Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, 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("98.67");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.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: | \(50.4735119441\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{43})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 43x^{2} + 1849 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.2 | ||
Root | \(3.27872 + 5.67891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.79 |
Dual form | 98.10.c.i.67.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | − | 13.8564i | 0.353553 | − | 0.612372i | ||||
\(3\) | 26.2298 | + | 45.4313i | 0.186960 | + | 0.323824i | 0.944235 | − | 0.329272i | \(-0.106803\pi\) |
−0.757275 | + | 0.653096i | \(0.773470\pi\) | |||||||
\(4\) | −128.000 | − | 221.703i | −0.250000 | − | 0.433013i | ||||
\(5\) | 918.041 | − | 1590.09i | 0.656897 | − | 1.13778i | −0.324518 | − | 0.945880i | \(-0.605202\pi\) |
0.981415 | − | 0.191899i | \(-0.0614647\pi\) | |||||||
\(6\) | 839.352 | 0.264401 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 8465.50 | − | 14662.7i | 0.430092 | − | 0.744941i | ||||
\(10\) | −14688.7 | − | 25441.5i | −0.464496 | − | 0.804531i | ||||
\(11\) | −4690.00 | − | 8123.32i | −0.0965841 | − | 0.167289i | 0.813685 | − | 0.581307i | \(-0.197458\pi\) |
−0.910269 | + | 0.414018i | \(0.864125\pi\) | |||||||
\(12\) | 6714.82 | − | 11630.4i | 0.0934800 | − | 0.161912i | ||||
\(13\) | −179044. | −1.73866 | −0.869332 | − | 0.494229i | \(-0.835450\pi\) | ||||
−0.869332 | + | 0.494229i | \(0.835450\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 96320.0 | 0.491254 | ||||||||
\(16\) | −32768.0 | + | 56755.8i | −0.125000 | + | 0.216506i | ||||
\(17\) | 48944.7 | + | 84774.7i | 0.142130 | + | 0.246176i | 0.928299 | − | 0.371836i | \(-0.121272\pi\) |
−0.786169 | + | 0.618012i | \(0.787938\pi\) | |||||||
\(18\) | −135448. | − | 234603.i | −0.304121 | − | 0.526753i | ||||
\(19\) | 281367. | − | 487341.i | 0.495315 | − | 0.857910i | −0.504671 | − | 0.863312i | \(-0.668386\pi\) |
0.999985 | + | 0.00540159i | \(0.00171939\pi\) | |||||||
\(20\) | −470037. | −0.656897 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −150080. | −0.136591 | ||||||||
\(23\) | 489468. | − | 847783.i | 0.364711 | − | 0.631698i | −0.624019 | − | 0.781409i | \(-0.714501\pi\) |
0.988730 | + | 0.149711i | \(0.0478344\pi\) | |||||||
\(24\) | −107437. | − | 186086.i | −0.0661003 | − | 0.114489i | ||||
\(25\) | −709038. | − | 1.22809e6i | −0.363027 | − | 0.628782i | ||||
\(26\) | −1.43235e6 | + | 2.48091e6i | −0.614710 | + | 1.06471i | ||||
\(27\) | 1.92075e6 | 0.695560 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.31721e6 | −1.13348 | −0.566738 | − | 0.823898i | \(-0.691795\pi\) | ||||
−0.566738 | + | 0.823898i | \(0.691795\pi\) | |||||||
\(30\) | 770560. | − | 1.33465e6i | 0.173684 | − | 0.300830i | ||||
\(31\) | 3.98729e6 | + | 6.90619e6i | 0.775444 | + | 1.34311i | 0.934545 | + | 0.355845i | \(0.115807\pi\) |
−0.159101 | + | 0.987262i | \(0.550860\pi\) | |||||||
\(32\) | 524288. | + | 908093.i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 246035. | − | 426145.i | 0.0361147 | − | 0.0625525i | ||||
\(34\) | 1.56623e6 | 0.201002 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.33434e6 | −0.430092 | ||||||||
\(37\) | −1.35720e6 | + | 2.35073e6i | −0.119052 | + | 0.206203i | −0.919392 | − | 0.393342i | \(-0.871319\pi\) |
0.800341 | + | 0.599546i | \(0.204652\pi\) | |||||||
\(38\) | −4.50187e6 | − | 7.79746e6i | −0.350240 | − | 0.606634i | ||||
\(39\) | −4.69629e6 | − | 8.13421e6i | −0.325060 | − | 0.563021i | ||||
\(40\) | −3.76030e6 | + | 6.51303e6i | −0.232248 | + | 0.402266i | ||||
\(41\) | −9.00237e6 | −0.497542 | −0.248771 | − | 0.968562i | \(-0.580027\pi\) | ||||
−0.248771 | + | 0.968562i | \(0.580027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.47557e7 | −1.55031 | −0.775154 | − | 0.631773i | \(-0.782328\pi\) | ||||
−0.775154 | + | 0.631773i | \(0.782328\pi\) | |||||||
\(44\) | −1.20064e6 | + | 2.07957e6i | −0.0482921 | + | 0.0836443i | ||||
\(45\) | −1.55434e7 | − | 2.69219e7i | −0.565052 | − | 0.978699i | ||||
\(46\) | −7.83149e6 | − | 1.35645e7i | −0.257890 | − | 0.446678i | ||||
\(47\) | 2.10888e7 | − | 3.65268e7i | 0.630392 | − | 1.09187i | −0.357079 | − | 0.934074i | \(-0.616227\pi\) |
0.987471 | − | 0.157798i | \(-0.0504393\pi\) | |||||||
\(48\) | −3.43799e6 | −0.0934800 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.26892e7 | −0.513398 | ||||||||
\(51\) | −2.56762e6 | + | 4.44724e6i | −0.0531452 | + | 0.0920502i | ||||
\(52\) | 2.29177e7 | + | 3.96946e7i | 0.434666 | + | 0.752863i | ||||
\(53\) | −3.40340e7 | − | 5.89486e7i | −0.592476 | − | 1.02620i | −0.993898 | − | 0.110306i | \(-0.964817\pi\) |
0.401421 | − | 0.915894i | \(-0.368516\pi\) | |||||||
\(54\) | 1.53660e7 | − | 2.66147e7i | 0.245918 | − | 0.425942i | ||||
\(55\) | −1.72225e7 | −0.253783 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.95207e7 | 0.370416 | ||||||||
\(58\) | −3.45377e7 | + | 5.98211e7i | −0.400745 | + | 0.694110i | ||||
\(59\) | −1.71159e7 | − | 2.96456e7i | −0.183893 | − | 0.318512i | 0.759310 | − | 0.650729i | \(-0.225537\pi\) |
−0.943203 | + | 0.332217i | \(0.892203\pi\) | |||||||
\(60\) | −1.23290e7 | − | 2.13544e7i | −0.122813 | − | 0.212719i | ||||
\(61\) | −8.29163e7 | + | 1.43615e8i | −0.766753 | + | 1.32806i | 0.172562 | + | 0.984999i | \(0.444796\pi\) |
−0.939315 | + | 0.343056i | \(0.888538\pi\) | |||||||
\(62\) | 1.27593e8 | 1.09664 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −1.64370e8 | + | 2.84697e8i | −1.14212 | + | 1.97821i | ||||
\(66\) | −3.93656e6 | − | 6.81832e6i | −0.0255370 | − | 0.0442313i | ||||
\(67\) | −1.21472e8 | − | 2.10396e8i | −0.736445 | − | 1.27556i | −0.954086 | − | 0.299531i | \(-0.903170\pi\) |
0.217641 | − | 0.976029i | \(-0.430164\pi\) | |||||||
\(68\) | 1.25298e7 | − | 2.17023e7i | 0.0710650 | − | 0.123088i | ||||
\(69\) | 5.13545e7 | 0.272746 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.42925e7 | −0.440367 | −0.220183 | − | 0.975459i | \(-0.570666\pi\) | ||||
−0.220183 | + | 0.975459i | \(0.570666\pi\) | |||||||
\(72\) | −3.46747e7 | + | 6.00583e7i | −0.152060 | + | 0.263376i | ||||
\(73\) | 6.66672e7 | + | 1.15471e8i | 0.274764 | + | 0.475905i | 0.970076 | − | 0.242803i | \(-0.0780670\pi\) |
−0.695312 | + | 0.718708i | \(0.744734\pi\) | |||||||
\(74\) | 2.17152e7 | + | 3.76117e7i | 0.0841822 | + | 0.145808i | ||||
\(75\) | 3.71958e7 | − | 6.44249e7i | 0.135743 | − | 0.235114i | ||||
\(76\) | −1.44060e8 | −0.495315 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.50281e8 | −0.459705 | ||||||||
\(79\) | −3.38813e8 | + | 5.86841e8i | −0.978673 | + | 1.69511i | −0.311434 | + | 0.950268i | \(0.600809\pi\) |
−0.667239 | + | 0.744844i | \(0.732524\pi\) | |||||||
\(80\) | 6.01648e7 | + | 1.04208e8i | 0.164224 | + | 0.284445i | ||||
\(81\) | −1.16246e8 | − | 2.01343e8i | −0.300050 | − | 0.519702i | ||||
\(82\) | −7.20189e7 | + | 1.24740e8i | −0.175907 | + | 0.304681i | ||||
\(83\) | −4.41313e8 | −1.02069 | −0.510347 | − | 0.859968i | \(-0.670483\pi\) | ||||
−0.510347 | + | 0.859968i | \(0.670483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.79733e8 | 0.373459 | ||||||||
\(86\) | −2.78046e8 | + | 4.81589e8i | −0.548117 | + | 0.949366i | ||||
\(87\) | −1.13239e8 | − | 1.96137e8i | −0.211915 | − | 0.367047i | ||||
\(88\) | 1.92102e7 | + | 3.32731e7i | 0.0341476 | + | 0.0591455i | ||||
\(89\) | 2.77639e8 | − | 4.80885e8i | 0.469056 | − | 0.812430i | −0.530318 | − | 0.847799i | \(-0.677927\pi\) |
0.999374 | + | 0.0353693i | \(0.0112607\pi\) | |||||||
\(90\) | −4.97387e8 | −0.799104 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.50608e8 | −0.364711 | ||||||||
\(93\) | −2.09171e8 | + | 3.62295e8i | −0.289954 | + | 0.502215i | ||||
\(94\) | −3.37420e8 | − | 5.84429e8i | −0.445755 | − | 0.772070i | ||||
\(95\) | −5.16612e8 | − | 8.94799e8i | −0.650742 | − | 1.12712i | ||||
\(96\) | −2.75039e7 | + | 4.76381e7i | −0.0330502 | + | 0.0572446i | ||||
\(97\) | 1.26895e9 | 1.45536 | 0.727680 | − | 0.685917i | \(-0.240599\pi\) | ||||
0.727680 | + | 0.685917i | \(0.240599\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.58813e8 | −0.166160 | ||||||||
\(100\) | −1.81514e8 | + | 3.14391e8i | −0.181514 | + | 0.314391i | ||||
\(101\) | 6.84150e8 | + | 1.18498e9i | 0.654191 | + | 1.13309i | 0.982096 | + | 0.188382i | \(0.0603243\pi\) |
−0.327904 | + | 0.944711i | \(0.606342\pi\) | |||||||
\(102\) | 4.10819e7 | + | 7.11559e7i | 0.0375794 | + | 0.0650893i | ||||
\(103\) | −9.60758e7 | + | 1.66408e8i | −0.0841097 | + | 0.145682i | −0.905012 | − | 0.425387i | \(-0.860138\pi\) |
0.820902 | + | 0.571069i | \(0.193471\pi\) | |||||||
\(104\) | 7.33365e8 | 0.614710 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.08909e9 | −0.837888 | ||||||||
\(107\) | 5.24275e8 | − | 9.08071e8i | 0.386663 | − | 0.669719i | −0.605336 | − | 0.795970i | \(-0.706961\pi\) |
0.991998 | + | 0.126251i | \(0.0402945\pi\) | |||||||
\(108\) | −2.45856e8 | − | 4.25836e8i | −0.173890 | − | 0.301186i | ||||
\(109\) | −1.01879e9 | − | 1.76459e9i | −0.691297 | − | 1.19736i | −0.971413 | − | 0.237395i | \(-0.923706\pi\) |
0.280116 | − | 0.959966i | \(-0.409627\pi\) | |||||||
\(110\) | −1.37780e8 | + | 2.38641e8i | −0.0897259 | + | 0.155410i | ||||
\(111\) | −1.42396e8 | −0.0890315 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.70999e8 | −0.271748 | −0.135874 | − | 0.990726i | \(-0.543384\pi\) | ||||
−0.135874 | + | 0.990726i | \(0.543384\pi\) | |||||||
\(114\) | 2.36166e8 | − | 4.09051e8i | 0.130962 | − | 0.226833i | ||||
\(115\) | −8.98704e8 | − | 1.55660e9i | −0.479155 | − | 0.829921i | ||||
\(116\) | 5.52603e8 | + | 9.57137e8i | 0.283369 | + | 0.490810i | ||||
\(117\) | −1.51570e9 | + | 2.62527e9i | −0.747785 | + | 1.29520i | ||||
\(118\) | −5.47708e8 | −0.260064 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.94527e8 | −0.173684 | ||||||||
\(121\) | 1.13498e9 | − | 1.96585e9i | 0.481343 | − | 0.833711i | ||||
\(122\) | 1.32666e9 | + | 2.29784e9i | 0.542176 | + | 0.939077i | ||||
\(123\) | −2.36130e8 | − | 4.08989e8i | −0.0930203 | − | 0.161116i | ||||
\(124\) | 1.02075e9 | − | 1.76798e9i | 0.387722 | − | 0.671554i | ||||
\(125\) | 9.82396e8 | 0.359908 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.87598e9 | 0.981001 | 0.490500 | − | 0.871441i | \(-0.336814\pi\) | ||||
0.490500 | + | 0.871441i | \(0.336814\pi\) | |||||||
\(128\) | 1.34218e8 | − | 2.32472e8i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −9.11633e8 | − | 1.57900e9i | −0.289845 | − | 0.502027i | ||||
\(130\) | 2.62992e9 | + | 4.55516e9i | 0.807603 | + | 1.39881i | ||||
\(131\) | 2.98553e9 | − | 5.17109e9i | 0.885729 | − | 1.53413i | 0.0408540 | − | 0.999165i | \(-0.486992\pi\) |
0.844875 | − | 0.534963i | \(-0.179675\pi\) | |||||||
\(132\) | −1.25970e8 | −0.0361147 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.88711e9 | −1.04149 | ||||||||
\(135\) | 1.76333e9 | − | 3.05418e9i | 0.456911 | − | 0.791393i | ||||
\(136\) | −2.00478e8 | − | 3.47237e8i | −0.0502505 | − | 0.0870365i | ||||
\(137\) | 6.98550e8 | + | 1.20992e9i | 0.169416 | + | 0.293437i | 0.938215 | − | 0.346054i | \(-0.112478\pi\) |
−0.768799 | + | 0.639491i | \(0.779145\pi\) | |||||||
\(138\) | 4.10836e8 | − | 7.11589e8i | 0.0964301 | − | 0.167022i | ||||
\(139\) | −7.96582e9 | −1.80994 | −0.904969 | − | 0.425477i | \(-0.860106\pi\) | ||||
−0.904969 | + | 0.425477i | \(0.860106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.21261e9 | 0.471433 | ||||||||
\(142\) | −7.54340e8 | + | 1.30655e9i | −0.155693 | + | 0.269668i | ||||
\(143\) | 8.39718e8 | + | 1.45443e9i | 0.167927 | + | 0.290859i | ||||
\(144\) | 5.54795e8 | + | 9.60933e8i | 0.107523 | + | 0.186235i | ||||
\(145\) | −3.96338e9 | + | 6.86478e9i | −0.744577 | + | 1.28965i | ||||
\(146\) | 2.13335e9 | 0.388575 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.94885e8 | 0.119052 | ||||||||
\(149\) | 5.51302e9 | − | 9.54884e9i | 0.916329 | − | 1.58713i | 0.111386 | − | 0.993777i | \(-0.464471\pi\) |
0.804943 | − | 0.593352i | \(-0.202196\pi\) | |||||||
\(150\) | −5.95132e8 | − | 1.03080e9i | −0.0959849 | − | 0.166251i | ||||
\(151\) | 1.97237e9 | + | 3.41624e9i | 0.308739 | + | 0.534752i | 0.978087 | − | 0.208197i | \(-0.0667596\pi\) |
−0.669348 | + | 0.742949i | \(0.733426\pi\) | |||||||
\(152\) | −1.15248e9 | + | 1.99615e9i | −0.175120 | + | 0.303317i | ||||
\(153\) | 1.65737e9 | 0.244516 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.46420e10 | 2.03755 | ||||||||
\(156\) | −1.20225e9 | + | 2.08236e9i | −0.162530 | + | 0.281511i | ||||
\(157\) | 3.38171e9 | + | 5.85729e9i | 0.444209 | + | 0.769393i | 0.997997 | − | 0.0632648i | \(-0.0201513\pi\) |
−0.553787 | + | 0.832658i | \(0.686818\pi\) | |||||||
\(158\) | 5.42100e9 | + | 9.38945e9i | 0.692026 | + | 1.19862i | ||||
\(159\) | 1.78540e9 | − | 3.09241e9i | 0.221539 | − | 0.383716i | ||||
\(160\) | 1.92527e9 | 0.232248 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.71986e9 | −0.424335 | ||||||||
\(163\) | 1.47237e9 | − | 2.55021e9i | 0.163370 | − | 0.282965i | −0.772705 | − | 0.634765i | \(-0.781097\pi\) |
0.936075 | + | 0.351800i | \(0.114430\pi\) | |||||||
\(164\) | 1.15230e9 | + | 1.99585e9i | 0.124385 | + | 0.215442i | ||||
\(165\) | −4.51741e8 | − | 7.82438e8i | −0.0474473 | − | 0.0821811i | ||||
\(166\) | −3.53051e9 | + | 6.11502e9i | −0.360870 | + | 0.625045i | ||||
\(167\) | 1.59064e10 | 1.58251 | 0.791256 | − | 0.611485i | \(-0.209427\pi\) | ||||
0.791256 | + | 0.611485i | \(0.209427\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.14524e10 | 2.02295 | ||||||||
\(170\) | 1.43786e9 | − | 2.49046e9i | 0.132038 | − | 0.228696i | ||||
\(171\) | −4.76382e9 | − | 8.25117e9i | −0.426062 | − | 0.737961i | ||||
\(172\) | 4.44873e9 | + | 7.70542e9i | 0.387577 | + | 0.671303i | ||||
\(173\) | 5.16493e9 | − | 8.94592e9i | 0.438386 | − | 0.759307i | −0.559179 | − | 0.829047i | \(-0.688884\pi\) |
0.997565 | + | 0.0697397i | \(0.0222169\pi\) | |||||||
\(174\) | −3.62366e9 | −0.299693 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.14728e8 | 0.0482921 | ||||||||
\(177\) | 8.97891e8 | − | 1.55519e9i | 0.0687613 | − | 0.119098i | ||||
\(178\) | −4.44222e9 | − | 7.69415e9i | −0.331673 | − | 0.574475i | ||||
\(179\) | −5.40127e9 | − | 9.35527e9i | −0.393239 | − | 0.681110i | 0.599635 | − | 0.800273i | \(-0.295312\pi\) |
−0.992875 | + | 0.119163i | \(0.961979\pi\) | |||||||
\(180\) | −3.97910e9 | + | 6.89200e9i | −0.282526 | + | 0.489350i | ||||
\(181\) | −6.13942e9 | −0.425181 | −0.212591 | − | 0.977141i | \(-0.568190\pi\) | ||||
−0.212591 | + | 0.977141i | \(0.568190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.69949e9 | −0.573408 | ||||||||
\(184\) | −2.00486e9 | + | 3.47252e9i | −0.128945 | + | 0.223339i | ||||
\(185\) | 2.49193e9 | + | 4.31614e9i | 0.156409 | + | 0.270909i | ||||
\(186\) | 3.34674e9 | + | 5.79672e9i | 0.205028 | + | 0.355119i | ||||
\(187\) | 4.59101e8 | − | 7.95187e8i | 0.0274550 | − | 0.0475535i | ||||
\(188\) | −1.07975e10 | −0.630392 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.65316e10 | −0.920288 | ||||||||
\(191\) | 4.69356e9 | − | 8.12948e9i | 0.255183 | − | 0.441990i | −0.709762 | − | 0.704441i | \(-0.751198\pi\) |
0.964945 | + | 0.262451i | \(0.0845309\pi\) | |||||||
\(192\) | 4.40062e8 | + | 7.62210e8i | 0.0233700 | + | 0.0404780i | ||||
\(193\) | −4.53204e9 | − | 7.84973e9i | −0.235118 | − | 0.407237i | 0.724189 | − | 0.689602i | \(-0.242214\pi\) |
−0.959307 | + | 0.282365i | \(0.908881\pi\) | |||||||
\(194\) | 1.01516e10 | − | 1.75830e10i | 0.514547 | − | 0.891222i | ||||
\(195\) | −1.72455e10 | −0.854125 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.31102e9 | −0.345844 | −0.172922 | − | 0.984936i | \(-0.555321\pi\) | ||||
−0.172922 | + | 0.984936i | \(0.555321\pi\) | |||||||
\(198\) | −1.27050e9 | + | 2.20057e9i | −0.0587465 | + | 0.101752i | ||||
\(199\) | −7.55250e8 | − | 1.30813e9i | −0.0341391 | − | 0.0591306i | 0.848451 | − | 0.529274i | \(-0.177536\pi\) |
−0.882590 | + | 0.470143i | \(0.844202\pi\) | |||||||
\(200\) | 2.90422e9 | + | 5.03025e9i | 0.128349 | + | 0.222308i | ||||
\(201\) | 6.37237e9 | − | 1.10373e10i | 0.275371 | − | 0.476957i | ||||
\(202\) | 2.18928e10 | 0.925166 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.31462e9 | 0.0531452 | ||||||||
\(205\) | −8.26454e9 | + | 1.43146e10i | −0.326834 | + | 0.566092i | ||||
\(206\) | 1.53721e9 | + | 2.66253e9i | 0.0594746 | + | 0.103013i | ||||
\(207\) | −8.28718e9 | − | 1.43538e10i | −0.313719 | − | 0.543377i | ||||
\(208\) | 5.86692e9 | − | 1.01618e10i | 0.217333 | − | 0.376432i | ||||
\(209\) | −5.27844e9 | −0.191358 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.89147e10 | −0.656945 | −0.328472 | − | 0.944514i | \(-0.606534\pi\) | ||||
−0.328472 | + | 0.944514i | \(0.606534\pi\) | |||||||
\(212\) | −8.71269e9 | + | 1.50908e10i | −0.296238 | + | 0.513100i | ||||
\(213\) | −2.47327e9 | − | 4.28383e9i | −0.0823309 | − | 0.142601i | ||||
\(214\) | −8.38840e9 | − | 1.45291e10i | −0.273412 | − | 0.473563i | ||||
\(215\) | −3.19072e10 | + | 5.52648e10i | −1.01839 | + | 1.76391i | ||||
\(216\) | −7.86740e9 | −0.245918 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.26012e10 | −0.977641 | ||||||||
\(219\) | −3.49733e9 | + | 6.05755e9i | −0.102740 | + | 0.177950i | ||||
\(220\) | 2.20447e9 | + | 3.81826e9i | 0.0634458 | + | 0.109891i | ||||
\(221\) | −8.76327e9 | − | 1.51784e10i | −0.247116 | − | 0.428018i | ||||
\(222\) | −1.13917e9 | + | 1.97309e9i | −0.0314774 | + | 0.0545204i | ||||
\(223\) | 5.37387e10 | 1.45518 | 0.727588 | − | 0.686015i | \(-0.240641\pi\) | ||||
0.727588 | + | 0.686015i | \(0.240641\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.40094e10 | −0.624540 | ||||||||
\(226\) | −3.76799e9 | + | 6.52635e9i | −0.0960775 | + | 0.166411i | ||||
\(227\) | −3.25667e9 | − | 5.64073e9i | −0.0814063 | − | 0.141000i | 0.822448 | − | 0.568840i | \(-0.192608\pi\) |
−0.903854 | + | 0.427841i | \(0.859274\pi\) | |||||||
\(228\) | −3.77865e9 | − | 6.54481e9i | −0.0926040 | − | 0.160395i | ||||
\(229\) | −1.04276e10 | + | 1.80611e10i | −0.250567 | + | 0.433995i | −0.963682 | − | 0.267052i | \(-0.913950\pi\) |
0.713115 | + | 0.701047i | \(0.247284\pi\) | |||||||
\(230\) | −2.87585e10 | −0.677628 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.76833e10 | 0.400745 | ||||||||
\(233\) | −9.57793e9 | + | 1.65895e10i | −0.212897 | + | 0.368749i | −0.952620 | − | 0.304163i | \(-0.901623\pi\) |
0.739723 | + | 0.672912i | \(0.234957\pi\) | |||||||
\(234\) | 2.42512e10 | + | 4.20043e10i | 0.528764 | + | 0.915846i | ||||
\(235\) | −3.87207e10 | − | 6.70663e10i | −0.828206 | − | 1.43449i | ||||
\(236\) | −4.38167e9 | + | 7.58927e9i | −0.0919465 | + | 0.159256i | ||||
\(237\) | −3.55479e10 | −0.731891 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.58648e10 | −0.512764 | −0.256382 | − | 0.966575i | \(-0.582531\pi\) | ||||
−0.256382 | + | 0.966575i | \(0.582531\pi\) | |||||||
\(240\) | −3.15621e9 | + | 5.46672e9i | −0.0614067 | + | 0.106360i | ||||
\(241\) | 1.60903e10 | + | 2.78692e10i | 0.307246 | + | 0.532167i | 0.977759 | − | 0.209732i | \(-0.0672591\pi\) |
−0.670512 | + | 0.741898i | \(0.733926\pi\) | |||||||
\(242\) | −1.81597e10 | − | 3.14535e10i | −0.340361 | − | 0.589522i | ||||
\(243\) | 2.50013e10 | − | 4.33035e10i | 0.459975 | − | 0.796699i | ||||
\(244\) | 4.24531e10 | 0.766753 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.55616e9 | −0.131551 | ||||||||
\(247\) | −5.03771e10 | + | 8.72557e10i | −0.861186 | + | 1.49162i | ||||
\(248\) | −1.63319e10 | − | 2.82877e10i | −0.274161 | − | 0.474860i | ||||
\(249\) | −1.15755e10 | − | 2.00494e10i | −0.190829 | − | 0.330525i | ||||
\(250\) | 7.85917e9 | − | 1.36125e10i | 0.127247 | − | 0.220398i | ||||
\(251\) | 2.42280e10 | 0.385288 | 0.192644 | − | 0.981269i | \(-0.438294\pi\) | ||||
0.192644 | + | 0.981269i | \(0.438294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.18242e9 | −0.140901 | ||||||||
\(254\) | 2.30079e10 | − | 3.98508e10i | 0.346836 | − | 0.600738i | ||||
\(255\) | 4.71436e9 | + | 8.16550e9i | 0.0698219 | + | 0.120935i | ||||
\(256\) | −2.14748e9 | − | 3.71955e9i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.78270e10 | − | 3.08773e10i | 0.254906 | − | 0.441510i | −0.709964 | − | 0.704238i | \(-0.751289\pi\) |
0.964870 | + | 0.262728i | \(0.0846222\pi\) | |||||||
\(258\) | −2.91723e10 | −0.409903 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.41575e10 | 1.14212 | ||||||||
\(261\) | −3.65474e10 | + | 6.33019e10i | −0.487499 | + | 0.844373i | ||||
\(262\) | −4.77685e10 | − | 8.27375e10i | −0.626305 | − | 1.08479i | ||||
\(263\) | 5.96845e10 | + | 1.03377e11i | 0.769238 | + | 1.33236i | 0.937977 | + | 0.346698i | \(0.112697\pi\) |
−0.168739 | + | 0.985661i | \(0.553970\pi\) | |||||||
\(264\) | −1.00776e9 | + | 1.74549e9i | −0.0127685 | + | 0.0221157i | ||||
\(265\) | −1.24978e11 | −1.55678 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.91296e10 | 0.350779 | ||||||||
\(268\) | −3.10969e10 | + | 5.38614e10i | −0.368223 | + | 0.637780i | ||||
\(269\) | −5.27901e10 | − | 9.14352e10i | −0.614706 | − | 1.06470i | −0.990436 | − | 0.137973i | \(-0.955941\pi\) |
0.375730 | − | 0.926729i | \(-0.377392\pi\) | |||||||
\(270\) | −2.82133e10 | − | 4.88668e10i | −0.323085 | − | 0.559600i | ||||
\(271\) | 3.15264e10 | − | 5.46053e10i | 0.355069 | − | 0.614997i | −0.632061 | − | 0.774919i | \(-0.717791\pi\) |
0.987130 | + | 0.159921i | \(0.0511241\pi\) | |||||||
\(272\) | −6.41528e9 | −0.0710650 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.23536e10 | 0.239591 | ||||||||
\(275\) | −6.65077e9 | + | 1.15195e10i | −0.0701253 | + | 0.121461i | ||||
\(276\) | −6.57338e9 | − | 1.13854e10i | −0.0681864 | − | 0.118102i | ||||
\(277\) | 4.41476e10 | + | 7.64659e10i | 0.450556 | + | 0.780385i | 0.998421 | − | 0.0561815i | \(-0.0178925\pi\) |
−0.547865 | + | 0.836567i | \(0.684559\pi\) | |||||||
\(278\) | −6.37265e10 | + | 1.10378e11i | −0.639910 | + | 1.10836i | ||||
\(279\) | 1.35018e11 | 1.33405 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.42216e10 | −0.136072 | −0.0680361 | − | 0.997683i | \(-0.521673\pi\) | ||||
−0.0680361 | + | 0.997683i | \(0.521673\pi\) | |||||||
\(282\) | 1.77009e10 | − | 3.06589e10i | 0.166677 | − | 0.288692i | ||||
\(283\) | 7.20956e10 | + | 1.24873e11i | 0.668144 | + | 1.15726i | 0.978423 | + | 0.206613i | \(0.0662442\pi\) |
−0.310279 | + | 0.950646i | \(0.600422\pi\) | |||||||
\(284\) | 1.20694e10 | + | 2.09049e10i | 0.110092 | + | 0.190684i | ||||
\(285\) | 2.71012e10 | − | 4.69407e10i | 0.243325 | − | 0.421452i | ||||
\(286\) | 2.68710e10 | 0.237485 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.77534e10 | 0.152060 | ||||||||
\(289\) | 5.45028e10 | − | 9.44016e10i | 0.459598 | − | 0.796047i | ||||
\(290\) | 6.34141e10 | + | 1.09836e11i | 0.526496 | + | 0.911917i | ||||
\(291\) | 3.32841e10 | + | 5.76498e10i | 0.272094 | + | 0.471280i | ||||
\(292\) | 1.70668e10 | − | 2.95606e10i | 0.137382 | − | 0.237952i | ||||
\(293\) | 7.39164e10 | 0.585918 | 0.292959 | − | 0.956125i | \(-0.405360\pi\) | ||||
0.292959 | + | 0.956125i | \(0.405360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.28524e10 | −0.483195 | ||||||||
\(296\) | 5.55908e9 | − | 9.62861e9i | 0.0420911 | − | 0.0729039i | ||||
\(297\) | −9.00833e9 | − | 1.56029e10i | −0.0671800 | − | 0.116359i | ||||
\(298\) | −8.82084e10 | − | 1.52781e11i | −0.647943 | − | 1.12227i | ||||
\(299\) | −8.76365e10 | + | 1.51791e11i | −0.634110 | + | 1.09831i | ||||
\(300\) | −1.90442e10 | −0.135743 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.31158e10 | 0.436623 | ||||||||
\(303\) | −3.58902e10 | + | 6.21636e10i | −0.244615 | + | 0.423686i | ||||
\(304\) | 1.84396e10 | + | 3.19384e10i | 0.123829 | + | 0.214478i | ||||
\(305\) | 1.52241e11 | + | 2.63689e11i | 1.00736 | + | 1.74479i | ||||
\(306\) | 1.32589e10 | − | 2.29651e10i | 0.0864494 | − | 0.149735i | ||||
\(307\) | −1.11736e11 | −0.717908 | −0.358954 | − | 0.933355i | \(-0.616866\pi\) | ||||
−0.358954 | + | 0.933355i | \(0.616866\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00802e10 | −0.0629006 | ||||||||
\(310\) | 1.17136e11 | − | 2.02885e11i | 0.720381 | − | 1.24774i | ||||
\(311\) | −1.10520e11 | − | 1.91426e11i | −0.669912 | − | 1.16032i | −0.977928 | − | 0.208940i | \(-0.932999\pi\) |
0.308017 | − | 0.951381i | \(-0.400335\pi\) | |||||||
\(312\) | 1.92360e10 | + | 3.33177e10i | 0.114926 | + | 0.199058i | ||||
\(313\) | −5.38133e10 | + | 9.32074e10i | −0.316913 | + | 0.548909i | −0.979842 | − | 0.199773i | \(-0.935980\pi\) |
0.662929 | + | 0.748682i | \(0.269313\pi\) | |||||||
\(314\) | 1.08215e11 | 0.628207 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.73472e11 | 0.978673 | ||||||||
\(317\) | 1.62817e11 | − | 2.82008e11i | 0.905594 | − | 1.56853i | 0.0854764 | − | 0.996340i | \(-0.472759\pi\) |
0.820118 | − | 0.572195i | \(-0.193908\pi\) | |||||||
\(318\) | −2.85665e10 | − | 4.94786e10i | −0.156652 | − | 0.271328i | ||||
\(319\) | 2.02477e10 | + | 3.50701e10i | 0.109476 | + | 0.189618i | ||||
\(320\) | 1.54022e10 | − | 2.66774e10i | 0.0821121 | − | 0.142222i | ||||
\(321\) | 5.50064e10 | 0.289162 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.50856e10 | 0.281596 | ||||||||
\(324\) | −2.97589e10 | + | 5.15439e10i | −0.150025 | + | 0.259851i | ||||
\(325\) | 1.26949e11 | + | 2.19882e11i | 0.631182 | + | 1.09324i | ||||
\(326\) | −2.35579e10 | − | 4.08034e10i | −0.115520 | − | 0.200086i | ||||
\(327\) | 5.34451e10 | − | 9.25697e10i | 0.258490 | − | 0.447717i | ||||
\(328\) | 3.68737e10 | 0.175907 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.44557e10 | −0.0671006 | ||||||||
\(331\) | 8.47723e10 | − | 1.46830e11i | 0.388175 | − | 0.672339i | −0.604029 | − | 0.796962i | \(-0.706439\pi\) |
0.992204 | + | 0.124623i | \(0.0397722\pi\) | |||||||
\(332\) | 5.64881e10 | + | 9.78403e10i | 0.255174 | + | 0.441974i | ||||
\(333\) | 2.29787e10 | + | 3.98003e10i | 0.102406 | + | 0.177373i | ||||
\(334\) | 1.27251e11 | − | 2.20405e11i | 0.559503 | − | 0.969087i | ||||
\(335\) | −4.46066e11 | −1.93507 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.26756e11 | −0.535347 | −0.267673 | − | 0.963510i | \(-0.586255\pi\) | ||||
−0.267673 | + | 0.963510i | \(0.586255\pi\) | |||||||
\(338\) | 1.71619e11 | − | 2.97253e11i | 0.715221 | − | 1.23880i | ||||
\(339\) | −1.23542e10 | − | 2.13981e10i | −0.0508060 | − | 0.0879986i | ||||
\(340\) | −2.30058e10 | − | 3.98473e10i | −0.0933648 | − | 0.161712i | ||||
\(341\) | 3.74008e10 | − | 6.47800e10i | 0.149791 | − | 0.259446i | ||||
\(342\) | −1.52442e11 | −0.602542 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.42359e11 | 0.548117 | ||||||||
\(345\) | 4.71456e10 | − | 8.16585e10i | 0.179166 | − | 0.310324i | ||||
\(346\) | −8.26389e10 | − | 1.43135e11i | −0.309986 | − | 0.536911i | ||||
\(347\) | 8.95539e10 | + | 1.55112e11i | 0.331590 | + | 0.574331i | 0.982824 | − | 0.184546i | \(-0.0590815\pi\) |
−0.651234 | + | 0.758877i | \(0.725748\pi\) | |||||||
\(348\) | −2.89893e10 | + | 5.02109e10i | −0.105957 | + | 0.183524i | ||||
\(349\) | 1.73876e11 | 0.627372 | 0.313686 | − | 0.949527i | \(-0.398436\pi\) | ||||
0.313686 | + | 0.949527i | \(0.398436\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.43900e11 | −1.20934 | ||||||||
\(352\) | 4.91782e9 | − | 8.51792e9i | 0.0170738 | − | 0.0295727i | ||||
\(353\) | −4.51749e10 | − | 7.82452e10i | −0.154850 | − | 0.268208i | 0.778154 | − | 0.628073i | \(-0.216156\pi\) |
−0.933004 | + | 0.359865i | \(0.882823\pi\) | |||||||
\(354\) | −1.43663e10 | − | 2.48831e10i | −0.0486216 | − | 0.0842150i | ||||
\(355\) | −8.65644e10 | + | 1.49934e11i | −0.289276 | + | 0.501040i | ||||
\(356\) | −1.42151e11 | −0.469056 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.72841e11 | −0.556124 | ||||||||
\(359\) | 9.19748e10 | − | 1.59305e11i | 0.292243 | − | 0.506180i | −0.682097 | − | 0.731262i | \(-0.738932\pi\) |
0.974340 | + | 0.225082i | \(0.0722651\pi\) | |||||||
\(360\) | 6.36656e10 | + | 1.10272e11i | 0.199776 | + | 0.346022i | ||||
\(361\) | 3.00955e9 | + | 5.21270e9i | 0.00932652 | + | 0.0161540i | ||||
\(362\) | −4.91154e10 | + | 8.50703e10i | −0.150324 | + | 0.260369i | ||||
\(363\) | 1.19081e11 | 0.359967 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.44813e11 | 0.721966 | ||||||||
\(366\) | −6.95959e10 | + | 1.20544e11i | −0.202730 | + | 0.351139i | ||||
\(367\) | −1.80656e11 | − | 3.12906e11i | −0.519823 | − | 0.900360i | −0.999734 | − | 0.0230430i | \(-0.992665\pi\) |
0.479911 | − | 0.877317i | \(-0.340669\pi\) | |||||||
\(368\) | 3.20778e10 | + | 5.55603e10i | 0.0911778 | + | 0.157925i | ||||
\(369\) | −7.62095e10 | + | 1.31999e11i | −0.213989 | + | 0.370639i | ||||
\(370\) | 7.97416e10 | 0.221196 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.07096e11 | 0.289954 | ||||||||
\(373\) | −8.12103e10 | + | 1.40660e11i | −0.217231 | + | 0.376255i | −0.953960 | − | 0.299933i | \(-0.903036\pi\) |
0.736730 | + | 0.676187i | \(0.236369\pi\) | |||||||
\(374\) | −7.34562e9 | − | 1.27230e10i | −0.0194136 | − | 0.0336254i | ||||
\(375\) | 2.57680e10 | + | 4.46315e10i | 0.0672884 | + | 0.116547i | ||||
\(376\) | −8.63796e10 | + | 1.49614e11i | −0.222877 | + | 0.386035i | ||||
\(377\) | 7.72973e11 | 1.97073 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.07832e10 | −0.0268455 | −0.0134227 | − | 0.999910i | \(-0.504273\pi\) | ||||
−0.0134227 | + | 0.999910i | \(0.504273\pi\) | |||||||
\(380\) | −1.32253e11 | + | 2.29068e11i | −0.325371 | + | 0.563559i | ||||
\(381\) | 7.54363e10 | + | 1.30660e11i | 0.183408 | + | 0.317672i | ||||
\(382\) | −7.50969e10 | − | 1.30072e11i | −0.180442 | − | 0.312534i | ||||
\(383\) | 3.48928e11 | − | 6.04362e11i | 0.828594 | − | 1.43517i | −0.0705472 | − | 0.997508i | \(-0.522475\pi\) |
0.899141 | − | 0.437659i | \(-0.144192\pi\) | |||||||
\(384\) | 1.40820e10 | 0.0330502 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.45025e11 | −0.332507 | ||||||||
\(387\) | −2.94224e11 | + | 5.09611e11i | −0.666775 | + | 1.15489i | ||||
\(388\) | −1.62425e11 | − | 2.81328e11i | −0.363840 | − | 0.630189i | ||||
\(389\) | 2.99480e11 | + | 5.18714e11i | 0.663123 | + | 1.14856i | 0.979791 | + | 0.200026i | \(0.0641028\pi\) |
−0.316667 | + | 0.948537i | \(0.602564\pi\) | |||||||
\(390\) | −1.37964e11 | + | 2.38961e11i | −0.301979 | + | 0.523042i | ||||
\(391\) | 9.58275e10 | 0.207346 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.13239e11 | 0.662384 | ||||||||
\(394\) | −5.84882e10 | + | 1.01305e11i | −0.122274 | + | 0.211785i | ||||
\(395\) | 6.22088e11 | + | 1.07749e12i | 1.28577 | + | 2.22703i | ||||
\(396\) | 2.03280e10 | + | 3.52092e10i | 0.0415401 | + | 0.0719495i | ||||
\(397\) | −1.84080e11 | + | 3.18835e11i | −0.371919 | + | 0.644183i | −0.989861 | − | 0.142041i | \(-0.954633\pi\) |
0.617942 | + | 0.786224i | \(0.287967\pi\) | |||||||
\(398\) | −2.41680e10 | −0.0482800 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.29350e10 | 0.181514 | ||||||||
\(401\) | −5.56095e10 | + | 9.63185e10i | −0.107399 | + | 0.186020i | −0.914716 | − | 0.404098i | \(-0.867586\pi\) |
0.807317 | + | 0.590118i | \(0.200919\pi\) | |||||||
\(402\) | −1.01958e11 | − | 1.76596e11i | −0.194717 | − | 0.337260i | ||||
\(403\) | −7.13902e11 | − | 1.23651e12i | −1.34824 | − | 2.33521i | ||||
\(404\) | 1.75142e11 | − | 3.03355e11i | 0.327096 | − | 0.566546i | ||||
\(405\) | −4.26873e11 | −0.788408 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.54610e10 | 0.0459940 | ||||||||
\(408\) | 1.05170e10 | − | 1.82159e10i | 0.0187897 | − | 0.0325447i | ||||
\(409\) | −2.21216e11 | − | 3.83157e11i | −0.390896 | − | 0.677051i | 0.601672 | − | 0.798743i | \(-0.294501\pi\) |
−0.992568 | + | 0.121692i | \(0.961168\pi\) | |||||||
\(410\) | 1.32233e11 | + | 2.29034e11i | 0.231106 | + | 0.400288i | ||||
\(411\) | −3.66456e10 | + | 6.34720e10i | −0.0633481 | + | 0.109722i | ||||
\(412\) | 4.91908e10 | 0.0841097 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.65190e11 | −0.443665 | ||||||||
\(415\) | −4.05144e11 | + | 7.01730e11i | −0.670491 | + | 1.16132i | ||||
\(416\) | −9.38708e10 | − | 1.62589e11i | −0.153678 | − | 0.266177i | ||||
\(417\) | −2.08941e11 | − | 3.61897e11i | −0.338386 | − | 0.586102i | ||||
\(418\) | −4.22275e10 | + | 7.31402e10i | −0.0676553 | + | 0.117182i | ||||
\(419\) | −7.54997e11 | −1.19669 | −0.598346 | − | 0.801238i | \(-0.704175\pi\) | ||||
−0.598346 | + | 0.801238i | \(0.704175\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.31285e11 | 0.669106 | 0.334553 | − | 0.942377i | \(-0.391415\pi\) | ||||
0.334553 | + | 0.942377i | \(0.391415\pi\) | |||||||
\(422\) | −1.51318e11 | + | 2.62090e11i | −0.232265 | + | 0.402295i | ||||
\(423\) | −3.57054e11 | − | 6.18436e11i | −0.542253 | − | 0.939210i | ||||
\(424\) | 1.39403e11 | + | 2.41453e11i | 0.209472 | + | 0.362816i | ||||
\(425\) | 6.94073e10 | − | 1.20217e11i | 0.103194 | − | 0.178737i | ||||
\(426\) | −7.91446e10 | −0.116434 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.68429e11 | −0.386663 | ||||||||
\(429\) | −4.40512e10 | + | 7.62989e10i | −0.0627913 | + | 0.108758i | ||||
\(430\) | 5.10515e11 | + | 8.84237e11i | 0.720112 | + | 1.24727i | ||||
\(431\) | −5.06876e11 | − | 8.77935e11i | −0.707545 | − | 1.22550i | −0.965765 | − | 0.259417i | \(-0.916470\pi\) |
0.258221 | − | 0.966086i | \(-0.416864\pi\) | |||||||
\(432\) | −6.29392e10 | + | 1.09014e11i | −0.0869450 | + | 0.150593i | ||||
\(433\) | −6.02971e11 | −0.824329 | −0.412165 | − | 0.911109i | \(-0.635227\pi\) | ||||
−0.412165 | + | 0.911109i | \(0.635227\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.15834e11 | −0.556825 | ||||||||
\(436\) | −2.60810e11 | + | 4.51736e11i | −0.345648 | + | 0.598681i | ||||
\(437\) | −2.75440e11 | − | 4.77076e11i | −0.361294 | − | 0.625779i | ||||
\(438\) | 5.59573e10 | + | 9.69208e10i | 0.0726479 | + | 0.125830i | ||||
\(439\) | 2.27143e11 | − | 3.93423e11i | 0.291883 | − | 0.505556i | −0.682372 | − | 0.731005i | \(-0.739052\pi\) |
0.974255 | + | 0.225449i | \(0.0723850\pi\) | |||||||
\(440\) | 7.05432e10 | 0.0897259 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.80425e11 | −0.349475 | ||||||||
\(443\) | −5.04444e11 | + | 8.73722e11i | −0.622294 | + | 1.07785i | 0.366763 | + | 0.930314i | \(0.380466\pi\) |
−0.989057 | + | 0.147531i | \(0.952867\pi\) | |||||||
\(444\) | 1.82267e10 | + | 3.15695e10i | 0.0222579 | + | 0.0385518i | ||||
\(445\) | −5.09768e11 | − | 8.82944e11i | −0.616244 | − | 1.06737i | ||||
\(446\) | 4.29910e11 | − | 7.44625e11i | 0.514482 | − | 0.891109i | ||||
\(447\) | 5.78421e11 | 0.685268 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.51070e10 | 0.0175416 | 0.00877082 | − | 0.999962i | \(-0.497208\pi\) | ||||
0.00877082 | + | 0.999962i | \(0.497208\pi\) | |||||||
\(450\) | −1.92075e11 | + | 3.32684e11i | −0.220808 | + | 0.382451i | ||||
\(451\) | 4.22211e10 | + | 7.31291e10i | 0.0480546 | + | 0.0832330i | ||||
\(452\) | 6.02878e10 | + | 1.04422e11i | 0.0679371 | + | 0.117670i | ||||
\(453\) | −1.03469e11 | + | 1.79214e11i | −0.115444 | + | 0.199954i | ||||
\(454\) | −1.04214e11 | −0.115126 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.20917e11 | −0.130962 | ||||||||
\(457\) | 5.16899e11 | − | 8.95295e11i | 0.554348 | − | 0.960159i | −0.443606 | − | 0.896222i | \(-0.646301\pi\) |
0.997954 | − | 0.0639369i | \(-0.0203657\pi\) | |||||||
\(458\) | 1.66841e11 | + | 2.88978e11i | 0.177178 | + | 0.306881i | ||||
\(459\) | 9.40107e10 | + | 1.62831e11i | 0.0988599 | + | 0.171230i | ||||
\(460\) | −2.30068e11 | + | 3.98490e11i | −0.239578 | + | 0.414961i | ||||
\(461\) | 6.16178e11 | 0.635407 | 0.317704 | − | 0.948190i | \(-0.397088\pi\) | ||||
0.317704 | + | 0.948190i | \(0.397088\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.87425e11 | 0.897464 | 0.448732 | − | 0.893666i | \(-0.351876\pi\) | ||||
0.448732 | + | 0.893666i | \(0.351876\pi\) | |||||||
\(464\) | 1.41466e11 | − | 2.45027e11i | 0.141685 | − | 0.245405i | ||||
\(465\) | 3.84056e11 | + | 6.65204e11i | 0.380939 | + | 0.659807i | ||||
\(466\) | 1.53247e11 | + | 2.65431e11i | 0.150541 | + | 0.260745i | ||||
\(467\) | −8.81241e11 | + | 1.52635e12i | −0.857371 | + | 1.48501i | 0.0170568 | + | 0.999855i | \(0.494570\pi\) |
−0.874428 | + | 0.485156i | \(0.838763\pi\) | |||||||
\(468\) | 7.76038e11 | 0.747785 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.23906e12 | −1.17126 | ||||||||
\(471\) | −1.77403e11 | + | 3.07271e11i | −0.166099 | + | 0.287691i | ||||
\(472\) | 7.01067e10 | + | 1.21428e11i | 0.0650160 | + | 0.112611i | ||||
\(473\) | 1.63004e11 | + | 2.82332e11i | 0.149735 | + | 0.259349i | ||||
\(474\) | −2.84383e11 | + | 4.92566e11i | −0.258762 | + | 0.448190i | ||||
\(475\) | −7.97998e11 | −0.719251 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.15246e12 | −1.01928 | ||||||||
\(478\) | −2.06918e11 | + | 3.58393e11i | −0.181290 | + | 0.314003i | ||||
\(479\) | −6.26066e10 | − | 1.08438e11i | −0.0543388 | − | 0.0941176i | 0.837576 | − | 0.546320i | \(-0.183972\pi\) |
−0.891915 | + | 0.452202i | \(0.850638\pi\) | |||||||
\(480\) | 5.04994e10 | + | 8.74676e10i | 0.0434211 | + | 0.0752076i | ||||
\(481\) | 2.42998e11 | − | 4.20886e11i | 0.206991 | − | 0.358518i | ||||
\(482\) | 5.14889e11 | 0.434512 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.81111e11 | −0.481343 | ||||||||
\(485\) | 1.16494e12 | − | 2.01774e12i | 0.956021 | − | 1.65588i | ||||
\(486\) | −4.00020e11 | − | 6.92856e11i | −0.325251 | − | 0.563352i | ||||
\(487\) | −9.59535e11 | − | 1.66196e12i | −0.773001 | − | 1.33888i | −0.935911 | − | 0.352237i | \(-0.885421\pi\) |
0.162909 | − | 0.986641i | \(-0.447912\pi\) | |||||||
\(488\) | 3.39625e11 | − | 5.88248e11i | 0.271088 | − | 0.469538i | ||||
\(489\) | 1.54479e11 | 0.122174 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.29801e12 | −1.00789 | −0.503944 | − | 0.863736i | \(-0.668118\pi\) | ||||
−0.503944 | + | 0.863736i | \(0.668118\pi\) | |||||||
\(492\) | −6.04492e10 | + | 1.04701e11i | −0.0465102 | + | 0.0805580i | ||||
\(493\) | −2.11305e11 | − | 3.65991e11i | −0.161101 | − | 0.279035i | ||||
\(494\) | 8.06033e11 | + | 1.39609e12i | 0.608950 | + | 1.05473i | ||||
\(495\) | −1.45797e11 | + | 2.52527e11i | −0.109150 | + | 0.189054i | ||||
\(496\) | −5.22622e11 | −0.387722 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.70417e11 | −0.269873 | ||||||||
\(499\) | 2.13038e11 | − | 3.68992e11i | 0.153817 | − | 0.266419i | −0.778811 | − | 0.627259i | \(-0.784177\pi\) |
0.932628 | + | 0.360840i | \(0.117510\pi\) | |||||||
\(500\) | −1.25747e11 | − | 2.17800e11i | −0.0899770 | − | 0.155845i | ||||
\(501\) | 4.17220e11 | + | 7.22647e11i | 0.295866 | + | 0.512456i | ||||
\(502\) | 1.93824e11 | − | 3.35713e11i | 0.136220 | − | 0.235940i | ||||
\(503\) | 1.75682e12 | 1.22369 | 0.611844 | − | 0.790978i | \(-0.290428\pi\) | ||||
0.611844 | + | 0.790978i | \(0.290428\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.51231e12 | 1.71895 | ||||||||
\(506\) | −7.34594e10 | + | 1.27235e11i | −0.0498161 | + | 0.0862840i | ||||
\(507\) | 5.62690e11 | + | 9.74608e11i | 0.378210 | + | 0.655080i | ||||
\(508\) | −3.68126e11 | − | 6.37612e11i | −0.245250 | − | 0.424786i | ||||
\(509\) | 1.29517e12 | − | 2.24330e12i | 0.855258 | − | 1.48135i | −0.0211477 | − | 0.999776i | \(-0.506732\pi\) |
0.876406 | − | 0.481574i | \(-0.159935\pi\) | |||||||
\(510\) | 1.50859e11 | 0.0987430 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | 5.40436e11 | − | 9.36062e11i | 0.344521 | − | 0.596728i | ||||
\(514\) | −2.85233e11 | − | 4.94037e11i | −0.180246 | − | 0.312195i | ||||
\(515\) | 1.76403e11 | + | 3.05539e11i | 0.110503 | + | 0.191397i | ||||
\(516\) | −2.33378e11 | + | 4.04223e11i | −0.144923 | + | 0.251014i | ||||
\(517\) | −3.95625e11 | −0.243544 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.41899e11 | 0.327843 | ||||||||
\(520\) | 6.73260e11 | − | 1.16612e12i | 0.403801 | − | 0.699404i | ||||
\(521\) | −4.81815e11 | − | 8.34527e11i | −0.286490 | − | 0.496216i | 0.686479 | − | 0.727150i | \(-0.259155\pi\) |
−0.972970 | + | 0.230933i | \(0.925822\pi\) | |||||||
\(522\) | 5.84758e11 | + | 1.01283e12i | 0.344714 | + | 0.597062i | ||||
\(523\) | 3.13995e11 | − | 5.43855e11i | 0.183512 | − | 0.317852i | −0.759562 | − | 0.650435i | \(-0.774587\pi\) |
0.943074 | + | 0.332582i | \(0.107920\pi\) | |||||||
\(524\) | −1.52859e12 | −0.885729 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.90990e12 | 1.08787 | ||||||||
\(527\) | −3.90314e11 | + | 6.76043e11i | −0.220428 | + | 0.381792i | ||||
\(528\) | 1.61242e10 | + | 2.79279e10i | 0.00902868 | + | 0.0156381i | ||||
\(529\) | 4.21418e11 | + | 7.29918e11i | 0.233972 | + | 0.405251i | ||||
\(530\) | −9.99827e11 | + | 1.73175e12i | −0.550406 | + | 0.953332i | ||||
\(531\) | −5.79578e11 | −0.316364 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.61182e12 | 0.865057 | ||||||||
\(534\) | 2.33037e11 | − | 4.03631e11i | 0.124019 | − | 0.214807i | ||||
\(535\) | −9.62612e11 | − | 1.66729e12i | −0.507995 | − | 0.879873i | ||||
\(536\) | 4.97550e11 | + | 8.61782e11i | 0.260373 | + | 0.450979i | ||||
\(537\) | 2.83348e11 | − | 4.90773e11i | 0.147040 | − | 0.254681i | ||||
\(538\) | −1.68928e12 | −0.869325 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.02825e11 | −0.456911 | ||||||||
\(541\) | 1.55786e12 | − | 2.69830e12i | 0.781884 | − | 1.35426i | −0.148960 | − | 0.988843i | \(-0.547592\pi\) |
0.930843 | − | 0.365419i | \(-0.119074\pi\) | |||||||
\(542\) | −5.04422e11 | − | 8.73685e11i | −0.251072 | − | 0.434869i | ||||
\(543\) | −1.61036e11 | − | 2.78922e11i | −0.0794918 | − | 0.137684i | ||||
\(544\) | −5.13223e10 | + | 8.88928e10i | −0.0251253 | + | 0.0435182i | ||||
\(545\) | −3.74116e12 | −1.81644 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.73766e12 | 0.829890 | 0.414945 | − | 0.909846i | \(-0.363801\pi\) | ||||
0.414945 | + | 0.909846i | \(0.363801\pi\) | |||||||
\(548\) | 1.78829e11 | − | 3.09740e11i | 0.0847081 | − | 0.146719i | ||||
\(549\) | 1.40386e12 | + | 2.43155e12i | 0.659549 | + | 1.14237i | ||||
\(550\) | 1.06412e11 | + | 1.84312e11i | 0.0495861 | + | 0.0858856i | ||||
\(551\) | −1.21472e12 | + | 2.10396e12i | −0.561428 | + | 0.972421i | ||||
\(552\) | −2.10348e11 | −0.0964301 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.41272e12 | 0.637182 | ||||||||
\(555\) | −1.30725e11 | + | 2.26423e11i | −0.0584845 | + | 0.101298i | ||||
\(556\) | 1.01962e12 | + | 1.76604e12i | 0.452485 | + | 0.783726i | ||||
\(557\) | 2.19213e12 | + | 3.79688e12i | 0.964980 | + | 1.67139i | 0.709668 | + | 0.704536i | \(0.248845\pi\) |
0.255312 | + | 0.966859i | \(0.417822\pi\) | |||||||
\(558\) | 1.08014e12 | − | 1.87086e12i | 0.471657 | − | 0.816934i | ||||
\(559\) | 6.22281e12 | 2.69546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.81685e10 | 0.0205319 | ||||||||
\(562\) | −1.13773e11 | + | 1.97060e11i | −0.0481088 | + | 0.0833269i | ||||
\(563\) | 1.30264e12 | + | 2.25625e12i | 0.546434 | + | 0.946452i | 0.998515 | + | 0.0544751i | \(0.0173486\pi\) |
−0.452081 | + | 0.891977i | \(0.649318\pi\) | |||||||
\(564\) | −2.83215e11 | − | 4.90542e11i | −0.117858 | − | 0.204136i | ||||
\(565\) | −4.32396e11 | + | 7.48932e11i | −0.178511 | + | 0.309189i | ||||
\(566\) | 2.30706e12 | 0.944898 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.86222e11 | 0.155693 | ||||||||
\(569\) | 5.10258e11 | − | 8.83793e11i | 0.204073 | − | 0.353464i | −0.745764 | − | 0.666210i | \(-0.767915\pi\) |
0.949837 | + | 0.312746i | \(0.101249\pi\) | |||||||
\(570\) | −4.33620e11 | − | 7.51051e11i | −0.172057 | − | 0.298011i | ||||
\(571\) | −1.51016e11 | − | 2.61567e11i | −0.0594512 | − | 0.102972i | 0.834768 | − | 0.550602i | \(-0.185602\pi\) |
−0.894219 | + | 0.447629i | \(0.852268\pi\) | |||||||
\(572\) | 2.14968e11 | − | 3.72335e11i | 0.0839636 | − | 0.145429i | ||||
\(573\) | 4.92443e11 | 0.190836 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.38820e12 | −0.529600 | ||||||||
\(576\) | 1.42028e11 | − | 2.45999e11i | 0.0537615 | − | 0.0931176i | ||||
\(577\) | −3.61791e11 | − | 6.26641e11i | −0.135884 | − | 0.235357i | 0.790051 | − | 0.613041i | \(-0.210054\pi\) |
−0.925935 | + | 0.377684i | \(0.876721\pi\) | |||||||
\(578\) | −8.72044e11 | − | 1.51042e12i | −0.324985 | − | 0.562890i | ||||
\(579\) | 2.37749e11 | − | 4.11793e11i | 0.0879154 | − | 0.152274i | ||||
\(580\) | 2.02925e12 | 0.744577 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.06509e12 | 0.384799 | ||||||||
\(583\) | −3.19239e11 | + | 5.52937e11i | −0.114448 | + | 0.198229i | ||||
\(584\) | −2.73069e11 | − | 4.72969e11i | −0.0971437 | − | 0.168258i | ||||
\(585\) | 2.78295e12 | + | 4.82021e12i | 0.982435 | + | 1.70163i | ||||
\(586\) | 5.91332e11 | − | 1.02422e12i | 0.207153 | − | 0.358800i | ||||
\(587\) | −4.21402e12 | −1.46496 | −0.732479 | − | 0.680789i | \(-0.761637\pi\) | ||||
−0.732479 | + | 0.680789i | \(0.761637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.48756e12 | 1.53635 | ||||||||
\(590\) | −5.02819e11 | + | 8.70908e11i | −0.170835 | + | 0.295895i | ||||
\(591\) | −1.91766e11 | − | 3.32149e11i | −0.0646590 | − | 0.111993i | ||||
\(592\) | −8.89453e10 | − | 1.54058e11i | −0.0297629 | − | 0.0515508i | ||||
\(593\) | −2.81140e12 | + | 4.86948e12i | −0.933633 | + | 1.61710i | −0.156578 | + | 0.987666i | \(0.550046\pi\) |
−0.777054 | + | 0.629434i | \(0.783287\pi\) | |||||||
\(594\) | −2.88267e11 | −0.0950069 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.82267e12 | −0.916329 | ||||||||
\(597\) | 3.96201e10 | − | 6.86239e10i | 0.0127653 | − | 0.0221101i | ||||
\(598\) | 1.40218e12 | + | 2.42865e12i | 0.448383 | + | 0.776623i | ||||
\(599\) | −3.82867e11 | − | 6.63145e11i | −0.121514 | − | 0.210469i | 0.798851 | − | 0.601529i | \(-0.205442\pi\) |
−0.920365 | + | 0.391060i | \(0.872108\pi\) | |||||||
\(600\) | −1.52354e11 | + | 2.63885e11i | −0.0479924 | + | 0.0831253i | ||||
\(601\) | 9.63630e11 | 0.301283 | 0.150642 | − | 0.988588i | \(-0.451866\pi\) | ||||
0.150642 | + | 0.988588i | \(0.451866\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.11329e12 | −1.26696 | ||||||||
\(604\) | 5.04926e11 | − | 8.74558e11i | 0.154370 | − | 0.267376i | ||||
\(605\) | −2.08392e12 | − | 3.60946e12i | −0.632386 | − | 1.09532i | ||||
\(606\) | 5.74242e11 | + | 9.94617e11i | 0.172969 | + | 0.299591i | ||||
\(607\) | 1.14247e12 | − | 1.97882e12i | 0.341583 | − | 0.591640i | −0.643144 | − | 0.765746i | \(-0.722370\pi\) |
0.984727 | + | 0.174106i | \(0.0557035\pi\) | |||||||
\(608\) | 5.90068e11 | 0.175120 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.87172e12 | 1.42462 | ||||||||
\(611\) | −3.77582e12 | + | 6.53992e12i | −1.09604 | + | 1.89840i | ||||
\(612\) | −2.12143e11 | − | 3.67442e11i | −0.0611290 | − | 0.105878i | ||||
\(613\) | −5.97297e11 | − | 1.03455e12i | −0.170851 | − | 0.295923i | 0.767866 | − | 0.640610i | \(-0.221318\pi\) |
−0.938718 | + | 0.344687i | \(0.887985\pi\) | |||||||
\(614\) | −8.93884e11 | + | 1.54825e12i | −0.253819 | + | 0.439627i | ||||
\(615\) | −8.67108e11 | −0.244419 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.40574e12 | −0.946082 | −0.473041 | − | 0.881040i | \(-0.656844\pi\) | ||||
−0.473041 | + | 0.881040i | \(0.656844\pi\) | |||||||
\(618\) | −8.06414e10 | + | 1.39675e11i | −0.0222387 | + | 0.0385186i | ||||
\(619\) | −8.08150e9 | − | 1.39976e10i | −0.00221250 | − | 0.00383217i | 0.864917 | − | 0.501915i | \(-0.167371\pi\) |
−0.867130 | + | 0.498083i | \(0.834038\pi\) | |||||||
\(620\) | −1.87417e12 | − | 3.24617e12i | −0.509386 | − | 0.882283i | ||||
\(621\) | 9.40147e11 | − | 1.62838e12i | 0.253678 | − | 0.439384i | ||||
\(622\) | −3.53663e12 | −0.947398 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.15552e11 | 0.162530 | ||||||||
\(625\) | 2.28672e12 | − | 3.96071e12i | 0.599450 | − | 1.03828i | ||||
\(626\) | 8.61013e11 | + | 1.49132e12i | 0.224091 | + | 0.388138i | ||||
\(627\) | −1.38452e11 | − | 2.39806e11i | −0.0357763 | − | 0.0619664i | ||||
\(628\) | 8.65718e11 | − | 1.49947e12i | 0.222105 | − | 0.384697i | ||||
\(629\) | −2.65711e11 | −0.0676832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.72735e12 | −1.18710 | −0.593548 | − | 0.804799i | \(-0.702273\pi\) | ||||
−0.593548 | + | 0.804799i | \(0.702273\pi\) | |||||||
\(632\) | 1.38778e12 | − | 2.40370e12i | 0.346013 | − | 0.599312i | ||||
\(633\) | −4.96128e11 | − | 8.59320e11i | −0.122822 | − | 0.212735i | ||||
\(634\) | −2.60508e12 | − | 4.51212e12i | −0.640352 | − | 1.10912i | ||||
\(635\) | 2.64027e12 | − | 4.57308e12i | 0.644416 | − | 1.11616i | ||||
\(636\) | −9.14127e11 | −0.221539 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.47927e11 | 0.154822 | ||||||||
\(639\) | −7.98233e11 | + | 1.38258e12i | −0.189398 | + | 0.328047i | ||||
\(640\) | −2.46435e11 | − | 4.26838e11i | −0.0580620 | − | 0.100566i | ||||
\(641\) | 9.17348e11 | + | 1.58889e12i | 0.214621 | + | 0.371735i | 0.953155 | − | 0.302481i | \(-0.0978149\pi\) |
−0.738534 | + | 0.674216i | \(0.764482\pi\) | |||||||
\(642\) | 4.40051e11 | − | 7.62191e11i | 0.102234 | − | 0.177075i | ||||
\(643\) | −3.00823e12 | −0.694003 | −0.347001 | − | 0.937865i | \(-0.612800\pi\) | ||||
−0.347001 | + | 0.937865i | \(0.612800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.34767e12 | −0.761594 | ||||||||
\(646\) | 4.40685e11 | − | 7.63289e11i | 0.0995593 | − | 0.172442i | ||||
\(647\) | −2.55178e12 | − | 4.41982e12i | −0.572499 | − | 0.991596i | −0.996308 | − | 0.0858454i | \(-0.972641\pi\) |
0.423810 | − | 0.905751i | \(-0.360692\pi\) | |||||||
\(648\) | 4.76142e11 | + | 8.24702e11i | 0.106084 | + | 0.183742i | ||||
\(649\) | −1.60547e11 | + | 2.78076e11i | −0.0355223 | + | 0.0615264i | ||||
\(650\) | 4.06237e12 | 0.892626 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.53852e11 | −0.163370 | ||||||||
\(653\) | −2.06171e12 | + | 3.57098e12i | −0.443729 | + | 0.768561i | −0.997963 | − | 0.0637999i | \(-0.979678\pi\) |
0.554234 | + | 0.832361i | \(0.313011\pi\) | |||||||
\(654\) | −8.55122e11 | − | 1.48111e12i | −0.182780 | − | 0.316584i | ||||
\(655\) | −5.48169e12 | − | 9.49456e12i | −1.16367 | − | 2.01553i | ||||
\(656\) | 2.94990e11 | − | 5.10937e11i | 0.0621927 | − | 0.107721i | ||||
\(657\) | 2.25749e12 | 0.472695 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.14612e12 | −1.47600 | −0.737999 | − | 0.674802i | \(-0.764229\pi\) | ||||
−0.737999 | + | 0.674802i | \(0.764229\pi\) | |||||||
\(660\) | −1.15646e11 | + | 2.00304e11i | −0.0237237 | + | 0.0410906i | ||||
\(661\) | 3.76809e12 | + | 6.52652e12i | 0.767740 | + | 1.32976i | 0.938786 | + | 0.344502i | \(0.111952\pi\) |
−0.171046 | + | 0.985263i | \(0.554715\pi\) | |||||||
\(662\) | −1.35636e12 | − | 2.34928e12i | −0.274481 | − | 0.475416i | ||||
\(663\) | 4.59717e11 | − | 7.96253e11i | 0.0924016 | − | 0.160044i | ||||
\(664\) | 1.80762e12 | 0.360870 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.35318e11 | 0.144824 | ||||||||
\(667\) | −2.11314e12 | + | 3.66006e12i | −0.413392 | + | 0.716015i | ||||
\(668\) | −2.03602e12 | − | 3.52648e12i | −0.395628 | − | 0.685248i | ||||
\(669\) | 1.40955e12 | + | 2.44142e12i | 0.272060 | + | 0.471221i | ||||
\(670\) | −3.56853e12 | + | 6.18087e12i | −0.684152 | + | 1.18499i | ||||
\(671\) | 1.55551e12 | 0.296225 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.71281e12 | 0.509743 | 0.254872 | − | 0.966975i | \(-0.417967\pi\) | ||||
0.254872 | + | 0.966975i | \(0.417967\pi\) | |||||||
\(674\) | −1.01405e12 | + | 1.75639e12i | −0.189274 | + | 0.327831i | ||||
\(675\) | −1.36189e12 | − | 2.35885e12i | −0.252507 | − | 0.437355i | ||||
\(676\) | −2.74590e12 | − | 4.75604e12i | −0.505737 | − | 0.875963i | ||||
\(677\) | −8.40789e11 | + | 1.45629e12i | −0.153829 | + | 0.266439i | −0.932632 | − | 0.360829i | \(-0.882494\pi\) |
0.778803 | + | 0.627268i | \(0.215827\pi\) | |||||||
\(678\) | −3.95334e11 | −0.0718506 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.36187e11 | −0.132038 | ||||||||
\(681\) | 1.70844e11 | − | 2.95910e11i | 0.0304394 | − | 0.0527226i | ||||
\(682\) | −5.98412e11 | − | 1.03648e12i | −0.105918 | − | 0.183456i | ||||
\(683\) | −1.78968e12 | − | 3.09982e12i | −0.314690 | − | 0.545059i | 0.664681 | − | 0.747127i | \(-0.268567\pi\) |
−0.979372 | + | 0.202067i | \(0.935234\pi\) | |||||||
\(684\) | −1.21954e12 | + | 2.11230e12i | −0.213031 | + | 0.368980i | ||||
\(685\) | 2.56519e12 | 0.445156 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.09405e12 | −0.187384 | ||||||||
\(688\) | 1.13887e12 | − | 1.97259e12i | 0.193788 | − | 0.335651i | ||||
\(689\) | 6.09359e12 | + | 1.05544e13i | 1.03012 | + | 1.78421i | ||||
\(690\) | −7.54329e11 | − | 1.30654e12i | −0.126689 | − | 0.219432i | ||||
\(691\) | −2.10678e12 | + | 3.64905e12i | −0.351535 | + | 0.608876i | −0.986519 | − | 0.163649i | \(-0.947673\pi\) |
0.634984 | + | 0.772525i | \(0.281007\pi\) | |||||||
\(692\) | −2.64444e12 | −0.438386 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.86572e12 | 0.468939 | ||||||||
\(695\) | −7.31295e12 | + | 1.26664e13i | −1.18894 | + | 2.05931i | ||||
\(696\) | 4.63829e11 | + | 8.03375e11i | 0.0749232 | + | 0.129771i | ||||
\(697\) | −4.40618e11 | − | 7.63173e11i | −0.0707156 | − | 0.122483i | ||||
\(698\) | 1.39101e12 | − | 2.40930e12i | 0.221810 | − | 0.384185i | ||||
\(699\) | −1.00491e12 | −0.159213 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.32382e12 | −0.989119 | −0.494560 | − | 0.869144i | \(-0.664671\pi\) | ||||
−0.494560 | + | 0.869144i | \(0.664671\pi\) | |||||||
\(702\) | −2.75120e12 | + | 4.76522e12i | −0.427568 | + | 0.740569i | ||||
\(703\) | 7.63740e11 | + | 1.32284e12i | 0.117936 | + | 0.204271i | ||||
\(704\) | −7.86851e10 | − | 1.36287e11i | −0.0120730 | − | 0.0209111i | ||||
\(705\) | 2.03127e12 | − | 3.51826e12i | 0.309683 | − | 0.536386i | ||||
\(706\) | −1.44560e12 | −0.218991 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.59720e11 | −0.0687613 | ||||||||
\(709\) | 4.00660e12 | − | 6.93964e12i | 0.595481 | − | 1.03140i | −0.397997 | − | 0.917387i | \(-0.630295\pi\) |
0.993479 | − | 0.114017i | \(-0.0363720\pi\) | |||||||
\(710\) | 1.38503e12 | + | 2.39894e12i | 0.204549 | + | 0.354289i | ||||
\(711\) | 5.73644e12 | + | 9.93580e12i | 0.841839 | + | 1.45811i | ||||
\(712\) | −1.13721e12 | + | 1.96970e12i | −0.165837 | + | 0.287237i | ||||
\(713\) | 7.80660e12 | 1.13125 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.08358e12 | 0.441244 | ||||||||
\(716\) | −1.38272e12 | + | 2.39495e12i | −0.196620 | + | 0.340555i | ||||
\(717\) | −6.78426e11 | − | 1.17507e12i | −0.0958664 | − | 0.166045i | ||||
\(718\) | −1.47160e12 | − | 2.54888e12i | −0.206647 | − | 0.357923i | ||||
\(719\) | 9.23989e11 | − | 1.60040e12i | 0.128940 | − | 0.223330i | −0.794326 | − | 0.607491i | \(-0.792176\pi\) |
0.923266 | + | 0.384161i | \(0.125509\pi\) | |||||||
\(720\) | 2.03730e12 | 0.282526 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.63057e10 | 0.0131897 | ||||||||
\(723\) | −8.44088e11 | + | 1.46200e12i | −0.114886 | + | 0.198988i | ||||
\(724\) | 7.85846e11 | + | 1.36113e12i | 0.106295 | + | 0.184109i | ||||
\(725\) | 3.06107e12 | + | 5.30192e12i | 0.411483 | + | 0.712709i | ||||
\(726\) | 9.52649e11 | − | 1.65004e12i | 0.127268 | − | 0.220434i | ||||
\(727\) | −9.54988e12 | −1.26792 | −0.633962 | − | 0.773365i | \(-0.718572\pi\) | ||||
−0.633962 | + | 0.773365i | \(0.718572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.95301e12 | −0.256113 | ||||||||
\(730\) | 1.95850e12 | − | 3.39223e12i | 0.255254 | − | 0.442112i | ||||
\(731\) | −1.70111e12 | − | 2.94640e12i | −0.220345 | − | 0.381649i | ||||
\(732\) | 1.11354e12 | + | 1.92870e12i | 0.143352 | + | 0.248293i | ||||
\(733\) | −1.22639e12 | + | 2.12417e12i | −0.156914 | + | 0.271783i | −0.933754 | − | 0.357915i | \(-0.883488\pi\) |
0.776840 | + | 0.629698i | \(0.216821\pi\) | |||||||
\(734\) | −5.78100e12 | −0.735141 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.02649e12 | 0.128945 | ||||||||
\(737\) | −1.13941e12 | + | 1.97351e12i | −0.142258 | + | 0.246398i | ||||
\(738\) | 1.21935e12 | + | 2.11198e12i | 0.151313 | + | 0.262081i | ||||
\(739\) | −5.16570e12 | − | 8.94725e12i | −0.637131 | − | 1.10354i | −0.986059 | − | 0.166394i | \(-0.946788\pi\) |
0.348928 | − | 0.937149i | \(-0.386546\pi\) | |||||||
\(740\) | 6.37933e11 | − | 1.10493e12i | 0.0782046 | − | 0.135454i | ||||
\(741\) | −5.28551e12 | −0.644029 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.90098e12 | 0.349216 | 0.174608 | − | 0.984638i | \(-0.444134\pi\) | ||||
0.174608 | + | 0.984638i | \(0.444134\pi\) | |||||||
\(744\) | 8.56765e11 | − | 1.48396e12i | 0.102514 | − | 0.177560i | ||||
\(745\) | −1.01224e13 | − | 1.75325e13i | −1.20387 | − | 2.08516i | ||||
\(746\) | 1.29936e12 | + | 2.25057e12i | 0.153605 | + | 0.266052i | ||||
\(747\) | −3.73594e12 | + | 6.47084e12i | −0.438992 | + | 0.760357i | ||||
\(748\) | −2.35060e11 | −0.0274550 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.24576e11 | 0.0951602 | ||||||||
\(751\) | −8.77661e11 | + | 1.52015e12i | −0.100681 | + | 0.174384i | −0.911965 | − | 0.410267i | \(-0.865435\pi\) |
0.811284 | + | 0.584652i | \(0.198769\pi\) | |||||||
\(752\) | 1.38207e12 | + | 2.39382e12i | 0.157598 | + | 0.272968i | ||||
\(753\) | 6.35494e11 | + | 1.10071e12i | 0.0720334 | + | 0.124765i | ||||
\(754\) | 6.18378e12 | − | 1.07106e13i | 0.696760 | − | 1.20682i | ||||
\(755\) | 7.24286e12 | 0.811240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.28835e13 | 1.42594 | 0.712972 | − | 0.701193i | \(-0.247349\pi\) | ||||
0.712972 | + | 0.701193i | \(0.247349\pi\) | |||||||
\(758\) | −8.62655e10 | + | 1.49416e11i | −0.00949130 | + | 0.0164394i | ||||
\(759\) | −2.40853e11 | − | 4.17169e11i | −0.0263429 | − | 0.0456272i | ||||
\(760\) | 2.11604e12 | + | 3.66510e12i | 0.230072 | + | 0.398496i | ||||
\(761\) | −9.85743e11 | + | 1.70736e12i | −0.106545 | + | 0.184541i | −0.914368 | − | 0.404883i | \(-0.867312\pi\) |
0.807823 | + | 0.589425i | \(0.200645\pi\) | |||||||
\(762\) | 2.41396e12 | 0.259378 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.40310e12 | −0.255183 | ||||||||
\(765\) | 1.52153e12 | − | 2.63537e12i | 0.160622 | − | 0.278205i | ||||
\(766\) | −5.58285e12 | − | 9.66979e12i | −0.585904 | − | 1.01482i | ||||
\(767\) | 3.06450e12 | + | 5.30787e12i | 0.319728 | + | 0.553785i | ||||
\(768\) | 1.12656e11 | − | 1.95126e11i | 0.0116850 | − | 0.0202390i | ||||
\(769\) | −8.44373e12 | −0.870694 | −0.435347 | − | 0.900263i | \(-0.643374\pi\) | ||||
−0.435347 | + | 0.900263i | \(0.643374\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.87039e12 | 0.190629 | ||||||||
\(772\) | −1.16020e12 | + | 2.00953e12i | −0.117559 | + | 0.203618i | ||||
\(773\) | 6.39625e12 | + | 1.10786e13i | 0.644344 | + | 1.11604i | 0.984453 | + | 0.175650i | \(0.0562027\pi\) |
−0.340109 | + | 0.940386i | \(0.610464\pi\) | |||||||
\(774\) | 4.70759e12 | + | 8.15378e12i | 0.471481 | + | 0.816629i | ||||
\(775\) | 5.65428e12 | − | 9.79349e12i | 0.563014 | − | 0.975169i | ||||
\(776\) | −5.19760e12 | −0.514547 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.58335e12 | 0.937798 | ||||||||
\(779\) | −2.53296e12 | + | 4.38722e12i | −0.246440 | + | 0.426846i | ||||
\(780\) | 2.20743e12 | + | 3.82338e12i | 0.213531 | + | 0.369847i | ||||
\(781\) | 4.42232e11 | + | 7.65968e11i | 0.0425324 | + | 0.0736683i | ||||
\(782\) | 7.66620e11 | − | 1.32782e12i | 0.0733077 | − | 0.126973i | ||||
\(783\) | −8.29230e12 | −0.788401 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.24182e13 | 1.16720 | ||||||||
\(786\) | 2.50591e12 | − | 4.34037e12i | 0.234188 | − | 0.405625i | ||||
\(787\) | 7.34166e12 | + | 1.27161e13i | 0.682194 | + | 1.18159i | 0.974310 | + | 0.225212i | \(0.0723074\pi\) |
−0.292116 | + | 0.956383i | \(0.594359\pi\) | |||||||
\(788\) | 9.35811e11 | + | 1.62087e12i | 0.0864610 | + | 0.149755i | ||||
\(789\) | −3.13102e12 | + | 5.42308e12i | −0.287633 | + | 0.498195i | ||||
\(790\) | 1.99068e13 | 1.81836 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.50497e11 | 0.0587465 | ||||||||
\(793\) | 1.48457e13 | − | 2.57135e13i | 1.33313 | − | 2.30904i | ||||
\(794\) | 2.94527e12 | + | 5.10136e12i | 0.262987 | + | 0.455506i | ||||
\(795\) | −3.27815e12 | − | 5.67792e12i | −0.291056 | − | 0.504124i | ||||
\(796\) | −1.93344e11 | + | 3.34882e11i | −0.0170695 | + | 0.0295653i | ||||
\(797\) | 1.35485e13 | 1.18940 | 0.594699 | − | 0.803948i | \(-0.297271\pi\) | ||||
0.594699 | + | 0.803948i | \(0.297271\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.12874e12 | 0.358391 | ||||||||
\(800\) | 7.43480e11 | − | 1.28774e12i | 0.0641747 | − | 0.111154i | ||||
\(801\) | −4.70070e12 | − | 8.14186e12i | −0.403475 | − | 0.698839i | ||||
\(802\) | 8.89753e11 | + | 1.54110e12i | 0.0759424 | + | 0.131536i | ||||
\(803\) | 6.25339e11 | − | 1.08312e12i | 0.0530756 | − | 0.0919297i | ||||
\(804\) | −3.26265e12 | −0.275371 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.28448e13 | −1.90669 | ||||||||
\(807\) | 2.76934e12 | − | 4.79664e12i | 0.229851 | − | 0.398113i | ||||
\(808\) | −2.80228e12 | − | 4.85369e12i | −0.231292 | − | 0.400609i | ||||
\(809\) | 7.16152e12 | + | 1.24041e13i | 0.587810 | + | 1.01812i | 0.994519 | + | 0.104559i | \(0.0333431\pi\) |
−0.406708 | + | 0.913558i | \(0.633324\pi\) | |||||||
\(810\) | −3.41498e12 | + | 5.91493e12i | −0.278744 | + | 0.482799i | ||||
\(811\) | 2.09686e13 | 1.70206 | 0.851030 | − | 0.525117i | \(-0.175979\pi\) | ||||
0.851030 | + | 0.525117i | \(0.175979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.30772e12 | 0.265535 | ||||||||
\(814\) | 2.03688e11 | − | 3.52798e11i | 0.0162613 | − | 0.0281654i | ||||
\(815\) | −2.70339e12 | − | 4.68241e12i | −0.214634 | − | 0.371758i | ||||
\(816\) | −1.68271e11 | − | 2.91454e11i | −0.0132863 | − | 0.0230126i | ||||
\(817\) | −9.77909e12 | + | 1.69379e13i | −0.767890 | + | 1.33003i | ||||
\(818\) | −7.07890e12 | −0.552810 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.23145e12 | 0.326834 | ||||||||
\(821\) | 7.26689e12 | − | 1.25866e13i | 0.558219 | − | 0.966863i | −0.439427 | − | 0.898279i | \(-0.644818\pi\) |
0.997645 | − | 0.0685847i | \(-0.0218483\pi\) | |||||||
\(822\) | 5.86329e11 | + | 1.01555e12i | 0.0447938 | + | 0.0775852i | ||||
\(823\) | −9.17660e12 | − | 1.58943e13i | −0.697240 | − | 1.20766i | −0.969420 | − | 0.245409i | \(-0.921078\pi\) |
0.272179 | − | 0.962247i | \(-0.412256\pi\) | |||||||
\(824\) | 3.93526e11 | − | 6.81608e11i | 0.0297373 | − | 0.0515065i | ||||
\(825\) | −6.97792e11 | −0.0524425 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.78350e11 | −0.0578629 | −0.0289315 | − | 0.999581i | \(-0.509210\pi\) | ||||
−0.0289315 | + | 0.999581i | \(0.509210\pi\) | |||||||
\(828\) | −2.12152e12 | + | 3.67458e12i | −0.156859 | + | 0.271688i | ||||
\(829\) | −4.89759e12 | − | 8.48288e12i | −0.360153 | − | 0.623803i | 0.627833 | − | 0.778348i | \(-0.283942\pi\) |
−0.987986 | + | 0.154545i | \(0.950609\pi\) | |||||||
\(830\) | 6.48230e12 | + | 1.12277e13i | 0.474109 | + | 0.821181i | ||||
\(831\) | −2.31596e12 | + | 4.01137e12i | −0.168472 | + | 0.291802i | ||||
\(832\) | −3.00386e12 | −0.217333 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.68613e12 | −0.478550 | ||||||||
\(835\) | 1.46027e13 | − | 2.52926e13i | 1.03955 | − | 1.80055i | ||||
\(836\) | 6.75640e11 | + | 1.17024e12i | 0.0478395 | + | 0.0828605i | ||||
\(837\) | 7.65860e12 | + | 1.32651e13i | 0.539367 | + | 0.934212i | ||||
\(838\) | −6.03998e12 | + | 1.04615e13i | −0.423094 | + | 0.732821i | ||||
\(839\) | −2.38998e12 | −0.166520 | −0.0832598 | − | 0.996528i | \(-0.526533\pi\) | ||||
−0.0832598 | + | 0.996528i | \(0.526533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.13119e12 | 0.284769 | ||||||||
\(842\) | 3.45028e12 | − | 5.97606e12i | 0.236565 | − | 0.409742i | ||||
\(843\) | −3.73029e11 | − | 6.46105e11i | −0.0254401 | − | 0.0440635i | ||||
\(844\) | 2.42108e12 | + | 4.19344e12i | 0.164236 | + | 0.284465i | ||||
\(845\) | 1.96942e13 | − | 3.41113e13i | 1.32887 | − | 2.30167i | ||||
\(846\) | −1.14257e13 | −0.766862 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.46090e12 | 0.296238 | ||||||||
\(849\) | −3.78210e12 | + | 6.55079e12i | −0.249832 | + | 0.432722i | ||||
\(850\) | −1.11052e12 | − | 1.92347e12i | −0.0729692 | − | 0.126386i | ||||
\(851\) | 1.32861e12 | + | 2.30122e12i | 0.0868389 | + | 0.150409i | ||||
\(852\) | −6.33157e11 | + | 1.09666e12i | −0.0411655 | + | 0.0713007i | ||||
\(853\) | −1.36355e13 | −0.881860 | −0.440930 | − | 0.897541i | \(-0.645351\pi\) | ||||
−0.440930 | + | 0.897541i | \(0.645351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.74935e13 | −1.11951 | ||||||||
\(856\) | −2.14743e12 | + | 3.71946e12i | −0.136706 | + | 0.236781i | ||||
\(857\) | 1.63491e12 | + | 2.83175e12i | 0.103533 | + | 0.179325i | 0.913138 | − | 0.407650i | \(-0.133652\pi\) |
−0.809605 | + | 0.586976i | \(0.800318\pi\) | |||||||
\(858\) | 7.04819e11 | + | 1.22078e12i | 0.0444002 | + | 0.0769034i | ||||
\(859\) | 9.81679e10 | − | 1.70032e11i | 0.00615177 | − | 0.0106552i | −0.862933 | − | 0.505318i | \(-0.831375\pi\) |
0.869085 | + | 0.494663i | \(0.164708\pi\) | |||||||
\(860\) | 1.63365e13 | 1.01839 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.62200e13 | −1.00062 | ||||||||
\(863\) | 4.51676e12 | − | 7.82325e12i | 0.277190 | − | 0.480108i | −0.693495 | − | 0.720461i | \(-0.743930\pi\) |
0.970685 | + | 0.240354i | \(0.0772634\pi\) | |||||||
\(864\) | 1.00703e12 | + | 1.74422e12i | 0.0614794 | + | 0.106485i | ||||
\(865\) | −9.48324e12 | − | 1.64255e13i | −0.575949 | − | 0.997573i | ||||
\(866\) | −4.82376e12 | + | 8.35501e12i | −0.291444 | + | 0.504796i | ||||
\(867\) | 5.71838e12 | 0.343706 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.35612e12 | 0.378097 | ||||||||
\(870\) | −3.32667e12 | + | 5.76197e12i | −0.196867 | + | 0.340984i | ||||
\(871\) | 2.17489e13 | + | 3.76702e13i | 1.28043 | + | 2.21777i | ||||
\(872\) | 4.17296e12 | + | 7.22777e12i | 0.244410 | + | 0.423331i | ||||
\(873\) | 1.07423e13 | − | 1.86061e13i | 0.625938 | − | 1.08416i | ||||
\(874\) | −8.81408e12 | −0.510946 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.79063e12 | 0.102740 | ||||||||
\(877\) | −3.52657e12 | + | 6.10819e12i | −0.201305 | + | 0.348670i | −0.948949 | − | 0.315429i | \(-0.897851\pi\) |
0.747644 | + | 0.664099i | \(0.231185\pi\) | |||||||
\(878\) | −3.63428e12 | − | 6.29476e12i | −0.206392 | − | 0.357482i | ||||
\(879\) | 1.93881e12 | + | 3.35812e12i | 0.109543 | + | 0.189734i | ||||
\(880\) | 5.64345e11 | − | 9.77475e11i | 0.0317229 | − | 0.0549457i | ||||
\(881\) | −3.36898e13 | −1.88411 | −0.942056 | − | 0.335456i | \(-0.891110\pi\) | ||||
−0.942056 | + | 0.335456i | \(0.891110\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.36891e13 | 1.31137 | 0.655686 | − | 0.755034i | \(-0.272379\pi\) | ||||
0.655686 | + | 0.755034i | \(0.272379\pi\) | |||||||
\(884\) | −2.24340e12 | + | 3.88568e12i | −0.123558 | + | 0.214009i | ||||
\(885\) | −1.64860e12 | − | 2.85546e12i | −0.0903381 | − | 0.156470i | ||||
\(886\) | 8.07110e12 | + | 1.39796e13i | 0.440029 | + | 0.762152i | ||||
\(887\) | −1.09498e13 | + | 1.89656e13i | −0.593948 | + | 1.02875i | 0.399746 | + | 0.916626i | \(0.369098\pi\) |
−0.993694 | + | 0.112123i | \(0.964235\pi\) | |||||||
\(888\) | 5.83253e11 | 0.0314774 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.63126e13 | −0.871500 | ||||||||
\(891\) | −1.09038e12 | + | 1.88860e12i | −0.0579602 | + | 0.100390i | ||||
\(892\) | −6.87856e12 | − | 1.19140e13i | −0.363794 | − | 0.630109i | ||||
\(893\) | −1.18674e13 | − | 2.05549e13i | −0.624485 | − | 1.08164i | ||||
\(894\) | 4.62737e12 | − | 8.01484e12i | 0.242279 | − | 0.419639i | ||||
\(895\) | −1.98343e13 | −1.03327 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.19473e12 | −0.474213 | ||||||||
\(898\) | 1.20856e11 | − | 2.09329e11i | 0.00620190 | − | 0.0107420i | ||||
\(899\) | −1.72140e13 | − | 2.98155e13i | −0.878947 | − | 1.52238i | ||||
\(900\) | 3.07321e12 | + | 5.32295e12i | 0.156135 | + | 0.270434i | ||||
\(901\) | 3.33157e12 | − | 5.77044e12i | 0.168417 | − | 0.291707i | ||||
\(902\) | 1.35108e12 | 0.0679595 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.92921e12 | 0.0960775 | ||||||||
\(905\) | −5.63624e12 | + | 9.76226e12i | −0.279300 | + | 0.483762i | ||||
\(906\) | 1.65551e12 | + | 2.86743e12i | 0.0816311 | + | 0.141389i | ||||
\(907\) | −7.08986e12 | − | 1.22800e13i | −0.347860 | − | 0.602511i | 0.638009 | − | 0.770029i | \(-0.279758\pi\) |
−0.985869 | + | 0.167518i | \(0.946425\pi\) | |||||||
\(908\) | −8.33709e11 | + | 1.44403e12i | −0.0407031 | + | 0.0704999i | ||||
\(909\) | 2.31667e13 | 1.12545 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.44567e12 | −0.261950 | −0.130975 | − | 0.991386i | \(-0.541811\pi\) | ||||
−0.130975 | + | 0.991386i | \(0.541811\pi\) | |||||||
\(912\) | −9.67334e11 | + | 1.67547e12i | −0.0463020 | + | 0.0801974i | ||||
\(913\) | 2.06976e12 | + | 3.58493e12i | 0.0985829 | + | 0.170751i | ||||
\(914\) | −8.27038e12 | − | 1.43247e13i | −0.391983 | − | 0.678935i | ||||
\(915\) | −7.98649e12 | + | 1.38330e13i | −0.376670 | + | 0.652412i | ||||
\(916\) | 5.33893e12 | 0.250567 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.00834e12 | 0.139809 | ||||||||
\(919\) | −1.37792e13 | + | 2.38662e13i | −0.637240 | + | 1.10373i | 0.348795 | + | 0.937199i | \(0.386591\pi\) |
−0.986036 | + | 0.166534i | \(0.946743\pi\) | |||||||
\(920\) | 3.68109e12 | + | 6.37584e12i | 0.169407 | + | 0.293421i | ||||
\(921\) | −2.93080e12 | − | 5.07629e12i | −0.134220 | − | 0.232476i | ||||
\(922\) | 4.92943e12 | − | 8.53802e12i | 0.224650 | − | 0.389106i | ||||
\(923\) | 1.68825e13 | 0.765649 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.84921e12 | 0.172876 | ||||||||
\(926\) | 7.09940e12 | − | 1.22965e13i | 0.317302 | − | 0.549582i | ||||
\(927\) | 1.62666e12 | + | 2.81746e12i | 0.0723498 | + | 0.125314i | ||||
\(928\) | −2.26346e12 | − | 3.92043e12i | −0.100186 | − | 0.173527i | ||||
\(929\) | −5.08846e12 | + | 8.81346e12i | −0.224138 | + | 0.388218i | −0.956060 | − | 0.293170i | \(-0.905290\pi\) |
0.731923 | + | 0.681388i | \(0.238623\pi\) | |||||||
\(930\) | 1.22898e13 | 0.538730 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.90390e12 | 0.212897 | ||||||||
\(933\) | 5.79781e12 | − | 1.00421e13i | 0.250493 | − | 0.433867i | ||||
\(934\) | 1.40999e13 | + | 2.44217e13i | 0.606253 | + | 1.05006i | ||||
\(935\) | −8.42948e11 | − | 1.46003e12i | −0.0360702 | − | 0.0624754i | ||||
\(936\) | 6.20831e12 | − | 1.07531e13i | 0.264382 | − | 0.457923i | ||||
\(937\) | 1.96831e13 | 0.834192 | 0.417096 | − | 0.908863i | \(-0.363048\pi\) | ||||
0.417096 | + | 0.908863i | \(0.363048\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.64604e12 | −0.237000 | ||||||||
\(940\) | −9.91251e12 | + | 1.71690e13i | −0.414103 | + | 0.717247i | ||||
\(941\) | −3.78017e12 | − | 6.54744e12i | −0.157166 | − | 0.272219i | 0.776680 | − | 0.629896i | \(-0.216902\pi\) |
−0.933845 | + | 0.357677i | \(0.883569\pi\) | |||||||
\(942\) | 2.83844e12 | + | 4.91633e12i | 0.117450 | + | 0.203429i | ||||
\(943\) | −4.40637e12 | + | 7.63206e12i | −0.181459 | + | 0.314296i | ||||
\(944\) | 2.24341e12 | 0.0919465 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.21613e12 | 0.211757 | ||||||||
\(947\) | −1.21185e13 | + | 2.09899e13i | −0.489637 | + | 0.848076i | −0.999929 | − | 0.0119251i | \(-0.996204\pi\) |
0.510292 | + | 0.860001i | \(0.329537\pi\) | |||||||
\(948\) | 4.55013e12 | + | 7.88105e12i | 0.182973 | + | 0.316918i | ||||
\(949\) | −1.19364e13 | − | 2.06744e13i | −0.477722 | − | 0.827438i | ||||
\(950\) | −6.38398e12 | + | 1.10574e13i | −0.254294 | + | 0.440449i | ||||
\(951\) | 1.70826e13 | 0.677239 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.69411e13 | 1.05803 | 0.529015 | − | 0.848613i | \(-0.322562\pi\) | ||||
0.529015 | + | 0.848613i | \(0.322562\pi\) | |||||||
\(954\) | −9.21966e12 | + | 1.59689e13i | −0.360369 | + | 0.624177i | ||||
\(955\) | −8.61776e12 | − | 1.49264e13i | −0.335258 | − | 0.580684i | ||||
\(956\) | 3.31069e12 | + | 5.73428e12i | 0.128191 | + | 0.222034i | ||||
\(957\) | −1.06219e12 | + | 1.83976e12i | −0.0409352 | + | 0.0709018i | ||||
\(958\) | −2.00341e12 | −0.0768467 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.61598e12 | 0.0614067 | ||||||||
\(961\) | −1.85771e13 | + | 3.21766e13i | −0.702625 | + | 1.21698i | ||||
\(962\) | −3.88797e12 | − | 6.73417e12i | −0.146364 | − | 0.253511i | ||||
\(963\) | −8.87650e12 | − | 1.53745e13i | −0.332601 | − | 0.576082i | ||||
\(964\) | 4.11911e12 | − | 7.13451e12i | 0.153623 | − | 0.266083i | ||||
\(965\) | −1.66424e13 | −0.617794 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.13513e13 | 0.785245 | 0.392623 | − | 0.919700i | \(-0.371568\pi\) | ||||
0.392623 | + | 0.919700i | \(0.371568\pi\) | |||||||
\(968\) | −4.64888e12 | + | 8.05210e12i | −0.170180 | + | 0.294761i | ||||
\(969\) | 1.44488e12 | + | 2.50261e12i | 0.0526472 | + | 0.0911877i | ||||
\(970\) | −1.86391e13 | − | 3.22839e13i | −0.676009 | − | 1.17088i | ||||
\(971\) | 3.10576e11 | − | 5.37933e11i | 0.0112119 | − | 0.0194197i | −0.860365 | − | 0.509678i | \(-0.829764\pi\) |
0.871577 | + | 0.490259i | \(0.163098\pi\) | |||||||
\(972\) | −1.28007e13 | −0.459975 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.07051e13 | −1.09319 | ||||||||
\(975\) | −6.65969e12 | + | 1.15349e13i | −0.236011 | + | 0.408784i | ||||
\(976\) | −5.43400e12 | − | 9.41196e12i | −0.191688 | − | 0.332014i | ||||
\(977\) | 1.06440e13 | + | 1.84359e13i | 0.373748 | + | 0.647350i | 0.990139 | − | 0.140090i | \(-0.0447392\pi\) |
−0.616391 | + | 0.787440i | \(0.711406\pi\) | |||||||
\(978\) | 1.23583e12 | − | 2.14053e12i | 0.0431952 | − | 0.0748163i | ||||
\(979\) | −5.20850e12 | −0.181214 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.44982e13 | −1.18928 | ||||||||
\(982\) | −1.03841e13 | + | 1.79858e13i | −0.356342 | + | 0.617203i | ||||
\(983\) | 2.82842e12 | + | 4.89897e12i | 0.0966169 | + | 0.167345i | 0.910282 | − | 0.413988i | \(-0.135865\pi\) |
−0.813665 | + | 0.581334i | \(0.802531\pi\) | |||||||
\(984\) | 9.67188e11 | + | 1.67522e12i | 0.0328877 | + | 0.0569631i | ||||
\(985\) | −6.71182e12 | + | 1.16252e13i | −0.227184 | + | 0.393494i | ||||
\(986\) | −6.76175e12 | −0.227831 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.57931e13 | 0.861186 | ||||||||
\(989\) | −1.70118e13 | + | 2.94653e13i | −0.565414 | + | 0.979327i | ||||
\(990\) | 2.33275e12 | + | 4.04044e12i | 0.0771808 | + | 0.133681i | ||||
\(991\) | 9.12288e12 | + | 1.58013e13i | 0.300469 | + | 0.520428i | 0.976242 | − | 0.216682i | \(-0.0695233\pi\) |
−0.675773 | + | 0.737110i | \(0.736190\pi\) | |||||||
\(992\) | −4.18098e12 | + | 7.24166e12i | −0.137080 | + | 0.237430i | ||||
\(993\) | 8.89422e12 | 0.290293 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.77340e12 | −0.0897035 | ||||||||
\(996\) | −2.96334e12 | + | 5.13265e12i | −0.0954145 | + | 0.165263i | ||||
\(997\) | −4.83657e12 | − | 8.37719e12i | −0.155028 | − | 0.268516i | 0.778041 | − | 0.628213i | \(-0.216213\pi\) |
−0.933069 | + | 0.359697i | \(0.882880\pi\) | |||||||
\(998\) | −3.40861e12 | − | 5.90388e12i | −0.108765 | − | 0.188387i | ||||
\(999\) | −2.60684e12 | + | 4.51518e12i | −0.0828075 | + | 0.143427i |
(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 | 98.10.c.i.79.2 | 4 | ||
7.2 | even | 3 | 98.10.a.d.1.1 | ✓ | 2 | ||
7.3 | odd | 6 | inner | 98.10.c.i.67.1 | 4 | ||
7.4 | even | 3 | inner | 98.10.c.i.67.2 | 4 | ||
7.5 | odd | 6 | 98.10.a.d.1.2 | yes | 2 | ||
7.6 | odd | 2 | inner | 98.10.c.i.79.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.10.a.d.1.1 | ✓ | 2 | 7.2 | even | 3 | ||
98.10.a.d.1.2 | yes | 2 | 7.5 | odd | 6 | ||
98.10.c.i.67.1 | 4 | 7.3 | odd | 6 | inner | ||
98.10.c.i.67.2 | 4 | 7.4 | even | 3 | inner | ||
98.10.c.i.79.1 | 4 | 7.6 | odd | 2 | inner | ||
98.10.c.i.79.2 | 4 | 1.1 | even | 1 | trivial |