Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,8,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), degree \(2\), not 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: | \(45.9205987462\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.8.e.a.79.1 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.00000 | − | 5.19615i | −0.265165 | − | 0.459279i | 0.702442 | − | 0.711741i | \(-0.252093\pi\) |
−0.967607 | + | 0.252462i | \(0.918760\pi\) | |||||||
\(3\) | −13.5000 | + | 23.3827i | −0.288675 | + | 0.500000i | ||||
\(4\) | 46.0000 | − | 79.6743i | 0.359375 | − | 0.622456i | ||||
\(5\) | 195.000 | + | 337.750i | 0.697653 | + | 1.20837i | 0.969278 | + | 0.245968i | \(0.0791057\pi\) |
−0.271625 | + | 0.962403i | \(0.587561\pi\) | |||||||
\(6\) | 162.000 | 0.306186 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1320.00 | −0.911505 | ||||||||
\(9\) | −364.500 | − | 631.333i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1170.00 | − | 2026.50i | 0.369986 | − | 0.640835i | ||||
\(11\) | 474.000 | − | 820.992i | 0.107375 | − | 0.185979i | −0.807331 | − | 0.590099i | \(-0.799089\pi\) |
0.914706 | + | 0.404120i | \(0.132422\pi\) | |||||||
\(12\) | 1242.00 | + | 2151.21i | 0.207485 | + | 0.359375i | ||||
\(13\) | 5098.00 | 0.643573 | 0.321787 | − | 0.946812i | \(-0.395717\pi\) | ||||
0.321787 | + | 0.946812i | \(0.395717\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10530.0 | −0.805581 | ||||||||
\(16\) | −1928.00 | − | 3339.39i | −0.117676 | − | 0.203820i | ||||
\(17\) | 14193.0 | − | 24583.0i | 0.700653 | − | 1.21357i | −0.267585 | − | 0.963534i | \(-0.586225\pi\) |
0.968238 | − | 0.250032i | \(-0.0804412\pi\) | |||||||
\(18\) | −2187.00 | + | 3788.00i | −0.0883883 | + | 0.153093i | ||||
\(19\) | −4310.00 | − | 7465.14i | −0.144158 | − | 0.249690i | 0.784900 | − | 0.619622i | \(-0.212714\pi\) |
−0.929059 | + | 0.369933i | \(0.879381\pi\) | |||||||
\(20\) | 35880.0 | 1.00288 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5688.00 | −0.113889 | ||||||||
\(23\) | 7644.00 | + | 13239.8i | 0.131001 | + | 0.226900i | 0.924063 | − | 0.382241i | \(-0.124848\pi\) |
−0.793062 | + | 0.609141i | \(0.791514\pi\) | |||||||
\(24\) | 17820.0 | − | 30865.1i | 0.263129 | − | 0.455752i | ||||
\(25\) | −36987.5 | + | 64064.2i | −0.473440 | + | 0.820022i | ||||
\(26\) | −15294.0 | − | 26490.0i | −0.170653 | − | 0.295580i | ||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 36510.0 | 0.277983 | 0.138992 | − | 0.990294i | \(-0.455614\pi\) | ||||
0.138992 | + | 0.990294i | \(0.455614\pi\) | |||||||
\(30\) | 31590.0 | + | 54715.5i | 0.213612 | + | 0.369986i | ||||
\(31\) | −138404. | + | 239723.i | −0.834416 | + | 1.44525i | 0.0600887 | + | 0.998193i | \(0.480862\pi\) |
−0.894505 | + | 0.447058i | \(0.852472\pi\) | |||||||
\(32\) | −96048.0 | + | 166360.i | −0.518159 | + | 0.897478i | ||||
\(33\) | 12798.0 | + | 22166.8i | 0.0619931 | + | 0.107375i | ||||
\(34\) | −170316. | −0.743155 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −67068.0 | −0.239583 | ||||||||
\(37\) | −134263. | − | 232550.i | −0.435763 | − | 0.754764i | 0.561595 | − | 0.827413i | \(-0.310188\pi\) |
−0.997358 | + | 0.0726489i | \(0.976855\pi\) | |||||||
\(38\) | −25860.0 | + | 44790.8i | −0.0764515 | + | 0.132418i | ||||
\(39\) | −68823.0 | + | 119205.i | −0.185784 | + | 0.321787i | ||||
\(40\) | −257400. | − | 445830.i | −0.635914 | − | 1.10144i | ||||
\(41\) | 629718. | 1.42693 | 0.713465 | − | 0.700691i | \(-0.247125\pi\) | ||||
0.713465 | + | 0.700691i | \(0.247125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 685772. | 1.31535 | 0.657673 | − | 0.753303i | \(-0.271541\pi\) | ||||
0.657673 | + | 0.753303i | \(0.271541\pi\) | |||||||
\(44\) | −43608.0 | − | 75531.3i | −0.0771759 | − | 0.133673i | ||||
\(45\) | 142155. | − | 246220.i | 0.232551 | − | 0.402790i | ||||
\(46\) | 45864.0 | − | 79438.8i | 0.0694736 | − | 0.120332i | ||||
\(47\) | 291648. | + | 505149.i | 0.409748 | + | 0.709704i | 0.994861 | − | 0.101248i | \(-0.0322834\pi\) |
−0.585114 | + | 0.810951i | \(0.698950\pi\) | |||||||
\(48\) | 104112. | 0.135880 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 443850. | 0.502159 | ||||||||
\(51\) | 383211. | + | 663741.i | 0.404522 | + | 0.700653i | ||||
\(52\) | 234508. | − | 406180.i | 0.231284 | − | 0.400596i | ||||
\(53\) | 214029. | − | 370709.i | 0.197473 | − | 0.342033i | −0.750236 | − | 0.661171i | \(-0.770060\pi\) |
0.947708 | + | 0.319138i | \(0.103393\pi\) | |||||||
\(54\) | −59049.0 | − | 102276.i | −0.0510310 | − | 0.0883883i | ||||
\(55\) | 369720. | 0.299643 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 232740. | 0.166460 | ||||||||
\(58\) | −109530. | − | 189712.i | −0.0737115 | − | 0.127672i | ||||
\(59\) | 653190. | − | 1.13136e6i | 0.414054 | − | 0.717163i | −0.581274 | − | 0.813708i | \(-0.697446\pi\) |
0.995329 | + | 0.0965444i | \(0.0307790\pi\) | |||||||
\(60\) | −484380. | + | 838971.i | −0.289506 | + | 0.501438i | ||||
\(61\) | 150331. | + | 260381.i | 0.0847997 | + | 0.146877i | 0.905306 | − | 0.424760i | \(-0.139642\pi\) |
−0.820506 | + | 0.571638i | \(0.806308\pi\) | |||||||
\(62\) | 1.66085e6 | 0.885032 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 659008. | 0.314240 | ||||||||
\(65\) | 994110. | + | 1.72185e6i | 0.448991 | + | 0.777675i | ||||
\(66\) | 76788.0 | − | 133001.i | 0.0328768 | − | 0.0569443i | ||||
\(67\) | 253622. | − | 439286.i | 0.103021 | − | 0.178437i | −0.809907 | − | 0.586558i | \(-0.800482\pi\) |
0.912928 | + | 0.408121i | \(0.133816\pi\) | |||||||
\(68\) | −1.30576e6 | − | 2.26164e6i | −0.503594 | − | 0.872251i | ||||
\(69\) | −412776. | −0.151266 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.56063e6 | 1.84383 | 0.921913 | − | 0.387397i | \(-0.126626\pi\) | ||||
0.921913 | + | 0.387397i | \(0.126626\pi\) | |||||||
\(72\) | 481140. | + | 833359.i | 0.151917 | + | 0.263129i | ||||
\(73\) | 684541. | − | 1.18566e6i | 0.205954 | − | 0.356722i | −0.744483 | − | 0.667642i | \(-0.767304\pi\) |
0.950436 | + | 0.310920i | \(0.100637\pi\) | |||||||
\(74\) | −805578. | + | 1.39530e6i | −0.231098 | + | 0.400274i | ||||
\(75\) | −998663. | − | 1.72973e6i | −0.273341 | − | 0.473440i | ||||
\(76\) | −793040. | −0.207228 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 825876. | 0.197053 | ||||||||
\(79\) | 3.45686e6 | + | 5.98746e6i | 0.788836 | + | 1.36630i | 0.926680 | + | 0.375851i | \(0.122649\pi\) |
−0.137844 | + | 0.990454i | \(0.544017\pi\) | |||||||
\(80\) | 751920. | − | 1.30236e6i | 0.164194 | − | 0.284392i | ||||
\(81\) | −265720. | + | 460241.i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.88915e6 | − | 3.27211e6i | −0.378372 | − | 0.655359i | ||||
\(83\) | 4.37675e6 | 0.840191 | 0.420096 | − | 0.907480i | \(-0.361997\pi\) | ||||
0.420096 | + | 0.907480i | \(0.361997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.10705e7 | 1.95525 | ||||||||
\(86\) | −2.05732e6 | − | 3.56338e6i | −0.348784 | − | 0.604111i | ||||
\(87\) | −492885. | + | 853702.i | −0.0802469 | + | 0.138992i | ||||
\(88\) | −625680. | + | 1.08371e6i | −0.0978730 | + | 0.169521i | ||||
\(89\) | −4.26416e6 | − | 7.38573e6i | −0.641162 | − | 1.11053i | −0.985174 | − | 0.171560i | \(-0.945119\pi\) |
0.344011 | − | 0.938965i | \(-0.388214\pi\) | |||||||
\(90\) | −1.70586e6 | −0.246658 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.40650e6 | 0.188313 | ||||||||
\(93\) | −3.73691e6 | − | 6.47251e6i | −0.481750 | − | 0.834416i | ||||
\(94\) | 1.74989e6 | − | 3.03089e6i | 0.217302 | − | 0.376377i | ||||
\(95\) | 1.68090e6 | − | 2.91140e6i | 0.201145 | − | 0.348393i | ||||
\(96\) | −2.59330e6 | − | 4.49172e6i | −0.299159 | − | 0.518159i | ||||
\(97\) | 8.82681e6 | 0.981981 | 0.490990 | − | 0.871165i | \(-0.336635\pi\) | ||||
0.490990 | + | 0.871165i | \(0.336635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −691092. | −0.0715835 | ||||||||
\(100\) | 3.40285e6 | + | 5.89391e6i | 0.340285 | + | 0.589391i | ||||
\(101\) | 5.99321e6 | − | 1.03805e7i | 0.578808 | − | 1.00253i | −0.416808 | − | 0.908995i | \(-0.636851\pi\) |
0.995616 | − | 0.0935309i | \(-0.0298154\pi\) | |||||||
\(102\) | 2.29927e6 | − | 3.98245e6i | 0.214530 | − | 0.371577i | ||||
\(103\) | 3.60470e6 | + | 6.24352e6i | 0.325041 | + | 0.562988i | 0.981521 | − | 0.191356i | \(-0.0612885\pi\) |
−0.656480 | + | 0.754344i | \(0.727955\pi\) | |||||||
\(104\) | −6.72936e6 | −0.586620 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.56835e6 | −0.209451 | ||||||||
\(107\) | −5.71304e6 | − | 9.89527e6i | −0.450842 | − | 0.780880i | 0.547597 | − | 0.836742i | \(-0.315543\pi\) |
−0.998439 | + | 0.0558618i | \(0.982209\pi\) | |||||||
\(108\) | 905418. | − | 1.56823e6i | 0.0691618 | − | 0.119792i | ||||
\(109\) | −2.01048e6 | + | 3.48224e6i | −0.148698 | + | 0.257553i | −0.930747 | − | 0.365665i | \(-0.880842\pi\) |
0.782048 | + | 0.623218i | \(0.214175\pi\) | |||||||
\(110\) | −1.10916e6 | − | 1.92112e6i | −0.0794547 | − | 0.137620i | ||||
\(111\) | 7.25020e6 | 0.503176 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.77063e7 | −1.15439 | −0.577197 | − | 0.816605i | \(-0.695853\pi\) | ||||
−0.577197 | + | 0.816605i | \(0.695853\pi\) | |||||||
\(114\) | −698220. | − | 1.20935e6i | −0.0441393 | − | 0.0764515i | ||||
\(115\) | −2.98116e6 | + | 5.16352e6i | −0.182786 | + | 0.316595i | ||||
\(116\) | 1.67946e6 | − | 2.90891e6i | 0.0999003 | − | 0.173032i | ||||
\(117\) | −1.85822e6 | − | 3.21853e6i | −0.107262 | − | 0.185784i | ||||
\(118\) | −7.83828e6 | −0.439171 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.38996e7 | 0.734291 | ||||||||
\(121\) | 9.29423e6 | + | 1.60981e7i | 0.476941 | + | 0.826086i | ||||
\(122\) | 901986. | − | 1.56229e6i | 0.0449718 | − | 0.0778935i | ||||
\(123\) | −8.50119e6 | + | 1.47245e7i | −0.411919 | + | 0.713465i | ||||
\(124\) | 1.27332e7 | + | 2.20545e7i | 0.599737 | + | 1.03877i | ||||
\(125\) | 1.61850e6 | 0.0741187 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.67883e7 | 0.727267 | 0.363633 | − | 0.931542i | \(-0.381536\pi\) | ||||
0.363633 | + | 0.931542i | \(0.381536\pi\) | |||||||
\(128\) | 1.03171e7 | + | 1.78698e7i | 0.434834 | + | 0.753155i | ||||
\(129\) | −9.25792e6 | + | 1.60352e7i | −0.379708 | + | 0.657673i | ||||
\(130\) | 5.96466e6 | − | 1.03311e7i | 0.238113 | − | 0.412425i | ||||
\(131\) | 8.41339e6 | + | 1.45724e7i | 0.326980 | + | 0.566346i | 0.981911 | − | 0.189343i | \(-0.0606357\pi\) |
−0.654931 | + | 0.755689i | \(0.727302\pi\) | |||||||
\(132\) | 2.35483e6 | 0.0891151 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.04346e6 | −0.109270 | ||||||||
\(135\) | 3.83818e6 | + | 6.64793e6i | 0.134263 | + | 0.232551i | ||||
\(136\) | −1.87348e7 | + | 3.24496e7i | −0.638649 | + | 1.10617i | ||||
\(137\) | −1.40225e7 | + | 2.42876e7i | −0.465910 | + | 0.806980i | −0.999242 | − | 0.0389262i | \(-0.987606\pi\) |
0.533332 | + | 0.845906i | \(0.320940\pi\) | |||||||
\(138\) | 1.23833e6 | + | 2.14485e6i | 0.0401106 | + | 0.0694736i | ||||
\(139\) | 1.18273e7 | 0.373537 | 0.186769 | − | 0.982404i | \(-0.440199\pi\) | ||||
0.186769 | + | 0.982404i | \(0.440199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.57490e7 | −0.473136 | ||||||||
\(142\) | −1.66819e7 | − | 2.88939e7i | −0.488918 | − | 0.846831i | ||||
\(143\) | 2.41645e6 | − | 4.18542e6i | 0.0691038 | − | 0.119691i | ||||
\(144\) | −1.40551e6 | + | 2.43442e6i | −0.0392253 | + | 0.0679401i | ||||
\(145\) | 7.11945e6 | + | 1.23312e7i | 0.193936 | + | 0.335907i | ||||
\(146\) | −8.21449e6 | −0.218447 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.47044e7 | −0.626409 | ||||||||
\(149\) | −1.03923e7 | − | 1.80000e7i | −0.257371 | − | 0.445780i | 0.708165 | − | 0.706046i | \(-0.249523\pi\) |
−0.965537 | + | 0.260266i | \(0.916190\pi\) | |||||||
\(150\) | −5.99198e6 | + | 1.03784e7i | −0.144961 | + | 0.251079i | ||||
\(151\) | −38056.0 | + | 65914.9i | −0.000899505 | + | 0.00155799i | −0.866475 | − | 0.499221i | \(-0.833620\pi\) |
0.865575 | + | 0.500779i | \(0.166953\pi\) | |||||||
\(152\) | 5.68920e6 | + | 9.85398e6i | 0.131401 | + | 0.227593i | ||||
\(153\) | −2.06934e7 | −0.467102 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.07955e8 | −2.32853 | ||||||||
\(156\) | 6.33172e6 | + | 1.09669e7i | 0.133532 | + | 0.231284i | ||||
\(157\) | −1.60912e7 | + | 2.78708e7i | −0.331849 | + | 0.574780i | −0.982874 | − | 0.184276i | \(-0.941006\pi\) |
0.651025 | + | 0.759056i | \(0.274339\pi\) | |||||||
\(158\) | 2.07412e7 | − | 3.59247e7i | 0.418344 | − | 0.724593i | ||||
\(159\) | 5.77878e6 | + | 1.00091e7i | 0.114011 | + | 0.197473i | ||||
\(160\) | −7.49174e7 | −1.44598 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.18865e6 | 0.0589256 | ||||||||
\(163\) | −2.91717e7 | − | 5.05269e7i | −0.527601 | − | 0.913832i | −0.999482 | − | 0.0321700i | \(-0.989758\pi\) |
0.471881 | − | 0.881662i | \(-0.343575\pi\) | |||||||
\(164\) | 2.89670e7 | − | 5.01724e7i | 0.512803 | − | 0.888201i | ||||
\(165\) | −4.99122e6 | + | 8.64505e6i | −0.0864994 | + | 0.149821i | ||||
\(166\) | −1.31302e7 | − | 2.27422e7i | −0.222789 | − | 0.385883i | ||||
\(167\) | 2.58365e7 | 0.429266 | 0.214633 | − | 0.976695i | \(-0.431145\pi\) | ||||
0.214633 | + | 0.976695i | \(0.431145\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.67589e7 | −0.585813 | ||||||||
\(170\) | −3.32116e7 | − | 5.75242e7i | −0.518464 | − | 0.898006i | ||||
\(171\) | −3.14199e6 | + | 5.44209e6i | −0.0480528 | + | 0.0832298i | ||||
\(172\) | 3.15455e7 | − | 5.46384e7i | 0.472703 | − | 0.818745i | ||||
\(173\) | 3.17600e7 | + | 5.50100e7i | 0.466358 | + | 0.807756i | 0.999262 | − | 0.0384200i | \(-0.0122325\pi\) |
−0.532904 | + | 0.846176i | \(0.678899\pi\) | |||||||
\(174\) | 5.91462e6 | 0.0851147 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.65549e6 | −0.0505418 | ||||||||
\(177\) | 1.76361e7 | + | 3.05467e7i | 0.239054 | + | 0.414054i | ||||
\(178\) | −2.55849e7 | + | 4.43144e7i | −0.340028 | + | 0.588945i | ||||
\(179\) | 4.04779e7 | − | 7.01099e7i | 0.527513 | − | 0.913679i | −0.471973 | − | 0.881613i | \(-0.656458\pi\) |
0.999486 | − | 0.0320658i | \(-0.0102086\pi\) | |||||||
\(180\) | −1.30783e7 | − | 2.26522e7i | −0.167146 | − | 0.289506i | ||||
\(181\) | −6.45032e7 | −0.808549 | −0.404274 | − | 0.914638i | \(-0.632476\pi\) | ||||
−0.404274 | + | 0.914638i | \(0.632476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.11787e6 | −0.0979182 | ||||||||
\(184\) | −1.00901e7 | − | 1.74765e7i | −0.119408 | − | 0.206820i | ||||
\(185\) | 5.23626e7 | − | 9.06946e7i | 0.608023 | − | 1.05313i | ||||
\(186\) | −2.24214e7 | + | 3.88351e7i | −0.255487 | + | 0.442516i | ||||
\(187\) | −1.34550e7 | − | 2.33047e7i | −0.150465 | − | 0.260614i | ||||
\(188\) | 5.36632e7 | 0.589012 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.01708e7 | −0.213346 | ||||||||
\(191\) | −2.84137e7 | − | 4.92140e7i | −0.295060 | − | 0.511060i | 0.679939 | − | 0.733269i | \(-0.262006\pi\) |
−0.974999 | + | 0.222209i | \(0.928673\pi\) | |||||||
\(192\) | −8.89661e6 | + | 1.54094e7i | −0.0907131 | + | 0.157120i | ||||
\(193\) | −5.81885e7 | + | 1.00785e8i | −0.582621 | + | 1.00913i | 0.412546 | + | 0.910937i | \(0.364640\pi\) |
−0.995167 | + | 0.0981931i | \(0.968694\pi\) | |||||||
\(194\) | −2.64804e7 | − | 4.58655e7i | −0.260387 | − | 0.451003i | ||||
\(195\) | −5.36819e7 | −0.518450 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.18816e8 | −1.10724 | −0.553622 | − | 0.832768i | \(-0.686755\pi\) | ||||
−0.553622 | + | 0.832768i | \(0.686755\pi\) | |||||||
\(198\) | 2.07328e6 | + | 3.59102e6i | 0.0189814 | + | 0.0328768i | ||||
\(199\) | −4.75053e7 | + | 8.22816e7i | −0.427323 | + | 0.740146i | −0.996634 | − | 0.0819767i | \(-0.973877\pi\) |
0.569311 | + | 0.822122i | \(0.307210\pi\) | |||||||
\(200\) | 4.88235e7 | − | 8.45648e7i | 0.431543 | − | 0.747454i | ||||
\(201\) | 6.84779e6 | + | 1.18607e7i | 0.0594791 | + | 0.103021i | ||||
\(202\) | −7.19185e7 | −0.613919 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.05108e7 | 0.581501 | ||||||||
\(205\) | 1.22795e8 | + | 2.12687e8i | 0.995502 | + | 1.72426i | ||||
\(206\) | 2.16282e7 | − | 3.74611e7i | 0.172379 | − | 0.298569i | ||||
\(207\) | 5.57248e6 | − | 9.65181e6i | 0.0436669 | − | 0.0756332i | ||||
\(208\) | −9.82894e6 | − | 1.70242e7i | −0.0757330 | − | 0.131173i | ||||
\(209\) | −8.17176e6 | −0.0619161 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.79246e8 | 1.31360 | 0.656798 | − | 0.754067i | \(-0.271910\pi\) | ||||
0.656798 | + | 0.754067i | \(0.271910\pi\) | |||||||
\(212\) | −1.96907e7 | − | 3.41052e7i | −0.141934 | − | 0.245836i | ||||
\(213\) | −7.50685e7 | + | 1.30023e8i | −0.532267 | + | 0.921913i | ||||
\(214\) | −3.42782e7 | + | 5.93716e7i | −0.239095 | + | 0.414124i | ||||
\(215\) | 1.33726e8 | + | 2.31619e8i | 0.917656 | + | 1.58943i | ||||
\(216\) | −2.59816e7 | −0.175419 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.41257e7 | 0.157718 | ||||||||
\(219\) | 1.84826e7 | + | 3.20128e7i | 0.118907 | + | 0.205954i | ||||
\(220\) | 1.70071e7 | − | 2.94572e7i | 0.107684 | − | 0.186514i | ||||
\(221\) | 7.23559e7 | − | 1.25324e8i | 0.450922 | − | 0.781019i | ||||
\(222\) | −2.17506e7 | − | 3.76732e7i | −0.133425 | − | 0.231098i | ||||
\(223\) | 2.06537e8 | 1.24718 | 0.623592 | − | 0.781750i | \(-0.285673\pi\) | ||||
0.623592 | + | 0.781750i | \(0.285673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.39278e7 | 0.315627 | ||||||||
\(226\) | 5.31190e7 | + | 9.20047e7i | 0.306105 | + | 0.530189i | ||||
\(227\) | 2.16977e7 | − | 3.75815e7i | 0.123118 | − | 0.213247i | −0.797877 | − | 0.602820i | \(-0.794044\pi\) |
0.920996 | + | 0.389572i | \(0.127377\pi\) | |||||||
\(228\) | 1.07060e7 | − | 1.85434e7i | 0.0598214 | − | 0.103614i | ||||
\(229\) | −1.80965e7 | − | 3.13441e7i | −0.0995799 | − | 0.172477i | 0.811931 | − | 0.583753i | \(-0.198417\pi\) |
−0.911511 | + | 0.411276i | \(0.865083\pi\) | |||||||
\(230\) | 3.57739e7 | 0.193874 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.81932e7 | −0.253383 | ||||||||
\(233\) | −4.61173e7 | − | 7.98776e7i | −0.238846 | − | 0.413694i | 0.721537 | − | 0.692376i | \(-0.243436\pi\) |
−0.960384 | + | 0.278682i | \(0.910103\pi\) | |||||||
\(234\) | −1.11493e7 | + | 1.93112e7i | −0.0568844 | + | 0.0985267i | ||||
\(235\) | −1.13743e8 | + | 1.97008e8i | −0.571724 | + | 0.990254i | ||||
\(236\) | −6.00935e7 | − | 1.04085e8i | −0.297602 | − | 0.515461i | ||||
\(237\) | −1.86670e8 | −0.910870 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.98468e7 | 0.236181 | 0.118090 | − | 0.993003i | \(-0.462323\pi\) | ||||
0.118090 | + | 0.993003i | \(0.462323\pi\) | |||||||
\(240\) | 2.03018e7 | + | 3.51638e7i | 0.0947973 | + | 0.164194i | ||||
\(241\) | 9.96870e7 | − | 1.72663e8i | 0.458753 | − | 0.794583i | −0.540142 | − | 0.841574i | \(-0.681630\pi\) |
0.998895 | + | 0.0469902i | \(0.0149630\pi\) | |||||||
\(242\) | 5.57654e7 | − | 9.65885e7i | 0.252936 | − | 0.438098i | ||||
\(243\) | −7.17445e6 | − | 1.24265e7i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 2.76609e7 | 0.121900 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.02014e8 | 0.436906 | ||||||||
\(247\) | −2.19724e7 | − | 3.80573e7i | −0.0927765 | − | 0.160694i | ||||
\(248\) | 1.82693e8 | − | 3.16434e8i | 0.760574 | − | 1.31735i | ||||
\(249\) | −5.90861e7 | + | 1.02340e8i | −0.242542 | + | 0.420096i | ||||
\(250\) | −4.85550e6 | − | 8.40997e6i | −0.0196537 | − | 0.0340412i | ||||
\(251\) | 3.94678e8 | 1.57538 | 0.787689 | − | 0.616073i | \(-0.211277\pi\) | ||||
0.787689 | + | 0.616073i | \(0.211277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.44930e7 | 0.0562649 | ||||||||
\(254\) | −5.03649e7 | − | 8.72345e7i | −0.192846 | − | 0.334018i | ||||
\(255\) | −1.49452e8 | + | 2.58859e8i | −0.564432 | + | 0.977626i | ||||
\(256\) | 1.04079e8 | − | 1.80271e8i | 0.387725 | − | 0.671560i | ||||
\(257\) | −7.14427e7 | − | 1.23742e8i | −0.262538 | − | 0.454729i | 0.704378 | − | 0.709825i | \(-0.251226\pi\) |
−0.966916 | + | 0.255096i | \(0.917893\pi\) | |||||||
\(258\) | 1.11095e8 | 0.402741 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.82916e8 | 0.645425 | ||||||||
\(261\) | −1.33079e7 | − | 2.30500e7i | −0.0463306 | − | 0.0802469i | ||||
\(262\) | 5.04803e7 | − | 8.74345e7i | 0.173407 | − | 0.300350i | ||||
\(263\) | −2.20120e8 | + | 3.81260e8i | −0.746131 | + | 1.29234i | 0.203533 | + | 0.979068i | \(0.434757\pi\) |
−0.949664 | + | 0.313269i | \(0.898576\pi\) | |||||||
\(264\) | −1.68934e7 | − | 2.92602e7i | −0.0565070 | − | 0.0978730i | ||||
\(265\) | 1.66943e8 | 0.551070 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.30264e8 | 0.740350 | ||||||||
\(268\) | −2.33332e7 | − | 4.04143e7i | −0.0740462 | − | 0.128252i | ||||
\(269\) | 1.37702e8 | − | 2.38507e8i | 0.431329 | − | 0.747083i | −0.565659 | − | 0.824639i | \(-0.691378\pi\) |
0.996988 | + | 0.0775560i | \(0.0247117\pi\) | |||||||
\(270\) | 2.30291e7 | − | 3.98876e7i | 0.0712039 | − | 0.123329i | ||||
\(271\) | −2.12335e8 | − | 3.67775e8i | −0.648080 | − | 1.12251i | −0.983581 | − | 0.180468i | \(-0.942239\pi\) |
0.335501 | − | 0.942040i | \(-0.391095\pi\) | |||||||
\(272\) | −1.09456e8 | −0.329800 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.68269e8 | 0.494172 | ||||||||
\(275\) | 3.50642e7 | + | 6.07329e7i | 0.101671 | + | 0.176100i | ||||
\(276\) | −1.89877e7 | + | 3.28877e7i | −0.0543614 | + | 0.0941567i | ||||
\(277\) | −2.58079e8 | + | 4.47006e8i | −0.729581 | + | 1.26367i | 0.227479 | + | 0.973783i | \(0.426952\pi\) |
−0.957060 | + | 0.289889i | \(0.906382\pi\) | |||||||
\(278\) | −3.54819e7 | − | 6.14565e7i | −0.0990490 | − | 0.171558i | ||||
\(279\) | 2.01793e8 | 0.556277 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.11043e8 | −0.836273 | −0.418137 | − | 0.908384i | \(-0.637317\pi\) | ||||
−0.418137 | + | 0.908384i | \(0.637317\pi\) | |||||||
\(282\) | 4.72470e7 | + | 8.18342e7i | 0.125459 | + | 0.217302i | ||||
\(283\) | −2.97154e8 | + | 5.14686e8i | −0.779344 | + | 1.34986i | 0.152976 | + | 0.988230i | \(0.451114\pi\) |
−0.932320 | + | 0.361634i | \(0.882219\pi\) | |||||||
\(284\) | 2.55789e8 | − | 4.43040e8i | 0.662625 | − | 1.14770i | ||||
\(285\) | 4.53843e7 | + | 7.86079e7i | 0.116131 | + | 0.201145i | ||||
\(286\) | −2.89974e7 | −0.0732957 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.40038e8 | 0.345440 | ||||||||
\(289\) | −1.97713e8 | − | 3.42449e8i | −0.481829 | − | 0.834553i | ||||
\(290\) | 4.27167e7 | − | 7.39875e7i | 0.102850 | − | 0.178142i | ||||
\(291\) | −1.19162e8 | + | 2.06395e8i | −0.283473 | + | 0.490990i | ||||
\(292\) | −6.29778e7 | − | 1.09081e8i | −0.148029 | − | 0.256394i | ||||
\(293\) | −1.15515e8 | −0.268288 | −0.134144 | − | 0.990962i | \(-0.542828\pi\) | ||||
−0.134144 | + | 0.990962i | \(0.542828\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.09488e8 | 1.15547 | ||||||||
\(296\) | 1.77227e8 | + | 3.06966e8i | 0.397200 | + | 0.687971i | ||||
\(297\) | 9.32974e6 | − | 1.61596e7i | 0.0206644 | − | 0.0357917i | ||||
\(298\) | −6.23539e7 | + | 1.08000e8i | −0.136492 | + | 0.236411i | ||||
\(299\) | 3.89691e7 | + | 6.74965e7i | 0.0843085 | + | 0.146027i | ||||
\(300\) | −1.83754e8 | −0.392927 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 456672. | 0.000954070 | ||||||||
\(303\) | 1.61817e8 | + | 2.80275e8i | 0.334175 | + | 0.578808i | ||||
\(304\) | −1.66194e7 | + | 2.87856e7i | −0.0339279 | + | 0.0587648i | ||||
\(305\) | −5.86291e7 | + | 1.01549e8i | −0.118322 | + | 0.204939i | ||||
\(306\) | 6.20802e7 | + | 1.07526e8i | 0.123859 | + | 0.214530i | ||||
\(307\) | 2.60600e8 | 0.514032 | 0.257016 | − | 0.966407i | \(-0.417261\pi\) | ||||
0.257016 | + | 0.966407i | \(0.417261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.94654e8 | −0.375325 | ||||||||
\(310\) | 3.23865e8 | + | 5.60951e8i | 0.617445 | + | 1.06945i | ||||
\(311\) | 2.88397e8 | − | 4.99519e8i | 0.543663 | − | 0.941652i | −0.455027 | − | 0.890478i | \(-0.650370\pi\) |
0.998690 | − | 0.0511744i | \(-0.0162964\pi\) | |||||||
\(312\) | 9.08464e7 | − | 1.57351e8i | 0.169343 | − | 0.293310i | ||||
\(313\) | −2.30037e8 | − | 3.98436e8i | −0.424026 | − | 0.734435i | 0.572303 | − | 0.820043i | \(-0.306050\pi\) |
−0.996329 | + | 0.0856073i | \(0.972717\pi\) | |||||||
\(314\) | 1.93095e8 | 0.351979 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.36062e8 | 1.13395 | ||||||||
\(317\) | −3.12781e7 | − | 5.41752e7i | −0.0551483 | − | 0.0955197i | 0.837133 | − | 0.546999i | \(-0.184230\pi\) |
−0.892282 | + | 0.451479i | \(0.850897\pi\) | |||||||
\(318\) | 3.46727e7 | − | 6.00549e7i | 0.0604634 | − | 0.104726i | ||||
\(319\) | 1.73057e7 | − | 2.99744e7i | 0.0298485 | − | 0.0516992i | ||||
\(320\) | 1.28507e8 | + | 2.22580e8i | 0.219230 | + | 0.379718i | ||||
\(321\) | 3.08504e8 | 0.520587 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.44687e8 | −0.404020 | ||||||||
\(324\) | 2.44463e7 | + | 4.23422e7i | 0.0399306 | + | 0.0691618i | ||||
\(325\) | −1.88562e8 | + | 3.26599e8i | −0.304693 | + | 0.527744i | ||||
\(326\) | −1.75030e8 | + | 3.03162e8i | −0.279803 | + | 0.484633i | ||||
\(327\) | −5.42828e7 | − | 9.40206e7i | −0.0858510 | − | 0.148698i | ||||
\(328\) | −8.31228e8 | −1.30065 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.98946e7 | 0.0917464 | ||||||||
\(331\) | −3.42118e8 | − | 5.92566e8i | −0.518535 | − | 0.898128i | −0.999768 | − | 0.0215359i | \(-0.993144\pi\) |
0.481233 | − | 0.876593i | \(-0.340189\pi\) | |||||||
\(332\) | 2.01330e8 | − | 3.48714e8i | 0.301944 | − | 0.522982i | ||||
\(333\) | −9.78777e7 | + | 1.69529e8i | −0.145254 | + | 0.251588i | ||||
\(334\) | −7.75095e7 | − | 1.34250e8i | −0.113826 | − | 0.197153i | ||||
\(335\) | 1.97825e8 | 0.287491 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.26313e8 | −0.891429 | −0.445714 | − | 0.895175i | \(-0.647050\pi\) | ||||
−0.445714 | + | 0.895175i | \(0.647050\pi\) | |||||||
\(338\) | 1.10277e8 | + | 1.91005e8i | 0.155337 | + | 0.269052i | ||||
\(339\) | 2.39035e8 | − | 4.14021e8i | 0.333245 | − | 0.577197i | ||||
\(340\) | 5.09245e8 | − | 8.82038e8i | 0.702668 | − | 1.21706i | ||||
\(341\) | 1.31207e8 | + | 2.27257e8i | 0.179191 | + | 0.310368i | ||||
\(342\) | 3.77039e7 | 0.0509677 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.05219e8 | −1.19894 | ||||||||
\(345\) | −8.04913e7 | − | 1.39415e8i | −0.105532 | − | 0.182786i | ||||
\(346\) | 1.90560e8 | − | 3.30060e8i | 0.247324 | − | 0.428377i | ||||
\(347\) | 6.26698e8 | − | 1.08547e9i | 0.805203 | − | 1.39465i | −0.110952 | − | 0.993826i | \(-0.535390\pi\) |
0.916154 | − | 0.400826i | \(-0.131277\pi\) | |||||||
\(348\) | 4.53454e7 | + | 7.85406e7i | 0.0576775 | + | 0.0999003i | ||||
\(349\) | −2.65350e8 | −0.334142 | −0.167071 | − | 0.985945i | \(-0.553431\pi\) | ||||
−0.167071 | + | 0.985945i | \(0.553431\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00344e8 | 0.123856 | ||||||||
\(352\) | 9.10535e7 | + | 1.57709e8i | 0.111275 | + | 0.192734i | ||||
\(353\) | −2.84818e8 | + | 4.93319e8i | −0.344632 | + | 0.596920i | −0.985287 | − | 0.170909i | \(-0.945330\pi\) |
0.640655 | + | 0.767829i | \(0.278663\pi\) | |||||||
\(354\) | 1.05817e8 | − | 1.83280e8i | 0.126778 | − | 0.219586i | ||||
\(355\) | 1.08432e9 | + | 1.87810e9i | 1.28635 | + | 2.22803i | ||||
\(356\) | −7.84605e8 | −0.921671 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.85735e8 | −0.559512 | ||||||||
\(359\) | −4.66270e8 | − | 8.07604e8i | −0.531872 | − | 0.921230i | −0.999308 | − | 0.0372025i | \(-0.988155\pi\) |
0.467436 | − | 0.884027i | \(-0.345178\pi\) | |||||||
\(360\) | −1.87645e8 | + | 3.25010e8i | −0.211971 | + | 0.367145i | ||||
\(361\) | 4.09784e8 | − | 7.09766e8i | 0.458437 | − | 0.794036i | ||||
\(362\) | 1.93510e8 | + | 3.35168e8i | 0.214399 | + | 0.371350i | ||||
\(363\) | −5.01889e8 | −0.550724 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.33942e8 | 0.574737 | ||||||||
\(366\) | 2.43536e7 | + | 4.21817e7i | 0.0259645 | + | 0.0449718i | ||||
\(367\) | −4.26282e8 | + | 7.38343e8i | −0.450159 | + | 0.779699i | −0.998396 | − | 0.0566249i | \(-0.981966\pi\) |
0.548236 | + | 0.836323i | \(0.315299\pi\) | |||||||
\(368\) | 2.94753e7 | − | 5.10527e7i | 0.0308312 | − | 0.0534012i | ||||
\(369\) | −2.29532e8 | − | 3.97561e8i | −0.237822 | − | 0.411919i | ||||
\(370\) | −6.28351e8 | −0.644906 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.87591e8 | −0.692516 | ||||||||
\(373\) | −1.90592e8 | − | 3.30115e8i | −0.190162 | − | 0.329370i | 0.755142 | − | 0.655561i | \(-0.227568\pi\) |
−0.945304 | + | 0.326192i | \(0.894235\pi\) | |||||||
\(374\) | −8.07298e7 | + | 1.39828e8i | −0.0797964 | + | 0.138211i | ||||
\(375\) | −2.18498e7 | + | 3.78449e7i | −0.0213962 | + | 0.0370593i | ||||
\(376\) | −3.84975e8 | − | 6.66797e8i | −0.373487 | − | 0.646898i | ||||
\(377\) | 1.86128e8 | 0.178903 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.48353e9 | −1.39978 | −0.699889 | − | 0.714251i | \(-0.746767\pi\) | ||||
−0.699889 | + | 0.714251i | \(0.746767\pi\) | |||||||
\(380\) | −1.54643e8 | − | 2.67849e8i | −0.144573 | − | 0.250408i | ||||
\(381\) | −2.26642e8 | + | 3.92555e8i | −0.209944 | + | 0.363633i | ||||
\(382\) | −1.70482e8 | + | 2.95284e8i | −0.156479 | + | 0.271030i | ||||
\(383\) | −3.80965e8 | − | 6.59851e8i | −0.346489 | − | 0.600136i | 0.639134 | − | 0.769095i | \(-0.279293\pi\) |
−0.985623 | + | 0.168959i | \(0.945959\pi\) | |||||||
\(384\) | −5.57124e8 | −0.502103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.98262e8 | 0.617963 | ||||||||
\(387\) | −2.49964e8 | − | 4.32950e8i | −0.219224 | − | 0.379708i | ||||
\(388\) | 4.06033e8 | − | 7.03271e8i | 0.352899 | − | 0.611239i | ||||
\(389\) | −8.04509e8 | + | 1.39345e9i | −0.692959 | + | 1.20024i | 0.277905 | + | 0.960608i | \(0.410360\pi\) |
−0.970864 | + | 0.239631i | \(0.922974\pi\) | |||||||
\(390\) | 1.61046e8 | + | 2.78940e8i | 0.137475 | + | 0.238113i | ||||
\(391\) | 4.33965e8 | 0.367144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.54323e8 | −0.377564 | ||||||||
\(394\) | 3.56448e8 | + | 6.17386e8i | 0.293602 | + | 0.508534i | ||||
\(395\) | −1.34818e9 | + | 2.33511e9i | −1.10067 | + | 1.90641i | ||||
\(396\) | −3.17902e7 | + | 5.50623e7i | −0.0257253 | + | 0.0445575i | ||||
\(397\) | 9.40079e8 | + | 1.62826e9i | 0.754046 | + | 1.30605i | 0.945847 | + | 0.324611i | \(0.105234\pi\) |
−0.191802 | + | 0.981434i | \(0.561433\pi\) | |||||||
\(398\) | 5.70064e8 | 0.453245 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.85248e8 | 0.222850 | ||||||||
\(401\) | −1.34296e8 | − | 2.32608e8i | −0.104006 | − | 0.180144i | 0.809326 | − | 0.587360i | \(-0.199833\pi\) |
−0.913332 | + | 0.407217i | \(0.866499\pi\) | |||||||
\(402\) | 4.10868e7 | − | 7.11644e7i | 0.0315436 | − | 0.0546351i | ||||
\(403\) | −7.05584e8 | + | 1.22211e9i | −0.537008 | + | 0.930125i | ||||
\(404\) | −5.51375e8 | − | 9.55010e8i | −0.416018 | − | 0.720565i | ||||
\(405\) | −2.07262e8 | −0.155034 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.54563e8 | −0.187161 | ||||||||
\(408\) | −5.05839e8 | − | 8.76138e8i | −0.368724 | − | 0.638649i | ||||
\(409\) | 4.49739e7 | − | 7.78971e7i | 0.0325034 | − | 0.0562976i | −0.849316 | − | 0.527885i | \(-0.822985\pi\) |
0.881820 | + | 0.471587i | \(0.156319\pi\) | |||||||
\(410\) | 7.36770e8 | − | 1.27612e9i | 0.527945 | − | 0.914427i | ||||
\(411\) | −3.78606e8 | − | 6.55765e8i | −0.268993 | − | 0.465910i | ||||
\(412\) | 6.63264e8 | 0.467247 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.68697e7 | −0.0463157 | ||||||||
\(415\) | 8.53466e8 | + | 1.47825e9i | 0.586162 | + | 1.01526i | ||||
\(416\) | −4.89653e8 | + | 8.48103e8i | −0.333474 | + | 0.577593i | ||||
\(417\) | −1.59669e8 | + | 2.76554e8i | −0.107831 | + | 0.186769i | ||||
\(418\) | 2.45153e7 | + | 4.24617e7i | 0.0164180 | + | 0.0284368i | ||||
\(419\) | −1.69054e9 | −1.12273 | −0.561367 | − | 0.827567i | \(-0.689724\pi\) | ||||
−0.561367 | + | 0.827567i | \(0.689724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.13333e9 | −0.740232 | −0.370116 | − | 0.928985i | \(-0.620682\pi\) | ||||
−0.370116 | + | 0.928985i | \(0.620682\pi\) | |||||||
\(422\) | −5.37739e8 | − | 9.31391e8i | −0.348320 | − | 0.603307i | ||||
\(423\) | 2.12611e8 | − | 3.68254e8i | 0.136583 | − | 0.236568i | ||||
\(424\) | −2.82518e8 | + | 4.89336e8i | −0.179997 | + | 0.311765i | ||||
\(425\) | 1.04993e9 | + | 1.81853e9i | 0.663434 | + | 1.14910i | ||||
\(426\) | 9.00822e8 | 0.564554 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.05120e9 | −0.648085 | ||||||||
\(429\) | 6.52442e7 | + | 1.13006e8i | 0.0398971 | + | 0.0691038i | ||||
\(430\) | 8.02353e8 | − | 1.38972e9i | 0.486660 | − | 0.842921i | ||||
\(431\) | −1.09971e9 | + | 1.90476e9i | −0.661621 | + | 1.14596i | 0.318569 | + | 0.947900i | \(0.396798\pi\) |
−0.980190 | + | 0.198061i | \(0.936536\pi\) | |||||||
\(432\) | −3.79488e7 | − | 6.57293e7i | −0.0226467 | − | 0.0392253i | ||||
\(433\) | 1.51738e8 | 0.0898227 | 0.0449114 | − | 0.998991i | \(-0.485699\pi\) | ||||
0.0449114 | + | 0.998991i | \(0.485699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.84450e8 | −0.223938 | ||||||||
\(436\) | 1.84964e8 | + | 3.20367e8i | 0.106877 | + | 0.185116i | ||||
\(437\) | 6.58913e7 | − | 1.14127e8i | 0.0377696 | − | 0.0654189i | ||||
\(438\) | 1.10896e8 | − | 1.92077e8i | 0.0630602 | − | 0.109223i | ||||
\(439\) | 4.95381e8 | + | 8.58026e8i | 0.279456 | + | 0.484032i | 0.971250 | − | 0.238063i | \(-0.0765125\pi\) |
−0.691793 | + | 0.722095i | \(0.743179\pi\) | |||||||
\(440\) | −4.88030e8 | −0.273126 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.68271e8 | −0.478275 | ||||||||
\(443\) | 8.86878e8 | + | 1.53612e9i | 0.484675 | + | 0.839482i | 0.999845 | − | 0.0176059i | \(-0.00560443\pi\) |
−0.515170 | + | 0.857088i | \(0.672271\pi\) | |||||||
\(444\) | 3.33509e8 | − | 5.77655e8i | 0.180829 | − | 0.313205i | ||||
\(445\) | 1.66302e9 | − | 2.88044e9i | 0.894618 | − | 1.54952i | ||||
\(446\) | −6.19611e8 | − | 1.07320e9i | −0.330710 | − | 0.572806i | ||||
\(447\) | 5.61185e8 | 0.297187 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.77010e8 | −0.144422 | −0.0722110 | − | 0.997389i | \(-0.523006\pi\) | ||||
−0.0722110 | + | 0.997389i | \(0.523006\pi\) | |||||||
\(450\) | −1.61783e8 | − | 2.80217e8i | −0.0836932 | − | 0.144961i | ||||
\(451\) | 2.98486e8 | − | 5.16993e8i | 0.153217 | − | 0.265379i | ||||
\(452\) | −8.14491e8 | + | 1.41074e9i | −0.414860 | + | 0.718559i | ||||
\(453\) | −1.02751e6 | − | 1.77970e6i | −0.000519330 | − | 0.000899505i | ||||
\(454\) | −2.60372e8 | −0.130587 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.07217e8 | −0.151729 | ||||||||
\(457\) | −1.47379e9 | − | 2.55268e9i | −0.722320 | − | 1.25109i | −0.960068 | − | 0.279768i | \(-0.909742\pi\) |
0.237748 | − | 0.971327i | \(-0.423591\pi\) | |||||||
\(458\) | −1.08579e8 | + | 1.88065e8i | −0.0528102 | + | 0.0914699i | ||||
\(459\) | 2.79361e8 | − | 4.83867e8i | 0.134841 | − | 0.233551i | ||||
\(460\) | 2.74267e8 | + | 4.75044e8i | 0.131377 | + | 0.227552i | ||||
\(461\) | 2.76687e9 | 1.31533 | 0.657667 | − | 0.753309i | \(-0.271543\pi\) | ||||
0.657667 | + | 0.753309i | \(0.271543\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.63553e8 | 0.217053 | 0.108527 | − | 0.994094i | \(-0.465387\pi\) | ||||
0.108527 | + | 0.994094i | \(0.465387\pi\) | |||||||
\(464\) | −7.03913e7 | − | 1.21921e8i | −0.0327119 | − | 0.0566587i | ||||
\(465\) | 1.45739e9 | − | 2.52428e9i | 0.672189 | − | 1.16427i | ||||
\(466\) | −2.76704e8 | + | 4.79265e8i | −0.126667 | + | 0.219394i | ||||
\(467\) | −2.08961e8 | − | 3.61931e8i | −0.0949415 | − | 0.164443i | 0.814643 | − | 0.579963i | \(-0.196933\pi\) |
−0.909584 | + | 0.415520i | \(0.863600\pi\) | |||||||
\(468\) | −3.41913e8 | −0.154189 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.36491e9 | 0.606404 | ||||||||
\(471\) | −4.34463e8 | − | 7.52513e8i | −0.191593 | − | 0.331849i | ||||
\(472\) | −8.62211e8 | + | 1.49339e9i | −0.377413 | + | 0.653698i | ||||
\(473\) | 3.25056e8 | − | 5.63013e8i | 0.141236 | − | 0.244627i | ||||
\(474\) | 5.60011e8 | + | 9.69968e8i | 0.241531 | + | 0.418344i | ||||
\(475\) | 6.37664e8 | 0.273001 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.12054e8 | −0.131648 | ||||||||
\(478\) | −1.49540e8 | − | 2.59012e8i | −0.0626269 | − | 0.108473i | ||||
\(479\) | −7.54864e8 | + | 1.30746e9i | −0.313830 | + | 0.543570i | −0.979188 | − | 0.202955i | \(-0.934946\pi\) |
0.665358 | + | 0.746524i | \(0.268279\pi\) | |||||||
\(480\) | 1.01139e9 | − | 1.75177e9i | 0.417419 | − | 0.722991i | ||||
\(481\) | −6.84473e8 | − | 1.18554e9i | −0.280445 | − | 0.485746i | ||||
\(482\) | −1.19624e9 | −0.486581 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.71014e9 | 0.685603 | ||||||||
\(485\) | 1.72123e9 | + | 2.98126e9i | 0.685082 | + | 1.18660i | ||||
\(486\) | −4.30467e7 | + | 7.45591e7i | −0.0170103 | + | 0.0294628i | ||||
\(487\) | −4.64730e8 | + | 8.04936e8i | −0.182326 | + | 0.315798i | −0.942672 | − | 0.333720i | \(-0.891696\pi\) |
0.760346 | + | 0.649518i | \(0.225029\pi\) | |||||||
\(488\) | −1.98437e8 | − | 3.43703e8i | −0.0772953 | − | 0.133879i | ||||
\(489\) | 1.57527e9 | 0.609221 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.12803e9 | 1.95508 | 0.977541 | − | 0.210743i | \(-0.0675885\pi\) | ||||
0.977541 | + | 0.210743i | \(0.0675885\pi\) | |||||||
\(492\) | 7.82110e8 | + | 1.35465e9i | 0.296067 | + | 0.512803i | ||||
\(493\) | 5.18186e8 | − | 8.97525e8i | 0.194770 | − | 0.337351i | ||||
\(494\) | −1.31834e8 | + | 2.28344e8i | −0.0492021 | + | 0.0852206i | ||||
\(495\) | −1.34763e8 | − | 2.33416e8i | −0.0499404 | − | 0.0864994i | ||||
\(496\) | 1.06737e9 | 0.392762 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.09033e8 | 0.257255 | ||||||||
\(499\) | 2.05325e8 | + | 3.55633e8i | 0.0739757 | + | 0.128130i | 0.900640 | − | 0.434565i | \(-0.143098\pi\) |
−0.826665 | + | 0.562695i | \(0.809765\pi\) | |||||||
\(500\) | 7.44510e7 | − | 1.28953e8i | 0.0266364 | − | 0.0461356i | ||||
\(501\) | −3.48793e8 | + | 6.04127e8i | −0.123918 | + | 0.214633i | ||||
\(502\) | −1.18403e9 | − | 2.05081e9i | −0.417735 | − | 0.723538i | ||||
\(503\) | −5.02041e9 | −1.75894 | −0.879470 | − | 0.475954i | \(-0.842103\pi\) | ||||
−0.879470 | + | 0.475954i | \(0.842103\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.67470e9 | 1.61523 | ||||||||
\(506\) | −4.34791e7 | − | 7.53080e7i | −0.0149195 | − | 0.0258413i | ||||
\(507\) | 4.96245e8 | − | 8.59522e8i | 0.169110 | − | 0.292907i | ||||
\(508\) | 7.72262e8 | − | 1.33760e9i | 0.261361 | − | 0.452691i | ||||
\(509\) | −1.62463e9 | − | 2.81394e9i | −0.546062 | − | 0.945807i | −0.998539 | − | 0.0540314i | \(-0.982793\pi\) |
0.452477 | − | 0.891776i | \(-0.350540\pi\) | |||||||
\(510\) | 1.79343e9 | 0.598671 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.39223e9 | 0.458423 | ||||||||
\(513\) | −8.48337e7 | − | 1.46936e8i | −0.0277433 | − | 0.0480528i | ||||
\(514\) | −4.28656e8 | + | 7.42454e8i | −0.139232 | + | 0.241156i | ||||
\(515\) | −1.40583e9 | + | 2.43497e9i | −0.453532 | + | 0.785540i | ||||
\(516\) | 8.51729e8 | + | 1.47524e9i | 0.272915 | + | 0.472703i | ||||
\(517\) | 5.52965e8 | 0.175987 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.71504e9 | −0.538504 | ||||||||
\(520\) | −1.31223e9 | − | 2.27284e9i | −0.409258 | − | 0.708855i | ||||
\(521\) | −1.05475e9 | + | 1.82688e9i | −0.326752 | + | 0.565951i | −0.981865 | − | 0.189580i | \(-0.939287\pi\) |
0.655114 | + | 0.755530i | \(0.272621\pi\) | |||||||
\(522\) | −7.98474e7 | + | 1.38300e8i | −0.0245705 | + | 0.0425573i | ||||
\(523\) | −2.64456e9 | − | 4.58051e9i | −0.808345 | − | 1.40009i | −0.914009 | − | 0.405693i | \(-0.867030\pi\) |
0.105664 | − | 0.994402i | \(-0.466303\pi\) | |||||||
\(524\) | 1.54806e9 | 0.470034 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.64144e9 | 0.791391 | ||||||||
\(527\) | 3.92874e9 | + | 6.80477e9i | 1.16927 | + | 2.02524i | ||||
\(528\) | 4.93491e7 | − | 8.54751e7i | 0.0145902 | − | 0.0252709i | ||||
\(529\) | 1.58555e9 | − | 2.74626e9i | 0.465678 | − | 0.806577i | ||||
\(530\) | −5.00828e8 | − | 8.67459e8i | −0.146124 | − | 0.253095i | ||||
\(531\) | −9.52351e8 | −0.276036 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.21030e9 | 0.918334 | ||||||||
\(534\) | −6.90793e8 | − | 1.19649e9i | −0.196315 | − | 0.340028i | ||||
\(535\) | 2.22808e9 | − | 3.85916e9i | 0.629062 | − | 1.08957i | ||||
\(536\) | −3.34781e8 | + | 5.79858e8i | −0.0939040 | + | 0.162646i | ||||
\(537\) | 1.09290e9 | + | 1.89297e9i | 0.304560 | + | 0.527513i | ||||
\(538\) | −1.65243e9 | −0.457493 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.06226e8 | 0.193004 | ||||||||
\(541\) | −1.52307e9 | − | 2.63803e9i | −0.413551 | − | 0.716291i | 0.581724 | − | 0.813386i | \(-0.302378\pi\) |
−0.995275 | + | 0.0970952i | \(0.969045\pi\) | |||||||
\(542\) | −1.27401e9 | + | 2.20665e9i | −0.343696 | + | 0.595300i | ||||
\(543\) | 8.70793e8 | − | 1.50826e9i | 0.233408 | − | 0.404274i | ||||
\(544\) | 2.72642e9 | + | 4.72230e9i | 0.726100 | + | 1.25764i | ||||
\(545\) | −1.56817e9 | −0.414959 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.85537e9 | −1.26843 | −0.634215 | − | 0.773157i | \(-0.718677\pi\) | ||||
−0.634215 | + | 0.773157i | \(0.718677\pi\) | |||||||
\(548\) | 1.29007e9 | + | 2.23446e9i | 0.334873 | + | 0.580017i | ||||
\(549\) | 1.09591e8 | − | 1.89818e8i | 0.0282666 | − | 0.0489591i | ||||
\(550\) | 2.10385e8 | − | 3.64397e8i | 0.0539194 | − | 0.0933912i | ||||
\(551\) | −1.57358e8 | − | 2.72552e8i | −0.0400736 | − | 0.0694095i | ||||
\(552\) | 5.44864e8 | 0.137880 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.09695e9 | 0.773838 | ||||||||
\(555\) | 1.41379e9 | + | 2.44876e9i | 0.351042 | + | 0.608023i | ||||
\(556\) | 5.44056e8 | − | 9.42332e8i | 0.134240 | − | 0.232510i | ||||
\(557\) | −6.38811e8 | + | 1.10645e9i | −0.156631 | + | 0.271294i | −0.933652 | − | 0.358182i | \(-0.883397\pi\) |
0.777020 | + | 0.629475i | \(0.216730\pi\) | |||||||
\(558\) | −6.05379e8 | − | 1.04855e9i | −0.147505 | − | 0.255487i | ||||
\(559\) | 3.49607e9 | 0.846522 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.26568e8 | 0.173743 | ||||||||
\(562\) | 9.33129e8 | + | 1.61623e9i | 0.221750 | + | 0.384083i | ||||
\(563\) | 2.35632e9 | − | 4.08127e9i | 0.556487 | − | 0.963865i | −0.441299 | − | 0.897360i | \(-0.645482\pi\) |
0.997786 | − | 0.0665042i | \(-0.0211846\pi\) | |||||||
\(564\) | −7.24454e8 | + | 1.25479e9i | −0.170033 | + | 0.294506i | ||||
\(565\) | −3.45273e9 | − | 5.98031e9i | −0.805366 | − | 1.39493i | ||||
\(566\) | 3.56585e9 | 0.826619 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.34003e9 | −1.68066 | ||||||||
\(569\) | −2.28900e9 | − | 3.96466e9i | −0.520898 | − | 0.902222i | −0.999705 | − | 0.0243013i | \(-0.992264\pi\) |
0.478807 | − | 0.877920i | \(-0.341069\pi\) | |||||||
\(570\) | 2.72306e8 | − | 4.71647e8i | 0.0615878 | − | 0.106673i | ||||
\(571\) | −2.47560e9 | + | 4.28786e9i | −0.556485 | + | 0.963860i | 0.441301 | + | 0.897359i | \(0.354517\pi\) |
−0.997786 | + | 0.0665012i | \(0.978816\pi\) | |||||||
\(572\) | −2.22314e8 | − | 3.85058e8i | −0.0496684 | − | 0.0860281i | ||||
\(573\) | 1.53434e9 | 0.340706 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.13093e9 | −0.248084 | ||||||||
\(576\) | −2.40208e8 | − | 4.16053e8i | −0.0523733 | − | 0.0907131i | ||||
\(577\) | 4.25924e9 | − | 7.37721e9i | 0.923031 | − | 1.59874i | 0.128334 | − | 0.991731i | \(-0.459037\pi\) |
0.794697 | − | 0.607006i | \(-0.207630\pi\) | |||||||
\(578\) | −1.18628e9 | + | 2.05470e9i | −0.255529 | + | 0.442588i | ||||
\(579\) | −1.57109e9 | − | 2.72121e9i | −0.336377 | − | 0.582621i | ||||
\(580\) | 1.30998e9 | 0.278783 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.42994e9 | 0.300669 | ||||||||
\(583\) | −2.02899e8 | − | 3.51432e8i | −0.0424073 | − | 0.0734517i | ||||
\(584\) | −9.03594e8 | + | 1.56507e9i | −0.187728 | + | 0.325154i | ||||
\(585\) | 7.24706e8 | − | 1.25523e9i | 0.149664 | − | 0.259225i | ||||
\(586\) | 3.46544e8 | + | 6.00232e8i | 0.0711405 | + | 0.123219i | ||||
\(587\) | 5.62247e8 | 0.114735 | 0.0573673 | − | 0.998353i | \(-0.481729\pi\) | ||||
0.0573673 | + | 0.998353i | \(0.481729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.38608e9 | 0.481152 | ||||||||
\(590\) | −1.52846e9 | − | 2.64738e9i | −0.306389 | − | 0.530682i | ||||
\(591\) | 1.60402e9 | − | 2.77824e9i | 0.319634 | − | 0.553622i | ||||
\(592\) | −5.17718e8 | + | 8.96714e8i | −0.102557 | + | 0.177635i | ||||
\(593\) | 1.81055e9 | + | 3.13597e9i | 0.356549 | + | 0.617561i | 0.987382 | − | 0.158358i | \(-0.0506198\pi\) |
−0.630833 | + | 0.775919i | \(0.717287\pi\) | |||||||
\(594\) | −1.11957e8 | −0.0219179 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.91219e9 | −0.369971 | ||||||||
\(597\) | −1.28264e9 | − | 2.22160e9i | −0.246715 | − | 0.427323i | ||||
\(598\) | 2.33815e8 | − | 4.04979e8i | 0.0447113 | − | 0.0774423i | ||||
\(599\) | 3.74052e9 | − | 6.47877e9i | 0.711112 | − | 1.23168i | −0.253328 | − | 0.967380i | \(-0.581525\pi\) |
0.964440 | − | 0.264301i | \(-0.0851414\pi\) | |||||||
\(600\) | 1.31823e9 | + | 2.28325e9i | 0.249151 | + | 0.431543i | ||||
\(601\) | 5.81270e9 | 1.09224 | 0.546119 | − | 0.837707i | \(-0.316105\pi\) | ||||
0.546119 | + | 0.837707i | \(0.316105\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.69781e8 | −0.0686806 | ||||||||
\(604\) | 3.50115e6 | + | 6.06417e6i | 0.000646520 | + | 0.00111980i | ||||
\(605\) | −3.62475e9 | + | 6.27825e9i | −0.665479 | + | 1.15264i | ||||
\(606\) | 9.70900e8 | − | 1.68165e9i | 0.177223 | − | 0.306959i | ||||
\(607\) | 1.92026e9 | + | 3.32598e9i | 0.348497 | + | 0.603614i | 0.985983 | − | 0.166848i | \(-0.0533590\pi\) |
−0.637486 | + | 0.770462i | \(0.720026\pi\) | |||||||
\(608\) | 1.65587e9 | 0.298788 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.03549e8 | 0.125499 | ||||||||
\(611\) | 1.48682e9 | + | 2.57525e9i | 0.263703 | + | 0.456746i | ||||
\(612\) | −9.51896e8 | + | 1.64873e9i | −0.167865 | + | 0.290750i | ||||
\(613\) | −8.52421e8 | + | 1.47644e9i | −0.149466 | + | 0.258883i | −0.931030 | − | 0.364942i | \(-0.881089\pi\) |
0.781564 | + | 0.623825i | \(0.214422\pi\) | |||||||
\(614\) | −7.81799e8 | − | 1.35412e9i | −0.136303 | − | 0.236084i | ||||
\(615\) | −6.63093e9 | −1.14951 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.80809e9 | −0.481297 | −0.240649 | − | 0.970612i | \(-0.577360\pi\) | ||||
−0.240649 | + | 0.970612i | \(0.577360\pi\) | |||||||
\(618\) | 5.83961e8 | + | 1.01145e9i | 0.0995231 | + | 0.172379i | ||||
\(619\) | −1.27183e9 | + | 2.20287e9i | −0.215532 | + | 0.373312i | −0.953437 | − | 0.301593i | \(-0.902482\pi\) |
0.737905 | + | 0.674904i | \(0.235815\pi\) | |||||||
\(620\) | −4.96594e9 | + | 8.60125e9i | −0.836816 | + | 1.44941i | ||||
\(621\) | 1.50457e8 | + | 2.60599e8i | 0.0252111 | + | 0.0436669i | ||||
\(622\) | −3.46077e9 | −0.576642 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.30763e8 | 0.0874489 | ||||||||
\(625\) | 3.20526e9 | + | 5.55167e9i | 0.525149 | + | 0.909585i | ||||
\(626\) | −1.38022e9 | + | 2.39062e9i | −0.224874 | + | 0.389493i | ||||
\(627\) | 1.10319e8 | − | 1.91078e8i | 0.0178736 | − | 0.0309581i | ||||
\(628\) | 1.48039e9 | + | 2.56412e9i | 0.238517 | + | 0.413123i | ||||
\(629\) | −7.62238e9 | −1.22127 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51146e8 | −0.0239494 | −0.0119747 | − | 0.999928i | \(-0.503812\pi\) | ||||
−0.0119747 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(632\) | −4.56306e9 | − | 7.90344e9i | −0.719028 | − | 1.24539i | ||||
\(633\) | −2.41983e9 | + | 4.19126e9i | −0.379202 | + | 0.656798i | ||||
\(634\) | −1.87668e8 | + | 3.25051e8i | −0.0292468 | + | 0.0506570i | ||||
\(635\) | 3.27372e9 | + | 5.67025e9i | 0.507380 | + | 0.878808i | ||||
\(636\) | 1.06330e9 | 0.163891 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.07669e8 | −0.0316591 | ||||||||
\(639\) | −2.02685e9 | − | 3.51061e9i | −0.307304 | − | 0.532267i | ||||
\(640\) | −4.02368e9 | + | 6.96921e9i | −0.606727 | + | 1.05088i | ||||
\(641\) | 6.18126e9 | − | 1.07062e10i | 0.926987 | − | 1.60559i | 0.138653 | − | 0.990341i | \(-0.455723\pi\) |
0.788334 | − | 0.615247i | \(-0.210944\pi\) | |||||||
\(642\) | −9.25512e8 | − | 1.60303e9i | −0.138041 | − | 0.239095i | ||||
\(643\) | −2.86744e9 | −0.425359 | −0.212680 | − | 0.977122i | \(-0.568219\pi\) | ||||
−0.212680 | + | 0.977122i | \(0.568219\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.22118e9 | −1.05962 | ||||||||
\(646\) | 7.34062e8 | + | 1.27143e9i | 0.107132 | + | 0.185558i | ||||
\(647\) | −2.05320e9 | + | 3.55624e9i | −0.298034 | + | 0.516210i | −0.975686 | − | 0.219172i | \(-0.929664\pi\) |
0.677652 | + | 0.735383i | \(0.262998\pi\) | |||||||
\(648\) | 3.50751e8 | − | 6.07519e8i | 0.0506392 | − | 0.0877096i | ||||
\(649\) | −6.19224e8 | − | 1.07253e9i | −0.0889184 | − | 0.154011i | ||||
\(650\) | 2.26275e9 | 0.323176 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.36760e9 | −0.758427 | ||||||||
\(653\) | −3.45550e9 | − | 5.98510e9i | −0.485640 | − | 0.841153i | 0.514224 | − | 0.857656i | \(-0.328080\pi\) |
−0.999864 | + | 0.0165027i | \(0.994747\pi\) | |||||||
\(654\) | −3.25697e8 | + | 5.64124e8i | −0.0455294 | + | 0.0788592i | ||||
\(655\) | −3.28122e9 | + | 5.68324e9i | −0.456237 | + | 0.790226i | ||||
\(656\) | −1.21410e9 | − | 2.10288e9i | −0.167915 | − | 0.290837i | ||||
\(657\) | −9.98061e8 | −0.137302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.42444e9 | 0.466112 | 0.233056 | − | 0.972463i | \(-0.425127\pi\) | ||||
0.233056 | + | 0.972463i | \(0.425127\pi\) | |||||||
\(660\) | 4.59192e8 | + | 7.95344e8i | 0.0621714 | + | 0.107684i | ||||
\(661\) | −3.38219e9 | + | 5.85812e9i | −0.455504 | + | 0.788956i | −0.998717 | − | 0.0506388i | \(-0.983874\pi\) |
0.543213 | + | 0.839595i | \(0.317208\pi\) | |||||||
\(662\) | −2.05271e9 | + | 3.55539e9i | −0.274995 | + | 0.476305i | ||||
\(663\) | 1.95361e9 | + | 3.38375e9i | 0.260340 | + | 0.450922i | ||||
\(664\) | −5.77731e9 | −0.765839 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.17453e9 | 0.154065 | ||||||||
\(667\) | 2.79082e8 | + | 4.83385e8i | 0.0364160 | + | 0.0630743i | ||||
\(668\) | 1.18848e9 | − | 2.05851e9i | 0.154267 | − | 0.267199i | ||||
\(669\) | −2.78825e9 | + | 4.82939e9i | −0.360031 | + | 0.623592i | ||||
\(670\) | −5.93475e8 | − | 1.02793e9i | −0.0762326 | − | 0.132039i | ||||
\(671\) | 2.85028e8 | 0.0364215 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.74959e9 | −0.221250 | −0.110625 | − | 0.993862i | \(-0.535285\pi\) | ||||
−0.110625 | + | 0.993862i | \(0.535285\pi\) | |||||||
\(674\) | 1.87894e9 | + | 3.25442e9i | 0.236376 | + | 0.409415i | ||||
\(675\) | −7.28025e8 | + | 1.26098e9i | −0.0911136 | + | 0.157813i | ||||
\(676\) | −1.69091e9 | + | 2.92874e9i | −0.210527 | + | 0.364643i | ||||
\(677\) | 4.15006e9 | + | 7.18811e9i | 0.514036 | + | 0.890337i | 0.999867 | + | 0.0162840i | \(0.00518358\pi\) |
−0.485831 | + | 0.874053i | \(0.661483\pi\) | |||||||
\(678\) | −2.86842e9 | −0.353459 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.46131e10 | −1.78222 | ||||||||
\(681\) | 5.85838e8 | + | 1.01470e9i | 0.0710825 | + | 0.123118i | ||||
\(682\) | 7.87242e8 | − | 1.36354e9i | 0.0950305 | − | 0.164598i | ||||
\(683\) | 6.06158e9 | − | 1.04990e10i | 0.727969 | − | 1.26088i | −0.229771 | − | 0.973245i | \(-0.573798\pi\) |
0.957740 | − | 0.287635i | \(-0.0928690\pi\) | |||||||
\(684\) | 2.89063e8 | + | 5.00672e8i | 0.0345379 | + | 0.0598214i | ||||
\(685\) | −1.09375e10 | −1.30017 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.77213e8 | 0.114985 | ||||||||
\(688\) | −1.32217e9 | − | 2.29006e9i | −0.154784 | − | 0.268094i | ||||
\(689\) | 1.09112e9 | − | 1.88988e9i | 0.127088 | − | 0.220123i | ||||
\(690\) | −4.82948e8 | + | 8.36490e8i | −0.0559665 | + | 0.0969369i | ||||
\(691\) | 4.10923e9 | + | 7.11739e9i | 0.473791 | + | 0.820631i | 0.999550 | − | 0.0300033i | \(-0.00955177\pi\) |
−0.525758 | + | 0.850634i | \(0.676218\pi\) | |||||||
\(692\) | 5.84385e9 | 0.670390 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.52038e9 | −0.854046 | ||||||||
\(695\) | 2.30632e9 | + | 3.99467e9i | 0.260599 | + | 0.451371i | ||||
\(696\) | 6.50608e8 | − | 1.12689e9i | 0.0731454 | − | 0.126692i | ||||
\(697\) | 8.93759e9 | − | 1.54804e10i | 0.999783 | − | 1.73167i | ||||
\(698\) | 7.96051e8 | + | 1.37880e9i | 0.0886027 | + | 0.153464i | ||||
\(699\) | 2.49034e9 | 0.275796 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.72231e9 | 0.517775 | 0.258888 | − | 0.965907i | \(-0.416644\pi\) | ||||
0.258888 | + | 0.965907i | \(0.416644\pi\) | |||||||
\(702\) | −3.01032e8 | − | 5.21402e8i | −0.0328422 | − | 0.0568844i | ||||
\(703\) | −1.15735e9 | + | 2.00458e9i | −0.125638 | + | 0.217611i | ||||
\(704\) | 3.12370e8 | − | 5.41040e8i | 0.0337415 | − | 0.0584420i | ||||
\(705\) | −3.07105e9 | − | 5.31922e9i | −0.330085 | − | 0.571724i | ||||
\(706\) | 3.41781e9 | 0.365537 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.24505e9 | 0.343641 | ||||||||
\(709\) | −1.39487e9 | − | 2.41599e9i | −0.146985 | − | 0.254585i | 0.783127 | − | 0.621862i | \(-0.213624\pi\) |
−0.930112 | + | 0.367277i | \(0.880290\pi\) | |||||||
\(710\) | 6.50594e9 | − | 1.12686e10i | 0.682191 | − | 1.18159i | ||||
\(711\) | 2.52005e9 | − | 4.36486e9i | 0.262945 | − | 0.455435i | ||||
\(712\) | 5.62868e9 | + | 9.74917e9i | 0.584423 | + | 1.01225i | ||||
\(713\) | −4.23184e9 | −0.437236 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.88483e9 | 0.192842 | ||||||||
\(716\) | −3.72397e9 | − | 6.45011e9i | −0.379150 | − | 0.656707i | ||||
\(717\) | −6.72932e8 | + | 1.16555e9i | −0.0681795 | + | 0.118090i | ||||
\(718\) | −2.79762e9 | + | 4.84562e9i | −0.282068 | + | 0.488556i | ||||
\(719\) | 7.59923e8 | + | 1.31623e9i | 0.0762463 | + | 0.132062i | 0.901628 | − | 0.432513i | \(-0.142373\pi\) |
−0.825381 | + | 0.564576i | \(0.809040\pi\) | |||||||
\(720\) | −1.09630e9 | −0.109463 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.91740e9 | −0.486246 | ||||||||
\(723\) | 2.69155e9 | + | 4.66190e9i | 0.264861 | + | 0.458753i | ||||
\(724\) | −2.96715e9 | + | 5.13925e9i | −0.290572 | + | 0.503286i | ||||
\(725\) | −1.35041e9 | + | 2.33899e9i | −0.131608 | + | 0.227953i | ||||
\(726\) | 1.50567e9 | + | 2.60789e9i | 0.146033 | + | 0.252936i | ||||
\(727\) | 8.11761e9 | 0.783534 | 0.391767 | − | 0.920065i | \(-0.371864\pi\) | ||||
0.391767 | + | 0.920065i | \(0.371864\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.60183e9 | − | 2.77444e9i | −0.152400 | − | 0.263965i | ||||
\(731\) | 9.73316e9 | − | 1.68583e10i | 0.921601 | − | 1.59626i | ||||
\(732\) | −3.73422e8 | + | 6.46786e8i | −0.0351894 | + | 0.0609498i | ||||
\(733\) | −5.16203e9 | − | 8.94090e9i | −0.484124 | − | 0.838528i | 0.515709 | − | 0.856764i | \(-0.327528\pi\) |
−0.999834 | + | 0.0182357i | \(0.994195\pi\) | |||||||
\(734\) | 5.11539e9 | 0.477466 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.93676e9 | −0.271517 | ||||||||
\(737\) | −2.40434e8 | − | 4.16443e8i | −0.0221238 | − | 0.0383195i | ||||
\(738\) | −1.37719e9 | + | 2.38537e9i | −0.126124 | + | 0.218453i | ||||
\(739\) | 6.76824e9 | − | 1.17229e10i | 0.616908 | − | 1.06852i | −0.373139 | − | 0.927776i | \(-0.621718\pi\) |
0.990047 | − | 0.140740i | \(-0.0449482\pi\) | |||||||
\(740\) | −4.81736e9 | − | 8.34391e9i | −0.437016 | − | 0.756935i | ||||
\(741\) | 1.18651e9 | 0.107129 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.71936e10 | −1.53782 | −0.768910 | − | 0.639356i | \(-0.779201\pi\) | ||||
−0.768910 | + | 0.639356i | \(0.779201\pi\) | |||||||
\(744\) | 4.93272e9 | + | 8.54372e9i | 0.439118 | + | 0.760574i | ||||
\(745\) | 4.05300e9 | − | 7.02001e9i | 0.359112 | − | 0.622000i | ||||
\(746\) | −1.14355e9 | + | 1.98069e9i | −0.100848 | + | 0.174675i | ||||
\(747\) | −1.59532e9 | − | 2.76318e9i | −0.140032 | − | 0.242542i | ||||
\(748\) | −2.47571e9 | −0.216294 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.62197e8 | 0.0226941 | ||||||||
\(751\) | −5.62392e9 | − | 9.74092e9i | −0.484506 | − | 0.839190i | 0.515335 | − | 0.856989i | \(-0.327667\pi\) |
−0.999842 | + | 0.0177991i | \(0.994334\pi\) | |||||||
\(752\) | 1.12459e9 | − | 1.94786e9i | 0.0964348 | − | 0.167030i | ||||
\(753\) | −5.32815e9 | + | 9.22863e9i | −0.454772 | + | 0.787689i | ||||
\(754\) | −5.58384e8 | − | 9.67149e8i | −0.0474387 | − | 0.0821663i | ||||
\(755\) | −2.96837e7 | −0.00251017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.63068e10 | 1.36626 | 0.683131 | − | 0.730296i | \(-0.260618\pi\) | ||||
0.683131 | + | 0.730296i | \(0.260618\pi\) | |||||||
\(758\) | 4.45059e9 | + | 7.70865e9i | 0.371172 | + | 0.642889i | ||||
\(759\) | −1.95656e8 | + | 3.38886e8i | −0.0162423 | + | 0.0281324i | ||||
\(760\) | −2.21879e9 | + | 3.84305e9i | −0.183345 | + | 0.317562i | ||||
\(761\) | 3.07035e9 | + | 5.31800e9i | 0.252546 | + | 0.437423i | 0.964226 | − | 0.265081i | \(-0.0853986\pi\) |
−0.711680 | + | 0.702504i | \(0.752065\pi\) | |||||||
\(762\) | 2.71970e9 | 0.222679 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.22812e9 | −0.424149 | ||||||||
\(765\) | −4.03521e9 | − | 6.98919e9i | −0.325875 | − | 0.564432i | ||||
\(766\) | −2.28579e9 | + | 3.95910e9i | −0.183753 | + | 0.318270i | ||||
\(767\) | 3.32996e9 | − | 5.76766e9i | 0.266474 | − | 0.461547i | ||||
\(768\) | 2.81014e9 | + | 4.86730e9i | 0.223853 | + | 0.387725i | ||||
\(769\) | −2.45069e10 | −1.94333 | −0.971664 | − | 0.236368i | \(-0.924043\pi\) | ||||
−0.971664 | + | 0.236368i | \(0.924043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.85791e9 | 0.303153 | ||||||||
\(772\) | 5.35334e9 | + | 9.27226e9i | 0.418759 | + | 0.725312i | ||||
\(773\) | −5.08608e9 | + | 8.80935e9i | −0.396055 | + | 0.685987i | −0.993235 | − | 0.116120i | \(-0.962954\pi\) |
0.597180 | + | 0.802107i | \(0.296288\pi\) | |||||||
\(774\) | −1.49978e9 | + | 2.59770e9i | −0.116261 | + | 0.201370i | ||||
\(775\) | −1.02384e10 | − | 1.77335e10i | −0.790092 | − | 1.36848i | ||||
\(776\) | −1.16514e10 | −0.895080 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.65411e9 | 0.734994 | ||||||||
\(779\) | −2.71408e9 | − | 4.70093e9i | −0.205704 | − | 0.356289i | ||||
\(780\) | −2.46937e9 | + | 4.27707e9i | −0.186318 | + | 0.322712i | ||||
\(781\) | 2.63574e9 | − | 4.56523e9i | 0.197981 | − | 0.342913i | ||||
\(782\) | −1.30190e9 | − | 2.25495e9i | −0.0973537 | − | 0.168622i | ||||
\(783\) | 7.18626e8 | 0.0534979 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.25512e10 | −0.926062 | ||||||||
\(786\) | 1.36297e9 | + | 2.36073e9i | 0.100117 | + | 0.173407i | ||||
\(787\) | −4.89567e9 | + | 8.47956e9i | −0.358015 | + | 0.620100i | −0.987629 | − | 0.156808i | \(-0.949880\pi\) |
0.629614 | + | 0.776908i | \(0.283213\pi\) | |||||||
\(788\) | −5.46554e9 | + | 9.46659e9i | −0.397916 | + | 0.689211i | ||||
\(789\) | −5.94325e9 | − | 1.02940e10i | −0.430779 | − | 0.746131i | ||||
\(790\) | 1.61781e10 | 1.16744 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.12241e8 | 0.0652487 | ||||||||
\(793\) | 7.66387e8 | + | 1.32742e9i | 0.0545748 | + | 0.0945263i | ||||
\(794\) | 5.64047e9 | − | 9.76959e9i | 0.399893 | − | 0.692635i | ||||
\(795\) | −2.25373e9 | + | 3.90357e9i | −0.159080 | + | 0.275535i | ||||
\(796\) | 4.37049e9 | + | 7.56991e9i | 0.307139 | + | 0.531980i | ||||
\(797\) | 9.75782e9 | 0.682729 | 0.341365 | − | 0.939931i | \(-0.389111\pi\) | ||||
0.341365 | + | 0.939931i | \(0.389111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.65574e10 | 1.14836 | ||||||||
\(800\) | −7.10515e9 | − | 1.23065e10i | −0.490635 | − | 0.849804i | ||||
\(801\) | −3.10857e9 | + | 5.38420e9i | −0.213721 | + | 0.370175i | ||||
\(802\) | −8.05777e8 | + | 1.39565e9i | −0.0551575 | + | 0.0955356i | ||||
\(803\) | −6.48945e8 | − | 1.12401e9i | −0.0442286 | − | 0.0766062i | ||||
\(804\) | 1.25999e9 | 0.0855012 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.46700e9 | 0.569583 | ||||||||
\(807\) | 3.71796e9 | + | 6.43970e9i | 0.249028 | + | 0.431329i | ||||
\(808\) | −7.91104e9 | + | 1.37023e10i | −0.527587 | + | 0.913807i | ||||
\(809\) | 1.39353e9 | − | 2.41366e9i | 0.0925330 | − | 0.160272i | −0.816043 | − | 0.577991i | \(-0.803837\pi\) |
0.908576 | + | 0.417719i | \(0.137170\pi\) | |||||||
\(810\) | 6.21786e8 | + | 1.07696e9i | 0.0411096 | + | 0.0712039i | ||||
\(811\) | 7.99983e9 | 0.526633 | 0.263316 | − | 0.964710i | \(-0.415184\pi\) | ||||
0.263316 | + | 0.964710i | \(0.415184\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.14661e10 | 0.748339 | ||||||||
\(814\) | 7.63688e8 | + | 1.32275e9i | 0.0496284 | + | 0.0859590i | ||||
\(815\) | 1.13770e10 | − | 1.97055e10i | 0.736165 | − | 1.27508i | ||||
\(816\) | 1.47766e9 | − | 2.55938e9i | 0.0952049 | − | 0.164900i | ||||
\(817\) | −2.95568e9 | − | 5.11938e9i | −0.189618 | − | 0.328428i | ||||
\(818\) | −5.39687e8 | −0.0344751 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.25943e10 | 1.43103 | ||||||||
\(821\) | 5.12009e9 | + | 8.86826e9i | 0.322906 | + | 0.559290i | 0.981086 | − | 0.193570i | \(-0.0620068\pi\) |
−0.658180 | + | 0.752861i | \(0.728673\pi\) | |||||||
\(822\) | −2.27164e9 | + | 3.93459e9i | −0.142655 | + | 0.247086i | ||||
\(823\) | −1.39341e10 | + | 2.41346e10i | −0.871324 | + | 1.50918i | −0.0106973 | + | 0.999943i | \(0.503405\pi\) |
−0.860627 | + | 0.509236i | \(0.829928\pi\) | |||||||
\(824\) | −4.75820e9 | − | 8.24144e9i | −0.296277 | − | 0.513166i | ||||
\(825\) | −1.89346e9 | −0.117400 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.35125e10 | 1.44554 | 0.722769 | − | 0.691090i | \(-0.242869\pi\) | ||||
0.722769 | + | 0.691090i | \(0.242869\pi\) | |||||||
\(828\) | −5.12668e8 | − | 8.87967e8i | −0.0313856 | − | 0.0543614i | ||||
\(829\) | −6.42991e9 | + | 1.11369e10i | −0.391980 | + | 0.678929i | −0.992711 | − | 0.120522i | \(-0.961543\pi\) |
0.600731 | + | 0.799451i | \(0.294876\pi\) | |||||||
\(830\) | 5.12080e9 | − | 8.86948e9i | 0.310859 | − | 0.538424i | ||||
\(831\) | −6.96813e9 | − | 1.20692e10i | −0.421224 | − | 0.729581i | ||||
\(832\) | 3.35962e9 | 0.202236 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.91602e9 | 0.114372 | ||||||||
\(835\) | 5.03812e9 | + | 8.72628e9i | 0.299479 | + | 0.518712i | ||||
\(836\) | −3.75901e8 | + | 6.51080e8i | −0.0222511 | + | 0.0385400i | ||||
\(837\) | −2.72421e9 | + | 4.71846e9i | −0.160583 | + | 0.278139i | ||||
\(838\) | 5.07163e9 | + | 8.78432e9i | 0.297710 | + | 0.515649i | ||||
\(839\) | 7.99832e9 | 0.467554 | 0.233777 | − | 0.972290i | \(-0.424891\pi\) | ||||
0.233777 | + | 0.972290i | \(0.424891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.59169e10 | −0.922725 | ||||||||
\(842\) | 3.39998e9 | + | 5.88894e9i | 0.196284 | + | 0.339973i | ||||
\(843\) | 4.19908e9 | − | 7.27302e9i | 0.241411 | − | 0.418137i | ||||
\(844\) | 8.24533e9 | − | 1.42813e10i | 0.472074 | − | 0.817655i | ||||
\(845\) | −7.16799e9 | − | 1.24153e10i | −0.408694 | − | 0.707880i | ||||
\(846\) | −2.55134e9 | −0.144868 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.65059e9 | −0.0929510 | ||||||||
\(849\) | −8.02316e9 | − | 1.38965e10i | −0.449955 | − | 0.779344i | ||||
\(850\) | 6.29956e9 | − | 1.09112e10i | 0.351839 | − | 0.609403i | ||||
\(851\) | 2.05261e9 | − | 3.55523e9i | 0.114170 | − | 0.197749i | ||||
\(852\) | 6.90630e9 | + | 1.19621e10i | 0.382567 | + | 0.662625i | ||||
\(853\) | −4.20827e9 | −0.232157 | −0.116079 | − | 0.993240i | \(-0.537032\pi\) | ||||
−0.116079 | + | 0.993240i | \(0.537032\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.45075e9 | −0.134097 | ||||||||
\(856\) | 7.54121e9 | + | 1.30618e10i | 0.410944 | + | 0.711776i | ||||
\(857\) | 1.59653e10 | − | 2.76528e10i | 0.866453 | − | 1.50074i | 0.000855933 | − | 1.00000i | \(-0.499728\pi\) |
0.865597 | − | 0.500741i | \(-0.166939\pi\) | |||||||
\(858\) | 3.91465e8 | − | 6.78038e8i | 0.0211586 | − | 0.0366478i | ||||
\(859\) | 1.09001e10 | + | 1.88795e10i | 0.586752 | + | 1.01628i | 0.994655 | + | 0.103259i | \(0.0329269\pi\) |
−0.407903 | + | 0.913025i | \(0.633740\pi\) | |||||||
\(860\) | 2.46055e10 | 1.31913 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.31966e10 | 0.701755 | ||||||||
\(863\) | −5.23639e9 | − | 9.06970e9i | −0.277329 | − | 0.480347i | 0.693391 | − | 0.720561i | \(-0.256116\pi\) |
−0.970720 | + | 0.240214i | \(0.922782\pi\) | |||||||
\(864\) | −1.89051e9 | + | 3.27446e9i | −0.0997198 | + | 0.172720i | ||||
\(865\) | −1.23864e10 | + | 2.14539e10i | −0.650712 | + | 1.12707i | ||||
\(866\) | −4.55214e8 | − | 7.88453e8i | −0.0238178 | − | 0.0412537i | ||||
\(867\) | 1.06765e10 | 0.556368 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.55421e9 | 0.338806 | ||||||||
\(870\) | 1.15335e9 | + | 1.99766e9i | 0.0593805 | + | 0.102850i | ||||
\(871\) | 1.29296e9 | − | 2.23948e9i | 0.0663015 | − | 0.114838i | ||||
\(872\) | 2.65383e9 | − | 4.59656e9i | 0.135539 | − | 0.234761i | ||||
\(873\) | −3.21737e9 | − | 5.57265e9i | −0.163663 | − | 0.283473i | ||||
\(874\) | −7.90695e8 | −0.0400608 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.40080e9 | 0.170929 | ||||||||
\(877\) | 8.88935e9 | + | 1.53968e10i | 0.445012 | + | 0.770783i | 0.998053 | − | 0.0623707i | \(-0.0198661\pi\) |
−0.553041 | + | 0.833154i | \(0.686533\pi\) | |||||||
\(878\) | 2.97229e9 | − | 5.14815e9i | 0.148204 | − | 0.256697i | ||||
\(879\) | 1.55945e9 | − | 2.70104e9i | 0.0774480 | − | 0.134144i | ||||
\(880\) | −7.12820e8 | − | 1.23464e9i | −0.0352607 | − | 0.0610733i | ||||
\(881\) | 7.64253e9 | 0.376549 | 0.188274 | − | 0.982116i | \(-0.439711\pi\) | ||||
0.188274 | + | 0.982116i | \(0.439711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.76375e10 | −1.35094 | −0.675472 | − | 0.737386i | \(-0.736060\pi\) | ||||
−0.675472 | + | 0.737386i | \(0.736060\pi\) | |||||||
\(884\) | −6.65674e9 | − | 1.15298e10i | −0.324100 | − | 0.561358i | ||||
\(885\) | −6.87809e9 | + | 1.19132e10i | −0.333554 | + | 0.577733i | ||||
\(886\) | 5.32127e9 | − | 9.21671e9i | 0.257038 | − | 0.445203i | ||||
\(887\) | 1.61544e10 | + | 2.79802e10i | 0.777243 | + | 1.34622i | 0.933525 | + | 0.358512i | \(0.116716\pi\) |
−0.156282 | + | 0.987713i | \(0.549951\pi\) | |||||||
\(888\) | −9.57027e9 | −0.458647 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.99562e10 | −0.948886 | ||||||||
\(891\) | 2.51903e8 | + | 4.36309e8i | 0.0119306 | + | 0.0206644i | ||||
\(892\) | 9.50070e9 | − | 1.64557e10i | 0.448207 | − | 0.776317i | ||||
\(893\) | 2.51401e9 | − | 4.35439e9i | 0.118137 | − | 0.204619i | ||||
\(894\) | −1.68356e9 | − | 2.91600e9i | −0.0788036 | − | 0.136492i | ||||
\(895\) | 3.15728e10 | 1.47208 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.10433e9 | −0.0973511 | ||||||||
\(898\) | 8.31031e8 | + | 1.43939e9i | 0.0382957 | + | 0.0663301i | ||||
\(899\) | −5.05313e9 | + | 8.75228e9i | −0.231954 | + | 0.401756i | ||||
\(900\) | 2.48068e9 | − | 4.29666e9i | 0.113428 | − | 0.196464i | ||||
\(901\) | −6.07543e9 | − | 1.05229e10i | −0.276720 | − | 0.479293i | ||||
\(902\) | −3.58184e9 | −0.162511 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.33723e10 | 1.05223 | ||||||||
\(905\) | −1.25781e10 | − | 2.17859e10i | −0.564087 | − | 0.977027i | ||||
\(906\) | −6.16507e6 | + | 1.06782e7i | −0.000275416 | + | 0.000477035i | ||||
\(907\) | −1.13571e10 | + | 1.96711e10i | −0.505409 | + | 0.875394i | 0.494572 | + | 0.869137i | \(0.335325\pi\) |
−0.999980 | + | 0.00625673i | \(0.998008\pi\) | |||||||
\(908\) | −1.99619e9 | − | 3.45750e9i | −0.0884914 | − | 0.153272i | ||||
\(909\) | −8.73810e9 | −0.385872 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.50925e9 | 0.329065 | 0.164533 | − | 0.986372i | \(-0.447388\pi\) | ||||
0.164533 | + | 0.986372i | \(0.447388\pi\) | |||||||
\(912\) | −4.48723e8 | − | 7.77211e8i | −0.0195883 | − | 0.0339279i | ||||
\(913\) | 2.07458e9 | − | 3.59328e9i | 0.0902157 | − | 0.156258i | ||||
\(914\) | −8.84275e9 | + | 1.53161e10i | −0.383068 | + | 0.663493i | ||||
\(915\) | −1.58299e9 | − | 2.74181e9i | −0.0683130 | − | 0.118322i | ||||
\(916\) | −3.32976e9 | −0.143146 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.35233e9 | −0.143020 | ||||||||
\(919\) | 1.24687e10 | + | 2.15964e10i | 0.529928 | + | 0.917862i | 0.999390 | + | 0.0349098i | \(0.0111144\pi\) |
−0.469462 | + | 0.882952i | \(0.655552\pi\) | |||||||
\(920\) | 3.93513e9 | − | 6.81585e9i | 0.166610 | − | 0.288577i | ||||
\(921\) | −3.51810e9 | + | 6.09352e9i | −0.148388 | + | 0.257016i | ||||
\(922\) | −8.30062e9 | − | 1.43771e10i | −0.348781 | − | 0.604106i | ||||
\(923\) | 2.83481e10 | 1.18664 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.98642e10 | 0.825230 | ||||||||
\(926\) | −1.39066e9 | − | 2.40869e9i | −0.0575549 | − | 0.0996880i | ||||
\(927\) | 2.62782e9 | − | 4.55152e9i | 0.108347 | − | 0.187663i | ||||
\(928\) | −3.50671e9 | + | 6.07380e9i | −0.144040 | + | 0.249484i | ||||
\(929\) | −4.33103e9 | − | 7.50156e9i | −0.177229 | − | 0.306970i | 0.763701 | − | 0.645570i | \(-0.223380\pi\) |
−0.940931 | + | 0.338600i | \(0.890047\pi\) | |||||||
\(930\) | −1.74887e10 | −0.712965 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.48559e9 | −0.343342 | ||||||||
\(933\) | 7.78673e9 | + | 1.34870e10i | 0.313884 | + | 0.543663i | ||||
\(934\) | −1.25377e9 | + | 2.17159e9i | −0.0503503 | + | 0.0872093i | ||||
\(935\) | 5.24744e9 | − | 9.08883e9i | 0.209945 | − | 0.363636i | ||||
\(936\) | 2.45285e9 | + | 4.24846e9i | 0.0977700 | + | 0.169343i | ||||
\(937\) | −2.82655e10 | −1.12245 | −0.561226 | − | 0.827663i | \(-0.689670\pi\) | ||||
−0.561226 | + | 0.827663i | \(0.689670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.24220e10 | 0.489623 | ||||||||
\(940\) | 1.04643e10 | + | 1.81248e10i | 0.410926 | + | 0.711745i | ||||
\(941\) | −2.33541e10 | + | 4.04505e10i | −0.913691 | + | 1.58256i | −0.104884 | + | 0.994484i | \(0.533447\pi\) |
−0.808807 | + | 0.588074i | \(0.799886\pi\) | |||||||
\(942\) | −2.60678e9 | + | 4.51508e9i | −0.101608 | + | 0.175990i | ||||
\(943\) | 4.81356e9 | + | 8.33734e9i | 0.186929 | + | 0.323770i | ||||
\(944\) | −5.03740e9 | −0.194897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.90067e9 | −0.149803 | ||||||||
\(947\) | 2.33696e10 | + | 4.04774e10i | 0.894184 | + | 1.54877i | 0.834812 | + | 0.550535i | \(0.185576\pi\) |
0.0593718 | + | 0.998236i | \(0.481090\pi\) | |||||||
\(948\) | −8.58684e9 | + | 1.48728e10i | −0.327344 | + | 0.566976i | ||||
\(949\) | 3.48979e9 | − | 6.04449e9i | 0.132546 | − | 0.229577i | ||||
\(950\) | −1.91299e9 | − | 3.31340e9i | −0.0723904 | − | 0.125384i | ||||
\(951\) | 1.68902e9 | 0.0636798 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.82420e10 | 1.43125 | 0.715625 | − | 0.698484i | \(-0.246142\pi\) | ||||
0.715625 | + | 0.698484i | \(0.246142\pi\) | |||||||
\(954\) | 9.36163e8 | + | 1.62148e9i | 0.0349086 | + | 0.0604634i | ||||
\(955\) | 1.10813e10 | − | 1.91934e10i | 0.411700 | − | 0.713085i | ||||
\(956\) | 2.29295e9 | − | 3.97151e9i | 0.0848775 | − | 0.147012i | ||||
\(957\) | 4.67255e8 | + | 8.09309e8i | 0.0172331 | + | 0.0298485i | ||||
\(958\) | 9.05837e9 | 0.332867 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.93935e9 | −0.253145 | ||||||||
\(961\) | −2.45550e10 | − | 4.25306e10i | −0.892501 | − | 1.54586i | ||||
\(962\) | −4.10684e9 | + | 7.11325e9i | −0.148729 | + | 0.257606i | ||||
\(963\) | −4.16480e9 | + | 7.21365e9i | −0.150281 | + | 0.260293i | ||||
\(964\) | −9.17120e9 | − | 1.58850e10i | −0.329729 | − | 0.571107i | ||||
\(965\) | −4.53870e10 | −1.62587 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.90012e10 | −1.74267 | −0.871333 | − | 0.490692i | \(-0.836744\pi\) | ||||
−0.871333 | + | 0.490692i | \(0.836744\pi\) | |||||||
\(968\) | −1.22684e10 | − | 2.12495e10i | −0.434734 | − | 0.752982i | ||||
\(969\) | 3.30328e9 | − | 5.72145e9i | 0.116630 | − | 0.202010i | ||||
\(970\) | 1.03274e10 | − | 1.78875e10i | 0.363320 | − | 0.629288i | ||||
\(971\) | 1.36464e10 | + | 2.36363e10i | 0.478357 | + | 0.828538i | 0.999692 | − | 0.0248138i | \(-0.00789928\pi\) |
−0.521335 | + | 0.853352i | \(0.674566\pi\) | |||||||
\(972\) | −1.32010e9 | −0.0461078 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.57676e9 | 0.193386 | ||||||||
\(975\) | −5.09118e9 | − | 8.81818e9i | −0.175915 | − | 0.304693i | ||||
\(976\) | 5.79676e8 | − | 1.00403e9i | 0.0199577 | − | 0.0345678i | ||||
\(977\) | −1.97241e9 | + | 3.41631e9i | −0.0676653 | + | 0.117200i | −0.897873 | − | 0.440254i | \(-0.854888\pi\) |
0.830208 | + | 0.557454i | \(0.188222\pi\) | |||||||
\(978\) | −4.72582e9 | − | 8.18537e9i | −0.161544 | − | 0.279803i | ||||
\(979\) | −8.08484e9 | −0.275380 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.93127e9 | 0.0991322 | ||||||||
\(982\) | −1.53841e10 | − | 2.66460e10i | −0.518420 | − | 0.897929i | ||||
\(983\) | 2.37160e8 | − | 4.10774e8i | 0.00796351 | − | 0.0137932i | −0.862016 | − | 0.506881i | \(-0.830798\pi\) |
0.869980 | + | 0.493088i | \(0.164132\pi\) | |||||||
\(984\) | 1.12216e10 | − | 1.94363e10i | 0.375466 | − | 0.650327i | ||||
\(985\) | −2.31691e10 | − | 4.01301e10i | −0.772472 | − | 1.33796i | ||||
\(986\) | −6.21824e9 | −0.206585 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.04292e9 | −0.133366 | ||||||||
\(989\) | 5.24204e9 | + | 9.07948e9i | 0.172311 | + | 0.298452i | ||||
\(990\) | −8.08578e8 | + | 1.40050e9i | −0.0264849 | + | 0.0458732i | ||||
\(991\) | −6.10984e9 | + | 1.05825e10i | −0.199421 | + | 0.345408i | −0.948341 | − | 0.317253i | \(-0.897240\pi\) |
0.748920 | + | 0.662661i | \(0.230573\pi\) | |||||||
\(992\) | −2.65869e10 | − | 4.60498e10i | −0.864721 | − | 1.49774i | ||||
\(993\) | 1.84744e10 | 0.598752 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.70541e10 | −1.19249 | ||||||||
\(996\) | 5.43592e9 | + | 9.41529e9i | 0.174327 | + | 0.301944i | ||||
\(997\) | −1.80345e10 | + | 3.12367e10i | −0.576330 | + | 0.998233i | 0.419566 | + | 0.907725i | \(0.362182\pi\) |
−0.995896 | + | 0.0905079i | \(0.971151\pi\) | |||||||
\(998\) | 1.23195e9 | − | 2.13380e9i | 0.0392316 | − | 0.0679510i | ||||
\(999\) | −2.64270e9 | − | 4.57729e9i | −0.0838626 | − | 0.145254i |
(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 | 147.8.e.a.67.1 | 2 | ||
7.2 | even | 3 | inner | 147.8.e.a.79.1 | 2 | ||
7.3 | odd | 6 | 3.8.a.a.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 147.8.a.b.1.1 | 1 | |||
7.5 | odd | 6 | 147.8.e.b.79.1 | 2 | |||
7.6 | odd | 2 | 147.8.e.b.67.1 | 2 | |||
21.11 | odd | 6 | 441.8.a.a.1.1 | 1 | |||
21.17 | even | 6 | 9.8.a.a.1.1 | 1 | |||
28.3 | even | 6 | 48.8.a.g.1.1 | 1 | |||
35.3 | even | 12 | 75.8.b.c.49.1 | 2 | |||
35.17 | even | 12 | 75.8.b.c.49.2 | 2 | |||
35.24 | odd | 6 | 75.8.a.a.1.1 | 1 | |||
56.3 | even | 6 | 192.8.a.a.1.1 | 1 | |||
56.45 | odd | 6 | 192.8.a.i.1.1 | 1 | |||
63.31 | odd | 6 | 81.8.c.a.55.1 | 2 | |||
63.38 | even | 6 | 81.8.c.c.28.1 | 2 | |||
63.52 | odd | 6 | 81.8.c.a.28.1 | 2 | |||
63.59 | even | 6 | 81.8.c.c.55.1 | 2 | |||
77.10 | even | 6 | 363.8.a.b.1.1 | 1 | |||
84.59 | odd | 6 | 144.8.a.b.1.1 | 1 | |||
91.38 | odd | 6 | 507.8.a.a.1.1 | 1 | |||
105.17 | odd | 12 | 225.8.b.f.199.1 | 2 | |||
105.38 | odd | 12 | 225.8.b.f.199.2 | 2 | |||
105.59 | even | 6 | 225.8.a.i.1.1 | 1 | |||
168.59 | odd | 6 | 576.8.a.x.1.1 | 1 | |||
168.101 | even | 6 | 576.8.a.w.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.8.a.a.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
9.8.a.a.1.1 | 1 | 21.17 | even | 6 | |||
48.8.a.g.1.1 | 1 | 28.3 | even | 6 | |||
75.8.a.a.1.1 | 1 | 35.24 | odd | 6 | |||
75.8.b.c.49.1 | 2 | 35.3 | even | 12 | |||
75.8.b.c.49.2 | 2 | 35.17 | even | 12 | |||
81.8.c.a.28.1 | 2 | 63.52 | odd | 6 | |||
81.8.c.a.55.1 | 2 | 63.31 | odd | 6 | |||
81.8.c.c.28.1 | 2 | 63.38 | even | 6 | |||
81.8.c.c.55.1 | 2 | 63.59 | even | 6 | |||
144.8.a.b.1.1 | 1 | 84.59 | odd | 6 | |||
147.8.a.b.1.1 | 1 | 7.4 | even | 3 | |||
147.8.e.a.67.1 | 2 | 1.1 | even | 1 | trivial | ||
147.8.e.a.79.1 | 2 | 7.2 | even | 3 | inner | ||
147.8.e.b.67.1 | 2 | 7.6 | odd | 2 | |||
147.8.e.b.79.1 | 2 | 7.5 | odd | 6 | |||
192.8.a.a.1.1 | 1 | 56.3 | even | 6 | |||
192.8.a.i.1.1 | 1 | 56.45 | odd | 6 | |||
225.8.a.i.1.1 | 1 | 105.59 | even | 6 | |||
225.8.b.f.199.1 | 2 | 105.17 | odd | 12 | |||
225.8.b.f.199.2 | 2 | 105.38 | odd | 12 | |||
363.8.a.b.1.1 | 1 | 77.10 | even | 6 | |||
441.8.a.a.1.1 | 1 | 21.11 | odd | 6 | |||
507.8.a.a.1.1 | 1 | 91.38 | odd | 6 | |||
576.8.a.w.1.1 | 1 | 168.101 | even | 6 | |||
576.8.a.x.1.1 | 1 | 168.59 | odd | 6 |