Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,32,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 32, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 32);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 32 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
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: | yes |
Analytic conductor: | \(60.8771328190\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 17573188320 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(132564.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32768.0 | −0.707107 | ||||||||
\(3\) | −2.68139e7 | −1.07890 | −0.539449 | − | 0.842018i | \(-0.681367\pi\) | ||||
−0.539449 | + | 0.842018i | \(0.681367\pi\) | |||||||
\(4\) | 1.07374e9 | 0.500000 | ||||||||
\(5\) | 3.05176e10 | 0.447214 | ||||||||
\(6\) | 8.78637e11 | 0.762896 | ||||||||
\(7\) | 7.28747e11 | 0.0580172 | 0.0290086 | − | 0.999579i | \(-0.490765\pi\) | ||||
0.0290086 | + | 0.999579i | \(0.490765\pi\) | |||||||
\(8\) | −3.51844e13 | −0.353553 | ||||||||
\(9\) | 1.01311e14 | 0.164020 | ||||||||
\(10\) | −1.00000e15 | −0.316228 | ||||||||
\(11\) | −3.37576e15 | −0.243661 | −0.121830 | − | 0.992551i | \(-0.538876\pi\) | ||||
−0.121830 | + | 0.992551i | \(0.538876\pi\) | |||||||
\(12\) | −2.87912e16 | −0.539449 | ||||||||
\(13\) | −1.37589e17 | −0.745527 | −0.372763 | − | 0.927926i | \(-0.621590\pi\) | ||||
−0.372763 | + | 0.927926i | \(0.621590\pi\) | |||||||
\(14\) | −2.38796e16 | −0.0410244 | ||||||||
\(15\) | −8.18295e17 | −0.482498 | ||||||||
\(16\) | 1.15292e18 | 0.250000 | ||||||||
\(17\) | 2.39641e18 | 0.203050 | 0.101525 | − | 0.994833i | \(-0.467628\pi\) | ||||
0.101525 | + | 0.994833i | \(0.467628\pi\) | |||||||
\(18\) | −3.31975e18 | −0.115980 | ||||||||
\(19\) | 9.48888e18 | 0.143395 | 0.0716975 | − | 0.997426i | \(-0.477158\pi\) | ||||
0.0716975 | + | 0.997426i | \(0.477158\pi\) | |||||||
\(20\) | 3.27680e19 | 0.223607 | ||||||||
\(21\) | −1.95405e19 | −0.0625947 | ||||||||
\(22\) | 1.10617e20 | 0.172294 | ||||||||
\(23\) | 1.89426e21 | 1.48135 | 0.740674 | − | 0.671865i | \(-0.234506\pi\) | ||||
0.740674 | + | 0.671865i | \(0.234506\pi\) | |||||||
\(24\) | 9.43430e20 | 0.381448 | ||||||||
\(25\) | 9.31323e20 | 0.200000 | ||||||||
\(26\) | 4.50853e21 | 0.527167 | ||||||||
\(27\) | 1.38457e22 | 0.901937 | ||||||||
\(28\) | 7.82486e20 | 0.0290086 | ||||||||
\(29\) | 5.03519e21 | 0.108354 | 0.0541772 | − | 0.998531i | \(-0.482746\pi\) | ||||
0.0541772 | + | 0.998531i | \(0.482746\pi\) | |||||||
\(30\) | 2.68139e22 | 0.341177 | ||||||||
\(31\) | −8.54182e22 | −0.653799 | −0.326899 | − | 0.945059i | \(-0.606004\pi\) | ||||
−0.326899 | + | 0.945059i | \(0.606004\pi\) | |||||||
\(32\) | −3.77789e22 | −0.176777 | ||||||||
\(33\) | 9.05173e22 | 0.262885 | ||||||||
\(34\) | −7.85254e22 | −0.143578 | ||||||||
\(35\) | 2.22396e22 | 0.0259461 | ||||||||
\(36\) | 1.08782e23 | 0.0820100 | ||||||||
\(37\) | 1.26772e24 | 0.625022 | 0.312511 | − | 0.949914i | \(-0.398830\pi\) | ||||
0.312511 | + | 0.949914i | \(0.398830\pi\) | |||||||
\(38\) | −3.10932e23 | −0.101396 | ||||||||
\(39\) | 3.68931e24 | 0.804347 | ||||||||
\(40\) | −1.07374e24 | −0.158114 | ||||||||
\(41\) | 8.53929e24 | 0.857574 | 0.428787 | − | 0.903406i | \(-0.358941\pi\) | ||||
0.428787 | + | 0.903406i | \(0.358941\pi\) | |||||||
\(42\) | 6.40304e23 | 0.0442611 | ||||||||
\(43\) | 2.40945e25 | 1.15653 | 0.578264 | − | 0.815850i | \(-0.303730\pi\) | ||||
0.578264 | + | 0.815850i | \(0.303730\pi\) | |||||||
\(44\) | −3.62470e24 | −0.121830 | ||||||||
\(45\) | 3.09176e24 | 0.0733520 | ||||||||
\(46\) | −6.20710e25 | −1.04747 | ||||||||
\(47\) | −3.96314e25 | −0.479207 | −0.239603 | − | 0.970871i | \(-0.577017\pi\) | ||||
−0.239603 | + | 0.970871i | \(0.577017\pi\) | |||||||
\(48\) | −3.09143e25 | −0.269724 | ||||||||
\(49\) | −1.57244e26 | −0.996634 | ||||||||
\(50\) | −3.05176e25 | −0.141421 | ||||||||
\(51\) | −6.42569e25 | −0.219070 | ||||||||
\(52\) | −1.47736e26 | −0.372763 | ||||||||
\(53\) | 7.23147e25 | 0.135816 | 0.0679080 | − | 0.997692i | \(-0.478368\pi\) | ||||
0.0679080 | + | 0.997692i | \(0.478368\pi\) | |||||||
\(54\) | −4.53695e26 | −0.637766 | ||||||||
\(55\) | −1.03020e26 | −0.108968 | ||||||||
\(56\) | −2.56405e25 | −0.0205122 | ||||||||
\(57\) | −2.54434e26 | −0.154709 | ||||||||
\(58\) | −1.64993e26 | −0.0766182 | ||||||||
\(59\) | −1.71371e27 | −0.610563 | −0.305281 | − | 0.952262i | \(-0.598751\pi\) | ||||
−0.305281 | + | 0.952262i | \(0.598751\pi\) | |||||||
\(60\) | −8.78637e26 | −0.241249 | ||||||||
\(61\) | 2.02558e27 | 0.430464 | 0.215232 | − | 0.976563i | \(-0.430949\pi\) | ||||
0.215232 | + | 0.976563i | \(0.430949\pi\) | |||||||
\(62\) | 2.79898e27 | 0.462305 | ||||||||
\(63\) | 7.38299e25 | 0.00951599 | ||||||||
\(64\) | 1.23794e27 | 0.125000 | ||||||||
\(65\) | −4.19890e27 | −0.333410 | ||||||||
\(66\) | −2.96607e27 | −0.185888 | ||||||||
\(67\) | −2.22923e28 | −1.10661 | −0.553307 | − | 0.832978i | \(-0.686634\pi\) | ||||
−0.553307 | + | 0.832978i | \(0.686634\pi\) | |||||||
\(68\) | 2.57312e27 | 0.101525 | ||||||||
\(69\) | −5.07923e28 | −1.59822 | ||||||||
\(70\) | −7.28747e26 | −0.0183467 | ||||||||
\(71\) | −8.76737e28 | −1.77160 | −0.885799 | − | 0.464069i | \(-0.846389\pi\) | ||||
−0.885799 | + | 0.464069i | \(0.846389\pi\) | |||||||
\(72\) | −3.56456e27 | −0.0579898 | ||||||||
\(73\) | −6.23103e28 | −0.818569 | −0.409285 | − | 0.912407i | \(-0.634222\pi\) | ||||
−0.409285 | + | 0.912407i | \(0.634222\pi\) | |||||||
\(74\) | −4.15405e28 | −0.441958 | ||||||||
\(75\) | −2.49724e28 | −0.215780 | ||||||||
\(76\) | 1.01886e28 | 0.0716975 | ||||||||
\(77\) | −2.46008e27 | −0.0141365 | ||||||||
\(78\) | −1.20891e29 | −0.568759 | ||||||||
\(79\) | 1.07042e29 | 0.413367 | 0.206683 | − | 0.978408i | \(-0.433733\pi\) | ||||
0.206683 | + | 0.978408i | \(0.433733\pi\) | |||||||
\(80\) | 3.51844e28 | 0.111803 | ||||||||
\(81\) | −4.33834e29 | −1.13712 | ||||||||
\(82\) | −2.79815e29 | −0.606397 | ||||||||
\(83\) | −5.93551e28 | −0.106598 | −0.0532988 | − | 0.998579i | \(-0.516974\pi\) | ||||
−0.0532988 | + | 0.998579i | \(0.516974\pi\) | |||||||
\(84\) | −2.09815e28 | −0.0312973 | ||||||||
\(85\) | 7.31325e28 | 0.0908065 | ||||||||
\(86\) | −7.89527e29 | −0.817789 | ||||||||
\(87\) | −1.35013e29 | −0.116903 | ||||||||
\(88\) | 1.18774e29 | 0.0861471 | ||||||||
\(89\) | 1.10405e30 | 0.672118 | 0.336059 | − | 0.941841i | \(-0.390906\pi\) | ||||
0.336059 | + | 0.941841i | \(0.390906\pi\) | |||||||
\(90\) | −1.01311e29 | −0.0518677 | ||||||||
\(91\) | −1.00268e29 | −0.0432534 | ||||||||
\(92\) | 2.03394e30 | 0.740674 | ||||||||
\(93\) | 2.29039e30 | 0.705382 | ||||||||
\(94\) | 1.29864e30 | 0.338850 | ||||||||
\(95\) | 2.89578e29 | 0.0641282 | ||||||||
\(96\) | 1.01300e30 | 0.190724 | ||||||||
\(97\) | 5.31660e30 | 0.852456 | 0.426228 | − | 0.904616i | \(-0.359842\pi\) | ||||
0.426228 | + | 0.904616i | \(0.359842\pi\) | |||||||
\(98\) | 5.15258e30 | 0.704727 | ||||||||
\(99\) | −3.42001e29 | −0.0399652 | ||||||||
\(100\) | 1.00000e30 | 0.100000 | ||||||||
\(101\) | −6.37914e30 | −0.546740 | −0.273370 | − | 0.961909i | \(-0.588138\pi\) | ||||
−0.273370 | + | 0.961909i | \(0.588138\pi\) | |||||||
\(102\) | 2.10557e30 | 0.154906 | ||||||||
\(103\) | 1.27411e31 | 0.805803 | 0.402901 | − | 0.915243i | \(-0.368002\pi\) | ||||
0.402901 | + | 0.915243i | \(0.368002\pi\) | |||||||
\(104\) | 4.84100e30 | 0.263583 | ||||||||
\(105\) | −5.96330e29 | −0.0279932 | ||||||||
\(106\) | −2.36961e30 | −0.0960364 | ||||||||
\(107\) | −1.47464e31 | −0.516698 | −0.258349 | − | 0.966052i | \(-0.583178\pi\) | ||||
−0.258349 | + | 0.966052i | \(0.583178\pi\) | |||||||
\(108\) | 1.48667e31 | 0.450968 | ||||||||
\(109\) | −2.43352e31 | −0.639917 | −0.319958 | − | 0.947432i | \(-0.603669\pi\) | ||||
−0.319958 | + | 0.947432i | \(0.603669\pi\) | |||||||
\(110\) | 3.37576e30 | 0.0770523 | ||||||||
\(111\) | −3.39924e31 | −0.674335 | ||||||||
\(112\) | 8.40188e29 | 0.0145043 | ||||||||
\(113\) | 1.29196e32 | 1.94327 | 0.971633 | − | 0.236495i | \(-0.0759987\pi\) | ||||
0.971633 | + | 0.236495i | \(0.0759987\pi\) | |||||||
\(114\) | 8.33729e30 | 0.109396 | ||||||||
\(115\) | 5.78081e31 | 0.662479 | ||||||||
\(116\) | 5.40649e30 | 0.0541772 | ||||||||
\(117\) | −1.39393e31 | −0.122281 | ||||||||
\(118\) | 5.61548e31 | 0.431733 | ||||||||
\(119\) | 1.74637e30 | 0.0117804 | ||||||||
\(120\) | 2.87912e31 | 0.170589 | ||||||||
\(121\) | −1.80548e32 | −0.940629 | ||||||||
\(122\) | −6.63742e31 | −0.304384 | ||||||||
\(123\) | −2.28971e32 | −0.925235 | ||||||||
\(124\) | −9.17171e31 | −0.326899 | ||||||||
\(125\) | 2.84217e31 | 0.0894427 | ||||||||
\(126\) | −2.41926e30 | −0.00672882 | ||||||||
\(127\) | −6.29352e32 | −1.54859 | −0.774294 | − | 0.632826i | \(-0.781895\pi\) | ||||
−0.774294 | + | 0.632826i | \(0.781895\pi\) | |||||||
\(128\) | −4.05648e31 | −0.0883883 | ||||||||
\(129\) | −6.46066e32 | −1.24778 | ||||||||
\(130\) | 1.37589e32 | 0.235756 | ||||||||
\(131\) | −1.13960e33 | −1.73400 | −0.866999 | − | 0.498310i | \(-0.833954\pi\) | ||||
−0.866999 | + | 0.498310i | \(0.833954\pi\) | |||||||
\(132\) | 9.71922e31 | 0.131442 | ||||||||
\(133\) | 6.91499e30 | 0.00831939 | ||||||||
\(134\) | 7.30475e32 | 0.782494 | ||||||||
\(135\) | 4.22537e32 | 0.403358 | ||||||||
\(136\) | −8.43160e31 | −0.0717889 | ||||||||
\(137\) | −1.23195e33 | −0.936318 | −0.468159 | − | 0.883644i | \(-0.655083\pi\) | ||||
−0.468159 | + | 0.883644i | \(0.655083\pi\) | |||||||
\(138\) | 1.66436e33 | 1.13011 | ||||||||
\(139\) | −1.10200e33 | −0.669042 | −0.334521 | − | 0.942388i | \(-0.608575\pi\) | ||||
−0.334521 | + | 0.942388i | \(0.608575\pi\) | |||||||
\(140\) | 2.38796e31 | 0.0129730 | ||||||||
\(141\) | 1.06267e33 | 0.517015 | ||||||||
\(142\) | 2.87289e33 | 1.25271 | ||||||||
\(143\) | 4.64470e32 | 0.181656 | ||||||||
\(144\) | 1.16803e32 | 0.0410050 | ||||||||
\(145\) | 1.53662e32 | 0.0484576 | ||||||||
\(146\) | 2.04178e33 | 0.578816 | ||||||||
\(147\) | 4.21633e33 | 1.07527 | ||||||||
\(148\) | 1.36120e33 | 0.312511 | ||||||||
\(149\) | −1.57024e33 | −0.324772 | −0.162386 | − | 0.986727i | \(-0.551919\pi\) | ||||
−0.162386 | + | 0.986727i | \(0.551919\pi\) | |||||||
\(150\) | 8.18295e32 | 0.152579 | ||||||||
\(151\) | −1.72612e33 | −0.290354 | −0.145177 | − | 0.989406i | \(-0.546375\pi\) | ||||
−0.145177 | + | 0.989406i | \(0.546375\pi\) | |||||||
\(152\) | −3.33860e32 | −0.0506978 | ||||||||
\(153\) | 2.42782e32 | 0.0333042 | ||||||||
\(154\) | 8.06118e31 | 0.00999603 | ||||||||
\(155\) | −2.60676e33 | −0.292388 | ||||||||
\(156\) | 3.96136e33 | 0.402173 | ||||||||
\(157\) | 1.22917e34 | 1.13023 | 0.565114 | − | 0.825013i | \(-0.308832\pi\) | ||||
0.565114 | + | 0.825013i | \(0.308832\pi\) | |||||||
\(158\) | −3.50756e33 | −0.292294 | ||||||||
\(159\) | −1.93904e33 | −0.146531 | ||||||||
\(160\) | −1.15292e33 | −0.0790569 | ||||||||
\(161\) | 1.38043e33 | 0.0859437 | ||||||||
\(162\) | 1.42159e34 | 0.804063 | ||||||||
\(163\) | −2.97139e34 | −1.52775 | −0.763874 | − | 0.645366i | \(-0.776705\pi\) | ||||
−0.763874 | + | 0.645366i | \(0.776705\pi\) | |||||||
\(164\) | 9.16899e33 | 0.428787 | ||||||||
\(165\) | 2.76237e33 | 0.117566 | ||||||||
\(166\) | 1.94495e33 | 0.0753759 | ||||||||
\(167\) | −1.23629e32 | −0.00436531 | −0.00218265 | − | 0.999998i | \(-0.500695\pi\) | ||||
−0.00218265 | + | 0.999998i | \(0.500695\pi\) | |||||||
\(168\) | 6.87521e32 | 0.0221306 | ||||||||
\(169\) | −1.51291e34 | −0.444190 | ||||||||
\(170\) | −2.39641e33 | −0.0642099 | ||||||||
\(171\) | 9.61326e32 | 0.0235197 | ||||||||
\(172\) | 2.58712e34 | 0.578264 | ||||||||
\(173\) | −8.47230e34 | −1.73096 | −0.865479 | − | 0.500945i | \(-0.832986\pi\) | ||||
−0.865479 | + | 0.500945i | \(0.832986\pi\) | |||||||
\(174\) | 4.42411e33 | 0.0826632 | ||||||||
\(175\) | 6.78698e32 | 0.0116034 | ||||||||
\(176\) | −3.89199e33 | −0.0609152 | ||||||||
\(177\) | 4.59511e34 | 0.658735 | ||||||||
\(178\) | −3.61776e34 | −0.475259 | ||||||||
\(179\) | −1.31638e35 | −1.58547 | −0.792736 | − | 0.609565i | \(-0.791344\pi\) | ||||
−0.792736 | + | 0.609565i | \(0.791344\pi\) | |||||||
\(180\) | 3.31975e33 | 0.0366760 | ||||||||
\(181\) | 7.25006e34 | 0.735062 | 0.367531 | − | 0.930011i | \(-0.380203\pi\) | ||||
0.367531 | + | 0.930011i | \(0.380203\pi\) | |||||||
\(182\) | 3.28558e33 | 0.0305848 | ||||||||
\(183\) | −5.43136e34 | −0.464426 | ||||||||
\(184\) | −6.66482e34 | −0.523736 | ||||||||
\(185\) | 3.86877e34 | 0.279519 | ||||||||
\(186\) | −7.50516e34 | −0.498780 | ||||||||
\(187\) | −8.08970e33 | −0.0494752 | ||||||||
\(188\) | −4.25539e34 | −0.239603 | ||||||||
\(189\) | 1.00900e34 | 0.0523279 | ||||||||
\(190\) | −9.48888e33 | −0.0453455 | ||||||||
\(191\) | 6.07467e34 | 0.267612 | 0.133806 | − | 0.991008i | \(-0.457280\pi\) | ||||
0.133806 | + | 0.991008i | \(0.457280\pi\) | |||||||
\(192\) | −3.31940e34 | −0.134862 | ||||||||
\(193\) | 3.30662e35 | 1.23950 | 0.619750 | − | 0.784799i | \(-0.287234\pi\) | ||||
0.619750 | + | 0.784799i | \(0.287234\pi\) | |||||||
\(194\) | −1.74214e35 | −0.602777 | ||||||||
\(195\) | 1.12589e35 | 0.359715 | ||||||||
\(196\) | −1.68840e35 | −0.498317 | ||||||||
\(197\) | 3.74089e35 | 1.02035 | 0.510174 | − | 0.860071i | \(-0.329581\pi\) | ||||
0.510174 | + | 0.860071i | \(0.329581\pi\) | |||||||
\(198\) | 1.12067e34 | 0.0282597 | ||||||||
\(199\) | −1.54190e35 | −0.359611 | −0.179805 | − | 0.983702i | \(-0.557547\pi\) | ||||
−0.179805 | + | 0.983702i | \(0.557547\pi\) | |||||||
\(200\) | −3.27680e34 | −0.0707107 | ||||||||
\(201\) | 5.97744e35 | 1.19392 | ||||||||
\(202\) | 2.09032e35 | 0.386604 | ||||||||
\(203\) | 3.66938e33 | 0.00628643 | ||||||||
\(204\) | −6.89954e34 | −0.109535 | ||||||||
\(205\) | 2.60598e35 | 0.383519 | ||||||||
\(206\) | −4.17499e35 | −0.569789 | ||||||||
\(207\) | 1.91909e35 | 0.242971 | ||||||||
\(208\) | −1.58630e35 | −0.186382 | ||||||||
\(209\) | −3.20322e34 | −0.0349397 | ||||||||
\(210\) | 1.95405e34 | 0.0197942 | ||||||||
\(211\) | −6.65945e35 | −0.626701 | −0.313350 | − | 0.949638i | \(-0.601451\pi\) | ||||
−0.313350 | + | 0.949638i | \(0.601451\pi\) | |||||||
\(212\) | 7.76473e34 | 0.0679080 | ||||||||
\(213\) | 2.35087e36 | 1.91137 | ||||||||
\(214\) | 4.83209e35 | 0.365361 | ||||||||
\(215\) | 7.35305e35 | 0.517215 | ||||||||
\(216\) | −4.87152e35 | −0.318883 | ||||||||
\(217\) | −6.22482e34 | −0.0379316 | ||||||||
\(218\) | 7.97415e35 | 0.452490 | ||||||||
\(219\) | 1.67078e36 | 0.883153 | ||||||||
\(220\) | −1.10617e35 | −0.0544842 | ||||||||
\(221\) | −3.29720e35 | −0.151379 | ||||||||
\(222\) | 1.11386e36 | 0.476827 | ||||||||
\(223\) | −1.97136e36 | −0.787117 | −0.393559 | − | 0.919299i | \(-0.628756\pi\) | ||||
−0.393559 | + | 0.919299i | \(0.628756\pi\) | |||||||
\(224\) | −2.75313e34 | −0.0102561 | ||||||||
\(225\) | 9.43530e34 | 0.0328040 | ||||||||
\(226\) | −4.23348e36 | −1.37410 | ||||||||
\(227\) | −5.24999e36 | −1.59132 | −0.795661 | − | 0.605743i | \(-0.792876\pi\) | ||||
−0.795661 | + | 0.605743i | \(0.792876\pi\) | |||||||
\(228\) | −2.73196e35 | −0.0773543 | ||||||||
\(229\) | −5.83672e36 | −1.54425 | −0.772127 | − | 0.635468i | \(-0.780807\pi\) | ||||
−0.772127 | + | 0.635468i | \(0.780807\pi\) | |||||||
\(230\) | −1.89426e36 | −0.468443 | ||||||||
\(231\) | 6.59642e34 | 0.0152519 | ||||||||
\(232\) | −1.77160e35 | −0.0383091 | ||||||||
\(233\) | −2.74902e36 | −0.556110 | −0.278055 | − | 0.960565i | \(-0.589690\pi\) | ||||
−0.278055 | + | 0.960565i | \(0.589690\pi\) | |||||||
\(234\) | 4.56763e35 | 0.0864659 | ||||||||
\(235\) | −1.20946e36 | −0.214308 | ||||||||
\(236\) | −1.84008e36 | −0.305281 | ||||||||
\(237\) | −2.87022e36 | −0.445980 | ||||||||
\(238\) | −5.72252e34 | −0.00832998 | ||||||||
\(239\) | −6.06727e35 | −0.0827610 | −0.0413805 | − | 0.999143i | \(-0.513176\pi\) | ||||
−0.0413805 | + | 0.999143i | \(0.513176\pi\) | |||||||
\(240\) | −9.43430e35 | −0.120624 | ||||||||
\(241\) | 9.96011e36 | 1.19399 | 0.596994 | − | 0.802246i | \(-0.296362\pi\) | ||||
0.596994 | + | 0.802246i | \(0.296362\pi\) | |||||||
\(242\) | 5.91619e36 | 0.665125 | ||||||||
\(243\) | 3.08065e36 | 0.324896 | ||||||||
\(244\) | 2.17495e36 | 0.215232 | ||||||||
\(245\) | −4.79872e36 | −0.445708 | ||||||||
\(246\) | 7.50293e36 | 0.654240 | ||||||||
\(247\) | −1.30557e36 | −0.106905 | ||||||||
\(248\) | 3.00538e36 | 0.231153 | ||||||||
\(249\) | 1.59154e36 | 0.115008 | ||||||||
\(250\) | −9.31323e35 | −0.0632456 | ||||||||
\(251\) | 2.33773e37 | 1.49228 | 0.746141 | − | 0.665788i | \(-0.231905\pi\) | ||||
0.746141 | + | 0.665788i | \(0.231905\pi\) | |||||||
\(252\) | 7.92743e34 | 0.00475799 | ||||||||
\(253\) | −6.39456e36 | −0.360946 | ||||||||
\(254\) | 2.06226e37 | 1.09502 | ||||||||
\(255\) | −1.96097e36 | −0.0979709 | ||||||||
\(256\) | 1.32923e36 | 0.0625000 | ||||||||
\(257\) | −3.78920e37 | −1.67720 | −0.838599 | − | 0.544749i | \(-0.816625\pi\) | ||||
−0.838599 | + | 0.544749i | \(0.816625\pi\) | |||||||
\(258\) | 2.11703e37 | 0.882310 | ||||||||
\(259\) | 9.23845e35 | 0.0362621 | ||||||||
\(260\) | −4.50853e36 | −0.166705 | ||||||||
\(261\) | 5.10119e35 | 0.0177723 | ||||||||
\(262\) | 3.73425e37 | 1.22612 | ||||||||
\(263\) | −1.23104e37 | −0.381029 | −0.190515 | − | 0.981684i | \(-0.561016\pi\) | ||||
−0.190515 | + | 0.981684i | \(0.561016\pi\) | |||||||
\(264\) | −3.18480e36 | −0.0929439 | ||||||||
\(265\) | 2.20687e36 | 0.0607387 | ||||||||
\(266\) | −2.26590e35 | −0.00588269 | ||||||||
\(267\) | −2.96040e37 | −0.725146 | ||||||||
\(268\) | −2.39362e37 | −0.553307 | ||||||||
\(269\) | −8.37019e36 | −0.182631 | −0.0913156 | − | 0.995822i | \(-0.529107\pi\) | ||||
−0.0913156 | + | 0.995822i | \(0.529107\pi\) | |||||||
\(270\) | −1.38457e37 | −0.285217 | ||||||||
\(271\) | 6.44376e37 | 1.25347 | 0.626737 | − | 0.779231i | \(-0.284390\pi\) | ||||
0.626737 | + | 0.779231i | \(0.284390\pi\) | |||||||
\(272\) | 2.76287e36 | 0.0507624 | ||||||||
\(273\) | 2.68857e36 | 0.0466660 | ||||||||
\(274\) | 4.03685e37 | 0.662077 | ||||||||
\(275\) | −3.14393e36 | −0.0487321 | ||||||||
\(276\) | −5.45379e37 | −0.799111 | ||||||||
\(277\) | 3.75754e37 | 0.520556 | 0.260278 | − | 0.965534i | \(-0.416186\pi\) | ||||
0.260278 | + | 0.965534i | \(0.416186\pi\) | |||||||
\(278\) | 3.61104e37 | 0.473084 | ||||||||
\(279\) | −8.65378e36 | −0.107236 | ||||||||
\(280\) | −7.82486e35 | −0.00917333 | ||||||||
\(281\) | −3.31550e37 | −0.367791 | −0.183896 | − | 0.982946i | \(-0.558871\pi\) | ||||
−0.183896 | + | 0.982946i | \(0.558871\pi\) | |||||||
\(282\) | −3.48216e37 | −0.365585 | ||||||||
\(283\) | 1.66415e38 | 1.65388 | 0.826938 | − | 0.562292i | \(-0.190080\pi\) | ||||
0.826938 | + | 0.562292i | \(0.190080\pi\) | |||||||
\(284\) | −9.41390e37 | −0.885799 | ||||||||
\(285\) | −7.76470e36 | −0.0691878 | ||||||||
\(286\) | −1.52197e37 | −0.128450 | ||||||||
\(287\) | 6.22298e36 | 0.0497541 | ||||||||
\(288\) | −3.82741e36 | −0.0289949 | ||||||||
\(289\) | −1.33546e38 | −0.958771 | ||||||||
\(290\) | −5.03519e36 | −0.0342647 | ||||||||
\(291\) | −1.42559e38 | −0.919713 | ||||||||
\(292\) | −6.69052e37 | −0.409285 | ||||||||
\(293\) | 5.69894e37 | 0.330633 | 0.165317 | − | 0.986241i | \(-0.447135\pi\) | ||||
0.165317 | + | 0.986241i | \(0.447135\pi\) | |||||||
\(294\) | −1.38161e38 | −0.760328 | ||||||||
\(295\) | −5.22982e37 | −0.273052 | ||||||||
\(296\) | −4.46038e37 | −0.220979 | ||||||||
\(297\) | −4.67398e37 | −0.219767 | ||||||||
\(298\) | 5.14536e37 | 0.229649 | ||||||||
\(299\) | −2.60630e38 | −1.10438 | ||||||||
\(300\) | −2.68139e37 | −0.107890 | ||||||||
\(301\) | 1.75588e37 | 0.0670986 | ||||||||
\(302\) | 5.65615e37 | 0.205311 | ||||||||
\(303\) | 1.71050e38 | 0.589877 | ||||||||
\(304\) | 1.09399e37 | 0.0358488 | ||||||||
\(305\) | 6.18158e37 | 0.192509 | ||||||||
\(306\) | −7.95547e36 | −0.0235496 | ||||||||
\(307\) | 3.60072e38 | 1.01331 | 0.506657 | − | 0.862147i | \(-0.330881\pi\) | ||||
0.506657 | + | 0.862147i | \(0.330881\pi\) | |||||||
\(308\) | −2.64149e36 | −0.00706826 | ||||||||
\(309\) | −3.41637e38 | −0.869379 | ||||||||
\(310\) | 8.54182e37 | 0.206749 | ||||||||
\(311\) | 2.32592e37 | 0.0535560 | 0.0267780 | − | 0.999641i | \(-0.491475\pi\) | ||||
0.0267780 | + | 0.999641i | \(0.491475\pi\) | |||||||
\(312\) | −1.29806e38 | −0.284380 | ||||||||
\(313\) | 7.58763e38 | 1.58186 | 0.790932 | − | 0.611904i | \(-0.209596\pi\) | ||||
0.790932 | + | 0.611904i | \(0.209596\pi\) | |||||||
\(314\) | −4.02773e38 | −0.799191 | ||||||||
\(315\) | 2.25311e36 | 0.00425568 | ||||||||
\(316\) | 1.14936e38 | 0.206683 | ||||||||
\(317\) | 6.69462e38 | 1.14632 | 0.573162 | − | 0.819442i | \(-0.305717\pi\) | ||||
0.573162 | + | 0.819442i | \(0.305717\pi\) | |||||||
\(318\) | 6.35384e37 | 0.103613 | ||||||||
\(319\) | −1.69976e37 | −0.0264017 | ||||||||
\(320\) | 3.77789e37 | 0.0559017 | ||||||||
\(321\) | 3.95408e38 | 0.557464 | ||||||||
\(322\) | −4.52340e37 | −0.0607714 | ||||||||
\(323\) | 2.27392e37 | 0.0291163 | ||||||||
\(324\) | −4.65825e38 | −0.568559 | ||||||||
\(325\) | −1.28140e38 | −0.149105 | ||||||||
\(326\) | 9.73664e38 | 1.08028 | ||||||||
\(327\) | 6.52520e38 | 0.690405 | ||||||||
\(328\) | −3.00449e38 | −0.303198 | ||||||||
\(329\) | −2.88813e37 | −0.0278023 | ||||||||
\(330\) | −9.05173e37 | −0.0831315 | ||||||||
\(331\) | 1.26121e39 | 1.10523 | 0.552615 | − | 0.833437i | \(-0.313630\pi\) | ||||
0.552615 | + | 0.833437i | \(0.313630\pi\) | |||||||
\(332\) | −6.37321e37 | −0.0532988 | ||||||||
\(333\) | 1.28433e38 | 0.102516 | ||||||||
\(334\) | 4.05107e36 | 0.00308674 | ||||||||
\(335\) | −6.80308e38 | −0.494893 | ||||||||
\(336\) | −2.25287e37 | −0.0156487 | ||||||||
\(337\) | 1.05833e39 | 0.702036 | 0.351018 | − | 0.936369i | \(-0.385836\pi\) | ||||
0.351018 | + | 0.936369i | \(0.385836\pi\) | |||||||
\(338\) | 4.95750e38 | 0.314090 | ||||||||
\(339\) | −3.46424e39 | −2.09658 | ||||||||
\(340\) | 7.85254e37 | 0.0454033 | ||||||||
\(341\) | 2.88352e38 | 0.159305 | ||||||||
\(342\) | −3.15007e37 | −0.0166309 | ||||||||
\(343\) | −2.29570e38 | −0.115839 | ||||||||
\(344\) | −8.47749e38 | −0.408894 | ||||||||
\(345\) | −1.55006e39 | −0.714747 | ||||||||
\(346\) | 2.77620e39 | 1.22397 | ||||||||
\(347\) | −5.76947e38 | −0.243237 | −0.121618 | − | 0.992577i | \(-0.538808\pi\) | ||||
−0.121618 | + | 0.992577i | \(0.538808\pi\) | |||||||
\(348\) | −1.44969e38 | −0.0584517 | ||||||||
\(349\) | −2.40704e39 | −0.928304 | −0.464152 | − | 0.885756i | \(-0.653641\pi\) | ||||
−0.464152 | + | 0.885756i | \(0.653641\pi\) | |||||||
\(350\) | −2.22396e37 | −0.00820488 | ||||||||
\(351\) | −1.90502e39 | −0.672418 | ||||||||
\(352\) | 1.27533e38 | 0.0430735 | ||||||||
\(353\) | 3.14178e38 | 0.101547 | 0.0507736 | − | 0.998710i | \(-0.483831\pi\) | ||||
0.0507736 | + | 0.998710i | \(0.483831\pi\) | |||||||
\(354\) | −1.50573e39 | −0.465796 | ||||||||
\(355\) | −2.67559e39 | −0.792283 | ||||||||
\(356\) | 1.18547e39 | 0.336059 | ||||||||
\(357\) | −4.68270e37 | −0.0127098 | ||||||||
\(358\) | 4.31351e39 | 1.12110 | ||||||||
\(359\) | −6.98872e39 | −1.73954 | −0.869768 | − | 0.493460i | \(-0.835732\pi\) | ||||
−0.869768 | + | 0.493460i | \(0.835732\pi\) | |||||||
\(360\) | −1.08782e38 | −0.0259338 | ||||||||
\(361\) | −4.28883e39 | −0.979438 | ||||||||
\(362\) | −2.37570e39 | −0.519767 | ||||||||
\(363\) | 4.84118e39 | 1.01484 | ||||||||
\(364\) | −1.07662e38 | −0.0216267 | ||||||||
\(365\) | −1.90156e39 | −0.366075 | ||||||||
\(366\) | 1.77975e39 | 0.328399 | ||||||||
\(367\) | −2.43434e39 | −0.430583 | −0.215292 | − | 0.976550i | \(-0.569070\pi\) | ||||
−0.215292 | + | 0.976550i | \(0.569070\pi\) | |||||||
\(368\) | 2.18393e39 | 0.370337 | ||||||||
\(369\) | 8.65122e38 | 0.140659 | ||||||||
\(370\) | −1.26772e39 | −0.197649 | ||||||||
\(371\) | 5.26991e37 | 0.00787966 | ||||||||
\(372\) | 2.45929e39 | 0.352691 | ||||||||
\(373\) | 1.04824e40 | 1.44203 | 0.721017 | − | 0.692917i | \(-0.243675\pi\) | ||||
0.721017 | + | 0.692917i | \(0.243675\pi\) | |||||||
\(374\) | 2.65083e38 | 0.0349842 | ||||||||
\(375\) | −7.62096e38 | −0.0964995 | ||||||||
\(376\) | 1.39441e39 | 0.169425 | ||||||||
\(377\) | −6.92789e38 | −0.0807812 | ||||||||
\(378\) | −3.30629e38 | −0.0370014 | ||||||||
\(379\) | 6.74056e39 | 0.724083 | 0.362041 | − | 0.932162i | \(-0.382080\pi\) | ||||
0.362041 | + | 0.932162i | \(0.382080\pi\) | |||||||
\(380\) | 3.10932e38 | 0.0320641 | ||||||||
\(381\) | 1.68754e40 | 1.67077 | ||||||||
\(382\) | −1.99055e39 | −0.189230 | ||||||||
\(383\) | 1.08157e40 | 0.987358 | 0.493679 | − | 0.869644i | \(-0.335652\pi\) | ||||
0.493679 | + | 0.869644i | \(0.335652\pi\) | |||||||
\(384\) | 1.08770e39 | 0.0953620 | ||||||||
\(385\) | −7.50756e37 | −0.00632204 | ||||||||
\(386\) | −1.08351e40 | −0.876459 | ||||||||
\(387\) | 2.44103e39 | 0.189694 | ||||||||
\(388\) | 5.70865e39 | 0.426228 | ||||||||
\(389\) | −2.00224e40 | −1.43647 | −0.718236 | − | 0.695800i | \(-0.755050\pi\) | ||||
−0.718236 | + | 0.695800i | \(0.755050\pi\) | |||||||
\(390\) | −3.68931e39 | −0.254357 | ||||||||
\(391\) | 4.53940e39 | 0.300787 | ||||||||
\(392\) | 5.53254e39 | 0.352363 | ||||||||
\(393\) | 3.05572e40 | 1.87081 | ||||||||
\(394\) | −1.22581e40 | −0.721495 | ||||||||
\(395\) | 3.26667e39 | 0.184863 | ||||||||
\(396\) | −3.67221e38 | −0.0199826 | ||||||||
\(397\) | −2.20892e40 | −1.15592 | −0.577958 | − | 0.816066i | \(-0.696150\pi\) | ||||
−0.577958 | + | 0.816066i | \(0.696150\pi\) | |||||||
\(398\) | 5.05249e39 | 0.254283 | ||||||||
\(399\) | −1.85418e38 | −0.00897577 | ||||||||
\(400\) | 1.07374e39 | 0.0500000 | ||||||||
\(401\) | −6.25993e39 | −0.280435 | −0.140217 | − | 0.990121i | \(-0.544780\pi\) | ||||
−0.140217 | + | 0.990121i | \(0.544780\pi\) | |||||||
\(402\) | −1.95869e40 | −0.844231 | ||||||||
\(403\) | 1.17526e40 | 0.487424 | ||||||||
\(404\) | −6.84955e39 | −0.273370 | ||||||||
\(405\) | −1.32395e40 | −0.508534 | ||||||||
\(406\) | −1.20238e38 | −0.00444518 | ||||||||
\(407\) | −4.27951e39 | −0.152293 | ||||||||
\(408\) | 2.26084e39 | 0.0774528 | ||||||||
\(409\) | −3.54495e40 | −1.16923 | −0.584614 | − | 0.811311i | \(-0.698754\pi\) | ||||
−0.584614 | + | 0.811311i | \(0.698754\pi\) | |||||||
\(410\) | −8.53929e39 | −0.271189 | ||||||||
\(411\) | 3.30333e40 | 1.01019 | ||||||||
\(412\) | 1.36806e40 | 0.402901 | ||||||||
\(413\) | −1.24886e39 | −0.0354232 | ||||||||
\(414\) | −6.28846e39 | −0.171806 | ||||||||
\(415\) | −1.81137e39 | −0.0476719 | ||||||||
\(416\) | 5.19798e39 | 0.131792 | ||||||||
\(417\) | 2.95490e40 | 0.721828 | ||||||||
\(418\) | 1.04963e39 | 0.0247061 | ||||||||
\(419\) | −2.98080e40 | −0.676106 | −0.338053 | − | 0.941127i | \(-0.609768\pi\) | ||||
−0.338053 | + | 0.941127i | \(0.609768\pi\) | |||||||
\(420\) | −6.40304e38 | −0.0139966 | ||||||||
\(421\) | 5.17658e40 | 1.09061 | 0.545307 | − | 0.838237i | \(-0.316413\pi\) | ||||
0.545307 | + | 0.838237i | \(0.316413\pi\) | |||||||
\(422\) | 2.18217e40 | 0.443144 | ||||||||
\(423\) | −4.01509e39 | −0.0785995 | ||||||||
\(424\) | −2.54435e39 | −0.0480182 | ||||||||
\(425\) | 2.23183e39 | 0.0406099 | ||||||||
\(426\) | −7.70334e40 | −1.35154 | ||||||||
\(427\) | 1.47613e39 | 0.0249743 | ||||||||
\(428\) | −1.58338e40 | −0.258349 | ||||||||
\(429\) | −1.24542e40 | −0.195988 | ||||||||
\(430\) | −2.40945e40 | −0.365726 | ||||||||
\(431\) | 3.26439e40 | 0.477973 | 0.238987 | − | 0.971023i | \(-0.423185\pi\) | ||||
0.238987 | + | 0.971023i | \(0.423185\pi\) | |||||||
\(432\) | 1.59630e40 | 0.225484 | ||||||||
\(433\) | −1.01421e41 | −1.38218 | −0.691092 | − | 0.722767i | \(-0.742870\pi\) | ||||
−0.691092 | + | 0.722767i | \(0.742870\pi\) | |||||||
\(434\) | 2.03975e39 | 0.0268217 | ||||||||
\(435\) | −4.12027e39 | −0.0522808 | ||||||||
\(436\) | −2.61297e40 | −0.319958 | ||||||||
\(437\) | 1.79744e40 | 0.212418 | ||||||||
\(438\) | −5.47482e40 | −0.624483 | ||||||||
\(439\) | −9.77448e40 | −1.07620 | −0.538101 | − | 0.842881i | \(-0.680858\pi\) | ||||
−0.538101 | + | 0.842881i | \(0.680858\pi\) | |||||||
\(440\) | 3.62470e39 | 0.0385261 | ||||||||
\(441\) | −1.59305e40 | −0.163468 | ||||||||
\(442\) | 1.08043e40 | 0.107041 | ||||||||
\(443\) | −8.28639e40 | −0.792698 | −0.396349 | − | 0.918100i | \(-0.629723\pi\) | ||||
−0.396349 | + | 0.918100i | \(0.629723\pi\) | |||||||
\(444\) | −3.64991e40 | −0.337168 | ||||||||
\(445\) | 3.36931e40 | 0.300580 | ||||||||
\(446\) | 6.45974e40 | 0.556576 | ||||||||
\(447\) | 4.21042e40 | 0.350396 | ||||||||
\(448\) | 9.02145e38 | 0.00725215 | ||||||||
\(449\) | 1.71749e41 | 1.33375 | 0.666875 | − | 0.745169i | \(-0.267631\pi\) | ||||
0.666875 | + | 0.745169i | \(0.267631\pi\) | |||||||
\(450\) | −3.09176e39 | −0.0231959 | ||||||||
\(451\) | −2.88266e40 | −0.208957 | ||||||||
\(452\) | 1.38723e41 | 0.971633 | ||||||||
\(453\) | 4.62839e40 | 0.313262 | ||||||||
\(454\) | 1.72032e41 | 1.12523 | ||||||||
\(455\) | −3.05993e39 | −0.0193435 | ||||||||
\(456\) | 8.95209e39 | 0.0546978 | ||||||||
\(457\) | 1.56497e41 | 0.924281 | 0.462140 | − | 0.886807i | \(-0.347082\pi\) | ||||
0.462140 | + | 0.886807i | \(0.347082\pi\) | |||||||
\(458\) | 1.91258e41 | 1.09195 | ||||||||
\(459\) | 3.31799e40 | 0.183138 | ||||||||
\(460\) | 6.20710e40 | 0.331239 | ||||||||
\(461\) | 8.09856e40 | 0.417872 | 0.208936 | − | 0.977929i | \(-0.433000\pi\) | ||||
0.208936 | + | 0.977929i | \(0.433000\pi\) | |||||||
\(462\) | −2.16152e39 | −0.0107847 | ||||||||
\(463\) | −5.84222e40 | −0.281885 | −0.140943 | − | 0.990018i | \(-0.545013\pi\) | ||||
−0.140943 | + | 0.990018i | \(0.545013\pi\) | |||||||
\(464\) | 5.80518e39 | 0.0270886 | ||||||||
\(465\) | 6.98972e40 | 0.315456 | ||||||||
\(466\) | 9.00799e40 | 0.393229 | ||||||||
\(467\) | −1.90743e41 | −0.805446 | −0.402723 | − | 0.915322i | \(-0.631936\pi\) | ||||
−0.402723 | + | 0.915322i | \(0.631936\pi\) | |||||||
\(468\) | −1.49672e40 | −0.0611406 | ||||||||
\(469\) | −1.62455e40 | −0.0642027 | ||||||||
\(470\) | 3.96314e40 | 0.151538 | ||||||||
\(471\) | −3.29587e41 | −1.21940 | ||||||||
\(472\) | 6.02957e40 | 0.215867 | ||||||||
\(473\) | −8.13372e40 | −0.281800 | ||||||||
\(474\) | 9.40514e40 | 0.315356 | ||||||||
\(475\) | 8.83721e39 | 0.0286790 | ||||||||
\(476\) | 1.87515e39 | 0.00589019 | ||||||||
\(477\) | 7.32626e39 | 0.0222765 | ||||||||
\(478\) | 1.98812e40 | 0.0585209 | ||||||||
\(479\) | −1.74507e41 | −0.497294 | −0.248647 | − | 0.968594i | \(-0.579986\pi\) | ||||
−0.248647 | + | 0.968594i | \(0.579986\pi\) | |||||||
\(480\) | 3.09143e40 | 0.0852943 | ||||||||
\(481\) | −1.74424e41 | −0.465971 | ||||||||
\(482\) | −3.26373e41 | −0.844277 | ||||||||
\(483\) | −3.70148e40 | −0.0927245 | ||||||||
\(484\) | −1.93862e41 | −0.470315 | ||||||||
\(485\) | 1.62250e41 | 0.381230 | ||||||||
\(486\) | −1.00947e41 | −0.229736 | ||||||||
\(487\) | −5.84025e41 | −1.28746 | −0.643728 | − | 0.765254i | \(-0.722613\pi\) | ||||
−0.643728 | + | 0.765254i | \(0.722613\pi\) | |||||||
\(488\) | −7.12687e40 | −0.152192 | ||||||||
\(489\) | 7.96744e41 | 1.64828 | ||||||||
\(490\) | 1.57244e41 | 0.315163 | ||||||||
\(491\) | −5.87015e41 | −1.13995 | −0.569975 | − | 0.821662i | \(-0.693047\pi\) | ||||
−0.569975 | + | 0.821662i | \(0.693047\pi\) | |||||||
\(492\) | −2.45856e41 | −0.462617 | ||||||||
\(493\) | 1.20664e40 | 0.0220013 | ||||||||
\(494\) | 4.27809e40 | 0.0755932 | ||||||||
\(495\) | −1.04371e40 | −0.0178730 | ||||||||
\(496\) | −9.84805e40 | −0.163450 | ||||||||
\(497\) | −6.38920e40 | −0.102783 | ||||||||
\(498\) | −5.21516e40 | −0.0813229 | ||||||||
\(499\) | 5.42200e41 | 0.819598 | 0.409799 | − | 0.912176i | \(-0.365599\pi\) | ||||
0.409799 | + | 0.912176i | \(0.365599\pi\) | |||||||
\(500\) | 3.05176e40 | 0.0447214 | ||||||||
\(501\) | 3.31497e39 | 0.00470972 | ||||||||
\(502\) | −7.66026e41 | −1.05520 | ||||||||
\(503\) | −1.24021e42 | −1.65651 | −0.828253 | − | 0.560354i | \(-0.810665\pi\) | ||||
−0.828253 | + | 0.560354i | \(0.810665\pi\) | |||||||
\(504\) | −2.59766e39 | −0.00336441 | ||||||||
\(505\) | −1.94676e41 | −0.244510 | ||||||||
\(506\) | 2.09537e41 | 0.255228 | ||||||||
\(507\) | 4.05669e41 | 0.479235 | ||||||||
\(508\) | −6.75761e41 | −0.774294 | ||||||||
\(509\) | 9.96253e41 | 1.10725 | 0.553623 | − | 0.832768i | \(-0.313245\pi\) | ||||
0.553623 | + | 0.832768i | \(0.313245\pi\) | |||||||
\(510\) | 6.42569e40 | 0.0692759 | ||||||||
\(511\) | −4.54084e40 | −0.0474911 | ||||||||
\(512\) | −4.35561e40 | −0.0441942 | ||||||||
\(513\) | 1.31380e41 | 0.129333 | ||||||||
\(514\) | 1.24165e42 | 1.18596 | ||||||||
\(515\) | 3.88826e41 | 0.360366 | ||||||||
\(516\) | −6.93708e41 | −0.623888 | ||||||||
\(517\) | 1.33786e41 | 0.116764 | ||||||||
\(518\) | −3.02725e40 | −0.0256412 | ||||||||
\(519\) | 2.27175e42 | 1.86753 | ||||||||
\(520\) | 1.47736e41 | 0.117878 | ||||||||
\(521\) | −4.81065e41 | −0.372579 | −0.186290 | − | 0.982495i | \(-0.559646\pi\) | ||||
−0.186290 | + | 0.982495i | \(0.559646\pi\) | |||||||
\(522\) | −1.67156e40 | −0.0125669 | ||||||||
\(523\) | −4.21516e41 | −0.307636 | −0.153818 | − | 0.988099i | \(-0.549157\pi\) | ||||
−0.153818 | + | 0.988099i | \(0.549157\pi\) | |||||||
\(524\) | −1.22364e42 | −0.866999 | ||||||||
\(525\) | −1.81985e40 | −0.0125189 | ||||||||
\(526\) | 4.03388e41 | 0.269428 | ||||||||
\(527\) | −2.04697e41 | −0.132754 | ||||||||
\(528\) | 1.04359e41 | 0.0657212 | ||||||||
\(529\) | 1.95303e42 | 1.19439 | ||||||||
\(530\) | −7.23147e40 | −0.0429488 | ||||||||
\(531\) | −1.73617e41 | −0.100145 | ||||||||
\(532\) | 7.42492e39 | 0.00415969 | ||||||||
\(533\) | −1.17492e42 | −0.639345 | ||||||||
\(534\) | 9.70063e41 | 0.512756 | ||||||||
\(535\) | −4.50024e41 | −0.231074 | ||||||||
\(536\) | 7.84342e41 | 0.391247 | ||||||||
\(537\) | 3.52972e42 | 1.71056 | ||||||||
\(538\) | 2.74274e41 | 0.129140 | ||||||||
\(539\) | 5.30820e41 | 0.242841 | ||||||||
\(540\) | 4.53695e41 | 0.201679 | ||||||||
\(541\) | 3.12292e42 | 1.34897 | 0.674486 | − | 0.738288i | \(-0.264365\pi\) | ||||
0.674486 | + | 0.738288i | \(0.264365\pi\) | |||||||
\(542\) | −2.11149e42 | −0.886340 | ||||||||
\(543\) | −1.94402e42 | −0.793056 | ||||||||
\(544\) | −9.05336e40 | −0.0358944 | ||||||||
\(545\) | −7.42650e41 | −0.286180 | ||||||||
\(546\) | −8.80991e40 | −0.0329978 | ||||||||
\(547\) | 8.44341e41 | 0.307407 | 0.153704 | − | 0.988117i | \(-0.450880\pi\) | ||||
0.153704 | + | 0.988117i | \(0.450880\pi\) | |||||||
\(548\) | −1.32279e42 | −0.468159 | ||||||||
\(549\) | 2.05213e41 | 0.0706047 | ||||||||
\(550\) | 1.03020e41 | 0.0344588 | ||||||||
\(551\) | 4.77783e40 | 0.0155375 | ||||||||
\(552\) | 1.78710e42 | 0.565057 | ||||||||
\(553\) | 7.80068e40 | 0.0239824 | ||||||||
\(554\) | −1.23127e42 | −0.368089 | ||||||||
\(555\) | −1.03737e42 | −0.301572 | ||||||||
\(556\) | −1.18327e42 | −0.334521 | ||||||||
\(557\) | −4.72577e42 | −1.29932 | −0.649662 | − | 0.760223i | \(-0.725089\pi\) | ||||
−0.649662 | + | 0.760223i | \(0.725089\pi\) | |||||||
\(558\) | 2.83567e41 | 0.0758273 | ||||||||
\(559\) | −3.31514e42 | −0.862223 | ||||||||
\(560\) | 2.56405e40 | 0.00648652 | ||||||||
\(561\) | 2.16916e41 | 0.0533787 | ||||||||
\(562\) | 1.08642e42 | 0.260068 | ||||||||
\(563\) | −5.45592e42 | −1.27054 | −0.635269 | − | 0.772291i | \(-0.719111\pi\) | ||||
−0.635269 | + | 0.772291i | \(0.719111\pi\) | |||||||
\(564\) | 1.14104e42 | 0.258508 | ||||||||
\(565\) | 3.94274e42 | 0.869055 | ||||||||
\(566\) | −5.45309e42 | −1.16947 | ||||||||
\(567\) | −3.16155e41 | −0.0659724 | ||||||||
\(568\) | 3.08475e42 | 0.626354 | ||||||||
\(569\) | −1.38927e42 | −0.274503 | −0.137251 | − | 0.990536i | \(-0.543827\pi\) | ||||
−0.137251 | + | 0.990536i | \(0.543827\pi\) | |||||||
\(570\) | 2.54434e41 | 0.0489232 | ||||||||
\(571\) | 7.44435e41 | 0.139305 | 0.0696526 | − | 0.997571i | \(-0.477811\pi\) | ||||
0.0696526 | + | 0.997571i | \(0.477811\pi\) | |||||||
\(572\) | 4.98720e41 | 0.0908278 | ||||||||
\(573\) | −1.62885e42 | −0.288726 | ||||||||
\(574\) | −2.03915e41 | −0.0351815 | ||||||||
\(575\) | 1.76416e42 | 0.296270 | ||||||||
\(576\) | 1.25417e41 | 0.0205025 | ||||||||
\(577\) | 3.47495e42 | 0.552998 | 0.276499 | − | 0.961014i | \(-0.410826\pi\) | ||||
0.276499 | + | 0.961014i | \(0.410826\pi\) | |||||||
\(578\) | 4.37604e42 | 0.677953 | ||||||||
\(579\) | −8.86634e42 | −1.33729 | ||||||||
\(580\) | 1.64993e41 | 0.0242288 | ||||||||
\(581\) | −4.32549e40 | −0.00618450 | ||||||||
\(582\) | 4.67136e42 | 0.650335 | ||||||||
\(583\) | −2.44117e41 | −0.0330930 | ||||||||
\(584\) | 2.19235e42 | 0.289408 | ||||||||
\(585\) | −4.25394e41 | −0.0546859 | ||||||||
\(586\) | −1.86743e42 | −0.233793 | ||||||||
\(587\) | −1.21331e43 | −1.47939 | −0.739694 | − | 0.672944i | \(-0.765030\pi\) | ||||
−0.739694 | + | 0.672944i | \(0.765030\pi\) | |||||||
\(588\) | 4.52725e42 | 0.537633 | ||||||||
\(589\) | −8.10523e41 | −0.0937515 | ||||||||
\(590\) | 1.71371e42 | 0.193077 | ||||||||
\(591\) | −1.00308e43 | −1.10085 | ||||||||
\(592\) | 1.46158e42 | 0.156256 | ||||||||
\(593\) | 6.01048e42 | 0.625981 | 0.312991 | − | 0.949756i | \(-0.398669\pi\) | ||||
0.312991 | + | 0.949756i | \(0.398669\pi\) | |||||||
\(594\) | 1.53157e42 | 0.155398 | ||||||||
\(595\) | 5.32951e40 | 0.00526834 | ||||||||
\(596\) | −1.68603e42 | −0.162386 | ||||||||
\(597\) | 4.13442e42 | 0.387983 | ||||||||
\(598\) | 8.54031e42 | 0.780918 | ||||||||
\(599\) | −1.66324e43 | −1.48197 | −0.740987 | − | 0.671520i | \(-0.765642\pi\) | ||||
−0.740987 | + | 0.671520i | \(0.765642\pi\) | |||||||
\(600\) | 8.78637e41 | 0.0762896 | ||||||||
\(601\) | 1.70666e43 | 1.44409 | 0.722043 | − | 0.691848i | \(-0.243203\pi\) | ||||
0.722043 | + | 0.691848i | \(0.243203\pi\) | |||||||
\(602\) | −5.75366e41 | −0.0474459 | ||||||||
\(603\) | −2.25845e42 | −0.181507 | ||||||||
\(604\) | −1.85341e42 | −0.145177 | ||||||||
\(605\) | −5.50988e42 | −0.420662 | ||||||||
\(606\) | −5.60495e42 | −0.417106 | ||||||||
\(607\) | 7.20634e42 | 0.522745 | 0.261373 | − | 0.965238i | \(-0.415825\pi\) | ||||
0.261373 | + | 0.965238i | \(0.415825\pi\) | |||||||
\(608\) | −3.58480e41 | −0.0253489 | ||||||||
\(609\) | −9.83903e40 | −0.00678241 | ||||||||
\(610\) | −2.02558e42 | −0.136125 | ||||||||
\(611\) | 5.45287e42 | 0.357261 | ||||||||
\(612\) | 2.60685e41 | 0.0166521 | ||||||||
\(613\) | 2.06526e43 | 1.28629 | 0.643144 | − | 0.765745i | \(-0.277630\pi\) | ||||
0.643144 | + | 0.765745i | \(0.277630\pi\) | |||||||
\(614\) | −1.17988e43 | −0.716522 | ||||||||
\(615\) | −6.98765e42 | −0.413778 | ||||||||
\(616\) | 8.65563e40 | 0.00499801 | ||||||||
\(617\) | 2.04236e43 | 1.15004 | 0.575018 | − | 0.818140i | \(-0.304995\pi\) | ||||
0.575018 | + | 0.818140i | \(0.304995\pi\) | |||||||
\(618\) | 1.11948e43 | 0.614744 | ||||||||
\(619\) | −2.85830e42 | −0.153074 | −0.0765372 | − | 0.997067i | \(-0.524386\pi\) | ||||
−0.0765372 | + | 0.997067i | \(0.524386\pi\) | |||||||
\(620\) | −2.79898e42 | −0.146194 | ||||||||
\(621\) | 2.62273e43 | 1.33608 | ||||||||
\(622\) | −7.62157e41 | −0.0378698 | ||||||||
\(623\) | 8.04576e41 | 0.0389944 | ||||||||
\(624\) | 4.25348e42 | 0.201087 | ||||||||
\(625\) | 8.67362e41 | 0.0400000 | ||||||||
\(626\) | −2.48632e43 | −1.11855 | ||||||||
\(627\) | 8.58908e41 | 0.0376964 | ||||||||
\(628\) | 1.31981e43 | 0.565114 | ||||||||
\(629\) | 3.03796e42 | 0.126911 | ||||||||
\(630\) | −7.38299e40 | −0.00300922 | ||||||||
\(631\) | 3.58197e43 | 1.42451 | 0.712257 | − | 0.701919i | \(-0.247673\pi\) | ||||
0.712257 | + | 0.701919i | \(0.247673\pi\) | |||||||
\(632\) | −3.76622e42 | −0.146147 | ||||||||
\(633\) | 1.78566e43 | 0.676146 | ||||||||
\(634\) | −2.19369e43 | −0.810573 | ||||||||
\(635\) | −1.92063e43 | −0.692549 | ||||||||
\(636\) | −2.08203e42 | −0.0732657 | ||||||||
\(637\) | 2.16352e43 | 0.743017 | ||||||||
\(638\) | 5.56978e41 | 0.0186688 | ||||||||
\(639\) | −8.88230e42 | −0.290577 | ||||||||
\(640\) | −1.23794e42 | −0.0395285 | ||||||||
\(641\) | 2.02115e43 | 0.629941 | 0.314971 | − | 0.949101i | \(-0.398005\pi\) | ||||
0.314971 | + | 0.949101i | \(0.398005\pi\) | |||||||
\(642\) | −1.29567e43 | −0.394187 | ||||||||
\(643\) | −1.67149e43 | −0.496401 | −0.248200 | − | 0.968709i | \(-0.579839\pi\) | ||||
−0.248200 | + | 0.968709i | \(0.579839\pi\) | |||||||
\(644\) | 1.48223e42 | 0.0429719 | ||||||||
\(645\) | −1.97164e43 | −0.558022 | ||||||||
\(646\) | −7.45118e41 | −0.0205883 | ||||||||
\(647\) | −4.63260e43 | −1.24971 | −0.624853 | − | 0.780742i | \(-0.714841\pi\) | ||||
−0.624853 | + | 0.780742i | \(0.714841\pi\) | |||||||
\(648\) | 1.52642e43 | 0.402032 | ||||||||
\(649\) | 5.78507e42 | 0.148770 | ||||||||
\(650\) | 4.19890e42 | 0.105433 | ||||||||
\(651\) | 1.66912e42 | 0.0409243 | ||||||||
\(652\) | −3.19050e43 | −0.763874 | ||||||||
\(653\) | −8.05067e43 | −1.88225 | −0.941126 | − | 0.338056i | \(-0.890231\pi\) | ||||
−0.941126 | + | 0.338056i | \(0.890231\pi\) | |||||||
\(654\) | −2.13818e43 | −0.488190 | ||||||||
\(655\) | −3.47779e43 | −0.775468 | ||||||||
\(656\) | 9.84513e42 | 0.214394 | ||||||||
\(657\) | −6.31271e42 | −0.134262 | ||||||||
\(658\) | 9.46382e41 | 0.0196592 | ||||||||
\(659\) | −6.45090e43 | −1.30887 | −0.654435 | − | 0.756118i | \(-0.727093\pi\) | ||||
−0.654435 | + | 0.756118i | \(0.727093\pi\) | |||||||
\(660\) | 2.96607e42 | 0.0587829 | ||||||||
\(661\) | −7.74577e42 | −0.149948 | −0.0749742 | − | 0.997185i | \(-0.523887\pi\) | ||||
−0.0749742 | + | 0.997185i | \(0.523887\pi\) | |||||||
\(662\) | −4.13272e43 | −0.781516 | ||||||||
\(663\) | 8.84108e42 | 0.163322 | ||||||||
\(664\) | 2.08837e42 | 0.0376880 | ||||||||
\(665\) | 2.11029e41 | 0.00372054 | ||||||||
\(666\) | −4.20851e42 | −0.0724899 | ||||||||
\(667\) | 9.53794e42 | 0.160511 | ||||||||
\(668\) | −1.32746e41 | −0.00218265 | ||||||||
\(669\) | 5.28597e43 | 0.849219 | ||||||||
\(670\) | 2.22923e43 | 0.349942 | ||||||||
\(671\) | −6.83787e42 | −0.104887 | ||||||||
\(672\) | 7.38220e41 | 0.0110653 | ||||||||
\(673\) | 4.06603e43 | 0.595576 | 0.297788 | − | 0.954632i | \(-0.403751\pi\) | ||||
0.297788 | + | 0.954632i | \(0.403751\pi\) | |||||||
\(674\) | −3.46795e43 | −0.496414 | ||||||||
\(675\) | 1.28948e43 | 0.180387 | ||||||||
\(676\) | −1.62447e43 | −0.222095 | ||||||||
\(677\) | 9.74695e42 | 0.130240 | 0.0651200 | − | 0.997877i | \(-0.479257\pi\) | ||||
0.0651200 | + | 0.997877i | \(0.479257\pi\) | |||||||
\(678\) | 1.13516e44 | 1.48251 | ||||||||
\(679\) | 3.87445e42 | 0.0494571 | ||||||||
\(680\) | −2.57312e42 | −0.0321050 | ||||||||
\(681\) | 1.40773e44 | 1.71687 | ||||||||
\(682\) | −9.44871e42 | −0.112646 | ||||||||
\(683\) | 1.36490e43 | 0.159067 | 0.0795337 | − | 0.996832i | \(-0.474657\pi\) | ||||
0.0795337 | + | 0.996832i | \(0.474657\pi\) | |||||||
\(684\) | 1.03222e42 | 0.0117598 | ||||||||
\(685\) | −3.75961e43 | −0.418734 | ||||||||
\(686\) | 7.52254e42 | 0.0819107 | ||||||||
\(687\) | 1.56505e44 | 1.66609 | ||||||||
\(688\) | 2.77790e43 | 0.289132 | ||||||||
\(689\) | −9.94974e42 | −0.101254 | ||||||||
\(690\) | 5.07923e43 | 0.505402 | ||||||||
\(691\) | −1.10022e42 | −0.0107046 | −0.00535229 | − | 0.999986i | \(-0.501704\pi\) | ||||
−0.00535229 | + | 0.999986i | \(0.501704\pi\) | |||||||
\(692\) | −9.09706e43 | −0.865479 | ||||||||
\(693\) | −2.49232e41 | −0.00231867 | ||||||||
\(694\) | 1.89054e43 | 0.171994 | ||||||||
\(695\) | −3.36305e43 | −0.299205 | ||||||||
\(696\) | 4.75035e42 | 0.0413316 | ||||||||
\(697\) | 2.04636e43 | 0.174130 | ||||||||
\(698\) | 7.88740e43 | 0.656410 | ||||||||
\(699\) | 7.37119e43 | 0.599986 | ||||||||
\(700\) | 7.28747e41 | 0.00580172 | ||||||||
\(701\) | −2.42614e44 | −1.88924 | −0.944619 | − | 0.328169i | \(-0.893568\pi\) | ||||
−0.944619 | + | 0.328169i | \(0.893568\pi\) | |||||||
\(702\) | 6.24237e43 | 0.475471 | ||||||||
\(703\) | 1.20292e43 | 0.0896251 | ||||||||
\(704\) | −4.17899e42 | −0.0304576 | ||||||||
\(705\) | 3.24302e43 | 0.231216 | ||||||||
\(706\) | −1.02950e43 | −0.0718048 | ||||||||
\(707\) | −4.64878e42 | −0.0317204 | ||||||||
\(708\) | 4.93397e43 | 0.329367 | ||||||||
\(709\) | −1.50345e44 | −0.981909 | −0.490954 | − | 0.871185i | \(-0.663352\pi\) | ||||
−0.490954 | + | 0.871185i | \(0.663352\pi\) | |||||||
\(710\) | 8.76737e43 | 0.560228 | ||||||||
\(711\) | 1.08445e43 | 0.0678004 | ||||||||
\(712\) | −3.88454e43 | −0.237629 | ||||||||
\(713\) | −1.61804e44 | −0.968503 | ||||||||
\(714\) | 1.53443e42 | 0.00898720 | ||||||||
\(715\) | 1.41745e43 | 0.0812388 | ||||||||
\(716\) | −1.41345e44 | −0.792736 | ||||||||
\(717\) | 1.62687e43 | 0.0892906 | ||||||||
\(718\) | 2.29006e44 | 1.23004 | ||||||||
\(719\) | 2.19794e43 | 0.115536 | 0.0577680 | − | 0.998330i | \(-0.481602\pi\) | ||||
0.0577680 | + | 0.998330i | \(0.481602\pi\) | |||||||
\(720\) | 3.56456e42 | 0.0183380 | ||||||||
\(721\) | 9.28501e42 | 0.0467505 | ||||||||
\(722\) | 1.40536e44 | 0.692567 | ||||||||
\(723\) | −2.67069e44 | −1.28819 | ||||||||
\(724\) | 7.78469e43 | 0.367531 | ||||||||
\(725\) | 4.68939e42 | 0.0216709 | ||||||||
\(726\) | −1.58636e44 | −0.717602 | ||||||||
\(727\) | 1.29172e43 | 0.0571987 | 0.0285993 | − | 0.999591i | \(-0.490895\pi\) | ||||
0.0285993 | + | 0.999591i | \(0.490895\pi\) | |||||||
\(728\) | 3.52786e42 | 0.0152924 | ||||||||
\(729\) | 1.85363e44 | 0.786587 | ||||||||
\(730\) | 6.23103e43 | 0.258854 | ||||||||
\(731\) | 5.77401e43 | 0.234833 | ||||||||
\(732\) | −5.83188e43 | −0.232213 | ||||||||
\(733\) | −3.65349e44 | −1.42428 | −0.712141 | − | 0.702037i | \(-0.752274\pi\) | ||||
−0.712141 | + | 0.702037i | \(0.752274\pi\) | |||||||
\(734\) | 7.97684e43 | 0.304468 | ||||||||
\(735\) | 1.28672e44 | 0.480874 | ||||||||
\(736\) | −7.15629e43 | −0.261868 | ||||||||
\(737\) | 7.52536e43 | 0.269638 | ||||||||
\(738\) | −2.83483e43 | −0.0994612 | ||||||||
\(739\) | 1.65100e44 | 0.567230 | 0.283615 | − | 0.958938i | \(-0.408466\pi\) | ||||
0.283615 | + | 0.958938i | \(0.408466\pi\) | |||||||
\(740\) | 4.15405e43 | 0.139759 | ||||||||
\(741\) | 3.50074e43 | 0.115339 | ||||||||
\(742\) | −1.72684e42 | −0.00557176 | ||||||||
\(743\) | −5.25353e44 | −1.66006 | −0.830031 | − | 0.557717i | \(-0.811677\pi\) | ||||
−0.830031 | + | 0.557717i | \(0.811677\pi\) | |||||||
\(744\) | −8.05860e43 | −0.249390 | ||||||||
\(745\) | −4.79199e43 | −0.145243 | ||||||||
\(746\) | −3.43489e44 | −1.01967 | ||||||||
\(747\) | −6.01331e42 | −0.0174841 | ||||||||
\(748\) | −8.68625e42 | −0.0247376 | ||||||||
\(749\) | −1.07464e43 | −0.0299774 | ||||||||
\(750\) | 2.49724e43 | 0.0682355 | ||||||||
\(751\) | 2.28749e44 | 0.612265 | 0.306132 | − | 0.951989i | \(-0.400965\pi\) | ||||
0.306132 | + | 0.951989i | \(0.400965\pi\) | |||||||
\(752\) | −4.56919e43 | −0.119802 | ||||||||
\(753\) | −6.26835e44 | −1.61002 | ||||||||
\(754\) | 2.27013e43 | 0.0571209 | ||||||||
\(755\) | −5.26770e43 | −0.129850 | ||||||||
\(756\) | 1.08341e43 | 0.0261639 | ||||||||
\(757\) | 3.96084e43 | 0.0937134 | 0.0468567 | − | 0.998902i | \(-0.485080\pi\) | ||||
0.0468567 | + | 0.998902i | \(0.485080\pi\) | |||||||
\(758\) | −2.20875e44 | −0.512004 | ||||||||
\(759\) | 1.71463e44 | 0.389424 | ||||||||
\(760\) | −1.01886e43 | −0.0226728 | ||||||||
\(761\) | 4.33856e44 | 0.945984 | 0.472992 | − | 0.881067i | \(-0.343174\pi\) | ||||
0.472992 | + | 0.881067i | \(0.343174\pi\) | |||||||
\(762\) | −5.52972e44 | −1.18141 | ||||||||
\(763\) | −1.77342e43 | −0.0371262 | ||||||||
\(764\) | 6.52262e43 | 0.133806 | ||||||||
\(765\) | 7.40911e42 | 0.0148941 | ||||||||
\(766\) | −3.54410e44 | −0.698168 | ||||||||
\(767\) | 2.35788e44 | 0.455191 | ||||||||
\(768\) | −3.56418e43 | −0.0674311 | ||||||||
\(769\) | 9.78759e44 | 1.81475 | 0.907377 | − | 0.420318i | \(-0.138082\pi\) | ||||
0.907377 | + | 0.420318i | \(0.138082\pi\) | |||||||
\(770\) | 2.46008e42 | 0.00447036 | ||||||||
\(771\) | 1.01603e45 | 1.80953 | ||||||||
\(772\) | 3.55046e44 | 0.619750 | ||||||||
\(773\) | −4.51209e44 | −0.771961 | −0.385981 | − | 0.922507i | \(-0.626137\pi\) | ||||
−0.385981 | + | 0.922507i | \(0.626137\pi\) | |||||||
\(774\) | −7.99876e43 | −0.134134 | ||||||||
\(775\) | −7.95519e43 | −0.130760 | ||||||||
\(776\) | −1.87061e44 | −0.301389 | ||||||||
\(777\) | −2.47719e43 | −0.0391231 | ||||||||
\(778\) | 6.56094e44 | 1.01574 | ||||||||
\(779\) | 8.10283e43 | 0.122972 | ||||||||
\(780\) | 1.20891e44 | 0.179857 | ||||||||
\(781\) | 2.95966e44 | 0.431669 | ||||||||
\(782\) | −1.48747e44 | −0.212689 | ||||||||
\(783\) | 6.97157e43 | 0.0977289 | ||||||||
\(784\) | −1.81290e44 | −0.249159 | ||||||||
\(785\) | 3.75112e44 | 0.505453 | ||||||||
\(786\) | −1.00130e45 | −1.32286 | ||||||||
\(787\) | 2.01056e44 | 0.260441 | 0.130220 | − | 0.991485i | \(-0.458431\pi\) | ||||
0.130220 | + | 0.991485i | \(0.458431\pi\) | |||||||
\(788\) | 4.01675e44 | 0.510174 | ||||||||
\(789\) | 3.30090e44 | 0.411092 | ||||||||
\(790\) | −1.07042e44 | −0.130718 | ||||||||
\(791\) | 9.41509e43 | 0.112743 | ||||||||
\(792\) | 1.20331e43 | 0.0141298 | ||||||||
\(793\) | −2.78698e44 | −0.320922 | ||||||||
\(794\) | 7.23818e44 | 0.817357 | ||||||||
\(795\) | −5.91747e43 | −0.0655309 | ||||||||
\(796\) | −1.65560e44 | −0.179805 | ||||||||
\(797\) | −1.47308e45 | −1.56900 | −0.784500 | − | 0.620129i | \(-0.787080\pi\) | ||||
−0.784500 | + | 0.620129i | \(0.787080\pi\) | |||||||
\(798\) | 6.07577e42 | 0.00634682 | ||||||||
\(799\) | −9.49730e43 | −0.0973027 | ||||||||
\(800\) | −3.51844e43 | −0.0353553 | ||||||||
\(801\) | 1.11853e44 | 0.110241 | ||||||||
\(802\) | 2.05125e44 | 0.198297 | ||||||||
\(803\) | 2.10345e44 | 0.199453 | ||||||||
\(804\) | 6.41823e44 | 0.596961 | ||||||||
\(805\) | 4.21275e43 | 0.0384352 | ||||||||
\(806\) | −3.85111e44 | −0.344661 | ||||||||
\(807\) | 2.24437e44 | 0.197040 | ||||||||
\(808\) | 2.24446e44 | 0.193302 | ||||||||
\(809\) | 1.82842e45 | 1.54481 | 0.772404 | − | 0.635131i | \(-0.219054\pi\) | ||||
0.772404 | + | 0.635131i | \(0.219054\pi\) | |||||||
\(810\) | 4.33834e44 | 0.359588 | ||||||||
\(811\) | 8.48526e44 | 0.689988 | 0.344994 | − | 0.938605i | \(-0.387881\pi\) | ||||
0.344994 | + | 0.938605i | \(0.387881\pi\) | |||||||
\(812\) | 3.93997e42 | 0.00314321 | ||||||||
\(813\) | −1.72782e45 | −1.35237 | ||||||||
\(814\) | 1.40231e44 | 0.107688 | ||||||||
\(815\) | −9.06796e44 | −0.683229 | ||||||||
\(816\) | −7.40832e43 | −0.0547674 | ||||||||
\(817\) | 2.28630e44 | 0.165840 | ||||||||
\(818\) | 1.16161e45 | 0.826769 | ||||||||
\(819\) | −1.01582e43 | −0.00709442 | ||||||||
\(820\) | 2.79815e44 | 0.191759 | ||||||||
\(821\) | −2.50451e45 | −1.68424 | −0.842119 | − | 0.539291i | \(-0.818692\pi\) | ||||
−0.842119 | + | 0.539291i | \(0.818692\pi\) | |||||||
\(822\) | −1.08244e45 | −0.714313 | ||||||||
\(823\) | 1.83581e45 | 1.18886 | 0.594430 | − | 0.804148i | \(-0.297378\pi\) | ||||
0.594430 | + | 0.804148i | \(0.297378\pi\) | |||||||
\(824\) | −4.48286e44 | −0.284894 | ||||||||
\(825\) | 8.43008e43 | 0.0525770 | ||||||||
\(826\) | 4.09226e43 | 0.0250480 | ||||||||
\(827\) | 1.18525e43 | 0.00711988 | 0.00355994 | − | 0.999994i | \(-0.498867\pi\) | ||||
0.00355994 | + | 0.999994i | \(0.498867\pi\) | |||||||
\(828\) | 2.06060e44 | 0.121485 | ||||||||
\(829\) | −1.49150e45 | −0.863034 | −0.431517 | − | 0.902105i | \(-0.642022\pi\) | ||||
−0.431517 | + | 0.902105i | \(0.642022\pi\) | |||||||
\(830\) | 5.93551e43 | 0.0337091 | ||||||||
\(831\) | −1.00754e45 | −0.561626 | ||||||||
\(832\) | −1.70328e44 | −0.0931908 | ||||||||
\(833\) | −3.76821e44 | −0.202366 | ||||||||
\(834\) | −9.68261e44 | −0.510409 | ||||||||
\(835\) | −3.77285e42 | −0.00195222 | ||||||||
\(836\) | −3.43943e43 | −0.0174699 | ||||||||
\(837\) | −1.18267e45 | −0.589685 | ||||||||
\(838\) | 9.76747e44 | 0.478079 | ||||||||
\(839\) | 7.17066e44 | 0.344547 | 0.172274 | − | 0.985049i | \(-0.444889\pi\) | ||||
0.172274 | + | 0.985049i | \(0.444889\pi\) | |||||||
\(840\) | 2.09815e43 | 0.00989708 | ||||||||
\(841\) | −2.13407e45 | −0.988259 | ||||||||
\(842\) | −1.69626e45 | −0.771180 | ||||||||
\(843\) | 8.89015e44 | 0.396809 | ||||||||
\(844\) | −7.15053e44 | −0.313350 | ||||||||
\(845\) | −4.61703e44 | −0.198648 | ||||||||
\(846\) | 1.31567e44 | 0.0555782 | ||||||||
\(847\) | −1.31574e44 | −0.0545727 | ||||||||
\(848\) | 8.33732e43 | 0.0339540 | ||||||||
\(849\) | −4.46224e45 | −1.78436 | ||||||||
\(850\) | −7.31325e43 | −0.0287155 | ||||||||
\(851\) | 2.40138e45 | 0.925876 | ||||||||
\(852\) | 2.52423e45 | 0.955686 | ||||||||
\(853\) | −2.17378e45 | −0.808176 | −0.404088 | − | 0.914720i | \(-0.632411\pi\) | ||||
−0.404088 | + | 0.914720i | \(0.632411\pi\) | |||||||
\(854\) | −4.83700e43 | −0.0176595 | ||||||||
\(855\) | 2.93373e43 | 0.0105183 | ||||||||
\(856\) | 5.18842e44 | 0.182680 | ||||||||
\(857\) | 1.46655e45 | 0.507102 | 0.253551 | − | 0.967322i | \(-0.418401\pi\) | ||||
0.253551 | + | 0.967322i | \(0.418401\pi\) | |||||||
\(858\) | 4.08100e44 | 0.138584 | ||||||||
\(859\) | −3.71283e45 | −1.23826 | −0.619129 | − | 0.785290i | \(-0.712514\pi\) | ||||
−0.619129 | + | 0.785290i | \(0.712514\pi\) | |||||||
\(860\) | 7.89527e44 | 0.258608 | ||||||||
\(861\) | −1.66862e44 | −0.0536796 | ||||||||
\(862\) | −1.06967e45 | −0.337978 | ||||||||
\(863\) | 2.28506e45 | 0.709138 | 0.354569 | − | 0.935030i | \(-0.384628\pi\) | ||||
0.354569 | + | 0.935030i | \(0.384628\pi\) | |||||||
\(864\) | −5.23075e44 | −0.159441 | ||||||||
\(865\) | −2.58554e45 | −0.774108 | ||||||||
\(866\) | 3.32337e45 | 0.977352 | ||||||||
\(867\) | 3.58089e45 | 1.03442 | ||||||||
\(868\) | −6.68385e43 | −0.0189658 | ||||||||
\(869\) | −3.61350e44 | −0.100721 | ||||||||
\(870\) | 1.35013e44 | 0.0369681 | ||||||||
\(871\) | 3.06719e45 | 0.825010 | ||||||||
\(872\) | 8.56218e44 | 0.226245 | ||||||||
\(873\) | 5.38629e44 | 0.139820 | ||||||||
\(874\) | −5.88984e44 | −0.150202 | ||||||||
\(875\) | 2.07122e43 | 0.00518922 | ||||||||
\(876\) | 1.79399e45 | 0.441576 | ||||||||
\(877\) | −1.08696e45 | −0.262858 | −0.131429 | − | 0.991326i | \(-0.541957\pi\) | ||||
−0.131429 | + | 0.991326i | \(0.541957\pi\) | |||||||
\(878\) | 3.20290e45 | 0.760989 | ||||||||
\(879\) | −1.52811e45 | −0.356719 | ||||||||
\(880\) | −1.18774e44 | −0.0272421 | ||||||||
\(881\) | 5.54107e45 | 1.24873 | 0.624363 | − | 0.781134i | \(-0.285359\pi\) | ||||
0.624363 | + | 0.781134i | \(0.285359\pi\) | |||||||
\(882\) | 5.22012e44 | 0.115589 | ||||||||
\(883\) | 2.97545e45 | 0.647384 | 0.323692 | − | 0.946162i | \(-0.395076\pi\) | ||||
0.323692 | + | 0.946162i | \(0.395076\pi\) | |||||||
\(884\) | −3.54034e44 | −0.0756894 | ||||||||
\(885\) | 1.40232e45 | 0.294595 | ||||||||
\(886\) | 2.71528e45 | 0.560522 | ||||||||
\(887\) | 9.12159e45 | 1.85035 | 0.925177 | − | 0.379537i | \(-0.123917\pi\) | ||||
0.925177 | + | 0.379537i | \(0.123917\pi\) | |||||||
\(888\) | 1.19600e45 | 0.238413 | ||||||||
\(889\) | −4.58638e44 | −0.0898448 | ||||||||
\(890\) | −1.10405e45 | −0.212542 | ||||||||
\(891\) | 1.46452e45 | 0.277071 | ||||||||
\(892\) | −2.11673e45 | −0.393559 | ||||||||
\(893\) | −3.76058e44 | −0.0687159 | ||||||||
\(894\) | −1.37967e45 | −0.247767 | ||||||||
\(895\) | −4.01727e45 | −0.709044 | ||||||||
\(896\) | −2.95615e43 | −0.00512805 | ||||||||
\(897\) | 6.98849e45 | 1.19152 | ||||||||
\(898\) | −5.62786e45 | −0.943104 | ||||||||
\(899\) | −4.30097e44 | −0.0708420 | ||||||||
\(900\) | 1.01311e44 | 0.0164020 | ||||||||
\(901\) | 1.73295e44 | 0.0275774 | ||||||||
\(902\) | 9.44590e44 | 0.147755 | ||||||||
\(903\) | −4.70819e44 | −0.0723925 | ||||||||
\(904\) | −4.54567e45 | −0.687048 | ||||||||
\(905\) | 2.21254e45 | 0.328730 | ||||||||
\(906\) | −1.51663e45 | −0.221510 | ||||||||
\(907\) | −5.68239e45 | −0.815865 | −0.407932 | − | 0.913012i | \(-0.633750\pi\) | ||||
−0.407932 | + | 0.913012i | \(0.633750\pi\) | |||||||
\(908\) | −5.63714e45 | −0.795661 | ||||||||
\(909\) | −6.46276e44 | −0.0896763 | ||||||||
\(910\) | 1.00268e44 | 0.0136779 | ||||||||
\(911\) | −2.79936e43 | −0.00375426 | −0.00187713 | − | 0.999998i | \(-0.500598\pi\) | ||||
−0.00187713 | + | 0.999998i | \(0.500598\pi\) | |||||||
\(912\) | −2.93342e44 | −0.0386772 | ||||||||
\(913\) | 2.00369e44 | 0.0259737 | ||||||||
\(914\) | −5.12808e45 | −0.653565 | ||||||||
\(915\) | −1.65752e45 | −0.207698 | ||||||||
\(916\) | −6.26713e45 | −0.772127 | ||||||||
\(917\) | −8.30482e44 | −0.100602 | ||||||||
\(918\) | −1.08724e45 | −0.129498 | ||||||||
\(919\) | −1.43630e46 | −1.68211 | −0.841055 | − | 0.540950i | \(-0.818065\pi\) | ||||
−0.841055 | + | 0.540950i | \(0.818065\pi\) | |||||||
\(920\) | −2.03394e45 | −0.234222 | ||||||||
\(921\) | −9.65493e45 | −1.09326 | ||||||||
\(922\) | −2.65374e45 | −0.295480 | ||||||||
\(923\) | 1.20630e46 | 1.32077 | ||||||||
\(924\) | 7.08285e43 | 0.00762593 | ||||||||
\(925\) | 1.18065e45 | 0.125004 | ||||||||
\(926\) | 1.91438e45 | 0.199323 | ||||||||
\(927\) | 1.29081e45 | 0.132168 | ||||||||
\(928\) | −1.90224e44 | −0.0191545 | ||||||||
\(929\) | 1.85223e46 | 1.83422 | 0.917108 | − | 0.398638i | \(-0.130517\pi\) | ||||
0.917108 | + | 0.398638i | \(0.130517\pi\) | |||||||
\(930\) | −2.29039e45 | −0.223061 | ||||||||
\(931\) | −1.49207e45 | −0.142912 | ||||||||
\(932\) | −2.95174e45 | −0.278055 | ||||||||
\(933\) | −6.23669e44 | −0.0577815 | ||||||||
\(934\) | 6.25026e45 | 0.569536 | ||||||||
\(935\) | −2.46878e44 | −0.0221260 | ||||||||
\(936\) | 4.90445e44 | 0.0432330 | ||||||||
\(937\) | −7.97850e45 | −0.691764 | −0.345882 | − | 0.938278i | \(-0.612420\pi\) | ||||
−0.345882 | + | 0.938278i | \(0.612420\pi\) | |||||||
\(938\) | 5.32331e44 | 0.0453981 | ||||||||
\(939\) | −2.03454e46 | −1.70667 | ||||||||
\(940\) | −1.29864e45 | −0.107154 | ||||||||
\(941\) | 7.58451e45 | 0.615585 | 0.307793 | − | 0.951453i | \(-0.400410\pi\) | ||||
0.307793 | + | 0.951453i | \(0.400410\pi\) | |||||||
\(942\) | 1.07999e46 | 0.862246 | ||||||||
\(943\) | 1.61756e46 | 1.27037 | ||||||||
\(944\) | −1.97577e45 | −0.152641 | ||||||||
\(945\) | 3.07922e44 | 0.0234017 | ||||||||
\(946\) | 2.66526e45 | 0.199263 | ||||||||
\(947\) | −1.64569e46 | −1.21038 | −0.605192 | − | 0.796079i | \(-0.706904\pi\) | ||||
−0.605192 | + | 0.796079i | \(0.706904\pi\) | |||||||
\(948\) | −3.08188e45 | −0.222990 | ||||||||
\(949\) | 8.57324e45 | 0.610265 | ||||||||
\(950\) | −2.89578e44 | −0.0202791 | ||||||||
\(951\) | −1.79509e46 | −1.23677 | ||||||||
\(952\) | −6.14450e43 | −0.00416499 | ||||||||
\(953\) | 1.88162e46 | 1.25485 | 0.627426 | − | 0.778676i | \(-0.284109\pi\) | ||||
0.627426 | + | 0.778676i | \(0.284109\pi\) | |||||||
\(954\) | −2.40067e44 | −0.0157519 | ||||||||
\(955\) | 1.85384e45 | 0.119680 | ||||||||
\(956\) | −6.51468e44 | −0.0413805 | ||||||||
\(957\) | 4.55772e44 | 0.0284848 | ||||||||
\(958\) | 5.71825e45 | 0.351640 | ||||||||
\(959\) | −8.97778e44 | −0.0543226 | ||||||||
\(960\) | −1.01300e45 | −0.0603122 | ||||||||
\(961\) | −9.77291e45 | −0.572547 | ||||||||
\(962\) | 5.71554e45 | 0.329491 | ||||||||
\(963\) | −1.49397e45 | −0.0847488 | ||||||||
\(964\) | 1.06946e46 | 0.596994 | ||||||||
\(965\) | 1.00910e46 | 0.554321 | ||||||||
\(966\) | 1.21290e45 | 0.0655661 | ||||||||
\(967\) | −2.62276e46 | −1.39524 | −0.697619 | − | 0.716469i | \(-0.745757\pi\) | ||||
−0.697619 | + | 0.716469i | \(0.745757\pi\) | |||||||
\(968\) | 6.35246e45 | 0.332563 | ||||||||
\(969\) | −6.09727e44 | −0.0314135 | ||||||||
\(970\) | −5.31660e45 | −0.269570 | ||||||||
\(971\) | 1.34449e46 | 0.670904 | 0.335452 | − | 0.942057i | \(-0.391111\pi\) | ||||
0.335452 | + | 0.942057i | \(0.391111\pi\) | |||||||
\(972\) | 3.30782e45 | 0.162448 | ||||||||
\(973\) | −8.03081e44 | −0.0388160 | ||||||||
\(974\) | 1.91373e46 | 0.910369 | ||||||||
\(975\) | 3.43594e45 | 0.160869 | ||||||||
\(976\) | 2.33533e45 | 0.107616 | ||||||||
\(977\) | −1.98144e46 | −0.898699 | −0.449350 | − | 0.893356i | \(-0.648344\pi\) | ||||
−0.449350 | + | 0.893356i | \(0.648344\pi\) | |||||||
\(978\) | −2.61077e46 | −1.16551 | ||||||||
\(979\) | −3.72703e45 | −0.163769 | ||||||||
\(980\) | −5.15258e45 | −0.222854 | ||||||||
\(981\) | −2.46541e45 | −0.104959 | ||||||||
\(982\) | 1.92353e46 | 0.806067 | ||||||||
\(983\) | −5.61388e44 | −0.0231571 | −0.0115785 | − | 0.999933i | \(-0.503686\pi\) | ||||
−0.0115785 | + | 0.999933i | \(0.503686\pi\) | |||||||
\(984\) | 8.05621e45 | 0.327120 | ||||||||
\(985\) | 1.14163e46 | 0.456313 | ||||||||
\(986\) | −3.95390e44 | −0.0155573 | ||||||||
\(987\) | 7.74419e44 | 0.0299958 | ||||||||
\(988\) | −1.40185e45 | −0.0534524 | ||||||||
\(989\) | 4.56411e46 | 1.71322 | ||||||||
\(990\) | 3.42001e44 | 0.0126381 | ||||||||
\(991\) | 9.54885e45 | 0.347384 | 0.173692 | − | 0.984800i | \(-0.444430\pi\) | ||||
0.173692 | + | 0.984800i | \(0.444430\pi\) | |||||||
\(992\) | 3.22701e45 | 0.115576 | ||||||||
\(993\) | −3.38179e46 | −1.19243 | ||||||||
\(994\) | 2.09361e45 | 0.0726787 | ||||||||
\(995\) | −4.70550e45 | −0.160823 | ||||||||
\(996\) | 1.70890e45 | 0.0575040 | ||||||||
\(997\) | −4.00436e45 | −0.132666 | −0.0663328 | − | 0.997798i | \(-0.521130\pi\) | ||||
−0.0663328 | + | 0.997798i | \(0.521130\pi\) | |||||||
\(998\) | −1.77668e46 | −0.579543 | ||||||||
\(999\) | 1.75524e46 | 0.563731 |
(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 | 10.32.a.a.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.32.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |