Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,8,Mod(1,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.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: | \(4.37339035678\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 14.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | −82.0000 | −1.75343 | −0.876717 | − | 0.481006i | \(-0.840271\pi\) | ||||
−0.876717 | + | 0.481006i | \(0.840271\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 448.000 | 1.60281 | 0.801407 | − | 0.598120i | \(-0.204085\pi\) | ||||
0.801407 | + | 0.598120i | \(0.204085\pi\) | |||||||
\(6\) | 656.000 | 1.23987 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 4537.00 | 2.07453 | ||||||||
\(10\) | −3584.00 | −1.13336 | ||||||||
\(11\) | 2408.00 | 0.545484 | 0.272742 | − | 0.962087i | \(-0.412069\pi\) | ||||
0.272742 | + | 0.962087i | \(0.412069\pi\) | |||||||
\(12\) | −5248.00 | −0.876717 | ||||||||
\(13\) | 7116.00 | 0.898326 | 0.449163 | − | 0.893450i | \(-0.351722\pi\) | ||||
0.449163 | + | 0.893450i | \(0.351722\pi\) | |||||||
\(14\) | 2744.00 | 0.267261 | ||||||||
\(15\) | −36736.0 | −2.81043 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 2486.00 | 0.122724 | 0.0613621 | − | 0.998116i | \(-0.480456\pi\) | ||||
0.0613621 | + | 0.998116i | \(0.480456\pi\) | |||||||
\(18\) | −36296.0 | −1.46692 | ||||||||
\(19\) | 36482.0 | 1.22023 | 0.610114 | − | 0.792314i | \(-0.291124\pi\) | ||||
0.610114 | + | 0.792314i | \(0.291124\pi\) | |||||||
\(20\) | 28672.0 | 0.801407 | ||||||||
\(21\) | 28126.0 | 0.662736 | ||||||||
\(22\) | −19264.0 | −0.385715 | ||||||||
\(23\) | −12880.0 | −0.220734 | −0.110367 | − | 0.993891i | \(-0.535203\pi\) | ||||
−0.110367 | + | 0.993891i | \(0.535203\pi\) | |||||||
\(24\) | 41984.0 | 0.619933 | ||||||||
\(25\) | 122579. | 1.56901 | ||||||||
\(26\) | −56928.0 | −0.635213 | ||||||||
\(27\) | −192700. | −1.88412 | ||||||||
\(28\) | −21952.0 | −0.188982 | ||||||||
\(29\) | −88094.0 | −0.670739 | −0.335369 | − | 0.942087i | \(-0.608861\pi\) | ||||
−0.335369 | + | 0.942087i | \(0.608861\pi\) | |||||||
\(30\) | 293888. | 1.98727 | ||||||||
\(31\) | 282636. | 1.70397 | 0.851984 | − | 0.523567i | \(-0.175399\pi\) | ||||
0.851984 | + | 0.523567i | \(0.175399\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | −197456. | −0.956470 | ||||||||
\(34\) | −19888.0 | −0.0867791 | ||||||||
\(35\) | −153664. | −0.605807 | ||||||||
\(36\) | 290368. | 1.03727 | ||||||||
\(37\) | −214534. | −0.696290 | −0.348145 | − | 0.937441i | \(-0.613188\pi\) | ||||
−0.348145 | + | 0.937441i | \(0.613188\pi\) | |||||||
\(38\) | −291856. | −0.862832 | ||||||||
\(39\) | −583512. | −1.57516 | ||||||||
\(40\) | −229376. | −0.566680 | ||||||||
\(41\) | −140874. | −0.319218 | −0.159609 | − | 0.987180i | \(-0.551023\pi\) | ||||
−0.159609 | + | 0.987180i | \(0.551023\pi\) | |||||||
\(42\) | −225008. | −0.468625 | ||||||||
\(43\) | 36464.0 | 0.0699399 | 0.0349699 | − | 0.999388i | \(-0.488866\pi\) | ||||
0.0349699 | + | 0.999388i | \(0.488866\pi\) | |||||||
\(44\) | 154112. | 0.272742 | ||||||||
\(45\) | 2.03258e6 | 3.32509 | ||||||||
\(46\) | 103040. | 0.156082 | ||||||||
\(47\) | 716868. | 1.00716 | 0.503578 | − | 0.863950i | \(-0.332017\pi\) | ||||
0.503578 | + | 0.863950i | \(0.332017\pi\) | |||||||
\(48\) | −335872. | −0.438359 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −980632. | −1.10946 | ||||||||
\(51\) | −203852. | −0.215189 | ||||||||
\(52\) | 455424. | 0.449163 | ||||||||
\(53\) | −56946.0 | −0.0525409 | −0.0262705 | − | 0.999655i | \(-0.508363\pi\) | ||||
−0.0262705 | + | 0.999655i | \(0.508363\pi\) | |||||||
\(54\) | 1.54160e6 | 1.33227 | ||||||||
\(55\) | 1.07878e6 | 0.874309 | ||||||||
\(56\) | 175616. | 0.133631 | ||||||||
\(57\) | −2.99152e6 | −2.13959 | ||||||||
\(58\) | 704752. | 0.474284 | ||||||||
\(59\) | −2.14986e6 | −1.36279 | −0.681394 | − | 0.731916i | \(-0.738626\pi\) | ||||
−0.681394 | + | 0.731916i | \(0.738626\pi\) | |||||||
\(60\) | −2.35110e6 | −1.40521 | ||||||||
\(61\) | 3.08436e6 | 1.73985 | 0.869923 | − | 0.493188i | \(-0.164169\pi\) | ||||
0.869923 | + | 0.493188i | \(0.164169\pi\) | |||||||
\(62\) | −2.26109e6 | −1.20489 | ||||||||
\(63\) | −1.55619e6 | −0.784099 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 3.18797e6 | 1.43985 | ||||||||
\(66\) | 1.57965e6 | 0.676327 | ||||||||
\(67\) | −3.03436e6 | −1.23255 | −0.616277 | − | 0.787530i | \(-0.711360\pi\) | ||||
−0.616277 | + | 0.787530i | \(0.711360\pi\) | |||||||
\(68\) | 159104. | 0.0613621 | ||||||||
\(69\) | 1.05616e6 | 0.387042 | ||||||||
\(70\) | 1.22931e6 | 0.428370 | ||||||||
\(71\) | −106624. | −0.0353550 | −0.0176775 | − | 0.999844i | \(-0.505627\pi\) | ||||
−0.0176775 | + | 0.999844i | \(0.505627\pi\) | |||||||
\(72\) | −2.32294e6 | −0.733458 | ||||||||
\(73\) | 988930. | 0.297533 | 0.148767 | − | 0.988872i | \(-0.452470\pi\) | ||||
0.148767 | + | 0.988872i | \(0.452470\pi\) | |||||||
\(74\) | 1.71627e6 | 0.492351 | ||||||||
\(75\) | −1.00515e7 | −2.75116 | ||||||||
\(76\) | 2.33485e6 | 0.610114 | ||||||||
\(77\) | −825944. | −0.206174 | ||||||||
\(78\) | 4.66810e6 | 1.11380 | ||||||||
\(79\) | 3.41590e6 | 0.779489 | 0.389744 | − | 0.920923i | \(-0.372563\pi\) | ||||
0.389744 | + | 0.920923i | \(0.372563\pi\) | |||||||
\(80\) | 1.83501e6 | 0.400703 | ||||||||
\(81\) | 5.87898e6 | 1.22915 | ||||||||
\(82\) | 1.12699e6 | 0.225721 | ||||||||
\(83\) | −15142.0 | −0.00290676 | −0.00145338 | − | 0.999999i | \(-0.500463\pi\) | ||||
−0.00145338 | + | 0.999999i | \(0.500463\pi\) | |||||||
\(84\) | 1.80006e6 | 0.331368 | ||||||||
\(85\) | 1.11373e6 | 0.196704 | ||||||||
\(86\) | −291712. | −0.0494549 | ||||||||
\(87\) | 7.22371e6 | 1.17610 | ||||||||
\(88\) | −1.23290e6 | −0.192858 | ||||||||
\(89\) | 174810. | 0.0262846 | 0.0131423 | − | 0.999914i | \(-0.495817\pi\) | ||||
0.0131423 | + | 0.999914i | \(0.495817\pi\) | |||||||
\(90\) | −1.62606e7 | −2.35119 | ||||||||
\(91\) | −2.44079e6 | −0.339535 | ||||||||
\(92\) | −824320. | −0.110367 | ||||||||
\(93\) | −2.31762e7 | −2.98780 | ||||||||
\(94\) | −5.73494e6 | −0.712167 | ||||||||
\(95\) | 1.63439e7 | 1.95580 | ||||||||
\(96\) | 2.68698e6 | 0.309966 | ||||||||
\(97\) | 1.35068e7 | 1.50263 | 0.751313 | − | 0.659946i | \(-0.229421\pi\) | ||||
0.751313 | + | 0.659946i | \(0.229421\pi\) | |||||||
\(98\) | −941192. | −0.101015 | ||||||||
\(99\) | 1.09251e7 | 1.13162 | ||||||||
\(100\) | 7.84506e6 | 0.784506 | ||||||||
\(101\) | −1.87645e7 | −1.81222 | −0.906112 | − | 0.423039i | \(-0.860963\pi\) | ||||
−0.906112 | + | 0.423039i | \(0.860963\pi\) | |||||||
\(102\) | 1.63082e6 | 0.152161 | ||||||||
\(103\) | −1.62080e7 | −1.46150 | −0.730751 | − | 0.682644i | \(-0.760830\pi\) | ||||
−0.730751 | + | 0.682644i | \(0.760830\pi\) | |||||||
\(104\) | −3.64339e6 | −0.317606 | ||||||||
\(105\) | 1.26004e7 | 1.06224 | ||||||||
\(106\) | 455568. | 0.0371520 | ||||||||
\(107\) | 6.96580e6 | 0.549702 | 0.274851 | − | 0.961487i | \(-0.411371\pi\) | ||||
0.274851 | + | 0.961487i | \(0.411371\pi\) | |||||||
\(108\) | −1.23328e7 | −0.942060 | ||||||||
\(109\) | −1.49039e7 | −1.10232 | −0.551159 | − | 0.834400i | \(-0.685814\pi\) | ||||
−0.551159 | + | 0.834400i | \(0.685814\pi\) | |||||||
\(110\) | −8.63027e6 | −0.618230 | ||||||||
\(111\) | 1.75918e7 | 1.22090 | ||||||||
\(112\) | −1.40493e6 | −0.0944911 | ||||||||
\(113\) | −2.60684e7 | −1.69958 | −0.849788 | − | 0.527125i | \(-0.823270\pi\) | ||||
−0.849788 | + | 0.527125i | \(0.823270\pi\) | |||||||
\(114\) | 2.39322e7 | 1.51292 | ||||||||
\(115\) | −5.77024e6 | −0.353795 | ||||||||
\(116\) | −5.63802e6 | −0.335369 | ||||||||
\(117\) | 3.22853e7 | 1.86361 | ||||||||
\(118\) | 1.71989e7 | 0.963637 | ||||||||
\(119\) | −852698. | −0.0463854 | ||||||||
\(120\) | 1.88088e7 | 0.993636 | ||||||||
\(121\) | −1.36887e7 | −0.702447 | ||||||||
\(122\) | −2.46749e7 | −1.23026 | ||||||||
\(123\) | 1.15517e7 | 0.559728 | ||||||||
\(124\) | 1.80887e7 | 0.851984 | ||||||||
\(125\) | 1.99154e7 | 0.912019 | ||||||||
\(126\) | 1.24495e7 | 0.554442 | ||||||||
\(127\) | 2.13136e7 | 0.923301 | 0.461651 | − | 0.887062i | \(-0.347257\pi\) | ||||
0.461651 | + | 0.887062i | \(0.347257\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | −2.99005e6 | −0.122635 | ||||||||
\(130\) | −2.55037e7 | −1.01813 | ||||||||
\(131\) | 1.04773e7 | 0.407194 | 0.203597 | − | 0.979055i | \(-0.434737\pi\) | ||||
0.203597 | + | 0.979055i | \(0.434737\pi\) | |||||||
\(132\) | −1.26372e7 | −0.478235 | ||||||||
\(133\) | −1.25133e7 | −0.461203 | ||||||||
\(134\) | 2.42749e7 | 0.871547 | ||||||||
\(135\) | −8.63296e7 | −3.01989 | ||||||||
\(136\) | −1.27283e6 | −0.0433895 | ||||||||
\(137\) | 3.61981e7 | 1.20272 | 0.601359 | − | 0.798979i | \(-0.294626\pi\) | ||||
0.601359 | + | 0.798979i | \(0.294626\pi\) | |||||||
\(138\) | −8.44928e6 | −0.273680 | ||||||||
\(139\) | −5.27655e7 | −1.66647 | −0.833237 | − | 0.552916i | \(-0.813515\pi\) | ||||
−0.833237 | + | 0.552916i | \(0.813515\pi\) | |||||||
\(140\) | −9.83450e6 | −0.302903 | ||||||||
\(141\) | −5.87832e7 | −1.76598 | ||||||||
\(142\) | 852992. | 0.0249998 | ||||||||
\(143\) | 1.71353e7 | 0.490023 | ||||||||
\(144\) | 1.85836e7 | 0.518633 | ||||||||
\(145\) | −3.94661e7 | −1.07507 | ||||||||
\(146\) | −7.91144e6 | −0.210388 | ||||||||
\(147\) | −9.64722e6 | −0.250491 | ||||||||
\(148\) | −1.37302e7 | −0.348145 | ||||||||
\(149\) | 7.36003e7 | 1.82275 | 0.911376 | − | 0.411575i | \(-0.135021\pi\) | ||||
0.911376 | + | 0.411575i | \(0.135021\pi\) | |||||||
\(150\) | 8.04118e7 | 1.94536 | ||||||||
\(151\) | 1.74289e7 | 0.411956 | 0.205978 | − | 0.978557i | \(-0.433963\pi\) | ||||
0.205978 | + | 0.978557i | \(0.433963\pi\) | |||||||
\(152\) | −1.86788e7 | −0.431416 | ||||||||
\(153\) | 1.12790e7 | 0.254595 | ||||||||
\(154\) | 6.60755e6 | 0.145787 | ||||||||
\(155\) | 1.26621e8 | 2.73114 | ||||||||
\(156\) | −3.73448e7 | −0.787578 | ||||||||
\(157\) | −2.22157e7 | −0.458154 | −0.229077 | − | 0.973408i | \(-0.573571\pi\) | ||||
−0.229077 | + | 0.973408i | \(0.573571\pi\) | |||||||
\(158\) | −2.73272e7 | −0.551182 | ||||||||
\(159\) | 4.66957e6 | 0.0921270 | ||||||||
\(160\) | −1.46801e7 | −0.283340 | ||||||||
\(161\) | 4.41784e6 | 0.0834295 | ||||||||
\(162\) | −4.70318e7 | −0.869140 | ||||||||
\(163\) | 6.23796e7 | 1.12820 | 0.564099 | − | 0.825707i | \(-0.309223\pi\) | ||||
0.564099 | + | 0.825707i | \(0.309223\pi\) | |||||||
\(164\) | −9.01594e6 | −0.159609 | ||||||||
\(165\) | −8.84603e7 | −1.53304 | ||||||||
\(166\) | 121136. | 0.00205539 | ||||||||
\(167\) | 3.31238e7 | 0.550343 | 0.275171 | − | 0.961395i | \(-0.411265\pi\) | ||||
0.275171 | + | 0.961395i | \(0.411265\pi\) | |||||||
\(168\) | −1.44005e7 | −0.234312 | ||||||||
\(169\) | −1.21111e7 | −0.193010 | ||||||||
\(170\) | −8.90982e6 | −0.139091 | ||||||||
\(171\) | 1.65519e8 | 2.53140 | ||||||||
\(172\) | 2.33370e6 | 0.0349699 | ||||||||
\(173\) | −7.05799e7 | −1.03638 | −0.518191 | − | 0.855265i | \(-0.673394\pi\) | ||||
−0.518191 | + | 0.855265i | \(0.673394\pi\) | |||||||
\(174\) | −5.77897e7 | −0.831626 | ||||||||
\(175\) | −4.20446e7 | −0.593030 | ||||||||
\(176\) | 9.86317e6 | 0.136371 | ||||||||
\(177\) | 1.76289e8 | 2.38956 | ||||||||
\(178\) | −1.39848e6 | −0.0185860 | ||||||||
\(179\) | −1.21176e8 | −1.57918 | −0.789590 | − | 0.613634i | \(-0.789707\pi\) | ||||
−0.789590 | + | 0.613634i | \(0.789707\pi\) | |||||||
\(180\) | 1.30085e8 | 1.66254 | ||||||||
\(181\) | 2.30550e7 | 0.288995 | 0.144498 | − | 0.989505i | \(-0.453843\pi\) | ||||
0.144498 | + | 0.989505i | \(0.453843\pi\) | |||||||
\(182\) | 1.95263e7 | 0.240088 | ||||||||
\(183\) | −2.52918e8 | −3.05070 | ||||||||
\(184\) | 6.59456e6 | 0.0780411 | ||||||||
\(185\) | −9.61112e7 | −1.11602 | ||||||||
\(186\) | 1.85409e8 | 2.11269 | ||||||||
\(187\) | 5.98629e6 | 0.0669441 | ||||||||
\(188\) | 4.58796e7 | 0.503578 | ||||||||
\(189\) | 6.60961e7 | 0.712130 | ||||||||
\(190\) | −1.30751e8 | −1.38296 | ||||||||
\(191\) | −2.02927e7 | −0.210728 | −0.105364 | − | 0.994434i | \(-0.533601\pi\) | ||||
−0.105364 | + | 0.994434i | \(0.533601\pi\) | |||||||
\(192\) | −2.14958e7 | −0.219179 | ||||||||
\(193\) | 2.26081e7 | 0.226367 | 0.113184 | − | 0.993574i | \(-0.463895\pi\) | ||||
0.113184 | + | 0.993574i | \(0.463895\pi\) | |||||||
\(194\) | −1.08054e8 | −1.06252 | ||||||||
\(195\) | −2.61413e8 | −2.52468 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | −3.27180e7 | −0.304898 | −0.152449 | − | 0.988311i | \(-0.548716\pi\) | ||||
−0.152449 | + | 0.988311i | \(0.548716\pi\) | |||||||
\(198\) | −8.74008e7 | −0.800179 | ||||||||
\(199\) | 7.24472e7 | 0.651682 | 0.325841 | − | 0.945424i | \(-0.394353\pi\) | ||||
0.325841 | + | 0.945424i | \(0.394353\pi\) | |||||||
\(200\) | −6.27604e7 | −0.554729 | ||||||||
\(201\) | 2.48818e8 | 2.16120 | ||||||||
\(202\) | 1.50116e8 | 1.28144 | ||||||||
\(203\) | 3.02162e7 | 0.253515 | ||||||||
\(204\) | −1.30465e7 | −0.107594 | ||||||||
\(205\) | −6.31116e7 | −0.511647 | ||||||||
\(206\) | 1.29664e8 | 1.03344 | ||||||||
\(207\) | −5.84366e7 | −0.457919 | ||||||||
\(208\) | 2.91471e7 | 0.224582 | ||||||||
\(209\) | 8.78487e7 | 0.665615 | ||||||||
\(210\) | −1.00804e8 | −0.751118 | ||||||||
\(211\) | 9.38006e7 | 0.687412 | 0.343706 | − | 0.939077i | \(-0.388318\pi\) | ||||
0.343706 | + | 0.939077i | \(0.388318\pi\) | |||||||
\(212\) | −3.64454e6 | −0.0262705 | ||||||||
\(213\) | 8.74317e6 | 0.0619927 | ||||||||
\(214\) | −5.57264e7 | −0.388698 | ||||||||
\(215\) | 1.63359e7 | 0.112101 | ||||||||
\(216\) | 9.86624e7 | 0.666137 | ||||||||
\(217\) | −9.69441e7 | −0.644040 | ||||||||
\(218\) | 1.19231e8 | 0.779457 | ||||||||
\(219\) | −8.10923e7 | −0.521705 | ||||||||
\(220\) | 6.90422e7 | 0.437155 | ||||||||
\(221\) | 1.76904e7 | 0.110246 | ||||||||
\(222\) | −1.40734e8 | −0.863306 | ||||||||
\(223\) | 1.62567e6 | 0.00981671 | 0.00490835 | − | 0.999988i | \(-0.498438\pi\) | ||||
0.00490835 | + | 0.999988i | \(0.498438\pi\) | |||||||
\(224\) | 1.12394e7 | 0.0668153 | ||||||||
\(225\) | 5.56141e8 | 3.25496 | ||||||||
\(226\) | 2.08548e8 | 1.20178 | ||||||||
\(227\) | −2.46153e8 | −1.39673 | −0.698367 | − | 0.715740i | \(-0.746090\pi\) | ||||
−0.698367 | + | 0.715740i | \(0.746090\pi\) | |||||||
\(228\) | −1.91458e8 | −1.06979 | ||||||||
\(229\) | −1.06041e8 | −0.583510 | −0.291755 | − | 0.956493i | \(-0.594239\pi\) | ||||
−0.291755 | + | 0.956493i | \(0.594239\pi\) | |||||||
\(230\) | 4.61619e7 | 0.250171 | ||||||||
\(231\) | 6.77274e7 | 0.361512 | ||||||||
\(232\) | 4.51041e7 | 0.237142 | ||||||||
\(233\) | −2.02206e8 | −1.04725 | −0.523623 | − | 0.851950i | \(-0.675420\pi\) | ||||
−0.523623 | + | 0.851950i | \(0.675420\pi\) | |||||||
\(234\) | −2.58282e8 | −1.31777 | ||||||||
\(235\) | 3.21157e8 | 1.61428 | ||||||||
\(236\) | −1.37591e8 | −0.681394 | ||||||||
\(237\) | −2.80103e8 | −1.36678 | ||||||||
\(238\) | 6.82158e6 | 0.0327994 | ||||||||
\(239\) | −3.67523e7 | −0.174137 | −0.0870687 | − | 0.996202i | \(-0.527750\pi\) | ||||
−0.0870687 | + | 0.996202i | \(0.527750\pi\) | |||||||
\(240\) | −1.50471e8 | −0.702607 | ||||||||
\(241\) | 5.76415e7 | 0.265262 | 0.132631 | − | 0.991165i | \(-0.457657\pi\) | ||||
0.132631 | + | 0.991165i | \(0.457657\pi\) | |||||||
\(242\) | 1.09510e8 | 0.496705 | ||||||||
\(243\) | −6.06415e7 | −0.271112 | ||||||||
\(244\) | 1.97399e8 | 0.869923 | ||||||||
\(245\) | 5.27068e7 | 0.228973 | ||||||||
\(246\) | −9.24133e7 | −0.395787 | ||||||||
\(247\) | 2.59606e8 | 1.09616 | ||||||||
\(248\) | −1.44710e8 | −0.602444 | ||||||||
\(249\) | 1.24164e6 | 0.00509682 | ||||||||
\(250\) | −1.59323e8 | −0.644895 | ||||||||
\(251\) | −2.61332e8 | −1.04312 | −0.521561 | − | 0.853214i | \(-0.674650\pi\) | ||||
−0.521561 | + | 0.853214i | \(0.674650\pi\) | |||||||
\(252\) | −9.95962e7 | −0.392050 | ||||||||
\(253\) | −3.10150e7 | −0.120407 | ||||||||
\(254\) | −1.70509e8 | −0.652873 | ||||||||
\(255\) | −9.13257e7 | −0.344907 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 3.47625e8 | 1.27745 | 0.638727 | − | 0.769433i | \(-0.279461\pi\) | ||||
0.638727 | + | 0.769433i | \(0.279461\pi\) | |||||||
\(258\) | 2.39204e7 | 0.0867160 | ||||||||
\(259\) | 7.35852e7 | 0.263173 | ||||||||
\(260\) | 2.04030e8 | 0.719925 | ||||||||
\(261\) | −3.99682e8 | −1.39147 | ||||||||
\(262\) | −8.38186e7 | −0.287929 | ||||||||
\(263\) | −1.76501e8 | −0.598278 | −0.299139 | − | 0.954210i | \(-0.596699\pi\) | ||||
−0.299139 | + | 0.954210i | \(0.596699\pi\) | |||||||
\(264\) | 1.01097e8 | 0.338163 | ||||||||
\(265\) | −2.55118e7 | −0.0842133 | ||||||||
\(266\) | 1.00107e8 | 0.326120 | ||||||||
\(267\) | −1.43344e7 | −0.0460883 | ||||||||
\(268\) | −1.94199e8 | −0.616277 | ||||||||
\(269\) | −4.07889e8 | −1.27764 | −0.638821 | − | 0.769356i | \(-0.720577\pi\) | ||||
−0.638821 | + | 0.769356i | \(0.720577\pi\) | |||||||
\(270\) | 6.90637e8 | 2.13539 | ||||||||
\(271\) | 3.17618e8 | 0.969422 | 0.484711 | − | 0.874674i | \(-0.338925\pi\) | ||||
0.484711 | + | 0.874674i | \(0.338925\pi\) | |||||||
\(272\) | 1.01827e7 | 0.0306810 | ||||||||
\(273\) | 2.00145e8 | 0.595353 | ||||||||
\(274\) | −2.89585e8 | −0.850450 | ||||||||
\(275\) | 2.95170e8 | 0.855871 | ||||||||
\(276\) | 6.75942e7 | 0.193521 | ||||||||
\(277\) | 2.93727e8 | 0.830356 | 0.415178 | − | 0.909740i | \(-0.363719\pi\) | ||||
0.415178 | + | 0.909740i | \(0.363719\pi\) | |||||||
\(278\) | 4.22124e8 | 1.17838 | ||||||||
\(279\) | 1.28232e9 | 3.53494 | ||||||||
\(280\) | 7.86760e7 | 0.214185 | ||||||||
\(281\) | −5.45027e7 | −0.146536 | −0.0732682 | − | 0.997312i | \(-0.523343\pi\) | ||||
−0.0732682 | + | 0.997312i | \(0.523343\pi\) | |||||||
\(282\) | 4.70265e8 | 1.24874 | ||||||||
\(283\) | 2.05409e8 | 0.538725 | 0.269362 | − | 0.963039i | \(-0.413187\pi\) | ||||
0.269362 | + | 0.963039i | \(0.413187\pi\) | |||||||
\(284\) | −6.82394e6 | −0.0176775 | ||||||||
\(285\) | −1.34020e9 | −3.42936 | ||||||||
\(286\) | −1.37083e8 | −0.346498 | ||||||||
\(287\) | 4.83198e7 | 0.120653 | ||||||||
\(288\) | −1.48668e8 | −0.366729 | ||||||||
\(289\) | −4.04158e8 | −0.984939 | ||||||||
\(290\) | 3.15729e8 | 0.760189 | ||||||||
\(291\) | −1.10756e9 | −2.63476 | ||||||||
\(292\) | 6.32915e7 | 0.148767 | ||||||||
\(293\) | −1.18887e8 | −0.276119 | −0.138059 | − | 0.990424i | \(-0.544087\pi\) | ||||
−0.138059 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(294\) | 7.71777e7 | 0.177124 | ||||||||
\(295\) | −9.63138e8 | −2.18430 | ||||||||
\(296\) | 1.09841e8 | 0.246176 | ||||||||
\(297\) | −4.64022e8 | −1.02776 | ||||||||
\(298\) | −5.88802e8 | −1.28888 | ||||||||
\(299\) | −9.16541e7 | −0.198291 | ||||||||
\(300\) | −6.43295e8 | −1.37558 | ||||||||
\(301\) | −1.25072e7 | −0.0264348 | ||||||||
\(302\) | −1.39431e8 | −0.291297 | ||||||||
\(303\) | 1.53869e9 | 3.17761 | ||||||||
\(304\) | 1.49430e8 | 0.305057 | ||||||||
\(305\) | 1.38179e9 | 2.78865 | ||||||||
\(306\) | −9.02319e7 | −0.180026 | ||||||||
\(307\) | 1.63581e8 | 0.322663 | 0.161332 | − | 0.986900i | \(-0.448421\pi\) | ||||
0.161332 | + | 0.986900i | \(0.448421\pi\) | |||||||
\(308\) | −5.28604e7 | −0.103087 | ||||||||
\(309\) | 1.32906e9 | 2.56265 | ||||||||
\(310\) | −1.01297e9 | −1.93121 | ||||||||
\(311\) | −4.32480e8 | −0.815276 | −0.407638 | − | 0.913144i | \(-0.633648\pi\) | ||||
−0.407638 | + | 0.913144i | \(0.633648\pi\) | |||||||
\(312\) | 2.98758e8 | 0.556902 | ||||||||
\(313\) | −4.27033e8 | −0.787148 | −0.393574 | − | 0.919293i | \(-0.628761\pi\) | ||||
−0.393574 | + | 0.919293i | \(0.628761\pi\) | |||||||
\(314\) | 1.77726e8 | 0.323964 | ||||||||
\(315\) | −6.97174e8 | −1.25676 | ||||||||
\(316\) | 2.18617e8 | 0.389744 | ||||||||
\(317\) | −3.47502e8 | −0.612703 | −0.306352 | − | 0.951918i | \(-0.599108\pi\) | ||||
−0.306352 | + | 0.951918i | \(0.599108\pi\) | |||||||
\(318\) | −3.73566e7 | −0.0651437 | ||||||||
\(319\) | −2.12130e8 | −0.365877 | ||||||||
\(320\) | 1.17441e8 | 0.200352 | ||||||||
\(321\) | −5.71195e8 | −0.963867 | ||||||||
\(322\) | −3.53427e7 | −0.0589935 | ||||||||
\(323\) | 9.06943e7 | 0.149751 | ||||||||
\(324\) | 3.76255e8 | 0.614574 | ||||||||
\(325\) | 8.72272e8 | 1.40948 | ||||||||
\(326\) | −4.99036e8 | −0.797757 | ||||||||
\(327\) | 1.22212e9 | 1.93284 | ||||||||
\(328\) | 7.21275e7 | 0.112861 | ||||||||
\(329\) | −2.45886e8 | −0.380669 | ||||||||
\(330\) | 7.07682e8 | 1.08403 | ||||||||
\(331\) | −8.15413e8 | −1.23589 | −0.617945 | − | 0.786221i | \(-0.712035\pi\) | ||||
−0.617945 | + | 0.786221i | \(0.712035\pi\) | |||||||
\(332\) | −969088. | −0.00145338 | ||||||||
\(333\) | −9.73341e8 | −1.44448 | ||||||||
\(334\) | −2.64991e8 | −0.389151 | ||||||||
\(335\) | −1.35940e9 | −1.97555 | ||||||||
\(336\) | 1.15204e8 | 0.165684 | ||||||||
\(337\) | −5.55790e8 | −0.791054 | −0.395527 | − | 0.918454i | \(-0.629438\pi\) | ||||
−0.395527 | + | 0.918454i | \(0.629438\pi\) | |||||||
\(338\) | 9.68885e7 | 0.136478 | ||||||||
\(339\) | 2.13761e9 | 2.98009 | ||||||||
\(340\) | 7.12786e7 | 0.0983519 | ||||||||
\(341\) | 6.80587e8 | 0.929488 | ||||||||
\(342\) | −1.32415e9 | −1.78997 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | −1.86696e7 | −0.0247275 | ||||||||
\(345\) | 4.73160e8 | 0.620356 | ||||||||
\(346\) | 5.64639e8 | 0.732832 | ||||||||
\(347\) | 1.07708e9 | 1.38387 | 0.691934 | − | 0.721961i | \(-0.256759\pi\) | ||||
0.691934 | + | 0.721961i | \(0.256759\pi\) | |||||||
\(348\) | 4.62317e8 | 0.588048 | ||||||||
\(349\) | 1.44167e9 | 1.81541 | 0.907707 | − | 0.419605i | \(-0.137831\pi\) | ||||
0.907707 | + | 0.419605i | \(0.137831\pi\) | |||||||
\(350\) | 3.36357e8 | 0.419336 | ||||||||
\(351\) | −1.37125e9 | −1.69255 | ||||||||
\(352\) | −7.89053e7 | −0.0964289 | ||||||||
\(353\) | 5.73266e8 | 0.693657 | 0.346829 | − | 0.937929i | \(-0.387259\pi\) | ||||
0.346829 | + | 0.937929i | \(0.387259\pi\) | |||||||
\(354\) | −1.41031e9 | −1.68967 | ||||||||
\(355\) | −4.77676e7 | −0.0566675 | ||||||||
\(356\) | 1.11878e7 | 0.0131423 | ||||||||
\(357\) | 6.99212e7 | 0.0813337 | ||||||||
\(358\) | 9.69410e8 | 1.11665 | ||||||||
\(359\) | −9.49335e8 | −1.08290 | −0.541451 | − | 0.840733i | \(-0.682125\pi\) | ||||
−0.541451 | + | 0.840733i | \(0.682125\pi\) | |||||||
\(360\) | −1.04068e9 | −1.17560 | ||||||||
\(361\) | 4.37065e8 | 0.488957 | ||||||||
\(362\) | −1.84440e8 | −0.204350 | ||||||||
\(363\) | 1.12247e9 | 1.23169 | ||||||||
\(364\) | −1.56210e8 | −0.169768 | ||||||||
\(365\) | 4.43041e8 | 0.476890 | ||||||||
\(366\) | 2.02334e9 | 2.15717 | ||||||||
\(367\) | −3.01771e8 | −0.318674 | −0.159337 | − | 0.987224i | \(-0.550936\pi\) | ||||
−0.159337 | + | 0.987224i | \(0.550936\pi\) | |||||||
\(368\) | −5.27565e7 | −0.0551834 | ||||||||
\(369\) | −6.39145e8 | −0.662228 | ||||||||
\(370\) | 7.68890e8 | 0.789147 | ||||||||
\(371\) | 1.95325e7 | 0.0198586 | ||||||||
\(372\) | −1.48327e9 | −1.49390 | ||||||||
\(373\) | −1.36182e9 | −1.35875 | −0.679374 | − | 0.733792i | \(-0.737749\pi\) | ||||
−0.679374 | + | 0.733792i | \(0.737749\pi\) | |||||||
\(374\) | −4.78903e7 | −0.0473366 | ||||||||
\(375\) | −1.63306e9 | −1.59916 | ||||||||
\(376\) | −3.67036e8 | −0.356083 | ||||||||
\(377\) | −6.26877e8 | −0.602542 | ||||||||
\(378\) | −5.28769e8 | −0.503552 | ||||||||
\(379\) | −1.51839e9 | −1.43267 | −0.716333 | − | 0.697758i | \(-0.754181\pi\) | ||||
−0.716333 | + | 0.697758i | \(0.754181\pi\) | |||||||
\(380\) | 1.04601e9 | 0.977899 | ||||||||
\(381\) | −1.74771e9 | −1.61895 | ||||||||
\(382\) | 1.62342e8 | 0.149007 | ||||||||
\(383\) | 4.54114e8 | 0.413018 | 0.206509 | − | 0.978445i | \(-0.433790\pi\) | ||||
0.206509 | + | 0.978445i | \(0.433790\pi\) | |||||||
\(384\) | 1.71966e8 | 0.154983 | ||||||||
\(385\) | −3.70023e8 | −0.330458 | ||||||||
\(386\) | −1.80865e8 | −0.160066 | ||||||||
\(387\) | 1.65437e8 | 0.145092 | ||||||||
\(388\) | 8.64435e8 | 0.751313 | ||||||||
\(389\) | −1.83700e9 | −1.58229 | −0.791143 | − | 0.611632i | \(-0.790514\pi\) | ||||
−0.791143 | + | 0.611632i | \(0.790514\pi\) | |||||||
\(390\) | 2.09131e9 | 1.78522 | ||||||||
\(391\) | −3.20197e7 | −0.0270893 | ||||||||
\(392\) | −6.02363e7 | −0.0505076 | ||||||||
\(393\) | −8.59141e8 | −0.713987 | ||||||||
\(394\) | 2.61744e8 | 0.215595 | ||||||||
\(395\) | 1.53032e9 | 1.24938 | ||||||||
\(396\) | 6.99206e8 | 0.565812 | ||||||||
\(397\) | 1.23668e9 | 0.991950 | 0.495975 | − | 0.868337i | \(-0.334811\pi\) | ||||
0.495975 | + | 0.868337i | \(0.334811\pi\) | |||||||
\(398\) | −5.79578e8 | −0.460809 | ||||||||
\(399\) | 1.02609e9 | 0.808689 | ||||||||
\(400\) | 5.02084e8 | 0.392253 | ||||||||
\(401\) | 1.57948e9 | 1.22323 | 0.611615 | − | 0.791156i | \(-0.290520\pi\) | ||||
0.611615 | + | 0.791156i | \(0.290520\pi\) | |||||||
\(402\) | −1.99054e9 | −1.52820 | ||||||||
\(403\) | 2.01124e9 | 1.53072 | ||||||||
\(404\) | −1.20093e9 | −0.906112 | ||||||||
\(405\) | 2.63378e9 | 1.97010 | ||||||||
\(406\) | −2.41730e8 | −0.179262 | ||||||||
\(407\) | −5.16598e8 | −0.379815 | ||||||||
\(408\) | 1.04372e8 | 0.0760807 | ||||||||
\(409\) | −1.92558e9 | −1.39165 | −0.695823 | − | 0.718213i | \(-0.744960\pi\) | ||||
−0.695823 | + | 0.718213i | \(0.744960\pi\) | |||||||
\(410\) | 5.04892e8 | 0.361789 | ||||||||
\(411\) | −2.96824e9 | −2.10889 | ||||||||
\(412\) | −1.03731e9 | −0.730751 | ||||||||
\(413\) | 7.37403e8 | 0.515086 | ||||||||
\(414\) | 4.67492e8 | 0.323797 | ||||||||
\(415\) | −6.78362e6 | −0.00465900 | ||||||||
\(416\) | −2.33177e8 | −0.158803 | ||||||||
\(417\) | 4.32677e9 | 2.92205 | ||||||||
\(418\) | −7.02789e8 | −0.470661 | ||||||||
\(419\) | −2.39996e9 | −1.59388 | −0.796938 | − | 0.604062i | \(-0.793548\pi\) | ||||
−0.796938 | + | 0.604062i | \(0.793548\pi\) | |||||||
\(420\) | 8.06429e8 | 0.531121 | ||||||||
\(421\) | 1.20940e9 | 0.789919 | 0.394960 | − | 0.918698i | \(-0.370759\pi\) | ||||
0.394960 | + | 0.918698i | \(0.370759\pi\) | |||||||
\(422\) | −7.50405e8 | −0.486074 | ||||||||
\(423\) | 3.25243e9 | 2.08938 | ||||||||
\(424\) | 2.91564e7 | 0.0185760 | ||||||||
\(425\) | 3.04731e8 | 0.192556 | ||||||||
\(426\) | −6.99453e7 | −0.0438354 | ||||||||
\(427\) | −1.05794e9 | −0.657600 | ||||||||
\(428\) | 4.45811e8 | 0.274851 | ||||||||
\(429\) | −1.40510e9 | −0.859223 | ||||||||
\(430\) | −1.30687e8 | −0.0792671 | ||||||||
\(431\) | −2.16285e9 | −1.30124 | −0.650618 | − | 0.759405i | \(-0.725490\pi\) | ||||
−0.650618 | + | 0.759405i | \(0.725490\pi\) | |||||||
\(432\) | −7.89299e8 | −0.471030 | ||||||||
\(433\) | 2.25750e9 | 1.33635 | 0.668174 | − | 0.744005i | \(-0.267076\pi\) | ||||
0.668174 | + | 0.744005i | \(0.267076\pi\) | |||||||
\(434\) | 7.75553e8 | 0.455405 | ||||||||
\(435\) | 3.23622e9 | 1.88506 | ||||||||
\(436\) | −9.53849e8 | −0.551159 | ||||||||
\(437\) | −4.69888e8 | −0.269345 | ||||||||
\(438\) | 6.48738e8 | 0.368901 | ||||||||
\(439\) | −7.45724e8 | −0.420680 | −0.210340 | − | 0.977628i | \(-0.567457\pi\) | ||||
−0.210340 | + | 0.977628i | \(0.567457\pi\) | |||||||
\(440\) | −5.52337e8 | −0.309115 | ||||||||
\(441\) | 5.33774e8 | 0.296362 | ||||||||
\(442\) | −1.41523e8 | −0.0779559 | ||||||||
\(443\) | −1.10215e9 | −0.602322 | −0.301161 | − | 0.953573i | \(-0.597374\pi\) | ||||
−0.301161 | + | 0.953573i | \(0.597374\pi\) | |||||||
\(444\) | 1.12587e9 | 0.610449 | ||||||||
\(445\) | 7.83149e7 | 0.0421293 | ||||||||
\(446\) | −1.30054e7 | −0.00694146 | ||||||||
\(447\) | −6.03522e9 | −3.19608 | ||||||||
\(448\) | −8.99154e7 | −0.0472456 | ||||||||
\(449\) | 3.41600e9 | 1.78097 | 0.890483 | − | 0.455017i | \(-0.150367\pi\) | ||||
0.890483 | + | 0.455017i | \(0.150367\pi\) | |||||||
\(450\) | −4.44913e9 | −2.30161 | ||||||||
\(451\) | −3.39225e8 | −0.174128 | ||||||||
\(452\) | −1.66838e9 | −0.849788 | ||||||||
\(453\) | −1.42917e9 | −0.722337 | ||||||||
\(454\) | 1.96922e9 | 0.987640 | ||||||||
\(455\) | −1.09347e9 | −0.544212 | ||||||||
\(456\) | 1.53166e9 | 0.756459 | ||||||||
\(457\) | 4.27310e8 | 0.209429 | 0.104714 | − | 0.994502i | \(-0.466607\pi\) | ||||
0.104714 | + | 0.994502i | \(0.466607\pi\) | |||||||
\(458\) | 8.48326e8 | 0.412604 | ||||||||
\(459\) | −4.79052e8 | −0.231227 | ||||||||
\(460\) | −3.69295e8 | −0.176897 | ||||||||
\(461\) | 2.18116e9 | 1.03690 | 0.518448 | − | 0.855109i | \(-0.326510\pi\) | ||||
0.518448 | + | 0.855109i | \(0.326510\pi\) | |||||||
\(462\) | −5.41819e8 | −0.255627 | ||||||||
\(463\) | 1.88134e8 | 0.0880916 | 0.0440458 | − | 0.999030i | \(-0.485975\pi\) | ||||
0.0440458 | + | 0.999030i | \(0.485975\pi\) | |||||||
\(464\) | −3.60833e8 | −0.167685 | ||||||||
\(465\) | −1.03829e10 | −4.78888 | ||||||||
\(466\) | 1.61765e9 | 0.740515 | ||||||||
\(467\) | 8.54534e8 | 0.388258 | 0.194129 | − | 0.980976i | \(-0.437812\pi\) | ||||
0.194129 | + | 0.980976i | \(0.437812\pi\) | |||||||
\(468\) | 2.06626e9 | 0.931803 | ||||||||
\(469\) | 1.04079e9 | 0.465862 | ||||||||
\(470\) | −2.56925e9 | −1.14147 | ||||||||
\(471\) | 1.82169e9 | 0.803342 | ||||||||
\(472\) | 1.10073e9 | 0.481819 | ||||||||
\(473\) | 8.78053e7 | 0.0381511 | ||||||||
\(474\) | 2.24083e9 | 0.966461 | ||||||||
\(475\) | 4.47193e9 | 1.91455 | ||||||||
\(476\) | −5.45727e7 | −0.0231927 | ||||||||
\(477\) | −2.58364e8 | −0.108998 | ||||||||
\(478\) | 2.94019e8 | 0.123134 | ||||||||
\(479\) | −6.82814e8 | −0.283876 | −0.141938 | − | 0.989876i | \(-0.545333\pi\) | ||||
−0.141938 | + | 0.989876i | \(0.545333\pi\) | |||||||
\(480\) | 1.20377e9 | 0.496818 | ||||||||
\(481\) | −1.52662e9 | −0.625496 | ||||||||
\(482\) | −4.61132e8 | −0.187569 | ||||||||
\(483\) | −3.62263e8 | −0.146288 | ||||||||
\(484\) | −8.76077e8 | −0.351224 | ||||||||
\(485\) | 6.05104e9 | 2.40843 | ||||||||
\(486\) | 4.85132e8 | 0.191705 | ||||||||
\(487\) | 4.15119e9 | 1.62863 | 0.814313 | − | 0.580425i | \(-0.197114\pi\) | ||||
0.814313 | + | 0.580425i | \(0.197114\pi\) | |||||||
\(488\) | −1.57919e9 | −0.615128 | ||||||||
\(489\) | −5.11512e9 | −1.97822 | ||||||||
\(490\) | −4.21654e8 | −0.161909 | ||||||||
\(491\) | 8.99538e8 | 0.342953 | 0.171476 | − | 0.985188i | \(-0.445146\pi\) | ||||
0.171476 | + | 0.985188i | \(0.445146\pi\) | |||||||
\(492\) | 7.39307e8 | 0.279864 | ||||||||
\(493\) | −2.19002e8 | −0.0823158 | ||||||||
\(494\) | −2.07685e9 | −0.775104 | ||||||||
\(495\) | 4.89444e9 | 1.81378 | ||||||||
\(496\) | 1.15768e9 | 0.425992 | ||||||||
\(497\) | 3.65720e7 | 0.0133629 | ||||||||
\(498\) | −9.93315e6 | −0.00360400 | ||||||||
\(499\) | −6.11110e8 | −0.220175 | −0.110087 | − | 0.993922i | \(-0.535113\pi\) | ||||
−0.110087 | + | 0.993922i | \(0.535113\pi\) | |||||||
\(500\) | 1.27459e9 | 0.456009 | ||||||||
\(501\) | −2.71616e9 | −0.964989 | ||||||||
\(502\) | 2.09066e9 | 0.737598 | ||||||||
\(503\) | 5.23241e9 | 1.83322 | 0.916608 | − | 0.399787i | \(-0.130916\pi\) | ||||
0.916608 | + | 0.399787i | \(0.130916\pi\) | |||||||
\(504\) | 7.96770e8 | 0.277221 | ||||||||
\(505\) | −8.40649e9 | −2.90466 | ||||||||
\(506\) | 2.48120e8 | 0.0851404 | ||||||||
\(507\) | 9.93107e8 | 0.338429 | ||||||||
\(508\) | 1.36407e9 | 0.461651 | ||||||||
\(509\) | 2.33531e8 | 0.0784931 | 0.0392465 | − | 0.999230i | \(-0.487504\pi\) | ||||
0.0392465 | + | 0.999230i | \(0.487504\pi\) | |||||||
\(510\) | 7.30606e8 | 0.243886 | ||||||||
\(511\) | −3.39203e8 | −0.112457 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | −7.03008e9 | −2.29906 | ||||||||
\(514\) | −2.78100e9 | −0.903297 | ||||||||
\(515\) | −7.26119e9 | −2.34252 | ||||||||
\(516\) | −1.91363e8 | −0.0613175 | ||||||||
\(517\) | 1.72622e9 | 0.549388 | ||||||||
\(518\) | −5.88681e8 | −0.186091 | ||||||||
\(519\) | 5.78755e9 | 1.81723 | ||||||||
\(520\) | −1.63224e9 | −0.509064 | ||||||||
\(521\) | 2.23029e9 | 0.690922 | 0.345461 | − | 0.938433i | \(-0.387723\pi\) | ||||
0.345461 | + | 0.938433i | \(0.387723\pi\) | |||||||
\(522\) | 3.19746e9 | 0.983917 | ||||||||
\(523\) | 4.74795e8 | 0.145128 | 0.0725638 | − | 0.997364i | \(-0.476882\pi\) | ||||
0.0725638 | + | 0.997364i | \(0.476882\pi\) | |||||||
\(524\) | 6.70549e8 | 0.203597 | ||||||||
\(525\) | 3.44766e9 | 1.03984 | ||||||||
\(526\) | 1.41201e9 | 0.423047 | ||||||||
\(527\) | 7.02633e8 | 0.209118 | ||||||||
\(528\) | −8.08780e8 | −0.239118 | ||||||||
\(529\) | −3.23893e9 | −0.951277 | ||||||||
\(530\) | 2.04094e8 | 0.0595478 | ||||||||
\(531\) | −9.75392e9 | −2.82715 | ||||||||
\(532\) | −8.00853e8 | −0.230601 | ||||||||
\(533\) | −1.00246e9 | −0.286762 | ||||||||
\(534\) | 1.14675e8 | 0.0325894 | ||||||||
\(535\) | 3.12068e9 | 0.881070 | ||||||||
\(536\) | 1.55359e9 | 0.435774 | ||||||||
\(537\) | 9.93645e9 | 2.76899 | ||||||||
\(538\) | 3.26311e9 | 0.903429 | ||||||||
\(539\) | 2.83299e8 | 0.0779263 | ||||||||
\(540\) | −5.52509e9 | −1.50995 | ||||||||
\(541\) | −8.47970e8 | −0.230245 | −0.115122 | − | 0.993351i | \(-0.536726\pi\) | ||||
−0.115122 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(542\) | −2.54095e9 | −0.685485 | ||||||||
\(543\) | −1.89051e9 | −0.506734 | ||||||||
\(544\) | −8.14612e7 | −0.0216948 | ||||||||
\(545\) | −6.67694e9 | −1.76681 | ||||||||
\(546\) | −1.60116e9 | −0.420978 | ||||||||
\(547\) | −6.55694e7 | −0.0171295 | −0.00856477 | − | 0.999963i | \(-0.502726\pi\) | ||||
−0.00856477 | + | 0.999963i | \(0.502726\pi\) | |||||||
\(548\) | 2.31668e9 | 0.601359 | ||||||||
\(549\) | 1.39937e10 | 3.60936 | ||||||||
\(550\) | −2.36136e9 | −0.605192 | ||||||||
\(551\) | −3.21385e9 | −0.818454 | ||||||||
\(552\) | −5.40754e8 | −0.136840 | ||||||||
\(553\) | −1.17165e9 | −0.294619 | ||||||||
\(554\) | −2.34981e9 | −0.587150 | ||||||||
\(555\) | 7.88112e9 | 1.95687 | ||||||||
\(556\) | −3.37699e9 | −0.833237 | ||||||||
\(557\) | 6.12524e8 | 0.150186 | 0.0750930 | − | 0.997177i | \(-0.476075\pi\) | ||||
0.0750930 | + | 0.997177i | \(0.476075\pi\) | |||||||
\(558\) | −1.02586e10 | −2.49958 | ||||||||
\(559\) | 2.59478e8 | 0.0628288 | ||||||||
\(560\) | −6.29408e8 | −0.151452 | ||||||||
\(561\) | −4.90876e8 | −0.117382 | ||||||||
\(562\) | 4.36021e8 | 0.103617 | ||||||||
\(563\) | 7.02101e8 | 0.165814 | 0.0829068 | − | 0.996557i | \(-0.473580\pi\) | ||||
0.0829068 | + | 0.996557i | \(0.473580\pi\) | |||||||
\(564\) | −3.76212e9 | −0.882991 | ||||||||
\(565\) | −1.16787e10 | −2.72410 | ||||||||
\(566\) | −1.64327e9 | −0.380936 | ||||||||
\(567\) | −2.01649e9 | −0.464575 | ||||||||
\(568\) | 5.45915e7 | 0.0124999 | ||||||||
\(569\) | 2.43577e8 | 0.0554298 | 0.0277149 | − | 0.999616i | \(-0.491177\pi\) | ||||
0.0277149 | + | 0.999616i | \(0.491177\pi\) | |||||||
\(570\) | 1.07216e10 | 2.42493 | ||||||||
\(571\) | 5.28919e9 | 1.18895 | 0.594474 | − | 0.804115i | \(-0.297360\pi\) | ||||
0.594474 | + | 0.804115i | \(0.297360\pi\) | |||||||
\(572\) | 1.09666e9 | 0.245011 | ||||||||
\(573\) | 1.66400e9 | 0.369498 | ||||||||
\(574\) | −3.86558e8 | −0.0853146 | ||||||||
\(575\) | −1.57882e9 | −0.346333 | ||||||||
\(576\) | 1.18935e9 | 0.259316 | ||||||||
\(577\) | −3.68455e9 | −0.798490 | −0.399245 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399245 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(578\) | 3.23327e9 | 0.696457 | ||||||||
\(579\) | −1.85387e9 | −0.396920 | ||||||||
\(580\) | −2.52583e9 | −0.537534 | ||||||||
\(581\) | 5.19371e6 | 0.00109865 | ||||||||
\(582\) | 8.86045e9 | 1.86305 | ||||||||
\(583\) | −1.37126e8 | −0.0286602 | ||||||||
\(584\) | −5.06332e8 | −0.105194 | ||||||||
\(585\) | 1.44638e10 | 2.98701 | ||||||||
\(586\) | 9.51093e8 | 0.195246 | ||||||||
\(587\) | −4.23510e9 | −0.864232 | −0.432116 | − | 0.901818i | \(-0.642233\pi\) | ||||
−0.432116 | + | 0.901818i | \(0.642233\pi\) | |||||||
\(588\) | −6.17422e8 | −0.125245 | ||||||||
\(589\) | 1.03111e10 | 2.07923 | ||||||||
\(590\) | 7.70511e9 | 1.54453 | ||||||||
\(591\) | 2.68287e9 | 0.534618 | ||||||||
\(592\) | −8.78731e8 | −0.174072 | ||||||||
\(593\) | 9.70955e9 | 1.91209 | 0.956043 | − | 0.293225i | \(-0.0947286\pi\) | ||||
0.956043 | + | 0.293225i | \(0.0947286\pi\) | |||||||
\(594\) | 3.71217e9 | 0.726734 | ||||||||
\(595\) | −3.82009e8 | −0.0743471 | ||||||||
\(596\) | 4.71042e9 | 0.911376 | ||||||||
\(597\) | −5.94067e9 | −1.14268 | ||||||||
\(598\) | 7.33233e8 | 0.140213 | ||||||||
\(599\) | −4.04176e9 | −0.768382 | −0.384191 | − | 0.923254i | \(-0.625520\pi\) | ||||
−0.384191 | + | 0.923254i | \(0.625520\pi\) | |||||||
\(600\) | 5.14636e9 | 0.972681 | ||||||||
\(601\) | −2.62572e7 | −0.00493387 | −0.00246694 | − | 0.999997i | \(-0.500785\pi\) | ||||
−0.00246694 | + | 0.999997i | \(0.500785\pi\) | |||||||
\(602\) | 1.00057e8 | 0.0186922 | ||||||||
\(603\) | −1.37669e10 | −2.55697 | ||||||||
\(604\) | 1.11545e9 | 0.205978 | ||||||||
\(605\) | −6.13254e9 | −1.12589 | ||||||||
\(606\) | −1.23095e10 | −2.24691 | ||||||||
\(607\) | −7.26489e9 | −1.31846 | −0.659232 | − | 0.751939i | \(-0.729119\pi\) | ||||
−0.659232 | + | 0.751939i | \(0.729119\pi\) | |||||||
\(608\) | −1.19544e9 | −0.215708 | ||||||||
\(609\) | −2.47773e9 | −0.444523 | ||||||||
\(610\) | −1.10543e10 | −1.97187 | ||||||||
\(611\) | 5.10123e9 | 0.904755 | ||||||||
\(612\) | 7.21855e8 | 0.127298 | ||||||||
\(613\) | −1.10037e10 | −1.92942 | −0.964712 | − | 0.263308i | \(-0.915186\pi\) | ||||
−0.964712 | + | 0.263308i | \(0.915186\pi\) | |||||||
\(614\) | −1.30865e9 | −0.228157 | ||||||||
\(615\) | 5.17515e9 | 0.897139 | ||||||||
\(616\) | 4.22883e8 | 0.0728934 | ||||||||
\(617\) | 8.50181e8 | 0.145718 | 0.0728590 | − | 0.997342i | \(-0.476788\pi\) | ||||
0.0728590 | + | 0.997342i | \(0.476788\pi\) | |||||||
\(618\) | −1.06325e10 | −1.81207 | ||||||||
\(619\) | 5.79271e9 | 0.981668 | 0.490834 | − | 0.871253i | \(-0.336692\pi\) | ||||
0.490834 | + | 0.871253i | \(0.336692\pi\) | |||||||
\(620\) | 8.10374e9 | 1.36557 | ||||||||
\(621\) | 2.48198e9 | 0.415889 | ||||||||
\(622\) | 3.45984e9 | 0.576488 | ||||||||
\(623\) | −5.99598e7 | −0.00993464 | ||||||||
\(624\) | −2.39007e9 | −0.393789 | ||||||||
\(625\) | −6.54389e8 | −0.107215 | ||||||||
\(626\) | 3.41626e9 | 0.556597 | ||||||||
\(627\) | −7.20359e9 | −1.16711 | ||||||||
\(628\) | −1.42180e9 | −0.229077 | ||||||||
\(629\) | −5.33332e8 | −0.0854516 | ||||||||
\(630\) | 5.57739e9 | 0.888667 | ||||||||
\(631\) | −6.69052e9 | −1.06012 | −0.530062 | − | 0.847959i | \(-0.677831\pi\) | ||||
−0.530062 | + | 0.847959i | \(0.677831\pi\) | |||||||
\(632\) | −1.74894e9 | −0.275591 | ||||||||
\(633\) | −7.69165e9 | −1.20533 | ||||||||
\(634\) | 2.78002e9 | 0.433246 | ||||||||
\(635\) | 9.54849e9 | 1.47988 | ||||||||
\(636\) | 2.98853e8 | 0.0460635 | ||||||||
\(637\) | 8.37190e8 | 0.128332 | ||||||||
\(638\) | 1.69704e9 | 0.258714 | ||||||||
\(639\) | −4.83753e8 | −0.0733450 | ||||||||
\(640\) | −9.39524e8 | −0.141670 | ||||||||
\(641\) | 4.77194e9 | 0.715636 | 0.357818 | − | 0.933791i | \(-0.383521\pi\) | ||||
0.357818 | + | 0.933791i | \(0.383521\pi\) | |||||||
\(642\) | 4.56956e9 | 0.681557 | ||||||||
\(643\) | 4.09295e9 | 0.607153 | 0.303576 | − | 0.952807i | \(-0.401819\pi\) | ||||
0.303576 | + | 0.952807i | \(0.401819\pi\) | |||||||
\(644\) | 2.82742e8 | 0.0417147 | ||||||||
\(645\) | −1.33954e9 | −0.196561 | ||||||||
\(646\) | −7.25554e8 | −0.105890 | ||||||||
\(647\) | −5.39902e9 | −0.783701 | −0.391850 | − | 0.920029i | \(-0.628165\pi\) | ||||
−0.391850 | + | 0.920029i | \(0.628165\pi\) | |||||||
\(648\) | −3.01004e9 | −0.434570 | ||||||||
\(649\) | −5.17687e9 | −0.743380 | ||||||||
\(650\) | −6.97818e9 | −0.996656 | ||||||||
\(651\) | 7.94942e9 | 1.12928 | ||||||||
\(652\) | 3.99229e9 | 0.564099 | ||||||||
\(653\) | −4.09787e9 | −0.575919 | −0.287960 | − | 0.957643i | \(-0.592977\pi\) | ||||
−0.287960 | + | 0.957643i | \(0.592977\pi\) | |||||||
\(654\) | −9.77695e9 | −1.36673 | ||||||||
\(655\) | 4.69384e9 | 0.652656 | ||||||||
\(656\) | −5.77020e8 | −0.0798045 | ||||||||
\(657\) | 4.48678e9 | 0.617242 | ||||||||
\(658\) | 1.96709e9 | 0.269174 | ||||||||
\(659\) | −3.77455e9 | −0.513766 | −0.256883 | − | 0.966442i | \(-0.582696\pi\) | ||||
−0.256883 | + | 0.966442i | \(0.582696\pi\) | |||||||
\(660\) | −5.66146e9 | −0.766522 | ||||||||
\(661\) | 9.81906e9 | 1.32241 | 0.661203 | − | 0.750207i | \(-0.270046\pi\) | ||||
0.661203 | + | 0.750207i | \(0.270046\pi\) | |||||||
\(662\) | 6.52331e9 | 0.873906 | ||||||||
\(663\) | −1.45061e9 | −0.193310 | ||||||||
\(664\) | 7.75270e6 | 0.00102770 | ||||||||
\(665\) | −5.60597e9 | −0.739222 | ||||||||
\(666\) | 7.78673e9 | 1.02140 | ||||||||
\(667\) | 1.13465e9 | 0.148055 | ||||||||
\(668\) | 2.11993e9 | 0.275171 | ||||||||
\(669\) | −1.33305e8 | −0.0172130 | ||||||||
\(670\) | 1.08752e10 | 1.39693 | ||||||||
\(671\) | 7.42714e9 | 0.949058 | ||||||||
\(672\) | −9.21633e8 | −0.117156 | ||||||||
\(673\) | 9.98739e9 | 1.26299 | 0.631494 | − | 0.775381i | \(-0.282442\pi\) | ||||
0.631494 | + | 0.775381i | \(0.282442\pi\) | |||||||
\(674\) | 4.44632e9 | 0.559359 | ||||||||
\(675\) | −2.36210e10 | −2.95621 | ||||||||
\(676\) | −7.75108e8 | −0.0965048 | ||||||||
\(677\) | 4.75559e8 | 0.0589040 | 0.0294520 | − | 0.999566i | \(-0.490624\pi\) | ||||
0.0294520 | + | 0.999566i | \(0.490624\pi\) | |||||||
\(678\) | −1.71009e10 | −2.10724 | ||||||||
\(679\) | −4.63283e9 | −0.567939 | ||||||||
\(680\) | −5.70229e8 | −0.0695453 | ||||||||
\(681\) | 2.01845e10 | 2.44908 | ||||||||
\(682\) | −5.44470e9 | −0.657247 | ||||||||
\(683\) | 2.76365e8 | 0.0331902 | 0.0165951 | − | 0.999862i | \(-0.494717\pi\) | ||||
0.0165951 | + | 0.999862i | \(0.494717\pi\) | |||||||
\(684\) | 1.05932e10 | 1.26570 | ||||||||
\(685\) | 1.62167e10 | 1.92773 | ||||||||
\(686\) | 3.22829e8 | 0.0381802 | ||||||||
\(687\) | 8.69534e9 | 1.02315 | ||||||||
\(688\) | 1.49357e8 | 0.0174850 | ||||||||
\(689\) | −4.05228e8 | −0.0471989 | ||||||||
\(690\) | −3.78528e9 | −0.438658 | ||||||||
\(691\) | 8.82482e9 | 1.01750 | 0.508748 | − | 0.860915i | \(-0.330108\pi\) | ||||
0.508748 | + | 0.860915i | \(0.330108\pi\) | |||||||
\(692\) | −4.51711e9 | −0.518191 | ||||||||
\(693\) | −3.74731e9 | −0.427714 | ||||||||
\(694\) | −8.61664e9 | −0.978542 | ||||||||
\(695\) | −2.36390e10 | −2.67105 | ||||||||
\(696\) | −3.69854e9 | −0.415813 | ||||||||
\(697\) | −3.50213e8 | −0.0391757 | ||||||||
\(698\) | −1.15333e10 | −1.28369 | ||||||||
\(699\) | 1.65809e10 | 1.83628 | ||||||||
\(700\) | −2.69085e9 | −0.296515 | ||||||||
\(701\) | 1.61615e10 | 1.77202 | 0.886012 | − | 0.463662i | \(-0.153465\pi\) | ||||
0.886012 | + | 0.463662i | \(0.153465\pi\) | |||||||
\(702\) | 1.09700e10 | 1.19682 | ||||||||
\(703\) | −7.82663e9 | −0.849633 | ||||||||
\(704\) | 6.31243e8 | 0.0681855 | ||||||||
\(705\) | −2.63349e10 | −2.83054 | ||||||||
\(706\) | −4.58613e9 | −0.490490 | ||||||||
\(707\) | 6.43622e9 | 0.684956 | ||||||||
\(708\) | 1.12825e10 | 1.19478 | ||||||||
\(709\) | −8.36102e9 | −0.881043 | −0.440522 | − | 0.897742i | \(-0.645207\pi\) | ||||
−0.440522 | + | 0.897742i | \(0.645207\pi\) | |||||||
\(710\) | 3.82140e8 | 0.0400699 | ||||||||
\(711\) | 1.54979e10 | 1.61707 | ||||||||
\(712\) | −8.95027e7 | −0.00929301 | ||||||||
\(713\) | −3.64035e9 | −0.376123 | ||||||||
\(714\) | −5.59370e8 | −0.0575116 | ||||||||
\(715\) | 7.67663e9 | 0.785415 | ||||||||
\(716\) | −7.75528e9 | −0.789590 | ||||||||
\(717\) | 3.01369e9 | 0.305339 | ||||||||
\(718\) | 7.59468e9 | 0.765727 | ||||||||
\(719\) | −8.18891e9 | −0.821627 | −0.410814 | − | 0.911719i | \(-0.634755\pi\) | ||||
−0.410814 | + | 0.911719i | \(0.634755\pi\) | |||||||
\(720\) | 8.32543e9 | 0.831272 | ||||||||
\(721\) | 5.55935e9 | 0.552396 | ||||||||
\(722\) | −3.49652e9 | −0.345745 | ||||||||
\(723\) | −4.72660e9 | −0.465120 | ||||||||
\(724\) | 1.47552e9 | 0.144498 | ||||||||
\(725\) | −1.07985e10 | −1.05240 | ||||||||
\(726\) | −8.97979e9 | −0.870940 | ||||||||
\(727\) | −1.40657e10 | −1.35766 | −0.678832 | − | 0.734294i | \(-0.737514\pi\) | ||||
−0.678832 | + | 0.734294i | \(0.737514\pi\) | |||||||
\(728\) | 1.24968e9 | 0.120044 | ||||||||
\(729\) | −7.88473e9 | −0.753772 | ||||||||
\(730\) | −3.54433e9 | −0.337212 | ||||||||
\(731\) | 9.06495e7 | 0.00858331 | ||||||||
\(732\) | −1.61867e10 | −1.52535 | ||||||||
\(733\) | −9.53632e9 | −0.894370 | −0.447185 | − | 0.894442i | \(-0.647573\pi\) | ||||
−0.447185 | + | 0.894442i | \(0.647573\pi\) | |||||||
\(734\) | 2.41417e9 | 0.225336 | ||||||||
\(735\) | −4.32195e9 | −0.401490 | ||||||||
\(736\) | 4.22052e8 | 0.0390206 | ||||||||
\(737\) | −7.30675e9 | −0.672338 | ||||||||
\(738\) | 5.11316e9 | 0.468266 | ||||||||
\(739\) | 1.45133e10 | 1.32285 | 0.661425 | − | 0.750011i | \(-0.269952\pi\) | ||||
0.661425 | + | 0.750011i | \(0.269952\pi\) | |||||||
\(740\) | −6.15112e9 | −0.558011 | ||||||||
\(741\) | −2.12877e10 | −1.92205 | ||||||||
\(742\) | −1.56260e8 | −0.0140422 | ||||||||
\(743\) | −1.88434e9 | −0.168538 | −0.0842692 | − | 0.996443i | \(-0.526856\pi\) | ||||
−0.0842692 | + | 0.996443i | \(0.526856\pi\) | |||||||
\(744\) | 1.18662e10 | 1.05635 | ||||||||
\(745\) | 3.29729e10 | 2.92153 | ||||||||
\(746\) | 1.08946e10 | 0.960780 | ||||||||
\(747\) | −6.86993e7 | −0.00603017 | ||||||||
\(748\) | 3.83122e8 | 0.0334720 | ||||||||
\(749\) | −2.38927e9 | −0.207768 | ||||||||
\(750\) | 1.30645e10 | 1.13078 | ||||||||
\(751\) | −1.71941e10 | −1.48129 | −0.740646 | − | 0.671895i | \(-0.765480\pi\) | ||||
−0.740646 | + | 0.671895i | \(0.765480\pi\) | |||||||
\(752\) | 2.93629e9 | 0.251789 | ||||||||
\(753\) | 2.14292e10 | 1.82904 | ||||||||
\(754\) | 5.01502e9 | 0.426062 | ||||||||
\(755\) | 7.80814e9 | 0.660288 | ||||||||
\(756\) | 4.23015e9 | 0.356065 | ||||||||
\(757\) | −1.02275e10 | −0.856909 | −0.428454 | − | 0.903563i | \(-0.640942\pi\) | ||||
−0.428454 | + | 0.903563i | \(0.640942\pi\) | |||||||
\(758\) | 1.21471e10 | 1.01305 | ||||||||
\(759\) | 2.54323e9 | 0.211125 | ||||||||
\(760\) | −8.36810e9 | −0.691479 | ||||||||
\(761\) | 2.93806e9 | 0.241666 | 0.120833 | − | 0.992673i | \(-0.461443\pi\) | ||||
0.120833 | + | 0.992673i | \(0.461443\pi\) | |||||||
\(762\) | 1.39817e10 | 1.14477 | ||||||||
\(763\) | 5.11204e9 | 0.416637 | ||||||||
\(764\) | −1.29873e9 | −0.105364 | ||||||||
\(765\) | 5.05298e9 | 0.408068 | ||||||||
\(766\) | −3.63291e9 | −0.292048 | ||||||||
\(767\) | −1.52984e10 | −1.22423 | ||||||||
\(768\) | −1.37573e9 | −0.109590 | ||||||||
\(769\) | −1.49710e10 | −1.18716 | −0.593579 | − | 0.804776i | \(-0.702286\pi\) | ||||
−0.593579 | + | 0.804776i | \(0.702286\pi\) | |||||||
\(770\) | 2.96018e9 | 0.233669 | ||||||||
\(771\) | −2.85053e10 | −2.23993 | ||||||||
\(772\) | 1.44692e9 | 0.113184 | ||||||||
\(773\) | −1.53271e10 | −1.19352 | −0.596762 | − | 0.802419i | \(-0.703546\pi\) | ||||
−0.596762 | + | 0.802419i | \(0.703546\pi\) | |||||||
\(774\) | −1.32350e9 | −0.102596 | ||||||||
\(775\) | 3.46452e10 | 2.67355 | ||||||||
\(776\) | −6.91548e9 | −0.531259 | ||||||||
\(777\) | −6.03398e9 | −0.461456 | ||||||||
\(778\) | 1.46960e10 | 1.11884 | ||||||||
\(779\) | −5.13937e9 | −0.389519 | ||||||||
\(780\) | −1.67305e10 | −1.26234 | ||||||||
\(781\) | −2.56751e8 | −0.0192856 | ||||||||
\(782\) | 2.56157e8 | 0.0191551 | ||||||||
\(783\) | 1.69757e10 | 1.26375 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −9.95263e9 | −0.734335 | ||||||||
\(786\) | 6.87313e9 | 0.504865 | ||||||||
\(787\) | −5.64462e8 | −0.0412784 | −0.0206392 | − | 0.999787i | \(-0.506570\pi\) | ||||
−0.0206392 | + | 0.999787i | \(0.506570\pi\) | |||||||
\(788\) | −2.09395e9 | −0.152449 | ||||||||
\(789\) | 1.44731e10 | 1.04904 | ||||||||
\(790\) | −1.22426e10 | −0.883442 | ||||||||
\(791\) | 8.94148e9 | 0.642379 | ||||||||
\(792\) | −5.59365e9 | −0.400089 | ||||||||
\(793\) | 2.19483e10 | 1.56295 | ||||||||
\(794\) | −9.89342e9 | −0.701414 | ||||||||
\(795\) | 2.09197e9 | 0.147662 | ||||||||
\(796\) | 4.63662e9 | 0.325841 | ||||||||
\(797\) | 2.02786e10 | 1.41884 | 0.709421 | − | 0.704785i | \(-0.248956\pi\) | ||||
0.709421 | + | 0.704785i | \(0.248956\pi\) | |||||||
\(798\) | −8.20874e9 | −0.571829 | ||||||||
\(799\) | 1.78213e9 | 0.123602 | ||||||||
\(800\) | −4.01667e9 | −0.277365 | ||||||||
\(801\) | 7.93113e8 | 0.0545282 | ||||||||
\(802\) | −1.26358e10 | −0.864954 | ||||||||
\(803\) | 2.38134e9 | 0.162300 | ||||||||
\(804\) | 1.59243e10 | 1.08060 | ||||||||
\(805\) | 1.97919e9 | 0.133722 | ||||||||
\(806\) | −1.60899e10 | −1.08238 | ||||||||
\(807\) | 3.34469e10 | 2.24026 | ||||||||
\(808\) | 9.60741e9 | 0.640718 | ||||||||
\(809\) | 3.20139e9 | 0.212578 | 0.106289 | − | 0.994335i | \(-0.466103\pi\) | ||||
0.106289 | + | 0.994335i | \(0.466103\pi\) | |||||||
\(810\) | −2.10703e10 | −1.39307 | ||||||||
\(811\) | −2.22219e10 | −1.46288 | −0.731439 | − | 0.681907i | \(-0.761151\pi\) | ||||
−0.731439 | + | 0.681907i | \(0.761151\pi\) | |||||||
\(812\) | 1.93384e9 | 0.126758 | ||||||||
\(813\) | −2.60447e10 | −1.69982 | ||||||||
\(814\) | 4.13278e9 | 0.268570 | ||||||||
\(815\) | 2.79460e10 | 1.80829 | ||||||||
\(816\) | −8.34978e8 | −0.0537972 | ||||||||
\(817\) | 1.33028e9 | 0.0853426 | ||||||||
\(818\) | 1.54046e10 | 0.984043 | ||||||||
\(819\) | −1.10739e10 | −0.704377 | ||||||||
\(820\) | −4.03914e9 | −0.255823 | ||||||||
\(821\) | 2.57309e9 | 0.162276 | 0.0811381 | − | 0.996703i | \(-0.474145\pi\) | ||||
0.0811381 | + | 0.996703i | \(0.474145\pi\) | |||||||
\(822\) | 2.37459e10 | 1.49121 | ||||||||
\(823\) | −5.15490e9 | −0.322345 | −0.161172 | − | 0.986926i | \(-0.551528\pi\) | ||||
−0.161172 | + | 0.986926i | \(0.551528\pi\) | |||||||
\(824\) | 8.29851e9 | 0.516719 | ||||||||
\(825\) | −2.42040e10 | −1.50071 | ||||||||
\(826\) | −5.89922e9 | −0.364221 | ||||||||
\(827\) | 2.02079e10 | 1.24237 | 0.621185 | − | 0.783664i | \(-0.286651\pi\) | ||||
0.621185 | + | 0.783664i | \(0.286651\pi\) | |||||||
\(828\) | −3.73994e9 | −0.228959 | ||||||||
\(829\) | −2.26920e10 | −1.38335 | −0.691676 | − | 0.722208i | \(-0.743127\pi\) | ||||
−0.691676 | + | 0.722208i | \(0.743127\pi\) | |||||||
\(830\) | 5.42689e7 | 0.00329441 | ||||||||
\(831\) | −2.40856e10 | −1.45597 | ||||||||
\(832\) | 1.86542e9 | 0.112291 | ||||||||
\(833\) | 2.92475e8 | 0.0175320 | ||||||||
\(834\) | −3.46142e10 | −2.06620 | ||||||||
\(835\) | 1.48395e10 | 0.882096 | ||||||||
\(836\) | 5.62231e9 | 0.332808 | ||||||||
\(837\) | −5.44640e10 | −3.21048 | ||||||||
\(838\) | 1.91997e10 | 1.12704 | ||||||||
\(839\) | −1.18283e10 | −0.691444 | −0.345722 | − | 0.938337i | \(-0.612366\pi\) | ||||
−0.345722 | + | 0.938337i | \(0.612366\pi\) | |||||||
\(840\) | −6.45143e9 | −0.375559 | ||||||||
\(841\) | −9.48932e9 | −0.550110 | ||||||||
\(842\) | −9.67520e9 | −0.558557 | ||||||||
\(843\) | 4.46922e9 | 0.256942 | ||||||||
\(844\) | 6.00324e9 | 0.343706 | ||||||||
\(845\) | −5.42576e9 | −0.309358 | ||||||||
\(846\) | −2.60194e10 | −1.47741 | ||||||||
\(847\) | 4.69523e9 | 0.265500 | ||||||||
\(848\) | −2.33251e8 | −0.0131352 | ||||||||
\(849\) | −1.68435e10 | −0.944618 | ||||||||
\(850\) | −2.43785e9 | −0.136157 | ||||||||
\(851\) | 2.76320e9 | 0.153695 | ||||||||
\(852\) | 5.59563e8 | 0.0309963 | ||||||||
\(853\) | 1.17141e10 | 0.646230 | 0.323115 | − | 0.946360i | \(-0.395270\pi\) | ||||
0.323115 | + | 0.946360i | \(0.395270\pi\) | |||||||
\(854\) | 8.46348e9 | 0.464993 | ||||||||
\(855\) | 7.41524e10 | 4.05736 | ||||||||
\(856\) | −3.56649e9 | −0.194349 | ||||||||
\(857\) | 1.67955e10 | 0.911506 | 0.455753 | − | 0.890106i | \(-0.349370\pi\) | ||||
0.455753 | + | 0.890106i | \(0.349370\pi\) | |||||||
\(858\) | 1.12408e10 | 0.607562 | ||||||||
\(859\) | −1.86233e10 | −1.00249 | −0.501244 | − | 0.865306i | \(-0.667124\pi\) | ||||
−0.501244 | + | 0.865306i | \(0.667124\pi\) | |||||||
\(860\) | 1.04550e9 | 0.0560503 | ||||||||
\(861\) | −3.96222e9 | −0.211557 | ||||||||
\(862\) | 1.73028e10 | 0.920113 | ||||||||
\(863\) | −1.95683e10 | −1.03637 | −0.518184 | − | 0.855269i | \(-0.673392\pi\) | ||||
−0.518184 | + | 0.855269i | \(0.673392\pi\) | |||||||
\(864\) | 6.31439e9 | 0.333068 | ||||||||
\(865\) | −3.16198e10 | −1.66113 | ||||||||
\(866\) | −1.80600e10 | −0.944941 | ||||||||
\(867\) | 3.31410e10 | 1.72703 | ||||||||
\(868\) | −6.20443e9 | −0.322020 | ||||||||
\(869\) | 8.22548e9 | 0.425199 | ||||||||
\(870\) | −2.58898e10 | −1.33294 | ||||||||
\(871\) | −2.15925e10 | −1.10724 | ||||||||
\(872\) | 7.63079e9 | 0.389728 | ||||||||
\(873\) | 6.12803e10 | 3.11725 | ||||||||
\(874\) | 3.75911e9 | 0.190456 | ||||||||
\(875\) | −6.83098e9 | −0.344711 | ||||||||
\(876\) | −5.18990e9 | −0.260853 | ||||||||
\(877\) | −8.76080e9 | −0.438576 | −0.219288 | − | 0.975660i | \(-0.570373\pi\) | ||||
−0.219288 | + | 0.975660i | \(0.570373\pi\) | |||||||
\(878\) | 5.96579e9 | 0.297466 | ||||||||
\(879\) | 9.74870e9 | 0.484156 | ||||||||
\(880\) | 4.41870e9 | 0.218577 | ||||||||
\(881\) | 3.59103e10 | 1.76931 | 0.884653 | − | 0.466250i | \(-0.154395\pi\) | ||||
0.884653 | + | 0.466250i | \(0.154395\pi\) | |||||||
\(882\) | −4.27019e9 | −0.209559 | ||||||||
\(883\) | −3.42420e10 | −1.67377 | −0.836887 | − | 0.547375i | \(-0.815627\pi\) | ||||
−0.836887 | + | 0.547375i | \(0.815627\pi\) | |||||||
\(884\) | 1.13218e9 | 0.0551232 | ||||||||
\(885\) | 7.89773e10 | 3.83002 | ||||||||
\(886\) | 8.81722e9 | 0.425906 | ||||||||
\(887\) | 1.33299e10 | 0.641350 | 0.320675 | − | 0.947189i | \(-0.396090\pi\) | ||||
0.320675 | + | 0.947189i | \(0.396090\pi\) | |||||||
\(888\) | −9.00700e9 | −0.431653 | ||||||||
\(889\) | −7.31056e9 | −0.348975 | ||||||||
\(890\) | −6.26519e8 | −0.0297899 | ||||||||
\(891\) | 1.41566e10 | 0.670481 | ||||||||
\(892\) | 1.04043e8 | 0.00490835 | ||||||||
\(893\) | 2.61528e10 | 1.22896 | ||||||||
\(894\) | 4.82818e10 | 2.25997 | ||||||||
\(895\) | −5.42870e10 | −2.53113 | ||||||||
\(896\) | 7.19323e8 | 0.0334077 | ||||||||
\(897\) | 7.51563e9 | 0.347690 | ||||||||
\(898\) | −2.73280e10 | −1.25933 | ||||||||
\(899\) | −2.48985e10 | −1.14292 | ||||||||
\(900\) | 3.55930e10 | 1.62748 | ||||||||
\(901\) | −1.41568e8 | −0.00644804 | ||||||||
\(902\) | 2.71380e9 | 0.123127 | ||||||||
\(903\) | 1.02559e9 | 0.0463516 | ||||||||
\(904\) | 1.33470e10 | 0.600891 | ||||||||
\(905\) | 1.03286e10 | 0.463205 | ||||||||
\(906\) | 1.14334e10 | 0.510769 | ||||||||
\(907\) | −3.95632e9 | −0.176062 | −0.0880310 | − | 0.996118i | \(-0.528057\pi\) | ||||
−0.0880310 | + | 0.996118i | \(0.528057\pi\) | |||||||
\(908\) | −1.57538e10 | −0.698367 | ||||||||
\(909\) | −8.51344e10 | −3.75951 | ||||||||
\(910\) | 8.74778e9 | 0.384816 | ||||||||
\(911\) | 1.77864e10 | 0.779426 | 0.389713 | − | 0.920936i | \(-0.372574\pi\) | ||||
0.389713 | + | 0.920936i | \(0.372574\pi\) | |||||||
\(912\) | −1.22533e10 | −0.534897 | ||||||||
\(913\) | −3.64619e7 | −0.00158559 | ||||||||
\(914\) | −3.41848e9 | −0.148088 | ||||||||
\(915\) | −1.13307e11 | −4.88971 | ||||||||
\(916\) | −6.78661e9 | −0.291755 | ||||||||
\(917\) | −3.59372e9 | −0.153905 | ||||||||
\(918\) | 3.83242e9 | 0.163502 | ||||||||
\(919\) | 3.79307e10 | 1.61208 | 0.806040 | − | 0.591862i | \(-0.201607\pi\) | ||||
0.806040 | + | 0.591862i | \(0.201607\pi\) | |||||||
\(920\) | 2.95436e9 | 0.125085 | ||||||||
\(921\) | −1.34137e10 | −0.565769 | ||||||||
\(922\) | −1.74493e10 | −0.733196 | ||||||||
\(923\) | −7.58736e8 | −0.0317603 | ||||||||
\(924\) | 4.33455e9 | 0.180756 | ||||||||
\(925\) | −2.62974e10 | −1.09249 | ||||||||
\(926\) | −1.50508e9 | −0.0622902 | ||||||||
\(927\) | −7.35358e10 | −3.03193 | ||||||||
\(928\) | 2.88666e9 | 0.118571 | ||||||||
\(929\) | 4.23414e10 | 1.73265 | 0.866323 | − | 0.499485i | \(-0.166477\pi\) | ||||
0.866323 | + | 0.499485i | \(0.166477\pi\) | |||||||
\(930\) | 8.30633e10 | 3.38625 | ||||||||
\(931\) | 4.29207e9 | 0.174318 | ||||||||
\(932\) | −1.29412e10 | −0.523623 | ||||||||
\(933\) | 3.54634e10 | 1.42953 | ||||||||
\(934\) | −6.83627e9 | −0.274540 | ||||||||
\(935\) | 2.68186e9 | 0.107299 | ||||||||
\(936\) | −1.65301e10 | −0.658884 | ||||||||
\(937\) | 1.65147e10 | 0.655817 | 0.327909 | − | 0.944709i | \(-0.393656\pi\) | ||||
0.327909 | + | 0.944709i | \(0.393656\pi\) | |||||||
\(938\) | −8.32629e9 | −0.329414 | ||||||||
\(939\) | 3.50167e10 | 1.38021 | ||||||||
\(940\) | 2.05540e10 | 0.807142 | ||||||||
\(941\) | −3.14329e10 | −1.22976 | −0.614881 | − | 0.788620i | \(-0.710796\pi\) | ||||
−0.614881 | + | 0.788620i | \(0.710796\pi\) | |||||||
\(942\) | −1.45735e10 | −0.568049 | ||||||||
\(943\) | 1.81446e9 | 0.0704621 | ||||||||
\(944\) | −8.80583e9 | −0.340697 | ||||||||
\(945\) | 2.96111e10 | 1.14141 | ||||||||
\(946\) | −7.02442e8 | −0.0269769 | ||||||||
\(947\) | −3.27114e10 | −1.25163 | −0.625813 | − | 0.779973i | \(-0.715233\pi\) | ||||
−0.625813 | + | 0.779973i | \(0.715233\pi\) | |||||||
\(948\) | −1.79266e10 | −0.683391 | ||||||||
\(949\) | 7.03723e9 | 0.267282 | ||||||||
\(950\) | −3.57754e10 | −1.35379 | ||||||||
\(951\) | 2.84952e10 | 1.07433 | ||||||||
\(952\) | 4.36581e8 | 0.0163997 | ||||||||
\(953\) | −2.62655e10 | −0.983017 | −0.491509 | − | 0.870873i | \(-0.663554\pi\) | ||||
−0.491509 | + | 0.870873i | \(0.663554\pi\) | |||||||
\(954\) | 2.06691e9 | 0.0770731 | ||||||||
\(955\) | −9.09113e9 | −0.337758 | ||||||||
\(956\) | −2.35215e9 | −0.0870687 | ||||||||
\(957\) | 1.73947e10 | 0.641542 | ||||||||
\(958\) | 5.46251e9 | 0.200730 | ||||||||
\(959\) | −1.24159e10 | −0.454584 | ||||||||
\(960\) | −9.63012e9 | −0.351303 | ||||||||
\(961\) | 5.23705e10 | 1.90351 | ||||||||
\(962\) | 1.22130e10 | 0.442292 | ||||||||
\(963\) | 3.16038e10 | 1.14037 | ||||||||
\(964\) | 3.68906e9 | 0.132631 | ||||||||
\(965\) | 1.01284e10 | 0.362825 | ||||||||
\(966\) | 2.89810e9 | 0.103441 | ||||||||
\(967\) | 2.58253e10 | 0.918443 | 0.459222 | − | 0.888322i | \(-0.348128\pi\) | ||||
0.459222 | + | 0.888322i | \(0.348128\pi\) | |||||||
\(968\) | 7.00862e9 | 0.248353 | ||||||||
\(969\) | −7.43693e9 | −0.262579 | ||||||||
\(970\) | −4.84083e10 | −1.70302 | ||||||||
\(971\) | 2.24102e10 | 0.785560 | 0.392780 | − | 0.919632i | \(-0.371513\pi\) | ||||
0.392780 | + | 0.919632i | \(0.371513\pi\) | |||||||
\(972\) | −3.88106e9 | −0.135556 | ||||||||
\(973\) | 1.80986e10 | 0.629868 | ||||||||
\(974\) | −3.32095e10 | −1.15161 | ||||||||
\(975\) | −7.15263e10 | −2.47144 | ||||||||
\(976\) | 1.26335e10 | 0.434961 | ||||||||
\(977\) | −3.54582e10 | −1.21643 | −0.608214 | − | 0.793773i | \(-0.708114\pi\) | ||||
−0.608214 | + | 0.793773i | \(0.708114\pi\) | |||||||
\(978\) | 4.09210e10 | 1.39881 | ||||||||
\(979\) | 4.20942e8 | 0.0143378 | ||||||||
\(980\) | 3.37323e9 | 0.114487 | ||||||||
\(981\) | −6.76190e10 | −2.28679 | ||||||||
\(982\) | −7.19631e9 | −0.242504 | ||||||||
\(983\) | −1.45767e10 | −0.489467 | −0.244733 | − | 0.969590i | \(-0.578700\pi\) | ||||
−0.244733 | + | 0.969590i | \(0.578700\pi\) | |||||||
\(984\) | −5.91445e9 | −0.197894 | ||||||||
\(985\) | −1.46576e10 | −0.488694 | ||||||||
\(986\) | 1.75201e9 | 0.0582061 | ||||||||
\(987\) | 2.01626e10 | 0.667478 | ||||||||
\(988\) | 1.66148e10 | 0.548082 | ||||||||
\(989\) | −4.69656e8 | −0.0154381 | ||||||||
\(990\) | −3.91555e10 | −1.28254 | ||||||||
\(991\) | 1.25713e10 | 0.410319 | 0.205160 | − | 0.978729i | \(-0.434229\pi\) | ||||
0.205160 | + | 0.978729i | \(0.434229\pi\) | |||||||
\(992\) | −9.26142e9 | −0.301222 | ||||||||
\(993\) | 6.68639e10 | 2.16705 | ||||||||
\(994\) | −2.92576e8 | −0.00944902 | ||||||||
\(995\) | 3.24564e10 | 1.04453 | ||||||||
\(996\) | 7.94652e7 | 0.00254841 | ||||||||
\(997\) | −1.04037e10 | −0.332471 | −0.166236 | − | 0.986086i | \(-0.553161\pi\) | ||||
−0.166236 | + | 0.986086i | \(0.553161\pi\) | |||||||
\(998\) | 4.88888e9 | 0.155687 | ||||||||
\(999\) | 4.13407e10 | 1.31189 |
(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 | 14.8.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 126.8.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 112.8.a.e.1.1 | 1 | |||
5.2 | odd | 4 | 350.8.c.d.99.1 | 2 | |||
5.3 | odd | 4 | 350.8.c.d.99.2 | 2 | |||
5.4 | even | 2 | 350.8.a.h.1.1 | 1 | |||
7.2 | even | 3 | 98.8.c.f.67.1 | 2 | |||
7.3 | odd | 6 | 98.8.c.c.79.1 | 2 | |||
7.4 | even | 3 | 98.8.c.f.79.1 | 2 | |||
7.5 | odd | 6 | 98.8.c.c.67.1 | 2 | |||
7.6 | odd | 2 | 98.8.a.b.1.1 | 1 | |||
8.3 | odd | 2 | 448.8.a.a.1.1 | 1 | |||
8.5 | even | 2 | 448.8.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.8.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
98.8.a.b.1.1 | 1 | 7.6 | odd | 2 | |||
98.8.c.c.67.1 | 2 | 7.5 | odd | 6 | |||
98.8.c.c.79.1 | 2 | 7.3 | odd | 6 | |||
98.8.c.f.67.1 | 2 | 7.2 | even | 3 | |||
98.8.c.f.79.1 | 2 | 7.4 | even | 3 | |||
112.8.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
126.8.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
350.8.a.h.1.1 | 1 | 5.4 | even | 2 | |||
350.8.c.d.99.1 | 2 | 5.2 | odd | 4 | |||
350.8.c.d.99.2 | 2 | 5.3 | odd | 4 | |||
448.8.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
448.8.a.j.1.1 | 1 | 8.5 | even | 2 |