Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,9,Mod(23,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.23");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4434941320\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 23.14 | ||
Character | \(\chi\) | \(=\) | 33.23 |
Dual form | 33.9.b.a.23.13 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.463681i | 0.0289801i | 0.999895 | + | 0.0144900i | \(0.00461248\pi\) | ||||
−0.999895 | + | 0.0144900i | \(0.995388\pi\) | |||||||
\(3\) | −38.1388 | − | 71.4593i | −0.470850 | − | 0.882213i | ||||
\(4\) | 255.785 | 0.999160 | ||||||||
\(5\) | 649.991i | 1.03999i | 0.854170 | + | 0.519993i | \(0.174066\pi\) | ||||
−0.854170 | + | 0.519993i | \(0.825934\pi\) | |||||||
\(6\) | 33.1343 | − | 17.6842i | 0.0255666 | − | 0.0136453i | ||||
\(7\) | −831.270 | −0.346218 | −0.173109 | − | 0.984903i | \(-0.555381\pi\) | ||||
−0.173109 | + | 0.984903i | \(0.555381\pi\) | |||||||
\(8\) | 237.305i | 0.0579358i | ||||||||
\(9\) | −3651.86 | + | 5450.75i | −0.556601 | + | 0.830780i | ||||
\(10\) | −301.389 | −0.0301389 | ||||||||
\(11\) | 4414.43i | 0.301511i | ||||||||
\(12\) | −9755.34 | − | 18278.2i | −0.470454 | − | 0.881472i | ||||
\(13\) | 43155.7 | 1.51100 | 0.755501 | − | 0.655147i | \(-0.227393\pi\) | ||||
0.755501 | + | 0.655147i | \(0.227393\pi\) | |||||||
\(14\) | − | 385.444i | − | 0.0100334i | ||||||
\(15\) | 46447.9 | − | 24789.9i | 0.917490 | − | 0.489677i | ||||
\(16\) | 65370.9 | 0.997481 | ||||||||
\(17\) | 104893.i | 1.25589i | 0.778259 | + | 0.627943i | \(0.216103\pi\) | ||||
−0.778259 | + | 0.627943i | \(0.783897\pi\) | |||||||
\(18\) | −2527.41 | − | 1693.30i | −0.0240760 | − | 0.0161303i | ||||
\(19\) | 75962.6 | 0.582889 | 0.291444 | − | 0.956588i | \(-0.405864\pi\) | ||||
0.291444 | + | 0.956588i | \(0.405864\pi\) | |||||||
\(20\) | 166258.i | 1.03911i | ||||||||
\(21\) | 31703.7 | + | 59401.9i | 0.163017 | + | 0.305438i | ||||
\(22\) | −2046.89 | −0.00873781 | ||||||||
\(23\) | − | 31800.2i | − | 0.113637i | −0.998385 | − | 0.0568183i | \(-0.981904\pi\) | ||
0.998385 | − | 0.0568183i | \(-0.0180956\pi\) | |||||||
\(24\) | 16957.6 | − | 9050.53i | 0.0511117 | − | 0.0272790i | ||||
\(25\) | −31863.9 | −0.0815716 | ||||||||
\(26\) | 20010.5i | 0.0437889i | ||||||||
\(27\) | 528784. | + | 53074.1i | 0.995001 | + | 0.0998683i | ||||
\(28\) | −212626. | −0.345927 | ||||||||
\(29\) | 33557.3i | 0.0474455i | 0.999719 | + | 0.0237227i | \(0.00755189\pi\) | ||||
−0.999719 | + | 0.0237227i | \(0.992448\pi\) | |||||||
\(30\) | 11494.6 | + | 21537.0i | 0.0141909 | + | 0.0265889i | ||||
\(31\) | 1.04649e6 | 1.13316 | 0.566578 | − | 0.824008i | \(-0.308267\pi\) | ||||
0.566578 | + | 0.824008i | \(0.308267\pi\) | |||||||
\(32\) | 91061.3i | 0.0868428i | ||||||||
\(33\) | 315452. | − | 168361.i | 0.265997 | − | 0.141967i | ||||
\(34\) | −48636.8 | −0.0363956 | ||||||||
\(35\) | − | 540318.i | − | 0.360062i | ||||||
\(36\) | −934091. | + | 1.39422e6i | −0.556134 | + | 0.830082i | ||||
\(37\) | −475780. | −0.253863 | −0.126931 | − | 0.991911i | \(-0.540513\pi\) | ||||
−0.126931 | + | 0.991911i | \(0.540513\pi\) | |||||||
\(38\) | 35222.4i | 0.0168921i | ||||||||
\(39\) | −1.64591e6 | − | 3.08388e6i | −0.711455 | − | 1.33303i | ||||
\(40\) | −154246. | −0.0602524 | ||||||||
\(41\) | − | 958455.i | − | 0.339185i | −0.985514 | − | 0.169592i | \(-0.945755\pi\) | ||
0.985514 | − | 0.169592i | \(-0.0542451\pi\) | |||||||
\(42\) | −27543.5 | + | 14700.4i | −0.00885162 | + | 0.00472423i | ||||
\(43\) | −5.21676e6 | −1.52590 | −0.762952 | − | 0.646456i | \(-0.776251\pi\) | ||||
−0.762952 | + | 0.646456i | \(0.776251\pi\) | |||||||
\(44\) | 1.12914e6i | 0.301258i | ||||||||
\(45\) | −3.54294e6 | − | 2.37368e6i | −0.864000 | − | 0.578857i | ||||
\(46\) | 14745.1 | 0.00329320 | ||||||||
\(47\) | 4.32434e6i | 0.886192i | 0.896474 | + | 0.443096i | \(0.146120\pi\) | ||||
−0.896474 | + | 0.443096i | \(0.853880\pi\) | |||||||
\(48\) | −2.49317e6 | − | 4.67136e6i | −0.469664 | − | 0.879991i | ||||
\(49\) | −5.07379e6 | −0.880133 | ||||||||
\(50\) | − | 14774.7i | − | 0.00236395i | ||||||
\(51\) | 7.49557e6 | − | 4.00049e6i | 1.10796 | − | 0.591333i | ||||
\(52\) | 1.10386e7 | 1.50973 | ||||||||
\(53\) | 1.46582e7i | 1.85771i | 0.370442 | + | 0.928856i | \(0.379206\pi\) | ||||
−0.370442 | + | 0.928856i | \(0.620794\pi\) | |||||||
\(54\) | −24609.4 | + | 245187.i | −0.00289419 | + | 0.0288352i | ||||
\(55\) | −2.86934e6 | −0.313568 | ||||||||
\(56\) | − | 197264.i | − | 0.0200584i | ||||||
\(57\) | −2.89713e6 | − | 5.42824e6i | −0.274453 | − | 0.514232i | ||||
\(58\) | −15559.9 | −0.00137497 | ||||||||
\(59\) | − | 1.53022e7i | − | 1.26284i | −0.775443 | − | 0.631418i | \(-0.782473\pi\) | ||
0.775443 | − | 0.631418i | \(-0.217527\pi\) | |||||||
\(60\) | 1.18807e7 | − | 6.34089e6i | 0.916719 | − | 0.489266i | ||||
\(61\) | −6.61576e6 | −0.477815 | −0.238908 | − | 0.971042i | \(-0.576789\pi\) | ||||
−0.238908 | + | 0.971042i | \(0.576789\pi\) | |||||||
\(62\) | 485239.i | 0.0328389i | ||||||||
\(63\) | 3.03568e6 | − | 4.53104e6i | 0.192705 | − | 0.287631i | ||||
\(64\) | 1.66927e7 | 0.994964 | ||||||||
\(65\) | 2.80509e7i | 1.57142i | ||||||||
\(66\) | 78065.8 | + | 146269.i | 0.00411420 | + | 0.00770862i | ||||
\(67\) | −8.92426e6 | −0.442867 | −0.221433 | − | 0.975176i | \(-0.571074\pi\) | ||||
−0.221433 | + | 0.975176i | \(0.571074\pi\) | |||||||
\(68\) | 2.68300e7i | 1.25483i | ||||||||
\(69\) | −2.27242e6 | + | 1.21282e6i | −0.100252 | + | 0.0535058i | ||||
\(70\) | 250535. | 0.0104346 | ||||||||
\(71\) | 1.10930e7i | 0.436532i | 0.975889 | + | 0.218266i | \(0.0700401\pi\) | ||||
−0.975889 | + | 0.218266i | \(0.929960\pi\) | |||||||
\(72\) | −1.29349e6 | − | 866604.i | −0.0481319 | − | 0.0322471i | ||||
\(73\) | 8.31278e6 | 0.292722 | 0.146361 | − | 0.989231i | \(-0.453244\pi\) | ||||
0.146361 | + | 0.989231i | \(0.453244\pi\) | |||||||
\(74\) | − | 220610.i | − | 0.00735696i | ||||||
\(75\) | 1.21525e6 | + | 2.27697e6i | 0.0384080 | + | 0.0719636i | ||||
\(76\) | 1.94301e7 | 0.582399 | ||||||||
\(77\) | − | 3.66958e6i | − | 0.104389i | ||||||
\(78\) | 1.42994e6 | − | 763177.i | 0.0386312 | − | 0.0206180i | ||||
\(79\) | 7.01564e7 | 1.80119 | 0.900593 | − | 0.434663i | \(-0.143133\pi\) | ||||
0.900593 | + | 0.434663i | \(0.143133\pi\) | |||||||
\(80\) | 4.24905e7i | 1.03737i | ||||||||
\(81\) | −1.63746e7 | − | 3.98107e7i | −0.380391 | − | 0.924826i | ||||
\(82\) | 444417. | 0.00982959 | ||||||||
\(83\) | − | 7.67533e7i | − | 1.61728i | −0.588305 | − | 0.808639i | \(-0.700204\pi\) | ||
0.588305 | − | 0.808639i | \(-0.299796\pi\) | |||||||
\(84\) | 8.10932e6 | + | 1.51941e7i | 0.162880 | + | 0.305182i | ||||
\(85\) | −6.81794e7 | −1.30610 | ||||||||
\(86\) | − | 2.41891e6i | − | 0.0442208i | ||||||
\(87\) | 2.39798e6 | − | 1.27984e6i | 0.0418570 | − | 0.0223397i | ||||
\(88\) | −1.04757e6 | −0.0174683 | ||||||||
\(89\) | 8.67620e6i | 0.138283i | 0.997607 | + | 0.0691416i | \(0.0220260\pi\) | ||||
−0.997607 | + | 0.0691416i | \(0.977974\pi\) | |||||||
\(90\) | 1.10063e6 | − | 1.64279e6i | 0.0167753 | − | 0.0250388i | ||||
\(91\) | −3.58741e7 | −0.523136 | ||||||||
\(92\) | − | 8.13402e6i | − | 0.113541i | ||||||
\(93\) | −3.99120e7 | − | 7.47817e7i | −0.533546 | − | 0.999686i | ||||
\(94\) | −2.00511e6 | −0.0256819 | ||||||||
\(95\) | 4.93751e7i | 0.606196i | ||||||||
\(96\) | 6.50718e6 | − | 3.47297e6i | 0.0766139 | − | 0.0408899i | ||||
\(97\) | −1.38818e8 | −1.56805 | −0.784025 | − | 0.620729i | \(-0.786837\pi\) | ||||
−0.784025 | + | 0.620729i | \(0.786837\pi\) | |||||||
\(98\) | − | 2.35262e6i | − | 0.0255063i | ||||||
\(99\) | −2.40619e7 | − | 1.61209e7i | −0.250490 | − | 0.167822i | ||||
\(100\) | −8.15031e6 | −0.0815031 | ||||||||
\(101\) | 9.38822e7i | 0.902189i | 0.892476 | + | 0.451095i | \(0.148966\pi\) | ||||
−0.892476 | + | 0.451095i | \(0.851034\pi\) | |||||||
\(102\) | 1.85495e6 | + | 3.47555e6i | 0.0171369 | + | 0.0321087i | ||||
\(103\) | −7.99315e7 | −0.710181 | −0.355091 | − | 0.934832i | \(-0.615550\pi\) | ||||
−0.355091 | + | 0.934832i | \(0.615550\pi\) | |||||||
\(104\) | 1.02411e7i | 0.0875411i | ||||||||
\(105\) | −3.86107e7 | + | 2.06071e7i | −0.317652 | + | 0.169535i | ||||
\(106\) | −6.79674e6 | −0.0538366 | ||||||||
\(107\) | − | 1.39281e8i | − | 1.06257i | −0.847195 | − | 0.531283i | \(-0.821710\pi\) | ||
0.847195 | − | 0.531283i | \(-0.178290\pi\) | |||||||
\(108\) | 1.35255e8 | + | 1.35756e7i | 0.994165 | + | 0.0997844i | ||||
\(109\) | 1.68855e8 | 1.19621 | 0.598104 | − | 0.801418i | \(-0.295921\pi\) | ||||
0.598104 | + | 0.801418i | \(0.295921\pi\) | |||||||
\(110\) | − | 1.33046e6i | − | 0.00908721i | ||||||
\(111\) | 1.81457e7 | + | 3.39989e7i | 0.119531 | + | 0.223961i | ||||
\(112\) | −5.43409e7 | −0.345346 | ||||||||
\(113\) | − | 2.75504e8i | − | 1.68972i | −0.534989 | − | 0.844859i | \(-0.679684\pi\) | ||
0.534989 | − | 0.844859i | \(-0.320316\pi\) | |||||||
\(114\) | 2.51697e6 | − | 1.34334e6i | 0.0149025 | − | 0.00795366i | ||||
\(115\) | 2.06699e7 | 0.118181 | ||||||||
\(116\) | 8.58345e6i | 0.0474056i | ||||||||
\(117\) | −1.57599e8 | + | 2.35231e8i | −0.841026 | + | 1.25531i | ||||
\(118\) | 7.09536e6 | 0.0365971 | ||||||||
\(119\) | − | 8.71942e7i | − | 0.434810i | ||||||
\(120\) | 5.88277e6 | + | 1.10223e7i | 0.0283698 | + | 0.0531555i | ||||
\(121\) | −1.94872e7 | −0.0909091 | ||||||||
\(122\) | − | 3.06760e6i | − | 0.0138471i | ||||||
\(123\) | −6.84905e7 | + | 3.65544e7i | −0.299233 | + | 0.159705i | ||||
\(124\) | 2.67677e8 | 1.13220 | ||||||||
\(125\) | 2.33192e8i | 0.955153i | ||||||||
\(126\) | 2.10096e6 | + | 1.40759e6i | 0.00833556 | + | 0.00558461i | ||||
\(127\) | 3.70029e8 | 1.42240 | 0.711199 | − | 0.702991i | \(-0.248153\pi\) | ||||
0.711199 | + | 0.702991i | \(0.248153\pi\) | |||||||
\(128\) | 3.10518e7i | 0.115677i | ||||||||
\(129\) | 1.98961e8 | + | 3.72786e8i | 0.718471 | + | 1.34617i | ||||
\(130\) | −1.30067e7 | −0.0455399 | ||||||||
\(131\) | − | 4.53608e8i | − | 1.54027i | −0.637883 | − | 0.770133i | \(-0.720190\pi\) | ||
0.637883 | − | 0.770133i | \(-0.279810\pi\) | |||||||
\(132\) | 8.06878e7 | − | 4.30642e7i | 0.265774 | − | 0.141847i | ||||
\(133\) | −6.31454e7 | −0.201807 | ||||||||
\(134\) | − | 4.13801e6i | − | 0.0128343i | ||||||
\(135\) | −3.44977e7 | + | 3.43705e8i | −0.103862 | + | 1.03479i | ||||
\(136\) | −2.48916e7 | −0.0727607 | ||||||||
\(137\) | 7.47078e7i | 0.212072i | 0.994362 | + | 0.106036i | \(0.0338159\pi\) | ||||
−0.994362 | + | 0.106036i | \(0.966184\pi\) | |||||||
\(138\) | −562363. | − | 1.05368e6i | −0.00155060 | − | 0.00290530i | ||||
\(139\) | −2.84891e7 | −0.0763167 | −0.0381584 | − | 0.999272i | \(-0.512149\pi\) | ||||
−0.0381584 | + | 0.999272i | \(0.512149\pi\) | |||||||
\(140\) | − | 1.38205e8i | − | 0.359760i | ||||||
\(141\) | 3.09014e8 | − | 1.64925e8i | 0.781811 | − | 0.417263i | ||||
\(142\) | −5.14362e6 | −0.0126507 | ||||||||
\(143\) | 1.90508e8i | 0.455584i | ||||||||
\(144\) | −2.38725e8 | + | 3.56320e8i | −0.555199 | + | 0.828687i | ||||
\(145\) | −2.18119e7 | −0.0493426 | ||||||||
\(146\) | 3.85448e6i | 0.00848309i | ||||||||
\(147\) | 1.93508e8 | + | 3.62570e8i | 0.414410 | + | 0.776465i | ||||
\(148\) | −1.21697e8 | −0.253650 | ||||||||
\(149\) | − | 6.68520e8i | − | 1.35634i | −0.734904 | − | 0.678171i | \(-0.762773\pi\) | ||
0.734904 | − | 0.678171i | \(-0.237227\pi\) | |||||||
\(150\) | −1.05579e6 | + | 563489.i | −0.00208551 | + | 0.00111307i | ||||
\(151\) | −1.10269e7 | −0.0212103 | −0.0106051 | − | 0.999944i | \(-0.503376\pi\) | ||||
−0.0106051 | + | 0.999944i | \(0.503376\pi\) | |||||||
\(152\) | 1.80263e7i | 0.0337701i | ||||||||
\(153\) | −5.71744e8 | − | 3.83054e8i | −1.04336 | − | 0.699027i | ||||
\(154\) | 1.70151e6 | 0.00302519 | ||||||||
\(155\) | 6.80212e8i | 1.17847i | ||||||||
\(156\) | −4.20999e8 | − | 7.88810e8i | −0.710858 | − | 1.33191i | ||||
\(157\) | −8.31454e8 | −1.36848 | −0.684242 | − | 0.729255i | \(-0.739867\pi\) | ||||
−0.684242 | + | 0.729255i | \(0.739867\pi\) | |||||||
\(158\) | 3.25302e7i | 0.0521985i | ||||||||
\(159\) | 1.04747e9 | − | 5.59048e8i | 1.63890 | − | 0.874703i | ||||
\(160\) | −5.91891e7 | −0.0903154 | ||||||||
\(161\) | 2.64345e7i | 0.0393431i | ||||||||
\(162\) | 1.84595e7 | − | 7.59258e6i | 0.0268015 | − | 0.0110237i | ||||
\(163\) | −1.27899e8 | −0.181183 | −0.0905916 | − | 0.995888i | \(-0.528876\pi\) | ||||
−0.0905916 | + | 0.995888i | \(0.528876\pi\) | |||||||
\(164\) | − | 2.45158e8i | − | 0.338900i | ||||||
\(165\) | 1.09433e8 | + | 2.05041e8i | 0.147643 | + | 0.276634i | ||||
\(166\) | 3.55891e7 | 0.0468688 | ||||||||
\(167\) | − | 1.99112e8i | − | 0.255995i | −0.991774 | − | 0.127998i | \(-0.959145\pi\) | ||
0.991774 | − | 0.127998i | \(-0.0408550\pi\) | |||||||
\(168\) | −1.40964e7 | + | 7.52343e6i | −0.0176958 | + | 0.00944450i | ||||
\(169\) | 1.04669e9 | 1.28313 | ||||||||
\(170\) | − | 3.16135e7i | − | 0.0378510i | ||||||
\(171\) | −2.77405e8 | + | 4.14053e8i | −0.324436 | + | 0.484252i | ||||
\(172\) | −1.33437e9 | −1.52462 | ||||||||
\(173\) | − | 1.14200e9i | − | 1.27492i | −0.770485 | − | 0.637458i | \(-0.779986\pi\) | ||
0.770485 | − | 0.637458i | \(-0.220014\pi\) | |||||||
\(174\) | 593435. | + | 1.11190e6i | 0.000647405 | + | 0.00121302i | ||||
\(175\) | 2.64875e7 | 0.0282416 | ||||||||
\(176\) | 2.88575e8i | 0.300752i | ||||||||
\(177\) | −1.09349e9 | + | 5.83610e8i | −1.11409 | + | 0.594606i | ||||
\(178\) | −4.02299e6 | −0.00400746 | ||||||||
\(179\) | 6.15680e8i | 0.599712i | 0.953984 | + | 0.299856i | \(0.0969387\pi\) | ||||
−0.953984 | + | 0.299856i | \(0.903061\pi\) | |||||||
\(180\) | −9.06231e8 | − | 6.07151e8i | −0.863274 | − | 0.578371i | ||||
\(181\) | 1.28354e8 | 0.119590 | 0.0597951 | − | 0.998211i | \(-0.480955\pi\) | ||||
0.0597951 | + | 0.998211i | \(0.480955\pi\) | |||||||
\(182\) | − | 1.66341e7i | − | 0.0151605i | ||||||
\(183\) | 2.52317e8 | + | 4.72757e8i | 0.224979 | + | 0.421535i | ||||
\(184\) | 7.54634e6 | 0.00658363 | ||||||||
\(185\) | − | 3.09253e8i | − | 0.264014i | ||||||
\(186\) | 3.46748e7 | − | 1.85064e7i | 0.0289709 | − | 0.0154622i | ||||
\(187\) | −4.63042e8 | −0.378664 | ||||||||
\(188\) | 1.10610e9i | 0.885448i | ||||||||
\(189\) | −4.39562e8 | − | 4.41189e7i | −0.344487 | − | 0.0345762i | ||||
\(190\) | −2.28943e7 | −0.0175676 | ||||||||
\(191\) | 1.24168e9i | 0.932986i | 0.884525 | + | 0.466493i | \(0.154483\pi\) | ||||
−0.884525 | + | 0.466493i | \(0.845517\pi\) | |||||||
\(192\) | −6.36641e8 | − | 1.19285e9i | −0.468479 | − | 0.877771i | ||||
\(193\) | 2.13484e9 | 1.53864 | 0.769318 | − | 0.638866i | \(-0.220596\pi\) | ||||
0.769318 | + | 0.638866i | \(0.220596\pi\) | |||||||
\(194\) | − | 6.43674e7i | − | 0.0454422i | ||||||
\(195\) | 2.00450e9 | − | 1.06983e9i | 1.38633 | − | 0.739904i | ||||
\(196\) | −1.29780e9 | −0.879394 | ||||||||
\(197\) | 9.17198e7i | 0.0608973i | 0.999536 | + | 0.0304487i | \(0.00969361\pi\) | ||||
−0.999536 | + | 0.0304487i | \(0.990306\pi\) | |||||||
\(198\) | 7.47494e6 | − | 1.11571e7i | 0.00486348 | − | 0.00725920i | ||||
\(199\) | −272964. | −0.000174058 | −8.70290e−5 | − | 1.00000i | \(-0.500028\pi\) | ||||
−8.70290e−5 | 1.00000i | \(0.500028\pi\) | ||||||||
\(200\) | − | 7.56146e6i | − | 0.00472591i | ||||||
\(201\) | 3.40361e8 | + | 6.37721e8i | 0.208524 | + | 0.390703i | ||||
\(202\) | −4.35314e7 | −0.0261455 | ||||||||
\(203\) | − | 2.78951e7i | − | 0.0164265i | ||||||
\(204\) | 1.91725e9 | − | 1.02327e9i | 1.10703 | − | 0.590837i | ||||
\(205\) | 6.22988e8 | 0.352748 | ||||||||
\(206\) | − | 3.70627e7i | − | 0.0205811i | ||||||
\(207\) | 1.73335e8 | + | 1.16130e8i | 0.0944071 | + | 0.0632503i | ||||
\(208\) | 2.82113e9 | 1.50720 | ||||||||
\(209\) | 3.35332e8i | 0.175748i | ||||||||
\(210\) | −9.55512e6 | − | 1.79031e7i | −0.00491314 | − | 0.00920556i | ||||
\(211\) | 2.45761e9 | 1.23989 | 0.619944 | − | 0.784646i | \(-0.287155\pi\) | ||||
0.619944 | + | 0.784646i | \(0.287155\pi\) | |||||||
\(212\) | 3.74936e9i | 1.85615i | ||||||||
\(213\) | 7.92699e8 | − | 4.23075e8i | 0.385115 | − | 0.205541i | ||||
\(214\) | 6.45818e7 | 0.0307932 | ||||||||
\(215\) | − | 3.39085e9i | − | 1.58692i | ||||||
\(216\) | −1.25947e7 | + | 1.25483e8i | −0.00578594 | + | 0.0576461i | ||||
\(217\) | −8.69918e8 | −0.392319 | ||||||||
\(218\) | 7.82946e7i | 0.0346662i | ||||||||
\(219\) | −3.17040e8 | − | 5.94025e8i | −0.137828 | − | 0.258243i | ||||
\(220\) | −7.33934e8 | −0.313304 | ||||||||
\(221\) | 4.52673e9i | 1.89765i | ||||||||
\(222\) | −1.57646e7 | + | 8.41381e6i | −0.00649041 | + | 0.00346402i | ||||
\(223\) | −3.21507e9 | −1.30008 | −0.650042 | − | 0.759898i | \(-0.725249\pi\) | ||||
−0.650042 | + | 0.759898i | \(0.725249\pi\) | |||||||
\(224\) | − | 7.56965e7i | − | 0.0300666i | ||||||
\(225\) | 1.16363e8 | − | 1.73682e8i | 0.0454028 | − | 0.0677681i | ||||
\(226\) | 1.27746e8 | 0.0489681 | ||||||||
\(227\) | 4.88497e9i | 1.83975i | 0.392215 | + | 0.919874i | \(0.371709\pi\) | ||||
−0.392215 | + | 0.919874i | \(0.628291\pi\) | |||||||
\(228\) | −7.41042e8 | − | 1.38846e9i | −0.274223 | − | 0.513800i | ||||
\(229\) | −1.14386e9 | −0.415942 | −0.207971 | − | 0.978135i | \(-0.566686\pi\) | ||||
−0.207971 | + | 0.978135i | \(0.566686\pi\) | |||||||
\(230\) | 9.58422e6i | 0.00342488i | ||||||||
\(231\) | −2.62226e8 | + | 1.39953e8i | −0.0920931 | + | 0.0491514i | ||||
\(232\) | −7.96331e6 | −0.00274879 | ||||||||
\(233\) | 2.06400e9i | 0.700304i | 0.936693 | + | 0.350152i | \(0.113870\pi\) | ||||
−0.936693 | + | 0.350152i | \(0.886130\pi\) | |||||||
\(234\) | −1.09072e8 | − | 7.30755e7i | −0.0363790 | − | 0.0243730i | ||||
\(235\) | −2.81078e9 | −0.921628 | ||||||||
\(236\) | − | 3.91408e9i | − | 1.26178i | ||||||
\(237\) | −2.67568e9 | − | 5.01332e9i | −0.848088 | − | 1.58903i | ||||
\(238\) | 4.04303e7 | 0.0126008 | ||||||||
\(239\) | − | 3.60302e9i | − | 1.10427i | −0.833755 | − | 0.552134i | \(-0.813814\pi\) | ||
0.833755 | − | 0.552134i | \(-0.186186\pi\) | |||||||
\(240\) | 3.03634e9 | − | 1.62054e9i | 0.915179 | − | 0.488444i | ||||
\(241\) | 1.93455e9 | 0.573470 | 0.286735 | − | 0.958010i | \(-0.407430\pi\) | ||||
0.286735 | + | 0.958010i | \(0.407430\pi\) | |||||||
\(242\) | − | 9.03583e6i | − | 0.00263455i | ||||||
\(243\) | −2.22034e9 | + | 2.68845e9i | −0.636787 | + | 0.771040i | ||||
\(244\) | −1.69221e9 | −0.477414 | ||||||||
\(245\) | − | 3.29792e9i | − | 0.915326i | ||||||
\(246\) | −1.69496e7 | − | 3.17577e7i | −0.00462826 | − | 0.00867180i | ||||
\(247\) | 3.27822e9 | 0.880747 | ||||||||
\(248\) | 2.48338e8i | 0.0656503i | ||||||||
\(249\) | −5.48474e9 | + | 2.92728e9i | −1.42679 | + | 0.761495i | ||||
\(250\) | −1.08127e8 | −0.0276804 | ||||||||
\(251\) | − | 2.48100e8i | − | 0.0625074i | −0.999511 | − | 0.0312537i | \(-0.990050\pi\) | ||
0.999511 | − | 0.0312537i | \(-0.00994999\pi\) | |||||||
\(252\) | 7.76481e8 | − | 1.15897e9i | 0.192543 | − | 0.287389i | ||||
\(253\) | 1.40380e8 | 0.0342627 | ||||||||
\(254\) | 1.71575e8i | 0.0412212i | ||||||||
\(255\) | 2.60028e9 | + | 4.87205e9i | 0.614979 | + | 1.15226i | ||||
\(256\) | 4.25894e9 | 0.991612 | ||||||||
\(257\) | − | 5.63936e9i | − | 1.29270i | −0.763042 | − | 0.646349i | \(-0.776295\pi\) | ||
0.763042 | − | 0.646349i | \(-0.223705\pi\) | |||||||
\(258\) | −1.72854e8 | + | 9.22545e7i | −0.0390121 | + | 0.0208213i | ||||
\(259\) | 3.95501e8 | 0.0878919 | ||||||||
\(260\) | 7.17499e9i | 1.57010i | ||||||||
\(261\) | −1.82912e8 | − | 1.22546e8i | −0.0394167 | − | 0.0264082i | ||||
\(262\) | 2.10330e8 | 0.0446370 | ||||||||
\(263\) | − | 7.53017e9i | − | 1.57392i | −0.617006 | − | 0.786959i | \(-0.711655\pi\) | ||
0.617006 | − | 0.786959i | \(-0.288345\pi\) | |||||||
\(264\) | 3.99529e7 | + | 7.48583e7i | 0.00822494 | + | 0.0154108i | ||||
\(265\) | −9.52773e9 | −1.93199 | ||||||||
\(266\) | − | 2.92793e7i | − | 0.00584837i | ||||||
\(267\) | 6.19995e8 | − | 3.30900e8i | 0.121995 | − | 0.0651106i | ||||
\(268\) | −2.28269e9 | −0.442495 | ||||||||
\(269\) | − | 6.86100e9i | − | 1.31032i | −0.755489 | − | 0.655161i | \(-0.772601\pi\) | ||
0.755489 | − | 0.655161i | \(-0.227399\pi\) | |||||||
\(270\) | −1.59370e8 | − | 1.59959e7i | −0.0299882 | − | 0.00300992i | ||||
\(271\) | −3.01473e9 | −0.558947 | −0.279474 | − | 0.960153i | \(-0.590160\pi\) | ||||
−0.279474 | + | 0.960153i | \(0.590160\pi\) | |||||||
\(272\) | 6.85694e9i | 1.25272i | ||||||||
\(273\) | 1.36819e9 | + | 2.56353e9i | 0.246319 | + | 0.461518i | ||||
\(274\) | −3.46406e7 | −0.00614586 | ||||||||
\(275\) | − | 1.40661e8i | − | 0.0245948i | ||||||
\(276\) | −5.81251e8 | + | 3.10222e8i | −0.100168 | + | 0.0534609i | ||||
\(277\) | −1.63933e9 | −0.278449 | −0.139225 | − | 0.990261i | \(-0.544461\pi\) | ||||
−0.139225 | + | 0.990261i | \(0.544461\pi\) | |||||||
\(278\) | − | 1.32099e7i | − | 0.00221166i | ||||||
\(279\) | −3.82165e9 | + | 5.70417e9i | −0.630716 | + | 0.941403i | ||||
\(280\) | 1.28220e8 | 0.0208605 | ||||||||
\(281\) | − | 1.15302e10i | − | 1.84932i | −0.380798 | − | 0.924658i | \(-0.624351\pi\) | ||
0.380798 | − | 0.924658i | \(-0.375649\pi\) | |||||||
\(282\) | 7.64726e7 | + | 1.43284e8i | 0.0120923 | + | 0.0226569i | ||||
\(283\) | 4.61179e9 | 0.718991 | 0.359496 | − | 0.933147i | \(-0.382949\pi\) | ||||
0.359496 | + | 0.933147i | \(0.382949\pi\) | |||||||
\(284\) | 2.83743e9i | 0.436166i | ||||||||
\(285\) | 3.52831e9 | − | 1.88311e9i | 0.534795 | − | 0.285427i | ||||
\(286\) | −8.83349e7 | −0.0132029 | ||||||||
\(287\) | 7.96735e8i | 0.117432i | ||||||||
\(288\) | −4.96352e8 | − | 3.32543e8i | −0.0721473 | − | 0.0483368i | ||||
\(289\) | −4.02675e9 | −0.577249 | ||||||||
\(290\) | − | 1.01138e7i | − | 0.00142995i | ||||||
\(291\) | 5.29437e9 | + | 9.91986e9i | 0.738316 | + | 1.38336i | ||||
\(292\) | 2.12628e9 | 0.292476 | ||||||||
\(293\) | 3.62605e9i | 0.491997i | 0.969270 | + | 0.245999i | \(0.0791159\pi\) | ||||
−0.969270 | + | 0.245999i | \(0.920884\pi\) | |||||||
\(294\) | −1.68117e8 | + | 8.97262e7i | −0.0225020 | + | 0.0120096i | ||||
\(295\) | 9.94633e9 | 1.31333 | ||||||||
\(296\) | − | 1.12905e8i | − | 0.0147077i | ||||||
\(297\) | −2.34292e8 | + | 2.33428e9i | −0.0301114 | + | 0.300004i | ||||
\(298\) | 3.09980e8 | 0.0393069 | ||||||||
\(299\) | − | 1.37236e9i | − | 0.171705i | ||||||
\(300\) | 3.10843e8 | + | 5.82415e8i | 0.0383757 | + | 0.0719031i | ||||
\(301\) | 4.33653e9 | 0.528295 | ||||||||
\(302\) | − | 5.11297e6i | − | 0.000614675i | ||||||
\(303\) | 6.70875e9 | − | 3.58056e9i | 0.795923 | − | 0.424796i | ||||
\(304\) | 4.96575e9 | 0.581421 | ||||||||
\(305\) | − | 4.30019e9i | − | 0.496922i | ||||||
\(306\) | 1.77615e8 | − | 2.65107e8i | 0.0202578 | − | 0.0302368i | ||||
\(307\) | −3.76730e9 | −0.424108 | −0.212054 | − | 0.977258i | \(-0.568015\pi\) | ||||
−0.212054 | + | 0.977258i | \(0.568015\pi\) | |||||||
\(308\) | − | 9.38623e8i | − | 0.104301i | ||||||
\(309\) | 3.04850e9 | + | 5.71185e9i | 0.334389 | + | 0.626531i | ||||
\(310\) | −3.15401e8 | −0.0341520 | ||||||||
\(311\) | 1.22053e10i | 1.30469i | 0.757924 | + | 0.652343i | \(0.226214\pi\) | ||||
−0.757924 | + | 0.652343i | \(0.773786\pi\) | |||||||
\(312\) | 7.31820e8 | − | 3.90582e8i | 0.0772299 | − | 0.0412187i | ||||
\(313\) | −1.33667e9 | −0.139267 | −0.0696335 | − | 0.997573i | \(-0.522183\pi\) | ||||
−0.0696335 | + | 0.997573i | \(0.522183\pi\) | |||||||
\(314\) | − | 3.85529e8i | − | 0.0396587i | ||||||
\(315\) | 2.94514e9 | + | 1.97317e9i | 0.299132 | + | 0.200411i | ||||
\(316\) | 1.79449e10 | 1.79967 | ||||||||
\(317\) | − | 1.19962e10i | − | 1.18797i | −0.804475 | − | 0.593986i | \(-0.797553\pi\) | ||
0.804475 | − | 0.593986i | \(-0.202447\pi\) | |||||||
\(318\) | 2.59220e8 | + | 4.85690e8i | 0.0253489 | + | 0.0474953i | ||||
\(319\) | −1.48136e8 | −0.0143053 | ||||||||
\(320\) | 1.08501e10i | 1.03475i | ||||||||
\(321\) | −9.95290e9 | + | 5.31200e9i | −0.937409 | + | 0.500309i | ||||
\(322\) | −1.22572e7 | −0.00114016 | ||||||||
\(323\) | 7.96794e9i | 0.732042i | ||||||||
\(324\) | −4.18837e9 | − | 1.01830e10i | −0.380071 | − | 0.924049i | ||||
\(325\) | −1.37511e9 | −0.123255 | ||||||||
\(326\) | − | 5.93045e7i | − | 0.00525070i | ||||||
\(327\) | −6.43992e9 | − | 1.20662e10i | −0.563234 | − | 1.05531i | ||||
\(328\) | 2.27446e8 | 0.0196509 | ||||||||
\(329\) | − | 3.59469e9i | − | 0.306816i | ||||||
\(330\) | −9.50736e7 | + | 5.07421e7i | −0.00801686 | + | 0.00427871i | ||||
\(331\) | 1.21367e9 | 0.101108 | 0.0505542 | − | 0.998721i | \(-0.483901\pi\) | ||||
0.0505542 | + | 0.998721i | \(0.483901\pi\) | |||||||
\(332\) | − | 1.96324e10i | − | 1.61592i | ||||||
\(333\) | 1.73748e9 | − | 2.59336e9i | 0.141300 | − | 0.210904i | ||||
\(334\) | 9.23245e7 | 0.00741876 | ||||||||
\(335\) | − | 5.80069e9i | − | 0.460575i | ||||||
\(336\) | 2.07250e9 | + | 3.88316e9i | 0.162606 | + | 0.304669i | ||||
\(337\) | −1.27229e10 | −0.986434 | −0.493217 | − | 0.869906i | \(-0.664179\pi\) | ||||
−0.493217 | + | 0.869906i | \(0.664179\pi\) | |||||||
\(338\) | 4.85329e8i | 0.0371852i | ||||||||
\(339\) | −1.96873e10 | + | 1.05074e10i | −1.49069 | + | 0.795603i | ||||
\(340\) | −1.74393e10 | −1.30501 | ||||||||
\(341\) | 4.61967e9i | 0.341659i | ||||||||
\(342\) | −1.91989e8 | − | 1.28627e8i | −0.0140337 | − | 0.00940219i | ||||
\(343\) | 9.00979e9 | 0.650936 | ||||||||
\(344\) | − | 1.23796e9i | − | 0.0884044i | ||||||
\(345\) | −7.88324e8 | − | 1.47705e9i | −0.0556453 | − | 0.104261i | ||||
\(346\) | 5.29524e8 | 0.0369471 | ||||||||
\(347\) | 1.72507e10i | 1.18984i | 0.803786 | + | 0.594919i | \(0.202816\pi\) | ||||
−0.803786 | + | 0.594919i | \(0.797184\pi\) | |||||||
\(348\) | 6.13367e8 | − | 3.27363e8i | 0.0418219 | − | 0.0223209i | ||||
\(349\) | −1.81850e10 | −1.22578 | −0.612888 | − | 0.790170i | \(-0.709992\pi\) | ||||
−0.612888 | + | 0.790170i | \(0.709992\pi\) | |||||||
\(350\) | 1.22817e7i | 0.000818442i | ||||||||
\(351\) | 2.28201e10 | + | 2.29045e9i | 1.50345 | + | 0.150901i | ||||
\(352\) | −4.01984e8 | −0.0261841 | ||||||||
\(353\) | − | 1.60479e9i | − | 0.103352i | −0.998664 | − | 0.0516762i | \(-0.983544\pi\) | ||
0.998664 | − | 0.0516762i | \(-0.0164564\pi\) | |||||||
\(354\) | −2.70609e8 | − | 5.07029e8i | −0.0172317 | − | 0.0322864i | ||||
\(355\) | −7.21037e9 | −0.453988 | ||||||||
\(356\) | 2.21924e9i | 0.138167i | ||||||||
\(357\) | −6.23084e9 | + | 3.32549e9i | −0.383595 | + | 0.204730i | ||||
\(358\) | −2.85479e8 | −0.0173797 | ||||||||
\(359\) | − | 2.19165e10i | − | 1.31945i | −0.751507 | − | 0.659725i | \(-0.770673\pi\) | ||
0.751507 | − | 0.659725i | \(-0.229327\pi\) | |||||||
\(360\) | 5.63285e8 | − | 8.40757e8i | 0.0335365 | − | 0.0500565i | ||||
\(361\) | −1.12132e10 | −0.660241 | ||||||||
\(362\) | 5.95154e7i | 0.00346573i | ||||||||
\(363\) | 7.43218e8 | + | 1.39254e9i | 0.0428045 | + | 0.0802012i | ||||
\(364\) | −9.17605e9 | −0.522697 | ||||||||
\(365\) | 5.40324e9i | 0.304427i | ||||||||
\(366\) | −2.19208e8 | + | 1.16995e8i | −0.0122161 | + | 0.00651991i | ||||
\(367\) | 2.66903e10 | 1.47126 | 0.735629 | − | 0.677385i | \(-0.236887\pi\) | ||||
0.735629 | + | 0.677385i | \(0.236887\pi\) | |||||||
\(368\) | − | 2.07881e9i | − | 0.113350i | ||||||
\(369\) | 5.22430e9 | + | 3.50014e9i | 0.281788 | + | 0.188791i | ||||
\(370\) | 1.43395e8 | 0.00765114 | ||||||||
\(371\) | − | 1.21849e10i | − | 0.643173i | ||||||
\(372\) | −1.02089e10 | − | 1.91280e10i | −0.533098 | − | 0.998846i | ||||
\(373\) | −1.19076e10 | −0.615162 | −0.307581 | − | 0.951522i | \(-0.599520\pi\) | ||||
−0.307581 | + | 0.951522i | \(0.599520\pi\) | |||||||
\(374\) | − | 2.14704e8i | − | 0.0109737i | ||||||
\(375\) | 1.66637e10 | − | 8.89366e9i | 0.842649 | − | 0.449734i | ||||
\(376\) | −1.02619e9 | −0.0513422 | ||||||||
\(377\) | 1.44819e9i | 0.0716902i | ||||||||
\(378\) | 2.04571e7 | − | 2.03817e8i | 0.00100202 | − | 0.00998326i | ||||
\(379\) | 2.09110e10 | 1.01349 | 0.506744 | − | 0.862097i | \(-0.330849\pi\) | ||||
0.506744 | + | 0.862097i | \(0.330849\pi\) | |||||||
\(380\) | 1.26294e10i | 0.605687i | ||||||||
\(381\) | −1.41125e10 | − | 2.64420e10i | −0.669735 | − | 1.25486i | ||||
\(382\) | −5.75742e8 | −0.0270380 | ||||||||
\(383\) | 8.11163e9i | 0.376975i | 0.982076 | + | 0.188488i | \(0.0603585\pi\) | ||||
−0.982076 | + | 0.188488i | \(0.939641\pi\) | |||||||
\(384\) | 2.21894e9 | − | 1.18428e9i | 0.102052 | − | 0.0544665i | ||||
\(385\) | 2.38520e9 | 0.108563 | ||||||||
\(386\) | 9.89884e8i | 0.0445898i | ||||||||
\(387\) | 1.90509e10 | − | 2.84352e10i | 0.849319 | − | 1.26769i | ||||
\(388\) | −3.55077e10 | −1.56673 | ||||||||
\(389\) | 2.20202e9i | 0.0961664i | 0.998843 | + | 0.0480832i | \(0.0153113\pi\) | ||||
−0.998843 | + | 0.0480832i | \(0.984689\pi\) | |||||||
\(390\) | 4.96058e8 | + | 9.29446e8i | 0.0214425 | + | 0.0401759i | ||||
\(391\) | 3.33561e9 | 0.142715 | ||||||||
\(392\) | − | 1.20404e9i | − | 0.0509912i | ||||||
\(393\) | −3.24145e10 | + | 1.73001e10i | −1.35884 | + | 0.725234i | ||||
\(394\) | −4.25287e7 | −0.00176481 | ||||||||
\(395\) | 4.56010e10i | 1.87321i | ||||||||
\(396\) | −6.15468e9 | − | 4.12348e9i | −0.250279 | − | 0.167681i | ||||
\(397\) | 1.81707e10 | 0.731493 | 0.365747 | − | 0.930714i | \(-0.380814\pi\) | ||||
0.365747 | + | 0.930714i | \(0.380814\pi\) | |||||||
\(398\) | − | 126568.i | − | 5.04421e-6i | ||||||
\(399\) | 2.40829e9 | + | 4.51233e9i | 0.0950206 | + | 0.178037i | ||||
\(400\) | −2.08297e9 | −0.0813662 | ||||||||
\(401\) | 4.26261e10i | 1.64854i | 0.566200 | + | 0.824268i | \(0.308413\pi\) | ||||
−0.566200 | + | 0.824268i | \(0.691587\pi\) | |||||||
\(402\) | −2.95699e8 | + | 1.57819e8i | −0.0113226 | + | 0.00604303i | ||||
\(403\) | 4.51622e10 | 1.71220 | ||||||||
\(404\) | 2.40136e10i | 0.901431i | ||||||||
\(405\) | 2.58766e10 | − | 1.06433e10i | 0.961806 | − | 0.395601i | ||||
\(406\) | 1.29344e7 | 0.000476040 | ||||||||
\(407\) | − | 2.10030e9i | − | 0.0765425i | ||||||
\(408\) | 9.49336e8 | + | 1.77873e9i | 0.0342594 | + | 0.0641905i | ||||
\(409\) | −1.92596e10 | −0.688263 | −0.344131 | − | 0.938921i | \(-0.611827\pi\) | ||||
−0.344131 | + | 0.938921i | \(0.611827\pi\) | |||||||
\(410\) | 2.88867e8i | 0.0102226i | ||||||||
\(411\) | 5.33856e9 | − | 2.84927e9i | 0.187093 | − | 0.0998541i | ||||
\(412\) | −2.04453e10 | −0.709585 | ||||||||
\(413\) | 1.27203e10i | 0.437217i | ||||||||
\(414\) | −5.38472e7 | + | 8.03721e7i | −0.00183300 | + | 0.00273592i | ||||
\(415\) | 4.98890e10 | 1.68195 | ||||||||
\(416\) | 3.92982e9i | 0.131220i | ||||||||
\(417\) | 1.08654e9 | + | 2.03581e9i | 0.0359337 | + | 0.0673276i | ||||
\(418\) | −1.55487e8 | −0.00509317 | ||||||||
\(419\) | − | 1.31277e10i | − | 0.425925i | −0.977060 | − | 0.212963i | \(-0.931689\pi\) | ||
0.977060 | − | 0.212963i | \(-0.0683112\pi\) | |||||||
\(420\) | −9.87605e9 | + | 5.27099e9i | −0.317385 | + | 0.169393i | ||||
\(421\) | 4.99077e10 | 1.58869 | 0.794346 | − | 0.607466i | \(-0.207814\pi\) | ||||
0.794346 | + | 0.607466i | \(0.207814\pi\) | |||||||
\(422\) | 1.13955e9i | 0.0359320i | ||||||||
\(423\) | −2.35709e10 | − | 1.57919e10i | −0.736231 | − | 0.493255i | ||||
\(424\) | −3.47847e9 | −0.107628 | ||||||||
\(425\) | − | 3.34230e9i | − | 0.102445i | ||||||
\(426\) | 1.96172e8 | + | 3.67560e8i | 0.00595659 | + | 0.0111606i | ||||
\(427\) | 5.49948e9 | 0.165428 | ||||||||
\(428\) | − | 3.56259e10i | − | 1.06167i | ||||||
\(429\) | 1.36136e10 | − | 7.26575e9i | 0.401923 | − | 0.214512i | ||||
\(430\) | 1.57227e9 | 0.0459890 | ||||||||
\(431\) | 5.19660e10i | 1.50595i | 0.658050 | + | 0.752975i | \(0.271382\pi\) | ||||
−0.658050 | + | 0.752975i | \(0.728618\pi\) | |||||||
\(432\) | 3.45671e10 | + | 3.46950e9i | 0.992494 | + | 0.0996167i | ||||
\(433\) | −3.51552e10 | −1.00009 | −0.500043 | − | 0.866001i | \(-0.666683\pi\) | ||||
−0.500043 | + | 0.866001i | \(0.666683\pi\) | |||||||
\(434\) | − | 4.03364e8i | − | 0.0113694i | ||||||
\(435\) | 8.31882e8 | + | 1.55867e9i | 0.0232330 | + | 0.0435307i | ||||
\(436\) | 4.31905e10 | 1.19520 | ||||||||
\(437\) | − | 2.41563e9i | − | 0.0662375i | ||||||
\(438\) | 2.75438e8 | − | 1.47005e8i | 0.00748389 | − | 0.00399426i | ||||
\(439\) | −2.78675e10 | −0.750308 | −0.375154 | − | 0.926963i | \(-0.622410\pi\) | ||||
−0.375154 | + | 0.926963i | \(0.622410\pi\) | |||||||
\(440\) | − | 6.80909e8i | − | 0.0181668i | ||||||
\(441\) | 1.85288e10 | − | 2.76560e10i | 0.489883 | − | 0.731197i | ||||
\(442\) | −2.09896e9 | −0.0549939 | ||||||||
\(443\) | − | 7.13519e10i | − | 1.85264i | −0.376740 | − | 0.926319i | \(-0.622955\pi\) | ||
0.376740 | − | 0.926319i | \(-0.377045\pi\) | |||||||
\(444\) | 4.64140e9 | + | 8.69641e9i | 0.119431 | + | 0.223773i | ||||
\(445\) | −5.63946e9 | −0.143813 | ||||||||
\(446\) | − | 1.49077e9i | − | 0.0376765i | ||||||
\(447\) | −4.77720e10 | + | 2.54966e10i | −1.19658 | + | 0.638634i | ||||
\(448\) | −1.38762e10 | −0.344475 | ||||||||
\(449\) | 2.72252e10i | 0.669863i | 0.942242 | + | 0.334932i | \(0.108713\pi\) | ||||
−0.942242 | + | 0.334932i | \(0.891287\pi\) | |||||||
\(450\) | 8.05331e7 | + | 5.39551e7i | 0.00196392 | + | 0.00131578i | ||||
\(451\) | 4.23103e9 | 0.102268 | ||||||||
\(452\) | − | 7.04698e10i | − | 1.68830i | ||||||
\(453\) | 4.20554e8 | + | 7.87975e8i | 0.00998685 | + | 0.0187120i | ||||
\(454\) | −2.26507e9 | −0.0533160 | ||||||||
\(455\) | − | 2.33178e10i | − | 0.544055i | ||||||
\(456\) | 1.28815e9 | − | 6.87502e8i | 0.0297924 | − | 0.0159006i | ||||
\(457\) | −8.26157e10 | −1.89408 | −0.947039 | − | 0.321119i | \(-0.895941\pi\) | ||||
−0.947039 | + | 0.321119i | \(0.895941\pi\) | |||||||
\(458\) | − | 5.30388e8i | − | 0.0120540i | ||||||
\(459\) | −5.56709e9 | + | 5.54657e10i | −0.125423 | + | 1.24961i | ||||
\(460\) | 5.28704e9 | 0.118081 | ||||||||
\(461\) | 1.73061e10i | 0.383173i | 0.981476 | + | 0.191586i | \(0.0613632\pi\) | ||||
−0.981476 | + | 0.191586i | \(0.938637\pi\) | |||||||
\(462\) | −6.48937e7 | − | 1.21589e8i | −0.00142441 | − | 0.00266886i | ||||
\(463\) | −3.11536e10 | −0.677930 | −0.338965 | − | 0.940799i | \(-0.610077\pi\) | ||||
−0.338965 | + | 0.940799i | \(0.610077\pi\) | |||||||
\(464\) | 2.19367e9i | 0.0473260i | ||||||||
\(465\) | 4.86075e10 | − | 2.59425e10i | 1.03966 | − | 0.554881i | ||||
\(466\) | −9.57039e8 | −0.0202949 | ||||||||
\(467\) | 4.46334e10i | 0.938410i | 0.883089 | + | 0.469205i | \(0.155459\pi\) | ||||
−0.883089 | + | 0.469205i | \(0.844541\pi\) | |||||||
\(468\) | −4.03114e10 | + | 6.01686e10i | −0.840319 | + | 1.25426i | ||||
\(469\) | 7.41846e9 | 0.153328 | ||||||||
\(470\) | − | 1.30331e9i | − | 0.0267088i | ||||||
\(471\) | 3.17107e10 | + | 5.94151e10i | 0.644351 | + | 1.20730i | ||||
\(472\) | 3.63130e9 | 0.0731634 | ||||||||
\(473\) | − | 2.30290e10i | − | 0.460077i | ||||||
\(474\) | 2.32458e9 | − | 1.24066e9i | 0.0460502 | − | 0.0245776i | ||||
\(475\) | −2.42047e9 | −0.0475472 | ||||||||
\(476\) | − | 2.23030e10i | − | 0.434445i | ||||||
\(477\) | −7.98983e10 | − | 5.35298e10i | −1.54335 | − | 1.03400i | ||||
\(478\) | 1.67065e9 | 0.0320018 | ||||||||
\(479\) | − | 2.84370e10i | − | 0.540184i | −0.962835 | − | 0.270092i | \(-0.912946\pi\) | ||
0.962835 | − | 0.270092i | \(-0.0870541\pi\) | |||||||
\(480\) | 2.25740e9 | + | 4.22961e9i | 0.0425250 | + | 0.0796774i | ||||
\(481\) | −2.05326e10 | −0.383588 | ||||||||
\(482\) | 8.97012e8i | 0.0166192i | ||||||||
\(483\) | 1.88899e9 | − | 1.00818e9i | 0.0347090 | − | 0.0185247i | ||||
\(484\) | −4.98453e9 | −0.0908327 | ||||||||
\(485\) | − | 9.02308e10i | − | 1.63075i | ||||||
\(486\) | −1.24658e9 | − | 1.02953e9i | −0.0223448 | − | 0.0184541i | ||||
\(487\) | −8.77522e10 | −1.56006 | −0.780031 | − | 0.625741i | \(-0.784797\pi\) | ||||
−0.780031 | + | 0.625741i | \(0.784797\pi\) | |||||||
\(488\) | − | 1.56995e9i | − | 0.0276826i | ||||||
\(489\) | 4.87793e9 | + | 9.13960e9i | 0.0853101 | + | 0.159842i | ||||
\(490\) | 1.52918e9 | 0.0265262 | ||||||||
\(491\) | − | 4.84047e10i | − | 0.832841i | −0.909172 | − | 0.416420i | \(-0.863285\pi\) | ||
0.909172 | − | 0.416420i | \(-0.136715\pi\) | |||||||
\(492\) | −1.75188e10 | + | 9.35006e9i | −0.298982 | + | 0.159571i | ||||
\(493\) | −3.51992e9 | −0.0595861 | ||||||||
\(494\) | 1.52005e9i | 0.0255241i | ||||||||
\(495\) | 1.04784e10 | − | 1.56400e10i | 0.174532 | − | 0.260506i | ||||
\(496\) | 6.84103e10 | 1.13030 | ||||||||
\(497\) | − | 9.22129e9i | − | 0.151135i | ||||||
\(498\) | −1.35732e9 | − | 2.54317e9i | −0.0220682 | − | 0.0413483i | ||||
\(499\) | 6.67276e10 | 1.07623 | 0.538113 | − | 0.842873i | \(-0.319137\pi\) | ||||
0.538113 | + | 0.842873i | \(0.319137\pi\) | |||||||
\(500\) | 5.96469e10i | 0.954351i | ||||||||
\(501\) | −1.42284e10 | + | 7.59391e9i | −0.225843 | + | 0.120535i | ||||
\(502\) | 1.15039e8 | 0.00181147 | ||||||||
\(503\) | 4.41867e10i | 0.690271i | 0.938553 | + | 0.345136i | \(0.112167\pi\) | ||||
−0.938553 | + | 0.345136i | \(0.887833\pi\) | |||||||
\(504\) | 1.07524e9 | + | 7.20382e8i | 0.0166641 | + | 0.0111645i | ||||
\(505\) | −6.10226e10 | −0.938264 | ||||||||
\(506\) | 6.50914e7i | 0.000992936i | ||||||||
\(507\) | −3.99195e10 | − | 7.47956e10i | −0.604161 | − | 1.13199i | ||||
\(508\) | 9.46479e10 | 1.42120 | ||||||||
\(509\) | 1.51164e10i | 0.225204i | 0.993640 | + | 0.112602i | \(0.0359186\pi\) | ||||
−0.993640 | + | 0.112602i | \(0.964081\pi\) | |||||||
\(510\) | −2.25908e9 | + | 1.20570e9i | −0.0333926 | + | 0.0178221i | ||||
\(511\) | −6.91016e9 | −0.101346 | ||||||||
\(512\) | 9.92405e9i | 0.144414i | ||||||||
\(513\) | 4.01678e10 | + | 4.03165e9i | 0.579975 | + | 0.0582121i | ||||
\(514\) | 2.61486e9 | 0.0374625 | ||||||||
\(515\) | − | 5.19548e10i | − | 0.738579i | ||||||
\(516\) | 5.08913e10 | + | 9.53530e10i | 0.717868 | + | 1.34504i | ||||
\(517\) | −1.90895e10 | −0.267197 | ||||||||
\(518\) | 1.83386e8i | 0.00254711i | ||||||||
\(519\) | −8.16065e10 | + | 4.35545e10i | −1.12475 | + | 0.600294i | ||||
\(520\) | −6.65661e9 | −0.0910416 | ||||||||
\(521\) | − | 3.51670e8i | − | 0.00477292i | −0.999997 | − | 0.00238646i | \(-0.999240\pi\) | ||
0.999997 | − | 0.00238646i | \(-0.000759635\pi\) | |||||||
\(522\) | 5.68224e7 | − | 8.48129e7i | 0.000765311 | − | 0.00114230i | ||||
\(523\) | 1.15691e10 | 0.154629 | 0.0773146 | − | 0.997007i | \(-0.475365\pi\) | ||||
0.0773146 | + | 0.997007i | \(0.475365\pi\) | |||||||
\(524\) | − | 1.16026e11i | − | 1.53897i | ||||||
\(525\) | −1.01020e9 | − | 1.89278e9i | −0.0132975 | − | 0.0249151i | ||||
\(526\) | 3.49160e9 | 0.0456122 | ||||||||
\(527\) | 1.09770e11i | 1.42311i | ||||||||
\(528\) | 2.06214e10 | − | 1.10059e10i | 0.265327 | − | 0.141609i | ||||
\(529\) | 7.72997e10 | 0.987087 | ||||||||
\(530\) | − | 4.41783e9i | − | 0.0559893i | ||||||
\(531\) | 8.34087e10 | + | 5.58816e10i | 1.04914 | + | 0.702896i | ||||
\(532\) | −1.61517e10 | −0.201637 | ||||||||
\(533\) | − | 4.13629e10i | − | 0.512509i | ||||||
\(534\) | 1.53432e8 | + | 2.87480e8i | 0.00188691 | + | 0.00353543i | ||||
\(535\) | 9.05312e10 | 1.10505 | ||||||||
\(536\) | − | 2.11777e9i | − | 0.0256578i | ||||||
\(537\) | 4.39961e10 | − | 2.34813e10i | 0.529074 | − | 0.282374i | ||||
\(538\) | 3.18131e9 | 0.0379732 | ||||||||
\(539\) | − | 2.23979e10i | − | 0.265370i | ||||||
\(540\) | −8.82399e9 | + | 8.79146e10i | −0.103774 | + | 1.03392i | ||||
\(541\) | 1.29152e11 | 1.50770 | 0.753848 | − | 0.657049i | \(-0.228196\pi\) | ||||
0.753848 | + | 0.657049i | \(0.228196\pi\) | |||||||
\(542\) | − | 1.39787e9i | − | 0.0161983i | ||||||
\(543\) | −4.89528e9 | − | 9.17210e9i | −0.0563090 | − | 0.105504i | ||||
\(544\) | −9.55168e9 | −0.109065 | ||||||||
\(545\) | 1.09754e11i | 1.24404i | ||||||||
\(546\) | −1.18866e9 | + | 6.34406e8i | −0.0133748 | + | 0.00713833i | ||||
\(547\) | −6.65377e10 | −0.743222 | −0.371611 | − | 0.928388i | \(-0.621195\pi\) | ||||
−0.371611 | + | 0.928388i | \(0.621195\pi\) | |||||||
\(548\) | 1.91091e10i | 0.211894i | ||||||||
\(549\) | 2.41598e10 | − | 3.60608e10i | 0.265953 | − | 0.396960i | ||||
\(550\) | 6.52218e7 | 0.000712758 | ||||||||
\(551\) | 2.54910e9i | 0.0276554i | ||||||||
\(552\) | −2.87809e8 | − | 5.39256e8i | −0.00309990 | − | 0.00580817i | ||||
\(553\) | −5.83188e10 | −0.623603 | ||||||||
\(554\) | − | 7.60124e8i | − | 0.00806948i | ||||||
\(555\) | −2.20990e10 | + | 1.17945e10i | −0.232917 | + | 0.124311i | ||||
\(556\) | −7.28709e9 | −0.0762526 | ||||||||
\(557\) | 3.91079e10i | 0.406297i | 0.979148 | + | 0.203149i | \(0.0651175\pi\) | ||||
−0.979148 | + | 0.203149i | \(0.934883\pi\) | |||||||
\(558\) | −2.64492e9 | − | 1.77202e9i | −0.0272819 | − | 0.0182782i | ||||
\(559\) | −2.25133e11 | −2.30564 | ||||||||
\(560\) | − | 3.53211e10i | − | 0.359155i | ||||||
\(561\) | 1.76599e10 | + | 3.30886e10i | 0.178294 | + | 0.334062i | ||||
\(562\) | 5.34633e9 | 0.0535933 | ||||||||
\(563\) | 4.37934e10i | 0.435889i | 0.975961 | + | 0.217944i | \(0.0699351\pi\) | ||||
−0.975961 | + | 0.217944i | \(0.930065\pi\) | |||||||
\(564\) | 7.90411e10 | − | 4.21854e10i | 0.781154 | − | 0.416913i | ||||
\(565\) | 1.79075e11 | 1.75728 | ||||||||
\(566\) | 2.13840e9i | 0.0208364i | ||||||||
\(567\) | 1.36117e10 | + | 3.30934e10i | 0.131698 | + | 0.320191i | ||||
\(568\) | −2.63243e9 | −0.0252908 | ||||||||
\(569\) | − | 6.48473e10i | − | 0.618647i | −0.950957 | − | 0.309324i | \(-0.899897\pi\) | ||
0.950957 | − | 0.309324i | \(-0.100103\pi\) | |||||||
\(570\) | 8.73161e8 | + | 1.63601e9i | 0.00827170 | + | 0.0154984i | ||||
\(571\) | −3.05163e10 | −0.287070 | −0.143535 | − | 0.989645i | \(-0.545847\pi\) | ||||
−0.143535 | + | 0.989645i | \(0.545847\pi\) | |||||||
\(572\) | 4.87291e10i | 0.455202i | ||||||||
\(573\) | 8.87293e10 | − | 4.73561e10i | 0.823092 | − | 0.439296i | ||||
\(574\) | −3.69431e8 | −0.00340318 | ||||||||
\(575\) | 1.01328e9i | 0.00926953i | ||||||||
\(576\) | −6.09595e10 | + | 9.09879e10i | −0.553798 | + | 0.826597i | ||||
\(577\) | −1.20546e11 | −1.08755 | −0.543773 | − | 0.839232i | \(-0.683005\pi\) | ||||
−0.543773 | + | 0.839232i | \(0.683005\pi\) | |||||||
\(578\) | − | 1.86713e9i | − | 0.0167287i | ||||||
\(579\) | −8.14203e10 | − | 1.52554e11i | −0.724467 | − | 1.35741i | ||||
\(580\) | −5.57917e9 | −0.0493012 | ||||||||
\(581\) | 6.38027e10i | 0.559931i | ||||||||
\(582\) | −4.59965e9 | + | 2.45490e9i | −0.0400897 | + | 0.0213964i | ||||
\(583\) | −6.47077e10 | −0.560121 | ||||||||
\(584\) | 1.97266e9i | 0.0169591i | ||||||||
\(585\) | −1.52898e11 | − | 1.02438e11i | −1.30551 | − | 0.874655i | ||||
\(586\) | −1.68133e9 | −0.0142581 | ||||||||
\(587\) | − | 1.51686e11i | − | 1.27759i | −0.769375 | − | 0.638797i | \(-0.779432\pi\) | ||
0.769375 | − | 0.638797i | \(-0.220568\pi\) | |||||||
\(588\) | 4.94966e10 | + | 9.27398e10i | 0.414062 | + | 0.775813i | ||||
\(589\) | 7.94944e10 | 0.660504 | ||||||||
\(590\) | 4.61192e9i | 0.0380604i | ||||||||
\(591\) | 6.55423e9 | − | 3.49809e9i | 0.0537245 | − | 0.0286735i | ||||
\(592\) | −3.11022e10 | −0.253223 | ||||||||
\(593\) | 6.17836e10i | 0.499637i | 0.968293 | + | 0.249819i | \(0.0803710\pi\) | ||||
−0.968293 | + | 0.249819i | \(0.919629\pi\) | |||||||
\(594\) | −1.08236e9 | − | 1.08637e8i | −0.00869413 | − | 0.000872630i | ||||
\(595\) | 5.66755e10 | 0.452197 | ||||||||
\(596\) | − | 1.70997e11i | − | 1.35520i | ||||||
\(597\) | 1.04105e7 | + | 1.95058e7i | 8.19551e−5 | + | 0.000153556i | ||||
\(598\) | 6.36338e8 | 0.00497603 | ||||||||
\(599\) | − | 8.72409e10i | − | 0.677661i | −0.940847 | − | 0.338831i | \(-0.889969\pi\) | ||
0.940847 | − | 0.338831i | \(-0.110031\pi\) | |||||||
\(600\) | −5.40337e8 | + | 2.88385e8i | −0.00416927 | + | 0.00222520i | ||||
\(601\) | 2.06867e11 | 1.58560 | 0.792800 | − | 0.609482i | \(-0.208622\pi\) | ||||
0.792800 | + | 0.609482i | \(0.208622\pi\) | |||||||
\(602\) | 2.01077e9i | 0.0153100i | ||||||||
\(603\) | 3.25901e10 | − | 4.86439e10i | 0.246500 | − | 0.367925i | ||||
\(604\) | −2.82052e9 | −0.0211925 | ||||||||
\(605\) | − | 1.26665e10i | − | 0.0945442i | ||||||
\(606\) | 1.66024e9 | + | 3.11072e9i | 0.0123106 | + | 0.0230659i | ||||
\(607\) | −7.90355e10 | −0.582193 | −0.291097 | − | 0.956694i | \(-0.594020\pi\) | ||||
−0.291097 | + | 0.956694i | \(0.594020\pi\) | |||||||
\(608\) | 6.91726e9i | 0.0506197i | ||||||||
\(609\) | −1.99337e9 | + | 1.06389e9i | −0.0144917 | + | 0.00773440i | ||||
\(610\) | 1.99391e9 | 0.0144008 | ||||||||
\(611\) | 1.86620e11i | 1.33904i | ||||||||
\(612\) | −1.46244e11 | − | 9.79794e10i | −1.04249 | − | 0.698440i | ||||
\(613\) | 2.14208e11 | 1.51703 | 0.758513 | − | 0.651658i | \(-0.225926\pi\) | ||||
0.758513 | + | 0.651658i | \(0.225926\pi\) | |||||||
\(614\) | − | 1.74682e9i | − | 0.0122907i | ||||||
\(615\) | −2.37600e10 | − | 4.45183e10i | −0.166091 | − | 0.311199i | ||||
\(616\) | 8.70809e8 | 0.00604784 | ||||||||
\(617\) | 1.13314e11i | 0.781884i | 0.920415 | + | 0.390942i | \(0.127851\pi\) | ||||
−0.920415 | + | 0.390942i | \(0.872149\pi\) | |||||||
\(618\) | −2.64848e9 | + | 1.41353e9i | −0.0181569 | + | 0.00969060i | ||||
\(619\) | −2.75385e11 | −1.87576 | −0.937880 | − | 0.346961i | \(-0.887214\pi\) | ||||
−0.937880 | + | 0.346961i | \(0.887214\pi\) | |||||||
\(620\) | 1.73988e11i | 1.17748i | ||||||||
\(621\) | 1.68777e9 | − | 1.68154e10i | 0.0113487 | − | 0.113069i | ||||
\(622\) | −5.65935e9 | −0.0378099 | ||||||||
\(623\) | − | 7.21226e9i | − | 0.0478762i | ||||||
\(624\) | −1.07595e11 | − | 2.01596e11i | −0.709663 | − | 1.32967i | ||||
\(625\) | −1.64019e11 | −1.07492 | ||||||||
\(626\) | − | 6.19790e8i | − | 0.00403596i | ||||||
\(627\) | 2.39626e10 | − | 1.27892e10i | 0.155047 | − | 0.0827507i | ||||
\(628\) | −2.12674e11 | −1.36734 | ||||||||
\(629\) | − | 4.99059e10i | − | 0.318823i | ||||||
\(630\) | −9.14919e8 | + | 1.36560e9i | −0.00580792 | + | 0.00866887i | ||||
\(631\) | 3.40330e10 | 0.214676 | 0.107338 | − | 0.994223i | \(-0.465767\pi\) | ||||
0.107338 | + | 0.994223i | \(0.465767\pi\) | |||||||
\(632\) | 1.66484e10i | 0.104353i | ||||||||
\(633\) | −9.37303e10 | − | 1.75619e11i | −0.583801 | − | 1.09385i | ||||
\(634\) | 5.56240e9 | 0.0344275 | ||||||||
\(635\) | 2.40516e11i | 1.47927i | ||||||||
\(636\) | 2.67926e11 | − | 1.42996e11i | 1.63752 | − | 0.873968i | ||||
\(637\) | −2.18963e11 | −1.32988 | ||||||||
\(638\) | − | 6.86879e7i | − | 0.000414570i | ||||||
\(639\) | −6.04653e10 | − | 4.05101e10i | −0.362662 | − | 0.242974i | ||||
\(640\) | −2.01834e10 | −0.120302 | ||||||||
\(641\) | 2.06072e11i | 1.22064i | 0.792155 | + | 0.610320i | \(0.208959\pi\) | ||||
−0.792155 | + | 0.610320i | \(0.791041\pi\) | |||||||
\(642\) | −2.46307e9 | − | 4.61497e9i | −0.0144990 | − | 0.0271662i | ||||
\(643\) | 1.22928e11 | 0.719130 | 0.359565 | − | 0.933120i | \(-0.382925\pi\) | ||||
0.359565 | + | 0.933120i | \(0.382925\pi\) | |||||||
\(644\) | 6.76156e9i | 0.0393100i | ||||||||
\(645\) | −2.42308e11 | + | 1.29323e11i | −1.40000 | + | 0.747200i | ||||
\(646\) | −3.69458e9 | −0.0212146 | ||||||||
\(647\) | − | 9.90239e10i | − | 0.565097i | −0.959253 | − | 0.282548i | \(-0.908820\pi\) | ||
0.959253 | − | 0.282548i | \(-0.0911797\pi\) | |||||||
\(648\) | 9.44728e9 | − | 3.88577e9i | 0.0535805 | − | 0.0220382i | ||||
\(649\) | 6.75506e10 | 0.380759 | ||||||||
\(650\) | − | 6.37613e8i | − | 0.00357193i | ||||||
\(651\) | 3.31777e10 | + | 6.21637e10i | 0.184723 | + | 0.346109i | ||||
\(652\) | −3.27147e10 | −0.181031 | ||||||||
\(653\) | 2.36684e11i | 1.30172i | 0.759199 | + | 0.650858i | \(0.225591\pi\) | ||||
−0.759199 | + | 0.650858i | \(0.774409\pi\) | |||||||
\(654\) | 5.59488e9 | − | 2.98607e9i | 0.0305830 | − | 0.0163226i | ||||
\(655\) | 2.94842e11 | 1.60186 | ||||||||
\(656\) | − | 6.26551e10i | − | 0.338330i | ||||||
\(657\) | −3.03571e10 | + | 4.53109e10i | −0.162929 | + | 0.243187i | ||||
\(658\) | 1.66679e9 | 0.00889154 | ||||||||
\(659\) | − | 1.89365e11i | − | 1.00405i | −0.864852 | − | 0.502027i | \(-0.832588\pi\) | ||
0.864852 | − | 0.502027i | \(-0.167412\pi\) | |||||||
\(660\) | 2.79914e10 | + | 5.24464e10i | 0.147519 | + | 0.276401i | ||||
\(661\) | −1.69454e10 | −0.0887658 | −0.0443829 | − | 0.999015i | \(-0.514132\pi\) | ||||
−0.0443829 | + | 0.999015i | \(0.514132\pi\) | |||||||
\(662\) | 5.62753e8i | 0.00293013i | ||||||||
\(663\) | 3.23477e11 | − | 1.72644e11i | 1.67413 | − | 0.893506i | ||||
\(664\) | 1.82139e10 | 0.0936983 | ||||||||
\(665\) | − | 4.10440e10i | − | 0.209876i | ||||||
\(666\) | 1.20249e9 | + | 8.05637e8i | 0.00611201 | + | 0.00409489i | ||||
\(667\) | 1.06713e9 | 0.00539155 | ||||||||
\(668\) | − | 5.09299e10i | − | 0.255780i | ||||||
\(669\) | 1.22619e11 | + | 2.29747e11i | 0.612144 | + | 1.14695i | ||||
\(670\) | 2.68967e9 | 0.0133475 | ||||||||
\(671\) | − | 2.92048e10i | − | 0.144067i | ||||||
\(672\) | −5.40922e9 | + | 2.88698e9i | −0.0265251 | + | 0.0141568i | ||||
\(673\) | 1.86567e11 | 0.909442 | 0.454721 | − | 0.890634i | \(-0.349739\pi\) | ||||
0.454721 | + | 0.890634i | \(0.349739\pi\) | |||||||
\(674\) | − | 5.89939e9i | − | 0.0285869i | ||||||
\(675\) | −1.68491e10 | − | 1.69115e9i | −0.0811638 | − | 0.00814642i | ||||
\(676\) | 2.67727e11 | 1.28205 | ||||||||
\(677\) | − | 3.01974e11i | − | 1.43752i | −0.695258 | − | 0.718760i | \(-0.744710\pi\) | ||
0.695258 | − | 0.718760i | \(-0.255290\pi\) | |||||||
\(678\) | −4.87208e9 | − | 9.12863e9i | −0.0230566 | − | 0.0432003i | ||||
\(679\) | 1.15396e11 | 0.542887 | ||||||||
\(680\) | − | 1.61793e10i | − | 0.0756701i | ||||||
\(681\) | 3.49076e11 | − | 1.86307e11i | 1.62305 | − | 0.866245i | ||||
\(682\) | −2.14205e9 | −0.00990131 | ||||||||
\(683\) | 1.83659e11i | 0.843976i | 0.906601 | + | 0.421988i | \(0.138668\pi\) | ||||
−0.906601 | + | 0.421988i | \(0.861332\pi\) | |||||||
\(684\) | −7.09560e10 | + | 1.05909e11i | −0.324164 | + | 0.483846i | ||||
\(685\) | −4.85594e10 | −0.220552 | ||||||||
\(686\) | 4.17767e9i | 0.0188642i | ||||||||
\(687\) | 4.36256e10 | + | 8.17397e10i | 0.195846 | + | 0.366949i | ||||
\(688\) | −3.41024e11 | −1.52206 | ||||||||
\(689\) | 6.32587e11i | 2.80701i | ||||||||
\(690\) | 6.84881e8 | − | 3.65531e8i | 0.00302148 | − | 0.00161260i | ||||
\(691\) | 1.81205e11 | 0.794799 | 0.397400 | − | 0.917646i | \(-0.369913\pi\) | ||||
0.397400 | + | 0.917646i | \(0.369913\pi\) | |||||||
\(692\) | − | 2.92106e11i | − | 1.27385i | ||||||
\(693\) | 2.00020e10 | + | 1.34008e10i | 0.0867240 | + | 0.0581028i | ||||
\(694\) | −7.99880e9 | −0.0344816 | ||||||||
\(695\) | − | 1.85177e10i | − | 0.0793684i | ||||||
\(696\) | 3.03711e8 | + | 5.69052e8i | 0.00129427 | + | 0.00242502i | ||||
\(697\) | 1.00535e11 | 0.425977 | ||||||||
\(698\) | − | 8.43203e9i | − | 0.0355231i | ||||||
\(699\) | 1.47492e11 | − | 7.87187e10i | 0.617818 | − | 0.329738i | ||||
\(700\) | 6.77511e9 | 0.0282179 | ||||||||
\(701\) | 2.12324e10i | 0.0879280i | 0.999033 | + | 0.0439640i | \(0.0139987\pi\) | ||||
−0.999033 | + | 0.0439640i | \(0.986001\pi\) | |||||||
\(702\) | −1.06204e9 | + | 1.05812e10i | −0.00437312 | + | 0.0435700i | ||||
\(703\) | −3.61415e10 | −0.147974 | ||||||||
\(704\) | 7.36889e10i | 0.299993i | ||||||||
\(705\) | 1.07200e11 | + | 2.00856e11i | 0.433948 | + | 0.813072i | ||||
\(706\) | 7.44113e8 | 0.00299516 | ||||||||
\(707\) | − | 7.80414e10i | − | 0.312354i | ||||||
\(708\) | −2.79698e11 | + | 1.49279e11i | −1.11316 | + | 0.594107i | ||||
\(709\) | −4.90836e10 | −0.194246 | −0.0971228 | − | 0.995272i | \(-0.530964\pi\) | ||||
−0.0971228 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(710\) | − | 3.34331e9i | − | 0.0131566i | ||||||
\(711\) | −2.56201e11 | + | 3.82405e11i | −1.00254 | + | 1.49639i | ||||
\(712\) | −2.05891e9 | −0.00801155 | ||||||||
\(713\) | − | 3.32787e10i | − | 0.128768i | ||||||
\(714\) | −1.54196e9 | − | 2.88912e9i | −0.00593310 | − | 0.0111166i | ||||
\(715\) | −1.23829e11 | −0.473802 | ||||||||
\(716\) | 1.57482e11i | 0.599209i | ||||||||
\(717\) | −2.57469e11 | + | 1.37415e11i | −0.974200 | + | 0.519944i | ||||
\(718\) | 1.01623e10 | 0.0382378 | ||||||||
\(719\) | − | 4.27110e11i | − | 1.59818i | −0.601214 | − | 0.799088i | \(-0.705316\pi\) | ||
0.601214 | − | 0.799088i | \(-0.294684\pi\) | |||||||
\(720\) | −2.31605e11 | − | 1.55169e11i | −0.861824 | − | 0.577399i | ||||
\(721\) | 6.64447e10 | 0.245878 | ||||||||
\(722\) | − | 5.19936e9i | − | 0.0191338i | ||||||
\(723\) | −7.37813e10 | − | 1.38241e11i | −0.270018 | − | 0.505923i | ||||
\(724\) | 3.28311e10 | 0.119490 | ||||||||
\(725\) | − | 1.06927e9i | − | 0.00387020i | ||||||
\(726\) | −6.45694e8 | + | 3.44616e8i | −0.00232424 | + | 0.00124048i | ||||
\(727\) | −3.02187e11 | −1.08178 | −0.540889 | − | 0.841094i | \(-0.681912\pi\) | ||||
−0.540889 | + | 0.841094i | \(0.681912\pi\) | |||||||
\(728\) | − | 8.51309e9i | − | 0.0303083i | ||||||
\(729\) | 2.76796e11 | + | 5.61295e10i | 0.980053 | + | 0.198738i | ||||
\(730\) | −2.50538e9 | −0.00882230 | ||||||||
\(731\) | − | 5.47201e11i | − | 1.91636i | ||||||
\(732\) | 6.45390e10 | + | 1.20924e11i | 0.224790 | + | 0.421181i | ||||
\(733\) | 2.32545e11 | 0.805547 | 0.402773 | − | 0.915300i | \(-0.368046\pi\) | ||||
0.402773 | + | 0.915300i | \(0.368046\pi\) | |||||||
\(734\) | 1.23758e10i | 0.0426371i | ||||||||
\(735\) | −2.35667e11 | + | 1.25779e11i | −0.807513 | + | 0.430981i | ||||
\(736\) | 2.89577e9 | 0.00986853 | ||||||||
\(737\) | − | 3.93955e10i | − | 0.133529i | ||||||
\(738\) | −1.62295e9 | + | 2.42241e9i | −0.00547116 | + | 0.00816623i | ||||
\(739\) | −7.16663e10 | −0.240291 | −0.120145 | − | 0.992756i | \(-0.538336\pi\) | ||||
−0.120145 | + | 0.992756i | \(0.538336\pi\) | |||||||
\(740\) | − | 7.91022e10i | − | 0.263792i | ||||||
\(741\) | −1.25028e11 | − | 2.34260e11i | −0.414699 | − | 0.777006i | ||||
\(742\) | 5.64993e9 | 0.0186392 | ||||||||
\(743\) | − | 5.62589e11i | − | 1.84602i | −0.384780 | − | 0.923008i | \(-0.625723\pi\) | ||
0.384780 | − | 0.923008i | \(-0.374277\pi\) | |||||||
\(744\) | 1.77461e10 | − | 9.47132e9i | 0.0579176 | − | 0.0309114i | ||||
\(745\) | 4.34532e11 | 1.41058 | ||||||||
\(746\) | − | 5.52134e9i | − | 0.0178274i | ||||||
\(747\) | 4.18363e11 | + | 2.80292e11i | 1.34360 | + | 0.900179i | ||||
\(748\) | −1.18439e11 | −0.378346 | ||||||||
\(749\) | 1.15780e11i | 0.367879i | ||||||||
\(750\) | 4.12382e9 | + | 7.72664e9i | 0.0130333 | + | 0.0244200i | ||||
\(751\) | −5.17774e11 | −1.62772 | −0.813862 | − | 0.581058i | \(-0.802639\pi\) | ||||
−0.813862 | + | 0.581058i | \(0.802639\pi\) | |||||||
\(752\) | 2.82686e11i | 0.883960i | ||||||||
\(753\) | −1.77290e10 | + | 9.46224e9i | −0.0551449 | + | 0.0294316i | ||||
\(754\) | −6.71498e8 | −0.00207759 | ||||||||
\(755\) | − | 7.16740e9i | − | 0.0220584i | ||||||
\(756\) | −1.12433e11 | − | 1.12849e10i | −0.344198 | − | 0.0345472i | ||||
\(757\) | 6.69784e10 | 0.203963 | 0.101981 | − | 0.994786i | \(-0.467482\pi\) | ||||
0.101981 | + | 0.994786i | \(0.467482\pi\) | |||||||
\(758\) | 9.69604e9i | 0.0293709i | ||||||||
\(759\) | −5.35392e9 | − | 1.00314e10i | −0.0161326 | − | 0.0302271i | ||||
\(760\) | −1.17169e10 | −0.0351205 | ||||||||
\(761\) | 4.30349e11i | 1.28316i | 0.767054 | + | 0.641582i | \(0.221722\pi\) | ||||
−0.767054 | + | 0.641582i | \(0.778278\pi\) | |||||||
\(762\) | 1.22607e10 | − | 6.54368e9i | 0.0363659 | − | 0.0194090i | ||||
\(763\) | −1.40364e11 | −0.414149 | ||||||||
\(764\) | 3.17602e11i | 0.932202i | ||||||||
\(765\) | 2.48982e11 | − | 3.71629e11i | 0.726979 | − | 1.08508i | ||||
\(766\) | −3.76121e9 | −0.0109248 | ||||||||
\(767\) | − | 6.60380e11i | − | 1.90815i | ||||||
\(768\) | −1.62431e11 | − | 3.04341e11i | −0.466900 | − | 0.874814i | ||||
\(769\) | −4.30496e11 | −1.23102 | −0.615509 | − | 0.788130i | \(-0.711049\pi\) | ||||
−0.615509 | + | 0.788130i | \(0.711049\pi\) | |||||||
\(770\) | 1.10597e9i | 0.00314616i | ||||||||
\(771\) | −4.02984e11 | + | 2.15078e11i | −1.14044 | + | 0.608667i | ||||
\(772\) | 5.46060e11 | 1.53734 | ||||||||
\(773\) | 2.25688e11i | 0.632108i | 0.948741 | + | 0.316054i | \(0.102358\pi\) | ||||
−0.948741 | + | 0.316054i | \(0.897642\pi\) | |||||||
\(774\) | 1.31849e10 | + | 8.83352e9i | 0.0367377 | + | 0.0246133i | ||||
\(775\) | −3.33454e10 | −0.0924334 | ||||||||
\(776\) | − | 3.29423e10i | − | 0.0908462i | ||||||
\(777\) | −1.50840e10 | − | 2.82622e10i | −0.0413839 | − | 0.0775394i | ||||
\(778\) | −1.02104e9 | −0.00278691 | ||||||||
\(779\) | − | 7.28068e10i | − | 0.197707i | ||||||
\(780\) | 5.12720e11 | − | 2.73646e11i | 1.38517 | − | 0.739282i | ||||
\(781\) | −4.89693e10 | −0.131619 | ||||||||
\(782\) | 1.54666e9i | 0.00413588i | ||||||||
\(783\) | −1.78102e9 | + | 1.77446e10i | −0.00473830 | + | 0.0472083i | ||||
\(784\) | −3.31678e11 | −0.877916 | ||||||||
\(785\) | − | 5.40438e11i | − | 1.42321i | ||||||
\(786\) | −8.02172e9 | − | 1.50300e10i | −0.0210173 | − | 0.0393794i | ||||
\(787\) | 1.20189e11 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(788\) | 2.34606e10i | 0.0608462i | ||||||||
\(789\) | −5.38101e11 | + | 2.87192e11i | −1.38853 | + | 0.741079i | ||||
\(790\) | −2.11443e10 | −0.0542857 | ||||||||
\(791\) | 2.29018e11i | 0.585011i | ||||||||
\(792\) | 3.82556e9 | − | 5.71001e9i | 0.00972287 | − | 0.0145123i | ||||
\(793\) | −2.85508e11 | −0.721980 | ||||||||
\(794\) | 8.42542e9i | 0.0211987i | ||||||||
\(795\) | 3.63376e11 | + | 6.80845e11i | 0.909679 | + | 1.70443i | ||||
\(796\) | −6.98202e7 | −0.000173912 | ||||||||
\(797\) | − | 4.17483e11i | − | 1.03468i | −0.855781 | − | 0.517339i | \(-0.826923\pi\) | ||
0.855781 | − | 0.517339i | \(-0.173077\pi\) | |||||||
\(798\) | −2.09228e9 | + | 1.11668e9i | −0.00515951 | + | 0.00275370i | ||||
\(799\) | −4.53592e11 | −1.11296 | ||||||||
\(800\) | − | 2.90157e9i | − | 0.00708391i | ||||||
\(801\) | −4.72918e10 | − | 3.16843e10i | −0.114883 | − | 0.0769686i | ||||
\(802\) | −1.97649e10 | −0.0477746 | ||||||||
\(803\) | 3.66962e10i | 0.0882589i | ||||||||
\(804\) | 8.70592e10 | + | 1.63119e11i | 0.208349 | + | 0.390375i | ||||
\(805\) | −1.71822e10 | −0.0409163 | ||||||||
\(806\) | 2.09409e10i | 0.0496197i | ||||||||
\(807\) | −4.90282e11 | + | 2.61670e11i | −1.15598 | + | 0.616965i | ||||
\(808\) | −2.22787e10 | −0.0522690 | ||||||||
\(809\) | − | 4.05365e11i | − | 0.946351i | −0.880968 | − | 0.473176i | \(-0.843108\pi\) | ||
0.880968 | − | 0.473176i | \(-0.156892\pi\) | |||||||
\(810\) | 4.93511e9 | + | 1.19985e10i | 0.0114645 | + | 0.0278732i | ||||
\(811\) | 3.83222e10 | 0.0885865 | 0.0442932 | − | 0.999019i | \(-0.485896\pi\) | ||||
0.0442932 | + | 0.999019i | \(0.485896\pi\) | |||||||
\(812\) | − | 7.13516e9i | − | 0.0164127i | ||||||
\(813\) | 1.14978e11 | + | 2.15430e11i | 0.263180 | + | 0.493111i | ||||
\(814\) | 9.73867e8 | 0.00221821 | ||||||||
\(815\) | − | 8.31335e10i | − | 0.188428i | ||||||
\(816\) | 4.89992e11 | − | 2.61516e11i | 1.10517 | − | 0.589844i | ||||
\(817\) | −3.96279e11 | −0.889432 | ||||||||
\(818\) | − | 8.93032e9i | − | 0.0199459i | ||||||
\(819\) | 1.31007e11 | − | 1.95540e11i | 0.291178 | − | 0.434611i | ||||
\(820\) | 1.59351e11 | 0.352451 | ||||||||
\(821\) | 2.97651e11i | 0.655140i | 0.944827 | + | 0.327570i | \(0.106230\pi\) | ||||
−0.944827 | + | 0.327570i | \(0.893770\pi\) | |||||||
\(822\) | 1.32115e9 | + | 2.47539e9i | 0.00289378 | + | 0.00542196i | ||||
\(823\) | 9.20530e10 | 0.200650 | 0.100325 | − | 0.994955i | \(-0.468012\pi\) | ||||
0.100325 | + | 0.994955i | \(0.468012\pi\) | |||||||
\(824\) | − | 1.89681e10i | − | 0.0411449i | ||||||
\(825\) | −1.00515e10 | + | 5.36464e9i | −0.0216978 | + | 0.0115804i | ||||
\(826\) | −5.89815e9 | −0.0126706 | ||||||||
\(827\) | 3.95331e11i | 0.845159i | 0.906326 | + | 0.422580i | \(0.138875\pi\) | ||||
−0.906326 | + | 0.422580i | \(0.861125\pi\) | |||||||
\(828\) | 4.43365e10 | + | 2.97043e10i | 0.0943278 | + | 0.0631972i | ||||
\(829\) | 8.27992e11 | 1.75311 | 0.876553 | − | 0.481305i | \(-0.159837\pi\) | ||||
0.876553 | + | 0.481305i | \(0.159837\pi\) | |||||||
\(830\) | 2.31326e10i | 0.0487429i | ||||||||
\(831\) | 6.25220e10 | + | 1.17145e11i | 0.131108 | + | 0.245652i | ||||
\(832\) | 7.20387e11 | 1.50339 | ||||||||
\(833\) | − | 5.32204e11i | − | 1.10535i | ||||||
\(834\) | −9.43967e8 | + | 5.03809e8i | −0.00195116 | + | 0.00104136i | ||||
\(835\) | 1.29421e11 | 0.266232 | ||||||||
\(836\) | 8.57728e10i | 0.175600i | ||||||||
\(837\) | 5.53369e11 | + | 5.55417e10i | 1.12749 | + | 0.113166i | ||||
\(838\) | 6.08707e9 | 0.0123433 | ||||||||
\(839\) | 1.83018e11i | 0.369357i | 0.982799 | + | 0.184679i | \(0.0591244\pi\) | ||||
−0.982799 | + | 0.184679i | \(0.940876\pi\) | |||||||
\(840\) | −4.89017e9 | − | 9.16252e9i | −0.00982215 | − | 0.0184034i | ||||
\(841\) | 4.99120e11 | 0.997749 | ||||||||
\(842\) | 2.31413e10i | 0.0460404i | ||||||||
\(843\) | −8.23939e11 | + | 4.39748e11i | −1.63149 | + | 0.870750i | ||||
\(844\) | 6.28619e11 | 1.23885 | ||||||||
\(845\) | 6.80338e11i | 1.33444i | ||||||||
\(846\) | 7.32238e9 | − | 1.09294e10i | 0.0142946 | − | 0.0213360i | ||||
\(847\) | 1.61991e10 | 0.0314744 | ||||||||
\(848\) | 9.58222e11i | 1.85303i | ||||||||
\(849\) | −1.75888e11 | − | 3.29555e11i | −0.338537 | − | 0.634304i | ||||
\(850\) | 1.54976e9 | 0.00296885 | ||||||||
\(851\) | 1.51299e10i | 0.0288481i | ||||||||
\(852\) | 2.02761e11 | − | 1.08216e11i | 0.384791 | − | 0.205369i | ||||
\(853\) | −4.43216e11 | −0.837182 | −0.418591 | − | 0.908175i | \(-0.637476\pi\) | ||||
−0.418591 | + | 0.908175i | \(0.637476\pi\) | |||||||
\(854\) | 2.55000e9i | 0.00479412i | ||||||||
\(855\) | −2.69131e11 | − | 1.80311e11i | −0.503616 | − | 0.337409i | ||||
\(856\) | 3.30520e10 | 0.0615605 | ||||||||
\(857\) | − | 2.91913e11i | − | 0.541166i | −0.962697 | − | 0.270583i | \(-0.912784\pi\) | ||
0.962697 | − | 0.270583i | \(-0.0872165\pi\) | |||||||
\(858\) | 3.36899e9 | + | 6.31235e9i | 0.00621656 | + | 0.0116477i | ||||
\(859\) | 1.85769e11 | 0.341194 | 0.170597 | − | 0.985341i | \(-0.445430\pi\) | ||||
0.170597 | + | 0.985341i | \(0.445430\pi\) | |||||||
\(860\) | − | 8.67328e11i | − | 1.58559i | ||||||
\(861\) | 5.69341e10 | − | 3.03865e10i | 0.103600 | − | 0.0552928i | ||||
\(862\) | −2.40956e10 | −0.0436425 | ||||||||
\(863\) | 4.04477e11i | 0.729207i | 0.931163 | + | 0.364604i | \(0.118796\pi\) | ||||
−0.931163 | + | 0.364604i | \(0.881204\pi\) | |||||||
\(864\) | −4.83300e9 | + | 4.81518e10i | −0.00867284 | + | 0.0864087i | ||||
\(865\) | 7.42290e11 | 1.32590 | ||||||||
\(866\) | − | 1.63008e10i | − | 0.0289826i | ||||||
\(867\) | 1.53575e11 | + | 2.87748e11i | 0.271797 | + | 0.509256i | ||||
\(868\) | −2.22512e11 | −0.391990 | ||||||||
\(869\) | 3.09700e11i | 0.543078i | ||||||||
\(870\) | −7.22723e8 | + | 3.85728e8i | −0.00126152 | + | 0.000673293i | ||||
\(871\) | −3.85133e11 | −0.669173 | ||||||||
\(872\) | 4.00700e10i | 0.0693032i | ||||||||
\(873\) | 5.06945e11 | − | 7.56664e11i | 0.872778 | − | 1.30270i | ||||
\(874\) | 1.12008e9 | 0.00191957 | ||||||||
\(875\) | − | 1.93845e11i | − | 0.330691i | ||||||
\(876\) | −8.10940e10 | − | 1.51943e11i | −0.137712 | − | 0.258026i | ||||
\(877\) | 5.64450e11 | 0.954173 | 0.477086 | − | 0.878856i | \(-0.341693\pi\) | ||||
0.477086 | + | 0.878856i | \(0.341693\pi\) | |||||||
\(878\) | − | 1.29216e10i | − | 0.0217440i | ||||||
\(879\) | 2.59115e11 | − | 1.38293e11i | 0.434047 | − | 0.231657i | ||||
\(880\) | −1.87571e11 | −0.312778 | ||||||||
\(881\) | − | 3.37942e11i | − | 0.560969i | −0.959859 | − | 0.280484i | \(-0.909505\pi\) | ||
0.959859 | − | 0.280484i | \(-0.0904951\pi\) | |||||||
\(882\) | 1.28235e10 | + | 8.59144e9i | 0.0211901 | + | 0.0141968i | ||||
\(883\) | −1.07671e11 | −0.177115 | −0.0885574 | − | 0.996071i | \(-0.528226\pi\) | ||||
−0.0885574 | + | 0.996071i | \(0.528226\pi\) | |||||||
\(884\) | 1.15787e12i | 1.89605i | ||||||||
\(885\) | −3.79341e11 | − | 7.10757e11i | −0.618382 | − | 1.15864i | ||||
\(886\) | 3.30845e10 | 0.0536895 | ||||||||
\(887\) | − | 6.80937e11i | − | 1.10005i | −0.835148 | − | 0.550025i | \(-0.814618\pi\) | ||
0.835148 | − | 0.550025i | \(-0.185382\pi\) | |||||||
\(888\) | −8.06810e9 | + | 4.30606e9i | −0.0129754 | + | 0.00692514i | ||||
\(889\) | −3.07594e11 | −0.492460 | ||||||||
\(890\) | − | 2.61491e9i | − | 0.00416770i | ||||||
\(891\) | 1.75742e11 | − | 7.22844e10i | 0.278845 | − | 0.114692i | ||||
\(892\) | −8.22367e11 | −1.29899 | ||||||||
\(893\) | 3.28488e11i | 0.516551i | ||||||||
\(894\) | −1.18223e10 | − | 2.21510e10i | −0.0185076 | − | 0.0346771i | ||||
\(895\) | −4.00187e11 | −0.623693 | ||||||||
\(896\) | − | 2.58124e10i | − | 0.0400495i | ||||||
\(897\) | −9.80680e10 | + | 5.23403e10i | −0.151481 | + | 0.0808474i | ||||
\(898\) | −1.26238e10 | −0.0194127 | ||||||||
\(899\) | 3.51175e10i | 0.0537631i | ||||||||
\(900\) | 2.97638e10 | − | 4.44253e10i | 0.0453647 | − | 0.0677112i | ||||
\(901\) | −1.53754e12 | −2.33307 | ||||||||
\(902\) | 1.96185e9i | 0.00296373i | ||||||||
\(903\) | −1.65390e11 | − | 3.09886e11i | −0.248748 | − | 0.466069i | ||||
\(904\) | 6.53785e10 | 0.0978951 | ||||||||
\(905\) | 8.34291e10i | 0.124372i | ||||||||
\(906\) | −3.65369e8 | + | 1.95003e8i | −0.000542274 | + | 0.000289419i | ||||
\(907\) | 6.14742e11 | 0.908372 | 0.454186 | − | 0.890907i | \(-0.349930\pi\) | ||||
0.454186 | + | 0.890907i | \(0.349930\pi\) | |||||||
\(908\) | 1.24950e12i | 1.83820i | ||||||||
\(909\) | −5.11728e11 | − | 3.42844e11i | −0.749521 | − | 0.502159i | ||||
\(910\) | 1.08120e10 | 0.0157667 | ||||||||
\(911\) | − | 5.19358e11i | − | 0.754038i | −0.926206 | − | 0.377019i | \(-0.876949\pi\) | ||
0.926206 | − | 0.377019i | \(-0.123051\pi\) | |||||||
\(912\) | −1.89388e11 | − | 3.54849e11i | −0.273762 | − | 0.512937i | ||||
\(913\) | 3.38822e11 | 0.487628 | ||||||||
\(914\) | − | 3.83073e10i | − | 0.0548905i | ||||||
\(915\) | −3.07288e11 | + | 1.64004e11i | −0.438391 | + | 0.233975i | ||||
\(916\) | −2.92583e11 | −0.415592 | ||||||||
\(917\) | 3.77071e11i | 0.533268i | ||||||||
\(918\) | −2.57184e10 | − | 2.58135e9i | −0.0362137 | − | 0.00363477i | ||||
\(919\) | 3.76611e11 | 0.527996 | 0.263998 | − | 0.964523i | \(-0.414959\pi\) | ||||
0.263998 | + | 0.964523i | \(0.414959\pi\) | |||||||
\(920\) | 4.90506e9i | 0.00684688i | ||||||||
\(921\) | 1.43680e11 | + | 2.69208e11i | 0.199691 | + | 0.374154i | ||||
\(922\) | −8.02449e9 | −0.0111044 | ||||||||
\(923\) | 4.78728e11i | 0.659602i | ||||||||
\(924\) | −6.70734e10 | + | 3.57980e10i | −0.0920157 | + | 0.0491101i | ||||
\(925\) | 1.51602e10 | 0.0207080 | ||||||||
\(926\) | − | 1.44453e10i | − | 0.0196464i | ||||||
\(927\) | 2.91899e11 | − | 4.35687e11i | 0.395288 | − | 0.590004i | ||||
\(928\) | −3.05577e9 | −0.00412030 | ||||||||
\(929\) | 1.34697e12i | 1.80841i | 0.427101 | + | 0.904204i | \(0.359535\pi\) | ||||
−0.427101 | + | 0.904204i | \(0.640465\pi\) | |||||||
\(930\) | 1.20290e10 | + | 2.25383e10i | 0.0160805 | + | 0.0301294i | ||||
\(931\) | −3.85419e11 | −0.513020 | ||||||||
\(932\) | 5.27941e11i | 0.699716i | ||||||||
\(933\) | 8.72180e11 | − | 4.65495e11i | 1.15101 | − | 0.614311i | ||||
\(934\) | −2.06957e10 | −0.0271952 | ||||||||
\(935\) | − | 3.00973e11i | − | 0.393805i | ||||||
\(936\) | −5.58215e10 | − | 3.73989e10i | −0.0727274 | − | 0.0487255i | ||||
\(937\) | −7.59940e11 | −0.985873 | −0.492937 | − | 0.870065i | \(-0.664077\pi\) | ||||
−0.492937 | + | 0.870065i | \(0.664077\pi\) | |||||||
\(938\) | 3.43980e9i | 0.00444347i | ||||||||
\(939\) | 5.09792e10 | + | 9.55177e10i | 0.0655738 | + | 0.122863i | ||||
\(940\) | −7.18956e11 | −0.920854 | ||||||||
\(941\) | − | 7.21405e11i | − | 0.920070i | −0.887901 | − | 0.460035i | \(-0.847837\pi\) | ||
0.887901 | − | 0.460035i | \(-0.152163\pi\) | |||||||
\(942\) | −2.75497e10 | + | 1.47036e10i | −0.0349875 | + | 0.0186733i | ||||
\(943\) | −3.04791e10 | −0.0385438 | ||||||||
\(944\) | − | 1.00032e12i | − | 1.25966i | ||||||
\(945\) | 2.86769e10 | − | 2.85712e11i | 0.0359588 | − | 0.358262i | ||||
\(946\) | 1.06781e10 | 0.0133331 | ||||||||
\(947\) | − | 3.20479e11i | − | 0.398474i | −0.979951 | − | 0.199237i | \(-0.936154\pi\) | ||
0.979951 | − | 0.199237i | \(-0.0638464\pi\) | |||||||
\(948\) | −6.84399e11 | − | 1.28233e12i | −0.847376 | − | 1.58770i | ||||
\(949\) | 3.58744e11 | 0.442303 | ||||||||
\(950\) | − | 1.12232e9i | − | 0.00137792i | ||||||
\(951\) | −8.57239e11 | + | 4.57521e11i | −1.04804 | + | 0.559356i | ||||
\(952\) | 2.06916e10 | 0.0251911 | ||||||||
\(953\) | − | 6.13488e11i | − | 0.743763i | −0.928280 | − | 0.371882i | \(-0.878713\pi\) | ||
0.928280 | − | 0.371882i | \(-0.121287\pi\) | |||||||
\(954\) | 2.48207e10 | − | 3.70473e10i | 0.0299655 | − | 0.0447263i | ||||
\(955\) | −8.07079e11 | −0.970292 | ||||||||
\(956\) | − | 9.21597e11i | − | 1.10334i | ||||||
\(957\) | 5.64974e9 | + | 1.05857e10i | 0.00673567 | + | 0.0126204i | ||||
\(958\) | 1.31857e10 | 0.0156545 | ||||||||
\(959\) | − | 6.21023e10i | − | 0.0734232i | ||||||
\(960\) | 7.75343e11 | − | 4.13811e11i | 0.912870 | − | 0.487212i | ||||
\(961\) | 2.42258e11 | 0.284043 | ||||||||
\(962\) | − | 9.52059e9i | − | 0.0111164i | ||||||
\(963\) | 7.59184e11 | + | 5.08633e11i | 0.882758 | + | 0.591425i | ||||
\(964\) | 4.94828e11 | 0.572989 | ||||||||
\(965\) | 1.38763e12i | 1.60016i | ||||||||
\(966\) | 4.67475e8 | + | 8.75890e8i | 0.000536846 | + | 0.00100587i | ||||
\(967\) | 9.10858e11 | 1.04171 | 0.520853 | − | 0.853647i | \(-0.325614\pi\) | ||||
0.520853 | + | 0.853647i | \(0.325614\pi\) | |||||||
\(968\) | − | 4.62440e9i | − | 0.00526689i | ||||||
\(969\) | 5.69383e11 | − | 3.03888e11i | 0.645817 | − | 0.344682i | ||||
\(970\) | 4.18383e10 | 0.0472593 | ||||||||
\(971\) | − | 1.29844e12i | − | 1.46065i | −0.683102 | − | 0.730323i | \(-0.739369\pi\) | ||
0.683102 | − | 0.730323i | \(-0.260631\pi\) | |||||||
\(972\) | −5.67929e11 | + | 6.87665e11i | −0.636252 | + | 0.770392i | ||||
\(973\) | 2.36821e10 | 0.0264222 | ||||||||
\(974\) | − | 4.06890e10i | − | 0.0452107i | ||||||
\(975\) | 5.24451e10 | + | 9.82645e10i | 0.0580346 | + | 0.108737i | ||||
\(976\) | −4.32478e11 | −0.476612 | ||||||||
\(977\) | 9.39096e11i | 1.03070i | 0.856980 | + | 0.515349i | \(0.172338\pi\) | ||||
−0.856980 | + | 0.515349i | \(0.827662\pi\) | |||||||
\(978\) | −4.23786e9 | + | 2.26180e9i | −0.00463224 | + | 0.00247229i | ||||
\(979\) | −3.83005e10 | −0.0416940 | ||||||||
\(980\) | − | 8.43559e11i | − | 0.914558i | ||||||
\(981\) | −6.16633e11 | + | 9.20384e11i | −0.665811 | + | 0.993786i | ||||
\(982\) | 2.24443e10 | 0.0241358 | ||||||||
\(983\) | − | 8.21237e10i | − | 0.0879538i | −0.999033 | − | 0.0439769i | \(-0.985997\pi\) | ||
0.999033 | − | 0.0439769i | \(-0.0140028\pi\) | |||||||
\(984\) | −8.67453e9 | − | 1.62531e10i | −0.00925264 | − | 0.0173363i | ||||
\(985\) | −5.96171e10 | −0.0633324 | ||||||||
\(986\) | − | 1.63212e9i | − | 0.00172681i | ||||||
\(987\) | −2.56874e11 | + | 1.37097e11i | −0.270677 | + | 0.144464i | ||||
\(988\) | 8.38521e11 | 0.880007 | ||||||||
\(989\) | 1.65894e11i | 0.173399i | ||||||||
\(990\) | 7.25199e9 | + | 4.85865e9i | 0.00754947 | + | 0.00505795i | ||||
\(991\) | 1.37543e12 | 1.42608 | 0.713039 | − | 0.701125i | \(-0.247318\pi\) | ||||
0.713039 | + | 0.701125i | \(0.247318\pi\) | |||||||
\(992\) | 9.52951e10i | 0.0984065i | ||||||||
\(993\) | −4.62878e10 | − | 8.67277e10i | −0.0476068 | − | 0.0891991i | ||||
\(994\) | 4.27574e9 | 0.00437991 | ||||||||
\(995\) | − | 1.77425e8i | − | 0.000181018i | ||||||
\(996\) | −1.40291e12 | + | 7.48755e11i | −1.42559 | + | 0.760856i | ||||
\(997\) | −4.03195e11 | −0.408070 | −0.204035 | − | 0.978964i | \(-0.565406\pi\) | ||||
−0.204035 | + | 0.978964i | \(0.565406\pi\) | |||||||
\(998\) | 3.09403e10i | 0.0311891i | ||||||||
\(999\) | −2.51585e11 | − | 2.52516e10i | −0.252594 | − | 0.0253528i |
(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 | 33.9.b.a.23.14 | yes | 26 | |
3.2 | odd | 2 | inner | 33.9.b.a.23.13 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.9.b.a.23.13 | ✓ | 26 | 3.2 | odd | 2 | inner | |
33.9.b.a.23.14 | yes | 26 | 1.1 | even | 1 | trivial |