Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [121,12,Mod(1,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("121.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.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: | \(92.9695248477\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 121.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 24.0000 | 0.530330 | 0.265165 | − | 0.964203i | \(-0.414574\pi\) | ||||
0.265165 | + | 0.964203i | \(0.414574\pi\) | |||||||
\(3\) | 252.000 | 0.598734 | 0.299367 | − | 0.954138i | \(-0.403225\pi\) | ||||
0.299367 | + | 0.954138i | \(0.403225\pi\) | |||||||
\(4\) | −1472.00 | −0.718750 | ||||||||
\(5\) | 4830.00 | 0.691213 | 0.345607 | − | 0.938379i | \(-0.387673\pi\) | ||||
0.345607 | + | 0.938379i | \(0.387673\pi\) | |||||||
\(6\) | 6048.00 | 0.317526 | ||||||||
\(7\) | 16744.0 | 0.376548 | 0.188274 | − | 0.982117i | \(-0.439711\pi\) | ||||
0.188274 | + | 0.982117i | \(0.439711\pi\) | |||||||
\(8\) | −84480.0 | −0.911505 | ||||||||
\(9\) | −113643. | −0.641518 | ||||||||
\(10\) | 115920. | 0.366571 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −370944. | −0.430340 | ||||||||
\(13\) | 577738. | 0.431561 | 0.215781 | − | 0.976442i | \(-0.430770\pi\) | ||||
0.215781 | + | 0.976442i | \(0.430770\pi\) | |||||||
\(14\) | 401856. | 0.199695 | ||||||||
\(15\) | 1.21716e6 | 0.413853 | ||||||||
\(16\) | 987136. | 0.235352 | ||||||||
\(17\) | 6.90593e6 | 1.17965 | 0.589825 | − | 0.807531i | \(-0.299197\pi\) | ||||
0.589825 | + | 0.807531i | \(0.299197\pi\) | |||||||
\(18\) | −2.72743e6 | −0.340216 | ||||||||
\(19\) | −1.06614e7 | −0.987803 | −0.493901 | − | 0.869518i | \(-0.664430\pi\) | ||||
−0.493901 | + | 0.869518i | \(0.664430\pi\) | |||||||
\(20\) | −7.10976e6 | −0.496810 | ||||||||
\(21\) | 4.21949e6 | 0.225452 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.86433e7 | 0.603975 | 0.301988 | − | 0.953312i | \(-0.402350\pi\) | ||||
0.301988 | + | 0.953312i | \(0.402350\pi\) | |||||||
\(24\) | −2.12890e7 | −0.545749 | ||||||||
\(25\) | −2.54992e7 | −0.522224 | ||||||||
\(26\) | 1.38657e7 | 0.228870 | ||||||||
\(27\) | −7.32791e7 | −0.982832 | ||||||||
\(28\) | −2.46472e7 | −0.270644 | ||||||||
\(29\) | −1.28407e8 | −1.16251 | −0.581257 | − | 0.813720i | \(-0.697439\pi\) | ||||
−0.581257 | + | 0.813720i | \(0.697439\pi\) | |||||||
\(30\) | 2.92118e7 | 0.219479 | ||||||||
\(31\) | −5.28432e7 | −0.331512 | −0.165756 | − | 0.986167i | \(-0.553006\pi\) | ||||
−0.165756 | + | 0.986167i | \(0.553006\pi\) | |||||||
\(32\) | 1.96706e8 | 1.03632 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.65742e8 | 0.625604 | ||||||||
\(35\) | 8.08735e7 | 0.260275 | ||||||||
\(36\) | 1.67282e8 | 0.461091 | ||||||||
\(37\) | −1.82213e8 | −0.431987 | −0.215993 | − | 0.976395i | \(-0.569299\pi\) | ||||
−0.215993 | + | 0.976395i | \(0.569299\pi\) | |||||||
\(38\) | −2.55874e8 | −0.523862 | ||||||||
\(39\) | 1.45590e8 | 0.258390 | ||||||||
\(40\) | −4.08038e8 | −0.630044 | ||||||||
\(41\) | −3.08120e8 | −0.415345 | −0.207673 | − | 0.978198i | \(-0.566589\pi\) | ||||
−0.207673 | + | 0.978198i | \(0.566589\pi\) | |||||||
\(42\) | 1.01268e8 | 0.119564 | ||||||||
\(43\) | 1.71257e7 | 0.0177653 | 0.00888264 | − | 0.999961i | \(-0.497173\pi\) | ||||
0.00888264 | + | 0.999961i | \(0.497173\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.48896e8 | −0.443426 | ||||||||
\(46\) | 4.47439e8 | 0.320306 | ||||||||
\(47\) | 2.68735e9 | 1.70917 | 0.854586 | − | 0.519310i | \(-0.173811\pi\) | ||||
0.854586 | + | 0.519310i | \(0.173811\pi\) | |||||||
\(48\) | 2.48758e8 | 0.140913 | ||||||||
\(49\) | −1.69697e9 | −0.858212 | ||||||||
\(50\) | −6.11981e8 | −0.276951 | ||||||||
\(51\) | 1.74030e9 | 0.706296 | ||||||||
\(52\) | −8.50430e8 | −0.310185 | ||||||||
\(53\) | −1.59606e9 | −0.524241 | −0.262120 | − | 0.965035i | \(-0.584422\pi\) | ||||
−0.262120 | + | 0.965035i | \(0.584422\pi\) | |||||||
\(54\) | −1.75870e9 | −0.521225 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.41453e9 | −0.343225 | ||||||||
\(57\) | −2.68668e9 | −0.591431 | ||||||||
\(58\) | −3.08176e9 | −0.616517 | ||||||||
\(59\) | −5.18920e9 | −0.944963 | −0.472481 | − | 0.881341i | \(-0.656642\pi\) | ||||
−0.472481 | + | 0.881341i | \(0.656642\pi\) | |||||||
\(60\) | −1.79166e9 | −0.297457 | ||||||||
\(61\) | −6.95648e9 | −1.05457 | −0.527285 | − | 0.849689i | \(-0.676790\pi\) | ||||
−0.527285 | + | 0.849689i | \(0.676790\pi\) | |||||||
\(62\) | −1.26824e9 | −0.175811 | ||||||||
\(63\) | −1.90284e9 | −0.241562 | ||||||||
\(64\) | 2.69930e9 | 0.314240 | ||||||||
\(65\) | 2.79047e9 | 0.298301 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.54818e10 | −1.40091 | −0.700456 | − | 0.713696i | \(-0.747020\pi\) | ||||
−0.700456 | + | 0.713696i | \(0.747020\pi\) | |||||||
\(68\) | −1.01655e10 | −0.847874 | ||||||||
\(69\) | 4.69810e9 | 0.361620 | ||||||||
\(70\) | 1.94096e9 | 0.138032 | ||||||||
\(71\) | 9.79149e9 | 0.644062 | 0.322031 | − | 0.946729i | \(-0.395634\pi\) | ||||
0.322031 | + | 0.946729i | \(0.395634\pi\) | |||||||
\(72\) | 9.60056e9 | 0.584747 | ||||||||
\(73\) | −1.46379e9 | −0.0826425 | −0.0413212 | − | 0.999146i | \(-0.513157\pi\) | ||||
−0.0413212 | + | 0.999146i | \(0.513157\pi\) | |||||||
\(74\) | −4.37312e9 | −0.229096 | ||||||||
\(75\) | −6.42580e9 | −0.312673 | ||||||||
\(76\) | 1.56936e10 | 0.709983 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.49416e9 | 0.137032 | ||||||||
\(79\) | −3.81168e10 | −1.39370 | −0.696848 | − | 0.717219i | \(-0.745415\pi\) | ||||
−0.696848 | + | 0.717219i | \(0.745415\pi\) | |||||||
\(80\) | 4.76787e9 | 0.162678 | ||||||||
\(81\) | 1.66519e9 | 0.0530635 | ||||||||
\(82\) | −7.39489e9 | −0.220270 | ||||||||
\(83\) | 2.93351e10 | 0.817444 | 0.408722 | − | 0.912659i | \(-0.365975\pi\) | ||||
0.408722 | + | 0.912659i | \(0.365975\pi\) | |||||||
\(84\) | −6.21109e9 | −0.162043 | ||||||||
\(85\) | 3.33557e10 | 0.815390 | ||||||||
\(86\) | 4.11017e8 | 0.00942146 | ||||||||
\(87\) | −3.23585e10 | −0.696037 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.49929e10 | −0.474430 | −0.237215 | − | 0.971457i | \(-0.576235\pi\) | ||||
−0.237215 | + | 0.971457i | \(0.576235\pi\) | |||||||
\(90\) | −1.31735e10 | −0.235162 | ||||||||
\(91\) | 9.67365e9 | 0.162503 | ||||||||
\(92\) | −2.74429e10 | −0.434107 | ||||||||
\(93\) | −1.33165e10 | −0.198488 | ||||||||
\(94\) | 6.44964e10 | 0.906425 | ||||||||
\(95\) | −5.14947e10 | −0.682782 | ||||||||
\(96\) | 4.95700e10 | 0.620479 | ||||||||
\(97\) | 7.50136e10 | 0.886942 | 0.443471 | − | 0.896289i | \(-0.353747\pi\) | ||||
0.443471 | + | 0.896289i | \(0.353747\pi\) | |||||||
\(98\) | −4.07272e10 | −0.455136 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.75349e10 | 0.375349 | ||||||||
\(101\) | −8.17430e10 | −0.773896 | −0.386948 | − | 0.922101i | \(-0.626471\pi\) | ||||
−0.386948 | + | 0.922101i | \(0.626471\pi\) | |||||||
\(102\) | 4.17671e10 | 0.374570 | ||||||||
\(103\) | −2.25755e11 | −1.91881 | −0.959407 | − | 0.282025i | \(-0.908994\pi\) | ||||
−0.959407 | + | 0.282025i | \(0.908994\pi\) | |||||||
\(104\) | −4.88073e10 | −0.393370 | ||||||||
\(105\) | 2.03801e10 | 0.155835 | ||||||||
\(106\) | −3.83053e10 | −0.278021 | ||||||||
\(107\) | −9.02413e10 | −0.622006 | −0.311003 | − | 0.950409i | \(-0.600665\pi\) | ||||
−0.311003 | + | 0.950409i | \(0.600665\pi\) | |||||||
\(108\) | 1.07867e11 | 0.706411 | ||||||||
\(109\) | −7.34827e10 | −0.457445 | −0.228723 | − | 0.973492i | \(-0.573455\pi\) | ||||
−0.228723 | + | 0.973492i | \(0.573455\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.59178e10 | −0.258645 | ||||||||
\(112\) | 1.65286e10 | 0.0886211 | ||||||||
\(113\) | −8.51469e10 | −0.434748 | −0.217374 | − | 0.976088i | \(-0.569749\pi\) | ||||
−0.217374 | + | 0.976088i | \(0.569749\pi\) | |||||||
\(114\) | −6.44803e10 | −0.313654 | ||||||||
\(115\) | 9.00470e10 | 0.417476 | ||||||||
\(116\) | 1.89015e11 | 0.835557 | ||||||||
\(117\) | −6.56559e10 | −0.276854 | ||||||||
\(118\) | −1.24541e11 | −0.501142 | ||||||||
\(119\) | 1.15633e11 | 0.444195 | ||||||||
\(120\) | −1.02826e11 | −0.377229 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.66955e11 | −0.559270 | ||||||||
\(123\) | −7.76464e10 | −0.248681 | ||||||||
\(124\) | 7.77851e10 | 0.238274 | ||||||||
\(125\) | −3.59001e11 | −1.05218 | ||||||||
\(126\) | −4.56681e10 | −0.128108 | ||||||||
\(127\) | 2.62717e11 | 0.705615 | 0.352808 | − | 0.935696i | \(-0.385227\pi\) | ||||
0.352808 | + | 0.935696i | \(0.385227\pi\) | |||||||
\(128\) | −3.38071e11 | −0.869668 | ||||||||
\(129\) | 4.31568e9 | 0.0106367 | ||||||||
\(130\) | 6.69714e10 | 0.158198 | ||||||||
\(131\) | −6.31529e11 | −1.43021 | −0.715107 | − | 0.699015i | \(-0.753622\pi\) | ||||
−0.715107 | + | 0.699015i | \(0.753622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.78515e11 | −0.371955 | ||||||||
\(134\) | −3.71564e11 | −0.742946 | ||||||||
\(135\) | −3.53938e11 | −0.679347 | ||||||||
\(136\) | −5.83413e11 | −1.07526 | ||||||||
\(137\) | −2.97199e11 | −0.526119 | −0.263059 | − | 0.964780i | \(-0.584732\pi\) | ||||
−0.263059 | + | 0.964780i | \(0.584732\pi\) | |||||||
\(138\) | 1.12755e11 | 0.191778 | ||||||||
\(139\) | −5.96794e11 | −0.975535 | −0.487767 | − | 0.872974i | \(-0.662189\pi\) | ||||
−0.487767 | + | 0.872974i | \(0.662189\pi\) | |||||||
\(140\) | −1.19046e11 | −0.187073 | ||||||||
\(141\) | 6.77212e11 | 1.02334 | ||||||||
\(142\) | 2.34996e11 | 0.341565 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.12181e11 | −0.150982 | ||||||||
\(145\) | −6.20204e11 | −0.803546 | ||||||||
\(146\) | −3.51310e10 | −0.0438278 | ||||||||
\(147\) | −4.27635e11 | −0.513840 | ||||||||
\(148\) | 2.68218e11 | 0.310491 | ||||||||
\(149\) | 1.11543e12 | 1.24428 | 0.622142 | − | 0.782905i | \(-0.286263\pi\) | ||||
0.622142 | + | 0.782905i | \(0.286263\pi\) | |||||||
\(150\) | −1.54219e11 | −0.165820 | ||||||||
\(151\) | 8.24447e11 | 0.854653 | 0.427326 | − | 0.904097i | \(-0.359456\pi\) | ||||
0.427326 | + | 0.904097i | \(0.359456\pi\) | |||||||
\(152\) | 9.00677e11 | 0.900387 | ||||||||
\(153\) | −7.84811e11 | −0.756767 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.55233e11 | −0.229146 | ||||||||
\(156\) | −2.14308e11 | −0.185718 | ||||||||
\(157\) | 1.31512e12 | 1.10031 | 0.550156 | − | 0.835062i | \(-0.314568\pi\) | ||||
0.550156 | + | 0.835062i | \(0.314568\pi\) | |||||||
\(158\) | −9.14804e11 | −0.739119 | ||||||||
\(159\) | −4.02206e11 | −0.313881 | ||||||||
\(160\) | 9.50091e11 | 0.716317 | ||||||||
\(161\) | 3.12163e11 | 0.227425 | ||||||||
\(162\) | 3.99645e10 | 0.0281412 | ||||||||
\(163\) | −3.57833e11 | −0.243584 | −0.121792 | − | 0.992556i | \(-0.538864\pi\) | ||||
−0.121792 | + | 0.992556i | \(0.538864\pi\) | |||||||
\(164\) | 4.53553e11 | 0.298529 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.04042e11 | 0.433515 | ||||||||
\(167\) | −2.75483e12 | −1.64117 | −0.820587 | − | 0.571521i | \(-0.806354\pi\) | ||||
−0.820587 | + | 0.571521i | \(0.806354\pi\) | |||||||
\(168\) | −3.56462e11 | −0.205500 | ||||||||
\(169\) | −1.45838e12 | −0.813755 | ||||||||
\(170\) | 8.00536e11 | 0.432426 | ||||||||
\(171\) | 1.21160e12 | 0.633693 | ||||||||
\(172\) | −2.52090e10 | −0.0127688 | ||||||||
\(173\) | 9.50387e11 | 0.466280 | 0.233140 | − | 0.972443i | \(-0.425100\pi\) | ||||
0.233140 | + | 0.972443i | \(0.425100\pi\) | |||||||
\(174\) | −7.76603e11 | −0.369129 | ||||||||
\(175\) | −4.26959e11 | −0.196642 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.30768e12 | −0.565781 | ||||||||
\(178\) | −5.99830e11 | −0.251604 | ||||||||
\(179\) | 1.68138e12 | 0.683873 | 0.341936 | − | 0.939723i | \(-0.388917\pi\) | ||||
0.341936 | + | 0.939723i | \(0.388917\pi\) | |||||||
\(180\) | 8.07974e11 | 0.318712 | ||||||||
\(181\) | −9.96774e11 | −0.381386 | −0.190693 | − | 0.981650i | \(-0.561073\pi\) | ||||
−0.190693 | + | 0.981650i | \(0.561073\pi\) | |||||||
\(182\) | 2.32167e11 | 0.0861804 | ||||||||
\(183\) | −1.75303e12 | −0.631406 | ||||||||
\(184\) | −1.57498e12 | −0.550526 | ||||||||
\(185\) | −8.80090e11 | −0.298595 | ||||||||
\(186\) | −3.19595e11 | −0.105264 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.95578e12 | −1.22847 | ||||||||
\(189\) | −1.22698e12 | −0.370083 | ||||||||
\(190\) | −1.23587e12 | −0.362100 | ||||||||
\(191\) | 2.76240e12 | 0.786328 | 0.393164 | − | 0.919468i | \(-0.371381\pi\) | ||||
0.393164 | + | 0.919468i | \(0.371381\pi\) | |||||||
\(192\) | 6.80223e11 | 0.188146 | ||||||||
\(193\) | −5.44239e12 | −1.46293 | −0.731466 | − | 0.681878i | \(-0.761164\pi\) | ||||
−0.731466 | + | 0.681878i | \(0.761164\pi\) | |||||||
\(194\) | 1.80033e12 | 0.470372 | ||||||||
\(195\) | 7.03200e11 | 0.178603 | ||||||||
\(196\) | 2.49793e12 | 0.616840 | ||||||||
\(197\) | 2.87609e12 | 0.690619 | 0.345309 | − | 0.938489i | \(-0.387774\pi\) | ||||
0.345309 | + | 0.938489i | \(0.387774\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.28391e11 | 0.165452 | 0.0827262 | − | 0.996572i | \(-0.473637\pi\) | ||||
0.0827262 | + | 0.996572i | \(0.473637\pi\) | |||||||
\(200\) | 2.15417e12 | 0.476010 | ||||||||
\(201\) | −3.90142e12 | −0.838773 | ||||||||
\(202\) | −1.96183e12 | −0.410421 | ||||||||
\(203\) | −2.15004e12 | −0.437742 | ||||||||
\(204\) | −2.56171e12 | −0.507651 | ||||||||
\(205\) | −1.48822e12 | −0.287092 | ||||||||
\(206\) | −5.41812e12 | −1.01760 | ||||||||
\(207\) | −2.11868e12 | −0.387461 | ||||||||
\(208\) | 5.70306e11 | 0.101569 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.89123e11 | 0.0826441 | ||||||||
\(211\) | 6.79317e12 | 1.11820 | 0.559099 | − | 0.829101i | \(-0.311147\pi\) | ||||
0.559099 | + | 0.829101i | \(0.311147\pi\) | |||||||
\(212\) | 2.34939e12 | 0.376798 | ||||||||
\(213\) | 2.46745e12 | 0.385622 | ||||||||
\(214\) | −2.16579e12 | −0.329868 | ||||||||
\(215\) | 8.27172e10 | 0.0122796 | ||||||||
\(216\) | 6.19062e12 | 0.895856 | ||||||||
\(217\) | −8.84806e11 | −0.124830 | ||||||||
\(218\) | −1.76358e12 | −0.242597 | ||||||||
\(219\) | −3.68875e11 | −0.0494808 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.98982e12 | 0.509092 | ||||||||
\(222\) | −1.10203e12 | −0.137167 | ||||||||
\(223\) | 7.33486e12 | 0.890667 | 0.445333 | − | 0.895365i | \(-0.353085\pi\) | ||||
0.445333 | + | 0.895365i | \(0.353085\pi\) | |||||||
\(224\) | 3.29365e12 | 0.390223 | ||||||||
\(225\) | 2.89781e12 | 0.335016 | ||||||||
\(226\) | −2.04352e12 | −0.230560 | ||||||||
\(227\) | 1.35984e12 | 0.149743 | 0.0748713 | − | 0.997193i | \(-0.476145\pi\) | ||||
0.0748713 | + | 0.997193i | \(0.476145\pi\) | |||||||
\(228\) | 3.95479e12 | 0.425091 | ||||||||
\(229\) | −1.18244e13 | −1.24075 | −0.620375 | − | 0.784305i | \(-0.713020\pi\) | ||||
−0.620375 | + | 0.784305i | \(0.713020\pi\) | |||||||
\(230\) | 2.16113e12 | 0.221400 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.08478e13 | 1.05964 | ||||||||
\(233\) | 1.75634e13 | 1.67552 | 0.837761 | − | 0.546038i | \(-0.183865\pi\) | ||||
0.837761 | + | 0.546038i | \(0.183865\pi\) | |||||||
\(234\) | −1.57574e12 | −0.146824 | ||||||||
\(235\) | 1.29799e13 | 1.18140 | ||||||||
\(236\) | 7.63851e12 | 0.679192 | ||||||||
\(237\) | −9.60545e12 | −0.834452 | ||||||||
\(238\) | 2.77519e12 | 0.235570 | ||||||||
\(239\) | 7.13958e12 | 0.592221 | 0.296111 | − | 0.955154i | \(-0.404310\pi\) | ||||
0.296111 | + | 0.955154i | \(0.404310\pi\) | |||||||
\(240\) | 1.20150e12 | 0.0974009 | ||||||||
\(241\) | 2.31307e11 | 0.0183271 | 0.00916357 | − | 0.999958i | \(-0.497083\pi\) | ||||
0.00916357 | + | 0.999958i | \(0.497083\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.34008e13 | 1.01460 | ||||||||
\(244\) | 1.02399e13 | 0.757972 | ||||||||
\(245\) | −8.19634e12 | −0.593207 | ||||||||
\(246\) | −1.86351e12 | −0.131883 | ||||||||
\(247\) | −6.15951e12 | −0.426297 | ||||||||
\(248\) | 4.46419e12 | 0.302175 | ||||||||
\(249\) | 7.39245e12 | 0.489431 | ||||||||
\(250\) | −8.61603e12 | −0.558004 | ||||||||
\(251\) | 1.29831e13 | 0.822567 | 0.411284 | − | 0.911507i | \(-0.365081\pi\) | ||||
0.411284 | + | 0.911507i | \(0.365081\pi\) | |||||||
\(252\) | 2.80098e12 | 0.173623 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.30521e12 | 0.374209 | ||||||||
\(255\) | 8.40563e12 | 0.488201 | ||||||||
\(256\) | −1.36419e13 | −0.775451 | ||||||||
\(257\) | 2.39612e13 | 1.33314 | 0.666571 | − | 0.745442i | \(-0.267761\pi\) | ||||
0.666571 | + | 0.745442i | \(0.267761\pi\) | |||||||
\(258\) | 1.03576e11 | 0.00564095 | ||||||||
\(259\) | −3.05098e12 | −0.162664 | ||||||||
\(260\) | −4.10758e12 | −0.214404 | ||||||||
\(261\) | 1.45925e13 | 0.745774 | ||||||||
\(262\) | −1.51567e13 | −0.758485 | ||||||||
\(263\) | 2.42737e13 | 1.18954 | 0.594771 | − | 0.803895i | \(-0.297243\pi\) | ||||
0.594771 | + | 0.803895i | \(0.297243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.70895e12 | −0.362362 | ||||||||
\(266\) | −4.28436e12 | −0.197259 | ||||||||
\(267\) | −6.29822e12 | −0.284057 | ||||||||
\(268\) | 2.27892e13 | 1.00691 | ||||||||
\(269\) | 2.58377e13 | 1.11845 | 0.559225 | − | 0.829016i | \(-0.311099\pi\) | ||||
0.559225 | + | 0.829016i | \(0.311099\pi\) | |||||||
\(270\) | −8.49451e12 | −0.360278 | ||||||||
\(271\) | 3.76793e12 | 0.156593 | 0.0782964 | − | 0.996930i | \(-0.475052\pi\) | ||||
0.0782964 | + | 0.996930i | \(0.475052\pi\) | |||||||
\(272\) | 6.81710e12 | 0.277633 | ||||||||
\(273\) | 2.43776e12 | 0.0972963 | ||||||||
\(274\) | −7.13277e12 | −0.279017 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.91561e12 | −0.259915 | ||||||||
\(277\) | 1.64189e13 | 0.604931 | 0.302466 | − | 0.953160i | \(-0.402190\pi\) | ||||
0.302466 | + | 0.953160i | \(0.402190\pi\) | |||||||
\(278\) | −1.43230e13 | −0.517355 | ||||||||
\(279\) | 6.00526e12 | 0.212671 | ||||||||
\(280\) | −6.83219e12 | −0.237242 | ||||||||
\(281\) | −2.10357e13 | −0.716263 | −0.358132 | − | 0.933671i | \(-0.616586\pi\) | ||||
−0.358132 | + | 0.933671i | \(0.616586\pi\) | |||||||
\(282\) | 1.62531e13 | 0.542707 | ||||||||
\(283\) | −1.67132e13 | −0.547310 | −0.273655 | − | 0.961828i | \(-0.588233\pi\) | ||||
−0.273655 | + | 0.961828i | \(0.588233\pi\) | |||||||
\(284\) | −1.44131e13 | −0.462920 | ||||||||
\(285\) | −1.29767e13 | −0.408805 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.15917e12 | −0.156397 | ||||||||
\(288\) | −2.23543e13 | −0.664817 | ||||||||
\(289\) | 1.34200e13 | 0.391575 | ||||||||
\(290\) | −1.48849e13 | −0.426144 | ||||||||
\(291\) | 1.89034e13 | 0.531042 | ||||||||
\(292\) | 2.15470e12 | 0.0593993 | ||||||||
\(293\) | 2.39269e13 | 0.647312 | 0.323656 | − | 0.946175i | \(-0.395088\pi\) | ||||
0.323656 | + | 0.946175i | \(0.395088\pi\) | |||||||
\(294\) | −1.02632e13 | −0.272505 | ||||||||
\(295\) | −2.50639e13 | −0.653171 | ||||||||
\(296\) | 1.53934e13 | 0.393758 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.67704e13 | 0.659881 | ||||||||
\(299\) | 1.07709e13 | 0.260652 | ||||||||
\(300\) | 9.45878e12 | 0.224734 | ||||||||
\(301\) | 2.86753e11 | 0.00668947 | ||||||||
\(302\) | 1.97867e13 | 0.453248 | ||||||||
\(303\) | −2.05992e13 | −0.463358 | ||||||||
\(304\) | −1.05243e13 | −0.232481 | ||||||||
\(305\) | −3.35998e13 | −0.728933 | ||||||||
\(306\) | −1.88355e13 | −0.401336 | ||||||||
\(307\) | −1.53111e13 | −0.320439 | −0.160219 | − | 0.987081i | \(-0.551220\pi\) | ||||
−0.160219 | + | 0.987081i | \(0.551220\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.68903e13 | −1.14886 | ||||||||
\(310\) | −6.12558e12 | −0.121523 | ||||||||
\(311\) | 4.98752e13 | 0.972080 | 0.486040 | − | 0.873936i | \(-0.338441\pi\) | ||||
0.486040 | + | 0.873936i | \(0.338441\pi\) | |||||||
\(312\) | −1.22994e13 | −0.235524 | ||||||||
\(313\) | −9.94808e13 | −1.87174 | −0.935870 | − | 0.352345i | \(-0.885384\pi\) | ||||
−0.935870 | + | 0.352345i | \(0.885384\pi\) | |||||||
\(314\) | 3.15628e13 | 0.583529 | ||||||||
\(315\) | −9.19071e12 | −0.166971 | ||||||||
\(316\) | 5.61080e13 | 1.00172 | ||||||||
\(317\) | 8.33692e13 | 1.46278 | 0.731392 | − | 0.681958i | \(-0.238871\pi\) | ||||
0.731392 | + | 0.681958i | \(0.238871\pi\) | |||||||
\(318\) | −9.65294e12 | −0.166460 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.30376e13 | 0.217207 | ||||||||
\(321\) | −2.27408e13 | −0.372416 | ||||||||
\(322\) | 7.49191e12 | 0.120611 | ||||||||
\(323\) | −7.36271e13 | −1.16526 | ||||||||
\(324\) | −2.45116e12 | −0.0381394 | ||||||||
\(325\) | −1.47319e13 | −0.225372 | ||||||||
\(326\) | −8.58799e12 | −0.129180 | ||||||||
\(327\) | −1.85176e13 | −0.273888 | ||||||||
\(328\) | 2.60300e13 | 0.378589 | ||||||||
\(329\) | 4.49970e13 | 0.643585 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.35840e13 | −0.879618 | −0.439809 | − | 0.898091i | \(-0.644954\pi\) | ||||
−0.439809 | + | 0.898091i | \(0.644954\pi\) | |||||||
\(332\) | −4.31813e13 | −0.587538 | ||||||||
\(333\) | 2.07073e13 | 0.277127 | ||||||||
\(334\) | −6.61160e13 | −0.870364 | ||||||||
\(335\) | −7.47772e13 | −0.968329 | ||||||||
\(336\) | 4.16521e12 | 0.0530604 | ||||||||
\(337\) | −1.21001e14 | −1.51644 | −0.758221 | − | 0.651997i | \(-0.773931\pi\) | ||||
−0.758221 | + | 0.651997i | \(0.773931\pi\) | |||||||
\(338\) | −3.50011e13 | −0.431559 | ||||||||
\(339\) | −2.14570e13 | −0.260298 | ||||||||
\(340\) | −4.90995e13 | −0.586062 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.90783e13 | 0.336067 | ||||||||
\(343\) | −6.15223e13 | −0.699705 | ||||||||
\(344\) | −1.44678e12 | −0.0161931 | ||||||||
\(345\) | 2.26918e13 | 0.249957 | ||||||||
\(346\) | 2.28093e13 | 0.247283 | ||||||||
\(347\) | 1.55662e14 | 1.66100 | 0.830499 | − | 0.557020i | \(-0.188055\pi\) | ||||
0.830499 | + | 0.557020i | \(0.188055\pi\) | |||||||
\(348\) | 4.76317e13 | 0.500276 | ||||||||
\(349\) | 2.56430e13 | 0.265112 | 0.132556 | − | 0.991176i | \(-0.457682\pi\) | ||||
0.132556 | + | 0.991176i | \(0.457682\pi\) | |||||||
\(350\) | −1.02470e13 | −0.104285 | ||||||||
\(351\) | −4.23361e13 | −0.424152 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.49098e13 | 0.241885 | 0.120943 | − | 0.992659i | \(-0.461408\pi\) | ||||
0.120943 | + | 0.992659i | \(0.461408\pi\) | |||||||
\(354\) | −3.13843e13 | −0.300051 | ||||||||
\(355\) | 4.72929e13 | 0.445184 | ||||||||
\(356\) | 3.67896e13 | 0.340996 | ||||||||
\(357\) | 2.91395e13 | 0.265954 | ||||||||
\(358\) | 4.03532e13 | 0.362678 | ||||||||
\(359\) | −1.57584e14 | −1.39474 | −0.697370 | − | 0.716712i | \(-0.745646\pi\) | ||||
−0.697370 | + | 0.716712i | \(0.745646\pi\) | |||||||
\(360\) | 4.63707e13 | 0.404185 | ||||||||
\(361\) | −2.82438e12 | −0.0242457 | ||||||||
\(362\) | −2.39226e13 | −0.202260 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.42396e13 | −0.116799 | ||||||||
\(365\) | −7.07011e12 | −0.0571236 | ||||||||
\(366\) | −4.20728e13 | −0.334854 | ||||||||
\(367\) | −1.77901e14 | −1.39481 | −0.697406 | − | 0.716676i | \(-0.745662\pi\) | ||||
−0.697406 | + | 0.716676i | \(0.745662\pi\) | |||||||
\(368\) | 1.84034e13 | 0.142146 | ||||||||
\(369\) | 3.50157e13 | 0.266452 | ||||||||
\(370\) | −2.11222e13 | −0.158354 | ||||||||
\(371\) | −2.67244e13 | −0.197402 | ||||||||
\(372\) | 1.96019e13 | 0.142663 | ||||||||
\(373\) | 5.51617e13 | 0.395585 | 0.197792 | − | 0.980244i | \(-0.436623\pi\) | ||||
0.197792 | + | 0.980244i | \(0.436623\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.04683e13 | −0.629976 | ||||||||
\(376\) | −2.27027e14 | −1.55792 | ||||||||
\(377\) | −7.41854e13 | −0.501696 | ||||||||
\(378\) | −2.94476e13 | −0.196266 | ||||||||
\(379\) | 1.46463e14 | 0.962083 | 0.481042 | − | 0.876698i | \(-0.340259\pi\) | ||||
0.481042 | + | 0.876698i | \(0.340259\pi\) | |||||||
\(380\) | 7.58001e13 | 0.490750 | ||||||||
\(381\) | 6.62047e13 | 0.422476 | ||||||||
\(382\) | 6.62977e13 | 0.417013 | ||||||||
\(383\) | 2.31450e14 | 1.43504 | 0.717519 | − | 0.696539i | \(-0.245278\pi\) | ||||
0.717519 | + | 0.696539i | \(0.245278\pi\) | |||||||
\(384\) | −8.51940e13 | −0.520700 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.30617e14 | −0.775837 | ||||||||
\(387\) | −1.94622e12 | −0.0113967 | ||||||||
\(388\) | −1.10420e14 | −0.637490 | ||||||||
\(389\) | −1.49872e14 | −0.853093 | −0.426547 | − | 0.904466i | \(-0.640270\pi\) | ||||
−0.426547 | + | 0.904466i | \(0.640270\pi\) | |||||||
\(390\) | 1.68768e13 | 0.0947184 | ||||||||
\(391\) | 1.28749e14 | 0.712480 | ||||||||
\(392\) | 1.43360e14 | 0.782264 | ||||||||
\(393\) | −1.59145e14 | −0.856317 | ||||||||
\(394\) | 6.90262e13 | 0.366256 | ||||||||
\(395\) | −1.84104e14 | −0.963341 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.08111e14 | 1.05912 | 0.529562 | − | 0.848271i | \(-0.322356\pi\) | ||||
0.529562 | + | 0.848271i | \(0.322356\pi\) | |||||||
\(398\) | 1.74814e13 | 0.0877443 | ||||||||
\(399\) | −4.49857e13 | −0.222702 | ||||||||
\(400\) | −2.51712e13 | −0.122906 | ||||||||
\(401\) | −1.33408e14 | −0.642521 | −0.321261 | − | 0.946991i | \(-0.604107\pi\) | ||||
−0.321261 | + | 0.946991i | \(0.604107\pi\) | |||||||
\(402\) | −9.36341e13 | −0.444827 | ||||||||
\(403\) | −3.05295e13 | −0.143068 | ||||||||
\(404\) | 1.20326e14 | 0.556238 | ||||||||
\(405\) | 8.04286e12 | 0.0366782 | ||||||||
\(406\) | −5.16010e13 | −0.232148 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.47020e14 | −0.643793 | ||||||||
\(409\) | 2.06168e14 | 0.890722 | 0.445361 | − | 0.895351i | \(-0.353075\pi\) | ||||
0.445361 | + | 0.895351i | \(0.353075\pi\) | |||||||
\(410\) | −3.57173e13 | −0.152254 | ||||||||
\(411\) | −7.48941e13 | −0.315005 | ||||||||
\(412\) | 3.32312e14 | 1.37915 | ||||||||
\(413\) | −8.68880e13 | −0.355824 | ||||||||
\(414\) | −5.08483e13 | −0.205482 | ||||||||
\(415\) | 1.41689e14 | 0.565028 | ||||||||
\(416\) | 1.13645e14 | 0.447235 | ||||||||
\(417\) | −1.50392e14 | −0.584085 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.34035e13 | 0.277677 | 0.138838 | − | 0.990315i | \(-0.455663\pi\) | ||||
0.138838 | + | 0.990315i | \(0.455663\pi\) | |||||||
\(420\) | −2.99995e13 | −0.112007 | ||||||||
\(421\) | 1.71112e14 | 0.630563 | 0.315282 | − | 0.948998i | \(-0.397901\pi\) | ||||
0.315282 | + | 0.948998i | \(0.397901\pi\) | |||||||
\(422\) | 1.63036e14 | 0.593014 | ||||||||
\(423\) | −3.05398e14 | −1.09646 | ||||||||
\(424\) | 1.34835e14 | 0.477848 | ||||||||
\(425\) | −1.76096e14 | −0.616042 | ||||||||
\(426\) | 5.92189e13 | 0.204507 | ||||||||
\(427\) | −1.16479e14 | −0.397096 | ||||||||
\(428\) | 1.32835e14 | 0.447067 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.98521e12 | 0.00651224 | ||||||||
\(431\) | 7.17758e13 | 0.232463 | 0.116231 | − | 0.993222i | \(-0.462919\pi\) | ||||
0.116231 | + | 0.993222i | \(0.462919\pi\) | |||||||
\(432\) | −7.23364e13 | −0.231311 | ||||||||
\(433\) | 9.98812e13 | 0.315356 | 0.157678 | − | 0.987491i | \(-0.449599\pi\) | ||||
0.157678 | + | 0.987491i | \(0.449599\pi\) | |||||||
\(434\) | −2.12353e13 | −0.0662012 | ||||||||
\(435\) | −1.56291e14 | −0.481110 | ||||||||
\(436\) | 1.08166e14 | 0.328789 | ||||||||
\(437\) | −1.98764e14 | −0.596608 | ||||||||
\(438\) | −8.85301e12 | −0.0262412 | ||||||||
\(439\) | 2.90312e13 | 0.0849788 | 0.0424894 | − | 0.999097i | \(-0.486471\pi\) | ||||
0.0424894 | + | 0.999097i | \(0.486471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.92848e14 | 0.550558 | ||||||||
\(442\) | 9.57557e13 | 0.269987 | ||||||||
\(443\) | 3.28370e14 | 0.914414 | 0.457207 | − | 0.889360i | \(-0.348850\pi\) | ||||
0.457207 | + | 0.889360i | \(0.348850\pi\) | |||||||
\(444\) | 6.75909e13 | 0.185901 | ||||||||
\(445\) | −1.20716e14 | −0.327932 | ||||||||
\(446\) | 1.76037e14 | 0.472347 | ||||||||
\(447\) | 2.81089e14 | 0.744994 | ||||||||
\(448\) | 4.51970e13 | 0.118326 | ||||||||
\(449\) | −6.12368e14 | −1.58364 | −0.791822 | − | 0.610752i | \(-0.790867\pi\) | ||||
−0.791822 | + | 0.610752i | \(0.790867\pi\) | |||||||
\(450\) | 6.95474e13 | 0.177669 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.25336e14 | 0.312475 | ||||||||
\(453\) | 2.07761e14 | 0.511709 | ||||||||
\(454\) | 3.26361e13 | 0.0794130 | ||||||||
\(455\) | 4.67237e13 | 0.112325 | ||||||||
\(456\) | 2.26971e14 | 0.539092 | ||||||||
\(457\) | −3.03483e14 | −0.712189 | −0.356095 | − | 0.934450i | \(-0.615892\pi\) | ||||
−0.356095 | + | 0.934450i | \(0.615892\pi\) | |||||||
\(458\) | −2.83786e14 | −0.658007 | ||||||||
\(459\) | −5.06060e14 | −1.15940 | ||||||||
\(460\) | −1.32549e14 | −0.300061 | ||||||||
\(461\) | 7.29308e14 | 1.63138 | 0.815691 | − | 0.578487i | \(-0.196357\pi\) | ||||
0.815691 | + | 0.578487i | \(0.196357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.22188e14 | 0.266891 | 0.133445 | − | 0.991056i | \(-0.457396\pi\) | ||||
0.133445 | + | 0.991056i | \(0.457396\pi\) | |||||||
\(464\) | −1.26755e14 | −0.273600 | ||||||||
\(465\) | −6.43186e13 | −0.137197 | ||||||||
\(466\) | 4.21520e14 | 0.888579 | ||||||||
\(467\) | −6.17381e14 | −1.28621 | −0.643103 | − | 0.765780i | \(-0.722353\pi\) | ||||
−0.643103 | + | 0.765780i | \(0.722353\pi\) | |||||||
\(468\) | 9.66455e13 | 0.198989 | ||||||||
\(469\) | −2.59228e14 | −0.527510 | ||||||||
\(470\) | 3.11517e14 | 0.626533 | ||||||||
\(471\) | 3.31409e14 | 0.658794 | ||||||||
\(472\) | 4.38384e14 | 0.861338 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.30531e14 | −0.442535 | ||||||||
\(475\) | 2.71858e14 | 0.515854 | ||||||||
\(476\) | −1.70212e14 | −0.319265 | ||||||||
\(477\) | 1.81381e14 | 0.336310 | ||||||||
\(478\) | 1.71350e14 | 0.314073 | ||||||||
\(479\) | −1.05084e15 | −1.90410 | −0.952052 | − | 0.305938i | \(-0.901030\pi\) | ||||
−0.952052 | + | 0.305938i | \(0.901030\pi\) | |||||||
\(480\) | 2.39423e14 | 0.428883 | ||||||||
\(481\) | −1.05272e14 | −0.186429 | ||||||||
\(482\) | 5.55137e12 | 0.00971944 | ||||||||
\(483\) | 7.86651e13 | 0.136167 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.62316e14 | 0.613066 | ||||||||
\(486\) | 3.21619e14 | 0.538074 | ||||||||
\(487\) | −2.19910e14 | −0.363777 | −0.181889 | − | 0.983319i | \(-0.558221\pi\) | ||||
−0.181889 | + | 0.983319i | \(0.558221\pi\) | |||||||
\(488\) | 5.87683e14 | 0.961246 | ||||||||
\(489\) | −9.01739e13 | −0.145842 | ||||||||
\(490\) | −1.96712e14 | −0.314596 | ||||||||
\(491\) | 4.83863e14 | 0.765199 | 0.382599 | − | 0.923914i | \(-0.375029\pi\) | ||||
0.382599 | + | 0.923914i | \(0.375029\pi\) | |||||||
\(492\) | 1.14295e14 | 0.178740 | ||||||||
\(493\) | −8.86768e14 | −1.37136 | ||||||||
\(494\) | −1.47828e14 | −0.226078 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.21634e13 | −0.0780219 | ||||||||
\(497\) | 1.63949e14 | 0.242520 | ||||||||
\(498\) | 1.77419e14 | 0.259560 | ||||||||
\(499\) | −1.08878e14 | −0.157538 | −0.0787691 | − | 0.996893i | \(-0.525099\pi\) | ||||
−0.0787691 | + | 0.996893i | \(0.525099\pi\) | |||||||
\(500\) | 5.28450e14 | 0.756256 | ||||||||
\(501\) | −6.94218e14 | −0.982626 | ||||||||
\(502\) | 3.11593e14 | 0.436232 | ||||||||
\(503\) | −5.06588e14 | −0.701506 | −0.350753 | − | 0.936468i | \(-0.614074\pi\) | ||||
−0.350753 | + | 0.936468i | \(0.614074\pi\) | |||||||
\(504\) | 1.60752e14 | 0.220185 | ||||||||
\(505\) | −3.94818e14 | −0.534927 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.67512e14 | −0.487222 | ||||||||
\(508\) | −3.86720e14 | −0.507161 | ||||||||
\(509\) | 8.57534e13 | 0.111251 | 0.0556254 | − | 0.998452i | \(-0.482285\pi\) | ||||
0.0556254 | + | 0.998452i | \(0.482285\pi\) | |||||||
\(510\) | 2.01735e14 | 0.258908 | ||||||||
\(511\) | −2.45097e13 | −0.0311188 | ||||||||
\(512\) | 3.64965e14 | 0.458423 | ||||||||
\(513\) | 7.81259e14 | 0.970844 | ||||||||
\(514\) | 5.75069e14 | 0.707005 | ||||||||
\(515\) | −1.09040e15 | −1.32631 | ||||||||
\(516\) | −6.35268e12 | −0.00764511 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −7.32235e13 | −0.0862654 | ||||||||
\(519\) | 2.39498e14 | 0.279178 | ||||||||
\(520\) | −2.35739e14 | −0.271903 | ||||||||
\(521\) | 9.27575e14 | 1.05862 | 0.529312 | − | 0.848428i | \(-0.322450\pi\) | ||||
0.529312 | + | 0.848428i | \(0.322450\pi\) | |||||||
\(522\) | 3.50220e14 | 0.395506 | ||||||||
\(523\) | 2.18187e13 | 0.0243820 | 0.0121910 | − | 0.999926i | \(-0.496119\pi\) | ||||
0.0121910 | + | 0.999926i | \(0.496119\pi\) | |||||||
\(524\) | 9.29610e14 | 1.02797 | ||||||||
\(525\) | −1.07594e14 | −0.117736 | ||||||||
\(526\) | 5.82569e14 | 0.630850 | ||||||||
\(527\) | −3.64931e14 | −0.391069 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.05238e14 | −0.635214 | ||||||||
\(530\) | −1.85015e14 | −0.192172 | ||||||||
\(531\) | 5.89717e14 | 0.606211 | ||||||||
\(532\) | 2.62774e14 | 0.267343 | ||||||||
\(533\) | −1.78013e14 | −0.179247 | ||||||||
\(534\) | −1.51157e14 | −0.150644 | ||||||||
\(535\) | −4.35865e14 | −0.429939 | ||||||||
\(536\) | 1.30790e15 | 1.27694 | ||||||||
\(537\) | 4.23709e14 | 0.409458 | ||||||||
\(538\) | 6.20105e14 | 0.593147 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.20997e14 | 0.488280 | ||||||||
\(541\) | 1.69527e15 | 1.57273 | 0.786363 | − | 0.617765i | \(-0.211962\pi\) | ||||
0.786363 | + | 0.617765i | \(0.211962\pi\) | |||||||
\(542\) | 9.04304e13 | 0.0830459 | ||||||||
\(543\) | −2.51187e14 | −0.228349 | ||||||||
\(544\) | 1.35844e15 | 1.22249 | ||||||||
\(545\) | −3.54921e14 | −0.316192 | ||||||||
\(546\) | 5.85062e13 | 0.0515991 | ||||||||
\(547\) | −7.52145e14 | −0.656706 | −0.328353 | − | 0.944555i | \(-0.606494\pi\) | ||||
−0.328353 | + | 0.944555i | \(0.606494\pi\) | |||||||
\(548\) | 4.37477e14 | 0.378148 | ||||||||
\(549\) | 7.90555e14 | 0.676526 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.36900e15 | 1.14834 | ||||||||
\(552\) | −3.96896e14 | −0.329619 | ||||||||
\(553\) | −6.38228e14 | −0.524793 | ||||||||
\(554\) | 3.94054e14 | 0.320813 | ||||||||
\(555\) | −2.21783e14 | −0.178779 | ||||||||
\(556\) | 8.78480e14 | 0.701166 | ||||||||
\(557\) | −1.87489e14 | −0.148174 | −0.0740870 | − | 0.997252i | \(-0.523604\pi\) | ||||
−0.0740870 | + | 0.997252i | \(0.523604\pi\) | |||||||
\(558\) | 1.44126e14 | 0.112786 | ||||||||
\(559\) | 9.89417e12 | 0.00766681 | ||||||||
\(560\) | 7.98332e13 | 0.0612561 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.04857e14 | −0.379856 | ||||||||
\(563\) | −2.44971e14 | −0.182524 | −0.0912618 | − | 0.995827i | \(-0.529090\pi\) | ||||
−0.0912618 | + | 0.995827i | \(0.529090\pi\) | |||||||
\(564\) | −9.96856e14 | −0.735525 | ||||||||
\(565\) | −4.11259e14 | −0.300503 | ||||||||
\(566\) | −4.01116e14 | −0.290255 | ||||||||
\(567\) | 2.78819e13 | 0.0199809 | ||||||||
\(568\) | −8.27185e14 | −0.587066 | ||||||||
\(569\) | −1.35243e15 | −0.950596 | −0.475298 | − | 0.879825i | \(-0.657660\pi\) | ||||
−0.475298 | + | 0.879825i | \(0.657660\pi\) | |||||||
\(570\) | −3.11440e14 | −0.216801 | ||||||||
\(571\) | −1.43223e15 | −0.987447 | −0.493723 | − | 0.869619i | \(-0.664364\pi\) | ||||
−0.493723 | + | 0.869619i | \(0.664364\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.96126e14 | 0.470801 | ||||||||
\(574\) | −1.23820e14 | −0.0829422 | ||||||||
\(575\) | −4.75389e14 | −0.315410 | ||||||||
\(576\) | −3.06756e14 | −0.201590 | ||||||||
\(577\) | −8.77659e14 | −0.571293 | −0.285647 | − | 0.958335i | \(-0.592208\pi\) | ||||
−0.285647 | + | 0.958335i | \(0.592208\pi\) | |||||||
\(578\) | 3.22081e14 | 0.207664 | ||||||||
\(579\) | −1.37148e15 | −0.875907 | ||||||||
\(580\) | 9.12940e14 | 0.577548 | ||||||||
\(581\) | 4.91187e14 | 0.307807 | ||||||||
\(582\) | 4.53682e14 | 0.281628 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.23661e14 | 0.0753290 | ||||||||
\(585\) | −3.17118e14 | −0.191365 | ||||||||
\(586\) | 5.74245e14 | 0.343289 | ||||||||
\(587\) | −2.43425e15 | −1.44164 | −0.720818 | − | 0.693124i | \(-0.756234\pi\) | ||||
−0.720818 | + | 0.693124i | \(0.756234\pi\) | |||||||
\(588\) | 6.29479e14 | 0.369323 | ||||||||
\(589\) | 5.63383e14 | 0.327469 | ||||||||
\(590\) | −6.01532e14 | −0.346396 | ||||||||
\(591\) | 7.24775e14 | 0.413497 | ||||||||
\(592\) | −1.79869e14 | −0.101669 | ||||||||
\(593\) | 3.03318e14 | 0.169863 | 0.0849313 | − | 0.996387i | \(-0.472933\pi\) | ||||
0.0849313 | + | 0.996387i | \(0.472933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.58507e14 | 0.307033 | ||||||||
\(596\) | −1.64192e15 | −0.894329 | ||||||||
\(597\) | 1.83555e14 | 0.0990619 | ||||||||
\(598\) | 2.58502e14 | 0.138232 | ||||||||
\(599\) | −1.70198e15 | −0.901795 | −0.450898 | − | 0.892576i | \(-0.648896\pi\) | ||||
−0.450898 | + | 0.892576i | \(0.648896\pi\) | |||||||
\(600\) | 5.42852e14 | 0.285003 | ||||||||
\(601\) | −2.33922e15 | −1.21692 | −0.608458 | − | 0.793586i | \(-0.708212\pi\) | ||||
−0.608458 | + | 0.793586i | \(0.708212\pi\) | |||||||
\(602\) | 6.88207e12 | 0.00354763 | ||||||||
\(603\) | 1.75940e15 | 0.898710 | ||||||||
\(604\) | −1.21359e15 | −0.614282 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.94381e14 | −0.245733 | ||||||||
\(607\) | 2.49607e15 | 1.22947 | 0.614737 | − | 0.788732i | \(-0.289262\pi\) | ||||
0.614737 | + | 0.788732i | \(0.289262\pi\) | |||||||
\(608\) | −2.09717e15 | −1.02368 | ||||||||
\(609\) | −5.41810e14 | −0.262091 | ||||||||
\(610\) | −8.06395e14 | −0.386575 | ||||||||
\(611\) | 1.55258e15 | 0.737612 | ||||||||
\(612\) | 1.15524e15 | 0.543926 | ||||||||
\(613\) | −2.47301e15 | −1.15397 | −0.576983 | − | 0.816756i | \(-0.695770\pi\) | ||||
−0.576983 | + | 0.816756i | \(0.695770\pi\) | |||||||
\(614\) | −3.67466e14 | −0.169938 | ||||||||
\(615\) | −3.75032e14 | −0.171892 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.43368e13 | 0.0109571 | 0.00547854 | − | 0.999985i | \(-0.498256\pi\) | ||||
0.00547854 | + | 0.999985i | \(0.498256\pi\) | |||||||
\(618\) | −1.36537e15 | −0.609274 | ||||||||
\(619\) | 4.22545e15 | 1.86885 | 0.934425 | − | 0.356160i | \(-0.115914\pi\) | ||||
0.934425 | + | 0.356160i | \(0.115914\pi\) | |||||||
\(620\) | 3.75702e14 | 0.164698 | ||||||||
\(621\) | −1.36616e15 | −0.593606 | ||||||||
\(622\) | 1.19700e15 | 0.515523 | ||||||||
\(623\) | −4.18481e14 | −0.178645 | ||||||||
\(624\) | 1.43717e14 | 0.0608126 | ||||||||
\(625\) | −4.88896e14 | −0.205058 | ||||||||
\(626\) | −2.38754e15 | −0.992640 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.93585e15 | −0.790850 | ||||||||
\(629\) | −1.25835e15 | −0.509594 | ||||||||
\(630\) | −2.20577e14 | −0.0885497 | ||||||||
\(631\) | −4.26326e15 | −1.69660 | −0.848302 | − | 0.529513i | \(-0.822375\pi\) | ||||
−0.848302 | + | 0.529513i | \(0.822375\pi\) | |||||||
\(632\) | 3.22011e15 | 1.27036 | ||||||||
\(633\) | 1.71188e15 | 0.669503 | ||||||||
\(634\) | 2.00086e15 | 0.775758 | ||||||||
\(635\) | 1.26892e15 | 0.487731 | ||||||||
\(636\) | 5.92047e14 | 0.225602 | ||||||||
\(637\) | −9.80401e14 | −0.370371 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.11273e15 | −0.413177 | ||||||||
\(640\) | −1.63288e15 | −0.601126 | ||||||||
\(641\) | 1.00830e15 | 0.368018 | 0.184009 | − | 0.982925i | \(-0.441092\pi\) | ||||
0.184009 | + | 0.982925i | \(0.441092\pi\) | |||||||
\(642\) | −5.45779e14 | −0.197503 | ||||||||
\(643\) | 3.03982e14 | 0.109066 | 0.0545328 | − | 0.998512i | \(-0.482633\pi\) | ||||
0.0545328 | + | 0.998512i | \(0.482633\pi\) | |||||||
\(644\) | −4.59504e14 | −0.163462 | ||||||||
\(645\) | 2.08447e13 | 0.00735221 | ||||||||
\(646\) | −1.76705e15 | −0.617974 | ||||||||
\(647\) | 3.43583e15 | 1.19140 | 0.595700 | − | 0.803207i | \(-0.296875\pi\) | ||||
0.595700 | + | 0.803207i | \(0.296875\pi\) | |||||||
\(648\) | −1.40675e14 | −0.0483676 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.53565e14 | −0.119521 | ||||||||
\(651\) | −2.22971e14 | −0.0747400 | ||||||||
\(652\) | 5.26730e14 | 0.175076 | ||||||||
\(653\) | −1.18539e15 | −0.390695 | −0.195347 | − | 0.980734i | \(-0.562583\pi\) | ||||
−0.195347 | + | 0.980734i | \(0.562583\pi\) | |||||||
\(654\) | −4.44423e14 | −0.145251 | ||||||||
\(655\) | −3.05028e15 | −0.988583 | ||||||||
\(656\) | −3.04157e14 | −0.0977522 | ||||||||
\(657\) | 1.66350e14 | 0.0530167 | ||||||||
\(658\) | 1.07993e15 | 0.341312 | ||||||||
\(659\) | 2.26510e15 | 0.709934 | 0.354967 | − | 0.934879i | \(-0.384492\pi\) | ||||
0.354967 | + | 0.934879i | \(0.384492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.33012e15 | −1.64297 | −0.821484 | − | 0.570232i | \(-0.806853\pi\) | ||||
−0.821484 | + | 0.570232i | \(0.806853\pi\) | |||||||
\(662\) | −1.52602e15 | −0.466488 | ||||||||
\(663\) | 1.00543e15 | 0.304810 | ||||||||
\(664\) | −2.47823e15 | −0.745104 | ||||||||
\(665\) | −8.62227e14 | −0.257100 | ||||||||
\(666\) | 4.96974e14 | 0.146969 | ||||||||
\(667\) | −2.39392e15 | −0.702130 | ||||||||
\(668\) | 4.05512e15 | 1.17959 | ||||||||
\(669\) | 1.84839e15 | 0.533272 | ||||||||
\(670\) | −1.79465e15 | −0.513534 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 8.30000e14 | 0.233640 | ||||||||
\(673\) | −4.74120e15 | −1.32375 | −0.661874 | − | 0.749615i | \(-0.730239\pi\) | ||||
−0.661874 | + | 0.749615i | \(0.730239\pi\) | |||||||
\(674\) | −2.90403e15 | −0.804215 | ||||||||
\(675\) | 1.86856e15 | 0.513259 | ||||||||
\(676\) | 2.14673e15 | 0.584886 | ||||||||
\(677\) | 1.41307e15 | 0.381880 | 0.190940 | − | 0.981602i | \(-0.438846\pi\) | ||||
0.190940 | + | 0.981602i | \(0.438846\pi\) | |||||||
\(678\) | −5.14968e14 | −0.138044 | ||||||||
\(679\) | 1.25603e15 | 0.333976 | ||||||||
\(680\) | −2.81789e15 | −0.743232 | ||||||||
\(681\) | 3.42680e14 | 0.0896559 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.03116e15 | −0.780359 | −0.390180 | − | 0.920739i | \(-0.627587\pi\) | ||||
−0.390180 | + | 0.920739i | \(0.627587\pi\) | |||||||
\(684\) | −1.78347e15 | −0.455467 | ||||||||
\(685\) | −1.43547e15 | −0.363660 | ||||||||
\(686\) | −1.47654e15 | −0.371075 | ||||||||
\(687\) | −2.97975e15 | −0.742879 | ||||||||
\(688\) | 1.69054e13 | 0.00418109 | ||||||||
\(689\) | −9.22102e14 | −0.226242 | ||||||||
\(690\) | 5.44604e14 | 0.132560 | ||||||||
\(691\) | −2.74731e15 | −0.663405 | −0.331703 | − | 0.943384i | \(-0.607623\pi\) | ||||
−0.331703 | + | 0.943384i | \(0.607623\pi\) | |||||||
\(692\) | −1.39897e15 | −0.335139 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.73588e15 | 0.880878 | ||||||||
\(695\) | −2.88251e15 | −0.674303 | ||||||||
\(696\) | 2.73364e15 | 0.634441 | ||||||||
\(697\) | −2.12786e15 | −0.489962 | ||||||||
\(698\) | 6.15433e14 | 0.140597 | ||||||||
\(699\) | 4.42597e15 | 1.00319 | ||||||||
\(700\) | 6.28484e14 | 0.141337 | ||||||||
\(701\) | −5.72747e15 | −1.27795 | −0.638974 | − | 0.769228i | \(-0.720641\pi\) | ||||
−0.638974 | + | 0.769228i | \(0.720641\pi\) | |||||||
\(702\) | −1.01607e15 | −0.224941 | ||||||||
\(703\) | 1.94265e15 | 0.426718 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.27093e15 | 0.707345 | ||||||||
\(706\) | 5.97836e14 | 0.128279 | ||||||||
\(707\) | −1.36870e15 | −0.291409 | ||||||||
\(708\) | 1.92490e15 | 0.406655 | ||||||||
\(709\) | 6.98326e14 | 0.146388 | 0.0731938 | − | 0.997318i | \(-0.476681\pi\) | ||||
0.0731938 | + | 0.997318i | \(0.476681\pi\) | |||||||
\(710\) | 1.13503e15 | 0.236095 | ||||||||
\(711\) | 4.33171e15 | 0.894081 | ||||||||
\(712\) | 2.11140e15 | 0.432445 | ||||||||
\(713\) | −9.85170e14 | −0.200225 | ||||||||
\(714\) | 6.99348e14 | 0.141044 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.47500e15 | −0.491534 | ||||||||
\(717\) | 1.79917e15 | 0.354583 | ||||||||
\(718\) | −3.78202e15 | −0.739672 | ||||||||
\(719\) | 9.70979e15 | 1.88452 | 0.942260 | − | 0.334882i | \(-0.108696\pi\) | ||||
0.942260 | + | 0.334882i | \(0.108696\pi\) | |||||||
\(720\) | −5.41835e14 | −0.104361 | ||||||||
\(721\) | −3.78004e15 | −0.722525 | ||||||||
\(722\) | −6.77852e13 | −0.0128582 | ||||||||
\(723\) | 5.82893e13 | 0.0109731 | ||||||||
\(724\) | 1.46725e15 | 0.274121 | ||||||||
\(725\) | 3.27427e15 | 0.607093 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.46469e15 | 0.450114 | 0.225057 | − | 0.974346i | \(-0.427743\pi\) | ||||
0.225057 | + | 0.974346i | \(0.427743\pi\) | |||||||
\(728\) | −8.17230e14 | −0.148123 | ||||||||
\(729\) | 3.08202e15 | 0.554413 | ||||||||
\(730\) | −1.69683e14 | −0.0302944 | ||||||||
\(731\) | 1.18269e14 | 0.0209568 | ||||||||
\(732\) | 2.58046e15 | 0.453823 | ||||||||
\(733\) | −7.91285e15 | −1.38121 | −0.690607 | − | 0.723230i | \(-0.742657\pi\) | ||||
−0.690607 | + | 0.723230i | \(0.742657\pi\) | |||||||
\(734\) | −4.26963e15 | −0.739711 | ||||||||
\(735\) | −2.06548e15 | −0.355173 | ||||||||
\(736\) | 3.66725e15 | 0.625911 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 8.40378e14 | 0.141307 | ||||||||
\(739\) | 8.40694e15 | 1.40312 | 0.701558 | − | 0.712613i | \(-0.252488\pi\) | ||||
0.701558 | + | 0.712613i | \(0.252488\pi\) | |||||||
\(740\) | 1.29549e15 | 0.214615 | ||||||||
\(741\) | −1.55220e15 | −0.255239 | ||||||||
\(742\) | −6.41385e14 | −0.104688 | ||||||||
\(743\) | −1.36287e15 | −0.220809 | −0.110404 | − | 0.993887i | \(-0.535215\pi\) | ||||
−0.110404 | + | 0.993887i | \(0.535215\pi\) | |||||||
\(744\) | 1.12498e15 | 0.180922 | ||||||||
\(745\) | 5.38754e15 | 0.860065 | ||||||||
\(746\) | 1.32388e15 | 0.209790 | ||||||||
\(747\) | −3.33373e15 | −0.524405 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.51100e15 | −0.234215 | ||||||||
\(750\) | −2.17124e15 | −0.334095 | ||||||||
\(751\) | 6.81722e15 | 1.04133 | 0.520664 | − | 0.853762i | \(-0.325684\pi\) | ||||
0.520664 | + | 0.853762i | \(0.325684\pi\) | |||||||
\(752\) | 2.65278e15 | 0.402256 | ||||||||
\(753\) | 3.27173e15 | 0.492499 | ||||||||
\(754\) | −1.78045e15 | −0.266065 | ||||||||
\(755\) | 3.98208e15 | 0.590747 | ||||||||
\(756\) | 1.80612e15 | 0.265997 | ||||||||
\(757\) | −6.67049e14 | −0.0975282 | −0.0487641 | − | 0.998810i | \(-0.515528\pi\) | ||||
−0.0487641 | + | 0.998810i | \(0.515528\pi\) | |||||||
\(758\) | 3.51511e15 | 0.510222 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.35027e15 | 0.622360 | ||||||||
\(761\) | 7.74408e15 | 1.09990 | 0.549951 | − | 0.835197i | \(-0.314646\pi\) | ||||
0.549951 | + | 0.835197i | \(0.314646\pi\) | |||||||
\(762\) | 1.58891e15 | 0.224052 | ||||||||
\(763\) | −1.23039e15 | −0.172250 | ||||||||
\(764\) | −4.06626e15 | −0.565173 | ||||||||
\(765\) | −3.79064e15 | −0.523088 | ||||||||
\(766\) | 5.55479e15 | 0.761043 | ||||||||
\(767\) | −2.99800e15 | −0.407809 | ||||||||
\(768\) | −3.43775e15 | −0.464288 | ||||||||
\(769\) | −2.52411e15 | −0.338465 | −0.169232 | − | 0.985576i | \(-0.554129\pi\) | ||||
−0.169232 | + | 0.985576i | \(0.554129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.03822e15 | 0.798197 | ||||||||
\(772\) | 8.01119e15 | 1.05148 | ||||||||
\(773\) | −1.11453e16 | −1.45246 | −0.726229 | − | 0.687453i | \(-0.758729\pi\) | ||||
−0.726229 | + | 0.687453i | \(0.758729\pi\) | |||||||
\(774\) | −4.67092e13 | −0.00604404 | ||||||||
\(775\) | 1.34746e15 | 0.173124 | ||||||||
\(776\) | −6.33715e15 | −0.808452 | ||||||||
\(777\) | −7.68847e14 | −0.0973922 | ||||||||
\(778\) | −3.59692e15 | −0.452421 | ||||||||
\(779\) | 3.28500e15 | 0.410279 | ||||||||
\(780\) | −1.03511e15 | −0.128371 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.08998e15 | 0.377849 | ||||||||
\(783\) | 9.40952e15 | 1.14256 | ||||||||
\(784\) | −1.67514e15 | −0.201981 | ||||||||
\(785\) | 6.35201e15 | 0.760551 | ||||||||
\(786\) | −3.81949e15 | −0.454131 | ||||||||
\(787\) | −1.32271e16 | −1.56172 | −0.780861 | − | 0.624705i | \(-0.785219\pi\) | ||||
−0.780861 | + | 0.624705i | \(0.785219\pi\) | |||||||
\(788\) | −4.23361e15 | −0.496382 | ||||||||
\(789\) | 6.11698e15 | 0.712219 | ||||||||
\(790\) | −4.41850e15 | −0.510889 | ||||||||
\(791\) | −1.42570e15 | −0.163703 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.01902e15 | −0.455112 | ||||||||
\(794\) | 4.99466e15 | 0.561685 | ||||||||
\(795\) | −1.94266e15 | −0.216958 | ||||||||
\(796\) | −1.07219e15 | −0.118919 | ||||||||
\(797\) | 2.30248e15 | 0.253615 | 0.126807 | − | 0.991927i | \(-0.459527\pi\) | ||||
0.126807 | + | 0.991927i | \(0.459527\pi\) | |||||||
\(798\) | −1.07966e15 | −0.118106 | ||||||||
\(799\) | 1.85587e16 | 2.01623 | ||||||||
\(800\) | −5.01586e15 | −0.541191 | ||||||||
\(801\) | 2.84027e15 | 0.304355 | ||||||||
\(802\) | −3.20179e15 | −0.340748 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.74289e15 | 0.602868 | ||||||||
\(805\) | 1.50775e15 | 0.157199 | ||||||||
\(806\) | −7.32708e14 | −0.0758732 | ||||||||
\(807\) | 6.51110e15 | 0.669653 | ||||||||
\(808\) | 6.90565e15 | 0.705410 | ||||||||
\(809\) | −5.60472e15 | −0.568639 | −0.284320 | − | 0.958730i | \(-0.591768\pi\) | ||||
−0.284320 | + | 0.958730i | \(0.591768\pi\) | |||||||
\(810\) | 1.93029e14 | 0.0194515 | ||||||||
\(811\) | 5.08516e15 | 0.508968 | 0.254484 | − | 0.967077i | \(-0.418094\pi\) | ||||
0.254484 | + | 0.967077i | \(0.418094\pi\) | |||||||
\(812\) | 3.16486e15 | 0.314627 | ||||||||
\(813\) | 9.49519e14 | 0.0937574 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.72833e15 | −0.168368 | ||||||||
\(816\) | 1.71791e15 | 0.166228 | ||||||||
\(817\) | −1.82584e14 | −0.0175486 | ||||||||
\(818\) | 4.94802e15 | 0.472377 | ||||||||
\(819\) | −1.09934e15 | −0.104249 | ||||||||
\(820\) | 2.19066e15 | 0.206348 | ||||||||
\(821\) | −2.79111e14 | −0.0261150 | −0.0130575 | − | 0.999915i | \(-0.504156\pi\) | ||||
−0.0130575 | + | 0.999915i | \(0.504156\pi\) | |||||||
\(822\) | −1.79746e15 | −0.167057 | ||||||||
\(823\) | −1.35265e16 | −1.24878 | −0.624391 | − | 0.781112i | \(-0.714653\pi\) | ||||
−0.624391 | + | 0.781112i | \(0.714653\pi\) | |||||||
\(824\) | 1.90718e16 | 1.74901 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.08531e15 | −0.188704 | ||||||||
\(827\) | −2.72544e14 | −0.0244994 | −0.0122497 | − | 0.999925i | \(-0.503899\pi\) | ||||
−0.0122497 | + | 0.999925i | \(0.503899\pi\) | |||||||
\(828\) | 3.11869e15 | 0.278488 | ||||||||
\(829\) | 1.80459e16 | 1.60077 | 0.800385 | − | 0.599486i | \(-0.204628\pi\) | ||||
0.800385 | + | 0.599486i | \(0.204628\pi\) | |||||||
\(830\) | 3.40052e15 | 0.299651 | ||||||||
\(831\) | 4.13757e15 | 0.362193 | ||||||||
\(832\) | 1.55949e15 | 0.135614 | ||||||||
\(833\) | −1.17191e16 | −1.01239 | ||||||||
\(834\) | −3.60941e15 | −0.309758 | ||||||||
\(835\) | −1.33058e16 | −1.13440 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.87230e15 | 0.325821 | ||||||||
\(838\) | 1.76168e15 | 0.147260 | ||||||||
\(839\) | −7.96183e15 | −0.661184 | −0.330592 | − | 0.943774i | \(-0.607248\pi\) | ||||
−0.330592 | + | 0.943774i | \(0.607248\pi\) | |||||||
\(840\) | −1.72171e15 | −0.142045 | ||||||||
\(841\) | 4.28775e15 | 0.351440 | ||||||||
\(842\) | 4.10669e15 | 0.334407 | ||||||||
\(843\) | −5.30100e15 | −0.428851 | ||||||||
\(844\) | −9.99954e15 | −0.803705 | ||||||||
\(845\) | −7.04397e15 | −0.562478 | ||||||||
\(846\) | −7.32956e15 | −0.581488 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.57552e15 | −0.123381 | ||||||||
\(849\) | −4.21172e15 | −0.327693 | ||||||||
\(850\) | −4.22630e15 | −0.326706 | ||||||||
\(851\) | −3.39705e15 | −0.260909 | ||||||||
\(852\) | −3.63209e15 | −0.277165 | ||||||||
\(853\) | 1.49826e16 | 1.13598 | 0.567988 | − | 0.823037i | \(-0.307722\pi\) | ||||
0.567988 | + | 0.823037i | \(0.307722\pi\) | |||||||
\(854\) | −2.79550e15 | −0.210592 | ||||||||
\(855\) | 5.85201e15 | 0.438017 | ||||||||
\(856\) | 7.62358e15 | 0.566961 | ||||||||
\(857\) | 2.22561e16 | 1.64458 | 0.822290 | − | 0.569068i | \(-0.192696\pi\) | ||||
0.822290 | + | 0.569068i | \(0.192696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.44237e15 | 0.397032 | 0.198516 | − | 0.980098i | \(-0.436388\pi\) | ||||
0.198516 | + | 0.980098i | \(0.436388\pi\) | |||||||
\(860\) | −1.21760e14 | −0.00882596 | ||||||||
\(861\) | −1.30011e15 | −0.0936403 | ||||||||
\(862\) | 1.72262e15 | 0.123282 | ||||||||
\(863\) | 1.08110e16 | 0.768787 | 0.384393 | − | 0.923169i | \(-0.374411\pi\) | ||||
0.384393 | + | 0.923169i | \(0.374411\pi\) | |||||||
\(864\) | −1.44145e16 | −1.01853 | ||||||||
\(865\) | 4.59037e15 | 0.322299 | ||||||||
\(866\) | 2.39715e15 | 0.167243 | ||||||||
\(867\) | 3.38185e15 | 0.234449 | ||||||||
\(868\) | 1.30243e15 | 0.0897217 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.75099e15 | −0.255147 | ||||||||
\(871\) | −8.94444e15 | −0.604579 | ||||||||
\(872\) | 6.20782e15 | 0.416964 | ||||||||
\(873\) | −8.52477e15 | −0.568989 | ||||||||
\(874\) | −4.77033e15 | −0.316399 | ||||||||
\(875\) | −6.01111e15 | −0.396197 | ||||||||
\(876\) | 5.42985e14 | 0.0355644 | ||||||||
\(877\) | 2.81024e16 | 1.82914 | 0.914568 | − | 0.404431i | \(-0.132530\pi\) | ||||
0.914568 | + | 0.404431i | \(0.132530\pi\) | |||||||
\(878\) | 6.96749e14 | 0.0450668 | ||||||||
\(879\) | 6.02957e15 | 0.387568 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.22209e15 | 0.268016 | 0.134008 | − | 0.990980i | \(-0.457215\pi\) | ||||
0.134008 | + | 0.990980i | \(0.457215\pi\) | |||||||
\(882\) | 4.62836e15 | 0.291978 | ||||||||
\(883\) | 5.16092e14 | 0.0323551 | 0.0161776 | − | 0.999869i | \(-0.494850\pi\) | ||||
0.0161776 | + | 0.999869i | \(0.494850\pi\) | |||||||
\(884\) | −5.87302e15 | −0.365910 | ||||||||
\(885\) | −6.31609e15 | −0.391075 | ||||||||
\(886\) | 7.88088e15 | 0.484941 | ||||||||
\(887\) | −5.71906e15 | −0.349740 | −0.174870 | − | 0.984592i | \(-0.555950\pi\) | ||||
−0.174870 | + | 0.984592i | \(0.555950\pi\) | |||||||
\(888\) | 3.87913e15 | 0.235756 | ||||||||
\(889\) | 4.39894e15 | 0.265698 | ||||||||
\(890\) | −2.89718e15 | −0.173912 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.07969e16 | −0.640167 | ||||||||
\(893\) | −2.86510e16 | −1.68832 | ||||||||
\(894\) | 6.74614e15 | 0.395093 | ||||||||
\(895\) | 8.12109e15 | 0.472702 | ||||||||
\(896\) | −5.66067e15 | −0.327472 | ||||||||
\(897\) | 2.71427e15 | 0.156061 | ||||||||
\(898\) | −1.46968e16 | −0.839854 | ||||||||
\(899\) | 6.78541e15 | 0.385388 | ||||||||
\(900\) | −4.26557e15 | −0.240793 | ||||||||
\(901\) | −1.10223e16 | −0.618421 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.22617e13 | 0.00400521 | ||||||||
\(904\) | 7.19321e15 | 0.396275 | ||||||||
\(905\) | −4.81442e15 | −0.263619 | ||||||||
\(906\) | 4.98626e15 | 0.271375 | ||||||||
\(907\) | −8.43778e13 | −0.00456445 | −0.00228222 | − | 0.999997i | \(-0.500726\pi\) | ||||
−0.00228222 | + | 0.999997i | \(0.500726\pi\) | |||||||
\(908\) | −2.00168e15 | −0.107628 | ||||||||
\(909\) | 9.28952e15 | 0.496468 | ||||||||
\(910\) | 1.12137e15 | 0.0595691 | ||||||||
\(911\) | −1.10091e16 | −0.581298 | −0.290649 | − | 0.956830i | \(-0.593871\pi\) | ||||
−0.290649 | + | 0.956830i | \(0.593871\pi\) | |||||||
\(912\) | −2.65212e15 | −0.139194 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −7.28359e15 | −0.377695 | ||||||||
\(915\) | −8.46715e15 | −0.436437 | ||||||||
\(916\) | 1.74055e16 | 0.891789 | ||||||||
\(917\) | −1.05743e16 | −0.538544 | ||||||||
\(918\) | −1.21455e16 | −0.614864 | ||||||||
\(919\) | 4.86351e15 | 0.244746 | 0.122373 | − | 0.992484i | \(-0.460950\pi\) | ||||
0.122373 | + | 0.992484i | \(0.460950\pi\) | |||||||
\(920\) | −7.60717e15 | −0.380531 | ||||||||
\(921\) | −3.85840e15 | −0.191857 | ||||||||
\(922\) | 1.75034e16 | 0.865171 | ||||||||
\(923\) | 5.65691e15 | 0.277952 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.64630e15 | 0.225594 | ||||||||
\(926\) | 2.93252e15 | 0.141540 | ||||||||
\(927\) | 2.56555e16 | 1.23095 | ||||||||
\(928\) | −2.52584e16 | −1.20474 | ||||||||
\(929\) | 3.57534e15 | 0.169524 | 0.0847620 | − | 0.996401i | \(-0.472987\pi\) | ||||
0.0847620 | + | 0.996401i | \(0.472987\pi\) | |||||||
\(930\) | −1.54365e15 | −0.0727598 | ||||||||
\(931\) | 1.80921e16 | 0.847744 | ||||||||
\(932\) | −2.58533e16 | −1.20428 | ||||||||
\(933\) | 1.25685e16 | 0.582017 | ||||||||
\(934\) | −1.48171e16 | −0.682113 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.54661e15 | 0.252354 | ||||||||
\(937\) | −3.86373e16 | −1.74759 | −0.873795 | − | 0.486295i | \(-0.838348\pi\) | ||||
−0.873795 | + | 0.486295i | \(0.838348\pi\) | |||||||
\(938\) | −6.22147e15 | −0.279754 | ||||||||
\(939\) | −2.50692e16 | −1.12067 | ||||||||
\(940\) | −1.91064e16 | −0.849133 | ||||||||
\(941\) | 3.48997e16 | 1.54198 | 0.770991 | − | 0.636846i | \(-0.219761\pi\) | ||||
0.770991 | + | 0.636846i | \(0.219761\pi\) | |||||||
\(942\) | 7.95383e15 | 0.349378 | ||||||||
\(943\) | −5.74437e15 | −0.250858 | ||||||||
\(944\) | −5.12245e15 | −0.222398 | ||||||||
\(945\) | −5.92634e15 | −0.255806 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.85123e16 | −1.21649 | −0.608243 | − | 0.793751i | \(-0.708125\pi\) | ||||
−0.608243 | + | 0.793751i | \(0.708125\pi\) | |||||||
\(948\) | 1.41392e16 | 0.599763 | ||||||||
\(949\) | −8.45688e14 | −0.0356653 | ||||||||
\(950\) | 6.52459e15 | 0.273573 | ||||||||
\(951\) | 2.10091e16 | 0.875817 | ||||||||
\(952\) | −9.76867e15 | −0.404886 | ||||||||
\(953\) | −4.00334e16 | −1.64973 | −0.824863 | − | 0.565332i | \(-0.808748\pi\) | ||||
−0.824863 | + | 0.565332i | \(0.808748\pi\) | |||||||
\(954\) | 4.35313e15 | 0.178355 | ||||||||
\(955\) | 1.33424e16 | 0.543520 | ||||||||
\(956\) | −1.05095e16 | −0.425659 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.52201e16 | −1.00980 | ||||||||
\(959\) | −4.97630e15 | −0.198109 | ||||||||
\(960\) | 3.28548e15 | 0.130049 | ||||||||
\(961\) | −2.26161e16 | −0.890100 | ||||||||
\(962\) | −2.52652e15 | −0.0988688 | ||||||||
\(963\) | 1.02553e16 | 0.399028 | ||||||||
\(964\) | −3.40484e14 | −0.0131726 | ||||||||
\(965\) | −2.62867e16 | −1.01120 | ||||||||
\(966\) | 1.88796e15 | 0.0722136 | ||||||||
\(967\) | −1.84953e16 | −0.703422 | −0.351711 | − | 0.936109i | \(-0.614400\pi\) | ||||
−0.351711 | + | 0.936109i | \(0.614400\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.85540e16 | −0.697682 | ||||||||
\(970\) | 8.69557e15 | 0.325127 | ||||||||
\(971\) | −2.14877e16 | −0.798884 | −0.399442 | − | 0.916759i | \(-0.630796\pi\) | ||||
−0.399442 | + | 0.916759i | \(0.630796\pi\) | |||||||
\(972\) | −1.97260e16 | −0.729246 | ||||||||
\(973\) | −9.99271e15 | −0.367335 | ||||||||
\(974\) | −5.27784e15 | −0.192922 | ||||||||
\(975\) | −3.71243e15 | −0.134938 | ||||||||
\(976\) | −6.86699e15 | −0.248195 | ||||||||
\(977\) | −8.73880e15 | −0.314074 | −0.157037 | − | 0.987593i | \(-0.550194\pi\) | ||||
−0.157037 | + | 0.987593i | \(0.550194\pi\) | |||||||
\(978\) | −2.16417e15 | −0.0773443 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.20650e16 | 0.426368 | ||||||||
\(981\) | 8.35079e15 | 0.293459 | ||||||||
\(982\) | 1.16127e16 | 0.405808 | ||||||||
\(983\) | 1.18924e16 | 0.413263 | 0.206631 | − | 0.978419i | \(-0.433750\pi\) | ||||
0.206631 | + | 0.978419i | \(0.433750\pi\) | |||||||
\(984\) | 6.55956e15 | 0.226674 | ||||||||
\(985\) | 1.38915e16 | 0.477365 | ||||||||
\(986\) | −2.12824e16 | −0.727274 | ||||||||
\(987\) | 1.13392e16 | 0.385336 | ||||||||
\(988\) | 9.06679e15 | 0.306401 | ||||||||
\(989\) | 3.19279e14 | 0.0107298 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.34409e16 | 0.779056 | 0.389528 | − | 0.921015i | \(-0.372638\pi\) | ||||
0.389528 | + | 0.921015i | \(0.372638\pi\) | |||||||
\(992\) | −1.03946e16 | −0.343552 | ||||||||
\(993\) | −1.60232e16 | −0.526657 | ||||||||
\(994\) | 3.93477e15 | 0.128616 | ||||||||
\(995\) | 3.51813e15 | 0.114363 | ||||||||
\(996\) | −1.08817e16 | −0.351779 | ||||||||
\(997\) | 2.14004e16 | 0.688016 | 0.344008 | − | 0.938967i | \(-0.388215\pi\) | ||||
0.344008 | + | 0.938967i | \(0.388215\pi\) | |||||||
\(998\) | −2.61307e15 | −0.0835473 | ||||||||
\(999\) | 1.33524e16 | 0.424571 |
(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 | 121.12.a.b.1.1 | 1 | ||
11.10 | odd | 2 | 1.12.a.a.1.1 | ✓ | 1 | ||
33.32 | even | 2 | 9.12.a.b.1.1 | 1 | |||
44.43 | even | 2 | 16.12.a.a.1.1 | 1 | |||
55.32 | even | 4 | 25.12.b.b.24.1 | 2 | |||
55.43 | even | 4 | 25.12.b.b.24.2 | 2 | |||
55.54 | odd | 2 | 25.12.a.b.1.1 | 1 | |||
77.10 | even | 6 | 49.12.c.c.30.1 | 2 | |||
77.32 | odd | 6 | 49.12.c.b.30.1 | 2 | |||
77.54 | even | 6 | 49.12.c.c.18.1 | 2 | |||
77.65 | odd | 6 | 49.12.c.b.18.1 | 2 | |||
77.76 | even | 2 | 49.12.a.a.1.1 | 1 | |||
88.21 | odd | 2 | 64.12.a.b.1.1 | 1 | |||
88.43 | even | 2 | 64.12.a.f.1.1 | 1 | |||
99.32 | even | 6 | 81.12.c.b.55.1 | 2 | |||
99.43 | odd | 6 | 81.12.c.d.28.1 | 2 | |||
99.65 | even | 6 | 81.12.c.b.28.1 | 2 | |||
99.76 | odd | 6 | 81.12.c.d.55.1 | 2 | |||
132.131 | odd | 2 | 144.12.a.d.1.1 | 1 | |||
143.142 | odd | 2 | 169.12.a.a.1.1 | 1 | |||
165.32 | odd | 4 | 225.12.b.d.199.2 | 2 | |||
165.98 | odd | 4 | 225.12.b.d.199.1 | 2 | |||
165.164 | even | 2 | 225.12.a.b.1.1 | 1 | |||
176.21 | odd | 4 | 256.12.b.e.129.1 | 2 | |||
176.43 | even | 4 | 256.12.b.c.129.2 | 2 | |||
176.109 | odd | 4 | 256.12.b.e.129.2 | 2 | |||
176.131 | even | 4 | 256.12.b.c.129.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.12.a.a.1.1 | ✓ | 1 | 11.10 | odd | 2 | ||
9.12.a.b.1.1 | 1 | 33.32 | even | 2 | |||
16.12.a.a.1.1 | 1 | 44.43 | even | 2 | |||
25.12.a.b.1.1 | 1 | 55.54 | odd | 2 | |||
25.12.b.b.24.1 | 2 | 55.32 | even | 4 | |||
25.12.b.b.24.2 | 2 | 55.43 | even | 4 | |||
49.12.a.a.1.1 | 1 | 77.76 | even | 2 | |||
49.12.c.b.18.1 | 2 | 77.65 | odd | 6 | |||
49.12.c.b.30.1 | 2 | 77.32 | odd | 6 | |||
49.12.c.c.18.1 | 2 | 77.54 | even | 6 | |||
49.12.c.c.30.1 | 2 | 77.10 | even | 6 | |||
64.12.a.b.1.1 | 1 | 88.21 | odd | 2 | |||
64.12.a.f.1.1 | 1 | 88.43 | even | 2 | |||
81.12.c.b.28.1 | 2 | 99.65 | even | 6 | |||
81.12.c.b.55.1 | 2 | 99.32 | even | 6 | |||
81.12.c.d.28.1 | 2 | 99.43 | odd | 6 | |||
81.12.c.d.55.1 | 2 | 99.76 | odd | 6 | |||
121.12.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
144.12.a.d.1.1 | 1 | 132.131 | odd | 2 | |||
169.12.a.a.1.1 | 1 | 143.142 | odd | 2 | |||
225.12.a.b.1.1 | 1 | 165.164 | even | 2 | |||
225.12.b.d.199.1 | 2 | 165.98 | odd | 4 | |||
225.12.b.d.199.2 | 2 | 165.32 | odd | 4 | |||
256.12.b.c.129.1 | 2 | 176.131 | even | 4 | |||
256.12.b.c.129.2 | 2 | 176.43 | even | 4 | |||
256.12.b.e.129.1 | 2 | 176.21 | odd | 4 | |||
256.12.b.e.129.2 | 2 | 176.109 | odd | 4 |