Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, 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("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.9493 | 0.528092 | 0.264046 | − | 0.964510i | \(-0.414943\pi\) | ||||
0.264046 | + | 0.964510i | \(0.414943\pi\) | |||||||
\(3\) | −87.8502 | −0.626177 | −0.313089 | − | 0.949724i | \(-0.601364\pi\) | ||||
−0.313089 | + | 0.949724i | \(0.601364\pi\) | |||||||
\(4\) | −369.213 | −0.721119 | ||||||||
\(5\) | −13.1947 | −0.00944138 | −0.00472069 | − | 0.999989i | \(-0.501503\pi\) | ||||
−0.00472069 | + | 0.999989i | \(0.501503\pi\) | |||||||
\(6\) | −1049.75 | −0.330679 | ||||||||
\(7\) | 9375.81 | 1.47594 | 0.737968 | − | 0.674835i | \(-0.235785\pi\) | ||||
0.737968 | + | 0.674835i | \(0.235785\pi\) | |||||||
\(8\) | −10529.9 | −0.908909 | ||||||||
\(9\) | −11965.3 | −0.607902 | ||||||||
\(10\) | −157.668 | −0.00498591 | ||||||||
\(11\) | 23234.7 | 0.478486 | 0.239243 | − | 0.970960i | \(-0.423101\pi\) | ||||
0.239243 | + | 0.970960i | \(0.423101\pi\) | |||||||
\(12\) | 32435.5 | 0.451549 | ||||||||
\(13\) | −19001.0 | −0.184515 | −0.0922573 | − | 0.995735i | \(-0.529408\pi\) | ||||
−0.0922573 | + | 0.995735i | \(0.529408\pi\) | |||||||
\(14\) | 112035. | 0.779430 | ||||||||
\(15\) | 1159.16 | 0.00591198 | ||||||||
\(16\) | 63211.4 | 0.241132 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −142978. | −0.321028 | ||||||||
\(19\) | −494664. | −0.870802 | −0.435401 | − | 0.900237i | \(-0.643393\pi\) | ||||
−0.435401 | + | 0.900237i | \(0.643393\pi\) | |||||||
\(20\) | 4871.67 | 0.00680836 | ||||||||
\(21\) | −823668. | −0.924198 | ||||||||
\(22\) | 277639. | 0.252685 | ||||||||
\(23\) | −1.11440e6 | −0.830356 | −0.415178 | − | 0.909740i | \(-0.636281\pi\) | ||||
−0.415178 | + | 0.909740i | \(0.636281\pi\) | |||||||
\(24\) | 925056. | 0.569138 | ||||||||
\(25\) | −1.95295e6 | −0.999911 | ||||||||
\(26\) | −227049. | −0.0974406 | ||||||||
\(27\) | 2.78031e6 | 1.00683 | ||||||||
\(28\) | −3.46167e6 | −1.06433 | ||||||||
\(29\) | 5.04385e6 | 1.32425 | 0.662126 | − | 0.749392i | \(-0.269654\pi\) | ||||
0.662126 | + | 0.749392i | \(0.269654\pi\) | |||||||
\(30\) | 13851.2 | 0.00312207 | ||||||||
\(31\) | 9.14986e6 | 1.77945 | 0.889727 | − | 0.456493i | \(-0.150895\pi\) | ||||
0.889727 | + | 0.456493i | \(0.150895\pi\) | |||||||
\(32\) | 6.14665e6 | 1.03625 | ||||||||
\(33\) | −2.04117e6 | −0.299617 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −123711. | −0.0139349 | ||||||||
\(36\) | 4.41776e6 | 0.438370 | ||||||||
\(37\) | −7.97118e6 | −0.699222 | −0.349611 | − | 0.936895i | \(-0.613686\pi\) | ||||
−0.349611 | + | 0.936895i | \(0.613686\pi\) | |||||||
\(38\) | −5.91092e6 | −0.459863 | ||||||||
\(39\) | 1.66924e6 | 0.115539 | ||||||||
\(40\) | 138939. | 0.00858135 | ||||||||
\(41\) | 1.11923e7 | 0.618576 | 0.309288 | − | 0.950968i | \(-0.399909\pi\) | ||||
0.309288 | + | 0.950968i | \(0.399909\pi\) | |||||||
\(42\) | −9.84229e6 | −0.488061 | ||||||||
\(43\) | −4.06201e6 | −0.181190 | −0.0905948 | − | 0.995888i | \(-0.528877\pi\) | ||||
−0.0905948 | + | 0.995888i | \(0.528877\pi\) | |||||||
\(44\) | −8.57855e6 | −0.345046 | ||||||||
\(45\) | 157879. | 0.00573943 | ||||||||
\(46\) | −1.33163e7 | −0.438504 | ||||||||
\(47\) | 1.71037e6 | 0.0511270 | 0.0255635 | − | 0.999673i | \(-0.491862\pi\) | ||||
0.0255635 | + | 0.999673i | \(0.491862\pi\) | |||||||
\(48\) | −5.55314e6 | −0.150992 | ||||||||
\(49\) | 4.75523e7 | 1.17839 | ||||||||
\(50\) | −2.33365e7 | −0.528044 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.01541e6 | 0.133057 | ||||||||
\(53\) | 4.70576e6 | 0.0819197 | 0.0409599 | − | 0.999161i | \(-0.486958\pi\) | ||||
0.0409599 | + | 0.999161i | \(0.486958\pi\) | |||||||
\(54\) | 3.32229e7 | 0.531699 | ||||||||
\(55\) | −306575. | −0.00451757 | ||||||||
\(56\) | −9.87266e7 | −1.34149 | ||||||||
\(57\) | 4.34564e7 | 0.545277 | ||||||||
\(58\) | 6.02707e7 | 0.699327 | ||||||||
\(59\) | 1.62484e8 | 1.74573 | 0.872864 | − | 0.487964i | \(-0.162260\pi\) | ||||
0.872864 | + | 0.487964i | \(0.162260\pi\) | |||||||
\(60\) | −427977. | −0.00426324 | ||||||||
\(61\) | −8.09997e7 | −0.749030 | −0.374515 | − | 0.927221i | \(-0.622191\pi\) | ||||
−0.374515 | + | 0.927221i | \(0.622191\pi\) | |||||||
\(62\) | 1.09335e8 | 0.939715 | ||||||||
\(63\) | −1.12185e8 | −0.897225 | ||||||||
\(64\) | 4.10843e7 | 0.306102 | ||||||||
\(65\) | 250713. | 0.00174207 | ||||||||
\(66\) | −2.43907e7 | −0.158225 | ||||||||
\(67\) | −1.08385e8 | −0.657100 | −0.328550 | − | 0.944487i | \(-0.606560\pi\) | ||||
−0.328550 | + | 0.944487i | \(0.606560\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.79000e7 | 0.519950 | ||||||||
\(70\) | −1.47827e6 | −0.00735889 | ||||||||
\(71\) | 2.89201e8 | 1.35063 | 0.675317 | − | 0.737527i | \(-0.264007\pi\) | ||||
0.675317 | + | 0.737527i | \(0.264007\pi\) | |||||||
\(72\) | 1.25994e8 | 0.552527 | ||||||||
\(73\) | 8.83100e7 | 0.363963 | 0.181981 | − | 0.983302i | \(-0.441749\pi\) | ||||
0.181981 | + | 0.983302i | \(0.441749\pi\) | |||||||
\(74\) | −9.52505e7 | −0.369253 | ||||||||
\(75\) | 1.71567e8 | 0.626122 | ||||||||
\(76\) | 1.82637e8 | 0.627952 | ||||||||
\(77\) | 2.17844e8 | 0.706216 | ||||||||
\(78\) | 1.99463e7 | 0.0610151 | ||||||||
\(79\) | −5.77142e8 | −1.66710 | −0.833549 | − | 0.552446i | \(-0.813695\pi\) | ||||
−0.833549 | + | 0.552446i | \(0.813695\pi\) | |||||||
\(80\) | −834057. | −0.00227662 | ||||||||
\(81\) | −8.73759e6 | −0.0225533 | ||||||||
\(82\) | 1.33741e8 | 0.326665 | ||||||||
\(83\) | 4.14681e8 | 0.959097 | 0.479549 | − | 0.877515i | \(-0.340800\pi\) | ||||
0.479549 | + | 0.877515i | \(0.340800\pi\) | |||||||
\(84\) | 3.04109e8 | 0.666457 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.85384e7 | −0.0956847 | ||||||||
\(87\) | −4.43103e8 | −0.829217 | ||||||||
\(88\) | −2.44659e8 | −0.434900 | ||||||||
\(89\) | −7.23081e8 | −1.22161 | −0.610804 | − | 0.791782i | \(-0.709154\pi\) | ||||
−0.610804 | + | 0.791782i | \(0.709154\pi\) | |||||||
\(90\) | 1.88655e6 | 0.00303095 | ||||||||
\(91\) | −1.78150e8 | −0.272332 | ||||||||
\(92\) | 4.11450e8 | 0.598786 | ||||||||
\(93\) | −8.03817e8 | −1.11425 | ||||||||
\(94\) | 2.04378e7 | 0.0269997 | ||||||||
\(95\) | 6.52696e6 | 0.00822157 | ||||||||
\(96\) | −5.39985e8 | −0.648875 | ||||||||
\(97\) | −3.43128e8 | −0.393534 | −0.196767 | − | 0.980450i | \(-0.563044\pi\) | ||||
−0.196767 | + | 0.980450i | \(0.563044\pi\) | |||||||
\(98\) | 5.68219e8 | 0.622298 | ||||||||
\(99\) | −2.78011e8 | −0.290873 | ||||||||
\(100\) | 7.21055e8 | 0.721055 | ||||||||
\(101\) | −7.19762e8 | −0.688244 | −0.344122 | − | 0.938925i | \(-0.611823\pi\) | ||||
−0.344122 | + | 0.938925i | \(0.611823\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.08162e9 | −0.946906 | −0.473453 | − | 0.880819i | \(-0.656993\pi\) | ||||
−0.473453 | + | 0.880819i | \(0.656993\pi\) | |||||||
\(104\) | 2.00079e8 | 0.167707 | ||||||||
\(105\) | 1.08681e7 | 0.00872570 | ||||||||
\(106\) | 5.62308e7 | 0.0432611 | ||||||||
\(107\) | −3.57334e7 | −0.0263540 | −0.0131770 | − | 0.999913i | \(-0.504194\pi\) | ||||
−0.0131770 | + | 0.999913i | \(0.504194\pi\) | |||||||
\(108\) | −1.02653e9 | −0.726046 | ||||||||
\(109\) | −2.26706e9 | −1.53831 | −0.769154 | − | 0.639064i | \(-0.779322\pi\) | ||||
−0.769154 | + | 0.639064i | \(0.779322\pi\) | |||||||
\(110\) | −3.66337e6 | −0.00238569 | ||||||||
\(111\) | 7.00271e8 | 0.437837 | ||||||||
\(112\) | 5.92658e8 | 0.355896 | ||||||||
\(113\) | −1.60055e9 | −0.923458 | −0.461729 | − | 0.887021i | \(-0.652771\pi\) | ||||
−0.461729 | + | 0.887021i | \(0.652771\pi\) | |||||||
\(114\) | 5.19276e8 | 0.287956 | ||||||||
\(115\) | 1.47042e7 | 0.00783971 | ||||||||
\(116\) | −1.86225e9 | −0.954944 | ||||||||
\(117\) | 2.27353e8 | 0.112167 | ||||||||
\(118\) | 1.94158e9 | 0.921904 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.22059e7 | −0.00537345 | ||||||||
\(121\) | −1.81810e9 | −0.771051 | ||||||||
\(122\) | −9.67894e8 | −0.395557 | ||||||||
\(123\) | −9.83248e8 | −0.387338 | ||||||||
\(124\) | −3.37825e9 | −1.28320 | ||||||||
\(125\) | 5.15396e7 | 0.0188819 | ||||||||
\(126\) | −1.34053e9 | −0.473817 | ||||||||
\(127\) | 2.56067e9 | 0.873448 | 0.436724 | − | 0.899596i | \(-0.356139\pi\) | ||||
0.436724 | + | 0.899596i | \(0.356139\pi\) | |||||||
\(128\) | −2.65616e9 | −0.874599 | ||||||||
\(129\) | 3.56849e8 | 0.113457 | ||||||||
\(130\) | 2.99585e6 | 0.000919973 0 | ||||||||
\(131\) | −4.64130e9 | −1.37695 | −0.688476 | − | 0.725259i | \(-0.741720\pi\) | ||||
−0.688476 | + | 0.725259i | \(0.741720\pi\) | |||||||
\(132\) | 7.53627e8 | 0.216060 | ||||||||
\(133\) | −4.63788e9 | −1.28525 | ||||||||
\(134\) | −1.29513e9 | −0.347009 | ||||||||
\(135\) | −3.66855e7 | −0.00950588 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.68686e9 | 1.86426 | 0.932130 | − | 0.362124i | \(-0.117948\pi\) | ||||
0.932130 | + | 0.362124i | \(0.117948\pi\) | |||||||
\(138\) | 1.16984e9 | 0.274581 | ||||||||
\(139\) | 6.96747e9 | 1.58310 | 0.791550 | − | 0.611105i | \(-0.209274\pi\) | ||||
0.791550 | + | 0.611105i | \(0.209274\pi\) | |||||||
\(140\) | 4.56758e7 | 0.0100487 | ||||||||
\(141\) | −1.50257e8 | −0.0320146 | ||||||||
\(142\) | 3.45577e9 | 0.713259 | ||||||||
\(143\) | −4.41481e8 | −0.0882877 | ||||||||
\(144\) | −7.56345e8 | −0.146585 | ||||||||
\(145\) | −6.65522e7 | −0.0125028 | ||||||||
\(146\) | 1.05525e9 | 0.192206 | ||||||||
\(147\) | −4.17748e9 | −0.737881 | ||||||||
\(148\) | 2.94307e9 | 0.504222 | ||||||||
\(149\) | −2.32799e9 | −0.386939 | −0.193470 | − | 0.981106i | \(-0.561974\pi\) | ||||
−0.193470 | + | 0.981106i | \(0.561974\pi\) | |||||||
\(150\) | 2.05012e9 | 0.330649 | ||||||||
\(151\) | −8.99613e9 | −1.40818 | −0.704092 | − | 0.710108i | \(-0.748646\pi\) | ||||
−0.704092 | + | 0.710108i | \(0.748646\pi\) | |||||||
\(152\) | 5.20878e9 | 0.791479 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.60309e9 | 0.372946 | ||||||||
\(155\) | −1.20730e8 | −0.0168005 | ||||||||
\(156\) | −6.16305e8 | −0.0833173 | ||||||||
\(157\) | −1.03091e10 | −1.35416 | −0.677082 | − | 0.735907i | \(-0.736756\pi\) | ||||
−0.677082 | + | 0.735907i | \(0.736756\pi\) | |||||||
\(158\) | −6.89648e9 | −0.880380 | ||||||||
\(159\) | −4.13402e8 | −0.0512963 | ||||||||
\(160\) | −8.11034e7 | −0.00978361 | ||||||||
\(161\) | −1.04484e10 | −1.22555 | ||||||||
\(162\) | −1.04409e8 | −0.0119102 | ||||||||
\(163\) | 3.32689e8 | 0.0369143 | 0.0184571 | − | 0.999830i | \(-0.494125\pi\) | ||||
0.0184571 | + | 0.999830i | \(0.494125\pi\) | |||||||
\(164\) | −4.13235e9 | −0.446067 | ||||||||
\(165\) | 2.69327e7 | 0.00282880 | ||||||||
\(166\) | 4.95517e9 | 0.506491 | ||||||||
\(167\) | 6.88418e9 | 0.684902 | 0.342451 | − | 0.939536i | \(-0.388743\pi\) | ||||
0.342451 | + | 0.939536i | \(0.388743\pi\) | |||||||
\(168\) | 8.67315e9 | 0.840012 | ||||||||
\(169\) | −1.02435e10 | −0.965954 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.91883e9 | 0.529362 | ||||||||
\(172\) | 1.49975e9 | 0.130659 | ||||||||
\(173\) | 6.01333e9 | 0.510396 | 0.255198 | − | 0.966889i | \(-0.417859\pi\) | ||||
0.255198 | + | 0.966889i | \(0.417859\pi\) | |||||||
\(174\) | −5.29479e9 | −0.437903 | ||||||||
\(175\) | −1.83105e10 | −1.47581 | ||||||||
\(176\) | 1.46870e9 | 0.115379 | ||||||||
\(177\) | −1.42743e10 | −1.09314 | ||||||||
\(178\) | −8.64034e9 | −0.645121 | ||||||||
\(179\) | −1.19820e10 | −0.872352 | −0.436176 | − | 0.899861i | \(-0.643668\pi\) | ||||
−0.436176 | + | 0.899861i | \(0.643668\pi\) | |||||||
\(180\) | −5.82911e7 | −0.00413882 | ||||||||
\(181\) | −1.48274e10 | −1.02686 | −0.513431 | − | 0.858131i | \(-0.671626\pi\) | ||||
−0.513431 | + | 0.858131i | \(0.671626\pi\) | |||||||
\(182\) | −2.12877e9 | −0.143816 | ||||||||
\(183\) | 7.11585e9 | 0.469026 | ||||||||
\(184\) | 1.17345e10 | 0.754718 | ||||||||
\(185\) | 1.05178e8 | 0.00660162 | ||||||||
\(186\) | −9.60509e9 | −0.588428 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.31492e8 | −0.0368687 | ||||||||
\(189\) | 2.60677e10 | 1.48602 | ||||||||
\(190\) | 7.79929e7 | 0.00434174 | ||||||||
\(191\) | −3.31620e10 | −1.80298 | −0.901490 | − | 0.432799i | \(-0.857526\pi\) | ||||
−0.901490 | + | 0.432799i | \(0.857526\pi\) | |||||||
\(192\) | −3.60926e9 | −0.191674 | ||||||||
\(193\) | 4.14885e9 | 0.215238 | 0.107619 | − | 0.994192i | \(-0.465677\pi\) | ||||
0.107619 | + | 0.994192i | \(0.465677\pi\) | |||||||
\(194\) | −4.10015e9 | −0.207822 | ||||||||
\(195\) | −2.20252e7 | −0.00109085 | ||||||||
\(196\) | −1.75569e10 | −0.849760 | ||||||||
\(197\) | −3.95264e10 | −1.86978 | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(198\) | −3.32205e9 | −0.153607 | ||||||||
\(199\) | 7.29277e9 | 0.329650 | 0.164825 | − | 0.986323i | \(-0.447294\pi\) | ||||
0.164825 | + | 0.986323i | \(0.447294\pi\) | |||||||
\(200\) | 2.05644e10 | 0.908828 | ||||||||
\(201\) | 9.52163e9 | 0.411461 | ||||||||
\(202\) | −8.60068e9 | −0.363456 | ||||||||
\(203\) | 4.72902e10 | 1.95451 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.47680e8 | −0.00584021 | ||||||||
\(206\) | −1.29246e10 | −0.500053 | ||||||||
\(207\) | 1.33341e10 | 0.504775 | ||||||||
\(208\) | −1.20108e9 | −0.0444924 | ||||||||
\(209\) | −1.14934e10 | −0.416667 | ||||||||
\(210\) | 1.29866e8 | 0.00460797 | ||||||||
\(211\) | −1.01627e10 | −0.352971 | −0.176486 | − | 0.984303i | \(-0.556473\pi\) | ||||
−0.176486 | + | 0.984303i | \(0.556473\pi\) | |||||||
\(212\) | −1.73743e9 | −0.0590739 | ||||||||
\(213\) | −2.54064e10 | −0.845737 | ||||||||
\(214\) | −4.26991e8 | −0.0139173 | ||||||||
\(215\) | 5.35972e7 | 0.00171068 | ||||||||
\(216\) | −2.92765e10 | −0.915118 | ||||||||
\(217\) | 8.57874e10 | 2.62636 | ||||||||
\(218\) | −2.70898e10 | −0.812367 | ||||||||
\(219\) | −7.75805e9 | −0.227905 | ||||||||
\(220\) | 1.13192e8 | 0.00325771 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 8.36778e9 | 0.231218 | ||||||||
\(223\) | 4.85121e10 | 1.31364 | 0.656822 | − | 0.754045i | \(-0.271900\pi\) | ||||
0.656822 | + | 0.754045i | \(0.271900\pi\) | |||||||
\(224\) | 5.76299e10 | 1.52944 | ||||||||
\(225\) | 2.33677e10 | 0.607848 | ||||||||
\(226\) | −1.91256e10 | −0.487670 | ||||||||
\(227\) | −3.09601e10 | −0.773901 | −0.386951 | − | 0.922100i | \(-0.626472\pi\) | ||||
−0.386951 | + | 0.922100i | \(0.626472\pi\) | |||||||
\(228\) | −1.60447e10 | −0.393209 | ||||||||
\(229\) | 1.33918e10 | 0.321795 | 0.160898 | − | 0.986971i | \(-0.448561\pi\) | ||||
0.160898 | + | 0.986971i | \(0.448561\pi\) | |||||||
\(230\) | 1.75705e8 | 0.00414008 | ||||||||
\(231\) | −1.91376e10 | −0.442216 | ||||||||
\(232\) | −5.31113e10 | −1.20362 | ||||||||
\(233\) | 4.68751e9 | 0.104193 | 0.0520967 | − | 0.998642i | \(-0.483410\pi\) | ||||
0.0520967 | + | 0.998642i | \(0.483410\pi\) | |||||||
\(234\) | 2.71672e9 | 0.0592343 | ||||||||
\(235\) | −2.25679e7 | −0.000482709 0 | ||||||||
\(236\) | −5.99912e10 | −1.25888 | ||||||||
\(237\) | 5.07021e10 | 1.04390 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.26030e10 | 0.646350 | 0.323175 | − | 0.946339i | \(-0.395250\pi\) | ||||
0.323175 | + | 0.946339i | \(0.395250\pi\) | |||||||
\(240\) | 7.32721e7 | 0.00142557 | ||||||||
\(241\) | 7.77778e10 | 1.48518 | 0.742590 | − | 0.669746i | \(-0.233597\pi\) | ||||
0.742590 | + | 0.669746i | \(0.233597\pi\) | |||||||
\(242\) | −2.17251e10 | −0.407185 | ||||||||
\(243\) | −5.39573e10 | −0.992709 | ||||||||
\(244\) | 2.99062e10 | 0.540140 | ||||||||
\(245\) | −6.27439e8 | −0.0111256 | ||||||||
\(246\) | −1.17492e10 | −0.204550 | ||||||||
\(247\) | 9.39910e9 | 0.160676 | ||||||||
\(248\) | −9.63473e10 | −1.61736 | ||||||||
\(249\) | −3.64298e10 | −0.600565 | ||||||||
\(250\) | 6.15865e8 | 0.00997138 | ||||||||
\(251\) | 8.26646e10 | 1.31458 | 0.657291 | − | 0.753637i | \(-0.271702\pi\) | ||||
0.657291 | + | 0.753637i | \(0.271702\pi\) | |||||||
\(252\) | 4.14201e10 | 0.647006 | ||||||||
\(253\) | −2.58926e10 | −0.397314 | ||||||||
\(254\) | 3.05983e10 | 0.461260 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.27745e10 | −0.767970 | ||||||||
\(257\) | −3.45108e10 | −0.493465 | −0.246732 | − | 0.969084i | \(-0.579357\pi\) | ||||
−0.246732 | + | 0.969084i | \(0.579357\pi\) | |||||||
\(258\) | 4.26411e9 | 0.0599156 | ||||||||
\(259\) | −7.47363e10 | −1.03201 | ||||||||
\(260\) | −9.25664e7 | −0.00125624 | ||||||||
\(261\) | −6.03513e10 | −0.805016 | ||||||||
\(262\) | −5.54605e10 | −0.727157 | ||||||||
\(263\) | −1.33213e11 | −1.71690 | −0.858452 | − | 0.512893i | \(-0.828574\pi\) | ||||
−0.858452 | + | 0.512893i | \(0.828574\pi\) | |||||||
\(264\) | 2.14934e10 | 0.272325 | ||||||||
\(265\) | −6.20912e7 | −0.000773435 0 | ||||||||
\(266\) | −5.54197e10 | −0.678729 | ||||||||
\(267\) | 6.35228e10 | 0.764943 | ||||||||
\(268\) | 4.00171e10 | 0.473848 | ||||||||
\(269\) | 5.04947e9 | 0.0587977 | 0.0293989 | − | 0.999568i | \(-0.490641\pi\) | ||||
0.0293989 | + | 0.999568i | \(0.490641\pi\) | |||||||
\(270\) | −4.38368e8 | −0.00501997 | ||||||||
\(271\) | 2.17449e9 | 0.0244903 | 0.0122452 | − | 0.999925i | \(-0.496102\pi\) | ||||
0.0122452 | + | 0.999925i | \(0.496102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.56505e10 | 0.170528 | ||||||||
\(274\) | 9.18530e10 | 0.984500 | ||||||||
\(275\) | −4.53762e10 | −0.478444 | ||||||||
\(276\) | −3.61460e10 | −0.374946 | ||||||||
\(277\) | −2.79184e10 | −0.284926 | −0.142463 | − | 0.989800i | \(-0.545502\pi\) | ||||
−0.142463 | + | 0.989800i | \(0.545502\pi\) | |||||||
\(278\) | 8.32567e10 | 0.836022 | ||||||||
\(279\) | −1.09481e11 | −1.08173 | ||||||||
\(280\) | 1.30267e9 | 0.0126655 | ||||||||
\(281\) | −1.56867e11 | −1.50090 | −0.750450 | − | 0.660927i | \(-0.770163\pi\) | ||||
−0.750450 | + | 0.660927i | \(0.770163\pi\) | |||||||
\(282\) | −1.79547e9 | −0.0169066 | ||||||||
\(283\) | −5.01719e10 | −0.464966 | −0.232483 | − | 0.972600i | \(-0.574685\pi\) | ||||
−0.232483 | + | 0.972600i | \(0.574685\pi\) | |||||||
\(284\) | −1.06777e11 | −0.973968 | ||||||||
\(285\) | −5.73395e8 | −0.00514816 | ||||||||
\(286\) | −5.27541e9 | −0.0466240 | ||||||||
\(287\) | 1.04937e11 | 0.912979 | ||||||||
\(288\) | −7.35468e10 | −0.629938 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −7.95255e8 | −0.00660261 | ||||||||
\(291\) | 3.01438e10 | 0.246422 | ||||||||
\(292\) | −3.26052e10 | −0.262460 | ||||||||
\(293\) | −2.31612e11 | −1.83593 | −0.917966 | − | 0.396658i | \(-0.870170\pi\) | ||||
−0.917966 | + | 0.396658i | \(0.870170\pi\) | |||||||
\(294\) | −4.99181e10 | −0.389669 | ||||||||
\(295\) | −2.14393e9 | −0.0164821 | ||||||||
\(296\) | 8.39359e10 | 0.635529 | ||||||||
\(297\) | 6.45997e10 | 0.481755 | ||||||||
\(298\) | −2.78179e10 | −0.204339 | ||||||||
\(299\) | 2.11746e10 | 0.153213 | ||||||||
\(300\) | −6.33449e10 | −0.451508 | ||||||||
\(301\) | −3.80847e10 | −0.267425 | ||||||||
\(302\) | −1.07498e11 | −0.743651 | ||||||||
\(303\) | 6.32312e10 | 0.430963 | ||||||||
\(304\) | −3.12684e10 | −0.209979 | ||||||||
\(305\) | 1.06877e9 | 0.00707188 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.57747e11 | 1.65604 | 0.828019 | − | 0.560699i | \(-0.189468\pi\) | ||||
0.828019 | + | 0.560699i | \(0.189468\pi\) | |||||||
\(308\) | −8.04308e10 | −0.509266 | ||||||||
\(309\) | 9.50205e10 | 0.592931 | ||||||||
\(310\) | −1.44264e9 | −0.00887220 | ||||||||
\(311\) | −1.32742e11 | −0.804611 | −0.402305 | − | 0.915506i | \(-0.631791\pi\) | ||||
−0.402305 | + | 0.915506i | \(0.631791\pi\) | |||||||
\(312\) | −1.75770e10 | −0.105014 | ||||||||
\(313\) | −1.55181e11 | −0.913879 | −0.456939 | − | 0.889498i | \(-0.651054\pi\) | ||||
−0.456939 | + | 0.889498i | \(0.651054\pi\) | |||||||
\(314\) | −1.23187e11 | −0.715123 | ||||||||
\(315\) | 1.48025e9 | 0.00847104 | ||||||||
\(316\) | 2.13089e11 | 1.20218 | ||||||||
\(317\) | 7.27830e10 | 0.404821 | 0.202411 | − | 0.979301i | \(-0.435122\pi\) | ||||
0.202411 | + | 0.979301i | \(0.435122\pi\) | |||||||
\(318\) | −4.93989e9 | −0.0270891 | ||||||||
\(319\) | 1.17192e11 | 0.633637 | ||||||||
\(320\) | −5.42096e8 | −0.00289002 | ||||||||
\(321\) | 3.13919e9 | 0.0165023 | ||||||||
\(322\) | −1.24851e11 | −0.647204 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3.22603e9 | 0.0162636 | ||||||||
\(325\) | 3.71080e10 | 0.184498 | ||||||||
\(326\) | 3.97542e9 | 0.0194941 | ||||||||
\(327\) | 1.99161e11 | 0.963253 | ||||||||
\(328\) | −1.17854e11 | −0.562229 | ||||||||
\(329\) | 1.60361e10 | 0.0754602 | ||||||||
\(330\) | 3.21828e8 | 0.00149387 | ||||||||
\(331\) | 1.77845e11 | 0.814357 | 0.407179 | − | 0.913349i | \(-0.366513\pi\) | ||||
0.407179 | + | 0.913349i | \(0.366513\pi\) | |||||||
\(332\) | −1.53106e11 | −0.691623 | ||||||||
\(333\) | 9.53779e10 | 0.425058 | ||||||||
\(334\) | 8.22615e10 | 0.361691 | ||||||||
\(335\) | 1.43011e9 | 0.00620393 | ||||||||
\(336\) | −5.20652e10 | −0.222854 | ||||||||
\(337\) | −2.89678e11 | −1.22344 | −0.611718 | − | 0.791076i | \(-0.709521\pi\) | ||||
−0.611718 | + | 0.791076i | \(0.709521\pi\) | |||||||
\(338\) | −1.22403e11 | −0.510112 | ||||||||
\(339\) | 1.40609e11 | 0.578248 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.12594e11 | 0.851444 | ||||||||
\(342\) | 7.07261e10 | 0.279552 | ||||||||
\(343\) | 6.74934e10 | 0.263292 | ||||||||
\(344\) | 4.27727e10 | 0.164685 | ||||||||
\(345\) | −1.29176e9 | −0.00490905 | ||||||||
\(346\) | 7.18554e10 | 0.269536 | ||||||||
\(347\) | 3.59514e11 | 1.33117 | 0.665585 | − | 0.746322i | \(-0.268182\pi\) | ||||
0.665585 | + | 0.746322i | \(0.268182\pi\) | |||||||
\(348\) | 1.63600e11 | 0.597965 | ||||||||
\(349\) | 3.06108e11 | 1.10448 | 0.552242 | − | 0.833684i | \(-0.313772\pi\) | ||||
0.552242 | + | 0.833684i | \(0.313772\pi\) | |||||||
\(350\) | −2.18799e11 | −0.779360 | ||||||||
\(351\) | −5.28287e10 | −0.185775 | ||||||||
\(352\) | 1.42816e11 | 0.495831 | ||||||||
\(353\) | −5.40179e11 | −1.85162 | −0.925809 | − | 0.377992i | \(-0.876615\pi\) | ||||
−0.925809 | + | 0.377992i | \(0.876615\pi\) | |||||||
\(354\) | −1.70568e11 | −0.577276 | ||||||||
\(355\) | −3.81593e9 | −0.0127518 | ||||||||
\(356\) | 2.66971e11 | 0.880925 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.43177e11 | −0.460682 | ||||||||
\(359\) | −5.90971e11 | −1.87777 | −0.938883 | − | 0.344237i | \(-0.888138\pi\) | ||||
−0.938883 | + | 0.344237i | \(0.888138\pi\) | |||||||
\(360\) | −1.66246e9 | −0.00521662 | ||||||||
\(361\) | −7.79948e10 | −0.241704 | ||||||||
\(362\) | −1.77178e11 | −0.542278 | ||||||||
\(363\) | 1.59720e11 | 0.482815 | ||||||||
\(364\) | 6.57751e10 | 0.196384 | ||||||||
\(365\) | −1.16523e9 | −0.00343631 | ||||||||
\(366\) | 8.50297e10 | 0.247689 | ||||||||
\(367\) | 1.30010e11 | 0.374092 | 0.187046 | − | 0.982351i | \(-0.440109\pi\) | ||||
0.187046 | + | 0.982351i | \(0.440109\pi\) | |||||||
\(368\) | −7.04425e10 | −0.200226 | ||||||||
\(369\) | −1.33920e11 | −0.376033 | ||||||||
\(370\) | 1.25680e9 | 0.00348626 | ||||||||
\(371\) | 4.41203e10 | 0.120908 | ||||||||
\(372\) | 2.96780e11 | 0.803510 | ||||||||
\(373\) | −4.27210e11 | −1.14275 | −0.571375 | − | 0.820689i | \(-0.693590\pi\) | ||||
−0.571375 | + | 0.820689i | \(0.693590\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.52777e9 | −0.0118234 | ||||||||
\(376\) | −1.80101e10 | −0.0464698 | ||||||||
\(377\) | −9.58380e10 | −0.244344 | ||||||||
\(378\) | 3.11492e11 | 0.784755 | ||||||||
\(379\) | 6.30202e11 | 1.56893 | 0.784465 | − | 0.620173i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620173i | \(0.212938\pi\) | |||||||
\(380\) | −2.40984e9 | −0.00592873 | ||||||||
\(381\) | −2.24955e11 | −0.546933 | ||||||||
\(382\) | −3.96265e11 | −0.952139 | ||||||||
\(383\) | 6.08533e11 | 1.44507 | 0.722537 | − | 0.691333i | \(-0.242976\pi\) | ||||
0.722537 | + | 0.691333i | \(0.242976\pi\) | |||||||
\(384\) | 2.33344e11 | 0.547654 | ||||||||
\(385\) | −2.87439e9 | −0.00666765 | ||||||||
\(386\) | 4.95760e10 | 0.113665 | ||||||||
\(387\) | 4.86034e10 | 0.110146 | ||||||||
\(388\) | 1.26687e11 | 0.283785 | ||||||||
\(389\) | −2.18499e10 | −0.0483811 | −0.0241906 | − | 0.999707i | \(-0.507701\pi\) | ||||
−0.0241906 | + | 0.999707i | \(0.507701\pi\) | |||||||
\(390\) | −2.63186e8 | −0.000576066 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.00722e11 | −1.07105 | ||||||||
\(393\) | 4.07739e11 | 0.862216 | ||||||||
\(394\) | −4.72315e11 | −0.987413 | ||||||||
\(395\) | 7.61524e9 | 0.0157397 | ||||||||
\(396\) | 1.02645e11 | 0.209754 | ||||||||
\(397\) | −8.30935e11 | −1.67884 | −0.839421 | − | 0.543482i | \(-0.817106\pi\) | ||||
−0.839421 | + | 0.543482i | \(0.817106\pi\) | |||||||
\(398\) | 8.71438e10 | 0.174086 | ||||||||
\(399\) | 4.07439e11 | 0.804794 | ||||||||
\(400\) | −1.23449e11 | −0.241111 | ||||||||
\(401\) | 6.07641e10 | 0.117354 | 0.0586769 | − | 0.998277i | \(-0.481312\pi\) | ||||
0.0586769 | + | 0.998277i | \(0.481312\pi\) | |||||||
\(402\) | 1.13777e11 | 0.217289 | ||||||||
\(403\) | −1.73856e11 | −0.328335 | ||||||||
\(404\) | 2.65745e11 | 0.496306 | ||||||||
\(405\) | 1.15290e8 | 0.000212934 0 | ||||||||
\(406\) | 5.65087e11 | 1.03216 | ||||||||
\(407\) | −1.85208e11 | −0.334568 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.81188e11 | −1.55709 | −0.778545 | − | 0.627588i | \(-0.784042\pi\) | ||||
−0.778545 | + | 0.627588i | \(0.784042\pi\) | |||||||
\(410\) | −1.76468e9 | −0.00308416 | ||||||||
\(411\) | −6.75293e11 | −1.16736 | ||||||||
\(412\) | 3.99348e11 | 0.682832 | ||||||||
\(413\) | 1.52342e12 | 2.57658 | ||||||||
\(414\) | 1.59334e11 | 0.266567 | ||||||||
\(415\) | −5.47160e9 | −0.00905520 | ||||||||
\(416\) | −1.16792e11 | −0.191203 | ||||||||
\(417\) | −6.12094e11 | −0.991301 | ||||||||
\(418\) | −1.37338e11 | −0.220038 | ||||||||
\(419\) | 3.41942e11 | 0.541988 | 0.270994 | − | 0.962581i | \(-0.412648\pi\) | ||||
0.270994 | + | 0.962581i | \(0.412648\pi\) | |||||||
\(420\) | −4.01263e9 | −0.00629227 | ||||||||
\(421\) | −4.41263e11 | −0.684585 | −0.342293 | − | 0.939593i | \(-0.611203\pi\) | ||||
−0.342293 | + | 0.939593i | \(0.611203\pi\) | |||||||
\(422\) | −1.21438e11 | −0.186401 | ||||||||
\(423\) | −2.04652e10 | −0.0310802 | ||||||||
\(424\) | −4.95513e10 | −0.0744575 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.03590e11 | −0.446626 | ||||||||
\(427\) | −7.59438e11 | −1.10552 | ||||||||
\(428\) | 1.31932e10 | 0.0190044 | ||||||||
\(429\) | 3.87842e10 | 0.0552837 | ||||||||
\(430\) | 6.40451e8 | 0.000903396 0 | ||||||||
\(431\) | −3.01082e11 | −0.420278 | −0.210139 | − | 0.977672i | \(-0.567392\pi\) | ||||
−0.210139 | + | 0.977672i | \(0.567392\pi\) | |||||||
\(432\) | 1.75748e11 | 0.242780 | ||||||||
\(433\) | 7.35571e11 | 1.00561 | 0.502805 | − | 0.864400i | \(-0.332302\pi\) | ||||
0.502805 | + | 0.864400i | \(0.332302\pi\) | |||||||
\(434\) | 1.02510e12 | 1.38696 | ||||||||
\(435\) | 5.84663e9 | 0.00782895 | ||||||||
\(436\) | 8.37027e11 | 1.10930 | ||||||||
\(437\) | 5.51252e11 | 0.723076 | ||||||||
\(438\) | −9.27037e10 | −0.120355 | ||||||||
\(439\) | 8.85875e11 | 1.13837 | 0.569183 | − | 0.822211i | \(-0.307259\pi\) | ||||
0.569183 | + | 0.822211i | \(0.307259\pi\) | |||||||
\(440\) | 3.22821e9 | 0.00410606 | ||||||||
\(441\) | −5.68979e11 | −0.716345 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.28950e11 | 0.159076 | 0.0795382 | − | 0.996832i | \(-0.474655\pi\) | ||||
0.0795382 | + | 0.996832i | \(0.474655\pi\) | |||||||
\(444\) | −2.58549e11 | −0.315733 | ||||||||
\(445\) | 9.54085e9 | 0.0115337 | ||||||||
\(446\) | 5.79688e11 | 0.693725 | ||||||||
\(447\) | 2.04514e11 | 0.242293 | ||||||||
\(448\) | 3.85199e11 | 0.451787 | ||||||||
\(449\) | 1.55749e12 | 1.80850 | 0.904249 | − | 0.427006i | \(-0.140432\pi\) | ||||
0.904249 | + | 0.427006i | \(0.140432\pi\) | |||||||
\(450\) | 2.79229e11 | 0.320999 | ||||||||
\(451\) | 2.60050e11 | 0.295980 | ||||||||
\(452\) | 5.90945e11 | 0.665923 | ||||||||
\(453\) | 7.90313e11 | 0.881773 | ||||||||
\(454\) | −3.69953e11 | −0.408691 | ||||||||
\(455\) | 2.35063e9 | 0.00257119 | ||||||||
\(456\) | −4.57592e11 | −0.495607 | ||||||||
\(457\) | −2.73319e11 | −0.293121 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(458\) | 1.60023e11 | 0.169937 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.42897e9 | −0.00565336 | ||||||||
\(461\) | 5.89272e11 | 0.607662 | 0.303831 | − | 0.952726i | \(-0.401734\pi\) | ||||
0.303831 | + | 0.952726i | \(0.401734\pi\) | |||||||
\(462\) | −2.28682e11 | −0.233531 | ||||||||
\(463\) | 1.34363e12 | 1.35883 | 0.679413 | − | 0.733756i | \(-0.262235\pi\) | ||||
0.679413 | + | 0.733756i | \(0.262235\pi\) | |||||||
\(464\) | 3.18829e11 | 0.319320 | ||||||||
\(465\) | 1.06062e10 | 0.0105201 | ||||||||
\(466\) | 5.60127e10 | 0.0550237 | ||||||||
\(467\) | 6.38082e10 | 0.0620798 | 0.0310399 | − | 0.999518i | \(-0.490118\pi\) | ||||
0.0310399 | + | 0.999518i | \(0.490118\pi\) | |||||||
\(468\) | −8.39417e10 | −0.0808856 | ||||||||
\(469\) | −1.01620e12 | −0.969839 | ||||||||
\(470\) | −2.69672e8 | −0.000254915 0 | ||||||||
\(471\) | 9.05655e11 | 0.847947 | ||||||||
\(472\) | −1.71094e12 | −1.58671 | ||||||||
\(473\) | −9.43796e10 | −0.0866968 | ||||||||
\(474\) | 6.05857e11 | 0.551274 | ||||||||
\(475\) | 9.66055e11 | 0.870724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.63060e10 | −0.0497992 | ||||||||
\(478\) | 3.89585e11 | 0.341332 | ||||||||
\(479\) | −1.15346e11 | −0.100114 | −0.0500568 | − | 0.998746i | \(-0.515940\pi\) | ||||
−0.0500568 | + | 0.998746i | \(0.515940\pi\) | |||||||
\(480\) | 7.12496e9 | 0.00612628 | ||||||||
\(481\) | 1.51460e11 | 0.129017 | ||||||||
\(482\) | 9.29394e11 | 0.784311 | ||||||||
\(483\) | 9.17892e11 | 0.767414 | ||||||||
\(484\) | 6.71265e11 | 0.556020 | ||||||||
\(485\) | 4.52747e9 | 0.00371551 | ||||||||
\(486\) | −6.44755e11 | −0.524241 | ||||||||
\(487\) | 1.92135e12 | 1.54784 | 0.773921 | − | 0.633283i | \(-0.218293\pi\) | ||||
0.773921 | + | 0.633283i | \(0.218293\pi\) | |||||||
\(488\) | 8.52921e11 | 0.680800 | ||||||||
\(489\) | −2.92268e10 | −0.0231149 | ||||||||
\(490\) | −7.49749e9 | −0.00587535 | ||||||||
\(491\) | −1.25106e12 | −0.971430 | −0.485715 | − | 0.874117i | \(-0.661441\pi\) | ||||
−0.485715 | + | 0.874117i | \(0.661441\pi\) | |||||||
\(492\) | 3.63028e11 | 0.279317 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.12313e11 | 0.0848515 | ||||||||
\(495\) | 3.66827e9 | 0.00274624 | ||||||||
\(496\) | 5.78375e11 | 0.429084 | ||||||||
\(497\) | 2.71150e12 | 1.99345 | ||||||||
\(498\) | −4.35313e11 | −0.317153 | ||||||||
\(499\) | 6.12106e11 | 0.441951 | 0.220975 | − | 0.975279i | \(-0.429076\pi\) | ||||
0.220975 | + | 0.975279i | \(0.429076\pi\) | |||||||
\(500\) | −1.90291e10 | −0.0136161 | ||||||||
\(501\) | −6.04777e11 | −0.428870 | ||||||||
\(502\) | 9.87788e11 | 0.694220 | ||||||||
\(503\) | 2.15448e12 | 1.50067 | 0.750337 | − | 0.661056i | \(-0.229891\pi\) | ||||
0.750337 | + | 0.661056i | \(0.229891\pi\) | |||||||
\(504\) | 1.18130e12 | 0.815495 | ||||||||
\(505\) | 9.49706e9 | 0.00649797 | ||||||||
\(506\) | −3.09400e11 | −0.209818 | ||||||||
\(507\) | 8.99891e11 | 0.604859 | ||||||||
\(508\) | −9.45433e11 | −0.629860 | ||||||||
\(509\) | −2.44832e12 | −1.61673 | −0.808367 | − | 0.588679i | \(-0.799648\pi\) | ||||
−0.808367 | + | 0.588679i | \(0.799648\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.27978e11 | 0.537186 | ||||||||
\(512\) | 7.29331e11 | 0.469040 | ||||||||
\(513\) | −1.37532e12 | −0.876751 | ||||||||
\(514\) | −4.12382e11 | −0.260594 | ||||||||
\(515\) | 1.42717e10 | 0.00894010 | ||||||||
\(516\) | −1.31753e11 | −0.0818159 | ||||||||
\(517\) | 3.97399e10 | 0.0244636 | ||||||||
\(518\) | −8.93051e11 | −0.544994 | ||||||||
\(519\) | −5.28273e11 | −0.319599 | ||||||||
\(520\) | −2.63998e9 | −0.00158338 | ||||||||
\(521\) | −4.93030e11 | −0.293159 | −0.146580 | − | 0.989199i | \(-0.546826\pi\) | ||||
−0.146580 | + | 0.989199i | \(0.546826\pi\) | |||||||
\(522\) | −7.21159e11 | −0.425122 | ||||||||
\(523\) | −7.48265e11 | −0.437318 | −0.218659 | − | 0.975801i | \(-0.570168\pi\) | ||||
−0.218659 | + | 0.975801i | \(0.570168\pi\) | |||||||
\(524\) | 1.71363e12 | 0.992947 | ||||||||
\(525\) | 1.60858e12 | 0.924116 | ||||||||
\(526\) | −1.59181e12 | −0.906683 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.29025e11 | −0.0722474 | ||||||||
\(529\) | −5.59274e11 | −0.310509 | ||||||||
\(530\) | −7.41950e8 | −0.000408445 0 | ||||||||
\(531\) | −1.94418e12 | −1.06123 | ||||||||
\(532\) | 1.71237e12 | 0.926818 | ||||||||
\(533\) | −2.12665e11 | −0.114136 | ||||||||
\(534\) | 7.59056e11 | 0.403960 | ||||||||
\(535\) | 4.71492e8 | 0.000248819 0 | ||||||||
\(536\) | 1.14128e12 | 0.597244 | ||||||||
\(537\) | 1.05262e12 | 0.546247 | ||||||||
\(538\) | 6.03379e10 | 0.0310506 | ||||||||
\(539\) | 1.10486e12 | 0.563843 | ||||||||
\(540\) | 1.35448e10 | 0.00685487 | ||||||||
\(541\) | −1.55217e12 | −0.779026 | −0.389513 | − | 0.921021i | \(-0.627357\pi\) | ||||
−0.389513 | + | 0.921021i | \(0.627357\pi\) | |||||||
\(542\) | 2.59837e10 | 0.0129331 | ||||||||
\(543\) | 1.30259e12 | 0.642998 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.99132e10 | 0.0145237 | ||||||||
\(546\) | 1.87013e11 | 0.0900544 | ||||||||
\(547\) | −3.78215e12 | −1.80632 | −0.903162 | − | 0.429300i | \(-0.858760\pi\) | ||||
−0.903162 | + | 0.429300i | \(0.858760\pi\) | |||||||
\(548\) | −2.83809e12 | −1.34435 | ||||||||
\(549\) | 9.69189e11 | 0.455337 | ||||||||
\(550\) | −5.42216e11 | −0.252662 | ||||||||
\(551\) | −2.49501e12 | −1.15316 | ||||||||
\(552\) | −1.03088e12 | −0.472587 | ||||||||
\(553\) | −5.41118e12 | −2.46053 | ||||||||
\(554\) | −3.33607e11 | −0.150467 | ||||||||
\(555\) | −9.23988e9 | −0.00413378 | ||||||||
\(556\) | −2.57248e12 | −1.14160 | ||||||||
\(557\) | −1.59132e12 | −0.700501 | −0.350251 | − | 0.936656i | \(-0.613904\pi\) | ||||
−0.350251 | + | 0.936656i | \(0.613904\pi\) | |||||||
\(558\) | −1.30823e12 | −0.571254 | ||||||||
\(559\) | 7.71822e10 | 0.0334321 | ||||||||
\(560\) | −7.81996e9 | −0.00336015 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.87445e12 | −0.792613 | ||||||||
\(563\) | −1.57665e12 | −0.661374 | −0.330687 | − | 0.943741i | \(-0.607280\pi\) | ||||
−0.330687 | + | 0.943741i | \(0.607280\pi\) | |||||||
\(564\) | 5.54767e10 | 0.0230863 | ||||||||
\(565\) | 2.11189e10 | 0.00871872 | ||||||||
\(566\) | −5.99521e11 | −0.245545 | ||||||||
\(567\) | −8.19220e10 | −0.0332872 | ||||||||
\(568\) | −3.04527e12 | −1.22760 | ||||||||
\(569\) | 2.23114e12 | 0.892321 | 0.446160 | − | 0.894953i | \(-0.352791\pi\) | ||||
0.446160 | + | 0.894953i | \(0.352791\pi\) | |||||||
\(570\) | −6.85170e9 | −0.00271870 | ||||||||
\(571\) | −9.16846e11 | −0.360939 | −0.180470 | − | 0.983581i | \(-0.557762\pi\) | ||||
−0.180470 | + | 0.983581i | \(0.557762\pi\) | |||||||
\(572\) | 1.63001e11 | 0.0636659 | ||||||||
\(573\) | 2.91329e12 | 1.12899 | ||||||||
\(574\) | 1.25393e12 | 0.482136 | ||||||||
\(575\) | 2.17636e12 | 0.830282 | ||||||||
\(576\) | −4.91587e11 | −0.186080 | ||||||||
\(577\) | 1.39411e12 | 0.523609 | 0.261804 | − | 0.965121i | \(-0.415682\pi\) | ||||
0.261804 | + | 0.965121i | \(0.415682\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.64477e11 | −0.134777 | ||||||||
\(580\) | 2.45719e10 | 0.00901599 | ||||||||
\(581\) | 3.88797e12 | 1.41557 | ||||||||
\(582\) | 3.60199e11 | 0.130134 | ||||||||
\(583\) | 1.09337e11 | 0.0391975 | ||||||||
\(584\) | −9.29897e11 | −0.330809 | ||||||||
\(585\) | −2.99986e9 | −0.00105901 | ||||||||
\(586\) | −2.76761e12 | −0.969541 | ||||||||
\(587\) | 3.69526e12 | 1.28462 | 0.642309 | − | 0.766446i | \(-0.277977\pi\) | ||||
0.642309 | + | 0.766446i | \(0.277977\pi\) | |||||||
\(588\) | 1.54238e12 | 0.532100 | ||||||||
\(589\) | −4.52611e12 | −1.54955 | ||||||||
\(590\) | −2.56186e10 | −0.00870405 | ||||||||
\(591\) | 3.47241e12 | 1.17081 | ||||||||
\(592\) | −5.03870e11 | −0.168605 | ||||||||
\(593\) | −1.83960e12 | −0.610911 | −0.305456 | − | 0.952206i | \(-0.598809\pi\) | ||||
−0.305456 | + | 0.952206i | \(0.598809\pi\) | |||||||
\(594\) | 7.71924e11 | 0.254411 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.59524e11 | 0.279029 | ||||||||
\(597\) | −6.40672e11 | −0.206420 | ||||||||
\(598\) | 2.53023e11 | 0.0809104 | ||||||||
\(599\) | 1.96213e12 | 0.622741 | 0.311370 | − | 0.950289i | \(-0.399212\pi\) | ||||
0.311370 | + | 0.950289i | \(0.399212\pi\) | |||||||
\(600\) | −1.80659e12 | −0.569087 | ||||||||
\(601\) | −4.32477e11 | −0.135216 | −0.0676080 | − | 0.997712i | \(-0.521537\pi\) | ||||
−0.0676080 | + | 0.997712i | \(0.521537\pi\) | |||||||
\(602\) | −4.55087e11 | −0.141225 | ||||||||
\(603\) | 1.29686e12 | 0.399453 | ||||||||
\(604\) | 3.32149e12 | 1.01547 | ||||||||
\(605\) | 2.39893e10 | 0.00727978 | ||||||||
\(606\) | 7.55572e11 | 0.227588 | ||||||||
\(607\) | −4.28237e12 | −1.28037 | −0.640185 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640185 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(608\) | −3.04053e12 | −0.902367 | ||||||||
\(609\) | −4.15445e12 | −1.22387 | ||||||||
\(610\) | 1.27711e10 | 0.00373460 | ||||||||
\(611\) | −3.24987e10 | −0.00943367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.51089e12 | 0.718217 | 0.359108 | − | 0.933296i | \(-0.383081\pi\) | ||||
0.359108 | + | 0.933296i | \(0.383081\pi\) | |||||||
\(614\) | 3.07991e12 | 0.874540 | ||||||||
\(615\) | 1.29737e10 | 0.00365701 | ||||||||
\(616\) | −2.29388e12 | −0.641885 | ||||||||
\(617\) | −4.14534e12 | −1.15153 | −0.575767 | − | 0.817614i | \(-0.695296\pi\) | ||||
−0.575767 | + | 0.817614i | \(0.695296\pi\) | |||||||
\(618\) | 1.13543e12 | 0.313122 | ||||||||
\(619\) | 2.30355e12 | 0.630651 | 0.315325 | − | 0.948984i | \(-0.397886\pi\) | ||||
0.315325 | + | 0.948984i | \(0.397886\pi\) | |||||||
\(620\) | 4.45751e10 | 0.0121152 | ||||||||
\(621\) | −3.09837e12 | −0.836029 | ||||||||
\(622\) | −1.58618e12 | −0.424908 | ||||||||
\(623\) | −6.77947e12 | −1.80302 | ||||||||
\(624\) | 1.05515e11 | 0.0278601 | ||||||||
\(625\) | 3.81368e12 | 0.999733 | ||||||||
\(626\) | −1.85431e12 | −0.482612 | ||||||||
\(627\) | 1.00970e12 | 0.260907 | ||||||||
\(628\) | 3.80625e12 | 0.976514 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.76880e10 | 0.00447348 | ||||||||
\(631\) | −3.70828e12 | −0.931195 | −0.465598 | − | 0.884997i | \(-0.654161\pi\) | ||||
−0.465598 | + | 0.884997i | \(0.654161\pi\) | |||||||
\(632\) | 6.07726e12 | 1.51524 | ||||||||
\(633\) | 8.92798e11 | 0.221023 | ||||||||
\(634\) | 8.69709e11 | 0.213783 | ||||||||
\(635\) | −3.37873e10 | −0.00824655 | ||||||||
\(636\) | 1.52634e11 | 0.0369907 | ||||||||
\(637\) | −9.03539e11 | −0.217430 | ||||||||
\(638\) | 1.40037e12 | 0.334618 | ||||||||
\(639\) | −3.46039e12 | −0.821053 | ||||||||
\(640\) | 3.50473e10 | 0.00825742 | ||||||||
\(641\) | 4.07381e11 | 0.0953102 | 0.0476551 | − | 0.998864i | \(-0.484825\pi\) | ||||
0.0476551 | + | 0.998864i | \(0.484825\pi\) | |||||||
\(642\) | 3.75112e10 | 0.00871473 | ||||||||
\(643\) | −4.35895e12 | −1.00562 | −0.502808 | − | 0.864398i | \(-0.667700\pi\) | ||||
−0.502808 | + | 0.864398i | \(0.667700\pi\) | |||||||
\(644\) | 3.85768e12 | 0.883770 | ||||||||
\(645\) | −4.70853e9 | −0.00107119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.35019e12 | 0.975975 | 0.487987 | − | 0.872851i | \(-0.337731\pi\) | ||||
0.487987 | + | 0.872851i | \(0.337731\pi\) | |||||||
\(648\) | 9.20062e10 | 0.0204988 | ||||||||
\(649\) | 3.77526e12 | 0.835307 | ||||||||
\(650\) | 4.43416e11 | 0.0974319 | ||||||||
\(651\) | −7.53644e12 | −1.64457 | ||||||||
\(652\) | −1.22833e11 | −0.0266196 | ||||||||
\(653\) | −9.70029e11 | −0.208773 | −0.104387 | − | 0.994537i | \(-0.533288\pi\) | ||||
−0.104387 | + | 0.994537i | \(0.533288\pi\) | |||||||
\(654\) | 2.37985e12 | 0.508686 | ||||||||
\(655\) | 6.12407e10 | 0.0130003 | ||||||||
\(656\) | 7.07482e11 | 0.149159 | ||||||||
\(657\) | −1.05666e12 | −0.221254 | ||||||||
\(658\) | 1.91621e11 | 0.0398499 | ||||||||
\(659\) | 8.95610e12 | 1.84984 | 0.924921 | − | 0.380160i | \(-0.124131\pi\) | ||||
0.924921 | + | 0.380160i | \(0.124131\pi\) | |||||||
\(660\) | −9.94391e9 | −0.00203990 | ||||||||
\(661\) | −3.58110e12 | −0.729643 | −0.364822 | − | 0.931077i | \(-0.618870\pi\) | ||||
−0.364822 | + | 0.931077i | \(0.618870\pi\) | |||||||
\(662\) | 2.12513e12 | 0.430055 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.36656e12 | −0.871732 | ||||||||
\(665\) | 6.11956e10 | 0.0121345 | ||||||||
\(666\) | 1.13970e12 | 0.224470 | ||||||||
\(667\) | −5.62084e12 | −1.09960 | ||||||||
\(668\) | −2.54173e12 | −0.493896 | ||||||||
\(669\) | −4.26180e12 | −0.822575 | ||||||||
\(670\) | 1.70889e10 | 0.00327624 | ||||||||
\(671\) | −1.88200e12 | −0.358401 | ||||||||
\(672\) | −5.06280e12 | −0.957699 | ||||||||
\(673\) | −2.42644e12 | −0.455933 | −0.227967 | − | 0.973669i | \(-0.573208\pi\) | ||||
−0.227967 | + | 0.973669i | \(0.573208\pi\) | |||||||
\(674\) | −3.46147e12 | −0.646087 | ||||||||
\(675\) | −5.42982e12 | −1.00674 | ||||||||
\(676\) | 3.78202e12 | 0.696568 | ||||||||
\(677\) | 5.57708e12 | 1.02037 | 0.510186 | − | 0.860064i | \(-0.329577\pi\) | ||||
0.510186 | + | 0.860064i | \(0.329577\pi\) | |||||||
\(678\) | 1.68019e12 | 0.305368 | ||||||||
\(679\) | −3.21710e12 | −0.580832 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.71985e12 | 0.484600 | ||||||||
\(682\) | 2.54036e12 | 0.449641 | ||||||||
\(683\) | −3.41770e12 | −0.600953 | −0.300476 | − | 0.953789i | \(-0.597146\pi\) | ||||
−0.300476 | + | 0.953789i | \(0.597146\pi\) | |||||||
\(684\) | −2.18531e12 | −0.381733 | ||||||||
\(685\) | −1.01426e11 | −0.0176012 | ||||||||
\(686\) | 8.06502e11 | 0.139042 | ||||||||
\(687\) | −1.17647e12 | −0.201501 | ||||||||
\(688\) | −2.56766e11 | −0.0436907 | ||||||||
\(689\) | −8.94140e10 | −0.0151154 | ||||||||
\(690\) | −1.54357e10 | −0.00259243 | ||||||||
\(691\) | −6.82270e12 | −1.13843 | −0.569213 | − | 0.822190i | \(-0.692752\pi\) | ||||
−0.569213 | + | 0.822190i | \(0.692752\pi\) | |||||||
\(692\) | −2.22020e12 | −0.368057 | ||||||||
\(693\) | −2.60658e12 | −0.429310 | ||||||||
\(694\) | 4.29596e12 | 0.702980 | ||||||||
\(695\) | −9.19338e10 | −0.0149466 | ||||||||
\(696\) | 4.66584e12 | 0.753683 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 3.65779e12 | 0.583269 | ||||||||
\(699\) | −4.11799e11 | −0.0652436 | ||||||||
\(700\) | 6.76048e12 | 1.06423 | ||||||||
\(701\) | −1.09353e13 | −1.71041 | −0.855205 | − | 0.518291i | \(-0.826569\pi\) | ||||
−0.855205 | + | 0.518291i | \(0.826569\pi\) | |||||||
\(702\) | −6.31268e11 | −0.0981063 | ||||||||
\(703\) | 3.94306e12 | 0.608884 | ||||||||
\(704\) | 9.54580e11 | 0.146466 | ||||||||
\(705\) | 1.98259e9 | 0.000302262 0 | ||||||||
\(706\) | −6.45478e12 | −0.977824 | ||||||||
\(707\) | −6.74835e12 | −1.01580 | ||||||||
\(708\) | 5.27024e12 | 0.788281 | ||||||||
\(709\) | 2.51896e12 | 0.374380 | 0.187190 | − | 0.982324i | \(-0.440062\pi\) | ||||
0.187190 | + | 0.982324i | \(0.440062\pi\) | |||||||
\(710\) | −4.55979e10 | −0.00673414 | ||||||||
\(711\) | 6.90570e12 | 1.01343 | ||||||||
\(712\) | 7.61398e12 | 1.11033 | ||||||||
\(713\) | −1.01966e13 | −1.47758 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.82522e9 | 0.000833557 0 | ||||||||
\(716\) | 4.42392e12 | 0.629070 | ||||||||
\(717\) | −2.86419e12 | −0.404730 | ||||||||
\(718\) | −7.06172e12 | −0.991632 | ||||||||
\(719\) | 1.02273e12 | 0.142719 | 0.0713595 | − | 0.997451i | \(-0.477266\pi\) | ||||
0.0713595 | + | 0.997451i | \(0.477266\pi\) | |||||||
\(720\) | 9.97977e9 | 0.00138396 | ||||||||
\(721\) | −1.01411e13 | −1.39757 | ||||||||
\(722\) | −9.31987e11 | −0.127642 | ||||||||
\(723\) | −6.83280e12 | −0.929986 | ||||||||
\(724\) | 5.47448e12 | 0.740491 | ||||||||
\(725\) | −9.85039e12 | −1.32413 | ||||||||
\(726\) | 1.90855e12 | 0.254970 | ||||||||
\(727\) | −2.78462e11 | −0.0369710 | −0.0184855 | − | 0.999829i | \(-0.505884\pi\) | ||||
−0.0184855 | + | 0.999829i | \(0.505884\pi\) | |||||||
\(728\) | 1.87590e12 | 0.247525 | ||||||||
\(729\) | 4.91215e12 | 0.644165 | ||||||||
\(730\) | −1.39237e10 | −0.00181469 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.62726e12 | −0.338224 | ||||||||
\(733\) | 5.30668e12 | 0.678977 | 0.339488 | − | 0.940610i | \(-0.389746\pi\) | ||||
0.339488 | + | 0.940610i | \(0.389746\pi\) | |||||||
\(734\) | 1.55353e12 | 0.197555 | ||||||||
\(735\) | 5.51207e10 | 0.00696661 | ||||||||
\(736\) | −6.84981e12 | −0.860455 | ||||||||
\(737\) | −2.51828e12 | −0.314413 | ||||||||
\(738\) | −1.60026e12 | −0.198580 | ||||||||
\(739\) | 3.78591e12 | 0.466950 | 0.233475 | − | 0.972363i | \(-0.424990\pi\) | ||||
0.233475 | + | 0.972363i | \(0.424990\pi\) | |||||||
\(740\) | −3.88329e10 | −0.00476056 | ||||||||
\(741\) | −8.25713e11 | −0.100611 | ||||||||
\(742\) | 5.27209e11 | 0.0638507 | ||||||||
\(743\) | −1.97364e12 | −0.237584 | −0.118792 | − | 0.992919i | \(-0.537902\pi\) | ||||
−0.118792 | + | 0.992919i | \(0.537902\pi\) | |||||||
\(744\) | 8.46413e12 | 1.01275 | ||||||||
\(745\) | 3.07172e10 | 0.00365324 | ||||||||
\(746\) | −5.10488e12 | −0.603477 | ||||||||
\(747\) | −4.96179e12 | −0.583037 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.35030e11 | −0.0388969 | ||||||||
\(750\) | −5.41039e10 | −0.00624385 | ||||||||
\(751\) | 3.16072e11 | 0.0362583 | 0.0181291 | − | 0.999836i | \(-0.494229\pi\) | ||||
0.0181291 | + | 0.999836i | \(0.494229\pi\) | |||||||
\(752\) | 1.08115e11 | 0.0123284 | ||||||||
\(753\) | −7.26210e12 | −0.823161 | ||||||||
\(754\) | −1.14520e12 | −0.129036 | ||||||||
\(755\) | 1.18702e11 | 0.0132952 | ||||||||
\(756\) | −9.62454e12 | −1.07160 | ||||||||
\(757\) | 1.03321e13 | 1.14355 | 0.571775 | − | 0.820411i | \(-0.306255\pi\) | ||||
0.571775 | + | 0.820411i | \(0.306255\pi\) | |||||||
\(758\) | 7.53051e12 | 0.828539 | ||||||||
\(759\) | 2.27467e12 | 0.248789 | ||||||||
\(760\) | −6.87284e10 | −0.00747266 | ||||||||
\(761\) | 1.77902e12 | 0.192287 | 0.0961435 | − | 0.995367i | \(-0.469349\pi\) | ||||
0.0961435 | + | 0.995367i | \(0.469349\pi\) | |||||||
\(762\) | −2.68807e12 | −0.288831 | ||||||||
\(763\) | −2.12555e13 | −2.27044 | ||||||||
\(764\) | 1.22439e13 | 1.30016 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.27158e12 | 0.763131 | ||||||||
\(767\) | −3.08735e12 | −0.322112 | ||||||||
\(768\) | 4.63625e12 | 0.480885 | ||||||||
\(769\) | 4.28074e12 | 0.441418 | 0.220709 | − | 0.975340i | \(-0.429163\pi\) | ||||
0.220709 | + | 0.975340i | \(0.429163\pi\) | |||||||
\(770\) | −3.43471e10 | −0.00352113 | ||||||||
\(771\) | 3.03178e12 | 0.308996 | ||||||||
\(772\) | −1.53181e12 | −0.155212 | ||||||||
\(773\) | −1.39043e13 | −1.40069 | −0.700343 | − | 0.713807i | \(-0.746970\pi\) | ||||
−0.700343 | + | 0.713807i | \(0.746970\pi\) | |||||||
\(774\) | 5.80779e11 | 0.0581669 | ||||||||
\(775\) | −1.78692e13 | −1.77930 | ||||||||
\(776\) | 3.61311e12 | 0.357687 | ||||||||
\(777\) | 6.56561e12 | 0.646220 | ||||||||
\(778\) | −2.61092e11 | −0.0255497 | ||||||||
\(779\) | −5.53644e12 | −0.538657 | ||||||||
\(780\) | 8.13198e9 | 0.000786630 0 | ||||||||
\(781\) | 6.71950e12 | 0.646260 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.40235e13 | 1.33330 | ||||||||
\(784\) | 3.00585e12 | 0.284148 | ||||||||
\(785\) | 1.36025e11 | 0.0127852 | ||||||||
\(786\) | 4.87222e12 | 0.455329 | ||||||||
\(787\) | 1.03400e13 | 0.960806 | 0.480403 | − | 0.877048i | \(-0.340490\pi\) | ||||
0.480403 | + | 0.877048i | \(0.340490\pi\) | |||||||
\(788\) | 1.45937e13 | 1.34833 | ||||||||
\(789\) | 1.17028e13 | 1.07509 | ||||||||
\(790\) | 9.09971e10 | 0.00831200 | ||||||||
\(791\) | −1.50065e13 | −1.36297 | ||||||||
\(792\) | 2.92743e12 | 0.264377 | ||||||||
\(793\) | 1.53907e12 | 0.138207 | ||||||||
\(794\) | −9.92913e12 | −0.886582 | ||||||||
\(795\) | 5.45473e9 | 0.000484307 0 | ||||||||
\(796\) | −2.69259e12 | −0.237717 | ||||||||
\(797\) | −1.22177e13 | −1.07257 | −0.536286 | − | 0.844036i | \(-0.680173\pi\) | ||||
−0.536286 | + | 0.844036i | \(0.680173\pi\) | |||||||
\(798\) | 4.86863e12 | 0.425005 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.20041e13 | −1.03616 | ||||||||
\(801\) | 8.65190e12 | 0.742617 | ||||||||
\(802\) | 7.26091e11 | 0.0619736 | ||||||||
\(803\) | 2.05185e12 | 0.174151 | ||||||||
\(804\) | −3.51551e12 | −0.296713 | ||||||||
\(805\) | 1.37863e11 | 0.0115709 | ||||||||
\(806\) | −2.07747e12 | −0.173391 | ||||||||
\(807\) | −4.43597e11 | −0.0368178 | ||||||||
\(808\) | 7.57903e12 | 0.625551 | ||||||||
\(809\) | −1.36574e13 | −1.12098 | −0.560490 | − | 0.828161i | \(-0.689387\pi\) | ||||
−0.560490 | + | 0.828161i | \(0.689387\pi\) | |||||||
\(810\) | 1.37764e9 | 0.000112449 0 | ||||||||
\(811\) | 2.08036e13 | 1.68867 | 0.844334 | − | 0.535817i | \(-0.179996\pi\) | ||||
0.844334 | + | 0.535817i | \(0.179996\pi\) | |||||||
\(812\) | −1.74602e13 | −1.40944 | ||||||||
\(813\) | −1.91029e11 | −0.0153353 | ||||||||
\(814\) | −2.21311e12 | −0.176683 | ||||||||
\(815\) | −4.38974e9 | −0.000348522 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00933e12 | 0.157780 | ||||||||
\(818\) | −1.05296e13 | −0.822286 | ||||||||
\(819\) | 2.13162e12 | 0.165551 | ||||||||
\(820\) | 5.45253e10 | 0.00421149 | ||||||||
\(821\) | −3.70041e12 | −0.284254 | −0.142127 | − | 0.989848i | \(-0.545394\pi\) | ||||
−0.142127 | + | 0.989848i | \(0.545394\pi\) | |||||||
\(822\) | −8.06931e12 | −0.616472 | ||||||||
\(823\) | −1.80532e13 | −1.37168 | −0.685842 | − | 0.727751i | \(-0.740566\pi\) | ||||
−0.685842 | + | 0.727751i | \(0.740566\pi\) | |||||||
\(824\) | 1.13894e13 | 0.860651 | ||||||||
\(825\) | 3.98631e12 | 0.299591 | ||||||||
\(826\) | 1.82039e13 | 1.36067 | ||||||||
\(827\) | 1.73862e13 | 1.29250 | 0.646249 | − | 0.763127i | \(-0.276337\pi\) | ||||
0.646249 | + | 0.763127i | \(0.276337\pi\) | |||||||
\(828\) | −4.92313e12 | −0.364003 | ||||||||
\(829\) | 1.39706e13 | 1.02735 | 0.513676 | − | 0.857984i | \(-0.328283\pi\) | ||||
0.513676 | + | 0.857984i | \(0.328283\pi\) | |||||||
\(830\) | −6.53821e10 | −0.00478197 | ||||||||
\(831\) | 2.45264e12 | 0.178414 | ||||||||
\(832\) | −7.80641e11 | −0.0564802 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.31412e12 | −0.523498 | ||||||||
\(835\) | −9.08349e10 | −0.00646642 | ||||||||
\(836\) | 4.24350e12 | 0.300467 | ||||||||
\(837\) | 2.54395e13 | 1.79161 | ||||||||
\(838\) | 4.08599e12 | 0.286219 | ||||||||
\(839\) | −9.86320e12 | −0.687209 | −0.343605 | − | 0.939114i | \(-0.611648\pi\) | ||||
−0.343605 | + | 0.939114i | \(0.611648\pi\) | |||||||
\(840\) | −1.14440e11 | −0.00793087 | ||||||||
\(841\) | 1.09333e13 | 0.753646 | ||||||||
\(842\) | −5.27280e12 | −0.361524 | ||||||||
\(843\) | 1.37808e13 | 0.939830 | ||||||||
\(844\) | 3.75221e12 | 0.254534 | ||||||||
\(845\) | 1.35160e11 | 0.00911994 | ||||||||
\(846\) | −2.44545e11 | −0.0164132 | ||||||||
\(847\) | −1.70461e13 | −1.13802 | ||||||||
\(848\) | 2.97458e11 | 0.0197535 | ||||||||
\(849\) | 4.40761e12 | 0.291151 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.88306e12 | 0.580603 | ||||||||
\(852\) | 9.38038e12 | 0.609877 | ||||||||
\(853\) | −2.33943e13 | −1.51300 | −0.756500 | − | 0.653994i | \(-0.773092\pi\) | ||||
−0.756500 | + | 0.653994i | \(0.773092\pi\) | |||||||
\(854\) | −9.07479e12 | −0.583817 | ||||||||
\(855\) | −7.80973e10 | −0.00499791 | ||||||||
\(856\) | 3.76270e11 | 0.0239534 | ||||||||
\(857\) | −2.44699e12 | −0.154960 | −0.0774799 | − | 0.996994i | \(-0.524687\pi\) | ||||
−0.0774799 | + | 0.996994i | \(0.524687\pi\) | |||||||
\(858\) | 4.63446e11 | 0.0291949 | ||||||||
\(859\) | −1.61824e11 | −0.0101409 | −0.00507043 | − | 0.999987i | \(-0.501614\pi\) | ||||
−0.00507043 | + | 0.999987i | \(0.501614\pi\) | |||||||
\(860\) | −1.97888e10 | −0.00123360 | ||||||||
\(861\) | −9.21875e12 | −0.571687 | ||||||||
\(862\) | −3.59773e12 | −0.221945 | ||||||||
\(863\) | −9.09905e12 | −0.558402 | −0.279201 | − | 0.960233i | \(-0.590070\pi\) | ||||
−0.279201 | + | 0.960233i | \(0.590070\pi\) | |||||||
\(864\) | 1.70896e13 | 1.04333 | ||||||||
\(865\) | −7.93443e10 | −0.00481885 | ||||||||
\(866\) | 8.78960e12 | 0.531054 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.16738e13 | −1.89392 | ||||||||
\(869\) | −1.34097e13 | −0.797683 | ||||||||
\(870\) | 6.98634e10 | 0.00413440 | ||||||||
\(871\) | 2.05942e12 | 0.121245 | ||||||||
\(872\) | 2.38719e13 | 1.39818 | ||||||||
\(873\) | 4.10564e12 | 0.239230 | ||||||||
\(874\) | 6.58710e12 | 0.381850 | ||||||||
\(875\) | 4.83226e11 | 0.0278685 | ||||||||
\(876\) | 2.86437e12 | 0.164347 | ||||||||
\(877\) | −2.44380e12 | −0.139498 | −0.0697489 | − | 0.997565i | \(-0.522220\pi\) | ||||
−0.0697489 | + | 0.997565i | \(0.522220\pi\) | |||||||
\(878\) | 1.05856e13 | 0.601162 | ||||||||
\(879\) | 2.03472e13 | 1.14962 | ||||||||
\(880\) | −1.93790e10 | −0.00108933 | ||||||||
\(881\) | −5.73549e11 | −0.0320759 | −0.0160379 | − | 0.999871i | \(-0.505105\pi\) | ||||
−0.0160379 | + | 0.999871i | \(0.505105\pi\) | |||||||
\(882\) | −6.79893e12 | −0.378296 | ||||||||
\(883\) | −1.23459e13 | −0.683441 | −0.341721 | − | 0.939802i | \(-0.611010\pi\) | ||||
−0.341721 | + | 0.939802i | \(0.611010\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.88345e11 | 0.0103207 | ||||||||
\(886\) | 1.54087e12 | 0.0840069 | ||||||||
\(887\) | −2.65385e13 | −1.43953 | −0.719765 | − | 0.694218i | \(-0.755750\pi\) | ||||
−0.719765 | + | 0.694218i | \(0.755750\pi\) | |||||||
\(888\) | −7.37379e12 | −0.397954 | ||||||||
\(889\) | 2.40084e13 | 1.28915 | ||||||||
\(890\) | 1.14007e11 | 0.00609083 | ||||||||
\(891\) | −2.03015e11 | −0.0107914 | ||||||||
\(892\) | −1.79113e13 | −0.947295 | ||||||||
\(893\) | −8.46060e11 | −0.0445215 | ||||||||
\(894\) | 2.44381e12 | 0.127953 | ||||||||
\(895\) | 1.58100e11 | 0.00823621 | ||||||||
\(896\) | −2.49036e13 | −1.29085 | ||||||||
\(897\) | −1.86019e12 | −0.0959384 | ||||||||
\(898\) | 1.86110e13 | 0.955053 | ||||||||
\(899\) | 4.61505e13 | 2.35645 | ||||||||
\(900\) | −8.62766e12 | −0.438331 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.10743e12 | 0.156305 | ||||||||
\(903\) | 3.34575e12 | 0.167455 | ||||||||
\(904\) | 1.68537e13 | 0.839339 | ||||||||
\(905\) | 1.95644e11 | 0.00969500 | ||||||||
\(906\) | 9.44372e12 | 0.465657 | ||||||||
\(907\) | −1.38313e13 | −0.678626 | −0.339313 | − | 0.940674i | \(-0.610194\pi\) | ||||
−0.339313 | + | 0.940674i | \(0.610194\pi\) | |||||||
\(908\) | 1.14309e13 | 0.558075 | ||||||||
\(909\) | 8.61219e12 | 0.418385 | ||||||||
\(910\) | 2.80885e10 | 0.00135782 | ||||||||
\(911\) | −2.14644e13 | −1.03249 | −0.516244 | − | 0.856441i | \(-0.672670\pi\) | ||||
−0.516244 | + | 0.856441i | \(0.672670\pi\) | |||||||
\(912\) | 2.74694e12 | 0.131484 | ||||||||
\(913\) | 9.63497e12 | 0.458915 | ||||||||
\(914\) | −3.26598e12 | −0.154794 | ||||||||
\(915\) | −9.38917e10 | −0.00442825 | ||||||||
\(916\) | −4.94443e12 | −0.232053 | ||||||||
\(917\) | −4.35160e13 | −2.03229 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.64775e13 | −1.22450 | −0.612248 | − | 0.790666i | \(-0.709734\pi\) | ||||
−0.612248 | + | 0.790666i | \(0.709734\pi\) | |||||||
\(920\) | −1.54834e11 | −0.00712558 | ||||||||
\(921\) | −2.26431e13 | −1.03697 | ||||||||
\(922\) | 7.04142e12 | 0.320901 | ||||||||
\(923\) | −5.49510e12 | −0.249212 | ||||||||
\(924\) | 7.06587e12 | 0.318891 | ||||||||
\(925\) | 1.55673e13 | 0.699160 | ||||||||
\(926\) | 1.60555e13 | 0.717585 | ||||||||
\(927\) | 1.29419e13 | 0.575626 | ||||||||
\(928\) | 3.10028e13 | 1.37226 | ||||||||
\(929\) | 2.21866e13 | 0.977281 | 0.488640 | − | 0.872485i | \(-0.337493\pi\) | ||||
0.488640 | + | 0.872485i | \(0.337493\pi\) | |||||||
\(930\) | 1.26737e11 | 0.00555557 | ||||||||
\(931\) | −2.35224e13 | −1.02614 | ||||||||
\(932\) | −1.73069e12 | −0.0751359 | ||||||||
\(933\) | 1.16614e13 | 0.503829 | ||||||||
\(934\) | 7.62466e11 | 0.0327838 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.39401e12 | −0.101949 | ||||||||
\(937\) | −2.22025e13 | −0.940966 | −0.470483 | − | 0.882409i | \(-0.655920\pi\) | ||||
−0.470483 | + | 0.882409i | \(0.655920\pi\) | |||||||
\(938\) | −1.21429e13 | −0.512164 | ||||||||
\(939\) | 1.36327e13 | 0.572250 | ||||||||
\(940\) | 8.33236e9 | 0.000348091 0 | ||||||||
\(941\) | −1.31832e12 | −0.0548108 | −0.0274054 | − | 0.999624i | \(-0.508725\pi\) | ||||
−0.0274054 | + | 0.999624i | \(0.508725\pi\) | |||||||
\(942\) | 1.08220e13 | 0.447794 | ||||||||
\(943\) | −1.24727e13 | −0.513638 | ||||||||
\(944\) | 1.02708e13 | 0.420951 | ||||||||
\(945\) | −3.43956e11 | −0.0140301 | ||||||||
\(946\) | −1.12777e12 | −0.0457838 | ||||||||
\(947\) | −6.19592e11 | −0.0250341 | −0.0125170 | − | 0.999922i | \(-0.503984\pi\) | ||||
−0.0125170 | + | 0.999922i | \(0.503984\pi\) | |||||||
\(948\) | −1.87199e13 | −0.752776 | ||||||||
\(949\) | −1.67797e12 | −0.0671564 | ||||||||
\(950\) | 1.15437e13 | 0.459822 | ||||||||
\(951\) | −6.39400e12 | −0.253490 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.01822e13 | 1.18531 | 0.592657 | − | 0.805455i | \(-0.298079\pi\) | ||||
0.592657 | + | 0.805455i | \(0.298079\pi\) | |||||||
\(954\) | −6.72820e11 | −0.0262985 | ||||||||
\(955\) | 4.37564e11 | 0.0170226 | ||||||||
\(956\) | −1.20375e13 | −0.466095 | ||||||||
\(957\) | −1.02954e13 | −0.396769 | ||||||||
\(958\) | −1.37831e12 | −0.0528692 | ||||||||
\(959\) | 7.20706e13 | 2.75153 | ||||||||
\(960\) | 4.76233e10 | 0.00180967 | ||||||||
\(961\) | 5.72803e13 | 2.16646 | ||||||||
\(962\) | 1.80985e12 | 0.0681326 | ||||||||
\(963\) | 4.27562e11 | 0.0160207 | ||||||||
\(964\) | −2.87166e13 | −1.07099 | ||||||||
\(965\) | −5.47429e10 | −0.00203215 | ||||||||
\(966\) | 1.09682e13 | 0.405265 | ||||||||
\(967\) | 1.16727e13 | 0.429291 | 0.214646 | − | 0.976692i | \(-0.431140\pi\) | ||||
0.214646 | + | 0.976692i | \(0.431140\pi\) | |||||||
\(968\) | 1.91444e13 | 0.700815 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.41004e10 | 0.00196213 | ||||||||
\(971\) | −1.98303e13 | −0.715885 | −0.357943 | − | 0.933744i | \(-0.616522\pi\) | ||||
−0.357943 | + | 0.933744i | \(0.616522\pi\) | |||||||
\(972\) | 1.99217e13 | 0.715862 | ||||||||
\(973\) | 6.53257e13 | 2.33656 | ||||||||
\(974\) | 2.29589e13 | 0.817402 | ||||||||
\(975\) | −3.25994e12 | −0.115529 | ||||||||
\(976\) | −5.12011e12 | −0.180615 | ||||||||
\(977\) | 3.14683e13 | 1.10496 | 0.552482 | − | 0.833525i | \(-0.313681\pi\) | ||||
0.552482 | + | 0.833525i | \(0.313681\pi\) | |||||||
\(978\) | −3.49241e11 | −0.0122068 | ||||||||
\(979\) | −1.68005e13 | −0.584522 | ||||||||
\(980\) | 2.31659e11 | 0.00802290 | ||||||||
\(981\) | 2.71261e13 | 0.935140 | ||||||||
\(982\) | −1.49494e13 | −0.513004 | ||||||||
\(983\) | −4.11496e13 | −1.40564 | −0.702821 | − | 0.711367i | \(-0.748076\pi\) | ||||
−0.702821 | + | 0.711367i | \(0.748076\pi\) | |||||||
\(984\) | 1.03535e13 | 0.352055 | ||||||||
\(985\) | 5.21540e11 | 0.0176533 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.40878e12 | −0.0472515 | ||||||||
\(988\) | −3.47027e12 | −0.115866 | ||||||||
\(989\) | 4.52669e12 | 0.150452 | ||||||||
\(990\) | 4.38335e10 | 0.00145027 | ||||||||
\(991\) | 1.78109e13 | 0.586615 | 0.293308 | − | 0.956018i | \(-0.405244\pi\) | ||||
0.293308 | + | 0.956018i | \(0.405244\pi\) | |||||||
\(992\) | 5.62410e13 | 1.84396 | ||||||||
\(993\) | −1.56237e13 | −0.509932 | ||||||||
\(994\) | 3.24006e13 | 1.05272 | ||||||||
\(995\) | −9.62261e10 | −0.00311235 | ||||||||
\(996\) | 1.34504e13 | 0.433079 | ||||||||
\(997\) | −5.88070e12 | −0.188495 | −0.0942476 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942476 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(998\) | 7.31427e12 | 0.233391 | ||||||||
\(999\) | −2.21624e13 | −0.703999 |
(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 | 289.10.a.g.1.23 | ✓ | 36 | |
17.16 | even | 2 | 289.10.a.h.1.23 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.23 | ✓ | 36 | 1.1 | even | 1 | trivial | |
289.10.a.h.1.23 | yes | 36 | 17.16 | even | 2 |