 0.748514 | − | 0.448420i | ||||
\(195\) | − | 8.20754e7i | − | 0.792669i | ||||||
\(196\) | 5.56959e6 | − | 1.04091e7i | 0.0528357 | − | 0.0987452i | ||||
\(197\) | − | 1.14882e8i | − | 1.07058i | −0.844668 | − | 0.535290i | \(-0.820202\pi\) | ||
0.844668 | − | 0.535290i | \(-0.179798\pi\) | |||||||
\(198\) | 1.80583e7 | + | 3.01434e7i | 0.165329 | + | 0.275971i | ||||
\(199\) | 1.20933e7 | 0.108782 | 0.0543911 | − | 0.998520i | \(-0.482678\pi\) | ||||
0.0543911 | + | 0.998520i | \(0.482678\pi\) | |||||||
\(200\) | −1.90496e6 | − | 3.93000e7i | −0.0168377 | − | 0.347366i | ||||
\(201\) | −1.27234e7 | −0.110514 | ||||||||
\(202\) | −3.60345e7 | − | 6.01496e7i | −0.307602 | − | 0.513456i | ||||
\(203\) | 1.63751e8i | 1.37388i | ||||||||
\(204\) | −1.56985e8 | − | 8.39979e7i | −1.29465 | − | 0.692728i | ||||
\(205\) | − | 2.32632e7i | − | 0.188596i | ||||||
\(206\) | 6.40375e7 | − | 3.83636e7i | 0.510386 | − | 0.305763i | ||||
\(207\) | −1.40518e7 | −0.110112 | ||||||||
\(208\) | 8.57287e7 | − | 5.71742e7i | 0.660548 | − | 0.440533i | ||||
\(209\) | 7.95784e7 | 0.602953 | ||||||||
\(210\) | −1.21202e8 | + | 7.26100e7i | −0.903116 | + | 0.541040i | ||||
\(211\) | 1.95850e8i | 1.43527i | 0.696418 | + | 0.717636i | \(0.254776\pi\) | ||||
−0.696418 | + | 0.717636i | \(0.745224\pi\) | |||||||
\(212\) | 1.17386e8 | + | 6.28098e7i | 0.846137 | + | 0.452743i | ||||
\(213\) | − | 2.16752e7i | − | 0.153686i | ||||||
\(214\) | 2.98183e6 | + | 4.97734e6i | 0.0207986 | + | 0.0347176i | ||||
\(215\) | 1.06569e8 | 0.731302 | ||||||||
\(216\) | 1.60357e8 | − | 7.77291e6i | 1.08268 | − | 0.0524802i | ||||
\(217\) | −1.06881e8 | −0.710057 | ||||||||
\(218\) | −1.13891e8 | − | 1.90110e8i | −0.744549 | − | 1.24282i | ||||
\(219\) | 1.07986e8i | 0.694723i | ||||||||
\(220\) | −1.06838e8 | + | 1.99671e8i | −0.676466 | + | 1.26426i | ||||
\(221\) | 2.17532e8i | 1.35566i | ||||||||
\(222\) | −4.04505e7 | + | 2.42331e7i | −0.248135 | + | 0.148653i | ||||
\(223\) | 1.08024e8 | 0.652311 | 0.326156 | − | 0.945316i | \(-0.394247\pi\) | ||||
0.326156 | + | 0.945316i | \(0.394247\pi\) | |||||||
\(224\) | −1.60272e8 | − | 7.60167e7i | −0.952775 | − | 0.451898i | ||||
\(225\) | −1.54773e7 | −0.0905851 | ||||||||
\(226\) | −1.83311e8 | + | 1.09818e8i | −1.05635 | + | 0.632841i | ||||
\(227\) | − | 1.61144e8i | − | 0.914374i | −0.889371 | − | 0.457187i | \(-0.848857\pi\) | ||
0.889371 | − | 0.457187i | \(-0.151143\pi\) | |||||||
\(228\) | 3.54466e7 | − | 6.62466e7i | 0.198063 | − | 0.370162i | ||||
\(229\) | − | 5.27173e7i | − | 0.290088i | −0.989425 | − | 0.145044i | \(-0.953668\pi\) | ||
0.989425 | − | 0.145044i | \(-0.0463323\pi\) | |||||||
\(230\) | −4.65399e7 | − | 7.76854e7i | −0.252219 | − | 0.421010i | ||||
\(231\) | 2.09830e8 | 1.12002 | ||||||||
\(232\) | 2.47511e8 | − | 1.19975e7i | 1.30133 | − | 0.0630786i | ||||
\(233\) | −1.79423e8 | −0.929249 | −0.464625 | − | 0.885508i | \(-0.653811\pi\) | ||||
−0.464625 | + | 0.885508i | \(0.653811\pi\) | |||||||
\(234\) | −2.08312e7 | − | 3.47718e7i | −0.106282 | − | 0.177408i | ||||
\(235\) | − | 3.86285e7i | − | 0.194165i | ||||||
\(236\) | 2.55044e7 | + | 1.36467e7i | 0.126306 | + | 0.0675826i | ||||
\(237\) | − | 3.30832e8i | − | 1.61431i | ||||||
\(238\) | 3.21234e8 | − | 1.92445e8i | 1.54455 | − | 0.925312i | ||||
\(239\) | −8.42441e7 | −0.399160 | −0.199580 | − | 0.979882i | \(-0.563958\pi\) | ||||
−0.199580 | + | 0.979882i | \(0.563958\pi\) | |||||||
\(240\) | 1.18631e8 | + | 1.77879e8i | 0.553935 | + | 0.830586i | ||||
\(241\) | −2.12302e8 | −0.977000 | −0.488500 | − | 0.872564i | \(-0.662456\pi\) | ||||
−0.488500 | + | 0.872564i | \(0.662456\pi\) | |||||||
\(242\) | 9.93766e7 | − | 5.95347e7i | 0.450745 | − | 0.270033i | ||||
\(243\) | − | 1.13255e8i | − | 0.506333i | ||||||
\(244\) | −1.75234e8 | − | 9.37629e7i | −0.772245 | − | 0.413206i | ||||
\(245\) | − | 2.99280e7i | − | 0.130016i | ||||||
\(246\) | 1.67635e7 | + | 2.79821e7i | 0.0717947 | + | 0.119841i | ||||
\(247\) | −9.17975e7 | −0.387607 | ||||||||
\(248\) | 7.83083e6 | + | 1.61552e8i | 0.0326007 | + | 0.672563i | ||||
\(249\) | 2.37079e8 | 0.973186 | ||||||||
\(250\) | 9.61366e7 | + | 1.60473e8i | 0.389134 | + | 0.649551i | ||||
\(251\) | 1.18102e8i | 0.471411i | 0.971825 | + | 0.235706i | \(0.0757401\pi\) | ||||
−0.971825 | + | 0.235706i | \(0.924260\pi\) | |||||||
\(252\) | −3.29194e7 | + | 6.15235e7i | −0.129584 | + | 0.242181i | ||||
\(253\) | 1.34492e8i | 0.522125i | ||||||||
\(254\) | −3.84637e8 | + | 2.30429e8i | −1.47276 | + | 0.882304i | ||||
\(255\) | −4.51359e8 | −1.70463 | ||||||||
\(256\) | −1.03157e8 | + | 2.47823e8i | −0.384291 | + | 0.923212i | ||||
\(257\) | 1.27463e8 | 0.468402 | 0.234201 | − | 0.972188i | \(-0.424753\pi\) | ||||
0.234201 | + | 0.972188i | \(0.424753\pi\) | |||||||
\(258\) | −1.28186e8 | + | 7.67940e7i | −0.464700 | + | 0.278393i | ||||
\(259\) | − | 9.91755e7i | − | 0.354695i | ||||||
\(260\) | 1.23243e8 | − | 2.30330e8i | 0.434865 | − | 0.812724i | ||||
\(261\) | − | 9.74762e7i | − | 0.339357i | ||||||
\(262\) | 2.12418e8 | + | 3.54573e8i | 0.729687 | + | 1.21801i | ||||
\(263\) | 4.33125e8 | 1.46814 | 0.734071 | − | 0.679073i | \(-0.237618\pi\) | ||||
0.734071 | + | 0.679073i | \(0.237618\pi\) | |||||||
\(264\) | −1.53735e7 | − | 3.17161e8i | −0.0514233 | − | 1.06088i | ||||
\(265\) | 3.37506e8 | 1.11409 | ||||||||
\(266\) | 8.12109e7 | + | 1.35559e8i | 0.264563 | + | 0.441614i | ||||
\(267\) | − | 1.75747e7i | − | 0.0565066i | ||||||
\(268\) | −3.57060e7 | − | 1.91052e7i | −0.113310 | − | 0.0606290i | ||||
\(269\) | 3.44748e8i | 1.07986i | 0.841709 | + | 0.539931i | \(0.181550\pi\) | ||||
−0.841709 | + | 0.539931i | \(0.818450\pi\) | |||||||
\(270\) | 3.49139e8 | − | 2.09163e8i | 1.07951 | − | 0.646712i | ||||
\(271\) | −4.42513e8 | −1.35062 | −0.675311 | − | 0.737533i | \(-0.735990\pi\) | ||||
−0.675311 | + | 0.737533i | \(0.735990\pi\) | |||||||
\(272\) | −3.14419e8 | − | 4.71450e8i | −0.947366 | − | 1.42051i | ||||
\(273\) | −2.42049e8 | −0.720003 | ||||||||
\(274\) | 2.49396e8 | − | 1.49408e8i | 0.732423 | − | 0.438781i | ||||
\(275\) | 1.48135e8i | 0.429531i | ||||||||
\(276\) | 1.11961e8 | + | 5.99068e7i | 0.320541 | + | 0.171512i | ||||
\(277\) | 3.18148e8i | 0.899395i | 0.893181 | + | 0.449697i | \(0.148468\pi\) | ||||
−0.893181 | + | 0.449697i | \(0.851532\pi\) | |||||||
\(278\) | −3.04088e8 | − | 5.07591e8i | −0.848873 | − | 1.41696i | ||||
\(279\) | 6.36234e7 | 0.175389 | ||||||||
\(280\) | −4.49162e8 | + | 2.17719e7i | −1.22278 | + | 0.0592713i | ||||
\(281\) | 1.28497e8 | 0.345478 | 0.172739 | − | 0.984968i | \(-0.444738\pi\) | ||||
0.172739 | + | 0.984968i | \(0.444738\pi\) | |||||||
\(282\) | 2.78358e7 | + | 4.64641e7i | 0.0739148 | + | 0.123380i | ||||
\(283\) | − | 3.98970e8i | − | 1.04637i | −0.852218 | − | 0.523187i | \(-0.824743\pi\) | ||
0.852218 | − | 0.523187i | \(-0.175257\pi\) | |||||||
\(284\) | 3.25470e7 | − | 6.08274e7i | 0.0843134 | − | 0.157574i | ||||
\(285\) | − | 1.90471e8i | − | 0.487384i | ||||||
\(286\) | −3.32806e8 | + | 1.99378e8i | −0.841221 | + | 0.503960i | ||||
\(287\) | −6.86057e7 | −0.171306 | ||||||||
\(288\) | 9.54054e7 | + | 4.52505e7i | 0.235342 | + | 0.111622i | ||||
\(289\) | 7.85942e8 | 1.91535 | ||||||||
\(290\) | 5.38896e8 | − | 3.22842e8i | 1.29751 | − | 0.777316i | ||||
\(291\) | 3.15425e8i | 0.750362i | ||||||||
\(292\) | −1.62149e8 | + | 3.03042e8i | −0.381131 | + | 0.712299i | ||||
\(293\) | 2.00958e8i | 0.466732i | 0.972389 | + | 0.233366i | \(0.0749741\pi\) | ||||
−0.972389 | + | 0.233366i | \(0.925026\pi\) | |||||||
\(294\) | 2.15662e7 | + | 3.59987e7i | 0.0494945 | + | 0.0826174i | ||||
\(295\) | 7.33298e7 | 0.166304 | ||||||||
\(296\) | −1.49905e8 | + | 7.26625e6i | −0.335965 | + | 0.0162850i | ||||
\(297\) | −6.04444e8 | −1.33878 | ||||||||
\(298\) | −1.04893e8 | − | 1.75090e8i | −0.229610 | − | 0.383270i | ||||
\(299\) | − | 1.55143e8i | − | 0.335647i | ||||||
\(300\) | 1.23318e8 | + | 6.59840e7i | 0.263696 | + | 0.141096i | ||||
\(301\) | − | 3.14284e8i | − | 0.664262i | ||||||
\(302\) | −3.75971e8 | + | 2.25237e8i | −0.785470 | + | 0.470560i | ||||
\(303\) | 2.49243e8 | 0.514724 | ||||||||
\(304\) | 1.98949e8 | − | 1.32683e8i | 0.406148 | − | 0.270868i | ||||
\(305\) | −5.03830e8 | −1.01680 | ||||||||
\(306\) | −1.91221e8 | + | 1.14557e8i | −0.381515 | + | 0.228558i | ||||
\(307\) | 1.58918e7i | 0.0313465i | 0.999877 | + | 0.0156733i | \(0.00498916\pi\) | ||||
−0.999877 | + | 0.0156733i | \(0.995011\pi\) | |||||||
\(308\) | 5.88850e8 | + | 3.15077e8i | 1.14836 | + | 0.614453i | ||||
\(309\) | 2.65353e8i | 0.511646i | ||||||||
\(310\) | 2.10722e8 | + | 3.51741e8i | 0.401738 | + | 0.670591i | ||||
\(311\) | 4.87710e8 | 0.919391 | 0.459695 | − | 0.888077i | \(-0.347959\pi\) | ||||
0.459695 | + | 0.888077i | \(0.347959\pi\) | |||||||
\(312\) | 1.77341e7 | + | 3.65860e8i | 0.0330574 | + | 0.681983i | ||||
\(313\) | −3.24731e8 | −0.598576 | −0.299288 | − | 0.954163i | \(-0.596749\pi\) | ||||
−0.299288 | + | 0.954163i | \(0.596749\pi\) | |||||||
\(314\) | 2.97890e8 | + | 4.97245e8i | 0.543003 | + | 0.906394i | ||||
\(315\) | 1.76891e8i | 0.318874i | ||||||||
\(316\) | 4.96770e8 | − | 9.28419e8i | 0.885627 | − | 1.65516i | ||||
\(317\) | − | 1.06084e9i | − | 1.87043i | −0.354086 | − | 0.935213i | \(-0.615208\pi\) | ||
0.354086 | − | 0.935213i | \(-0.384792\pi\) | |||||||
\(318\) | −4.05967e8 | + | 2.43207e8i | −0.707939 | + | 0.424113i | ||||
\(319\) | −9.32958e8 | −1.60914 | ||||||||
\(320\) | 6.58171e7 | + | 6.77318e8i | 0.112283 | + | 1.15549i | ||||
\(321\) | −2.06247e7 | −0.0348033 | ||||||||
\(322\) | −2.29102e8 | + | 1.37251e8i | −0.382414 | + | 0.229097i | ||||
\(323\) | 5.04824e8i | 0.833548i | ||||||||
\(324\) | −1.94005e8 | + | 3.62578e8i | −0.316887 | + | 0.592234i | ||||
\(325\) | − | 1.70881e8i | − | 0.276123i | ||||||
\(326\) | −4.98618e8 | − | 8.32304e8i | −0.797088 | − | 1.33052i | ||||
\(327\) | 7.87763e8 | 1.24589 | ||||||||
\(328\) | 5.02651e6 | + | 1.03698e8i | 0.00786516 | + | 0.162261i | ||||
\(329\) | −1.13919e8 | −0.176365 | ||||||||
\(330\) | −4.13690e8 | − | 6.90540e8i | −0.633689 | − | 1.05777i | ||||
\(331\) | − | 2.88487e8i | − | 0.437249i | −0.975809 | − | 0.218624i | \(-0.929843\pi\) | ||
0.975809 | − | 0.218624i | \(-0.0701569\pi\) | |||||||
\(332\) | 6.65319e8 | + | 3.55993e8i | 0.997808 | + | 0.533898i | ||||
\(333\) | 5.90363e7i | 0.0876121i | ||||||||
\(334\) | 1.02751e9 | − | 6.15563e8i | 1.50895 | − | 0.903982i | ||||
\(335\) | −1.02661e8 | −0.149193 | ||||||||
\(336\) | 5.24583e8 | − | 3.49855e8i | 0.754444 | − | 0.503154i | ||||
\(337\) | −1.10595e8 | −0.157410 | −0.0787051 | − | 0.996898i | \(-0.525079\pi\) | ||||
−0.0787051 | + | 0.996898i | \(0.525079\pi\) | |||||||
\(338\) | −2.25089e8 | + | 1.34847e8i | −0.317063 | + | 0.189947i | ||||
\(339\) | − | 7.59590e8i | − | 1.05896i | ||||||
\(340\) | −1.26666e9 | − | 6.77751e8i | −1.74776 | − | 0.935177i | ||||
\(341\) | − | 6.08948e8i | − | 0.831649i | ||||||
\(342\) | −4.83425e7 | − | 8.06944e7i | −0.0653488 | − | 0.109082i | ||||
\(343\) | 6.99837e8 | 0.936414 | ||||||||
\(344\) | −4.75044e8 | + | 2.30265e7i | −0.629186 | + | 0.0304981i | ||||
\(345\) | 3.21907e8 | 0.422049 | ||||||||
\(346\) | 1.15209e8 | + | 1.92309e8i | 0.149527 | + | 0.249594i | ||||
\(347\) | 1.10651e9i | 1.42168i | 0.703352 | + | 0.710841i | \(0.251686\pi\) | ||||
−0.703352 | + | 0.710841i | \(0.748314\pi\) | |||||||
\(348\) | −4.15568e8 | + | 7.76659e8i | −0.528585 | + | 0.987878i | ||||
\(349\) | 1.38337e9i | 1.74201i | 0.491278 | + | 0.871003i | \(0.336530\pi\) | ||||
−0.491278 | + | 0.871003i | \(0.663470\pi\) | |||||||
\(350\) | −2.52344e8 | + | 1.51174e8i | −0.314597 | + | 0.188469i | ||||
\(351\) | 6.97254e8 | 0.860630 | ||||||||
\(352\) | 4.33099e8 | − | 9.13138e8i | 0.529283 | − | 1.11593i | ||||
\(353\) | −2.47617e8 | −0.299618 | −0.149809 | − | 0.988715i | \(-0.547866\pi\) | ||||
−0.149809 | + | 0.988715i | \(0.547866\pi\) | |||||||
\(354\) | −8.82044e7 | + | 5.28416e7i | −0.105677 | + | 0.0633089i | ||||
\(355\) | − | 1.74890e8i | − | 0.207475i | ||||||
\(356\) | 2.63898e7 | − | 4.93202e7i | 0.0310000 | − | 0.0579362i | ||||
\(357\) | 1.33111e9i | 1.54837i | ||||||||
\(358\) | 1.73150e8 | + | 2.89026e8i | 0.199449 | + | 0.332925i | ||||
\(359\) | −1.38641e9 | −1.58148 | −0.790738 | − | 0.612155i | \(-0.790303\pi\) | ||||
−0.790738 | + | 0.612155i | \(0.790303\pi\) | |||||||
\(360\) | 2.67373e8 | − | 1.29602e7i | 0.302036 | − | 0.0146404i | ||||
\(361\) | 6.80839e8 | 0.761674 | ||||||||
\(362\) | 2.30378e7 | + | 3.84552e7i | 0.0255247 | + | 0.0426064i | ||||
\(363\) | 4.11789e8i | 0.451858i | ||||||||
\(364\) | −6.79267e8 | − | 3.63456e8i | −0.738219 | − | 0.395000i | ||||
\(365\) | 8.71299e8i | 0.937869i | ||||||||
\(366\) | 6.06030e8 | − | 3.63061e8i | 0.646116 | − | 0.387076i | ||||
\(367\) | −7.49367e8 | −0.791341 | −0.395670 | − | 0.918393i | \(-0.629488\pi\) | ||||
−0.395670 | + | 0.918393i | \(0.629488\pi\) | |||||||
\(368\) | 2.24242e8 | + | 3.36235e8i | 0.234558 | + | 0.351703i | ||||
\(369\) | 4.08390e7 | 0.0423139 | ||||||||
\(370\) | −3.26381e8 | + | 1.95529e8i | −0.334980 | + | 0.200680i | ||||
\(371\) | − | 9.95340e8i | − | 1.01196i | ||||||
\(372\) | −5.06931e8 | − | 2.71244e8i | −0.510562 | − | 0.273187i | ||||
\(373\) | − | 1.49519e9i | − | 1.49181i | −0.666051 | − | 0.745906i | \(-0.732017\pi\) | ||
0.666051 | − | 0.745906i | \(-0.267983\pi\) | |||||||
\(374\) | 1.09644e9 | + | 1.83021e9i | 1.08377 | + | 1.80905i | ||||
\(375\) | −6.64957e8 | −0.651155 | ||||||||
\(376\) | 8.34649e6 | + | 1.72191e8i | 0.00809741 | + | 0.167052i | ||||
\(377\) | 1.07621e9 | 1.03443 | ||||||||
\(378\) | −6.16843e8 | − | 1.02965e9i | −0.587426 | − | 0.980546i | ||||
\(379\) | 7.92096e7i | 0.0747379i | 0.999302 | + | 0.0373689i | \(0.0118977\pi\) | ||||
−0.999302 | + | 0.0373689i | \(0.988102\pi\) | |||||||
\(380\) | 2.86007e8 | − | 5.34522e8i | 0.267383 | − | 0.499715i | ||||
\(381\) | − | 1.59383e9i | − | 1.47640i | ||||||
\(382\) | 4.65959e8 | − | 2.79147e8i | 0.427687 | − | 0.256219i | ||||
\(383\) | 4.80285e8 | 0.436820 | 0.218410 | − | 0.975857i | \(-0.429913\pi\) | ||||
0.218410 | + | 0.975857i | \(0.429913\pi\) | |||||||
\(384\) | −5.67245e8 | − | 7.67281e8i | −0.511224 | − | 0.691505i | ||||
\(385\) | 1.69305e9 | 1.51202 | ||||||||
\(386\) | 4.58580e7 | − | 2.74726e7i | 0.0405844 | − | 0.0243134i | ||||
\(387\) | 1.87084e8i | 0.164077i | ||||||||
\(388\) | −4.73636e8 | + | 8.85183e8i | −0.411655 | + | 0.769346i | ||||
\(389\) | − | 1.07150e9i | − | 0.922928i | −0.887159 | − | 0.461464i | \(-0.847324\pi\) | ||
0.887159 | − | 0.461464i | \(-0.152676\pi\) | |||||||
\(390\) | 4.77211e8 | + | 7.96571e8i | 0.407365 | + | 0.679984i | ||||
\(391\) | −8.53180e8 | −0.721809 | ||||||||
\(392\) | 6.46656e6 | + | 1.33407e8i | 0.00542216 | + | 0.111861i | ||||
\(393\) | −1.46925e9 | −1.22102 | ||||||||
\(394\) | 6.67957e8 | + | 1.11497e9i | 0.550189 | + | 0.918387i | ||||
\(395\) | − | 2.66937e9i | − | 2.17931i | ||||||
\(396\) | −3.50525e8 | − | 1.87556e8i | −0.283652 | − | 0.151774i | ||||
\(397\) | 2.03185e9i | 1.62976i | 0.579627 | + | 0.814882i | \(0.303198\pi\) | ||||
−0.579627 | + | 0.814882i | \(0.696802\pi\) | |||||||
\(398\) | −1.17369e8 | + | 7.03138e7i | −0.0933178 | + | 0.0559049i | ||||
\(399\) | −5.61719e8 | −0.442705 | ||||||||
\(400\) | 2.46990e8 | + | 3.70344e8i | 0.192961 | + | 0.289331i | ||||
\(401\) | −2.57759e9 | −1.99622 | −0.998111 | − | 0.0614301i | \(-0.980434\pi\) | ||||
−0.998111 | + | 0.0614301i | \(0.980434\pi\) | |||||||
\(402\) | 1.23485e8 | − | 7.39778e7i | 0.0948035 | − | 0.0567950i | ||||
\(403\) | 7.02451e8i | 0.534624i | ||||||||
\(404\) | 6.99455e8 | + | 3.74258e8i | 0.527746 | + | 0.282382i | ||||
\(405\) | 1.04248e9i | 0.779782i | ||||||||
\(406\) | −9.52097e8 | − | 1.58926e9i | −0.706057 | − | 1.17857i | ||||
\(407\) | 5.65044e8 | 0.415434 | ||||||||
\(408\) | 2.01198e9 | − | 9.75255e7i | 1.46661 | − | 0.0710899i | ||||
\(409\) | 3.30242e8 | 0.238672 | 0.119336 | − | 0.992854i | \(-0.461923\pi\) | ||||
0.119336 | + | 0.992854i | \(0.461923\pi\) | |||||||
\(410\) | 1.35259e8 | + | 2.25778e8i | 0.0969223 | + | 0.161785i | ||||
\(411\) | 1.03343e9i | 0.734232i | ||||||||
\(412\) | −3.98449e8 | + | 7.44666e8i | −0.280693 | + | 0.524591i | ||||
\(413\) | − | 2.16257e8i | − | 0.151059i | ||||||
\(414\) | 1.36378e8 | − | 8.17015e7i | 0.0944590 | − | 0.0565886i | ||||
\(415\) | 1.91291e9 | 1.31379 | ||||||||
\(416\) | −4.99600e8 | + | 1.05335e9i | −0.340248 | + | 0.717374i | ||||
\(417\) | 2.10331e9 | 1.42046 | ||||||||
\(418\) | −7.72337e8 | + | 4.62692e8i | −0.517237 | + | 0.309867i | ||||
\(419\) | 5.80021e7i | 0.0385207i | 0.999815 | + | 0.0192604i | \(0.00613114\pi\) | ||||
−0.999815 | + | 0.0192604i | \(0.993869\pi\) | |||||||
\(420\) | 7.54136e8 | − | 1.40941e9i | 0.496680 | − | 0.928251i | ||||
\(421\) | 1.90609e8i | 0.124496i | 0.998061 | + | 0.0622480i | \(0.0198270\pi\) | ||||
−0.998061 | + | 0.0622480i | \(0.980173\pi\) | |||||||
\(422\) | −1.13873e9 | − | 1.90079e9i | −0.737610 | − | 1.23123i | ||||
\(423\) | 6.78129e7 | 0.0435633 | ||||||||
\(424\) | −1.50447e9 | + | 7.29251e7i | −0.958523 | + | 0.0464619i | ||||
\(425\) | −9.39731e8 | −0.593803 | ||||||||
\(426\) | 1.26026e8 | + | 2.10365e8i | 0.0789817 | + | 0.131838i | ||||
\(427\) | 1.48585e9i | 0.923586i | ||||||||
\(428\) | −5.78795e7 | − | 3.09696e7i | −0.0356838 | − | 0.0190934i | ||||
\(429\) | − | 1.37906e9i | − | 0.843298i | ||||||
\(430\) | −1.03429e9 | + | 6.19625e8i | −0.627341 | + | 0.375828i | ||||
\(431\) | 2.42923e9 | 1.46150 | 0.730749 | − | 0.682646i | \(-0.239171\pi\) | ||||
0.730749 | + | 0.682646i | \(0.239171\pi\) | |||||||
\(432\) | −1.51113e9 | + | 1.00780e9i | −0.901798 | + | 0.601427i | ||||
\(433\) | −2.37902e9 | −1.40828 | −0.704141 | − | 0.710060i | \(-0.748668\pi\) | ||||
−0.704141 | + | 0.710060i | \(0.748668\pi\) | |||||||
\(434\) | 1.03732e9 | − | 6.21440e8i | 0.609116 | − | 0.364910i | ||||
\(435\) | 2.23303e9i | 1.30072i | ||||||||
\(436\) | 2.21071e9 | + | 1.18289e9i | 1.27741 | + | 0.683504i | ||||
\(437\) | − | 3.60037e8i | − | 0.206378i | ||||||
\(438\) | −6.27860e8 | − | 1.04804e9i | −0.357029 | − | 0.595961i | ||||
\(439\) | −1.33161e9 | −0.751194 | −0.375597 | − | 0.926783i | \(-0.622562\pi\) | ||||
−0.375597 | + | 0.926783i | \(0.622562\pi\) | |||||||
\(440\) | −1.24044e8 | − | 2.55906e9i | −0.0694210 | − | 1.43218i | ||||
\(441\) | 5.25390e7 | 0.0291707 | ||||||||
\(442\) | −1.26480e9 | − | 2.11123e9i | −0.696696 | − | 1.16294i | ||||
\(443\) | 5.02643e8i | 0.274692i | 0.990523 | + | 0.137346i | \(0.0438573\pi\) | ||||
−0.990523 | + | 0.137346i | \(0.956143\pi\) | |||||||
\(444\) | 2.51688e8 | − | 4.70382e8i | 0.136465 | − | 0.255041i | ||||
\(445\) | − | 1.41805e8i | − | 0.0762834i | ||||||
\(446\) | −1.04842e9 | + | 6.28086e8i | −0.559579 | + | 0.335233i | ||||
\(447\) | 7.25525e8 | 0.384217 | ||||||||
\(448\) | 1.99748e9 | − | 1.94102e8i | 1.04957 | − | 0.101990i | ||||
\(449\) | 3.14785e9 | 1.64116 | 0.820580 | − | 0.571531i | \(-0.193650\pi\) | ||||
0.820580 | + | 0.571531i | \(0.193650\pi\) | |||||||
\(450\) | 1.50213e8 | − | 8.99897e7i | 0.0777075 | − | 0.0465531i | ||||
\(451\) | − | 3.90876e8i | − | 0.200641i | ||||||
\(452\) | 1.14058e9 | − | 2.13165e9i | 0.580955 | − | 1.08575i | ||||
\(453\) | − | 1.55792e9i | − | 0.787410i | ||||||
\(454\) | 9.36939e8 | + | 1.56396e9i | 0.469911 | + | 0.784387i | ||||
\(455\) | −1.95301e9 | −0.971998 | ||||||||
\(456\) | 4.11552e7 | + | 8.49044e8i | 0.0203258 | + | 0.419328i | ||||
\(457\) | −2.68422e9 | −1.31556 | −0.657782 | − | 0.753209i | \(-0.728505\pi\) | ||||
−0.657782 | + | 0.753209i | \(0.728505\pi\) | |||||||
\(458\) | 3.06514e8 | + | 5.11641e8i | 0.149081 | + | 0.248849i | ||||
\(459\) | − | 3.83442e9i | − | 1.85078i | ||||||
\(460\) | 9.03372e8 | + | 4.83368e8i | 0.432727 | + | 0.231540i | ||||
\(461\) | 1.30434e9i | 0.620065i | 0.950726 | + | 0.310033i | \(0.100340\pi\) | ||||
−0.950726 | + | 0.310033i | \(0.899660\pi\) | |||||||
\(462\) | −2.03648e9 | + | 1.22002e9i | −0.960799 | + | 0.575597i | ||||
\(463\) | 2.86853e9 | 1.34315 | 0.671577 | − | 0.740934i | \(-0.265617\pi\) | ||||
0.671577 | + | 0.740934i | \(0.265617\pi\) | |||||||
\(464\) | −2.33243e9 | + | 1.55554e9i | −1.08392 | + | 0.722886i | ||||
\(465\) | −1.45752e9 | −0.672246 | ||||||||
\(466\) | 1.74136e9 | − | 1.04322e9i | 0.797148 | − | 0.477556i | ||||
\(467\) | 5.96519e8i | 0.271029i | 0.990775 | + | 0.135514i | \(0.0432687\pi\) | ||||
−0.990775 | + | 0.135514i | \(0.956731\pi\) | |||||||
\(468\) | 4.04348e8 | + | 2.16355e8i | 0.182345 | + | 0.0975676i | ||||
\(469\) | 3.02758e8i | 0.135516i | ||||||||
\(470\) | 2.24597e8 | + | 3.74903e8i | 0.0997843 | + | 0.166562i | ||||
\(471\) | −2.06045e9 | −0.908632 | ||||||||
\(472\) | −3.26875e8 | + | 1.58444e7i | −0.143082 | + | 0.00693553i | ||||
\(473\) | 1.79061e9 | 0.778012 | ||||||||
\(474\) | 1.92355e9 | + | 3.21084e9i | 0.829622 | + | 1.38482i | ||||
\(475\) | − | 3.96561e8i | − | 0.169778i | ||||||
\(476\) | −1.99876e9 | + | 3.73550e9i | −0.849447 | + | 1.58754i | ||||
\(477\) | 5.92497e8i | 0.249961i | ||||||||
\(478\) | 8.17619e8 | − | 4.89820e8i | 0.342416 | − | 0.205135i | ||||
\(479\) | −2.16068e9 | −0.898289 | −0.449144 | − | 0.893459i | \(-0.648271\pi\) | ||||
−0.449144 | + | 0.893459i | \(0.648271\pi\) | |||||||
\(480\) | −2.18560e9 | − | 1.03662e9i | −0.902039 | − | 0.427835i | ||||
\(481\) | −6.51805e8 | −0.267061 | ||||||||
\(482\) | 2.06047e9 | − | 1.23439e9i | 0.838110 | − | 0.502096i | ||||
\(483\) | − | 9.49337e8i | − | 0.383359i | ||||||
\(484\) | −6.18334e8 | + | 1.15561e9i | −0.247893 | + | 0.463290i | ||||
\(485\) | 2.54506e9i | 1.01298i | ||||||||
\(486\) | 6.58499e8 | + | 1.09918e9i | 0.260213 | + | 0.434353i | ||||
\(487\) | 1.41934e8 | 0.0556847 | 0.0278424 | − | 0.999612i | \(-0.491136\pi\) | ||||
0.0278424 | + | 0.999612i | \(0.491136\pi\) | |||||||
\(488\) | 2.24588e9 | − | 1.08863e8i | 0.874816 | − | 0.0424044i | ||||
\(489\) | 3.44884e9 | 1.33380 | ||||||||
\(490\) | 1.74010e8 | + | 2.90462e8i | 0.0668172 | + | 0.111533i | ||||
\(491\) | 2.38677e9i | 0.909966i | 0.890500 | + | 0.454983i | \(0.150355\pi\) | ||||
−0.890500 | + | 0.454983i | \(0.849645\pi\) | |||||||
\(492\) | −3.25392e8 | − | 1.74108e8i | −0.123177 | − | 0.0659084i | ||||
\(493\) | − | 5.91843e9i | − | 2.22455i | ||||||
\(494\) | 8.90927e8 | − | 5.33738e8i | 0.332505 | − | 0.199197i | ||||
\(495\) | −1.00782e9 | −0.373479 | ||||||||
\(496\) | −1.01532e9 | − | 1.52239e9i | −0.373607 | − | 0.560197i | ||||
\(497\) | −5.15769e8 | −0.188455 | ||||||||
\(498\) | −2.30094e9 | + | 1.37845e9i | −0.834838 | + | 0.500136i | ||||
\(499\) | − | 5.23900e9i | − | 1.88754i | −0.330601 | − | 0.943771i | \(-0.607251\pi\) | ||
0.330601 | − | 0.943771i | \(-0.392749\pi\) | |||||||
\(500\) | −1.86608e9 | − | 9.98486e8i | −0.667629 | − | 0.357229i | ||||
\(501\) | 4.25772e9i | 1.51267i | ||||||||
\(502\) | −6.86681e8 | − | 1.14622e9i | −0.242266 | − | 0.404396i | ||||
\(503\) | −3.63292e9 | −1.27282 | −0.636411 | − | 0.771350i | \(-0.719582\pi\) | ||||
−0.636411 | + | 0.771350i | \(0.719582\pi\) | |||||||
\(504\) | −3.82210e7 | − | 7.88511e8i | −0.0132983 | − | 0.274347i | ||||
\(505\) | 2.01106e9 | 0.694872 | ||||||||
\(506\) | −7.81976e8 | − | 1.30529e9i | −0.268328 | − | 0.447900i | ||||
\(507\) | − | 9.32706e8i | − | 0.317846i | ||||||
\(508\) | 2.39326e9 | − | 4.47278e9i | 0.809965 | − | 1.51375i | ||||
\(509\) | 2.58693e9i | 0.869505i | 0.900550 | + | 0.434753i | \(0.143164\pi\) | ||||
−0.900550 | + | 0.434753i | \(0.856836\pi\) | |||||||
\(510\) | 4.38060e9 | − | 2.62433e9i | 1.46230 | − | 0.876039i | ||||
\(511\) | 2.56955e9 | 0.851892 | ||||||||
\(512\) | −4.39735e8 | − | 3.00500e9i | −0.144793 | − | 0.989462i | ||||
\(513\) | 1.61811e9 | 0.529171 | ||||||||
\(514\) | −1.23708e9 | + | 7.41108e8i | −0.401814 | + | 0.240719i | ||||
\(515\) | 2.14105e9i | 0.690718i | ||||||||
\(516\) | 7.97591e8 | − | 1.49063e9i | 0.255568 | − | 0.477633i | ||||
\(517\) | − | 6.49047e8i | − | 0.206566i | ||||||
\(518\) | 5.76636e8 | + | 9.62533e8i | 0.182283 | + | 0.304272i | ||||
\(519\) | −7.96876e8 | −0.250210 | ||||||||
\(520\) | 1.43091e8 | + | 2.95200e9i | 0.0446272 | + | 0.920672i | ||||
\(521\) | 1.08542e8 | 0.0336253 | 0.0168127 | − | 0.999859i | \(-0.494648\pi\) | ||||
0.0168127 | + | 0.999859i | \(0.494648\pi\) | |||||||
\(522\) | 5.66755e8 | + | 9.46041e8i | 0.174401 | + | 0.291114i | ||||
\(523\) | 6.10725e9i | 1.86676i | 0.358884 | + | 0.933382i | \(0.383157\pi\) | ||||
−0.358884 | + | 0.933382i | \(0.616843\pi\) | |||||||
\(524\) | −4.12318e9 | − | 2.20620e9i | −1.25191 | − | 0.669861i | ||||
\(525\) | − | 1.04564e9i | − | 0.315374i | ||||||
\(526\) | −4.20363e9 | + | 2.51832e9i | −1.25943 | + | 0.754502i | ||||
\(527\) | 3.86300e9 | 1.14971 | ||||||||
\(528\) | 1.99327e9 | + | 2.98877e9i | 0.589315 | + | 0.883637i | ||||
\(529\) | −2.79634e9 | −0.821288 | ||||||||
\(530\) | −3.27561e9 | + | 1.96236e9i | −0.955712 | + | 0.572549i | ||||
\(531\) | 1.28732e8i | 0.0373125i | ||||||||
\(532\) | −1.57636e9 | − | 8.43465e8i | −0.453905 | − | 0.242871i | ||||
\(533\) | 4.50894e8i | 0.128982i | ||||||||
\(534\) | 1.02185e8 | + | 1.70569e8i | 0.0290396 | + | 0.0484736i | ||||
\(535\) | −1.66414e8 | −0.0469841 | ||||||||
\(536\) | 4.57623e8 | − | 2.21821e7i | 0.128360 | − | 0.00622193i | ||||
\(537\) | −1.19764e9 | −0.333747 | ||||||||
\(538\) | −2.00446e9 | − | 3.34590e9i | −0.554958 | − | 0.926349i | ||||
\(539\) | − | 5.02858e8i | − | 0.138320i | ||||||
\(540\) | −2.17239e9 | + | 4.06000e9i | −0.593689 | + | 1.10955i | ||||
\(541\) | 5.39345e8i | 0.146445i | 0.997316 | + | 0.0732227i | \(0.0233284\pi\) | ||||
−0.997316 | + | 0.0732227i | \(0.976672\pi\) | |||||||
\(542\) | 4.29475e9 | − | 2.57290e9i | 1.15862 | − | 0.694106i | ||||
\(543\) | −1.59348e8 | −0.0427116 | ||||||||
\(544\) | 5.79270e9 | + | 2.74746e9i | 1.54271 | + | 0.731704i | ||||
\(545\) | 6.35620e9 | 1.68194 | ||||||||
\(546\) | 2.34917e9 | − | 1.40735e9i | 0.617648 | − | 0.370021i | ||||
\(547\) | 8.82287e7i | 0.0230491i | 0.999934 | + | 0.0115246i | \(0.00366846\pi\) | ||||
−0.999934 | + | 0.0115246i | \(0.996332\pi\) | |||||||
\(548\) | −1.55177e9 | + | 2.90012e9i | −0.402806 | + | 0.752808i | ||||
\(549\) | − | 8.84483e8i | − | 0.228132i | ||||||
\(550\) | −8.61304e8 | − | 1.43771e9i | −0.220743 | − | 0.368469i | ||||
\(551\) | 2.49754e9 | 0.636037 | ||||||||
\(552\) | −1.43493e9 | + | 6.95546e7i | −0.363116 | + | 0.0176011i | ||||
\(553\) | −7.87226e9 | −1.97953 | ||||||||
\(554\) | −1.84981e9 | − | 3.08774e9i | −0.462213 | − | 0.771537i | ||||
\(555\) | − | 1.35243e9i | − | 0.335807i | ||||||
\(556\) | 5.90257e9 | + | 3.15829e9i | 1.45639 | + | 0.779274i | ||||
\(557\) | − | 5.57233e8i | − | 0.136629i | −0.997664 | − | 0.0683147i | \(-0.978238\pi\) | ||
0.997664 | − | 0.0683147i | \(-0.0217622\pi\) | |||||||
\(558\) | −6.17488e8 | + | 3.69925e8i | −0.150456 | + | 0.0901352i | ||||
\(559\) | −2.06555e9 | −0.500143 | ||||||||
\(560\) | 4.23269e9 | − | 2.82286e9i | 1.01849 | − | 0.679254i | ||||
\(561\) | −7.58386e9 | −1.81351 | ||||||||
\(562\) | −1.24711e9 | + | 7.47119e8i | −0.296365 | + | 0.177547i | ||||
\(563\) | − | 1.17012e9i | − | 0.276344i | −0.990408 | − | 0.138172i | \(-0.955877\pi\) | ||
0.990408 | − | 0.138172i | \(-0.0441227\pi\) | |||||||
\(564\) | −5.40312e8 | − | 2.89105e8i | −0.126814 | − | 0.0678546i | ||||
\(565\) | − | 6.12887e9i | − | 1.42959i | ||||||
\(566\) | 2.31973e9 | + | 3.87214e9i | 0.537749 | + | 0.897623i | ||||
\(567\) | 3.07437e9 | 0.708297 | ||||||||
\(568\) | 3.77886e7 | + | 7.79590e8i | 0.00865250 | + | 0.178504i | ||||
\(569\) | −2.39181e9 | −0.544295 | −0.272147 | − | 0.962256i | \(-0.587734\pi\) | ||||
−0.272147 | + | 0.962256i | \(0.587734\pi\) | |||||||
\(570\) | 1.10745e9 | + | 1.84859e9i | 0.250475 | + | 0.418098i | ||||
\(571\) | − | 3.15823e9i | − | 0.709933i | −0.934879 | − | 0.354966i | \(-0.884492\pi\) | ||
0.934879 | − | 0.354966i | \(-0.115508\pi\) | |||||||
\(572\) | 2.07076e9 | − | 3.87007e9i | 0.462640 | − | 0.864634i | ||||
\(573\) | 1.93080e9i | 0.428743i | ||||||||
\(574\) | 6.65843e8 | − | 3.98894e8i | 0.146954 | − | 0.0880371i | ||||
\(575\) | 6.70211e8 | 0.147019 | ||||||||
\(576\) | −1.18904e9 | + | 1.15543e8i | −0.259250 | + | 0.0251921i | ||||
\(577\) | 4.03435e9 | 0.874296 | 0.437148 | − | 0.899390i | \(-0.355989\pi\) | ||||
0.437148 | + | 0.899390i | \(0.355989\pi\) | |||||||
\(578\) | −7.62785e9 | + | 4.56970e9i | −1.64306 | + | 0.984329i | ||||
\(579\) | 1.90023e8i | 0.0406846i | ||||||||
\(580\) | −3.35308e9 | + | 6.26660e9i | −0.713585 | + | 1.33363i | ||||
\(581\) | − | 5.64138e9i | − | 1.19335i | ||||||
\(582\) | −1.83398e9 | − | 3.06131e9i | −0.385623 | − | 0.643691i | ||||
\(583\) | 5.67087e9 | 1.18525 | ||||||||
\(584\) | −1.88262e8 | − | 3.88391e9i | −0.0391128 | − | 0.806908i | ||||
\(585\) | 1.16257e9 | 0.240090 | ||||||||
\(586\) | −1.16843e9 | − | 1.95037e9i | −0.239861 | − | 0.400382i | ||||
\(587\) | − | 2.72240e9i | − | 0.555544i | −0.960647 | − | 0.277772i | \(-0.910404\pi\) | ||
0.960647 | − | 0.277772i | \(-0.0895960\pi\) | |||||||
\(588\) | −4.18614e8 | − | 2.23988e8i | −0.0849168 | − | 0.0454365i | ||||
\(589\) | 1.63016e9i | 0.328721i | ||||||||
\(590\) | −7.11692e8 | + | 4.26361e8i | −0.142662 | + | 0.0854664i | ||||
\(591\) | −4.62012e9 | −0.920655 | ||||||||
\(592\) | 1.41263e9 | − | 9.42113e8i | 0.279836 | − | 0.186628i | ||||
\(593\) | −2.29251e9 | −0.451460 | −0.225730 | − | 0.974190i | \(-0.572477\pi\) | ||||
−0.225730 | + | 0.974190i | \(0.572477\pi\) | |||||||
\(594\) | 5.86634e9 | − | 3.51441e9i | 1.14846 | − | 0.688019i | ||||
\(595\) | 1.07402e10i | 2.09028i | ||||||||
\(596\) | 2.03605e9 | + | 1.08943e9i | 0.393937 | + | 0.210784i | ||||
\(597\) | − | 4.86346e8i | − | 0.0935482i | ||||||
\(598\) | 9.02047e8 | + | 1.50572e9i | 0.172494 | + | 0.287932i | ||||
\(599\) | −3.58734e9 | −0.681991 | −0.340995 | − | 0.940065i | \(-0.610764\pi\) | ||||
−0.340995 | + | 0.940065i | \(0.610764\pi\) | |||||||
\(600\) | −1.58050e9 | + | 7.66106e7i | −0.298720 | + | 0.0144797i | ||||
\(601\) | 8.20369e9 | 1.54152 | 0.770759 | − | 0.637127i | \(-0.219877\pi\) | ||||
0.770759 | + | 0.637127i | \(0.219877\pi\) | |||||||
\(602\) | 1.82734e9 | + | 3.05024e9i | 0.341375 | + | 0.569831i | ||||
\(603\) | − | 1.80223e8i | − | 0.0334734i | ||||||
\(604\) | 2.33934e9 | − | 4.37201e9i | 0.431980 | − | 0.807332i | ||||
\(605\) | 3.32259e9i | 0.610004i | ||||||||
\(606\) | −2.41899e9 | + | 1.44917e9i | −0.441551 | + | 0.264525i | ||||
\(607\) | −4.60087e9 | −0.834986 | −0.417493 | − | 0.908680i | \(-0.637091\pi\) | ||||
−0.417493 | + | 0.908680i | \(0.637091\pi\) | |||||||
\(608\) | −1.15941e9 | + | 2.44449e9i | −0.209207 | + | 0.441088i | ||||
\(609\) | 6.58546e9 | 1.18148 | ||||||||
\(610\) | 4.88985e9 | − | 2.92942e9i | 0.872251 | − | 0.522549i | ||||
\(611\) | 7.48707e8i | 0.132791i | ||||||||
\(612\) | 1.18980e9 | − | 2.22364e9i | 0.209819 | − | 0.392133i | ||||
\(613\) | 8.55728e9i | 1.50046i | 0.661178 | + | 0.750229i | \(0.270057\pi\) | ||||
−0.661178 | + | 0.750229i | \(0.729943\pi\) | |||||||
\(614\) | −9.23998e7 | − | 1.54236e8i | −0.0161095 | − | 0.0268903i | ||||
\(615\) | −9.35561e8 | −0.162184 | ||||||||
\(616\) | −7.54695e9 | + | 3.65819e8i | −1.30089 | + | 0.0630570i | ||||
\(617\) | −2.58089e9 | −0.442355 | −0.221178 | − | 0.975234i | \(-0.570990\pi\) | ||||
−0.221178 | + | 0.975234i | \(0.570990\pi\) | |||||||
\(618\) | −1.54284e9 | − | 2.57535e9i | −0.262943 | − | 0.438911i | ||||
\(619\) | 5.26641e9i | 0.892478i | 0.894914 | + | 0.446239i | \(0.147237\pi\) | ||||
−0.894914 | + | 0.446239i | \(0.852763\pi\) | |||||||
\(620\) | −4.09026e9 | − | 2.18858e9i | −0.689255 | − | 0.368800i | ||||
\(621\) | 2.73469e9i | 0.458234i | ||||||||
\(622\) | −4.73340e9 | + | 2.83569e9i | −0.788690 | + | 0.472490i | ||||
\(623\) | −4.18197e8 | −0.0692903 | ||||||||
\(624\) | −2.29933e9 | − | 3.44769e9i | −0.378840 | − | 0.568044i | ||||
\(625\) | −7.48796e9 | −1.22683 | ||||||||
\(626\) | 3.15164e9 | − | 1.88809e9i | 0.513483 | − | 0.307618i | ||||
\(627\) | − | 3.20035e9i | − | 0.518514i | ||||||
\(628\) | −5.78226e9 | − | 3.09392e9i | −0.931621 | − | 0.498483i | ||||
\(629\) | 3.58449e9i | 0.574314i | ||||||||
\(630\) | −1.02850e9 | − | 1.71679e9i | −0.163874 | − | 0.273543i | ||||
\(631\) | 8.32515e9 | 1.31914 | 0.659568 | − | 0.751645i | \(-0.270739\pi\) | ||||
0.659568 | + | 0.751645i | \(0.270739\pi\) | |||||||
\(632\) | 5.76773e8 | + | 1.18990e10i | 0.0908857 | + | 1.87500i | ||||
\(633\) | 7.87635e9 | 1.23428 | ||||||||
\(634\) | 6.16801e9 | + | 1.02958e10i | 0.961242 | + | 1.60453i | ||||
\(635\) | − | 1.28601e10i | − | 1.99313i | ||||||
\(636\) | 2.52598e9 | − | 4.72083e9i | 0.389341 | − | 0.727643i | ||||
\(637\) | 5.80071e8i | 0.0889187i | ||||||||
\(638\) | 9.05469e9 | − | 5.42449e9i | 1.38039 | − | 0.826965i | ||||
\(639\) | 3.07022e8 | 0.0465496 | ||||||||
\(640\) | −4.57691e9 | − | 6.19093e9i | −0.690148 | − | 0.933526i | ||||
\(641\) | 4.26190e9 | 0.639146 | 0.319573 | − | 0.947562i | \(-0.396460\pi\) | ||||
0.319573 | + | 0.947562i | \(0.396460\pi\) | |||||||
\(642\) | 2.00170e8 | − | 1.19918e8i | 0.0298557 | − | 0.0178860i | ||||
\(643\) | − | 1.26588e10i | − | 1.87782i | −0.344167 | − | 0.938908i | \(-0.611839\pi\) | ||
0.344167 | − | 0.938908i | \(-0.388161\pi\) | |||||||
\(644\) | 1.42550e9 | − | 2.66414e9i | 0.210314 | − | 0.393058i | ||||
\(645\) | − | 4.28582e9i | − | 0.628890i | ||||||
\(646\) | −2.93519e9 | − | 4.89949e9i | −0.428374 | − | 0.715052i | ||||
\(647\) | −7.38061e9 | −1.07134 | −0.535670 | − | 0.844427i | \(-0.679941\pi\) | ||||
−0.535670 | + | 0.844427i | \(0.679941\pi\) | |||||||
\(648\) | −2.25249e8 | − | 4.64695e9i | −0.0325199 | − | 0.670896i | ||||
\(649\) | 1.23211e9 | 0.176926 | ||||||||
\(650\) | 9.93555e8 | + | 1.65846e9i | 0.141904 | + | 0.236870i | ||||
\(651\) | 4.29837e9i | 0.610620i | ||||||||
\(652\) | 9.67853e9 | + | 5.17870e9i | 1.36755 | + | 0.731735i | ||||
\(653\) | − | 3.21579e9i | − | 0.451951i | −0.974133 | − | 0.225975i | \(-0.927443\pi\) | ||
0.974133 | − | 0.225975i | \(-0.0725569\pi\) | |||||||
\(654\) | −7.64552e9 | + | 4.58029e9i | −1.06877 | + | 0.640281i | ||||
\(655\) | −1.18549e10 | −1.64836 | ||||||||
\(656\) | −6.51717e8 | − | 9.77204e8i | −0.0901354 | − | 0.135152i | ||||
\(657\) | −1.52958e9 | −0.210423 | ||||||||
\(658\) | 1.10563e9 | − | 6.62362e8i | 0.151293 | − | 0.0906368i | ||||
\(659\) | 5.17004e9i | 0.703711i | 0.936054 | + | 0.351856i | \(0.114449\pi\) | ||||
−0.936054 | + | 0.351856i | \(0.885551\pi\) | |||||||
\(660\) | 8.03001e9 | + | 4.29663e9i | 1.08721 | + | 0.581733i | ||||
\(661\) | − | 1.95604e9i | − | 0.263435i | −0.991287 | − | 0.131717i | \(-0.957951\pi\) | ||
0.991287 | − | 0.131717i | \(-0.0420491\pi\) | |||||||
\(662\) | 1.67735e9 | + | 2.79987e9i | 0.224709 | + | 0.375090i | ||||
\(663\) | 8.74835e9 | 1.16581 | ||||||||
\(664\) | −8.52701e9 | + | 4.13325e8i | −1.13034 | + | 0.0547902i | ||||
\(665\) | −4.53232e9 | −0.597647 | ||||||||
\(666\) | −3.43254e8 | − | 5.72968e8i | −0.0450253 | − | 0.0751572i | ||||
\(667\) | 4.22099e9i | 0.550775i | ||||||||
\(668\) | −6.39330e9 | + | 1.19485e10i | −0.829865 | + | 1.55094i | ||||
\(669\) | − | 4.34434e9i | − | 0.560961i | ||||||
\(670\) | 9.96362e8 | − | 5.96902e8i | 0.127984 | − | 0.0766727i | ||||
\(671\) | −8.46551e9 | −1.08174 | ||||||||
\(672\) | −3.05711e9 | + | 6.44555e9i | −0.388614 | + | 0.819347i | ||||
\(673\) | 1.54679e9 | 0.195605 | 0.0978024 | − | 0.995206i | \(-0.468819\pi\) | ||||
0.0978024 | + | 0.995206i | \(0.468819\pi\) | |||||||
\(674\) | 1.07337e9 | − | 6.43035e8i | 0.135033 | − | 0.0808956i | ||||
\(675\) | 3.01211e9i | 0.376971i | ||||||||
\(676\) | 1.40053e9 | − | 2.61747e9i | 0.174373 | − | 0.325888i | ||||
\(677\) | − | 8.55209e9i | − | 1.05928i | −0.848222 | − | 0.529642i | \(-0.822326\pi\) | ||
0.848222 | − | 0.529642i | \(-0.177674\pi\) | |||||||
\(678\) | 4.41648e9 | + | 7.37209e9i | 0.544217 | + | 0.908420i | ||||
\(679\) | 7.50565e9 | 0.920119 | ||||||||
\(680\) | 1.62340e10 | − | 7.86900e8i | 1.97990 | − | 0.0959707i | ||||
\(681\) | −6.48061e9 | −0.786323 | ||||||||
\(682\) | 3.54061e9 | + | 5.91006e9i | 0.427398 | + | 0.713422i | ||||
\(683\) | 7.26976e9i | 0.873067i | 0.899688 | + | 0.436534i | \(0.143794\pi\) | ||||
−0.899688 | + | 0.436534i | \(0.856206\pi\) | |||||||
\(684\) | 9.38362e8 | + | 5.02090e8i | 0.112118 | + | 0.0599909i | ||||
\(685\) | 8.33837e9i | 0.991206i | ||||||||
\(686\) | −6.79217e9 | + | 4.06906e9i | −0.803293 | + | 0.481238i | ||||
\(687\) | −2.12010e9 | −0.249463 | ||||||||
\(688\) | 4.47658e9 | − | 2.98552e9i | 0.524068 | − | 0.349511i | ||||
\(689\) | −6.54162e9 | −0.761935 | ||||||||
\(690\) | −3.12422e9 | + | 1.87166e9i | −0.362051 | + | 0.216898i | ||||
\(691\) | − | 5.19893e9i | − | 0.599434i | −0.954028 | − | 0.299717i | \(-0.903108\pi\) | ||
0.954028 | − | 0.299717i | \(-0.0968922\pi\) | |||||||
\(692\) | −2.23629e9 | − | 1.19657e9i | −0.256541 | − | 0.137268i | ||||
\(693\) | 2.97218e9i | 0.339241i | ||||||||
\(694\) | −6.43358e9 | − | 1.07391e10i | −0.730626 | − | 1.21958i | ||||
\(695\) | 1.69709e10 | 1.91760 | ||||||||
\(696\) | −4.82494e8 | − | 9.95399e9i | −0.0542449 | − | 1.11909i | ||||
\(697\) | 2.47961e9 | 0.277376 | ||||||||
\(698\) | −8.04333e9 | − | 1.34261e10i | −0.895245 | − | 1.49436i | ||||
\(699\) | 7.21572e9i | 0.799116i | ||||||||
\(700\) | 1.57011e9 | − | 2.93440e9i | 0.173017 | − | 0.323353i | ||||
\(701\) | − | 1.35221e10i | − | 1.48262i | −0.671163 | − | 0.741310i | \(-0.734205\pi\) | ||
0.671163 | − | 0.741310i | \(-0.265795\pi\) | |||||||
\(702\) | −6.76710e9 | + | 4.05404e9i | −0.738283 | + | 0.442291i | ||||
\(703\) | −1.51263e9 | −0.164206 | ||||||||
\(704\) | 1.10588e9 | + | 1.13805e10i | 0.119455 | + | 1.22930i | ||||
\(705\) | −1.55349e9 | −0.166974 | ||||||||
\(706\) | 2.40321e9 | − | 1.43972e9i | 0.257025 | − | 0.153979i | ||||
\(707\) | − | 5.93083e9i | − | 0.631172i | ||||||
\(708\) | 5.48819e8 | − | 1.02569e9i | 0.0581182 | − | 0.108618i | ||||
\(709\) | 1.05901e10i | 1.11594i | 0.829862 | + | 0.557969i | \(0.188419\pi\) | ||||
−0.829862 | + | 0.557969i | \(0.811581\pi\) | |||||||
\(710\) | 1.01686e9 | + | 1.69737e9i | 0.106625 | + | 0.177980i | ||||
\(711\) | 4.68613e9 | 0.488957 | ||||||||
\(712\) | 3.06398e7 | + | 6.32109e8i | 0.00318131 | + | 0.0656314i | ||||
\(713\) | −2.75507e9 | −0.284655 | ||||||||
\(714\) | −7.73944e9 | − | 1.29189e10i | −0.795730 | − | 1.32825i | ||||
\(715\) | − | 1.11271e10i | − | 1.13845i | ||||||
\(716\) | −3.36096e9 | − | 1.79835e9i | −0.342191 | − | 0.183096i | ||||
\(717\) | 3.38799e9i | 0.343261i | ||||||||
\(718\) | 1.34556e10 | − | 8.06102e9i | 1.35665 | − | 0.812746i | ||||
\(719\) | 1.49161e10 | 1.49659 | 0.748297 | − | 0.663363i | \(-0.230872\pi\) | ||||
0.748297 | + | 0.663363i | \(0.230872\pi\) | |||||||
\(720\) | −2.51959e9 | + | 1.68037e9i | −0.251575 | + | 0.167780i | ||||
\(721\) | 6.31417e9 | 0.627398 | ||||||||
\(722\) | −6.60779e9 | + | 3.95860e9i | −0.653395 | + | 0.391437i | ||||
\(723\) | 8.53800e9i | 0.840180i | ||||||||
\(724\) | −4.47180e8 | − | 2.39273e8i | −0.0437923 | − | 0.0234320i | ||||
\(725\) | 4.64919e9i | 0.453100i | ||||||||
\(726\) | −2.39426e9 | − | 3.99656e9i | −0.232217 | − | 0.387622i | ||||
\(727\) | −8.90159e9 | −0.859206 | −0.429603 | − | 0.903018i | \(-0.641346\pi\) | ||||
−0.429603 | + | 0.903018i | \(0.641346\pi\) | |||||||
\(728\) | 8.70577e9 | − | 4.21989e8i | 0.836271 | − | 0.0405361i | ||||
\(729\) | −1.15808e10 | −1.10711 | ||||||||
\(730\) | −5.06599e9 | − | 8.45627e9i | −0.481986 | − | 0.804542i | ||||
\(731\) | 1.13591e10i | 1.07556i | ||||||||
\(732\) | −3.77079e9 | + | 7.04728e9i | −0.355340 | + | 0.664099i | ||||
\(733\) | − | 7.99792e9i | − | 0.750090i | −0.927007 | − | 0.375045i | \(-0.877627\pi\) | ||
0.927007 | − | 0.375045i | \(-0.122373\pi\) | |||||||
\(734\) | 7.27288e9 | − | 4.35704e9i | 0.678844 | − | 0.406683i | ||||
\(735\) | −1.20359e9 | −0.111808 | ||||||||
\(736\) | −4.13132e9 | − | 1.95947e9i | −0.381959 | − | 0.181162i | ||||
\(737\) | −1.72494e9 | −0.158722 | ||||||||
\(738\) | −3.96357e8 | + | 2.37450e8i | −0.0362985 | + | 0.0217458i | ||||
\(739\) | 1.03852e10i | 0.946588i | 0.880905 | + | 0.473294i | \(0.156935\pi\) | ||||
−0.880905 | + | 0.473294i | \(0.843065\pi\) | |||||||
\(740\) | 2.03078e9 | − | 3.79536e9i | 0.184227 | − | 0.344304i | ||||
\(741\) | 3.69175e9i | 0.333326i | ||||||||
\(742\) | 5.78720e9 | + | 9.66013e9i | 0.520062 | + | 0.868099i | ||||
\(743\) | −3.73477e9 | −0.334044 | −0.167022 | − | 0.985953i | \(-0.553415\pi\) | ||||
−0.167022 | + | 0.985953i | \(0.553415\pi\) | |||||||
\(744\) | 6.49704e9 | − | 3.14927e8i | 0.578376 | − | 0.0280353i | ||||
\(745\) | 5.85402e9 | 0.518689 | ||||||||
\(746\) | 8.69345e9 | + | 1.45113e10i | 0.766666 | + | 1.27974i | ||||
\(747\) | 3.35815e9i | 0.294766i | ||||||||
\(748\) | −2.12827e10 | − | 1.13878e10i | −1.85940 | − | 0.994908i | ||||
\(749\) | 4.90772e8i | 0.0426770i | ||||||||
\(750\) | 6.45365e9 | − | 3.86626e9i | 0.558587 | − | 0.334639i | ||||
\(751\) | −1.34330e10 | −1.15726 | −0.578631 | − | 0.815589i | \(-0.696413\pi\) | ||||
−0.578631 | + | 0.815589i | \(0.696413\pi\) | |||||||
\(752\) | −1.08217e9 | − | 1.62264e9i | −0.0927970 | − | 0.139143i | ||||
\(753\) | 4.74963e9 | 0.405394 | ||||||||
\(754\) | −1.04450e10 | + | 6.25741e9i | −0.887379 | + | 0.531612i | ||||
\(755\) | − | 1.25703e10i | − | 1.06300i | ||||||
\(756\) | 1.19734e10 | + | 6.40660e9i | 1.00784 | + | 0.539264i | ||||
\(757\) | − | 6.78007e9i | − | 0.568065i | −0.958815 | − | 0.284033i | \(-0.908328\pi\) | ||
0.958815 | − | 0.284033i | \(-0.0916724\pi\) | |||||||
\(758\) | −4.60548e8 | − | 7.68758e8i | −0.0384090 | − | 0.0641132i | ||||
\(759\) | 5.40877e9 | 0.449006 | ||||||||
\(760\) | 3.32068e8 | + | 6.85065e9i | 0.0274397 | + | 0.566089i | ||||
\(761\) | 8.01137e9 | 0.658962 | 0.329481 | − | 0.944162i | \(-0.393126\pi\) | ||||
0.329481 | + | 0.944162i | \(0.393126\pi\) | |||||||
\(762\) | 9.26698e9 | + | 1.54687e10i | 0.758745 | + | 1.26652i | ||||
\(763\) | − | 1.87451e10i | − | 1.52775i | ||||||
\(764\) | −2.89925e9 | + | 5.41845e9i | −0.235212 | + | 0.439590i | ||||
\(765\) | − | 6.39335e9i | − | 0.516314i | ||||||
\(766\) | −4.66133e9 | + | 2.79252e9i | −0.374722 | + | 0.224489i | ||||
\(767\) | −1.42130e9 | −0.113737 | ||||||||
\(768\) | 9.96651e9 | + | 4.14861e9i | 0.793924 | + | 0.330475i | ||||
\(769\) | 1.46553e10 | 1.16213 | 0.581063 | − | 0.813858i | \(-0.302637\pi\) | ||||
0.581063 | + | 0.813858i | \(0.302637\pi\) | |||||||
\(770\) | −1.64316e10 | + | 9.84389e9i | −1.29707 | + | 0.777051i | ||||
\(771\) | − | 5.12609e9i | − | 0.402806i | ||||||
\(772\) | −2.85334e8 | + | 5.33264e8i | −0.0223199 | + | 0.0417140i | ||||
\(773\) | 2.33296e10i | 1.81668i | 0.418233 | + | 0.908340i | \(0.362650\pi\) | ||||
−0.418233 | + | 0.908340i | \(0.637350\pi\) | |||||||
\(774\) | −1.08776e9 | − | 1.81572e9i | −0.0843219 | − | 0.140752i | ||||
\(775\) | −3.03456e9 | −0.234174 | ||||||||
\(776\) | −5.49913e8 | − | 1.13449e10i | −0.0422453 | − | 0.871533i | ||||
\(777\) | −3.98847e9 | −0.305023 | ||||||||
\(778\) | 6.23001e9 | + | 1.03993e10i | 0.474307 | + | 0.791725i | ||||
\(779\) | 1.04638e9i | 0.0793064i | ||||||||
\(780\) | −9.26300e9 | − | 4.95636e9i | −0.698909 | − | 0.373966i | ||||
\(781\) | − | 2.93855e9i | − | 0.220726i | ||||||
\(782\) | 8.28042e9 | − | 4.96064e9i | 0.619197 | − | 0.370949i | ||||
\(783\) | −1.89703e10 | −1.41224 | ||||||||
\(784\) | −8.38429e8 | − | 1.25716e9i | −0.0621384 | − | 0.0931721i | ||||
\(785\) | −1.66250e10 | −1.22664 | ||||||||
\(786\) | 1.42596e10 | − | 8.54266e9i | 1.04744 | − | 0.627501i | ||||
\(787\) | − | 5.27740e8i | − | 0.0385930i | −0.999814 | − | 0.0192965i | \(-0.993857\pi\) | ||
0.999814 | − | 0.0192965i | \(-0.00614264\pi\) | |||||||
\(788\) | −1.29655e10 | − | 6.93747e9i | −0.943948 | − | 0.505079i | ||||
\(789\) | − | 1.74187e10i | − | 1.26254i | ||||||
\(790\) | 1.55205e10 | + | 2.59072e10i | 1.11998 | + | 1.86950i | ||||
\(791\) | −1.80747e10 | −1.29853 | ||||||||
\(792\) | 4.49248e9 | − | 2.17761e8i | 0.321327 | − | 0.0155755i | ||||
\(793\) | 9.76536e9 | 0.695396 | ||||||||
\(794\) | −1.18138e10 | − | 1.97198e10i | −0.837562 | − | 1.39808i | ||||
\(795\) | − | 1.35732e10i | − | 0.958072i | ||||||
\(796\) | 7.30287e8 | − | 1.36484e9i | 0.0513213 | − | 0.0959150i | ||||
\(797\) | 2.41514e9i | 0.168981i | 0.996424 | + | 0.0844907i | \(0.0269263\pi\) | ||||
−0.996424 | + | 0.0844907i | \(0.973074\pi\) | |||||||
\(798\) | 5.45168e9 | − | 3.26600e9i | 0.379770 | − | 0.227513i | ||||
\(799\) | 4.11738e9 | 0.285566 | ||||||||
\(800\) | −4.55042e9 | − | 2.15825e9i | −0.314222 | − | 0.149034i | ||||
\(801\) | 2.48940e8 | 0.0171152 | ||||||||
\(802\) | 2.50165e10 | − | 1.49869e10i | 1.71244 | − | 1.02589i | ||||
\(803\) | 1.46398e10i | 0.997773i | ||||||||
\(804\) | −7.68341e8 | + | 1.43596e9i | −0.0521384 | + | 0.0974421i | ||||
\(805\) | − | 7.65988e9i | − | 0.517531i | ||||||
\(806\) | −4.08426e9 | − | 6.81754e9i | −0.274752 | − | 0.458622i | ||||
\(807\) | 1.38645e10 | 0.928636 | ||||||||
\(808\) | −8.96451e9 | + | 4.34531e8i | −0.597843 | + | 0.0289789i | ||||
\(809\) | 1.16364e10 | 0.772679 | 0.386340 | − | 0.922357i | \(-0.373739\pi\) | ||||
0.386340 | + | 0.922357i | \(0.373739\pi\) | |||||||
\(810\) | −6.06126e9 | − | 1.01176e10i | −0.400743 | − | 0.668929i | ||||
\(811\) | − | 1.44359e10i | − | 0.950320i | −0.879899 | − | 0.475160i | \(-0.842390\pi\) | ||
0.879899 | − | 0.475160i | \(-0.157610\pi\) | |||||||
\(812\) | 1.84809e10 | + | 9.88858e9i | 1.21137 | + | 0.648168i | ||||
\(813\) | 1.77962e10i | 1.16148i | ||||||||
\(814\) | −5.48396e9 | + | 3.28533e9i | −0.356376 | + | 0.213498i | ||||
\(815\) | 2.78275e10 | 1.80062 | ||||||||
\(816\) | −1.89599e10 | + | 1.26448e10i | −1.22158 | + | 0.814696i | ||||
\(817\) | −4.79348e9 | −0.307521 | ||||||||
\(818\) | −3.20512e9 | + | 1.92013e9i | −0.204742 | + | 0.122657i | ||||
\(819\) | − | 3.42855e9i | − | 0.218080i | ||||||
\(820\) | −2.62548e9 | − | 1.40482e9i | −0.166288 | − | 0.0889757i | ||||
\(821\) | 7.63805e9i | 0.481706i | 0.970562 | + | 0.240853i | \(0.0774271\pi\) | ||||
−0.970562 | + | 0.240853i | \(0.922573\pi\) | |||||||
\(822\) | −6.00865e9 | − | 1.00298e10i | −0.377333 | − | 0.629854i | ||||
\(823\) | −2.16446e10 | −1.35348 | −0.676738 | − | 0.736224i | \(-0.736607\pi\) | ||||
−0.676738 | + | 0.736224i | \(0.736607\pi\) | |||||||
\(824\) | −4.62618e8 | − | 9.54395e9i | −0.0288056 | − | 0.594268i | ||||
\(825\) | 5.95746e9 | 0.369379 | ||||||||
\(826\) | 1.25738e9 | + | 2.09885e9i | 0.0776315 | + | 0.129584i | ||||
\(827\) | 1.57823e10i | 0.970288i | 0.874434 | + | 0.485144i | \(0.161233\pi\) | ||||
−0.874434 | + | 0.485144i | \(0.838767\pi\) | |||||||
\(828\) | −8.48561e8 | + | 1.58588e9i | −0.0519489 | + | 0.0970879i | ||||
\(829\) | 2.63296e10i | 1.60510i | 0.596582 | + | 0.802552i | \(0.296525\pi\) | ||||
−0.596582 | + | 0.802552i | \(0.703475\pi\) | |||||||
\(830\) | −1.85655e10 | + | 1.11222e10i | −1.12702 | + | 0.675179i | ||||
\(831\) | 1.27947e10 | 0.773442 | ||||||||
\(832\) | −1.27568e9 | − | 1.31279e10i | −0.0767911 | − | 0.790251i | ||||
\(833\) | 3.19000e9 | 0.191220 | ||||||||
\(834\) | −2.04134e10 | + | 1.22293e10i | −1.21852 | + | 0.729995i | ||||
\(835\) | 3.43541e10i | 2.04210i | ||||||||
\(836\) | 4.80557e9 | − | 8.98119e9i | 0.284461 | − | 0.531633i | ||||
\(837\) | − | 1.23820e10i | − | 0.729882i | ||||||
\(838\) | −3.37241e8 | − | 5.62931e8i | −0.0197964 | − | 0.0330446i | ||||
\(839\) | −1.84995e9 | −0.108142 | −0.0540710 | − | 0.998537i | \(-0.517220\pi\) | ||||
−0.0540710 | + | 0.998537i | \(0.517220\pi\) | |||||||
\(840\) | 8.75587e8 | + | 1.80636e10i | 0.0509708 | + | 1.05154i | ||||
\(841\) | −1.20307e10 | −0.697438 | ||||||||
\(842\) | −1.10826e9 | − | 1.84993e9i | −0.0639805 | − | 0.106798i | ||||
\(843\) | − | 5.16767e9i | − | 0.297097i | ||||||
\(844\) | 2.21035e10 | + | 1.18270e10i | 1.26550 | + | 0.677134i | ||||
\(845\) | − | 7.52569e9i | − | 0.429090i | ||||||
\(846\) | −6.58149e8 | + | 3.94285e8i | −0.0373704 | + | 0.0223879i | ||||
\(847\) | 9.79866e9 | 0.554083 | ||||||||
\(848\) | 1.41774e10 | − | 9.45519e9i | 0.798382 | − | 0.532457i | ||||
\(849\) | −1.60451e10 | −0.899839 | ||||||||
\(850\) | 9.12042e9 | − | 5.46387e9i | 0.509388 | − | 0.305165i | ||||
\(851\) | − | 2.55643e9i | − | 0.142194i | ||||||
\(852\) | −2.44625e9 | − | 1.30892e9i | −0.135507 | − | 0.0725060i | ||||
\(853\) | 6.28088e7i | 0.00346496i | 0.999998 | + | 0.00173248i | \(0.000551466\pi\) | ||||
−0.999998 | + | 0.00173248i | \(0.999449\pi\) | |||||||
\(854\) | −8.63917e9 | − | 1.44207e10i | −0.474646 | − | 0.792289i | ||||
\(855\) | 2.69796e9 | 0.147623 | ||||||||
\(856\) | 7.41808e8 | − | 3.59572e7i | 0.0404234 | − | 0.00195942i | ||||
\(857\) | −6.25595e9 | −0.339516 | −0.169758 | − | 0.985486i | \(-0.554299\pi\) | ||||
−0.169758 | + | 0.985486i | \(0.554299\pi\) | |||||||
\(858\) | 8.01824e9 | + | 1.33842e10i | 0.433384 | + | 0.723415i | ||||
\(859\) | 2.48119e10i | 1.33562i | 0.744331 | + | 0.667811i | \(0.232769\pi\) | ||||
−0.744331 | + | 0.667811i | \(0.767231\pi\) | |||||||
\(860\) | 6.43549e9 | − | 1.20274e10i | 0.345014 | − | 0.644801i | ||||
\(861\) | 2.75907e9i | 0.147316i | ||||||||
\(862\) | −2.35765e10 | + | 1.41243e10i | −1.25373 | + | 0.751087i | ||||
\(863\) | 1.28944e10 | 0.682909 | 0.341455 | − | 0.939898i | \(-0.389080\pi\) | ||||
0.341455 | + | 0.939898i | \(0.389080\pi\) | |||||||
\(864\) | 8.80640e9 | − | 1.85673e10i | 0.464516 | − | 0.979377i | ||||
\(865\) | −6.42973e9 | −0.337782 | ||||||||
\(866\) | 2.30892e10 | − | 1.38323e10i | 1.20808 | − | 0.723739i | ||||
\(867\) | − | 3.16077e10i | − | 1.64712i | ||||||
\(868\) | −6.45435e9 | + | 1.20626e10i | −0.334991 | + | 0.626069i | ||||
\(869\) | − | 4.48516e10i | − | 2.31851i | ||||||
\(870\) | −1.29835e10 | − | 2.16724e10i | −0.668460 | − | 1.11581i | ||||
\(871\) | 1.98980e9 | 0.102034 | ||||||||
\(872\) | −2.83334e10 | + | 1.37339e9i | −1.44708 | + | 0.0701432i | ||||
\(873\) | −4.46789e9 | −0.227276 | ||||||||
\(874\) | 2.09336e9 | + | 3.49429e9i | 0.106061 | + | 0.177039i | ||||
\(875\) | 1.58229e10i | 0.798468i | ||||||||
\(876\) | 1.21872e10 | + | 6.52102e9i | 0.612548 | + | 0.327757i | ||||
\(877\) | − | 2.75670e10i | − | 1.38004i | −0.723792 | − | 0.690018i | \(-0.757603\pi\) | ||
0.723792 | − | 0.690018i | \(-0.242397\pi\) | |||||||
\(878\) | 1.29238e10 | − | 7.74239e9i | 0.644404 | − | 0.386051i | ||||
\(879\) | 8.08177e9 | 0.401371 | ||||||||
\(880\) | 1.60830e10 | + | 2.41154e10i | 0.795571 | + | 1.19290i | ||||
\(881\) | 2.74343e10 | 1.35169 | 0.675847 | − | 0.737042i | \(-0.263778\pi\) | ||||
0.675847 | + | 0.737042i | \(0.263778\pi\) | |||||||
\(882\) | −5.09910e8 | + | 3.05478e8i | −0.0250238 | + | 0.0149913i | ||||
\(883\) | − | 2.09906e10i | − | 1.02604i | −0.858378 | − | 0.513018i | \(-0.828527\pi\) | ||
0.858378 | − | 0.513018i | \(-0.171473\pi\) | |||||||
\(884\) | 2.45506e10 | + | 1.31363e10i | 1.19531 | + | 0.639575i | ||||
\(885\) | − | 2.94905e9i | − | 0.143015i | ||||||
\(886\) | −2.92251e9 | − | 4.87833e9i | −0.141169 | − | 0.235642i | ||||
\(887\) | −2.39134e10 | −1.15056 | −0.575280 | − | 0.817957i | \(-0.695107\pi\) | ||||
−0.575280 | + | 0.817957i | \(0.695107\pi\) | |||||||
\(888\) | 2.92221e8 | + | 6.02862e9i | 0.0140045 | + | 0.288916i | ||||
\(889\) | −3.79257e10 | −1.81041 | ||||||||
\(890\) | 8.24493e8 | + | 1.37626e9i | 0.0392033 | + | 0.0654390i | ||||
\(891\) | 1.75160e10i | 0.829588i | ||||||||
\(892\) | 6.52337e9 | − | 1.21916e10i | 0.307748 | − | 0.575153i | ||||
\(893\) | 1.73751e9i | 0.0816483i | ||||||||
\(894\) | −7.04148e9 | + | 4.21842e9i | −0.329596 | + | 0.197455i | ||||
\(895\) | −9.66337e9 | −0.450555 | ||||||||
\(896\) | −1.82577e10 | + | 1.34978e10i | −0.847947 | + | 0.626880i | ||||
\(897\) | −6.23927e9 | −0.288643 | ||||||||
\(898\) | −3.05510e10 | + | 1.83025e10i | −1.40785 | + | 0.843419i | ||||
\(899\) | − | 1.91117e10i | − | 0.877282i | ||||||
\(900\) | −9.34642e8 | + | 1.74676e9i | −0.0427363 | + | 0.0798703i | ||||
\(901\) | 3.59744e10i | 1.63854i | ||||||||
\(902\) | 2.27267e9 | + | 3.79359e9i | 0.103113 | + | 0.172118i | ||||
\(903\) | −1.26393e10 | −0.571238 | ||||||||
\(904\) | 1.32427e9 | + | 2.73201e10i | 0.0596194 | + | 1.22997i | ||||
\(905\) | −1.28572e9 | −0.0576603 | ||||||||
\(906\) | 9.05819e9 | + | 1.51201e10i | 0.404662 | + | 0.675472i | ||||
\(907\) | − | 3.84425e10i | − | 1.71075i | −0.518012 | − | 0.855373i | \(-0.673328\pi\) | ||
0.518012 | − | 0.855373i | \(-0.326672\pi\) | |||||||
\(908\) | −1.81867e10 | − | 9.73115e9i | −0.806218 | − | 0.431384i | ||||
\(909\) | 3.53045e9i | 0.155904i | ||||||||
\(910\) | 1.89547e10 | − | 1.13554e10i | 0.833819 | − | 0.499525i | ||||
\(911\) | 3.64507e10 | 1.59732 | 0.798660 | − | 0.601783i | \(-0.205543\pi\) | ||||
0.798660 | + | 0.601783i | \(0.205543\pi\) | |||||||
\(912\) | −5.33602e9 | − | 8.00099e9i | −0.232936 | − | 0.349270i | ||||
\(913\) | 3.21413e10 | 1.39771 | ||||||||
\(914\) | 2.60513e10 | − | 1.56069e10i | 1.12854 | − | 0.676089i | ||||
\(915\) | 2.02622e10i | 0.874405i | ||||||||
\(916\) | −5.94966e9 | − | 3.18349e9i | −0.255775 | − | 0.136858i | ||||
\(917\) | 3.49613e10i | 1.49725i | ||||||||
\(918\) | 2.22945e10 | + | 3.72145e10i | 0.951148 | + | 1.58768i | ||||
\(919\) | 2.37343e10 | 1.00872 | 0.504361 | − | 0.863493i | \(-0.331728\pi\) | ||||
0.504361 | + | 0.863493i | \(0.331728\pi\) | |||||||
\(920\) | −1.15780e10 | + | 5.61213e8i | −0.490203 | + | 0.0237613i | ||||
\(921\) | 6.39111e8 | 0.0269567 | ||||||||
\(922\) | −7.58382e9 | − | 1.26591e10i | −0.318662 | − | 0.531917i | ||||
\(923\) | 3.38976e9i | 0.141894i | ||||||||
\(924\) | 1.26712e10 | − | 2.36814e10i | 0.528404 | − | 0.987540i | ||||
\(925\) | − | 2.81577e9i | − | 0.116977i | ||||||
\(926\) | −2.78401e10 | + | 1.66785e10i | −1.15221 | + | 0.690269i | ||||
\(927\) | −3.75864e9 | −0.154972 | ||||||||
\(928\) | 1.35927e10 | − | 2.86586e10i | 0.558325 | − | 1.17716i | ||||
\(929\) | −4.23952e10 | −1.73485 | −0.867424 | − | 0.497570i | \(-0.834226\pi\) | ||||
−0.867424 | + | 0.497570i | \(0.834226\pi\) | |||||||
\(930\) | 1.41457e10 | − | 8.47444e9i | 0.576680 | − | 0.345478i | ||||
\(931\) | 1.34616e9i | 0.0546730i | ||||||||
\(932\) | −1.08350e10 | + | 2.02496e10i | −0.438402 | + | 0.819334i | ||||
\(933\) | − | 1.96139e10i | − | 0.790638i | ||||||
\(934\) | −3.46834e9 | − | 5.78943e9i | −0.139286 | − | 0.232499i | ||||
\(935\) | −6.11916e10 | −2.44823 | ||||||||
\(936\) | −5.18229e9 | + | 2.51198e8i | −0.206565 | + | 0.0100127i | ||||
\(937\) | 3.70014e10 | 1.46937 | 0.734683 | − | 0.678411i | \(-0.237331\pi\) | ||||
0.734683 | + | 0.678411i | \(0.237331\pi\) | |||||||
\(938\) | −1.76033e9 | − | 2.93838e9i | −0.0696439 | − | 0.116251i | ||||
\(939\) | 1.30595e10i | 0.514750i | ||||||||
\(940\) | −4.35960e9 | − | 2.33269e9i | −0.171198 | − | 0.0916031i | ||||
\(941\) | 2.10617e10i | 0.824005i | 0.911183 | + | 0.412003i | \(0.135171\pi\) | ||||
−0.911183 | + | 0.412003i | \(0.864829\pi\) | |||||||
\(942\) | 1.99974e10 | − | 1.19800e10i | 0.779461 | − | 0.466960i | ||||
\(943\) | −1.76844e9 | −0.0686752 | ||||||||
\(944\) | 3.08032e9 | − | 2.05433e9i | 0.119177 | − | 0.0794817i | ||||
\(945\) | 3.44256e10 | 1.32700 | ||||||||
\(946\) | −1.73785e10 | + | 1.04111e10i | −0.667410 | + | 0.399833i | ||||
\(947\) | 1.35146e10i | 0.517104i | 0.965997 | + | 0.258552i | \(0.0832454\pi\) | ||||
−0.965997 | + | 0.258552i | \(0.916755\pi\) | |||||||
\(948\) | −3.73376e10 | − | 1.99782e10i | −1.42337 | − | 0.761602i | ||||
\(949\) | − | 1.68877e10i | − | 0.641416i | ||||||
\(950\) | 2.30572e9 | + | 3.84877e9i | 0.0872519 | + | 0.145643i | ||||
\(951\) | −4.26628e10 | −1.60849 | ||||||||
\(952\) | −2.32065e9 | − | 4.78758e10i | −0.0871728 | − | 1.79840i | ||||
\(953\) | 4.26831e10 | 1.59746 | 0.798731 | − | 0.601688i | \(-0.205505\pi\) | ||||
0.798731 | + | 0.601688i | \(0.205505\pi\) | |||||||
\(954\) | −3.44495e9 | − | 5.75039e9i | −0.128459 | − | 0.214426i | ||||
\(955\) | 1.55790e10i | 0.578799i | ||||||||
\(956\) | −5.08733e9 | + | 9.50776e9i | −0.188316 | + | 0.351946i | ||||
\(957\) | 3.75201e10i | 1.38380i | ||||||||
\(958\) | 2.09702e10 | − | 1.25628e10i | 0.770588 | − | 0.461645i | ||||
\(959\) | 2.45907e10 | 0.900340 | ||||||||
\(960\) | 2.72392e10 | − | 2.64692e9i | 0.993677 | − | 0.0965587i | ||||
\(961\) | −1.50383e10 | −0.546597 | ||||||||
\(962\) | 6.32600e9 | − | 3.78979e9i | 0.229096 | − | 0.137247i | ||||
\(963\) | − | 2.92142e8i | − | 0.0105415i | ||||||
\(964\) | −1.28205e10 | + | 2.39603e10i | −0.460930 | + | 0.861437i | ||||
\(965\) | 1.53323e9i | 0.0549239i | ||||||||
\(966\) | 5.51972e9 | + | 9.21365e9i | 0.197014 | + | 0.328861i | ||||
\(967\) | 2.32274e10 | 0.826053 | 0.413026 | − | 0.910719i | \(-0.364472\pi\) | ||||
0.413026 | + | 0.910719i | \(0.364472\pi\) | |||||||
\(968\) | −7.17914e8 | − | 1.48108e10i | −0.0254395 | − | 0.524825i | ||||
\(969\) | 2.03021e10 | 0.716817 | ||||||||
\(970\) | −1.47977e10 | − | 2.47007e10i | −0.520588 | − | 0.868977i | ||||
\(971\) | − | 4.85678e10i | − | 1.70248i | −0.524780 | − | 0.851238i | \(-0.675852\pi\) | ||
0.524780 | − | 0.851238i | \(-0.324148\pi\) | |||||||
\(972\) | −1.27819e10 | − | 6.83925e9i | −0.446442 | − | 0.238878i | ||||
\(973\) | − | 5.00491e10i | − | 1.74181i | ||||||
\(974\) | −1.37752e9 | + | 8.25248e8i | −0.0477686 | + | 0.0286173i | ||||
\(975\) | −6.87221e9 | −0.237454 | ||||||||
\(976\) | −2.11641e10 | + | 1.41148e10i | −0.728660 | + | 0.485958i | ||||
\(977\) | 1.54549e10 | 0.530193 | 0.265096 | − | 0.964222i | \(-0.414596\pi\) | ||||
0.265096 | + | 0.964222i | \(0.414596\pi\) | |||||||
\(978\) | −3.34722e10 | + | 2.00526e10i | −1.14419 | + | 0.685463i | ||||
\(979\) | − | 2.38264e9i | − | 0.0811557i | ||||||
\(980\) | −3.37766e9 | − | 1.80729e9i | −0.114637 | − | 0.0613389i | ||||
\(981\) | 1.11584e10i | 0.377364i | ||||||||
\(982\) | −1.38774e10 | − | 2.31644e10i | −0.467646 | − | 0.780606i | ||||
\(983\) | −1.59192e10 | −0.534546 | −0.267273 | − | 0.963621i | \(-0.586123\pi\) | ||||
−0.267273 | + | 0.963621i | \(0.586123\pi\) | |||||||
\(984\) | 4.17036e9 | − | 2.02147e8i | 0.139537 | − | 0.00676371i | ||||
\(985\) | −3.72782e10 | −1.24288 | ||||||||
\(986\) | 3.44115e10 | + | 5.74405e10i | 1.14323 | + | 1.90831i | ||||
\(987\) | 4.58142e9i | 0.151667i | ||||||||
\(988\) | −5.54346e9 | + | 1.03602e10i | −0.182865 | + | 0.341759i | ||||
\(989\) | − | 8.10126e9i | − | 0.266296i | ||||||
\(990\) | 9.78128e9 | − | 5.85978e9i | 0.320385 | − | 0.191937i | ||||
\(991\) | 1.49883e10 | 0.489208 | 0.244604 | − | 0.969623i | \(-0.421342\pi\) | ||||
0.244604 | + | 0.969623i | \(0.421342\pi\) | |||||||
\(992\) | 1.87056e10 | + | 8.87203e9i | 0.608390 | + | 0.288557i | ||||
\(993\) | −1.16019e10 | −0.376016 | ||||||||
\(994\) | 5.00572e9 | − | 2.99883e9i | 0.161664 | − | 0.0968500i | ||||
\(995\) | − | 3.92416e9i | − | 0.126289i | ||||||
\(996\) | 1.43167e10 | − | 2.67567e10i | 0.459130 | − | 0.858073i | ||||
\(997\) | 3.44101e10i | 1.09965i | 0.835281 | + | 0.549824i | \(0.185305\pi\) | ||||
−0.835281 | + | 0.549824i | \(0.814695\pi\) | |||||||
\(998\) | 3.04611e10 | + | 5.08464e10i | 0.970038 | + | 1.61921i | ||||
\(999\) | 1.14893e10 | 0.364598 |
(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 | 8.8.b.a.5.2 | yes | 6 | |
3.2 | odd | 2 | 72.8.d.b.37.5 | 6 | |||
4.3 | odd | 2 | 32.8.b.a.17.5 | 6 | |||
8.3 | odd | 2 | 32.8.b.a.17.2 | 6 | |||
8.5 | even | 2 | inner | 8.8.b.a.5.1 | ✓ | 6 | |
12.11 | even | 2 | 288.8.d.b.145.5 | 6 | |||
16.3 | odd | 4 | 256.8.a.q.1.2 | 6 | |||
16.5 | even | 4 | 256.8.a.r.1.2 | 6 | |||
16.11 | odd | 4 | 256.8.a.q.1.5 | 6 | |||
16.13 | even | 4 | 256.8.a.r.1.5 | 6 | |||
24.5 | odd | 2 | 72.8.d.b.37.6 | 6 | |||
24.11 | even | 2 | 288.8.d.b.145.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.8.b.a.5.1 | ✓ | 6 | 8.5 | even | 2 | inner | |
8.8.b.a.5.2 | yes | 6 | 1.1 | even | 1 | trivial | |
32.8.b.a.17.2 | 6 | 8.3 | odd | 2 | |||
32.8.b.a.17.5 | 6 | 4.3 | odd | 2 | |||
72.8.d.b.37.5 | 6 | 3.2 | odd | 2 | |||
72.8.d.b.37.6 | 6 | 24.5 | odd | 2 | |||
256.8.a.q.1.2 | 6 | 16.3 | odd | 4 | |||
256.8.a.q.1.5 | 6 | 16.11 | odd | 4 | |||
256.8.a.r.1.2 | 6 | 16.5 | even | 4 | |||
256.8.a.r.1.5 | 6 | 16.13 | even | 4 | |||
288.8.d.b.145.2 | 6 | 24.11 | even | 2 | |||
288.8.d.b.145.5 | 6 | 12.11 | even | 2 |