Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,10,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (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: | \(25.2367559720\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 427x^{4} - 3606x^{3} + 183492x^{2} - 858816x + 4064256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 18.1 | ||
Root | \(2.48064 + 4.29659i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.18 |
Dual form | 49.10.c.d.30.1 |
$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −20.9010 | − | 36.2015i | −0.923701 | − | 1.59990i | −0.793637 | − | 0.608392i | \(-0.791815\pi\) |
−0.130065 | − | 0.991506i | \(-0.541518\pi\) | |||||||
\(3\) | −0.116170 | + | 0.201212i | −0.000828031 | + | 0.00143419i | −0.866439 | − | 0.499283i | \(-0.833597\pi\) |
0.865611 | + | 0.500717i | \(0.166930\pi\) | |||||||
\(4\) | −617.701 | + | 1069.89i | −1.20645 | + | 2.08963i | ||||
\(5\) | 895.944 | + | 1551.82i | 0.641086 | + | 1.11039i | 0.985191 | + | 0.171462i | \(0.0548490\pi\) |
−0.344105 | + | 0.938931i | \(0.611818\pi\) | |||||||
\(6\) | 9.71222 | 0.00305941 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 30239.6 | 2.61019 | ||||||||
\(9\) | 9841.47 | + | 17045.9i | 0.499999 | + | 0.866023i | ||||
\(10\) | 37452.2 | − | 64869.1i | 1.18434 | − | 2.05134i | ||||
\(11\) | −8700.77 | + | 15070.2i | −0.179180 | + | 0.310350i | −0.941600 | − | 0.336733i | \(-0.890678\pi\) |
0.762420 | + | 0.647083i | \(0.224011\pi\) | |||||||
\(12\) | −143.516 | − | 248.577i | −0.00199795 | − | 0.00346056i | ||||
\(13\) | −122541. | −1.18997 | −0.594986 | − | 0.803736i | \(-0.702842\pi\) | ||||
−0.594986 | + | 0.803736i | \(0.702842\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −416.326 | −0.00212335 | ||||||||
\(16\) | −315775. | − | 546938.i | −1.20459 | − | 2.08640i | ||||
\(17\) | −165966. | + | 287462.i | −0.481948 | + | 0.834758i | −0.999785 | − | 0.0207211i | \(-0.993404\pi\) |
0.517838 | + | 0.855479i | \(0.326737\pi\) | |||||||
\(18\) | 411393. | − | 712553.i | 0.923699 | − | 1.59989i | ||||
\(19\) | −380853. | − | 659658.i | −0.670450 | − | 1.16125i | −0.977777 | − | 0.209650i | \(-0.932768\pi\) |
0.307326 | − | 0.951604i | \(-0.400566\pi\) | |||||||
\(20\) | −2.21370e6 | −3.09375 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 727418. | 0.662037 | ||||||||
\(23\) | −616243. | − | 1.06736e6i | −0.459173 | − | 0.795312i | 0.539744 | − | 0.841829i | \(-0.318521\pi\) |
−0.998917 | + | 0.0465175i | \(0.985188\pi\) | |||||||
\(24\) | −3512.93 | + | 6084.57i | −0.00216132 | + | 0.00374351i | ||||
\(25\) | −628870. | + | 1.08923e6i | −0.321981 | + | 0.557688i | ||||
\(26\) | 2.56123e6 | + | 4.43618e6i | 1.09918 | + | 1.90383i | ||||
\(27\) | −9146.25 | −0.00331212 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 634604. | 0.166614 | 0.0833071 | − | 0.996524i | \(-0.473452\pi\) | ||||
0.0833071 | + | 0.996524i | \(0.473452\pi\) | |||||||
\(30\) | 8701.61 | + | 15071.6i | 0.00196135 | + | 0.00339715i | ||||
\(31\) | 2.69034e6 | − | 4.65981e6i | 0.523215 | − | 0.906235i | −0.476420 | − | 0.879218i | \(-0.658066\pi\) |
0.999635 | − | 0.0270171i | \(-0.00860085\pi\) | |||||||
\(32\) | −5.45866e6 | + | 9.45467e6i | −0.920261 | + | 1.59394i | ||||
\(33\) | −2021.53 | − | 3501.39i | −0.000296734 | − | 0.000513958i | ||||
\(34\) | 1.38754e7 | 1.78070 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.43164e7 | −2.41289 | ||||||||
\(37\) | 1.51806e6 | + | 2.62935e6i | 0.133162 | + | 0.230643i | 0.924894 | − | 0.380226i | \(-0.124154\pi\) |
−0.791732 | + | 0.610869i | \(0.790820\pi\) | |||||||
\(38\) | −1.59204e7 | + | 2.75750e7i | −1.23859 | + | 2.14530i | ||||
\(39\) | 14235.5 | − | 24656.7i | 0.000985334 | − | 0.00170665i | ||||
\(40\) | 2.70930e7 | + | 4.69265e7i | 1.67335 | + | 2.89833i | ||||
\(41\) | −7.37009e6 | −0.407329 | −0.203665 | − | 0.979041i | \(-0.565285\pi\) | ||||
−0.203665 | + | 0.979041i | \(0.565285\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.06990e7 | −0.923297 | −0.461649 | − | 0.887063i | \(-0.652742\pi\) | ||||
−0.461649 | + | 0.887063i | \(0.652742\pi\) | |||||||
\(44\) | −1.07490e7 | − | 1.86177e7i | −0.432344 | − | 0.748841i | ||||
\(45\) | −1.76348e7 | + | 3.05444e7i | −0.641084 | + | 1.11039i | ||||
\(46\) | −2.57602e7 | + | 4.46179e7i | −0.848278 | + | 1.46926i | ||||
\(47\) | −1.01816e7 | − | 1.76350e7i | −0.304351 | − | 0.527152i | 0.672766 | − | 0.739856i | \(-0.265106\pi\) |
−0.977117 | + | 0.212704i | \(0.931773\pi\) | |||||||
\(48\) | 146734. | 0.00398974 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.25760e7 | 1.18966 | ||||||||
\(51\) | −38560.5 | − | 66788.7i | −0.000798135 | − | 0.00138241i | ||||
\(52\) | 7.56938e7 | − | 1.31106e8i | 1.43564 | − | 2.48660i | ||||
\(53\) | 2.98690e7 | − | 5.17346e7i | 0.519971 | − | 0.900616i | −0.479759 | − | 0.877400i | \(-0.659276\pi\) |
0.999730 | − | 0.0232162i | \(-0.00739062\pi\) | |||||||
\(54\) | 191165. | + | 331108.i | 0.00305941 | + | 0.00529905i | ||||
\(55\) | −3.11816e7 | −0.459480 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 176974. | 0.00222061 | ||||||||
\(58\) | −1.32638e7 | − | 2.29736e7i | −0.153902 | − | 0.266565i | ||||
\(59\) | −3.01730e7 | + | 5.22612e7i | −0.324179 | + | 0.561495i | −0.981346 | − | 0.192250i | \(-0.938421\pi\) |
0.657167 | + | 0.753745i | \(0.271755\pi\) | |||||||
\(60\) | 257165. | − | 445423.i | 0.00256172 | − | 0.00443702i | ||||
\(61\) | 4.72179e6 | + | 8.17837e6i | 0.0436639 | + | 0.0756280i | 0.887031 | − | 0.461709i | \(-0.152764\pi\) |
−0.843368 | + | 0.537337i | \(0.819430\pi\) | |||||||
\(62\) | −2.24923e8 | −1.93318 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.33012e8 | 0.991013 | ||||||||
\(65\) | −1.09790e8 | − | 1.90162e8i | −0.762874 | − | 1.32134i | ||||
\(66\) | −84503.8 | + | 146365.i | −0.000548187 | + | 0.000949487i | ||||
\(67\) | 1.09593e8 | − | 1.89821e8i | 0.664427 | − | 1.15082i | −0.315013 | − | 0.949087i | \(-0.602009\pi\) |
0.979440 | − | 0.201734i | \(-0.0646577\pi\) | |||||||
\(68\) | −2.05035e8 | − | 3.55132e8i | −1.16289 | − | 2.01418i | ||||
\(69\) | 286355. | 0.00152084 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.58741e7 | −0.260944 | −0.130472 | − | 0.991452i | \(-0.541649\pi\) | ||||
−0.130472 | + | 0.991452i | \(0.541649\pi\) | |||||||
\(72\) | 2.97603e8 | + | 5.15463e8i | 1.30509 | + | 2.26048i | ||||
\(73\) | −2.27166e8 | + | 3.93463e8i | −0.936248 | + | 1.62163i | −0.163855 | + | 0.986485i | \(0.552393\pi\) |
−0.772393 | + | 0.635144i | \(0.780941\pi\) | |||||||
\(74\) | 6.34577e7 | − | 1.09912e8i | 0.246004 | − | 0.426091i | ||||
\(75\) | −146111. | − | 253072.i | −0.000533221 | − | 0.000923566i | ||||
\(76\) | 9.41015e8 | 3.23545 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.19015e6 | −0.00364062 | ||||||||
\(79\) | −2.25528e7 | − | 3.90627e7i | −0.0651447 | − | 0.112834i | 0.831613 | − | 0.555355i | \(-0.187418\pi\) |
−0.896758 | + | 0.442521i | \(0.854084\pi\) | |||||||
\(80\) | 5.65834e8 | − | 9.80053e8i | 1.54449 | − | 2.67513i | ||||
\(81\) | −1.93709e8 | + | 3.35513e8i | −0.499996 | + | 0.866018i | ||||
\(82\) | 1.54042e8 | + | 2.66809e8i | 0.376250 | + | 0.651685i | ||||
\(83\) | −3.34665e8 | −0.774031 | −0.387016 | − | 0.922073i | \(-0.626494\pi\) | ||||
−0.387016 | + | 0.922073i | \(0.626494\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.94786e8 | −1.23588 | ||||||||
\(86\) | 4.32629e8 | + | 7.49336e8i | 0.852851 | + | 1.47718i | ||||
\(87\) | −73721.6 | + | 127690.i | −0.000137962 | + | 0.000238957i | ||||
\(88\) | −2.63108e8 | + | 4.55717e8i | −0.467695 | + | 0.810071i | ||||
\(89\) | −3.25943e8 | − | 5.64550e8i | −0.550664 | − | 0.953777i | −0.998227 | − | 0.0595250i | \(-0.981041\pi\) |
0.447563 | − | 0.894252i | \(-0.352292\pi\) | |||||||
\(90\) | 1.47434e9 | 2.36868 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.52262e9 | 2.21588 | ||||||||
\(93\) | 625072. | + | 1.08266e6i | 0.000866476 | + | 0.00150078i | ||||
\(94\) | −4.25610e8 | + | 7.37178e8i | −0.562259 | + | 0.973861i | ||||
\(95\) | 6.82447e8 | − | 1.18203e9i | 0.859632 | − | 1.48893i | ||||
\(96\) | −1.26826e6 | − | 2.19669e6i | −0.00152401 | − | 0.00263966i | ||||
\(97\) | −1.42804e9 | −1.63783 | −0.818914 | − | 0.573916i | \(-0.805424\pi\) | ||||
−0.818914 | + | 0.573916i | \(0.805424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.42514e8 | −0.358360 | ||||||||
\(100\) | −7.76908e8 | − | 1.34564e9i | −0.776908 | − | 1.34564i | ||||
\(101\) | −4.45766e8 | + | 7.72090e8i | −0.426247 | + | 0.738281i | −0.996536 | − | 0.0831631i | \(-0.973498\pi\) |
0.570289 | + | 0.821444i | \(0.306831\pi\) | |||||||
\(102\) | −1.61190e6 | + | 2.79190e6i | −0.00147448 | + | 0.00255387i | ||||
\(103\) | 3.56000e8 | + | 6.16610e8i | 0.311661 | + | 0.539813i | 0.978722 | − | 0.205190i | \(-0.0657813\pi\) |
−0.667061 | + | 0.745003i | \(0.732448\pi\) | |||||||
\(104\) | −3.70560e9 | −3.10605 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.49716e9 | −1.92119 | ||||||||
\(107\) | −1.24299e9 | − | 2.15292e9i | −0.916729 | − | 1.58782i | −0.804350 | − | 0.594156i | \(-0.797486\pi\) |
−0.112379 | − | 0.993665i | \(-0.535847\pi\) | |||||||
\(108\) | 5.64965e6 | − | 9.78548e6i | 0.00399590 | − | 0.00692110i | ||||
\(109\) | −1.91728e8 | + | 3.32082e8i | −0.130096 | + | 0.225334i | −0.923714 | − | 0.383084i | \(-0.874862\pi\) |
0.793617 | + | 0.608418i | \(0.208195\pi\) | |||||||
\(110\) | 6.51726e8 | + | 1.12882e9i | 0.424422 | + | 0.735121i | ||||
\(111\) | −705407. | −0.000441048 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.39582e9 | 1.38230 | 0.691148 | − | 0.722713i | \(-0.257105\pi\) | ||||
0.691148 | + | 0.722713i | \(0.257105\pi\) | |||||||
\(114\) | −3.69893e6 | − | 6.40674e6i | −0.00205118 | − | 0.00355276i | ||||
\(115\) | 1.10424e9 | − | 1.91260e9i | 0.588739 | − | 1.01973i | ||||
\(116\) | −3.91996e8 | + | 6.78957e8i | −0.201011 | + | 0.348162i | ||||
\(117\) | −1.20599e9 | − | 2.08883e9i | −0.594985 | − | 1.03054i | ||||
\(118\) | 2.52258e9 | 1.19778 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.25895e7 | −0.00554235 | ||||||||
\(121\) | 1.02757e9 | + | 1.77980e9i | 0.435789 | + | 0.754808i | ||||
\(122\) | 1.97380e8 | − | 3.41872e8i | 0.0806647 | − | 0.139715i | ||||
\(123\) | 856180. | − | 1.48295e6i | 0.000337281 | − | 0.000584188i | ||||
\(124\) | 3.32366e9 | + | 5.75675e9i | 1.26246 | + | 2.18665i | ||||
\(125\) | 1.24605e9 | 0.456501 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.88261e9 | 0.642161 | 0.321080 | − | 0.947052i | \(-0.395954\pi\) | ||||
0.321080 | + | 0.947052i | \(0.395954\pi\) | |||||||
\(128\) | 1.47619e7 | + | 2.55683e7i | 0.00486067 | + | 0.00841893i | ||||
\(129\) | 2.40459e6 | − | 4.16488e6i | 0.000764519 | − | 0.00132419i | ||||
\(130\) | −4.58944e9 | + | 7.94914e9i | −1.40934 | + | 2.44104i | ||||
\(131\) | 7.46207e8 | + | 1.29247e9i | 0.221380 | + | 0.383442i | 0.955227 | − | 0.295873i | \(-0.0956105\pi\) |
−0.733847 | + | 0.679315i | \(0.762277\pi\) | |||||||
\(132\) | 4.99480e6 | 0.00143198 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.16242e9 | −2.45493 | ||||||||
\(135\) | −8.19453e6 | − | 1.41933e7i | −0.00212335 | − | 0.00367775i | ||||
\(136\) | −5.01876e9 | + | 8.69275e9i | −1.25797 | + | 2.17887i | ||||
\(137\) | 1.60559e9 | − | 2.78096e9i | 0.389396 | − | 0.674454i | −0.602972 | − | 0.797762i | \(-0.706017\pi\) |
0.992368 | + | 0.123308i | \(0.0393504\pi\) | |||||||
\(138\) | −5.98509e6 | − | 1.03665e7i | −0.00140480 | − | 0.00243319i | ||||
\(139\) | −3.03934e9 | −0.690577 | −0.345289 | − | 0.938497i | \(-0.612219\pi\) | ||||
−0.345289 | + | 0.938497i | \(0.612219\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.73116e6 | 0.00100805 | ||||||||
\(142\) | 1.16782e9 | + | 2.02273e9i | 0.241035 | + | 0.417484i | ||||
\(143\) | 1.06620e9 | − | 1.84672e9i | 0.213220 | − | 0.369307i | ||||
\(144\) | 6.21538e9 | − | 1.07654e10i | 1.20458 | − | 2.08640i | ||||
\(145\) | 5.68570e8 | + | 9.84792e8i | 0.106814 | + | 0.185007i | ||||
\(146\) | 1.89920e10 | 3.45925 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.75082e9 | −0.642611 | ||||||||
\(149\) | 1.82143e9 | + | 3.15481e9i | 0.302743 | + | 0.524367i | 0.976756 | − | 0.214353i | \(-0.0687642\pi\) |
−0.674013 | + | 0.738719i | \(0.735431\pi\) | |||||||
\(150\) | −6.10773e6 | + | 1.05789e7i | −0.000985074 | + | 0.00170620i | ||||
\(151\) | −2.52931e9 | + | 4.38089e9i | −0.395919 | + | 0.685751i | −0.993218 | − | 0.116267i | \(-0.962907\pi\) |
0.597299 | + | 0.802018i | \(0.296240\pi\) | |||||||
\(152\) | −1.15169e10 | − | 1.99478e10i | −1.75000 | − | 3.03109i | ||||
\(153\) | −6.53341e9 | −0.963893 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.64159e9 | 1.34170 | ||||||||
\(156\) | 1.75866e7 | + | 3.04609e7i | 0.00237751 | + | 0.00411797i | ||||
\(157\) | 5.98434e9 | − | 1.03652e10i | 0.786082 | − | 1.36153i | −0.142269 | − | 0.989828i | \(-0.545440\pi\) |
0.928351 | − | 0.371706i | \(-0.121227\pi\) | |||||||
\(158\) | −9.42753e8 | + | 1.63290e9i | −0.120349 | + | 0.208450i | ||||
\(159\) | 6.93973e6 | + | 1.20200e7i | 0.000861104 | + | 0.00149148i | ||||
\(160\) | −1.95626e10 | −2.35986 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.61948e10 | 1.84739 | ||||||||
\(163\) | −7.04800e9 | − | 1.22075e10i | −0.782027 | − | 1.35451i | −0.930759 | − | 0.365633i | \(-0.880853\pi\) |
0.148733 | − | 0.988877i | \(-0.452481\pi\) | |||||||
\(164\) | 4.55251e9 | − | 7.88519e9i | 0.491421 | − | 0.851167i | ||||
\(165\) | 3.62235e6 | − | 6.27410e6i | 0.000380464 | − | 0.000658982i | ||||
\(166\) | 6.99482e9 | + | 1.21154e10i | 0.714974 | + | 1.23837i | ||||
\(167\) | 3.56028e9 | 0.354210 | 0.177105 | − | 0.984192i | \(-0.443327\pi\) | ||||
0.177105 | + | 0.984192i | \(0.443327\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.41184e9 | 0.416034 | ||||||||
\(170\) | 1.24316e10 | + | 2.15322e10i | 1.14158 | + | 1.97728i | ||||
\(171\) | 7.49632e9 | − | 1.29840e10i | 0.670449 | − | 1.16125i | ||||
\(172\) | 1.27858e10 | − | 2.21457e10i | 1.11391 | − | 1.92935i | ||||
\(173\) | −1.32034e9 | − | 2.28689e9i | −0.112067 | − | 0.194106i | 0.804537 | − | 0.593903i | \(-0.202414\pi\) |
−0.916604 | + | 0.399797i | \(0.869080\pi\) | |||||||
\(174\) | 6.16342e6 | 0.000509741 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.09899e10 | 0.863353 | ||||||||
\(177\) | −7.01038e6 | − | 1.21423e7i | −0.000536861 | − | 0.000929870i | ||||
\(178\) | −1.36250e10 | + | 2.35993e10i | −1.01730 | + | 1.76201i | ||||
\(179\) | −6.34867e8 | + | 1.09962e9i | −0.0462215 | + | 0.0800580i | −0.888211 | − | 0.459437i | \(-0.848051\pi\) |
0.841989 | + | 0.539495i | \(0.181385\pi\) | |||||||
\(180\) | −2.17861e10 | − | 3.77347e10i | −1.54687 | − | 2.67926i | ||||
\(181\) | −2.17242e10 | −1.50449 | −0.752247 | − | 0.658881i | \(-0.771030\pi\) | ||||
−0.752247 | + | 0.658881i | \(0.771030\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.19411e6 | −0.000144620 | ||||||||
\(184\) | −1.86350e10 | − | 3.22767e10i | −1.19853 | − | 2.07591i | ||||
\(185\) | −2.72019e9 | + | 4.71150e9i | −0.170736 | + | 0.295724i | ||||
\(186\) | 2.61292e7 | − | 4.52571e7i | 0.00160073 | − | 0.00277255i | ||||
\(187\) | −2.88807e9 | − | 5.00228e9i | −0.172711 | − | 0.299144i | ||||
\(188\) | 2.51567e10 | 1.46874 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.70552e10 | −3.17617 | ||||||||
\(191\) | 5.35175e9 | + | 9.26950e9i | 0.290968 | + | 0.503972i | 0.974039 | − | 0.226380i | \(-0.0726893\pi\) |
−0.683071 | + | 0.730352i | \(0.739356\pi\) | |||||||
\(192\) | −1.54519e7 | + | 2.67635e7i | −0.000820590 | + | 0.00142130i | ||||
\(193\) | −3.83031e9 | + | 6.63430e9i | −0.198713 | + | 0.344181i | −0.948111 | − | 0.317938i | \(-0.897010\pi\) |
0.749398 | + | 0.662119i | \(0.230343\pi\) | |||||||
\(194\) | 2.98475e10 | + | 5.16974e10i | 1.51286 | + | 2.62036i | ||||
\(195\) | 5.10170e7 | 0.00252673 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.26160e9 | −0.201592 | −0.100796 | − | 0.994907i | \(-0.532139\pi\) | ||||
−0.100796 | + | 0.994907i | \(0.532139\pi\) | |||||||
\(198\) | 7.15887e9 | + | 1.23995e10i | 0.331017 | + | 0.573339i | ||||
\(199\) | −1.58146e10 | + | 2.73916e10i | −0.714856 | + | 1.23817i | 0.248159 | + | 0.968719i | \(0.420174\pi\) |
−0.963015 | + | 0.269448i | \(0.913159\pi\) | |||||||
\(200\) | −1.90168e10 | + | 3.29381e10i | −0.840432 | + | 1.45567i | ||||
\(201\) | 2.54628e7 | + | 4.41029e7i | 0.00110033 | + | 0.00190583i | ||||
\(202\) | 3.72678e10 | 1.57490 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.52754e7 | 0.00385163 | ||||||||
\(205\) | −6.60319e9 | − | 1.14371e10i | −0.261133 | − | 0.452295i | ||||
\(206\) | 1.48815e10 | − | 2.57755e10i | 0.575763 | − | 0.997251i | ||||
\(207\) | 1.21295e10 | − | 2.10089e10i | 0.459172 | − | 0.795310i | ||||
\(208\) | 3.86954e10 | + | 6.70225e10i | 1.43342 | + | 2.48276i | ||||
\(209\) | 1.32549e10 | 0.480526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.76561e10 | 0.613229 | 0.306615 | − | 0.951834i | \(-0.400804\pi\) | ||||
0.306615 | + | 0.951834i | \(0.400804\pi\) | |||||||
\(212\) | 3.69002e10 | + | 6.39131e10i | 1.25464 | + | 2.17309i | ||||
\(213\) | 6.49087e6 | − | 1.12425e7i | 0.000216070 | − | 0.000374244i | ||||
\(214\) | −5.19594e10 | + | 8.99964e10i | −1.69357 | + | 2.93334i | ||||
\(215\) | −1.85452e10 | − | 3.21212e10i | −0.591913 | − | 1.02522i | ||||
\(216\) | −2.76579e8 | −0.00864525 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.60292e10 | 0.480681 | ||||||||
\(219\) | −5.27796e7 | − | 9.14169e7i | −0.00155048 | − | 0.00268552i | ||||
\(220\) | 1.92609e10 | − | 3.33609e10i | 0.554339 | − | 0.960143i | ||||
\(221\) | 2.03377e10 | − | 3.52259e10i | 0.573504 | − | 0.993339i | ||||
\(222\) | 1.47437e7 | + | 2.55368e7i | 0.000407397 | + | 0.000705632i | ||||
\(223\) | −1.04686e10 | −0.283476 | −0.141738 | − | 0.989904i | \(-0.545269\pi\) | ||||
−0.141738 | + | 0.989904i | \(0.545269\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.47560e10 | −0.643961 | ||||||||
\(226\) | −5.00749e10 | − | 8.67323e10i | −1.27683 | − | 2.21153i | ||||
\(227\) | −9.75213e9 | + | 1.68912e10i | −0.243772 | + | 0.422225i | −0.961786 | − | 0.273804i | \(-0.911718\pi\) |
0.718014 | + | 0.696029i | \(0.245051\pi\) | |||||||
\(228\) | −1.09317e8 | + | 1.89343e8i | −0.00267906 | + | 0.00464026i | ||||
\(229\) | 2.98067e10 | + | 5.16268e10i | 0.716234 | + | 1.24055i | 0.962482 | + | 0.271347i | \(0.0874690\pi\) |
−0.246248 | + | 0.969207i | \(0.579198\pi\) | |||||||
\(230\) | −9.23187e10 | −2.17528 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.91902e10 | 0.434894 | ||||||||
\(233\) | −4.21309e10 | − | 7.29729e10i | −0.936482 | − | 1.62203i | −0.771970 | − | 0.635659i | \(-0.780728\pi\) |
−0.164512 | − | 0.986375i | \(-0.552605\pi\) | |||||||
\(234\) | −5.04125e10 | + | 8.73171e10i | −1.09918 | + | 1.90383i | ||||
\(235\) | 1.82443e10 | − | 3.16000e10i | 0.390230 | − | 0.675899i | ||||
\(236\) | −3.72759e10 | − | 6.45637e10i | −0.782211 | − | 1.35483i | ||||
\(237\) | 1.04798e7 | 0.000215767 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.28353e10 | −1.44395 | −0.721974 | − | 0.691920i | \(-0.756765\pi\) | ||||
−0.721974 | + | 0.691920i | \(0.756765\pi\) | |||||||
\(240\) | 1.31465e8 | + | 2.27704e8i | 0.00255776 | + | 0.00443018i | ||||
\(241\) | −2.22778e10 | + | 3.85862e10i | −0.425397 | + | 0.736810i | −0.996457 | − | 0.0840985i | \(-0.973199\pi\) |
0.571060 | + | 0.820908i | \(0.306532\pi\) | |||||||
\(242\) | 4.29543e10 | − | 7.43990e10i | 0.805077 | − | 1.39443i | ||||
\(243\) | −1.35019e8 | − | 2.33860e8i | −0.00248408 | − | 0.00430256i | ||||
\(244\) | −1.16666e10 | −0.210713 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.15800e7 | −0.00124619 | ||||||||
\(247\) | 4.66702e10 | + | 8.08352e10i | 0.797818 | + | 1.38186i | ||||
\(248\) | 8.13550e10 | − | 1.40911e11i | 1.36569 | − | 2.36544i | ||||
\(249\) | 3.88778e7 | − | 6.73384e7i | 0.000640922 | − | 0.00111011i | ||||
\(250\) | −2.60437e10 | − | 4.51090e10i | −0.421670 | − | 0.730354i | ||||
\(251\) | −9.55068e10 | −1.51881 | −0.759404 | − | 0.650620i | \(-0.774509\pi\) | ||||
−0.759404 | + | 0.650620i | \(0.774509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.14472e10 | 0.329100 | ||||||||
\(254\) | −3.93484e10 | − | 6.81534e10i | −0.593165 | − | 1.02739i | ||||
\(255\) | 6.90960e7 | − | 1.19678e8i | 0.00102335 | − | 0.00177249i | ||||
\(256\) | 3.46680e10 | − | 6.00468e10i | 0.504486 | − | 0.873796i | ||||
\(257\) | −4.56397e10 | − | 7.90503e10i | −0.652595 | − | 1.13033i | −0.982491 | − | 0.186310i | \(-0.940347\pi\) |
0.329896 | − | 0.944017i | \(-0.392986\pi\) | |||||||
\(258\) | −2.01033e8 | −0.00282475 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.71270e11 | 3.68147 | ||||||||
\(261\) | 6.24544e9 | + | 1.08174e10i | 0.0833068 | + | 0.144292i | ||||
\(262\) | 3.11929e10 | − | 5.40277e10i | 0.408978 | − | 0.708371i | ||||
\(263\) | −7.54881e10 | + | 1.30749e11i | −0.972921 | + | 1.68515i | −0.286289 | + | 0.958143i | \(0.592422\pi\) |
−0.686632 | + | 0.727005i | \(0.740912\pi\) | |||||||
\(264\) | −6.11303e7 | − | 1.05881e8i | −0.000774531 | − | 0.00134153i | ||||
\(265\) | 1.07044e11 | 1.33338 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.51458e8 | 0.00182387 | ||||||||
\(268\) | 1.35392e11 | + | 2.34506e11i | 1.60319 | + | 2.77681i | ||||
\(269\) | −1.19811e10 | + | 2.07519e10i | −0.139512 | + | 0.241642i | −0.927312 | − | 0.374289i | \(-0.877887\pi\) |
0.787800 | + | 0.615931i | \(0.211220\pi\) | |||||||
\(270\) | −3.42547e8 | + | 5.93309e8i | −0.00392269 | + | 0.00679429i | ||||
\(271\) | 2.75624e10 | + | 4.77395e10i | 0.310424 | + | 0.537670i | 0.978454 | − | 0.206464i | \(-0.0661956\pi\) |
−0.668030 | + | 0.744134i | \(0.732862\pi\) | |||||||
\(272\) | 2.09632e11 | 2.32219 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.34233e11 | −1.43874 | ||||||||
\(275\) | −1.09433e10 | − | 1.89544e10i | −0.115386 | − | 0.199854i | ||||
\(276\) | −1.76882e8 | + | 3.06368e8i | −0.00183481 | + | 0.00317799i | ||||
\(277\) | −1.09816e10 | + | 1.90207e10i | −0.112074 | + | 0.194118i | −0.916606 | − | 0.399791i | \(-0.869083\pi\) |
0.804532 | + | 0.593909i | \(0.202416\pi\) | |||||||
\(278\) | 6.35251e10 | + | 1.10029e11i | 0.637887 | + | 1.10485i | ||||
\(279\) | 1.05908e11 | 1.04643 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.62670e10 | −0.155643 | −0.0778213 | − | 0.996967i | \(-0.524796\pi\) | ||||
−0.0778213 | + | 0.996967i | \(0.524796\pi\) | |||||||
\(282\) | −9.88858e7 | − | 1.71275e8i | −0.000931136 | − | 0.00161277i | ||||
\(283\) | −6.77949e9 | + | 1.17424e10i | −0.0628287 | + | 0.108823i | −0.895729 | − | 0.444601i | \(-0.853346\pi\) |
0.832900 | + | 0.553423i | \(0.186679\pi\) | |||||||
\(284\) | 3.45135e10 | − | 5.97792e10i | 0.314816 | − | 0.545277i | ||||
\(285\) | 1.58559e8 | + | 2.74632e8i | 0.00142360 | + | 0.00246575i | ||||
\(286\) | −8.91387e10 | −0.787805 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.14885e11 | −1.84052 | ||||||||
\(289\) | 4.20429e9 | + | 7.28205e9i | 0.0354530 | + | 0.0614063i | ||||
\(290\) | 2.37673e10 | − | 4.11662e10i | 0.197328 | − | 0.341783i | ||||
\(291\) | 1.65895e8 | − | 2.87339e8i | 0.00135617 | − | 0.00234896i | ||||
\(292\) | −2.80642e11 | − | 4.86086e11i | −2.25907 | − | 3.91282i | ||||
\(293\) | 5.41900e10 | 0.429551 | 0.214776 | − | 0.976663i | \(-0.431098\pi\) | ||||
0.214776 | + | 0.976663i | \(0.431098\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.08133e11 | −0.831306 | ||||||||
\(296\) | 4.59055e10 | + | 7.95106e10i | 0.347577 | + | 0.602022i | ||||
\(297\) | 7.95794e7 | − | 1.37836e8i | 0.000593467 | − | 0.00102791i | ||||
\(298\) | 7.61394e10 | − | 1.31877e11i | 0.559289 | − | 0.968716i | ||||
\(299\) | 7.55151e10 | + | 1.30796e11i | 0.546404 | + | 0.946399i | ||||
\(300\) | 3.61012e8 | 0.00257321 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.11460e11 | 1.46284 | ||||||||
\(303\) | −1.03569e8 | − | 1.79387e8i | −0.000705891 | − | 0.00122264i | ||||
\(304\) | −2.40528e11 | + | 4.16607e11i | −1.61523 | + | 2.79766i | ||||
\(305\) | −8.46092e9 | + | 1.46547e10i | −0.0559845 | + | 0.0969681i | ||||
\(306\) | 1.36555e11 | + | 2.36520e11i | 0.890349 | + | 1.54213i | ||||
\(307\) | 7.32498e10 | 0.470634 | 0.235317 | − | 0.971919i | \(-0.424387\pi\) | ||||
0.235317 | + | 0.971919i | \(0.424387\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.65425e8 | −0.00103226 | ||||||||
\(310\) | −2.01519e11 | − | 3.49041e11i | −1.23933 | − | 2.14659i | ||||
\(311\) | 1.22251e11 | − | 2.11745e11i | 0.741021 | − | 1.28349i | −0.211010 | − | 0.977484i | \(-0.567675\pi\) |
0.952031 | − | 0.306002i | \(-0.0989914\pi\) | |||||||
\(312\) | 4.30478e8 | − | 7.45610e8i | 0.00257191 | − | 0.00445467i | ||||
\(313\) | 2.19948e10 | + | 3.80960e10i | 0.129530 | + | 0.224352i | 0.923494 | − | 0.383612i | \(-0.125320\pi\) |
−0.793965 | + | 0.607964i | \(0.791987\pi\) | |||||||
\(314\) | −5.00314e11 | −2.90442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.57237e10 | 0.314375 | ||||||||
\(317\) | 1.08827e11 | + | 1.88493e11i | 0.605297 | + | 1.04841i | 0.992004 | + | 0.126203i | \(0.0402792\pi\) |
−0.386707 | + | 0.922203i | \(0.626387\pi\) | |||||||
\(318\) | 2.90094e8 | − | 5.02458e8i | 0.00159081 | − | 0.00275536i | ||||
\(319\) | −5.52154e9 | + | 9.56359e9i | −0.0298540 | + | 0.0517086i | ||||
\(320\) | 1.19171e11 | + | 2.06410e11i | 0.635324 | + | 1.10041i | ||||
\(321\) | 5.77591e8 | 0.00303632 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.52835e11 | 1.29249 | ||||||||
\(324\) | −2.39308e11 | − | 4.14494e11i | −1.20644 | − | 2.08961i | ||||
\(325\) | 7.70625e10 | − | 1.33476e11i | 0.383149 | − | 0.663634i | ||||
\(326\) | −2.94620e11 | + | 5.10297e11i | −1.44472 | + | 2.50233i | ||||
\(327\) | −4.45458e7 | − | 7.71556e7i | −0.000215448 | − | 0.000373167i | ||||
\(328\) | −2.22869e11 | −1.06321 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.02843e8 | −0.00140574 | ||||||||
\(331\) | 1.83473e11 | + | 3.17784e11i | 0.840128 | + | 1.45514i | 0.889786 | + | 0.456377i | \(0.150853\pi\) |
−0.0496587 | + | 0.998766i | \(0.515813\pi\) | |||||||
\(332\) | 2.06723e11 | − | 3.58055e11i | 0.933829 | − | 1.61744i | ||||
\(333\) | −2.98798e10 | + | 5.17533e10i | −0.133161 | + | 0.230642i | ||||
\(334\) | −7.44134e10 | − | 1.28888e11i | −0.327184 | − | 0.566699i | ||||
\(335\) | 3.92758e11 | 1.70382 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.99451e11 | 0.842367 | 0.421183 | − | 0.906976i | \(-0.361615\pi\) | ||||
0.421183 | + | 0.906976i | \(0.361615\pi\) | |||||||
\(338\) | −9.22117e10 | − | 1.59715e11i | −0.384291 | − | 0.665612i | ||||
\(339\) | −2.78321e8 | + | 4.82066e8i | −0.00114458 | + | 0.00198248i | ||||
\(340\) | 3.67400e11 | − | 6.36356e11i | 1.49102 | − | 2.58253i | ||||
\(341\) | 4.68161e10 | + | 8.10879e10i | 0.187500 | + | 0.324759i | ||||
\(342\) | −6.26721e11 | −2.47718 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.25931e11 | −2.40998 | ||||||||
\(345\) | 2.56558e8 | + | 4.44371e8i | 0.000974988 | + | 0.00168873i | ||||
\(346\) | −5.51927e10 | + | 9.55966e10i | −0.207033 | + | 0.358591i | ||||
\(347\) | −3.31590e10 | + | 5.74330e10i | −0.122777 | + | 0.212657i | −0.920862 | − | 0.389889i | \(-0.872513\pi\) |
0.798085 | + | 0.602545i | \(0.205847\pi\) | |||||||
\(348\) | −9.10759e7 | − | 1.57748e8i | −0.000332887 | − | 0.000576577i | ||||
\(349\) | −1.20301e11 | −0.434065 | −0.217033 | − | 0.976164i | \(-0.569638\pi\) | ||||
−0.217033 | + | 0.976164i | \(0.569638\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.12079e9 | 0.00394133 | ||||||||
\(352\) | −9.49890e10 | − | 1.64526e11i | −0.329786 | − | 0.571205i | ||||
\(353\) | −1.21530e11 | + | 2.10497e11i | −0.416580 | + | 0.721537i | −0.995593 | − | 0.0937810i | \(-0.970105\pi\) |
0.579013 | + | 0.815318i | \(0.303438\pi\) | |||||||
\(354\) | −2.93047e8 | + | 5.07573e8i | −0.000991798 | + | 0.00171784i | ||||
\(355\) | −5.00601e10 | − | 8.67066e10i | −0.167288 | − | 0.289751i | ||||
\(356\) | 8.05341e11 | 2.65739 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.30773e10 | 0.170779 | ||||||||
\(359\) | −1.40827e11 | − | 2.43919e11i | −0.447466 | − | 0.775034i | 0.550754 | − | 0.834668i | \(-0.314340\pi\) |
−0.998220 | + | 0.0596332i | \(0.981007\pi\) | |||||||
\(360\) | −5.33271e11 | + | 9.23652e11i | −1.67335 | + | 2.89833i | ||||
\(361\) | −1.28755e11 | + | 2.23010e11i | −0.399008 | + | 0.691101i | ||||
\(362\) | 4.54057e11 | + | 7.86450e11i | 1.38970 | + | 2.40704i | ||||
\(363\) | −4.77488e8 | −0.00144339 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.14113e11 | −2.40086 | ||||||||
\(366\) | 4.58591e7 | + | 7.94302e7i | 0.000133586 | + | 0.000231377i | ||||
\(367\) | 1.20500e11 | − | 2.08712e11i | 0.346729 | − | 0.600552i | −0.638937 | − | 0.769259i | \(-0.720626\pi\) |
0.985666 | + | 0.168707i | \(0.0539590\pi\) | |||||||
\(368\) | −3.89188e11 | + | 6.74094e11i | −1.10623 | + | 1.91604i | ||||
\(369\) | −7.25325e10 | − | 1.25630e11i | −0.203664 | − | 0.352756i | ||||
\(370\) | 2.27418e11 | 0.630837 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.54443e9 | −0.00418143 | ||||||||
\(373\) | 6.69605e10 | + | 1.15979e11i | 0.179114 | + | 0.310234i | 0.941577 | − | 0.336797i | \(-0.109344\pi\) |
−0.762464 | + | 0.647031i | \(0.776010\pi\) | |||||||
\(374\) | −1.20727e11 | + | 2.09105e11i | −0.319067 | + | 0.552640i | ||||
\(375\) | −1.44753e8 | + | 2.50720e8i | −0.000377997 | + | 0.000654709i | ||||
\(376\) | −3.07887e11 | − | 5.33277e11i | −0.794414 | − | 1.37596i | ||||
\(377\) | −7.77651e10 | −0.198266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.67201e11 | 1.41208 | 0.706042 | − | 0.708170i | \(-0.250479\pi\) | ||||
0.706042 | + | 0.708170i | \(0.250479\pi\) | |||||||
\(380\) | 8.43097e11 | + | 1.46029e12i | 2.07420 | + | 3.59263i | ||||
\(381\) | −2.18702e8 | + | 3.78803e8i | −0.000531729 | + | 0.000920982i | ||||
\(382\) | 2.23714e11 | − | 3.87483e11i | 0.537536 | − | 0.931039i | ||||
\(383\) | 5.17543e10 | + | 8.96411e10i | 0.122900 | + | 0.212869i | 0.920910 | − | 0.389775i | \(-0.127447\pi\) |
−0.798010 | + | 0.602644i | \(0.794114\pi\) | |||||||
\(384\) | −6.85951e6 | −1.60991e−5 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.20229e11 | 0.734206 | ||||||||
\(387\) | −2.03709e11 | − | 3.52834e11i | −0.461647 | − | 0.799597i | ||||
\(388\) | 8.82104e11 | − | 1.52785e12i | 1.97596 | − | 3.42245i | ||||
\(389\) | 2.91800e11 | − | 5.05413e11i | 0.646119 | − | 1.11911i | −0.337923 | − | 0.941174i | \(-0.609724\pi\) |
0.984042 | − | 0.177937i | \(-0.0569422\pi\) | |||||||
\(390\) | −1.06631e9 | − | 1.84690e9i | −0.00233395 | − | 0.00404251i | ||||
\(391\) | 4.09102e11 | 0.885190 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.46746e8 | −0.000733238 | ||||||||
\(394\) | 8.90715e10 | + | 1.54276e11i | 0.186211 | + | 0.322527i | ||||
\(395\) | 4.04122e10 | − | 6.99959e10i | 0.0835267 | − | 0.144672i | ||||
\(396\) | 2.11571e11 | − | 3.66452e11i | 0.432343 | − | 0.748839i | ||||
\(397\) | 3.27271e10 | + | 5.66850e10i | 0.0661226 | + | 0.114528i | 0.897191 | − | 0.441642i | \(-0.145604\pi\) |
−0.831069 | + | 0.556170i | \(0.812270\pi\) | |||||||
\(398\) | 1.32216e12 | 2.64125 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.94326e11 | 1.55142 | ||||||||
\(401\) | −2.03324e10 | − | 3.52167e10i | −0.0392679 | − | 0.0680141i | 0.845723 | − | 0.533621i | \(-0.179169\pi\) |
−0.884991 | + | 0.465607i | \(0.845836\pi\) | |||||||
\(402\) | 1.06439e9 | − | 1.84359e9i | 0.00203276 | − | 0.00352084i | ||||
\(403\) | −3.29678e11 | + | 5.71019e11i | −0.622611 | + | 1.07839i | ||||
\(404\) | −5.50701e11 | − | 9.53842e11i | −1.02849 | − | 1.78139i | ||||
\(405\) | −6.94209e11 | −1.28216 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.28330e10 | −0.0954400 | ||||||||
\(408\) | −1.16605e9 | − | 2.01967e9i | −0.00208328 | − | 0.00360835i | ||||
\(409\) | −5.30816e11 | + | 9.19400e11i | −0.937970 | + | 1.62461i | −0.168720 | + | 0.985664i | \(0.553963\pi\) |
−0.769250 | + | 0.638948i | \(0.779370\pi\) | |||||||
\(410\) | −2.76026e11 | + | 4.78091e11i | −0.482417 | + | 0.835571i | ||||
\(411\) | 3.73041e8 | + | 6.46126e8i | 0.000644864 | + | 0.00111694i | ||||
\(412\) | −8.79607e11 | −1.50401 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.01407e12 | −1.69655 | ||||||||
\(415\) | −2.99841e11 | − | 5.19340e11i | −0.496220 | − | 0.859479i | ||||
\(416\) | 6.68910e11 | − | 1.15859e12i | 1.09509 | − | 1.89674i | ||||
\(417\) | 3.53078e8 | − | 6.11550e8i | 0.000571819 | − | 0.000990420i | ||||
\(418\) | −2.77040e11 | − | 4.79847e11i | −0.443863 | − | 0.768793i | ||||
\(419\) | −1.19335e12 | −1.89149 | −0.945744 | − | 0.324912i | \(-0.894665\pi\) | ||||
−0.945744 | + | 0.324912i | \(0.894665\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.88397e11 | −0.912853 | −0.456427 | − | 0.889761i | \(-0.650871\pi\) | ||||
−0.456427 | + | 0.889761i | \(0.650871\pi\) | |||||||
\(422\) | −3.69029e11 | − | 6.39177e11i | −0.566441 | − | 0.981104i | ||||
\(423\) | 2.00404e11 | − | 3.47109e11i | 0.304350 | − | 0.527150i | ||||
\(424\) | 9.03228e11 | − | 1.56444e12i | 1.35722 | − | 2.35078i | ||||
\(425\) | −2.08742e11 | − | 3.61553e11i | −0.310356 | − | 0.537553i | ||||
\(426\) | −5.42662e8 | −0.000798337 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.07119e12 | 4.42394 | ||||||||
\(429\) | 2.47720e8 | + | 4.29064e8i | 0.000353105 | + | 0.000611596i | ||||
\(430\) | −7.75224e11 | + | 1.34273e12i | −1.09350 | + | 1.89400i | ||||
\(431\) | 6.14658e11 | − | 1.06462e12i | 0.857997 | − | 1.48609i | −0.0158402 | − | 0.999875i | \(-0.505042\pi\) |
0.873837 | − | 0.486219i | \(-0.161624\pi\) | |||||||
\(432\) | 2.88816e9 | + | 5.00243e9i | 0.00398973 | + | 0.00691042i | ||||
\(433\) | −4.73819e10 | −0.0647764 | −0.0323882 | − | 0.999475i | \(-0.510311\pi\) | ||||
−0.0323882 | + | 0.999475i | \(0.510311\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.64202e8 | −0.000353781 | ||||||||
\(436\) | −2.36861e11 | − | 4.10255e11i | −0.313909 | − | 0.543707i | ||||
\(437\) | −4.69397e11 | + | 8.13019e11i | −0.615706 | + | 1.06643i | ||||
\(438\) | −2.20629e9 | + | 3.82141e9i | −0.00286437 | + | 0.00496123i | ||||
\(439\) | −3.07118e11 | − | 5.31944e11i | −0.394652 | − | 0.683558i | 0.598404 | − | 0.801194i | \(-0.295802\pi\) |
−0.993057 | + | 0.117636i | \(0.962468\pi\) | |||||||
\(440\) | −9.42921e11 | −1.19933 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.70031e12 | −2.11899 | ||||||||
\(443\) | 4.09600e11 | + | 7.09447e11i | 0.505292 | + | 0.875192i | 0.999981 | + | 0.00612197i | \(0.00194869\pi\) |
−0.494689 | + | 0.869070i | \(0.664718\pi\) | |||||||
\(444\) | 4.35731e8 | − | 7.54708e8i | 0.000532102 | − | 0.000921628i | ||||
\(445\) | 5.84053e11 | − | 1.01161e12i | 0.706045 | − | 1.22291i | ||||
\(446\) | 2.18804e11 | + | 3.78979e11i | 0.261847 | + | 0.453532i | ||||
\(447\) | −8.46379e8 | −0.00100272 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.81029e11 | 0.558551 | 0.279276 | − | 0.960211i | \(-0.409906\pi\) | ||||
0.279276 | + | 0.960211i | \(0.409906\pi\) | |||||||
\(450\) | 5.17425e11 | + | 8.96207e11i | 0.594828 | + | 1.03027i | ||||
\(451\) | 6.41254e10 | − | 1.11069e11i | 0.0729854 | − | 0.126414i | ||||
\(452\) | −1.47990e12 | + | 2.56326e12i | −1.66767 | + | 2.88849i | ||||
\(453\) | −5.87658e8 | − | 1.01785e9i | −0.000655666 | − | 0.00113565i | ||||
\(454\) | 8.15316e11 | 0.900689 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.35164e9 | 0.00579622 | ||||||||
\(457\) | −5.76641e11 | − | 9.98771e11i | −0.618419 | − | 1.07113i | −0.989774 | − | 0.142642i | \(-0.954440\pi\) |
0.371356 | − | 0.928491i | \(-0.378893\pi\) | |||||||
\(458\) | 1.24598e12 | − | 2.15810e12i | 1.32317 | − | 2.29180i | ||||
\(459\) | 1.51797e9 | − | 2.62920e9i | 0.00159627 | − | 0.00276482i | ||||
\(460\) | 1.36418e12 | + | 2.36283e12i | 1.42057 | + | 2.46049i | ||||
\(461\) | −6.06986e11 | −0.625928 | −0.312964 | − | 0.949765i | \(-0.601322\pi\) | ||||
−0.312964 | + | 0.949765i | \(0.601322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.87758e11 | −0.897801 | −0.448900 | − | 0.893582i | \(-0.648184\pi\) | ||||
−0.448900 | + | 0.893582i | \(0.648184\pi\) | |||||||
\(464\) | −2.00392e11 | − | 3.47089e11i | −0.200701 | − | 0.347624i | ||||
\(465\) | −1.12006e9 | + | 1.94000e9i | −0.00111097 | + | 0.00192426i | ||||
\(466\) | −1.76115e12 | + | 3.05041e12i | −1.73006 | + | 2.99655i | ||||
\(467\) | 5.48897e11 | + | 9.50717e11i | 0.534029 | + | 0.924965i | 0.999210 | + | 0.0397495i | \(0.0126560\pi\) |
−0.465181 | + | 0.885216i | \(0.654011\pi\) | |||||||
\(468\) | 2.97976e12 | 2.87127 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.52529e12 | −1.44182 | ||||||||
\(471\) | 1.39040e9 | + | 2.40824e9i | 0.00130180 | + | 0.00225478i | ||||
\(472\) | −9.12422e11 | + | 1.58036e12i | −0.846169 | + | 1.46561i | ||||
\(473\) | 1.80097e11 | − | 3.11938e11i | 0.165437 | − | 0.286545i | ||||
\(474\) | −2.19038e8 | − | 3.79385e8i | −0.000199305 | − | 0.000345206i | ||||
\(475\) | 9.58029e11 | 0.863490 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.17582e12 | 1.03994 | ||||||||
\(478\) | 1.52233e12 | + | 2.63675e12i | 1.33378 | + | 2.31017i | ||||
\(479\) | 1.56114e11 | − | 2.70398e11i | 0.135498 | − | 0.234690i | −0.790290 | − | 0.612734i | \(-0.790070\pi\) |
0.925788 | + | 0.378044i | \(0.123403\pi\) | |||||||
\(480\) | 2.27258e9 | − | 3.93622e9i | 0.00195404 | − | 0.00338450i | ||||
\(481\) | −1.86024e11 | − | 3.22203e11i | −0.158459 | − | 0.274459i | ||||
\(482\) | 1.86251e12 | 1.57176 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.53892e12 | −2.10303 | ||||||||
\(485\) | −1.27945e12 | − | 2.21607e12i | −1.04999 | − | 1.81863i | ||||
\(486\) | −5.64405e9 | + | 9.77578e9i | −0.00458910 | + | 0.00794856i | ||||
\(487\) | −5.41887e11 | + | 9.38575e11i | −0.436544 | + | 0.756116i | −0.997420 | − | 0.0717832i | \(-0.977131\pi\) |
0.560876 | + | 0.827900i | \(0.310464\pi\) | |||||||
\(488\) | 1.42785e11 | + | 2.47311e11i | 0.113971 | + | 0.197403i | ||||
\(489\) | 3.27505e9 | 0.00259017 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.14702e12 | 1.66713 | 0.833567 | − | 0.552419i | \(-0.186295\pi\) | ||||
0.833567 | + | 0.552419i | \(0.186295\pi\) | |||||||
\(492\) | 1.05773e9 | + | 1.83204e9i | 0.000813824 | + | 0.00140958i | ||||
\(493\) | −1.05323e11 | + | 1.82425e11i | −0.0802993 | + | 0.139082i | ||||
\(494\) | 1.95091e12 | − | 3.37907e12i | 1.47389 | − | 2.55285i | ||||
\(495\) | −3.06873e11 | − | 5.31520e11i | −0.229739 | − | 0.397920i | ||||
\(496\) | −3.39817e12 | −2.52103 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.25034e9 | −0.00236808 | ||||||||
\(499\) | 9.28525e11 | + | 1.60825e12i | 0.670411 | + | 1.16119i | 0.977788 | + | 0.209598i | \(0.0672154\pi\) |
−0.307377 | + | 0.951588i | \(0.599451\pi\) | |||||||
\(500\) | −7.69688e11 | + | 1.33314e12i | −0.550744 | + | 0.953917i | ||||
\(501\) | −4.13596e8 | + | 7.16370e8i | −0.000293297 | + | 0.000508005i | ||||
\(502\) | 1.99619e12 | + | 3.45750e12i | 1.40292 | + | 2.42994i | ||||
\(503\) | −1.59040e12 | −1.10777 | −0.553885 | − | 0.832593i | \(-0.686855\pi\) | ||||
−0.553885 | + | 0.832593i | \(0.686855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.59753e12 | −1.09304 | ||||||||
\(506\) | −4.48266e11 | − | 7.76420e11i | −0.303990 | − | 0.526526i | ||||
\(507\) | −5.12521e8 | + | 8.87712e8i | −0.000344489 | + | 0.000596673i | ||||
\(508\) | −1.16289e12 | + | 2.01419e12i | −0.774734 | + | 1.34188i | ||||
\(509\) | −1.16432e12 | − | 2.01667e12i | −0.768853 | − | 1.33169i | −0.938185 | − | 0.346133i | \(-0.887495\pi\) |
0.169333 | − | 0.985559i | \(-0.445839\pi\) | |||||||
\(510\) | −5.77670e9 | −0.00378106 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.88327e12 | −1.85426 | ||||||||
\(513\) | 3.48338e9 | + | 6.03339e9i | 0.00222061 | + | 0.00384621i | ||||
\(514\) | −1.90783e12 | + | 3.30446e12i | −1.20561 | + | 2.08817i | ||||
\(515\) | −6.37912e11 | + | 1.10490e12i | −0.399603 | + | 0.692132i | ||||
\(516\) | 2.97064e9 | + | 5.14530e9i | 0.00184470 | + | 0.00319512i | ||||
\(517\) | 3.54350e11 | 0.218135 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.13532e8 | 0.000371180 | ||||||||
\(520\) | −3.32001e12 | − | 5.75043e12i | −1.99124 | − | 3.44894i | ||||
\(521\) | 7.41832e11 | − | 1.28489e12i | 0.441099 | − | 0.764005i | −0.556673 | − | 0.830732i | \(-0.687922\pi\) |
0.997771 | + | 0.0667268i | \(0.0212556\pi\) | |||||||
\(522\) | 2.61071e11 | − | 4.52189e11i | 0.153901 | − | 0.266565i | ||||
\(523\) | 9.77922e11 | + | 1.69381e12i | 0.571540 | + | 0.989936i | 0.996408 | + | 0.0846808i | \(0.0269871\pi\) |
−0.424868 | + | 0.905255i | \(0.639680\pi\) | |||||||
\(524\) | −1.84373e12 | −1.06833 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.31110e12 | 3.59475 | ||||||||
\(527\) | 8.93013e11 | + | 1.54674e12i | 0.504324 | + | 0.873516i | ||||
\(528\) | −1.27670e9 | + | 2.21130e9i | −0.000714883 | + | 0.00123821i | ||||
\(529\) | 1.41065e11 | − | 2.44332e11i | 0.0783195 | − | 0.135653i | ||||
\(530\) | −2.23732e12 | − | 3.87515e12i | −1.23165 | − | 2.13328i | ||||
\(531\) | −1.18779e12 | −0.648357 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.03139e11 | 0.484710 | ||||||||
\(534\) | −3.16563e9 | − | 5.48303e9i | −0.00168471 | − | 0.00291800i | ||||
\(535\) | 2.22730e12 | − | 3.85780e12i | 1.17540 | − | 2.03586i | ||||
\(536\) | 3.31406e12 | − | 5.74012e12i | 1.73428 | − | 3.00386i | ||||
\(537\) | −1.47504e8 | − | 2.55485e8i | −7.65457e−5 | − | 0.000132581i | ||||
\(538\) | 1.00167e12 | 0.515470 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.02471e10 | 0.0102469 | ||||||||
\(541\) | 6.74009e11 | + | 1.16742e12i | 0.338281 | + | 0.585921i | 0.984110 | − | 0.177562i | \(-0.0568211\pi\) |
−0.645828 | + | 0.763483i | \(0.723488\pi\) | |||||||
\(542\) | 1.15216e12 | − | 1.99560e12i | 0.573478 | − | 0.993294i | ||||
\(543\) | 2.52369e9 | − | 4.37116e9i | 0.00124577 | − | 0.00215773i | ||||
\(544\) | −1.81191e12 | − | 3.13832e12i | −0.887035 | − | 1.53639i | ||||
\(545\) | −6.87109e11 | −0.333612 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.02503e12 | 0.489548 | 0.244774 | − | 0.969580i | \(-0.421286\pi\) | ||||
0.244774 | + | 0.969580i | \(0.421286\pi\) | |||||||
\(548\) | 1.98355e12 | + | 3.43561e12i | 0.939572 | + | 1.62739i | ||||
\(549\) | −9.29387e10 | + | 1.60975e11i | −0.0436637 | + | 0.0756278i | ||||
\(550\) | −4.57451e11 | + | 7.92329e11i | −0.213164 | + | 0.369210i | ||||
\(551\) | −2.41691e11 | − | 4.18621e11i | −0.111706 | − | 0.193481i | ||||
\(552\) | 8.65926e9 | 0.00396968 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.18103e11 | 0.414093 | ||||||||
\(555\) | −6.32005e8 | − | 1.09467e9i | −0.000282750 | − | 0.000489737i | ||||
\(556\) | 1.87740e12 | − | 3.25176e12i | 0.833146 | − | 1.44305i | ||||
\(557\) | −8.76717e11 | + | 1.51852e12i | −0.385932 | + | 0.668454i | −0.991898 | − | 0.127037i | \(-0.959453\pi\) |
0.605966 | + | 0.795491i | \(0.292787\pi\) | |||||||
\(558\) | −2.21358e12 | − | 3.83403e12i | −0.966586 | − | 1.67418i | ||||
\(559\) | 2.53648e12 | 1.09870 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.34202e9 | 0.000572041 | ||||||||
\(562\) | 3.39996e11 | + | 5.88890e11i | 0.143767 | + | 0.249012i | ||||
\(563\) | 1.08728e12 | − | 1.88322e12i | 0.456092 | − | 0.789975i | −0.542658 | − | 0.839954i | \(-0.682582\pi\) |
0.998750 | + | 0.0499786i | \(0.0159153\pi\) | |||||||
\(564\) | −2.92244e9 | + | 5.06182e9i | −0.00121616 | + | 0.00210645i | ||||
\(565\) | 2.14652e12 | + | 3.71788e12i | 0.886170 | + | 1.53489i | ||||
\(566\) | 5.66792e11 | 0.232140 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.68961e12 | −0.681114 | ||||||||
\(569\) | −1.56906e12 | − | 2.71770e12i | −0.627531 | − | 1.08692i | −0.988046 | − | 0.154162i | \(-0.950732\pi\) |
0.360515 | − | 0.932753i | \(-0.382601\pi\) | |||||||
\(570\) | 6.62808e9 | − | 1.14802e10i | 0.00262997 | − | 0.00455524i | ||||
\(571\) | −1.02990e12 | + | 1.78383e12i | −0.405444 | + | 0.702249i | −0.994373 | − | 0.105935i | \(-0.966216\pi\) |
0.588929 | + | 0.808185i | \(0.299550\pi\) | |||||||
\(572\) | 1.31719e12 | + | 2.28144e12i | 0.514477 | + | 0.891100i | ||||
\(573\) | −2.48684e9 | −0.000963723 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.55015e12 | 0.591381 | ||||||||
\(576\) | 1.30903e12 | + | 2.26731e12i | 0.495505 | + | 0.858240i | ||||
\(577\) | −1.97190e12 | + | 3.41543e12i | −0.740617 | + | 1.28279i | 0.211597 | + | 0.977357i | \(0.432134\pi\) |
−0.952214 | + | 0.305430i | \(0.901200\pi\) | |||||||
\(578\) | 1.75748e11 | − | 3.04404e11i | 0.0654959 | − | 0.113442i | ||||
\(579\) | −8.89931e8 | − | 1.54141e9i | −0.000329081 | − | 0.000569985i | ||||
\(580\) | −1.40483e12 | −0.515462 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.38695e10 | −0.00501079 | ||||||||
\(583\) | 5.19766e11 | + | 9.00262e11i | 0.186337 | + | 0.322746i | ||||
\(584\) | −6.86943e12 | + | 1.18982e13i | −2.44378 | + | 4.23276i | ||||
\(585\) | 2.16099e12 | − | 3.74295e12i | 0.762872 | − | 1.32133i | ||||
\(586\) | −1.13262e12 | − | 1.96176e12i | −0.396777 | − | 0.687238i | ||||
\(587\) | 3.68239e12 | 1.28014 | 0.640071 | − | 0.768315i | \(-0.278905\pi\) | ||||
0.640071 | + | 0.768315i | \(0.278905\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.09851e12 | −1.40316 | ||||||||
\(590\) | 2.26009e12 | + | 3.91460e12i | 0.767879 | + | 1.33000i | ||||
\(591\) | 4.95068e8 | − | 8.57482e8i | 0.000166925 | − | 0.000289122i | ||||
\(592\) | 9.58728e11 | − | 1.66057e12i | 0.320810 | − | 0.555659i | ||||
\(593\) | 5.85568e11 | + | 1.01423e12i | 0.194460 | + | 0.336815i | 0.946724 | − | 0.322048i | \(-0.104371\pi\) |
−0.752263 | + | 0.658863i | \(0.771038\pi\) | |||||||
\(594\) | −6.65315e9 | −0.00219274 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.50040e12 | −1.46098 | ||||||||
\(597\) | −3.67434e9 | − | 6.36415e9i | −0.00118385 | − | 0.00205048i | ||||
\(598\) | 3.15668e12 | − | 5.46753e12i | 1.00943 | − | 1.74838i | ||||
\(599\) | −1.41878e12 | + | 2.45740e12i | −0.450293 | + | 0.779931i | −0.998404 | − | 0.0564751i | \(-0.982014\pi\) |
0.548111 | + | 0.836406i | \(0.315347\pi\) | |||||||
\(600\) | −4.41835e9 | − | 7.65280e9i | −0.00139181 | − | 0.00241068i | ||||
\(601\) | 2.37066e12 | 0.741198 | 0.370599 | − | 0.928793i | \(-0.379152\pi\) | ||||
0.370599 | + | 0.928793i | \(0.379152\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.31424e12 | 1.32885 | ||||||||
\(604\) | −3.12472e12 | − | 5.41217e12i | −0.955310 | − | 1.65465i | ||||
\(605\) | −1.84129e12 | + | 3.18920e12i | −0.558756 | + | 0.967793i | ||||
\(606\) | −4.32938e9 | + | 7.49871e9i | −0.00130406 | + | 0.00225871i | ||||
\(607\) | −2.20040e12 | − | 3.81120e12i | −0.657889 | − | 1.13950i | −0.981161 | − | 0.193191i | \(-0.938116\pi\) |
0.323273 | − | 0.946306i | \(-0.395217\pi\) | |||||||
\(608\) | 8.31580e12 | 2.46796 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.07366e11 | 0.206852 | ||||||||
\(611\) | 1.24766e12 | + | 2.16102e12i | 0.362169 | + | 0.627296i | ||||
\(612\) | 4.03570e12 | − | 6.99003e12i | 1.16289 | − | 2.01418i | ||||
\(613\) | 9.37851e11 | − | 1.62441e12i | 0.268264 | − | 0.464646i | −0.700150 | − | 0.713996i | \(-0.746883\pi\) |
0.968414 | + | 0.249350i | \(0.0802168\pi\) | |||||||
\(614\) | −1.53099e12 | − | 2.65176e12i | −0.434726 | − | 0.752967i | ||||
\(615\) | 3.06836e9 | 0.000864904 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.18170e12 | −0.883845 | −0.441922 | − | 0.897053i | \(-0.645703\pi\) | ||||
−0.441922 | + | 0.897053i | \(0.645703\pi\) | |||||||
\(618\) | 3.45755e9 | + | 5.98865e9i | 0.000953500 | + | 0.00165151i | ||||
\(619\) | 5.82378e10 | − | 1.00871e11i | 0.0159440 | − | 0.0276158i | −0.857943 | − | 0.513744i | \(-0.828258\pi\) |
0.873887 | + | 0.486129i | \(0.161591\pi\) | |||||||
\(620\) | −5.95563e12 | + | 1.03154e13i | −1.61869 | + | 2.80366i | ||||
\(621\) | 5.63631e9 | + | 9.76238e9i | 0.00152084 | + | 0.00263417i | ||||
\(622\) | −1.02207e13 | −2.73793 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.79809e10 | −0.00474768 | ||||||||
\(625\) | 2.34466e12 | + | 4.06106e12i | 0.614637 | + | 1.06458i | ||||
\(626\) | 9.19423e11 | − | 1.59249e12i | 0.239294 | − | 0.414469i | ||||
\(627\) | −1.53981e9 | + | 2.66703e9i | −0.000397891 | + | 0.000689167i | ||||
\(628\) | 7.39307e12 | + | 1.28052e13i | 1.89673 | + | 3.28524i | ||||
\(629\) | −1.00778e12 | −0.256708 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.71283e12 | −0.932338 | −0.466169 | − | 0.884696i | \(-0.654366\pi\) | ||||
−0.466169 | + | 0.884696i | \(0.654366\pi\) | |||||||
\(632\) | −6.81990e11 | − | 1.18124e12i | −0.170040 | − | 0.294518i | ||||
\(633\) | −2.05110e9 | + | 3.55260e9i | −0.000507773 | + | 0.000879488i | ||||
\(634\) | 4.54917e12 | − | 7.87939e12i | 1.11823 | − | 1.93683i | ||||
\(635\) | 1.68671e12 | + | 2.92148e12i | 0.411680 | + | 0.713051i | ||||
\(636\) | −1.71467e10 | −0.00415551 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.61622e11 | 0.110305 | ||||||||
\(639\) | −5.49884e11 | − | 9.52426e11i | −0.130472 | − | 0.225984i | ||||
\(640\) | −2.64516e10 | + | 4.58155e10i | −0.00623221 | + | 0.0107945i | ||||
\(641\) | −1.46882e11 | + | 2.54407e11i | −0.0343642 | + | 0.0595206i | −0.882696 | − | 0.469944i | \(-0.844274\pi\) |
0.848332 | + | 0.529465i | \(0.177607\pi\) | |||||||
\(642\) | −1.20722e10 | − | 2.09097e10i | −0.00280465 | − | 0.00485780i | ||||
\(643\) | 5.27980e12 | 1.21806 | 0.609029 | − | 0.793148i | \(-0.291559\pi\) | ||||
0.609029 | + | 0.793148i | \(0.291559\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.61753e9 | 0.00196049 | ||||||||
\(646\) | −5.28451e12 | − | 9.15303e12i | −1.19387 | − | 2.06785i | ||||
\(647\) | 1.31000e12 | − | 2.26899e12i | 0.293902 | − | 0.509053i | −0.680827 | − | 0.732444i | \(-0.738379\pi\) |
0.974729 | + | 0.223391i | \(0.0717128\pi\) | |||||||
\(648\) | −5.85768e12 | + | 1.01458e13i | −1.30508 | + | 2.26047i | ||||
\(649\) | −5.25057e11 | − | 9.09426e11i | −0.116173 | − | 0.201218i | ||||
\(650\) | −6.44272e12 | −1.41566 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.74142e13 | 3.77390 | ||||||||
\(653\) | −1.57959e12 | − | 2.73593e12i | −0.339965 | − | 0.588837i | 0.644460 | − | 0.764638i | \(-0.277082\pi\) |
−0.984426 | + | 0.175800i | \(0.943749\pi\) | |||||||
\(654\) | −1.86210e9 | + | 3.22526e9i | −0.000398019 | + | 0.000689389i | ||||
\(655\) | −1.33712e12 | + | 2.31596e12i | −0.283847 | + | 0.491638i | ||||
\(656\) | 2.32729e12 | + | 4.03098e12i | 0.490663 | + | 0.849853i | ||||
\(657\) | −8.94260e12 | −1.87249 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.77292e11 | 0.181201 | 0.0906004 | − | 0.995887i | \(-0.471121\pi\) | ||||
0.0906004 | + | 0.995887i | \(0.471121\pi\) | |||||||
\(660\) | 4.47507e9 | + | 7.75104e9i | 0.000918019 | + | 0.00159006i | ||||
\(661\) | −4.11054e12 | + | 7.11966e12i | −0.837514 | + | 1.45062i | 0.0544528 | + | 0.998516i | \(0.482659\pi\) |
−0.891967 | + | 0.452101i | \(0.850675\pi\) | |||||||
\(662\) | 7.66951e12 | − | 1.32840e13i | 1.55205 | − | 2.68824i | ||||
\(663\) | 4.72524e9 | + | 8.18436e9i | 0.000949759 | + | 0.00164503i | ||||
\(664\) | −1.01201e13 | −2.02037 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.49807e12 | 0.492006 | ||||||||
\(667\) | −3.91070e11 | − | 6.77354e11i | −0.0765048 | − | 0.132510i | ||||
\(668\) | −2.19919e12 | + | 3.80911e12i | −0.427336 | + | 0.740167i | ||||
\(669\) | 1.21613e9 | − | 2.10640e9i | 0.000234727 | − | 0.000406559i | ||||
\(670\) | −8.20902e12 | − | 1.42184e13i | −1.57382 | − | 2.72593i | ||||
\(671\) | −1.64333e11 | −0.0312948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.47304e12 | −1.40420 | −0.702101 | − | 0.712077i | \(-0.747754\pi\) | ||||
−0.702101 | + | 0.712077i | \(0.747754\pi\) | |||||||
\(674\) | −4.16872e12 | − | 7.22043e12i | −0.778095 | − | 1.34770i | ||||
\(675\) | 5.75180e9 | − | 9.96241e9i | 0.00106644 | − | 0.00184713i | ||||
\(676\) | −2.72520e12 | + | 4.72018e12i | −0.501924 | + | 0.869358i | ||||
\(677\) | −4.35654e12 | − | 7.54575e12i | −0.797064 | − | 1.38055i | −0.921521 | − | 0.388330i | \(-0.873052\pi\) |
0.124457 | − | 0.992225i | \(-0.460281\pi\) | |||||||
\(678\) | 2.32687e10 | 0.00422901 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.79861e13 | −3.22588 | ||||||||
\(681\) | −2.26580e9 | − | 3.92448e9i | −0.000403701 | − | 0.000699231i | ||||
\(682\) | 1.95700e12 | − | 3.38963e12i | 0.346387 | − | 0.599961i | ||||
\(683\) | 1.86952e12 | − | 3.23810e12i | 0.328727 | − | 0.569373i | −0.653532 | − | 0.756899i | \(-0.726714\pi\) |
0.982260 | + | 0.187526i | \(0.0600469\pi\) | |||||||
\(684\) | 9.26097e12 | + | 1.60405e13i | 1.61772 | + | 2.80198i | ||||
\(685\) | 5.75407e12 | 0.998545 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.38505e10 | −0.00237226 | ||||||||
\(688\) | 6.53623e12 | + | 1.13211e13i | 1.11219 | + | 1.92637i | ||||
\(689\) | −3.66018e12 | + | 6.33962e12i | −0.618751 | + | 1.07171i | ||||
\(690\) | 1.07246e10 | − | 1.85756e10i | 0.00180120 | − | 0.00311976i | ||||
\(691\) | 3.13485e12 | + | 5.42973e12i | 0.523078 | + | 0.905997i | 0.999639 | + | 0.0268559i | \(0.00854954\pi\) |
−0.476562 | + | 0.879141i | \(0.658117\pi\) | |||||||
\(692\) | 3.26230e12 | 0.540812 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.77222e12 | 0.453639 | ||||||||
\(695\) | −2.72308e12 | − | 4.71651e12i | −0.442719 | − | 0.766812i | ||||
\(696\) | −2.22932e9 | + | 3.86129e9i | −0.000360106 | + | 0.000623721i | ||||
\(697\) | 1.22319e12 | − | 2.11862e12i | 0.196311 | − | 0.340021i | ||||
\(698\) | 2.51441e12 | + | 4.35508e12i | 0.400947 | + | 0.694460i | ||||
\(699\) | 1.95773e10 | 0.00310174 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.13904e12 | −0.803805 | −0.401903 | − | 0.915682i | \(-0.631651\pi\) | ||||
−0.401903 | + | 0.915682i | \(0.631651\pi\) | |||||||
\(702\) | −2.34256e10 | − | 4.05744e10i | −0.00364061 | − | 0.00630572i | ||||
\(703\) | 1.15631e12 | − | 2.00279e12i | 0.178557 | − | 0.309270i | ||||
\(704\) | −1.15730e12 | + | 2.00451e12i | −0.177570 | + | 0.307561i | ||||
\(705\) | 4.23885e9 | + | 7.34191e9i | 0.000646245 | + | 0.00111933i | ||||
\(706\) | 1.01604e13 | 1.53918 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.73213e10 | 0.00259078 | ||||||||
\(709\) | 1.47719e12 | + | 2.55857e12i | 0.219547 | + | 0.380267i | 0.954670 | − | 0.297667i | \(-0.0962087\pi\) |
−0.735122 | + | 0.677934i | \(0.762875\pi\) | |||||||
\(710\) | −2.09261e12 | + | 3.62451e12i | −0.309048 | + | 0.535287i | ||||
\(711\) | 4.43906e11 | − | 7.68868e11i | 0.0651445 | − | 0.112834i | ||||
\(712\) | −9.85640e12 | − | 1.70718e13i | −1.43734 | − | 2.48954i | ||||
\(713\) | −6.63162e12 | −0.960986 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.82103e12 | 0.546768 | ||||||||
\(716\) | −7.84316e11 | − | 1.35848e12i | −0.111528 | − | 0.193172i | ||||
\(717\) | 8.46125e9 | − | 1.46553e10i | 0.00119563 | − | 0.00207090i | ||||
\(718\) | −5.88684e12 | + | 1.01963e13i | −0.826650 | + | 1.43180i | ||||
\(719\) | 6.09094e12 | + | 1.05498e13i | 0.849971 | + | 1.47219i | 0.881233 | + | 0.472682i | \(0.156714\pi\) |
−0.0312620 | + | 0.999511i | \(0.509953\pi\) | |||||||
\(720\) | 2.22745e13 | 3.08896 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.07644e13 | 1.47426 | ||||||||
\(723\) | −5.17599e9 | − | 8.96508e9i | −0.000704484 | − | 0.00122020i | ||||
\(724\) | 1.34191e13 | − | 2.32425e13i | 1.81509 | − | 3.14384i | ||||
\(725\) | −3.99083e11 | + | 6.91233e11i | −0.0536466 | + | 0.0929187i | ||||
\(726\) | 9.97996e9 | + | 1.72858e10i | 0.00133326 | + | 0.00230927i | ||||
\(727\) | 1.26291e13 | 1.67675 | 0.838376 | − | 0.545093i | \(-0.183506\pi\) | ||||
0.838376 | + | 0.545093i | \(0.183506\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.62547e12 | −0.999984 | ||||||||
\(730\) | 1.70158e13 | + | 2.94722e13i | 2.21768 | + | 3.84113i | ||||
\(731\) | 3.43534e12 | − | 5.95018e12i | 0.444981 | − | 0.770730i | ||||
\(732\) | 1.35531e9 | − | 2.34746e9i | 0.000174477 | − | 0.000302202i | ||||
\(733\) | −4.58297e12 | − | 7.93794e12i | −0.586380 | − | 1.01564i | −0.994702 | − | 0.102802i | \(-0.967219\pi\) |
0.408322 | − | 0.912838i | \(-0.366114\pi\) | |||||||
\(734\) | −1.00743e13 | −1.28110 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.34554e13 | 1.69024 | ||||||||
\(737\) | 1.90709e12 | + | 3.30318e12i | 0.238105 | + | 0.412409i | ||||
\(738\) | −3.03200e12 | + | 5.25158e12i | −0.376249 | + | 0.651683i | ||||
\(739\) | −5.53289e12 | + | 9.58324e12i | −0.682420 | + | 1.18199i | 0.291820 | + | 0.956473i | \(0.405739\pi\) |
−0.974240 | + | 0.225513i | \(0.927594\pi\) | |||||||
\(740\) | −3.36053e12 | − | 5.82060e12i | −0.411969 | − | 0.713551i | ||||
\(741\) | −2.16866e10 | −0.00264247 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.84642e12 | 0.222270 | 0.111135 | − | 0.993805i | \(-0.464551\pi\) | ||||
0.111135 | + | 0.993805i | \(0.464551\pi\) | |||||||
\(744\) | 1.89020e10 | + | 3.27391e10i | 0.00226167 | + | 0.00391732i | ||||
\(745\) | −3.26380e12 | + | 5.65307e12i | −0.388169 | + | 0.672328i | ||||
\(746\) | 2.79908e12 | − | 4.84815e12i | 0.330895 | − | 0.573127i | ||||
\(747\) | −3.29359e12 | − | 5.70467e12i | −0.387015 | − | 0.670329i | ||||
\(748\) | 7.13586e12 | 0.833468 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.21019e10 | 0.00139662 | ||||||||
\(751\) | 4.59836e12 | + | 7.96459e12i | 0.527501 | + | 0.913658i | 0.999486 | + | 0.0320518i | \(0.0102041\pi\) |
−0.471985 | + | 0.881606i | \(0.656463\pi\) | |||||||
\(752\) | −6.43018e12 | + | 1.11374e13i | −0.733234 | + | 1.27000i | ||||
\(753\) | 1.10950e10 | − | 1.92171e10i | 0.00125762 | − | 0.00217826i | ||||
\(754\) | 1.62537e12 | + | 2.81522e12i | 0.183139 | + | 0.317206i | ||||
\(755\) | −9.06449e12 | −1.01527 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.81778e12 | 0.975950 | 0.487975 | − | 0.872858i | \(-0.337736\pi\) | ||||
0.487975 | + | 0.872858i | \(0.337736\pi\) | |||||||
\(758\) | −1.18551e13 | − | 2.05336e13i | −1.30434 | − | 2.25919i | ||||
\(759\) | −2.49151e9 | + | 4.31541e9i | −0.000272505 | + | 0.000471992i | ||||
\(760\) | 2.06370e13 | − | 3.57443e13i | 2.24380 | − | 3.88638i | ||||
\(761\) | 1.21021e12 | + | 2.09615e12i | 0.130807 | + | 0.226564i | 0.923988 | − | 0.382422i | \(-0.124910\pi\) |
−0.793181 | + | 0.608986i | \(0.791577\pi\) | |||||||
\(762\) | 1.82843e10 | 0.00196464 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.32231e13 | −1.40415 | ||||||||
\(765\) | −5.85357e12 | − | 1.01387e13i | −0.617938 | − | 1.07030i | ||||
\(766\) | 2.16343e12 | − | 3.74717e12i | 0.227046 | − | 0.393255i | ||||
\(767\) | 3.69744e12 | − | 6.40415e12i | 0.385764 | − | 0.668163i | ||||
\(768\) | 8.05474e9 | + | 1.39512e10i | 0.000835461 | + | 0.00144706i | ||||
\(769\) | 7.67945e12 | 0.791885 | 0.395942 | − | 0.918275i | \(-0.370418\pi\) | ||||
0.395942 | + | 0.918275i | \(0.370418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.12078e10 | 0.00216148 | ||||||||
\(772\) | −4.73198e12 | − | 8.19603e12i | −0.479474 | − | 0.830473i | ||||
\(773\) | −5.23466e12 | + | 9.06670e12i | −0.527328 | + | 0.913359i | 0.472165 | + | 0.881510i | \(0.343473\pi\) |
−0.999493 | + | 0.0318488i | \(0.989861\pi\) | |||||||
\(774\) | −8.51542e12 | + | 1.47491e13i | −0.852848 | + | 1.47718i | ||||
\(775\) | 3.38375e12 | + | 5.86083e12i | 0.336931 | + | 0.583582i | ||||
\(776\) | −4.31835e13 | −4.27504 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.43956e13 | −2.38728 | ||||||||
\(779\) | 2.80692e12 | + | 4.86173e12i | 0.273094 | + | 0.473013i | ||||
\(780\) | −3.15133e10 | + | 5.45826e10i | −0.00304837 | + | 0.00527994i | ||||
\(781\) | 4.86148e11 | − | 8.42033e11i | 0.0467561 | − | 0.0809840i | ||||
\(782\) | −8.55064e12 | − | 1.48101e13i | −0.817651 | − | 1.41621i | ||||
\(783\) | −5.80424e9 | −0.000551846 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.14465e13 | 2.01578 | ||||||||
\(786\) | 7.24733e9 | + | 1.25527e10i | 0.000677293 | + | 0.00117311i | ||||
\(787\) | 6.32449e12 | − | 1.09543e13i | 0.587677 | − | 1.01789i | −0.406858 | − | 0.913491i | \(-0.633376\pi\) |
0.994536 | − | 0.104396i | \(-0.0332909\pi\) | |||||||
\(788\) | 2.63239e12 | − | 4.55944e12i | 0.243211 | − | 0.421254i | ||||
\(789\) | −1.75388e10 | − | 3.03781e10i | −0.00161122 | − | 0.00279071i | ||||
\(790\) | −3.37862e12 | −0.308615 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.03575e13 | −0.935387 | ||||||||
\(793\) | −5.78613e11 | − | 1.00219e12i | −0.0519588 | − | 0.0899953i | ||||
\(794\) | 1.36806e12 | − | 2.36954e12i | 0.122155 | − | 0.211579i | ||||
\(795\) | −1.24352e10 | + | 2.15384e10i | −0.00110408 | + | 0.00191233i | ||||
\(796\) | −1.95374e13 | − | 3.38397e13i | −1.72487 | − | 2.98757i | ||||
\(797\) | −6.02337e11 | −0.0528782 | −0.0264391 | − | 0.999650i | \(-0.508417\pi\) | ||||
−0.0264391 | + | 0.999650i | \(0.508417\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.75920e12 | 0.586725 | ||||||||
\(800\) | −6.86557e12 | − | 1.18915e13i | −0.592614 | − | 1.02644i | ||||
\(801\) | 6.41551e12 | − | 1.11120e13i | 0.550662 | − | 0.953775i | ||||
\(802\) | −8.49932e11 | + | 1.47213e12i | −0.0725437 | + | 0.125649i | ||||
\(803\) | −3.95304e12 | − | 6.84687e12i | −0.335515 | − | 0.581128i | ||||
\(804\) | −6.29136e10 | −0.00530997 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.75624e13 | 2.30043 | ||||||||
\(807\) | −2.78368e9 | − | 4.82148e9i | −0.000231041 | − | 0.000400174i | ||||
\(808\) | −1.34798e13 | + | 2.33477e13i | −1.11258 | + | 1.92705i | ||||
\(809\) | 3.86484e12 | − | 6.69409e12i | 0.317222 | − | 0.549444i | −0.662686 | − | 0.748898i | \(-0.730583\pi\) |
0.979907 | + | 0.199454i | \(0.0639167\pi\) | |||||||
\(810\) | 1.45096e13 | + | 2.51314e13i | 1.18433 | + | 2.05133i | ||||
\(811\) | −1.20157e13 | −0.975335 | −0.487668 | − | 0.873029i | \(-0.662152\pi\) | ||||
−0.487668 | + | 0.873029i | \(0.662152\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.28077e10 | −0.00102816 | ||||||||
\(814\) | 1.10426e12 | + | 1.91264e12i | 0.0881580 | + | 0.152694i | ||||
\(815\) | 1.26292e13 | − | 2.18745e13i | 1.00269 | − | 1.73671i | ||||
\(816\) | −2.43529e10 | + | 4.21804e10i | −0.00192284 | + | 0.00333046i | ||||
\(817\) | 7.88329e12 | + | 1.36543e13i | 0.619025 | + | 1.07218i | ||||
\(818\) | 4.43783e13 | 3.46562 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.63152e13 | 1.26017 | ||||||||
\(821\) | −6.99760e12 | − | 1.21202e13i | −0.537533 | − | 0.931035i | −0.999036 | − | 0.0438959i | \(-0.986023\pi\) |
0.461503 | − | 0.887139i | \(-0.347310\pi\) | |||||||
\(822\) | 1.55938e10 | − | 2.70093e10i | 0.00119132 | − | 0.00206343i | ||||
\(823\) | −8.09909e12 | + | 1.40280e13i | −0.615371 | + | 1.06585i | 0.374948 | + | 0.927046i | \(0.377661\pi\) |
−0.990319 | + | 0.138808i | \(0.955673\pi\) | |||||||
\(824\) | 1.07653e13 | + | 1.86461e13i | 0.813494 | + | 1.40901i | ||||
\(825\) | 5.08511e9 | 0.000382171 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.30127e13 | −0.967374 | −0.483687 | − | 0.875241i | \(-0.660703\pi\) | ||||
−0.483687 | + | 0.875241i | \(0.660703\pi\) | |||||||
\(828\) | 1.49848e13 | + | 2.59544e13i | 1.10793 | + | 1.91900i | ||||
\(829\) | 6.56819e12 | − | 1.13764e13i | 0.483004 | − | 0.836587i | −0.516806 | − | 0.856103i | \(-0.672879\pi\) |
0.999810 | + | 0.0195157i | \(0.00621243\pi\) | |||||||
\(830\) | −1.25339e13 | + | 2.17094e13i | −0.916719 | + | 1.58780i | ||||
\(831\) | −2.55145e9 | − | 4.41924e9i | −0.000185602 | − | 0.000321472i | ||||
\(832\) | −1.62994e13 | −1.17928 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.95187e10 | −0.00211276 | ||||||||
\(835\) | 3.18982e12 | + | 5.52492e12i | 0.227079 | + | 0.393312i | ||||
\(836\) | −8.18755e12 | + | 1.41813e13i | −0.579730 | + | 1.00412i | ||||
\(837\) | −2.46065e10 | + | 4.26198e10i | −0.00173295 | + | 0.00300156i | ||||
\(838\) | 2.49421e13 | + | 4.32010e13i | 1.74717 | + | 3.02619i | ||||
\(839\) | −5.22420e12 | −0.363991 | −0.181996 | − | 0.983299i | \(-0.558256\pi\) | ||||
−0.181996 | + | 0.983299i | \(0.558256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.41044e13 | −0.972240 | ||||||||
\(842\) | 1.22981e13 | + | 2.13009e13i | 0.843204 | + | 1.46047i | ||||
\(843\) | 1.88973e9 | − | 3.27310e9i | 0.000128877 | − | 0.000223221i | ||||
\(844\) | −1.09062e13 | + | 1.88901e13i | −0.739829 | + | 1.28142i | ||||
\(845\) | 3.95276e12 | + | 6.84638e12i | 0.266714 | + | 0.461962i | ||||
\(846\) | −1.67545e13 | −1.12452 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.77275e13 | −2.50540 | ||||||||
\(849\) | −1.57514e9 | − | 2.72822e9i | −0.000104048 | − | 0.000180217i | ||||
\(850\) | −8.72584e12 | + | 1.51136e13i | −0.573353 | + | 0.993077i | ||||
\(851\) | 1.87098e12 | − | 3.24064e12i | 0.122289 | − | 0.211810i | ||||
\(852\) | 8.01884e9 | + | 1.38890e10i | 0.000521355 | + | 0.000903013i | ||||
\(853\) | −5.65076e12 | −0.365457 | −0.182728 | − | 0.983163i | \(-0.558493\pi\) | ||||
−0.182728 | + | 0.983163i | \(0.558493\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.68651e13 | 1.71926 | ||||||||
\(856\) | −3.75876e13 | − | 6.51036e13i | −2.39283 | − | 4.14451i | ||||
\(857\) | −7.12578e11 | + | 1.23422e12i | −0.0451251 | + | 0.0781590i | −0.887706 | − | 0.460411i | \(-0.847702\pi\) |
0.842581 | + | 0.538570i | \(0.181035\pi\) | |||||||
\(858\) | 1.03552e10 | − | 1.79357e10i | 0.000652327 | − | 0.00112986i | ||||
\(859\) | −1.38980e13 | − | 2.40721e13i | −0.870932 | − | 1.50850i | −0.861034 | − | 0.508547i | \(-0.830183\pi\) |
−0.00989732 | − | 0.999951i | \(-0.503150\pi\) | |||||||
\(860\) | 4.58215e13 | 2.85645 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.13878e13 | −3.17013 | ||||||||
\(863\) | 5.70583e12 | + | 9.88279e12i | 0.350163 | + | 0.606500i | 0.986278 | − | 0.165094i | \(-0.0527928\pi\) |
−0.636115 | + | 0.771595i | \(0.719459\pi\) | |||||||
\(864\) | 4.99262e10 | − | 8.64748e10i | 0.00304801 | − | 0.00527932i | ||||
\(865\) | 2.36590e12 | − | 4.09786e12i | 0.143689 | − | 0.248877i | ||||
\(866\) | 9.90328e11 | + | 1.71530e12i | 0.0598341 | + | 0.103636i | ||||
\(867\) | −1.95364e9 | −0.000117425 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.84908e11 | 0.0466906 | ||||||||
\(870\) | 5.52208e9 | + | 9.56452e9i | 0.000326788 | + | 0.000566013i | ||||
\(871\) | −1.34297e13 | + | 2.32609e13i | −0.790650 | + | 1.36945i | ||||
\(872\) | −5.79778e12 | + | 1.00420e13i | −0.339576 | + | 0.588163i | ||||
\(873\) | −1.40540e13 | − | 2.43423e13i | −0.818912 | − | 1.41840i | ||||
\(874\) | 3.92434e13 | 2.27491 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.30408e11 | 0.00748232 | ||||||||
\(877\) | 6.05939e12 | + | 1.04952e13i | 0.345884 | + | 0.599089i | 0.985514 | − | 0.169594i | \(-0.0542456\pi\) |
−0.639630 | + | 0.768683i | \(0.720912\pi\) | |||||||
\(878\) | −1.28381e13 | + | 2.22363e13i | −0.729082 | + | 1.26281i | ||||
\(879\) | −6.29523e9 | + | 1.09037e10i | −0.000355682 | + | 0.000616059i | ||||
\(880\) | 9.84637e12 | + | 1.70544e13i | 0.553483 | + | 0.958661i | ||||
\(881\) | −4.60741e12 | −0.257671 | −0.128836 | − | 0.991666i | \(-0.541124\pi\) | ||||
−0.128836 | + | 0.991666i | \(0.541124\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.04709e13 | 0.579642 | 0.289821 | − | 0.957081i | \(-0.406404\pi\) | ||||
0.289821 | + | 0.957081i | \(0.406404\pi\) | |||||||
\(884\) | 2.51253e13 | + | 4.35182e13i | 1.38381 | + | 2.39682i | ||||
\(885\) | 1.25618e10 | − | 2.17577e10i | 0.000688347 | − | 0.00119225i | ||||
\(886\) | 1.71221e13 | − | 2.96563e13i | 0.933478 | − | 1.61683i | ||||
\(887\) | 1.84355e12 | + | 3.19313e12i | 0.0999999 | + | 0.173205i | 0.911684 | − | 0.410891i | \(-0.134782\pi\) |
−0.811684 | + | 0.584096i | \(0.801449\pi\) | |||||||
\(888\) | −2.13313e10 | −0.00115122 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.88291e13 | −2.60870 | ||||||||
\(891\) | −3.37083e12 | − | 5.83845e12i | −0.179179 | − | 0.310347i | ||||
\(892\) | 6.46646e12 | − | 1.12002e13i | 0.341999 | − | 0.592360i | ||||
\(893\) | −7.75538e12 | + | 1.34327e13i | −0.408105 | + | 0.706858i | ||||
\(894\) | 1.76901e10 | + | 3.06402e10i | 0.000926217 | + | 0.00160425i | ||||
\(895\) | −2.27522e12 | −0.118528 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.50902e10 | −0.00180976 | ||||||||
\(898\) | −1.00540e13 | − | 1.74140e13i | −0.515935 | − | 0.893625i | ||||
\(899\) | 1.70730e12 | − | 2.95713e12i | 0.0871750 | − | 0.150992i | ||||
\(900\) | 1.52918e13 | − | 2.64862e13i | 0.776906 | − | 1.34564i | ||||
\(901\) | 9.91449e12 | + | 1.71724e13i | 0.501198 | + | 0.868100i | ||||
\(902\) | −5.36114e12 | −0.269667 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.24487e13 | 3.60805 | ||||||||
\(905\) | −1.94637e13 | − | 3.37121e13i | −0.964510 | − | 1.67058i | ||||
\(906\) | −2.45652e10 | + | 4.25482e10i | −0.00121128 | + | 0.00209800i | ||||
\(907\) | 3.02605e11 | − | 5.24126e11i | 0.0148471 | − | 0.0257160i | −0.858506 | − | 0.512803i | \(-0.828607\pi\) |
0.873354 | + | 0.487087i | \(0.161941\pi\) | |||||||
\(908\) | −1.20478e13 | − | 2.08674e13i | −0.588196 | − | 1.01878i | ||||
\(909\) | −1.75480e13 | −0.852491 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.27450e12 | −0.157512 | −0.0787559 | − | 0.996894i | \(-0.525095\pi\) | ||||
−0.0787559 | + | 0.996894i | \(0.525095\pi\) | |||||||
\(912\) | −5.58840e10 | − | 9.67940e10i | −0.00267492 | − | 0.00463310i | ||||
\(913\) | 2.91184e12 | − | 5.04346e12i | 0.138691 | − | 0.240220i | ||||
\(914\) | −2.41047e13 | + | 4.17506e13i | −1.14247 | + | 1.97881i | ||||
\(915\) | −1.96580e9 | − | 3.40487e9i | −9.27139e−5 | − | 0.000160585i | ||||
\(916\) | −7.36467e13 | −3.45640 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.26908e11 | −0.00589790 | ||||||||
\(919\) | −1.10558e11 | − | 1.91493e11i | −0.00511295 | − | 0.00885589i | 0.863458 | − | 0.504421i | \(-0.168294\pi\) |
−0.868571 | + | 0.495566i | \(0.834961\pi\) | |||||||
\(920\) | 3.33918e13 | − | 5.78363e13i | 1.53672 | − | 2.66168i | ||||
\(921\) | −8.50939e9 | + | 1.47387e10i | −0.000389700 | + | 0.000674980i | ||||
\(922\) | 1.26866e13 | + | 2.19738e13i | 0.578171 | + | 1.00142i | ||||
\(923\) | 6.84688e12 | 0.310517 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.81864e12 | −0.171503 | ||||||||
\(926\) | 1.85550e13 | + | 3.21382e13i | 0.829300 | + | 1.43639i | ||||
\(927\) | −7.00713e12 | + | 1.21367e13i | −0.311660 | + | 0.539811i | ||||
\(928\) | −3.46409e12 | + | 5.99997e12i | −0.153328 | + | 0.265573i | ||||
\(929\) | 2.00073e12 | + | 3.46537e12i | 0.0881290 | + | 0.152644i | 0.906720 | − | 0.421733i | \(-0.138578\pi\) |
−0.818591 | + | 0.574376i | \(0.805245\pi\) | |||||||
\(930\) | 9.36413e10 | 0.00410482 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.04097e14 | 4.51927 | ||||||||
\(933\) | 2.84037e10 | + | 4.91966e10i | 0.00122718 | + | 0.00212553i | ||||
\(934\) | 2.29450e13 | − | 3.97418e13i | 0.986566 | − | 1.70878i | ||||
\(935\) | 5.17510e12 | − | 8.96353e12i | 0.221445 | − | 0.383554i | ||||
\(936\) | −3.64686e13 | − | 6.31654e13i | −1.55302 | − | 2.68991i | ||||
\(937\) | −3.76138e10 | −0.00159411 | −0.000797056 | − | 1.00000i | \(-0.500254\pi\) | ||||
−0.000797056 | 1.00000i | \(0.500254\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.02205e10 | −0.000429019 | ||||||||
\(940\) | 2.25390e13 | + | 3.90387e13i | 0.941585 | + | 1.63087i | ||||
\(941\) | 1.10747e12 | − | 1.91820e12i | 0.0460447 | − | 0.0797518i | −0.842085 | − | 0.539346i | \(-0.818672\pi\) |
0.888129 | + | 0.459594i | \(0.152005\pi\) | |||||||
\(942\) | 5.81212e10 | − | 1.00669e11i | 0.00240495 | − | 0.00416549i | ||||
\(943\) | 4.54177e12 | + | 7.86657e12i | 0.187035 | + | 0.323954i | ||||
\(944\) | 3.81116e13 | 1.56201 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.50568e13 | −0.611257 | ||||||||
\(947\) | −1.18133e13 | − | 2.04612e13i | −0.477305 | − | 0.826716i | 0.522357 | − | 0.852727i | \(-0.325053\pi\) |
−0.999662 | + | 0.0260107i | \(0.991720\pi\) | |||||||
\(948\) | −6.47339e9 | + | 1.12122e10i | −0.000260312 | + | 0.000450874i | ||||
\(949\) | 2.78372e13 | − | 4.82155e13i | 1.11411 | − | 1.92969i | ||||
\(950\) | −2.00237e13 | − | 3.46821e13i | −0.797607 | − | 1.38150i | ||||
\(951\) | −5.05694e10 | −0.00200482 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.15037e13 | −0.451771 | −0.225885 | − | 0.974154i | \(-0.572527\pi\) | ||||
−0.225885 | + | 0.974154i | \(0.572527\pi\) | |||||||
\(954\) | −2.45758e13 | − | 4.25665e13i | −0.960593 | − | 1.66380i | ||||
\(955\) | −9.58974e12 | + | 1.66099e13i | −0.373071 | + | 0.646178i | ||||
\(956\) | 4.49905e13 | − | 7.79258e13i | 1.74205 | − | 3.01732i | ||||
\(957\) | −1.28287e9 | − | 2.22200e9i | −4.94400e−5 | − | 8.56327e-5i | ||||
\(958\) | −1.30518e13 | −0.500639 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.53761e10 | −0.00210427 | ||||||||
\(961\) | −1.25609e12 | − | 2.17561e12i | −0.0475078 | − | 0.0822859i | ||||
\(962\) | −7.77618e12 | + | 1.34687e13i | −0.292737 | + | 0.507036i | ||||
\(963\) | 2.44657e13 | − | 4.23759e13i | 0.916726 | − | 1.58782i | ||||
\(964\) | −2.75220e13 | − | 4.76695e13i | −1.02644 | − | 1.77785i | ||||
\(965\) | −1.37270e13 | −0.509568 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.36863e13 | −0.503346 | −0.251673 | − | 0.967812i | \(-0.580981\pi\) | ||||
−0.251673 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(968\) | 3.10733e13 | + | 5.38205e13i | 1.13749 | + | 1.97019i | ||||
\(969\) | −2.93718e10 | + | 5.08734e10i | −0.00107022 | + | 0.00185368i | ||||
\(970\) | −5.34834e13 | + | 9.26359e13i | −1.93975 | + | 3.35975i | ||||
\(971\) | −4.97630e12 | − | 8.61920e12i | −0.179647 | − | 0.311158i | 0.762113 | − | 0.647444i | \(-0.224162\pi\) |
−0.941760 | + | 0.336287i | \(0.890829\pi\) | |||||||
\(972\) | 3.33605e11 | 0.0119877 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.53038e13 | 1.61295 | ||||||||
\(975\) | 1.79046e10 | + | 3.10117e10i | 0.000634518 | + | 0.00109902i | ||||
\(976\) | 2.98204e12 | − | 5.16505e12i | 0.105194 | − | 0.182201i | ||||
\(977\) | −7.56937e12 | + | 1.31105e13i | −0.265787 | + | 0.460357i | −0.967770 | − | 0.251837i | \(-0.918965\pi\) |
0.701982 | + | 0.712194i | \(0.252299\pi\) | |||||||
\(978\) | −6.84517e10 | − | 1.18562e11i | −0.00239254 | − | 0.00414401i | ||||
\(979\) | 1.13438e13 | 0.394673 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.54753e12 | −0.260192 | ||||||||
\(982\) | −4.48749e13 | − | 7.77256e13i | −1.53993 | − | 2.66724i | ||||
\(983\) | −2.73570e13 | + | 4.73838e13i | −0.934497 | + | 1.61860i | −0.158970 | + | 0.987283i | \(0.550817\pi\) |
−0.775528 | + | 0.631314i | \(0.782516\pi\) | |||||||
\(984\) | 2.58906e10 | − | 4.48438e10i | 0.000880367 | − | 0.00152484i | ||||
\(985\) | −3.81815e12 | − | 6.61324e12i | −0.129238 | − | 0.223847i | ||||
\(986\) | 8.80540e12 | 0.296690 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.15313e14 | −3.85010 | ||||||||
\(989\) | 1.27556e13 | + | 2.20934e13i | 0.423954 | + | 0.734309i | ||||
\(990\) | −1.28279e13 | + | 2.22186e13i | −0.424421 | + | 0.735119i | ||||
\(991\) | −2.43192e13 | + | 4.21221e13i | −0.800974 | + | 1.38733i | 0.118002 | + | 0.993013i | \(0.462351\pi\) |
−0.918976 | + | 0.394314i | \(0.870982\pi\) | |||||||
\(992\) | 2.93713e13 | + | 5.08726e13i | 0.962989 | + | 1.66795i | ||||
\(993\) | −8.52557e10 | −0.00278261 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.66759e13 | −1.83314 | ||||||||
\(996\) | 4.80298e10 | + | 8.31901e10i | 0.00154648 | + | 0.00267858i | ||||
\(997\) | −1.38879e13 | + | 2.40545e13i | −0.445152 | + | 0.771026i | −0.998063 | − | 0.0622146i | \(-0.980184\pi\) |
0.552911 | + | 0.833240i | \(0.313517\pi\) | |||||||
\(998\) | 3.88141e13 | − | 6.72281e13i | 1.23852 | − | 2.14518i | ||||
\(999\) | −1.38845e10 | − | 2.40487e10i | −0.000441048 | − | 0.000763917i |
(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 | 49.10.c.d.18.1 | 6 | ||
7.2 | even | 3 | inner | 49.10.c.d.30.1 | 6 | ||
7.3 | odd | 6 | 49.10.a.c.1.3 | 3 | |||
7.4 | even | 3 | 7.10.a.b.1.3 | ✓ | 3 | ||
7.5 | odd | 6 | 49.10.c.e.30.1 | 6 | |||
7.6 | odd | 2 | 49.10.c.e.18.1 | 6 | |||
21.11 | odd | 6 | 63.10.a.e.1.1 | 3 | |||
28.11 | odd | 6 | 112.10.a.h.1.2 | 3 | |||
35.4 | even | 6 | 175.10.a.d.1.1 | 3 | |||
35.18 | odd | 12 | 175.10.b.d.99.1 | 6 | |||
35.32 | odd | 12 | 175.10.b.d.99.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.10.a.b.1.3 | ✓ | 3 | 7.4 | even | 3 | ||
49.10.a.c.1.3 | 3 | 7.3 | odd | 6 | |||
49.10.c.d.18.1 | 6 | 1.1 | even | 1 | trivial | ||
49.10.c.d.30.1 | 6 | 7.2 | even | 3 | inner | ||
49.10.c.e.18.1 | 6 | 7.6 | odd | 2 | |||
49.10.c.e.30.1 | 6 | 7.5 | odd | 6 | |||
63.10.a.e.1.1 | 3 | 21.11 | odd | 6 | |||
112.10.a.h.1.2 | 3 | 28.11 | odd | 6 | |||
175.10.a.d.1.1 | 3 | 35.4 | even | 6 | |||
175.10.b.d.99.1 | 6 | 35.18 | odd | 12 | |||
175.10.b.d.99.6 | 6 | 35.32 | odd | 12 |