Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(7,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.7");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1485512441856.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 119x^{4} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(2.30795 - 2.30795i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.43 |
Dual form | 75.9.f.b.7.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.85713 | + | 5.85713i | −0.366071 | + | 0.366071i | −0.866042 | − | 0.499971i | \(-0.833344\pi\) |
0.499971 | + | 0.866042i | \(0.333344\pi\) | |||||||
\(3\) | 33.0681 | + | 33.0681i | 0.408248 | + | 0.408248i | ||||
\(4\) | 187.388i | 0.731984i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −387.369 | −0.298896 | ||||||||
\(7\) | 1106.65 | − | 1106.65i | 0.460911 | − | 0.460911i | −0.438043 | − | 0.898954i | \(-0.644328\pi\) |
0.898954 | + | 0.438043i | \(0.144328\pi\) | |||||||
\(8\) | −2596.98 | − | 2596.98i | −0.634029 | − | 0.634029i | ||||
\(9\) | 2187.00i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20307.9 | 1.38705 | 0.693527 | − | 0.720430i | \(-0.256056\pi\) | ||||
0.693527 | + | 0.720430i | \(0.256056\pi\) | |||||||
\(12\) | −6196.57 | + | 6196.57i | −0.298831 | + | 0.298831i | ||||
\(13\) | 38060.2 | + | 38060.2i | 1.33259 | + | 1.33259i | 0.903044 | + | 0.429549i | \(0.141327\pi\) |
0.429549 | + | 0.903044i | \(0.358673\pi\) | |||||||
\(14\) | 12963.6i | 0.337452i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −17549.6 | −0.267785 | ||||||||
\(17\) | 35079.5 | − | 35079.5i | 0.420008 | − | 0.420008i | −0.465199 | − | 0.885206i | \(-0.654017\pi\) |
0.885206 | + | 0.465199i | \(0.154017\pi\) | |||||||
\(18\) | −12809.6 | − | 12809.6i | −0.122024 | − | 0.122024i | ||||
\(19\) | − | 33759.4i | − | 0.259048i | −0.991576 | − | 0.129524i | \(-0.958655\pi\) | ||
0.991576 | − | 0.129524i | \(-0.0413450\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 73189.5 | 0.376332 | ||||||||
\(22\) | −118946. | + | 118946.i | −0.507760 | + | 0.507760i | ||||
\(23\) | 180062. | + | 180062.i | 0.643445 | + | 0.643445i | 0.951401 | − | 0.307956i | \(-0.0996449\pi\) |
−0.307956 | + | 0.951401i | \(0.599645\pi\) | |||||||
\(24\) | − | 171755.i | − | 0.517683i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −445847. | −0.975647 | ||||||||
\(27\) | −72320.0 | + | 72320.0i | −0.136083 | + | 0.136083i | ||||
\(28\) | 207372. | + | 207372.i | 0.337380 | + | 0.337380i | ||||
\(29\) | − | 126808.i | − | 0.179289i | −0.995974 | − | 0.0896444i | \(-0.971427\pi\) | ||
0.995974 | − | 0.0896444i | \(-0.0285731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −606669. | −0.656909 | −0.328455 | − | 0.944520i | \(-0.606528\pi\) | ||||
−0.328455 | + | 0.944520i | \(0.606528\pi\) | |||||||
\(32\) | 767618. | − | 767618.i | 0.732057 | − | 0.732057i | ||||
\(33\) | 671543. | + | 671543.i | 0.566263 | + | 0.566263i | ||||
\(34\) | 410930.i | 0.307505i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −409817. | −0.243995 | ||||||||
\(37\) | −32513.8 | + | 32513.8i | −0.0173485 | + | 0.0173485i | −0.715728 | − | 0.698379i | \(-0.753905\pi\) |
0.698379 | + | 0.715728i | \(0.253905\pi\) | |||||||
\(38\) | 197734. | + | 197734.i | 0.0948300 | + | 0.0948300i | ||||
\(39\) | 2.51716e6i | 1.08806i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.66638e6 | −1.65137 | −0.825686 | − | 0.564130i | \(-0.809212\pi\) | ||||
−0.825686 | + | 0.564130i | \(0.809212\pi\) | |||||||
\(42\) | −428680. | + | 428680.i | −0.137764 | + | 0.137764i | ||||
\(43\) | 2.52144e6 | + | 2.52144e6i | 0.737521 | + | 0.737521i | 0.972098 | − | 0.234576i | \(-0.0753703\pi\) |
−0.234576 | + | 0.972098i | \(0.575370\pi\) | |||||||
\(44\) | 3.80545e6i | 1.01530i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.10930e6 | −0.471093 | ||||||||
\(47\) | −2.01575e6 | + | 2.01575e6i | −0.413090 | + | 0.413090i | −0.882814 | − | 0.469724i | \(-0.844354\pi\) |
0.469724 | + | 0.882814i | \(0.344354\pi\) | |||||||
\(48\) | −580331. | − | 580331.i | −0.109323 | − | 0.109323i | ||||
\(49\) | 3.31547e6i | 0.575122i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.32002e6 | 0.342935 | ||||||||
\(52\) | −7.13202e6 | + | 7.13202e6i | −0.975437 | + | 0.975437i | ||||
\(53\) | 6.90838e6 | + | 6.90838e6i | 0.875533 | + | 0.875533i | 0.993069 | − | 0.117535i | \(-0.0374993\pi\) |
−0.117535 | + | 0.993069i | \(0.537499\pi\) | |||||||
\(54\) | − | 847175.i | − | 0.0996319i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.74789e6 | −0.584462 | ||||||||
\(57\) | 1.11636e6 | − | 1.11636e6i | 0.105756 | − | 0.105756i | ||||
\(58\) | 742729. | + | 742729.i | 0.0656324 | + | 0.0656324i | ||||
\(59\) | 3.09316e6i | 0.255266i | 0.991821 | + | 0.127633i | \(0.0407380\pi\) | ||||
−0.991821 | + | 0.127633i | \(0.959262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.67808e7 | −1.93422 | −0.967108 | − | 0.254366i | \(-0.918133\pi\) | ||||
−0.967108 | + | 0.254366i | \(0.918133\pi\) | |||||||
\(62\) | 3.55334e6 | − | 3.55334e6i | 0.240475 | − | 0.240475i | ||||
\(63\) | 2.42024e6 | + | 2.42024e6i | 0.153637 | + | 0.153637i | ||||
\(64\) | 4.49939e6i | 0.268185i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.86663e6 | −0.414585 | ||||||||
\(67\) | −5.43157e6 | + | 5.43157e6i | −0.269542 | + | 0.269542i | −0.828915 | − | 0.559374i | \(-0.811042\pi\) |
0.559374 | + | 0.828915i | \(0.311042\pi\) | |||||||
\(68\) | 6.57347e6 | + | 6.57347e6i | 0.307439 | + | 0.307439i | ||||
\(69\) | 1.19086e7i | 0.525370i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.05288e7 | 1.59489 | 0.797445 | − | 0.603392i | \(-0.206185\pi\) | ||||
0.797445 | + | 0.603392i | \(0.206185\pi\) | |||||||
\(72\) | 5.67960e6 | − | 5.67960e6i | 0.211343 | − | 0.211343i | ||||
\(73\) | −1.17468e6 | − | 1.17468e6i | −0.0413644 | − | 0.0413644i | 0.686122 | − | 0.727486i | \(-0.259312\pi\) |
−0.727486 | + | 0.686122i | \(0.759312\pi\) | |||||||
\(74\) | − | 380876.i | − | 0.0127015i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.32611e6 | 0.189619 | ||||||||
\(77\) | 2.24736e7 | − | 2.24736e7i | 0.639309 | − | 0.639309i | ||||
\(78\) | −1.47433e7 | − | 1.47433e7i | −0.398306 | − | 0.398306i | ||||
\(79\) | − | 5.57922e7i | − | 1.43240i | −0.697893 | − | 0.716202i | \(-0.745879\pi\) | ||
0.697893 | − | 0.716202i | \(-0.254121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.78297e6 | −0.111111 | ||||||||
\(82\) | 2.73316e7 | − | 2.73316e7i | 0.604519 | − | 0.604519i | ||||
\(83\) | 3.11112e7 | + | 3.11112e7i | 0.655548 | + | 0.655548i | 0.954323 | − | 0.298776i | \(-0.0965782\pi\) |
−0.298776 | + | 0.954323i | \(0.596578\pi\) | |||||||
\(84\) | 1.37148e7i | 0.275469i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.95368e7 | −0.539970 | ||||||||
\(87\) | 4.19329e6 | − | 4.19329e6i | 0.0731944 | − | 0.0731944i | ||||
\(88\) | −5.27392e7 | − | 5.27392e7i | −0.879433 | − | 0.879433i | ||||
\(89\) | − | 5.37783e7i | − | 0.857131i | −0.903511 | − | 0.428565i | \(-0.859019\pi\) | ||
0.903511 | − | 0.428565i | \(-0.140981\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.42384e7 | 1.22841 | ||||||||
\(92\) | −3.37415e7 | + | 3.37415e7i | −0.470991 | + | 0.470991i | ||||
\(93\) | −2.00614e7 | − | 2.00614e7i | −0.268182 | − | 0.268182i | ||||
\(94\) | − | 2.36130e7i | − | 0.302440i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.07673e7 | 0.597722 | ||||||||
\(97\) | −9.15785e7 | + | 9.15785e7i | −1.03444 | + | 1.03444i | −0.0350572 | + | 0.999385i | \(0.511161\pi\) |
−0.999385 | + | 0.0350572i | \(0.988839\pi\) | |||||||
\(98\) | −1.94191e7 | − | 1.94191e7i | −0.210536 | − | 0.210536i | ||||
\(99\) | 4.44133e7i | 0.462352i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.86102e8 | 1.78841 | 0.894203 | − | 0.447662i | \(-0.147743\pi\) | ||||
0.894203 | + | 0.447662i | \(0.147743\pi\) | |||||||
\(102\) | −1.35887e7 | + | 1.35887e7i | −0.125538 | + | 0.125538i | ||||
\(103\) | −8.62396e7 | − | 8.62396e7i | −0.766227 | − | 0.766227i | 0.211213 | − | 0.977440i | \(-0.432259\pi\) |
−0.977440 | + | 0.211213i | \(0.932259\pi\) | |||||||
\(104\) | − | 1.97683e8i | − | 1.68980i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.09266e7 | −0.641015 | ||||||||
\(107\) | 1.42221e8 | − | 1.42221e8i | 1.08500 | − | 1.08500i | 0.0889663 | − | 0.996035i | \(-0.471644\pi\) |
0.996035 | − | 0.0889663i | \(-0.0283563\pi\) | |||||||
\(108\) | −1.35519e7 | − | 1.35519e7i | −0.0996104 | − | 0.0996104i | ||||
\(109\) | 2.30661e8i | 1.63406i | 0.576595 | + | 0.817030i | \(0.304381\pi\) | ||||
−0.576595 | + | 0.817030i | \(0.695619\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.15034e6 | −0.0141650 | ||||||||
\(112\) | −1.94212e7 | + | 1.94212e7i | −0.123425 | + | 0.123425i | ||||
\(113\) | −3.83447e7 | − | 3.83447e7i | −0.235175 | − | 0.235175i | 0.579674 | − | 0.814849i | \(-0.303180\pi\) |
−0.814849 | + | 0.579674i | \(0.803180\pi\) | |||||||
\(114\) | 1.30773e7i | 0.0774284i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.37622e7 | 0.131237 | ||||||||
\(117\) | −8.32376e7 | + | 8.32376e7i | −0.444197 | + | 0.444197i | ||||
\(118\) | −1.81170e7 | − | 1.81170e7i | −0.0934456 | − | 0.0934456i | ||||
\(119\) | − | 7.76412e7i | − | 0.387172i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.98051e8 | 0.923921 | ||||||||
\(122\) | 1.56859e8 | − | 1.56859e8i | 0.708060 | − | 0.708060i | ||||
\(123\) | −1.54308e8 | − | 1.54308e8i | −0.674170 | − | 0.674170i | ||||
\(124\) | − | 1.13683e8i | − | 0.480847i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.83513e7 | −0.112484 | ||||||||
\(127\) | 1.07039e8 | − | 1.07039e8i | 0.411460 | − | 0.411460i | −0.470787 | − | 0.882247i | \(-0.656030\pi\) |
0.882247 | + | 0.470787i | \(0.156030\pi\) | |||||||
\(128\) | 1.70157e8 | + | 1.70157e8i | 0.633883 | + | 0.633883i | ||||
\(129\) | 1.66758e8i | 0.602184i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.75517e8 | −1.27510 | −0.637551 | − | 0.770408i | \(-0.720052\pi\) | ||||
−0.637551 | + | 0.770408i | \(0.720052\pi\) | |||||||
\(132\) | −1.25839e8 | + | 1.25839e8i | −0.414495 | + | 0.414495i | ||||
\(133\) | −3.73598e7 | − | 3.73598e7i | −0.119398 | − | 0.119398i | ||||
\(134\) | − | 6.36268e7i | − | 0.197343i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.82202e8 | −0.532594 | ||||||||
\(137\) | 4.18355e7 | − | 4.18355e7i | 0.118758 | − | 0.118758i | −0.645230 | − | 0.763988i | \(-0.723239\pi\) |
0.763988 | + | 0.645230i | \(0.223239\pi\) | |||||||
\(138\) | −6.97505e7 | − | 6.97505e7i | −0.192323 | − | 0.192323i | ||||
\(139\) | 3.73312e8i | 1.00003i | 0.866017 | + | 0.500015i | \(0.166672\pi\) | ||||
−0.866017 | + | 0.500015i | \(0.833328\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.33314e8 | −0.337287 | ||||||||
\(142\) | −2.37383e8 | + | 2.37383e8i | −0.583842 | + | 0.583842i | ||||
\(143\) | 7.72921e8 | + | 7.72921e8i | 1.84838 | + | 1.84838i | ||||
\(144\) | − | 3.83809e7i | − | 0.0892617i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.37605e7 | 0.0302846 | ||||||||
\(147\) | −1.09636e8 | + | 1.09636e8i | −0.234793 | + | 0.234793i | ||||
\(148\) | −6.09270e6 | − | 6.09270e6i | −0.0126988 | − | 0.0126988i | ||||
\(149\) | − | 7.24478e8i | − | 1.46987i | −0.678136 | − | 0.734937i | \(-0.737212\pi\) | ||
0.678136 | − | 0.734937i | \(-0.262788\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.28197e8 | −0.438937 | −0.219468 | − | 0.975620i | \(-0.570432\pi\) | ||||
−0.219468 | + | 0.975620i | \(0.570432\pi\) | |||||||
\(152\) | −8.76727e7 | + | 8.76727e7i | −0.164244 | + | 0.164244i | ||||
\(153\) | 7.67188e7 | + | 7.67188e7i | 0.140003 | + | 0.140003i | ||||
\(154\) | 2.63262e8i | 0.468065i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.71685e8 | −0.796441 | ||||||||
\(157\) | 3.20804e8 | − | 3.20804e8i | 0.528008 | − | 0.528008i | −0.391970 | − | 0.919978i | \(-0.628206\pi\) |
0.919978 | + | 0.391970i | \(0.128206\pi\) | |||||||
\(158\) | 3.26783e8 | + | 3.26783e8i | 0.524361 | + | 0.524361i | ||||
\(159\) | 4.56894e8i | 0.714870i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.98531e8 | 0.593141 | ||||||||
\(162\) | 2.80145e7 | − | 2.80145e7i | 0.0406745 | − | 0.0406745i | ||||
\(163\) | 1.31891e8 | + | 1.31891e8i | 0.186838 | + | 0.186838i | 0.794328 | − | 0.607489i | \(-0.207823\pi\) |
−0.607489 | + | 0.794328i | \(0.707823\pi\) | |||||||
\(164\) | − | 8.74424e8i | − | 1.20878i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.64445e8 | −0.479954 | ||||||||
\(167\) | 8.72543e7 | − | 8.72543e7i | 0.112181 | − | 0.112181i | −0.648788 | − | 0.760969i | \(-0.724724\pi\) |
0.760969 | + | 0.648788i | \(0.224724\pi\) | |||||||
\(168\) | −1.90072e8 | − | 1.90072e8i | −0.238606 | − | 0.238606i | ||||
\(169\) | 2.08142e9i | 2.55161i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.38319e7 | 0.0863494 | ||||||||
\(172\) | −4.72487e8 | + | 4.72487e8i | −0.539854 | + | 0.539854i | ||||
\(173\) | 8.30340e8 | + | 8.30340e8i | 0.926983 | + | 0.926983i | 0.997510 | − | 0.0705268i | \(-0.0224680\pi\) |
−0.0705268 | + | 0.997510i | \(0.522468\pi\) | |||||||
\(174\) | 4.91213e7i | 0.0535887i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.56394e8 | −0.371433 | ||||||||
\(177\) | −1.02285e8 | + | 1.02285e8i | −0.104212 | + | 0.104212i | ||||
\(178\) | 3.14987e8 | + | 3.14987e8i | 0.313771 | + | 0.313771i | ||||
\(179\) | 1.18482e9i | 1.15409i | 0.816711 | + | 0.577047i | \(0.195795\pi\) | ||||
−0.816711 | + | 0.577047i | \(0.804205\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.64466e8 | −0.246408 | −0.123204 | − | 0.992381i | \(-0.539317\pi\) | ||||
−0.123204 | + | 0.992381i | \(0.539317\pi\) | |||||||
\(182\) | −4.93395e8 | + | 4.93395e8i | −0.449686 | + | 0.449686i | ||||
\(183\) | −8.85592e8 | − | 8.85592e8i | −0.789640 | − | 0.789640i | ||||
\(184\) | − | 9.35237e8i | − | 0.815925i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.35005e8 | 0.196347 | ||||||||
\(187\) | 7.12389e8 | − | 7.12389e8i | 0.582574 | − | 0.582574i | ||||
\(188\) | −3.77727e8 | − | 3.77727e8i | −0.302375 | − | 0.302375i | ||||
\(189\) | 1.60065e8i | 0.125444i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.35604e8 | −0.177031 | −0.0885154 | − | 0.996075i | \(-0.528212\pi\) | ||||
−0.0885154 | + | 0.996075i | \(0.528212\pi\) | |||||||
\(192\) | −1.48786e8 | + | 1.48786e8i | −0.109486 | + | 0.109486i | ||||
\(193\) | −1.36934e9 | − | 1.36934e9i | −0.986920 | − | 0.986920i | 0.0129952 | − | 0.999916i | \(-0.495863\pi\) |
−0.999916 | + | 0.0129952i | \(0.995863\pi\) | |||||||
\(194\) | − | 1.07277e9i | − | 0.757359i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.21278e8 | −0.420980 | ||||||||
\(197\) | 2.01542e9 | − | 2.01542e9i | 1.33814 | − | 1.33814i | 0.440274 | − | 0.897864i | \(-0.354881\pi\) |
0.897864 | − | 0.440274i | \(-0.145119\pi\) | |||||||
\(198\) | −2.60135e8 | − | 2.60135e8i | −0.169253 | − | 0.169253i | ||||
\(199\) | − | 2.07907e9i | − | 1.32573i | −0.748737 | − | 0.662867i | \(-0.769339\pi\) | ||
0.748737 | − | 0.662867i | \(-0.230661\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.59223e8 | −0.220080 | ||||||||
\(202\) | −1.09003e9 | + | 1.09003e9i | −0.654683 | + | 0.654683i | ||||
\(203\) | −1.40331e8 | − | 1.40331e8i | −0.0826362 | − | 0.0826362i | ||||
\(204\) | 4.34744e8i | 0.251023i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.01023e9 | 0.560987 | ||||||||
\(207\) | −3.93796e8 | + | 3.93796e8i | −0.214482 | + | 0.214482i | ||||
\(208\) | −6.67939e8 | − | 6.67939e8i | −0.356848 | − | 0.356848i | ||||
\(209\) | − | 6.85582e8i | − | 0.359314i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.81393e9 | 1.41966 | 0.709829 | − | 0.704374i | \(-0.248772\pi\) | ||||
0.709829 | + | 0.704374i | \(0.248772\pi\) | |||||||
\(212\) | −1.29455e9 | + | 1.29455e9i | −0.640877 | + | 0.640877i | ||||
\(213\) | 1.34021e9 | + | 1.34021e9i | 0.651111 | + | 0.651111i | ||||
\(214\) | 1.66602e9i | 0.794374i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.75627e8 | 0.172561 | ||||||||
\(217\) | −6.71369e8 | + | 6.71369e8i | −0.302777 | + | 0.302777i | ||||
\(218\) | −1.35101e9 | − | 1.35101e9i | −0.598182 | − | 0.598182i | ||||
\(219\) | − | 7.76886e7i | − | 0.0337739i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.67026e9 | 1.11940 | ||||||||
\(222\) | 1.25948e7 | − | 1.25948e7i | 0.00518538 | − | 0.00518538i | ||||
\(223\) | −8.44395e8 | − | 8.44395e8i | −0.341449 | − | 0.341449i | 0.515463 | − | 0.856912i | \(-0.327620\pi\) |
−0.856912 | + | 0.515463i | \(0.827620\pi\) | |||||||
\(224\) | − | 1.69896e9i | − | 0.674826i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.49180e8 | 0.172181 | ||||||||
\(227\) | 3.17731e9 | − | 3.17731e9i | 1.19662 | − | 1.19662i | 0.221445 | − | 0.975173i | \(-0.428923\pi\) |
0.975173 | − | 0.221445i | \(-0.0710774\pi\) | |||||||
\(228\) | 2.09193e8 | + | 2.09193e8i | 0.0774117 | + | 0.0774117i | ||||
\(229\) | − | 1.98891e9i | − | 0.723225i | −0.932329 | − | 0.361612i | \(-0.882226\pi\) | ||
0.932329 | − | 0.361612i | \(-0.117774\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.48632e9 | 0.521993 | ||||||||
\(232\) | −3.29317e8 | + | 3.29317e8i | −0.113674 | + | 0.113674i | ||||
\(233\) | −1.15947e9 | − | 1.15947e9i | −0.393402 | − | 0.393402i | 0.482496 | − | 0.875898i | \(-0.339730\pi\) |
−0.875898 | + | 0.482496i | \(0.839730\pi\) | |||||||
\(234\) | − | 9.75068e8i | − | 0.325216i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.79620e8 | −0.186851 | ||||||||
\(237\) | 1.84494e9 | − | 1.84494e9i | 0.584776 | − | 0.584776i | ||||
\(238\) | 4.54755e8 | + | 4.54755e8i | 0.141732 | + | 0.141732i | ||||
\(239\) | 2.87212e9i | 0.880261i | 0.897934 | + | 0.440131i | \(0.145068\pi\) | ||||
−0.897934 | + | 0.440131i | \(0.854932\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.92807e9 | 0.867988 | 0.433994 | − | 0.900916i | \(-0.357104\pi\) | ||||
0.433994 | + | 0.900916i | \(0.357104\pi\) | |||||||
\(242\) | −1.16001e9 | + | 1.16001e9i | −0.338221 | + | 0.338221i | ||||
\(243\) | −1.58164e8 | − | 1.58164e8i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 5.01841e9i | − | 1.41582i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.80761e9 | 0.493588 | ||||||||
\(247\) | 1.28489e9 | − | 1.28489e9i | 0.345206 | − | 0.345206i | ||||
\(248\) | 1.57551e9 | + | 1.57551e9i | 0.416500 | + | 0.416500i | ||||
\(249\) | 2.05758e9i | 0.535253i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.42046e9 | −0.609822 | −0.304911 | − | 0.952381i | \(-0.598627\pi\) | ||||
−0.304911 | + | 0.952381i | \(0.598627\pi\) | |||||||
\(252\) | −4.53523e8 | + | 4.53523e8i | −0.112460 | + | 0.112460i | ||||
\(253\) | 3.65668e9 | + | 3.65668e9i | 0.892493 | + | 0.892493i | ||||
\(254\) | 1.25389e9i | 0.301247i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.14510e9 | −0.732277 | ||||||||
\(257\) | −3.61426e9 | + | 3.61426e9i | −0.828490 | + | 0.828490i | −0.987308 | − | 0.158818i | \(-0.949232\pi\) |
0.158818 | + | 0.987308i | \(0.449232\pi\) | |||||||
\(258\) | −9.76727e8 | − | 9.76727e8i | −0.220442 | − | 0.220442i | ||||
\(259\) | 7.19626e7i | 0.0159922i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.77328e8 | 0.0597630 | ||||||||
\(262\) | 2.19946e9 | − | 2.19946e9i | 0.466778 | − | 0.466778i | ||||
\(263\) | −4.87560e9 | − | 4.87560e9i | −1.01907 | − | 1.01907i | −0.999815 | − | 0.0192588i | \(-0.993869\pi\) |
−0.0192588 | − | 0.999815i | \(-0.506131\pi\) | |||||||
\(264\) | − | 3.48797e9i | − | 0.718054i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.37643e8 | 0.0874164 | ||||||||
\(267\) | 1.77835e9 | − | 1.77835e9i | 0.349922 | − | 0.349922i | ||||
\(268\) | −1.01781e9 | − | 1.01781e9i | −0.197300 | − | 0.197300i | ||||
\(269\) | 2.34422e9i | 0.447703i | 0.974623 | + | 0.223851i | \(0.0718630\pi\) | ||||
−0.974623 | + | 0.223851i | \(0.928137\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.34686e9 | −0.805931 | −0.402966 | − | 0.915215i | \(-0.632021\pi\) | ||||
−0.402966 | + | 0.915215i | \(0.632021\pi\) | |||||||
\(272\) | −6.15629e8 | + | 6.15629e8i | −0.112472 | + | 0.112472i | ||||
\(273\) | 2.78560e9 | + | 2.78560e9i | 0.501497 | + | 0.501497i | ||||
\(274\) | 4.90072e8i | 0.0869477i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.23153e9 | −0.384563 | ||||||||
\(277\) | −2.78931e9 | + | 2.78931e9i | −0.473781 | + | 0.473781i | −0.903136 | − | 0.429355i | \(-0.858741\pi\) |
0.429355 | + | 0.903136i | \(0.358741\pi\) | |||||||
\(278\) | −2.18654e9 | − | 2.18654e9i | −0.366082 | − | 0.366082i | ||||
\(279\) | − | 1.32679e9i | − | 0.218970i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.37876e9 | −0.381526 | −0.190763 | − | 0.981636i | \(-0.561096\pi\) | ||||
−0.190763 | + | 0.981636i | \(0.561096\pi\) | |||||||
\(282\) | 7.80838e8 | − | 7.80838e8i | 0.123471 | − | 0.123471i | ||||
\(283\) | 2.50114e9 | + | 2.50114e9i | 0.389935 | + | 0.389935i | 0.874664 | − | 0.484729i | \(-0.161082\pi\) |
−0.484729 | + | 0.874664i | \(0.661082\pi\) | |||||||
\(284\) | 7.59461e9i | 1.16743i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.05420e9 | −1.35328 | ||||||||
\(287\) | −5.16404e9 | + | 5.16404e9i | −0.761135 | + | 0.761135i | ||||
\(288\) | 1.67878e9 | + | 1.67878e9i | 0.244019 | + | 0.244019i | ||||
\(289\) | 4.51462e9i | 0.647187i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.05665e9 | −0.844619 | ||||||||
\(292\) | 2.20120e8 | − | 2.20120e8i | 0.0302781 | − | 0.0302781i | ||||
\(293\) | 9.38037e8 | + | 9.38037e8i | 0.127277 | + | 0.127277i | 0.767876 | − | 0.640599i | \(-0.221314\pi\) |
−0.640599 | + | 0.767876i | \(0.721314\pi\) | |||||||
\(294\) | − | 1.28431e9i | − | 0.171902i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.68876e8 | 0.0219989 | ||||||||
\(297\) | −1.46866e9 | + | 1.46866e9i | −0.188754 | + | 0.188754i | ||||
\(298\) | 4.24336e9 | + | 4.24336e9i | 0.538078 | + | 0.538078i | ||||
\(299\) | 1.37064e10i | 1.71490i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.58069e9 | 0.679863 | ||||||||
\(302\) | 1.33658e9 | − | 1.33658e9i | 0.160682 | − | 0.160682i | ||||
\(303\) | 6.15405e9 | + | 6.15405e9i | 0.730114 | + | 0.730114i | ||||
\(304\) | 5.92463e8i | 0.0693693i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.98704e8 | −0.102502 | ||||||||
\(307\) | 5.86175e9 | − | 5.86175e9i | 0.659893 | − | 0.659893i | −0.295462 | − | 0.955355i | \(-0.595473\pi\) |
0.955355 | + | 0.295462i | \(0.0954734\pi\) | |||||||
\(308\) | 4.21129e9 | + | 4.21129e9i | 0.467964 | + | 0.467964i | ||||
\(309\) | − | 5.70356e9i | − | 0.625622i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.11229e9 | −0.974061 | −0.487030 | − | 0.873385i | \(-0.661920\pi\) | ||||
−0.487030 | + | 0.873385i | \(0.661920\pi\) | |||||||
\(312\) | 6.53701e9 | − | 6.53701e9i | 0.689860 | − | 0.689860i | ||||
\(313\) | −4.02063e9 | − | 4.02063e9i | −0.418906 | − | 0.418906i | 0.465920 | − | 0.884827i | \(-0.345723\pi\) |
−0.884827 | + | 0.465920i | \(0.845723\pi\) | |||||||
\(314\) | 3.75798e9i | 0.386577i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.04548e10 | 1.04850 | ||||||||
\(317\) | −9.03622e9 | + | 9.03622e9i | −0.894849 | + | 0.894849i | −0.994975 | − | 0.100126i | \(-0.968076\pi\) |
0.100126 | + | 0.994975i | \(0.468076\pi\) | |||||||
\(318\) | −2.67609e9 | − | 2.67609e9i | −0.261693 | − | 0.261693i | ||||
\(319\) | − | 2.57519e9i | − | 0.248684i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.40599e9 | 0.885900 | ||||||||
\(322\) | −2.33425e9 | + | 2.33425e9i | −0.217132 | + | 0.217132i | ||||
\(323\) | −1.18426e9 | − | 1.18426e9i | −0.108802 | − | 0.108802i | ||||
\(324\) | − | 8.96271e8i | − | 0.0813316i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.54501e9 | −0.136792 | ||||||||
\(327\) | −7.62752e9 | + | 7.62752e9i | −0.667102 | + | 0.667102i | ||||
\(328\) | 1.21185e10 | + | 1.21185e10i | 1.04702 | + | 1.04702i | ||||
\(329\) | 4.46144e9i | 0.380795i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.22140e8 | −0.0101753 | −0.00508765 | − | 0.999987i | \(-0.501619\pi\) | ||||
−0.00508765 | + | 0.999987i | \(0.501619\pi\) | |||||||
\(332\) | −5.82986e9 | + | 5.82986e9i | −0.479851 | + | 0.479851i | ||||
\(333\) | −7.11077e7 | − | 7.11077e7i | −0.00578282 | − | 0.00578282i | ||||
\(334\) | 1.02212e9i | 0.0821327i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.28444e9 | −0.100776 | ||||||||
\(337\) | 5.75655e9 | − | 5.75655e9i | 0.446316 | − | 0.446316i | −0.447812 | − | 0.894128i | \(-0.647797\pi\) |
0.894128 | + | 0.447812i | \(0.147797\pi\) | |||||||
\(338\) | −1.21912e10 | − | 1.21912e10i | −0.934068 | − | 0.934068i | ||||
\(339\) | − | 2.53597e9i | − | 0.192020i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.23202e10 | −0.911169 | ||||||||
\(342\) | −4.32443e8 | + | 4.32443e8i | −0.0316100 | + | 0.0316100i | ||||
\(343\) | 1.00487e10 | + | 1.00487e10i | 0.725991 | + | 0.725991i | ||||
\(344\) | − | 1.30963e10i | − | 0.935220i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.72683e9 | −0.678683 | ||||||||
\(347\) | 1.02276e10 | − | 1.02276e10i | 0.705431 | − | 0.705431i | −0.260140 | − | 0.965571i | \(-0.583769\pi\) |
0.965571 | + | 0.260140i | \(0.0837688\pi\) | |||||||
\(348\) | 7.85772e8 | + | 7.85772e8i | 0.0535771 | + | 0.0535771i | ||||
\(349\) | − | 1.35109e10i | − | 0.910712i | −0.890309 | − | 0.455356i | \(-0.849512\pi\) | ||
0.890309 | − | 0.455356i | \(-0.150488\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.50502e9 | −0.362686 | ||||||||
\(352\) | 1.55887e10 | − | 1.55887e10i | 1.01540 | − | 1.01540i | ||||
\(353\) | −1.50393e10 | − | 1.50393e10i | −0.968564 | − | 0.968564i | 0.0309571 | − | 0.999521i | \(-0.490144\pi\) |
−0.999521 | + | 0.0309571i | \(0.990144\pi\) | |||||||
\(354\) | − | 1.19819e9i | − | 0.0762980i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.00774e10 | 0.627406 | ||||||||
\(357\) | 2.56745e9 | − | 2.56745e9i | 0.158062 | − | 0.158062i | ||||
\(358\) | −6.93966e9 | − | 6.93966e9i | −0.422480 | − | 0.422480i | ||||
\(359\) | − | 2.41219e10i | − | 1.45222i | −0.687577 | − | 0.726111i | \(-0.741326\pi\) | ||
0.687577 | − | 0.726111i | \(-0.258674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.58439e10 | 0.932894 | ||||||||
\(362\) | 1.54901e9 | − | 1.54901e9i | 0.0902029 | − | 0.0902029i | ||||
\(363\) | 6.54916e9 | + | 6.54916e9i | 0.377189 | + | 0.377189i | ||||
\(364\) | 1.57853e10i | 0.899179i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.03741e10 | 0.578129 | ||||||||
\(367\) | −1.77795e10 | + | 1.77795e10i | −0.980068 | + | 0.980068i | −0.999805 | − | 0.0197370i | \(-0.993717\pi\) |
0.0197370 | + | 0.999805i | \(0.493717\pi\) | |||||||
\(368\) | −3.16001e9 | − | 3.16001e9i | −0.172305 | − | 0.172305i | ||||
\(369\) | − | 1.02054e10i | − | 0.550457i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52903e10 | 0.807086 | ||||||||
\(372\) | 3.75927e9 | − | 3.75927e9i | 0.196305 | − | 0.196305i | ||||
\(373\) | −9.55861e9 | − | 9.55861e9i | −0.493810 | − | 0.493810i | 0.415695 | − | 0.909504i | \(-0.363539\pi\) |
−0.909504 | + | 0.415695i | \(0.863539\pi\) | |||||||
\(374\) | 8.34512e9i | 0.426527i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.04697e10 | 0.523822 | ||||||||
\(377\) | 4.82632e9 | − | 4.82632e9i | 0.238919 | − | 0.238919i | ||||
\(378\) | −9.37524e8 | − | 9.37524e8i | −0.0459214 | − | 0.0459214i | ||||
\(379\) | − | 1.39162e10i | − | 0.674474i | −0.941420 | − | 0.337237i | \(-0.890508\pi\) | ||
0.941420 | − | 0.337237i | \(-0.109492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.07917e9 | 0.335956 | ||||||||
\(382\) | 1.37996e9 | − | 1.37996e9i | 0.0648058 | − | 0.0648058i | ||||
\(383\) | 3.87421e8 | + | 3.87421e8i | 0.0180048 | + | 0.0180048i | 0.716052 | − | 0.698047i | \(-0.245947\pi\) |
−0.698047 | + | 0.716052i | \(0.745947\pi\) | |||||||
\(384\) | 1.12535e10i | 0.517563i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.60408e10 | 0.722566 | ||||||||
\(387\) | −5.51439e9 | + | 5.51439e9i | −0.245840 | + | 0.245840i | ||||
\(388\) | −1.71607e10 | − | 1.71607e10i | −0.757196 | − | 0.757196i | ||||
\(389\) | − | 6.64677e9i | − | 0.290277i | −0.989411 | − | 0.145138i | \(-0.953637\pi\) | ||
0.989411 | − | 0.145138i | \(-0.0463627\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.26330e10 | 0.540503 | ||||||||
\(392\) | 8.61021e9 | − | 8.61021e9i | 0.364644 | − | 0.364644i | ||||
\(393\) | −1.24177e10 | − | 1.24177e10i | −0.520558 | − | 0.520558i | ||||
\(394\) | 2.36092e10i | 0.979706i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.32252e9 | −0.338434 | ||||||||
\(397\) | −5.86473e9 | + | 5.86473e9i | −0.236095 | + | 0.236095i | −0.815231 | − | 0.579136i | \(-0.803390\pi\) |
0.579136 | + | 0.815231i | \(0.303390\pi\) | |||||||
\(398\) | 1.21774e10 | + | 1.21774e10i | 0.485313 | + | 0.485313i | ||||
\(399\) | − | 2.47083e9i | − | 0.0974882i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.20472e10 | −1.23940 | −0.619701 | − | 0.784838i | \(-0.712746\pi\) | ||||
−0.619701 | + | 0.784838i | \(0.712746\pi\) | |||||||
\(402\) | 2.10402e9 | − | 2.10402e9i | 0.0805648 | − | 0.0805648i | ||||
\(403\) | −2.30899e10 | − | 2.30899e10i | −0.875392 | − | 0.875392i | ||||
\(404\) | 3.48733e10i | 1.30908i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.64388e9 | 0.0605014 | ||||||||
\(407\) | −6.60286e8 | + | 6.60286e8i | −0.0240633 | + | 0.0240633i | ||||
\(408\) | −6.02506e9 | − | 6.02506e9i | −0.217431 | − | 0.217431i | ||||
\(409\) | − | 2.75999e10i | − | 0.986313i | −0.869941 | − | 0.493157i | \(-0.835843\pi\) | ||
0.869941 | − | 0.493157i | \(-0.164157\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.76684e9 | 0.0969655 | ||||||||
\(412\) | 1.61603e10 | − | 1.61603e10i | 0.560866 | − | 0.560866i | ||||
\(413\) | 3.42303e9 | + | 3.42303e9i | 0.117655 | + | 0.117655i | ||||
\(414\) | − | 4.61303e9i | − | 0.157031i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.84313e10 | 1.95107 | ||||||||
\(417\) | −1.23447e10 | + | 1.23447e10i | −0.408261 | + | 0.408261i | ||||
\(418\) | 4.01555e9 | + | 4.01555e9i | 0.131534 | + | 0.131534i | ||||
\(419\) | − | 2.09715e10i | − | 0.680414i | −0.940351 | − | 0.340207i | \(-0.889503\pi\) | ||
0.940351 | − | 0.340207i | \(-0.110497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.19854e10 | 0.381526 | 0.190763 | − | 0.981636i | \(-0.438904\pi\) | ||||
0.190763 | + | 0.981636i | \(0.438904\pi\) | |||||||
\(422\) | −1.64816e10 | + | 1.64816e10i | −0.519695 | + | 0.519695i | ||||
\(423\) | −4.40844e9 | − | 4.40844e9i | −0.137697 | − | 0.137697i | ||||
\(424\) | − | 3.58819e10i | − | 1.11023i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.56996e10 | −0.476705 | ||||||||
\(427\) | −2.96369e10 | + | 2.96369e10i | −0.891501 | + | 0.891501i | ||||
\(428\) | 2.66506e10 | + | 2.66506e10i | 0.794204 | + | 0.794204i | ||||
\(429\) | 5.11181e10i | 1.50920i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.29044e9 | −0.269232 | −0.134616 | − | 0.990898i | \(-0.542980\pi\) | ||||
−0.134616 | + | 0.990898i | \(0.542980\pi\) | |||||||
\(432\) | 1.26918e9 | − | 1.26918e9i | 0.0364409 | − | 0.0364409i | ||||
\(433\) | 1.48436e10 | + | 1.48436e10i | 0.422267 | + | 0.422267i | 0.885984 | − | 0.463717i | \(-0.153484\pi\) |
−0.463717 | + | 0.885984i | \(0.653484\pi\) | |||||||
\(434\) | − | 7.86460e9i | − | 0.221675i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.32231e10 | −1.19611 | ||||||||
\(437\) | 6.07880e9 | − | 6.07880e9i | 0.166683 | − | 0.166683i | ||||
\(438\) | 4.55032e8 | + | 4.55032e8i | 0.0123636 | + | 0.0123636i | ||||
\(439\) | 3.74565e10i | 1.00848i | 0.863562 | + | 0.504242i | \(0.168228\pi\) | ||||
−0.863562 | + | 0.504242i | \(0.831772\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.25092e9 | −0.191707 | ||||||||
\(442\) | −1.56401e10 | + | 1.56401e10i | −0.409779 | + | 0.409779i | ||||
\(443\) | 1.12412e10 | + | 1.12412e10i | 0.291877 | + | 0.291877i | 0.837821 | − | 0.545945i | \(-0.183829\pi\) |
−0.545945 | + | 0.837821i | \(0.683829\pi\) | |||||||
\(444\) | − | 4.02948e8i | − | 0.0103685i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.89147e9 | 0.249989 | ||||||||
\(447\) | 2.39571e10 | − | 2.39571e10i | 0.600073 | − | 0.600073i | ||||
\(448\) | 4.97924e9 | + | 4.97924e9i | 0.123609 | + | 0.123609i | ||||
\(449\) | − | 6.71064e10i | − | 1.65112i | −0.564315 | − | 0.825560i | \(-0.690860\pi\) | ||
0.564315 | − | 0.825560i | \(-0.309140\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.47643e10 | −2.29054 | ||||||||
\(452\) | 7.18533e9 | − | 7.18533e9i | 0.172144 | − | 0.172144i | ||||
\(453\) | −7.54604e9 | − | 7.54604e9i | −0.179195 | − | 0.179195i | ||||
\(454\) | 3.72198e10i | 0.876094i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.79834e9 | −0.134105 | ||||||||
\(457\) | 5.45475e9 | − | 5.45475e9i | 0.125058 | − | 0.125058i | −0.641808 | − | 0.766865i | \(-0.721815\pi\) |
0.766865 | + | 0.641808i | \(0.221815\pi\) | |||||||
\(458\) | 1.16493e10 | + | 1.16493e10i | 0.264751 | + | 0.264751i | ||||
\(459\) | 5.07389e9i | 0.114312i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.99346e10 | −0.662780 | −0.331390 | − | 0.943494i | \(-0.607518\pi\) | ||||
−0.331390 | + | 0.943494i | \(0.607518\pi\) | |||||||
\(462\) | −8.70559e9 | + | 8.70559e9i | −0.191087 | + | 0.191087i | ||||
\(463\) | 7.39909e9 | + | 7.39909e9i | 0.161011 | + | 0.161011i | 0.783014 | − | 0.622004i | \(-0.213681\pi\) |
−0.622004 | + | 0.783014i | \(0.713681\pi\) | |||||||
\(464\) | 2.22542e9i | 0.0480109i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.35824e10 | 0.288026 | ||||||||
\(467\) | 5.76602e10 | − | 5.76602e10i | 1.21230 | − | 1.21230i | 0.242025 | − | 0.970270i | \(-0.422188\pi\) |
0.970270 | − | 0.242025i | \(-0.0778117\pi\) | |||||||
\(468\) | −1.55977e10 | − | 1.55977e10i | −0.325146 | − | 0.325146i | ||||
\(469\) | 1.20217e10i | 0.248469i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.12167e10 | 0.431117 | ||||||||
\(472\) | 8.03287e9 | − | 8.03287e9i | 0.161846 | − | 0.161846i | ||||
\(473\) | 5.12051e10 | + | 5.12051e10i | 1.02298 | + | 1.02298i | ||||
\(474\) | 2.16122e10i | 0.428139i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.45490e10 | 0.283404 | ||||||||
\(477\) | −1.51086e10 | + | 1.51086e10i | −0.291844 | + | 0.291844i | ||||
\(478\) | −1.68224e10 | − | 1.68224e10i | −0.322238 | − | 0.322238i | ||||
\(479\) | − | 8.46861e9i | − | 0.160868i | −0.996760 | − | 0.0804341i | \(-0.974369\pi\) | ||
0.996760 | − | 0.0804341i | \(-0.0256307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.47496e9 | −0.0462369 | ||||||||
\(482\) | −1.71501e10 | + | 1.71501e10i | −0.317745 | + | 0.317745i | ||||
\(483\) | 1.31787e10 | + | 1.31787e10i | 0.242149 | + | 0.242149i | ||||
\(484\) | 3.71123e10i | 0.676296i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.85277e9 | 0.0332106 | ||||||||
\(487\) | −3.40281e10 | + | 3.40281e10i | −0.604954 | + | 0.604954i | −0.941623 | − | 0.336669i | \(-0.890700\pi\) |
0.336669 | + | 0.941623i | \(0.390700\pi\) | |||||||
\(488\) | 6.95494e10 | + | 6.95494e10i | 1.22635 | + | 1.22635i | ||||
\(489\) | 8.72280e9i | 0.152553i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.86536e10 | −1.52535 | −0.762677 | − | 0.646780i | \(-0.776115\pi\) | ||||
−0.762677 | + | 0.646780i | \(0.776115\pi\) | |||||||
\(492\) | 2.89155e10 | − | 2.89155e10i | 0.493482 | − | 0.493482i | ||||
\(493\) | −4.44834e9 | − | 4.44834e9i | −0.0753027 | − | 0.0753027i | ||||
\(494\) | 1.50515e10i | 0.252740i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.06468e10 | 0.175911 | ||||||||
\(497\) | 4.48511e10 | − | 4.48511e10i | 0.735102 | − | 0.735102i | ||||
\(498\) | −1.20515e10 | − | 1.20515e10i | −0.195940 | − | 0.195940i | ||||
\(499\) | 2.44875e10i | 0.394949i | 0.980308 | + | 0.197475i | \(0.0632740\pi\) | ||||
−0.980308 | + | 0.197475i | \(0.936726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.77067e9 | 0.0915957 | ||||||||
\(502\) | 1.41770e10 | − | 1.41770e10i | 0.223238 | − | 0.223238i | ||||
\(503\) | 2.95139e10 | + | 2.95139e10i | 0.461057 | + | 0.461057i | 0.899002 | − | 0.437945i | \(-0.144293\pi\) |
−0.437945 | + | 0.899002i | \(0.644293\pi\) | |||||||
\(504\) | − | 1.25706e10i | − | 0.194821i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.28353e10 | −0.653431 | ||||||||
\(507\) | −6.88287e10 | + | 6.88287e10i | −1.04169 | + | 1.04169i | ||||
\(508\) | 2.00579e10 | + | 2.00579e10i | 0.301183 | + | 0.301183i | ||||
\(509\) | − | 9.36366e9i | − | 0.139500i | −0.997565 | − | 0.0697500i | \(-0.977780\pi\) | ||
0.997565 | − | 0.0697500i | \(-0.0222202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.59990e9 | −0.0381306 | ||||||||
\(512\) | −2.51388e10 | + | 2.51388e10i | −0.365818 | + | 0.365818i | ||||
\(513\) | 2.44148e9 | + | 2.44148e9i | 0.0352520 | + | 0.0352520i | ||||
\(514\) | − | 4.23385e10i | − | 0.606572i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.12485e10 | −0.440789 | ||||||||
\(517\) | −4.09355e10 | + | 4.09355e10i | −0.572979 | + | 0.572979i | ||||
\(518\) | −4.21495e8 | − | 4.21495e8i | −0.00585428 | − | 0.00585428i | ||||
\(519\) | 5.49156e10i | 0.756879i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.05168e11 | 1.42735 | 0.713675 | − | 0.700477i | \(-0.247029\pi\) | ||||
0.713675 | + | 0.700477i | \(0.247029\pi\) | |||||||
\(522\) | −1.62435e9 | + | 1.62435e9i | −0.0218775 | + | 0.0218775i | ||||
\(523\) | 3.38658e9 | + | 3.38658e9i | 0.0452642 | + | 0.0452642i | 0.729377 | − | 0.684112i | \(-0.239810\pi\) |
−0.684112 | + | 0.729377i | \(0.739810\pi\) | |||||||
\(524\) | − | 7.03674e10i | − | 0.933355i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.71141e10 | 0.746106 | ||||||||
\(527\) | −2.12816e10 | + | 2.12816e10i | −0.275907 | + | 0.275907i | ||||
\(528\) | −1.17853e10 | − | 1.17853e10i | −0.151637 | − | 0.151637i | ||||
\(529\) | − | 1.34662e10i | − | 0.171958i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.76473e9 | −0.0850888 | ||||||||
\(532\) | 7.00077e9 | − | 7.00077e9i | 0.0873976 | − | 0.0873976i | ||||
\(533\) | −1.77603e11 | − | 1.77603e11i | −2.20061 | − | 2.20061i | ||||
\(534\) | 2.08320e10i | 0.256193i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.82114e10 | 0.341794 | ||||||||
\(537\) | −3.91798e10 | + | 3.91798e10i | −0.471157 | + | 0.471157i | ||||
\(538\) | −1.37304e10 | − | 1.37304e10i | −0.163891 | − | 0.163891i | ||||
\(539\) | 6.73300e10i | 0.797726i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.94182e10 | 0.460159 | 0.230080 | − | 0.973172i | \(-0.426101\pi\) | ||||
0.230080 | + | 0.973172i | \(0.426101\pi\) | |||||||
\(542\) | 2.54601e10 | − | 2.54601e10i | 0.295028 | − | 0.295028i | ||||
\(543\) | −8.74539e9 | − | 8.74539e9i | −0.100596 | − | 0.100596i | ||||
\(544\) | − | 5.38552e10i | − | 0.614939i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.26313e10 | −0.367167 | ||||||||
\(547\) | −1.18155e10 | + | 1.18155e10i | −0.131978 | + | 0.131978i | −0.770010 | − | 0.638032i | \(-0.779749\pi\) |
0.638032 | + | 0.770010i | \(0.279749\pi\) | |||||||
\(548\) | 7.83947e9 | + | 7.83947e9i | 0.0869289 | + | 0.0869289i | ||||
\(549\) | − | 5.85697e10i | − | 0.644739i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.28095e9 | −0.0464445 | ||||||||
\(552\) | 3.09265e10 | − | 3.09265e10i | 0.333100 | − | 0.333100i | ||||
\(553\) | −6.17423e10 | − | 6.17423e10i | −0.660211 | − | 0.660211i | ||||
\(554\) | − | 3.26747e10i | − | 0.346875i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.99542e10 | −0.732006 | ||||||||
\(557\) | 1.10650e11 | − | 1.10650e11i | 1.14956 | − | 1.14956i | 0.162917 | − | 0.986640i | \(-0.447910\pi\) |
0.986640 | − | 0.162917i | \(-0.0520903\pi\) | |||||||
\(558\) | 7.77116e9 | + | 7.77116e9i | 0.0801584 | + | 0.0801584i | ||||
\(559\) | 1.91933e11i | 1.96563i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.71147e10 | 0.475669 | ||||||||
\(562\) | 1.39327e10 | − | 1.39327e10i | 0.139666 | − | 0.139666i | ||||
\(563\) | 7.40471e10 | + | 7.40471e10i | 0.737012 | + | 0.737012i | 0.971999 | − | 0.234987i | \(-0.0755046\pi\) |
−0.234987 | + | 0.971999i | \(0.575505\pi\) | |||||||
\(564\) | − | 2.49814e10i | − | 0.246888i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.92990e10 | −0.285488 | ||||||||
\(567\) | −5.29306e9 | + | 5.29306e9i | −0.0512123 | + | 0.0512123i | ||||
\(568\) | −1.05253e11 | − | 1.05253e11i | −1.01121 | − | 1.01121i | ||||
\(569\) | − | 1.23910e11i | − | 1.18211i | −0.806631 | − | 0.591056i | \(-0.798711\pi\) | ||
0.806631 | − | 0.591056i | \(-0.201289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.83145e11 | 1.72286 | 0.861429 | − | 0.507877i | \(-0.169570\pi\) | ||||
0.861429 | + | 0.507877i | \(0.169570\pi\) | |||||||
\(572\) | −1.44836e11 | + | 1.44836e11i | −1.35298 | + | 1.35298i | ||||
\(573\) | −7.79098e9 | − | 7.79098e9i | −0.0722725 | − | 0.0722725i | ||||
\(574\) | − | 6.04929e10i | − | 0.557259i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.84017e9 | −0.0893949 | ||||||||
\(577\) | 1.40883e11 | − | 1.40883e11i | 1.27103 | − | 1.27103i | 0.325481 | − | 0.945549i | \(-0.394474\pi\) |
0.945549 | − | 0.325481i | \(-0.105526\pi\) | |||||||
\(578\) | −2.64427e10 | − | 2.64427e10i | −0.236916 | − | 0.236916i | ||||
\(579\) | − | 9.05630e10i | − | 0.805817i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.88582e10 | 0.604298 | ||||||||
\(582\) | 3.54746e10 | − | 3.54746e10i | 0.309190 | − | 0.309190i | ||||
\(583\) | 1.40294e11 | + | 1.40294e11i | 1.21441 | + | 1.21441i | ||||
\(584\) | 6.10122e9i | 0.0524524i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.09884e10 | −0.0931847 | ||||||||
\(587\) | −2.56405e10 | + | 2.56405e10i | −0.215960 | + | 0.215960i | −0.806794 | − | 0.590833i | \(-0.798799\pi\) |
0.590833 | + | 0.806794i | \(0.298799\pi\) | |||||||
\(588\) | −2.05445e10 | − | 2.05445e10i | −0.171865 | − | 0.171865i | ||||
\(589\) | 2.04808e10i | 0.170171i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.33292e11 | 1.09258 | ||||||||
\(592\) | 5.70603e8 | − | 5.70603e8i | 0.00464566 | − | 0.00464566i | ||||
\(593\) | −9.86176e10 | − | 9.86176e10i | −0.797509 | − | 0.797509i | 0.185193 | − | 0.982702i | \(-0.440709\pi\) |
−0.982702 | + | 0.185193i | \(0.940709\pi\) | |||||||
\(594\) | − | 1.72043e10i | − | 0.138195i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.35758e11 | 1.07592 | ||||||||
\(597\) | 6.87509e10 | − | 6.87509e10i | 0.541229 | − | 0.541229i | ||||
\(598\) | −8.02802e10 | − | 8.02802e10i | −0.627775 | − | 0.627775i | ||||
\(599\) | 5.83980e10i | 0.453619i | 0.973939 | + | 0.226809i | \(0.0728294\pi\) | ||||
−0.973939 | + | 0.226809i | \(0.927171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.35703e10 | 0.180662 | 0.0903309 | − | 0.995912i | \(-0.471208\pi\) | ||||
0.0903309 | + | 0.995912i | \(0.471208\pi\) | |||||||
\(602\) | −3.26868e10 | + | 3.26868e10i | −0.248878 | + | 0.248878i | ||||
\(603\) | −1.18788e10 | − | 1.18788e10i | −0.0898472 | − | 0.0898472i | ||||
\(604\) | − | 4.27613e10i | − | 0.321295i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.20902e10 | −0.534547 | ||||||||
\(607\) | 6.46123e10 | − | 6.46123e10i | 0.475949 | − | 0.475949i | −0.427884 | − | 0.903833i | \(-0.640741\pi\) |
0.903833 | + | 0.427884i | \(0.140741\pi\) | |||||||
\(608\) | −2.59143e10 | − | 2.59143e10i | −0.189638 | − | 0.189638i | ||||
\(609\) | − | 9.28098e9i | − | 0.0674722i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.53439e11 | −1.10096 | ||||||||
\(612\) | −1.43762e10 | + | 1.43762e10i | −0.102480 | + | 0.102480i | ||||
\(613\) | 3.03819e10 | + | 3.03819e10i | 0.215165 | + | 0.215165i | 0.806457 | − | 0.591292i | \(-0.201382\pi\) |
−0.591292 | + | 0.806457i | \(0.701382\pi\) | |||||||
\(614\) | 6.86661e10i | 0.483135i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.16727e11 | −0.810681 | ||||||||
\(617\) | 2.55523e10 | − | 2.55523e10i | 0.176315 | − | 0.176315i | −0.613432 | − | 0.789747i | \(-0.710212\pi\) |
0.789747 | + | 0.613432i | \(0.210212\pi\) | |||||||
\(618\) | 3.34065e10 | + | 3.34065e10i | 0.229022 | + | 0.229022i | ||||
\(619\) | − | 1.91818e11i | − | 1.30655i | −0.757121 | − | 0.653275i | \(-0.773395\pi\) | ||
0.757121 | − | 0.653275i | \(-0.226605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.60442e10 | −0.175123 | ||||||||
\(622\) | 5.33719e10 | − | 5.33719e10i | 0.356575 | − | 0.356575i | ||||
\(623\) | −5.95136e10 | − | 5.95136e10i | −0.395061 | − | 0.395061i | ||||
\(624\) | − | 4.41750e10i | − | 0.291366i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.70987e10 | 0.306699 | ||||||||
\(627\) | 2.26709e10 | − | 2.26709e10i | 0.146689 | − | 0.146689i | ||||
\(628\) | 6.01147e10 | + | 6.01147e10i | 0.386494 | + | 0.386494i | ||||
\(629\) | 2.28113e9i | 0.0145730i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.85374e10 | 0.621561 | 0.310781 | − | 0.950482i | \(-0.399410\pi\) | ||||
0.310781 | + | 0.950482i | \(0.399410\pi\) | |||||||
\(632\) | −1.44891e11 | + | 1.44891e11i | −0.908186 | + | 0.908186i | ||||
\(633\) | 9.30514e10 | + | 9.30514e10i | 0.579573 | + | 0.579573i | ||||
\(634\) | − | 1.05853e11i | − | 0.655156i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.56165e10 | −0.523274 | ||||||||
\(637\) | −1.26187e11 | + | 1.26187e11i | −0.766404 | + | 0.766404i | ||||
\(638\) | 1.50832e10 | + | 1.50832e10i | 0.0910358 | + | 0.0910358i | ||||
\(639\) | 8.86365e10i | 0.531630i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.97357e10 | 0.590770 | 0.295385 | − | 0.955378i | \(-0.404552\pi\) | ||||
0.295385 | + | 0.955378i | \(0.404552\pi\) | |||||||
\(642\) | −5.50922e10 | + | 5.50922e10i | −0.324302 | + | 0.324302i | ||||
\(643\) | 2.05223e11 | + | 2.05223e11i | 1.20056 | + | 1.20056i | 0.973997 | + | 0.226559i | \(0.0727478\pi\) |
0.226559 | + | 0.973997i | \(0.427252\pi\) | |||||||
\(644\) | 7.46798e10i | 0.434170i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.38728e10 | 0.0796587 | ||||||||
\(647\) | −9.08930e10 | + | 9.08930e10i | −0.518696 | + | 0.518696i | −0.917177 | − | 0.398480i | \(-0.869538\pi\) |
0.398480 | + | 0.917177i | \(0.369538\pi\) | |||||||
\(648\) | 1.24213e10 | + | 1.24213e10i | 0.0704477 | + | 0.0704477i | ||||
\(649\) | 6.28154e10i | 0.354069i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.44018e10 | −0.247216 | ||||||||
\(652\) | −2.47148e10 | + | 2.47148e10i | −0.136763 | + | 0.136763i | ||||
\(653\) | −6.42783e10 | − | 6.42783e10i | −0.353518 | − | 0.353518i | 0.507899 | − | 0.861417i | \(-0.330422\pi\) |
−0.861417 | + | 0.507899i | \(0.830422\pi\) | |||||||
\(654\) | − | 8.93508e10i | − | 0.488413i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.18930e10 | 0.442213 | ||||||||
\(657\) | 2.56901e9 | − | 2.56901e9i | 0.0137881 | − | 0.0137881i | ||||
\(658\) | −2.61313e10 | − | 2.61313e10i | −0.139398 | − | 0.139398i | ||||
\(659\) | 2.78073e11i | 1.47441i | 0.675670 | + | 0.737204i | \(0.263854\pi\) | ||||
−0.675670 | + | 0.737204i | \(0.736146\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.68908e11 | 0.884799 | 0.442400 | − | 0.896818i | \(-0.354127\pi\) | ||||
0.442400 | + | 0.896818i | \(0.354127\pi\) | |||||||
\(662\) | 7.15393e8 | − | 7.15393e8i | 0.00372488 | − | 0.00372488i | ||||
\(663\) | 8.83005e10 | + | 8.83005e10i | 0.456992 | + | 0.456992i | ||||
\(664\) | − | 1.61590e11i | − | 0.831273i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.32975e8 | 0.00423385 | ||||||||
\(667\) | 2.28333e10 | − | 2.28333e10i | 0.115362 | − | 0.115362i | ||||
\(668\) | 1.63504e10 | + | 1.63504e10i | 0.0821150 | + | 0.0821150i | ||||
\(669\) | − | 5.58451e10i | − | 0.278792i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.43862e11 | −2.68286 | ||||||||
\(672\) | 5.61815e10 | − | 5.61815e10i | 0.275497 | − | 0.275497i | ||||
\(673\) | 2.63803e10 | + | 2.63803e10i | 0.128593 | + | 0.128593i | 0.768474 | − | 0.639881i | \(-0.221016\pi\) |
−0.639881 | + | 0.768474i | \(0.721016\pi\) | |||||||
\(674\) | 6.74337e10i | 0.326766i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.90034e11 | −1.86773 | ||||||||
\(677\) | 1.77432e11 | − | 1.77432e11i | 0.844652 | − | 0.844652i | −0.144808 | − | 0.989460i | \(-0.546256\pi\) |
0.989460 | + | 0.144808i | \(0.0462565\pi\) | |||||||
\(678\) | 1.48535e10 | + | 1.48535e10i | 0.0702928 | + | 0.0702928i | ||||
\(679\) | 2.02690e11i | 0.953572i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.10135e11 | 0.977034 | ||||||||
\(682\) | 7.21609e10 | − | 7.21609e10i | 0.333553 | − | 0.333553i | ||||
\(683\) | −2.40451e10 | − | 2.40451e10i | −0.110495 | − | 0.110495i | 0.649697 | − | 0.760193i | \(-0.274896\pi\) |
−0.760193 | + | 0.649697i | \(0.774896\pi\) | |||||||
\(684\) | 1.38352e10i | 0.0632064i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.17713e11 | −0.531528 | ||||||||
\(687\) | 6.57695e10 | − | 6.57695e10i | 0.295255 | − | 0.295255i | ||||
\(688\) | −4.42502e10 | − | 4.42502e10i | −0.197497 | − | 0.197497i | ||||
\(689\) | 5.25868e11i | 2.33346i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.97853e11 | −1.30644 | −0.653221 | − | 0.757168i | \(-0.726583\pi\) | ||||
−0.653221 | + | 0.757168i | \(0.726583\pi\) | |||||||
\(692\) | −1.55596e11 | + | 1.55596e11i | −0.678537 | + | 0.678537i | ||||
\(693\) | 4.91499e10 | + | 4.91499e10i | 0.213103 | + | 0.213103i | ||||
\(694\) | 1.19808e11i | 0.516475i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.17798e10 | −0.0928147 | ||||||||
\(697\) | −1.63694e11 | + | 1.63694e11i | −0.693589 | + | 0.693589i | ||||
\(698\) | 7.91349e10 | + | 7.91349e10i | 0.333385 | + | 0.333385i | ||||
\(699\) | − | 7.66831e10i | − | 0.321211i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.00659e10 | −0.0830973 | −0.0415487 | − | 0.999136i | \(-0.513229\pi\) | ||||
−0.0415487 | + | 0.999136i | \(0.513229\pi\) | |||||||
\(702\) | 3.22436e10 | − | 3.22436e10i | 0.132769 | − | 0.132769i | ||||
\(703\) | 1.09765e9 | + | 1.09765e9i | 0.00449409 | + | 0.00449409i | ||||
\(704\) | 9.13731e10i | 0.371987i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.76174e11 | 0.709126 | ||||||||
\(707\) | 2.05949e11 | − | 2.05949e11i | 0.824296 | − | 0.824296i | ||||
\(708\) | −1.91669e10 | − | 1.91669e10i | −0.0762816 | − | 0.0762816i | ||||
\(709\) | − | 3.15404e10i | − | 0.124820i | −0.998051 | − | 0.0624098i | \(-0.980121\pi\) | ||
0.998051 | − | 0.0624098i | \(-0.0198786\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.22018e11 | 0.477468 | ||||||||
\(712\) | −1.39661e11 | + | 1.39661e11i | −0.543446 | + | 0.543446i | ||||
\(713\) | −1.09238e11 | − | 1.09238e11i | −0.422685 | − | 0.422685i | ||||
\(714\) | 3.00758e10i | 0.115724i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.22021e11 | −0.844778 | ||||||||
\(717\) | −9.49757e10 | + | 9.49757e10i | −0.359365 | + | 0.359365i | ||||
\(718\) | 1.41285e11 | + | 1.41285e11i | 0.531616 | + | 0.531616i | ||||
\(719\) | − | 3.58390e10i | − | 0.134104i | −0.997749 | − | 0.0670518i | \(-0.978641\pi\) | ||
0.997749 | − | 0.0670518i | \(-0.0213593\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.90873e11 | −0.706325 | ||||||||
\(722\) | −9.27996e10 | + | 9.27996e10i | −0.341505 | + | 0.341505i | ||||
\(723\) | 9.68259e10 | + | 9.68259e10i | 0.354355 | + | 0.354355i | ||||
\(724\) | − | 4.95577e10i | − | 0.180367i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.67187e10 | −0.276156 | ||||||||
\(727\) | 1.18145e11 | − | 1.18145e11i | 0.422940 | − | 0.422940i | −0.463274 | − | 0.886215i | \(-0.653326\pi\) |
0.886215 | + | 0.463274i | \(0.153326\pi\) | |||||||
\(728\) | −2.18766e11 | − | 2.18766e11i | −0.778849 | − | 0.778849i | ||||
\(729\) | − | 1.04604e10i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.76901e11 | 0.619529 | ||||||||
\(732\) | 1.65949e11 | − | 1.65949e11i | 0.578004 | − | 0.578004i | ||||
\(733\) | 4.46957e10 | + | 4.46957e10i | 0.154828 | + | 0.154828i | 0.780270 | − | 0.625442i | \(-0.215081\pi\) |
−0.625442 | + | 0.780270i | \(0.715081\pi\) | |||||||
\(734\) | − | 2.08274e11i | − | 0.717549i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.76438e11 | 0.942077 | ||||||||
\(737\) | −1.10304e11 | + | 1.10304e11i | −0.373869 | + | 0.373869i | ||||
\(738\) | 5.97743e10 | + | 5.97743e10i | 0.201506 | + | 0.201506i | ||||
\(739\) | − | 3.09256e11i | − | 1.03691i | −0.855105 | − | 0.518454i | \(-0.826508\pi\) | ||
0.855105 | − | 0.518454i | \(-0.173492\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.49778e10 | 0.281859 | ||||||||
\(742\) | −8.95572e10 | + | 8.95572e10i | −0.295451 | + | 0.295451i | ||||
\(743\) | −1.52845e11 | − | 1.52845e11i | −0.501529 | − | 0.501529i | 0.410384 | − | 0.911913i | \(-0.365395\pi\) |
−0.911913 | + | 0.410384i | \(0.865395\pi\) | |||||||
\(744\) | 1.04198e11i | 0.340070i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.11972e11 | 0.361539 | ||||||||
\(747\) | −6.80402e10 | + | 6.80402e10i | −0.218516 | + | 0.218516i | ||||
\(748\) | 1.33493e11 | + | 1.33493e11i | 0.426435 | + | 0.426435i | ||||
\(749\) | − | 3.14778e11i | − | 1.00018i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.96392e11 | −1.24613 | −0.623067 | − | 0.782168i | \(-0.714114\pi\) | ||||
−0.623067 | + | 0.782168i | \(0.714114\pi\) | |||||||
\(752\) | 3.53755e10 | − | 3.53755e10i | 0.110619 | − | 0.110619i | ||||
\(753\) | −8.00401e10 | − | 8.00401e10i | −0.248959 | − | 0.248959i | ||||
\(754\) | 5.65368e10i | 0.174923i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.99943e10 | −0.0918231 | ||||||||
\(757\) | 4.74476e10 | − | 4.74476e10i | 0.144488 | − | 0.144488i | −0.631163 | − | 0.775650i | \(-0.717422\pi\) |
0.775650 | + | 0.631163i | \(0.217422\pi\) | |||||||
\(758\) | 8.15093e10 | + | 8.15093e10i | 0.246905 | + | 0.246905i | ||||
\(759\) | 2.41839e11i | 0.728718i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.88001e10 | −0.0858727 | −0.0429363 | − | 0.999078i | \(-0.513671\pi\) | ||||
−0.0429363 | + | 0.999078i | \(0.513671\pi\) | |||||||
\(762\) | −4.14636e10 | + | 4.14636e10i | −0.122984 | + | 0.122984i | ||||
\(763\) | 2.55260e11 | + | 2.55260e11i | 0.753156 | + | 0.753156i | ||||
\(764\) | − | 4.41493e10i | − | 0.129584i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.53835e9 | −0.0131820 | ||||||||
\(767\) | −1.17726e11 | + | 1.17726e11i | −0.340166 | + | 0.340166i | ||||
\(768\) | −1.04003e11 | − | 1.04003e11i | −0.298951 | − | 0.298951i | ||||
\(769\) | − | 2.37524e11i | − | 0.679207i | −0.940569 | − | 0.339604i | \(-0.889707\pi\) | ||
0.940569 | − | 0.339604i | \(-0.110293\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.39034e11 | −0.676459 | ||||||||
\(772\) | 2.56598e11 | − | 2.56598e11i | 0.722410 | − | 0.722410i | ||||
\(773\) | 2.30602e10 | + | 2.30602e10i | 0.0645869 | + | 0.0645869i | 0.738662 | − | 0.674076i | \(-0.235458\pi\) |
−0.674076 | + | 0.738662i | \(0.735458\pi\) | |||||||
\(774\) | − | 6.45970e10i | − | 0.179990i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.75655e11 | 1.31173 | ||||||||
\(777\) | −2.37967e9 | + | 2.37967e9i | −0.00652879 | + | 0.00652879i | ||||
\(778\) | 3.89310e10 | + | 3.89310e10i | 0.106262 | + | 0.106262i | ||||
\(779\) | 1.57534e11i | 0.427785i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.23054e11 | 2.21220 | ||||||||
\(782\) | −7.39930e10 | + | 7.39930e10i | −0.197863 | + | 0.197863i | ||||
\(783\) | 9.17072e9 | + | 9.17072e9i | 0.0243981 | + | 0.0243981i | ||||
\(784\) | − | 5.81850e10i | − | 0.154009i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.45464e11 | 0.381122 | ||||||||
\(787\) | −2.21187e11 | + | 2.21187e11i | −0.576582 | + | 0.576582i | −0.933960 | − | 0.357378i | \(-0.883671\pi\) |
0.357378 | + | 0.933960i | \(0.383671\pi\) | |||||||
\(788\) | 3.77665e11 | + | 3.77665e11i | 0.979495 | + | 0.979495i | ||||
\(789\) | − | 3.22454e11i | − | 0.832070i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.48680e10 | −0.216789 | ||||||||
\(792\) | 1.15341e11 | − | 1.15341e11i | 0.293144 | − | 0.293144i | ||||
\(793\) | −1.01928e12 | − | 1.01928e12i | −2.57752 | − | 2.57752i | ||||
\(794\) | − | 6.87010e10i | − | 0.172855i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.89592e11 | 0.970417 | ||||||||
\(797\) | 2.59953e11 | − | 2.59953e11i | 0.644260 | − | 0.644260i | −0.307340 | − | 0.951600i | \(-0.599439\pi\) |
0.951600 | + | 0.307340i | \(0.0994387\pi\) | |||||||
\(798\) | 1.44720e10 | + | 1.44720e10i | 0.0356876 | + | 0.0356876i | ||||
\(799\) | 1.41423e11i | 0.347002i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.17613e11 | 0.285710 | ||||||||
\(802\) | 1.87704e11 | − | 1.87704e11i | 0.453709 | − | 0.453709i | ||||
\(803\) | −2.38551e10 | − | 2.38551e10i | −0.0573746 | − | 0.0573746i | ||||
\(804\) | − | 6.73141e10i | − | 0.161095i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.70482e11 | 0.640911 | ||||||||
\(807\) | −7.75190e10 | + | 7.75190e10i | −0.182774 | + | 0.182774i | ||||
\(808\) | −4.83304e11 | − | 4.83304e11i | −1.13390 | − | 1.13390i | ||||
\(809\) | − | 4.01818e11i | − | 0.938071i | −0.883179 | − | 0.469036i | \(-0.844602\pi\) | ||
0.883179 | − | 0.469036i | \(-0.155398\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.61109e11 | −0.603584 | −0.301792 | − | 0.953374i | \(-0.597585\pi\) | ||||
−0.301792 | + | 0.953374i | \(0.597585\pi\) | |||||||
\(812\) | 2.62964e10 | − | 2.62964e10i | 0.0604884 | − | 0.0604884i | ||||
\(813\) | −1.43742e11 | − | 1.43742e11i | −0.329020 | − | 0.329020i | ||||
\(814\) | − | 7.73477e9i | − | 0.0176177i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.07154e10 | −0.0918328 | ||||||||
\(817\) | 8.51224e10 | − | 8.51224e10i | 0.191054 | − | 0.191054i | ||||
\(818\) | 1.61657e11 | + | 1.61657e11i | 0.361061 | + | 0.361061i | ||||
\(819\) | 1.84229e11i | 0.409471i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.19668e11 | 0.923704 | 0.461852 | − | 0.886957i | \(-0.347185\pi\) | ||||
0.461852 | + | 0.886957i | \(0.347185\pi\) | |||||||
\(822\) | −1.62058e10 | + | 1.62058e10i | −0.0354962 | + | 0.0354962i | ||||
\(823\) | 2.76519e11 | + | 2.76519e11i | 0.602734 | + | 0.602734i | 0.941037 | − | 0.338303i | \(-0.109853\pi\) |
−0.338303 | + | 0.941037i | \(0.609853\pi\) | |||||||
\(824\) | 4.47925e11i | 0.971621i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.00983e10 | −0.0861402 | ||||||||
\(827\) | 2.50038e11 | − | 2.50038e11i | 0.534545 | − | 0.534545i | −0.387377 | − | 0.921922i | \(-0.626619\pi\) |
0.921922 | + | 0.387377i | \(0.126619\pi\) | |||||||
\(828\) | −7.37926e10 | − | 7.37926e10i | −0.156997 | − | 0.156997i | ||||
\(829\) | − | 3.03680e11i | − | 0.642981i | −0.946913 | − | 0.321491i | \(-0.895816\pi\) | ||
0.946913 | − | 0.321491i | \(-0.104184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.84475e11 | −0.386841 | ||||||||
\(832\) | −1.71248e11 | + | 1.71248e11i | −0.357381 | + | 0.357381i | ||||
\(833\) | 1.16305e11 | + | 1.16305e11i | 0.241556 | + | 0.241556i | ||||
\(834\) | − | 1.44610e11i | − | 0.298905i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.28470e11 | 0.263012 | ||||||||
\(837\) | 4.38743e10 | − | 4.38743e10i | 0.0893940 | − | 0.0893940i | ||||
\(838\) | 1.22833e11 | + | 1.22833e11i | 0.249080 | + | 0.249080i | ||||
\(839\) | − | 7.68316e11i | − | 1.55057i | −0.631610 | − | 0.775286i | \(-0.717606\pi\) | ||
0.631610 | − | 0.775286i | \(-0.282394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.84166e11 | 0.967856 | ||||||||
\(842\) | −7.02002e10 | + | 7.02002e10i | −0.139666 | + | 0.139666i | ||||
\(843\) | −7.86610e10 | − | 7.86610e10i | −0.155757 | − | 0.155757i | ||||
\(844\) | 5.27297e11i | 1.03917i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.16416e10 | 0.100813 | ||||||||
\(847\) | 2.19172e11 | − | 2.19172e11i | 0.425845 | − | 0.425845i | ||||
\(848\) | −1.21239e11 | − | 1.21239e11i | −0.234455 | − | 0.234455i | ||||
\(849\) | 1.65416e11i | 0.318381i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.17090e10 | −0.0223256 | ||||||||
\(852\) | −2.51139e11 | + | 2.51139e11i | −0.476603 | + | 0.476603i | ||||
\(853\) | −1.03763e11 | − | 1.03763e11i | −0.195995 | − | 0.195995i | 0.602286 | − | 0.798281i | \(-0.294257\pi\) |
−0.798281 | + | 0.602286i | \(0.794257\pi\) | |||||||
\(854\) | − | 3.47175e11i | − | 0.652705i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.38694e11 | −1.37584 | ||||||||
\(857\) | −6.22521e10 | + | 6.22521e10i | −0.115407 | + | 0.115407i | −0.762452 | − | 0.647045i | \(-0.776005\pi\) |
0.647045 | + | 0.762452i | \(0.276005\pi\) | |||||||
\(858\) | −2.99405e11 | − | 2.99405e11i | −0.552472 | − | 0.552472i | ||||
\(859\) | 1.01381e12i | 1.86203i | 0.364986 | + | 0.931013i | \(0.381074\pi\) | ||||
−0.364986 | + | 0.931013i | \(0.618926\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.41530e11 | −0.621464 | ||||||||
\(862\) | 5.44154e10 | − | 5.44154e10i | 0.0985581 | − | 0.0985581i | ||||
\(863\) | −1.41738e11 | − | 1.41738e11i | −0.255531 | − | 0.255531i | 0.567703 | − | 0.823234i | \(-0.307832\pi\) |
−0.823234 | + | 0.567703i | \(0.807832\pi\) | |||||||
\(864\) | 1.11028e11i | 0.199241i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.73882e11 | −0.309159 | ||||||||
\(867\) | −1.49290e11 | + | 1.49290e11i | −0.264213 | + | 0.264213i | ||||
\(868\) | −1.25806e11 | − | 1.25806e11i | −0.221628 | − | 0.221628i | ||||
\(869\) | − | 1.13302e12i | − | 1.98682i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.13453e11 | −0.718378 | ||||||||
\(872\) | 5.99022e11 | − | 5.99022e11i | 1.03604 | − | 1.03604i | ||||
\(873\) | −2.00282e11 | − | 2.00282e11i | −0.344814 | − | 0.344814i | ||||
\(874\) | 7.12087e10i | 0.122036i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.45579e10 | 0.0247219 | ||||||||
\(877\) | −2.65966e11 | + | 2.65966e11i | −0.449601 | + | 0.449601i | −0.895222 | − | 0.445621i | \(-0.852983\pi\) |
0.445621 | + | 0.895222i | \(0.352983\pi\) | |||||||
\(878\) | −2.19388e11 | − | 2.19388e11i | −0.369177 | − | 0.369177i | ||||
\(879\) | 6.20382e10i | 0.103921i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.64084e11 | −0.272372 | −0.136186 | − | 0.990683i | \(-0.543484\pi\) | ||||
−0.136186 | + | 0.990683i | \(0.543484\pi\) | |||||||
\(882\) | 4.24696e10 | − | 4.24696e10i | 0.0701785 | − | 0.0701785i | ||||
\(883\) | −1.00861e11 | − | 1.00861e11i | −0.165912 | − | 0.165912i | 0.619268 | − | 0.785180i | \(-0.287430\pi\) |
−0.785180 | + | 0.619268i | \(0.787430\pi\) | |||||||
\(884\) | 5.00375e11i | 0.819382i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.31683e11 | −0.213695 | ||||||||
\(887\) | −7.92983e11 | + | 7.92983e11i | −1.28106 | + | 1.28106i | −0.340993 | + | 0.940066i | \(0.610763\pi\) |
−0.940066 | + | 0.340993i | \(0.889237\pi\) | |||||||
\(888\) | 5.58440e9 | + | 5.58440e9i | 0.00898100 | + | 0.00898100i | ||||
\(889\) | − | 2.36909e11i | − | 0.379293i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.71319e10 | −0.154117 | ||||||||
\(892\) | 1.58230e11 | − | 1.58230e11i | 0.249936 | − | 0.249936i | ||||
\(893\) | 6.80505e10 | + | 6.80505e10i | 0.107010 | + | 0.107010i | ||||
\(894\) | 2.80640e11i | 0.439339i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.76607e11 | 0.584327 | ||||||||
\(897\) | −4.53245e11 | + | 4.53245e11i | −0.700105 | + | 0.700105i | ||||
\(898\) | 3.93051e11 | + | 3.93051e11i | 0.604427 | + | 0.604427i | ||||
\(899\) | 7.69303e10i | 0.117777i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.84685e11 | 0.735462 | ||||||||
\(902\) | 5.55047e11 | − | 5.55047e11i | 0.838501 | − | 0.838501i | ||||
\(903\) | 1.84543e11 | + | 1.84543e11i | 0.277553 | + | 0.277553i | ||||
\(904\) | 1.99161e11i | 0.298216i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.83963e10 | 0.131196 | ||||||||
\(907\) | −8.20854e11 | + | 8.20854e11i | −1.21293 | + | 1.21293i | −0.242875 | + | 0.970058i | \(0.578090\pi\) |
−0.970058 | + | 0.242875i | \(0.921910\pi\) | |||||||
\(908\) | 5.95389e11 | + | 5.95389e11i | 0.875905 | + | 0.875905i | ||||
\(909\) | 4.07006e11i | 0.596135i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.34207e12 | −1.94851 | −0.974254 | − | 0.225454i | \(-0.927613\pi\) | ||||
−0.974254 | + | 0.225454i | \(0.927613\pi\) | |||||||
\(912\) | −1.95916e10 | + | 1.95916e10i | −0.0283199 | + | 0.0283199i | ||||
\(913\) | 6.31802e11 | + | 6.31802e11i | 0.909281 | + | 0.909281i | ||||
\(914\) | 6.38984e10i | 0.0915598i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.72698e11 | 0.529389 | ||||||||
\(917\) | −4.15565e11 | + | 4.15565e11i | −0.587708 | + | 0.587708i | ||||
\(918\) | −2.97185e10 | − | 2.97185e10i | −0.0418462 | − | 0.0418462i | ||||
\(919\) | 4.14286e11i | 0.580815i | 0.956903 | + | 0.290408i | \(0.0937909\pi\) | ||||
−0.956903 | + | 0.290408i | \(0.906209\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.87674e11 | 0.538800 | ||||||||
\(922\) | 1.75331e11 | − | 1.75331e11i | 0.242625 | − | 0.242625i | ||||
\(923\) | 1.54253e12 | + | 1.54253e12i | 2.12534 | + | 2.12534i | ||||
\(924\) | 2.78519e11i | 0.382091i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.66750e10 | −0.117883 | ||||||||
\(927\) | 1.88606e11 | − | 1.88606e11i | 0.255409 | − | 0.255409i | ||||
\(928\) | −9.73398e10 | − | 9.73398e10i | −0.131250 | − | 0.131250i | ||||
\(929\) | − | 3.44057e11i | − | 0.461920i | −0.972963 | − | 0.230960i | \(-0.925813\pi\) | ||
0.972963 | − | 0.230960i | \(-0.0741867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.11928e11 | 0.148984 | ||||||||
\(932\) | 2.17271e11 | − | 2.17271e11i | 0.287964 | − | 0.287964i | ||||
\(933\) | −3.01326e11 | − | 3.01326e11i | −0.397659 | − | 0.397659i | ||||
\(934\) | 6.75447e11i | 0.887572i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.32333e11 | 0.563268 | ||||||||
\(937\) | 6.64709e11 | − | 6.64709e11i | 0.862329 | − | 0.862329i | −0.129279 | − | 0.991608i | \(-0.541266\pi\) |
0.991608 | + | 0.129279i | \(0.0412664\pi\) | |||||||
\(938\) | −7.04124e10 | − | 7.04124e10i | −0.0909574 | − | 0.0909574i | ||||
\(939\) | − | 2.65909e11i | − | 0.342035i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.87481e11 | −0.494187 | −0.247094 | − | 0.968992i | \(-0.579476\pi\) | ||||
−0.247094 | + | 0.968992i | \(0.579476\pi\) | |||||||
\(942\) | −1.24269e11 | + | 1.24269e11i | −0.157819 | + | 0.157819i | ||||
\(943\) | −8.40239e11 | − | 8.40239e11i | −1.06257 | − | 1.06257i | ||||
\(944\) | − | 5.42835e10i | − | 0.0683566i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.99830e11 | −0.748968 | ||||||||
\(947\) | 9.94316e11 | − | 9.94316e11i | 1.23630 | − | 1.23630i | 0.274800 | − | 0.961501i | \(-0.411388\pi\) |
0.961501 | − | 0.274800i | \(-0.0886118\pi\) | |||||||
\(948\) | 3.45720e11 | + | 3.45720e11i | 0.428047 | + | 0.428047i | ||||
\(949\) | − | 8.94167e10i | − | 0.110244i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.97622e11 | −0.730641 | ||||||||
\(952\) | −2.01633e11 | + | 2.01633e11i | −0.245478 | + | 0.245478i | ||||
\(953\) | 5.07969e11 | + | 5.07969e11i | 0.615836 | + | 0.615836i | 0.944461 | − | 0.328624i | \(-0.106585\pi\) |
−0.328624 | + | 0.944461i | \(0.606585\pi\) | |||||||
\(954\) | − | 1.76987e11i | − | 0.213672i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.38201e11 | −0.644337 | ||||||||
\(957\) | 8.51568e10 | − | 8.51568e10i | 0.101525 | − | 0.101525i | ||||
\(958\) | 4.96018e10 | + | 4.96018e10i | 0.0588892 | + | 0.0588892i | ||||
\(959\) | − | 9.25943e10i | − | 0.109474i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.84843e11 | −0.568470 | ||||||||
\(962\) | 1.44962e10 | − | 1.44962e10i | 0.0169260 | − | 0.0169260i | ||||
\(963\) | 3.11038e11 | + | 3.11038e11i | 0.361667 | + | 0.361667i | ||||
\(964\) | 5.48686e11i | 0.635354i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.54378e11 | −0.177287 | ||||||||
\(967\) | −8.82088e11 | + | 8.82088e11i | −1.00880 | + | 1.00880i | −0.00884150 | + | 0.999961i | \(0.502814\pi\) |
−0.999961 | + | 0.00884150i | \(0.997186\pi\) | |||||||
\(968\) | −5.14334e11 | − | 5.14334e11i | −0.585793 | − | 0.585793i | ||||
\(969\) | − | 7.83227e10i | − | 0.0888367i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.47801e11 | 0.391249 | 0.195625 | − | 0.980679i | \(-0.437327\pi\) | ||||
0.195625 | + | 0.980679i | \(0.437327\pi\) | |||||||
\(972\) | 2.96380e10 | − | 2.96380e10i | 0.0332035 | − | 0.0332035i | ||||
\(973\) | 4.13125e11 | + | 4.13125e11i | 0.460925 | + | 0.460925i | ||||
\(974\) | − | 3.98615e11i | − | 0.442912i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.69992e11 | 0.517954 | ||||||||
\(977\) | 1.23243e11 | − | 1.23243e11i | 0.135265 | − | 0.135265i | −0.636232 | − | 0.771497i | \(-0.719508\pi\) |
0.771497 | + | 0.636232i | \(0.219508\pi\) | |||||||
\(978\) | −5.10906e10 | − | 5.10906e10i | −0.0558451 | − | 0.0558451i | ||||
\(979\) | − | 1.09212e12i | − | 1.18889i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.04455e11 | −0.544687 | ||||||||
\(982\) | 5.19256e11 | − | 5.19256e11i | 0.558387 | − | 0.558387i | ||||
\(983\) | 5.87218e11 | + | 5.87218e11i | 0.628905 | + | 0.628905i | 0.947793 | − | 0.318887i | \(-0.103309\pi\) |
−0.318887 | + | 0.947793i | \(0.603309\pi\) | |||||||
\(984\) | 8.01473e11i | 0.854886i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.21091e10 | 0.0551323 | ||||||||
\(987\) | −1.47531e11 | + | 1.47531e11i | −0.155459 | + | 0.155459i | ||||
\(988\) | 2.40773e11 | + | 2.40773e11i | 0.252685 | + | 0.252685i | ||||
\(989\) | 9.08032e11i | 0.949108i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.33829e12 | −1.38757 | −0.693786 | − | 0.720181i | \(-0.744059\pi\) | ||||
−0.693786 | + | 0.720181i | \(0.744059\pi\) | |||||||
\(992\) | −4.65690e11 | + | 4.65690e11i | −0.480895 | + | 0.480895i | ||||
\(993\) | −4.03895e9 | − | 4.03895e9i | −0.00415405 | − | 0.00415405i | ||||
\(994\) | 5.25398e11i | 0.538199i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.85565e11 | −0.391796 | ||||||||
\(997\) | −6.49580e11 | + | 6.49580e11i | −0.657433 | + | 0.657433i | −0.954772 | − | 0.297339i | \(-0.903901\pi\) |
0.297339 | + | 0.954772i | \(0.403901\pi\) | |||||||
\(998\) | −1.43426e11 | − | 1.43426e11i | −0.144579 | − | 0.144579i | ||||
\(999\) | − | 4.70280e9i | − | 0.00472165i |
(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 | 75.9.f.b.43.2 | yes | 8 | |
5.2 | odd | 4 | inner | 75.9.f.b.7.2 | ✓ | 8 | |
5.3 | odd | 4 | inner | 75.9.f.b.7.3 | yes | 8 | |
5.4 | even | 2 | inner | 75.9.f.b.43.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.9.f.b.7.2 | ✓ | 8 | 5.2 | odd | 4 | inner | |
75.9.f.b.7.3 | yes | 8 | 5.3 | odd | 4 | inner | |
75.9.f.b.43.2 | yes | 8 | 1.1 | even | 1 | trivial | |
75.9.f.b.43.3 | yes | 8 | 5.4 | even | 2 | inner |