Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −141.008 | −1.55794 | −0.778968 | − | 0.627064i | \(-0.784256\pi\) | ||||
−0.778968 | + | 0.627064i | \(0.784256\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 11691.3 | 1.42716 | ||||||||
\(5\) | −32545.4 | −0.931504 | −0.465752 | − | 0.884915i | \(-0.654216\pi\) | ||||
−0.465752 | + | 0.884915i | \(0.654216\pi\) | |||||||
\(6\) | −102795. | −0.899474 | ||||||||
\(7\) | −339369. | −1.09027 | −0.545136 | − | 0.838348i | \(-0.683522\pi\) | ||||
−0.545136 | + | 0.838348i | \(0.683522\pi\) | |||||||
\(8\) | −493432. | −0.665491 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 4.58917e6 | 1.45122 | ||||||||
\(11\) | 3.57384e6 | 0.608251 | 0.304126 | − | 0.952632i | \(-0.401636\pi\) | ||||
0.304126 | + | 0.952632i | \(0.401636\pi\) | |||||||
\(12\) | 8.52297e6 | 0.823973 | ||||||||
\(13\) | −2.09171e7 | −1.20190 | −0.600952 | − | 0.799285i | \(-0.705212\pi\) | ||||
−0.600952 | + | 0.799285i | \(0.705212\pi\) | |||||||
\(14\) | 4.78538e7 | 1.69857 | ||||||||
\(15\) | −2.37256e7 | −0.537804 | ||||||||
\(16\) | −2.61973e7 | −0.390370 | ||||||||
\(17\) | 9.09292e6 | 0.0913662 | 0.0456831 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456831 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(18\) | −7.49375e7 | −0.519312 | ||||||||
\(19\) | 1.92711e8 | 0.939742 | 0.469871 | − | 0.882735i | \(-0.344300\pi\) | ||||
0.469871 | + | 0.882735i | \(0.344300\pi\) | |||||||
\(20\) | −3.80499e8 | −1.32941 | ||||||||
\(21\) | −2.47400e8 | −0.629468 | ||||||||
\(22\) | −5.03941e8 | −0.947616 | ||||||||
\(23\) | −8.21298e8 | −1.15683 | −0.578415 | − | 0.815742i | \(-0.696329\pi\) | ||||
−0.578415 | + | 0.815742i | \(0.696329\pi\) | |||||||
\(24\) | −3.59712e8 | −0.384222 | ||||||||
\(25\) | −1.61499e8 | −0.132300 | ||||||||
\(26\) | 2.94948e9 | 1.87249 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −3.96767e9 | −1.55599 | ||||||||
\(29\) | −5.08788e8 | −0.158836 | −0.0794182 | − | 0.996841i | \(-0.525306\pi\) | ||||
−0.0794182 | + | 0.996841i | \(0.525306\pi\) | |||||||
\(30\) | 3.34550e9 | 0.837864 | ||||||||
\(31\) | 4.32040e9 | 0.874326 | 0.437163 | − | 0.899382i | \(-0.355983\pi\) | ||||
0.437163 | + | 0.899382i | \(0.355983\pi\) | |||||||
\(32\) | 7.73623e9 | 1.27366 | ||||||||
\(33\) | 2.60533e9 | 0.351174 | ||||||||
\(34\) | −1.28218e9 | −0.142343 | ||||||||
\(35\) | 1.10449e10 | 1.01559 | ||||||||
\(36\) | 6.21324e9 | 0.475721 | ||||||||
\(37\) | −6.74260e9 | −0.432033 | −0.216016 | − | 0.976390i | \(-0.569306\pi\) | ||||
−0.216016 | + | 0.976390i | \(0.569306\pi\) | |||||||
\(38\) | −2.71739e10 | −1.46406 | ||||||||
\(39\) | −1.52486e10 | −0.693919 | ||||||||
\(40\) | 1.60589e10 | 0.619908 | ||||||||
\(41\) | 4.16817e10 | 1.37041 | 0.685204 | − | 0.728351i | \(-0.259713\pi\) | ||||
0.685204 | + | 0.728351i | \(0.259713\pi\) | |||||||
\(42\) | 3.48854e10 | 0.980671 | ||||||||
\(43\) | 6.89112e10 | 1.66244 | 0.831218 | − | 0.555947i | \(-0.187644\pi\) | ||||
0.831218 | + | 0.555947i | \(0.187644\pi\) | |||||||
\(44\) | 4.17829e10 | 0.868074 | ||||||||
\(45\) | −1.72960e10 | −0.310501 | ||||||||
\(46\) | 1.15810e11 | 1.80227 | ||||||||
\(47\) | −6.47713e10 | −0.876489 | −0.438244 | − | 0.898856i | \(-0.644400\pi\) | ||||
−0.438244 | + | 0.898856i | \(0.644400\pi\) | |||||||
\(48\) | −1.90978e10 | −0.225380 | ||||||||
\(49\) | 1.82821e10 | 0.188691 | ||||||||
\(50\) | 2.27728e10 | 0.206115 | ||||||||
\(51\) | 6.62874e9 | 0.0527503 | ||||||||
\(52\) | −2.44548e11 | −1.71531 | ||||||||
\(53\) | 8.27456e10 | 0.512805 | 0.256402 | − | 0.966570i | \(-0.417463\pi\) | ||||
0.256402 | + | 0.966570i | \(0.417463\pi\) | |||||||
\(54\) | −5.46295e10 | −0.299825 | ||||||||
\(55\) | −1.16312e11 | −0.566589 | ||||||||
\(56\) | 1.67455e11 | 0.725566 | ||||||||
\(57\) | 1.40486e11 | 0.542560 | ||||||||
\(58\) | 7.17433e10 | 0.247457 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | −2.77383e11 | −0.767534 | ||||||||
\(61\) | −3.81752e11 | −0.948719 | −0.474360 | − | 0.880331i | \(-0.657320\pi\) | ||||
−0.474360 | + | 0.880331i | \(0.657320\pi\) | |||||||
\(62\) | −6.09212e11 | −1.36214 | ||||||||
\(63\) | −1.80354e11 | −0.363424 | ||||||||
\(64\) | −8.76263e11 | −1.59391 | ||||||||
\(65\) | 6.80755e11 | 1.11958 | ||||||||
\(66\) | −3.67373e11 | −0.547107 | ||||||||
\(67\) | −8.52576e11 | −1.15146 | −0.575728 | − | 0.817641i | \(-0.695281\pi\) | ||||
−0.575728 | + | 0.817641i | \(0.695281\pi\) | |||||||
\(68\) | 1.06308e11 | 0.130394 | ||||||||
\(69\) | −5.98726e11 | −0.667896 | ||||||||
\(70\) | −1.55742e12 | −1.58223 | ||||||||
\(71\) | −1.49429e12 | −1.38438 | −0.692188 | − | 0.721717i | \(-0.743353\pi\) | ||||
−0.692188 | + | 0.721717i | \(0.743353\pi\) | |||||||
\(72\) | −2.62230e11 | −0.221830 | ||||||||
\(73\) | 1.20889e11 | 0.0934952 | 0.0467476 | − | 0.998907i | \(-0.485114\pi\) | ||||
0.0467476 | + | 0.998907i | \(0.485114\pi\) | |||||||
\(74\) | 9.50763e11 | 0.673079 | ||||||||
\(75\) | −1.17733e11 | −0.0763837 | ||||||||
\(76\) | 2.25305e12 | 1.34116 | ||||||||
\(77\) | −1.21285e12 | −0.663159 | ||||||||
\(78\) | 2.15017e12 | 1.08108 | ||||||||
\(79\) | 3.34434e12 | 1.54787 | 0.773936 | − | 0.633264i | \(-0.218285\pi\) | ||||
0.773936 | + | 0.633264i | \(0.218285\pi\) | |||||||
\(80\) | 8.52601e11 | 0.363631 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −5.87746e12 | −2.13501 | ||||||||
\(83\) | 2.74183e12 | 0.920520 | 0.460260 | − | 0.887784i | \(-0.347756\pi\) | ||||
0.460260 | + | 0.887784i | \(0.347756\pi\) | |||||||
\(84\) | −2.89243e12 | −0.898354 | ||||||||
\(85\) | −2.95933e11 | −0.0851080 | ||||||||
\(86\) | −9.71705e12 | −2.58997 | ||||||||
\(87\) | −3.70906e11 | −0.0917042 | ||||||||
\(88\) | −1.76345e12 | −0.404786 | ||||||||
\(89\) | 5.23866e12 | 1.11734 | 0.558670 | − | 0.829390i | \(-0.311312\pi\) | ||||
0.558670 | + | 0.829390i | \(0.311312\pi\) | |||||||
\(90\) | 2.43887e12 | 0.483741 | ||||||||
\(91\) | 7.09861e12 | 1.31040 | ||||||||
\(92\) | −9.60205e12 | −1.65099 | ||||||||
\(93\) | 3.14957e12 | 0.504792 | ||||||||
\(94\) | 9.13328e12 | 1.36551 | ||||||||
\(95\) | −6.27186e12 | −0.875373 | ||||||||
\(96\) | 5.63971e12 | 0.735349 | ||||||||
\(97\) | 9.88927e12 | 1.20545 | 0.602723 | − | 0.797950i | \(-0.294082\pi\) | ||||
0.602723 | + | 0.797950i | \(0.294082\pi\) | |||||||
\(98\) | −2.57793e12 | −0.293969 | ||||||||
\(99\) | 1.89929e12 | 0.202750 | ||||||||
\(100\) | −1.88814e12 | −0.188814 | ||||||||
\(101\) | 5.89937e12 | 0.552989 | 0.276495 | − | 0.961015i | \(-0.410827\pi\) | ||||
0.276495 | + | 0.961015i | \(0.410827\pi\) | |||||||
\(102\) | −9.34707e11 | −0.0821816 | ||||||||
\(103\) | 2.03940e13 | 1.68291 | 0.841454 | − | 0.540328i | \(-0.181700\pi\) | ||||
0.841454 | + | 0.540328i | \(0.181700\pi\) | |||||||
\(104\) | 1.03212e13 | 0.799856 | ||||||||
\(105\) | 8.05173e12 | 0.586352 | ||||||||
\(106\) | −1.16678e13 | −0.798916 | ||||||||
\(107\) | −1.02325e13 | −0.659156 | −0.329578 | − | 0.944128i | \(-0.606906\pi\) | ||||
−0.329578 | + | 0.944128i | \(0.606906\pi\) | |||||||
\(108\) | 4.52945e12 | 0.274658 | ||||||||
\(109\) | 2.01100e13 | 1.14852 | 0.574260 | − | 0.818673i | \(-0.305290\pi\) | ||||
0.574260 | + | 0.818673i | \(0.305290\pi\) | |||||||
\(110\) | 1.64010e13 | 0.882708 | ||||||||
\(111\) | −4.91536e12 | −0.249434 | ||||||||
\(112\) | 8.89054e12 | 0.425609 | ||||||||
\(113\) | −4.04662e13 | −1.82845 | −0.914223 | − | 0.405211i | \(-0.867198\pi\) | ||||
−0.914223 | + | 0.405211i | \(0.867198\pi\) | |||||||
\(114\) | −1.98097e13 | −0.845274 | ||||||||
\(115\) | 2.67295e13 | 1.07759 | ||||||||
\(116\) | −5.94840e12 | −0.226685 | ||||||||
\(117\) | −1.11162e13 | −0.400634 | ||||||||
\(118\) | −5.94780e12 | −0.202826 | ||||||||
\(119\) | −3.08585e12 | −0.0996139 | ||||||||
\(120\) | 1.17070e13 | 0.357904 | ||||||||
\(121\) | −2.17503e13 | −0.630030 | ||||||||
\(122\) | 5.38302e13 | 1.47804 | ||||||||
\(123\) | 3.03859e13 | 0.791206 | ||||||||
\(124\) | 5.05112e13 | 1.24781 | ||||||||
\(125\) | 4.49843e13 | 1.05474 | ||||||||
\(126\) | 2.54315e13 | 0.566191 | ||||||||
\(127\) | 4.59756e13 | 0.972307 | 0.486154 | − | 0.873873i | \(-0.338400\pi\) | ||||
0.486154 | + | 0.873873i | \(0.338400\pi\) | |||||||
\(128\) | 6.01852e13 | 1.20955 | ||||||||
\(129\) | 5.02363e13 | 0.959808 | ||||||||
\(130\) | −9.59921e13 | −1.74423 | ||||||||
\(131\) | 6.31090e13 | 1.09101 | 0.545504 | − | 0.838108i | \(-0.316338\pi\) | ||||
0.545504 | + | 0.838108i | \(0.316338\pi\) | |||||||
\(132\) | 3.04598e13 | 0.501183 | ||||||||
\(133\) | −6.54001e13 | −1.02457 | ||||||||
\(134\) | 1.20220e14 | 1.79389 | ||||||||
\(135\) | −1.26088e13 | −0.179268 | ||||||||
\(136\) | −4.48674e12 | −0.0608034 | ||||||||
\(137\) | −5.15109e13 | −0.665603 | −0.332802 | − | 0.942997i | \(-0.607994\pi\) | ||||
−0.332802 | + | 0.942997i | \(0.607994\pi\) | |||||||
\(138\) | 8.44253e13 | 1.04054 | ||||||||
\(139\) | 2.20544e13 | 0.259358 | 0.129679 | − | 0.991556i | \(-0.458605\pi\) | ||||
0.129679 | + | 0.991556i | \(0.458605\pi\) | |||||||
\(140\) | 1.29129e14 | 1.44941 | ||||||||
\(141\) | −4.72183e13 | −0.506041 | ||||||||
\(142\) | 2.10707e14 | 2.15677 | ||||||||
\(143\) | −7.47544e13 | −0.731059 | ||||||||
\(144\) | −1.39223e13 | −0.130123 | ||||||||
\(145\) | 1.65587e13 | 0.147957 | ||||||||
\(146\) | −1.70464e13 | −0.145659 | ||||||||
\(147\) | 1.33277e13 | 0.108941 | ||||||||
\(148\) | −7.88299e13 | −0.616581 | ||||||||
\(149\) | −5.03518e13 | −0.376968 | −0.188484 | − | 0.982076i | \(-0.560357\pi\) | ||||
−0.188484 | + | 0.982076i | \(0.560357\pi\) | |||||||
\(150\) | 1.66013e13 | 0.119001 | ||||||||
\(151\) | 1.20657e14 | 0.828327 | 0.414163 | − | 0.910203i | \(-0.364074\pi\) | ||||
0.414163 | + | 0.910203i | \(0.364074\pi\) | |||||||
\(152\) | −9.50899e13 | −0.625390 | ||||||||
\(153\) | 4.83235e12 | 0.0304554 | ||||||||
\(154\) | 1.71022e14 | 1.03316 | ||||||||
\(155\) | −1.40609e14 | −0.814438 | ||||||||
\(156\) | −1.78276e14 | −0.990335 | ||||||||
\(157\) | −6.09316e13 | −0.324710 | −0.162355 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(158\) | −4.71580e14 | −2.41148 | ||||||||
\(159\) | 6.03216e13 | 0.296068 | ||||||||
\(160\) | −2.51779e14 | −1.18642 | ||||||||
\(161\) | 2.78723e14 | 1.26126 | ||||||||
\(162\) | −3.98249e13 | −0.173104 | ||||||||
\(163\) | 1.45321e14 | 0.606890 | 0.303445 | − | 0.952849i | \(-0.401863\pi\) | ||||
0.303445 | + | 0.952849i | \(0.401863\pi\) | |||||||
\(164\) | 4.87314e14 | 1.95580 | ||||||||
\(165\) | −8.47916e13 | −0.327120 | ||||||||
\(166\) | −3.86621e14 | −1.43411 | ||||||||
\(167\) | −1.87744e14 | −0.669743 | −0.334872 | − | 0.942264i | \(-0.608693\pi\) | ||||
−0.334872 | + | 0.942264i | \(0.608693\pi\) | |||||||
\(168\) | 1.22075e14 | 0.418906 | ||||||||
\(169\) | 1.34650e14 | 0.444571 | ||||||||
\(170\) | 4.17290e13 | 0.132593 | ||||||||
\(171\) | 1.02415e14 | 0.313247 | ||||||||
\(172\) | 8.05663e14 | 2.37257 | ||||||||
\(173\) | −6.04115e14 | −1.71325 | −0.856623 | − | 0.515942i | \(-0.827442\pi\) | ||||
−0.856623 | + | 0.515942i | \(0.827442\pi\) | |||||||
\(174\) | 5.23009e13 | 0.142869 | ||||||||
\(175\) | 5.48079e13 | 0.144243 | ||||||||
\(176\) | −9.36250e13 | −0.237443 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −7.38694e14 | −1.74074 | ||||||||
\(179\) | −6.12062e14 | −1.39075 | −0.695377 | − | 0.718645i | \(-0.744763\pi\) | ||||
−0.695377 | + | 0.718645i | \(0.744763\pi\) | |||||||
\(180\) | −2.02213e14 | −0.443136 | ||||||||
\(181\) | 7.61474e14 | 1.60970 | 0.804849 | − | 0.593480i | \(-0.202246\pi\) | ||||
0.804849 | + | 0.593480i | \(0.202246\pi\) | |||||||
\(182\) | −1.00096e15 | −2.04152 | ||||||||
\(183\) | −2.78297e14 | −0.547743 | ||||||||
\(184\) | 4.05255e14 | 0.769861 | ||||||||
\(185\) | 2.19441e14 | 0.402440 | ||||||||
\(186\) | −4.44116e14 | −0.786434 | ||||||||
\(187\) | 3.24967e13 | 0.0555736 | ||||||||
\(188\) | −7.57261e14 | −1.25089 | ||||||||
\(189\) | −1.31478e14 | −0.209823 | ||||||||
\(190\) | 8.84384e14 | 1.36377 | ||||||||
\(191\) | 5.67015e14 | 0.845041 | 0.422521 | − | 0.906353i | \(-0.361145\pi\) | ||||
0.422521 | + | 0.906353i | \(0.361145\pi\) | |||||||
\(192\) | −6.38796e14 | −0.920247 | ||||||||
\(193\) | 5.03814e14 | 0.701694 | 0.350847 | − | 0.936433i | \(-0.385894\pi\) | ||||
0.350847 | + | 0.936433i | \(0.385894\pi\) | |||||||
\(194\) | −1.39447e15 | −1.87801 | ||||||||
\(195\) | 4.96271e14 | 0.646388 | ||||||||
\(196\) | 2.13742e14 | 0.269293 | ||||||||
\(197\) | 1.05639e15 | 1.28764 | 0.643821 | − | 0.765176i | \(-0.277348\pi\) | ||||
0.643821 | + | 0.765176i | \(0.277348\pi\) | |||||||
\(198\) | −2.67815e14 | −0.315872 | ||||||||
\(199\) | 1.18175e15 | 1.34891 | 0.674454 | − | 0.738317i | \(-0.264379\pi\) | ||||
0.674454 | + | 0.738317i | \(0.264379\pi\) | |||||||
\(200\) | 7.96890e13 | 0.0880448 | ||||||||
\(201\) | −6.21528e14 | −0.664793 | ||||||||
\(202\) | −8.31859e14 | −0.861521 | ||||||||
\(203\) | 1.72667e14 | 0.173175 | ||||||||
\(204\) | 7.74987e13 | 0.0752833 | ||||||||
\(205\) | −1.35655e15 | −1.27654 | ||||||||
\(206\) | −2.87572e15 | −2.62186 | ||||||||
\(207\) | −4.36471e14 | −0.385610 | ||||||||
\(208\) | 5.47971e14 | 0.469187 | ||||||||
\(209\) | 6.88720e14 | 0.571599 | ||||||||
\(210\) | −1.13536e15 | −0.913499 | ||||||||
\(211\) | 8.28907e14 | 0.646651 | 0.323326 | − | 0.946288i | \(-0.395199\pi\) | ||||
0.323326 | + | 0.946288i | \(0.395199\pi\) | |||||||
\(212\) | 9.67405e14 | 0.731855 | ||||||||
\(213\) | −1.08933e15 | −0.799270 | ||||||||
\(214\) | 1.44287e15 | 1.02692 | ||||||||
\(215\) | −2.24274e15 | −1.54857 | ||||||||
\(216\) | −1.91166e14 | −0.128074 | ||||||||
\(217\) | −1.46621e15 | −0.953252 | ||||||||
\(218\) | −2.83567e15 | −1.78932 | ||||||||
\(219\) | 8.81283e13 | 0.0539795 | ||||||||
\(220\) | −1.35984e15 | −0.808614 | ||||||||
\(221\) | −1.90198e14 | −0.109813 | ||||||||
\(222\) | 6.93106e14 | 0.388602 | ||||||||
\(223\) | −2.60795e15 | −1.42010 | −0.710048 | − | 0.704153i | \(-0.751327\pi\) | ||||
−0.710048 | + | 0.704153i | \(0.751327\pi\) | |||||||
\(224\) | −2.62543e15 | −1.38864 | ||||||||
\(225\) | −8.58275e13 | −0.0441001 | ||||||||
\(226\) | 5.70606e15 | 2.84860 | ||||||||
\(227\) | 3.19516e15 | 1.54997 | 0.774987 | − | 0.631978i | \(-0.217757\pi\) | ||||
0.774987 | + | 0.631978i | \(0.217757\pi\) | |||||||
\(228\) | 1.64247e15 | 0.774321 | ||||||||
\(229\) | −2.26829e15 | −1.03936 | −0.519682 | − | 0.854360i | \(-0.673950\pi\) | ||||
−0.519682 | + | 0.854360i | \(0.673950\pi\) | |||||||
\(230\) | −3.76908e15 | −1.67882 | ||||||||
\(231\) | −8.84168e14 | −0.382875 | ||||||||
\(232\) | 2.51052e14 | 0.105704 | ||||||||
\(233\) | −3.28473e15 | −1.34489 | −0.672443 | − | 0.740149i | \(-0.734755\pi\) | ||||
−0.672443 | + | 0.740149i | \(0.734755\pi\) | |||||||
\(234\) | 1.56748e15 | 0.624162 | ||||||||
\(235\) | 2.10801e15 | 0.816453 | ||||||||
\(236\) | 4.93146e14 | 0.185801 | ||||||||
\(237\) | 2.43803e15 | 0.893664 | ||||||||
\(238\) | 4.35131e14 | 0.155192 | ||||||||
\(239\) | −8.22938e14 | −0.285615 | −0.142807 | − | 0.989751i | \(-0.545613\pi\) | ||||
−0.142807 | + | 0.989751i | \(0.545613\pi\) | |||||||
\(240\) | 6.21546e14 | 0.209942 | ||||||||
\(241\) | −3.01011e13 | −0.00989626 | −0.00494813 | − | 0.999988i | \(-0.501575\pi\) | ||||
−0.00494813 | + | 0.999988i | \(0.501575\pi\) | |||||||
\(242\) | 3.06698e15 | 0.981546 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −4.46319e15 | −1.35398 | ||||||||
\(245\) | −5.94999e14 | −0.175767 | ||||||||
\(246\) | −4.28467e15 | −1.23265 | ||||||||
\(247\) | −4.03096e15 | −1.12948 | ||||||||
\(248\) | −2.13183e15 | −0.581856 | ||||||||
\(249\) | 1.99880e15 | 0.531462 | ||||||||
\(250\) | −6.34316e15 | −1.64322 | ||||||||
\(251\) | −5.39725e15 | −1.36236 | −0.681182 | − | 0.732114i | \(-0.738534\pi\) | ||||
−0.681182 | + | 0.732114i | \(0.738534\pi\) | |||||||
\(252\) | −2.10858e15 | −0.518665 | ||||||||
\(253\) | −2.93519e15 | −0.703644 | ||||||||
\(254\) | −6.48294e15 | −1.51479 | ||||||||
\(255\) | −2.15735e14 | −0.0491371 | ||||||||
\(256\) | −1.30825e15 | −0.290490 | ||||||||
\(257\) | −2.41508e15 | −0.522837 | −0.261419 | − | 0.965226i | \(-0.584190\pi\) | ||||
−0.261419 | + | 0.965226i | \(0.584190\pi\) | |||||||
\(258\) | −7.08373e15 | −1.49532 | ||||||||
\(259\) | 2.28823e15 | 0.471033 | ||||||||
\(260\) | 7.95892e15 | 1.59782 | ||||||||
\(261\) | −2.70391e14 | −0.0529454 | ||||||||
\(262\) | −8.89888e15 | −1.69972 | ||||||||
\(263\) | −6.62502e15 | −1.23445 | −0.617227 | − | 0.786785i | \(-0.711744\pi\) | ||||
−0.617227 | + | 0.786785i | \(0.711744\pi\) | |||||||
\(264\) | −1.28555e15 | −0.233703 | ||||||||
\(265\) | −2.69299e15 | −0.477679 | ||||||||
\(266\) | 9.22196e15 | 1.59622 | ||||||||
\(267\) | 3.81898e15 | 0.645096 | ||||||||
\(268\) | −9.96774e15 | −1.64331 | ||||||||
\(269\) | −2.15137e15 | −0.346199 | −0.173100 | − | 0.984904i | \(-0.555378\pi\) | ||||
−0.173100 | + | 0.984904i | \(0.555378\pi\) | |||||||
\(270\) | 1.77794e15 | 0.279288 | ||||||||
\(271\) | −4.01545e15 | −0.615792 | −0.307896 | − | 0.951420i | \(-0.599625\pi\) | ||||
−0.307896 | + | 0.951420i | \(0.599625\pi\) | |||||||
\(272\) | −2.38210e14 | −0.0356666 | ||||||||
\(273\) | 5.17488e15 | 0.756560 | ||||||||
\(274\) | 7.26346e15 | 1.03697 | ||||||||
\(275\) | −5.77174e14 | −0.0804719 | ||||||||
\(276\) | −6.99990e15 | −0.953197 | ||||||||
\(277\) | 1.33580e15 | 0.177674 | 0.0888369 | − | 0.996046i | \(-0.471685\pi\) | ||||
0.0888369 | + | 0.996046i | \(0.471685\pi\) | |||||||
\(278\) | −3.10986e15 | −0.404063 | ||||||||
\(279\) | 2.29604e15 | 0.291442 | ||||||||
\(280\) | −5.44990e15 | −0.675868 | ||||||||
\(281\) | 1.02666e16 | 1.24405 | 0.622024 | − | 0.782998i | \(-0.286311\pi\) | ||||
0.622024 | + | 0.782998i | \(0.286311\pi\) | |||||||
\(282\) | 6.65816e15 | 0.788379 | ||||||||
\(283\) | 5.11351e15 | 0.591708 | 0.295854 | − | 0.955233i | \(-0.404396\pi\) | ||||
0.295854 | + | 0.955233i | \(0.404396\pi\) | |||||||
\(284\) | −1.74702e16 | −1.97573 | ||||||||
\(285\) | −4.57219e15 | −0.505397 | ||||||||
\(286\) | 1.05410e16 | 1.13894 | ||||||||
\(287\) | −1.41455e16 | −1.49412 | ||||||||
\(288\) | 4.11135e15 | 0.424554 | ||||||||
\(289\) | −9.82190e15 | −0.991652 | ||||||||
\(290\) | −2.33491e15 | −0.230507 | ||||||||
\(291\) | 7.20928e15 | 0.695965 | ||||||||
\(292\) | 1.41335e15 | 0.133433 | ||||||||
\(293\) | −1.05264e16 | −0.971942 | −0.485971 | − | 0.873975i | \(-0.661534\pi\) | ||||
−0.485971 | + | 0.873975i | \(0.661534\pi\) | |||||||
\(294\) | −1.87931e15 | −0.169723 | ||||||||
\(295\) | −1.37278e15 | −0.121271 | ||||||||
\(296\) | 3.32702e15 | 0.287514 | ||||||||
\(297\) | 1.38458e15 | 0.117058 | ||||||||
\(298\) | 7.10002e15 | 0.587292 | ||||||||
\(299\) | 1.71792e16 | 1.39040 | ||||||||
\(300\) | −1.37646e15 | −0.109012 | ||||||||
\(301\) | −2.33863e16 | −1.81251 | ||||||||
\(302\) | −1.70136e16 | −1.29048 | ||||||||
\(303\) | 4.30064e15 | 0.319268 | ||||||||
\(304\) | −5.04851e15 | −0.366847 | ||||||||
\(305\) | 1.24243e16 | 0.883736 | ||||||||
\(306\) | −6.81401e14 | −0.0474475 | ||||||||
\(307\) | 1.98222e15 | 0.135130 | 0.0675651 | − | 0.997715i | \(-0.478477\pi\) | ||||
0.0675651 | + | 0.997715i | \(0.478477\pi\) | |||||||
\(308\) | −1.41798e16 | −0.946436 | ||||||||
\(309\) | 1.48672e16 | 0.971628 | ||||||||
\(310\) | 1.98271e16 | 1.26884 | ||||||||
\(311\) | 1.40014e16 | 0.877461 | 0.438731 | − | 0.898619i | \(-0.355428\pi\) | ||||
0.438731 | + | 0.898619i | \(0.355428\pi\) | |||||||
\(312\) | 7.52413e15 | 0.461797 | ||||||||
\(313\) | 3.90874e15 | 0.234963 | 0.117481 | − | 0.993075i | \(-0.462518\pi\) | ||||
0.117481 | + | 0.993075i | \(0.462518\pi\) | |||||||
\(314\) | 8.59186e15 | 0.505877 | ||||||||
\(315\) | 5.86971e15 | 0.338531 | ||||||||
\(316\) | 3.90998e16 | 2.20906 | ||||||||
\(317\) | −2.27057e16 | −1.25675 | −0.628377 | − | 0.777909i | \(-0.716281\pi\) | ||||
−0.628377 | + | 0.777909i | \(0.716281\pi\) | |||||||
\(318\) | −8.50583e15 | −0.461255 | ||||||||
\(319\) | −1.81833e15 | −0.0966124 | ||||||||
\(320\) | 2.85183e16 | 1.48474 | ||||||||
\(321\) | −7.45950e15 | −0.380564 | ||||||||
\(322\) | −3.93022e16 | −1.96496 | ||||||||
\(323\) | 1.75231e15 | 0.0858606 | ||||||||
\(324\) | 3.30197e15 | 0.158574 | ||||||||
\(325\) | 3.37810e15 | 0.159012 | ||||||||
\(326\) | −2.04915e16 | −0.945495 | ||||||||
\(327\) | 1.46602e16 | 0.663099 | ||||||||
\(328\) | −2.05671e16 | −0.911995 | ||||||||
\(329\) | 2.19813e16 | 0.955610 | ||||||||
\(330\) | 1.19563e16 | 0.509632 | ||||||||
\(331\) | 2.83737e14 | 0.0118586 | 0.00592932 | − | 0.999982i | \(-0.498113\pi\) | ||||
0.00592932 | + | 0.999982i | \(0.498113\pi\) | |||||||
\(332\) | 3.20556e16 | 1.31373 | ||||||||
\(333\) | −3.58330e15 | −0.144011 | ||||||||
\(334\) | 2.64734e16 | 1.04342 | ||||||||
\(335\) | 2.77474e16 | 1.07259 | ||||||||
\(336\) | 6.48120e15 | 0.245725 | ||||||||
\(337\) | −1.94267e16 | −0.722445 | −0.361222 | − | 0.932480i | \(-0.617641\pi\) | ||||
−0.361222 | + | 0.932480i | \(0.617641\pi\) | |||||||
\(338\) | −1.89867e16 | −0.692613 | ||||||||
\(339\) | −2.94998e16 | −1.05565 | ||||||||
\(340\) | −3.45985e15 | −0.121463 | ||||||||
\(341\) | 1.54405e16 | 0.531810 | ||||||||
\(342\) | −1.44413e16 | −0.488019 | ||||||||
\(343\) | 2.66767e16 | 0.884546 | ||||||||
\(344\) | −3.40030e16 | −1.10634 | ||||||||
\(345\) | 1.94858e16 | 0.622148 | ||||||||
\(346\) | 8.51852e16 | 2.66913 | ||||||||
\(347\) | −9.23354e15 | −0.283940 | −0.141970 | − | 0.989871i | \(-0.545344\pi\) | ||||
−0.141970 | + | 0.989871i | \(0.545344\pi\) | |||||||
\(348\) | −4.33638e15 | −0.130877 | ||||||||
\(349\) | −4.15080e16 | −1.22961 | −0.614803 | − | 0.788681i | \(-0.710765\pi\) | ||||
−0.614803 | + | 0.788681i | \(0.710765\pi\) | |||||||
\(350\) | −7.72836e15 | −0.224722 | ||||||||
\(351\) | −8.10371e15 | −0.231306 | ||||||||
\(352\) | 2.76481e16 | 0.774707 | ||||||||
\(353\) | 1.29564e15 | 0.0356410 | 0.0178205 | − | 0.999841i | \(-0.494327\pi\) | ||||
0.0178205 | + | 0.999841i | \(0.494327\pi\) | |||||||
\(354\) | −4.33595e15 | −0.117102 | ||||||||
\(355\) | 4.86321e16 | 1.28955 | ||||||||
\(356\) | 6.12468e16 | 1.59463 | ||||||||
\(357\) | −2.24959e15 | −0.0575121 | ||||||||
\(358\) | 8.63057e16 | 2.16671 | ||||||||
\(359\) | −4.33504e16 | −1.06876 | −0.534379 | − | 0.845245i | \(-0.679454\pi\) | ||||
−0.534379 | + | 0.845245i | \(0.679454\pi\) | |||||||
\(360\) | 8.53438e15 | 0.206636 | ||||||||
\(361\) | −4.91539e15 | −0.116886 | ||||||||
\(362\) | −1.07374e17 | −2.50780 | ||||||||
\(363\) | −1.58560e16 | −0.363748 | ||||||||
\(364\) | 8.29920e16 | 1.87015 | ||||||||
\(365\) | −3.93439e15 | −0.0870911 | ||||||||
\(366\) | 3.92422e16 | 0.853349 | ||||||||
\(367\) | −6.62560e16 | −1.41545 | −0.707727 | − | 0.706486i | \(-0.750279\pi\) | ||||
−0.707727 | + | 0.706486i | \(0.750279\pi\) | |||||||
\(368\) | 2.15158e16 | 0.451592 | ||||||||
\(369\) | 2.21513e16 | 0.456803 | ||||||||
\(370\) | −3.09430e16 | −0.626976 | ||||||||
\(371\) | −2.80813e16 | −0.559096 | ||||||||
\(372\) | 3.68227e16 | 0.720421 | ||||||||
\(373\) | −6.77688e16 | −1.30293 | −0.651467 | − | 0.758677i | \(-0.725846\pi\) | ||||
−0.651467 | + | 0.758677i | \(0.725846\pi\) | |||||||
\(374\) | −4.58230e15 | −0.0865801 | ||||||||
\(375\) | 3.27936e16 | 0.608956 | ||||||||
\(376\) | 3.19602e16 | 0.583296 | ||||||||
\(377\) | 1.06424e16 | 0.190906 | ||||||||
\(378\) | 1.85395e16 | 0.326890 | ||||||||
\(379\) | 3.45510e15 | 0.0598834 | 0.0299417 | − | 0.999552i | \(-0.490468\pi\) | ||||
0.0299417 | + | 0.999552i | \(0.490468\pi\) | |||||||
\(380\) | −7.33263e16 | −1.24930 | ||||||||
\(381\) | 3.35162e16 | 0.561362 | ||||||||
\(382\) | −7.99538e16 | −1.31652 | ||||||||
\(383\) | −4.03416e16 | −0.653072 | −0.326536 | − | 0.945185i | \(-0.605881\pi\) | ||||
−0.326536 | + | 0.945185i | \(0.605881\pi\) | |||||||
\(384\) | 4.38750e16 | 0.698335 | ||||||||
\(385\) | 3.94727e16 | 0.617735 | ||||||||
\(386\) | −7.10419e16 | −1.09319 | ||||||||
\(387\) | 3.66222e16 | 0.554145 | ||||||||
\(388\) | 1.15619e17 | 1.72037 | ||||||||
\(389\) | −4.77579e16 | −0.698832 | −0.349416 | − | 0.936968i | \(-0.613620\pi\) | ||||
−0.349416 | + | 0.936968i | \(0.613620\pi\) | |||||||
\(390\) | −6.99782e16 | −1.00703 | ||||||||
\(391\) | −7.46800e15 | −0.105695 | ||||||||
\(392\) | −9.02098e15 | −0.125572 | ||||||||
\(393\) | 4.60064e16 | 0.629893 | ||||||||
\(394\) | −1.48960e17 | −2.00606 | ||||||||
\(395\) | −1.08843e17 | −1.44185 | ||||||||
\(396\) | 2.22052e16 | 0.289358 | ||||||||
\(397\) | −8.13622e16 | −1.04300 | −0.521500 | − | 0.853251i | \(-0.674627\pi\) | ||||
−0.521500 | + | 0.853251i | \(0.674627\pi\) | |||||||
\(398\) | −1.66637e17 | −2.10151 | ||||||||
\(399\) | −4.76767e16 | −0.591538 | ||||||||
\(400\) | 4.23085e15 | 0.0516461 | ||||||||
\(401\) | −6.34120e16 | −0.761610 | −0.380805 | − | 0.924655i | \(-0.624353\pi\) | ||||
−0.380805 | + | 0.924655i | \(0.624353\pi\) | |||||||
\(402\) | 8.76406e16 | 1.03570 | ||||||||
\(403\) | −9.03703e16 | −1.05086 | ||||||||
\(404\) | 6.89714e16 | 0.789205 | ||||||||
\(405\) | −9.19178e15 | −0.103500 | ||||||||
\(406\) | −2.43474e16 | −0.269795 | ||||||||
\(407\) | −2.40970e16 | −0.262784 | ||||||||
\(408\) | −3.27083e15 | −0.0351049 | ||||||||
\(409\) | −1.46971e17 | −1.55250 | −0.776248 | − | 0.630427i | \(-0.782880\pi\) | ||||
−0.776248 | + | 0.630427i | \(0.782880\pi\) | |||||||
\(410\) | 1.91284e17 | 1.98877 | ||||||||
\(411\) | −3.75514e16 | −0.384286 | ||||||||
\(412\) | 2.38433e17 | 2.40178 | ||||||||
\(413\) | −1.43148e16 | −0.141941 | ||||||||
\(414\) | 6.15460e16 | 0.600756 | ||||||||
\(415\) | −8.92340e16 | −0.857468 | ||||||||
\(416\) | −1.61819e17 | −1.53082 | ||||||||
\(417\) | 1.60777e16 | 0.149740 | ||||||||
\(418\) | −9.71151e16 | −0.890515 | ||||||||
\(419\) | −8.53034e16 | −0.770150 | −0.385075 | − | 0.922885i | \(-0.625824\pi\) | ||||
−0.385075 | + | 0.922885i | \(0.625824\pi\) | |||||||
\(420\) | 9.41353e16 | 0.836820 | ||||||||
\(421\) | 4.86032e16 | 0.425433 | 0.212716 | − | 0.977114i | \(-0.431769\pi\) | ||||
0.212716 | + | 0.977114i | \(0.431769\pi\) | |||||||
\(422\) | −1.16883e17 | −1.00744 | ||||||||
\(423\) | −3.44221e16 | −0.292163 | ||||||||
\(424\) | −4.08293e16 | −0.341267 | ||||||||
\(425\) | −1.46850e15 | −0.0120878 | ||||||||
\(426\) | 1.53605e17 | 1.24521 | ||||||||
\(427\) | 1.29555e17 | 1.03436 | ||||||||
\(428\) | −1.19632e17 | −0.940722 | ||||||||
\(429\) | −5.44960e16 | −0.422077 | ||||||||
\(430\) | 3.16245e17 | 2.41257 | ||||||||
\(431\) | 1.32000e17 | 0.991910 | 0.495955 | − | 0.868348i | \(-0.334818\pi\) | ||||
0.495955 | + | 0.868348i | \(0.334818\pi\) | |||||||
\(432\) | −1.01494e16 | −0.0751267 | ||||||||
\(433\) | 9.75130e16 | 0.711036 | 0.355518 | − | 0.934670i | \(-0.384305\pi\) | ||||
0.355518 | + | 0.934670i | \(0.384305\pi\) | |||||||
\(434\) | 2.06748e17 | 1.48511 | ||||||||
\(435\) | 1.20713e16 | 0.0854228 | ||||||||
\(436\) | 2.35112e17 | 1.63913 | ||||||||
\(437\) | −1.58273e17 | −1.08712 | ||||||||
\(438\) | −1.24268e16 | −0.0840965 | ||||||||
\(439\) | 4.19591e16 | 0.279774 | 0.139887 | − | 0.990167i | \(-0.455326\pi\) | ||||
0.139887 | + | 0.990167i | \(0.455326\pi\) | |||||||
\(440\) | 5.73922e16 | 0.377060 | ||||||||
\(441\) | 9.71587e15 | 0.0628971 | ||||||||
\(442\) | 2.68194e16 | 0.171082 | ||||||||
\(443\) | −1.52350e17 | −0.957677 | −0.478839 | − | 0.877903i | \(-0.658942\pi\) | ||||
−0.478839 | + | 0.877903i | \(0.658942\pi\) | |||||||
\(444\) | −5.74670e16 | −0.355983 | ||||||||
\(445\) | −1.70494e17 | −1.04081 | ||||||||
\(446\) | 3.67742e17 | 2.21242 | ||||||||
\(447\) | −3.67065e16 | −0.217643 | ||||||||
\(448\) | 2.97376e17 | 1.73780 | ||||||||
\(449\) | −2.14314e17 | −1.23438 | −0.617190 | − | 0.786814i | \(-0.711729\pi\) | ||||
−0.617190 | + | 0.786814i | \(0.711729\pi\) | |||||||
\(450\) | 1.21024e16 | 0.0687051 | ||||||||
\(451\) | 1.48964e17 | 0.833553 | ||||||||
\(452\) | −4.73103e17 | −2.60949 | ||||||||
\(453\) | 8.79588e16 | 0.478235 | ||||||||
\(454\) | −4.50543e17 | −2.41476 | ||||||||
\(455\) | −2.31027e17 | −1.22064 | ||||||||
\(456\) | −6.93205e16 | −0.361069 | ||||||||
\(457\) | 3.07100e17 | 1.57697 | 0.788486 | − | 0.615052i | \(-0.210865\pi\) | ||||
0.788486 | + | 0.615052i | \(0.210865\pi\) | |||||||
\(458\) | 3.19847e17 | 1.61926 | ||||||||
\(459\) | 3.52279e15 | 0.0175834 | ||||||||
\(460\) | 3.12503e17 | 1.53790 | ||||||||
\(461\) | −2.40168e17 | −1.16536 | −0.582678 | − | 0.812703i | \(-0.697995\pi\) | ||||
−0.582678 | + | 0.812703i | \(0.697995\pi\) | |||||||
\(462\) | 1.24675e17 | 0.596495 | ||||||||
\(463\) | −2.41166e17 | −1.13773 | −0.568865 | − | 0.822431i | \(-0.692617\pi\) | ||||
−0.568865 | + | 0.822431i | \(0.692617\pi\) | |||||||
\(464\) | 1.33289e16 | 0.0620049 | ||||||||
\(465\) | −1.02504e17 | −0.470216 | ||||||||
\(466\) | 4.63173e17 | 2.09525 | ||||||||
\(467\) | 2.51988e17 | 1.12414 | 0.562070 | − | 0.827090i | \(-0.310005\pi\) | ||||
0.562070 | + | 0.827090i | \(0.310005\pi\) | |||||||
\(468\) | −1.29963e17 | −0.571770 | ||||||||
\(469\) | 2.89338e17 | 1.25540 | ||||||||
\(470\) | −2.97246e17 | −1.27198 | ||||||||
\(471\) | −4.44192e16 | −0.187471 | ||||||||
\(472\) | −2.08132e16 | −0.0866396 | ||||||||
\(473\) | 2.46278e17 | 1.01118 | ||||||||
\(474\) | −3.43782e17 | −1.39227 | ||||||||
\(475\) | −3.11228e16 | −0.124328 | ||||||||
\(476\) | −3.60777e16 | −0.142165 | ||||||||
\(477\) | 4.39744e16 | 0.170935 | ||||||||
\(478\) | 1.16041e17 | 0.444969 | ||||||||
\(479\) | 6.98532e16 | 0.264244 | 0.132122 | − | 0.991233i | \(-0.457821\pi\) | ||||
0.132122 | + | 0.991233i | \(0.457821\pi\) | |||||||
\(480\) | −1.83547e17 | −0.684981 | ||||||||
\(481\) | 1.41036e17 | 0.519261 | ||||||||
\(482\) | 4.24450e15 | 0.0154177 | ||||||||
\(483\) | 2.03189e17 | 0.728188 | ||||||||
\(484\) | −2.54290e17 | −0.899155 | ||||||||
\(485\) | −3.21850e17 | −1.12288 | ||||||||
\(486\) | −2.90323e16 | −0.0999416 | ||||||||
\(487\) | −1.64688e16 | −0.0559402 | −0.0279701 | − | 0.999609i | \(-0.508904\pi\) | ||||
−0.0279701 | + | 0.999609i | \(0.508904\pi\) | |||||||
\(488\) | 1.88369e17 | 0.631365 | ||||||||
\(489\) | 1.05939e17 | 0.350388 | ||||||||
\(490\) | 8.38997e16 | 0.273833 | ||||||||
\(491\) | −1.43797e17 | −0.463149 | −0.231574 | − | 0.972817i | \(-0.574388\pi\) | ||||
−0.231574 | + | 0.972817i | \(0.574388\pi\) | |||||||
\(492\) | 3.55252e17 | 1.12918 | ||||||||
\(493\) | −4.62637e15 | −0.0145123 | ||||||||
\(494\) | 5.68398e17 | 1.75965 | ||||||||
\(495\) | −6.18131e16 | −0.188863 | ||||||||
\(496\) | −1.13183e17 | −0.341310 | ||||||||
\(497\) | 5.07114e17 | 1.50935 | ||||||||
\(498\) | −2.81847e17 | −0.827984 | ||||||||
\(499\) | 1.98943e17 | 0.576867 | 0.288434 | − | 0.957500i | \(-0.406866\pi\) | ||||
0.288434 | + | 0.957500i | \(0.406866\pi\) | |||||||
\(500\) | 5.25926e17 | 1.50529 | ||||||||
\(501\) | −1.36865e17 | −0.386676 | ||||||||
\(502\) | 7.61056e17 | 2.12247 | ||||||||
\(503\) | −5.36371e17 | −1.47664 | −0.738318 | − | 0.674453i | \(-0.764379\pi\) | ||||
−0.738318 | + | 0.674453i | \(0.764379\pi\) | |||||||
\(504\) | 8.89927e16 | 0.241855 | ||||||||
\(505\) | −1.91997e17 | −0.515112 | ||||||||
\(506\) | 4.13886e17 | 1.09623 | ||||||||
\(507\) | 9.81595e16 | 0.256673 | ||||||||
\(508\) | 5.37516e17 | 1.38764 | ||||||||
\(509\) | 2.34622e17 | 0.598002 | 0.299001 | − | 0.954253i | \(-0.403347\pi\) | ||||
0.299001 | + | 0.954253i | \(0.403347\pi\) | |||||||
\(510\) | 3.04204e16 | 0.0765524 | ||||||||
\(511\) | −4.10260e16 | −0.101935 | ||||||||
\(512\) | −3.08563e17 | −0.756987 | ||||||||
\(513\) | 7.46603e16 | 0.180853 | ||||||||
\(514\) | 3.40546e17 | 0.814546 | ||||||||
\(515\) | −6.63731e17 | −1.56764 | ||||||||
\(516\) | 5.87328e17 | 1.36980 | ||||||||
\(517\) | −2.31482e17 | −0.533126 | ||||||||
\(518\) | −3.22659e17 | −0.733838 | ||||||||
\(519\) | −4.40400e17 | −0.989143 | ||||||||
\(520\) | −3.35906e17 | −0.745069 | ||||||||
\(521\) | 8.13954e17 | 1.78301 | 0.891507 | − | 0.453007i | \(-0.149649\pi\) | ||||
0.891507 | + | 0.453007i | \(0.149649\pi\) | |||||||
\(522\) | 3.81273e16 | 0.0824856 | ||||||||
\(523\) | 2.03568e17 | 0.434959 | 0.217480 | − | 0.976065i | \(-0.430216\pi\) | ||||
0.217480 | + | 0.976065i | \(0.430216\pi\) | |||||||
\(524\) | 7.37827e17 | 1.55704 | ||||||||
\(525\) | 3.99549e16 | 0.0832789 | ||||||||
\(526\) | 9.34182e17 | 1.92320 | ||||||||
\(527\) | 3.92851e16 | 0.0798838 | ||||||||
\(528\) | −6.82526e16 | −0.137088 | ||||||||
\(529\) | 1.70494e17 | 0.338257 | ||||||||
\(530\) | 3.79734e17 | 0.744194 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | −7.64614e17 | −1.46223 | ||||||||
\(533\) | −8.71859e17 | −1.64710 | ||||||||
\(534\) | −5.38508e17 | −1.00502 | ||||||||
\(535\) | 3.33021e17 | 0.614006 | ||||||||
\(536\) | 4.20689e17 | 0.766284 | ||||||||
\(537\) | −4.46193e17 | −0.802953 | ||||||||
\(538\) | 3.03361e17 | 0.539356 | ||||||||
\(539\) | 6.53374e16 | 0.114772 | ||||||||
\(540\) | −1.47413e17 | −0.255845 | ||||||||
\(541\) | −3.12937e17 | −0.536629 | −0.268315 | − | 0.963331i | \(-0.586467\pi\) | ||||
−0.268315 | + | 0.963331i | \(0.586467\pi\) | |||||||
\(542\) | 5.66211e17 | 0.959363 | ||||||||
\(543\) | 5.55114e17 | 0.929359 | ||||||||
\(544\) | 7.03449e16 | 0.116370 | ||||||||
\(545\) | −6.54487e17 | −1.06985 | ||||||||
\(546\) | −7.29701e17 | −1.17867 | ||||||||
\(547\) | 4.64466e16 | 0.0741372 | 0.0370686 | − | 0.999313i | \(-0.488198\pi\) | ||||
0.0370686 | + | 0.999313i | \(0.488198\pi\) | |||||||
\(548\) | −6.02230e17 | −0.949924 | ||||||||
\(549\) | −2.02879e17 | −0.316240 | ||||||||
\(550\) | 8.13863e16 | 0.125370 | ||||||||
\(551\) | −9.80491e16 | −0.149265 | ||||||||
\(552\) | 2.95431e17 | 0.444479 | ||||||||
\(553\) | −1.13497e18 | −1.68760 | ||||||||
\(554\) | −1.88359e17 | −0.276804 | ||||||||
\(555\) | 1.59972e17 | 0.232349 | ||||||||
\(556\) | 2.57845e17 | 0.370146 | ||||||||
\(557\) | 4.79880e17 | 0.680885 | 0.340442 | − | 0.940265i | \(-0.389423\pi\) | ||||
0.340442 | + | 0.940265i | \(0.389423\pi\) | |||||||
\(558\) | −3.23760e17 | −0.454048 | ||||||||
\(559\) | −1.44142e18 | −1.99809 | ||||||||
\(560\) | −2.89346e17 | −0.396456 | ||||||||
\(561\) | 2.36901e16 | 0.0320855 | ||||||||
\(562\) | −1.44768e18 | −1.93815 | ||||||||
\(563\) | −1.23803e18 | −1.63843 | −0.819215 | − | 0.573486i | \(-0.805591\pi\) | ||||
−0.819215 | + | 0.573486i | \(0.805591\pi\) | |||||||
\(564\) | −5.52043e17 | −0.722203 | ||||||||
\(565\) | 1.31699e18 | 1.70321 | ||||||||
\(566\) | −7.21047e17 | −0.921843 | ||||||||
\(567\) | −9.58478e16 | −0.121141 | ||||||||
\(568\) | 7.37328e17 | 0.921291 | ||||||||
\(569\) | −8.42942e17 | −1.04128 | −0.520641 | − | 0.853776i | \(-0.674307\pi\) | ||||
−0.520641 | + | 0.853776i | \(0.674307\pi\) | |||||||
\(570\) | 6.44716e17 | 0.787376 | ||||||||
\(571\) | 8.26813e16 | 0.0998326 | 0.0499163 | − | 0.998753i | \(-0.484105\pi\) | ||||
0.0499163 | + | 0.998753i | \(0.484105\pi\) | |||||||
\(572\) | −8.73977e17 | −1.04334 | ||||||||
\(573\) | 4.13354e17 | 0.487885 | ||||||||
\(574\) | 1.99463e18 | 2.32774 | ||||||||
\(575\) | 1.32639e17 | 0.153049 | ||||||||
\(576\) | −4.65682e17 | −0.531305 | ||||||||
\(577\) | 1.46434e17 | 0.165196 | 0.0825978 | − | 0.996583i | \(-0.473678\pi\) | ||||
0.0825978 | + | 0.996583i | \(0.473678\pi\) | |||||||
\(578\) | 1.38497e18 | 1.54493 | ||||||||
\(579\) | 3.67280e17 | 0.405123 | ||||||||
\(580\) | 1.93593e17 | 0.211158 | ||||||||
\(581\) | −9.30492e17 | −1.00362 | ||||||||
\(582\) | −1.01657e18 | −1.08427 | ||||||||
\(583\) | 2.95720e17 | 0.311914 | ||||||||
\(584\) | −5.96506e16 | −0.0622202 | ||||||||
\(585\) | 3.61781e17 | 0.373193 | ||||||||
\(586\) | 1.48431e18 | 1.51422 | ||||||||
\(587\) | −2.12057e17 | −0.213947 | −0.106973 | − | 0.994262i | \(-0.534116\pi\) | ||||
−0.106973 | + | 0.994262i | \(0.534116\pi\) | |||||||
\(588\) | 1.55818e17 | 0.155477 | ||||||||
\(589\) | 8.32590e17 | 0.821640 | ||||||||
\(590\) | 1.93574e17 | 0.188933 | ||||||||
\(591\) | 7.70111e17 | 0.743420 | ||||||||
\(592\) | 1.76638e17 | 0.168652 | ||||||||
\(593\) | 4.33421e16 | 0.0409312 | 0.0204656 | − | 0.999791i | \(-0.493485\pi\) | ||||
0.0204656 | + | 0.999791i | \(0.493485\pi\) | |||||||
\(594\) | −1.95237e17 | −0.182369 | ||||||||
\(595\) | 1.00430e17 | 0.0927908 | ||||||||
\(596\) | −5.88679e17 | −0.537995 | ||||||||
\(597\) | 8.61499e17 | 0.778792 | ||||||||
\(598\) | −2.42240e18 | −2.16615 | ||||||||
\(599\) | 7.59124e17 | 0.671489 | 0.335744 | − | 0.941953i | \(-0.391012\pi\) | ||||
0.335744 | + | 0.941953i | \(0.391012\pi\) | |||||||
\(600\) | 5.80933e16 | 0.0508327 | ||||||||
\(601\) | 7.45965e17 | 0.645705 | 0.322853 | − | 0.946449i | \(-0.395358\pi\) | ||||
0.322853 | + | 0.946449i | \(0.395358\pi\) | |||||||
\(602\) | 3.29766e18 | 2.82377 | ||||||||
\(603\) | −4.53094e17 | −0.383818 | ||||||||
\(604\) | 1.41064e18 | 1.18216 | ||||||||
\(605\) | 7.07874e17 | 0.586876 | ||||||||
\(606\) | −6.06426e17 | −0.497400 | ||||||||
\(607\) | 1.44337e18 | 1.17126 | 0.585629 | − | 0.810579i | \(-0.300848\pi\) | ||||
0.585629 | + | 0.810579i | \(0.300848\pi\) | |||||||
\(608\) | 1.49086e18 | 1.19691 | ||||||||
\(609\) | 1.25874e17 | 0.0999825 | ||||||||
\(610\) | −1.75193e18 | −1.37680 | ||||||||
\(611\) | 1.35483e18 | 1.05345 | ||||||||
\(612\) | 5.64966e16 | 0.0434648 | ||||||||
\(613\) | −2.40464e18 | −1.83044 | −0.915221 | − | 0.402951i | \(-0.867984\pi\) | ||||
−0.915221 | + | 0.402951i | \(0.867984\pi\) | |||||||
\(614\) | −2.79509e17 | −0.210524 | ||||||||
\(615\) | −9.88923e17 | −0.737011 | ||||||||
\(616\) | 5.98460e17 | 0.441327 | ||||||||
\(617\) | 1.89253e17 | 0.138099 | 0.0690493 | − | 0.997613i | \(-0.478003\pi\) | ||||
0.0690493 | + | 0.997613i | \(0.478003\pi\) | |||||||
\(618\) | −2.09640e18 | −1.51373 | ||||||||
\(619\) | 4.43390e17 | 0.316808 | 0.158404 | − | 0.987374i | \(-0.449365\pi\) | ||||
0.158404 | + | 0.987374i | \(0.449365\pi\) | |||||||
\(620\) | −1.64391e18 | −1.16234 | ||||||||
\(621\) | −3.18188e17 | −0.222632 | ||||||||
\(622\) | −1.97431e18 | −1.36703 | ||||||||
\(623\) | −1.77784e18 | −1.21820 | ||||||||
\(624\) | 3.99471e17 | 0.270885 | ||||||||
\(625\) | −1.26689e18 | −0.850196 | ||||||||
\(626\) | −5.51165e17 | −0.366057 | ||||||||
\(627\) | 5.02077e17 | 0.330013 | ||||||||
\(628\) | −7.12371e17 | −0.463413 | ||||||||
\(629\) | −6.13100e16 | −0.0394732 | ||||||||
\(630\) | −8.27677e17 | −0.527409 | ||||||||
\(631\) | −2.89290e17 | −0.182450 | −0.0912248 | − | 0.995830i | \(-0.529078\pi\) | ||||
−0.0912248 | + | 0.995830i | \(0.529078\pi\) | |||||||
\(632\) | −1.65021e18 | −1.03009 | ||||||||
\(633\) | 6.04273e17 | 0.373344 | ||||||||
\(634\) | 3.20170e18 | 1.95794 | ||||||||
\(635\) | −1.49630e18 | −0.905708 | ||||||||
\(636\) | 7.05238e17 | 0.422537 | ||||||||
\(637\) | −3.82409e17 | −0.226789 | ||||||||
\(638\) | 2.56399e17 | 0.150516 | ||||||||
\(639\) | −7.94125e17 | −0.461459 | ||||||||
\(640\) | −1.95875e18 | −1.12670 | ||||||||
\(641\) | 1.36610e17 | 0.0777868 | 0.0388934 | − | 0.999243i | \(-0.487617\pi\) | ||||
0.0388934 | + | 0.999243i | \(0.487617\pi\) | |||||||
\(642\) | 1.05185e18 | 0.592894 | ||||||||
\(643\) | 2.08256e17 | 0.116205 | 0.0581026 | − | 0.998311i | \(-0.481495\pi\) | ||||
0.0581026 | + | 0.998311i | \(0.481495\pi\) | |||||||
\(644\) | 3.25864e18 | 1.80002 | ||||||||
\(645\) | −1.63496e18 | −0.894065 | ||||||||
\(646\) | −2.47090e17 | −0.133765 | ||||||||
\(647\) | 1.55341e18 | 0.832548 | 0.416274 | − | 0.909239i | \(-0.363336\pi\) | ||||
0.416274 | + | 0.909239i | \(0.363336\pi\) | |||||||
\(648\) | −1.39360e17 | −0.0739435 | ||||||||
\(649\) | 1.50747e17 | 0.0791876 | ||||||||
\(650\) | −4.76340e17 | −0.247731 | ||||||||
\(651\) | −1.06887e18 | −0.550361 | ||||||||
\(652\) | 1.69900e18 | 0.866131 | ||||||||
\(653\) | 2.82346e18 | 1.42510 | 0.712550 | − | 0.701621i | \(-0.247540\pi\) | ||||
0.712550 | + | 0.701621i | \(0.247540\pi\) | |||||||
\(654\) | −2.06720e18 | −1.03306 | ||||||||
\(655\) | −2.05391e18 | −1.01628 | ||||||||
\(656\) | −1.09195e18 | −0.534966 | ||||||||
\(657\) | 6.42455e16 | 0.0311651 | ||||||||
\(658\) | −3.09955e18 | −1.48878 | ||||||||
\(659\) | −1.08635e18 | −0.516674 | −0.258337 | − | 0.966055i | \(-0.583174\pi\) | ||||
−0.258337 | + | 0.966055i | \(0.583174\pi\) | |||||||
\(660\) | −9.91325e17 | −0.466854 | ||||||||
\(661\) | −4.65670e17 | −0.217154 | −0.108577 | − | 0.994088i | \(-0.534629\pi\) | ||||
−0.108577 | + | 0.994088i | \(0.534629\pi\) | |||||||
\(662\) | −4.00093e16 | −0.0184750 | ||||||||
\(663\) | −1.38654e17 | −0.0634008 | ||||||||
\(664\) | −1.35291e18 | −0.612598 | ||||||||
\(665\) | 2.12847e18 | 0.954394 | ||||||||
\(666\) | 5.05274e17 | 0.224360 | ||||||||
\(667\) | 4.17866e17 | 0.183747 | ||||||||
\(668\) | −2.19497e18 | −0.955832 | ||||||||
\(669\) | −1.90120e18 | −0.819893 | ||||||||
\(670\) | −3.91262e18 | −1.67102 | ||||||||
\(671\) | −1.36432e18 | −0.577060 | ||||||||
\(672\) | −1.91394e18 | −0.801730 | ||||||||
\(673\) | 1.31869e18 | 0.547072 | 0.273536 | − | 0.961862i | \(-0.411807\pi\) | ||||
0.273536 | + | 0.961862i | \(0.411807\pi\) | |||||||
\(674\) | 2.73932e18 | 1.12552 | ||||||||
\(675\) | −6.25682e16 | −0.0254612 | ||||||||
\(676\) | 1.57423e18 | 0.634475 | ||||||||
\(677\) | 4.38276e18 | 1.74953 | 0.874765 | − | 0.484547i | \(-0.161015\pi\) | ||||
0.874765 | + | 0.484547i | \(0.161015\pi\) | |||||||
\(678\) | 4.15972e18 | 1.64464 | ||||||||
\(679\) | −3.35611e18 | −1.31426 | ||||||||
\(680\) | 1.46023e17 | 0.0566386 | ||||||||
\(681\) | 2.32927e18 | 0.894877 | ||||||||
\(682\) | −2.17723e18 | −0.828526 | ||||||||
\(683\) | −2.95888e18 | −1.11530 | −0.557650 | − | 0.830076i | \(-0.688297\pi\) | ||||
−0.557650 | + | 0.830076i | \(0.688297\pi\) | |||||||
\(684\) | 1.19736e18 | 0.447055 | ||||||||
\(685\) | 1.67644e18 | 0.620012 | ||||||||
\(686\) | −3.76164e18 | −1.37807 | ||||||||
\(687\) | −1.65358e18 | −0.600077 | ||||||||
\(688\) | −1.80529e18 | −0.648965 | ||||||||
\(689\) | −1.73080e18 | −0.616341 | ||||||||
\(690\) | −2.74766e18 | −0.969267 | ||||||||
\(691\) | 1.39667e18 | 0.488073 | 0.244037 | − | 0.969766i | \(-0.421528\pi\) | ||||
0.244037 | + | 0.969766i | \(0.421528\pi\) | |||||||
\(692\) | −7.06290e18 | −2.44508 | ||||||||
\(693\) | −6.44559e17 | −0.221053 | ||||||||
\(694\) | 1.30201e18 | 0.442360 | ||||||||
\(695\) | −7.17771e17 | −0.241593 | ||||||||
\(696\) | 1.83017e17 | 0.0610284 | ||||||||
\(697\) | 3.79008e17 | 0.125209 | ||||||||
\(698\) | 5.85296e18 | 1.91565 | ||||||||
\(699\) | −2.39456e18 | −0.776471 | ||||||||
\(700\) | 6.40776e17 | 0.205859 | ||||||||
\(701\) | 3.20852e18 | 1.02126 | 0.510631 | − | 0.859800i | \(-0.329412\pi\) | ||||
0.510631 | + | 0.859800i | \(0.329412\pi\) | |||||||
\(702\) | 1.14269e18 | 0.360360 | ||||||||
\(703\) | −1.29938e18 | −0.405999 | ||||||||
\(704\) | −3.13163e18 | −0.969500 | ||||||||
\(705\) | 1.53674e18 | 0.471379 | ||||||||
\(706\) | −1.82697e17 | −0.0555264 | ||||||||
\(707\) | −2.00206e18 | −0.602908 | ||||||||
\(708\) | 3.59503e17 | 0.107272 | ||||||||
\(709\) | −3.96499e18 | −1.17231 | −0.586154 | − | 0.810200i | \(-0.699359\pi\) | ||||
−0.586154 | + | 0.810200i | \(0.699359\pi\) | |||||||
\(710\) | −6.85753e18 | −2.00904 | ||||||||
\(711\) | 1.77732e18 | 0.515957 | ||||||||
\(712\) | −2.58492e18 | −0.743580 | ||||||||
\(713\) | −3.54834e18 | −1.01145 | ||||||||
\(714\) | 3.17210e17 | 0.0896002 | ||||||||
\(715\) | 2.43291e18 | 0.680985 | ||||||||
\(716\) | −7.15581e18 | −1.98483 | ||||||||
\(717\) | −5.99922e17 | −0.164900 | ||||||||
\(718\) | 6.11276e18 | 1.66505 | ||||||||
\(719\) | 3.22681e17 | 0.0871036 | 0.0435518 | − | 0.999051i | \(-0.486133\pi\) | ||||
0.0435518 | + | 0.999051i | \(0.486133\pi\) | |||||||
\(720\) | 4.53107e17 | 0.121210 | ||||||||
\(721\) | −6.92109e18 | −1.83483 | ||||||||
\(722\) | 6.93110e17 | 0.182100 | ||||||||
\(723\) | −2.19437e16 | −0.00571361 | ||||||||
\(724\) | 8.90263e18 | 2.29730 | ||||||||
\(725\) | 8.21690e16 | 0.0210141 | ||||||||
\(726\) | 2.23583e18 | 0.566696 | ||||||||
\(727\) | −3.93382e18 | −0.988191 | −0.494095 | − | 0.869408i | \(-0.664501\pi\) | ||||
−0.494095 | + | 0.869408i | \(0.664501\pi\) | |||||||
\(728\) | −3.50268e18 | −0.872060 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 5.54781e17 | 0.135682 | ||||||||
\(731\) | 6.26604e17 | 0.151890 | ||||||||
\(732\) | −3.25366e18 | −0.781719 | ||||||||
\(733\) | −3.56933e18 | −0.849985 | −0.424993 | − | 0.905197i | \(-0.639723\pi\) | ||||
−0.424993 | + | 0.905197i | \(0.639723\pi\) | |||||||
\(734\) | 9.34264e18 | 2.20519 | ||||||||
\(735\) | −4.33754e17 | −0.101479 | ||||||||
\(736\) | −6.35375e18 | −1.47341 | ||||||||
\(737\) | −3.04698e18 | −0.700374 | ||||||||
\(738\) | −3.12352e18 | −0.711669 | ||||||||
\(739\) | −3.49941e18 | −0.790325 | −0.395163 | − | 0.918611i | \(-0.629312\pi\) | ||||
−0.395163 | + | 0.918611i | \(0.629312\pi\) | |||||||
\(740\) | 2.56555e18 | 0.574347 | ||||||||
\(741\) | −2.93857e18 | −0.652105 | ||||||||
\(742\) | 3.95969e18 | 0.871035 | ||||||||
\(743\) | −2.67608e18 | −0.583542 | −0.291771 | − | 0.956488i | \(-0.594244\pi\) | ||||
−0.291771 | + | 0.956488i | \(0.594244\pi\) | |||||||
\(744\) | −1.55410e18 | −0.335935 | ||||||||
\(745\) | 1.63872e18 | 0.351147 | ||||||||
\(746\) | 9.55596e18 | 2.02989 | ||||||||
\(747\) | 1.45712e18 | 0.306840 | ||||||||
\(748\) | 3.79929e17 | 0.0793126 | ||||||||
\(749\) | 3.47260e18 | 0.718658 | ||||||||
\(750\) | −4.62417e18 | −0.948714 | ||||||||
\(751\) | 5.54941e18 | 1.12872 | 0.564361 | − | 0.825528i | \(-0.309122\pi\) | ||||
0.564361 | + | 0.825528i | \(0.309122\pi\) | |||||||
\(752\) | 1.69683e18 | 0.342155 | ||||||||
\(753\) | −3.93459e18 | −0.786561 | ||||||||
\(754\) | −1.50066e18 | −0.297419 | ||||||||
\(755\) | −3.92683e18 | −0.771590 | ||||||||
\(756\) | −1.53716e18 | −0.299451 | ||||||||
\(757\) | −3.98699e18 | −0.770056 | −0.385028 | − | 0.922905i | \(-0.625808\pi\) | ||||
−0.385028 | + | 0.922905i | \(0.625808\pi\) | |||||||
\(758\) | −4.87198e17 | −0.0932944 | ||||||||
\(759\) | −2.13975e18 | −0.406249 | ||||||||
\(760\) | 3.09474e18 | 0.582553 | ||||||||
\(761\) | −4.32091e18 | −0.806445 | −0.403222 | − | 0.915102i | \(-0.632110\pi\) | ||||
−0.403222 | + | 0.915102i | \(0.632110\pi\) | |||||||
\(762\) | −4.72606e18 | −0.874566 | ||||||||
\(763\) | −6.82469e18 | −1.25220 | ||||||||
\(764\) | 6.62915e18 | 1.20601 | ||||||||
\(765\) | −1.57271e17 | −0.0283693 | ||||||||
\(766\) | 5.68850e18 | 1.01744 | ||||||||
\(767\) | −8.82294e17 | −0.156474 | ||||||||
\(768\) | −9.53715e17 | −0.167715 | ||||||||
\(769\) | −3.75159e18 | −0.654175 | −0.327088 | − | 0.944994i | \(-0.606067\pi\) | ||||
−0.327088 | + | 0.944994i | \(0.606067\pi\) | |||||||
\(770\) | −5.56598e18 | −0.962392 | ||||||||
\(771\) | −1.76059e18 | −0.301860 | ||||||||
\(772\) | 5.89025e18 | 1.00143 | ||||||||
\(773\) | 3.44844e18 | 0.581374 | 0.290687 | − | 0.956818i | \(-0.406116\pi\) | ||||
0.290687 | + | 0.956818i | \(0.406116\pi\) | |||||||
\(774\) | −5.16404e18 | −0.863323 | ||||||||
\(775\) | −6.97743e17 | −0.115674 | ||||||||
\(776\) | −4.87968e18 | −0.802214 | ||||||||
\(777\) | 1.66812e18 | 0.271951 | ||||||||
\(778\) | 6.73425e18 | 1.08873 | ||||||||
\(779\) | 8.03252e18 | 1.28783 | ||||||||
\(780\) | 5.80206e18 | 0.922501 | ||||||||
\(781\) | −5.34034e18 | −0.842049 | ||||||||
\(782\) | 1.05305e18 | 0.164666 | ||||||||
\(783\) | −1.97115e17 | −0.0305681 | ||||||||
\(784\) | −4.78942e17 | −0.0736594 | ||||||||
\(785\) | 1.98305e18 | 0.302468 | ||||||||
\(786\) | −6.48729e18 | −0.981333 | ||||||||
\(787\) | 5.71704e18 | 0.857701 | 0.428850 | − | 0.903376i | \(-0.358919\pi\) | ||||
0.428850 | + | 0.903376i | \(0.358919\pi\) | |||||||
\(788\) | 1.23506e19 | 1.83767 | ||||||||
\(789\) | −4.82964e18 | −0.712712 | ||||||||
\(790\) | 1.53478e19 | 2.24631 | ||||||||
\(791\) | 1.37330e19 | 1.99350 | ||||||||
\(792\) | −9.37169e17 | −0.134929 | ||||||||
\(793\) | 7.98515e18 | 1.14027 | ||||||||
\(794\) | 1.14727e19 | 1.62493 | ||||||||
\(795\) | −1.96319e18 | −0.275788 | ||||||||
\(796\) | 1.38163e19 | 1.92511 | ||||||||
\(797\) | −1.02867e19 | −1.42166 | −0.710829 | − | 0.703364i | \(-0.751680\pi\) | ||||
−0.710829 | + | 0.703364i | \(0.751680\pi\) | |||||||
\(798\) | 6.72281e18 | 0.921577 | ||||||||
\(799\) | −5.88960e17 | −0.0800814 | ||||||||
\(800\) | −1.24940e18 | −0.168506 | ||||||||
\(801\) | 2.78404e18 | 0.372447 | ||||||||
\(802\) | 8.94161e18 | 1.18654 | ||||||||
\(803\) | 4.32039e17 | 0.0568686 | ||||||||
\(804\) | −7.26648e18 | −0.948768 | ||||||||
\(805\) | −9.07115e18 | −1.17487 | ||||||||
\(806\) | 1.27430e19 | 1.63716 | ||||||||
\(807\) | −1.56835e18 | −0.199878 | ||||||||
\(808\) | −2.91094e18 | −0.368010 | ||||||||
\(809\) | 8.06911e18 | 1.01195 | 0.505977 | − | 0.862547i | \(-0.331132\pi\) | ||||
0.505977 | + | 0.862547i | \(0.331132\pi\) | |||||||
\(810\) | 1.29612e18 | 0.161247 | ||||||||
\(811\) | 1.58560e19 | 1.95685 | 0.978425 | − | 0.206603i | \(-0.0662407\pi\) | ||||
0.978425 | + | 0.206603i | \(0.0662407\pi\) | |||||||
\(812\) | 2.01870e18 | 0.247148 | ||||||||
\(813\) | −2.92726e18 | −0.355527 | ||||||||
\(814\) | 3.39788e18 | 0.409401 | ||||||||
\(815\) | −4.72954e18 | −0.565320 | ||||||||
\(816\) | −1.73655e17 | −0.0205921 | ||||||||
\(817\) | 1.32800e19 | 1.56226 | ||||||||
\(818\) | 2.07241e19 | 2.41869 | ||||||||
\(819\) | 3.77249e18 | 0.436800 | ||||||||
\(820\) | −1.58598e19 | −1.82183 | ||||||||
\(821\) | −1.61392e19 | −1.83929 | −0.919646 | − | 0.392749i | \(-0.871524\pi\) | ||||
−0.919646 | + | 0.392749i | \(0.871524\pi\) | |||||||
\(822\) | 5.29506e18 | 0.598693 | ||||||||
\(823\) | 1.13957e19 | 1.27833 | 0.639163 | − | 0.769071i | \(-0.279281\pi\) | ||||
0.639163 | + | 0.769071i | \(0.279281\pi\) | |||||||
\(824\) | −1.00631e19 | −1.11996 | ||||||||
\(825\) | −4.20760e17 | −0.0464605 | ||||||||
\(826\) | 2.01850e18 | 0.221135 | ||||||||
\(827\) | −3.46550e18 | −0.376686 | −0.188343 | − | 0.982103i | \(-0.560312\pi\) | ||||
−0.188343 | + | 0.982103i | \(0.560312\pi\) | |||||||
\(828\) | −5.10292e18 | −0.550328 | ||||||||
\(829\) | 2.23042e17 | 0.0238662 | 0.0119331 | − | 0.999929i | \(-0.496201\pi\) | ||||
0.0119331 | + | 0.999929i | \(0.496201\pi\) | |||||||
\(830\) | 1.25827e19 | 1.33588 | ||||||||
\(831\) | 9.73800e17 | 0.102580 | ||||||||
\(832\) | 1.83289e19 | 1.91573 | ||||||||
\(833\) | 1.66238e17 | 0.0172400 | ||||||||
\(834\) | −2.26709e18 | −0.233286 | ||||||||
\(835\) | 6.11020e18 | 0.623868 | ||||||||
\(836\) | 8.05204e18 | 0.815765 | ||||||||
\(837\) | 1.67381e18 | 0.168264 | ||||||||
\(838\) | 1.20285e19 | 1.19984 | ||||||||
\(839\) | −1.29547e19 | −1.28226 | −0.641128 | − | 0.767434i | \(-0.721533\pi\) | ||||
−0.641128 | + | 0.767434i | \(0.721533\pi\) | |||||||
\(840\) | −3.97298e18 | −0.390212 | ||||||||
\(841\) | −1.00018e19 | −0.974771 | ||||||||
\(842\) | −6.85345e18 | −0.662797 | ||||||||
\(843\) | 7.48438e18 | 0.718251 | ||||||||
\(844\) | 9.69102e18 | 0.922876 | ||||||||
\(845\) | −4.38222e18 | −0.414120 | ||||||||
\(846\) | 4.85380e18 | 0.455171 | ||||||||
\(847\) | 7.38139e18 | 0.686904 | ||||||||
\(848\) | −2.16771e18 | −0.200183 | ||||||||
\(849\) | 3.72775e18 | 0.341623 | ||||||||
\(850\) | 2.07071e17 | 0.0188320 | ||||||||
\(851\) | 5.53769e18 | 0.499788 | ||||||||
\(852\) | −1.27357e19 | −1.14069 | ||||||||
\(853\) | 2.04089e19 | 1.81406 | 0.907029 | − | 0.421069i | \(-0.138345\pi\) | ||||
0.907029 | + | 0.421069i | \(0.138345\pi\) | |||||||
\(854\) | −1.82683e19 | −1.61147 | ||||||||
\(855\) | −3.33313e18 | −0.291791 | ||||||||
\(856\) | 5.04905e18 | 0.438662 | ||||||||
\(857\) | −6.96086e17 | −0.0600188 | −0.0300094 | − | 0.999550i | \(-0.509554\pi\) | ||||
−0.0300094 | + | 0.999550i | \(0.509554\pi\) | |||||||
\(858\) | 7.68438e18 | 0.657569 | ||||||||
\(859\) | 1.63956e19 | 1.39242 | 0.696212 | − | 0.717836i | \(-0.254867\pi\) | ||||
0.696212 | + | 0.717836i | \(0.254867\pi\) | |||||||
\(860\) | −2.62206e19 | −2.21005 | ||||||||
\(861\) | −1.03120e19 | −0.862629 | ||||||||
\(862\) | −1.86131e19 | −1.54533 | ||||||||
\(863\) | 1.62974e19 | 1.34291 | 0.671457 | − | 0.741043i | \(-0.265669\pi\) | ||||
0.671457 | + | 0.741043i | \(0.265669\pi\) | |||||||
\(864\) | 2.99717e18 | 0.245116 | ||||||||
\(865\) | 1.96612e19 | 1.59590 | ||||||||
\(866\) | −1.37501e19 | −1.10775 | ||||||||
\(867\) | −7.16016e18 | −0.572531 | ||||||||
\(868\) | −1.71419e19 | −1.36045 | ||||||||
\(869\) | 1.19522e19 | 0.941495 | ||||||||
\(870\) | −1.70215e18 | −0.133083 | ||||||||
\(871\) | 1.78334e19 | 1.38394 | ||||||||
\(872\) | −9.92289e18 | −0.764331 | ||||||||
\(873\) | 5.25556e18 | 0.401816 | ||||||||
\(874\) | 2.23178e19 | 1.69367 | ||||||||
\(875\) | −1.52663e19 | −1.14996 | ||||||||
\(876\) | 1.03034e18 | 0.0770375 | ||||||||
\(877\) | −2.11466e19 | −1.56944 | −0.784718 | − | 0.619853i | \(-0.787192\pi\) | ||||
−0.784718 | + | 0.619853i | \(0.787192\pi\) | |||||||
\(878\) | −5.91658e18 | −0.435869 | ||||||||
\(879\) | −7.67375e18 | −0.561151 | ||||||||
\(880\) | 3.04706e18 | 0.221179 | ||||||||
\(881\) | 1.78682e19 | 1.28747 | 0.643734 | − | 0.765249i | \(-0.277384\pi\) | ||||
0.643734 | + | 0.765249i | \(0.277384\pi\) | |||||||
\(882\) | −1.37002e18 | −0.0979896 | ||||||||
\(883\) | −1.04409e19 | −0.741302 | −0.370651 | − | 0.928772i | \(-0.620865\pi\) | ||||
−0.370651 | + | 0.928772i | \(0.620865\pi\) | |||||||
\(884\) | −2.22366e18 | −0.156721 | ||||||||
\(885\) | −1.00076e18 | −0.0700161 | ||||||||
\(886\) | 2.14827e19 | 1.49200 | ||||||||
\(887\) | 2.06682e19 | 1.42495 | 0.712474 | − | 0.701699i | \(-0.247575\pi\) | ||||
0.712474 | + | 0.701699i | \(0.247575\pi\) | |||||||
\(888\) | 2.42540e18 | 0.165996 | ||||||||
\(889\) | −1.56027e19 | −1.06008 | ||||||||
\(890\) | 2.40411e19 | 1.62151 | ||||||||
\(891\) | 1.00936e18 | 0.0675835 | ||||||||
\(892\) | −3.04904e19 | −2.02671 | ||||||||
\(893\) | −1.24821e19 | −0.823673 | ||||||||
\(894\) | 5.17591e18 | 0.339073 | ||||||||
\(895\) | 1.99198e19 | 1.29549 | ||||||||
\(896\) | −2.04250e19 | −1.31874 | ||||||||
\(897\) | 1.25236e19 | 0.802747 | ||||||||
\(898\) | 3.02200e19 | 1.92309 | ||||||||
\(899\) | −2.19817e18 | −0.138875 | ||||||||
\(900\) | −1.00344e18 | −0.0629380 | ||||||||
\(901\) | 7.52400e17 | 0.0468530 | ||||||||
\(902\) | −2.10051e19 | −1.29862 | ||||||||
\(903\) | −1.70486e19 | −1.04645 | ||||||||
\(904\) | 1.99673e19 | 1.21682 | ||||||||
\(905\) | −2.47825e19 | −1.49944 | ||||||||
\(906\) | −1.24029e19 | −0.745059 | ||||||||
\(907\) | 2.43732e19 | 1.45367 | 0.726835 | − | 0.686812i | \(-0.240991\pi\) | ||||
0.726835 | + | 0.686812i | \(0.240991\pi\) | |||||||
\(908\) | 3.73556e19 | 2.21206 | ||||||||
\(909\) | 3.13517e18 | 0.184330 | ||||||||
\(910\) | 3.25767e19 | 1.90168 | ||||||||
\(911\) | 5.74736e18 | 0.333119 | 0.166559 | − | 0.986031i | \(-0.446734\pi\) | ||||
0.166559 | + | 0.986031i | \(0.446734\pi\) | |||||||
\(912\) | −3.68036e18 | −0.211799 | ||||||||
\(913\) | 9.79888e18 | 0.559908 | ||||||||
\(914\) | −4.33036e19 | −2.45682 | ||||||||
\(915\) | 9.05730e18 | 0.510225 | ||||||||
\(916\) | −2.65193e19 | −1.48334 | ||||||||
\(917\) | −2.14172e19 | −1.18949 | ||||||||
\(918\) | −4.96742e17 | −0.0273939 | ||||||||
\(919\) | 1.79988e19 | 0.985584 | 0.492792 | − | 0.870147i | \(-0.335976\pi\) | ||||
0.492792 | + | 0.870147i | \(0.335976\pi\) | |||||||
\(920\) | −1.31892e19 | −0.717128 | ||||||||
\(921\) | 1.44504e18 | 0.0780175 | ||||||||
\(922\) | 3.38656e19 | 1.81555 | ||||||||
\(923\) | 3.12561e19 | 1.66389 | ||||||||
\(924\) | −1.03371e19 | −0.546425 | ||||||||
\(925\) | 1.08893e18 | 0.0571581 | ||||||||
\(926\) | 3.40063e19 | 1.77251 | ||||||||
\(927\) | 1.08382e19 | 0.560969 | ||||||||
\(928\) | −3.93610e18 | −0.202304 | ||||||||
\(929\) | 1.51694e18 | 0.0774224 | 0.0387112 | − | 0.999250i | \(-0.487675\pi\) | ||||
0.0387112 | + | 0.999250i | \(0.487675\pi\) | |||||||
\(930\) | 1.44539e19 | 0.732566 | ||||||||
\(931\) | 3.52317e18 | 0.177321 | ||||||||
\(932\) | −3.84028e19 | −1.91937 | ||||||||
\(933\) | 1.02070e19 | 0.506603 | ||||||||
\(934\) | −3.55324e19 | −1.75134 | ||||||||
\(935\) | −1.05762e18 | −0.0517671 | ||||||||
\(936\) | 5.48509e18 | 0.266619 | ||||||||
\(937\) | −2.76656e19 | −1.33547 | −0.667733 | − | 0.744401i | \(-0.732735\pi\) | ||||
−0.667733 | + | 0.744401i | \(0.732735\pi\) | |||||||
\(938\) | −4.07990e19 | −1.95583 | ||||||||
\(939\) | 2.84947e18 | 0.135656 | ||||||||
\(940\) | 2.46454e19 | 1.16521 | ||||||||
\(941\) | −1.97743e19 | −0.928474 | −0.464237 | − | 0.885711i | \(-0.653671\pi\) | ||||
−0.464237 | + | 0.885711i | \(0.653671\pi\) | |||||||
\(942\) | 6.26347e18 | 0.292068 | ||||||||
\(943\) | −3.42331e19 | −1.58533 | ||||||||
\(944\) | −1.10502e18 | −0.0508218 | ||||||||
\(945\) | 4.27902e18 | 0.195451 | ||||||||
\(946\) | −3.47272e19 | −1.57535 | ||||||||
\(947\) | 9.54996e18 | 0.430256 | 0.215128 | − | 0.976586i | \(-0.430983\pi\) | ||||
0.215128 | + | 0.976586i | \(0.430983\pi\) | |||||||
\(948\) | 2.85037e19 | 1.27540 | ||||||||
\(949\) | −2.52865e18 | −0.112372 | ||||||||
\(950\) | 4.38856e18 | 0.193695 | ||||||||
\(951\) | −1.65525e19 | −0.725587 | ||||||||
\(952\) | 1.52266e18 | 0.0662922 | ||||||||
\(953\) | −2.35086e19 | −1.01654 | −0.508269 | − | 0.861198i | \(-0.669714\pi\) | ||||
−0.508269 | + | 0.861198i | \(0.669714\pi\) | |||||||
\(954\) | −6.20075e18 | −0.266305 | ||||||||
\(955\) | −1.84537e19 | −0.787159 | ||||||||
\(956\) | −9.62122e18 | −0.407619 | ||||||||
\(957\) | −1.32556e18 | −0.0557792 | ||||||||
\(958\) | −9.84988e18 | −0.411675 | ||||||||
\(959\) | 1.74812e19 | 0.725688 | ||||||||
\(960\) | 2.07899e19 | 0.857213 | ||||||||
\(961\) | −5.75166e18 | −0.235554 | ||||||||
\(962\) | −1.98872e19 | −0.808976 | ||||||||
\(963\) | −5.43798e18 | −0.219719 | ||||||||
\(964\) | −3.51921e17 | −0.0141236 | ||||||||
\(965\) | −1.63968e19 | −0.653630 | ||||||||
\(966\) | −2.86513e19 | −1.13447 | ||||||||
\(967\) | −3.01315e19 | −1.18508 | −0.592541 | − | 0.805540i | \(-0.701875\pi\) | ||||
−0.592541 | + | 0.805540i | \(0.701875\pi\) | |||||||
\(968\) | 1.07323e19 | 0.419280 | ||||||||
\(969\) | 1.27743e18 | 0.0495717 | ||||||||
\(970\) | 4.53835e19 | 1.74937 | ||||||||
\(971\) | 1.65229e19 | 0.632648 | 0.316324 | − | 0.948651i | \(-0.397551\pi\) | ||||
0.316324 | + | 0.948651i | \(0.397551\pi\) | |||||||
\(972\) | 2.40714e18 | 0.0915525 | ||||||||
\(973\) | −7.48459e18 | −0.282771 | ||||||||
\(974\) | 2.32224e18 | 0.0871512 | ||||||||
\(975\) | 2.46263e18 | 0.0918058 | ||||||||
\(976\) | 1.00009e19 | 0.370351 | ||||||||
\(977\) | −1.30217e19 | −0.479019 | −0.239510 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239510 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(978\) | −1.49383e19 | −0.545882 | ||||||||
\(979\) | 1.87222e19 | 0.679623 | ||||||||
\(980\) | −6.95632e18 | −0.250848 | ||||||||
\(981\) | 1.06873e19 | 0.382840 | ||||||||
\(982\) | 2.02766e19 | 0.721556 | ||||||||
\(983\) | 3.54880e19 | 1.25454 | 0.627269 | − | 0.778803i | \(-0.284173\pi\) | ||||
0.627269 | + | 0.778803i | \(0.284173\pi\) | |||||||
\(984\) | −1.49934e19 | −0.526541 | ||||||||
\(985\) | −3.43807e19 | −1.19944 | ||||||||
\(986\) | 6.52356e17 | 0.0226092 | ||||||||
\(987\) | 1.60244e19 | 0.551722 | ||||||||
\(988\) | −4.71272e19 | −1.61195 | ||||||||
\(989\) | −5.65966e19 | −1.92316 | ||||||||
\(990\) | 8.71615e18 | 0.294236 | ||||||||
\(991\) | −1.14308e19 | −0.383354 | −0.191677 | − | 0.981458i | \(-0.561393\pi\) | ||||
−0.191677 | + | 0.981458i | \(0.561393\pi\) | |||||||
\(992\) | 3.34236e19 | 1.11360 | ||||||||
\(993\) | 2.06845e17 | 0.00684659 | ||||||||
\(994\) | −7.15072e19 | −2.35146 | ||||||||
\(995\) | −3.84607e19 | −1.25651 | ||||||||
\(996\) | 2.33685e19 | 0.758483 | ||||||||
\(997\) | 3.63547e19 | 1.17231 | 0.586155 | − | 0.810199i | \(-0.300641\pi\) | ||||
0.586155 | + | 0.810199i | \(0.300641\pi\) | |||||||
\(998\) | −2.80526e19 | −0.898722 | ||||||||
\(999\) | −2.61222e18 | −0.0831447 |
(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 | 177.14.a.a.1.6 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.6 | ✓ | 30 | 1.1 | even | 1 | trivial |