Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,10,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, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(38.6276877123\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 469x^{2} + 4449x - 5580 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(13.6993\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −20.9703 | −0.926764 | −0.463382 | − | 0.886159i | \(-0.653364\pi\) | ||||
−0.463382 | + | 0.886159i | \(0.653364\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −72.2477 | −0.141109 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1698.59 | 0.535067 | ||||||||
\(7\) | −3575.78 | −0.562898 | −0.281449 | − | 0.959576i | \(-0.590815\pi\) | ||||
−0.281449 | + | 0.959576i | \(0.590815\pi\) | |||||||
\(8\) | 12251.8 | 1.05754 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −74517.5 | −1.53458 | −0.767292 | − | 0.641297i | \(-0.778397\pi\) | ||||
−0.767292 | + | 0.641297i | \(0.778397\pi\) | |||||||
\(12\) | 5852.07 | 0.0814692 | ||||||||
\(13\) | 34478.5 | 0.334814 | 0.167407 | − | 0.985888i | \(-0.446461\pi\) | ||||
0.167407 | + | 0.985888i | \(0.446461\pi\) | |||||||
\(14\) | 74985.1 | 0.521674 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −219933. | −0.838979 | ||||||||
\(17\) | −372733. | −1.08237 | −0.541187 | − | 0.840902i | \(-0.682025\pi\) | ||||
−0.541187 | + | 0.840902i | \(0.682025\pi\) | |||||||
\(18\) | −137586. | −0.308921 | ||||||||
\(19\) | −835114. | −1.47013 | −0.735063 | − | 0.677998i | \(-0.762848\pi\) | ||||
−0.735063 | + | 0.677998i | \(0.762848\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 289638. | 0.324989 | ||||||||
\(22\) | 1.56265e6 | 1.42220 | ||||||||
\(23\) | −31807.7 | −0.0237005 | −0.0118503 | − | 0.999930i | \(-0.503772\pi\) | ||||
−0.0118503 | + | 0.999930i | \(0.503772\pi\) | |||||||
\(24\) | −992398. | −0.610570 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −723024. | −0.310294 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 258342. | 0.0794299 | ||||||||
\(29\) | −6.73894e6 | −1.76930 | −0.884649 | − | 0.466258i | \(-0.845602\pi\) | ||||
−0.884649 | + | 0.466258i | \(0.845602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.04277e6 | −0.786232 | −0.393116 | − | 0.919489i | \(-0.628603\pi\) | ||||
−0.393116 | + | 0.919489i | \(0.628603\pi\) | |||||||
\(32\) | −1.66087e6 | −0.280003 | ||||||||
\(33\) | 6.03591e6 | 0.885993 | ||||||||
\(34\) | 7.81631e6 | 1.00311 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −474017. | −0.0470363 | ||||||||
\(37\) | 6.29831e6 | 0.552480 | 0.276240 | − | 0.961089i | \(-0.410912\pi\) | ||||
0.276240 | + | 0.961089i | \(0.410912\pi\) | |||||||
\(38\) | 1.75126e7 | 1.36246 | ||||||||
\(39\) | −2.79276e6 | −0.193305 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.10746e7 | 0.612072 | 0.306036 | − | 0.952020i | \(-0.400997\pi\) | ||||
0.306036 | + | 0.952020i | \(0.400997\pi\) | |||||||
\(42\) | −6.07379e6 | −0.301188 | ||||||||
\(43\) | −1.42409e7 | −0.635226 | −0.317613 | − | 0.948220i | \(-0.602881\pi\) | ||||
−0.317613 | + | 0.948220i | \(0.602881\pi\) | |||||||
\(44\) | 5.38372e6 | 0.216543 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 667017. | 0.0219648 | ||||||||
\(47\) | 2.76408e7 | 0.826249 | 0.413124 | − | 0.910675i | \(-0.364437\pi\) | ||||
0.413124 | + | 0.910675i | \(0.364437\pi\) | |||||||
\(48\) | 1.78146e7 | 0.484385 | ||||||||
\(49\) | −2.75674e7 | −0.683146 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.01914e7 | 0.624909 | ||||||||
\(52\) | −2.49100e6 | −0.0472452 | ||||||||
\(53\) | 8.30946e7 | 1.44654 | 0.723272 | − | 0.690564i | \(-0.242637\pi\) | ||||
0.723272 | + | 0.690564i | \(0.242637\pi\) | |||||||
\(54\) | 1.11445e7 | 0.178356 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.38099e7 | −0.595286 | ||||||||
\(57\) | 6.76443e7 | 0.848778 | ||||||||
\(58\) | 1.41317e8 | 1.63972 | ||||||||
\(59\) | 1.04437e8 | 1.12207 | 0.561034 | − | 0.827793i | \(-0.310404\pi\) | ||||
0.561034 | + | 0.827793i | \(0.310404\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.99467e7 | 0.369400 | 0.184700 | − | 0.982795i | \(-0.440869\pi\) | ||||
0.184700 | + | 0.982795i | \(0.440869\pi\) | |||||||
\(62\) | 8.47779e7 | 0.728652 | ||||||||
\(63\) | −2.34607e7 | −0.187633 | ||||||||
\(64\) | 1.47435e8 | 1.09848 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.26575e8 | −0.821106 | ||||||||
\(67\) | −1.98351e8 | −1.20254 | −0.601268 | − | 0.799047i | \(-0.705338\pi\) | ||||
−0.601268 | + | 0.799047i | \(0.705338\pi\) | |||||||
\(68\) | 2.69291e7 | 0.152733 | ||||||||
\(69\) | 2.57643e6 | 0.0136835 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.52976e7 | 0.211550 | 0.105775 | − | 0.994390i | \(-0.466268\pi\) | ||||
0.105775 | + | 0.994390i | \(0.466268\pi\) | |||||||
\(72\) | 8.03843e7 | 0.352513 | ||||||||
\(73\) | 3.64162e8 | 1.50087 | 0.750433 | − | 0.660947i | \(-0.229845\pi\) | ||||
0.750433 | + | 0.660947i | \(0.229845\pi\) | |||||||
\(74\) | −1.32077e8 | −0.512018 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.03351e7 | 0.207448 | ||||||||
\(77\) | 2.66458e8 | 0.863815 | ||||||||
\(78\) | 5.85650e7 | 0.179148 | ||||||||
\(79\) | −4.55156e8 | −1.31473 | −0.657367 | − | 0.753570i | \(-0.728330\pi\) | ||||
−0.657367 | + | 0.753570i | \(0.728330\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −2.32238e8 | −0.567246 | ||||||||
\(83\) | 3.16569e7 | 0.0732178 | 0.0366089 | − | 0.999330i | \(-0.488344\pi\) | ||||
0.0366089 | + | 0.999330i | \(0.488344\pi\) | |||||||
\(84\) | −2.09257e7 | −0.0458589 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.98635e8 | 0.588704 | ||||||||
\(87\) | 5.45854e8 | 1.02150 | ||||||||
\(88\) | −9.12975e8 | −1.62288 | ||||||||
\(89\) | 2.77919e8 | 0.469530 | 0.234765 | − | 0.972052i | \(-0.424568\pi\) | ||||
0.234765 | + | 0.972052i | \(0.424568\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.23288e8 | −0.188466 | ||||||||
\(92\) | 2.29804e6 | 0.00334435 | ||||||||
\(93\) | 3.27464e8 | 0.453932 | ||||||||
\(94\) | −5.79636e8 | −0.765737 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.34531e8 | 0.161660 | ||||||||
\(97\) | −1.06978e9 | −1.22694 | −0.613468 | − | 0.789720i | \(-0.710226\pi\) | ||||
−0.613468 | + | 0.789720i | \(0.710226\pi\) | |||||||
\(98\) | 5.78096e8 | 0.633115 | ||||||||
\(99\) | −4.88909e8 | −0.511528 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.28777e8 | −0.505623 | −0.252811 | − | 0.967516i | \(-0.581355\pi\) | ||||
−0.252811 | + | 0.967516i | \(0.581355\pi\) | |||||||
\(102\) | −6.33121e8 | −0.579143 | ||||||||
\(103\) | −1.45019e9 | −1.26957 | −0.634786 | − | 0.772688i | \(-0.718912\pi\) | ||||
−0.634786 | + | 0.772688i | \(0.718912\pi\) | |||||||
\(104\) | 4.22425e8 | 0.354079 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.74252e9 | −1.34060 | ||||||||
\(107\) | −1.18511e8 | −0.0874043 | −0.0437021 | − | 0.999045i | \(-0.513915\pi\) | ||||
−0.0437021 | + | 0.999045i | \(0.513915\pi\) | |||||||
\(108\) | 3.83954e7 | 0.0271564 | ||||||||
\(109\) | 1.47459e9 | 1.00058 | 0.500289 | − | 0.865859i | \(-0.333227\pi\) | ||||
0.500289 | + | 0.865859i | \(0.333227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.10163e8 | −0.318974 | ||||||||
\(112\) | 7.86434e8 | 0.472260 | ||||||||
\(113\) | −1.73649e9 | −1.00189 | −0.500943 | − | 0.865480i | \(-0.667013\pi\) | ||||
−0.500943 | + | 0.865480i | \(0.667013\pi\) | |||||||
\(114\) | −1.41852e9 | −0.786617 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.86873e8 | 0.249663 | ||||||||
\(117\) | 2.26214e8 | 0.111605 | ||||||||
\(118\) | −2.19006e9 | −1.03989 | ||||||||
\(119\) | 1.33281e9 | 0.609267 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.19490e9 | 1.35495 | ||||||||
\(122\) | −8.37694e8 | −0.342347 | ||||||||
\(123\) | −8.97046e8 | −0.353380 | ||||||||
\(124\) | 2.92081e8 | 0.110944 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.91977e8 | 0.173891 | ||||||||
\(127\) | −2.07925e9 | −0.709235 | −0.354618 | − | 0.935011i | \(-0.615389\pi\) | ||||
−0.354618 | + | 0.935011i | \(0.615389\pi\) | |||||||
\(128\) | −2.24138e9 | −0.738025 | ||||||||
\(129\) | 1.15351e9 | 0.366748 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.49740e9 | 1.92761 | 0.963804 | − | 0.266612i | \(-0.0859043\pi\) | ||||
0.963804 | + | 0.266612i | \(0.0859043\pi\) | |||||||
\(132\) | −4.36081e8 | −0.125021 | ||||||||
\(133\) | 2.98619e9 | 0.827532 | ||||||||
\(134\) | 4.15948e9 | 1.11447 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.56666e9 | −1.14465 | ||||||||
\(137\) | 2.45780e9 | 0.596080 | 0.298040 | − | 0.954553i | \(-0.403667\pi\) | ||||
0.298040 | + | 0.954553i | \(0.403667\pi\) | |||||||
\(138\) | −5.40284e7 | −0.0126814 | ||||||||
\(139\) | −5.53229e9 | −1.25701 | −0.628505 | − | 0.777806i | \(-0.716333\pi\) | ||||
−0.628505 | + | 0.777806i | \(0.716333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.23891e9 | −0.477035 | ||||||||
\(142\) | −9.49903e8 | −0.196057 | ||||||||
\(143\) | −2.56925e9 | −0.513801 | ||||||||
\(144\) | −1.44298e9 | −0.279660 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.63657e9 | −1.39095 | ||||||||
\(147\) | 2.23296e9 | 0.394414 | ||||||||
\(148\) | −4.55038e8 | −0.0779597 | ||||||||
\(149\) | 1.06402e10 | 1.76852 | 0.884261 | − | 0.466994i | \(-0.154663\pi\) | ||||
0.884261 | + | 0.466994i | \(0.154663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.40470e9 | 0.846009 | 0.423005 | − | 0.906128i | \(-0.360975\pi\) | ||||
0.423005 | + | 0.906128i | \(0.360975\pi\) | |||||||
\(152\) | −1.02317e10 | −1.55472 | ||||||||
\(153\) | −2.44550e9 | −0.360792 | ||||||||
\(154\) | −5.58770e9 | −0.800553 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.01771e8 | 0.0272770 | ||||||||
\(157\) | 7.89002e9 | 1.03641 | 0.518203 | − | 0.855258i | \(-0.326601\pi\) | ||||
0.518203 | + | 0.855258i | \(0.326601\pi\) | |||||||
\(158\) | 9.54474e9 | 1.21845 | ||||||||
\(159\) | −6.73066e9 | −0.835162 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.13738e8 | 0.0133410 | ||||||||
\(162\) | −9.02701e8 | −0.102974 | ||||||||
\(163\) | 1.43411e10 | 1.59125 | 0.795627 | − | 0.605787i | \(-0.207142\pi\) | ||||
0.795627 | + | 0.605787i | \(0.207142\pi\) | |||||||
\(164\) | −8.00118e8 | −0.0863688 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.63853e8 | −0.0678556 | ||||||||
\(167\) | 1.43038e10 | 1.42308 | 0.711539 | − | 0.702647i | \(-0.247999\pi\) | ||||
0.711539 | + | 0.702647i | \(0.247999\pi\) | |||||||
\(168\) | 3.54860e9 | 0.343689 | ||||||||
\(169\) | −9.41573e9 | −0.887900 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.47919e9 | −0.490042 | ||||||||
\(172\) | 1.02887e9 | 0.0896360 | ||||||||
\(173\) | 3.74604e9 | 0.317955 | 0.158977 | − | 0.987282i | \(-0.449180\pi\) | ||||
0.158977 | + | 0.987282i | \(0.449180\pi\) | |||||||
\(174\) | −1.14467e10 | −0.946693 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.63889e10 | 1.28749 | ||||||||
\(177\) | −8.45937e9 | −0.647826 | ||||||||
\(178\) | −5.82804e9 | −0.435144 | ||||||||
\(179\) | 2.22667e9 | 0.162113 | 0.0810565 | − | 0.996710i | \(-0.474171\pi\) | ||||
0.0810565 | + | 0.996710i | \(0.474171\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.08908e10 | −1.44678 | −0.723388 | − | 0.690442i | \(-0.757416\pi\) | ||||
−0.723388 | + | 0.690442i | \(0.757416\pi\) | |||||||
\(182\) | 2.58538e9 | 0.174664 | ||||||||
\(183\) | −3.23569e9 | −0.213273 | ||||||||
\(184\) | −3.89703e8 | −0.0250642 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.86701e9 | −0.420687 | ||||||||
\(187\) | 2.77751e10 | 1.66100 | ||||||||
\(188\) | −1.99699e9 | −0.116591 | ||||||||
\(189\) | 1.90032e9 | 0.108330 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.10380e9 | 0.0600125 | 0.0300062 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300062 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(192\) | −1.19422e10 | −0.634205 | ||||||||
\(193\) | 2.76093e10 | 1.43234 | 0.716171 | − | 0.697925i | \(-0.245893\pi\) | ||||
0.716171 | + | 0.697925i | \(0.245893\pi\) | |||||||
\(194\) | 2.24336e10 | 1.13708 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.99168e9 | 0.0963979 | ||||||||
\(197\) | −3.05799e10 | −1.44656 | −0.723282 | − | 0.690553i | \(-0.757367\pi\) | ||||
−0.723282 | + | 0.690553i | \(0.757367\pi\) | |||||||
\(198\) | 1.02526e10 | 0.474066 | ||||||||
\(199\) | 7.92786e9 | 0.358358 | 0.179179 | − | 0.983816i | \(-0.442656\pi\) | ||||
0.179179 | + | 0.983816i | \(0.442656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.60664e10 | 0.694285 | ||||||||
\(202\) | 1.10886e10 | 0.468593 | ||||||||
\(203\) | 2.40970e10 | 0.995934 | ||||||||
\(204\) | −2.18126e9 | −0.0881802 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.04109e10 | 1.17659 | ||||||||
\(207\) | −2.08691e8 | −0.00790017 | ||||||||
\(208\) | −7.58298e9 | −0.280902 | ||||||||
\(209\) | 6.22306e10 | 2.25603 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.97409e9 | −0.138028 | −0.0690139 | − | 0.997616i | \(-0.521985\pi\) | ||||
−0.0690139 | + | 0.997616i | \(0.521985\pi\) | |||||||
\(212\) | −6.00340e9 | −0.204120 | ||||||||
\(213\) | −3.66911e9 | −0.122138 | ||||||||
\(214\) | 2.48521e9 | 0.0810031 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.51113e9 | −0.203523 | ||||||||
\(217\) | 1.44561e10 | 0.442569 | ||||||||
\(218\) | −3.09225e10 | −0.927299 | ||||||||
\(219\) | −2.94971e10 | −0.866525 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.28513e10 | −0.362394 | ||||||||
\(222\) | 1.06983e10 | 0.295614 | ||||||||
\(223\) | −4.90677e10 | −1.32869 | −0.664345 | − | 0.747426i | \(-0.731289\pi\) | ||||
−0.664345 | + | 0.747426i | \(0.731289\pi\) | |||||||
\(224\) | 5.93893e9 | 0.157613 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.64146e10 | 0.928512 | ||||||||
\(227\) | 4.97991e10 | 1.24482 | 0.622408 | − | 0.782693i | \(-0.286154\pi\) | ||||
0.622408 | + | 0.782693i | \(0.286154\pi\) | |||||||
\(228\) | −4.88714e9 | −0.119770 | ||||||||
\(229\) | −3.84531e10 | −0.923999 | −0.462000 | − | 0.886880i | \(-0.652868\pi\) | ||||
−0.462000 | + | 0.886880i | \(0.652868\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.15831e10 | −0.498724 | ||||||||
\(232\) | −8.25644e10 | −1.87110 | ||||||||
\(233\) | 5.45563e9 | 0.121267 | 0.0606336 | − | 0.998160i | \(-0.480688\pi\) | ||||
0.0606336 | + | 0.998160i | \(0.480688\pi\) | |||||||
\(234\) | −4.74376e9 | −0.103431 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.54531e9 | −0.158334 | ||||||||
\(237\) | 3.68676e10 | 0.759062 | ||||||||
\(238\) | −2.79494e10 | −0.564646 | ||||||||
\(239\) | −5.86338e10 | −1.16240 | −0.581202 | − | 0.813759i | \(-0.697418\pi\) | ||||
−0.581202 | + | 0.813759i | \(0.697418\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.28707e10 | −0.436719 | −0.218360 | − | 0.975868i | \(-0.570071\pi\) | ||||
−0.218360 | + | 0.975868i | \(0.570071\pi\) | |||||||
\(242\) | −6.69980e10 | −1.25572 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −2.88606e9 | −0.0521256 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.88113e10 | 0.327500 | ||||||||
\(247\) | −2.87935e10 | −0.492219 | ||||||||
\(248\) | −4.95313e10 | −0.831471 | ||||||||
\(249\) | −2.56421e9 | −0.0422723 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.14619e10 | −0.182275 | −0.0911374 | − | 0.995838i | \(-0.529050\pi\) | ||||
−0.0911374 | + | 0.995838i | \(0.529050\pi\) | |||||||
\(252\) | 1.69498e9 | 0.0264766 | ||||||||
\(253\) | 2.37023e9 | 0.0363704 | ||||||||
\(254\) | 4.36025e10 | 0.657293 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.84843e10 | −0.414501 | ||||||||
\(257\) | 7.03335e10 | 1.00569 | 0.502844 | − | 0.864377i | \(-0.332287\pi\) | ||||
0.502844 | + | 0.864377i | \(0.332287\pi\) | |||||||
\(258\) | −2.41894e10 | −0.339889 | ||||||||
\(259\) | −2.25214e10 | −0.310990 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.42142e10 | −0.589766 | ||||||||
\(262\) | −1.36252e11 | −1.78644 | ||||||||
\(263\) | −1.11602e11 | −1.43838 | −0.719188 | − | 0.694815i | \(-0.755486\pi\) | ||||
−0.719188 | + | 0.694815i | \(0.755486\pi\) | |||||||
\(264\) | 7.39510e10 | 0.936972 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.26212e10 | −0.766926 | ||||||||
\(267\) | −2.25115e10 | −0.271083 | ||||||||
\(268\) | 1.43304e10 | 0.169688 | ||||||||
\(269\) | −6.35228e10 | −0.739680 | −0.369840 | − | 0.929095i | \(-0.620588\pi\) | ||||
−0.369840 | + | 0.929095i | \(0.620588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.97056e8 | −0.00897691 | −0.00448845 | − | 0.999990i | \(-0.501429\pi\) | ||||
−0.00448845 | + | 0.999990i | \(0.501429\pi\) | |||||||
\(272\) | 8.19764e10 | 0.908090 | ||||||||
\(273\) | 9.98631e9 | 0.108811 | ||||||||
\(274\) | −5.15408e10 | −0.552425 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.86141e8 | −0.00193086 | ||||||||
\(277\) | 3.68479e10 | 0.376057 | 0.188029 | − | 0.982164i | \(-0.439790\pi\) | ||||
0.188029 | + | 0.982164i | \(0.439790\pi\) | |||||||
\(278\) | 1.16014e11 | 1.16495 | ||||||||
\(279\) | −2.65246e10 | −0.262077 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.86433e10 | 0.752460 | 0.376230 | − | 0.926526i | \(-0.377220\pi\) | ||||
0.376230 | + | 0.926526i | \(0.377220\pi\) | |||||||
\(282\) | 4.69505e10 | 0.442099 | ||||||||
\(283\) | 3.08266e10 | 0.285685 | 0.142842 | − | 0.989745i | \(-0.454376\pi\) | ||||
0.142842 | + | 0.989745i | \(0.454376\pi\) | |||||||
\(284\) | −3.27265e9 | −0.0298515 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.38779e10 | 0.476172 | ||||||||
\(287\) | −3.96005e10 | −0.344534 | ||||||||
\(288\) | −1.08970e10 | −0.0933342 | ||||||||
\(289\) | 2.03420e10 | 0.171535 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.66522e10 | 0.708372 | ||||||||
\(292\) | −2.63099e10 | −0.211785 | ||||||||
\(293\) | 6.04362e10 | 0.479064 | 0.239532 | − | 0.970889i | \(-0.423006\pi\) | ||||
0.239532 | + | 0.970889i | \(0.423006\pi\) | |||||||
\(294\) | −4.68257e10 | −0.365529 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.71658e10 | 0.584268 | ||||||||
\(297\) | 3.96016e10 | 0.295331 | ||||||||
\(298\) | −2.23127e11 | −1.63900 | ||||||||
\(299\) | −1.09668e9 | −0.00793526 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.09222e10 | 0.357568 | ||||||||
\(302\) | −1.13338e11 | −0.784051 | ||||||||
\(303\) | 4.28309e10 | 0.291921 | ||||||||
\(304\) | 1.83670e11 | 1.23341 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.12828e10 | 0.334369 | ||||||||
\(307\) | 2.37829e11 | 1.52807 | 0.764034 | − | 0.645176i | \(-0.223216\pi\) | ||||
0.764034 | + | 0.645176i | \(0.223216\pi\) | |||||||
\(308\) | −1.92510e10 | −0.121892 | ||||||||
\(309\) | 1.17465e11 | 0.732988 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.05237e11 | −0.637892 | −0.318946 | − | 0.947773i | \(-0.603329\pi\) | ||||
−0.318946 | + | 0.947773i | \(0.603329\pi\) | |||||||
\(312\) | −3.42164e10 | −0.204427 | ||||||||
\(313\) | 1.21699e11 | 0.716702 | 0.358351 | − | 0.933587i | \(-0.383339\pi\) | ||||
0.358351 | + | 0.933587i | \(0.383339\pi\) | |||||||
\(314\) | −1.65456e11 | −0.960504 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.28840e10 | 0.185521 | ||||||||
\(317\) | 8.05511e10 | 0.448028 | 0.224014 | − | 0.974586i | \(-0.428084\pi\) | ||||
0.224014 | + | 0.974586i | \(0.428084\pi\) | |||||||
\(318\) | 1.41144e11 | 0.773998 | ||||||||
\(319\) | 5.02169e11 | 2.71514 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.59941e9 | 0.0504629 | ||||||||
\(322\) | −2.38511e9 | −0.0123639 | ||||||||
\(323\) | 3.11275e11 | 1.59123 | ||||||||
\(324\) | −3.11003e9 | −0.0156788 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.00738e11 | −1.47472 | ||||||||
\(327\) | −1.19441e11 | −0.577684 | ||||||||
\(328\) | 1.35685e11 | 0.647290 | ||||||||
\(329\) | −9.88376e10 | −0.465094 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.15934e11 | −0.988769 | −0.494385 | − | 0.869243i | \(-0.664607\pi\) | ||||
−0.494385 | + | 0.869243i | \(0.664607\pi\) | |||||||
\(332\) | −2.28714e9 | −0.0103317 | ||||||||
\(333\) | 4.13232e10 | 0.184160 | ||||||||
\(334\) | −2.99955e11 | −1.31886 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.37012e10 | −0.272659 | ||||||||
\(337\) | 1.13654e10 | 0.0480010 | 0.0240005 | − | 0.999712i | \(-0.492360\pi\) | ||||
0.0240005 | + | 0.999712i | \(0.492360\pi\) | |||||||
\(338\) | 1.97450e11 | 0.822873 | ||||||||
\(339\) | 1.40655e11 | 0.578439 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.01257e11 | 1.20654 | ||||||||
\(342\) | 1.14900e11 | 0.454153 | ||||||||
\(343\) | 2.42871e11 | 0.947440 | ||||||||
\(344\) | −1.74477e11 | −0.671776 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.85555e10 | −0.294669 | ||||||||
\(347\) | −1.23817e11 | −0.458455 | −0.229228 | − | 0.973373i | \(-0.573620\pi\) | ||||
−0.229228 | + | 0.973373i | \(0.573620\pi\) | |||||||
\(348\) | −3.94367e10 | −0.144143 | ||||||||
\(349\) | −1.76035e11 | −0.635161 | −0.317580 | − | 0.948231i | \(-0.602870\pi\) | ||||
−0.317580 | + | 0.948231i | \(0.602870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.83233e10 | −0.0644350 | ||||||||
\(352\) | 1.23764e11 | 0.429688 | ||||||||
\(353\) | −5.17450e11 | −1.77371 | −0.886853 | − | 0.462051i | \(-0.847114\pi\) | ||||
−0.886853 | + | 0.462051i | \(0.847114\pi\) | |||||||
\(354\) | 1.77395e11 | 0.600381 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.00790e10 | −0.0662549 | ||||||||
\(357\) | −1.07958e11 | −0.351760 | ||||||||
\(358\) | −4.66939e10 | −0.150240 | ||||||||
\(359\) | −2.86436e11 | −0.910128 | −0.455064 | − | 0.890459i | \(-0.650384\pi\) | ||||
−0.455064 | + | 0.890459i | \(0.650384\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.74728e11 | 1.16127 | ||||||||
\(362\) | 4.38086e11 | 1.34082 | ||||||||
\(363\) | −2.58787e11 | −0.782281 | ||||||||
\(364\) | 8.90726e9 | 0.0265943 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.78532e10 | 0.197654 | ||||||||
\(367\) | 1.20491e11 | 0.346704 | 0.173352 | − | 0.984860i | \(-0.444540\pi\) | ||||
0.173352 | + | 0.984860i | \(0.444540\pi\) | |||||||
\(368\) | 6.99559e9 | 0.0198842 | ||||||||
\(369\) | 7.26607e10 | 0.204024 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.97128e11 | −0.814257 | ||||||||
\(372\) | −2.36585e10 | −0.0640537 | ||||||||
\(373\) | 4.05791e11 | 1.08546 | 0.542728 | − | 0.839909i | \(-0.317391\pi\) | ||||
0.542728 | + | 0.839909i | \(0.317391\pi\) | |||||||
\(374\) | −5.82452e11 | −1.53935 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.38651e11 | 0.873790 | ||||||||
\(377\) | −2.32349e11 | −0.592386 | ||||||||
\(378\) | −3.98502e10 | −0.100396 | ||||||||
\(379\) | −2.12253e11 | −0.528418 | −0.264209 | − | 0.964465i | \(-0.585111\pi\) | ||||
−0.264209 | + | 0.964465i | \(0.585111\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.68419e11 | 0.409477 | ||||||||
\(382\) | −2.31470e10 | −0.0556174 | ||||||||
\(383\) | −4.96937e10 | −0.118007 | −0.0590034 | − | 0.998258i | \(-0.518792\pi\) | ||||
−0.0590034 | + | 0.998258i | \(0.518792\pi\) | |||||||
\(384\) | 1.81552e11 | 0.426099 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.78974e11 | −1.32744 | ||||||||
\(387\) | −9.34343e10 | −0.211742 | ||||||||
\(388\) | 7.72892e10 | 0.173131 | ||||||||
\(389\) | 2.74472e11 | 0.607750 | 0.303875 | − | 0.952712i | \(-0.401720\pi\) | ||||
0.303875 | + | 0.952712i | \(0.401720\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18558e10 | 0.0256528 | ||||||||
\(392\) | −3.37751e11 | −0.722453 | ||||||||
\(393\) | −5.26289e11 | −1.11290 | ||||||||
\(394\) | 6.41268e11 | 1.34062 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.53226e10 | 0.0721812 | ||||||||
\(397\) | −2.17106e10 | −0.0438646 | −0.0219323 | − | 0.999759i | \(-0.506982\pi\) | ||||
−0.0219323 | + | 0.999759i | \(0.506982\pi\) | |||||||
\(398\) | −1.66249e11 | −0.332113 | ||||||||
\(399\) | −2.41881e11 | −0.477776 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.16300e11 | 0.417741 | 0.208871 | − | 0.977943i | \(-0.433021\pi\) | ||||
0.208871 | + | 0.977943i | \(0.433021\pi\) | |||||||
\(402\) | −3.36918e11 | −0.643438 | ||||||||
\(403\) | −1.39389e11 | −0.263242 | ||||||||
\(404\) | 3.82029e10 | 0.0713478 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.05320e11 | −0.922996 | ||||||||
\(407\) | −4.69334e11 | −0.847827 | ||||||||
\(408\) | 3.69900e11 | 0.660866 | ||||||||
\(409\) | −2.30916e11 | −0.408037 | −0.204019 | − | 0.978967i | \(-0.565400\pi\) | ||||
−0.204019 | + | 0.978967i | \(0.565400\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.99082e11 | −0.344147 | ||||||||
\(412\) | 1.04773e11 | 0.179148 | ||||||||
\(413\) | −3.73443e11 | −0.631610 | ||||||||
\(414\) | 4.37630e9 | 0.00732159 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.72645e10 | −0.0937488 | ||||||||
\(417\) | 4.48116e11 | 0.725735 | ||||||||
\(418\) | −1.30499e12 | −2.09081 | ||||||||
\(419\) | 2.38946e11 | 0.378736 | 0.189368 | − | 0.981906i | \(-0.439356\pi\) | ||||
0.189368 | + | 0.981906i | \(0.439356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.09581e11 | 0.635434 | 0.317717 | − | 0.948186i | \(-0.397084\pi\) | ||||
0.317717 | + | 0.948186i | \(0.397084\pi\) | |||||||
\(422\) | 8.33377e10 | 0.127919 | ||||||||
\(423\) | 1.81352e11 | 0.275416 | ||||||||
\(424\) | 1.01806e12 | 1.52977 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.69421e10 | 0.113193 | ||||||||
\(427\) | −1.42841e11 | −0.207935 | ||||||||
\(428\) | 8.56217e9 | 0.0123335 | ||||||||
\(429\) | 2.08109e11 | 0.296643 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.29879e11 | 0.739655 | 0.369828 | − | 0.929100i | \(-0.379417\pi\) | ||||
0.369828 | + | 0.929100i | \(0.379417\pi\) | |||||||
\(432\) | 1.16882e11 | 0.161462 | ||||||||
\(433\) | −1.70997e11 | −0.233772 | −0.116886 | − | 0.993145i | \(-0.537291\pi\) | ||||
−0.116886 | + | 0.993145i | \(0.537291\pi\) | |||||||
\(434\) | −3.03147e11 | −0.410157 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.06535e11 | −0.141190 | ||||||||
\(437\) | 2.65631e10 | 0.0348427 | ||||||||
\(438\) | 6.18563e11 | 0.803064 | ||||||||
\(439\) | −2.23652e11 | −0.287398 | −0.143699 | − | 0.989621i | \(-0.545900\pi\) | ||||
−0.143699 | + | 0.989621i | \(0.545900\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.80870e11 | −0.227715 | ||||||||
\(442\) | 2.69495e11 | 0.335854 | ||||||||
\(443\) | −8.32773e11 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671712\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671712\pi\) | |||||||
\(444\) | 3.68581e10 | 0.0450101 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.02896e12 | 1.23138 | ||||||||
\(447\) | −8.61854e11 | −1.02106 | ||||||||
\(448\) | −5.27195e11 | −0.618330 | ||||||||
\(449\) | −5.62842e11 | −0.653549 | −0.326774 | − | 0.945102i | \(-0.605962\pi\) | ||||
−0.326774 | + | 0.945102i | \(0.605962\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.25254e11 | −0.939276 | ||||||||
\(452\) | 1.25457e11 | 0.141375 | ||||||||
\(453\) | −4.37780e11 | −0.488444 | ||||||||
\(454\) | −1.04430e12 | −1.15365 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.28766e11 | 0.897615 | ||||||||
\(457\) | −7.43811e11 | −0.797700 | −0.398850 | − | 0.917016i | \(-0.630591\pi\) | ||||
−0.398850 | + | 0.917016i | \(0.630591\pi\) | |||||||
\(458\) | 8.06372e11 | 0.856329 | ||||||||
\(459\) | 1.98086e11 | 0.208303 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.90060e11 | −1.02096 | −0.510478 | − | 0.859891i | \(-0.670532\pi\) | ||||
−0.510478 | + | 0.859891i | \(0.670532\pi\) | |||||||
\(462\) | 4.52604e11 | 0.462199 | ||||||||
\(463\) | −7.40358e11 | −0.748734 | −0.374367 | − | 0.927281i | \(-0.622140\pi\) | ||||
−0.374367 | + | 0.927281i | \(0.622140\pi\) | |||||||
\(464\) | 1.48212e12 | 1.48440 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.14406e11 | −0.112386 | ||||||||
\(467\) | 1.86063e11 | 0.181023 | 0.0905114 | − | 0.995895i | \(-0.471150\pi\) | ||||
0.0905114 | + | 0.995895i | \(0.471150\pi\) | |||||||
\(468\) | −1.63434e10 | −0.0157484 | ||||||||
\(469\) | 7.09261e11 | 0.676906 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.39092e11 | −0.598369 | ||||||||
\(472\) | 1.27954e12 | 1.18663 | ||||||||
\(473\) | 1.06119e12 | 0.974808 | ||||||||
\(474\) | −7.73124e11 | −0.703472 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.62926e10 | −0.0859729 | ||||||||
\(477\) | 5.45184e11 | 0.482181 | ||||||||
\(478\) | 1.22957e12 | 1.07727 | ||||||||
\(479\) | 5.77280e11 | 0.501045 | 0.250522 | − | 0.968111i | \(-0.419398\pi\) | ||||
0.250522 | + | 0.968111i | \(0.419398\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.17156e11 | 0.184978 | ||||||||
\(482\) | 4.79604e11 | 0.404736 | ||||||||
\(483\) | −9.21274e9 | −0.00770241 | ||||||||
\(484\) | −2.30824e11 | −0.191196 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.31188e10 | 0.0594519 | ||||||||
\(487\) | −2.33534e12 | −1.88135 | −0.940675 | − | 0.339310i | \(-0.889806\pi\) | ||||
−0.940675 | + | 0.339310i | \(0.889806\pi\) | |||||||
\(488\) | 4.89421e11 | 0.390655 | ||||||||
\(489\) | −1.16163e12 | −0.918711 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.07091e11 | 0.704343 | 0.352171 | − | 0.935936i | \(-0.385443\pi\) | ||||
0.352171 | + | 0.935936i | \(0.385443\pi\) | |||||||
\(492\) | 6.48095e10 | 0.0498650 | ||||||||
\(493\) | 2.51183e12 | 1.91504 | ||||||||
\(494\) | 6.03808e11 | 0.456171 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.89139e11 | 0.659633 | ||||||||
\(497\) | −1.61974e11 | −0.119081 | ||||||||
\(498\) | 5.37721e10 | 0.0391764 | ||||||||
\(499\) | −1.13701e12 | −0.820937 | −0.410469 | − | 0.911875i | \(-0.634635\pi\) | ||||
−0.410469 | + | 0.911875i | \(0.634635\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.15861e12 | −0.821614 | ||||||||
\(502\) | 2.40360e11 | 0.168926 | ||||||||
\(503\) | −1.85806e11 | −0.129421 | −0.0647103 | − | 0.997904i | \(-0.520612\pi\) | ||||
−0.0647103 | + | 0.997904i | \(0.520612\pi\) | |||||||
\(504\) | −2.87437e11 | −0.198429 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.97044e10 | −0.0337068 | ||||||||
\(507\) | 7.62674e11 | 0.512629 | ||||||||
\(508\) | 1.50221e11 | 0.100079 | ||||||||
\(509\) | 7.38201e11 | 0.487466 | 0.243733 | − | 0.969842i | \(-0.421628\pi\) | ||||
0.243733 | + | 0.969842i | \(0.421628\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.30216e12 | −0.844834 | ||||||||
\(512\) | 1.74491e12 | 1.12217 | ||||||||
\(513\) | 4.43814e11 | 0.282926 | ||||||||
\(514\) | −1.47491e12 | −0.932035 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.33384e10 | −0.0517514 | ||||||||
\(517\) | −2.05972e12 | −1.26795 | ||||||||
\(518\) | 4.72279e11 | 0.288214 | ||||||||
\(519\) | −3.03429e11 | −0.183571 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.17044e11 | −0.0695955 | −0.0347977 | − | 0.999394i | \(-0.511079\pi\) | ||||
−0.0347977 | + | 0.999394i | \(0.511079\pi\) | |||||||
\(522\) | 9.27184e11 | 0.546573 | ||||||||
\(523\) | −1.53771e12 | −0.898707 | −0.449354 | − | 0.893354i | \(-0.648346\pi\) | ||||
−0.449354 | + | 0.893354i | \(0.648346\pi\) | |||||||
\(524\) | −4.69422e11 | −0.272002 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.34033e12 | 1.33304 | ||||||||
\(527\) | 1.50687e12 | 0.850998 | ||||||||
\(528\) | −1.32750e12 | −0.743330 | ||||||||
\(529\) | −1.80014e12 | −0.999438 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.85209e11 | 0.374022 | ||||||||
\(532\) | −2.15745e11 | −0.116772 | ||||||||
\(533\) | 3.81838e11 | 0.204930 | ||||||||
\(534\) | 4.72072e11 | 0.251230 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.43017e12 | −1.27173 | ||||||||
\(537\) | −1.80360e11 | −0.0935960 | ||||||||
\(538\) | 1.33209e12 | 0.685509 | ||||||||
\(539\) | 2.05425e12 | 1.04834 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.24717e12 | −1.12784 | −0.563922 | − | 0.825828i | \(-0.690708\pi\) | ||||
−0.563922 | + | 0.825828i | \(0.690708\pi\) | |||||||
\(542\) | 1.67145e10 | 0.00831947 | ||||||||
\(543\) | 1.69215e12 | 0.835297 | ||||||||
\(544\) | 6.19063e11 | 0.303068 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.09416e11 | −0.100842 | ||||||||
\(547\) | 2.72880e12 | 1.30325 | 0.651625 | − | 0.758541i | \(-0.274087\pi\) | ||||
0.651625 | + | 0.758541i | \(0.274087\pi\) | |||||||
\(548\) | −1.77571e11 | −0.0841122 | ||||||||
\(549\) | 2.62091e11 | 0.123133 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.62779e12 | 2.60109 | ||||||||
\(552\) | 3.15660e10 | 0.0144708 | ||||||||
\(553\) | 1.62754e12 | 0.740062 | ||||||||
\(554\) | −7.72711e11 | −0.348516 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.99695e11 | 0.177375 | ||||||||
\(557\) | −1.50494e12 | −0.662477 | −0.331238 | − | 0.943547i | \(-0.607466\pi\) | ||||
−0.331238 | + | 0.943547i | \(0.607466\pi\) | |||||||
\(558\) | 5.56228e11 | 0.242884 | ||||||||
\(559\) | −4.91004e11 | −0.212683 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.24978e12 | −0.958976 | ||||||||
\(562\) | −1.64917e12 | −0.697353 | ||||||||
\(563\) | 1.28466e12 | 0.538892 | 0.269446 | − | 0.963015i | \(-0.413159\pi\) | ||||
0.269446 | + | 0.963015i | \(0.413159\pi\) | |||||||
\(564\) | 1.61756e11 | 0.0673138 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.46443e11 | −0.264762 | ||||||||
\(567\) | −1.53926e11 | −0.0625442 | ||||||||
\(568\) | 5.54979e11 | 0.223722 | ||||||||
\(569\) | 4.36230e12 | 1.74466 | 0.872329 | − | 0.488920i | \(-0.162609\pi\) | ||||
0.872329 | + | 0.488920i | \(0.162609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.22894e12 | −0.877475 | −0.438738 | − | 0.898615i | \(-0.644574\pi\) | ||||
−0.438738 | + | 0.898615i | \(0.644574\pi\) | |||||||
\(572\) | 1.85623e11 | 0.0725018 | ||||||||
\(573\) | −8.94080e10 | −0.0346482 | ||||||||
\(574\) | 8.30434e11 | 0.319302 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.67320e11 | 0.366159 | ||||||||
\(577\) | 2.37578e12 | 0.892307 | 0.446153 | − | 0.894956i | \(-0.352794\pi\) | ||||
0.446153 | + | 0.894956i | \(0.352794\pi\) | |||||||
\(578\) | −4.26576e11 | −0.158972 | ||||||||
\(579\) | −2.23635e12 | −0.826963 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.13198e11 | −0.0412142 | ||||||||
\(582\) | −1.81712e12 | −0.656493 | ||||||||
\(583\) | −6.19200e12 | −2.21984 | ||||||||
\(584\) | 4.46165e12 | 1.58722 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.26736e12 | −0.443979 | ||||||||
\(587\) | −4.85338e12 | −1.68722 | −0.843612 | − | 0.536954i | \(-0.819575\pi\) | ||||
−0.843612 | + | 0.536954i | \(0.819575\pi\) | |||||||
\(588\) | −1.61326e11 | −0.0556553 | ||||||||
\(589\) | 3.37617e12 | 1.15586 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.47697e12 | 0.835174 | ||||||||
\(592\) | −1.38521e12 | −0.463519 | ||||||||
\(593\) | −3.40807e12 | −1.13178 | −0.565891 | − | 0.824480i | \(-0.691468\pi\) | ||||
−0.565891 | + | 0.824480i | \(0.691468\pi\) | |||||||
\(594\) | −8.30457e11 | −0.273702 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.68728e11 | −0.249554 | ||||||||
\(597\) | −6.42157e11 | −0.206898 | ||||||||
\(598\) | 2.29978e10 | 0.00735412 | ||||||||
\(599\) | −9.36596e11 | −0.297257 | −0.148628 | − | 0.988893i | \(-0.547486\pi\) | ||||
−0.148628 | + | 0.988893i | \(0.547486\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.48082e12 | 0.775639 | 0.387820 | − | 0.921735i | \(-0.373228\pi\) | ||||
0.387820 | + | 0.921735i | \(0.373228\pi\) | |||||||
\(602\) | −1.06785e12 | −0.331381 | ||||||||
\(603\) | −1.30138e12 | −0.400845 | ||||||||
\(604\) | −3.90477e11 | −0.119379 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.98176e11 | −0.270542 | ||||||||
\(607\) | 5.87176e12 | 1.75557 | 0.877787 | − | 0.479052i | \(-0.159019\pi\) | ||||
0.877787 | + | 0.479052i | \(0.159019\pi\) | |||||||
\(608\) | 1.38702e12 | 0.411639 | ||||||||
\(609\) | −1.95186e12 | −0.575003 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.53015e11 | 0.276640 | ||||||||
\(612\) | 1.76682e11 | 0.0509109 | ||||||||
\(613\) | −3.44781e11 | −0.0986215 | −0.0493108 | − | 0.998783i | \(-0.515702\pi\) | ||||
−0.0493108 | + | 0.998783i | \(0.515702\pi\) | |||||||
\(614\) | −4.98734e12 | −1.41616 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.26460e12 | 0.913518 | ||||||||
\(617\) | 3.81915e12 | 1.06092 | 0.530461 | − | 0.847709i | \(-0.322019\pi\) | ||||
0.530461 | + | 0.847709i | \(0.322019\pi\) | |||||||
\(618\) | −2.46328e12 | −0.679306 | ||||||||
\(619\) | 8.91644e11 | 0.244109 | 0.122055 | − | 0.992523i | \(-0.461052\pi\) | ||||
0.122055 | + | 0.992523i | \(0.461052\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.69039e10 | 0.00456116 | ||||||||
\(622\) | 2.20685e12 | 0.591176 | ||||||||
\(623\) | −9.93779e11 | −0.264298 | ||||||||
\(624\) | 6.14222e11 | 0.162179 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.55207e12 | −0.664213 | ||||||||
\(627\) | −5.04068e12 | −1.30252 | ||||||||
\(628\) | −5.70036e11 | −0.146246 | ||||||||
\(629\) | −2.34759e12 | −0.597990 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.72749e12 | 0.684907 | 0.342453 | − | 0.939535i | \(-0.388742\pi\) | ||||
0.342453 | + | 0.939535i | \(0.388742\pi\) | |||||||
\(632\) | −5.57649e12 | −1.39038 | ||||||||
\(633\) | 3.21901e11 | 0.0796904 | ||||||||
\(634\) | −1.68918e12 | −0.415216 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.86275e11 | 0.117849 | ||||||||
\(637\) | −9.50483e11 | −0.228727 | ||||||||
\(638\) | −1.05306e13 | −2.51629 | ||||||||
\(639\) | 2.97198e11 | 0.0705166 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.88474e12 | 1.37678 | 0.688392 | − | 0.725339i | \(-0.258317\pi\) | ||||
0.688392 | + | 0.725339i | \(0.258317\pi\) | |||||||
\(642\) | −2.01302e11 | −0.0467672 | ||||||||
\(643\) | −8.44268e11 | −0.194774 | −0.0973870 | − | 0.995247i | \(-0.531048\pi\) | ||||
−0.0973870 | + | 0.995247i | \(0.531048\pi\) | |||||||
\(644\) | −8.21728e9 | −0.00188253 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.52751e12 | −1.47469 | ||||||||
\(647\) | −1.54662e12 | −0.346988 | −0.173494 | − | 0.984835i | \(-0.555506\pi\) | ||||
−0.173494 | + | 0.984835i | \(0.555506\pi\) | |||||||
\(648\) | 5.27401e11 | 0.117504 | ||||||||
\(649\) | −7.78235e12 | −1.72191 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.17094e12 | −0.255517 | ||||||||
\(652\) | −1.03611e12 | −0.224540 | ||||||||
\(653\) | 7.20565e12 | 1.55083 | 0.775414 | − | 0.631453i | \(-0.217541\pi\) | ||||
0.775414 | + | 0.631453i | \(0.217541\pi\) | |||||||
\(654\) | 2.50472e12 | 0.535376 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.43568e12 | −0.513516 | ||||||||
\(657\) | 2.38927e12 | 0.500288 | ||||||||
\(658\) | 2.07265e12 | 0.431032 | ||||||||
\(659\) | −1.96856e12 | −0.406597 | −0.203299 | − | 0.979117i | \(-0.565166\pi\) | ||||
−0.203299 | + | 0.979117i | \(0.565166\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.75497e12 | −1.78381 | −0.891904 | − | 0.452225i | \(-0.850630\pi\) | ||||
−0.891904 | + | 0.452225i | \(0.850630\pi\) | |||||||
\(662\) | 4.52819e12 | 0.916356 | ||||||||
\(663\) | 1.04095e12 | 0.209228 | ||||||||
\(664\) | 3.87855e11 | 0.0774306 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.66559e11 | −0.170673 | ||||||||
\(667\) | 2.14351e11 | 0.0419332 | ||||||||
\(668\) | −1.03342e12 | −0.200809 | ||||||||
\(669\) | 3.97448e12 | 0.767119 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.97673e12 | −0.566876 | ||||||||
\(672\) | −4.81053e11 | −0.0909979 | ||||||||
\(673\) | 1.73755e12 | 0.326489 | 0.163244 | − | 0.986586i | \(-0.447804\pi\) | ||||
0.163244 | + | 0.986586i | \(0.447804\pi\) | |||||||
\(674\) | −2.38336e11 | −0.0444856 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.80265e11 | 0.125290 | ||||||||
\(677\) | 1.87762e12 | 0.343526 | 0.171763 | − | 0.985138i | \(-0.445054\pi\) | ||||
0.171763 | + | 0.985138i | \(0.445054\pi\) | |||||||
\(678\) | −2.94958e12 | −0.536077 | ||||||||
\(679\) | 3.82530e12 | 0.690640 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.03373e12 | −0.718695 | ||||||||
\(682\) | −6.31743e12 | −1.11818 | ||||||||
\(683\) | −3.03387e11 | −0.0533463 | −0.0266731 | − | 0.999644i | \(-0.508491\pi\) | ||||
−0.0266731 | + | 0.999644i | \(0.508491\pi\) | |||||||
\(684\) | 3.95859e11 | 0.0691493 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.09306e12 | −0.878053 | ||||||||
\(687\) | 3.11470e12 | 0.533471 | ||||||||
\(688\) | 3.13204e12 | 0.532941 | ||||||||
\(689\) | 2.86498e12 | 0.484323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.73855e12 | 1.29124 | 0.645622 | − | 0.763657i | \(-0.276598\pi\) | ||||
0.645622 | + | 0.763657i | \(0.276598\pi\) | |||||||
\(692\) | −2.70643e11 | −0.0448662 | ||||||||
\(693\) | 1.74823e12 | 0.287938 | ||||||||
\(694\) | 2.59647e12 | 0.424880 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.68772e12 | 1.08028 | ||||||||
\(697\) | −4.12789e12 | −0.662491 | ||||||||
\(698\) | 3.69149e12 | 0.588644 | ||||||||
\(699\) | −4.41906e11 | −0.0700137 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.29003e12 | −0.201776 | −0.100888 | − | 0.994898i | \(-0.532168\pi\) | ||||
−0.100888 | + | 0.994898i | \(0.532168\pi\) | |||||||
\(702\) | 3.84245e11 | 0.0597160 | ||||||||
\(703\) | −5.25981e12 | −0.812215 | ||||||||
\(704\) | −1.09865e13 | −1.68570 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.08511e13 | 1.64381 | ||||||||
\(707\) | 1.89079e12 | 0.284614 | ||||||||
\(708\) | 6.11170e11 | 0.0914139 | ||||||||
\(709\) | 1.80911e12 | 0.268879 | 0.134440 | − | 0.990922i | \(-0.457077\pi\) | ||||
0.134440 | + | 0.990922i | \(0.457077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.98628e12 | −0.438245 | ||||||||
\(712\) | 3.40502e12 | 0.496546 | ||||||||
\(713\) | 1.28591e11 | 0.0186341 | ||||||||
\(714\) | 2.26390e12 | 0.325999 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.60872e11 | −0.0228756 | ||||||||
\(717\) | 4.74934e12 | 0.671115 | ||||||||
\(718\) | 6.00664e12 | 0.843473 | ||||||||
\(719\) | −8.24498e11 | −0.115056 | −0.0575280 | − | 0.998344i | \(-0.518322\pi\) | ||||
−0.0575280 | + | 0.998344i | \(0.518322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.18556e12 | 0.714640 | ||||||||
\(722\) | −7.85816e12 | −1.07623 | ||||||||
\(723\) | 1.85252e12 | 0.252140 | ||||||||
\(724\) | 1.50931e12 | 0.204153 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.42684e12 | 0.724990 | ||||||||
\(727\) | 4.26121e12 | 0.565754 | 0.282877 | − | 0.959156i | \(-0.408711\pi\) | ||||
0.282877 | + | 0.959156i | \(0.408711\pi\) | |||||||
\(728\) | −1.51050e12 | −0.199310 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.30804e12 | 0.687552 | ||||||||
\(732\) | 2.33771e11 | 0.0300947 | ||||||||
\(733\) | 1.17006e13 | 1.49707 | 0.748535 | − | 0.663095i | \(-0.230758\pi\) | ||||
0.748535 | + | 0.663095i | \(0.230758\pi\) | |||||||
\(734\) | −2.52674e12 | −0.321313 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.28287e10 | 0.00663620 | ||||||||
\(737\) | 1.47806e13 | 1.84539 | ||||||||
\(738\) | −1.52372e12 | −0.189082 | ||||||||
\(739\) | 1.30351e13 | 1.60773 | 0.803866 | − | 0.594811i | \(-0.202773\pi\) | ||||
0.803866 | + | 0.594811i | \(0.202773\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.33228e12 | 0.284183 | ||||||||
\(742\) | 6.23086e12 | 0.754624 | ||||||||
\(743\) | 8.72982e12 | 1.05089 | 0.525443 | − | 0.850829i | \(-0.323900\pi\) | ||||
0.525443 | + | 0.850829i | \(0.323900\pi\) | |||||||
\(744\) | 4.01203e12 | 0.480050 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.50954e12 | −1.00596 | ||||||||
\(747\) | 2.07701e11 | 0.0244059 | ||||||||
\(748\) | −2.00669e12 | −0.234381 | ||||||||
\(749\) | 4.23770e11 | 0.0491997 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.03083e13 | −1.18252 | −0.591259 | − | 0.806482i | \(-0.701369\pi\) | ||||
−0.591259 | + | 0.806482i | \(0.701369\pi\) | |||||||
\(752\) | −6.07914e12 | −0.693206 | ||||||||
\(753\) | 9.28418e11 | 0.105236 | ||||||||
\(754\) | 4.87242e12 | 0.549001 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.37294e11 | −0.0152863 | ||||||||
\(757\) | −5.42609e12 | −0.600559 | −0.300280 | − | 0.953851i | \(-0.597080\pi\) | ||||
−0.300280 | + | 0.953851i | \(0.597080\pi\) | |||||||
\(758\) | 4.45101e12 | 0.489719 | ||||||||
\(759\) | −1.91989e11 | −0.0209985 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.12828e12 | 0.986639 | 0.493319 | − | 0.869848i | \(-0.335783\pi\) | ||||
0.493319 | + | 0.869848i | \(0.335783\pi\) | |||||||
\(762\) | −3.53180e12 | −0.379489 | ||||||||
\(763\) | −5.27280e12 | −0.563223 | ||||||||
\(764\) | −7.97473e10 | −0.00846829 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.04209e12 | 0.109364 | ||||||||
\(767\) | 3.60082e12 | 0.375684 | ||||||||
\(768\) | 2.30723e12 | 0.239312 | ||||||||
\(769\) | −5.29627e12 | −0.546137 | −0.273069 | − | 0.961995i | \(-0.588039\pi\) | ||||
−0.273069 | + | 0.961995i | \(0.588039\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.69701e12 | −0.580634 | ||||||||
\(772\) | −1.99471e12 | −0.202116 | ||||||||
\(773\) | 1.45554e13 | 1.46628 | 0.733138 | − | 0.680080i | \(-0.238055\pi\) | ||||
0.733138 | + | 0.680080i | \(0.238055\pi\) | |||||||
\(774\) | 1.95934e12 | 0.196235 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.31068e13 | −1.29753 | ||||||||
\(777\) | 1.82423e12 | 0.179550 | ||||||||
\(778\) | −5.75575e12 | −0.563240 | ||||||||
\(779\) | −9.24860e12 | −0.899823 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.37546e12 | −0.324641 | ||||||||
\(782\) | −2.48619e11 | −0.0237741 | ||||||||
\(783\) | 3.58135e12 | 0.340501 | ||||||||
\(784\) | 6.06299e12 | 0.573145 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.10364e13 | 1.03140 | ||||||||
\(787\) | −1.36878e13 | −1.27188 | −0.635941 | − | 0.771737i | \(-0.719388\pi\) | ||||
−0.635941 | + | 0.771737i | \(0.719388\pi\) | |||||||
\(788\) | 2.20932e12 | 0.204123 | ||||||||
\(789\) | 9.03979e12 | 0.830447 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.20930e12 | 0.563960 | ||||||||
\(792\) | −5.99003e12 | −0.540961 | ||||||||
\(793\) | 1.37730e12 | 0.123680 | ||||||||
\(794\) | 4.55277e11 | 0.0406522 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.72770e11 | −0.0505675 | ||||||||
\(797\) | 1.44438e13 | 1.26800 | 0.633999 | − | 0.773334i | \(-0.281413\pi\) | ||||
0.633999 | + | 0.773334i | \(0.281413\pi\) | |||||||
\(798\) | 5.07231e12 | 0.442785 | ||||||||
\(799\) | −1.03026e13 | −0.894311 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.82343e12 | 0.156510 | ||||||||
\(802\) | −4.53588e12 | −0.387147 | ||||||||
\(803\) | −2.71364e13 | −2.30321 | ||||||||
\(804\) | −1.16076e12 | −0.0979697 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.92302e12 | 0.243963 | ||||||||
\(807\) | 5.14534e12 | 0.427055 | ||||||||
\(808\) | −6.47849e12 | −0.534715 | ||||||||
\(809\) | −2.28499e13 | −1.87550 | −0.937749 | − | 0.347314i | \(-0.887094\pi\) | ||||
−0.937749 | + | 0.347314i | \(0.887094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.16202e13 | −1.75495 | −0.877477 | − | 0.479618i | \(-0.840775\pi\) | ||||
−0.877477 | + | 0.479618i | \(0.840775\pi\) | |||||||
\(812\) | −1.74095e12 | −0.140535 | ||||||||
\(813\) | 6.45615e10 | 0.00518282 | ||||||||
\(814\) | 9.84206e12 | 0.785735 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.64009e12 | −0.524286 | ||||||||
\(817\) | 1.18927e13 | 0.933863 | ||||||||
\(818\) | 4.84238e12 | 0.378154 | ||||||||
\(819\) | −8.08891e11 | −0.0628221 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.90438e12 | −0.760822 | −0.380411 | − | 0.924817i | \(-0.624218\pi\) | ||||
−0.380411 | + | 0.924817i | \(0.624218\pi\) | |||||||
\(822\) | 4.17480e12 | 0.318943 | ||||||||
\(823\) | −1.33090e13 | −1.01122 | −0.505610 | − | 0.862762i | \(-0.668733\pi\) | ||||
−0.505610 | + | 0.862762i | \(0.668733\pi\) | |||||||
\(824\) | −1.77675e13 | −1.34262 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.83119e12 | 0.585353 | ||||||||
\(827\) | −9.27779e12 | −0.689715 | −0.344858 | − | 0.938655i | \(-0.612073\pi\) | ||||
−0.344858 | + | 0.938655i | \(0.612073\pi\) | |||||||
\(828\) | 1.50774e10 | 0.00111478 | ||||||||
\(829\) | −1.67554e13 | −1.23214 | −0.616071 | − | 0.787691i | \(-0.711276\pi\) | ||||
−0.616071 | + | 0.787691i | \(0.711276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.98468e12 | −0.217117 | ||||||||
\(832\) | 5.08334e12 | 0.367785 | ||||||||
\(833\) | 1.02753e13 | 0.739419 | ||||||||
\(834\) | −9.39711e12 | −0.672585 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.49602e12 | −0.318346 | ||||||||
\(837\) | 2.14849e12 | 0.151311 | ||||||||
\(838\) | −5.01076e12 | −0.350998 | ||||||||
\(839\) | 1.08548e13 | 0.756295 | 0.378147 | − | 0.925745i | \(-0.376561\pi\) | ||||
0.378147 | + | 0.925745i | \(0.376561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.09062e13 | 2.13041 | ||||||||
\(842\) | −8.58902e12 | −0.588897 | ||||||||
\(843\) | −6.37011e12 | −0.434433 | ||||||||
\(844\) | 2.87119e11 | 0.0194769 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.80299e12 | −0.255246 | ||||||||
\(847\) | −1.14243e13 | −0.762699 | ||||||||
\(848\) | −1.82753e13 | −1.21362 | ||||||||
\(849\) | −2.49696e12 | −0.164940 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00335e11 | −0.0130940 | ||||||||
\(852\) | 2.65085e11 | 0.0172348 | ||||||||
\(853\) | −1.55815e12 | −0.100772 | −0.0503858 | − | 0.998730i | \(-0.516045\pi\) | ||||
−0.0503858 | + | 0.998730i | \(0.516045\pi\) | |||||||
\(854\) | 2.99541e12 | 0.192706 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.45198e12 | −0.0924334 | ||||||||
\(857\) | −1.18714e13 | −0.751778 | −0.375889 | − | 0.926665i | \(-0.622663\pi\) | ||||
−0.375889 | + | 0.926665i | \(0.622663\pi\) | |||||||
\(858\) | −4.36411e12 | −0.274918 | ||||||||
\(859\) | 8.41923e12 | 0.527598 | 0.263799 | − | 0.964578i | \(-0.415024\pi\) | ||||
0.263799 | + | 0.964578i | \(0.415024\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.20764e12 | 0.198917 | ||||||||
\(862\) | −1.11117e13 | −0.685486 | ||||||||
\(863\) | −1.09630e13 | −0.672790 | −0.336395 | − | 0.941721i | \(-0.609208\pi\) | ||||
−0.336395 | + | 0.941721i | \(0.609208\pi\) | |||||||
\(864\) | 8.82657e11 | 0.0538865 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.58585e12 | 0.216651 | ||||||||
\(867\) | −1.64770e12 | −0.0990357 | ||||||||
\(868\) | −1.04442e12 | −0.0624504 | ||||||||
\(869\) | 3.39170e13 | 2.01757 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.83886e12 | −0.402626 | ||||||||
\(872\) | 1.80664e13 | 1.05815 | ||||||||
\(873\) | −7.01883e12 | −0.408979 | ||||||||
\(874\) | −5.57036e11 | −0.0322910 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.13110e12 | 0.122274 | ||||||||
\(877\) | −1.49209e12 | −0.0851723 | −0.0425861 | − | 0.999093i | \(-0.513560\pi\) | ||||
−0.0425861 | + | 0.999093i | \(0.513560\pi\) | |||||||
\(878\) | 4.69005e12 | 0.266350 | ||||||||
\(879\) | −4.89533e12 | −0.276587 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.94363e12 | 0.332399 | 0.166200 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166200 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(882\) | 3.79289e12 | 0.211038 | ||||||||
\(883\) | 1.57021e13 | 0.869230 | 0.434615 | − | 0.900616i | \(-0.356884\pi\) | ||||
0.434615 | + | 0.900616i | \(0.356884\pi\) | |||||||
\(884\) | 9.28476e11 | 0.0511370 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.74635e13 | 0.952092 | ||||||||
\(887\) | −2.07953e13 | −1.12800 | −0.564001 | − | 0.825774i | \(-0.690738\pi\) | ||||
−0.564001 | + | 0.825774i | \(0.690738\pi\) | |||||||
\(888\) | −6.25043e12 | −0.337327 | ||||||||
\(889\) | 7.43495e12 | 0.399227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.20773e12 | −0.170509 | ||||||||
\(892\) | 3.54503e12 | 0.187490 | ||||||||
\(893\) | −2.30833e13 | −1.21469 | ||||||||
\(894\) | 1.80733e13 | 0.946278 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.01469e12 | 0.415433 | ||||||||
\(897\) | 8.88314e10 | 0.00458143 | ||||||||
\(898\) | 1.18029e13 | 0.605685 | ||||||||
\(899\) | 2.72440e13 | 1.39108 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.09721e13 | −1.56570 | ||||||||
\(902\) | 1.73058e13 | 0.870487 | ||||||||
\(903\) | −4.12470e12 | −0.206442 | ||||||||
\(904\) | −2.12751e13 | −1.05953 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.18038e12 | 0.452672 | ||||||||
\(907\) | −5.16199e12 | −0.253270 | −0.126635 | − | 0.991949i | \(-0.540418\pi\) | ||||
−0.126635 | + | 0.991949i | \(0.540418\pi\) | |||||||
\(908\) | −3.59787e12 | −0.175655 | ||||||||
\(909\) | −3.46931e12 | −0.168541 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.23036e13 | −0.591834 | −0.295917 | − | 0.955214i | \(-0.595625\pi\) | ||||
−0.295917 | + | 0.955214i | \(0.595625\pi\) | |||||||
\(912\) | −1.48772e13 | −0.712107 | ||||||||
\(913\) | −2.35899e12 | −0.112359 | ||||||||
\(914\) | 1.55979e13 | 0.739280 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.77815e12 | 0.130384 | ||||||||
\(917\) | −2.32333e13 | −1.08505 | ||||||||
\(918\) | −4.15391e12 | −0.193048 | ||||||||
\(919\) | −6.62689e12 | −0.306471 | −0.153236 | − | 0.988190i | \(-0.548969\pi\) | ||||
−0.153236 | + | 0.988190i | \(0.548969\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.92642e13 | −0.882230 | ||||||||
\(922\) | 2.07618e13 | 0.946185 | ||||||||
\(923\) | 1.56179e12 | 0.0708299 | ||||||||
\(924\) | 1.55933e12 | 0.0703743 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.55255e13 | 0.693900 | ||||||||
\(927\) | −9.51469e12 | −0.423191 | ||||||||
\(928\) | 1.11925e13 | 0.495408 | ||||||||
\(929\) | −1.50849e12 | −0.0664466 | −0.0332233 | − | 0.999448i | \(-0.510577\pi\) | ||||
−0.0332233 | + | 0.999448i | \(0.510577\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.30219e13 | 1.00431 | ||||||||
\(932\) | −3.94157e11 | −0.0171119 | ||||||||
\(933\) | 8.52421e12 | 0.368287 | ||||||||
\(934\) | −3.90179e12 | −0.167765 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.77153e12 | 0.118026 | ||||||||
\(937\) | 2.83761e13 | 1.20261 | 0.601305 | − | 0.799019i | \(-0.294648\pi\) | ||||
0.601305 | + | 0.799019i | \(0.294648\pi\) | |||||||
\(938\) | −1.48734e13 | −0.627332 | ||||||||
\(939\) | −9.85764e12 | −0.413788 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.17067e13 | 0.902488 | 0.451244 | − | 0.892401i | \(-0.350980\pi\) | ||||
0.451244 | + | 0.892401i | \(0.350980\pi\) | |||||||
\(942\) | 1.34019e13 | 0.554547 | ||||||||
\(943\) | −3.52260e11 | −0.0145064 | ||||||||
\(944\) | −2.29691e13 | −0.941391 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.22535e13 | −0.903417 | ||||||||
\(947\) | 1.50628e13 | 0.608600 | 0.304300 | − | 0.952576i | \(-0.401578\pi\) | ||||
0.304300 | + | 0.952576i | \(0.401578\pi\) | |||||||
\(948\) | −2.66360e12 | −0.107110 | ||||||||
\(949\) | 1.25558e13 | 0.502511 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.52464e12 | −0.258669 | ||||||||
\(952\) | 1.63294e13 | 0.644323 | ||||||||
\(953\) | 3.10734e13 | 1.22031 | 0.610156 | − | 0.792281i | \(-0.291107\pi\) | ||||
0.610156 | + | 0.792281i | \(0.291107\pi\) | |||||||
\(954\) | −1.14326e13 | −0.446868 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.23616e12 | 0.164026 | ||||||||
\(957\) | −4.06757e13 | −1.56758 | ||||||||
\(958\) | −1.21057e13 | −0.464350 | ||||||||
\(959\) | −8.78857e12 | −0.335532 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.00957e13 | −0.381839 | ||||||||
\(962\) | −4.55383e12 | −0.171431 | ||||||||
\(963\) | −7.77552e11 | −0.0291348 | ||||||||
\(964\) | 1.65235e12 | 0.0616249 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.93194e11 | 0.00713832 | ||||||||
\(967\) | 1.56729e13 | 0.576408 | 0.288204 | − | 0.957569i | \(-0.406942\pi\) | ||||
0.288204 | + | 0.957569i | \(0.406942\pi\) | |||||||
\(968\) | 3.91434e13 | 1.43291 | ||||||||
\(969\) | −2.52132e13 | −0.918696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.46434e13 | 0.889641 | 0.444820 | − | 0.895620i | \(-0.353267\pi\) | ||||
0.444820 | + | 0.895620i | \(0.353267\pi\) | |||||||
\(972\) | 2.51912e11 | 0.00905214 | ||||||||
\(973\) | 1.97823e13 | 0.707568 | ||||||||
\(974\) | 4.89727e13 | 1.74357 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.78562e12 | −0.309919 | ||||||||
\(977\) | 1.86706e13 | 0.655591 | 0.327796 | − | 0.944749i | \(-0.393694\pi\) | ||||
0.327796 | + | 0.944749i | \(0.393694\pi\) | |||||||
\(978\) | 2.43597e13 | 0.851428 | ||||||||
\(979\) | −2.07098e13 | −0.720534 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.67476e12 | 0.333526 | ||||||||
\(982\) | −1.90219e13 | −0.652759 | ||||||||
\(983\) | −2.04996e13 | −0.700252 | −0.350126 | − | 0.936703i | \(-0.613861\pi\) | ||||
−0.350126 | + | 0.936703i | \(0.613861\pi\) | |||||||
\(984\) | −1.09905e13 | −0.373713 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.26737e13 | −1.77479 | ||||||||
\(987\) | 8.00585e12 | 0.268522 | ||||||||
\(988\) | 2.08027e12 | 0.0694565 | ||||||||
\(989\) | 4.52970e11 | 0.0150552 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.90837e12 | −0.227533 | −0.113766 | − | 0.993508i | \(-0.536292\pi\) | ||||
−0.113766 | + | 0.993508i | \(0.536292\pi\) | |||||||
\(992\) | 6.71453e12 | 0.220147 | ||||||||
\(993\) | 1.74907e13 | 0.570866 | ||||||||
\(994\) | 3.39665e12 | 0.110360 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.85258e11 | 0.00596500 | ||||||||
\(997\) | 2.80773e13 | 0.899969 | 0.449984 | − | 0.893036i | \(-0.351430\pi\) | ||||
0.449984 | + | 0.893036i | \(0.351430\pi\) | |||||||
\(998\) | 2.38433e13 | 0.760815 | ||||||||
\(999\) | −3.34718e12 | −0.106325 |
(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 | 75.10.a.i.1.2 | 4 | ||
3.2 | odd | 2 | 225.10.a.u.1.3 | 4 | |||
5.2 | odd | 4 | 15.10.b.a.4.3 | ✓ | 8 | ||
5.3 | odd | 4 | 15.10.b.a.4.6 | yes | 8 | ||
5.4 | even | 2 | 75.10.a.l.1.3 | 4 | |||
15.2 | even | 4 | 45.10.b.c.19.6 | 8 | |||
15.8 | even | 4 | 45.10.b.c.19.3 | 8 | |||
15.14 | odd | 2 | 225.10.a.q.1.2 | 4 | |||
20.3 | even | 4 | 240.10.f.c.49.6 | 8 | |||
20.7 | even | 4 | 240.10.f.c.49.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.b.a.4.3 | ✓ | 8 | 5.2 | odd | 4 | ||
15.10.b.a.4.6 | yes | 8 | 5.3 | odd | 4 | ||
45.10.b.c.19.3 | 8 | 15.8 | even | 4 | |||
45.10.b.c.19.6 | 8 | 15.2 | even | 4 | |||
75.10.a.i.1.2 | 4 | 1.1 | even | 1 | trivial | ||
75.10.a.l.1.3 | 4 | 5.4 | even | 2 | |||
225.10.a.q.1.2 | 4 | 15.14 | odd | 2 | |||
225.10.a.u.1.3 | 4 | 3.2 | odd | 2 | |||
240.10.f.c.49.2 | 8 | 20.7 | even | 4 | |||
240.10.f.c.49.6 | 8 | 20.3 | even | 4 |