Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,10,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(12.8758959041\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1009}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 252 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-15.3824\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 36.7648 | 1.62479 | 0.812394 | − | 0.583109i | \(-0.198164\pi\) | ||||
0.812394 | + | 0.583109i | \(0.198164\pi\) | |||||||
\(3\) | −193.530 | −1.37944 | −0.689718 | − | 0.724078i | \(-0.742266\pi\) | ||||
−0.689718 | + | 0.724078i | \(0.742266\pi\) | |||||||
\(4\) | 839.648 | 1.63994 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −7115.07 | −2.24129 | ||||||||
\(7\) | −7647.66 | −1.20389 | −0.601946 | − | 0.798537i | \(-0.705608\pi\) | ||||
−0.601946 | + | 0.798537i | \(0.705608\pi\) | |||||||
\(8\) | 12045.9 | 1.03976 | ||||||||
\(9\) | 17770.7 | 0.902844 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −48361.0 | −0.995929 | −0.497965 | − | 0.867197i | \(-0.665919\pi\) | ||||
−0.497965 | + | 0.867197i | \(0.665919\pi\) | |||||||
\(12\) | −162497. | −2.26219 | ||||||||
\(13\) | −100456. | −0.975507 | −0.487754 | − | 0.872981i | \(-0.662184\pi\) | ||||
−0.487754 | + | 0.872981i | \(0.662184\pi\) | |||||||
\(14\) | −281164. | −1.95607 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12964.5 | 0.0494557 | ||||||||
\(17\) | 201958. | 0.586463 | 0.293231 | − | 0.956042i | \(-0.405269\pi\) | ||||
0.293231 | + | 0.956042i | \(0.405269\pi\) | |||||||
\(18\) | 653335. | 1.46693 | ||||||||
\(19\) | −58048.1 | −0.102187 | −0.0510936 | − | 0.998694i | \(-0.516271\pi\) | ||||
−0.0510936 | + | 0.998694i | \(0.516271\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.48005e6 | 1.66069 | ||||||||
\(22\) | −1.77798e6 | −1.61817 | ||||||||
\(23\) | 1.14078e6 | 0.850017 | 0.425009 | − | 0.905189i | \(-0.360271\pi\) | ||||
0.425009 | + | 0.905189i | \(0.360271\pi\) | |||||||
\(24\) | −2.33123e6 | −1.43428 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.69324e6 | −1.58499 | ||||||||
\(27\) | 370091. | 0.134021 | ||||||||
\(28\) | −6.42134e6 | −1.97431 | ||||||||
\(29\) | 1.56407e6 | 0.410643 | 0.205322 | − | 0.978695i | \(-0.434176\pi\) | ||||
0.205322 | + | 0.978695i | \(0.434176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.10744e6 | −0.798810 | −0.399405 | − | 0.916775i | \(-0.630783\pi\) | ||||
−0.399405 | + | 0.916775i | \(0.630783\pi\) | |||||||
\(32\) | −5.69086e6 | −0.959407 | ||||||||
\(33\) | 9.35929e6 | 1.37382 | ||||||||
\(34\) | 7.42493e6 | 0.952878 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.49211e7 | 1.48061 | ||||||||
\(37\) | 1.70821e7 | 1.49842 | 0.749212 | − | 0.662330i | \(-0.230432\pi\) | ||||
0.749212 | + | 0.662330i | \(0.230432\pi\) | |||||||
\(38\) | −2.13412e6 | −0.166033 | ||||||||
\(39\) | 1.94412e7 | 1.34565 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.52969e6 | −0.471418 | −0.235709 | − | 0.971824i | \(-0.575741\pi\) | ||||
−0.235709 | + | 0.971824i | \(0.575741\pi\) | |||||||
\(42\) | 5.44136e7 | 2.69827 | ||||||||
\(43\) | −2.56254e7 | −1.14304 | −0.571521 | − | 0.820587i | \(-0.693646\pi\) | ||||
−0.571521 | + | 0.820587i | \(0.693646\pi\) | |||||||
\(44\) | −4.06062e7 | −1.63326 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.19406e7 | 1.38110 | ||||||||
\(47\) | −4.58297e7 | −1.36996 | −0.684978 | − | 0.728564i | \(-0.740188\pi\) | ||||
−0.684978 | + | 0.728564i | \(0.740188\pi\) | |||||||
\(48\) | −2.50902e6 | −0.0682210 | ||||||||
\(49\) | 1.81331e7 | 0.449355 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.90848e7 | −0.808988 | ||||||||
\(52\) | −8.43476e7 | −1.59977 | ||||||||
\(53\) | 5.56483e7 | 0.968748 | 0.484374 | − | 0.874861i | \(-0.339047\pi\) | ||||
0.484374 | + | 0.874861i | \(0.339047\pi\) | |||||||
\(54\) | 1.36063e7 | 0.217755 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.21228e7 | −1.25176 | ||||||||
\(57\) | 1.12340e7 | 0.140961 | ||||||||
\(58\) | 5.75026e7 | 0.667209 | ||||||||
\(59\) | 2.15699e7 | 0.231747 | 0.115873 | − | 0.993264i | \(-0.463033\pi\) | ||||
0.115873 | + | 0.993264i | \(0.463033\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.15309e8 | −1.06630 | −0.533148 | − | 0.846022i | \(-0.678991\pi\) | ||||
−0.533148 | + | 0.846022i | \(0.678991\pi\) | |||||||
\(62\) | −1.51009e8 | −1.29790 | ||||||||
\(63\) | −1.35904e8 | −1.08693 | ||||||||
\(64\) | −2.15861e8 | −1.60829 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.44092e8 | 2.23217 | ||||||||
\(67\) | 7.69254e7 | 0.466373 | 0.233186 | − | 0.972432i | \(-0.425085\pi\) | ||||
0.233186 | + | 0.972432i | \(0.425085\pi\) | |||||||
\(68\) | 1.69573e8 | 0.961762 | ||||||||
\(69\) | −2.20775e8 | −1.17254 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.95870e8 | 0.914754 | 0.457377 | − | 0.889273i | \(-0.348789\pi\) | ||||
0.457377 | + | 0.889273i | \(0.348789\pi\) | |||||||
\(72\) | 2.14064e8 | 0.938742 | ||||||||
\(73\) | −3.40942e8 | −1.40517 | −0.702583 | − | 0.711601i | \(-0.747970\pi\) | ||||
−0.702583 | + | 0.711601i | \(0.747970\pi\) | |||||||
\(74\) | 6.28021e8 | 2.43462 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.87399e7 | −0.167581 | ||||||||
\(77\) | 3.69849e8 | 1.19899 | ||||||||
\(78\) | 7.14751e8 | 2.18640 | ||||||||
\(79\) | −5.92965e8 | −1.71280 | −0.856401 | − | 0.516311i | \(-0.827305\pi\) | ||||
−0.856401 | + | 0.516311i | \(0.827305\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.21404e8 | −1.08772 | ||||||||
\(82\) | −3.13592e8 | −0.765954 | ||||||||
\(83\) | −7.88477e8 | −1.82363 | −0.911817 | − | 0.410598i | \(-0.865320\pi\) | ||||
−0.911817 | + | 0.410598i | \(0.865320\pi\) | |||||||
\(84\) | 1.24272e9 | 2.72343 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.42111e8 | −1.85720 | ||||||||
\(87\) | −3.02693e8 | −0.566456 | ||||||||
\(88\) | −5.82552e8 | −1.03553 | ||||||||
\(89\) | 8.40110e8 | 1.41932 | 0.709661 | − | 0.704543i | \(-0.248848\pi\) | ||||
0.709661 | + | 0.704543i | \(0.248848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.68253e8 | 1.17441 | ||||||||
\(92\) | 9.57856e8 | 1.39397 | ||||||||
\(93\) | 7.94910e8 | 1.10191 | ||||||||
\(94\) | −1.68492e9 | −2.22589 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.10135e9 | 1.32344 | ||||||||
\(97\) | −2.35903e8 | −0.270558 | −0.135279 | − | 0.990808i | \(-0.543193\pi\) | ||||
−0.135279 | + | 0.990808i | \(0.543193\pi\) | |||||||
\(98\) | 6.66658e8 | 0.730106 | ||||||||
\(99\) | −8.59408e8 | −0.899169 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.52957e8 | −0.624365 | −0.312182 | − | 0.950022i | \(-0.601060\pi\) | ||||
−0.312182 | + | 0.950022i | \(0.601060\pi\) | |||||||
\(102\) | −1.43694e9 | −1.31443 | ||||||||
\(103\) | −9.53214e8 | −0.834493 | −0.417247 | − | 0.908793i | \(-0.637005\pi\) | ||||
−0.417247 | + | 0.908793i | \(0.637005\pi\) | |||||||
\(104\) | −1.21008e9 | −1.01430 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.04590e9 | 1.57401 | ||||||||
\(107\) | 1.33363e9 | 0.983573 | 0.491787 | − | 0.870716i | \(-0.336344\pi\) | ||||
0.491787 | + | 0.870716i | \(0.336344\pi\) | |||||||
\(108\) | 3.10746e8 | 0.219785 | ||||||||
\(109\) | 1.93368e9 | 1.31210 | 0.656049 | − | 0.754718i | \(-0.272226\pi\) | ||||
0.656049 | + | 0.754718i | \(0.272226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.30590e9 | −2.06698 | ||||||||
\(112\) | −9.91483e7 | −0.0595393 | ||||||||
\(113\) | 9.74289e8 | 0.562128 | 0.281064 | − | 0.959689i | \(-0.409313\pi\) | ||||
0.281064 | + | 0.959689i | \(0.409313\pi\) | |||||||
\(114\) | 4.13016e8 | 0.229031 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.31327e9 | 0.673429 | ||||||||
\(117\) | −1.78517e9 | −0.880731 | ||||||||
\(118\) | 7.93011e8 | 0.376539 | ||||||||
\(119\) | −1.54450e9 | −0.706037 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.91571e7 | −0.00812446 | ||||||||
\(122\) | −4.23929e9 | −1.73250 | ||||||||
\(123\) | 1.65075e9 | 0.650290 | ||||||||
\(124\) | −3.44880e9 | −1.31000 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.99648e9 | −1.76602 | ||||||||
\(127\) | −1.25137e9 | −0.426845 | −0.213422 | − | 0.976960i | \(-0.568461\pi\) | ||||
−0.213422 | + | 0.976960i | \(0.568461\pi\) | |||||||
\(128\) | −5.02235e9 | −1.65372 | ||||||||
\(129\) | 4.95927e9 | 1.57675 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.23060e9 | 0.661760 | 0.330880 | − | 0.943673i | \(-0.392655\pi\) | ||||
0.330880 | + | 0.943673i | \(0.392655\pi\) | |||||||
\(132\) | 7.85851e9 | 2.25298 | ||||||||
\(133\) | 4.43932e8 | 0.123022 | ||||||||
\(134\) | 2.82814e9 | 0.757757 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.43276e9 | 0.609781 | ||||||||
\(137\) | 3.91202e9 | 0.948764 | 0.474382 | − | 0.880319i | \(-0.342672\pi\) | ||||
0.474382 | + | 0.880319i | \(0.342672\pi\) | |||||||
\(138\) | −8.11675e9 | −1.90514 | ||||||||
\(139\) | 1.64295e9 | 0.373299 | 0.186649 | − | 0.982427i | \(-0.440237\pi\) | ||||
0.186649 | + | 0.982427i | \(0.440237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.86939e9 | 1.88977 | ||||||||
\(142\) | 7.20110e9 | 1.48628 | ||||||||
\(143\) | 4.85815e9 | 0.971537 | ||||||||
\(144\) | 2.30388e8 | 0.0446508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.25347e10 | −2.28310 | ||||||||
\(147\) | −3.50929e9 | −0.619856 | ||||||||
\(148\) | 1.43430e10 | 2.45732 | ||||||||
\(149\) | −6.33624e9 | −1.05316 | −0.526579 | − | 0.850126i | \(-0.676525\pi\) | ||||
−0.526579 | + | 0.850126i | \(0.676525\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.67989e9 | 0.889086 | 0.444543 | − | 0.895757i | \(-0.353366\pi\) | ||||
0.444543 | + | 0.895757i | \(0.353366\pi\) | |||||||
\(152\) | −6.99241e8 | −0.106250 | ||||||||
\(153\) | 3.58893e9 | 0.529484 | ||||||||
\(154\) | 1.35974e10 | 1.94811 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.63238e10 | 2.20678 | ||||||||
\(157\) | 4.23621e9 | 0.556454 | 0.278227 | − | 0.960515i | \(-0.410253\pi\) | ||||
0.278227 | + | 0.960515i | \(0.410253\pi\) | |||||||
\(158\) | −2.18002e10 | −2.78294 | ||||||||
\(159\) | −1.07696e10 | −1.33633 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.72432e9 | −1.02333 | ||||||||
\(162\) | −1.54928e10 | −1.76731 | ||||||||
\(163\) | −8.56450e9 | −0.950293 | −0.475147 | − | 0.879907i | \(-0.657605\pi\) | ||||
−0.475147 | + | 0.879907i | \(0.657605\pi\) | |||||||
\(164\) | −7.16193e9 | −0.773095 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.89882e10 | −2.96302 | ||||||||
\(167\) | −5.87750e9 | −0.584748 | −0.292374 | − | 0.956304i | \(-0.594445\pi\) | ||||
−0.292374 | + | 0.956304i | \(0.594445\pi\) | |||||||
\(168\) | 1.78285e10 | 1.72672 | ||||||||
\(169\) | −5.13100e8 | −0.0483851 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.03155e9 | −0.0922591 | ||||||||
\(172\) | −2.15163e10 | −1.87452 | ||||||||
\(173\) | −1.48147e10 | −1.25743 | −0.628715 | − | 0.777635i | \(-0.716419\pi\) | ||||
−0.628715 | + | 0.777635i | \(0.716419\pi\) | |||||||
\(174\) | −1.11285e10 | −0.920372 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.26978e8 | −0.0492544 | ||||||||
\(177\) | −4.17441e9 | −0.319680 | ||||||||
\(178\) | 3.08864e10 | 2.30610 | ||||||||
\(179\) | 5.95512e9 | 0.433563 | 0.216781 | − | 0.976220i | \(-0.430444\pi\) | ||||
0.216781 | + | 0.976220i | \(0.430444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.02707e10 | 0.711290 | 0.355645 | − | 0.934621i | \(-0.384261\pi\) | ||||
0.355645 | + | 0.934621i | \(0.384261\pi\) | |||||||
\(182\) | 2.82446e10 | 1.90816 | ||||||||
\(183\) | 2.23156e10 | 1.47089 | ||||||||
\(184\) | 1.37417e10 | 0.883815 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.92247e10 | 1.79036 | ||||||||
\(187\) | −9.76689e9 | −0.584075 | ||||||||
\(188\) | −3.84808e10 | −2.24664 | ||||||||
\(189\) | −2.83033e9 | −0.161346 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.09899e9 | 0.114120 | 0.0570599 | − | 0.998371i | \(-0.481827\pi\) | ||||
0.0570599 | + | 0.998371i | \(0.481827\pi\) | |||||||
\(192\) | 4.17754e10 | 2.21853 | ||||||||
\(193\) | 1.95026e10 | 1.01178 | 0.505888 | − | 0.862599i | \(-0.331165\pi\) | ||||
0.505888 | + | 0.862599i | \(0.331165\pi\) | |||||||
\(194\) | −8.67293e9 | −0.439600 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.52254e10 | 0.736913 | ||||||||
\(197\) | −6.38850e9 | −0.302204 | −0.151102 | − | 0.988518i | \(-0.548282\pi\) | ||||
−0.151102 | + | 0.988518i | \(0.548282\pi\) | |||||||
\(198\) | −3.15959e10 | −1.46096 | ||||||||
\(199\) | 1.32140e10 | 0.597303 | 0.298652 | − | 0.954362i | \(-0.403463\pi\) | ||||
0.298652 | + | 0.954362i | \(0.403463\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.48873e10 | −0.643331 | ||||||||
\(202\) | −2.40058e10 | −1.01446 | ||||||||
\(203\) | −1.19615e10 | −0.494370 | ||||||||
\(204\) | −3.28174e10 | −1.32669 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.50447e10 | −1.35588 | ||||||||
\(207\) | 2.02725e10 | 0.767433 | ||||||||
\(208\) | −1.30236e9 | −0.0482444 | ||||||||
\(209\) | 2.80727e9 | 0.101771 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.06410e9 | 0.0716901 | 0.0358450 | − | 0.999357i | \(-0.488588\pi\) | ||||
0.0358450 | + | 0.999357i | \(0.488588\pi\) | |||||||
\(212\) | 4.67250e10 | 1.58869 | ||||||||
\(213\) | −3.79065e10 | −1.26184 | ||||||||
\(214\) | 4.90304e10 | 1.59810 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.45808e9 | 0.139350 | ||||||||
\(217\) | 3.14123e10 | 0.961680 | ||||||||
\(218\) | 7.10915e10 | 2.13188 | ||||||||
\(219\) | 6.59824e10 | 1.93834 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.02879e10 | −0.572099 | ||||||||
\(222\) | −1.21541e11 | −3.35840 | ||||||||
\(223\) | 1.59589e10 | 0.432145 | 0.216073 | − | 0.976377i | \(-0.430675\pi\) | ||||
0.216073 | + | 0.976377i | \(0.430675\pi\) | |||||||
\(224\) | 4.35217e10 | 1.15502 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.58195e10 | 0.913338 | ||||||||
\(227\) | −4.86308e10 | −1.21561 | −0.607807 | − | 0.794085i | \(-0.707950\pi\) | ||||
−0.607807 | + | 0.794085i | \(0.707950\pi\) | |||||||
\(228\) | 9.43262e9 | 0.231167 | ||||||||
\(229\) | −6.34109e10 | −1.52372 | −0.761858 | − | 0.647744i | \(-0.775713\pi\) | ||||
−0.761858 | + | 0.647744i | \(0.775713\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.15767e10 | −1.65393 | ||||||||
\(232\) | 1.88406e10 | 0.426971 | ||||||||
\(233\) | −2.45281e10 | −0.545209 | −0.272605 | − | 0.962126i | \(-0.587885\pi\) | ||||
−0.272605 | + | 0.962126i | \(0.587885\pi\) | |||||||
\(234\) | −6.56314e10 | −1.43100 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.81111e10 | 0.380050 | ||||||||
\(237\) | 1.14756e11 | 2.36270 | ||||||||
\(238\) | −5.67833e10 | −1.14716 | ||||||||
\(239\) | −7.82086e10 | −1.55047 | −0.775236 | − | 0.631671i | \(-0.782369\pi\) | ||||
−0.775236 | + | 0.631671i | \(0.782369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.59331e10 | 1.25900 | 0.629502 | − | 0.776999i | \(-0.283259\pi\) | ||||
0.629502 | + | 0.776999i | \(0.283259\pi\) | |||||||
\(242\) | −7.04304e8 | −0.0132005 | ||||||||
\(243\) | 7.42696e10 | 1.36642 | ||||||||
\(244\) | −9.68186e10 | −1.74866 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.06893e10 | 1.05658 | ||||||||
\(247\) | 5.83128e9 | 0.0996844 | ||||||||
\(248\) | −4.94777e10 | −0.830571 | ||||||||
\(249\) | 1.52594e11 | 2.51559 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.83321e10 | 0.291527 | 0.145764 | − | 0.989319i | \(-0.453436\pi\) | ||||
0.145764 | + | 0.989319i | \(0.453436\pi\) | |||||||
\(252\) | −1.14112e11 | −1.78249 | ||||||||
\(253\) | −5.51694e10 | −0.846557 | ||||||||
\(254\) | −4.60064e10 | −0.693533 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.41248e10 | −1.07866 | ||||||||
\(257\) | −6.41469e10 | −0.917227 | −0.458613 | − | 0.888636i | \(-0.651654\pi\) | ||||
−0.458613 | + | 0.888636i | \(0.651654\pi\) | |||||||
\(258\) | 1.82326e11 | 2.56189 | ||||||||
\(259\) | −1.30638e11 | −1.80394 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.77946e10 | 0.370747 | ||||||||
\(262\) | 8.20074e10 | 1.07522 | ||||||||
\(263\) | −2.20901e10 | −0.284706 | −0.142353 | − | 0.989816i | \(-0.545467\pi\) | ||||
−0.142353 | + | 0.989816i | \(0.545467\pi\) | |||||||
\(264\) | 1.12741e11 | 1.42845 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.63211e10 | 0.199885 | ||||||||
\(267\) | −1.62586e11 | −1.95787 | ||||||||
\(268\) | 6.45902e10 | 0.764822 | ||||||||
\(269\) | 7.78901e10 | 0.906978 | 0.453489 | − | 0.891262i | \(-0.350179\pi\) | ||||
0.453489 | + | 0.891262i | \(0.350179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.36671e10 | −1.05493 | −0.527467 | − | 0.849576i | \(-0.676858\pi\) | ||||
−0.527467 | + | 0.849576i | \(0.676858\pi\) | |||||||
\(272\) | 2.61829e9 | 0.0290039 | ||||||||
\(273\) | −1.48680e11 | −1.62002 | ||||||||
\(274\) | 1.43824e11 | 1.54154 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.85373e11 | −1.92290 | ||||||||
\(277\) | 7.45925e10 | 0.761266 | 0.380633 | − | 0.924726i | \(-0.375706\pi\) | ||||
0.380633 | + | 0.924726i | \(0.375706\pi\) | |||||||
\(278\) | 6.04025e10 | 0.606532 | ||||||||
\(279\) | −7.29919e10 | −0.721200 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.10771e11 | −1.05986 | −0.529930 | − | 0.848041i | \(-0.677782\pi\) | ||||
−0.529930 | + | 0.848041i | \(0.677782\pi\) | |||||||
\(282\) | 3.26081e11 | 3.07047 | ||||||||
\(283\) | −1.44123e11 | −1.33566 | −0.667830 | − | 0.744314i | \(-0.732777\pi\) | ||||
−0.667830 | + | 0.744314i | \(0.732777\pi\) | |||||||
\(284\) | 1.64461e11 | 1.50014 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.78609e11 | 1.57854 | ||||||||
\(287\) | 6.52321e10 | 0.567536 | ||||||||
\(288\) | −1.01130e11 | −0.866194 | ||||||||
\(289\) | −7.78009e10 | −0.656061 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.56542e10 | 0.373218 | ||||||||
\(292\) | −2.86271e11 | −2.30438 | ||||||||
\(293\) | 1.39037e11 | 1.10211 | 0.551056 | − | 0.834469i | \(-0.314225\pi\) | ||||
0.551056 | + | 0.834469i | \(0.314225\pi\) | |||||||
\(294\) | −1.29018e11 | −1.00713 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.05770e11 | 1.55800 | ||||||||
\(297\) | −1.78980e10 | −0.133475 | ||||||||
\(298\) | −2.32950e11 | −1.71116 | ||||||||
\(299\) | −1.14598e11 | −0.829198 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.95974e11 | 1.37610 | ||||||||
\(302\) | 2.08820e11 | 1.44458 | ||||||||
\(303\) | 1.26366e11 | 0.861271 | ||||||||
\(304\) | −7.52566e8 | −0.00505375 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.31946e11 | 0.860300 | ||||||||
\(307\) | 2.71765e10 | 0.174611 | 0.0873053 | − | 0.996182i | \(-0.472174\pi\) | ||||
0.0873053 | + | 0.996182i | \(0.472174\pi\) | |||||||
\(308\) | 3.10543e11 | 1.96627 | ||||||||
\(309\) | 1.84475e11 | 1.15113 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.82604e10 | 0.595603 | 0.297802 | − | 0.954628i | \(-0.403747\pi\) | ||||
0.297802 | + | 0.954628i | \(0.403747\pi\) | |||||||
\(312\) | 2.34186e11 | 1.39916 | ||||||||
\(313\) | 1.82397e11 | 1.07416 | 0.537078 | − | 0.843533i | \(-0.319528\pi\) | ||||
0.537078 | + | 0.843533i | \(0.319528\pi\) | |||||||
\(314\) | 1.55743e11 | 0.904120 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.97882e11 | −2.80889 | ||||||||
\(317\) | 1.52524e11 | 0.848341 | 0.424170 | − | 0.905582i | \(-0.360566\pi\) | ||||
0.424170 | + | 0.905582i | \(0.360566\pi\) | |||||||
\(318\) | −3.95942e11 | −2.17125 | ||||||||
\(319\) | −7.56400e10 | −0.408972 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.58096e11 | −1.35678 | ||||||||
\(322\) | −3.20747e11 | −1.66269 | ||||||||
\(323\) | −1.17233e10 | −0.0599290 | ||||||||
\(324\) | −3.53831e11 | −1.78379 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.14872e11 | −1.54403 | ||||||||
\(327\) | −3.74225e11 | −1.80996 | ||||||||
\(328\) | −1.02748e11 | −0.490162 | ||||||||
\(329\) | 3.50490e11 | 1.64928 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.08043e11 | 1.86845 | 0.934223 | − | 0.356690i | \(-0.116095\pi\) | ||||
0.934223 | + | 0.356690i | \(0.116095\pi\) | |||||||
\(332\) | −6.62043e11 | −2.99064 | ||||||||
\(333\) | 3.03561e11 | 1.35284 | ||||||||
\(334\) | −2.16085e11 | −0.950092 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.91881e10 | 0.0821307 | ||||||||
\(337\) | 2.48513e11 | 1.04958 | 0.524789 | − | 0.851233i | \(-0.324144\pi\) | ||||
0.524789 | + | 0.851233i | \(0.324144\pi\) | |||||||
\(338\) | −1.88640e10 | −0.0786156 | ||||||||
\(339\) | −1.88554e11 | −0.775419 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.98640e11 | 0.795558 | ||||||||
\(342\) | −3.79248e10 | −0.149902 | ||||||||
\(343\) | 1.69935e11 | 0.662917 | ||||||||
\(344\) | −3.08680e11 | −1.18849 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.44657e11 | −2.04306 | ||||||||
\(347\) | −3.44769e11 | −1.27657 | −0.638287 | − | 0.769799i | \(-0.720356\pi\) | ||||
−0.638287 | + | 0.769799i | \(0.720356\pi\) | |||||||
\(348\) | −2.54156e11 | −0.928953 | ||||||||
\(349\) | 4.24804e11 | 1.53276 | 0.766380 | − | 0.642388i | \(-0.222056\pi\) | ||||
0.766380 | + | 0.642388i | \(0.222056\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.71779e10 | −0.130738 | ||||||||
\(352\) | 2.75216e11 | 0.955501 | ||||||||
\(353\) | −1.53549e11 | −0.526334 | −0.263167 | − | 0.964750i | \(-0.584767\pi\) | ||||
−0.263167 | + | 0.964750i | \(0.584767\pi\) | |||||||
\(354\) | −1.53471e11 | −0.519412 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.05397e11 | 2.32760 | ||||||||
\(357\) | 2.98907e11 | 0.973933 | ||||||||
\(358\) | 2.18938e11 | 0.704447 | ||||||||
\(359\) | −3.08800e11 | −0.981189 | −0.490594 | − | 0.871388i | \(-0.663220\pi\) | ||||
−0.490594 | + | 0.871388i | \(0.663220\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.19318e11 | −0.989558 | ||||||||
\(362\) | 3.77600e11 | 1.15570 | ||||||||
\(363\) | 3.70745e9 | 0.0112072 | ||||||||
\(364\) | 6.45062e11 | 1.92595 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.20429e11 | 2.38988 | ||||||||
\(367\) | 1.26543e11 | 0.364116 | 0.182058 | − | 0.983288i | \(-0.441724\pi\) | ||||
0.182058 | + | 0.983288i | \(0.441724\pi\) | |||||||
\(368\) | 1.47897e10 | 0.0420382 | ||||||||
\(369\) | −1.51578e11 | −0.425616 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.25579e11 | −1.16627 | ||||||||
\(372\) | 6.67444e11 | 1.80706 | ||||||||
\(373\) | −2.88008e10 | −0.0770397 | −0.0385199 | − | 0.999258i | \(-0.512264\pi\) | ||||
−0.0385199 | + | 0.999258i | \(0.512264\pi\) | |||||||
\(374\) | −3.59077e11 | −0.948999 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.52059e11 | −1.42443 | ||||||||
\(377\) | −1.57120e11 | −0.400586 | ||||||||
\(378\) | −1.04056e11 | −0.262154 | ||||||||
\(379\) | 5.21974e11 | 1.29949 | 0.649744 | − | 0.760153i | \(-0.274876\pi\) | ||||
0.649744 | + | 0.760153i | \(0.274876\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.42178e11 | 0.588805 | ||||||||
\(382\) | 7.71690e10 | 0.185421 | ||||||||
\(383\) | 1.77381e10 | 0.0421223 | 0.0210611 | − | 0.999778i | \(-0.493296\pi\) | ||||
0.0210611 | + | 0.999778i | \(0.493296\pi\) | |||||||
\(384\) | 9.71973e11 | 2.28120 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.17007e11 | 1.64392 | ||||||||
\(387\) | −4.55380e11 | −1.03199 | ||||||||
\(388\) | −1.98076e11 | −0.443699 | ||||||||
\(389\) | −2.05874e10 | −0.0455856 | −0.0227928 | − | 0.999740i | \(-0.507256\pi\) | ||||
−0.0227928 | + | 0.999740i | \(0.507256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.30390e11 | 0.498503 | ||||||||
\(392\) | 2.18429e11 | 0.467222 | ||||||||
\(393\) | −4.31686e11 | −0.912855 | ||||||||
\(394\) | −2.34872e11 | −0.491018 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.21600e11 | −1.47458 | ||||||||
\(397\) | 8.47450e11 | 1.71221 | 0.856105 | − | 0.516803i | \(-0.172878\pi\) | ||||
0.856105 | + | 0.516803i | \(0.172878\pi\) | |||||||
\(398\) | 4.85809e11 | 0.970491 | ||||||||
\(399\) | −8.59139e10 | −0.169701 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.81253e11 | −0.543185 | −0.271592 | − | 0.962412i | \(-0.587550\pi\) | ||||
−0.271592 | + | 0.962412i | \(0.587550\pi\) | |||||||
\(402\) | −5.47329e11 | −1.04528 | ||||||||
\(403\) | 4.12616e11 | 0.779245 | ||||||||
\(404\) | −5.48254e11 | −1.02392 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.39760e11 | −0.803247 | ||||||||
\(407\) | −8.26111e11 | −1.49232 | ||||||||
\(408\) | −4.70811e11 | −0.841154 | ||||||||
\(409\) | −6.89579e11 | −1.21851 | −0.609255 | − | 0.792975i | \(-0.708531\pi\) | ||||
−0.609255 | + | 0.792975i | \(0.708531\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.57091e11 | −1.30876 | ||||||||
\(412\) | −8.00364e11 | −1.36852 | ||||||||
\(413\) | −1.64959e11 | −0.278998 | ||||||||
\(414\) | 7.45313e11 | 1.24692 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.71680e11 | 0.935908 | ||||||||
\(417\) | −3.17958e11 | −0.514942 | ||||||||
\(418\) | 1.03208e11 | 0.165357 | ||||||||
\(419\) | −4.76873e11 | −0.755857 | −0.377928 | − | 0.925835i | \(-0.623363\pi\) | ||||
−0.377928 | + | 0.925835i | \(0.623363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.08180e12 | 1.67833 | 0.839165 | − | 0.543877i | \(-0.183044\pi\) | ||||
0.839165 | + | 0.543877i | \(0.183044\pi\) | |||||||
\(422\) | 7.58860e10 | 0.116481 | ||||||||
\(423\) | −8.14424e11 | −1.23686 | ||||||||
\(424\) | 6.70333e11 | 1.00727 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.39363e12 | −2.05023 | ||||||||
\(427\) | 8.81841e11 | 1.28370 | ||||||||
\(428\) | 1.11978e12 | 1.61300 | ||||||||
\(429\) | −9.40196e11 | −1.34017 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.36212e11 | −0.469316 | −0.234658 | − | 0.972078i | \(-0.575397\pi\) | ||||
−0.234658 | + | 0.972078i | \(0.575397\pi\) | |||||||
\(432\) | 4.79806e9 | 0.00662809 | ||||||||
\(433\) | −1.26577e12 | −1.73045 | −0.865225 | − | 0.501383i | \(-0.832825\pi\) | ||||
−0.865225 | + | 0.501383i | \(0.832825\pi\) | |||||||
\(434\) | 1.15486e12 | 1.56253 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.62361e12 | 2.15176 | ||||||||
\(437\) | −6.62203e10 | −0.0868609 | ||||||||
\(438\) | 2.42583e12 | 3.14939 | ||||||||
\(439\) | 2.16378e11 | 0.278050 | 0.139025 | − | 0.990289i | \(-0.455603\pi\) | ||||
0.139025 | + | 0.990289i | \(0.455603\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.22237e11 | 0.405697 | ||||||||
\(442\) | −7.45878e11 | −0.929539 | ||||||||
\(443\) | 3.36288e11 | 0.414853 | 0.207426 | − | 0.978251i | \(-0.433491\pi\) | ||||
0.207426 | + | 0.978251i | \(0.433491\pi\) | |||||||
\(444\) | −2.77579e12 | −3.38972 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.86724e11 | 0.702145 | ||||||||
\(447\) | 1.22625e12 | 1.45276 | ||||||||
\(448\) | 1.65083e12 | 1.93620 | ||||||||
\(449\) | 1.40309e12 | 1.62922 | 0.814608 | − | 0.580012i | \(-0.196952\pi\) | ||||
0.814608 | + | 0.580012i | \(0.196952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.12505e11 | 0.469499 | ||||||||
\(452\) | 8.18060e11 | 0.921854 | ||||||||
\(453\) | −1.09923e12 | −1.22644 | ||||||||
\(454\) | −1.78790e12 | −1.97511 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.35324e11 | 0.146566 | ||||||||
\(457\) | −1.26840e12 | −1.36030 | −0.680148 | − | 0.733075i | \(-0.738084\pi\) | ||||
−0.680148 | + | 0.733075i | \(0.738084\pi\) | |||||||
\(458\) | −2.33129e12 | −2.47572 | ||||||||
\(459\) | 7.47428e10 | 0.0785981 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.57771e11 | −0.368936 | −0.184468 | − | 0.982839i | \(-0.559056\pi\) | ||||
−0.184468 | + | 0.982839i | \(0.559056\pi\) | |||||||
\(462\) | −2.63150e12 | −2.68729 | ||||||||
\(463\) | 3.72773e11 | 0.376990 | 0.188495 | − | 0.982074i | \(-0.439639\pi\) | ||||
0.188495 | + | 0.982074i | \(0.439639\pi\) | |||||||
\(464\) | 2.02774e10 | 0.0203087 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.01771e11 | −0.885849 | ||||||||
\(467\) | 1.30696e12 | 1.27155 | 0.635777 | − | 0.771873i | \(-0.280680\pi\) | ||||
0.635777 | + | 0.771873i | \(0.280680\pi\) | |||||||
\(468\) | −1.49891e12 | −1.44434 | ||||||||
\(469\) | −5.88299e11 | −0.561462 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.19832e11 | −0.767593 | ||||||||
\(472\) | 2.59828e11 | 0.240961 | ||||||||
\(473\) | 1.23927e12 | 1.13839 | ||||||||
\(474\) | 4.21898e12 | 3.83889 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.29684e12 | −1.15786 | ||||||||
\(477\) | 9.88908e11 | 0.874628 | ||||||||
\(478\) | −2.87532e12 | −2.51919 | ||||||||
\(479\) | 3.77216e10 | 0.0327402 | 0.0163701 | − | 0.999866i | \(-0.494789\pi\) | ||||
0.0163701 | + | 0.999866i | \(0.494789\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.71600e12 | −1.46172 | ||||||||
\(482\) | 2.42401e12 | 2.04561 | ||||||||
\(483\) | 1.68841e12 | 1.41162 | ||||||||
\(484\) | −1.60852e10 | −0.0133236 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.73050e12 | 2.22014 | ||||||||
\(487\) | −1.89303e12 | −1.52503 | −0.762513 | − | 0.646973i | \(-0.776035\pi\) | ||||
−0.762513 | + | 0.646973i | \(0.776035\pi\) | |||||||
\(488\) | −1.38899e12 | −1.10869 | ||||||||
\(489\) | 1.65748e12 | 1.31087 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.57823e11 | −0.588438 | −0.294219 | − | 0.955738i | \(-0.595060\pi\) | ||||
−0.294219 | + | 0.955738i | \(0.595060\pi\) | |||||||
\(492\) | 1.38605e12 | 1.06644 | ||||||||
\(493\) | 3.15876e11 | 0.240827 | ||||||||
\(494\) | 2.14385e11 | 0.161966 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.32510e10 | −0.0395057 | ||||||||
\(497\) | −1.49794e12 | −1.10126 | ||||||||
\(498\) | 5.61006e12 | 4.08729 | ||||||||
\(499\) | 3.90008e11 | 0.281593 | 0.140796 | − | 0.990039i | \(-0.455034\pi\) | ||||
0.140796 | + | 0.990039i | \(0.455034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.13747e12 | 0.806623 | ||||||||
\(502\) | 6.73973e11 | 0.473670 | ||||||||
\(503\) | 3.44868e11 | 0.240213 | 0.120107 | − | 0.992761i | \(-0.461676\pi\) | ||||
0.120107 | + | 0.992761i | \(0.461676\pi\) | |||||||
\(504\) | −1.63708e12 | −1.13014 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.02829e12 | −1.37548 | ||||||||
\(507\) | 9.93001e10 | 0.0667442 | ||||||||
\(508\) | −1.05071e12 | −0.699999 | ||||||||
\(509\) | −1.33209e12 | −0.879636 | −0.439818 | − | 0.898087i | \(-0.644957\pi\) | ||||
−0.439818 | + | 0.898087i | \(0.644957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.60741e12 | 1.69167 | ||||||||
\(512\) | −1.53738e11 | −0.0988703 | ||||||||
\(513\) | −2.14831e10 | −0.0136952 | ||||||||
\(514\) | −2.35835e12 | −1.49030 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.16404e12 | 2.58578 | ||||||||
\(517\) | 2.21637e12 | 1.36438 | ||||||||
\(518\) | −4.80289e12 | −2.93102 | ||||||||
\(519\) | 2.86707e12 | 1.73455 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.31345e12 | −0.780985 | −0.390493 | − | 0.920606i | \(-0.627695\pi\) | ||||
−0.390493 | + | 0.920606i | \(0.627695\pi\) | |||||||
\(522\) | 1.02186e12 | 0.602385 | ||||||||
\(523\) | −1.60667e12 | −0.939006 | −0.469503 | − | 0.882931i | \(-0.655567\pi\) | ||||
−0.469503 | + | 0.882931i | \(0.655567\pi\) | |||||||
\(524\) | 1.87292e12 | 1.08524 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.12136e11 | −0.462587 | ||||||||
\(527\) | −8.29529e11 | −0.468472 | ||||||||
\(528\) | 1.21339e11 | 0.0679433 | ||||||||
\(529\) | −4.99767e11 | −0.277471 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.83311e11 | 0.209231 | ||||||||
\(532\) | 3.72746e11 | 0.201749 | ||||||||
\(533\) | 8.56858e11 | 0.459871 | ||||||||
\(534\) | −5.97744e12 | −3.18112 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.26634e11 | 0.484916 | ||||||||
\(537\) | −1.15249e12 | −0.598072 | ||||||||
\(538\) | 2.86361e12 | 1.47365 | ||||||||
\(539\) | −8.76935e11 | −0.447525 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.22163e12 | −0.613132 | −0.306566 | − | 0.951849i | \(-0.599180\pi\) | ||||
−0.306566 | + | 0.951849i | \(0.599180\pi\) | |||||||
\(542\) | −3.44365e12 | −1.71404 | ||||||||
\(543\) | −1.98769e12 | −0.981179 | ||||||||
\(544\) | −1.14931e12 | −0.562656 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.46617e12 | −2.63218 | ||||||||
\(547\) | −1.65203e11 | −0.0788996 | −0.0394498 | − | 0.999222i | \(-0.512561\pi\) | ||||
−0.0394498 | + | 0.999222i | \(0.512561\pi\) | |||||||
\(548\) | 3.28472e12 | 1.55591 | ||||||||
\(549\) | −2.04911e12 | −0.962698 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.07912e10 | −0.0419625 | ||||||||
\(552\) | −2.65943e12 | −1.21917 | ||||||||
\(553\) | 4.53479e12 | 2.06203 | ||||||||
\(554\) | 2.74238e12 | 1.23690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.37950e12 | 0.612186 | ||||||||
\(557\) | −3.45024e12 | −1.51880 | −0.759401 | − | 0.650623i | \(-0.774508\pi\) | ||||
−0.759401 | + | 0.650623i | \(0.774508\pi\) | |||||||
\(558\) | −2.68353e12 | −1.17180 | ||||||||
\(559\) | 2.57422e12 | 1.11505 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.89018e12 | 0.805695 | ||||||||
\(562\) | −4.07248e12 | −1.72205 | ||||||||
\(563\) | −4.38944e11 | −0.184129 | −0.0920643 | − | 0.995753i | \(-0.529347\pi\) | ||||
−0.0920643 | + | 0.995753i | \(0.529347\pi\) | |||||||
\(564\) | 7.44717e12 | 3.09910 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.29867e12 | −2.17016 | ||||||||
\(567\) | 3.22275e12 | 1.30949 | ||||||||
\(568\) | 2.35942e12 | 0.951126 | ||||||||
\(569\) | −2.03068e12 | −0.812150 | −0.406075 | − | 0.913840i | \(-0.633103\pi\) | ||||
−0.406075 | + | 0.913840i | \(0.633103\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.25554e12 | 0.494276 | 0.247138 | − | 0.968980i | \(-0.420510\pi\) | ||||
0.247138 | + | 0.968980i | \(0.420510\pi\) | |||||||
\(572\) | 4.07914e12 | 1.59326 | ||||||||
\(573\) | −4.06217e11 | −0.157421 | ||||||||
\(574\) | 2.39824e12 | 0.922125 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.83599e12 | −1.45203 | ||||||||
\(577\) | 1.45596e12 | 0.546838 | 0.273419 | − | 0.961895i | \(-0.411845\pi\) | ||||
0.273419 | + | 0.961895i | \(0.411845\pi\) | |||||||
\(578\) | −2.86033e12 | −1.06596 | ||||||||
\(579\) | −3.77432e12 | −1.39568 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.03000e12 | 2.19546 | ||||||||
\(582\) | 1.67847e12 | 0.606400 | ||||||||
\(583\) | −2.69121e12 | −0.964805 | ||||||||
\(584\) | −4.10695e12 | −1.46104 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.11165e12 | 1.79070 | ||||||||
\(587\) | 7.51503e11 | 0.261252 | 0.130626 | − | 0.991432i | \(-0.458301\pi\) | ||||
0.130626 | + | 0.991432i | \(0.458301\pi\) | |||||||
\(588\) | −2.94656e12 | −1.01652 | ||||||||
\(589\) | 2.38429e11 | 0.0816281 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.23636e12 | 0.416872 | ||||||||
\(592\) | 2.21462e11 | 0.0741057 | ||||||||
\(593\) | 1.95284e12 | 0.648514 | 0.324257 | − | 0.945969i | \(-0.394886\pi\) | ||||
0.324257 | + | 0.945969i | \(0.394886\pi\) | |||||||
\(594\) | −6.58016e11 | −0.216869 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.32021e12 | −1.72711 | ||||||||
\(597\) | −2.55730e12 | −0.823942 | ||||||||
\(598\) | −4.21318e12 | −1.34727 | ||||||||
\(599\) | −4.92766e12 | −1.56394 | −0.781969 | − | 0.623317i | \(-0.785785\pi\) | ||||
−0.781969 | + | 0.623317i | \(0.785785\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.36498e12 | −1.36473 | −0.682366 | − | 0.731011i | \(-0.739049\pi\) | ||||
−0.682366 | + | 0.731011i | \(0.739049\pi\) | |||||||
\(602\) | 7.20494e12 | 2.23587 | ||||||||
\(603\) | 1.36702e12 | 0.421062 | ||||||||
\(604\) | 4.76911e12 | 1.45805 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.64583e12 | 1.39938 | ||||||||
\(607\) | 1.49883e12 | 0.448128 | 0.224064 | − | 0.974574i | \(-0.428068\pi\) | ||||
0.224064 | + | 0.974574i | \(0.428068\pi\) | |||||||
\(608\) | 3.30343e11 | 0.0980391 | ||||||||
\(609\) | 2.31490e12 | 0.681952 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.60386e12 | 1.33640 | ||||||||
\(612\) | 3.01343e12 | 0.868321 | ||||||||
\(613\) | 3.19261e12 | 0.913216 | 0.456608 | − | 0.889668i | \(-0.349064\pi\) | ||||
0.456608 | + | 0.889668i | \(0.349064\pi\) | |||||||
\(614\) | 9.99137e11 | 0.283705 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.45516e12 | 1.24666 | ||||||||
\(617\) | 1.58167e12 | 0.439371 | 0.219685 | − | 0.975571i | \(-0.429497\pi\) | ||||
0.219685 | + | 0.975571i | \(0.429497\pi\) | |||||||
\(618\) | 6.78218e12 | 1.87034 | ||||||||
\(619\) | 2.53778e12 | 0.694777 | 0.347389 | − | 0.937721i | \(-0.387068\pi\) | ||||
0.347389 | + | 0.937721i | \(0.387068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.22194e11 | 0.113920 | ||||||||
\(622\) | 3.61252e12 | 0.967729 | ||||||||
\(623\) | −6.42488e12 | −1.70871 | ||||||||
\(624\) | 2.52046e11 | 0.0665501 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.70576e12 | 1.74527 | ||||||||
\(627\) | −5.43289e11 | −0.140387 | ||||||||
\(628\) | 3.55693e12 | 0.912550 | ||||||||
\(629\) | 3.44987e12 | 0.878770 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.66150e12 | −1.67278 | −0.836392 | − | 0.548131i | \(-0.815339\pi\) | ||||
−0.836392 | + | 0.548131i | \(0.815339\pi\) | |||||||
\(632\) | −7.14279e12 | −1.78091 | ||||||||
\(633\) | −3.99464e11 | −0.0988918 | ||||||||
\(634\) | 5.60749e12 | 1.37837 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.04266e12 | −2.19149 | ||||||||
\(637\) | −1.82158e12 | −0.438349 | ||||||||
\(638\) | −2.78089e12 | −0.664493 | ||||||||
\(639\) | 3.48073e12 | 0.825880 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.22257e12 | −1.45582 | −0.727911 | − | 0.685671i | \(-0.759509\pi\) | ||||
−0.727911 | + | 0.685671i | \(0.759509\pi\) | |||||||
\(642\) | −9.48883e12 | −2.20447 | ||||||||
\(643\) | 4.55187e11 | 0.105012 | 0.0525061 | − | 0.998621i | \(-0.483279\pi\) | ||||
0.0525061 | + | 0.998621i | \(0.483279\pi\) | |||||||
\(644\) | −7.32535e12 | −1.67819 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.31003e11 | −0.0973719 | ||||||||
\(647\) | 2.50192e12 | 0.561312 | 0.280656 | − | 0.959808i | \(-0.409448\pi\) | ||||
0.280656 | + | 0.959808i | \(0.409448\pi\) | |||||||
\(648\) | −5.07618e12 | −1.13097 | ||||||||
\(649\) | −1.04314e12 | −0.230803 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.07920e12 | −1.32658 | ||||||||
\(652\) | −7.19116e12 | −1.55842 | ||||||||
\(653\) | −3.54499e12 | −0.762966 | −0.381483 | − | 0.924376i | \(-0.624587\pi\) | ||||
−0.381483 | + | 0.924376i | \(0.624587\pi\) | |||||||
\(654\) | −1.37583e13 | −2.94080 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.10583e11 | −0.0233143 | ||||||||
\(657\) | −6.05877e12 | −1.26865 | ||||||||
\(658\) | 1.28857e13 | 2.67973 | ||||||||
\(659\) | 5.93850e12 | 1.22657 | 0.613285 | − | 0.789862i | \(-0.289848\pi\) | ||||
0.613285 | + | 0.789862i | \(0.289848\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.68673e12 | −1.36241 | −0.681204 | − | 0.732093i | \(-0.738543\pi\) | ||||
−0.681204 | + | 0.732093i | \(0.738543\pi\) | |||||||
\(662\) | 1.50016e13 | 3.03583 | ||||||||
\(663\) | 3.92630e12 | 0.789174 | ||||||||
\(664\) | −9.49790e12 | −1.89614 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.11604e13 | 2.19808 | ||||||||
\(667\) | 1.78426e12 | 0.349054 | ||||||||
\(668\) | −4.93503e12 | −0.958950 | ||||||||
\(669\) | −3.08851e12 | −0.596117 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.57645e12 | 1.06196 | ||||||||
\(672\) | −8.42274e12 | −1.59328 | ||||||||
\(673\) | −8.43444e12 | −1.58485 | −0.792425 | − | 0.609969i | \(-0.791182\pi\) | ||||
−0.792425 | + | 0.609969i | \(0.791182\pi\) | |||||||
\(674\) | 9.13652e12 | 1.70534 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.30823e11 | −0.0793486 | ||||||||
\(677\) | −9.48091e12 | −1.73461 | −0.867303 | − | 0.497781i | \(-0.834148\pi\) | ||||
−0.867303 | + | 0.497781i | \(0.834148\pi\) | |||||||
\(678\) | −6.93213e12 | −1.25989 | ||||||||
\(679\) | 1.80411e12 | 0.325723 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.41150e12 | 1.67686 | ||||||||
\(682\) | 7.30295e12 | 1.29261 | ||||||||
\(683\) | 1.00045e13 | 1.75914 | 0.879571 | − | 0.475768i | \(-0.157830\pi\) | ||||
0.879571 | + | 0.475768i | \(0.157830\pi\) | |||||||
\(684\) | −8.66142e11 | −0.151299 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.24762e12 | 1.07710 | ||||||||
\(687\) | 1.22719e13 | 2.10187 | ||||||||
\(688\) | −3.32221e11 | −0.0565300 | ||||||||
\(689\) | −5.59021e12 | −0.945021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.59146e12 | 0.932983 | 0.466491 | − | 0.884526i | \(-0.345518\pi\) | ||||
0.466491 | + | 0.884526i | \(0.345518\pi\) | |||||||
\(692\) | −1.24391e13 | −2.06211 | ||||||||
\(693\) | 6.57246e12 | 1.08250 | ||||||||
\(694\) | −1.26754e13 | −2.07416 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.64621e12 | −0.588980 | ||||||||
\(697\) | −1.72264e12 | −0.276469 | ||||||||
\(698\) | 1.56178e13 | 2.49041 | ||||||||
\(699\) | 4.74692e12 | 0.752081 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.41878e12 | −1.00397 | −0.501986 | − | 0.864876i | \(-0.667397\pi\) | ||||
−0.501986 | + | 0.864876i | \(0.667397\pi\) | |||||||
\(702\) | −1.36684e12 | −0.212422 | ||||||||
\(703\) | −9.91586e11 | −0.153120 | ||||||||
\(704\) | 1.04393e13 | 1.60174 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.64520e12 | −0.855181 | ||||||||
\(707\) | 4.99359e12 | 0.751667 | ||||||||
\(708\) | −3.50503e12 | −0.524255 | ||||||||
\(709\) | 1.98300e12 | 0.294724 | 0.147362 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147362 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.05374e13 | −1.54639 | ||||||||
\(712\) | 1.01199e13 | 1.47576 | ||||||||
\(713\) | −4.68569e12 | −0.679002 | ||||||||
\(714\) | 1.09892e13 | 1.58244 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.00020e12 | 0.711015 | ||||||||
\(717\) | 1.51357e13 | 2.13878 | ||||||||
\(718\) | −1.13530e13 | −1.59422 | ||||||||
\(719\) | −9.53823e12 | −1.33103 | −0.665515 | − | 0.746385i | \(-0.731788\pi\) | ||||
−0.665515 | + | 0.746385i | \(0.731788\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.28986e12 | 1.00464 | ||||||||
\(722\) | −1.17397e13 | −1.60782 | ||||||||
\(723\) | −1.27600e13 | −1.73671 | ||||||||
\(724\) | 8.62377e12 | 1.16647 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.36304e11 | 0.0182093 | ||||||||
\(727\) | 6.30135e11 | 0.0836621 | 0.0418310 | − | 0.999125i | \(-0.486681\pi\) | ||||
0.0418310 | + | 0.999125i | \(0.486681\pi\) | |||||||
\(728\) | 9.25429e12 | 1.22110 | ||||||||
\(729\) | −6.07886e12 | −0.797165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.17524e12 | −0.670352 | ||||||||
\(732\) | 1.87373e13 | 2.41216 | ||||||||
\(733\) | −2.79069e12 | −0.357061 | −0.178531 | − | 0.983934i | \(-0.557134\pi\) | ||||
−0.178531 | + | 0.983934i | \(0.557134\pi\) | |||||||
\(734\) | 4.65232e12 | 0.591612 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.49203e12 | −0.815512 | ||||||||
\(737\) | −3.72019e12 | −0.464474 | ||||||||
\(738\) | −5.57274e12 | −0.691537 | ||||||||
\(739\) | 7.26759e12 | 0.896376 | 0.448188 | − | 0.893939i | \(-0.352069\pi\) | ||||
0.448188 | + | 0.893939i | \(0.352069\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.12852e12 | −0.137508 | ||||||||
\(742\) | −1.56463e13 | −1.89494 | ||||||||
\(743\) | 9.19047e12 | 1.10634 | 0.553169 | − | 0.833069i | \(-0.313418\pi\) | ||||
0.553169 | + | 0.833069i | \(0.313418\pi\) | |||||||
\(744\) | 9.57540e12 | 1.14572 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.05885e12 | −0.125173 | ||||||||
\(747\) | −1.40118e13 | −1.64646 | ||||||||
\(748\) | −8.20074e12 | −0.957847 | ||||||||
\(749\) | −1.01991e13 | −1.18412 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.21242e11 | −0.0597943 | −0.0298972 | − | 0.999553i | \(-0.509518\pi\) | ||||
−0.0298972 | + | 0.999553i | \(0.509518\pi\) | |||||||
\(752\) | −5.94160e11 | −0.0677521 | ||||||||
\(753\) | −3.54779e12 | −0.402143 | ||||||||
\(754\) | −5.77648e12 | −0.650867 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.37648e12 | −0.264598 | ||||||||
\(757\) | −1.15123e13 | −1.27417 | −0.637087 | − | 0.770792i | \(-0.719861\pi\) | ||||
−0.637087 | + | 0.770792i | \(0.719861\pi\) | |||||||
\(758\) | 1.91903e13 | 2.11139 | ||||||||
\(759\) | 1.06769e13 | 1.16777 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.43517e13 | 1.55121 | 0.775607 | − | 0.631217i | \(-0.217444\pi\) | ||||
0.775607 | + | 0.631217i | \(0.217444\pi\) | |||||||
\(762\) | 8.90360e12 | 0.956684 | ||||||||
\(763\) | −1.47882e13 | −1.57962 | ||||||||
\(764\) | 1.76242e12 | 0.187149 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.52136e11 | 0.0684398 | ||||||||
\(767\) | −2.16682e12 | −0.226071 | ||||||||
\(768\) | 1.43453e13 | 1.48794 | ||||||||
\(769\) | −7.42318e12 | −0.765458 | −0.382729 | − | 0.923861i | \(-0.625016\pi\) | ||||
−0.382729 | + | 0.923861i | \(0.625016\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.24143e13 | 1.26526 | ||||||||
\(772\) | 1.63753e13 | 1.65925 | ||||||||
\(773\) | −5.82774e12 | −0.587074 | −0.293537 | − | 0.955948i | \(-0.594832\pi\) | ||||
−0.293537 | + | 0.955948i | \(0.594832\pi\) | |||||||
\(774\) | −1.67419e13 | −1.67676 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.84166e12 | −0.281316 | ||||||||
\(777\) | 2.52824e13 | 2.48842 | ||||||||
\(778\) | −7.56890e11 | −0.0740670 | ||||||||
\(779\) | 4.95132e11 | 0.0481729 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.47246e12 | −0.911031 | ||||||||
\(782\) | 8.47023e12 | 0.809962 | ||||||||
\(783\) | 5.78848e11 | 0.0550347 | ||||||||
\(784\) | 2.35087e11 | 0.0222232 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.58708e13 | −1.48320 | ||||||||
\(787\) | −7.20033e11 | −0.0669061 | −0.0334531 | − | 0.999440i | \(-0.510650\pi\) | ||||
−0.0334531 | + | 0.999440i | \(0.510650\pi\) | |||||||
\(788\) | −5.36409e12 | −0.495596 | ||||||||
\(789\) | 4.27508e12 | 0.392733 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.45103e12 | −0.676741 | ||||||||
\(792\) | −1.03523e13 | −0.934921 | ||||||||
\(793\) | 1.15834e13 | 1.04018 | ||||||||
\(794\) | 3.11563e13 | 2.78198 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.10951e13 | 0.979539 | ||||||||
\(797\) | −9.03491e12 | −0.793161 | −0.396580 | − | 0.918000i | \(-0.629803\pi\) | ||||
−0.396580 | + | 0.918000i | \(0.629803\pi\) | |||||||
\(798\) | −3.15861e12 | −0.275729 | ||||||||
\(799\) | −9.25566e12 | −0.803428 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.49293e13 | 1.28143 | ||||||||
\(802\) | −1.03402e13 | −0.882560 | ||||||||
\(803\) | 1.64883e13 | 1.39945 | ||||||||
\(804\) | −1.25001e13 | −1.05502 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.51697e13 | 1.26611 | ||||||||
\(807\) | −1.50740e13 | −1.25112 | ||||||||
\(808\) | −7.86544e12 | −0.649190 | ||||||||
\(809\) | −2.33217e13 | −1.91422 | −0.957111 | − | 0.289721i | \(-0.906438\pi\) | ||||
−0.957111 | + | 0.289721i | \(0.906438\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.16365e13 | 0.944555 | 0.472277 | − | 0.881450i | \(-0.343432\pi\) | ||||
0.472277 | + | 0.881450i | \(0.343432\pi\) | |||||||
\(812\) | −1.00434e13 | −0.810736 | ||||||||
\(813\) | 1.81273e13 | 1.45521 | ||||||||
\(814\) | −3.03718e13 | −2.42471 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.06716e11 | −0.0400091 | ||||||||
\(817\) | 1.48750e12 | 0.116804 | ||||||||
\(818\) | −2.53522e13 | −1.97982 | ||||||||
\(819\) | 1.36524e13 | 1.06030 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.36931e13 | −1.05186 | −0.525931 | − | 0.850527i | \(-0.676283\pi\) | ||||
−0.525931 | + | 0.850527i | \(0.676283\pi\) | |||||||
\(822\) | −2.78343e13 | −2.12646 | ||||||||
\(823\) | −8.13478e12 | −0.618083 | −0.309041 | − | 0.951049i | \(-0.600008\pi\) | ||||
−0.309041 | + | 0.951049i | \(0.600008\pi\) | |||||||
\(824\) | −1.14823e13 | −0.867674 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.06468e12 | −0.453313 | ||||||||
\(827\) | −9.52838e12 | −0.708344 | −0.354172 | − | 0.935180i | \(-0.615237\pi\) | ||||
−0.354172 | + | 0.935180i | \(0.615237\pi\) | |||||||
\(828\) | 1.70217e13 | 1.25854 | ||||||||
\(829\) | 2.36561e13 | 1.73960 | 0.869798 | − | 0.493407i | \(-0.164249\pi\) | ||||
0.869798 | + | 0.493407i | \(0.164249\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.44359e13 | −1.05012 | ||||||||
\(832\) | 2.16845e13 | 1.56890 | ||||||||
\(833\) | 3.66212e12 | 0.263530 | ||||||||
\(834\) | −1.16897e13 | −0.836671 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.35711e12 | 0.166898 | ||||||||
\(837\) | −1.52013e12 | −0.107057 | ||||||||
\(838\) | −1.75321e13 | −1.22811 | ||||||||
\(839\) | −1.43311e12 | −0.0998509 | −0.0499255 | − | 0.998753i | \(-0.515898\pi\) | ||||
−0.0499255 | + | 0.998753i | \(0.515898\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20608e13 | −0.831372 | ||||||||
\(842\) | 3.97721e13 | 2.72693 | ||||||||
\(843\) | 2.14375e13 | 1.46201 | ||||||||
\(844\) | 1.73311e12 | 0.117567 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.99421e13 | −2.00963 | ||||||||
\(847\) | 1.46507e11 | 0.00978097 | ||||||||
\(848\) | 7.21454e11 | 0.0479101 | ||||||||
\(849\) | 2.78921e13 | 1.84246 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.94870e13 | 1.27369 | ||||||||
\(852\) | −3.18281e13 | −2.06935 | ||||||||
\(853\) | −2.03077e13 | −1.31338 | −0.656690 | − | 0.754161i | \(-0.728044\pi\) | ||||
−0.656690 | + | 0.754161i | \(0.728044\pi\) | |||||||
\(854\) | 3.24207e13 | 2.08575 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.60647e13 | 1.02268 | ||||||||
\(857\) | 1.23092e12 | 0.0779498 | 0.0389749 | − | 0.999240i | \(-0.487591\pi\) | ||||
0.0389749 | + | 0.999240i | \(0.487591\pi\) | |||||||
\(858\) | −3.45661e13 | −2.17750 | ||||||||
\(859\) | −1.69941e13 | −1.06495 | −0.532476 | − | 0.846445i | \(-0.678738\pi\) | ||||
−0.532476 | + | 0.846445i | \(0.678738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.26243e13 | −0.782879 | ||||||||
\(862\) | −1.23607e13 | −0.762538 | ||||||||
\(863\) | 3.86270e12 | 0.237051 | 0.118526 | − | 0.992951i | \(-0.462183\pi\) | ||||
0.118526 | + | 0.992951i | \(0.462183\pi\) | |||||||
\(864\) | −2.10614e12 | −0.128580 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.65357e13 | −2.81162 | ||||||||
\(867\) | 1.50568e13 | 0.904995 | ||||||||
\(868\) | 2.63752e13 | 1.57709 | ||||||||
\(869\) | 2.86764e13 | 1.70583 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.72761e12 | −0.454950 | ||||||||
\(872\) | 2.32929e13 | 1.36427 | ||||||||
\(873\) | −4.19216e12 | −0.244272 | ||||||||
\(874\) | −2.43457e12 | −0.141131 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.54019e13 | 3.17875 | ||||||||
\(877\) | 3.44305e12 | 0.196538 | 0.0982688 | − | 0.995160i | \(-0.468670\pi\) | ||||
0.0982688 | + | 0.995160i | \(0.468670\pi\) | |||||||
\(878\) | 7.95508e12 | 0.451772 | ||||||||
\(879\) | −2.69077e13 | −1.52029 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.37092e13 | 1.32594 | 0.662971 | − | 0.748645i | \(-0.269295\pi\) | ||||
0.662971 | + | 0.748645i | \(0.269295\pi\) | |||||||
\(882\) | 1.18470e13 | 0.659172 | ||||||||
\(883\) | 3.07625e13 | 1.70294 | 0.851468 | − | 0.524407i | \(-0.175713\pi\) | ||||
0.851468 | + | 0.524407i | \(0.175713\pi\) | |||||||
\(884\) | −1.70347e13 | −0.938206 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.23635e13 | 0.674048 | ||||||||
\(887\) | 1.39503e13 | 0.756706 | 0.378353 | − | 0.925661i | \(-0.376491\pi\) | ||||
0.378353 | + | 0.925661i | \(0.376491\pi\) | |||||||
\(888\) | −3.98225e13 | −2.14917 | ||||||||
\(889\) | 9.57008e12 | 0.513875 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.03795e13 | 1.08329 | ||||||||
\(892\) | 1.33998e13 | 0.708691 | ||||||||
\(893\) | 2.66032e12 | 0.139992 | ||||||||
\(894\) | 4.50828e13 | 2.36043 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.84092e13 | 1.99090 | ||||||||
\(897\) | 2.21782e13 | 1.14383 | ||||||||
\(898\) | 5.15844e13 | 2.64713 | ||||||||
\(899\) | −6.42431e12 | −0.328026 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.12386e13 | 0.568134 | ||||||||
\(902\) | 1.51656e13 | 0.762836 | ||||||||
\(903\) | −3.79268e13 | −1.89824 | ||||||||
\(904\) | 1.17362e13 | 0.584479 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.04128e13 | −1.99270 | ||||||||
\(907\) | −9.36080e12 | −0.459283 | −0.229641 | − | 0.973275i | \(-0.573755\pi\) | ||||
−0.229641 | + | 0.973275i | \(0.573755\pi\) | |||||||
\(908\) | −4.08328e13 | −1.99353 | ||||||||
\(909\) | −1.16035e13 | −0.563704 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.17441e12 | 0.297004 | 0.148502 | − | 0.988912i | \(-0.452555\pi\) | ||||
0.148502 | + | 0.988912i | \(0.452555\pi\) | |||||||
\(912\) | 1.45644e11 | 0.00697132 | ||||||||
\(913\) | 3.81316e13 | 1.81621 | ||||||||
\(914\) | −4.66324e13 | −2.21019 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.32428e13 | −2.49880 | ||||||||
\(917\) | −1.70588e13 | −0.796687 | ||||||||
\(918\) | 2.74790e12 | 0.127705 | ||||||||
\(919\) | 3.99328e12 | 0.184676 | 0.0923380 | − | 0.995728i | \(-0.470566\pi\) | ||||
0.0923380 | + | 0.995728i | \(0.470566\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.25945e12 | −0.240864 | ||||||||
\(922\) | −1.31534e13 | −0.599443 | ||||||||
\(923\) | −1.96763e13 | −0.892350 | ||||||||
\(924\) | −6.00992e13 | −2.71234 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.37049e13 | 0.612529 | ||||||||
\(927\) | −1.69393e13 | −0.753417 | ||||||||
\(928\) | −8.90089e12 | −0.393974 | ||||||||
\(929\) | 1.84456e13 | 0.812496 | 0.406248 | − | 0.913763i | \(-0.366837\pi\) | ||||
0.406248 | + | 0.913763i | \(0.366837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.05259e12 | −0.0459183 | ||||||||
\(932\) | −2.05950e13 | −0.894108 | ||||||||
\(933\) | −1.90163e13 | −0.821596 | ||||||||
\(934\) | 4.80499e13 | 2.06601 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.15040e13 | −0.915750 | ||||||||
\(937\) | 8.90163e12 | 0.377261 | 0.188630 | − | 0.982048i | \(-0.439595\pi\) | ||||
0.188630 | + | 0.982048i | \(0.439595\pi\) | |||||||
\(938\) | −2.16287e13 | −0.912257 | ||||||||
\(939\) | −3.52991e13 | −1.48173 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.64341e13 | −0.683270 | −0.341635 | − | 0.939833i | \(-0.610981\pi\) | ||||
−0.341635 | + | 0.939833i | \(0.610981\pi\) | |||||||
\(942\) | −3.01409e13 | −1.24718 | ||||||||
\(943\) | −9.73052e12 | −0.400713 | ||||||||
\(944\) | 2.79643e11 | 0.0114612 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.55615e13 | 1.84964 | ||||||||
\(947\) | −4.26042e13 | −1.72138 | −0.860691 | − | 0.509128i | \(-0.829968\pi\) | ||||
−0.860691 | + | 0.509128i | \(0.829968\pi\) | |||||||
\(948\) | 9.63548e13 | 3.87468 | ||||||||
\(949\) | 3.42497e13 | 1.37075 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.95178e13 | −1.17023 | ||||||||
\(952\) | −1.86049e13 | −0.734111 | ||||||||
\(953\) | −3.52200e12 | −0.138316 | −0.0691578 | − | 0.997606i | \(-0.522031\pi\) | ||||
−0.0691578 | + | 0.997606i | \(0.522031\pi\) | |||||||
\(954\) | 3.63570e13 | 1.42109 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.56677e13 | −2.54268 | ||||||||
\(957\) | 1.46386e13 | 0.564151 | ||||||||
\(958\) | 1.38683e12 | 0.0531958 | ||||||||
\(959\) | −2.99178e13 | −1.14221 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.56859e12 | −0.361903 | ||||||||
\(962\) | −6.30885e13 | −2.37499 | ||||||||
\(963\) | 2.36994e13 | 0.888013 | ||||||||
\(964\) | 5.53606e13 | 2.06469 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.20741e13 | 2.29358 | ||||||||
\(967\) | 3.34889e13 | 1.23163 | 0.615816 | − | 0.787890i | \(-0.288826\pi\) | ||||
0.615816 | + | 0.787890i | \(0.288826\pi\) | |||||||
\(968\) | −2.30764e11 | −0.00844750 | ||||||||
\(969\) | 2.26880e12 | 0.0826682 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.77122e13 | −1.36143 | −0.680715 | − | 0.732548i | \(-0.738331\pi\) | ||||
−0.680715 | + | 0.732548i | \(0.738331\pi\) | |||||||
\(972\) | 6.23603e13 | 2.24083 | ||||||||
\(973\) | −1.25647e13 | −0.449411 | ||||||||
\(974\) | −6.95968e13 | −2.47784 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.49492e12 | −0.0527344 | ||||||||
\(977\) | 4.00215e13 | 1.40530 | 0.702648 | − | 0.711537i | \(-0.252001\pi\) | ||||
0.702648 | + | 0.711537i | \(0.252001\pi\) | |||||||
\(978\) | 6.09370e13 | 2.12988 | ||||||||
\(979\) | −4.06286e13 | −1.41355 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.43629e13 | 1.18462 | ||||||||
\(982\) | −2.78612e13 | −0.956088 | ||||||||
\(983\) | −3.31096e13 | −1.13100 | −0.565500 | − | 0.824748i | \(-0.691317\pi\) | ||||
−0.565500 | + | 0.824748i | \(0.691317\pi\) | |||||||
\(984\) | 1.98847e13 | 0.676147 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.16131e13 | 0.391293 | ||||||||
\(987\) | −6.78301e13 | −2.27507 | ||||||||
\(988\) | 4.89622e12 | 0.163476 | ||||||||
\(989\) | −2.92330e13 | −0.971606 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.90619e12 | 0.0627820 | 0.0313910 | − | 0.999507i | \(-0.490006\pi\) | ||||
0.0313910 | + | 0.999507i | \(0.490006\pi\) | |||||||
\(992\) | 2.33748e13 | 0.766383 | ||||||||
\(993\) | −7.89684e13 | −2.57740 | ||||||||
\(994\) | −5.50715e13 | −1.78932 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.28125e14 | 4.12540 | ||||||||
\(997\) | 2.13028e13 | 0.682823 | 0.341411 | − | 0.939914i | \(-0.389095\pi\) | ||||
0.341411 | + | 0.939914i | \(0.389095\pi\) | |||||||
\(998\) | 1.43386e13 | 0.457529 | ||||||||
\(999\) | 6.32195e12 | 0.200820 |
(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 | 25.10.a.b.1.2 | 2 | ||
3.2 | odd | 2 | 225.10.a.h.1.1 | 2 | |||
4.3 | odd | 2 | 400.10.a.t.1.2 | 2 | |||
5.2 | odd | 4 | 25.10.b.b.24.4 | 4 | |||
5.3 | odd | 4 | 25.10.b.b.24.1 | 4 | |||
5.4 | even | 2 | 5.10.a.b.1.1 | ✓ | 2 | ||
15.2 | even | 4 | 225.10.b.h.199.1 | 4 | |||
15.8 | even | 4 | 225.10.b.h.199.4 | 4 | |||
15.14 | odd | 2 | 45.10.a.f.1.2 | 2 | |||
20.3 | even | 4 | 400.10.c.p.49.4 | 4 | |||
20.7 | even | 4 | 400.10.c.p.49.1 | 4 | |||
20.19 | odd | 2 | 80.10.a.f.1.1 | 2 | |||
35.34 | odd | 2 | 245.10.a.d.1.1 | 2 | |||
40.19 | odd | 2 | 320.10.a.s.1.2 | 2 | |||
40.29 | even | 2 | 320.10.a.k.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.10.a.b.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
25.10.a.b.1.2 | 2 | 1.1 | even | 1 | trivial | ||
25.10.b.b.24.1 | 4 | 5.3 | odd | 4 | |||
25.10.b.b.24.4 | 4 | 5.2 | odd | 4 | |||
45.10.a.f.1.2 | 2 | 15.14 | odd | 2 | |||
80.10.a.f.1.1 | 2 | 20.19 | odd | 2 | |||
225.10.a.h.1.1 | 2 | 3.2 | odd | 2 | |||
225.10.b.h.199.1 | 4 | 15.2 | even | 4 | |||
225.10.b.h.199.4 | 4 | 15.8 | even | 4 | |||
245.10.a.d.1.1 | 2 | 35.34 | odd | 2 | |||
320.10.a.k.1.1 | 2 | 40.29 | even | 2 | |||
320.10.a.s.1.2 | 2 | 40.19 | odd | 2 | |||
400.10.a.t.1.2 | 2 | 4.3 | odd | 2 | |||
400.10.c.p.49.1 | 4 | 20.7 | even | 4 | |||
400.10.c.p.49.4 | 4 | 20.3 | even | 4 |