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: | \(24\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 12.9147 | 0.570755 | 0.285378 | − | 0.958415i | \(-0.407881\pi\) | ||||
0.285378 | + | 0.958415i | \(0.407881\pi\) | |||||||
\(3\) | −101.422 | −0.722917 | −0.361459 | − | 0.932388i | \(-0.617721\pi\) | ||||
−0.361459 | + | 0.932388i | \(0.617721\pi\) | |||||||
\(4\) | −345.210 | −0.674238 | ||||||||
\(5\) | −2078.59 | −1.48732 | −0.743658 | − | 0.668560i | \(-0.766911\pi\) | ||||
−0.743658 | + | 0.668560i | \(0.766911\pi\) | |||||||
\(6\) | −1309.84 | −0.412609 | ||||||||
\(7\) | −2161.61 | −0.340280 | −0.170140 | − | 0.985420i | \(-0.554422\pi\) | ||||
−0.170140 | + | 0.985420i | \(0.554422\pi\) | |||||||
\(8\) | −11070.6 | −0.955580 | ||||||||
\(9\) | −9396.49 | −0.477391 | ||||||||
\(10\) | −26844.4 | −0.848893 | ||||||||
\(11\) | 13147.0 | 0.270745 | 0.135372 | − | 0.990795i | \(-0.456777\pi\) | ||||
0.135372 | + | 0.990795i | \(0.456777\pi\) | |||||||
\(12\) | 35012.1 | 0.487418 | ||||||||
\(13\) | −17852.0 | −0.173357 | −0.0866785 | − | 0.996236i | \(-0.527625\pi\) | ||||
−0.0866785 | + | 0.996236i | \(0.527625\pi\) | |||||||
\(14\) | −27916.6 | −0.194217 | ||||||||
\(15\) | 210815. | 1.07521 | ||||||||
\(16\) | 33773.6 | 0.128836 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −121353. | −0.272473 | ||||||||
\(19\) | −30951.0 | −0.0544858 | −0.0272429 | − | 0.999629i | \(-0.508673\pi\) | ||||
−0.0272429 | + | 0.999629i | \(0.508673\pi\) | |||||||
\(20\) | 717549. | 1.00281 | ||||||||
\(21\) | 219236. | 0.245994 | ||||||||
\(22\) | 169790. | 0.154529 | ||||||||
\(23\) | 193663. | 0.144302 | 0.0721510 | − | 0.997394i | \(-0.477014\pi\) | ||||
0.0721510 | + | 0.997394i | \(0.477014\pi\) | |||||||
\(24\) | 1.12281e6 | 0.690805 | ||||||||
\(25\) | 2.36740e6 | 1.21211 | ||||||||
\(26\) | −230553. | −0.0989444 | ||||||||
\(27\) | 2.94931e6 | 1.06803 | ||||||||
\(28\) | 746210. | 0.229430 | ||||||||
\(29\) | −1.83211e6 | −0.481017 | −0.240508 | − | 0.970647i | \(-0.577314\pi\) | ||||
−0.240508 | + | 0.970647i | \(0.577314\pi\) | |||||||
\(30\) | 2.72262e6 | 0.613680 | ||||||||
\(31\) | 525734. | 0.102244 | 0.0511221 | − | 0.998692i | \(-0.483720\pi\) | ||||
0.0511221 | + | 0.998692i | \(0.483720\pi\) | |||||||
\(32\) | 6.10434e6 | 1.02911 | ||||||||
\(33\) | −1.33340e6 | −0.195726 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.49310e6 | 0.506104 | ||||||||
\(36\) | 3.24376e6 | 0.321875 | ||||||||
\(37\) | 1.78204e7 | 1.56318 | 0.781591 | − | 0.623791i | \(-0.214408\pi\) | ||||
0.781591 | + | 0.623791i | \(0.214408\pi\) | |||||||
\(38\) | −399723. | −0.0310981 | ||||||||
\(39\) | 1.81059e6 | 0.125323 | ||||||||
\(40\) | 2.30113e7 | 1.42125 | ||||||||
\(41\) | 1.53721e7 | 0.849582 | 0.424791 | − | 0.905291i | \(-0.360348\pi\) | ||||
0.424791 | + | 0.905291i | \(0.360348\pi\) | |||||||
\(42\) | 2.83137e6 | 0.140402 | ||||||||
\(43\) | −4.23089e7 | −1.88723 | −0.943613 | − | 0.331051i | \(-0.892597\pi\) | ||||
−0.943613 | + | 0.331051i | \(0.892597\pi\) | |||||||
\(44\) | −4.53848e6 | −0.182547 | ||||||||
\(45\) | 1.95314e7 | 0.710031 | ||||||||
\(46\) | 2.50111e6 | 0.0823611 | ||||||||
\(47\) | 5.91782e7 | 1.76897 | 0.884487 | − | 0.466565i | \(-0.154509\pi\) | ||||
0.884487 | + | 0.466565i | \(0.154509\pi\) | |||||||
\(48\) | −3.42540e6 | −0.0931377 | ||||||||
\(49\) | −3.56810e7 | −0.884210 | ||||||||
\(50\) | 3.05743e7 | 0.691817 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.16269e6 | 0.116884 | ||||||||
\(53\) | −8.32863e7 | −1.44988 | −0.724941 | − | 0.688811i | \(-0.758133\pi\) | ||||
−0.724941 | + | 0.688811i | \(0.758133\pi\) | |||||||
\(54\) | 3.80895e7 | 0.609584 | ||||||||
\(55\) | −2.73272e7 | −0.402683 | ||||||||
\(56\) | 2.39304e7 | 0.325165 | ||||||||
\(57\) | 3.13913e6 | 0.0393887 | ||||||||
\(58\) | −2.36612e7 | −0.274543 | ||||||||
\(59\) | 9.24034e7 | 0.992782 | 0.496391 | − | 0.868099i | \(-0.334658\pi\) | ||||
0.496391 | + | 0.868099i | \(0.334658\pi\) | |||||||
\(60\) | −7.27756e7 | −0.724945 | ||||||||
\(61\) | 1.01929e8 | 0.942568 | 0.471284 | − | 0.881981i | \(-0.343791\pi\) | ||||
0.471284 | + | 0.881981i | \(0.343791\pi\) | |||||||
\(62\) | 6.78970e6 | 0.0583564 | ||||||||
\(63\) | 2.03115e7 | 0.162447 | ||||||||
\(64\) | 6.15437e7 | 0.458536 | ||||||||
\(65\) | 3.71069e7 | 0.257837 | ||||||||
\(66\) | −1.72205e7 | −0.111712 | ||||||||
\(67\) | 1.25363e8 | 0.760031 | 0.380015 | − | 0.924980i | \(-0.375919\pi\) | ||||
0.380015 | + | 0.924980i | \(0.375919\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.96418e7 | −0.104318 | ||||||||
\(70\) | 5.80271e7 | 0.288861 | ||||||||
\(71\) | −2.14775e8 | −1.00305 | −0.501523 | − | 0.865144i | \(-0.667227\pi\) | ||||
−0.501523 | + | 0.865144i | \(0.667227\pi\) | |||||||
\(72\) | 1.04025e8 | 0.456185 | ||||||||
\(73\) | 1.02966e8 | 0.424365 | 0.212182 | − | 0.977230i | \(-0.431943\pi\) | ||||
0.212182 | + | 0.977230i | \(0.431943\pi\) | |||||||
\(74\) | 2.30145e8 | 0.892194 | ||||||||
\(75\) | −2.40108e8 | −0.876254 | ||||||||
\(76\) | 1.06846e7 | 0.0367364 | ||||||||
\(77\) | −2.84187e7 | −0.0921290 | ||||||||
\(78\) | 2.33833e7 | 0.0715286 | ||||||||
\(79\) | 9.58995e6 | 0.0277009 | 0.0138505 | − | 0.999904i | \(-0.495591\pi\) | ||||
0.0138505 | + | 0.999904i | \(0.495591\pi\) | |||||||
\(80\) | −7.02013e7 | −0.191620 | ||||||||
\(81\) | −1.14176e8 | −0.294707 | ||||||||
\(82\) | 1.98526e8 | 0.484904 | ||||||||
\(83\) | −6.13699e8 | −1.41940 | −0.709699 | − | 0.704505i | \(-0.751169\pi\) | ||||
−0.709699 | + | 0.704505i | \(0.751169\pi\) | |||||||
\(84\) | −7.56824e7 | −0.165859 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.46408e8 | −1.07714 | ||||||||
\(87\) | 1.85817e8 | 0.347735 | ||||||||
\(88\) | −1.45546e8 | −0.258718 | ||||||||
\(89\) | 5.89040e8 | 0.995153 | 0.497576 | − | 0.867420i | \(-0.334223\pi\) | ||||
0.497576 | + | 0.867420i | \(0.334223\pi\) | |||||||
\(90\) | 2.52243e8 | 0.405254 | ||||||||
\(91\) | 3.85890e7 | 0.0589899 | ||||||||
\(92\) | −6.68545e7 | −0.0972939 | ||||||||
\(93\) | −5.33212e7 | −0.0739140 | ||||||||
\(94\) | 7.64270e8 | 1.00965 | ||||||||
\(95\) | 6.43343e7 | 0.0810376 | ||||||||
\(96\) | −6.19117e8 | −0.743964 | ||||||||
\(97\) | −8.70682e8 | −0.998589 | −0.499295 | − | 0.866432i | \(-0.666407\pi\) | ||||
−0.499295 | + | 0.866432i | \(0.666407\pi\) | |||||||
\(98\) | −4.60811e8 | −0.504667 | ||||||||
\(99\) | −1.23536e8 | −0.129251 | ||||||||
\(100\) | −8.17250e8 | −0.817250 | ||||||||
\(101\) | −1.76796e9 | −1.69054 | −0.845271 | − | 0.534338i | \(-0.820561\pi\) | ||||
−0.845271 | + | 0.534338i | \(0.820561\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.32197e8 | 0.728549 | 0.364275 | − | 0.931292i | \(-0.381317\pi\) | ||||
0.364275 | + | 0.931292i | \(0.381317\pi\) | |||||||
\(104\) | 1.97633e8 | 0.165657 | ||||||||
\(105\) | −4.55701e8 | −0.365871 | ||||||||
\(106\) | −1.07562e9 | −0.827527 | ||||||||
\(107\) | 1.49690e9 | 1.10399 | 0.551994 | − | 0.833848i | \(-0.313867\pi\) | ||||
0.551994 | + | 0.833848i | \(0.313867\pi\) | |||||||
\(108\) | −1.01813e9 | −0.720108 | ||||||||
\(109\) | −1.25120e9 | −0.848998 | −0.424499 | − | 0.905428i | \(-0.639550\pi\) | ||||
−0.424499 | + | 0.905428i | \(0.639550\pi\) | |||||||
\(110\) | −3.52923e8 | −0.229833 | ||||||||
\(111\) | −1.80739e9 | −1.13005 | ||||||||
\(112\) | −7.30053e7 | −0.0438403 | ||||||||
\(113\) | 2.62190e9 | 1.51274 | 0.756369 | − | 0.654145i | \(-0.226971\pi\) | ||||
0.756369 | + | 0.654145i | \(0.226971\pi\) | |||||||
\(114\) | 4.05409e7 | 0.0224813 | ||||||||
\(115\) | −4.02546e8 | −0.214623 | ||||||||
\(116\) | 6.32462e8 | 0.324320 | ||||||||
\(117\) | 1.67746e8 | 0.0827591 | ||||||||
\(118\) | 1.19336e9 | 0.566636 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.33386e9 | −1.02745 | ||||||||
\(121\) | −2.18510e9 | −0.926697 | ||||||||
\(122\) | 1.31638e9 | 0.537976 | ||||||||
\(123\) | −1.55907e9 | −0.614178 | ||||||||
\(124\) | −1.81489e8 | −0.0689369 | ||||||||
\(125\) | −8.61107e8 | −0.315473 | ||||||||
\(126\) | 2.62318e8 | 0.0927172 | ||||||||
\(127\) | −3.13001e9 | −1.06765 | −0.533825 | − | 0.845595i | \(-0.679246\pi\) | ||||
−0.533825 | + | 0.845595i | \(0.679246\pi\) | |||||||
\(128\) | −2.33060e9 | −0.767402 | ||||||||
\(129\) | 4.29107e9 | 1.36431 | ||||||||
\(130\) | 4.79225e8 | 0.147162 | ||||||||
\(131\) | −1.31489e9 | −0.390094 | −0.195047 | − | 0.980794i | \(-0.562486\pi\) | ||||
−0.195047 | + | 0.980794i | \(0.562486\pi\) | |||||||
\(132\) | 4.60304e8 | 0.131966 | ||||||||
\(133\) | 6.69040e7 | 0.0185404 | ||||||||
\(134\) | 1.61902e9 | 0.433792 | ||||||||
\(135\) | −6.13040e9 | −1.58850 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.14400e8 | 0.124755 | 0.0623775 | − | 0.998053i | \(-0.480132\pi\) | ||||
0.0623775 | + | 0.998053i | \(0.480132\pi\) | |||||||
\(138\) | −2.53668e8 | −0.0595402 | ||||||||
\(139\) | 7.81812e9 | 1.77638 | 0.888189 | − | 0.459478i | \(-0.151963\pi\) | ||||
0.888189 | + | 0.459478i | \(0.151963\pi\) | |||||||
\(140\) | −1.55106e9 | −0.341235 | ||||||||
\(141\) | −6.00200e9 | −1.27882 | ||||||||
\(142\) | −2.77376e9 | −0.572494 | ||||||||
\(143\) | −2.34700e8 | −0.0469355 | ||||||||
\(144\) | −3.17353e8 | −0.0615051 | ||||||||
\(145\) | 3.80820e9 | 0.715424 | ||||||||
\(146\) | 1.32977e9 | 0.242208 | ||||||||
\(147\) | 3.61886e9 | 0.639210 | ||||||||
\(148\) | −6.15178e9 | −1.05396 | ||||||||
\(149\) | 8.47199e9 | 1.40814 | 0.704072 | − | 0.710128i | \(-0.251363\pi\) | ||||
0.704072 | + | 0.710128i | \(0.251363\pi\) | |||||||
\(150\) | −3.10092e9 | −0.500127 | ||||||||
\(151\) | −1.13940e9 | −0.178353 | −0.0891766 | − | 0.996016i | \(-0.528424\pi\) | ||||
−0.0891766 | + | 0.996016i | \(0.528424\pi\) | |||||||
\(152\) | 3.42647e8 | 0.0520656 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.67020e8 | −0.0525831 | ||||||||
\(155\) | −1.09278e9 | −0.152069 | ||||||||
\(156\) | −6.25035e8 | −0.0844974 | ||||||||
\(157\) | −3.27009e9 | −0.429547 | −0.214774 | − | 0.976664i | \(-0.568901\pi\) | ||||
−0.214774 | + | 0.976664i | \(0.568901\pi\) | |||||||
\(158\) | 1.23851e8 | 0.0158105 | ||||||||
\(159\) | 8.44711e9 | 1.04814 | ||||||||
\(160\) | −1.26884e10 | −1.53062 | ||||||||
\(161\) | −4.18625e8 | −0.0491030 | ||||||||
\(162\) | −1.47454e9 | −0.168206 | ||||||||
\(163\) | 2.09512e9 | 0.232468 | 0.116234 | − | 0.993222i | \(-0.462918\pi\) | ||||
0.116234 | + | 0.993222i | \(0.462918\pi\) | |||||||
\(164\) | −5.30660e9 | −0.572821 | ||||||||
\(165\) | 2.77159e9 | 0.291106 | ||||||||
\(166\) | −7.92575e9 | −0.810129 | ||||||||
\(167\) | −1.40830e10 | −1.40110 | −0.700551 | − | 0.713603i | \(-0.747062\pi\) | ||||
−0.700551 | + | 0.713603i | \(0.747062\pi\) | |||||||
\(168\) | −2.42708e9 | −0.235067 | ||||||||
\(169\) | −1.02858e10 | −0.969947 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.90831e8 | 0.0260110 | ||||||||
\(172\) | 1.46055e10 | 1.27244 | ||||||||
\(173\) | 3.98665e9 | 0.338377 | 0.169188 | − | 0.985584i | \(-0.445885\pi\) | ||||
0.169188 | + | 0.985584i | \(0.445885\pi\) | |||||||
\(174\) | 2.39977e9 | 0.198472 | ||||||||
\(175\) | −5.11740e9 | −0.412456 | ||||||||
\(176\) | 4.44022e8 | 0.0348817 | ||||||||
\(177\) | −9.37178e9 | −0.717699 | ||||||||
\(178\) | 7.60728e9 | 0.567989 | ||||||||
\(179\) | 1.82891e10 | 1.33154 | 0.665769 | − | 0.746158i | \(-0.268104\pi\) | ||||
0.665769 | + | 0.746158i | \(0.268104\pi\) | |||||||
\(180\) | −6.74244e9 | −0.478730 | ||||||||
\(181\) | 1.12163e10 | 0.776775 | 0.388387 | − | 0.921496i | \(-0.373032\pi\) | ||||
0.388387 | + | 0.921496i | \(0.373032\pi\) | |||||||
\(182\) | 4.98367e8 | 0.0336688 | ||||||||
\(183\) | −1.03379e10 | −0.681399 | ||||||||
\(184\) | −2.14397e9 | −0.137892 | ||||||||
\(185\) | −3.70412e10 | −2.32495 | ||||||||
\(186\) | −6.88628e8 | −0.0421868 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.04289e10 | −1.19271 | ||||||||
\(189\) | −6.37527e9 | −0.363430 | ||||||||
\(190\) | 8.30860e8 | 0.0462526 | ||||||||
\(191\) | −6.63597e9 | −0.360790 | −0.180395 | − | 0.983594i | \(-0.557738\pi\) | ||||
−0.180395 | + | 0.983594i | \(0.557738\pi\) | |||||||
\(192\) | −6.24191e9 | −0.331484 | ||||||||
\(193\) | −1.28453e10 | −0.666404 | −0.333202 | − | 0.942856i | \(-0.608129\pi\) | ||||
−0.333202 | + | 0.942856i | \(0.608129\pi\) | |||||||
\(194\) | −1.12446e10 | −0.569950 | ||||||||
\(195\) | −3.76347e9 | −0.186395 | ||||||||
\(196\) | 1.23175e10 | 0.596168 | ||||||||
\(197\) | 9.15030e9 | 0.432850 | 0.216425 | − | 0.976299i | \(-0.430560\pi\) | ||||
0.216425 | + | 0.976299i | \(0.430560\pi\) | |||||||
\(198\) | −1.59543e9 | −0.0737707 | ||||||||
\(199\) | 4.02134e10 | 1.81774 | 0.908870 | − | 0.417079i | \(-0.136946\pi\) | ||||
0.908870 | + | 0.417079i | \(0.136946\pi\) | |||||||
\(200\) | −2.62086e10 | −1.15827 | ||||||||
\(201\) | −1.27146e10 | −0.549439 | ||||||||
\(202\) | −2.28327e10 | −0.964886 | ||||||||
\(203\) | 3.96030e9 | 0.163680 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.19522e10 | −1.26360 | ||||||||
\(206\) | 1.07476e10 | 0.415823 | ||||||||
\(207\) | −1.81975e9 | −0.0688884 | ||||||||
\(208\) | −6.02925e8 | −0.0223346 | ||||||||
\(209\) | −4.06913e8 | −0.0147517 | ||||||||
\(210\) | −5.88525e9 | −0.208823 | ||||||||
\(211\) | −9.07065e9 | −0.315041 | −0.157521 | − | 0.987516i | \(-0.550350\pi\) | ||||
−0.157521 | + | 0.987516i | \(0.550350\pi\) | |||||||
\(212\) | 2.87513e10 | 0.977566 | ||||||||
\(213\) | 2.17830e10 | 0.725119 | ||||||||
\(214\) | 1.93320e10 | 0.630107 | ||||||||
\(215\) | 8.79428e10 | 2.80690 | ||||||||
\(216\) | −3.26507e10 | −1.02059 | ||||||||
\(217\) | −1.13643e9 | −0.0347916 | ||||||||
\(218\) | −1.61589e10 | −0.484570 | ||||||||
\(219\) | −1.04430e10 | −0.306781 | ||||||||
\(220\) | 9.43363e9 | 0.271504 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.33419e10 | −0.644982 | ||||||||
\(223\) | 2.83923e10 | 0.768827 | 0.384414 | − | 0.923161i | \(-0.374404\pi\) | ||||
0.384414 | + | 0.923161i | \(0.374404\pi\) | |||||||
\(224\) | −1.31952e10 | −0.350187 | ||||||||
\(225\) | −2.22452e10 | −0.578650 | ||||||||
\(226\) | 3.38611e10 | 0.863403 | ||||||||
\(227\) | 7.74085e10 | 1.93496 | 0.967480 | − | 0.252946i | \(-0.0813997\pi\) | ||||
0.967480 | + | 0.252946i | \(0.0813997\pi\) | |||||||
\(228\) | −1.08366e9 | −0.0265574 | ||||||||
\(229\) | −1.04661e9 | −0.0251492 | −0.0125746 | − | 0.999921i | \(-0.504003\pi\) | ||||
−0.0125746 | + | 0.999921i | \(0.504003\pi\) | |||||||
\(230\) | −5.19877e9 | −0.122497 | ||||||||
\(231\) | 2.88230e9 | 0.0666016 | ||||||||
\(232\) | 2.02826e10 | 0.459650 | ||||||||
\(233\) | −6.08121e10 | −1.35172 | −0.675862 | − | 0.737028i | \(-0.736229\pi\) | ||||
−0.675862 | + | 0.737028i | \(0.736229\pi\) | |||||||
\(234\) | 2.16639e9 | 0.0472352 | ||||||||
\(235\) | −1.23007e11 | −2.63102 | ||||||||
\(236\) | −3.18986e10 | −0.669372 | ||||||||
\(237\) | −9.72636e8 | −0.0200255 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.87053e10 | −0.965574 | −0.482787 | − | 0.875738i | \(-0.660375\pi\) | ||||
−0.482787 | + | 0.875738i | \(0.660375\pi\) | |||||||
\(240\) | 7.11999e9 | 0.138525 | ||||||||
\(241\) | 8.61021e10 | 1.64413 | 0.822067 | − | 0.569391i | \(-0.192821\pi\) | ||||
0.822067 | + | 0.569391i | \(0.192821\pi\) | |||||||
\(242\) | −2.82200e10 | −0.528917 | ||||||||
\(243\) | −4.64714e10 | −0.854982 | ||||||||
\(244\) | −3.51869e10 | −0.635516 | ||||||||
\(245\) | 7.41662e10 | 1.31510 | ||||||||
\(246\) | −2.01350e10 | −0.350545 | ||||||||
\(247\) | 5.52537e8 | 0.00944550 | ||||||||
\(248\) | −5.82020e9 | −0.0977025 | ||||||||
\(249\) | 6.22429e10 | 1.02611 | ||||||||
\(250\) | −1.11209e10 | −0.180058 | ||||||||
\(251\) | 1.62824e10 | 0.258933 | 0.129466 | − | 0.991584i | \(-0.458674\pi\) | ||||
0.129466 | + | 0.991584i | \(0.458674\pi\) | |||||||
\(252\) | −7.01175e9 | −0.109528 | ||||||||
\(253\) | 2.54609e9 | 0.0390690 | ||||||||
\(254\) | −4.04232e10 | −0.609366 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.16094e10 | −0.896535 | ||||||||
\(257\) | −5.50549e10 | −0.787221 | −0.393611 | − | 0.919277i | \(-0.628774\pi\) | ||||
−0.393611 | + | 0.919277i | \(0.628774\pi\) | |||||||
\(258\) | 5.54180e10 | 0.778686 | ||||||||
\(259\) | −3.85208e10 | −0.531919 | ||||||||
\(260\) | −1.28097e10 | −0.173843 | ||||||||
\(261\) | 1.72154e10 | 0.229633 | ||||||||
\(262\) | −1.69814e10 | −0.222648 | ||||||||
\(263\) | 1.36741e10 | 0.176237 | 0.0881186 | − | 0.996110i | \(-0.471915\pi\) | ||||
0.0881186 | + | 0.996110i | \(0.471915\pi\) | |||||||
\(264\) | 1.47616e10 | 0.187032 | ||||||||
\(265\) | 1.73118e11 | 2.15643 | ||||||||
\(266\) | 8.64046e8 | 0.0105820 | ||||||||
\(267\) | −5.97419e10 | −0.719413 | ||||||||
\(268\) | −4.32764e10 | −0.512442 | ||||||||
\(269\) | −9.50088e10 | −1.10631 | −0.553157 | − | 0.833077i | \(-0.686577\pi\) | ||||
−0.553157 | + | 0.833077i | \(0.686577\pi\) | |||||||
\(270\) | −7.91724e10 | −0.906645 | ||||||||
\(271\) | 7.91380e10 | 0.891299 | 0.445650 | − | 0.895208i | \(-0.352973\pi\) | ||||
0.445650 | + | 0.895208i | \(0.352973\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.91380e9 | −0.0426448 | ||||||||
\(274\) | 6.64333e9 | 0.0712046 | ||||||||
\(275\) | 3.11242e10 | 0.328172 | ||||||||
\(276\) | 6.78055e9 | 0.0703354 | ||||||||
\(277\) | 2.52889e10 | 0.258090 | 0.129045 | − | 0.991639i | \(-0.458809\pi\) | ||||
0.129045 | + | 0.991639i | \(0.458809\pi\) | |||||||
\(278\) | 1.00969e11 | 1.01388 | ||||||||
\(279\) | −4.94005e9 | −0.0488104 | ||||||||
\(280\) | −4.97414e10 | −0.483623 | ||||||||
\(281\) | 9.53062e8 | 0.00911891 | 0.00455946 | − | 0.999990i | \(-0.498549\pi\) | ||||
0.00455946 | + | 0.999990i | \(0.498549\pi\) | |||||||
\(282\) | −7.75141e10 | −0.729894 | ||||||||
\(283\) | 3.78782e10 | 0.351035 | 0.175517 | − | 0.984476i | \(-0.443840\pi\) | ||||
0.175517 | + | 0.984476i | \(0.443840\pi\) | |||||||
\(284\) | 7.41425e10 | 0.676292 | ||||||||
\(285\) | −6.52495e9 | −0.0585835 | ||||||||
\(286\) | −3.03109e9 | −0.0267887 | ||||||||
\(287\) | −3.32285e10 | −0.289096 | ||||||||
\(288\) | −5.73593e10 | −0.491290 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 4.91818e10 | 0.408332 | ||||||||
\(291\) | 8.83067e10 | 0.721897 | ||||||||
\(292\) | −3.55448e10 | −0.286123 | ||||||||
\(293\) | −1.17365e11 | −0.930325 | −0.465163 | − | 0.885225i | \(-0.654004\pi\) | ||||
−0.465163 | + | 0.885225i | \(0.654004\pi\) | |||||||
\(294\) | 4.67365e10 | 0.364833 | ||||||||
\(295\) | −1.92069e11 | −1.47658 | ||||||||
\(296\) | −1.97283e11 | −1.49375 | ||||||||
\(297\) | 3.87747e10 | 0.289164 | ||||||||
\(298\) | 1.09413e11 | 0.803706 | ||||||||
\(299\) | −3.45727e9 | −0.0250157 | ||||||||
\(300\) | 8.28875e10 | 0.590804 | ||||||||
\(301\) | 9.14554e10 | 0.642185 | ||||||||
\(302\) | −1.47151e10 | −0.101796 | ||||||||
\(303\) | 1.79311e11 | 1.22212 | ||||||||
\(304\) | −1.04533e9 | −0.00701973 | ||||||||
\(305\) | −2.11868e11 | −1.40190 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.18712e10 | −0.526028 | −0.263014 | − | 0.964792i | \(-0.584717\pi\) | ||||
−0.263014 | + | 0.964792i | \(0.584717\pi\) | |||||||
\(308\) | 9.81043e9 | 0.0621169 | ||||||||
\(309\) | −8.44035e10 | −0.526681 | ||||||||
\(310\) | −1.41130e10 | −0.0867943 | ||||||||
\(311\) | −1.69662e11 | −1.02840 | −0.514201 | − | 0.857670i | \(-0.671912\pi\) | ||||
−0.514201 | + | 0.857670i | \(0.671912\pi\) | |||||||
\(312\) | −2.00444e10 | −0.119756 | ||||||||
\(313\) | −3.25773e11 | −1.91852 | −0.959258 | − | 0.282533i | \(-0.908825\pi\) | ||||
−0.959258 | + | 0.282533i | \(0.908825\pi\) | |||||||
\(314\) | −4.22323e10 | −0.245166 | ||||||||
\(315\) | −4.22193e10 | −0.241609 | ||||||||
\(316\) | −3.31055e9 | −0.0186770 | ||||||||
\(317\) | −1.30550e11 | −0.726124 | −0.363062 | − | 0.931765i | \(-0.618269\pi\) | ||||
−0.363062 | + | 0.931765i | \(0.618269\pi\) | |||||||
\(318\) | 1.09092e11 | 0.598234 | ||||||||
\(319\) | −2.40868e10 | −0.130233 | ||||||||
\(320\) | −1.27924e11 | −0.681988 | ||||||||
\(321\) | −1.51819e11 | −0.798092 | ||||||||
\(322\) | −5.40642e9 | −0.0280258 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3.94145e10 | 0.198703 | ||||||||
\(325\) | −4.22628e10 | −0.210128 | ||||||||
\(326\) | 2.70578e10 | 0.132683 | ||||||||
\(327\) | 1.26900e11 | 0.613755 | ||||||||
\(328\) | −1.70179e11 | −0.811844 | ||||||||
\(329\) | −1.27920e11 | −0.601946 | ||||||||
\(330\) | 3.57943e10 | 0.166151 | ||||||||
\(331\) | 1.07749e11 | 0.493385 | 0.246692 | − | 0.969094i | \(-0.420656\pi\) | ||||
0.246692 | + | 0.969094i | \(0.420656\pi\) | |||||||
\(332\) | 2.11855e11 | 0.957013 | ||||||||
\(333\) | −1.67449e11 | −0.746249 | ||||||||
\(334\) | −1.81877e11 | −0.799686 | ||||||||
\(335\) | −2.60577e11 | −1.13041 | ||||||||
\(336\) | 7.40438e9 | 0.0316929 | ||||||||
\(337\) | 2.54399e11 | 1.07444 | 0.537218 | − | 0.843444i | \(-0.319475\pi\) | ||||
0.537218 | + | 0.843444i | \(0.319475\pi\) | |||||||
\(338\) | −1.32838e11 | −0.553603 | ||||||||
\(339\) | −2.65920e11 | −1.09358 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.91183e9 | 0.0276821 | ||||||||
\(342\) | 3.75599e9 | 0.0148459 | ||||||||
\(343\) | 1.64357e11 | 0.641159 | ||||||||
\(344\) | 4.68386e11 | 1.80340 | ||||||||
\(345\) | 4.08272e10 | 0.155154 | ||||||||
\(346\) | 5.14864e10 | 0.193130 | ||||||||
\(347\) | −4.03414e10 | −0.149372 | −0.0746859 | − | 0.997207i | \(-0.523795\pi\) | ||||
−0.0746859 | + | 0.997207i | \(0.523795\pi\) | |||||||
\(348\) | −6.41459e10 | −0.234456 | ||||||||
\(349\) | −2.78080e11 | −1.00336 | −0.501679 | − | 0.865054i | \(-0.667284\pi\) | ||||
−0.501679 | + | 0.865054i | \(0.667284\pi\) | |||||||
\(350\) | −6.60897e10 | −0.235412 | ||||||||
\(351\) | −5.26511e10 | −0.185151 | ||||||||
\(352\) | 8.02538e10 | 0.278627 | ||||||||
\(353\) | 2.25144e11 | 0.771746 | 0.385873 | − | 0.922552i | \(-0.373900\pi\) | ||||
0.385873 | + | 0.922552i | \(0.373900\pi\) | |||||||
\(354\) | −1.21034e11 | −0.409630 | ||||||||
\(355\) | 4.46428e11 | 1.49185 | ||||||||
\(356\) | −2.03343e11 | −0.670970 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.36198e11 | 0.759982 | ||||||||
\(359\) | 2.26898e11 | 0.720952 | 0.360476 | − | 0.932768i | \(-0.382614\pi\) | ||||
0.360476 | + | 0.932768i | \(0.382614\pi\) | |||||||
\(360\) | −2.16225e11 | −0.678492 | ||||||||
\(361\) | −3.21730e11 | −0.997031 | ||||||||
\(362\) | 1.44855e11 | 0.443348 | ||||||||
\(363\) | 2.21619e11 | 0.669925 | ||||||||
\(364\) | −1.33213e10 | −0.0397733 | ||||||||
\(365\) | −2.14023e11 | −0.631164 | ||||||||
\(366\) | −1.33511e11 | −0.388912 | ||||||||
\(367\) | 3.78313e11 | 1.08856 | 0.544281 | − | 0.838903i | \(-0.316802\pi\) | ||||
0.544281 | + | 0.838903i | \(0.316802\pi\) | |||||||
\(368\) | 6.54070e9 | 0.0185913 | ||||||||
\(369\) | −1.44444e11 | −0.405583 | ||||||||
\(370\) | −4.78377e11 | −1.32697 | ||||||||
\(371\) | 1.80033e11 | 0.493365 | ||||||||
\(372\) | 1.84070e10 | 0.0498357 | ||||||||
\(373\) | 6.56421e11 | 1.75587 | 0.877935 | − | 0.478779i | \(-0.158921\pi\) | ||||
0.877935 | + | 0.478779i | \(0.158921\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.73355e10 | 0.228061 | ||||||||
\(376\) | −6.55140e11 | −1.69040 | ||||||||
\(377\) | 3.27068e10 | 0.0833876 | ||||||||
\(378\) | −8.23348e10 | −0.207429 | ||||||||
\(379\) | 5.04568e11 | 1.25615 | 0.628077 | − | 0.778151i | \(-0.283842\pi\) | ||||
0.628077 | + | 0.778151i | \(0.283842\pi\) | |||||||
\(380\) | −2.22089e10 | −0.0546387 | ||||||||
\(381\) | 3.17453e11 | 0.771822 | ||||||||
\(382\) | −8.57017e10 | −0.205923 | ||||||||
\(383\) | −3.41936e11 | −0.811990 | −0.405995 | − | 0.913875i | \(-0.633075\pi\) | ||||
−0.405995 | + | 0.913875i | \(0.633075\pi\) | |||||||
\(384\) | 2.36375e11 | 0.554768 | ||||||||
\(385\) | 5.90708e10 | 0.137025 | ||||||||
\(386\) | −1.65894e11 | −0.380353 | ||||||||
\(387\) | 3.97555e11 | 0.900945 | ||||||||
\(388\) | 3.00568e11 | 0.673287 | ||||||||
\(389\) | 7.41610e11 | 1.64211 | 0.821055 | − | 0.570849i | \(-0.193386\pi\) | ||||
0.821055 | + | 0.570849i | \(0.193386\pi\) | |||||||
\(390\) | −4.86042e10 | −0.106386 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.95012e11 | 0.844933 | ||||||||
\(393\) | 1.33359e11 | 0.282005 | ||||||||
\(394\) | 1.18174e11 | 0.247051 | ||||||||
\(395\) | −1.99335e10 | −0.0412000 | ||||||||
\(396\) | 4.26458e10 | 0.0871461 | ||||||||
\(397\) | −2.44352e11 | −0.493695 | −0.246848 | − | 0.969054i | \(-0.579395\pi\) | ||||
−0.246848 | + | 0.969054i | \(0.579395\pi\) | |||||||
\(398\) | 5.19345e11 | 1.03748 | ||||||||
\(399\) | −6.78557e9 | −0.0134032 | ||||||||
\(400\) | 7.99555e10 | 0.156163 | ||||||||
\(401\) | −4.19091e11 | −0.809392 | −0.404696 | − | 0.914451i | \(-0.632623\pi\) | ||||
−0.404696 | + | 0.914451i | \(0.632623\pi\) | |||||||
\(402\) | −1.64205e11 | −0.313595 | ||||||||
\(403\) | −9.38539e9 | −0.0177247 | ||||||||
\(404\) | 6.10317e11 | 1.13983 | ||||||||
\(405\) | 2.37324e11 | 0.438322 | ||||||||
\(406\) | 5.11462e10 | 0.0934214 | ||||||||
\(407\) | 2.34285e11 | 0.423223 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.47241e11 | −0.966994 | −0.483497 | − | 0.875346i | \(-0.660634\pi\) | ||||
−0.483497 | + | 0.875346i | \(0.660634\pi\) | |||||||
\(410\) | −4.12654e11 | −0.721205 | ||||||||
\(411\) | −5.21717e10 | −0.0901876 | ||||||||
\(412\) | −2.87283e11 | −0.491216 | ||||||||
\(413\) | −1.99740e11 | −0.337824 | ||||||||
\(414\) | −2.35016e10 | −0.0393184 | ||||||||
\(415\) | 1.27563e12 | 2.11109 | ||||||||
\(416\) | −1.08975e11 | −0.178404 | ||||||||
\(417\) | −7.92933e11 | −1.28417 | ||||||||
\(418\) | −5.25517e9 | −0.00841964 | ||||||||
\(419\) | −6.31112e11 | −1.00033 | −0.500165 | − | 0.865930i | \(-0.666727\pi\) | ||||
−0.500165 | + | 0.865930i | \(0.666727\pi\) | |||||||
\(420\) | 1.57313e11 | 0.246684 | ||||||||
\(421\) | 2.59316e11 | 0.402309 | 0.201154 | − | 0.979560i | \(-0.435531\pi\) | ||||
0.201154 | + | 0.979560i | \(0.435531\pi\) | |||||||
\(422\) | −1.17145e11 | −0.179811 | ||||||||
\(423\) | −5.56067e11 | −0.844492 | ||||||||
\(424\) | 9.22032e11 | 1.38548 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.81321e11 | 0.413866 | ||||||||
\(427\) | −2.20330e11 | −0.320737 | ||||||||
\(428\) | −5.16744e11 | −0.744351 | ||||||||
\(429\) | 2.38039e10 | 0.0339305 | ||||||||
\(430\) | 1.13576e12 | 1.60205 | ||||||||
\(431\) | 3.20451e11 | 0.447315 | 0.223658 | − | 0.974668i | \(-0.428200\pi\) | ||||
0.223658 | + | 0.974668i | \(0.428200\pi\) | |||||||
\(432\) | 9.96088e10 | 0.137601 | ||||||||
\(433\) | 6.08153e11 | 0.831414 | 0.415707 | − | 0.909499i | \(-0.363534\pi\) | ||||
0.415707 | + | 0.909499i | \(0.363534\pi\) | |||||||
\(434\) | −1.46767e10 | −0.0198575 | ||||||||
\(435\) | −3.86237e11 | −0.517192 | ||||||||
\(436\) | 4.31926e11 | 0.572427 | ||||||||
\(437\) | −5.99407e9 | −0.00786241 | ||||||||
\(438\) | −1.34869e11 | −0.175097 | ||||||||
\(439\) | 9.67705e11 | 1.24352 | 0.621760 | − | 0.783208i | \(-0.286418\pi\) | ||||
0.621760 | + | 0.783208i | \(0.286418\pi\) | |||||||
\(440\) | 3.02529e11 | 0.384796 | ||||||||
\(441\) | 3.35276e11 | 0.422114 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.00554e11 | 1.11095 | 0.555473 | − | 0.831535i | \(-0.312537\pi\) | ||||
0.555473 | + | 0.831535i | \(0.312537\pi\) | |||||||
\(444\) | 6.23929e11 | 0.761924 | ||||||||
\(445\) | −1.22437e12 | −1.48011 | ||||||||
\(446\) | 3.66679e11 | 0.438812 | ||||||||
\(447\) | −8.59250e11 | −1.01797 | ||||||||
\(448\) | −1.33034e11 | −0.156031 | ||||||||
\(449\) | 2.53168e11 | 0.293968 | 0.146984 | − | 0.989139i | \(-0.453043\pi\) | ||||
0.146984 | + | 0.989139i | \(0.453043\pi\) | |||||||
\(450\) | −2.87291e11 | −0.330267 | ||||||||
\(451\) | 2.02097e11 | 0.230020 | ||||||||
\(452\) | −9.05108e11 | −1.01995 | ||||||||
\(453\) | 1.15561e11 | 0.128935 | ||||||||
\(454\) | 9.99708e11 | 1.10439 | ||||||||
\(455\) | −8.02107e10 | −0.0877366 | ||||||||
\(456\) | −3.47521e10 | −0.0376391 | ||||||||
\(457\) | 1.51148e12 | 1.62099 | 0.810495 | − | 0.585745i | \(-0.199198\pi\) | ||||
0.810495 | + | 0.585745i | \(0.199198\pi\) | |||||||
\(458\) | −1.35166e10 | −0.0143540 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.38963e11 | 0.144707 | ||||||||
\(461\) | 8.09197e11 | 0.834450 | 0.417225 | − | 0.908803i | \(-0.363003\pi\) | ||||
0.417225 | + | 0.908803i | \(0.363003\pi\) | |||||||
\(462\) | 3.72241e10 | 0.0380132 | ||||||||
\(463\) | 1.55999e12 | 1.57764 | 0.788819 | − | 0.614625i | \(-0.210693\pi\) | ||||
0.788819 | + | 0.614625i | \(0.210693\pi\) | |||||||
\(464\) | −6.18768e10 | −0.0619722 | ||||||||
\(465\) | 1.10833e11 | 0.109933 | ||||||||
\(466\) | −7.85371e11 | −0.771504 | ||||||||
\(467\) | 3.66882e11 | 0.356944 | 0.178472 | − | 0.983945i | \(-0.442885\pi\) | ||||
0.178472 | + | 0.983945i | \(0.442885\pi\) | |||||||
\(468\) | −5.79076e10 | −0.0557993 | ||||||||
\(469\) | −2.70985e11 | −0.258623 | ||||||||
\(470\) | −1.58860e12 | −1.50167 | ||||||||
\(471\) | 3.31660e11 | 0.310527 | ||||||||
\(472\) | −1.02296e12 | −0.948683 | ||||||||
\(473\) | −5.56236e11 | −0.510957 | ||||||||
\(474\) | −1.25613e10 | −0.0114296 | ||||||||
\(475\) | −7.32734e10 | −0.0660427 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.82599e11 | 0.692160 | ||||||||
\(478\) | −6.29015e11 | −0.551106 | ||||||||
\(479\) | −5.73621e11 | −0.497869 | −0.248935 | − | 0.968520i | \(-0.580080\pi\) | ||||
−0.248935 | + | 0.968520i | \(0.580080\pi\) | |||||||
\(480\) | 1.28689e12 | 1.10651 | ||||||||
\(481\) | −3.18129e11 | −0.270989 | ||||||||
\(482\) | 1.11198e12 | 0.938398 | ||||||||
\(483\) | 4.24579e10 | 0.0354974 | ||||||||
\(484\) | 7.54320e11 | 0.624815 | ||||||||
\(485\) | 1.80979e12 | 1.48522 | ||||||||
\(486\) | −6.00164e11 | −0.487986 | ||||||||
\(487\) | −1.56412e12 | −1.26006 | −0.630028 | − | 0.776572i | \(-0.716957\pi\) | ||||
−0.630028 | + | 0.776572i | \(0.716957\pi\) | |||||||
\(488\) | −1.12842e12 | −0.900700 | ||||||||
\(489\) | −2.12492e11 | −0.168055 | ||||||||
\(490\) | 9.57835e11 | 0.750600 | ||||||||
\(491\) | −1.20510e11 | −0.0935743 | −0.0467872 | − | 0.998905i | \(-0.514898\pi\) | ||||
−0.0467872 | + | 0.998905i | \(0.514898\pi\) | |||||||
\(492\) | 5.38208e11 | 0.414102 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 7.13585e9 | 0.00539107 | ||||||||
\(495\) | 2.56780e11 | 0.192237 | ||||||||
\(496\) | 1.77559e10 | 0.0131727 | ||||||||
\(497\) | 4.64260e11 | 0.341316 | ||||||||
\(498\) | 8.03849e11 | 0.585656 | ||||||||
\(499\) | −4.96049e11 | −0.358156 | −0.179078 | − | 0.983835i | \(-0.557311\pi\) | ||||
−0.179078 | + | 0.983835i | \(0.557311\pi\) | |||||||
\(500\) | 2.97263e11 | 0.212704 | ||||||||
\(501\) | 1.42833e12 | 1.01288 | ||||||||
\(502\) | 2.10283e11 | 0.147787 | ||||||||
\(503\) | 1.48407e11 | 0.103371 | 0.0516853 | − | 0.998663i | \(-0.483541\pi\) | ||||
0.0516853 | + | 0.998663i | \(0.483541\pi\) | |||||||
\(504\) | −2.24861e11 | −0.155231 | ||||||||
\(505\) | 3.67486e12 | 2.51437 | ||||||||
\(506\) | 3.28821e10 | 0.0222988 | ||||||||
\(507\) | 1.04321e12 | 0.701191 | ||||||||
\(508\) | 1.08051e12 | 0.719850 | ||||||||
\(509\) | 8.49687e11 | 0.561085 | 0.280543 | − | 0.959842i | \(-0.409486\pi\) | ||||
0.280543 | + | 0.959842i | \(0.409486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.22572e11 | −0.144403 | ||||||||
\(512\) | 3.97599e11 | 0.255700 | ||||||||
\(513\) | −9.12842e10 | −0.0581925 | ||||||||
\(514\) | −7.11018e11 | −0.449311 | ||||||||
\(515\) | −1.72979e12 | −1.08358 | ||||||||
\(516\) | −1.48132e12 | −0.919869 | ||||||||
\(517\) | 7.78017e11 | 0.478941 | ||||||||
\(518\) | −4.97485e11 | −0.303596 | ||||||||
\(519\) | −4.04336e11 | −0.244618 | ||||||||
\(520\) | −4.10797e11 | −0.246384 | ||||||||
\(521\) | −4.63859e11 | −0.275814 | −0.137907 | − | 0.990445i | \(-0.544038\pi\) | ||||
−0.137907 | + | 0.990445i | \(0.544038\pi\) | |||||||
\(522\) | 2.22332e11 | 0.131064 | ||||||||
\(523\) | −3.01502e11 | −0.176211 | −0.0881054 | − | 0.996111i | \(-0.528081\pi\) | ||||
−0.0881054 | + | 0.996111i | \(0.528081\pi\) | |||||||
\(524\) | 4.53913e11 | 0.263016 | ||||||||
\(525\) | 5.19019e11 | 0.298172 | ||||||||
\(526\) | 1.76597e11 | 0.100588 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −4.50338e10 | −0.0252165 | ||||||||
\(529\) | −1.76365e12 | −0.979177 | ||||||||
\(530\) | 2.23577e12 | 1.23079 | ||||||||
\(531\) | −8.68267e11 | −0.473945 | ||||||||
\(532\) | −2.30959e10 | −0.0125007 | ||||||||
\(533\) | −2.74422e11 | −0.147281 | ||||||||
\(534\) | −7.71550e11 | −0.410609 | ||||||||
\(535\) | −3.11143e12 | −1.64198 | ||||||||
\(536\) | −1.38784e12 | −0.726271 | ||||||||
\(537\) | −1.85492e12 | −0.962591 | ||||||||
\(538\) | −1.22701e12 | −0.631435 | ||||||||
\(539\) | −4.69099e11 | −0.239395 | ||||||||
\(540\) | 2.11628e12 | 1.07103 | ||||||||
\(541\) | −2.05647e12 | −1.03213 | −0.516066 | − | 0.856549i | \(-0.672604\pi\) | ||||
−0.516066 | + | 0.856549i | \(0.672604\pi\) | |||||||
\(542\) | 1.02205e12 | 0.508714 | ||||||||
\(543\) | −1.13758e12 | −0.561544 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.60072e12 | 1.26273 | ||||||||
\(546\) | −5.05456e10 | −0.0243398 | ||||||||
\(547\) | −3.11555e12 | −1.48796 | −0.743981 | − | 0.668201i | \(-0.767065\pi\) | ||||
−0.743981 | + | 0.668201i | \(0.767065\pi\) | |||||||
\(548\) | −1.77576e11 | −0.0841147 | ||||||||
\(549\) | −9.57773e11 | −0.449973 | ||||||||
\(550\) | 4.01961e11 | 0.187306 | ||||||||
\(551\) | 5.67056e10 | 0.0262086 | ||||||||
\(552\) | 2.17447e11 | 0.0996845 | ||||||||
\(553\) | −2.07297e10 | −0.00942607 | ||||||||
\(554\) | 3.26599e11 | 0.147306 | ||||||||
\(555\) | 3.75681e12 | 1.68074 | ||||||||
\(556\) | −2.69889e12 | −1.19770 | ||||||||
\(557\) | 2.06457e12 | 0.908828 | 0.454414 | − | 0.890791i | \(-0.349849\pi\) | ||||
0.454414 | + | 0.890791i | \(0.349849\pi\) | |||||||
\(558\) | −6.37993e10 | −0.0278588 | ||||||||
\(559\) | 7.55298e11 | 0.327164 | ||||||||
\(560\) | 1.51748e11 | 0.0652043 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.23085e10 | 0.00520467 | ||||||||
\(563\) | 3.11121e12 | 1.30509 | 0.652547 | − | 0.757748i | \(-0.273700\pi\) | ||||
0.652547 | + | 0.757748i | \(0.273700\pi\) | |||||||
\(564\) | 2.07195e12 | 0.862231 | ||||||||
\(565\) | −5.44986e12 | −2.24992 | ||||||||
\(566\) | 4.89186e11 | 0.200355 | ||||||||
\(567\) | 2.46803e11 | 0.100283 | ||||||||
\(568\) | 2.37769e12 | 0.958491 | ||||||||
\(569\) | 4.33084e11 | 0.173207 | 0.0866037 | − | 0.996243i | \(-0.472399\pi\) | ||||
0.0866037 | + | 0.996243i | \(0.472399\pi\) | |||||||
\(570\) | −8.42678e10 | −0.0334368 | ||||||||
\(571\) | 4.07139e12 | 1.60280 | 0.801402 | − | 0.598126i | \(-0.204088\pi\) | ||||
0.801402 | + | 0.598126i | \(0.204088\pi\) | |||||||
\(572\) | 8.10209e10 | 0.0316457 | ||||||||
\(573\) | 6.73037e11 | 0.260821 | ||||||||
\(574\) | −4.29136e11 | −0.165003 | ||||||||
\(575\) | 4.58478e11 | 0.174910 | ||||||||
\(576\) | −5.78295e11 | −0.218901 | ||||||||
\(577\) | −2.10704e12 | −0.791375 | −0.395687 | − | 0.918385i | \(-0.629494\pi\) | ||||
−0.395687 | + | 0.918385i | \(0.629494\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.30280e12 | 0.481754 | ||||||||
\(580\) | −1.31463e12 | −0.482366 | ||||||||
\(581\) | 1.32658e12 | 0.482993 | ||||||||
\(582\) | 1.14046e12 | 0.412027 | ||||||||
\(583\) | −1.09497e12 | −0.392548 | ||||||||
\(584\) | −1.13989e12 | −0.405515 | ||||||||
\(585\) | −3.48675e11 | −0.123089 | ||||||||
\(586\) | −1.51574e12 | −0.530988 | ||||||||
\(587\) | −1.65360e12 | −0.574857 | −0.287428 | − | 0.957802i | \(-0.592800\pi\) | ||||
−0.287428 | + | 0.957802i | \(0.592800\pi\) | |||||||
\(588\) | −1.24927e12 | −0.430980 | ||||||||
\(589\) | −1.62720e10 | −0.00557085 | ||||||||
\(590\) | −2.48051e12 | −0.842766 | ||||||||
\(591\) | −9.28046e11 | −0.312915 | ||||||||
\(592\) | 6.01858e11 | 0.201394 | ||||||||
\(593\) | −1.28308e12 | −0.426096 | −0.213048 | − | 0.977042i | \(-0.568339\pi\) | ||||
−0.213048 | + | 0.977042i | \(0.568339\pi\) | |||||||
\(594\) | 5.00764e11 | 0.165042 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.92462e12 | −0.949425 | ||||||||
\(597\) | −4.07854e12 | −1.31408 | ||||||||
\(598\) | −4.46497e10 | −0.0142779 | ||||||||
\(599\) | 2.16567e12 | 0.687341 | 0.343671 | − | 0.939090i | \(-0.388330\pi\) | ||||
0.343671 | + | 0.939090i | \(0.388330\pi\) | |||||||
\(600\) | 2.65814e12 | 0.837331 | ||||||||
\(601\) | −7.68293e11 | −0.240210 | −0.120105 | − | 0.992761i | \(-0.538323\pi\) | ||||
−0.120105 | + | 0.992761i | \(0.538323\pi\) | |||||||
\(602\) | 1.18112e12 | 0.366531 | ||||||||
\(603\) | −1.17797e12 | −0.362832 | ||||||||
\(604\) | 3.93333e11 | 0.120253 | ||||||||
\(605\) | 4.54193e12 | 1.37829 | ||||||||
\(606\) | 2.31575e12 | 0.697532 | ||||||||
\(607\) | −2.89113e12 | −0.864406 | −0.432203 | − | 0.901776i | \(-0.642264\pi\) | ||||
−0.432203 | + | 0.901776i | \(0.642264\pi\) | |||||||
\(608\) | −1.88935e11 | −0.0560721 | ||||||||
\(609\) | −4.01664e11 | −0.118327 | ||||||||
\(610\) | −2.73621e12 | −0.800140 | ||||||||
\(611\) | −1.05645e12 | −0.306664 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.08236e12 | −1.45376 | −0.726881 | − | 0.686763i | \(-0.759031\pi\) | ||||
−0.726881 | + | 0.686763i | \(0.759031\pi\) | |||||||
\(614\) | −1.05734e12 | −0.300233 | ||||||||
\(615\) | 3.24067e12 | 0.913476 | ||||||||
\(616\) | 3.14613e11 | 0.0880367 | ||||||||
\(617\) | 2.83974e12 | 0.788852 | 0.394426 | − | 0.918928i | \(-0.370944\pi\) | ||||
0.394426 | + | 0.918928i | \(0.370944\pi\) | |||||||
\(618\) | −1.09005e12 | −0.300606 | ||||||||
\(619\) | −2.75485e12 | −0.754206 | −0.377103 | − | 0.926171i | \(-0.623080\pi\) | ||||
−0.377103 | + | 0.926171i | \(0.623080\pi\) | |||||||
\(620\) | 3.77240e11 | 0.102531 | ||||||||
\(621\) | 5.71174e11 | 0.154119 | ||||||||
\(622\) | −2.19114e12 | −0.586966 | ||||||||
\(623\) | −1.27328e12 | −0.338630 | ||||||||
\(624\) | 6.11502e10 | 0.0161461 | ||||||||
\(625\) | −2.83394e12 | −0.742901 | ||||||||
\(626\) | −4.20726e12 | −1.09500 | ||||||||
\(627\) | 4.12701e10 | 0.0106643 | ||||||||
\(628\) | 1.12887e12 | 0.289617 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −5.45250e11 | −0.137900 | ||||||||
\(631\) | 4.35581e12 | 1.09380 | 0.546899 | − | 0.837199i | \(-0.315808\pi\) | ||||
0.546899 | + | 0.837199i | \(0.315808\pi\) | |||||||
\(632\) | −1.06167e11 | −0.0264705 | ||||||||
\(633\) | 9.19968e11 | 0.227749 | ||||||||
\(634\) | −1.68602e12 | −0.414439 | ||||||||
\(635\) | 6.50599e12 | 1.58793 | ||||||||
\(636\) | −2.91603e12 | −0.706699 | ||||||||
\(637\) | 6.36978e11 | 0.153284 | ||||||||
\(638\) | −3.11074e11 | −0.0743310 | ||||||||
\(639\) | 2.01813e12 | 0.478845 | ||||||||
\(640\) | 4.84436e12 | 1.14137 | ||||||||
\(641\) | −9.78124e11 | −0.228840 | −0.114420 | − | 0.993432i | \(-0.536501\pi\) | ||||
−0.114420 | + | 0.993432i | \(0.536501\pi\) | |||||||
\(642\) | −1.96070e12 | −0.455515 | ||||||||
\(643\) | 6.72829e11 | 0.155223 | 0.0776114 | − | 0.996984i | \(-0.475271\pi\) | ||||
0.0776114 | + | 0.996984i | \(0.475271\pi\) | |||||||
\(644\) | 1.44513e11 | 0.0331072 | ||||||||
\(645\) | −8.91937e12 | −2.02916 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.23882e12 | −1.39969 | −0.699847 | − | 0.714293i | \(-0.746748\pi\) | ||||
−0.699847 | + | 0.714293i | \(0.746748\pi\) | |||||||
\(648\) | 1.26399e12 | 0.281616 | ||||||||
\(649\) | 1.21483e12 | 0.268791 | ||||||||
\(650\) | −5.45812e11 | −0.119931 | ||||||||
\(651\) | 1.15260e11 | 0.0251515 | ||||||||
\(652\) | −7.23255e11 | −0.156739 | ||||||||
\(653\) | −9.10099e12 | −1.95875 | −0.979375 | − | 0.202049i | \(-0.935240\pi\) | ||||
−0.979375 | + | 0.202049i | \(0.935240\pi\) | |||||||
\(654\) | 1.63887e12 | 0.350304 | ||||||||
\(655\) | 2.73311e12 | 0.580192 | ||||||||
\(656\) | 5.19170e11 | 0.109457 | ||||||||
\(657\) | −9.67515e11 | −0.202588 | ||||||||
\(658\) | −1.65205e12 | −0.343564 | ||||||||
\(659\) | −5.03909e12 | −1.04080 | −0.520400 | − | 0.853922i | \(-0.674217\pi\) | ||||
−0.520400 | + | 0.853922i | \(0.674217\pi\) | |||||||
\(660\) | −9.56782e11 | −0.196275 | ||||||||
\(661\) | −8.54137e12 | −1.74029 | −0.870144 | − | 0.492798i | \(-0.835974\pi\) | ||||
−0.870144 | + | 0.492798i | \(0.835974\pi\) | |||||||
\(662\) | 1.39154e12 | 0.281602 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.79404e12 | 1.35635 | ||||||||
\(665\) | −1.39066e11 | −0.0275755 | ||||||||
\(666\) | −2.16256e12 | −0.425925 | ||||||||
\(667\) | −3.54812e11 | −0.0694116 | ||||||||
\(668\) | 4.86158e12 | 0.944676 | ||||||||
\(669\) | −2.87962e12 | −0.555798 | ||||||||
\(670\) | −3.36528e12 | −0.645185 | ||||||||
\(671\) | 1.34006e12 | 0.255195 | ||||||||
\(672\) | 1.33829e12 | 0.253156 | ||||||||
\(673\) | 1.57979e12 | 0.296846 | 0.148423 | − | 0.988924i | \(-0.452580\pi\) | ||||
0.148423 | + | 0.988924i | \(0.452580\pi\) | |||||||
\(674\) | 3.28549e12 | 0.613240 | ||||||||
\(675\) | 6.98220e12 | 1.29457 | ||||||||
\(676\) | 3.55076e12 | 0.653976 | ||||||||
\(677\) | −1.28465e12 | −0.235037 | −0.117519 | − | 0.993071i | \(-0.537494\pi\) | ||||
−0.117519 | + | 0.993071i | \(0.537494\pi\) | |||||||
\(678\) | −3.43428e12 | −0.624169 | ||||||||
\(679\) | 1.88208e12 | 0.339800 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.85096e12 | −1.39882 | ||||||||
\(682\) | 8.92643e10 | 0.0157997 | ||||||||
\(683\) | −7.81658e12 | −1.37443 | −0.687217 | − | 0.726453i | \(-0.741168\pi\) | ||||
−0.687217 | + | 0.726453i | \(0.741168\pi\) | |||||||
\(684\) | −1.00398e11 | −0.0175376 | ||||||||
\(685\) | −1.06922e12 | −0.185550 | ||||||||
\(686\) | 2.12263e12 | 0.365945 | ||||||||
\(687\) | 1.06149e11 | 0.0181808 | ||||||||
\(688\) | −1.42892e12 | −0.243143 | ||||||||
\(689\) | 1.48683e12 | 0.251347 | ||||||||
\(690\) | 5.27272e11 | 0.0885551 | ||||||||
\(691\) | 5.29472e12 | 0.883470 | 0.441735 | − | 0.897146i | \(-0.354363\pi\) | ||||
0.441735 | + | 0.897146i | \(0.354363\pi\) | |||||||
\(692\) | −1.37623e12 | −0.228147 | ||||||||
\(693\) | 2.67036e11 | 0.0439816 | ||||||||
\(694\) | −5.20998e11 | −0.0852547 | ||||||||
\(695\) | −1.62506e13 | −2.64204 | ||||||||
\(696\) | −2.05711e12 | −0.332289 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −3.59133e12 | −0.572672 | ||||||||
\(699\) | 6.16771e12 | 0.977185 | ||||||||
\(700\) | 1.76658e12 | 0.278094 | ||||||||
\(701\) | −4.08705e12 | −0.639262 | −0.319631 | − | 0.947542i | \(-0.603559\pi\) | ||||
−0.319631 | + | 0.947542i | \(0.603559\pi\) | |||||||
\(702\) | −6.79974e11 | −0.105676 | ||||||||
\(703\) | −5.51559e11 | −0.0851712 | ||||||||
\(704\) | 8.09116e11 | 0.124146 | ||||||||
\(705\) | 1.24757e13 | 1.90201 | ||||||||
\(706\) | 2.90767e12 | 0.440478 | ||||||||
\(707\) | 3.82164e12 | 0.575257 | ||||||||
\(708\) | 3.23523e12 | 0.483900 | ||||||||
\(709\) | −7.02438e12 | −1.04400 | −0.522000 | − | 0.852946i | \(-0.674814\pi\) | ||||
−0.522000 | + | 0.852946i | \(0.674814\pi\) | |||||||
\(710\) | 5.76550e12 | 0.851479 | ||||||||
\(711\) | −9.01118e10 | −0.0132242 | ||||||||
\(712\) | −6.52104e12 | −0.950948 | ||||||||
\(713\) | 1.01815e11 | 0.0147540 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.87845e11 | 0.0698079 | ||||||||
\(716\) | −6.31358e12 | −0.897773 | ||||||||
\(717\) | 4.93981e12 | 0.698030 | ||||||||
\(718\) | 2.93033e12 | 0.411487 | ||||||||
\(719\) | −1.05283e13 | −1.46919 | −0.734594 | − | 0.678507i | \(-0.762627\pi\) | ||||
−0.734594 | + | 0.678507i | \(0.762627\pi\) | |||||||
\(720\) | 6.59646e11 | 0.0914775 | ||||||||
\(721\) | −1.79889e12 | −0.247911 | ||||||||
\(722\) | −4.15505e12 | −0.569061 | ||||||||
\(723\) | −8.73269e12 | −1.18857 | ||||||||
\(724\) | −3.87197e12 | −0.523731 | ||||||||
\(725\) | −4.33733e12 | −0.583044 | ||||||||
\(726\) | 2.86214e12 | 0.382363 | ||||||||
\(727\) | −9.94519e11 | −0.132041 | −0.0660204 | − | 0.997818i | \(-0.521030\pi\) | ||||
−0.0660204 | + | 0.997818i | \(0.521030\pi\) | |||||||
\(728\) | −4.27205e11 | −0.0563696 | ||||||||
\(729\) | 6.96056e12 | 0.912788 | ||||||||
\(730\) | −2.76405e12 | −0.360240 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 3.56874e12 | 0.459425 | ||||||||
\(733\) | 3.00202e12 | 0.384101 | 0.192051 | − | 0.981385i | \(-0.438486\pi\) | ||||
0.192051 | + | 0.981385i | \(0.438486\pi\) | |||||||
\(734\) | 4.88580e12 | 0.621303 | ||||||||
\(735\) | −7.52211e12 | −0.950708 | ||||||||
\(736\) | 1.18219e12 | 0.148503 | ||||||||
\(737\) | 1.64814e12 | 0.205774 | ||||||||
\(738\) | −1.86545e12 | −0.231489 | ||||||||
\(739\) | −1.31885e13 | −1.62665 | −0.813325 | − | 0.581810i | \(-0.802345\pi\) | ||||
−0.813325 | + | 0.581810i | \(0.802345\pi\) | |||||||
\(740\) | 1.27870e13 | 1.56757 | ||||||||
\(741\) | −5.60396e10 | −0.00682831 | ||||||||
\(742\) | 2.32507e12 | 0.281591 | ||||||||
\(743\) | 4.22387e12 | 0.508464 | 0.254232 | − | 0.967143i | \(-0.418177\pi\) | ||||
0.254232 | + | 0.967143i | \(0.418177\pi\) | |||||||
\(744\) | 5.90299e11 | 0.0706308 | ||||||||
\(745\) | −1.76098e13 | −2.09436 | ||||||||
\(746\) | 8.47749e12 | 1.00217 | ||||||||
\(747\) | 5.76662e12 | 0.677608 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.23571e12 | −0.375665 | ||||||||
\(750\) | 1.12791e12 | 0.130167 | ||||||||
\(751\) | 8.30449e12 | 0.952649 | 0.476325 | − | 0.879270i | \(-0.341969\pi\) | ||||
0.476325 | + | 0.879270i | \(0.341969\pi\) | |||||||
\(752\) | 1.99866e12 | 0.227907 | ||||||||
\(753\) | −1.65140e12 | −0.187187 | ||||||||
\(754\) | 4.22399e11 | 0.0475939 | ||||||||
\(755\) | 2.36835e12 | 0.265268 | ||||||||
\(756\) | 2.20081e12 | 0.245038 | ||||||||
\(757\) | −9.58086e12 | −1.06041 | −0.530204 | − | 0.847870i | \(-0.677885\pi\) | ||||
−0.530204 | + | 0.847870i | \(0.677885\pi\) | |||||||
\(758\) | 6.51635e12 | 0.716957 | ||||||||
\(759\) | −2.58231e11 | −0.0282436 | ||||||||
\(760\) | −7.12221e11 | −0.0774379 | ||||||||
\(761\) | −3.82260e12 | −0.413169 | −0.206585 | − | 0.978429i | \(-0.566235\pi\) | ||||
−0.206585 | + | 0.978429i | \(0.566235\pi\) | |||||||
\(762\) | 4.09982e12 | 0.440521 | ||||||||
\(763\) | 2.70460e12 | 0.288897 | ||||||||
\(764\) | 2.29081e12 | 0.243259 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.41601e12 | −0.463448 | ||||||||
\(767\) | −1.64958e12 | −0.172106 | ||||||||
\(768\) | 6.24858e12 | 0.648121 | ||||||||
\(769\) | −1.25991e13 | −1.29919 | −0.649595 | − | 0.760281i | \(-0.725061\pi\) | ||||
−0.649595 | + | 0.760281i | \(0.725061\pi\) | |||||||
\(770\) | 7.62883e11 | 0.0782077 | ||||||||
\(771\) | 5.58380e12 | 0.569096 | ||||||||
\(772\) | 4.43434e12 | 0.449315 | ||||||||
\(773\) | 3.83859e12 | 0.386691 | 0.193345 | − | 0.981131i | \(-0.438066\pi\) | ||||
0.193345 | + | 0.981131i | \(0.438066\pi\) | |||||||
\(774\) | 5.13431e12 | 0.514219 | ||||||||
\(775\) | 1.24462e12 | 0.123931 | ||||||||
\(776\) | 9.63900e12 | 0.954232 | ||||||||
\(777\) | 3.90687e12 | 0.384534 | ||||||||
\(778\) | 9.57768e12 | 0.937243 | ||||||||
\(779\) | −4.75781e11 | −0.0462902 | ||||||||
\(780\) | 1.29919e12 | 0.125674 | ||||||||
\(781\) | −2.82365e12 | −0.271570 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.40346e12 | −0.513741 | ||||||||
\(784\) | −1.20508e12 | −0.113918 | ||||||||
\(785\) | 6.79716e12 | 0.638873 | ||||||||
\(786\) | 1.72230e12 | 0.160956 | ||||||||
\(787\) | −2.26189e12 | −0.210177 | −0.105089 | − | 0.994463i | \(-0.533513\pi\) | ||||
−0.105089 | + | 0.994463i | \(0.533513\pi\) | |||||||
\(788\) | −3.15878e12 | −0.291844 | ||||||||
\(789\) | −1.38686e12 | −0.127405 | ||||||||
\(790\) | −2.57436e11 | −0.0235151 | ||||||||
\(791\) | −5.66754e12 | −0.514754 | ||||||||
\(792\) | 1.36762e12 | 0.123510 | ||||||||
\(793\) | −1.81963e12 | −0.163401 | ||||||||
\(794\) | −3.15574e12 | −0.281779 | ||||||||
\(795\) | −1.75580e13 | −1.55892 | ||||||||
\(796\) | −1.38821e13 | −1.22559 | ||||||||
\(797\) | 1.88804e13 | 1.65748 | 0.828741 | − | 0.559632i | \(-0.189058\pi\) | ||||
0.828741 | + | 0.559632i | \(0.189058\pi\) | |||||||
\(798\) | −8.76337e10 | −0.00764994 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.44514e13 | 1.24740 | ||||||||
\(801\) | −5.53491e12 | −0.475077 | ||||||||
\(802\) | −5.41245e12 | −0.461965 | ||||||||
\(803\) | 1.35369e12 | 0.114895 | ||||||||
\(804\) | 4.38920e12 | 0.370453 | ||||||||
\(805\) | 8.70148e11 | 0.0730317 | ||||||||
\(806\) | −1.21210e11 | −0.0101165 | ||||||||
\(807\) | 9.63602e12 | 0.799773 | ||||||||
\(808\) | 1.95724e13 | 1.61545 | ||||||||
\(809\) | −3.59571e11 | −0.0295132 | −0.0147566 | − | 0.999891i | \(-0.504697\pi\) | ||||
−0.0147566 | + | 0.999891i | \(0.504697\pi\) | |||||||
\(810\) | 3.06497e12 | 0.250175 | ||||||||
\(811\) | −1.94199e13 | −1.57635 | −0.788174 | − | 0.615452i | \(-0.788973\pi\) | ||||
−0.788174 | + | 0.615452i | \(0.788973\pi\) | |||||||
\(812\) | −1.36714e12 | −0.110360 | ||||||||
\(813\) | −8.02637e12 | −0.644335 | ||||||||
\(814\) | 3.02572e12 | 0.241557 | ||||||||
\(815\) | −4.35488e12 | −0.345754 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.30950e12 | 0.102827 | ||||||||
\(818\) | −7.06746e12 | −0.551917 | ||||||||
\(819\) | −3.62601e11 | −0.0281612 | ||||||||
\(820\) | 1.10302e13 | 0.851966 | ||||||||
\(821\) | −1.20567e13 | −0.926153 | −0.463077 | − | 0.886318i | \(-0.653255\pi\) | ||||
−0.463077 | + | 0.886318i | \(0.653255\pi\) | |||||||
\(822\) | −6.73783e11 | −0.0514750 | ||||||||
\(823\) | 1.80283e13 | 1.36979 | 0.684897 | − | 0.728640i | \(-0.259847\pi\) | ||||
0.684897 | + | 0.728640i | \(0.259847\pi\) | |||||||
\(824\) | −9.21295e12 | −0.696187 | ||||||||
\(825\) | −3.15670e12 | −0.237241 | ||||||||
\(826\) | −2.57959e12 | −0.192815 | ||||||||
\(827\) | −1.53472e13 | −1.14092 | −0.570458 | − | 0.821326i | \(-0.693234\pi\) | ||||
−0.570458 | + | 0.821326i | \(0.693234\pi\) | |||||||
\(828\) | 6.28198e11 | 0.0464472 | ||||||||
\(829\) | 1.06941e13 | 0.786412 | 0.393206 | − | 0.919450i | \(-0.371366\pi\) | ||||
0.393206 | + | 0.919450i | \(0.371366\pi\) | |||||||
\(830\) | 1.64744e13 | 1.20492 | ||||||||
\(831\) | −2.56487e12 | −0.186578 | ||||||||
\(832\) | −1.09868e12 | −0.0794905 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.02405e13 | −0.732949 | ||||||||
\(835\) | 2.92726e13 | 2.08388 | ||||||||
\(836\) | 1.40471e11 | 0.00994620 | ||||||||
\(837\) | 1.55055e12 | 0.109200 | ||||||||
\(838\) | −8.15064e12 | −0.570944 | ||||||||
\(839\) | −1.24511e13 | −0.867518 | −0.433759 | − | 0.901029i | \(-0.642813\pi\) | ||||
−0.433759 | + | 0.901029i | \(0.642813\pi\) | |||||||
\(840\) | 5.04489e12 | 0.349619 | ||||||||
\(841\) | −1.11505e13 | −0.768623 | ||||||||
\(842\) | 3.34899e12 | 0.229620 | ||||||||
\(843\) | −9.66619e10 | −0.00659222 | ||||||||
\(844\) | 3.13128e12 | 0.212413 | ||||||||
\(845\) | 2.13799e13 | 1.44262 | ||||||||
\(846\) | −7.18145e12 | −0.481998 | ||||||||
\(847\) | 4.72334e12 | 0.315336 | ||||||||
\(848\) | −2.81288e12 | −0.186797 | ||||||||
\(849\) | −3.84170e12 | −0.253769 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.45116e12 | 0.225570 | ||||||||
\(852\) | −7.51971e12 | −0.488903 | ||||||||
\(853\) | −1.72550e13 | −1.11595 | −0.557974 | − | 0.829858i | \(-0.688421\pi\) | ||||
−0.557974 | + | 0.829858i | \(0.688421\pi\) | |||||||
\(854\) | −2.84551e12 | −0.183062 | ||||||||
\(855\) | −6.04517e11 | −0.0386866 | ||||||||
\(856\) | −1.65716e13 | −1.05495 | ||||||||
\(857\) | −5.66030e12 | −0.358447 | −0.179224 | − | 0.983808i | \(-0.557359\pi\) | ||||
−0.179224 | + | 0.983808i | \(0.557359\pi\) | |||||||
\(858\) | 3.07420e11 | 0.0193660 | ||||||||
\(859\) | −6.43103e12 | −0.403006 | −0.201503 | − | 0.979488i | \(-0.564583\pi\) | ||||
−0.201503 | + | 0.979488i | \(0.564583\pi\) | |||||||
\(860\) | −3.03587e13 | −1.89252 | ||||||||
\(861\) | 3.37011e12 | 0.208992 | ||||||||
\(862\) | 4.13853e12 | 0.255307 | ||||||||
\(863\) | −1.51972e13 | −0.932645 | −0.466322 | − | 0.884615i | \(-0.654421\pi\) | ||||
−0.466322 | + | 0.884615i | \(0.654421\pi\) | |||||||
\(864\) | 1.80036e13 | 1.09913 | ||||||||
\(865\) | −8.28660e12 | −0.503273 | ||||||||
\(866\) | 7.85412e12 | 0.474534 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.92308e11 | 0.0234578 | ||||||||
\(869\) | 1.26079e11 | 0.00749988 | ||||||||
\(870\) | −4.98814e12 | −0.295190 | ||||||||
\(871\) | −2.23797e12 | −0.131757 | ||||||||
\(872\) | 1.38515e13 | 0.811286 | ||||||||
\(873\) | 8.18135e12 | 0.476718 | ||||||||
\(874\) | −7.74117e10 | −0.00448751 | ||||||||
\(875\) | 1.86138e12 | 0.107349 | ||||||||
\(876\) | 3.60504e12 | 0.206843 | ||||||||
\(877\) | −1.55933e13 | −0.890104 | −0.445052 | − | 0.895505i | \(-0.646815\pi\) | ||||
−0.445052 | + | 0.895505i | \(0.646815\pi\) | |||||||
\(878\) | 1.24976e13 | 0.709745 | ||||||||
\(879\) | 1.19035e13 | 0.672548 | ||||||||
\(880\) | −9.22938e11 | −0.0518800 | ||||||||
\(881\) | −6.53525e12 | −0.365486 | −0.182743 | − | 0.983161i | \(-0.558498\pi\) | ||||
−0.182743 | + | 0.983161i | \(0.558498\pi\) | |||||||
\(882\) | 4.33000e12 | 0.240924 | ||||||||
\(883\) | 7.83304e12 | 0.433618 | 0.216809 | − | 0.976214i | \(-0.430435\pi\) | ||||
0.216809 | + | 0.976214i | \(0.430435\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.94801e13 | 1.06745 | ||||||||
\(886\) | 1.16304e13 | 0.634078 | ||||||||
\(887\) | −1.69970e13 | −0.921967 | −0.460983 | − | 0.887409i | \(-0.652503\pi\) | ||||
−0.460983 | + | 0.887409i | \(0.652503\pi\) | |||||||
\(888\) | 2.00089e13 | 1.07985 | ||||||||
\(889\) | 6.76586e12 | 0.363300 | ||||||||
\(890\) | −1.58124e13 | −0.844779 | ||||||||
\(891\) | −1.50107e12 | −0.0797904 | ||||||||
\(892\) | −9.80131e12 | −0.518373 | ||||||||
\(893\) | −1.83162e12 | −0.0963840 | ||||||||
\(894\) | −1.10970e13 | −0.581013 | ||||||||
\(895\) | −3.80154e13 | −1.98042 | ||||||||
\(896\) | 5.03785e12 | 0.261132 | ||||||||
\(897\) | 3.50645e11 | 0.0180843 | ||||||||
\(898\) | 3.26959e12 | 0.167784 | ||||||||
\(899\) | −9.63201e11 | −0.0491811 | ||||||||
\(900\) | 7.67928e12 | 0.390148 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 2.61003e12 | 0.131285 | ||||||||
\(903\) | −9.27563e12 | −0.464247 | ||||||||
\(904\) | −2.90261e13 | −1.44554 | ||||||||
\(905\) | −2.33140e13 | −1.15531 | ||||||||
\(906\) | 1.49244e12 | 0.0735901 | ||||||||
\(907\) | 2.70047e13 | 1.32497 | 0.662486 | − | 0.749075i | \(-0.269502\pi\) | ||||
0.662486 | + | 0.749075i | \(0.269502\pi\) | |||||||
\(908\) | −2.67222e13 | −1.30462 | ||||||||
\(909\) | 1.66126e13 | 0.807049 | ||||||||
\(910\) | −1.03590e12 | −0.0500761 | ||||||||
\(911\) | 4.11523e13 | 1.97953 | 0.989763 | − | 0.142722i | \(-0.0455854\pi\) | ||||
0.989763 | + | 0.142722i | \(0.0455854\pi\) | |||||||
\(912\) | 1.06019e11 | 0.00507468 | ||||||||
\(913\) | −8.06832e12 | −0.384295 | ||||||||
\(914\) | 1.95204e13 | 0.925189 | ||||||||
\(915\) | 2.14882e13 | 1.01345 | ||||||||
\(916\) | 3.61299e11 | 0.0169566 | ||||||||
\(917\) | 2.84228e12 | 0.132741 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.01787e12 | −0.139566 | −0.0697832 | − | 0.997562i | \(-0.522231\pi\) | ||||
−0.0697832 | + | 0.997562i | \(0.522231\pi\) | |||||||
\(920\) | 4.45644e12 | 0.205089 | ||||||||
\(921\) | 8.30358e12 | 0.380274 | ||||||||
\(922\) | 1.04506e13 | 0.476267 | ||||||||
\(923\) | 3.83416e12 | 0.173885 | ||||||||
\(924\) | −9.94998e11 | −0.0449054 | ||||||||
\(925\) | 4.21880e13 | 1.89475 | ||||||||
\(926\) | 2.01468e13 | 0.900445 | ||||||||
\(927\) | −7.81973e12 | −0.347803 | ||||||||
\(928\) | −1.11838e13 | −0.495021 | ||||||||
\(929\) | −2.85800e13 | −1.25890 | −0.629449 | − | 0.777041i | \(-0.716720\pi\) | ||||
−0.629449 | + | 0.777041i | \(0.716720\pi\) | |||||||
\(930\) | 1.43137e12 | 0.0627451 | ||||||||
\(931\) | 1.10436e12 | 0.0481769 | ||||||||
\(932\) | 2.09929e13 | 0.911385 | ||||||||
\(933\) | 1.72075e13 | 0.743450 | ||||||||
\(934\) | 4.73818e12 | 0.203728 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.85705e12 | −0.0790829 | ||||||||
\(937\) | −3.78192e13 | −1.60282 | −0.801409 | − | 0.598117i | \(-0.795916\pi\) | ||||
−0.801409 | + | 0.598117i | \(0.795916\pi\) | |||||||
\(938\) | −3.49969e12 | −0.147611 | ||||||||
\(939\) | 3.30407e13 | 1.38693 | ||||||||
\(940\) | 4.24633e13 | 1.77394 | ||||||||
\(941\) | 2.17056e13 | 0.902441 | 0.451220 | − | 0.892413i | \(-0.350989\pi\) | ||||
0.451220 | + | 0.892413i | \(0.350989\pi\) | |||||||
\(942\) | 4.28330e12 | 0.177235 | ||||||||
\(943\) | 2.97701e12 | 0.122596 | ||||||||
\(944\) | 3.12079e12 | 0.127906 | ||||||||
\(945\) | 1.32515e13 | 0.540535 | ||||||||
\(946\) | −7.18363e12 | −0.291631 | ||||||||
\(947\) | 1.29191e13 | 0.521986 | 0.260993 | − | 0.965341i | \(-0.415950\pi\) | ||||
0.260993 | + | 0.965341i | \(0.415950\pi\) | |||||||
\(948\) | 3.35764e11 | 0.0135019 | ||||||||
\(949\) | −1.83814e12 | −0.0735666 | ||||||||
\(950\) | −9.46305e11 | −0.0376942 | ||||||||
\(951\) | 1.32407e13 | 0.524927 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.66939e13 | 1.04832 | 0.524159 | − | 0.851620i | \(-0.324380\pi\) | ||||
0.524159 | + | 0.851620i | \(0.324380\pi\) | |||||||
\(954\) | 1.01070e13 | 0.395054 | ||||||||
\(955\) | 1.37935e13 | 0.536609 | ||||||||
\(956\) | 1.68135e13 | 0.651027 | ||||||||
\(957\) | 2.44294e12 | 0.0941475 | ||||||||
\(958\) | −7.40815e12 | −0.284162 | ||||||||
\(959\) | −1.11193e12 | −0.0424517 | ||||||||
\(960\) | 1.29744e13 | 0.493021 | ||||||||
\(961\) | −2.61632e13 | −0.989546 | ||||||||
\(962\) | −4.10855e12 | −0.154668 | ||||||||
\(963\) | −1.40656e13 | −0.527034 | ||||||||
\(964\) | −2.97233e13 | −1.10854 | ||||||||
\(965\) | 2.67001e13 | 0.991153 | ||||||||
\(966\) | 5.48332e11 | 0.0202603 | ||||||||
\(967\) | 2.52091e13 | 0.927124 | 0.463562 | − | 0.886064i | \(-0.346571\pi\) | ||||
0.463562 | + | 0.886064i | \(0.346571\pi\) | |||||||
\(968\) | 2.41905e13 | 0.885534 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.33729e13 | 0.847696 | ||||||||
\(971\) | −3.23630e13 | −1.16832 | −0.584161 | − | 0.811638i | \(-0.698576\pi\) | ||||
−0.584161 | + | 0.811638i | \(0.698576\pi\) | |||||||
\(972\) | 1.60424e13 | 0.576462 | ||||||||
\(973\) | −1.68997e13 | −0.604466 | ||||||||
\(974\) | −2.02002e13 | −0.719184 | ||||||||
\(975\) | 4.28640e12 | 0.151905 | ||||||||
\(976\) | 3.44250e12 | 0.121437 | ||||||||
\(977\) | −3.01878e13 | −1.06000 | −0.530001 | − | 0.847997i | \(-0.677808\pi\) | ||||
−0.530001 | + | 0.847997i | \(0.677808\pi\) | |||||||
\(978\) | −2.74427e12 | −0.0959184 | ||||||||
\(979\) | 7.74412e12 | 0.269432 | ||||||||
\(980\) | −2.56029e13 | −0.886690 | ||||||||
\(981\) | 1.17569e13 | 0.405304 | ||||||||
\(982\) | −1.55635e12 | −0.0534080 | ||||||||
\(983\) | 4.00385e13 | 1.36769 | 0.683843 | − | 0.729629i | \(-0.260307\pi\) | ||||
0.683843 | + | 0.729629i | \(0.260307\pi\) | |||||||
\(984\) | 1.72599e13 | 0.586896 | ||||||||
\(985\) | −1.90197e13 | −0.643785 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.29740e13 | 0.435157 | ||||||||
\(988\) | −1.90741e11 | −0.00636852 | ||||||||
\(989\) | −8.19369e12 | −0.272330 | ||||||||
\(990\) | 3.31624e12 | 0.109720 | ||||||||
\(991\) | −1.77191e13 | −0.583593 | −0.291796 | − | 0.956480i | \(-0.594253\pi\) | ||||
−0.291796 | + | 0.956480i | \(0.594253\pi\) | |||||||
\(992\) | 3.20926e12 | 0.105221 | ||||||||
\(993\) | −1.09281e13 | −0.356676 | ||||||||
\(994\) | 5.99578e12 | 0.194808 | ||||||||
\(995\) | −8.35870e13 | −2.70355 | ||||||||
\(996\) | −2.14869e13 | −0.691841 | ||||||||
\(997\) | 1.52000e13 | 0.487210 | 0.243605 | − | 0.969875i | \(-0.421670\pi\) | ||||
0.243605 | + | 0.969875i | \(0.421670\pi\) | |||||||
\(998\) | −6.40633e12 | −0.204419 | ||||||||
\(999\) | 5.25579e13 | 1.66953 |
(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.f.1.15 | 24 | ||
17.2 | even | 8 | 17.10.c.a.4.8 | ✓ | 24 | ||
17.9 | even | 8 | 17.10.c.a.13.5 | yes | 24 | ||
17.16 | even | 2 | inner | 289.10.a.f.1.16 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.c.a.4.8 | ✓ | 24 | 17.2 | even | 8 | ||
17.10.c.a.13.5 | yes | 24 | 17.9 | even | 8 | ||
289.10.a.f.1.15 | 24 | 1.1 | even | 1 | trivial | ||
289.10.a.f.1.16 | 24 | 17.16 | even | 2 | inner |