Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,10,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(2.57517918082\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.49740556.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 45x^{2} + 304 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.2 | ||
Root | \(-6.05982i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.10.b.a.4.3 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.843944i | − | 0.0372974i | −0.999826 | − | 0.0186487i | \(-0.994064\pi\) | ||
0.999826 | − | 0.0186487i | \(-0.00593641\pi\) | |||||||
\(3\) | − | 179.263i | − | 1.27775i | −0.769312 | − | 0.638873i | \(-0.779401\pi\) | ||
0.769312 | − | 0.638873i | \(-0.220599\pi\) | |||||||
\(4\) | 511.288 | 0.998609 | ||||||||
\(5\) | −568.288 | − | 1276.78i | −0.406634 | − | 0.913591i | ||||
\(6\) | −151.288 | −0.0476566 | ||||||||
\(7\) | 8712.99i | 1.37160i | 0.727792 | + | 0.685798i | \(0.240547\pi\) | ||||
−0.727792 | + | 0.685798i | \(0.759453\pi\) | |||||||
\(8\) | − | 863.597i | − | 0.0745429i | ||||||
\(9\) | −12452.2 | −0.632636 | ||||||||
\(10\) | −1077.53 | + | 479.603i | −0.0340746 | + | 0.0151664i | ||||
\(11\) | 44557.8 | 0.917606 | 0.458803 | − | 0.888538i | \(-0.348278\pi\) | ||||
0.458803 | + | 0.888538i | \(0.348278\pi\) | |||||||
\(12\) | − | 91654.9i | − | 1.27597i | ||||||
\(13\) | 21430.4i | 0.208107i | 0.994572 | + | 0.104053i | \(0.0331813\pi\) | ||||
−0.994572 | + | 0.104053i | \(0.966819\pi\) | |||||||
\(14\) | 7353.27 | 0.0511569 | ||||||||
\(15\) | −228880. | + | 101873.i | −1.16734 | + | 0.519575i | ||||
\(16\) | 261051. | 0.995829 | ||||||||
\(17\) | 300220.i | 0.871805i | 0.899994 | + | 0.435903i | \(0.143571\pi\) | ||||
−0.899994 | + | 0.435903i | \(0.856429\pi\) | |||||||
\(18\) | 10508.9i | 0.0235957i | ||||||||
\(19\) | −565385. | −0.995298 | −0.497649 | − | 0.867379i | \(-0.665803\pi\) | ||||
−0.497649 | + | 0.867379i | \(0.665803\pi\) | |||||||
\(20\) | −290559. | − | 652803.i | −0.406068 | − | 0.912320i | ||||
\(21\) | 1.56192e6 | 1.75255 | ||||||||
\(22\) | − | 37604.2i | − | 0.0342243i | ||||||
\(23\) | − | 950727.i | − | 0.708403i | −0.935169 | − | 0.354202i | \(-0.884753\pi\) | ||
0.935169 | − | 0.354202i | \(-0.115247\pi\) | |||||||
\(24\) | −154811. | −0.0952469 | ||||||||
\(25\) | −1.30722e6 | + | 1.45116e6i | −0.669298 | + | 0.742994i | ||||
\(26\) | 18086.1 | 0.00776183 | ||||||||
\(27\) | − | 1.29622e6i | − | 0.469398i | ||||||
\(28\) | 4.45485e6i | 1.36969i | ||||||||
\(29\) | 803167. | 0.210870 | 0.105435 | − | 0.994426i | \(-0.466377\pi\) | ||||
0.105435 | + | 0.994426i | \(0.466377\pi\) | |||||||
\(30\) | 85975.0 | + | 193162.i | 0.0193788 | + | 0.0435387i | ||||
\(31\) | −1.99843e6 | −0.388652 | −0.194326 | − | 0.980937i | \(-0.562252\pi\) | ||||
−0.194326 | + | 0.980937i | \(0.562252\pi\) | |||||||
\(32\) | − | 662474.i | − | 0.111685i | ||||||
\(33\) | − | 7.98755e6i | − | 1.17247i | ||||||
\(34\) | 253369. | 0.0325161 | ||||||||
\(35\) | 1.11246e7 | − | 4.95149e6i | 1.25308 | − | 0.557737i | ||||
\(36\) | −6.36665e6 | −0.631756 | ||||||||
\(37\) | 9.53656e6i | 0.836535i | 0.908324 | + | 0.418267i | \(0.137363\pi\) | ||||
−0.908324 | + | 0.418267i | \(0.862637\pi\) | |||||||
\(38\) | 477153.i | 0.0371220i | ||||||||
\(39\) | 3.84168e6 | 0.265908 | ||||||||
\(40\) | −1.10263e6 | + | 490772.i | −0.0681017 | + | 0.0303116i | ||||
\(41\) | −2.54355e7 | −1.40576 | −0.702882 | − | 0.711306i | \(-0.748104\pi\) | ||||
−0.702882 | + | 0.711306i | \(0.748104\pi\) | |||||||
\(42\) | − | 1.31817e6i | − | 0.0653656i | ||||||
\(43\) | 2.32830e7i | 1.03856i | 0.854605 | + | 0.519279i | \(0.173800\pi\) | ||||
−0.854605 | + | 0.519279i | \(0.826200\pi\) | |||||||
\(44\) | 2.27818e7 | 0.916329 | ||||||||
\(45\) | 7.07642e6 | + | 1.58987e7i | 0.257251 | + | 0.577971i | ||||
\(46\) | −802360. | −0.0264216 | ||||||||
\(47\) | − | 3.77353e7i | − | 1.12800i | −0.825776 | − | 0.563998i | \(-0.809262\pi\) | ||
0.825776 | − | 0.563998i | \(-0.190738\pi\) | |||||||
\(48\) | − | 4.67967e7i | − | 1.27242i | ||||||
\(49\) | −3.55626e7 | −0.881274 | ||||||||
\(50\) | 1.22470e6 | + | 1.10322e6i | 0.0277117 | + | 0.0249631i | ||||
\(51\) | 5.38183e7 | 1.11395 | ||||||||
\(52\) | 1.09571e7i | 0.207817i | ||||||||
\(53\) | 4.79297e7i | 0.834379i | 0.908819 | + | 0.417190i | \(0.136985\pi\) | ||||
−0.908819 | + | 0.417190i | \(0.863015\pi\) | |||||||
\(54\) | −1.09393e6 | −0.0175073 | ||||||||
\(55\) | −2.53216e7 | − | 5.68906e7i | −0.373129 | − | 0.838317i | ||||
\(56\) | 7.52451e6 | 0.102243 | ||||||||
\(57\) | 1.01353e8i | 1.27174i | ||||||||
\(58\) | − | 677827.i | − | 0.00786490i | ||||||
\(59\) | −7.00069e7 | −0.752154 | −0.376077 | − | 0.926588i | \(-0.622727\pi\) | ||||
−0.376077 | + | 0.926588i | \(0.622727\pi\) | |||||||
\(60\) | −1.17023e8 | + | 5.20864e7i | −1.16571 | + | 0.518852i | ||||
\(61\) | 1.26942e8 | 1.17387 | 0.586936 | − | 0.809633i | \(-0.300334\pi\) | ||||
0.586936 | + | 0.809633i | \(0.300334\pi\) | |||||||
\(62\) | 1.68656e6i | 0.0144957i | ||||||||
\(63\) | − | 1.08496e8i | − | 0.867721i | ||||||
\(64\) | 1.33099e8 | 0.991663 | ||||||||
\(65\) | 2.73620e7 | − | 1.21787e7i | 0.190124 | − | 0.0846231i | ||||
\(66\) | −6.74104e6 | −0.0437300 | ||||||||
\(67\) | − | 2.66595e8i | − | 1.61628i | −0.588993 | − | 0.808138i | \(-0.700475\pi\) | ||
0.588993 | − | 0.808138i | \(-0.299525\pi\) | |||||||
\(68\) | 1.53499e8i | 0.870593i | ||||||||
\(69\) | −1.70430e8 | −0.905160 | ||||||||
\(70\) | −4.17877e6 | − | 9.38853e6i | −0.0208021 | − | 0.0467365i | ||||
\(71\) | 6.59169e7 | 0.307846 | 0.153923 | − | 0.988083i | \(-0.450809\pi\) | ||||
0.153923 | + | 0.988083i | \(0.450809\pi\) | |||||||
\(72\) | 1.07537e7i | 0.0471585i | ||||||||
\(73\) | − | 1.47516e7i | − | 0.0607977i | −0.999538 | − | 0.0303989i | \(-0.990322\pi\) | ||
0.999538 | − | 0.0303989i | \(-0.00967775\pi\) | |||||||
\(74\) | 8.04832e6 | 0.0312006 | ||||||||
\(75\) | 2.60139e8 | + | 2.34337e8i | 0.949358 | + | 0.855193i | ||||
\(76\) | −2.89074e8 | −0.993913 | ||||||||
\(77\) | 3.88231e8i | 1.25858i | ||||||||
\(78\) | − | 3.24216e6i | − | 0.00991766i | ||||||
\(79\) | 4.66498e7 | 0.134750 | 0.0673748 | − | 0.997728i | \(-0.478538\pi\) | ||||
0.0673748 | + | 0.997728i | \(0.478538\pi\) | |||||||
\(80\) | −1.48352e8 | − | 3.33305e8i | −0.404937 | − | 0.909780i | ||||
\(81\) | −4.77460e8 | −1.23241 | ||||||||
\(82\) | 2.14661e7i | 0.0524313i | ||||||||
\(83\) | − | 2.01840e8i | − | 0.466826i | −0.972378 | − | 0.233413i | \(-0.925011\pi\) | ||
0.972378 | − | 0.233413i | \(-0.0749895\pi\) | |||||||
\(84\) | 7.98588e8 | 1.75011 | ||||||||
\(85\) | 3.83316e8 | − | 1.70611e8i | 0.796474 | − | 0.354505i | ||||
\(86\) | 1.96495e7 | 0.0387355 | ||||||||
\(87\) | − | 1.43978e8i | − | 0.269438i | ||||||
\(88\) | − | 3.84800e7i | − | 0.0684010i | ||||||
\(89\) | −5.54039e8 | −0.936020 | −0.468010 | − | 0.883723i | \(-0.655029\pi\) | ||||
−0.468010 | + | 0.883723i | \(0.655029\pi\) | |||||||
\(90\) | 1.34176e7 | − | 5.97210e6i | 0.0215568 | − | 0.00959480i | ||||
\(91\) | −1.86723e8 | −0.285438 | ||||||||
\(92\) | − | 4.86095e8i | − | 0.707418i | ||||||
\(93\) | 3.58244e8i | 0.496599i | ||||||||
\(94\) | −3.18465e7 | −0.0420713 | ||||||||
\(95\) | 3.21301e8 | + | 7.21874e8i | 0.404722 | + | 0.909295i | ||||
\(96\) | −1.18757e8 | −0.142705 | ||||||||
\(97\) | 3.39489e8i | 0.389361i | 0.980867 | + | 0.194681i | \(0.0623670\pi\) | ||||
−0.980867 | + | 0.194681i | \(0.937633\pi\) | |||||||
\(98\) | 3.00128e7i | 0.0328692i | ||||||||
\(99\) | −5.54841e8 | −0.580511 | ||||||||
\(100\) | −6.68367e8 | + | 7.41960e8i | −0.668367 | + | 0.741960i | ||||
\(101\) | 1.33921e9 | 1.28056 | 0.640282 | − | 0.768140i | \(-0.278817\pi\) | ||||
0.640282 | + | 0.768140i | \(0.278817\pi\) | |||||||
\(102\) | − | 4.54196e7i | − | 0.0415473i | ||||||
\(103\) | 3.84306e8i | 0.336442i | 0.985749 | + | 0.168221i | \(0.0538022\pi\) | ||||
−0.985749 | + | 0.168221i | \(0.946198\pi\) | |||||||
\(104\) | 1.85073e7 | 0.0155129 | ||||||||
\(105\) | −8.87618e8 | − | 1.99423e9i | −0.712646 | − | 1.60112i | ||||
\(106\) | 4.04500e7 | 0.0311202 | ||||||||
\(107\) | − | 7.97379e8i | − | 0.588082i | −0.955793 | − | 0.294041i | \(-0.905000\pi\) | ||
0.955793 | − | 0.294041i | \(-0.0950002\pi\) | |||||||
\(108\) | − | 6.62740e8i | − | 0.468745i | ||||||
\(109\) | 6.63230e8 | 0.450034 | 0.225017 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225017 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(110\) | −4.80124e7 | + | 2.13700e7i | −0.0312670 | + | 0.0139168i | ||||
\(111\) | 1.70955e9 | 1.06888 | ||||||||
\(112\) | 2.27453e9i | 1.36587i | ||||||||
\(113\) | − | 1.48164e9i | − | 0.854847i | −0.904051 | − | 0.427424i | \(-0.859421\pi\) | ||
0.904051 | − | 0.427424i | \(-0.140579\pi\) | |||||||
\(114\) | 8.55358e7 | 0.0474325 | ||||||||
\(115\) | −1.21387e9 | + | 5.40286e8i | −0.647191 | + | 0.288060i | ||||
\(116\) | 4.10649e8 | 0.210577 | ||||||||
\(117\) | − | 2.66856e8i | − | 0.131656i | ||||||
\(118\) | 5.90819e7i | 0.0280534i | ||||||||
\(119\) | −2.61581e9 | −1.19576 | ||||||||
\(120\) | 8.79771e7 | + | 1.97660e8i | 0.0387306 | + | 0.0870168i | ||||
\(121\) | −3.72554e8 | −0.157999 | ||||||||
\(122\) | − | 1.07132e8i | − | 0.0437824i | ||||||
\(123\) | 4.55964e9i | 1.79621i | ||||||||
\(124\) | −1.02177e9 | −0.388112 | ||||||||
\(125\) | 2.59569e9 | + | 8.44363e8i | 0.950952 | + | 0.309339i | ||||
\(126\) | −9.15643e7 | −0.0323637 | ||||||||
\(127\) | − | 2.28772e9i | − | 0.780344i | −0.920742 | − | 0.390172i | \(-0.872416\pi\) | ||
0.920742 | − | 0.390172i | \(-0.127584\pi\) | |||||||
\(128\) | − | 4.51514e8i | − | 0.148671i | ||||||
\(129\) | 4.17378e9 | 1.32701 | ||||||||
\(130\) | −1.02781e7 | − | 2.30920e7i | −0.00315622 | − | 0.00709114i | ||||
\(131\) | −3.83999e9 | −1.13922 | −0.569612 | − | 0.821914i | \(-0.692906\pi\) | ||||
−0.569612 | + | 0.821914i | \(0.692906\pi\) | |||||||
\(132\) | − | 4.08394e9i | − | 1.17084i | ||||||
\(133\) | − | 4.92619e9i | − | 1.36515i | ||||||
\(134\) | −2.24991e8 | −0.0602829 | ||||||||
\(135\) | −1.65499e9 | + | 7.36625e8i | −0.428838 | + | 0.190873i | ||||
\(136\) | 2.59269e8 | 0.0649869 | ||||||||
\(137\) | 5.82666e9i | 1.41311i | 0.707657 | + | 0.706556i | \(0.249752\pi\) | ||||
−0.707657 | + | 0.706556i | \(0.750248\pi\) | |||||||
\(138\) | 1.43833e8i | 0.0337601i | ||||||||
\(139\) | 5.89895e9 | 1.34032 | 0.670159 | − | 0.742217i | \(-0.266226\pi\) | ||||
0.670159 | + | 0.742217i | \(0.266226\pi\) | |||||||
\(140\) | 5.68787e9 | − | 2.53163e9i | 1.25133 | − | 0.556961i | ||||
\(141\) | −6.76455e9 | −1.44129 | ||||||||
\(142\) | − | 5.56301e7i | − | 0.0114819i | ||||||
\(143\) | 9.54892e8i | 0.190960i | ||||||||
\(144\) | −3.25065e9 | −0.629997 | ||||||||
\(145\) | −4.56430e8 | − | 1.02547e9i | −0.0857468 | − | 0.192649i | ||||
\(146\) | −1.24495e7 | −0.00226760 | ||||||||
\(147\) | 6.37505e9i | 1.12604i | ||||||||
\(148\) | 4.87593e9i | 0.835371i | ||||||||
\(149\) | −5.39333e9 | −0.896436 | −0.448218 | − | 0.893924i | \(-0.647941\pi\) | ||||
−0.448218 | + | 0.893924i | \(0.647941\pi\) | |||||||
\(150\) | 1.97767e8 | − | 2.19543e8i | 0.0318965 | − | 0.0354086i | ||||
\(151\) | 7.92204e8 | 0.124005 | 0.0620027 | − | 0.998076i | \(-0.480251\pi\) | ||||
0.0620027 | + | 0.998076i | \(0.480251\pi\) | |||||||
\(152\) | 4.88265e8i | 0.0741924i | ||||||||
\(153\) | − | 3.73839e9i | − | 0.551536i | ||||||
\(154\) | 3.27645e8 | 0.0469419 | ||||||||
\(155\) | 1.13568e9 | + | 2.55156e9i | 0.158039 | + | 0.355069i | ||||
\(156\) | 1.96420e9 | 0.265538 | ||||||||
\(157\) | − | 1.18606e10i | − | 1.55797i | −0.627042 | − | 0.778985i | \(-0.715735\pi\) | ||
0.627042 | − | 0.778985i | \(-0.284265\pi\) | |||||||
\(158\) | − | 3.93698e7i | − | 0.00502581i | ||||||
\(159\) | 8.59202e9 | 1.06613 | ||||||||
\(160\) | −8.45835e8 | + | 3.76476e8i | −0.102034 | + | 0.0454148i | ||||
\(161\) | 8.28367e9 | 0.971642 | ||||||||
\(162\) | 4.02949e8i | 0.0459656i | ||||||||
\(163\) | − | 3.99906e9i | − | 0.443724i | −0.975078 | − | 0.221862i | \(-0.928787\pi\) | ||
0.975078 | − | 0.221862i | \(-0.0712135\pi\) | |||||||
\(164\) | −1.30048e10 | −1.40381 | ||||||||
\(165\) | −1.01984e10 | + | 4.53923e9i | −1.07116 | + | 0.476765i | ||||
\(166\) | −1.70341e8 | −0.0174114 | ||||||||
\(167\) | − | 1.09118e10i | − | 1.08560i | −0.839861 | − | 0.542802i | \(-0.817363\pi\) | ||
0.839861 | − | 0.542802i | \(-0.182637\pi\) | |||||||
\(168\) | − | 1.34887e9i | − | 0.130640i | ||||||
\(169\) | 1.01452e10 | 0.956692 | ||||||||
\(170\) | −1.43986e8 | − | 3.23497e8i | −0.0132221 | − | 0.0297064i | ||||
\(171\) | 7.04028e9 | 0.629662 | ||||||||
\(172\) | 1.19043e10i | 1.03711i | ||||||||
\(173\) | 1.89328e10i | 1.60696i | 0.595329 | + | 0.803482i | \(0.297022\pi\) | ||||
−0.595329 | + | 0.803482i | \(0.702978\pi\) | |||||||
\(174\) | −1.21509e8 | −0.0100493 | ||||||||
\(175\) | −1.26439e10 | − | 1.13898e10i | −1.01909 | − | 0.918006i | ||||
\(176\) | 1.16318e10 | 0.913778 | ||||||||
\(177\) | 1.25496e10i | 0.961062i | ||||||||
\(178\) | 4.67577e8i | 0.0349111i | ||||||||
\(179\) | −2.09763e10 | −1.52718 | −0.763592 | − | 0.645699i | \(-0.776566\pi\) | ||||
−0.763592 | + | 0.645699i | \(0.776566\pi\) | |||||||
\(180\) | 3.61809e9 | + | 8.12882e9i | 0.256893 | + | 0.577167i | ||||
\(181\) | −7.16950e9 | −0.496518 | −0.248259 | − | 0.968694i | \(-0.579858\pi\) | ||||
−0.248259 | + | 0.968694i | \(0.579858\pi\) | |||||||
\(182\) | 1.57584e8i | 0.0106461i | ||||||||
\(183\) | − | 2.27560e10i | − | 1.49991i | ||||||
\(184\) | −8.21045e8 | −0.0528064 | ||||||||
\(185\) | 1.21761e10 | − | 5.41951e9i | 0.764251 | − | 0.340163i | ||||
\(186\) | 3.02338e8 | 0.0185218 | ||||||||
\(187\) | 1.33771e10i | 0.799974i | ||||||||
\(188\) | − | 1.92936e10i | − | 1.12643i | ||||||
\(189\) | 1.12939e10 | 0.643824 | ||||||||
\(190\) | 6.09221e8 | − | 2.71160e8i | 0.0339143 | − | 0.0150951i | ||||
\(191\) | 1.75301e10 | 0.953091 | 0.476545 | − | 0.879150i | \(-0.341889\pi\) | ||||
0.476545 | + | 0.879150i | \(0.341889\pi\) | |||||||
\(192\) | − | 2.38597e10i | − | 1.26709i | ||||||
\(193\) | 3.13528e10i | 1.62655i | 0.581877 | + | 0.813277i | \(0.302319\pi\) | ||||
−0.581877 | + | 0.813277i | \(0.697681\pi\) | |||||||
\(194\) | 2.86509e8 | 0.0145222 | ||||||||
\(195\) | −2.18318e9 | − | 4.90499e9i | −0.108127 | − | 0.242931i | ||||
\(196\) | −1.81827e10 | −0.880048 | ||||||||
\(197\) | − | 1.85971e10i | − | 0.879725i | −0.898065 | − | 0.439862i | \(-0.855027\pi\) | ||
0.898065 | − | 0.439862i | \(-0.144973\pi\) | |||||||
\(198\) | 4.68255e8i | 0.0216515i | ||||||||
\(199\) | 1.26662e10 | 0.572544 | 0.286272 | − | 0.958148i | \(-0.407584\pi\) | ||||
0.286272 | + | 0.958148i | \(0.407584\pi\) | |||||||
\(200\) | 1.25322e9 | + | 1.12891e9i | 0.0553849 | + | 0.0498914i | ||||
\(201\) | −4.77906e10 | −2.06519 | ||||||||
\(202\) | − | 1.13021e9i | − | 0.0477617i | ||||||
\(203\) | 6.99798e9i | 0.289228i | ||||||||
\(204\) | 2.75166e10 | 1.11240 | ||||||||
\(205\) | 1.44547e10 | + | 3.24756e10i | 0.571631 | + | 1.28429i | ||||
\(206\) | 3.24333e8 | 0.0125484 | ||||||||
\(207\) | 1.18386e10i | 0.448161i | ||||||||
\(208\) | 5.59443e9i | 0.207239i | ||||||||
\(209\) | −2.51923e10 | −0.913291 | ||||||||
\(210\) | −1.68301e9 | + | 7.49099e8i | −0.0597174 | + | 0.0265798i | ||||
\(211\) | −6.20579e9 | −0.215539 | −0.107770 | − | 0.994176i | \(-0.534371\pi\) | ||||
−0.107770 | + | 0.994176i | \(0.534371\pi\) | |||||||
\(212\) | 2.45059e10i | 0.833218i | ||||||||
\(213\) | − | 1.18164e10i | − | 0.393350i | ||||||
\(214\) | −6.72943e8 | −0.0219339 | ||||||||
\(215\) | 2.97273e10 | − | 1.32314e10i | 0.948818 | − | 0.422313i | ||||
\(216\) | −1.11941e9 | −0.0349903 | ||||||||
\(217\) | − | 1.74123e10i | − | 0.533074i | ||||||
\(218\) | − | 5.59729e8i | − | 0.0167851i | ||||||
\(219\) | −2.64442e9 | −0.0776841 | ||||||||
\(220\) | −1.29466e10 | − | 2.90875e10i | −0.372610 | − | 0.837151i | ||||
\(221\) | −6.43385e9 | −0.181428 | ||||||||
\(222\) | − | 1.44277e9i | − | 0.0398664i | ||||||
\(223\) | − | 4.30855e10i | − | 1.16670i | −0.812221 | − | 0.583350i | \(-0.801742\pi\) | ||
0.812221 | − | 0.583350i | \(-0.198258\pi\) | |||||||
\(224\) | 5.77213e9 | 0.153186 | ||||||||
\(225\) | 1.62778e10 | − | 1.80701e10i | 0.423422 | − | 0.470045i | ||||
\(226\) | −1.25042e9 | −0.0318836 | ||||||||
\(227\) | 2.28857e10i | 0.572068i | 0.958219 | + | 0.286034i | \(0.0923371\pi\) | ||||
−0.958219 | + | 0.286034i | \(0.907663\pi\) | |||||||
\(228\) | 5.18203e10i | 1.26997i | ||||||||
\(229\) | 5.26747e9 | 0.126573 | 0.0632867 | − | 0.997995i | \(-0.479842\pi\) | ||||
0.0632867 | + | 0.997995i | \(0.479842\pi\) | |||||||
\(230\) | 4.55971e8 | + | 1.02444e9i | 0.0107439 | + | 0.0241385i | ||||
\(231\) | 6.95955e10 | 1.60815 | ||||||||
\(232\) | − | 6.93612e8i | − | 0.0157189i | ||||||
\(233\) | − | 3.55179e10i | − | 0.789488i | −0.918791 | − | 0.394744i | \(-0.870833\pi\) | ||
0.918791 | − | 0.394744i | \(-0.129167\pi\) | |||||||
\(234\) | −2.25211e8 | −0.00491042 | ||||||||
\(235\) | −4.81798e10 | + | 2.14445e10i | −1.03053 | + | 0.458681i | ||||
\(236\) | −3.57937e10 | −0.751108 | ||||||||
\(237\) | − | 8.36257e9i | − | 0.172176i | ||||||
\(238\) | 2.20760e9i | 0.0445989i | ||||||||
\(239\) | −5.72471e10 | −1.13491 | −0.567457 | − | 0.823403i | \(-0.692073\pi\) | ||||
−0.567457 | + | 0.823403i | \(0.692073\pi\) | |||||||
\(240\) | −5.97492e10 | + | 2.65940e10i | −1.16247 | + | 0.517407i | ||||
\(241\) | 3.89830e10 | 0.744386 | 0.372193 | − | 0.928155i | \(-0.378606\pi\) | ||||
0.372193 | + | 0.928155i | \(0.378606\pi\) | |||||||
\(242\) | 3.14415e8i | 0.00589296i | ||||||||
\(243\) | 6.00774e10i | 1.10531i | ||||||||
\(244\) | 6.49039e10 | 1.17224 | ||||||||
\(245\) | 2.02098e10 | + | 4.54057e10i | 0.358356 | + | 0.805124i | ||||
\(246\) | 3.84808e9 | 0.0669939 | ||||||||
\(247\) | − | 1.21164e10i | − | 0.207128i | ||||||
\(248\) | 1.72584e9i | 0.0289713i | ||||||||
\(249\) | −3.61824e10 | −0.596486 | ||||||||
\(250\) | 7.12595e8 | − | 2.19062e9i | 0.0115375 | − | 0.0354680i | ||||
\(251\) | 4.56895e10 | 0.726581 | 0.363291 | − | 0.931676i | \(-0.381653\pi\) | ||||
0.363291 | + | 0.931676i | \(0.381653\pi\) | |||||||
\(252\) | − | 5.54725e10i | − | 0.866514i | ||||||
\(253\) | − | 4.23622e10i | − | 0.650035i | ||||||
\(254\) | −1.93071e9 | −0.0291048 | ||||||||
\(255\) | −3.05843e10 | − | 6.87143e10i | −0.452968 | − | 1.01769i | ||||
\(256\) | 6.77655e10 | 0.986118 | ||||||||
\(257\) | − | 1.29955e10i | − | 0.185821i | −0.995674 | − | 0.0929104i | \(-0.970383\pi\) | ||
0.995674 | − | 0.0929104i | \(-0.0296170\pi\) | |||||||
\(258\) | − | 3.52243e9i | − | 0.0494942i | ||||||
\(259\) | −8.30920e10 | −1.14739 | ||||||||
\(260\) | 1.39899e10 | − | 6.22680e9i | 0.189860 | − | 0.0845054i | ||||
\(261\) | −1.00012e10 | −0.133404 | ||||||||
\(262\) | 3.24073e9i | 0.0424901i | ||||||||
\(263\) | 4.80103e10i | 0.618776i | 0.950936 | + | 0.309388i | \(0.100124\pi\) | ||||
−0.950936 | + | 0.309388i | \(0.899876\pi\) | |||||||
\(264\) | −6.89803e9 | −0.0873991 | ||||||||
\(265\) | 6.11958e10 | − | 2.72379e10i | 0.762282 | − | 0.339287i | ||||
\(266\) | −4.15743e9 | −0.0509164 | ||||||||
\(267\) | 9.93185e10i | 1.19600i | ||||||||
\(268\) | − | 1.36307e11i | − | 1.61403i | ||||||
\(269\) | 9.98823e10 | 1.16306 | 0.581531 | − | 0.813524i | \(-0.302454\pi\) | ||||
0.581531 | + | 0.813524i | \(0.302454\pi\) | |||||||
\(270\) | 6.21670e8 | + | 1.39672e9i | 0.00711906 | + | 0.0159945i | ||||
\(271\) | −4.80217e10 | −0.540849 | −0.270424 | − | 0.962741i | \(-0.587164\pi\) | ||||
−0.270424 | + | 0.962741i | \(0.587164\pi\) | |||||||
\(272\) | 7.83726e10i | 0.868169i | ||||||||
\(273\) | 3.34725e10i | 0.364718i | ||||||||
\(274\) | 4.91737e9 | 0.0527054 | ||||||||
\(275\) | −5.82469e10 | + | 6.46604e10i | −0.614152 | + | 0.681776i | ||||
\(276\) | −8.71388e10 | −0.903900 | ||||||||
\(277\) | 1.77838e10i | 0.181495i | 0.995874 | + | 0.0907477i | \(0.0289257\pi\) | ||||
−0.995874 | + | 0.0907477i | \(0.971074\pi\) | |||||||
\(278\) | − | 4.97838e9i | − | 0.0499904i | ||||||
\(279\) | 2.48848e10 | 0.245875 | ||||||||
\(280\) | −4.27609e9 | − | 9.60717e9i | −0.0415753 | − | 0.0934080i | ||||
\(281\) | −1.52044e11 | −1.45476 | −0.727379 | − | 0.686236i | \(-0.759262\pi\) | ||||
−0.727379 | + | 0.686236i | \(0.759262\pi\) | |||||||
\(282\) | 5.70890e9i | 0.0537565i | ||||||||
\(283\) | 1.86733e11i | 1.73055i | 0.501301 | + | 0.865273i | \(0.332855\pi\) | ||||
−0.501301 | + | 0.865273i | \(0.667145\pi\) | |||||||
\(284\) | 3.37025e10 | 0.307418 | ||||||||
\(285\) | 1.29405e11 | − | 5.75974e10i | 1.16185 | − | 0.517132i | ||||
\(286\) | 8.05875e8 | 0.00712230 | ||||||||
\(287\) | − | 2.21619e11i | − | 1.92814i | ||||||
\(288\) | 8.24924e9i | 0.0706558i | ||||||||
\(289\) | 2.84558e10 | 0.239955 | ||||||||
\(290\) | −8.65438e8 | + | 3.85201e8i | −0.00718530 | + | 0.00319813i | ||||
\(291\) | 6.08577e10 | 0.497505 | ||||||||
\(292\) | − | 7.54233e9i | − | 0.0607132i | ||||||
\(293\) | − | 1.28928e11i | − | 1.02198i | −0.859586 | − | 0.510991i | \(-0.829278\pi\) | ||
0.859586 | − | 0.510991i | \(-0.170722\pi\) | |||||||
\(294\) | 5.38018e9 | 0.0419985 | ||||||||
\(295\) | 3.97841e10 | + | 8.93836e10i | 0.305851 | + | 0.687161i | ||||
\(296\) | 8.23575e9 | 0.0623577 | ||||||||
\(297\) | − | 5.77565e10i | − | 0.430722i | ||||||
\(298\) | 4.55167e9i | 0.0334347i | ||||||||
\(299\) | 2.03745e10 | 0.147423 | ||||||||
\(300\) | 1.33006e11 | + | 1.19813e11i | 0.948037 | + | 0.854004i | ||||
\(301\) | −2.02865e11 | −1.42448 | ||||||||
\(302\) | − | 6.68575e8i | − | 0.00462508i | ||||||
\(303\) | − | 2.40070e11i | − | 1.63624i | ||||||
\(304\) | −1.47594e11 | −0.991146 | ||||||||
\(305\) | −7.21396e10 | − | 1.62077e11i | −0.477336 | − | 1.07244i | ||||
\(306\) | −3.15499e9 | −0.0205708 | ||||||||
\(307\) | 8.78331e10i | 0.564333i | 0.959365 | + | 0.282167i | \(0.0910531\pi\) | ||||
−0.959365 | + | 0.282167i | \(0.908947\pi\) | |||||||
\(308\) | 1.98498e11i | 1.25683i | ||||||||
\(309\) | 6.88919e10 | 0.429887 | ||||||||
\(310\) | 2.15337e9 | − | 9.58452e8i | 0.0132432 | − | 0.00589444i | ||||
\(311\) | 2.76204e11 | 1.67420 | 0.837101 | − | 0.547049i | \(-0.184249\pi\) | ||||
0.837101 | + | 0.547049i | \(0.184249\pi\) | |||||||
\(312\) | − | 3.31767e9i | − | 0.0198215i | ||||||
\(313\) | 1.84107e11i | 1.08423i | 0.840304 | + | 0.542115i | \(0.182376\pi\) | ||||
−0.840304 | + | 0.542115i | \(0.817624\pi\) | |||||||
\(314\) | −1.00097e10 | −0.0581082 | ||||||||
\(315\) | −1.38525e11 | + | 6.16568e10i | −0.792742 | + | 0.352845i | ||||
\(316\) | 2.38515e10 | 0.134562 | ||||||||
\(317\) | 3.48865e11i | 1.94040i | 0.242313 | + | 0.970198i | \(0.422094\pi\) | ||||
−0.242313 | + | 0.970198i | \(0.577906\pi\) | |||||||
\(318\) | − | 7.25118e9i | − | 0.0397637i | ||||||
\(319\) | 3.57873e10 | 0.193496 | ||||||||
\(320\) | −7.56384e10 | − | 1.69938e11i | −0.403244 | − | 0.905975i | ||||
\(321\) | −1.42940e11 | −0.751419 | ||||||||
\(322\) | − | 6.99095e9i | − | 0.0362397i | ||||||
\(323\) | − | 1.69740e11i | − | 0.867706i | ||||||
\(324\) | −2.44119e11 | −1.23069 | ||||||||
\(325\) | −3.10990e10 | − | 2.80144e10i | −0.154622 | − | 0.139285i | ||||
\(326\) | −3.37498e9 | −0.0165498 | ||||||||
\(327\) | − | 1.18893e11i | − | 0.575029i | ||||||
\(328\) | 2.19660e10i | 0.104790i | ||||||||
\(329\) | 3.28788e11 | 1.54716 | ||||||||
\(330\) | 3.83085e9 | + | 8.60685e9i | 0.0177821 | + | 0.0399513i | ||||
\(331\) | 2.88744e11 | 1.32217 | 0.661084 | − | 0.750312i | \(-0.270097\pi\) | ||||
0.661084 | + | 0.750312i | \(0.270097\pi\) | |||||||
\(332\) | − | 1.03198e11i | − | 0.466177i | ||||||
\(333\) | − | 1.18751e11i | − | 0.529222i | ||||||
\(334\) | −9.20892e9 | −0.0404902 | ||||||||
\(335\) | −3.40384e11 | + | 1.51503e11i | −1.47662 | + | 0.657232i | ||||
\(336\) | 4.07739e11 | 1.74524 | ||||||||
\(337\) | − | 1.25882e11i | − | 0.531654i | −0.964021 | − | 0.265827i | \(-0.914355\pi\) | ||
0.964021 | − | 0.265827i | \(-0.0856450\pi\) | |||||||
\(338\) | − | 8.56201e9i | − | 0.0356821i | ||||||
\(339\) | −2.65602e11 | −1.09228 | ||||||||
\(340\) | 1.95985e11 | − | 8.72315e10i | 0.795366 | − | 0.354012i | ||||
\(341\) | −8.90455e10 | −0.356630 | ||||||||
\(342\) | − | 5.94160e9i | − | 0.0234847i | ||||||
\(343\) | 4.17441e10i | 0.162844i | ||||||||
\(344\) | 2.01071e10 | 0.0774172 | ||||||||
\(345\) | 9.68533e10 | + | 2.17602e11i | 0.368068 | + | 0.826946i | ||||
\(346\) | 1.59782e10 | 0.0599356 | ||||||||
\(347\) | − | 2.95822e11i | − | 1.09534i | −0.836695 | − | 0.547669i | \(-0.815515\pi\) | ||
0.836695 | − | 0.547669i | \(-0.184485\pi\) | |||||||
\(348\) | − | 7.36142e10i | − | 0.269064i | ||||||
\(349\) | −3.73474e11 | −1.34755 | −0.673777 | − | 0.738934i | \(-0.735329\pi\) | ||||
−0.673777 | + | 0.738934i | \(0.735329\pi\) | |||||||
\(350\) | −9.61237e9 | + | 1.06708e10i | −0.0342392 | + | 0.0380093i | ||||
\(351\) | 2.77785e10 | 0.0976848 | ||||||||
\(352\) | − | 2.95183e10i | − | 0.102483i | ||||||
\(353\) | 4.89872e11i | 1.67918i | 0.543223 | + | 0.839589i | \(0.317204\pi\) | ||||
−0.543223 | + | 0.839589i | \(0.682796\pi\) | |||||||
\(354\) | 1.05912e10 | 0.0358451 | ||||||||
\(355\) | −3.74598e10 | − | 8.41615e10i | −0.125181 | − | 0.281246i | ||||
\(356\) | −2.83273e11 | −0.934718 | ||||||||
\(357\) | 4.68918e11i | 1.52788i | ||||||||
\(358\) | 1.77029e10i | 0.0569600i | ||||||||
\(359\) | 4.27559e11 | 1.35854 | 0.679268 | − | 0.733891i | \(-0.262298\pi\) | ||||
0.679268 | + | 0.733891i | \(0.262298\pi\) | |||||||
\(360\) | 1.37301e10 | − | 6.11118e9i | 0.0430836 | − | 0.0191762i | ||||
\(361\) | −3.02753e9 | −0.00938223 | ||||||||
\(362\) | 6.05065e9i | 0.0185188i | ||||||||
\(363\) | 6.67851e10i | 0.201883i | ||||||||
\(364\) | −9.54693e10 | −0.285041 | ||||||||
\(365\) | −1.88346e10 | + | 8.38317e9i | −0.0555443 | + | 0.0247224i | ||||
\(366\) | −1.92048e10 | −0.0559428 | ||||||||
\(367\) | 2.54403e10i | 0.0732023i | 0.999330 | + | 0.0366012i | \(0.0116531\pi\) | ||||
−0.999330 | + | 0.0366012i | \(0.988347\pi\) | |||||||
\(368\) | − | 2.48188e11i | − | 0.705448i | ||||||
\(369\) | 3.16727e11 | 0.889337 | ||||||||
\(370\) | −4.57376e9 | − | 1.02760e10i | −0.0126872 | − | 0.0285046i | ||||
\(371\) | −4.17611e11 | −1.14443 | ||||||||
\(372\) | 1.83166e11i | 0.495908i | ||||||||
\(373\) | − | 7.26003e11i | − | 1.94200i | −0.239087 | − | 0.970998i | \(-0.576848\pi\) | ||
0.239087 | − | 0.970998i | \(-0.423152\pi\) | |||||||
\(374\) | 1.12895e10 | 0.0298369 | ||||||||
\(375\) | 1.51363e11 | − | 4.65312e11i | 0.395256 | − | 1.21508i | ||||
\(376\) | −3.25881e10 | −0.0840842 | ||||||||
\(377\) | 1.72122e10i | 0.0438834i | ||||||||
\(378\) | − | 9.53144e9i | − | 0.0240129i | ||||||
\(379\) | 2.76699e11 | 0.688859 | 0.344430 | − | 0.938812i | \(-0.388072\pi\) | ||||
0.344430 | + | 0.938812i | \(0.388072\pi\) | |||||||
\(380\) | 1.64277e11 | + | 3.69085e11i | 0.404159 | + | 0.908031i | ||||
\(381\) | −4.10103e11 | −0.997082 | ||||||||
\(382\) | − | 1.47944e10i | − | 0.0355478i | ||||||
\(383\) | 1.71143e11i | 0.406410i | 0.979136 | + | 0.203205i | \(0.0651358\pi\) | ||||
−0.979136 | + | 0.203205i | \(0.934864\pi\) | |||||||
\(384\) | −8.09398e10 | −0.189964 | ||||||||
\(385\) | 4.95687e11 | − | 2.20627e11i | 1.14983 | − | 0.511783i | ||||
\(386\) | 2.64600e10 | 0.0606662 | ||||||||
\(387\) | − | 2.89924e11i | − | 0.657030i | ||||||
\(388\) | 1.73576e11i | 0.388819i | ||||||||
\(389\) | −3.92384e10 | −0.0868837 | −0.0434419 | − | 0.999056i | \(-0.513832\pi\) | ||||
−0.0434419 | + | 0.999056i | \(0.513832\pi\) | |||||||
\(390\) | −4.13954e9 | + | 1.84248e9i | −0.00906068 | + | 0.00403285i | ||||
\(391\) | 2.85427e11 | 0.617590 | ||||||||
\(392\) | 3.07117e10i | 0.0656927i | ||||||||
\(393\) | 6.88367e11i | 1.45564i | ||||||||
\(394\) | −1.56949e10 | −0.0328114 | ||||||||
\(395\) | −2.65105e10 | − | 5.95616e10i | −0.0547937 | − | 0.123106i | ||||
\(396\) | −2.83684e11 | −0.579703 | ||||||||
\(397\) | − | 3.91381e11i | − | 0.790756i | −0.918519 | − | 0.395378i | \(-0.870614\pi\) | ||
0.918519 | − | 0.395378i | \(-0.129386\pi\) | |||||||
\(398\) | − | 1.06896e10i | − | 0.0213544i | ||||||
\(399\) | −8.83084e11 | −1.74431 | ||||||||
\(400\) | −3.41251e11 | + | 3.78826e11i | −0.666506 | + | 0.739895i | ||||
\(401\) | −5.04969e11 | −0.975248 | −0.487624 | − | 0.873054i | \(-0.662136\pi\) | ||||
−0.487624 | + | 0.873054i | \(0.662136\pi\) | |||||||
\(402\) | 4.03326e10i | 0.0770263i | ||||||||
\(403\) | − | 4.28272e10i | − | 0.0808811i | ||||||
\(404\) | 6.84720e11 | 1.27878 | ||||||||
\(405\) | 2.71335e11 | + | 6.09613e11i | 0.501138 | + | 1.12592i | ||||
\(406\) | 5.90590e9 | 0.0107875 | ||||||||
\(407\) | 4.24928e11i | 0.767609i | ||||||||
\(408\) | − | 4.64773e10i | − | 0.0830368i | ||||||
\(409\) | −9.44998e9 | −0.0166985 | −0.00834923 | − | 0.999965i | \(-0.502658\pi\) | ||||
−0.00834923 | + | 0.999965i | \(0.502658\pi\) | |||||||
\(410\) | 2.74075e10 | − | 1.21989e10i | 0.0479008 | − | 0.0213203i | ||||
\(411\) | 1.04450e12 | 1.80560 | ||||||||
\(412\) | 1.96491e11i | 0.335974i | ||||||||
\(413\) | − | 6.09969e11i | − | 1.03165i | ||||||
\(414\) | 9.99113e9 | 0.0167153 | ||||||||
\(415\) | −2.57706e11 | + | 1.14703e11i | −0.426488 | + | 0.189827i | ||||
\(416\) | 1.41971e10 | 0.0232423 | ||||||||
\(417\) | − | 1.05746e12i | − | 1.71259i | ||||||
\(418\) | 2.12609e10i | 0.0340634i | ||||||||
\(419\) | 5.77328e10 | 0.0915081 | 0.0457541 | − | 0.998953i | \(-0.485431\pi\) | ||||
0.0457541 | + | 0.998953i | \(0.485431\pi\) | |||||||
\(420\) | −4.53828e11 | − | 1.01962e12i | −0.711655 | − | 1.59889i | ||||
\(421\) | 4.38976e9 | 0.00681038 | 0.00340519 | − | 0.999994i | \(-0.498916\pi\) | ||||
0.00340519 | + | 0.999994i | \(0.498916\pi\) | |||||||
\(422\) | 5.23734e9i | 0.00803905i | ||||||||
\(423\) | 4.69887e11i | 0.713612i | ||||||||
\(424\) | 4.13920e10 | 0.0621970 | ||||||||
\(425\) | −4.35667e11 | − | 3.92455e11i | −0.647746 | − | 0.583498i | ||||
\(426\) | −9.97242e9 | −0.0146709 | ||||||||
\(427\) | 1.10604e12i | 1.61008i | ||||||||
\(428\) | − | 4.07690e11i | − | 0.587264i | ||||||
\(429\) | 1.71177e11 | 0.243998 | ||||||||
\(430\) | −1.11666e10 | − | 2.50882e10i | −0.0157512 | − | 0.0353884i | ||||
\(431\) | 9.94476e11 | 1.38818 | 0.694091 | − | 0.719887i | \(-0.255807\pi\) | ||||
0.694091 | + | 0.719887i | \(0.255807\pi\) | |||||||
\(432\) | − | 3.38378e11i | − | 0.467440i | ||||||
\(433\) | − | 1.91618e11i | − | 0.261963i | −0.991385 | − | 0.130982i | \(-0.958187\pi\) | ||
0.991385 | − | 0.130982i | \(-0.0418129\pi\) | |||||||
\(434\) | −1.46950e10 | −0.0198823 | ||||||||
\(435\) | −1.83829e11 | + | 8.18209e10i | −0.246157 | + | 0.109563i | ||||
\(436\) | 3.39101e11 | 0.449407 | ||||||||
\(437\) | 5.37527e11i | 0.705072i | ||||||||
\(438\) | 2.23174e9i | 0.00289741i | ||||||||
\(439\) | −1.38202e12 | −1.77592 | −0.887962 | − | 0.459917i | \(-0.847879\pi\) | ||||
−0.887962 | + | 0.459917i | \(0.847879\pi\) | |||||||
\(440\) | −4.91305e10 | + | 2.18677e10i | −0.0624906 | + | 0.0278141i | ||||
\(441\) | 4.42832e11 | 0.557526 | ||||||||
\(442\) | 5.42980e9i | 0.00676681i | ||||||||
\(443\) | − | 3.05660e11i | − | 0.377070i | −0.982066 | − | 0.188535i | \(-0.939626\pi\) | ||
0.982066 | − | 0.188535i | \(-0.0603740\pi\) | |||||||
\(444\) | 8.74073e11 | 1.06739 | ||||||||
\(445\) | 3.14853e11 | + | 7.07387e11i | 0.380617 | + | 0.855139i | ||||
\(446\) | −3.63617e10 | −0.0435148 | ||||||||
\(447\) | 9.66825e11i | 1.14542i | ||||||||
\(448\) | 1.15969e12i | 1.36016i | ||||||||
\(449\) | −1.49518e12 | −1.73614 | −0.868069 | − | 0.496444i | \(-0.834639\pi\) | ||||
−0.868069 | + | 0.496444i | \(0.834639\pi\) | |||||||
\(450\) | −1.52501e10 | − | 1.37375e10i | −0.0175314 | − | 0.0157925i | ||||
\(451\) | −1.13335e12 | −1.28994 | ||||||||
\(452\) | − | 7.57542e11i | − | 0.853658i | ||||||
\(453\) | − | 1.42013e11i | − | 0.158447i | ||||||
\(454\) | 1.93142e10 | 0.0213367 | ||||||||
\(455\) | 1.06112e11 | + | 2.38405e11i | 0.116069 | + | 0.260774i | ||||
\(456\) | 8.75278e10 | 0.0947991 | ||||||||
\(457\) | − | 1.17977e12i | − | 1.26525i | −0.774459 | − | 0.632624i | \(-0.781978\pi\) | ||
0.774459 | − | 0.632624i | \(-0.218022\pi\) | |||||||
\(458\) | − | 4.44545e9i | − | 0.00472086i | ||||||
\(459\) | 3.89151e11 | 0.409223 | ||||||||
\(460\) | −6.20638e11 | + | 2.76242e11i | −0.646291 | + | 0.287660i | ||||
\(461\) | 1.54415e12 | 1.59234 | 0.796170 | − | 0.605074i | \(-0.206856\pi\) | ||||
0.796170 | + | 0.605074i | \(0.206856\pi\) | |||||||
\(462\) | − | 5.87346e10i | − | 0.0599799i | ||||||
\(463\) | − | 4.55769e11i | − | 0.460926i | −0.973081 | − | 0.230463i | \(-0.925976\pi\) | ||
0.973081 | − | 0.230463i | \(-0.0740240\pi\) | |||||||
\(464\) | 2.09667e11 | 0.209990 | ||||||||
\(465\) | 4.57400e11 | − | 2.03586e11i | 0.453689 | − | 0.201934i | ||||
\(466\) | −2.99751e10 | −0.0294458 | ||||||||
\(467\) | − | 6.97342e11i | − | 0.678454i | −0.940705 | − | 0.339227i | \(-0.889835\pi\) | ||
0.940705 | − | 0.339227i | \(-0.110165\pi\) | |||||||
\(468\) | − | 1.36440e11i | − | 0.131473i | ||||||
\(469\) | 2.32284e12 | 2.21688 | ||||||||
\(470\) | 1.80980e10 | + | 4.06611e10i | 0.0171076 | + | 0.0384360i | ||||
\(471\) | −2.12617e12 | −1.99069 | ||||||||
\(472\) | 6.04578e10i | 0.0560677i | ||||||||
\(473\) | 1.03744e12i | 0.952987i | ||||||||
\(474\) | −7.05754e9 | −0.00642171 | ||||||||
\(475\) | 7.39084e11 | − | 8.20464e11i | 0.666151 | − | 0.739500i | ||||
\(476\) | −1.33743e12 | −1.19410 | ||||||||
\(477\) | − | 5.96829e11i | − | 0.527858i | ||||||
\(478\) | 4.83134e10i | 0.0423294i | ||||||||
\(479\) | −2.43471e11 | −0.211318 | −0.105659 | − | 0.994402i | \(-0.533695\pi\) | ||||
−0.105659 | + | 0.994402i | \(0.533695\pi\) | |||||||
\(480\) | 6.74881e10 | + | 1.51627e11i | 0.0580285 | + | 0.130374i | ||||
\(481\) | −2.04373e11 | −0.174088 | ||||||||
\(482\) | − | 3.28994e10i | − | 0.0277637i | ||||||
\(483\) | − | 1.48495e12i | − | 1.24151i | ||||||
\(484\) | −1.90482e11 | −0.157780 | ||||||||
\(485\) | 4.33453e11 | − | 1.92927e11i | 0.355717 | − | 0.158327i | ||||
\(486\) | 5.07019e10 | 0.0412251 | ||||||||
\(487\) | 1.56961e12i | 1.26448i | 0.774773 | + | 0.632239i | \(0.217864\pi\) | ||||
−0.774773 | + | 0.632239i | \(0.782136\pi\) | |||||||
\(488\) | − | 1.09627e11i | − | 0.0875039i | ||||||
\(489\) | −7.16882e11 | −0.566967 | ||||||||
\(490\) | 3.83198e10 | − | 1.70559e10i | 0.0300290 | − | 0.0133657i | ||||
\(491\) | 6.52870e11 | 0.506944 | 0.253472 | − | 0.967343i | \(-0.418427\pi\) | ||||
0.253472 | + | 0.967343i | \(0.418427\pi\) | |||||||
\(492\) | 2.33129e12i | 1.79371i | ||||||||
\(493\) | 2.41127e11i | 0.183838i | ||||||||
\(494\) | −1.02256e10 | −0.00772534 | ||||||||
\(495\) | 3.15309e11 | + | 7.08412e11i | 0.236055 | + | 0.530350i | ||||
\(496\) | −5.21691e11 | −0.387031 | ||||||||
\(497\) | 5.74333e11i | 0.422241i | ||||||||
\(498\) | 3.05359e10i | 0.0222474i | ||||||||
\(499\) | 7.51465e11 | 0.542571 | 0.271285 | − | 0.962499i | \(-0.412551\pi\) | ||||
0.271285 | + | 0.962499i | \(0.412551\pi\) | |||||||
\(500\) | 1.32715e12 | + | 4.31713e11i | 0.949629 | + | 0.308908i | ||||
\(501\) | −1.95608e12 | −1.38713 | ||||||||
\(502\) | − | 3.85593e10i | − | 0.0270996i | ||||||
\(503\) | 1.31120e12i | 0.913299i | 0.889647 | + | 0.456649i | \(0.150951\pi\) | ||||
−0.889647 | + | 0.456649i | \(0.849049\pi\) | |||||||
\(504\) | −9.36966e10 | −0.0646824 | ||||||||
\(505\) | −7.61055e11 | − | 1.70988e12i | −0.520721 | − | 1.16991i | ||||
\(506\) | −3.57513e10 | −0.0242446 | ||||||||
\(507\) | − | 1.81866e12i | − | 1.22241i | ||||||
\(508\) | − | 1.16968e12i | − | 0.779259i | ||||||
\(509\) | −1.78629e12 | −1.17957 | −0.589783 | − | 0.807561i | \(-0.700787\pi\) | ||||
−0.589783 | + | 0.807561i | \(0.700787\pi\) | |||||||
\(510\) | −5.79910e10 | + | 2.58114e10i | −0.0379572 | + | 0.0168945i | ||||
\(511\) | 1.28531e11 | 0.0833899 | ||||||||
\(512\) | − | 2.88366e11i | − | 0.185451i | ||||||
\(513\) | 7.32862e11i | 0.467191i | ||||||||
\(514\) | −1.09675e10 | −0.00693063 | ||||||||
\(515\) | 4.90676e11 | − | 2.18397e11i | 0.307370 | − | 0.136809i | ||||
\(516\) | 2.13400e12 | 1.32517 | ||||||||
\(517\) | − | 1.68140e12i | − | 1.03506i | ||||||
\(518\) | 7.01249e10i | 0.0427946i | ||||||||
\(519\) | 3.39394e12 | 2.05329 | ||||||||
\(520\) | −1.05175e10 | − | 2.36298e10i | −0.00630805 | − | 0.0141724i | ||||
\(521\) | 5.88627e11 | 0.350002 | 0.175001 | − | 0.984568i | \(-0.444007\pi\) | ||||
0.175001 | + | 0.984568i | \(0.444007\pi\) | |||||||
\(522\) | 8.44043e9i | 0.00497562i | ||||||||
\(523\) | 6.01202e11i | 0.351369i | 0.984447 | + | 0.175684i | \(0.0562138\pi\) | ||||
−0.984447 | + | 0.175684i | \(0.943786\pi\) | |||||||
\(524\) | −1.96334e12 | −1.13764 | ||||||||
\(525\) | −2.04177e12 | + | 2.26659e12i | −1.17298 | + | 1.30213i | ||||
\(526\) | 4.05180e10 | 0.0230787 | ||||||||
\(527\) | − | 5.99968e11i | − | 0.338829i | ||||||
\(528\) | − | 2.08515e12i | − | 1.16758i | ||||||
\(529\) | 8.97272e11 | 0.498165 | ||||||||
\(530\) | −2.29872e10 | − | 5.16458e10i | −0.0126545 | − | 0.0284311i | ||||
\(531\) | 8.71739e11 | 0.475840 | ||||||||
\(532\) | − | 2.51870e12i | − | 1.36325i | ||||||
\(533\) | − | 5.45093e11i | − | 0.292549i | ||||||
\(534\) | 8.38193e10 | 0.0446075 | ||||||||
\(535\) | −1.01808e12 | + | 4.53141e11i | −0.537266 | + | 0.239134i | ||||
\(536\) | −2.30231e11 | −0.120482 | ||||||||
\(537\) | 3.76028e12i | 1.95135i | ||||||||
\(538\) | − | 8.42950e10i | − | 0.0433792i | ||||||
\(539\) | −1.58459e12 | −0.808662 | ||||||||
\(540\) | −8.46175e11 | + | 3.76627e11i | −0.428241 | + | 0.190607i | ||||
\(541\) | 1.40863e12 | 0.706982 | 0.353491 | − | 0.935438i | \(-0.384995\pi\) | ||||
0.353491 | + | 0.935438i | \(0.384995\pi\) | |||||||
\(542\) | 4.05276e10i | 0.0201723i | ||||||||
\(543\) | 1.28522e12i | 0.634424i | ||||||||
\(544\) | 1.98888e11 | 0.0973673 | ||||||||
\(545\) | −3.76905e11 | − | 8.46800e11i | −0.182999 | − | 0.411147i | ||||
\(546\) | 2.82489e10 | 0.0136030 | ||||||||
\(547\) | 8.05933e10i | 0.0384907i | 0.999815 | + | 0.0192454i | \(0.00612636\pi\) | ||||
−0.999815 | + | 0.0192454i | \(0.993874\pi\) | |||||||
\(548\) | 2.97910e12i | 1.41115i | ||||||||
\(549\) | −1.58070e12 | −0.742635 | ||||||||
\(550\) | 5.45698e10 | + | 4.91571e10i | 0.0254285 | + | 0.0229063i | ||||
\(551\) | −4.54098e11 | −0.209878 | ||||||||
\(552\) | 1.47183e11i | 0.0674732i | ||||||||
\(553\) | 4.06459e11i | 0.184822i | ||||||||
\(554\) | 1.50085e10 | 0.00676930 | ||||||||
\(555\) | −9.71517e11 | − | 2.18273e12i | −0.434642 | − | 0.976519i | ||||
\(556\) | 3.01606e12 | 1.33845 | ||||||||
\(557\) | 3.92066e12i | 1.72588i | 0.505305 | + | 0.862941i | \(0.331380\pi\) | ||||
−0.505305 | + | 0.862941i | \(0.668620\pi\) | |||||||
\(558\) | − | 2.10014e10i | − | 0.00917051i | ||||||
\(559\) | −4.98965e11 | −0.216131 | ||||||||
\(560\) | 2.90408e12 | − | 1.29259e12i | 1.24785 | − | 0.555410i | ||||
\(561\) | 2.39802e12 | 1.02216 | ||||||||
\(562\) | 1.28317e11i | 0.0542587i | ||||||||
\(563\) | − | 3.86627e12i | − | 1.62182i | −0.585168 | − | 0.810912i | \(-0.698971\pi\) | ||
0.585168 | − | 0.810912i | \(-0.301029\pi\) | |||||||
\(564\) | −3.45863e12 | −1.43929 | ||||||||
\(565\) | −1.89173e12 | + | 8.41996e11i | −0.780981 | + | 0.347610i | ||||
\(566\) | 1.57592e11 | 0.0645448 | ||||||||
\(567\) | − | 4.16010e12i | − | 1.69036i | ||||||
\(568\) | − | 5.69256e10i | − | 0.0229478i | ||||||
\(569\) | 1.87990e12 | 0.751849 | 0.375924 | − | 0.926650i | \(-0.377325\pi\) | ||||
0.375924 | + | 0.926650i | \(0.377325\pi\) | |||||||
\(570\) | −4.86090e10 | − | 1.09211e11i | −0.0192877 | − | 0.0433339i | ||||
\(571\) | −3.44726e12 | −1.35710 | −0.678550 | − | 0.734554i | \(-0.737391\pi\) | ||||
−0.678550 | + | 0.734554i | \(0.737391\pi\) | |||||||
\(572\) | 4.88225e11i | 0.190694i | ||||||||
\(573\) | − | 3.14250e12i | − | 1.21781i | ||||||
\(574\) | −1.87034e11 | −0.0719146 | ||||||||
\(575\) | 1.37966e12 | + | 1.24281e12i | 0.526339 | + | 0.474133i | ||||
\(576\) | −1.65737e12 | −0.627362 | ||||||||
\(577\) | 1.68433e12i | 0.632608i | 0.948658 | + | 0.316304i | \(0.102442\pi\) | ||||
−0.948658 | + | 0.316304i | \(0.897558\pi\) | |||||||
\(578\) | − | 2.40151e10i | − | 0.00894971i | ||||||
\(579\) | 5.62039e12 | 2.07832 | ||||||||
\(580\) | −2.33367e11 | − | 5.24310e11i | −0.0856275 | − | 0.192381i | ||||
\(581\) | 1.75863e12 | 0.640297 | ||||||||
\(582\) | − | 5.13605e10i | − | 0.0185556i | ||||||
\(583\) | 2.13564e12i | 0.765631i | ||||||||
\(584\) | −1.27395e10 | −0.00453204 | ||||||||
\(585\) | −3.40717e11 | + | 1.51651e11i | −0.120280 | + | 0.0535357i | ||||
\(586\) | −1.08808e11 | −0.0381173 | ||||||||
\(587\) | − | 5.04715e12i | − | 1.75458i | −0.479956 | − | 0.877292i | \(-0.659348\pi\) | ||
0.479956 | − | 0.877292i | \(-0.340652\pi\) | |||||||
\(588\) | 3.25949e12i | 1.12448i | ||||||||
\(589\) | 1.12988e12 | 0.386825 | ||||||||
\(590\) | 7.54347e10 | − | 3.35755e10i | 0.0256293 | − | 0.0114074i | ||||
\(591\) | −3.33377e12 | −1.12407 | ||||||||
\(592\) | 2.48952e12i | 0.833045i | ||||||||
\(593\) | − | 6.66924e11i | − | 0.221478i | −0.993850 | − | 0.110739i | \(-0.964678\pi\) | ||
0.993850 | − | 0.110739i | \(-0.0353217\pi\) | |||||||
\(594\) | −4.87433e10 | −0.0160648 | ||||||||
\(595\) | 1.48654e12 | + | 3.33983e12i | 0.486238 | + | 1.09244i | ||||
\(596\) | −2.75755e12 | −0.895189 | ||||||||
\(597\) | − | 2.27059e12i | − | 0.731566i | ||||||
\(598\) | − | 1.71949e10i | − | 0.00549851i | ||||||
\(599\) | −3.36479e12 | −1.06792 | −0.533958 | − | 0.845511i | \(-0.679296\pi\) | ||||
−0.533958 | + | 0.845511i | \(0.679296\pi\) | |||||||
\(600\) | 2.02372e11 | − | 2.24655e11i | 0.0637486 | − | 0.0707679i | ||||
\(601\) | −2.79891e12 | −0.875092 | −0.437546 | − | 0.899196i | \(-0.644152\pi\) | ||||
−0.437546 | + | 0.899196i | \(0.644152\pi\) | |||||||
\(602\) | 1.71206e11i | 0.0531295i | ||||||||
\(603\) | 3.31969e12i | 1.02251i | ||||||||
\(604\) | 4.05044e11 | 0.123833 | ||||||||
\(605\) | 2.11718e11 | + | 4.75671e11i | 0.0642478 | + | 0.144347i | ||||
\(606\) | −2.02606e11 | −0.0610274 | ||||||||
\(607\) | 3.38683e12i | 1.01261i | 0.862353 | + | 0.506307i | \(0.168990\pi\) | ||||
−0.862353 | + | 0.506307i | \(0.831010\pi\) | |||||||
\(608\) | 3.74553e11i | 0.111160i | ||||||||
\(609\) | 1.25448e12 | 0.369560 | ||||||||
\(610\) | −1.36784e11 | + | 6.08817e10i | −0.0399992 | + | 0.0178034i | ||||
\(611\) | 8.08685e11 | 0.234744 | ||||||||
\(612\) | − | 1.91139e12i | − | 0.550768i | ||||||
\(613\) | − | 7.53866e11i | − | 0.215636i | −0.994171 | − | 0.107818i | \(-0.965614\pi\) | ||
0.994171 | − | 0.107818i | \(-0.0343864\pi\) | |||||||
\(614\) | 7.41262e10 | 0.0210482 | ||||||||
\(615\) | 5.82166e12 | − | 2.59119e12i | 1.64100 | − | 0.730399i | ||||
\(616\) | 3.35275e11 | 0.0938185 | ||||||||
\(617\) | − | 1.42132e11i | − | 0.0394827i | −0.999805 | − | 0.0197414i | \(-0.993716\pi\) | ||
0.999805 | − | 0.0197414i | \(-0.00628428\pi\) | |||||||
\(618\) | − | 5.81408e10i | − | 0.0160337i | ||||||
\(619\) | 1.03073e12 | 0.282186 | 0.141093 | − | 0.989996i | \(-0.454938\pi\) | ||||
0.141093 | + | 0.989996i | \(0.454938\pi\) | |||||||
\(620\) | 5.80661e11 | + | 1.30458e12i | 0.157819 | + | 0.354575i | ||||
\(621\) | −1.23235e12 | −0.332523 | ||||||||
\(622\) | − | 2.33100e11i | − | 0.0624433i | ||||||
\(623\) | − | 4.82733e12i | − | 1.28384i | ||||||
\(624\) | 1.00287e12 | 0.264798 | ||||||||
\(625\) | −3.97033e11 | − | 3.79398e12i | −0.104080 | − | 0.994569i | ||||
\(626\) | 1.55376e11 | 0.0404390 | ||||||||
\(627\) | 4.51604e12i | 1.16695i | ||||||||
\(628\) | − | 6.06419e12i | − | 1.55580i | ||||||
\(629\) | −2.86307e12 | −0.729296 | ||||||||
\(630\) | 5.20349e10 | + | 1.16908e11i | 0.0131602 | + | 0.0295672i | ||||
\(631\) | −4.61780e12 | −1.15959 | −0.579793 | − | 0.814764i | \(-0.696867\pi\) | ||||
−0.579793 | + | 0.814764i | \(0.696867\pi\) | |||||||
\(632\) | − | 4.02866e10i | − | 0.0100446i | ||||||
\(633\) | 1.11247e12i | 0.275404i | ||||||||
\(634\) | 2.94422e11 | 0.0723717 | ||||||||
\(635\) | −2.92092e12 | + | 1.30008e12i | −0.712916 | + | 0.317314i | ||||
\(636\) | 4.39299e12 | 1.06464 | ||||||||
\(637\) | − | 7.62122e11i | − | 0.183399i | ||||||
\(638\) | − | 3.02025e10i | − | 0.00721688i | ||||||
\(639\) | −8.20809e11 | −0.194755 | ||||||||
\(640\) | −5.76486e11 | + | 2.56590e11i | −0.135825 | + | 0.0604547i | ||||
\(641\) | 7.51099e12 | 1.75726 | 0.878630 | − | 0.477503i | \(-0.158458\pi\) | ||||
0.878630 | + | 0.477503i | \(0.158458\pi\) | |||||||
\(642\) | 1.20634e11i | 0.0280260i | ||||||||
\(643\) | 4.42841e12i | 1.02164i | 0.859687 | + | 0.510821i | \(0.170659\pi\) | ||||
−0.859687 | + | 0.510821i | \(0.829341\pi\) | |||||||
\(644\) | 4.23534e12 | 0.970291 | ||||||||
\(645\) | −2.37191e12 | − | 5.32901e12i | −0.539609 | − | 1.21235i | ||||
\(646\) | −1.43251e11 | −0.0323632 | ||||||||
\(647\) | 1.09396e12i | 0.245432i | 0.992442 | + | 0.122716i | \(0.0391604\pi\) | ||||
−0.992442 | + | 0.122716i | \(0.960840\pi\) | |||||||
\(648\) | 4.12333e11i | 0.0918672i | ||||||||
\(649\) | −3.11935e12 | −0.690181 | ||||||||
\(650\) | −2.36425e10 | + | 2.62458e10i | −0.00519498 | + | 0.00576699i | ||||
\(651\) | −3.12138e12 | −0.681133 | ||||||||
\(652\) | − | 2.04467e12i | − | 0.443107i | ||||||
\(653\) | 8.24881e12i | 1.77534i | 0.460477 | + | 0.887671i | \(0.347678\pi\) | ||||
−0.460477 | + | 0.887671i | \(0.652322\pi\) | |||||||
\(654\) | −1.00339e11 | −0.0214471 | ||||||||
\(655\) | 2.18222e12 | + | 4.90283e12i | 0.463247 | + | 1.04078i | ||||
\(656\) | −6.63994e12 | −1.39990 | ||||||||
\(657\) | 1.83690e11i | 0.0384628i | ||||||||
\(658\) | − | 2.77478e11i | − | 0.0577049i | ||||||
\(659\) | 2.64086e12 | 0.545458 | 0.272729 | − | 0.962091i | \(-0.412074\pi\) | ||||
0.272729 | + | 0.962091i | \(0.412074\pi\) | |||||||
\(660\) | −5.21430e12 | + | 2.32085e12i | −1.06967 | + | 0.476102i | ||||
\(661\) | 8.94654e12 | 1.82284 | 0.911420 | − | 0.411478i | \(-0.134987\pi\) | ||||
0.911420 | + | 0.411478i | \(0.134987\pi\) | |||||||
\(662\) | − | 2.43683e11i | − | 0.0493134i | ||||||
\(663\) | 1.15335e12i | 0.231820i | ||||||||
\(664\) | −1.74308e11 | −0.0347986 | ||||||||
\(665\) | −6.28968e12 | + | 2.79950e12i | −1.24719 | + | 0.555114i | ||||
\(666\) | −1.00219e11 | −0.0197386 | ||||||||
\(667\) | − | 7.63592e11i | − | 0.149381i | ||||||
\(668\) | − | 5.57906e12i | − | 1.08409i | ||||||
\(669\) | −7.72362e12 | −1.49075 | ||||||||
\(670\) | 1.27860e11 | + | 2.87265e11i | 0.0245130 | + | 0.0550739i | ||||
\(671\) | 5.65625e12 | 1.07715 | ||||||||
\(672\) | − | 1.03473e12i | − | 0.195733i | ||||||
\(673\) | − | 6.40541e12i | − | 1.20359i | −0.798650 | − | 0.601796i | \(-0.794452\pi\) | ||
0.798650 | − | 0.601796i | \(-0.205548\pi\) | |||||||
\(674\) | −1.06237e11 | −0.0198293 | ||||||||
\(675\) | 1.88102e12 | + | 1.69445e12i | 0.348760 | + | 0.314167i | ||||
\(676\) | 5.18713e12 | 0.955361 | ||||||||
\(677\) | − | 6.41491e12i | − | 1.17366i | −0.809711 | − | 0.586829i | \(-0.800376\pi\) | ||
0.809711 | − | 0.586829i | \(-0.199624\pi\) | |||||||
\(678\) | 2.24153e11i | 0.0407391i | ||||||||
\(679\) | −2.95796e12 | −0.534046 | ||||||||
\(680\) | −1.47339e11 | − | 3.31030e11i | −0.0264259 | − | 0.0593715i | ||||
\(681\) | 4.10256e12 | 0.730958 | ||||||||
\(682\) | 7.51494e10i | 0.0133014i | ||||||||
\(683\) | 2.15592e12i | 0.379088i | 0.981872 | + | 0.189544i | \(0.0607009\pi\) | ||||
−0.981872 | + | 0.189544i | \(0.939299\pi\) | |||||||
\(684\) | 3.59961e12 | 0.628786 | ||||||||
\(685\) | 7.43937e12 | − | 3.31122e12i | 1.29101 | − | 0.574619i | ||||
\(686\) | 3.52297e10 | 0.00607366 | ||||||||
\(687\) | − | 9.44262e11i | − | 0.161729i | ||||||
\(688\) | 6.07804e12i | 1.03423i | ||||||||
\(689\) | −1.02715e12 | −0.173640 | ||||||||
\(690\) | 1.83644e11 | − | 8.17387e10i | 0.0308429 | − | 0.0137280i | ||||
\(691\) | −4.58074e12 | −0.764336 | −0.382168 | − | 0.924093i | \(-0.624822\pi\) | ||||
−0.382168 | + | 0.924093i | \(0.624822\pi\) | |||||||
\(692\) | 9.68009e12i | 1.60473i | ||||||||
\(693\) | − | 4.83433e12i | − | 0.796226i | ||||||
\(694\) | −2.49657e11 | −0.0408533 | ||||||||
\(695\) | −3.35230e12 | − | 7.53168e12i | −0.545019 | − | 1.22450i | ||||
\(696\) | −1.24339e11 | −0.0200847 | ||||||||
\(697\) | − | 7.63624e12i | − | 1.22555i | ||||||
\(698\) | 3.15191e11i | 0.0502603i | ||||||||
\(699\) | −6.36704e12 | −1.00877 | ||||||||
\(700\) | −6.46469e12 | − | 5.82348e12i | −1.01767 | − | 0.916729i | ||||
\(701\) | −1.22474e12 | −0.191564 | −0.0957819 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957819 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(702\) | − | 2.34435e10i | − | 0.00364339i | ||||||
\(703\) | − | 5.39183e12i | − | 0.832601i | ||||||
\(704\) | 5.93058e12 | 0.909956 | ||||||||
\(705\) | 3.84421e12 | + | 8.63686e12i | 0.586079 | + | 1.31675i | ||||
\(706\) | 4.13424e11 | 0.0626289 | ||||||||
\(707\) | 1.16685e13i | 1.75642i | ||||||||
\(708\) | 6.41648e12i | 0.959725i | ||||||||
\(709\) | 5.65887e12 | 0.841049 | 0.420525 | − | 0.907281i | \(-0.361846\pi\) | ||||
0.420525 | + | 0.907281i | \(0.361846\pi\) | |||||||
\(710\) | −7.10276e10 | + | 3.16139e10i | −0.0104897 | + | 0.00466891i | ||||
\(711\) | −5.80891e11 | −0.0852475 | ||||||||
\(712\) | 4.78466e11i | 0.0697736i | ||||||||
\(713\) | 1.89996e12i | 0.275322i | ||||||||
\(714\) | 3.95741e11 | 0.0569861 | ||||||||
\(715\) | 1.21919e12 | − | 5.42653e11i | 0.174459 | − | 0.0776507i | ||||
\(716\) | −1.07250e13 | −1.52506 | ||||||||
\(717\) | 1.02623e13i | 1.45013i | ||||||||
\(718\) | − | 3.60836e11i | − | 0.0506698i | ||||||
\(719\) | 6.02904e12 | 0.841333 | 0.420667 | − | 0.907215i | \(-0.361796\pi\) | ||||
0.420667 | + | 0.907215i | \(0.361796\pi\) | |||||||
\(720\) | 1.84730e12 | + | 4.15037e12i | 0.256178 | + | 0.575560i | ||||
\(721\) | −3.34846e12 | −0.461462 | ||||||||
\(722\) | 2.55506e9i | 0.000349933i | ||||||||
\(723\) | − | 6.98820e12i | − | 0.951137i | ||||||
\(724\) | −3.66568e12 | −0.495827 | ||||||||
\(725\) | −1.04992e12 | + | 1.16552e12i | −0.141135 | + | 0.156675i | ||||
\(726\) | 5.63629e10 | 0.00752971 | ||||||||
\(727\) | − | 2.63469e12i | − | 0.349805i | −0.984586 | − | 0.174902i | \(-0.944039\pi\) | ||
0.984586 | − | 0.174902i | \(-0.0559609\pi\) | |||||||
\(728\) | 1.61254e11i | 0.0212774i | ||||||||
\(729\) | 1.37180e12 | 0.179894 | ||||||||
\(730\) | 7.07493e9 | + | 1.58954e10i | 0.000922081 | + | 0.00207166i | ||||
\(731\) | −6.99002e12 | −0.905421 | ||||||||
\(732\) | − | 1.16349e13i | − | 1.49783i | ||||||
\(733\) | 5.28609e12i | 0.676343i | 0.941085 | + | 0.338171i | \(0.109808\pi\) | ||||
−0.941085 | + | 0.338171i | \(0.890192\pi\) | |||||||
\(734\) | 2.14702e10 | 0.00273026 | ||||||||
\(735\) | 8.13955e12 | − | 3.62286e12i | 1.02874 | − | 0.457888i | ||||
\(736\) | −6.29831e11 | −0.0791178 | ||||||||
\(737\) | − | 1.18789e13i | − | 1.48310i | ||||||
\(738\) | − | 2.67300e11i | − | 0.0331700i | ||||||
\(739\) | −2.51810e12 | −0.310580 | −0.155290 | − | 0.987869i | \(-0.549631\pi\) | ||||
−0.155290 | + | 0.987869i | \(0.549631\pi\) | |||||||
\(740\) | 6.22550e12 | − | 2.77093e12i | 0.763188 | − | 0.339690i | ||||
\(741\) | −2.17203e12 | −0.264657 | ||||||||
\(742\) | 3.52440e11i | 0.0426843i | ||||||||
\(743\) | 7.02537e11i | 0.0845706i | 0.999106 | + | 0.0422853i | \(0.0134638\pi\) | ||||
−0.999106 | + | 0.0422853i | \(0.986536\pi\) | |||||||
\(744\) | 3.09379e11 | 0.0370179 | ||||||||
\(745\) | 3.06497e12 | + | 6.88612e12i | 0.364521 | + | 0.818976i | ||||
\(746\) | −6.12705e11 | −0.0724314 | ||||||||
\(747\) | 2.51335e12i | 0.295331i | ||||||||
\(748\) | 6.83956e12i | 0.798861i | ||||||||
\(749\) | 6.94755e12 | 0.806610 | ||||||||
\(750\) | −3.92697e11 | − | 1.27742e11i | −0.0453191 | − | 0.0147420i | ||||
\(751\) | 4.60108e12 | 0.527813 | 0.263907 | − | 0.964548i | \(-0.414989\pi\) | ||||
0.263907 | + | 0.964548i | \(0.414989\pi\) | |||||||
\(752\) | − | 9.85083e12i | − | 1.12329i | ||||||
\(753\) | − | 8.19042e12i | − | 0.928387i | ||||||
\(754\) | 1.45261e10 | 0.00163674 | ||||||||
\(755\) | −4.50200e11 | − | 1.01147e12i | −0.0504248 | − | 0.113290i | ||||
\(756\) | 5.77445e12 | 0.642928 | ||||||||
\(757\) | 3.05764e12i | 0.338419i | 0.985580 | + | 0.169210i | \(0.0541215\pi\) | ||||
−0.985580 | + | 0.169210i | \(0.945878\pi\) | |||||||
\(758\) | − | 2.33518e11i | − | 0.0256927i | ||||||
\(759\) | −7.59398e12 | −0.830580 | ||||||||
\(760\) | 6.23408e11 | − | 2.77475e11i | 0.0677815 | − | 0.0301691i | ||||
\(761\) | −9.86753e12 | −1.06654 | −0.533270 | − | 0.845945i | \(-0.679037\pi\) | ||||
−0.533270 | + | 0.845945i | \(0.679037\pi\) | |||||||
\(762\) | 3.46104e11i | 0.0371886i | ||||||||
\(763\) | 5.77872e12i | 0.617264i | ||||||||
\(764\) | 8.96293e12 | 0.951765 | ||||||||
\(765\) | −4.77312e12 | + | 2.12448e12i | −0.503878 | + | 0.224273i | ||||
\(766\) | 1.44435e11 | 0.0151580 | ||||||||
\(767\) | − | 1.50028e12i | − | 0.156528i | ||||||
\(768\) | − | 1.21478e13i | − | 1.26001i | ||||||
\(769\) | −1.65694e13 | −1.70859 | −0.854294 | − | 0.519790i | \(-0.826010\pi\) | ||||
−0.854294 | + | 0.519790i | \(0.826010\pi\) | |||||||
\(770\) | −1.86197e11 | − | 4.18332e11i | −0.0190882 | − | 0.0428857i | ||||
\(771\) | −2.32961e12 | −0.237432 | ||||||||
\(772\) | 1.60303e13i | 1.62429i | ||||||||
\(773\) | 1.10674e13i | 1.11490i | 0.830210 | + | 0.557451i | \(0.188221\pi\) | ||||
−0.830210 | + | 0.557451i | \(0.811779\pi\) | |||||||
\(774\) | −2.44680e11 | −0.0245055 | ||||||||
\(775\) | 2.61239e12 | − | 2.90004e12i | 0.260124 | − | 0.288766i | ||||
\(776\) | 2.93181e11 | 0.0290241 | ||||||||
\(777\) | 1.48953e13i | 1.46607i | ||||||||
\(778\) | 3.31150e10i | 0.00324054i | ||||||||
\(779\) | 1.43808e13 | 1.39915 | ||||||||
\(780\) | −1.11623e12 | − | 2.50786e12i | −0.107977 | − | 0.242593i | ||||
\(781\) | 2.93711e12 | 0.282482 | ||||||||
\(782\) | − | 2.40884e11i | − | 0.0230345i | ||||||
\(783\) | − | 1.04108e12i | − | 0.0989819i | ||||||
\(784\) | −9.28363e12 | −0.877598 | ||||||||
\(785\) | −1.51434e13 | + | 6.74025e12i | −1.42335 | + | 0.633523i | ||||
\(786\) | 5.80943e11 | 0.0542915 | ||||||||
\(787\) | 1.67201e12i | 0.155365i | 0.996978 | + | 0.0776825i | \(0.0247520\pi\) | ||||
−0.996978 | + | 0.0776825i | \(0.975248\pi\) | |||||||
\(788\) | − | 9.50846e12i | − | 0.878501i | ||||||
\(789\) | 8.60646e12 | 0.790638 | ||||||||
\(790\) | −5.02666e10 | + | 2.23734e10i | −0.00459154 | + | 0.00204366i | ||||
\(791\) | 1.29095e13 | 1.17250 | ||||||||
\(792\) | 4.79159e11i | 0.0432730i | ||||||||
\(793\) | 2.72042e12i | 0.244291i | ||||||||
\(794\) | −3.30303e11 | −0.0294931 | ||||||||
\(795\) | −4.88274e12 | − | 1.09701e13i | −0.433522 | − | 0.974003i | ||||
\(796\) | 6.47609e12 | 0.571748 | ||||||||
\(797\) | − | 6.97864e12i | − | 0.612644i | −0.951928 | − | 0.306322i | \(-0.900902\pi\) | ||
0.951928 | − | 0.306322i | \(-0.0990985\pi\) | |||||||
\(798\) | 7.45273e11i | 0.0650582i | ||||||||
\(799\) | 1.13289e13 | 0.983394 | ||||||||
\(800\) | 9.61355e11 | + | 8.66001e11i | 0.0829811 | + | 0.0747504i | ||||
\(801\) | 6.89899e12 | 0.592160 | ||||||||
\(802\) | 4.26165e11i | 0.0363742i | ||||||||
\(803\) | − | 6.57300e11i | − | 0.0557884i | ||||||
\(804\) | −2.44348e13 | −2.06232 | ||||||||
\(805\) | −4.70751e12 | − | 1.05764e13i | −0.395102 | − | 0.887684i | ||||
\(806\) | −3.61437e10 | −0.00301665 | ||||||||
\(807\) | − | 1.79052e13i | − | 1.48610i | ||||||
\(808\) | − | 1.15654e12i | − | 0.0954570i | ||||||
\(809\) | −5.27673e12 | −0.433108 | −0.216554 | − | 0.976271i | \(-0.569482\pi\) | ||||
−0.216554 | + | 0.976271i | \(0.569482\pi\) | |||||||
\(810\) | 5.14479e11 | − | 2.28991e11i | 0.0419938 | − | 0.0186912i | ||||
\(811\) | −1.43675e12 | −0.116624 | −0.0583118 | − | 0.998298i | \(-0.518572\pi\) | ||||
−0.0583118 | + | 0.998298i | \(0.518572\pi\) | |||||||
\(812\) | 3.57798e12i | 0.288826i | ||||||||
\(813\) | 8.60851e12i | 0.691068i | ||||||||
\(814\) | 3.58615e11 | 0.0286298 | ||||||||
\(815\) | −5.10592e12 | + | 2.27261e12i | −0.405383 | + | 0.180433i | ||||
\(816\) | 1.40493e13 | 1.10930 | ||||||||
\(817\) | − | 1.31639e13i | − | 1.03367i | ||||||
\(818\) | 7.97525e9i | 0.000622809i | ||||||||
\(819\) | 2.32511e12 | 0.180578 | ||||||||
\(820\) | 7.39049e12 | + | 1.66044e13i | 0.570836 | + | 1.28251i | ||||
\(821\) | 9.44899e12 | 0.725840 | 0.362920 | − | 0.931820i | \(-0.381780\pi\) | ||||
0.362920 | + | 0.931820i | \(0.381780\pi\) | |||||||
\(822\) | − | 8.81502e11i | − | 0.0673442i | ||||||
\(823\) | − | 1.20237e13i | − | 0.913562i | −0.889579 | − | 0.456781i | \(-0.849002\pi\) | ||
0.889579 | − | 0.456781i | \(-0.150998\pi\) | |||||||
\(824\) | 3.31886e11 | 0.0250794 | ||||||||
\(825\) | 1.15912e13 | + | 1.04415e13i | 0.871136 | + | 0.784731i | ||||
\(826\) | −5.14780e11 | −0.0384779 | ||||||||
\(827\) | 7.86848e12i | 0.584947i | 0.956274 | + | 0.292473i | \(0.0944782\pi\) | ||||
−0.956274 | + | 0.292473i | \(0.905522\pi\) | |||||||
\(828\) | 6.05294e12i | 0.447538i | ||||||||
\(829\) | −4.86184e12 | −0.357524 | −0.178762 | − | 0.983892i | \(-0.557209\pi\) | ||||
−0.178762 | + | 0.983892i | \(0.557209\pi\) | |||||||
\(830\) | 9.68029e10 | + | 2.17489e11i | 0.00708006 | + | 0.0159069i | ||||
\(831\) | 3.18798e12 | 0.231905 | ||||||||
\(832\) | 2.85236e12i | 0.206372i | ||||||||
\(833\) | − | 1.06766e13i | − | 0.768299i | ||||||
\(834\) | −8.92439e11 | −0.0638750 | ||||||||
\(835\) | −1.39320e13 | + | 6.20103e12i | −0.991798 | + | 0.441443i | ||||
\(836\) | −1.28805e13 | −0.912021 | ||||||||
\(837\) | 2.59040e12i | 0.182432i | ||||||||
\(838\) | − | 4.87232e10i | − | 0.00341301i | ||||||
\(839\) | −1.76025e13 | −1.22644 | −0.613218 | − | 0.789914i | \(-0.710125\pi\) | ||||
−0.613218 | + | 0.789914i | \(0.710125\pi\) | |||||||
\(840\) | −1.72221e12 | + | 7.66544e11i | −0.119352 | + | 0.0531227i | ||||
\(841\) | −1.38621e13 | −0.955534 | ||||||||
\(842\) | − | 3.70471e9i | − | 0.000254009i | ||||||
\(843\) | 2.72559e13i | 1.85881i | ||||||||
\(844\) | −3.17294e12 | −0.215239 | ||||||||
\(845\) | −5.76541e12 | − | 1.29533e13i | −0.389023 | − | 0.874025i | ||||
\(846\) | 3.96558e11 | 0.0266159 | ||||||||
\(847\) | − | 3.24606e12i | − | 0.216711i | ||||||
\(848\) | 1.25121e13i | 0.830899i | ||||||||
\(849\) | 3.34744e13 | 2.21120 | ||||||||
\(850\) | −3.31209e11 | + | 3.67679e11i | −0.0217629 | + | 0.0241592i | ||||
\(851\) | 9.06666e12 | 0.592604 | ||||||||
\(852\) | − | 6.04161e12i | − | 0.392802i | ||||||
\(853\) | 9.20458e11i | 0.0595296i | 0.999557 | + | 0.0297648i | \(0.00947584\pi\) | ||||
−0.999557 | + | 0.0297648i | \(0.990524\pi\) | |||||||
\(854\) | 9.33439e11 | 0.0600517 | ||||||||
\(855\) | −4.00090e12 | − | 8.98890e12i | −0.256042 | − | 0.575253i | ||||
\(856\) | −6.88614e11 | −0.0438373 | ||||||||
\(857\) | 2.35047e13i | 1.48847i | 0.667915 | + | 0.744237i | \(0.267187\pi\) | ||||
−0.667915 | + | 0.744237i | \(0.732813\pi\) | |||||||
\(858\) | − | 1.44463e11i | − | 0.00910050i | ||||||
\(859\) | 2.02385e13 | 1.26826 | 0.634132 | − | 0.773225i | \(-0.281357\pi\) | ||||
0.634132 | + | 0.773225i | \(0.281357\pi\) | |||||||
\(860\) | 1.51992e13 | − | 6.76508e12i | 0.947498 | − | 0.421725i | ||||
\(861\) | −3.97281e13 | −2.46367 | ||||||||
\(862\) | − | 8.39281e11i | − | 0.0517756i | ||||||
\(863\) | − | 3.07364e13i | − | 1.88627i | −0.332406 | − | 0.943136i | \(-0.607860\pi\) | ||
0.332406 | − | 0.943136i | \(-0.392140\pi\) | |||||||
\(864\) | −8.58710e11 | −0.0524245 | ||||||||
\(865\) | 2.41730e13 | − | 1.07593e13i | 1.46811 | − | 0.653446i | ||||
\(866\) | −1.61715e11 | −0.00977055 | ||||||||
\(867\) | − | 5.10107e12i | − | 0.306602i | ||||||
\(868\) | − | 8.90269e12i | − | 0.532332i | ||||||
\(869\) | 2.07861e12 | 0.123647 | ||||||||
\(870\) | 6.90522e10 | + | 1.55141e11i | 0.00408640 | + | 0.00918100i | ||||
\(871\) | 5.71325e12 | 0.336358 | ||||||||
\(872\) | − | 5.72763e11i | − | 0.0335468i | ||||||
\(873\) | − | 4.22737e12i | − | 0.246324i | ||||||
\(874\) | 4.53642e11 | 0.0262973 | ||||||||
\(875\) | −7.35693e12 | + | 2.26163e13i | −0.424288 | + | 1.30432i | ||||
\(876\) | −1.35206e12 | −0.0775760 | ||||||||
\(877\) | 6.65840e12i | 0.380077i | 0.981777 | + | 0.190039i | \(0.0608613\pi\) | ||||
−0.981777 | + | 0.190039i | \(0.939139\pi\) | |||||||
\(878\) | 1.16635e12i | 0.0662373i | ||||||||
\(879\) | −2.31120e13 | −1.30584 | ||||||||
\(880\) | −6.61022e12 | − | 1.48513e13i | −0.371573 | − | 0.834820i | ||||
\(881\) | 3.41842e12 | 0.191176 | 0.0955882 | − | 0.995421i | \(-0.469527\pi\) | ||||
0.0955882 | + | 0.995421i | \(0.469527\pi\) | |||||||
\(882\) | − | 3.73725e11i | − | 0.0207943i | ||||||
\(883\) | − | 1.92500e13i | − | 1.06563i | −0.846231 | − | 0.532815i | \(-0.821134\pi\) | ||
0.846231 | − | 0.532815i | \(-0.178866\pi\) | |||||||
\(884\) | −3.28955e12 | −0.181176 | ||||||||
\(885\) | 1.60232e13 | − | 7.13181e12i | 0.878018 | − | 0.390800i | ||||
\(886\) | −2.57960e11 | −0.0140637 | ||||||||
\(887\) | 1.48977e13i | 0.808095i | 0.914738 | + | 0.404048i | \(0.132397\pi\) | ||||
−0.914738 | + | 0.404048i | \(0.867603\pi\) | |||||||
\(888\) | − | 1.47636e12i | − | 0.0796774i | ||||||
\(889\) | 1.99329e13 | 1.07032 | ||||||||
\(890\) | 5.96995e11 | − | 2.65718e11i | 0.0318945 | − | 0.0141960i | ||||
\(891\) | −2.12745e13 | −1.13086 | ||||||||
\(892\) | − | 2.20291e13i | − | 1.16508i | ||||||
\(893\) | 2.13350e13i | 1.12269i | ||||||||
\(894\) | 8.15946e11 | 0.0427211 | ||||||||
\(895\) | 1.19206e13 | + | 2.67822e13i | 0.621004 | + | 1.39522i | ||||
\(896\) | 3.93404e12 | 0.203917 | ||||||||
\(897\) | − | 3.65239e12i | − | 0.188370i | ||||||
\(898\) | 1.26185e12i | 0.0647534i | ||||||||
\(899\) | −1.60507e12 | −0.0819551 | ||||||||
\(900\) | 8.32263e12 | − | 9.23902e12i | 0.422833 | − | 0.469391i | ||||
\(901\) | −1.43895e13 | −0.727416 | ||||||||
\(902\) | 9.56481e11i | 0.0481113i | ||||||||
\(903\) | 3.63661e13i | 1.82013i | ||||||||
\(904\) | −1.27954e12 | −0.0637228 | ||||||||
\(905\) | 4.07434e12 | + | 9.15389e12i | 0.201901 | + | 0.453615i | ||||
\(906\) | −1.19851e11 | −0.00590968 | ||||||||
\(907\) | − | 1.11529e13i | − | 0.547210i | −0.961842 | − | 0.273605i | \(-0.911784\pi\) | ||
0.961842 | − | 0.273605i | \(-0.0882162\pi\) | |||||||
\(908\) | 1.17012e13i | 0.571273i | ||||||||
\(909\) | −1.66760e13 | −0.810132 | ||||||||
\(910\) | 2.01200e11 | − | 8.95530e10i | 0.00972618 | − | 0.00432906i | ||||
\(911\) | −2.25248e12 | −0.108350 | −0.0541750 | − | 0.998531i | \(-0.517253\pi\) | ||||
−0.0541750 | + | 0.998531i | \(0.517253\pi\) | |||||||
\(912\) | 2.64581e13i | 1.26643i | ||||||||
\(913\) | − | 8.99353e12i | − | 0.428363i | ||||||
\(914\) | −9.95663e11 | −0.0471905 | ||||||||
\(915\) | −2.90545e13 | + | 1.29320e13i | −1.37031 | + | 0.609915i | ||||
\(916\) | 2.69319e12 | 0.126397 | ||||||||
\(917\) | − | 3.34578e13i | − | 1.56255i | ||||||
\(918\) | − | 3.28421e11i | − | 0.0152630i | ||||||
\(919\) | −1.40633e13 | −0.650380 | −0.325190 | − | 0.945649i | \(-0.605428\pi\) | ||||
−0.325190 | + | 0.945649i | \(0.605428\pi\) | |||||||
\(920\) | 4.66590e11 | + | 1.04830e12i | 0.0214729 | + | 0.0482435i | ||||
\(921\) | 1.57452e13 | 0.721075 | ||||||||
\(922\) | − | 1.30318e12i | − | 0.0593901i | ||||||
\(923\) | 1.41263e12i | 0.0640649i | ||||||||
\(924\) | 3.55833e13 | 1.60591 | ||||||||
\(925\) | −1.38391e13 | − | 1.24664e13i | −0.621540 | − | 0.559891i | ||||
\(926\) | −3.84644e11 | −0.0171913 | ||||||||
\(927\) | − | 4.78545e12i | − | 0.212845i | ||||||
\(928\) | − | 5.32077e11i | − | 0.0235509i | ||||||
\(929\) | −1.04912e13 | −0.462118 | −0.231059 | − | 0.972940i | \(-0.574219\pi\) | ||||
−0.231059 | + | 0.972940i | \(0.574219\pi\) | |||||||
\(930\) | −1.71815e11 | − | 3.86020e11i | −0.00753161 | − | 0.0169214i | ||||
\(931\) | 2.01066e13 | 0.877130 | ||||||||
\(932\) | − | 1.81599e13i | − | 0.788389i | ||||||
\(933\) | − | 4.95131e13i | − | 2.13920i | ||||||
\(934\) | −5.88518e11 | −0.0253045 | ||||||||
\(935\) | 1.70797e13 | − | 7.60206e12i | 0.730849 | − | 0.325296i | ||||
\(936\) | −2.30456e11 | −0.00981400 | ||||||||
\(937\) | 3.77841e13i | 1.60133i | 0.599111 | + | 0.800666i | \(0.295521\pi\) | ||||
−0.599111 | + | 0.800666i | \(0.704479\pi\) | |||||||
\(938\) | − | 1.96035e12i | − | 0.0826837i | ||||||
\(939\) | 3.30036e13 | 1.38537 | ||||||||
\(940\) | −2.46338e13 | + | 1.09643e13i | −1.02909 | + | 0.458043i | ||||
\(941\) | 1.11142e13 | 0.462088 | 0.231044 | − | 0.972943i | \(-0.425786\pi\) | ||||
0.231044 | + | 0.972943i | \(0.425786\pi\) | |||||||
\(942\) | 1.79437e12i | 0.0742476i | ||||||||
\(943\) | 2.41822e13i | 0.995847i | ||||||||
\(944\) | −1.82753e13 | −0.749017 | ||||||||
\(945\) | −6.41820e12 | − | 1.44199e13i | −0.261800 | − | 0.588192i | ||||
\(946\) | 8.75539e11 | 0.0355439 | ||||||||
\(947\) | 4.96563e12i | 0.200631i | 0.994956 | + | 0.100316i | \(0.0319853\pi\) | ||||
−0.994956 | + | 0.100316i | \(0.968015\pi\) | |||||||
\(948\) | − | 4.27568e12i | − | 0.171936i | ||||||
\(949\) | 3.16134e11 | 0.0126524 | ||||||||
\(950\) | −6.92425e11 | − | 6.23745e11i | −0.0275814 | − | 0.0248457i | ||||
\(951\) | 6.25385e13 | 2.47933 | ||||||||
\(952\) | 2.25901e12i | 0.0891357i | ||||||||
\(953\) | − | 3.02750e13i | − | 1.18896i | −0.804111 | − | 0.594479i | \(-0.797358\pi\) | ||
0.804111 | − | 0.594479i | \(-0.202642\pi\) | |||||||
\(954\) | −5.03690e11 | −0.0196877 | ||||||||
\(955\) | −9.96214e12 | − | 2.23821e13i | −0.387559 | − | 0.870736i | ||||
\(956\) | −2.92698e13 | −1.13334 | ||||||||
\(957\) | − | 6.41533e12i | − | 0.247238i | ||||||
\(958\) | 2.05476e11i | 0.00788162i | ||||||||
\(959\) | −5.07676e13 | −1.93822 | ||||||||
\(960\) | −3.04636e13 | + | 1.35592e13i | −1.15761 | + | 0.515243i | ||||
\(961\) | −2.24459e13 | −0.848949 | ||||||||
\(962\) | 1.72479e11i | 0.00649304i | ||||||||
\(963\) | 9.92910e12i | 0.372042i | ||||||||
\(964\) | 1.99315e13 | 0.743351 | ||||||||
\(965\) | 4.00307e13 | − | 1.78174e13i | 1.48601 | − | 0.661412i | ||||
\(966\) | −1.25322e12 | −0.0463052 | ||||||||
\(967\) | 2.48487e13i | 0.913869i | 0.889500 | + | 0.456934i | \(0.151053\pi\) | ||||
−0.889500 | + | 0.456934i | \(0.848947\pi\) | |||||||
\(968\) | 3.21737e11i | 0.0117777i | ||||||||
\(969\) | −3.04281e13 | −1.10871 | ||||||||
\(970\) | −1.62820e11 | − | 3.65810e11i | −0.00590519 | − | 0.0132673i | ||||
\(971\) | 4.43278e13 | 1.60026 | 0.800128 | − | 0.599829i | \(-0.204765\pi\) | ||||
0.800128 | + | 0.599829i | \(0.204765\pi\) | |||||||
\(972\) | 3.07168e13i | 1.10377i | ||||||||
\(973\) | 5.13975e13i | 1.83837i | ||||||||
\(974\) | 1.32466e12 | 0.0471618 | ||||||||
\(975\) | −5.02193e12 | + | 5.57489e12i | −0.177971 | + | 0.197568i | ||||
\(976\) | 3.31383e13 | 1.16898 | ||||||||
\(977\) | − | 9.73746e11i | − | 0.0341917i | −0.999854 | − | 0.0170958i | \(-0.994558\pi\) | ||
0.999854 | − | 0.0170958i | \(-0.00544204\pi\) | |||||||
\(978\) | 6.05008e11i | 0.0211464i | ||||||||
\(979\) | −2.46867e13 | −0.858897 | ||||||||
\(980\) | 1.03330e13 | + | 2.32154e13i | 0.357857 | + | 0.804004i | ||||
\(981\) | −8.25866e12 | −0.284708 | ||||||||
\(982\) | − | 5.50985e11i | − | 0.0189077i | ||||||
\(983\) | 2.85792e13i | 0.976247i | 0.872775 | + | 0.488123i | \(0.162318\pi\) | ||||
−0.872775 | + | 0.488123i | \(0.837682\pi\) | |||||||
\(984\) | 3.93769e12 | 0.133895 | ||||||||
\(985\) | −2.37444e13 | + | 1.05685e13i | −0.803709 | + | 0.357726i | ||||
\(986\) | 2.03497e11 | 0.00685666 | ||||||||
\(987\) | − | 5.89394e13i | − | 1.97687i | ||||||
\(988\) | − | 6.19499e12i | − | 0.206840i | ||||||
\(989\) | 2.21358e13 | 0.735718 | ||||||||
\(990\) | 5.97859e11 | − | 2.66103e11i | 0.0197807 | − | 0.00880424i | ||||
\(991\) | −3.49036e13 | −1.14958 | −0.574789 | − | 0.818302i | \(-0.694916\pi\) | ||||
−0.574789 | + | 0.818302i | \(0.694916\pi\) | |||||||
\(992\) | 1.32391e12i | 0.0434065i | ||||||||
\(993\) | − | 5.17610e13i | − | 1.68940i | ||||||
\(994\) | 4.84705e11 | 0.0157485 | ||||||||
\(995\) | −7.19807e12 | − | 1.61720e13i | −0.232816 | − | 0.523071i | ||||
\(996\) | −1.84996e13 | −0.595656 | ||||||||
\(997\) | − | 8.78834e12i | − | 0.281695i | −0.990031 | − | 0.140847i | \(-0.955017\pi\) | ||
0.990031 | − | 0.140847i | \(-0.0449827\pi\) | |||||||
\(998\) | − | 6.34194e11i | − | 0.0202365i | ||||||
\(999\) | 1.23615e13 | 0.392668 |
(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 | 5.10.b.a.4.2 | ✓ | 4 | |
3.2 | odd | 2 | 45.10.b.b.19.3 | 4 | |||
4.3 | odd | 2 | 80.10.c.c.49.4 | 4 | |||
5.2 | odd | 4 | 25.10.a.e.1.3 | 4 | |||
5.3 | odd | 4 | 25.10.a.e.1.2 | 4 | |||
5.4 | even | 2 | inner | 5.10.b.a.4.3 | yes | 4 | |
15.2 | even | 4 | 225.10.a.s.1.2 | 4 | |||
15.8 | even | 4 | 225.10.a.s.1.3 | 4 | |||
15.14 | odd | 2 | 45.10.b.b.19.2 | 4 | |||
20.3 | even | 4 | 400.10.a.ba.1.1 | 4 | |||
20.7 | even | 4 | 400.10.a.ba.1.4 | 4 | |||
20.19 | odd | 2 | 80.10.c.c.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.10.b.a.4.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
5.10.b.a.4.3 | yes | 4 | 5.4 | even | 2 | inner | |
25.10.a.e.1.2 | 4 | 5.3 | odd | 4 | |||
25.10.a.e.1.3 | 4 | 5.2 | odd | 4 | |||
45.10.b.b.19.2 | 4 | 15.14 | odd | 2 | |||
45.10.b.b.19.3 | 4 | 3.2 | odd | 2 | |||
80.10.c.c.49.1 | 4 | 20.19 | odd | 2 | |||
80.10.c.c.49.4 | 4 | 4.3 | odd | 2 | |||
225.10.a.s.1.2 | 4 | 15.2 | even | 4 | |||
225.10.a.s.1.3 | 4 | 15.8 | even | 4 | |||
400.10.a.ba.1.1 | 4 | 20.3 | even | 4 | |||
400.10.a.ba.1.4 | 4 | 20.7 | even | 4 |