Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 157936x - 9799664 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{4}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(425.878\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2787.27 | −1.92470 | −0.962352 | − | 0.271805i | \(-0.912379\pi\) | ||||
−0.962352 | + | 0.271805i | \(0.912379\pi\) | |||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | 5.67172e6 | 2.70449 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.64586e8 | −1.11123 | ||||||||
\(7\) | 1.37938e9 | 1.84567 | 0.922836 | − | 0.385194i | \(-0.125866\pi\) | ||||
0.922836 | + | 0.385194i | \(0.125866\pi\) | |||||||
\(8\) | −9.96329e9 | −3.28064 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.99797e10 | 0.348501 | 0.174250 | − | 0.984701i | \(-0.444250\pi\) | ||||
0.174250 | + | 0.984701i | \(0.444250\pi\) | |||||||
\(12\) | 3.34910e11 | 1.56144 | ||||||||
\(13\) | 7.63100e11 | 1.53524 | 0.767619 | − | 0.640906i | \(-0.221441\pi\) | ||||
0.767619 | + | 0.640906i | \(0.221441\pi\) | |||||||
\(14\) | −3.84470e12 | −3.55237 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.58759e13 | 3.60977 | ||||||||
\(17\) | 1.14939e13 | 1.38278 | 0.691391 | − | 0.722480i | \(-0.256998\pi\) | ||||
0.691391 | + | 0.722480i | \(0.256998\pi\) | |||||||
\(18\) | −9.71861e12 | −0.641568 | ||||||||
\(19\) | −5.19898e12 | −0.194538 | −0.0972692 | − | 0.995258i | \(-0.531011\pi\) | ||||
−0.0972692 | + | 0.995258i | \(0.531011\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.14510e13 | 1.06560 | ||||||||
\(22\) | −8.35614e13 | −0.670761 | ||||||||
\(23\) | 8.03048e13 | 0.404203 | 0.202101 | − | 0.979365i | \(-0.435223\pi\) | ||||
0.202101 | + | 0.979365i | \(0.435223\pi\) | |||||||
\(24\) | −5.88322e14 | −1.89408 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.12696e15 | −2.95488 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | 7.82346e15 | 4.99159 | ||||||||
\(29\) | −2.01015e14 | −0.0887259 | −0.0443629 | − | 0.999015i | \(-0.514126\pi\) | ||||
−0.0443629 | + | 0.999015i | \(0.514126\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.53535e15 | 0.336442 | 0.168221 | − | 0.985749i | \(-0.446198\pi\) | ||||
0.168221 | + | 0.985749i | \(0.446198\pi\) | |||||||
\(32\) | −2.33559e16 | −3.66710 | ||||||||
\(33\) | 1.77027e15 | 0.201207 | ||||||||
\(34\) | −3.20366e16 | −2.66145 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.97761e16 | 0.901496 | ||||||||
\(37\) | −1.53969e16 | −0.526401 | −0.263200 | − | 0.964741i | \(-0.584778\pi\) | ||||
−0.263200 | + | 0.964741i | \(0.584778\pi\) | |||||||
\(38\) | 1.44910e16 | 0.374429 | ||||||||
\(39\) | 4.50603e16 | 0.886371 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.88656e16 | −0.917608 | −0.458804 | − | 0.888538i | \(-0.651722\pi\) | ||||
−0.458804 | + | 0.888538i | \(0.651722\pi\) | |||||||
\(42\) | −2.27026e17 | −2.05096 | ||||||||
\(43\) | 1.61914e17 | 1.14253 | 0.571264 | − | 0.820766i | \(-0.306453\pi\) | ||||
0.571264 | + | 0.820766i | \(0.306453\pi\) | |||||||
\(44\) | 1.70036e17 | 0.942516 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.23831e17 | −0.777971 | ||||||||
\(47\) | 3.76922e17 | 1.04526 | 0.522629 | − | 0.852560i | \(-0.324951\pi\) | ||||
0.522629 | + | 0.852560i | \(0.324951\pi\) | |||||||
\(48\) | 9.37457e17 | 2.08410 | ||||||||
\(49\) | 1.34414e18 | 2.40650 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.78704e17 | 0.798350 | ||||||||
\(52\) | 4.32809e18 | 4.15204 | ||||||||
\(53\) | −3.24880e17 | −0.255168 | −0.127584 | − | 0.991828i | \(-0.540722\pi\) | ||||
−0.127584 | + | 0.991828i | \(0.540722\pi\) | |||||||
\(54\) | −5.73874e17 | −0.370410 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.37432e19 | −6.05497 | ||||||||
\(57\) | −3.06994e17 | −0.112317 | ||||||||
\(58\) | 5.60284e17 | 0.170771 | ||||||||
\(59\) | −9.88461e17 | −0.251775 | −0.125888 | − | 0.992044i | \(-0.540178\pi\) | ||||
−0.125888 | + | 0.992044i | \(0.540178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.01280e19 | 1.81786 | 0.908929 | − | 0.416951i | \(-0.136901\pi\) | ||||
0.908929 | + | 0.416951i | \(0.136901\pi\) | |||||||
\(62\) | −4.27945e18 | −0.647552 | ||||||||
\(63\) | 4.80960e18 | 0.615224 | ||||||||
\(64\) | 3.18051e19 | 3.44832 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.93422e18 | −0.387264 | ||||||||
\(67\) | 1.02596e19 | 0.687616 | 0.343808 | − | 0.939040i | \(-0.388283\pi\) | ||||
0.343808 | + | 0.939040i | \(0.388283\pi\) | |||||||
\(68\) | 6.51902e19 | 3.73972 | ||||||||
\(69\) | 4.74192e18 | 0.233367 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.23535e19 | 1.17953 | 0.589765 | − | 0.807575i | \(-0.299220\pi\) | ||||
0.589765 | + | 0.807575i | \(0.299220\pi\) | |||||||
\(72\) | −3.47399e19 | −1.09355 | ||||||||
\(73\) | 2.89708e19 | 0.788987 | 0.394494 | − | 0.918899i | \(-0.370920\pi\) | ||||
0.394494 | + | 0.918899i | \(0.370920\pi\) | |||||||
\(74\) | 4.29154e19 | 1.01317 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.94872e19 | −0.526126 | ||||||||
\(77\) | 4.13533e19 | 0.643218 | ||||||||
\(78\) | −1.25595e20 | −1.70600 | ||||||||
\(79\) | 3.51920e19 | 0.418176 | 0.209088 | − | 0.977897i | \(-0.432950\pi\) | ||||
0.209088 | + | 0.977897i | \(0.432950\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 2.19820e20 | 1.76612 | ||||||||
\(83\) | −2.86096e19 | −0.202391 | −0.101196 | − | 0.994867i | \(-0.532267\pi\) | ||||
−0.101196 | + | 0.994867i | \(0.532267\pi\) | |||||||
\(84\) | 4.61967e20 | 2.88190 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.51299e20 | −2.19903 | ||||||||
\(87\) | −1.18698e19 | −0.0512259 | ||||||||
\(88\) | −2.98696e20 | −1.14330 | ||||||||
\(89\) | 5.20282e19 | 0.176866 | 0.0884328 | − | 0.996082i | \(-0.471814\pi\) | ||||
0.0884328 | + | 0.996082i | \(0.471814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.05260e21 | 2.83355 | ||||||||
\(92\) | 4.55467e20 | 1.09316 | ||||||||
\(93\) | 9.06611e19 | 0.194245 | ||||||||
\(94\) | −1.05058e21 | −2.01181 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.37915e21 | −2.11720 | ||||||||
\(97\) | −7.90419e20 | −1.08831 | −0.544157 | − | 0.838983i | \(-0.683150\pi\) | ||||
−0.544157 | + | 0.838983i | \(0.683150\pi\) | |||||||
\(98\) | −3.74649e21 | −4.63180 | ||||||||
\(99\) | 1.04533e20 | 0.116167 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.18585e21 | −1.06821 | −0.534105 | − | 0.845418i | \(-0.679351\pi\) | ||||
−0.534105 | + | 0.845418i | \(0.679351\pi\) | |||||||
\(102\) | −1.89173e21 | −1.53659 | ||||||||
\(103\) | −1.17111e21 | −0.858632 | −0.429316 | − | 0.903154i | \(-0.641245\pi\) | ||||
−0.429316 | + | 0.903154i | \(0.641245\pi\) | |||||||
\(104\) | −7.60298e21 | −5.03656 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.05529e20 | 0.491123 | ||||||||
\(107\) | −1.02156e21 | −0.502035 | −0.251018 | − | 0.967983i | \(-0.580765\pi\) | ||||
−0.251018 | + | 0.967983i | \(0.580765\pi\) | |||||||
\(108\) | 1.16776e21 | 0.520479 | ||||||||
\(109\) | −8.82895e20 | −0.357216 | −0.178608 | − | 0.983920i | \(-0.557159\pi\) | ||||
−0.178608 | + | 0.983920i | \(0.557159\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.09174e20 | −0.303917 | ||||||||
\(112\) | 2.18989e22 | 6.66244 | ||||||||
\(113\) | −3.34874e21 | −0.928022 | −0.464011 | − | 0.885829i | \(-0.653590\pi\) | ||||
−0.464011 | + | 0.885829i | \(0.653590\pi\) | |||||||
\(114\) | 8.55676e20 | 0.216177 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.14010e21 | −0.239958 | ||||||||
\(117\) | 2.66076e21 | 0.511746 | ||||||||
\(118\) | 2.75511e21 | 0.484593 | ||||||||
\(119\) | 1.58545e22 | 2.55216 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.50147e21 | −0.878547 | ||||||||
\(122\) | −2.82294e22 | −3.49884 | ||||||||
\(123\) | −4.65694e21 | −0.529781 | ||||||||
\(124\) | 8.70810e21 | 0.909905 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.34056e22 | −1.18412 | ||||||||
\(127\) | −1.00016e20 | −0.00813076 | −0.00406538 | − | 0.999992i | \(-0.501294\pi\) | ||||
−0.00406538 | + | 0.999992i | \(0.501294\pi\) | |||||||
\(128\) | −3.96684e22 | −2.96989 | ||||||||
\(129\) | 9.56089e21 | 0.659639 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.82022e21 | 0.106850 | 0.0534252 | − | 0.998572i | \(-0.482986\pi\) | ||||
0.0534252 | + | 0.998572i | \(0.482986\pi\) | |||||||
\(132\) | 1.00405e22 | 0.544162 | ||||||||
\(133\) | −7.17136e21 | −0.359054 | ||||||||
\(134\) | −2.85964e22 | −1.32346 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.14517e23 | −4.53641 | ||||||||
\(137\) | 3.39671e22 | 1.24593 | 0.622963 | − | 0.782251i | \(-0.285929\pi\) | ||||
0.622963 | + | 0.782251i | \(0.285929\pi\) | |||||||
\(138\) | −1.32170e22 | −0.449162 | ||||||||
\(139\) | 5.60010e21 | 0.176417 | 0.0882085 | − | 0.996102i | \(-0.471886\pi\) | ||||
0.0882085 | + | 0.996102i | \(0.471886\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.22568e22 | 0.603480 | ||||||||
\(142\) | −9.01780e22 | −2.27025 | ||||||||
\(143\) | 2.28775e22 | 0.535032 | ||||||||
\(144\) | 5.53559e22 | 1.20326 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.07494e22 | −1.51857 | ||||||||
\(147\) | 7.93702e22 | 1.38939 | ||||||||
\(148\) | −8.73272e22 | −1.42364 | ||||||||
\(149\) | −3.33164e22 | −0.506060 | −0.253030 | − | 0.967458i | \(-0.581427\pi\) | ||||
−0.253030 | + | 0.967458i | \(0.581427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.19754e22 | −1.08249 | −0.541247 | − | 0.840863i | \(-0.682048\pi\) | ||||
−0.541247 | + | 0.840863i | \(0.682048\pi\) | |||||||
\(152\) | 5.17989e22 | 0.638209 | ||||||||
\(153\) | 4.00768e22 | 0.460928 | ||||||||
\(154\) | −1.15263e23 | −1.23800 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.55569e23 | 2.39718 | ||||||||
\(157\) | 1.47933e23 | 1.29754 | 0.648769 | − | 0.760986i | \(-0.275284\pi\) | ||||
0.648769 | + | 0.760986i | \(0.275284\pi\) | |||||||
\(158\) | −9.80896e22 | −0.804866 | ||||||||
\(159\) | −1.91839e22 | −0.147321 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.10771e23 | 0.746025 | ||||||||
\(162\) | −3.38867e22 | −0.213856 | ||||||||
\(163\) | −5.52958e22 | −0.327132 | −0.163566 | − | 0.986532i | \(-0.552300\pi\) | ||||
−0.163566 | + | 0.986532i | \(0.552300\pi\) | |||||||
\(164\) | −4.47304e23 | −2.48166 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.97426e22 | 0.389543 | ||||||||
\(167\) | 4.62356e22 | 0.212058 | 0.106029 | − | 0.994363i | \(-0.466186\pi\) | ||||
0.106029 | + | 0.994363i | \(0.466186\pi\) | |||||||
\(168\) | −8.11520e23 | −3.49584 | ||||||||
\(169\) | 3.35256e23 | 1.35696 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.81277e22 | −0.0648461 | ||||||||
\(172\) | 9.18334e23 | 3.08995 | ||||||||
\(173\) | 4.87339e23 | 1.54293 | 0.771466 | − | 0.636270i | \(-0.219524\pi\) | ||||
0.771466 | + | 0.636270i | \(0.219524\pi\) | |||||||
\(174\) | 3.30842e22 | 0.0985947 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.75955e23 | 1.25801 | ||||||||
\(177\) | −5.83676e22 | −0.145363 | ||||||||
\(178\) | −1.45017e23 | −0.340414 | ||||||||
\(179\) | −4.33940e23 | −0.960446 | −0.480223 | − | 0.877146i | \(-0.659444\pi\) | ||||
−0.480223 | + | 0.877146i | \(0.659444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.08757e23 | −1.39596 | −0.697979 | − | 0.716118i | \(-0.745917\pi\) | ||||
−0.697979 | + | 0.716118i | \(0.745917\pi\) | |||||||
\(182\) | −2.93389e24 | −5.45374 | ||||||||
\(183\) | 5.98048e23 | 1.04954 | ||||||||
\(184\) | −8.00100e23 | −1.32604 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.52697e23 | −0.373865 | ||||||||
\(187\) | 3.44583e23 | 0.481901 | ||||||||
\(188\) | 2.13779e24 | 2.82689 | ||||||||
\(189\) | 2.84002e23 | 0.355200 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.37779e24 | −1.54289 | −0.771443 | − | 0.636299i | \(-0.780464\pi\) | ||||
−0.771443 | + | 0.636299i | \(0.780464\pi\) | |||||||
\(192\) | 1.87806e24 | 1.99089 | ||||||||
\(193\) | −4.06115e23 | −0.407659 | −0.203829 | − | 0.979006i | \(-0.565339\pi\) | ||||
−0.203829 | + | 0.979006i | \(0.565339\pi\) | |||||||
\(194\) | 2.20311e24 | 2.09468 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.62360e24 | 6.50835 | ||||||||
\(197\) | −1.19621e24 | −0.968083 | −0.484041 | − | 0.875045i | \(-0.660832\pi\) | ||||
−0.484041 | + | 0.875045i | \(0.660832\pi\) | |||||||
\(198\) | −2.91361e23 | −0.223587 | ||||||||
\(199\) | 1.89020e24 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258535\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258535\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.05821e23 | 0.396995 | ||||||||
\(202\) | 3.30529e24 | 2.05599 | ||||||||
\(203\) | −2.77276e23 | −0.163759 | ||||||||
\(204\) | 3.84942e24 | 2.15913 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.26420e24 | 1.65261 | ||||||||
\(207\) | 2.80006e23 | 0.134734 | ||||||||
\(208\) | 1.21149e25 | 5.54185 | ||||||||
\(209\) | −1.55864e23 | −0.0677967 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.61070e24 | −1.42110 | −0.710552 | − | 0.703645i | \(-0.751555\pi\) | ||||
−0.710552 | + | 0.703645i | \(0.751555\pi\) | |||||||
\(212\) | −1.84263e24 | −0.690099 | ||||||||
\(213\) | 1.91044e24 | 0.681002 | ||||||||
\(214\) | 2.84736e24 | 0.966270 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.05135e24 | −0.631359 | ||||||||
\(217\) | 2.11784e24 | 0.620962 | ||||||||
\(218\) | 2.46087e24 | 0.687535 | ||||||||
\(219\) | 1.71070e24 | 0.455522 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.77099e24 | 2.12290 | ||||||||
\(222\) | 2.53411e24 | 0.584951 | ||||||||
\(223\) | −2.51046e24 | −0.552780 | −0.276390 | − | 0.961046i | \(-0.589138\pi\) | ||||
−0.276390 | + | 0.961046i | \(0.589138\pi\) | |||||||
\(224\) | −3.22167e25 | −6.76826 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.33385e24 | 1.78617 | ||||||||
\(227\) | −9.57954e24 | −1.75014 | −0.875071 | − | 0.483995i | \(-0.839185\pi\) | ||||
−0.875071 | + | 0.483995i | \(0.839185\pi\) | |||||||
\(228\) | −1.74119e24 | −0.303759 | ||||||||
\(229\) | −9.71373e24 | −1.61850 | −0.809251 | − | 0.587463i | \(-0.800127\pi\) | ||||
−0.809251 | + | 0.587463i | \(0.800127\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.44187e24 | 0.371362 | ||||||||
\(232\) | 2.00277e24 | 0.291077 | ||||||||
\(233\) | 9.68019e24 | 1.34477 | 0.672383 | − | 0.740204i | \(-0.265271\pi\) | ||||
0.672383 | + | 0.740204i | \(0.265271\pi\) | |||||||
\(234\) | −7.41627e24 | −0.984961 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.60628e24 | −0.680924 | ||||||||
\(237\) | 2.07805e24 | 0.241434 | ||||||||
\(238\) | −4.41907e25 | −4.91216 | ||||||||
\(239\) | −1.36780e25 | −1.45494 | −0.727471 | − | 0.686138i | \(-0.759305\pi\) | ||||
−0.727471 | + | 0.686138i | \(0.759305\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.69789e25 | −1.65474 | −0.827372 | − | 0.561654i | \(-0.810165\pi\) | ||||
−0.827372 | + | 0.561654i | \(0.810165\pi\) | |||||||
\(242\) | 1.81214e25 | 1.69094 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | 5.74432e25 | 4.91638 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.29801e25 | 1.01967 | ||||||||
\(247\) | −3.96734e24 | −0.298663 | ||||||||
\(248\) | −1.52972e25 | −1.10375 | ||||||||
\(249\) | −1.68937e24 | −0.116851 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.20909e25 | 0.768929 | 0.384465 | − | 0.923140i | \(-0.374386\pi\) | ||||
0.384465 | + | 0.923140i | \(0.374386\pi\) | |||||||
\(252\) | 2.72787e25 | 1.66386 | ||||||||
\(253\) | 2.40751e24 | 0.140865 | ||||||||
\(254\) | 2.78772e23 | 0.0156493 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.38665e25 | 2.26785 | ||||||||
\(257\) | 1.47338e25 | 0.731167 | 0.365584 | − | 0.930779i | \(-0.380869\pi\) | ||||
0.365584 | + | 0.930779i | \(0.380869\pi\) | |||||||
\(258\) | −2.66488e25 | −1.26961 | ||||||||
\(259\) | −2.12382e25 | −0.971562 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.00897e23 | −0.0295753 | ||||||||
\(262\) | −5.07346e24 | −0.205656 | ||||||||
\(263\) | −3.43475e25 | −1.33770 | −0.668852 | − | 0.743396i | \(-0.733214\pi\) | ||||
−0.668852 | + | 0.743396i | \(0.733214\pi\) | |||||||
\(264\) | −1.76377e25 | −0.660087 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.99885e25 | 0.691072 | ||||||||
\(267\) | 3.07221e24 | 0.102113 | ||||||||
\(268\) | 5.81898e25 | 1.85965 | ||||||||
\(269\) | 3.49311e25 | 1.07353 | 0.536764 | − | 0.843733i | \(-0.319647\pi\) | ||||
0.536764 | + | 0.843733i | \(0.319647\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.04797e25 | −1.43529 | −0.717644 | − | 0.696410i | \(-0.754779\pi\) | ||||
−0.717644 | + | 0.696410i | \(0.754779\pi\) | |||||||
\(272\) | 1.82476e26 | 4.99152 | ||||||||
\(273\) | 6.21552e25 | 1.63595 | ||||||||
\(274\) | −9.46755e25 | −2.39804 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.68949e25 | 0.631137 | ||||||||
\(277\) | 3.43914e24 | 0.0776985 | 0.0388492 | − | 0.999245i | \(-0.487631\pi\) | ||||
0.0388492 | + | 0.999245i | \(0.487631\pi\) | |||||||
\(278\) | −1.56090e25 | −0.339551 | ||||||||
\(279\) | 5.35345e24 | 0.112147 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.07634e25 | −1.56963 | −0.784817 | − | 0.619727i | \(-0.787243\pi\) | ||||
−0.784817 | + | 0.619727i | \(0.787243\pi\) | |||||||
\(282\) | −6.20358e25 | −1.16152 | ||||||||
\(283\) | 2.52971e25 | 0.456366 | 0.228183 | − | 0.973618i | \(-0.426722\pi\) | ||||
0.228183 | + | 0.973618i | \(0.426722\pi\) | |||||||
\(284\) | 1.83500e26 | 3.19002 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.37657e25 | −1.02978 | ||||||||
\(287\) | −1.08786e26 | −1.69360 | ||||||||
\(288\) | −8.14371e25 | −1.22237 | ||||||||
\(289\) | 6.30180e25 | 0.912088 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.66735e25 | −0.628338 | ||||||||
\(292\) | 1.64314e26 | 2.13381 | ||||||||
\(293\) | −1.39891e26 | −1.75259 | −0.876295 | − | 0.481775i | \(-0.839992\pi\) | ||||
−0.876295 | + | 0.481775i | \(0.839992\pi\) | |||||||
\(294\) | −2.21226e26 | −2.67417 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.53404e26 | 1.72693 | ||||||||
\(297\) | 6.17255e24 | 0.0670690 | ||||||||
\(298\) | 9.28617e25 | 0.974016 | ||||||||
\(299\) | 6.12806e25 | 0.620548 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.23341e26 | 2.10873 | ||||||||
\(302\) | 2.28488e26 | 2.08348 | ||||||||
\(303\) | −7.00235e25 | −0.616731 | ||||||||
\(304\) | −8.25386e25 | −0.702238 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.11705e26 | −0.887150 | ||||||||
\(307\) | 1.66063e26 | 1.27444 | 0.637222 | − | 0.770681i | \(-0.280084\pi\) | ||||
0.637222 | + | 0.770681i | \(0.280084\pi\) | |||||||
\(308\) | 2.34545e26 | 1.73957 | ||||||||
\(309\) | −6.91529e25 | −0.495732 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.85915e26 | 1.91537 | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) | ||||
0.957685 | + | 0.287819i | \(0.0929302\pi\) | |||||||
\(312\) | −4.48949e26 | −2.90786 | ||||||||
\(313\) | −6.78268e25 | −0.424801 | −0.212401 | − | 0.977183i | \(-0.568128\pi\) | ||||
−0.212401 | + | 0.977183i | \(0.568128\pi\) | |||||||
\(314\) | −4.12330e26 | −2.49738 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.99599e26 | 1.13095 | ||||||||
\(317\) | 3.05982e25 | 0.167716 | 0.0838579 | − | 0.996478i | \(-0.473276\pi\) | ||||
0.0838579 | + | 0.996478i | \(0.473276\pi\) | |||||||
\(318\) | 5.34706e25 | 0.283550 | ||||||||
\(319\) | −6.02637e24 | −0.0309210 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.03221e25 | −0.289850 | ||||||||
\(322\) | −3.08748e26 | −1.43588 | ||||||||
\(323\) | −5.97566e25 | −0.269004 | ||||||||
\(324\) | 6.89549e25 | 0.300499 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.54124e26 | 0.629632 | ||||||||
\(327\) | −5.21341e25 | −0.206239 | ||||||||
\(328\) | 7.85761e26 | 3.01034 | ||||||||
\(329\) | 5.19918e26 | 1.92920 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.97902e26 | 1.03724 | 0.518620 | − | 0.855005i | \(-0.326446\pi\) | ||||
0.518620 | + | 0.855005i | \(0.326446\pi\) | |||||||
\(332\) | −1.62266e26 | −0.547364 | ||||||||
\(333\) | −5.36858e25 | −0.175467 | ||||||||
\(334\) | −1.28871e26 | −0.408148 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.29311e27 | 3.84656 | ||||||||
\(337\) | −1.35212e26 | −0.389852 | −0.194926 | − | 0.980818i | \(-0.562447\pi\) | ||||
−0.194926 | + | 0.980818i | \(0.562447\pi\) | |||||||
\(338\) | −9.34450e26 | −2.61174 | ||||||||
\(339\) | −1.97740e26 | −0.535794 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.60294e25 | 0.117250 | ||||||||
\(342\) | 5.05268e25 | 0.124810 | ||||||||
\(343\) | 1.08363e27 | 2.59594 | ||||||||
\(344\) | −1.61320e27 | −3.74822 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.35834e27 | −2.96969 | ||||||||
\(347\) | −2.89431e26 | −0.613884 | −0.306942 | − | 0.951728i | \(-0.599306\pi\) | ||||
−0.306942 | + | 0.951728i | \(0.599306\pi\) | |||||||
\(348\) | −6.73220e25 | −0.138540 | ||||||||
\(349\) | 5.89250e26 | 1.17661 | 0.588306 | − | 0.808639i | \(-0.299795\pi\) | ||||
0.588306 | + | 0.808639i | \(0.299795\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57115e26 | 0.295457 | ||||||||
\(352\) | −7.00203e26 | −1.27799 | ||||||||
\(353\) | −6.63803e25 | −0.117599 | −0.0587996 | − | 0.998270i | \(-0.518727\pi\) | ||||
−0.0587996 | + | 0.998270i | \(0.518727\pi\) | |||||||
\(354\) | 1.62686e26 | 0.279780 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.95089e26 | 0.478331 | ||||||||
\(357\) | 9.36190e26 | 1.47349 | ||||||||
\(358\) | 1.20951e27 | 1.84858 | ||||||||
\(359\) | 9.35962e26 | 1.38921 | 0.694603 | − | 0.719393i | \(-0.255580\pi\) | ||||
0.694603 | + | 0.719393i | \(0.255580\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.87180e26 | −0.962155 | ||||||||
\(362\) | 1.97550e27 | 2.68681 | ||||||||
\(363\) | −3.83905e26 | −0.507230 | ||||||||
\(364\) | 5.97008e27 | 7.66329 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.66692e27 | −2.02006 | ||||||||
\(367\) | −1.41202e27 | −1.66282 | −0.831411 | − | 0.555658i | \(-0.812466\pi\) | ||||
−0.831411 | + | 0.555658i | \(0.812466\pi\) | |||||||
\(368\) | 1.27491e27 | 1.45908 | ||||||||
\(369\) | −2.74987e26 | −0.305869 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.48133e26 | −0.470957 | ||||||||
\(372\) | 5.14205e26 | 0.525334 | ||||||||
\(373\) | 4.21905e26 | 0.419056 | 0.209528 | − | 0.977803i | \(-0.432807\pi\) | ||||
0.209528 | + | 0.977803i | \(0.432807\pi\) | |||||||
\(374\) | −9.60447e26 | −0.927517 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.75538e27 | −3.42911 | ||||||||
\(377\) | −1.53395e26 | −0.136215 | ||||||||
\(378\) | −7.91590e26 | −0.683654 | ||||||||
\(379\) | −1.82216e27 | −1.53065 | −0.765325 | − | 0.643644i | \(-0.777422\pi\) | ||||
−0.765325 | + | 0.643644i | \(0.777422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.90586e24 | −0.00469430 | ||||||||
\(382\) | 3.84028e27 | 2.96960 | ||||||||
\(383\) | 3.47058e26 | 0.261105 | 0.130552 | − | 0.991441i | \(-0.458325\pi\) | ||||
0.130552 | + | 0.991441i | \(0.458325\pi\) | |||||||
\(384\) | −2.34238e27 | −1.71467 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.13195e27 | 0.784623 | ||||||||
\(387\) | 5.64561e26 | 0.380843 | ||||||||
\(388\) | −4.48304e27 | −2.94333 | ||||||||
\(389\) | −1.66189e27 | −1.06202 | −0.531009 | − | 0.847366i | \(-0.678187\pi\) | ||||
−0.531009 | + | 0.847366i | \(0.678187\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.23016e26 | 0.558925 | ||||||||
\(392\) | −1.33921e28 | −7.89485 | ||||||||
\(393\) | 1.07482e26 | 0.0616902 | ||||||||
\(394\) | 3.33416e27 | 1.86327 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.92880e26 | 0.314172 | ||||||||
\(397\) | 3.53949e27 | 1.82659 | 0.913293 | − | 0.407304i | \(-0.133531\pi\) | ||||
0.913293 | + | 0.407304i | \(0.133531\pi\) | |||||||
\(398\) | −5.26851e27 | −2.64798 | ||||||||
\(399\) | −4.23462e26 | −0.207300 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.58374e27 | −0.735644 | −0.367822 | − | 0.929896i | \(-0.619896\pi\) | ||||
−0.367822 | + | 0.929896i | \(0.619896\pi\) | |||||||
\(402\) | −1.68859e27 | −0.764099 | ||||||||
\(403\) | 1.17163e27 | 0.516520 | ||||||||
\(404\) | −6.72583e27 | −2.88896 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.72844e26 | 0.315187 | ||||||||
\(407\) | −4.61595e26 | −0.183451 | ||||||||
\(408\) | −6.76212e27 | −2.61910 | ||||||||
\(409\) | 2.05726e27 | 0.776596 | 0.388298 | − | 0.921534i | \(-0.373063\pi\) | ||||
0.388298 | + | 0.921534i | \(0.373063\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00572e27 | 0.719336 | ||||||||
\(412\) | −6.64222e27 | −2.32216 | ||||||||
\(413\) | −1.36346e27 | −0.464695 | ||||||||
\(414\) | −7.80451e26 | −0.259324 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.78229e28 | −5.62987 | ||||||||
\(417\) | 3.30680e26 | 0.101854 | ||||||||
\(418\) | 4.34434e26 | 0.130489 | ||||||||
\(419\) | 1.53990e27 | 0.451071 | 0.225536 | − | 0.974235i | \(-0.427587\pi\) | ||||
0.225536 | + | 0.974235i | \(0.427587\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.15043e27 | 0.877824 | 0.438912 | − | 0.898530i | \(-0.355364\pi\) | ||||
0.438912 | + | 0.898530i | \(0.355364\pi\) | |||||||
\(422\) | 1.00640e28 | 2.73521 | ||||||||
\(423\) | 1.31424e27 | 0.348419 | ||||||||
\(424\) | 3.23688e27 | 0.837114 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.32492e27 | −1.31073 | ||||||||
\(427\) | 1.39703e28 | 3.35517 | ||||||||
\(428\) | −5.79400e27 | −1.35775 | ||||||||
\(429\) | 1.35089e27 | 0.308901 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.98201e27 | 0.431614 | 0.215807 | − | 0.976436i | \(-0.430762\pi\) | ||||
0.215807 | + | 0.976436i | \(0.430762\pi\) | |||||||
\(432\) | 3.26871e27 | 0.694700 | ||||||||
\(433\) | −5.59999e27 | −1.16162 | −0.580810 | − | 0.814039i | \(-0.697264\pi\) | ||||
−0.580810 | + | 0.814039i | \(0.697264\pi\) | |||||||
\(434\) | −5.90298e27 | −1.19517 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.00754e27 | −0.966087 | ||||||||
\(437\) | −4.17503e26 | −0.0786329 | ||||||||
\(438\) | −4.76817e27 | −0.876746 | ||||||||
\(439\) | 1.53894e27 | 0.276277 | 0.138138 | − | 0.990413i | \(-0.455888\pi\) | ||||
0.138138 | + | 0.990413i | \(0.455888\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.68673e27 | 0.802167 | ||||||||
\(442\) | −2.44471e28 | −4.08596 | ||||||||
\(443\) | 3.27390e27 | 0.534351 | 0.267175 | − | 0.963648i | \(-0.413910\pi\) | ||||
0.267175 | + | 0.963648i | \(0.413910\pi\) | |||||||
\(444\) | −5.15658e27 | −0.821941 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.99733e27 | 1.06394 | ||||||||
\(447\) | −1.96730e27 | −0.292174 | ||||||||
\(448\) | 4.38713e28 | 6.36446 | ||||||||
\(449\) | 3.04397e27 | 0.431374 | 0.215687 | − | 0.976463i | \(-0.430801\pi\) | ||||
0.215687 | + | 0.976463i | \(0.430801\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.36436e27 | −0.319787 | ||||||||
\(452\) | −1.89931e28 | −2.50982 | ||||||||
\(453\) | −4.84057e27 | −0.624979 | ||||||||
\(454\) | 2.67008e28 | 3.36850 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.05868e27 | 0.368470 | ||||||||
\(457\) | 4.76153e26 | 0.0560566 | 0.0280283 | − | 0.999607i | \(-0.491077\pi\) | ||||
0.0280283 | + | 0.999607i | \(0.491077\pi\) | |||||||
\(458\) | 2.70748e28 | 3.11514 | ||||||||
\(459\) | 2.36649e27 | 0.266117 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.99698e27 | −1.07401 | −0.537006 | − | 0.843578i | \(-0.680445\pi\) | ||||
−0.537006 | + | 0.843578i | \(0.680445\pi\) | |||||||
\(462\) | −6.80616e27 | −0.714762 | ||||||||
\(463\) | −1.40995e28 | −1.44745 | −0.723723 | − | 0.690090i | \(-0.757571\pi\) | ||||
−0.723723 | + | 0.690090i | \(0.757571\pi\) | |||||||
\(464\) | −3.19130e27 | −0.320280 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.69813e28 | −2.58828 | ||||||||
\(467\) | −3.82873e25 | −0.00359110 | −0.00179555 | − | 0.999998i | \(-0.500572\pi\) | ||||
−0.00179555 | + | 0.999998i | \(0.500572\pi\) | |||||||
\(468\) | 1.50911e28 | 1.38401 | ||||||||
\(469\) | 1.41519e28 | 1.26911 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.73532e27 | 0.749133 | ||||||||
\(472\) | 9.84832e27 | 0.825983 | ||||||||
\(473\) | 4.85414e27 | 0.398172 | ||||||||
\(474\) | −5.79209e27 | −0.464690 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.99221e28 | 6.90229 | ||||||||
\(477\) | −1.13279e27 | −0.0850561 | ||||||||
\(478\) | 3.81244e28 | 2.80033 | ||||||||
\(479\) | 9.30936e27 | 0.668955 | 0.334477 | − | 0.942404i | \(-0.391440\pi\) | ||||
0.334477 | + | 0.942404i | \(0.391440\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.17494e28 | −0.808151 | ||||||||
\(482\) | 4.73248e28 | 3.18490 | ||||||||
\(483\) | 6.54091e27 | 0.430718 | ||||||||
\(484\) | −3.68745e28 | −2.37602 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.00098e27 | −0.123470 | ||||||||
\(487\) | 1.33180e28 | 0.804239 | 0.402119 | − | 0.915587i | \(-0.368274\pi\) | ||||
0.402119 | + | 0.915587i | \(0.368274\pi\) | |||||||
\(488\) | −1.00908e29 | −5.96373 | ||||||||
\(489\) | −3.26516e27 | −0.188869 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.75994e27 | −0.319199 | −0.159600 | − | 0.987182i | \(-0.551020\pi\) | ||||
−0.159600 | + | 0.987182i | \(0.551020\pi\) | |||||||
\(492\) | −2.64128e28 | −1.43279 | ||||||||
\(493\) | −2.31045e27 | −0.122689 | ||||||||
\(494\) | 1.10580e28 | 0.574838 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.43752e28 | 1.21448 | ||||||||
\(497\) | 4.46278e28 | 2.17702 | ||||||||
\(498\) | 4.70872e27 | 0.224903 | ||||||||
\(499\) | 1.10496e28 | 0.516763 | 0.258382 | − | 0.966043i | \(-0.416811\pi\) | ||||
0.258382 | + | 0.966043i | \(0.416811\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.73017e27 | 0.122432 | ||||||||
\(502\) | −3.37007e28 | −1.47996 | ||||||||
\(503\) | −2.38869e28 | −1.02730 | −0.513649 | − | 0.858001i | \(-0.671706\pi\) | ||||
−0.513649 | + | 0.858001i | \(0.671706\pi\) | |||||||
\(504\) | −4.79194e28 | −2.01832 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.71039e27 | −0.271123 | ||||||||
\(507\) | 1.97966e28 | 0.783440 | ||||||||
\(508\) | −5.67264e26 | −0.0219896 | ||||||||
\(509\) | 7.62092e27 | 0.289381 | 0.144691 | − | 0.989477i | \(-0.453781\pi\) | ||||
0.144691 | + | 0.989477i | \(0.453781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.99617e28 | 1.45621 | ||||||||
\(512\) | −3.90771e28 | −1.39504 | ||||||||
\(513\) | −1.07042e27 | −0.0374389 | ||||||||
\(514\) | −4.10671e28 | −1.40728 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.42267e28 | 1.78399 | ||||||||
\(517\) | 1.13000e28 | 0.364273 | ||||||||
\(518\) | 5.91967e28 | 1.86997 | ||||||||
\(519\) | 2.87769e28 | 0.890813 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.68092e28 | −0.797055 | −0.398527 | − | 0.917156i | \(-0.630479\pi\) | ||||
−0.398527 | + | 0.917156i | \(0.630479\pi\) | |||||||
\(522\) | 1.95359e27 | 0.0569237 | ||||||||
\(523\) | 1.54301e28 | 0.440657 | 0.220328 | − | 0.975426i | \(-0.429287\pi\) | ||||
0.220328 | + | 0.975426i | \(0.429287\pi\) | |||||||
\(524\) | 1.03238e28 | 0.288976 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.57358e28 | 2.57469 | ||||||||
\(527\) | 1.76472e28 | 0.465227 | ||||||||
\(528\) | 2.81047e28 | 0.726310 | ||||||||
\(529\) | −3.30227e28 | −0.836620 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.44655e27 | −0.0839251 | ||||||||
\(532\) | −4.06740e28 | −0.971056 | ||||||||
\(533\) | −6.01823e28 | −1.40875 | ||||||||
\(534\) | −8.56308e27 | −0.196538 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.02220e29 | −2.25582 | ||||||||
\(537\) | −2.56237e28 | −0.554514 | ||||||||
\(538\) | −9.73623e28 | −2.06622 | ||||||||
\(539\) | 4.02969e28 | 0.838667 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.53635e28 | −1.10829 | −0.554143 | − | 0.832421i | \(-0.686954\pi\) | ||||
−0.554143 | + | 0.832421i | \(0.686954\pi\) | |||||||
\(542\) | 1.40700e29 | 2.76250 | ||||||||
\(543\) | −4.18514e28 | −0.805957 | ||||||||
\(544\) | −2.68451e29 | −5.07080 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.73243e29 | −3.14872 | ||||||||
\(547\) | 3.14951e28 | 0.561535 | 0.280767 | − | 0.959776i | \(-0.409411\pi\) | ||||
0.280767 | + | 0.959776i | \(0.409411\pi\) | |||||||
\(548\) | 1.92652e29 | 3.36959 | ||||||||
\(549\) | 3.53141e28 | 0.605953 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.04507e27 | 0.0172606 | ||||||||
\(552\) | −4.72451e28 | −0.765591 | ||||||||
\(553\) | 4.85431e28 | 0.771816 | ||||||||
\(554\) | −9.58581e27 | −0.149547 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.17622e28 | 0.477118 | ||||||||
\(557\) | −4.25159e28 | −0.626717 | −0.313358 | − | 0.949635i | \(-0.601454\pi\) | ||||
−0.313358 | + | 0.949635i | \(0.601454\pi\) | |||||||
\(558\) | −1.49215e28 | −0.215851 | ||||||||
\(559\) | 1.23557e29 | 1.75405 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.03473e28 | 0.278226 | ||||||||
\(562\) | 2.25110e29 | 3.02108 | ||||||||
\(563\) | 7.19780e28 | 0.948116 | 0.474058 | − | 0.880494i | \(-0.342789\pi\) | ||||
0.474058 | + | 0.880494i | \(0.342789\pi\) | |||||||
\(564\) | 1.26235e29 | 1.63210 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.05098e28 | −0.878369 | ||||||||
\(567\) | 1.67700e28 | 0.205075 | ||||||||
\(568\) | −3.22348e29 | −3.86961 | ||||||||
\(569\) | 1.32568e29 | 1.56228 | 0.781142 | − | 0.624353i | \(-0.214637\pi\) | ||||
0.781142 | + | 0.624353i | \(0.214637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.77857e28 | 0.656359 | 0.328179 | − | 0.944615i | \(-0.393565\pi\) | ||||
0.328179 | + | 0.944615i | \(0.393565\pi\) | |||||||
\(572\) | 1.29755e29 | 1.44699 | ||||||||
\(573\) | −8.13573e28 | −0.890785 | ||||||||
\(574\) | 3.03215e29 | 3.25968 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.10898e29 | 1.14944 | ||||||||
\(577\) | 1.02641e29 | 1.04466 | 0.522332 | − | 0.852742i | \(-0.325062\pi\) | ||||
0.522332 | + | 0.852742i | \(0.325062\pi\) | |||||||
\(578\) | −1.75648e29 | −1.75550 | ||||||||
\(579\) | −2.39807e28 | −0.235362 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.94635e28 | −0.373547 | ||||||||
\(582\) | 1.30092e29 | 1.20937 | ||||||||
\(583\) | −9.73980e27 | −0.0889263 | ||||||||
\(584\) | −2.88644e29 | −2.58838 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.89914e29 | 3.37322 | ||||||||
\(587\) | −1.42995e29 | −1.21512 | −0.607562 | − | 0.794272i | \(-0.707852\pi\) | ||||
−0.607562 | + | 0.794272i | \(0.707852\pi\) | |||||||
\(588\) | 4.50166e29 | 3.75760 | ||||||||
\(589\) | −7.98227e27 | −0.0654510 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.06351e28 | −0.558923 | ||||||||
\(592\) | −2.44441e29 | −1.90018 | ||||||||
\(593\) | −1.90982e29 | −1.45854 | −0.729270 | − | 0.684226i | \(-0.760140\pi\) | ||||
−0.729270 | + | 0.684226i | \(0.760140\pi\) | |||||||
\(594\) | −1.72046e28 | −0.129088 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.88961e29 | −1.36863 | ||||||||
\(597\) | 1.11615e29 | 0.794311 | ||||||||
\(598\) | −1.70806e29 | −1.19437 | ||||||||
\(599\) | 1.17313e29 | 0.806053 | 0.403027 | − | 0.915188i | \(-0.367958\pi\) | ||||
0.403027 | + | 0.915188i | \(0.367958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.19161e29 | −1.45405 | −0.727027 | − | 0.686609i | \(-0.759099\pi\) | ||||
−0.727027 | + | 0.686609i | \(0.759099\pi\) | |||||||
\(602\) | −6.22513e29 | −4.05868 | ||||||||
\(603\) | 3.57731e28 | 0.229205 | ||||||||
\(604\) | −4.64942e29 | −2.92759 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.95174e29 | 1.18703 | ||||||||
\(607\) | −1.48966e29 | −0.890445 | −0.445222 | − | 0.895420i | \(-0.646875\pi\) | ||||
−0.445222 | + | 0.895420i | \(0.646875\pi\) | |||||||
\(608\) | 1.21427e29 | 0.713391 | ||||||||
\(609\) | −1.63729e28 | −0.0945462 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.87629e29 | 1.60472 | ||||||||
\(612\) | 2.27304e29 | 1.24657 | ||||||||
\(613\) | −2.26313e29 | −1.22004 | −0.610022 | − | 0.792385i | \(-0.708839\pi\) | ||||
−0.610022 | + | 0.792385i | \(0.708839\pi\) | |||||||
\(614\) | −4.62863e29 | −2.45293 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.12015e29 | −2.11016 | ||||||||
\(617\) | 3.85893e29 | 1.94300 | 0.971500 | − | 0.237040i | \(-0.0761773\pi\) | ||||
0.971500 | + | 0.237040i | \(0.0761773\pi\) | |||||||
\(618\) | 1.92748e29 | 0.954137 | ||||||||
\(619\) | −1.80368e29 | −0.877823 | −0.438912 | − | 0.898530i | \(-0.644636\pi\) | ||||
−0.438912 | + | 0.898530i | \(0.644636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.65341e28 | 0.0777889 | ||||||||
\(622\) | −7.96922e29 | −3.68652 | ||||||||
\(623\) | 7.17666e28 | 0.326436 | ||||||||
\(624\) | 7.15373e29 | 3.19959 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.89052e29 | 0.817617 | ||||||||
\(627\) | −9.20359e27 | −0.0391425 | ||||||||
\(628\) | 8.39037e29 | 3.50917 | ||||||||
\(629\) | −1.76971e29 | −0.727898 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.76208e29 | 1.09882 | 0.549411 | − | 0.835552i | \(-0.314852\pi\) | ||||
0.549411 | + | 0.835552i | \(0.314852\pi\) | |||||||
\(632\) | −3.50628e29 | −1.37188 | ||||||||
\(633\) | −2.13208e29 | −0.820475 | ||||||||
\(634\) | −8.52855e28 | −0.322803 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.08805e29 | −0.398429 | ||||||||
\(637\) | 1.02571e30 | 3.69455 | ||||||||
\(638\) | 1.67971e28 | 0.0595138 | ||||||||
\(639\) | 1.12810e29 | 0.393177 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.28643e29 | 0.433889 | 0.216944 | − | 0.976184i | \(-0.430391\pi\) | ||||
0.216944 | + | 0.976184i | \(0.430391\pi\) | |||||||
\(642\) | 1.68134e29 | 0.557876 | ||||||||
\(643\) | 3.99417e29 | 1.30380 | 0.651900 | − | 0.758305i | \(-0.273972\pi\) | ||||
0.651900 | + | 0.758305i | \(0.273972\pi\) | |||||||
\(644\) | 6.28261e29 | 2.01762 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.66558e29 | 0.517754 | ||||||||
\(647\) | 2.80444e29 | 0.857730 | 0.428865 | − | 0.903368i | \(-0.358914\pi\) | ||||
0.428865 | + | 0.903368i | \(0.358914\pi\) | |||||||
\(648\) | −1.21130e29 | −0.364515 | ||||||||
\(649\) | −2.96337e28 | −0.0877439 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.25056e29 | 0.358513 | ||||||||
\(652\) | −3.13623e29 | −0.884723 | ||||||||
\(653\) | 1.79013e29 | 0.496931 | 0.248466 | − | 0.968641i | \(-0.420074\pi\) | ||||
0.248466 | + | 0.968641i | \(0.420074\pi\) | |||||||
\(654\) | 1.45312e29 | 0.396949 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.25206e30 | −3.31235 | ||||||||
\(657\) | 1.01015e29 | 0.262996 | ||||||||
\(658\) | −1.44915e30 | −3.71314 | ||||||||
\(659\) | 7.33826e29 | 1.85053 | 0.925265 | − | 0.379320i | \(-0.123842\pi\) | ||||
0.925265 | + | 0.379320i | \(0.123842\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.96638e29 | −1.45746 | −0.728728 | − | 0.684803i | \(-0.759888\pi\) | ||||
−0.728728 | + | 0.684803i | \(0.759888\pi\) | |||||||
\(662\) | −8.30333e29 | −1.99638 | ||||||||
\(663\) | 5.17918e29 | 1.22566 | ||||||||
\(664\) | 2.85046e29 | 0.663971 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.49637e29 | 0.337722 | ||||||||
\(667\) | −1.61425e28 | −0.0358632 | ||||||||
\(668\) | 2.62236e29 | 0.573507 | ||||||||
\(669\) | −1.48240e29 | −0.319148 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.03634e29 | 0.633525 | ||||||||
\(672\) | −1.90236e30 | −3.90766 | ||||||||
\(673\) | 1.89245e28 | 0.0382706 | 0.0191353 | − | 0.999817i | \(-0.493909\pi\) | ||||
0.0191353 | + | 0.999817i | \(0.493909\pi\) | |||||||
\(674\) | 3.76871e29 | 0.750350 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.90148e30 | 3.66988 | ||||||||
\(677\) | 2.47018e28 | 0.0469405 | 0.0234703 | − | 0.999725i | \(-0.492529\pi\) | ||||
0.0234703 | + | 0.999725i | \(0.492529\pi\) | |||||||
\(678\) | 5.51155e29 | 1.03124 | ||||||||
\(679\) | −1.09029e30 | −2.00867 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.65662e29 | −1.01044 | ||||||||
\(682\) | −1.28296e29 | −0.225672 | ||||||||
\(683\) | 2.88518e29 | 0.499752 | 0.249876 | − | 0.968278i | \(-0.419610\pi\) | ||||
0.249876 | + | 0.968278i | \(0.419610\pi\) | |||||||
\(684\) | −1.02815e29 | −0.175375 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.02038e30 | −4.99642 | ||||||||
\(687\) | −5.73586e29 | −0.934443 | ||||||||
\(688\) | 2.57054e30 | 4.12426 | ||||||||
\(689\) | −2.47916e29 | −0.391744 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.59152e29 | −0.550502 | −0.275251 | − | 0.961372i | \(-0.588761\pi\) | ||||
−0.275251 | + | 0.961372i | \(0.588761\pi\) | |||||||
\(692\) | 2.76405e30 | 4.17284 | ||||||||
\(693\) | 1.44190e29 | 0.214406 | ||||||||
\(694\) | 8.06723e29 | 1.18154 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.18262e29 | 0.168054 | ||||||||
\(697\) | −9.06474e29 | −1.26885 | ||||||||
\(698\) | −1.64240e30 | −2.26463 | ||||||||
\(699\) | 5.71605e29 | 0.776401 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.21736e30 | 1.60465 | 0.802327 | − | 0.596885i | \(-0.203595\pi\) | ||||
0.802327 | + | 0.596885i | \(0.203595\pi\) | |||||||
\(702\) | −4.37923e29 | −0.568667 | ||||||||
\(703\) | 8.00483e28 | 0.102405 | ||||||||
\(704\) | 9.53506e29 | 1.20174 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.85020e29 | 0.226344 | ||||||||
\(707\) | −1.63574e30 | −1.97156 | ||||||||
\(708\) | −3.31045e29 | −0.393131 | ||||||||
\(709\) | 1.19822e30 | 1.40202 | 0.701008 | − | 0.713154i | \(-0.252734\pi\) | ||||
0.701008 | + | 0.713154i | \(0.252734\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.22707e29 | 0.139392 | ||||||||
\(712\) | −5.18372e29 | −0.580232 | ||||||||
\(713\) | 1.23296e29 | 0.135991 | ||||||||
\(714\) | −2.60941e30 | −2.83604 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.46119e30 | −2.59752 | ||||||||
\(717\) | −8.07674e29 | −0.840011 | ||||||||
\(718\) | −2.60878e30 | −2.67381 | ||||||||
\(719\) | −2.33520e29 | −0.235869 | −0.117935 | − | 0.993021i | \(-0.537627\pi\) | ||||
−0.117935 | + | 0.993021i | \(0.537627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.61541e30 | −1.58475 | ||||||||
\(722\) | 1.91536e30 | 1.85186 | ||||||||
\(723\) | −1.00259e30 | −0.955367 | ||||||||
\(724\) | −4.01987e30 | −3.77535 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.07005e30 | 0.976267 | ||||||||
\(727\) | 5.30551e29 | 0.477107 | 0.238554 | − | 0.971129i | \(-0.423327\pi\) | ||||
0.238554 | + | 0.971129i | \(0.423327\pi\) | |||||||
\(728\) | −1.04874e31 | −9.29583 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.86103e30 | 1.57987 | ||||||||
\(732\) | 3.39196e30 | 2.83847 | ||||||||
\(733\) | −4.20011e28 | −0.0346473 | −0.0173236 | − | 0.999850i | \(-0.505515\pi\) | ||||
−0.0173236 | + | 0.999850i | \(0.505515\pi\) | |||||||
\(734\) | 3.93567e30 | 3.20044 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.87559e30 | −1.48225 | ||||||||
\(737\) | 3.07580e29 | 0.239635 | ||||||||
\(738\) | 7.66464e29 | 0.588708 | ||||||||
\(739\) | −8.41533e28 | −0.0637243 | −0.0318621 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318621 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.34267e29 | −0.172433 | ||||||||
\(742\) | 1.24907e30 | 0.906452 | ||||||||
\(743\) | 1.91121e30 | 1.36749 | 0.683746 | − | 0.729720i | \(-0.260350\pi\) | ||||
0.683746 | + | 0.729720i | \(0.260350\pi\) | |||||||
\(744\) | −9.03283e29 | −0.637248 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.17596e30 | −0.806559 | ||||||||
\(747\) | −9.97554e28 | −0.0674637 | ||||||||
\(748\) | 1.95438e30 | 1.30329 | ||||||||
\(749\) | −1.40912e30 | −0.926592 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.07482e29 | −0.0687250 | −0.0343625 | − | 0.999409i | \(-0.510940\pi\) | ||||
−0.0343625 | + | 0.999409i | \(0.510940\pi\) | |||||||
\(752\) | 5.98398e30 | 3.77314 | ||||||||
\(753\) | 7.13958e29 | 0.443941 | ||||||||
\(754\) | 4.27553e29 | 0.262174 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.61078e30 | 0.960633 | ||||||||
\(757\) | −3.00991e30 | −1.77030 | −0.885149 | − | 0.465307i | \(-0.845944\pi\) | ||||
−0.885149 | + | 0.465307i | \(0.845944\pi\) | |||||||
\(758\) | 5.07887e30 | 2.94605 | ||||||||
\(759\) | 1.42161e29 | 0.0813284 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.13756e29 | −0.0633049 | −0.0316524 | − | 0.999499i | \(-0.510077\pi\) | ||||
−0.0316524 | + | 0.999499i | \(0.510077\pi\) | |||||||
\(762\) | 1.64612e28 | 0.00903514 | ||||||||
\(763\) | −1.21785e30 | −0.659303 | ||||||||
\(764\) | −7.81446e30 | −4.17271 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.67344e29 | −0.502549 | ||||||||
\(767\) | −7.54294e29 | −0.386535 | ||||||||
\(768\) | 2.59027e30 | 1.30934 | ||||||||
\(769\) | 2.78880e29 | 0.139056 | 0.0695281 | − | 0.997580i | \(-0.477851\pi\) | ||||
0.0695281 | + | 0.997580i | \(0.477851\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.70016e29 | 0.422140 | ||||||||
\(772\) | −2.30337e30 | −1.10251 | ||||||||
\(773\) | −1.53967e30 | −0.727012 | −0.363506 | − | 0.931592i | \(-0.618420\pi\) | ||||
−0.363506 | + | 0.931592i | \(0.618420\pi\) | |||||||
\(774\) | −1.57358e30 | −0.733010 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.87518e30 | 3.57036 | ||||||||
\(777\) | −1.25410e30 | −0.560932 | ||||||||
\(778\) | 4.63214e30 | 2.04407 | ||||||||
\(779\) | 4.10021e29 | 0.178510 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.69948e29 | 0.411067 | ||||||||
\(782\) | −2.57270e30 | −1.07577 | ||||||||
\(783\) | −4.13873e28 | −0.0170753 | ||||||||
\(784\) | 2.13395e31 | 8.68691 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.99583e29 | −0.118735 | ||||||||
\(787\) | −7.03087e29 | −0.274963 | −0.137482 | − | 0.990504i | \(-0.543901\pi\) | ||||
−0.137482 | + | 0.990504i | \(0.543901\pi\) | |||||||
\(788\) | −6.78458e30 | −2.61817 | ||||||||
\(789\) | −2.02819e30 | −0.772324 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.61919e30 | −1.71282 | ||||||||
\(792\) | −1.04149e30 | −0.381101 | ||||||||
\(793\) | 7.72867e30 | 2.79085 | ||||||||
\(794\) | −9.86551e30 | −3.51564 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.07207e31 | 3.72080 | ||||||||
\(797\) | 2.01448e30 | 0.690001 | 0.345001 | − | 0.938602i | \(-0.387879\pi\) | ||||
0.345001 | + | 0.938602i | \(0.387879\pi\) | |||||||
\(798\) | 1.18030e30 | 0.398991 | ||||||||
\(799\) | 4.33230e30 | 1.44536 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.81411e29 | 0.0589552 | ||||||||
\(802\) | 4.41431e30 | 1.41590 | ||||||||
\(803\) | 8.68534e29 | 0.274963 | ||||||||
\(804\) | 3.43605e30 | 1.07367 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.26564e30 | −0.994148 | ||||||||
\(807\) | 2.06264e30 | 0.619801 | ||||||||
\(808\) | 1.18150e31 | 3.50441 | ||||||||
\(809\) | −5.38496e30 | −1.57660 | −0.788302 | − | 0.615288i | \(-0.789040\pi\) | ||||
−0.788302 | + | 0.615288i | \(0.789040\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.66080e30 | 0.473804 | 0.236902 | − | 0.971534i | \(-0.423868\pi\) | ||||
0.236902 | + | 0.971534i | \(0.423868\pi\) | |||||||
\(812\) | −1.57263e30 | −0.442884 | ||||||||
\(813\) | −2.98077e30 | −0.828664 | ||||||||
\(814\) | 1.28659e30 | 0.353089 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.07750e31 | 2.88186 | ||||||||
\(817\) | −8.41790e29 | −0.222265 | ||||||||
\(818\) | −5.73415e30 | −1.49472 | ||||||||
\(819\) | 3.67020e30 | 0.944515 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.71407e30 | −0.931638 | −0.465819 | − | 0.884880i | \(-0.654240\pi\) | ||||
−0.465819 | + | 0.884880i | \(0.654240\pi\) | |||||||
\(822\) | −5.59049e30 | −1.38451 | ||||||||
\(823\) | −1.83682e30 | −0.449126 | −0.224563 | − | 0.974460i | \(-0.572096\pi\) | ||||
−0.224563 | + | 0.974460i | \(0.572096\pi\) | |||||||
\(824\) | 1.16681e31 | 2.81686 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.80034e30 | 0.894400 | ||||||||
\(827\) | −4.85542e30 | −1.12828 | −0.564142 | − | 0.825678i | \(-0.690793\pi\) | ||||
−0.564142 | + | 0.825678i | \(0.690793\pi\) | |||||||
\(828\) | 1.58811e30 | 0.364387 | ||||||||
\(829\) | −6.43767e30 | −1.45850 | −0.729249 | − | 0.684248i | \(-0.760130\pi\) | ||||
−0.729249 | + | 0.684248i | \(0.760130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.03078e29 | 0.0448592 | ||||||||
\(832\) | 2.42705e31 | 5.29399 | ||||||||
\(833\) | 1.54494e31 | 3.32767 | ||||||||
\(834\) | −9.21696e29 | −0.196040 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.84015e29 | −0.183355 | ||||||||
\(837\) | 3.16116e29 | 0.0647484 | ||||||||
\(838\) | −4.29212e30 | −0.868179 | ||||||||
\(839\) | 3.48676e30 | 0.696500 | 0.348250 | − | 0.937402i | \(-0.386776\pi\) | ||||
0.348250 | + | 0.937402i | \(0.386776\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.09244e30 | −0.992128 | ||||||||
\(842\) | −8.78109e30 | −1.68955 | ||||||||
\(843\) | −4.76900e30 | −0.906229 | ||||||||
\(844\) | −2.04789e31 | −3.84336 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.66315e30 | −0.670604 | ||||||||
\(847\) | −8.96799e30 | −1.62151 | ||||||||
\(848\) | −5.15777e30 | −0.921098 | ||||||||
\(849\) | 1.49377e30 | 0.263483 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.23645e30 | −0.212773 | ||||||||
\(852\) | 1.08355e31 | 1.84176 | ||||||||
\(853\) | 5.20313e30 | 0.873575 | 0.436788 | − | 0.899565i | \(-0.356116\pi\) | ||||
0.436788 | + | 0.899565i | \(0.356116\pi\) | |||||||
\(854\) | −3.89391e31 | −6.45771 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.01781e31 | 1.64699 | ||||||||
\(857\) | −6.67513e30 | −1.06699 | −0.533496 | − | 0.845803i | \(-0.679122\pi\) | ||||
−0.533496 | + | 0.845803i | \(0.679122\pi\) | |||||||
\(858\) | −3.76530e30 | −0.594543 | ||||||||
\(859\) | 7.89066e29 | 0.123079 | 0.0615397 | − | 0.998105i | \(-0.480399\pi\) | ||||
0.0615397 | + | 0.998105i | \(0.480399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.42368e30 | −0.977802 | ||||||||
\(862\) | −5.52440e30 | −0.830729 | ||||||||
\(863\) | −1.23936e31 | −1.84113 | −0.920564 | − | 0.390591i | \(-0.872271\pi\) | ||||
−0.920564 | + | 0.390591i | \(0.872271\pi\) | |||||||
\(864\) | −4.80878e30 | −0.705734 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.56087e31 | 2.23578 | ||||||||
\(867\) | 3.72115e30 | 0.526594 | ||||||||
\(868\) | 1.20118e31 | 1.67938 | ||||||||
\(869\) | 1.05504e30 | 0.145735 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.82912e30 | 1.05566 | ||||||||
\(872\) | 8.79654e30 | 1.17190 | ||||||||
\(873\) | −2.75602e30 | −0.362771 | ||||||||
\(874\) | 1.16369e30 | 0.151345 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.70259e30 | 1.23195 | ||||||||
\(877\) | 8.03560e30 | 1.00814 | 0.504072 | − | 0.863662i | \(-0.331835\pi\) | ||||
0.504072 | + | 0.863662i | \(0.331835\pi\) | |||||||
\(878\) | −4.28944e30 | −0.531751 | ||||||||
\(879\) | −8.26043e30 | −1.01186 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.43033e30 | 0.769106 | 0.384553 | − | 0.923103i | \(-0.374356\pi\) | ||||
0.384553 | + | 0.923103i | \(0.374356\pi\) | |||||||
\(882\) | −1.30632e31 | −1.54393 | ||||||||
\(883\) | −1.16447e31 | −1.36000 | −0.680002 | − | 0.733210i | \(-0.738021\pi\) | ||||
−0.680002 | + | 0.733210i | \(0.738021\pi\) | |||||||
\(884\) | 4.97466e31 | 5.74136 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.12525e30 | −1.02847 | ||||||||
\(887\) | 1.24369e30 | 0.138520 | 0.0692601 | − | 0.997599i | \(-0.477936\pi\) | ||||
0.0692601 | + | 0.997599i | \(0.477936\pi\) | |||||||
\(888\) | 9.05837e30 | 0.997043 | ||||||||
\(889\) | −1.37960e29 | −0.0150067 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.64483e29 | 0.0387223 | ||||||||
\(892\) | −1.42386e31 | −1.49499 | ||||||||
\(893\) | −1.95961e30 | −0.203343 | ||||||||
\(894\) | 5.48339e30 | 0.562348 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.47178e31 | −5.48144 | ||||||||
\(897\) | 3.61856e30 | 0.358274 | ||||||||
\(898\) | −8.48436e30 | −0.830267 | ||||||||
\(899\) | −3.08630e29 | −0.0298512 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.73414e30 | −0.352842 | ||||||||
\(902\) | 6.59012e30 | 0.615495 | ||||||||
\(903\) | 1.31881e31 | 1.21748 | ||||||||
\(904\) | 3.33645e31 | 3.04450 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.34920e31 | 1.20290 | ||||||||
\(907\) | 3.37302e30 | 0.297264 | 0.148632 | − | 0.988893i | \(-0.452513\pi\) | ||||
0.148632 | + | 0.988893i | \(0.452513\pi\) | |||||||
\(908\) | −5.43325e31 | −4.73324 | ||||||||
\(909\) | −4.13482e30 | −0.356070 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.99391e31 | −1.67789 | −0.838945 | − | 0.544216i | \(-0.816827\pi\) | ||||
−0.838945 | + | 0.544216i | \(0.816827\pi\) | |||||||
\(912\) | −4.87382e30 | −0.405437 | ||||||||
\(913\) | −8.57705e29 | −0.0705334 | ||||||||
\(914\) | −1.32717e30 | −0.107892 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.50936e31 | −4.37722 | ||||||||
\(917\) | 2.51078e30 | 0.197211 | ||||||||
\(918\) | −6.59606e30 | −0.512196 | ||||||||
\(919\) | −3.09702e30 | −0.237756 | −0.118878 | − | 0.992909i | \(-0.537930\pi\) | ||||
−0.118878 | + | 0.992909i | \(0.537930\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.80587e30 | 0.735800 | ||||||||
\(922\) | 2.78643e31 | 2.06716 | ||||||||
\(923\) | 2.46890e31 | 1.81086 | ||||||||
\(924\) | 1.38496e31 | 1.00434 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.92990e31 | 2.78591 | ||||||||
\(927\) | −4.08341e30 | −0.286211 | ||||||||
\(928\) | 4.69490e30 | 0.325367 | ||||||||
\(929\) | 3.21440e30 | 0.220260 | 0.110130 | − | 0.993917i | \(-0.464873\pi\) | ||||
0.110130 | + | 0.993917i | \(0.464873\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.98816e30 | −0.468157 | ||||||||
\(932\) | 5.49033e31 | 3.63690 | ||||||||
\(933\) | 1.68830e31 | 1.10584 | ||||||||
\(934\) | 1.06717e29 | 0.00691181 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.65100e31 | −1.67885 | ||||||||
\(937\) | −4.96558e30 | −0.310960 | −0.155480 | − | 0.987839i | \(-0.549692\pi\) | ||||
−0.155480 | + | 0.987839i | \(0.549692\pi\) | |||||||
\(938\) | −3.94452e31 | −2.44267 | ||||||||
\(939\) | −4.00511e30 | −0.245259 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.65186e30 | 0.0989193 | 0.0494597 | − | 0.998776i | \(-0.484250\pi\) | ||||
0.0494597 | + | 0.998776i | \(0.484250\pi\) | |||||||
\(942\) | −2.43477e31 | −1.44186 | ||||||||
\(943\) | −6.33329e30 | −0.370900 | ||||||||
\(944\) | −1.56927e31 | −0.908851 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.35298e31 | −0.766363 | ||||||||
\(947\) | −1.15884e31 | −0.649155 | −0.324578 | − | 0.945859i | \(-0.605222\pi\) | ||||
−0.324578 | + | 0.945859i | \(0.605222\pi\) | |||||||
\(948\) | 1.17861e31 | 0.652956 | ||||||||
\(949\) | 2.21076e31 | 1.21128 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.80679e30 | 0.0968308 | ||||||||
\(952\) | −1.57963e32 | −8.37271 | ||||||||
\(953\) | 3.38294e31 | 1.77345 | 0.886724 | − | 0.462299i | \(-0.152975\pi\) | ||||
0.886724 | + | 0.462299i | \(0.152975\pi\) | |||||||
\(954\) | 3.15738e30 | 0.163708 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.75780e31 | −3.93487 | ||||||||
\(957\) | −3.55851e29 | −0.0178523 | ||||||||
\(958\) | −2.59477e31 | −1.28754 | ||||||||
\(959\) | 4.68535e31 | 2.29957 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.84682e31 | −0.886806 | ||||||||
\(962\) | 3.27487e31 | 1.55545 | ||||||||
\(963\) | −3.56196e30 | −0.167345 | ||||||||
\(964\) | −9.62997e31 | −4.47524 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.82313e31 | −0.829005 | ||||||||
\(967\) | 1.15852e30 | 0.0521104 | 0.0260552 | − | 0.999661i | \(-0.491705\pi\) | ||||
0.0260552 | + | 0.999661i | \(0.491705\pi\) | |||||||
\(968\) | 6.47760e31 | 2.88219 | ||||||||
\(969\) | −3.52857e30 | −0.155310 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.52187e30 | 0.237840 | 0.118920 | − | 0.992904i | \(-0.462057\pi\) | ||||
0.118920 | + | 0.992904i | \(0.462057\pi\) | |||||||
\(972\) | 4.07172e30 | 0.173493 | ||||||||
\(973\) | 7.72467e30 | 0.325608 | ||||||||
\(974\) | −3.71209e31 | −1.54792 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.60791e32 | 6.56204 | ||||||||
\(977\) | −4.51123e29 | −0.0182139 | −0.00910693 | − | 0.999959i | \(-0.502899\pi\) | ||||
−0.00910693 | + | 0.999959i | \(0.502899\pi\) | |||||||
\(978\) | 9.10089e30 | 0.363518 | ||||||||
\(979\) | 1.55979e30 | 0.0616378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.07847e30 | −0.119072 | ||||||||
\(982\) | 1.60545e31 | 0.614365 | ||||||||
\(983\) | −4.25669e31 | −1.61161 | −0.805805 | − | 0.592180i | \(-0.798267\pi\) | ||||
−0.805805 | + | 0.592180i | \(0.798267\pi\) | |||||||
\(984\) | 4.63984e31 | 1.73802 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.43985e30 | 0.236139 | ||||||||
\(987\) | 3.07006e31 | 1.11383 | ||||||||
\(988\) | −2.25016e31 | −0.807730 | ||||||||
\(989\) | 1.30025e31 | 0.461813 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.26274e30 | 0.113451 | 0.0567256 | − | 0.998390i | \(-0.481934\pi\) | ||||
0.0567256 | + | 0.998390i | \(0.481934\pi\) | |||||||
\(992\) | −3.58596e31 | −1.23377 | ||||||||
\(993\) | 1.75908e31 | 0.598851 | ||||||||
\(994\) | −1.24390e32 | −4.19013 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.58162e30 | −0.316021 | ||||||||
\(997\) | 3.92458e31 | 1.28084 | 0.640419 | − | 0.768026i | \(-0.278761\pi\) | ||||
0.640419 | + | 0.768026i | \(0.278761\pi\) | |||||||
\(998\) | −3.07983e31 | −0.994617 | ||||||||
\(999\) | −3.17009e30 | −0.101306 |
(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 | 75.22.a.f.1.1 | 3 | ||
5.2 | odd | 4 | 75.22.b.f.49.1 | 6 | |||
5.3 | odd | 4 | 75.22.b.f.49.6 | 6 | |||
5.4 | even | 2 | 15.22.a.c.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 45.22.a.c.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.22.a.c.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
45.22.a.c.1.1 | 3 | 15.14 | odd | 2 | |||
75.22.a.f.1.1 | 3 | 1.1 | even | 1 | trivial | ||
75.22.b.f.49.1 | 6 | 5.2 | odd | 4 | |||
75.22.b.f.49.6 | 6 | 5.3 | odd | 4 |