Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [285,10,Mod(1,285)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(285, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("285.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.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: | \(146.785213307\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 5365 x^{12} + 7107 x^{11} + 10970098 x^{10} - 19024208 x^{9} - 10608934432 x^{8} + \cdots - 480881506516992 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{8}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(33.9313\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 285.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −33.9313 | −1.49956 | −0.749782 | − | 0.661685i | \(-0.769842\pi\) | ||||
−0.749782 | + | 0.661685i | \(0.769842\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 639.331 | 1.24869 | ||||||||
\(5\) | −625.000 | −0.447214 | ||||||||
\(6\) | 2748.43 | 0.865774 | ||||||||
\(7\) | 9880.04 | 1.55531 | 0.777656 | − | 0.628690i | \(-0.216409\pi\) | ||||
0.777656 | + | 0.628690i | \(0.216409\pi\) | |||||||
\(8\) | −4320.49 | −0.372931 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 21207.0 | 0.670626 | ||||||||
\(11\) | −69660.6 | −1.43456 | −0.717282 | − | 0.696782i | \(-0.754614\pi\) | ||||
−0.717282 | + | 0.696782i | \(0.754614\pi\) | |||||||
\(12\) | −51785.8 | −0.720933 | ||||||||
\(13\) | −176048. | −1.70956 | −0.854782 | − | 0.518987i | \(-0.826309\pi\) | ||||
−0.854782 | + | 0.518987i | \(0.826309\pi\) | |||||||
\(14\) | −335242. | −2.33229 | ||||||||
\(15\) | 50625.0 | 0.258199 | ||||||||
\(16\) | −180738. | −0.689459 | ||||||||
\(17\) | −491581. | −1.42750 | −0.713748 | − | 0.700402i | \(-0.753004\pi\) | ||||
−0.713748 | + | 0.700402i | \(0.753004\pi\) | |||||||
\(18\) | −222623. | −0.499855 | ||||||||
\(19\) | 130321. | 0.229416 | ||||||||
\(20\) | −399582. | −0.558432 | ||||||||
\(21\) | −800283. | −0.897960 | ||||||||
\(22\) | 2.36367e6 | 2.15122 | ||||||||
\(23\) | −712914. | −0.531205 | −0.265602 | − | 0.964083i | \(-0.585571\pi\) | ||||
−0.265602 | + | 0.964083i | \(0.585571\pi\) | |||||||
\(24\) | 349960. | 0.215312 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | 5.97353e6 | 2.56360 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 6.31661e6 | 1.94211 | ||||||||
\(29\) | −134373. | −0.0352794 | −0.0176397 | − | 0.999844i | \(-0.505615\pi\) | ||||
−0.0176397 | + | 0.999844i | \(0.505615\pi\) | |||||||
\(30\) | −1.71777e6 | −0.387186 | ||||||||
\(31\) | −2.59229e6 | −0.504145 | −0.252073 | − | 0.967708i | \(-0.581112\pi\) | ||||
−0.252073 | + | 0.967708i | \(0.581112\pi\) | |||||||
\(32\) | 8.34475e6 | 1.40682 | ||||||||
\(33\) | 5.64251e6 | 0.828246 | ||||||||
\(34\) | 1.66800e7 | 2.14062 | ||||||||
\(35\) | −6.17502e6 | −0.695557 | ||||||||
\(36\) | 4.19465e6 | 0.416231 | ||||||||
\(37\) | −3.66220e6 | −0.321243 | −0.160622 | − | 0.987016i | \(-0.551350\pi\) | ||||
−0.160622 | + | 0.987016i | \(0.551350\pi\) | |||||||
\(38\) | −4.42196e6 | −0.344024 | ||||||||
\(39\) | 1.42599e7 | 0.987018 | ||||||||
\(40\) | 2.70031e6 | 0.166780 | ||||||||
\(41\) | −9.74654e6 | −0.538670 | −0.269335 | − | 0.963047i | \(-0.586804\pi\) | ||||
−0.269335 | + | 0.963047i | \(0.586804\pi\) | |||||||
\(42\) | 2.71546e7 | 1.34655 | ||||||||
\(43\) | 4.21021e6 | 0.187800 | 0.0938999 | − | 0.995582i | \(-0.470067\pi\) | ||||
0.0938999 | + | 0.995582i | \(0.470067\pi\) | |||||||
\(44\) | −4.45362e7 | −1.79133 | ||||||||
\(45\) | −4.10062e6 | −0.149071 | ||||||||
\(46\) | 2.41901e7 | 0.796575 | ||||||||
\(47\) | −6.41652e7 | −1.91805 | −0.959024 | − | 0.283325i | \(-0.908562\pi\) | ||||
−0.959024 | + | 0.283325i | \(0.908562\pi\) | |||||||
\(48\) | 1.46397e7 | 0.398059 | ||||||||
\(49\) | 5.72616e7 | 1.41900 | ||||||||
\(50\) | −1.32544e7 | −0.299913 | ||||||||
\(51\) | 3.98181e7 | 0.824166 | ||||||||
\(52\) | −1.12553e8 | −2.13472 | ||||||||
\(53\) | −2.38522e7 | −0.415228 | −0.207614 | − | 0.978211i | \(-0.566570\pi\) | ||||
−0.207614 | + | 0.978211i | \(0.566570\pi\) | |||||||
\(54\) | 1.80325e7 | 0.288591 | ||||||||
\(55\) | 4.35379e7 | 0.641557 | ||||||||
\(56\) | −4.26866e7 | −0.580024 | ||||||||
\(57\) | −1.05560e7 | −0.132453 | ||||||||
\(58\) | 4.55945e6 | 0.0529037 | ||||||||
\(59\) | −1.02156e8 | −1.09757 | −0.548783 | − | 0.835965i | \(-0.684909\pi\) | ||||
−0.548783 | + | 0.835965i | \(0.684909\pi\) | |||||||
\(60\) | 3.23661e7 | 0.322411 | ||||||||
\(61\) | −1.25148e8 | −1.15728 | −0.578642 | − | 0.815582i | \(-0.696417\pi\) | ||||
−0.578642 | + | 0.815582i | \(0.696417\pi\) | |||||||
\(62\) | 8.79596e7 | 0.755998 | ||||||||
\(63\) | 6.48229e7 | 0.518437 | ||||||||
\(64\) | −1.90610e8 | −1.42016 | ||||||||
\(65\) | 1.10030e8 | 0.764541 | ||||||||
\(66\) | −1.91457e8 | −1.24201 | ||||||||
\(67\) | −9.38601e6 | −0.0569042 | −0.0284521 | − | 0.999595i | \(-0.509058\pi\) | ||||
−0.0284521 | + | 0.999595i | \(0.509058\pi\) | |||||||
\(68\) | −3.14283e8 | −1.78250 | ||||||||
\(69\) | 5.77460e7 | 0.306691 | ||||||||
\(70\) | 2.09526e8 | 1.04303 | ||||||||
\(71\) | 1.74680e8 | 0.815792 | 0.407896 | − | 0.913028i | \(-0.366263\pi\) | ||||
0.407896 | + | 0.913028i | \(0.366263\pi\) | |||||||
\(72\) | −2.83468e7 | −0.124310 | ||||||||
\(73\) | 3.17964e8 | 1.31046 | 0.655232 | − | 0.755428i | \(-0.272571\pi\) | ||||
0.655232 | + | 0.755428i | \(0.272571\pi\) | |||||||
\(74\) | 1.24263e8 | 0.481725 | ||||||||
\(75\) | −3.16406e7 | −0.115470 | ||||||||
\(76\) | 8.33182e7 | 0.286470 | ||||||||
\(77\) | −6.88250e8 | −2.23120 | ||||||||
\(78\) | −4.83856e8 | −1.48010 | ||||||||
\(79\) | 4.82600e7 | 0.139401 | 0.0697004 | − | 0.997568i | \(-0.477796\pi\) | ||||
0.0697004 | + | 0.997568i | \(0.477796\pi\) | |||||||
\(80\) | 1.12961e8 | 0.308335 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 3.30712e8 | 0.807771 | ||||||||
\(83\) | 3.83115e8 | 0.886090 | 0.443045 | − | 0.896499i | \(-0.353898\pi\) | ||||
0.443045 | + | 0.896499i | \(0.353898\pi\) | |||||||
\(84\) | −5.11646e8 | −1.12128 | ||||||||
\(85\) | 3.07238e8 | 0.638396 | ||||||||
\(86\) | −1.42858e8 | −0.281618 | ||||||||
\(87\) | 1.08842e7 | 0.0203686 | ||||||||
\(88\) | 3.00968e8 | 0.534994 | ||||||||
\(89\) | −1.01770e9 | −1.71936 | −0.859678 | − | 0.510836i | \(-0.829336\pi\) | ||||
−0.859678 | + | 0.510836i | \(0.829336\pi\) | |||||||
\(90\) | 1.39139e8 | 0.223542 | ||||||||
\(91\) | −1.73936e9 | −2.65891 | ||||||||
\(92\) | −4.55788e8 | −0.663311 | ||||||||
\(93\) | 2.09975e8 | 0.291068 | ||||||||
\(94\) | 2.17721e9 | 2.87624 | ||||||||
\(95\) | −8.14506e7 | −0.102598 | ||||||||
\(96\) | −6.75924e8 | −0.812227 | ||||||||
\(97\) | −1.08495e9 | −1.24434 | −0.622168 | − | 0.782883i | \(-0.713748\pi\) | ||||
−0.622168 | + | 0.782883i | \(0.713748\pi\) | |||||||
\(98\) | −1.94296e9 | −2.12787 | ||||||||
\(99\) | −4.57043e8 | −0.478188 | ||||||||
\(100\) | 2.49739e8 | 0.249739 | ||||||||
\(101\) | −2.54570e8 | −0.243423 | −0.121711 | − | 0.992566i | \(-0.538838\pi\) | ||||
−0.121711 | + | 0.992566i | \(0.538838\pi\) | |||||||
\(102\) | −1.35108e9 | −1.23589 | ||||||||
\(103\) | 1.61531e6 | 0.00141413 | 0.000707063 | − | 1.00000i | \(-0.499775\pi\) | ||||
0.000707063 | 1.00000i | \(0.499775\pi\) | ||||||||
\(104\) | 7.60613e8 | 0.637549 | ||||||||
\(105\) | 5.00177e8 | 0.401580 | ||||||||
\(106\) | 8.09335e8 | 0.622661 | ||||||||
\(107\) | 1.89093e9 | 1.39460 | 0.697299 | − | 0.716780i | \(-0.254385\pi\) | ||||
0.697299 | + | 0.716780i | \(0.254385\pi\) | |||||||
\(108\) | −3.39767e8 | −0.240311 | ||||||||
\(109\) | 6.16231e8 | 0.418142 | 0.209071 | − | 0.977900i | \(-0.432956\pi\) | ||||
0.209071 | + | 0.977900i | \(0.432956\pi\) | |||||||
\(110\) | −1.47730e9 | −0.962056 | ||||||||
\(111\) | 2.96638e8 | 0.185470 | ||||||||
\(112\) | −1.78569e9 | −1.07232 | ||||||||
\(113\) | −3.36282e9 | −1.94022 | −0.970110 | − | 0.242666i | \(-0.921978\pi\) | ||||
−0.970110 | + | 0.242666i | \(0.921978\pi\) | |||||||
\(114\) | 3.58178e8 | 0.198622 | ||||||||
\(115\) | 4.45571e8 | 0.237562 | ||||||||
\(116\) | −8.59088e7 | −0.0440531 | ||||||||
\(117\) | −1.15505e9 | −0.569855 | ||||||||
\(118\) | 3.46629e9 | 1.64587 | ||||||||
\(119\) | −4.85684e9 | −2.22020 | ||||||||
\(120\) | −2.18725e8 | −0.0962903 | ||||||||
\(121\) | 2.49465e9 | 1.05798 | ||||||||
\(122\) | 4.24643e9 | 1.73542 | ||||||||
\(123\) | 7.89470e8 | 0.311001 | ||||||||
\(124\) | −1.65733e9 | −0.629522 | ||||||||
\(125\) | −2.44141e8 | −0.0894427 | ||||||||
\(126\) | −2.19952e9 | −0.777430 | ||||||||
\(127\) | −2.51900e9 | −0.859232 | −0.429616 | − | 0.903012i | \(-0.641351\pi\) | ||||
−0.429616 | + | 0.903012i | \(0.641351\pi\) | |||||||
\(128\) | 2.19513e9 | 0.722797 | ||||||||
\(129\) | −3.41027e8 | −0.108426 | ||||||||
\(130\) | −3.73345e9 | −1.14648 | ||||||||
\(131\) | −5.00056e9 | −1.48353 | −0.741767 | − | 0.670657i | \(-0.766012\pi\) | ||||
−0.741767 | + | 0.670657i | \(0.766012\pi\) | |||||||
\(132\) | 3.60743e9 | 1.03423 | ||||||||
\(133\) | 1.28758e9 | 0.356813 | ||||||||
\(134\) | 3.18479e8 | 0.0853315 | ||||||||
\(135\) | 3.32151e8 | 0.0860663 | ||||||||
\(136\) | 2.12387e9 | 0.532358 | ||||||||
\(137\) | −2.10286e9 | −0.509998 | −0.254999 | − | 0.966941i | \(-0.582075\pi\) | ||||
−0.254999 | + | 0.966941i | \(0.582075\pi\) | |||||||
\(138\) | −1.95940e9 | −0.459903 | ||||||||
\(139\) | −1.92992e9 | −0.438503 | −0.219251 | − | 0.975668i | \(-0.570362\pi\) | ||||
−0.219251 | + | 0.975668i | \(0.570362\pi\) | |||||||
\(140\) | −3.94788e9 | −0.868537 | ||||||||
\(141\) | 5.19738e9 | 1.10739 | ||||||||
\(142\) | −5.92710e9 | −1.22333 | ||||||||
\(143\) | 1.22636e10 | 2.45248 | ||||||||
\(144\) | −1.18582e9 | −0.229820 | ||||||||
\(145\) | 8.39831e7 | 0.0157774 | ||||||||
\(146\) | −1.07889e10 | −1.96512 | ||||||||
\(147\) | −4.63819e9 | −0.819257 | ||||||||
\(148\) | −2.34136e9 | −0.401134 | ||||||||
\(149\) | 7.40405e9 | 1.23064 | 0.615320 | − | 0.788277i | \(-0.289027\pi\) | ||||
0.615320 | + | 0.788277i | \(0.289027\pi\) | |||||||
\(150\) | 1.07361e9 | 0.173155 | ||||||||
\(151\) | 1.15986e9 | 0.181555 | 0.0907776 | − | 0.995871i | \(-0.471065\pi\) | ||||
0.0907776 | + | 0.995871i | \(0.471065\pi\) | |||||||
\(152\) | −5.63051e8 | −0.0855562 | ||||||||
\(153\) | −3.22526e9 | −0.475832 | ||||||||
\(154\) | 2.33532e10 | 3.34582 | ||||||||
\(155\) | 1.62018e9 | 0.225461 | ||||||||
\(156\) | 9.11678e9 | 1.23248 | ||||||||
\(157\) | −7.39247e9 | −0.971049 | −0.485525 | − | 0.874223i | \(-0.661371\pi\) | ||||
−0.485525 | + | 0.874223i | \(0.661371\pi\) | |||||||
\(158\) | −1.63752e9 | −0.209041 | ||||||||
\(159\) | 1.93203e9 | 0.239732 | ||||||||
\(160\) | −5.21547e9 | −0.629149 | ||||||||
\(161\) | −7.04362e9 | −0.826189 | ||||||||
\(162\) | −1.46063e9 | −0.166618 | ||||||||
\(163\) | 2.42581e9 | 0.269162 | 0.134581 | − | 0.990903i | \(-0.457031\pi\) | ||||
0.134581 | + | 0.990903i | \(0.457031\pi\) | |||||||
\(164\) | −6.23126e9 | −0.672634 | ||||||||
\(165\) | −3.52657e9 | −0.370403 | ||||||||
\(166\) | −1.29996e10 | −1.32875 | ||||||||
\(167\) | −1.27031e10 | −1.26382 | −0.631911 | − | 0.775041i | \(-0.717729\pi\) | ||||
−0.631911 | + | 0.775041i | \(0.717729\pi\) | |||||||
\(168\) | 3.45762e9 | 0.334877 | ||||||||
\(169\) | 2.03883e10 | 1.92261 | ||||||||
\(170\) | −1.04250e10 | −0.957316 | ||||||||
\(171\) | 8.55036e8 | 0.0764719 | ||||||||
\(172\) | 2.69171e9 | 0.234504 | ||||||||
\(173\) | 1.98216e10 | 1.68240 | 0.841202 | − | 0.540721i | \(-0.181849\pi\) | ||||
0.841202 | + | 0.540721i | \(0.181849\pi\) | |||||||
\(174\) | −3.69315e8 | −0.0305440 | ||||||||
\(175\) | 3.85939e9 | 0.311062 | ||||||||
\(176\) | 1.25903e10 | 0.989074 | ||||||||
\(177\) | 8.27466e9 | 0.633680 | ||||||||
\(178\) | 3.45319e10 | 2.57828 | ||||||||
\(179\) | 1.27221e10 | 0.926230 | 0.463115 | − | 0.886298i | \(-0.346732\pi\) | ||||
0.463115 | + | 0.886298i | \(0.346732\pi\) | |||||||
\(180\) | −2.62166e9 | −0.186144 | ||||||||
\(181\) | 6.13497e9 | 0.424873 | 0.212436 | − | 0.977175i | \(-0.431860\pi\) | ||||
0.212436 | + | 0.977175i | \(0.431860\pi\) | |||||||
\(182\) | 5.90187e10 | 3.98720 | ||||||||
\(183\) | 1.01370e10 | 0.668158 | ||||||||
\(184\) | 3.08014e9 | 0.198103 | ||||||||
\(185\) | 2.28888e9 | 0.143664 | ||||||||
\(186\) | −7.12473e9 | −0.436476 | ||||||||
\(187\) | 3.42438e10 | 2.04784 | ||||||||
\(188\) | −4.10228e10 | −2.39505 | ||||||||
\(189\) | −5.25066e9 | −0.299320 | ||||||||
\(190\) | 2.76372e9 | 0.153852 | ||||||||
\(191\) | −3.51221e10 | −1.90955 | −0.954774 | − | 0.297331i | \(-0.903903\pi\) | ||||
−0.954774 | + | 0.297331i | \(0.903903\pi\) | |||||||
\(192\) | 1.54394e10 | 0.819928 | ||||||||
\(193\) | 3.31686e10 | 1.72075 | 0.860377 | − | 0.509657i | \(-0.170228\pi\) | ||||
0.860377 | + | 0.509657i | \(0.170228\pi\) | |||||||
\(194\) | 3.68138e10 | 1.86596 | ||||||||
\(195\) | −8.91242e9 | −0.441408 | ||||||||
\(196\) | 3.66091e10 | 1.77189 | ||||||||
\(197\) | 1.17394e10 | 0.555324 | 0.277662 | − | 0.960679i | \(-0.410441\pi\) | ||||
0.277662 | + | 0.960679i | \(0.410441\pi\) | |||||||
\(198\) | 1.55081e10 | 0.717074 | ||||||||
\(199\) | −3.84124e10 | −1.73633 | −0.868166 | − | 0.496273i | \(-0.834701\pi\) | ||||
−0.868166 | + | 0.496273i | \(0.834701\pi\) | |||||||
\(200\) | −1.68769e9 | −0.0745862 | ||||||||
\(201\) | 7.60267e8 | 0.0328536 | ||||||||
\(202\) | 8.63789e9 | 0.365028 | ||||||||
\(203\) | −1.32761e9 | −0.0548705 | ||||||||
\(204\) | 2.54569e10 | 1.02913 | ||||||||
\(205\) | 6.09159e9 | 0.240901 | ||||||||
\(206\) | −5.48095e7 | −0.00212057 | ||||||||
\(207\) | −4.67743e9 | −0.177068 | ||||||||
\(208\) | 3.18185e10 | 1.17867 | ||||||||
\(209\) | −9.07824e9 | −0.329112 | ||||||||
\(210\) | −1.69716e10 | −0.602195 | ||||||||
\(211\) | 9.53224e9 | 0.331073 | 0.165537 | − | 0.986204i | \(-0.447064\pi\) | ||||
0.165537 | + | 0.986204i | \(0.447064\pi\) | |||||||
\(212\) | −1.52494e10 | −0.518492 | ||||||||
\(213\) | −1.41490e10 | −0.470998 | ||||||||
\(214\) | −6.41618e10 | −2.09129 | ||||||||
\(215\) | −2.63138e9 | −0.0839867 | ||||||||
\(216\) | 2.29609e9 | 0.0717706 | ||||||||
\(217\) | −2.56119e10 | −0.784103 | ||||||||
\(218\) | −2.09095e10 | −0.627031 | ||||||||
\(219\) | −2.57551e10 | −0.756596 | ||||||||
\(220\) | 2.78351e10 | 0.801108 | ||||||||
\(221\) | 8.65418e10 | 2.44040 | ||||||||
\(222\) | −1.00653e10 | −0.278124 | ||||||||
\(223\) | −3.45762e10 | −0.936280 | −0.468140 | − | 0.883654i | \(-0.655076\pi\) | ||||
−0.468140 | + | 0.883654i | \(0.655076\pi\) | |||||||
\(224\) | 8.24464e10 | 2.18804 | ||||||||
\(225\) | 2.56289e9 | 0.0666667 | ||||||||
\(226\) | 1.14105e11 | 2.90948 | ||||||||
\(227\) | 2.09866e10 | 0.524597 | 0.262299 | − | 0.964987i | \(-0.415519\pi\) | ||||
0.262299 | + | 0.964987i | \(0.415519\pi\) | |||||||
\(228\) | −6.74878e9 | −0.165393 | ||||||||
\(229\) | −5.45785e10 | −1.31148 | −0.655741 | − | 0.754986i | \(-0.727643\pi\) | ||||
−0.655741 | + | 0.754986i | \(0.727643\pi\) | |||||||
\(230\) | −1.51188e10 | −0.356239 | ||||||||
\(231\) | 5.57482e10 | 1.28818 | ||||||||
\(232\) | 5.80558e8 | 0.0131568 | ||||||||
\(233\) | 2.43534e10 | 0.541324 | 0.270662 | − | 0.962674i | \(-0.412757\pi\) | ||||
0.270662 | + | 0.962674i | \(0.412757\pi\) | |||||||
\(234\) | 3.91923e10 | 0.854534 | ||||||||
\(235\) | 4.01033e10 | 0.857777 | ||||||||
\(236\) | −6.53116e10 | −1.37052 | ||||||||
\(237\) | −3.90906e9 | −0.0804831 | ||||||||
\(238\) | 1.64799e11 | 3.32934 | ||||||||
\(239\) | −9.34512e10 | −1.85265 | −0.926327 | − | 0.376720i | \(-0.877052\pi\) | ||||
−0.926327 | + | 0.376720i | \(0.877052\pi\) | |||||||
\(240\) | −9.14984e9 | −0.178018 | ||||||||
\(241\) | −7.79516e10 | −1.48850 | −0.744250 | − | 0.667902i | \(-0.767193\pi\) | ||||
−0.744250 | + | 0.667902i | \(0.767193\pi\) | |||||||
\(242\) | −8.46468e10 | −1.58650 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −8.00109e10 | −1.44509 | ||||||||
\(245\) | −3.57885e10 | −0.634594 | ||||||||
\(246\) | −2.67877e10 | −0.466367 | ||||||||
\(247\) | −2.29427e10 | −0.392201 | ||||||||
\(248\) | 1.12000e10 | 0.188011 | ||||||||
\(249\) | −3.10323e10 | −0.511584 | ||||||||
\(250\) | 8.28400e9 | 0.134125 | ||||||||
\(251\) | −8.60114e10 | −1.36781 | −0.683903 | − | 0.729573i | \(-0.739719\pi\) | ||||
−0.683903 | + | 0.729573i | \(0.739719\pi\) | |||||||
\(252\) | 4.14433e10 | 0.647369 | ||||||||
\(253\) | 4.96620e10 | 0.762048 | ||||||||
\(254\) | 8.54727e10 | 1.28847 | ||||||||
\(255\) | −2.48863e10 | −0.368578 | ||||||||
\(256\) | 2.31087e10 | 0.336276 | ||||||||
\(257\) | 3.35045e10 | 0.479076 | 0.239538 | − | 0.970887i | \(-0.423004\pi\) | ||||
0.239538 | + | 0.970887i | \(0.423004\pi\) | |||||||
\(258\) | 1.15715e10 | 0.162592 | ||||||||
\(259\) | −3.61827e10 | −0.499634 | ||||||||
\(260\) | 7.03455e10 | 0.954676 | ||||||||
\(261\) | −8.81621e8 | −0.0117598 | ||||||||
\(262\) | 1.69675e11 | 2.22466 | ||||||||
\(263\) | −1.25298e11 | −1.61490 | −0.807449 | − | 0.589938i | \(-0.799152\pi\) | ||||
−0.807449 | + | 0.589938i | \(0.799152\pi\) | |||||||
\(264\) | −2.43784e10 | −0.308879 | ||||||||
\(265\) | 1.49076e10 | 0.185696 | ||||||||
\(266\) | −4.36891e10 | −0.535064 | ||||||||
\(267\) | 8.24339e10 | 0.992671 | ||||||||
\(268\) | −6.00076e9 | −0.0710559 | ||||||||
\(269\) | −3.18538e10 | −0.370917 | −0.185458 | − | 0.982652i | \(-0.559377\pi\) | ||||
−0.185458 | + | 0.982652i | \(0.559377\pi\) | |||||||
\(270\) | −1.12703e10 | −0.129062 | ||||||||
\(271\) | −3.80191e10 | −0.428193 | −0.214097 | − | 0.976812i | \(-0.568681\pi\) | ||||
−0.214097 | + | 0.976812i | \(0.568681\pi\) | |||||||
\(272\) | 8.88472e10 | 0.984201 | ||||||||
\(273\) | 1.40888e11 | 1.53512 | ||||||||
\(274\) | 7.13529e10 | 0.764775 | ||||||||
\(275\) | −2.72112e10 | −0.286913 | ||||||||
\(276\) | 3.69188e10 | 0.382963 | ||||||||
\(277\) | 1.05646e11 | 1.07819 | 0.539095 | − | 0.842245i | \(-0.318766\pi\) | ||||
0.539095 | + | 0.842245i | \(0.318766\pi\) | |||||||
\(278\) | 6.54846e10 | 0.657563 | ||||||||
\(279\) | −1.70080e10 | −0.168048 | ||||||||
\(280\) | 2.66792e10 | 0.259395 | ||||||||
\(281\) | −4.31314e10 | −0.412682 | −0.206341 | − | 0.978480i | \(-0.566156\pi\) | ||||
−0.206341 | + | 0.978480i | \(0.566156\pi\) | |||||||
\(282\) | −1.76354e11 | −1.66060 | ||||||||
\(283\) | 1.39197e11 | 1.29000 | 0.645002 | − | 0.764181i | \(-0.276857\pi\) | ||||
0.645002 | + | 0.764181i | \(0.276857\pi\) | |||||||
\(284\) | 1.11678e11 | 1.01867 | ||||||||
\(285\) | 6.59750e9 | 0.0592349 | ||||||||
\(286\) | −4.16119e11 | −3.67765 | ||||||||
\(287\) | −9.62962e10 | −0.837800 | ||||||||
\(288\) | 5.47499e10 | 0.468940 | ||||||||
\(289\) | 1.23064e11 | 1.03775 | ||||||||
\(290\) | −2.84965e9 | −0.0236593 | ||||||||
\(291\) | 8.78812e10 | 0.718418 | ||||||||
\(292\) | 2.03284e11 | 1.63637 | ||||||||
\(293\) | 1.18645e11 | 0.940473 | 0.470236 | − | 0.882541i | \(-0.344169\pi\) | ||||
0.470236 | + | 0.882541i | \(0.344169\pi\) | |||||||
\(294\) | 1.57380e11 | 1.22853 | ||||||||
\(295\) | 6.38477e10 | 0.490847 | ||||||||
\(296\) | 1.58225e10 | 0.119802 | ||||||||
\(297\) | 3.70205e10 | 0.276082 | ||||||||
\(298\) | −2.51229e11 | −1.84542 | ||||||||
\(299\) | 1.25507e11 | 0.908129 | ||||||||
\(300\) | −2.02288e10 | −0.144187 | ||||||||
\(301\) | 4.15970e10 | 0.292087 | ||||||||
\(302\) | −3.93555e10 | −0.272254 | ||||||||
\(303\) | 2.06202e10 | 0.140540 | ||||||||
\(304\) | −2.35539e10 | −0.158173 | ||||||||
\(305\) | 7.82175e10 | 0.517553 | ||||||||
\(306\) | 1.09437e11 | 0.713541 | ||||||||
\(307\) | 1.54568e11 | 0.993109 | 0.496554 | − | 0.868006i | \(-0.334598\pi\) | ||||
0.496554 | + | 0.868006i | \(0.334598\pi\) | |||||||
\(308\) | −4.40019e11 | −2.78608 | ||||||||
\(309\) | −1.30840e8 | −0.000816446 0 | ||||||||
\(310\) | −5.49747e10 | −0.338093 | ||||||||
\(311\) | −5.00657e10 | −0.303472 | −0.151736 | − | 0.988421i | \(-0.548486\pi\) | ||||
−0.151736 | + | 0.988421i | \(0.548486\pi\) | |||||||
\(312\) | −6.16097e10 | −0.368089 | ||||||||
\(313\) | 1.63498e11 | 0.962858 | 0.481429 | − | 0.876485i | \(-0.340118\pi\) | ||||
0.481429 | + | 0.876485i | \(0.340118\pi\) | |||||||
\(314\) | 2.50836e11 | 1.45615 | ||||||||
\(315\) | −4.05143e10 | −0.231852 | ||||||||
\(316\) | 3.08541e10 | 0.174069 | ||||||||
\(317\) | 1.23719e11 | 0.688129 | 0.344064 | − | 0.938946i | \(-0.388196\pi\) | ||||
0.344064 | + | 0.938946i | \(0.388196\pi\) | |||||||
\(318\) | −6.55561e10 | −0.359494 | ||||||||
\(319\) | 9.36051e9 | 0.0506106 | ||||||||
\(320\) | 1.19131e11 | 0.635113 | ||||||||
\(321\) | −1.53166e11 | −0.805172 | ||||||||
\(322\) | 2.38999e11 | 1.23892 | ||||||||
\(323\) | −6.40634e10 | −0.327490 | ||||||||
\(324\) | 2.75211e10 | 0.138744 | ||||||||
\(325\) | −6.87687e10 | −0.341913 | ||||||||
\(326\) | −8.23109e10 | −0.403625 | ||||||||
\(327\) | −4.99147e10 | −0.241415 | ||||||||
\(328\) | 4.21098e10 | 0.200887 | ||||||||
\(329\) | −6.33955e11 | −2.98316 | ||||||||
\(330\) | 1.19661e11 | 0.555443 | ||||||||
\(331\) | −3.51714e11 | −1.61051 | −0.805255 | − | 0.592929i | \(-0.797972\pi\) | ||||
−0.805255 | + | 0.592929i | \(0.797972\pi\) | |||||||
\(332\) | 2.44937e11 | 1.10645 | ||||||||
\(333\) | −2.40277e10 | −0.107081 | ||||||||
\(334\) | 4.31033e11 | 1.89518 | ||||||||
\(335\) | 5.86625e9 | 0.0254483 | ||||||||
\(336\) | 1.44641e11 | 0.619106 | ||||||||
\(337\) | 4.10219e11 | 1.73253 | 0.866267 | − | 0.499582i | \(-0.166513\pi\) | ||||
0.866267 | + | 0.499582i | \(0.166513\pi\) | |||||||
\(338\) | −6.91802e11 | −2.88308 | ||||||||
\(339\) | 2.72389e11 | 1.12019 | ||||||||
\(340\) | 1.96427e11 | 0.797160 | ||||||||
\(341\) | 1.80580e11 | 0.723229 | ||||||||
\(342\) | −2.90125e10 | −0.114675 | ||||||||
\(343\) | 1.67051e11 | 0.651668 | ||||||||
\(344\) | −1.81902e10 | −0.0700364 | ||||||||
\(345\) | −3.60913e10 | −0.137156 | ||||||||
\(346\) | −6.72570e11 | −2.52287 | ||||||||
\(347\) | 4.08881e11 | 1.51396 | 0.756979 | − | 0.653439i | \(-0.226674\pi\) | ||||
0.756979 | + | 0.653439i | \(0.226674\pi\) | |||||||
\(348\) | 6.95861e9 | 0.0254341 | ||||||||
\(349\) | −4.04337e11 | −1.45891 | −0.729457 | − | 0.684027i | \(-0.760227\pi\) | ||||
−0.729457 | + | 0.684027i | \(0.760227\pi\) | |||||||
\(350\) | −1.30954e11 | −0.466458 | ||||||||
\(351\) | 9.35590e10 | 0.329006 | ||||||||
\(352\) | −5.81300e11 | −2.01817 | ||||||||
\(353\) | −1.14276e11 | −0.391714 | −0.195857 | − | 0.980633i | \(-0.562749\pi\) | ||||
−0.195857 | + | 0.980633i | \(0.562749\pi\) | |||||||
\(354\) | −2.80770e11 | −0.950245 | ||||||||
\(355\) | −1.09175e11 | −0.364833 | ||||||||
\(356\) | −6.50649e11 | −2.14695 | ||||||||
\(357\) | 3.93404e11 | 1.28183 | ||||||||
\(358\) | −4.31676e11 | −1.38894 | ||||||||
\(359\) | 2.73301e11 | 0.868393 | 0.434197 | − | 0.900818i | \(-0.357032\pi\) | ||||
0.434197 | + | 0.900818i | \(0.357032\pi\) | |||||||
\(360\) | 1.77167e10 | 0.0555933 | ||||||||
\(361\) | 1.69836e10 | 0.0526316 | ||||||||
\(362\) | −2.08167e11 | −0.637124 | ||||||||
\(363\) | −2.02067e11 | −0.610823 | ||||||||
\(364\) | −1.11203e12 | −3.32016 | ||||||||
\(365\) | −1.98727e11 | −0.586057 | ||||||||
\(366\) | −3.43961e11 | −1.00195 | ||||||||
\(367\) | 3.97112e11 | 1.14266 | 0.571328 | − | 0.820722i | \(-0.306428\pi\) | ||||
0.571328 | + | 0.820722i | \(0.306428\pi\) | |||||||
\(368\) | 1.28850e11 | 0.366244 | ||||||||
\(369\) | −6.39470e10 | −0.179557 | ||||||||
\(370\) | −7.76644e10 | −0.215434 | ||||||||
\(371\) | −2.35661e11 | −0.645809 | ||||||||
\(372\) | 1.34244e11 | 0.363455 | ||||||||
\(373\) | −2.90603e11 | −0.777338 | −0.388669 | − | 0.921378i | \(-0.627065\pi\) | ||||
−0.388669 | + | 0.921378i | \(0.627065\pi\) | |||||||
\(374\) | −1.16194e12 | −3.07086 | ||||||||
\(375\) | 1.97754e10 | 0.0516398 | ||||||||
\(376\) | 2.77225e11 | 0.715299 | ||||||||
\(377\) | 2.36561e10 | 0.0603124 | ||||||||
\(378\) | 1.78161e11 | 0.448849 | ||||||||
\(379\) | 3.42610e11 | 0.852949 | 0.426474 | − | 0.904500i | \(-0.359755\pi\) | ||||
0.426474 | + | 0.904500i | \(0.359755\pi\) | |||||||
\(380\) | −5.20739e10 | −0.128113 | ||||||||
\(381\) | 2.04039e11 | 0.496078 | ||||||||
\(382\) | 1.19174e12 | 2.86349 | ||||||||
\(383\) | −1.05333e11 | −0.250133 | −0.125066 | − | 0.992148i | \(-0.539914\pi\) | ||||
−0.125066 | + | 0.992148i | \(0.539914\pi\) | |||||||
\(384\) | −1.77806e11 | −0.417307 | ||||||||
\(385\) | 4.30156e11 | 0.997821 | ||||||||
\(386\) | −1.12545e12 | −2.58038 | ||||||||
\(387\) | 2.76232e10 | 0.0626000 | ||||||||
\(388\) | −6.93643e11 | −1.55379 | ||||||||
\(389\) | −7.35118e11 | −1.62774 | −0.813868 | − | 0.581050i | \(-0.802642\pi\) | ||||
−0.813868 | + | 0.581050i | \(0.802642\pi\) | |||||||
\(390\) | 3.02410e11 | 0.661919 | ||||||||
\(391\) | 3.50455e11 | 0.758293 | ||||||||
\(392\) | −2.47398e11 | −0.529187 | ||||||||
\(393\) | 4.05045e11 | 0.856519 | ||||||||
\(394\) | −3.98331e11 | −0.832743 | ||||||||
\(395\) | −3.01625e10 | −0.0623420 | ||||||||
\(396\) | −2.92202e11 | −0.597110 | ||||||||
\(397\) | −1.30600e11 | −0.263868 | −0.131934 | − | 0.991258i | \(-0.542119\pi\) | ||||
−0.131934 | + | 0.991258i | \(0.542119\pi\) | |||||||
\(398\) | 1.30338e12 | 2.60374 | ||||||||
\(399\) | −1.04294e11 | −0.206006 | ||||||||
\(400\) | −7.06006e10 | −0.137892 | ||||||||
\(401\) | 3.26468e11 | 0.630509 | 0.315254 | − | 0.949007i | \(-0.397910\pi\) | ||||
0.315254 | + | 0.949007i | \(0.397910\pi\) | |||||||
\(402\) | −2.57968e10 | −0.0492662 | ||||||||
\(403\) | 4.56366e11 | 0.861869 | ||||||||
\(404\) | −1.62755e11 | −0.303960 | ||||||||
\(405\) | −2.69042e10 | −0.0496904 | ||||||||
\(406\) | 4.50475e10 | 0.0822818 | ||||||||
\(407\) | 2.55111e11 | 0.460845 | ||||||||
\(408\) | −1.72034e11 | −0.307357 | ||||||||
\(409\) | 9.96939e11 | 1.76163 | 0.880813 | − | 0.473464i | \(-0.156997\pi\) | ||||
0.880813 | + | 0.473464i | \(0.156997\pi\) | |||||||
\(410\) | −2.06695e11 | −0.361246 | ||||||||
\(411\) | 1.70332e11 | 0.294448 | ||||||||
\(412\) | 1.03272e9 | 0.00176581 | ||||||||
\(413\) | −1.00931e12 | −1.70706 | ||||||||
\(414\) | 1.58711e11 | 0.265525 | ||||||||
\(415\) | −2.39447e11 | −0.396272 | ||||||||
\(416\) | −1.46907e12 | −2.40505 | ||||||||
\(417\) | 1.56323e11 | 0.253170 | ||||||||
\(418\) | 3.08036e11 | 0.493524 | ||||||||
\(419\) | 1.41597e11 | 0.224435 | 0.112217 | − | 0.993684i | \(-0.464205\pi\) | ||||
0.112217 | + | 0.993684i | \(0.464205\pi\) | |||||||
\(420\) | 3.19779e11 | 0.501450 | ||||||||
\(421\) | 7.96738e11 | 1.23608 | 0.618039 | − | 0.786147i | \(-0.287927\pi\) | ||||
0.618039 | + | 0.786147i | \(0.287927\pi\) | |||||||
\(422\) | −3.23441e11 | −0.496465 | ||||||||
\(423\) | −4.20988e11 | −0.639349 | ||||||||
\(424\) | 1.03053e11 | 0.154851 | ||||||||
\(425\) | −1.92024e11 | −0.285499 | ||||||||
\(426\) | 4.80095e11 | 0.706291 | ||||||||
\(427\) | −1.23647e12 | −1.79994 | ||||||||
\(428\) | 1.20893e12 | 1.74143 | ||||||||
\(429\) | −9.93352e11 | −1.41594 | ||||||||
\(430\) | 8.92860e10 | 0.125943 | ||||||||
\(431\) | −4.11727e11 | −0.574727 | −0.287364 | − | 0.957822i | \(-0.592779\pi\) | ||||
−0.287364 | + | 0.957822i | \(0.592779\pi\) | |||||||
\(432\) | 9.60513e10 | 0.132686 | ||||||||
\(433\) | −5.25038e11 | −0.717787 | −0.358893 | − | 0.933379i | \(-0.616846\pi\) | ||||
−0.358893 | + | 0.933379i | \(0.616846\pi\) | |||||||
\(434\) | 8.69044e11 | 1.17581 | ||||||||
\(435\) | −6.80263e9 | −0.00910910 | ||||||||
\(436\) | 3.93975e11 | 0.522131 | ||||||||
\(437\) | −9.29077e10 | −0.121867 | ||||||||
\(438\) | 8.73902e11 | 1.13456 | ||||||||
\(439\) | 5.92349e11 | 0.761180 | 0.380590 | − | 0.924744i | \(-0.375721\pi\) | ||||
0.380590 | + | 0.924744i | \(0.375721\pi\) | |||||||
\(440\) | −1.88105e11 | −0.239256 | ||||||||
\(441\) | 3.75693e11 | 0.472998 | ||||||||
\(442\) | −2.93647e12 | −3.65953 | ||||||||
\(443\) | −3.46221e11 | −0.427107 | −0.213553 | − | 0.976931i | \(-0.568504\pi\) | ||||
−0.213553 | + | 0.976931i | \(0.568504\pi\) | |||||||
\(444\) | 1.89650e11 | 0.231595 | ||||||||
\(445\) | 6.36064e11 | 0.768919 | ||||||||
\(446\) | 1.17322e12 | 1.40401 | ||||||||
\(447\) | −5.99728e11 | −0.710511 | ||||||||
\(448\) | −1.88324e12 | −2.20879 | ||||||||
\(449\) | −1.90995e11 | −0.221775 | −0.110888 | − | 0.993833i | \(-0.535369\pi\) | ||||
−0.110888 | + | 0.993833i | \(0.535369\pi\) | |||||||
\(450\) | −8.69621e10 | −0.0999709 | ||||||||
\(451\) | 6.78950e11 | 0.772758 | ||||||||
\(452\) | −2.14996e12 | −2.42274 | ||||||||
\(453\) | −9.39485e10 | −0.104821 | ||||||||
\(454\) | −7.12102e11 | −0.786667 | ||||||||
\(455\) | 1.08710e12 | 1.18910 | ||||||||
\(456\) | 4.56071e10 | 0.0493959 | ||||||||
\(457\) | −8.99317e11 | −0.964472 | −0.482236 | − | 0.876041i | \(-0.660175\pi\) | ||||
−0.482236 | + | 0.876041i | \(0.660175\pi\) | |||||||
\(458\) | 1.85192e12 | 1.96665 | ||||||||
\(459\) | 2.61246e11 | 0.274722 | ||||||||
\(460\) | 2.84867e11 | 0.296642 | ||||||||
\(461\) | −2.78718e11 | −0.287416 | −0.143708 | − | 0.989620i | \(-0.545903\pi\) | ||||
−0.143708 | + | 0.989620i | \(0.545903\pi\) | |||||||
\(462\) | −1.89161e12 | −1.93171 | ||||||||
\(463\) | 7.59495e11 | 0.768087 | 0.384044 | − | 0.923315i | \(-0.374531\pi\) | ||||
0.384044 | + | 0.923315i | \(0.374531\pi\) | |||||||
\(464\) | 2.42863e10 | 0.0243237 | ||||||||
\(465\) | −1.31235e11 | −0.130170 | ||||||||
\(466\) | −8.26341e11 | −0.811751 | ||||||||
\(467\) | 9.77081e11 | 0.950615 | 0.475307 | − | 0.879820i | \(-0.342337\pi\) | ||||
0.475307 | + | 0.879820i | \(0.342337\pi\) | |||||||
\(468\) | −7.38459e11 | −0.711574 | ||||||||
\(469\) | −9.27341e10 | −0.0885038 | ||||||||
\(470\) | −1.36075e12 | −1.28629 | ||||||||
\(471\) | 5.98790e11 | 0.560636 | ||||||||
\(472\) | 4.41365e11 | 0.409317 | ||||||||
\(473\) | −2.93286e11 | −0.269411 | ||||||||
\(474\) | 1.32639e11 | 0.120690 | ||||||||
\(475\) | 5.09066e10 | 0.0458831 | ||||||||
\(476\) | −3.10513e12 | −2.77235 | ||||||||
\(477\) | −1.56494e11 | −0.138409 | ||||||||
\(478\) | 3.17092e12 | 2.77817 | ||||||||
\(479\) | −1.93121e12 | −1.67617 | −0.838086 | − | 0.545538i | \(-0.816325\pi\) | ||||
−0.838086 | + | 0.545538i | \(0.816325\pi\) | |||||||
\(480\) | 4.22453e11 | 0.363239 | ||||||||
\(481\) | 6.44722e11 | 0.549187 | ||||||||
\(482\) | 2.64500e12 | 2.23210 | ||||||||
\(483\) | 5.70533e11 | 0.477000 | ||||||||
\(484\) | 1.59491e12 | 1.32109 | ||||||||
\(485\) | 6.78095e11 | 0.556484 | ||||||||
\(486\) | 1.18311e11 | 0.0961971 | ||||||||
\(487\) | 1.99512e12 | 1.60727 | 0.803634 | − | 0.595124i | \(-0.202897\pi\) | ||||
0.803634 | + | 0.595124i | \(0.202897\pi\) | |||||||
\(488\) | 5.40701e11 | 0.431587 | ||||||||
\(489\) | −1.96491e11 | −0.155401 | ||||||||
\(490\) | 1.21435e12 | 0.951614 | ||||||||
\(491\) | 1.79495e12 | 1.39375 | 0.696876 | − | 0.717192i | \(-0.254573\pi\) | ||||
0.696876 | + | 0.717192i | \(0.254573\pi\) | |||||||
\(492\) | 5.04732e11 | 0.388345 | ||||||||
\(493\) | 6.60553e10 | 0.0503612 | ||||||||
\(494\) | 7.78476e11 | 0.588131 | ||||||||
\(495\) | 2.85652e11 | 0.213852 | ||||||||
\(496\) | 4.68524e11 | 0.347587 | ||||||||
\(497\) | 1.72584e12 | 1.26881 | ||||||||
\(498\) | 1.05297e12 | 0.767154 | ||||||||
\(499\) | −5.00717e11 | −0.361526 | −0.180763 | − | 0.983527i | \(-0.557857\pi\) | ||||
−0.180763 | + | 0.983527i | \(0.557857\pi\) | |||||||
\(500\) | −1.56087e11 | −0.111686 | ||||||||
\(501\) | 1.02895e12 | 0.729669 | ||||||||
\(502\) | 2.91848e12 | 2.05111 | ||||||||
\(503\) | −2.44897e12 | −1.70580 | −0.852900 | − | 0.522074i | \(-0.825158\pi\) | ||||
−0.852900 | + | 0.522074i | \(0.825158\pi\) | |||||||
\(504\) | −2.80067e11 | −0.193341 | ||||||||
\(505\) | 1.59106e11 | 0.108862 | ||||||||
\(506\) | −1.68510e12 | −1.14274 | ||||||||
\(507\) | −1.65146e12 | −1.11002 | ||||||||
\(508\) | −1.61047e12 | −1.07292 | ||||||||
\(509\) | 1.39357e12 | 0.920235 | 0.460117 | − | 0.887858i | \(-0.347807\pi\) | ||||
0.460117 | + | 0.887858i | \(0.347807\pi\) | |||||||
\(510\) | 8.44424e11 | 0.552706 | ||||||||
\(511\) | 3.14150e12 | 2.03818 | ||||||||
\(512\) | −1.90802e12 | −1.22706 | ||||||||
\(513\) | −6.92579e10 | −0.0441511 | ||||||||
\(514\) | −1.13685e12 | −0.718405 | ||||||||
\(515\) | −1.00957e9 | −0.000632417 0 | ||||||||
\(516\) | −2.18029e11 | −0.135391 | ||||||||
\(517\) | 4.46979e12 | 2.75156 | ||||||||
\(518\) | 1.22772e12 | 0.749233 | ||||||||
\(519\) | −1.60555e12 | −0.971336 | ||||||||
\(520\) | −4.75383e11 | −0.285121 | ||||||||
\(521\) | 1.18713e12 | 0.705875 | 0.352937 | − | 0.935647i | \(-0.385183\pi\) | ||||
0.352937 | + | 0.935647i | \(0.385183\pi\) | |||||||
\(522\) | 2.99145e10 | 0.0176346 | ||||||||
\(523\) | 7.35893e11 | 0.430088 | 0.215044 | − | 0.976604i | \(-0.431011\pi\) | ||||
0.215044 | + | 0.976604i | \(0.431011\pi\) | |||||||
\(524\) | −3.19701e12 | −1.85248 | ||||||||
\(525\) | −3.12611e11 | −0.179592 | ||||||||
\(526\) | 4.25154e12 | 2.42164 | ||||||||
\(527\) | 1.27432e12 | 0.719665 | ||||||||
\(528\) | −1.01981e12 | −0.571042 | ||||||||
\(529\) | −1.29291e12 | −0.717822 | ||||||||
\(530\) | −5.05834e11 | −0.278463 | ||||||||
\(531\) | −6.70247e11 | −0.365856 | ||||||||
\(532\) | 8.23187e11 | 0.445550 | ||||||||
\(533\) | 1.71586e12 | 0.920892 | ||||||||
\(534\) | −2.79709e12 | −1.48857 | ||||||||
\(535\) | −1.18183e12 | −0.623683 | ||||||||
\(536\) | 4.05522e10 | 0.0212213 | ||||||||
\(537\) | −1.03049e12 | −0.534759 | ||||||||
\(538\) | 1.08084e12 | 0.556213 | ||||||||
\(539\) | −3.98888e12 | −2.03564 | ||||||||
\(540\) | 2.12354e11 | 0.107470 | ||||||||
\(541\) | 3.42601e12 | 1.71950 | 0.859748 | − | 0.510719i | \(-0.170621\pi\) | ||||
0.859748 | + | 0.510719i | \(0.170621\pi\) | |||||||
\(542\) | 1.29004e12 | 0.642103 | ||||||||
\(543\) | −4.96932e11 | −0.245300 | ||||||||
\(544\) | −4.10212e12 | −2.00823 | ||||||||
\(545\) | −3.85144e11 | −0.186999 | ||||||||
\(546\) | −4.78051e12 | −2.30201 | ||||||||
\(547\) | −2.19990e11 | −0.105065 | −0.0525327 | − | 0.998619i | \(-0.516729\pi\) | ||||
−0.0525327 | + | 0.998619i | \(0.516729\pi\) | |||||||
\(548\) | −1.34443e12 | −0.636831 | ||||||||
\(549\) | −8.21096e11 | −0.385761 | ||||||||
\(550\) | 9.23310e11 | 0.430244 | ||||||||
\(551\) | −1.75116e10 | −0.00809365 | ||||||||
\(552\) | −2.49491e11 | −0.114375 | ||||||||
\(553\) | 4.76811e11 | 0.216812 | ||||||||
\(554\) | −3.58471e12 | −1.61681 | ||||||||
\(555\) | −1.85399e11 | −0.0829447 | ||||||||
\(556\) | −1.23386e12 | −0.547556 | ||||||||
\(557\) | −4.44924e11 | −0.195856 | −0.0979281 | − | 0.995193i | \(-0.531222\pi\) | ||||
−0.0979281 | + | 0.995193i | \(0.531222\pi\) | |||||||
\(558\) | 5.77103e11 | 0.251999 | ||||||||
\(559\) | −7.41198e11 | −0.321056 | ||||||||
\(560\) | 1.11606e12 | 0.479558 | ||||||||
\(561\) | −2.77375e12 | −1.18232 | ||||||||
\(562\) | 1.46350e12 | 0.618843 | ||||||||
\(563\) | −2.85252e12 | −1.19658 | −0.598289 | − | 0.801281i | \(-0.704152\pi\) | ||||
−0.598289 | + | 0.801281i | \(0.704152\pi\) | |||||||
\(564\) | 3.32285e12 | 1.38278 | ||||||||
\(565\) | 2.10176e12 | 0.867693 | ||||||||
\(566\) | −4.72313e12 | −1.93444 | ||||||||
\(567\) | 4.25303e11 | 0.172812 | ||||||||
\(568\) | −7.54702e11 | −0.304234 | ||||||||
\(569\) | 3.03910e12 | 1.21546 | 0.607729 | − | 0.794144i | \(-0.292081\pi\) | ||||
0.607729 | + | 0.794144i | \(0.292081\pi\) | |||||||
\(570\) | −2.23862e11 | −0.0888265 | ||||||||
\(571\) | 8.39653e11 | 0.330550 | 0.165275 | − | 0.986248i | \(-0.447149\pi\) | ||||
0.165275 | + | 0.986248i | \(0.447149\pi\) | |||||||
\(572\) | 7.84050e12 | 3.06240 | ||||||||
\(573\) | 2.84489e12 | 1.10248 | ||||||||
\(574\) | 3.26745e12 | 1.25634 | ||||||||
\(575\) | −2.78482e11 | −0.106241 | ||||||||
\(576\) | −1.25059e12 | −0.473385 | ||||||||
\(577\) | −2.51851e12 | −0.945914 | −0.472957 | − | 0.881085i | \(-0.656813\pi\) | ||||
−0.472957 | + | 0.881085i | \(0.656813\pi\) | |||||||
\(578\) | −4.17572e12 | −1.55617 | ||||||||
\(579\) | −2.68666e12 | −0.993478 | ||||||||
\(580\) | 5.36930e10 | 0.0197012 | ||||||||
\(581\) | 3.78519e12 | 1.37815 | ||||||||
\(582\) | −2.98192e12 | −1.07731 | ||||||||
\(583\) | 1.66156e12 | 0.595672 | ||||||||
\(584\) | −1.37376e12 | −0.488712 | ||||||||
\(585\) | 7.21906e11 | 0.254847 | ||||||||
\(586\) | −4.02578e12 | −1.41030 | ||||||||
\(587\) | −7.40507e11 | −0.257429 | −0.128715 | − | 0.991682i | \(-0.541085\pi\) | ||||
−0.128715 | + | 0.991682i | \(0.541085\pi\) | |||||||
\(588\) | −2.96534e12 | −1.02300 | ||||||||
\(589\) | −3.37829e11 | −0.115659 | ||||||||
\(590\) | −2.16643e12 | −0.736056 | ||||||||
\(591\) | −9.50887e11 | −0.320616 | ||||||||
\(592\) | 6.61897e11 | 0.221484 | ||||||||
\(593\) | 1.87921e12 | 0.624066 | 0.312033 | − | 0.950071i | \(-0.398990\pi\) | ||||
0.312033 | + | 0.950071i | \(0.398990\pi\) | |||||||
\(594\) | −1.25615e12 | −0.414003 | ||||||||
\(595\) | 3.03553e12 | 0.992905 | ||||||||
\(596\) | 4.73364e12 | 1.53669 | ||||||||
\(597\) | 3.11141e12 | 1.00247 | ||||||||
\(598\) | −4.25861e12 | −1.36180 | ||||||||
\(599\) | 5.78020e11 | 0.183452 | 0.0917259 | − | 0.995784i | \(-0.470762\pi\) | ||||
0.0917259 | + | 0.995784i | \(0.470762\pi\) | |||||||
\(600\) | 1.36703e11 | 0.0430623 | ||||||||
\(601\) | −3.96250e12 | −1.23889 | −0.619447 | − | 0.785038i | \(-0.712643\pi\) | ||||
−0.619447 | + | 0.785038i | \(0.712643\pi\) | |||||||
\(602\) | −1.41144e12 | −0.438004 | ||||||||
\(603\) | −6.15816e10 | −0.0189681 | ||||||||
\(604\) | 7.41533e11 | 0.226707 | ||||||||
\(605\) | −1.55916e12 | −0.473142 | ||||||||
\(606\) | −6.99669e11 | −0.210749 | ||||||||
\(607\) | −3.06642e12 | −0.916817 | −0.458408 | − | 0.888742i | \(-0.651580\pi\) | ||||
−0.458408 | + | 0.888742i | \(0.651580\pi\) | |||||||
\(608\) | 1.08750e12 | 0.322746 | ||||||||
\(609\) | 1.07536e11 | 0.0316795 | ||||||||
\(610\) | −2.65402e12 | −0.776104 | ||||||||
\(611\) | 1.12961e13 | 3.27903 | ||||||||
\(612\) | −2.06201e12 | −0.594168 | ||||||||
\(613\) | −4.26173e12 | −1.21903 | −0.609514 | − | 0.792775i | \(-0.708636\pi\) | ||||
−0.609514 | + | 0.792775i | \(0.708636\pi\) | |||||||
\(614\) | −5.24469e12 | −1.48923 | ||||||||
\(615\) | −4.93419e11 | −0.139084 | ||||||||
\(616\) | 2.97358e12 | 0.832082 | ||||||||
\(617\) | 6.21898e12 | 1.72757 | 0.863785 | − | 0.503860i | \(-0.168087\pi\) | ||||
0.863785 | + | 0.503860i | \(0.168087\pi\) | |||||||
\(618\) | 4.43957e9 | 0.00122431 | ||||||||
\(619\) | 1.11768e12 | 0.305992 | 0.152996 | − | 0.988227i | \(-0.451108\pi\) | ||||
0.152996 | + | 0.988227i | \(0.451108\pi\) | |||||||
\(620\) | 1.03583e12 | 0.281531 | ||||||||
\(621\) | 3.78872e11 | 0.102230 | ||||||||
\(622\) | 1.69879e12 | 0.455076 | ||||||||
\(623\) | −1.00549e13 | −2.67414 | ||||||||
\(624\) | −2.57729e12 | −0.680508 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | −5.54768e12 | −1.44387 | ||||||||
\(627\) | 7.35338e11 | 0.190013 | ||||||||
\(628\) | −4.72624e12 | −1.21254 | ||||||||
\(629\) | 1.80027e12 | 0.458574 | ||||||||
\(630\) | 1.37470e12 | 0.347677 | ||||||||
\(631\) | −2.69935e12 | −0.677839 | −0.338920 | − | 0.940815i | \(-0.610061\pi\) | ||||
−0.338920 | + | 0.940815i | \(0.610061\pi\) | |||||||
\(632\) | −2.08507e11 | −0.0519869 | ||||||||
\(633\) | −7.72111e11 | −0.191145 | ||||||||
\(634\) | −4.19794e12 | −1.03189 | ||||||||
\(635\) | 1.57437e12 | 0.384260 | ||||||||
\(636\) | 1.23520e12 | 0.299352 | ||||||||
\(637\) | −1.00808e13 | −2.42586 | ||||||||
\(638\) | −3.17614e11 | −0.0758938 | ||||||||
\(639\) | 1.14607e12 | 0.271931 | ||||||||
\(640\) | −1.37196e12 | −0.323244 | ||||||||
\(641\) | −1.19746e12 | −0.280157 | −0.140078 | − | 0.990140i | \(-0.544735\pi\) | ||||
−0.140078 | + | 0.990140i | \(0.544735\pi\) | |||||||
\(642\) | 5.19710e12 | 1.20741 | ||||||||
\(643\) | −7.98005e11 | −0.184101 | −0.0920505 | − | 0.995754i | \(-0.529342\pi\) | ||||
−0.0920505 | + | 0.995754i | \(0.529342\pi\) | |||||||
\(644\) | −4.50320e12 | −1.03166 | ||||||||
\(645\) | 2.13142e11 | 0.0484897 | ||||||||
\(646\) | 2.17375e12 | 0.491093 | ||||||||
\(647\) | 2.32481e12 | 0.521577 | 0.260788 | − | 0.965396i | \(-0.416017\pi\) | ||||
0.260788 | + | 0.965396i | \(0.416017\pi\) | |||||||
\(648\) | −1.85983e11 | −0.0414368 | ||||||||
\(649\) | 7.11627e12 | 1.57453 | ||||||||
\(650\) | 2.33341e12 | 0.512720 | ||||||||
\(651\) | 2.07456e12 | 0.452702 | ||||||||
\(652\) | 1.55090e12 | 0.336100 | ||||||||
\(653\) | −2.42366e12 | −0.521630 | −0.260815 | − | 0.965389i | \(-0.583991\pi\) | ||||
−0.260815 | + | 0.965389i | \(0.583991\pi\) | |||||||
\(654\) | 1.69367e12 | 0.362017 | ||||||||
\(655\) | 3.12535e12 | 0.663457 | ||||||||
\(656\) | 1.76157e12 | 0.371391 | ||||||||
\(657\) | 2.08616e12 | 0.436821 | ||||||||
\(658\) | 2.15109e13 | 4.47344 | ||||||||
\(659\) | 2.04543e12 | 0.422474 | 0.211237 | − | 0.977435i | \(-0.432251\pi\) | ||||
0.211237 | + | 0.977435i | \(0.432251\pi\) | |||||||
\(660\) | −2.25464e12 | −0.462520 | ||||||||
\(661\) | −1.14535e12 | −0.233363 | −0.116682 | − | 0.993169i | \(-0.537226\pi\) | ||||
−0.116682 | + | 0.993169i | \(0.537226\pi\) | |||||||
\(662\) | 1.19341e13 | 2.41506 | ||||||||
\(663\) | −7.00989e12 | −1.40896 | ||||||||
\(664\) | −1.65525e12 | −0.330450 | ||||||||
\(665\) | −8.04735e11 | −0.159572 | ||||||||
\(666\) | 8.15290e11 | 0.160575 | ||||||||
\(667\) | 9.57964e10 | 0.0187406 | ||||||||
\(668\) | −8.12149e12 | −1.57813 | ||||||||
\(669\) | 2.80067e12 | 0.540561 | ||||||||
\(670\) | −1.99049e11 | −0.0381614 | ||||||||
\(671\) | 8.71789e12 | 1.66020 | ||||||||
\(672\) | −6.67816e12 | −1.26327 | ||||||||
\(673\) | 4.53266e12 | 0.851697 | 0.425848 | − | 0.904795i | \(-0.359976\pi\) | ||||
0.425848 | + | 0.904795i | \(0.359976\pi\) | |||||||
\(674\) | −1.39193e13 | −2.59805 | ||||||||
\(675\) | −2.07594e11 | −0.0384900 | ||||||||
\(676\) | 1.30349e13 | 2.40075 | ||||||||
\(677\) | 3.07988e12 | 0.563489 | 0.281744 | − | 0.959489i | \(-0.409087\pi\) | ||||
0.281744 | + | 0.959489i | \(0.409087\pi\) | |||||||
\(678\) | −9.24249e12 | −1.67979 | ||||||||
\(679\) | −1.07194e13 | −1.93533 | ||||||||
\(680\) | −1.32742e12 | −0.238078 | ||||||||
\(681\) | −1.69992e12 | −0.302876 | ||||||||
\(682\) | −6.12732e12 | −1.08453 | ||||||||
\(683\) | 8.81574e12 | 1.55012 | 0.775060 | − | 0.631887i | \(-0.217719\pi\) | ||||
0.775060 | + | 0.631887i | \(0.217719\pi\) | |||||||
\(684\) | 5.46651e11 | 0.0954899 | ||||||||
\(685\) | 1.31429e12 | 0.228078 | ||||||||
\(686\) | −5.66827e12 | −0.977219 | ||||||||
\(687\) | 4.42086e12 | 0.757184 | ||||||||
\(688\) | −7.60942e11 | −0.129480 | ||||||||
\(689\) | 4.19912e12 | 0.709859 | ||||||||
\(690\) | 1.22462e12 | 0.205675 | ||||||||
\(691\) | −1.13198e12 | −0.188880 | −0.0944401 | − | 0.995531i | \(-0.530106\pi\) | ||||
−0.0944401 | + | 0.995531i | \(0.530106\pi\) | |||||||
\(692\) | 1.26725e13 | 2.10081 | ||||||||
\(693\) | −4.51561e12 | −0.743732 | ||||||||
\(694\) | −1.38738e13 | −2.27028 | ||||||||
\(695\) | 1.20620e12 | 0.196104 | ||||||||
\(696\) | −4.70252e10 | −0.00759607 | ||||||||
\(697\) | 4.79121e12 | 0.768950 | ||||||||
\(698\) | 1.37197e13 | 2.18773 | ||||||||
\(699\) | −1.97262e12 | −0.312534 | ||||||||
\(700\) | 2.46743e12 | 0.388421 | ||||||||
\(701\) | 9.40714e12 | 1.47138 | 0.735692 | − | 0.677316i | \(-0.236857\pi\) | ||||
0.735692 | + | 0.677316i | \(0.236857\pi\) | |||||||
\(702\) | −3.17458e12 | −0.493365 | ||||||||
\(703\) | −4.77262e11 | −0.0736983 | ||||||||
\(704\) | 1.32780e13 | 2.03731 | ||||||||
\(705\) | −3.24836e12 | −0.495238 | ||||||||
\(706\) | 3.87753e12 | 0.587400 | ||||||||
\(707\) | −2.51516e12 | −0.378598 | ||||||||
\(708\) | 5.29024e12 | 0.791272 | ||||||||
\(709\) | −6.66779e12 | −0.991001 | −0.495500 | − | 0.868608i | \(-0.665015\pi\) | ||||
−0.495500 | + | 0.868608i | \(0.665015\pi\) | |||||||
\(710\) | 3.70444e12 | 0.547091 | ||||||||
\(711\) | 3.16634e11 | 0.0464670 | ||||||||
\(712\) | 4.39698e12 | 0.641201 | ||||||||
\(713\) | 1.84808e12 | 0.267804 | ||||||||
\(714\) | −1.33487e13 | −1.92219 | ||||||||
\(715\) | −7.66475e12 | −1.09678 | ||||||||
\(716\) | 8.13361e12 | 1.15658 | ||||||||
\(717\) | 7.56955e12 | 1.06963 | ||||||||
\(718\) | −9.27346e12 | −1.30221 | ||||||||
\(719\) | 2.41689e12 | 0.337269 | 0.168635 | − | 0.985679i | \(-0.446064\pi\) | ||||
0.168635 | + | 0.985679i | \(0.446064\pi\) | |||||||
\(720\) | 7.41137e11 | 0.102778 | ||||||||
\(721\) | 1.59593e10 | 0.00219941 | ||||||||
\(722\) | −5.76274e11 | −0.0789244 | ||||||||
\(723\) | 6.31408e12 | 0.859385 | ||||||||
\(724\) | 3.92227e12 | 0.530535 | ||||||||
\(725\) | −5.24895e10 | −0.00705588 | ||||||||
\(726\) | 6.85639e12 | 0.915968 | ||||||||
\(727\) | −7.53146e12 | −0.999941 | −0.499970 | − | 0.866043i | \(-0.666656\pi\) | ||||
−0.499970 | + | 0.866043i | \(0.666656\pi\) | |||||||
\(728\) | 7.51489e12 | 0.991588 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 6.74307e12 | 0.878830 | ||||||||
\(731\) | −2.06966e12 | −0.268084 | ||||||||
\(732\) | 6.48089e12 | 0.834324 | ||||||||
\(733\) | −2.65885e11 | −0.0340194 | −0.0170097 | − | 0.999855i | \(-0.505415\pi\) | ||||
−0.0170097 | + | 0.999855i | \(0.505415\pi\) | |||||||
\(734\) | −1.34745e13 | −1.71349 | ||||||||
\(735\) | 2.89887e12 | 0.366383 | ||||||||
\(736\) | −5.94909e12 | −0.747309 | ||||||||
\(737\) | 6.53835e11 | 0.0816328 | ||||||||
\(738\) | 2.16980e12 | 0.269257 | ||||||||
\(739\) | −7.54408e12 | −0.930478 | −0.465239 | − | 0.885185i | \(-0.654032\pi\) | ||||
−0.465239 | + | 0.885185i | \(0.654032\pi\) | |||||||
\(740\) | 1.46335e12 | 0.179393 | ||||||||
\(741\) | 1.85836e12 | 0.226437 | ||||||||
\(742\) | 7.99626e12 | 0.968432 | ||||||||
\(743\) | −9.27540e12 | −1.11656 | −0.558281 | − | 0.829652i | \(-0.688539\pi\) | ||||
−0.558281 | + | 0.829652i | \(0.688539\pi\) | |||||||
\(744\) | −9.07197e11 | −0.108548 | ||||||||
\(745\) | −4.62753e12 | −0.550359 | ||||||||
\(746\) | 9.86051e12 | 1.16567 | ||||||||
\(747\) | 2.51362e12 | 0.295363 | ||||||||
\(748\) | 2.18931e13 | 2.55712 | ||||||||
\(749\) | 1.86825e13 | 2.16904 | ||||||||
\(750\) | −6.71004e11 | −0.0774372 | ||||||||
\(751\) | −3.97286e12 | −0.455747 | −0.227874 | − | 0.973691i | \(-0.573177\pi\) | ||||
−0.227874 | + | 0.973691i | \(0.573177\pi\) | |||||||
\(752\) | 1.15971e13 | 1.32242 | ||||||||
\(753\) | 6.96693e12 | 0.789703 | ||||||||
\(754\) | −8.02681e11 | −0.0904423 | ||||||||
\(755\) | −7.24912e11 | −0.0811940 | ||||||||
\(756\) | −3.35691e12 | −0.373759 | ||||||||
\(757\) | −3.95644e12 | −0.437899 | −0.218949 | − | 0.975736i | \(-0.570263\pi\) | ||||
−0.218949 | + | 0.975736i | \(0.570263\pi\) | |||||||
\(758\) | −1.16252e13 | −1.27905 | ||||||||
\(759\) | −4.02262e12 | −0.439968 | ||||||||
\(760\) | 3.51907e11 | 0.0382619 | ||||||||
\(761\) | 4.02381e12 | 0.434917 | 0.217458 | − | 0.976070i | \(-0.430223\pi\) | ||||
0.217458 | + | 0.976070i | \(0.430223\pi\) | |||||||
\(762\) | −6.92329e12 | −0.743901 | ||||||||
\(763\) | 6.08838e12 | 0.650342 | ||||||||
\(764\) | −2.24547e13 | −2.38444 | ||||||||
\(765\) | 2.01579e12 | 0.212799 | ||||||||
\(766\) | 3.57409e12 | 0.375090 | ||||||||
\(767\) | 1.79844e13 | 1.87636 | ||||||||
\(768\) | −1.87181e12 | −0.194149 | ||||||||
\(769\) | 1.47012e13 | 1.51595 | 0.757976 | − | 0.652283i | \(-0.226188\pi\) | ||||
0.757976 | + | 0.652283i | \(0.226188\pi\) | |||||||
\(770\) | −1.45957e13 | −1.49630 | ||||||||
\(771\) | −2.71387e12 | −0.276595 | ||||||||
\(772\) | 2.12057e13 | 2.14869 | ||||||||
\(773\) | 5.27223e12 | 0.531113 | 0.265556 | − | 0.964095i | \(-0.414444\pi\) | ||||
0.265556 | + | 0.964095i | \(0.414444\pi\) | |||||||
\(774\) | −9.37289e11 | −0.0938727 | ||||||||
\(775\) | −1.01261e12 | −0.100829 | ||||||||
\(776\) | 4.68753e12 | 0.464052 | ||||||||
\(777\) | 2.93080e12 | 0.288464 | ||||||||
\(778\) | 2.49435e13 | 2.44090 | ||||||||
\(779\) | −1.27018e12 | −0.123579 | ||||||||
\(780\) | −5.69798e12 | −0.551183 | ||||||||
\(781\) | −1.21683e13 | −1.17031 | ||||||||
\(782\) | −1.18914e13 | −1.13711 | ||||||||
\(783\) | 7.14113e10 | 0.00678952 | ||||||||
\(784\) | −1.03493e13 | −0.978339 | ||||||||
\(785\) | 4.62030e12 | 0.434267 | ||||||||
\(786\) | −1.37437e13 | −1.28441 | ||||||||
\(787\) | 1.14758e13 | 1.06634 | 0.533169 | − | 0.846009i | \(-0.321001\pi\) | ||||
0.533169 | + | 0.846009i | \(0.321001\pi\) | |||||||
\(788\) | 7.50533e12 | 0.693428 | ||||||||
\(789\) | 1.01492e13 | 0.932362 | ||||||||
\(790\) | 1.02345e12 | 0.0934858 | ||||||||
\(791\) | −3.32248e13 | −3.01765 | ||||||||
\(792\) | 1.97465e12 | 0.178331 | ||||||||
\(793\) | 2.20320e13 | 1.97845 | ||||||||
\(794\) | 4.43144e12 | 0.395688 | ||||||||
\(795\) | −1.20752e12 | −0.107211 | ||||||||
\(796\) | −2.45582e13 | −2.16815 | ||||||||
\(797\) | −8.04453e12 | −0.706217 | −0.353108 | − | 0.935582i | \(-0.614875\pi\) | ||||
−0.353108 | + | 0.935582i | \(0.614875\pi\) | |||||||
\(798\) | 3.53882e12 | 0.308919 | ||||||||
\(799\) | 3.15424e13 | 2.73801 | ||||||||
\(800\) | 3.25967e12 | 0.281364 | ||||||||
\(801\) | −6.67715e12 | −0.573119 | ||||||||
\(802\) | −1.10775e13 | −0.945489 | ||||||||
\(803\) | −2.21496e13 | −1.87995 | ||||||||
\(804\) | 4.86062e11 | 0.0410241 | ||||||||
\(805\) | 4.40226e12 | 0.369483 | ||||||||
\(806\) | −1.54851e13 | −1.29243 | ||||||||
\(807\) | 2.58016e12 | 0.214149 | ||||||||
\(808\) | 1.09987e12 | 0.0907799 | ||||||||
\(809\) | −1.46887e13 | −1.20563 | −0.602814 | − | 0.797882i | \(-0.705954\pi\) | ||||
−0.602814 | + | 0.797882i | \(0.705954\pi\) | |||||||
\(810\) | 9.12894e11 | 0.0745139 | ||||||||
\(811\) | 5.18047e12 | 0.420509 | 0.210255 | − | 0.977647i | \(-0.432571\pi\) | ||||
0.210255 | + | 0.977647i | \(0.432571\pi\) | |||||||
\(812\) | −8.48782e11 | −0.0685164 | ||||||||
\(813\) | 3.07955e12 | 0.247218 | ||||||||
\(814\) | −8.65624e12 | −0.691066 | ||||||||
\(815\) | −1.51613e12 | −0.120373 | ||||||||
\(816\) | −7.19662e12 | −0.568228 | ||||||||
\(817\) | 5.48678e11 | 0.0430842 | ||||||||
\(818\) | −3.38274e13 | −2.64167 | ||||||||
\(819\) | −1.14119e13 | −0.886302 | ||||||||
\(820\) | 3.89454e12 | 0.300811 | ||||||||
\(821\) | 2.10676e13 | 1.61834 | 0.809172 | − | 0.587572i | \(-0.199916\pi\) | ||||
0.809172 | + | 0.587572i | \(0.199916\pi\) | |||||||
\(822\) | −5.77958e12 | −0.441543 | ||||||||
\(823\) | −1.23011e12 | −0.0934644 | −0.0467322 | − | 0.998907i | \(-0.514881\pi\) | ||||
−0.0467322 | + | 0.998907i | \(0.514881\pi\) | |||||||
\(824\) | −6.97893e9 | −0.000527371 0 | ||||||||
\(825\) | 2.20411e12 | 0.165649 | ||||||||
\(826\) | 3.42471e13 | 2.55984 | ||||||||
\(827\) | −1.85555e12 | −0.137942 | −0.0689712 | − | 0.997619i | \(-0.521972\pi\) | ||||
−0.0689712 | + | 0.997619i | \(0.521972\pi\) | |||||||
\(828\) | −2.99042e12 | −0.221104 | ||||||||
\(829\) | 9.09884e12 | 0.669099 | 0.334550 | − | 0.942378i | \(-0.391416\pi\) | ||||
0.334550 | + | 0.942378i | \(0.391416\pi\) | |||||||
\(830\) | 8.12474e12 | 0.594235 | ||||||||
\(831\) | −8.55734e12 | −0.622493 | ||||||||
\(832\) | 3.35565e13 | 2.42785 | ||||||||
\(833\) | −2.81487e13 | −2.02561 | ||||||||
\(834\) | −5.30425e12 | −0.379644 | ||||||||
\(835\) | 7.93945e12 | 0.565199 | ||||||||
\(836\) | −5.80400e12 | −0.410960 | ||||||||
\(837\) | 1.37765e12 | 0.0970228 | ||||||||
\(838\) | −4.80455e12 | −0.336554 | ||||||||
\(839\) | 1.12716e13 | 0.785341 | 0.392670 | − | 0.919679i | \(-0.371551\pi\) | ||||
0.392670 | + | 0.919679i | \(0.371551\pi\) | |||||||
\(840\) | −2.16101e12 | −0.149762 | ||||||||
\(841\) | −1.44891e13 | −0.998755 | ||||||||
\(842\) | −2.70343e13 | −1.85358 | ||||||||
\(843\) | 3.49364e12 | 0.238262 | ||||||||
\(844\) | 6.09425e12 | 0.413409 | ||||||||
\(845\) | −1.27427e13 | −0.859818 | ||||||||
\(846\) | 1.42847e13 | 0.958745 | ||||||||
\(847\) | 2.46473e13 | 1.64548 | ||||||||
\(848\) | 4.31098e12 | 0.286283 | ||||||||
\(849\) | −1.12750e13 | −0.744784 | ||||||||
\(850\) | 6.51561e12 | 0.428125 | ||||||||
\(851\) | 2.61083e12 | 0.170646 | ||||||||
\(852\) | −9.04592e12 | −0.588131 | ||||||||
\(853\) | 9.70339e12 | 0.627556 | 0.313778 | − | 0.949496i | \(-0.398405\pi\) | ||||
0.313778 | + | 0.949496i | \(0.398405\pi\) | |||||||
\(854\) | 4.19549e13 | 2.69912 | ||||||||
\(855\) | −5.34398e11 | −0.0341993 | ||||||||
\(856\) | −8.16976e12 | −0.520089 | ||||||||
\(857\) | 2.75330e13 | 1.74357 | 0.871787 | − | 0.489885i | \(-0.162961\pi\) | ||||
0.871787 | + | 0.489885i | \(0.162961\pi\) | |||||||
\(858\) | 3.37057e13 | 2.12329 | ||||||||
\(859\) | −1.21276e13 | −0.759989 | −0.379994 | − | 0.924989i | \(-0.624074\pi\) | ||||
−0.379994 | + | 0.924989i | \(0.624074\pi\) | |||||||
\(860\) | −1.68232e12 | −0.104874 | ||||||||
\(861\) | 7.79999e12 | 0.483704 | ||||||||
\(862\) | 1.39704e13 | 0.861841 | ||||||||
\(863\) | 1.58553e13 | 0.973032 | 0.486516 | − | 0.873672i | \(-0.338268\pi\) | ||||
0.486516 | + | 0.873672i | \(0.338268\pi\) | |||||||
\(864\) | −4.43474e12 | −0.270742 | ||||||||
\(865\) | −1.23885e13 | −0.752394 | ||||||||
\(866\) | 1.78152e13 | 1.07637 | ||||||||
\(867\) | −9.96820e12 | −0.599143 | ||||||||
\(868\) | −1.63745e13 | −0.979104 | ||||||||
\(869\) | −3.36182e12 | −0.199980 | ||||||||
\(870\) | 2.30822e11 | 0.0136597 | ||||||||
\(871\) | 1.65239e12 | 0.0972814 | ||||||||
\(872\) | −2.66242e12 | −0.155938 | ||||||||
\(873\) | −7.11837e12 | −0.414779 | ||||||||
\(874\) | 3.15247e12 | 0.182747 | ||||||||
\(875\) | −2.41212e12 | −0.139111 | ||||||||
\(876\) | −1.64660e13 | −0.944757 | ||||||||
\(877\) | −2.86146e13 | −1.63339 | −0.816695 | − | 0.577069i | \(-0.804196\pi\) | ||||
−0.816695 | + | 0.577069i | \(0.804196\pi\) | |||||||
\(878\) | −2.00992e13 | −1.14144 | ||||||||
\(879\) | −9.61027e12 | −0.542982 | ||||||||
\(880\) | −7.86893e12 | −0.442327 | ||||||||
\(881\) | −1.23867e13 | −0.692729 | −0.346365 | − | 0.938100i | \(-0.612584\pi\) | ||||
−0.346365 | + | 0.938100i | \(0.612584\pi\) | |||||||
\(882\) | −1.27477e13 | −0.709292 | ||||||||
\(883\) | −3.23596e12 | −0.179135 | −0.0895673 | − | 0.995981i | \(-0.528548\pi\) | ||||
−0.0895673 | + | 0.995981i | \(0.528548\pi\) | |||||||
\(884\) | 5.53288e13 | 3.04731 | ||||||||
\(885\) | −5.17166e12 | −0.283391 | ||||||||
\(886\) | 1.17477e13 | 0.640474 | ||||||||
\(887\) | −2.35148e11 | −0.0127551 | −0.00637757 | − | 0.999980i | \(-0.502030\pi\) | ||||
−0.00637757 | + | 0.999980i | \(0.502030\pi\) | |||||||
\(888\) | −1.28162e12 | −0.0691675 | ||||||||
\(889\) | −2.48878e13 | −1.33637 | ||||||||
\(890\) | −2.15825e13 | −1.15304 | ||||||||
\(891\) | −2.99866e12 | −0.159396 | ||||||||
\(892\) | −2.21056e13 | −1.16913 | ||||||||
\(893\) | −8.36208e12 | −0.440030 | ||||||||
\(894\) | 2.03495e13 | 1.06546 | ||||||||
\(895\) | −7.95129e12 | −0.414223 | ||||||||
\(896\) | 2.16880e13 | 1.12417 | ||||||||
\(897\) | −1.01661e13 | −0.524308 | ||||||||
\(898\) | 6.48070e12 | 0.332566 | ||||||||
\(899\) | 3.48333e11 | 0.0177859 | ||||||||
\(900\) | 1.63853e12 | 0.0832462 | ||||||||
\(901\) | 1.17253e13 | 0.592737 | ||||||||
\(902\) | −2.30376e13 | −1.15880 | ||||||||
\(903\) | −3.36936e12 | −0.168637 | ||||||||
\(904\) | 1.45291e13 | 0.723568 | ||||||||
\(905\) | −3.83435e12 | −0.190009 | ||||||||
\(906\) | 3.18779e12 | 0.157186 | ||||||||
\(907\) | 3.22682e13 | 1.58322 | 0.791611 | − | 0.611026i | \(-0.209243\pi\) | ||||
0.791611 | + | 0.611026i | \(0.209243\pi\) | |||||||
\(908\) | 1.34174e13 | 0.655061 | ||||||||
\(909\) | −1.67023e12 | −0.0811409 | ||||||||
\(910\) | −3.68867e13 | −1.78313 | ||||||||
\(911\) | 2.50945e13 | 1.20711 | 0.603553 | − | 0.797323i | \(-0.293751\pi\) | ||||
0.603553 | + | 0.797323i | \(0.293751\pi\) | |||||||
\(912\) | 1.90787e12 | 0.0913211 | ||||||||
\(913\) | −2.66880e13 | −1.27115 | ||||||||
\(914\) | 3.05149e13 | 1.44629 | ||||||||
\(915\) | −6.33562e12 | −0.298809 | ||||||||
\(916\) | −3.48937e13 | −1.63764 | ||||||||
\(917\) | −4.94057e13 | −2.30736 | ||||||||
\(918\) | −8.86442e12 | −0.411963 | ||||||||
\(919\) | 1.22135e13 | 0.564835 | 0.282418 | − | 0.959292i | \(-0.408864\pi\) | ||||
0.282418 | + | 0.959292i | \(0.408864\pi\) | |||||||
\(920\) | −1.92509e12 | −0.0885942 | ||||||||
\(921\) | −1.25200e13 | −0.573372 | ||||||||
\(922\) | 9.45727e12 | 0.430999 | ||||||||
\(923\) | −3.07519e13 | −1.39465 | ||||||||
\(924\) | 3.56416e13 | 1.60854 | ||||||||
\(925\) | −1.43055e12 | −0.0642487 | ||||||||
\(926\) | −2.57706e13 | −1.15180 | ||||||||
\(927\) | 1.05980e10 | 0.000471376 0 | ||||||||
\(928\) | −1.12131e12 | −0.0496317 | ||||||||
\(929\) | −2.81613e13 | −1.24046 | −0.620228 | − | 0.784422i | \(-0.712960\pi\) | ||||
−0.620228 | + | 0.784422i | \(0.712960\pi\) | |||||||
\(930\) | 4.45295e12 | 0.195198 | ||||||||
\(931\) | 7.46239e12 | 0.325540 | ||||||||
\(932\) | 1.55699e13 | 0.675948 | ||||||||
\(933\) | 4.05532e12 | 0.175210 | ||||||||
\(934\) | −3.31536e13 | −1.42551 | ||||||||
\(935\) | −2.14024e13 | −0.915820 | ||||||||
\(936\) | 4.99038e12 | 0.212516 | ||||||||
\(937\) | 4.52888e12 | 0.191939 | 0.0959695 | − | 0.995384i | \(-0.469405\pi\) | ||||
0.0959695 | + | 0.995384i | \(0.469405\pi\) | |||||||
\(938\) | 3.14659e12 | 0.132717 | ||||||||
\(939\) | −1.32433e13 | −0.555906 | ||||||||
\(940\) | 2.56393e13 | 1.07110 | ||||||||
\(941\) | 3.51517e13 | 1.46148 | 0.730741 | − | 0.682655i | \(-0.239175\pi\) | ||||
0.730741 | + | 0.682655i | \(0.239175\pi\) | |||||||
\(942\) | −2.03177e13 | −0.840709 | ||||||||
\(943\) | 6.94844e12 | 0.286144 | ||||||||
\(944\) | 1.84635e13 | 0.756727 | ||||||||
\(945\) | 3.28166e12 | 0.133860 | ||||||||
\(946\) | 9.95155e12 | 0.403999 | ||||||||
\(947\) | −1.47283e13 | −0.595083 | −0.297541 | − | 0.954709i | \(-0.596167\pi\) | ||||
−0.297541 | + | 0.954709i | \(0.596167\pi\) | |||||||
\(948\) | −2.49918e12 | −0.100499 | ||||||||
\(949\) | −5.59768e13 | −2.24032 | ||||||||
\(950\) | −1.72733e12 | −0.0688047 | ||||||||
\(951\) | −1.00212e13 | −0.397291 | ||||||||
\(952\) | 2.09839e13 | 0.827982 | ||||||||
\(953\) | 7.97246e12 | 0.313094 | 0.156547 | − | 0.987671i | \(-0.449964\pi\) | ||||
0.156547 | + | 0.987671i | \(0.449964\pi\) | |||||||
\(954\) | 5.31004e12 | 0.207554 | ||||||||
\(955\) | 2.19513e13 | 0.853976 | ||||||||
\(956\) | −5.97462e13 | −2.31340 | ||||||||
\(957\) | −7.58201e11 | −0.0292200 | ||||||||
\(958\) | 6.55282e13 | 2.51353 | ||||||||
\(959\) | −2.07764e13 | −0.793207 | ||||||||
\(960\) | −9.64964e12 | −0.366683 | ||||||||
\(961\) | −1.97197e13 | −0.745838 | ||||||||
\(962\) | −2.18762e13 | −0.823541 | ||||||||
\(963\) | 1.24064e13 | 0.464866 | ||||||||
\(964\) | −4.98369e13 | −1.85868 | ||||||||
\(965\) | −2.07304e13 | −0.769545 | ||||||||
\(966\) | −1.93589e13 | −0.715293 | ||||||||
\(967\) | −4.87770e13 | −1.79389 | −0.896945 | − | 0.442143i | \(-0.854218\pi\) | ||||
−0.896945 | + | 0.442143i | \(0.854218\pi\) | |||||||
\(968\) | −1.07781e13 | −0.394552 | ||||||||
\(969\) | 5.18913e12 | 0.189077 | ||||||||
\(970\) | −2.30086e13 | −0.834484 | ||||||||
\(971\) | −4.14096e13 | −1.49491 | −0.747454 | − | 0.664314i | \(-0.768724\pi\) | ||||
−0.747454 | + | 0.664314i | \(0.768724\pi\) | |||||||
\(972\) | −2.22921e12 | −0.0801037 | ||||||||
\(973\) | −1.90677e13 | −0.682009 | ||||||||
\(974\) | −6.76969e13 | −2.41020 | ||||||||
\(975\) | 5.57026e12 | 0.197404 | ||||||||
\(976\) | 2.26189e13 | 0.797899 | ||||||||
\(977\) | −4.15877e13 | −1.46029 | −0.730145 | − | 0.683292i | \(-0.760547\pi\) | ||||
−0.730145 | + | 0.683292i | \(0.760547\pi\) | |||||||
\(978\) | 6.66718e12 | 0.233033 | ||||||||
\(979\) | 7.08938e13 | 2.46653 | ||||||||
\(980\) | −2.28807e13 | −0.792413 | ||||||||
\(981\) | 4.04309e12 | 0.139381 | ||||||||
\(982\) | −6.09049e13 | −2.09002 | ||||||||
\(983\) | 3.82096e13 | 1.30522 | 0.652608 | − | 0.757696i | \(-0.273675\pi\) | ||||
0.652608 | + | 0.757696i | \(0.273675\pi\) | |||||||
\(984\) | −3.41090e12 | −0.115982 | ||||||||
\(985\) | −7.33709e12 | −0.248348 | ||||||||
\(986\) | −2.24134e12 | −0.0755199 | ||||||||
\(987\) | 5.13504e13 | 1.72233 | ||||||||
\(988\) | −1.46680e13 | −0.489739 | ||||||||
\(989\) | −3.00151e12 | −0.0997602 | ||||||||
\(990\) | −9.69254e12 | −0.320685 | ||||||||
\(991\) | 3.49657e13 | 1.15163 | 0.575813 | − | 0.817582i | \(-0.304686\pi\) | ||||
0.575813 | + | 0.817582i | \(0.304686\pi\) | |||||||
\(992\) | −2.16320e13 | −0.709241 | ||||||||
\(993\) | 2.84888e13 | 0.929828 | ||||||||
\(994\) | −5.85600e13 | −1.90266 | ||||||||
\(995\) | 2.40078e13 | 0.776512 | ||||||||
\(996\) | −1.98399e13 | −0.638812 | ||||||||
\(997\) | −2.24998e13 | −0.721193 | −0.360596 | − | 0.932722i | \(-0.617427\pi\) | ||||
−0.360596 | + | 0.932722i | \(0.617427\pi\) | |||||||
\(998\) | 1.69900e13 | 0.542132 | ||||||||
\(999\) | 1.94624e12 | 0.0618233 |
(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 | 285.10.a.f.1.3 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.10.a.f.1.3 | ✓ | 14 | 1.1 | even | 1 | trivial |