Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,12,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(151.363606570\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −87.1440 | −1.92563 | −0.962814 | − | 0.270165i | \(-0.912922\pi\) | ||||
−0.962814 | + | 0.270165i | \(0.912922\pi\) | |||||||
\(3\) | 786.167 | 1.86788 | 0.933938 | − | 0.357435i | \(-0.116349\pi\) | ||||
0.933938 | + | 0.357435i | \(0.116349\pi\) | |||||||
\(4\) | 5546.07 | 2.70804 | ||||||||
\(5\) | 12634.2 | 1.80805 | 0.904026 | − | 0.427477i | \(-0.140597\pi\) | ||||
0.904026 | + | 0.427477i | \(0.140597\pi\) | |||||||
\(6\) | −68509.7 | −3.59683 | ||||||||
\(7\) | −52867.9 | −1.18892 | −0.594460 | − | 0.804125i | \(-0.702634\pi\) | ||||
−0.594460 | + | 0.804125i | \(0.702634\pi\) | |||||||
\(8\) | −304836. | −3.28906 | ||||||||
\(9\) | 440912. | 2.48896 | ||||||||
\(10\) | −1.10099e6 | −3.48164 | ||||||||
\(11\) | −243497. | −0.455863 | −0.227931 | − | 0.973677i | \(-0.573196\pi\) | ||||
−0.227931 | + | 0.973677i | \(0.573196\pi\) | |||||||
\(12\) | 4.36014e6 | 5.05829 | ||||||||
\(13\) | 1.64401e6 | 1.22805 | 0.614024 | − | 0.789288i | \(-0.289550\pi\) | ||||
0.614024 | + | 0.789288i | \(0.289550\pi\) | |||||||
\(14\) | 4.60712e6 | 2.28942 | ||||||||
\(15\) | 9.93256e6 | 3.37722 | ||||||||
\(16\) | 1.52063e7 | 3.62545 | ||||||||
\(17\) | −3.18554e6 | −0.544144 | −0.272072 | − | 0.962277i | \(-0.587709\pi\) | ||||
−0.272072 | + | 0.962277i | \(0.587709\pi\) | |||||||
\(18\) | −3.84228e7 | −4.79281 | ||||||||
\(19\) | −1.13223e6 | −0.104904 | −0.0524519 | − | 0.998623i | \(-0.516704\pi\) | ||||
−0.0524519 | + | 0.998623i | \(0.516704\pi\) | |||||||
\(20\) | 7.00699e7 | 4.89628 | ||||||||
\(21\) | −4.15630e7 | −2.22076 | ||||||||
\(22\) | 2.12193e7 | 0.877822 | ||||||||
\(23\) | −5.58534e7 | −1.80945 | −0.904724 | − | 0.425998i | \(-0.859923\pi\) | ||||
−0.904724 | + | 0.425998i | \(0.859923\pi\) | |||||||
\(24\) | −2.39652e8 | −6.14355 | ||||||||
\(25\) | 1.10794e8 | 2.26905 | ||||||||
\(26\) | −1.43265e8 | −2.36476 | ||||||||
\(27\) | 2.07363e8 | 2.78119 | ||||||||
\(28\) | −2.93209e8 | −3.21965 | ||||||||
\(29\) | 7.30013e7 | 0.660909 | 0.330454 | − | 0.943822i | \(-0.392798\pi\) | ||||
0.330454 | + | 0.943822i | \(0.392798\pi\) | |||||||
\(30\) | −8.65562e8 | −6.50327 | ||||||||
\(31\) | 1.66906e8 | 1.04709 | 0.523544 | − | 0.851999i | \(-0.324610\pi\) | ||||
0.523544 | + | 0.851999i | \(0.324610\pi\) | |||||||
\(32\) | −7.00830e8 | −3.69222 | ||||||||
\(33\) | −1.91429e8 | −0.851495 | ||||||||
\(34\) | 2.77600e8 | 1.04782 | ||||||||
\(35\) | −6.67941e8 | −2.14963 | ||||||||
\(36\) | 2.44533e9 | 6.74021 | ||||||||
\(37\) | −2.24431e8 | −0.532075 | −0.266037 | − | 0.963963i | \(-0.585714\pi\) | ||||
−0.266037 | + | 0.963963i | \(0.585714\pi\) | |||||||
\(38\) | 9.86673e7 | 0.202006 | ||||||||
\(39\) | 1.29246e9 | 2.29384 | ||||||||
\(40\) | −3.85134e9 | −5.94679 | ||||||||
\(41\) | −3.79319e8 | −0.511321 | −0.255660 | − | 0.966767i | \(-0.582293\pi\) | ||||
−0.255660 | + | 0.966767i | \(0.582293\pi\) | |||||||
\(42\) | 3.62197e9 | 4.27635 | ||||||||
\(43\) | 2.22500e8 | 0.230810 | 0.115405 | − | 0.993319i | \(-0.463183\pi\) | ||||
0.115405 | + | 0.993319i | \(0.463183\pi\) | |||||||
\(44\) | −1.35045e9 | −1.23450 | ||||||||
\(45\) | 5.57055e9 | 4.50017 | ||||||||
\(46\) | 4.86728e9 | 3.48432 | ||||||||
\(47\) | 2.25481e9 | 1.43408 | 0.717038 | − | 0.697034i | \(-0.245498\pi\) | ||||
0.717038 | + | 0.697034i | \(0.245498\pi\) | |||||||
\(48\) | 1.19547e10 | 6.77190 | ||||||||
\(49\) | 8.17688e8 | 0.413532 | ||||||||
\(50\) | −9.65500e9 | −4.36935 | ||||||||
\(51\) | −2.50437e9 | −1.01639 | ||||||||
\(52\) | 9.11778e9 | 3.32561 | ||||||||
\(53\) | −5.59241e7 | −0.0183689 | −0.00918443 | − | 0.999958i | \(-0.502924\pi\) | ||||
−0.00918443 | + | 0.999958i | \(0.502924\pi\) | |||||||
\(54\) | −1.80705e10 | −5.35555 | ||||||||
\(55\) | −3.07638e9 | −0.824223 | ||||||||
\(56\) | 1.61160e10 | 3.91043 | ||||||||
\(57\) | −8.90124e8 | −0.195947 | ||||||||
\(58\) | −6.36162e9 | −1.27266 | ||||||||
\(59\) | 2.40144e9 | 0.437307 | 0.218653 | − | 0.975803i | \(-0.429834\pi\) | ||||
0.218653 | + | 0.975803i | \(0.429834\pi\) | |||||||
\(60\) | 5.50867e10 | 9.14565 | ||||||||
\(61\) | −5.86229e9 | −0.888696 | −0.444348 | − | 0.895854i | \(-0.646565\pi\) | ||||
−0.444348 | + | 0.895854i | \(0.646565\pi\) | |||||||
\(62\) | −1.45449e10 | −2.01630 | ||||||||
\(63\) | −2.33101e10 | −2.95918 | ||||||||
\(64\) | 2.99307e10 | 3.48439 | ||||||||
\(65\) | 2.07706e10 | 2.22037 | ||||||||
\(66\) | 1.66819e10 | 1.63966 | ||||||||
\(67\) | 7.91950e9 | 0.716616 | 0.358308 | − | 0.933603i | \(-0.383354\pi\) | ||||
0.358308 | + | 0.933603i | \(0.383354\pi\) | |||||||
\(68\) | −1.76672e10 | −1.47357 | ||||||||
\(69\) | −4.39101e10 | −3.37983 | ||||||||
\(70\) | 5.82070e10 | 4.13939 | ||||||||
\(71\) | 2.05210e10 | 1.34982 | 0.674911 | − | 0.737899i | \(-0.264182\pi\) | ||||
0.674911 | + | 0.737899i | \(0.264182\pi\) | |||||||
\(72\) | −1.34406e11 | −8.18633 | ||||||||
\(73\) | 1.74831e10 | 0.987060 | 0.493530 | − | 0.869729i | \(-0.335706\pi\) | ||||
0.493530 | + | 0.869729i | \(0.335706\pi\) | |||||||
\(74\) | 1.95578e10 | 1.02458 | ||||||||
\(75\) | 8.71024e10 | 4.23831 | ||||||||
\(76\) | −6.27944e9 | −0.284084 | ||||||||
\(77\) | 1.28732e10 | 0.541984 | ||||||||
\(78\) | −1.12630e11 | −4.41708 | ||||||||
\(79\) | 2.82858e10 | 1.03423 | 0.517117 | − | 0.855915i | \(-0.327005\pi\) | ||||
0.517117 | + | 0.855915i | \(0.327005\pi\) | |||||||
\(80\) | 1.92118e11 | 6.55501 | ||||||||
\(81\) | 8.49161e10 | 2.70597 | ||||||||
\(82\) | 3.30554e10 | 0.984614 | ||||||||
\(83\) | 6.22953e10 | 1.73590 | 0.867952 | − | 0.496649i | \(-0.165436\pi\) | ||||
0.867952 | + | 0.496649i | \(0.165436\pi\) | |||||||
\(84\) | −2.30511e11 | −6.01390 | ||||||||
\(85\) | −4.02466e10 | −0.983841 | ||||||||
\(86\) | −1.93896e10 | −0.444453 | ||||||||
\(87\) | 5.73912e10 | 1.23450 | ||||||||
\(88\) | 7.42266e10 | 1.49936 | ||||||||
\(89\) | −8.70641e10 | −1.65270 | −0.826350 | − | 0.563156i | \(-0.809587\pi\) | ||||
−0.826350 | + | 0.563156i | \(0.809587\pi\) | |||||||
\(90\) | −4.85440e11 | −8.66566 | ||||||||
\(91\) | −8.69152e10 | −1.46005 | ||||||||
\(92\) | −3.09767e11 | −4.90006 | ||||||||
\(93\) | 1.31216e11 | 1.95583 | ||||||||
\(94\) | −1.96493e11 | −2.76150 | ||||||||
\(95\) | −1.43048e10 | −0.189671 | ||||||||
\(96\) | −5.50969e11 | −6.89661 | ||||||||
\(97\) | 1.00198e11 | 1.18471 | 0.592356 | − | 0.805676i | \(-0.298198\pi\) | ||||
0.592356 | + | 0.805676i | \(0.298198\pi\) | |||||||
\(98\) | −7.12566e10 | −0.796309 | ||||||||
\(99\) | −1.07361e11 | −1.13462 | ||||||||
\(100\) | 6.14470e11 | 6.14470 | ||||||||
\(101\) | 1.32458e11 | 1.25404 | 0.627021 | − | 0.779002i | \(-0.284274\pi\) | ||||
0.627021 | + | 0.779002i | \(0.284274\pi\) | |||||||
\(102\) | 2.18240e11 | 1.95720 | ||||||||
\(103\) | 1.10119e11 | 0.935959 | 0.467979 | − | 0.883739i | \(-0.344982\pi\) | ||||
0.467979 | + | 0.883739i | \(0.344982\pi\) | |||||||
\(104\) | −5.01152e11 | −4.03912 | ||||||||
\(105\) | −5.25113e11 | −4.01524 | ||||||||
\(106\) | 4.87345e9 | 0.0353716 | ||||||||
\(107\) | 7.80172e10 | 0.537749 | 0.268875 | − | 0.963175i | \(-0.413348\pi\) | ||||
0.268875 | + | 0.963175i | \(0.413348\pi\) | |||||||
\(108\) | 1.15005e12 | 7.53160 | ||||||||
\(109\) | −3.81290e10 | −0.237361 | −0.118681 | − | 0.992932i | \(-0.537866\pi\) | ||||
−0.118681 | + | 0.992932i | \(0.537866\pi\) | |||||||
\(110\) | 2.68088e11 | 1.58715 | ||||||||
\(111\) | −1.76440e11 | −0.993850 | ||||||||
\(112\) | −8.03923e11 | −4.31038 | ||||||||
\(113\) | 2.06621e11 | 1.05498 | 0.527490 | − | 0.849561i | \(-0.323133\pi\) | ||||
0.527490 | + | 0.849561i | \(0.323133\pi\) | |||||||
\(114\) | 7.75690e10 | 0.377321 | ||||||||
\(115\) | −7.05660e11 | −3.27158 | ||||||||
\(116\) | 4.04871e11 | 1.78977 | ||||||||
\(117\) | 7.24862e11 | 3.05656 | ||||||||
\(118\) | −2.09271e11 | −0.842090 | ||||||||
\(119\) | 1.68413e11 | 0.646944 | ||||||||
\(120\) | −3.02780e12 | −11.1079 | ||||||||
\(121\) | −2.26021e11 | −0.792189 | ||||||||
\(122\) | 5.10863e11 | 1.71130 | ||||||||
\(123\) | −2.98208e11 | −0.955084 | ||||||||
\(124\) | 9.25674e11 | 2.83556 | ||||||||
\(125\) | 7.82882e11 | 2.29452 | ||||||||
\(126\) | 2.03133e12 | 5.69827 | ||||||||
\(127\) | −5.46793e11 | −1.46860 | −0.734299 | − | 0.678826i | \(-0.762489\pi\) | ||||
−0.734299 | + | 0.678826i | \(0.762489\pi\) | |||||||
\(128\) | −1.17298e12 | −3.01742 | ||||||||
\(129\) | 1.74922e11 | 0.431124 | ||||||||
\(130\) | −1.81004e12 | −4.27561 | ||||||||
\(131\) | −3.13074e11 | −0.709014 | −0.354507 | − | 0.935053i | \(-0.615351\pi\) | ||||
−0.354507 | + | 0.935053i | \(0.615351\pi\) | |||||||
\(132\) | −1.06168e12 | −2.30588 | ||||||||
\(133\) | 5.98588e10 | 0.124722 | ||||||||
\(134\) | −6.90137e11 | −1.37994 | ||||||||
\(135\) | 2.61986e12 | 5.02855 | ||||||||
\(136\) | 9.71066e11 | 1.78972 | ||||||||
\(137\) | 5.60447e11 | 0.992136 | 0.496068 | − | 0.868284i | \(-0.334777\pi\) | ||||
0.496068 | + | 0.868284i | \(0.334777\pi\) | |||||||
\(138\) | 3.82650e12 | 6.50829 | ||||||||
\(139\) | 3.59980e11 | 0.588432 | 0.294216 | − | 0.955739i | \(-0.404941\pi\) | ||||
0.294216 | + | 0.955739i | \(0.404941\pi\) | |||||||
\(140\) | −3.70445e12 | −5.82129 | ||||||||
\(141\) | 1.77266e12 | 2.67868 | ||||||||
\(142\) | −1.78828e12 | −2.59926 | ||||||||
\(143\) | −4.00311e11 | −0.559821 | ||||||||
\(144\) | 6.70462e12 | 9.02361 | ||||||||
\(145\) | 9.22310e11 | 1.19496 | ||||||||
\(146\) | −1.52355e12 | −1.90071 | ||||||||
\(147\) | 6.42840e11 | 0.772427 | ||||||||
\(148\) | −1.24471e12 | −1.44088 | ||||||||
\(149\) | −1.32672e12 | −1.47998 | −0.739990 | − | 0.672618i | \(-0.765170\pi\) | ||||
−0.739990 | + | 0.672618i | \(0.765170\pi\) | |||||||
\(150\) | −7.59045e12 | −8.16141 | ||||||||
\(151\) | 1.54430e12 | 1.60088 | 0.800438 | − | 0.599416i | \(-0.204600\pi\) | ||||
0.800438 | + | 0.599416i | \(0.204600\pi\) | |||||||
\(152\) | 3.45145e11 | 0.345034 | ||||||||
\(153\) | −1.40454e12 | −1.35435 | ||||||||
\(154\) | −1.12182e12 | −1.04366 | ||||||||
\(155\) | 2.10872e12 | 1.89319 | ||||||||
\(156\) | 7.16810e12 | 6.21182 | ||||||||
\(157\) | 1.54023e12 | 1.28865 | 0.644327 | − | 0.764750i | \(-0.277138\pi\) | ||||
0.644327 | + | 0.764750i | \(0.277138\pi\) | |||||||
\(158\) | −2.46493e12 | −1.99155 | ||||||||
\(159\) | −4.39657e10 | −0.0343107 | ||||||||
\(160\) | −8.85439e12 | −6.67573 | ||||||||
\(161\) | 2.95285e12 | 2.15129 | ||||||||
\(162\) | −7.39993e12 | −5.21068 | ||||||||
\(163\) | −2.89330e11 | −0.196952 | −0.0984762 | − | 0.995139i | \(-0.531397\pi\) | ||||
−0.0984762 | + | 0.995139i | \(0.531397\pi\) | |||||||
\(164\) | −2.10373e12 | −1.38468 | ||||||||
\(165\) | −2.41855e12 | −1.53955 | ||||||||
\(166\) | −5.42866e12 | −3.34270 | ||||||||
\(167\) | −2.72326e11 | −0.162237 | −0.0811183 | − | 0.996704i | \(-0.525849\pi\) | ||||
−0.0811183 | + | 0.996704i | \(0.525849\pi\) | |||||||
\(168\) | 1.26699e13 | 7.30419 | ||||||||
\(169\) | 9.10598e11 | 0.508100 | ||||||||
\(170\) | 3.50725e12 | 1.89451 | ||||||||
\(171\) | −4.99215e11 | −0.261101 | ||||||||
\(172\) | 1.23400e12 | 0.625042 | ||||||||
\(173\) | −8.95594e11 | −0.439397 | −0.219699 | − | 0.975568i | \(-0.570507\pi\) | ||||
−0.219699 | + | 0.975568i | \(0.570507\pi\) | |||||||
\(174\) | −5.00130e12 | −2.37718 | ||||||||
\(175\) | −5.85743e12 | −2.69773 | ||||||||
\(176\) | −3.70268e12 | −1.65271 | ||||||||
\(177\) | 1.88794e12 | 0.816835 | ||||||||
\(178\) | 7.58711e12 | 3.18249 | ||||||||
\(179\) | −1.68681e12 | −0.686081 | −0.343041 | − | 0.939321i | \(-0.611457\pi\) | ||||
−0.343041 | + | 0.939321i | \(0.611457\pi\) | |||||||
\(180\) | 3.08947e13 | 12.1867 | ||||||||
\(181\) | −1.70026e12 | −0.650555 | −0.325278 | − | 0.945619i | \(-0.605458\pi\) | ||||
−0.325278 | + | 0.945619i | \(0.605458\pi\) | |||||||
\(182\) | 7.57413e12 | 2.81151 | ||||||||
\(183\) | −4.60874e12 | −1.65997 | ||||||||
\(184\) | 1.70261e13 | 5.95138 | ||||||||
\(185\) | −2.83549e12 | −0.962019 | ||||||||
\(186\) | −1.14347e13 | −3.76620 | ||||||||
\(187\) | 7.75669e11 | 0.248055 | ||||||||
\(188\) | 1.25053e13 | 3.88354 | ||||||||
\(189\) | −1.09629e13 | −3.30662 | ||||||||
\(190\) | 1.24658e12 | 0.365237 | ||||||||
\(191\) | 2.77001e12 | 0.788493 | 0.394246 | − | 0.919005i | \(-0.371006\pi\) | ||||
0.394246 | + | 0.919005i | \(0.371006\pi\) | |||||||
\(192\) | 2.35305e13 | 6.50841 | ||||||||
\(193\) | 2.80210e11 | 0.0753214 | 0.0376607 | − | 0.999291i | \(-0.488009\pi\) | ||||
0.0376607 | + | 0.999291i | \(0.488009\pi\) | |||||||
\(194\) | −8.73162e12 | −2.28132 | ||||||||
\(195\) | 1.63292e13 | 4.14738 | ||||||||
\(196\) | 4.53496e12 | 1.11986 | ||||||||
\(197\) | −2.96709e11 | −0.0712470 | ||||||||
\(198\) | 9.35584e12 | 2.18486 | ||||||||
\(199\) | 2.56480e12 | 0.582588 | 0.291294 | − | 0.956634i | \(-0.405914\pi\) | ||||
0.291294 | + | 0.956634i | \(0.405914\pi\) | |||||||
\(200\) | −3.37739e13 | −7.46304 | ||||||||
\(201\) | 6.22606e12 | 1.33855 | ||||||||
\(202\) | −1.15430e13 | −2.41482 | ||||||||
\(203\) | −3.85943e12 | −0.785768 | ||||||||
\(204\) | −1.38894e13 | −2.75244 | ||||||||
\(205\) | −4.79237e12 | −0.924495 | ||||||||
\(206\) | −9.59619e12 | −1.80231 | ||||||||
\(207\) | −2.46264e13 | −4.50365 | ||||||||
\(208\) | 2.49992e13 | 4.45223 | ||||||||
\(209\) | 2.75695e11 | 0.0478217 | ||||||||
\(210\) | 4.57605e13 | 7.73187 | ||||||||
\(211\) | −6.35815e11 | −0.104659 | −0.0523295 | − | 0.998630i | \(-0.516665\pi\) | ||||
−0.0523295 | + | 0.998630i | \(0.516665\pi\) | |||||||
\(212\) | −3.10159e11 | −0.0497436 | ||||||||
\(213\) | 1.61329e13 | 2.52130 | ||||||||
\(214\) | −6.79873e12 | −1.03550 | ||||||||
\(215\) | 2.81110e12 | 0.417316 | ||||||||
\(216\) | −6.32118e13 | −9.14750 | ||||||||
\(217\) | −8.82398e12 | −1.24490 | ||||||||
\(218\) | 3.32272e12 | 0.457070 | ||||||||
\(219\) | 1.37447e13 | 1.84371 | ||||||||
\(220\) | −1.70618e13 | −2.23203 | ||||||||
\(221\) | −5.23705e12 | −0.668235 | ||||||||
\(222\) | 1.53757e13 | 1.91378 | ||||||||
\(223\) | 8.89651e12 | 1.08030 | 0.540148 | − | 0.841570i | \(-0.318368\pi\) | ||||
0.540148 | + | 0.841570i | \(0.318368\pi\) | |||||||
\(224\) | 3.70514e13 | 4.38976 | ||||||||
\(225\) | 4.88503e13 | 5.64759 | ||||||||
\(226\) | −1.80058e13 | −2.03150 | ||||||||
\(227\) | −7.22778e12 | −0.795908 | −0.397954 | − | 0.917405i | \(-0.630280\pi\) | ||||
−0.397954 | + | 0.917405i | \(0.630280\pi\) | |||||||
\(228\) | −4.93669e12 | −0.530633 | ||||||||
\(229\) | −5.30547e12 | −0.556709 | −0.278355 | − | 0.960478i | \(-0.589789\pi\) | ||||
−0.278355 | + | 0.960478i | \(0.589789\pi\) | |||||||
\(230\) | 6.14940e13 | 6.29984 | ||||||||
\(231\) | 1.01205e13 | 1.01236 | ||||||||
\(232\) | −2.22534e13 | −2.17377 | ||||||||
\(233\) | −9.75341e11 | −0.0930462 | −0.0465231 | − | 0.998917i | \(-0.514814\pi\) | ||||
−0.0465231 | + | 0.998917i | \(0.514814\pi\) | |||||||
\(234\) | −6.31674e13 | −5.88580 | ||||||||
\(235\) | 2.84876e13 | 2.59288 | ||||||||
\(236\) | 1.33186e13 | 1.18425 | ||||||||
\(237\) | 2.22373e13 | 1.93182 | ||||||||
\(238\) | −1.46762e13 | −1.24577 | ||||||||
\(239\) | −1.61817e13 | −1.34226 | −0.671129 | − | 0.741341i | \(-0.734190\pi\) | ||||
−0.671129 | + | 0.741341i | \(0.734190\pi\) | |||||||
\(240\) | 1.51037e14 | 12.2439 | ||||||||
\(241\) | 3.10447e10 | 0.00245976 | 0.00122988 | − | 0.999999i | \(-0.499609\pi\) | ||||
0.00122988 | + | 0.999999i | \(0.499609\pi\) | |||||||
\(242\) | 1.96964e13 | 1.52546 | ||||||||
\(243\) | 3.00244e13 | 2.27321 | ||||||||
\(244\) | −3.25127e13 | −2.40663 | ||||||||
\(245\) | 1.03308e13 | 0.747688 | ||||||||
\(246\) | 2.59871e13 | 1.83914 | ||||||||
\(247\) | −1.86140e12 | −0.128827 | ||||||||
\(248\) | −5.08790e13 | −3.44393 | ||||||||
\(249\) | 4.89745e13 | 3.24245 | ||||||||
\(250\) | −6.82234e13 | −4.41839 | ||||||||
\(251\) | −9.77956e12 | −0.619604 | −0.309802 | − | 0.950801i | \(-0.600263\pi\) | ||||
−0.309802 | + | 0.950801i | \(0.600263\pi\) | |||||||
\(252\) | −1.29279e14 | −8.01358 | ||||||||
\(253\) | 1.36001e13 | 0.824860 | ||||||||
\(254\) | 4.76498e13 | 2.82797 | ||||||||
\(255\) | −3.16405e13 | −1.83769 | ||||||||
\(256\) | 4.09200e13 | 2.32603 | ||||||||
\(257\) | −3.13864e13 | −1.74626 | −0.873132 | − | 0.487484i | \(-0.837915\pi\) | ||||
−0.873132 | + | 0.487484i | \(0.837915\pi\) | |||||||
\(258\) | −1.52434e13 | −0.830184 | ||||||||
\(259\) | 1.18652e13 | 0.632595 | ||||||||
\(260\) | 1.15195e14 | 6.01287 | ||||||||
\(261\) | 3.21872e13 | 1.64498 | ||||||||
\(262\) | 2.72825e13 | 1.36530 | ||||||||
\(263\) | 1.19615e13 | 0.586177 | 0.293089 | − | 0.956085i | \(-0.405317\pi\) | ||||
0.293089 | + | 0.956085i | \(0.405317\pi\) | |||||||
\(264\) | 5.83546e13 | 2.80061 | ||||||||
\(265\) | −7.06554e11 | −0.0332119 | ||||||||
\(266\) | −5.21633e12 | −0.240169 | ||||||||
\(267\) | −6.84470e13 | −3.08704 | ||||||||
\(268\) | 4.39221e13 | 1.94063 | ||||||||
\(269\) | −2.88848e13 | −1.25035 | −0.625175 | − | 0.780485i | \(-0.714972\pi\) | ||||
−0.625175 | + | 0.780485i | \(0.714972\pi\) | |||||||
\(270\) | −2.28305e14 | −9.68311 | ||||||||
\(271\) | −1.75361e13 | −0.728790 | −0.364395 | − | 0.931245i | \(-0.618724\pi\) | ||||
−0.364395 | + | 0.931245i | \(0.618724\pi\) | |||||||
\(272\) | −4.84401e13 | −1.97277 | ||||||||
\(273\) | −6.83299e13 | −2.72719 | ||||||||
\(274\) | −4.88396e13 | −1.91049 | ||||||||
\(275\) | −2.69779e13 | −1.03438 | ||||||||
\(276\) | −2.43528e14 | −9.15271 | ||||||||
\(277\) | −4.89346e13 | −1.80292 | −0.901462 | − | 0.432859i | \(-0.857505\pi\) | ||||
−0.901462 | + | 0.432859i | \(0.857505\pi\) | |||||||
\(278\) | −3.13701e13 | −1.13310 | ||||||||
\(279\) | 7.35909e13 | 2.60616 | ||||||||
\(280\) | 2.03612e14 | 7.07026 | ||||||||
\(281\) | −6.93651e12 | −0.236187 | −0.118094 | − | 0.993002i | \(-0.537678\pi\) | ||||
−0.118094 | + | 0.993002i | \(0.537678\pi\) | |||||||
\(282\) | −1.54477e14 | −5.15813 | ||||||||
\(283\) | 5.95228e13 | 1.94921 | 0.974604 | − | 0.223935i | \(-0.0718905\pi\) | ||||
0.974604 | + | 0.223935i | \(0.0718905\pi\) | |||||||
\(284\) | 1.13811e14 | 3.65538 | ||||||||
\(285\) | −1.12460e13 | −0.354283 | ||||||||
\(286\) | 3.48847e13 | 1.07801 | ||||||||
\(287\) | 2.00538e13 | 0.607920 | ||||||||
\(288\) | −3.09004e14 | −9.18979 | ||||||||
\(289\) | −2.41242e13 | −0.703907 | ||||||||
\(290\) | −8.03737e13 | −2.30104 | ||||||||
\(291\) | 7.87721e13 | 2.21290 | ||||||||
\(292\) | 9.69627e13 | 2.67300 | ||||||||
\(293\) | 4.44871e12 | 0.120355 | 0.0601773 | − | 0.998188i | \(-0.480833\pi\) | ||||
0.0601773 | + | 0.998188i | \(0.480833\pi\) | |||||||
\(294\) | −5.60196e13 | −1.48741 | ||||||||
\(295\) | 3.03402e13 | 0.790673 | ||||||||
\(296\) | 6.84145e13 | 1.75002 | ||||||||
\(297\) | −5.04924e13 | −1.26784 | ||||||||
\(298\) | 1.15616e14 | 2.84989 | ||||||||
\(299\) | −9.18233e13 | −2.22209 | ||||||||
\(300\) | 4.83076e14 | 11.4775 | ||||||||
\(301\) | −1.17631e13 | −0.274414 | ||||||||
\(302\) | −1.34576e14 | −3.08269 | ||||||||
\(303\) | 1.04134e14 | 2.34239 | ||||||||
\(304\) | −1.72170e13 | −0.380324 | ||||||||
\(305\) | −7.40651e13 | −1.60681 | ||||||||
\(306\) | 1.22397e14 | 2.60798 | ||||||||
\(307\) | 4.35234e13 | 0.910881 | 0.455441 | − | 0.890266i | \(-0.349482\pi\) | ||||
0.455441 | + | 0.890266i | \(0.349482\pi\) | |||||||
\(308\) | 7.13956e13 | 1.46772 | ||||||||
\(309\) | 8.65718e13 | 1.74825 | ||||||||
\(310\) | −1.83762e14 | −3.64558 | ||||||||
\(311\) | 5.89792e12 | 0.114952 | 0.0574761 | − | 0.998347i | \(-0.481695\pi\) | ||||
0.0574761 | + | 0.998347i | \(0.481695\pi\) | |||||||
\(312\) | −3.93990e14 | −7.54457 | ||||||||
\(313\) | 3.03098e13 | 0.570281 | 0.285141 | − | 0.958486i | \(-0.407960\pi\) | ||||
0.285141 | + | 0.958486i | \(0.407960\pi\) | |||||||
\(314\) | −1.34221e14 | −2.48147 | ||||||||
\(315\) | −2.94503e14 | −5.35035 | ||||||||
\(316\) | 1.56875e14 | 2.80075 | ||||||||
\(317\) | −8.45658e12 | −0.148378 | −0.0741889 | − | 0.997244i | \(-0.523637\pi\) | ||||
−0.0741889 | + | 0.997244i | \(0.523637\pi\) | |||||||
\(318\) | 3.83135e12 | 0.0660697 | ||||||||
\(319\) | −1.77756e13 | −0.301284 | ||||||||
\(320\) | 3.78149e14 | 6.29996 | ||||||||
\(321\) | 6.13346e13 | 1.00445 | ||||||||
\(322\) | −2.57323e14 | −4.14259 | ||||||||
\(323\) | 3.60677e12 | 0.0570827 | ||||||||
\(324\) | 4.70951e14 | 7.32787 | ||||||||
\(325\) | 1.82146e14 | 2.78651 | ||||||||
\(326\) | 2.52133e13 | 0.379257 | ||||||||
\(327\) | −2.99758e13 | −0.443362 | ||||||||
\(328\) | 1.15630e14 | 1.68176 | ||||||||
\(329\) | −1.19207e14 | −1.70500 | ||||||||
\(330\) | 2.10762e14 | 2.96460 | ||||||||
\(331\) | −1.08434e14 | −1.50007 | −0.750037 | − | 0.661396i | \(-0.769964\pi\) | ||||
−0.750037 | + | 0.661396i | \(0.769964\pi\) | |||||||
\(332\) | 3.45494e14 | 4.70090 | ||||||||
\(333\) | −9.89541e13 | −1.32431 | ||||||||
\(334\) | 2.37316e13 | 0.312408 | ||||||||
\(335\) | 1.00056e14 | 1.29568 | ||||||||
\(336\) | −6.32018e14 | −8.05125 | ||||||||
\(337\) | 1.08104e14 | 1.35480 | 0.677401 | − | 0.735613i | \(-0.263106\pi\) | ||||
0.677401 | + | 0.735613i | \(0.263106\pi\) | |||||||
\(338\) | −7.93531e13 | −0.978412 | ||||||||
\(339\) | 1.62439e14 | 1.97057 | ||||||||
\(340\) | −2.23210e14 | −2.66428 | ||||||||
\(341\) | −4.06412e13 | −0.477328 | ||||||||
\(342\) | 4.35036e13 | 0.502784 | ||||||||
\(343\) | 6.13077e13 | 0.697264 | ||||||||
\(344\) | −6.78261e13 | −0.759146 | ||||||||
\(345\) | −5.54767e14 | −6.11090 | ||||||||
\(346\) | 7.80456e13 | 0.846116 | ||||||||
\(347\) | −6.13520e13 | −0.654661 | −0.327331 | − | 0.944910i | \(-0.606149\pi\) | ||||
−0.327331 | + | 0.944910i | \(0.606149\pi\) | |||||||
\(348\) | 3.18296e14 | 3.34307 | ||||||||
\(349\) | −6.29685e13 | −0.651004 | −0.325502 | − | 0.945541i | \(-0.605533\pi\) | ||||
−0.325502 | + | 0.945541i | \(0.605533\pi\) | |||||||
\(350\) | 5.10440e14 | 5.19482 | ||||||||
\(351\) | 3.40907e14 | 3.41544 | ||||||||
\(352\) | 1.70650e14 | 1.68314 | ||||||||
\(353\) | 3.83303e13 | 0.372204 | 0.186102 | − | 0.982530i | \(-0.440415\pi\) | ||||
0.186102 | + | 0.982530i | \(0.440415\pi\) | |||||||
\(354\) | −1.64522e14 | −1.57292 | ||||||||
\(355\) | 2.59265e14 | 2.44055 | ||||||||
\(356\) | −4.82864e14 | −4.47558 | ||||||||
\(357\) | 1.32401e14 | 1.20841 | ||||||||
\(358\) | 1.46996e14 | 1.32114 | ||||||||
\(359\) | 1.77156e14 | 1.56796 | 0.783982 | − | 0.620784i | \(-0.213186\pi\) | ||||
0.783982 | + | 0.620784i | \(0.213186\pi\) | |||||||
\(360\) | −1.69810e15 | −14.8013 | ||||||||
\(361\) | −1.15208e14 | −0.988995 | ||||||||
\(362\) | 1.48168e14 | 1.25273 | ||||||||
\(363\) | −1.77690e14 | −1.47971 | ||||||||
\(364\) | −4.82038e14 | −3.95388 | ||||||||
\(365\) | 2.20884e14 | 1.78466 | ||||||||
\(366\) | 4.01624e14 | 3.19649 | ||||||||
\(367\) | −5.67164e13 | −0.444677 | −0.222339 | − | 0.974969i | \(-0.571369\pi\) | ||||
−0.222339 | + | 0.974969i | \(0.571369\pi\) | |||||||
\(368\) | −8.49321e14 | −6.56007 | ||||||||
\(369\) | −1.67246e14 | −1.27266 | ||||||||
\(370\) | 2.47096e14 | 1.85249 | ||||||||
\(371\) | 2.95659e12 | 0.0218391 | ||||||||
\(372\) | 7.27734e14 | 5.29647 | ||||||||
\(373\) | 1.04076e14 | 0.746363 | 0.373182 | − | 0.927758i | \(-0.378267\pi\) | ||||
0.373182 | + | 0.927758i | \(0.378267\pi\) | |||||||
\(374\) | −6.75949e13 | −0.477661 | ||||||||
\(375\) | 6.15476e14 | 4.28587 | ||||||||
\(376\) | −6.87347e14 | −4.71675 | ||||||||
\(377\) | 1.20015e14 | 0.811628 | ||||||||
\(378\) | 9.55348e14 | 6.36732 | ||||||||
\(379\) | −9.10659e12 | −0.0598191 | −0.0299096 | − | 0.999553i | \(-0.509522\pi\) | ||||
−0.0299096 | + | 0.999553i | \(0.509522\pi\) | |||||||
\(380\) | −7.93354e13 | −0.513638 | ||||||||
\(381\) | −4.29871e14 | −2.74316 | ||||||||
\(382\) | −2.41390e14 | −1.51834 | ||||||||
\(383\) | 4.60884e13 | 0.285758 | 0.142879 | − | 0.989740i | \(-0.454364\pi\) | ||||
0.142879 | + | 0.989740i | \(0.454364\pi\) | |||||||
\(384\) | −9.22157e14 | −5.63616 | ||||||||
\(385\) | 1.62642e14 | 0.979936 | ||||||||
\(386\) | −2.44186e13 | −0.145041 | ||||||||
\(387\) | 9.81030e13 | 0.574476 | ||||||||
\(388\) | 5.55703e14 | 3.20825 | ||||||||
\(389\) | −2.14867e14 | −1.22306 | −0.611530 | − | 0.791221i | \(-0.709446\pi\) | ||||
−0.611530 | + | 0.791221i | \(0.709446\pi\) | |||||||
\(390\) | −1.42299e15 | −7.98632 | ||||||||
\(391\) | 1.77923e14 | 0.984600 | ||||||||
\(392\) | −2.49261e14 | −1.36013 | ||||||||
\(393\) | −2.46129e14 | −1.32435 | ||||||||
\(394\) | 2.58564e13 | 0.137195 | ||||||||
\(395\) | 3.57366e14 | 1.86995 | ||||||||
\(396\) | −5.95431e14 | −3.07261 | ||||||||
\(397\) | −1.39664e14 | −0.710783 | −0.355392 | − | 0.934717i | \(-0.615653\pi\) | ||||
−0.355392 | + | 0.934717i | \(0.615653\pi\) | |||||||
\(398\) | −2.23507e14 | −1.12185 | ||||||||
\(399\) | 4.70590e13 | 0.232966 | ||||||||
\(400\) | 1.68476e15 | 8.22635 | ||||||||
\(401\) | −3.58063e14 | −1.72451 | −0.862255 | − | 0.506474i | \(-0.830949\pi\) | ||||
−0.862255 | + | 0.506474i | \(0.830949\pi\) | |||||||
\(402\) | −5.42563e14 | −2.57755 | ||||||||
\(403\) | 2.74395e14 | 1.28587 | ||||||||
\(404\) | 7.34624e14 | 3.39600 | ||||||||
\(405\) | 1.07284e15 | 4.89253 | ||||||||
\(406\) | 3.36326e14 | 1.51310 | ||||||||
\(407\) | 5.46482e13 | 0.242553 | ||||||||
\(408\) | 7.63421e14 | 3.34297 | ||||||||
\(409\) | 1.52082e14 | 0.657050 | 0.328525 | − | 0.944495i | \(-0.393449\pi\) | ||||
0.328525 | + | 0.944495i | \(0.393449\pi\) | |||||||
\(410\) | 4.17627e14 | 1.78023 | ||||||||
\(411\) | 4.40605e14 | 1.85319 | ||||||||
\(412\) | 6.10727e14 | 2.53462 | ||||||||
\(413\) | −1.26959e14 | −0.519923 | ||||||||
\(414\) | 2.14604e15 | 8.67235 | ||||||||
\(415\) | 7.87048e14 | 3.13860 | ||||||||
\(416\) | −1.15217e15 | −4.53422 | ||||||||
\(417\) | 2.83004e14 | 1.09912 | ||||||||
\(418\) | −2.40252e13 | −0.0920868 | ||||||||
\(419\) | −2.33547e14 | −0.883480 | −0.441740 | − | 0.897143i | \(-0.645639\pi\) | ||||
−0.441740 | + | 0.897143i | \(0.645639\pi\) | |||||||
\(420\) | −2.91232e15 | −10.8735 | ||||||||
\(421\) | 8.00503e13 | 0.294993 | 0.147496 | − | 0.989063i | \(-0.452879\pi\) | ||||
0.147496 | + | 0.989063i | \(0.452879\pi\) | |||||||
\(422\) | 5.54074e13 | 0.201534 | ||||||||
\(423\) | 9.94173e14 | 3.56936 | ||||||||
\(424\) | 1.70477e13 | 0.0604162 | ||||||||
\(425\) | −3.52937e14 | −1.23469 | ||||||||
\(426\) | −1.40589e15 | −4.85509 | ||||||||
\(427\) | 3.09927e14 | 1.05659 | ||||||||
\(428\) | 4.32689e14 | 1.45625 | ||||||||
\(429\) | −3.14711e14 | −1.04568 | ||||||||
\(430\) | −2.44971e14 | −0.803595 | ||||||||
\(431\) | 3.50083e14 | 1.13383 | 0.566913 | − | 0.823777i | \(-0.308137\pi\) | ||||
0.566913 | + | 0.823777i | \(0.308137\pi\) | |||||||
\(432\) | 3.15322e15 | 10.0831 | ||||||||
\(433\) | −1.57619e14 | −0.497651 | −0.248826 | − | 0.968548i | \(-0.580045\pi\) | ||||
−0.248826 | + | 0.968548i | \(0.580045\pi\) | |||||||
\(434\) | 7.68957e14 | 2.39722 | ||||||||
\(435\) | 7.25090e14 | 2.23203 | ||||||||
\(436\) | −2.11466e14 | −0.642785 | ||||||||
\(437\) | 6.32390e13 | 0.189818 | ||||||||
\(438\) | −1.19776e15 | −3.55029 | ||||||||
\(439\) | −5.00298e14 | −1.46445 | −0.732225 | − | 0.681063i | \(-0.761518\pi\) | ||||
−0.732225 | + | 0.681063i | \(0.761518\pi\) | |||||||
\(440\) | 9.37791e14 | 2.71092 | ||||||||
\(441\) | 3.60529e14 | 1.02927 | ||||||||
\(442\) | 4.56377e14 | 1.28677 | ||||||||
\(443\) | 2.78354e14 | 0.775133 | 0.387567 | − | 0.921842i | \(-0.373316\pi\) | ||||
0.387567 | + | 0.921842i | \(0.373316\pi\) | |||||||
\(444\) | −9.78549e14 | −2.69139 | ||||||||
\(445\) | −1.09998e15 | −2.98817 | ||||||||
\(446\) | −7.75277e14 | −2.08025 | ||||||||
\(447\) | −1.04303e15 | −2.76442 | ||||||||
\(448\) | −1.58237e15 | −4.14266 | ||||||||
\(449\) | −4.73886e14 | −1.22552 | −0.612758 | − | 0.790270i | \(-0.709940\pi\) | ||||
−0.612758 | + | 0.790270i | \(0.709940\pi\) | |||||||
\(450\) | −4.25701e15 | −10.8752 | ||||||||
\(451\) | 9.23631e13 | 0.233092 | ||||||||
\(452\) | 1.14594e15 | 2.85693 | ||||||||
\(453\) | 1.21408e15 | 2.99024 | ||||||||
\(454\) | 6.29857e14 | 1.53262 | ||||||||
\(455\) | −1.09810e15 | −2.63985 | ||||||||
\(456\) | 2.71342e14 | 0.644481 | ||||||||
\(457\) | −4.20915e14 | −0.987769 | −0.493884 | − | 0.869528i | \(-0.664423\pi\) | ||||
−0.493884 | + | 0.869528i | \(0.664423\pi\) | |||||||
\(458\) | 4.62339e14 | 1.07201 | ||||||||
\(459\) | −6.60564e14 | −1.51337 | ||||||||
\(460\) | −3.91364e15 | −8.85957 | ||||||||
\(461\) | 5.26897e14 | 1.17861 | 0.589306 | − | 0.807910i | \(-0.299401\pi\) | ||||
0.589306 | + | 0.807910i | \(0.299401\pi\) | |||||||
\(462\) | −8.81938e14 | −1.94943 | ||||||||
\(463\) | 4.35851e14 | 0.952012 | 0.476006 | − | 0.879442i | \(-0.342084\pi\) | ||||
0.476006 | + | 0.879442i | \(0.342084\pi\) | |||||||
\(464\) | 1.11008e15 | 2.39610 | ||||||||
\(465\) | 1.65781e15 | 3.53624 | ||||||||
\(466\) | 8.49951e13 | 0.179172 | ||||||||
\(467\) | 3.98633e14 | 0.830483 | 0.415241 | − | 0.909711i | \(-0.363697\pi\) | ||||
0.415241 | + | 0.909711i | \(0.363697\pi\) | |||||||
\(468\) | 4.02014e15 | 8.27730 | ||||||||
\(469\) | −4.18688e14 | −0.852000 | ||||||||
\(470\) | −2.48253e15 | −4.99293 | ||||||||
\(471\) | 1.21088e15 | 2.40705 | ||||||||
\(472\) | −7.32046e14 | −1.43833 | ||||||||
\(473\) | −5.41781e13 | −0.105217 | ||||||||
\(474\) | −1.93785e15 | −3.71997 | ||||||||
\(475\) | −1.25444e14 | −0.238032 | ||||||||
\(476\) | 9.34029e14 | 1.75195 | ||||||||
\(477\) | −2.46576e13 | −0.0457194 | ||||||||
\(478\) | 1.41014e15 | 2.58469 | ||||||||
\(479\) | 1.15602e14 | 0.209468 | 0.104734 | − | 0.994500i | \(-0.466601\pi\) | ||||
0.104734 | + | 0.994500i | \(0.466601\pi\) | |||||||
\(480\) | −6.96103e15 | −12.4694 | ||||||||
\(481\) | −3.68965e14 | −0.653413 | ||||||||
\(482\) | −2.70536e12 | −0.00473659 | ||||||||
\(483\) | 2.32143e15 | 4.01834 | ||||||||
\(484\) | −1.25353e15 | −2.14528 | ||||||||
\(485\) | 1.26591e15 | 2.14202 | ||||||||
\(486\) | −2.61645e15 | −4.37737 | ||||||||
\(487\) | 4.03307e14 | 0.667155 | 0.333577 | − | 0.942723i | \(-0.391744\pi\) | ||||
0.333577 | + | 0.942723i | \(0.391744\pi\) | |||||||
\(488\) | 1.78704e15 | 2.92297 | ||||||||
\(489\) | −2.27461e14 | −0.367883 | ||||||||
\(490\) | −9.00267e14 | −1.43977 | ||||||||
\(491\) | 4.64426e14 | 0.734461 | 0.367230 | − | 0.930130i | \(-0.380306\pi\) | ||||
0.367230 | + | 0.930130i | \(0.380306\pi\) | |||||||
\(492\) | −1.65388e15 | −2.58641 | ||||||||
\(493\) | −2.32548e14 | −0.359630 | ||||||||
\(494\) | 1.62210e14 | 0.248072 | ||||||||
\(495\) | −1.35641e15 | −2.05146 | ||||||||
\(496\) | 2.53802e15 | 3.79617 | ||||||||
\(497\) | −1.08490e15 | −1.60483 | ||||||||
\(498\) | −4.26783e15 | −6.24376 | ||||||||
\(499\) | 3.73382e14 | 0.540257 | 0.270128 | − | 0.962824i | \(-0.412934\pi\) | ||||
0.270128 | + | 0.962824i | \(0.412934\pi\) | |||||||
\(500\) | 4.34192e15 | 6.21365 | ||||||||
\(501\) | −2.14094e14 | −0.303038 | ||||||||
\(502\) | 8.52230e14 | 1.19313 | ||||||||
\(503\) | −9.19697e14 | −1.27356 | −0.636782 | − | 0.771044i | \(-0.719735\pi\) | ||||
−0.636782 | + | 0.771044i | \(0.719735\pi\) | |||||||
\(504\) | 7.10575e15 | 9.73290 | ||||||||
\(505\) | 1.67350e15 | 2.26737 | ||||||||
\(506\) | −1.18517e15 | −1.58837 | ||||||||
\(507\) | 7.15882e14 | 0.949069 | ||||||||
\(508\) | −3.03256e15 | −3.97703 | ||||||||
\(509\) | −5.01368e14 | −0.650442 | −0.325221 | − | 0.945638i | \(-0.605439\pi\) | ||||
−0.325221 | + | 0.945638i | \(0.605439\pi\) | |||||||
\(510\) | 2.75728e15 | 3.53871 | ||||||||
\(511\) | −9.24296e14 | −1.17354 | ||||||||
\(512\) | −1.16367e15 | −1.46166 | ||||||||
\(513\) | −2.34784e14 | −0.291758 | ||||||||
\(514\) | 2.73514e15 | 3.36266 | ||||||||
\(515\) | 1.39126e15 | 1.69226 | ||||||||
\(516\) | 9.70132e14 | 1.16750 | ||||||||
\(517\) | −5.49040e14 | −0.653741 | ||||||||
\(518\) | −1.03398e15 | −1.21814 | ||||||||
\(519\) | −7.04086e14 | −0.820740 | ||||||||
\(520\) | −6.33163e15 | −7.30293 | ||||||||
\(521\) | −8.34015e14 | −0.951845 | −0.475922 | − | 0.879487i | \(-0.657886\pi\) | ||||
−0.475922 | + | 0.879487i | \(0.657886\pi\) | |||||||
\(522\) | −2.80492e15 | −3.16761 | ||||||||
\(523\) | −7.13094e14 | −0.796870 | −0.398435 | − | 0.917197i | \(-0.630447\pi\) | ||||
−0.398435 | + | 0.917197i | \(0.630447\pi\) | |||||||
\(524\) | −1.73633e15 | −1.92004 | ||||||||
\(525\) | −4.60492e15 | −5.03902 | ||||||||
\(526\) | −1.04237e15 | −1.12876 | ||||||||
\(527\) | −5.31686e14 | −0.569766 | ||||||||
\(528\) | −2.91092e15 | −3.08706 | ||||||||
\(529\) | 2.16679e15 | 2.27410 | ||||||||
\(530\) | 6.15719e13 | 0.0639537 | ||||||||
\(531\) | 1.05882e15 | 1.08844 | ||||||||
\(532\) | 3.31981e14 | 0.337753 | ||||||||
\(533\) | −6.23603e14 | −0.627926 | ||||||||
\(534\) | 5.96474e15 | 5.94449 | ||||||||
\(535\) | 9.85681e14 | 0.972279 | ||||||||
\(536\) | −2.41415e15 | −2.35699 | ||||||||
\(537\) | −1.32612e15 | −1.28152 | ||||||||
\(538\) | 2.51713e15 | 2.40771 | ||||||||
\(539\) | −1.99105e14 | −0.188514 | ||||||||
\(540\) | 1.45299e16 | 13.6175 | ||||||||
\(541\) | −1.58429e15 | −1.46977 | −0.734885 | − | 0.678192i | \(-0.762764\pi\) | ||||
−0.734885 | + | 0.678192i | \(0.762764\pi\) | |||||||
\(542\) | 1.52817e15 | 1.40338 | ||||||||
\(543\) | −1.33669e15 | −1.21516 | ||||||||
\(544\) | 2.23252e15 | 2.00910 | ||||||||
\(545\) | −4.81728e14 | −0.429162 | ||||||||
\(546\) | 5.95454e15 | 5.25156 | ||||||||
\(547\) | −2.40211e14 | −0.209731 | −0.104866 | − | 0.994486i | \(-0.533441\pi\) | ||||
−0.104866 | + | 0.994486i | \(0.533441\pi\) | |||||||
\(548\) | 3.10828e15 | 2.68675 | ||||||||
\(549\) | −2.58475e15 | −2.21193 | ||||||||
\(550\) | 2.35096e15 | 1.99182 | ||||||||
\(551\) | −8.26545e13 | −0.0693318 | ||||||||
\(552\) | 1.33854e16 | 11.1164 | ||||||||
\(553\) | −1.49541e15 | −1.22962 | ||||||||
\(554\) | 4.26435e15 | 3.47176 | ||||||||
\(555\) | −2.22917e15 | −1.79693 | ||||||||
\(556\) | 1.99647e15 | 1.59350 | ||||||||
\(557\) | 4.00785e14 | 0.316744 | 0.158372 | − | 0.987380i | \(-0.449375\pi\) | ||||
0.158372 | + | 0.987380i | \(0.449375\pi\) | |||||||
\(558\) | −6.41301e15 | −5.01850 | ||||||||
\(559\) | 3.65792e14 | 0.283445 | ||||||||
\(560\) | −1.01569e16 | −7.79339 | ||||||||
\(561\) | 6.09806e14 | 0.463336 | ||||||||
\(562\) | 6.04475e14 | 0.454809 | ||||||||
\(563\) | −1.30980e15 | −0.975906 | −0.487953 | − | 0.872870i | \(-0.662256\pi\) | ||||
−0.487953 | + | 0.872870i | \(0.662256\pi\) | |||||||
\(564\) | 9.83129e15 | 7.25397 | ||||||||
\(565\) | 2.61049e15 | 1.90746 | ||||||||
\(566\) | −5.18706e15 | −3.75345 | ||||||||
\(567\) | −4.48934e15 | −3.21718 | ||||||||
\(568\) | −6.25552e15 | −4.43964 | ||||||||
\(569\) | −9.61821e14 | −0.676047 | −0.338024 | − | 0.941138i | \(-0.609758\pi\) | ||||
−0.338024 | + | 0.941138i | \(0.609758\pi\) | |||||||
\(570\) | 9.80018e14 | 0.682217 | ||||||||
\(571\) | 2.05240e15 | 1.41503 | 0.707513 | − | 0.706700i | \(-0.249817\pi\) | ||||
0.707513 | + | 0.706700i | \(0.249817\pi\) | |||||||
\(572\) | −2.22015e15 | −1.51602 | ||||||||
\(573\) | 2.17769e15 | 1.47281 | ||||||||
\(574\) | −1.74757e15 | −1.17063 | ||||||||
\(575\) | −6.18820e15 | −4.10574 | ||||||||
\(576\) | 1.31968e16 | 8.67251 | ||||||||
\(577\) | 5.64715e14 | 0.367589 | 0.183794 | − | 0.982965i | \(-0.441162\pi\) | ||||
0.183794 | + | 0.982965i | \(0.441162\pi\) | |||||||
\(578\) | 2.10228e15 | 1.35546 | ||||||||
\(579\) | 2.20292e14 | 0.140691 | ||||||||
\(580\) | 5.11520e15 | 3.23600 | ||||||||
\(581\) | −3.29342e15 | −2.06385 | ||||||||
\(582\) | −6.86451e15 | −4.26121 | ||||||||
\(583\) | 1.36174e13 | 0.00837367 | ||||||||
\(584\) | −5.32949e15 | −3.24649 | ||||||||
\(585\) | 9.15802e15 | 5.52643 | ||||||||
\(586\) | −3.87679e14 | −0.231758 | ||||||||
\(587\) | 4.21382e14 | 0.249555 | 0.124778 | − | 0.992185i | \(-0.460178\pi\) | ||||
0.124778 | + | 0.992185i | \(0.460178\pi\) | |||||||
\(588\) | 3.56524e15 | 2.09177 | ||||||||
\(589\) | −1.88977e14 | −0.109843 | ||||||||
\(590\) | −2.64396e15 | −1.52254 | ||||||||
\(591\) | −2.33263e14 | −0.133081 | ||||||||
\(592\) | −3.41275e15 | −1.92901 | ||||||||
\(593\) | −4.78325e14 | −0.267869 | −0.133934 | − | 0.990990i | \(-0.542761\pi\) | ||||
−0.133934 | + | 0.990990i | \(0.542761\pi\) | |||||||
\(594\) | 4.40011e15 | 2.44139 | ||||||||
\(595\) | 2.12775e15 | 1.16971 | ||||||||
\(596\) | −7.35810e15 | −4.00785 | ||||||||
\(597\) | 2.01636e15 | 1.08820 | ||||||||
\(598\) | 8.00185e15 | 4.27892 | ||||||||
\(599\) | −5.93499e14 | −0.314465 | −0.157232 | − | 0.987562i | \(-0.550257\pi\) | ||||
−0.157232 | + | 0.987562i | \(0.550257\pi\) | |||||||
\(600\) | −2.65519e16 | −13.9400 | ||||||||
\(601\) | 3.22160e15 | 1.67596 | 0.837978 | − | 0.545704i | \(-0.183738\pi\) | ||||
0.837978 | + | 0.545704i | \(0.183738\pi\) | |||||||
\(602\) | 1.02509e15 | 0.528420 | ||||||||
\(603\) | 3.49180e15 | 1.78363 | ||||||||
\(604\) | 8.56478e15 | 4.33524 | ||||||||
\(605\) | −2.85558e15 | −1.43232 | ||||||||
\(606\) | −9.07469e15 | −4.51058 | ||||||||
\(607\) | −3.13500e15 | −1.54419 | −0.772093 | − | 0.635509i | \(-0.780790\pi\) | ||||
−0.772093 | + | 0.635509i | \(0.780790\pi\) | |||||||
\(608\) | 7.93502e14 | 0.387328 | ||||||||
\(609\) | −3.03415e15 | −1.46772 | ||||||||
\(610\) | 6.45432e15 | 3.09412 | ||||||||
\(611\) | 3.70692e15 | 1.76111 | ||||||||
\(612\) | −7.78969e15 | −3.66765 | ||||||||
\(613\) | 1.54585e15 | 0.721332 | 0.360666 | − | 0.932695i | \(-0.382549\pi\) | ||||
0.360666 | + | 0.932695i | \(0.382549\pi\) | |||||||
\(614\) | −3.79280e15 | −1.75402 | ||||||||
\(615\) | −3.76761e15 | −1.72684 | ||||||||
\(616\) | −3.92421e15 | −1.78262 | ||||||||
\(617\) | −1.75213e15 | −0.788855 | −0.394428 | − | 0.918927i | \(-0.629057\pi\) | ||||
−0.394428 | + | 0.918927i | \(0.629057\pi\) | |||||||
\(618\) | −7.54421e15 | −3.36649 | ||||||||
\(619\) | 4.13897e15 | 1.83060 | 0.915300 | − | 0.402773i | \(-0.131954\pi\) | ||||
0.915300 | + | 0.402773i | \(0.131954\pi\) | |||||||
\(620\) | 1.16951e16 | 5.12684 | ||||||||
\(621\) | −1.15819e16 | −5.03243 | ||||||||
\(622\) | −5.13969e14 | −0.221355 | ||||||||
\(623\) | 4.60290e15 | 1.96493 | ||||||||
\(624\) | 1.96535e16 | 8.31621 | ||||||||
\(625\) | 4.48120e15 | 1.87955 | ||||||||
\(626\) | −2.64131e15 | −1.09815 | ||||||||
\(627\) | 2.16743e14 | 0.0893250 | ||||||||
\(628\) | 8.54220e15 | 3.48973 | ||||||||
\(629\) | 7.14932e14 | 0.289525 | ||||||||
\(630\) | 2.56642e16 | 10.3028 | ||||||||
\(631\) | 1.34196e15 | 0.534046 | 0.267023 | − | 0.963690i | \(-0.413960\pi\) | ||||
0.267023 | + | 0.963690i | \(0.413960\pi\) | |||||||
\(632\) | −8.62251e15 | −3.40165 | ||||||||
\(633\) | −4.99857e14 | −0.195490 | ||||||||
\(634\) | 7.36940e14 | 0.285721 | ||||||||
\(635\) | −6.90827e15 | −2.65530 | ||||||||
\(636\) | −2.43837e14 | −0.0929150 | ||||||||
\(637\) | 1.34428e15 | 0.507837 | ||||||||
\(638\) | 1.54904e15 | 0.580160 | ||||||||
\(639\) | 9.04794e15 | 3.35966 | ||||||||
\(640\) | −1.48196e16 | −5.45565 | ||||||||
\(641\) | 2.56166e15 | 0.934978 | 0.467489 | − | 0.883999i | \(-0.345159\pi\) | ||||
0.467489 | + | 0.883999i | \(0.345159\pi\) | |||||||
\(642\) | −5.34494e15 | −1.93419 | ||||||||
\(643\) | 1.86299e15 | 0.668420 | 0.334210 | − | 0.942499i | \(-0.391531\pi\) | ||||
0.334210 | + | 0.942499i | \(0.391531\pi\) | |||||||
\(644\) | 1.63767e16 | 5.82579 | ||||||||
\(645\) | 2.21000e15 | 0.779495 | ||||||||
\(646\) | −3.14308e14 | −0.109920 | ||||||||
\(647\) | −2.31615e15 | −0.803144 | −0.401572 | − | 0.915827i | \(-0.631536\pi\) | ||||
−0.401572 | + | 0.915827i | \(0.631536\pi\) | |||||||
\(648\) | −2.58855e16 | −8.90007 | ||||||||
\(649\) | −5.84744e14 | −0.199352 | ||||||||
\(650\) | −1.58729e16 | −5.36577 | ||||||||
\(651\) | −6.93712e15 | −2.32533 | ||||||||
\(652\) | −1.60464e15 | −0.533355 | ||||||||
\(653\) | 3.45678e15 | 1.13933 | 0.569665 | − | 0.821877i | \(-0.307073\pi\) | ||||
0.569665 | + | 0.821877i | \(0.307073\pi\) | |||||||
\(654\) | 2.61221e15 | 0.853749 | ||||||||
\(655\) | −3.95542e15 | −1.28193 | ||||||||
\(656\) | −5.76802e15 | −1.85377 | ||||||||
\(657\) | 7.70852e15 | 2.45675 | ||||||||
\(658\) | 1.03882e16 | 3.28320 | ||||||||
\(659\) | −1.88198e15 | −0.589856 | −0.294928 | − | 0.955519i | \(-0.595296\pi\) | ||||
−0.294928 | + | 0.955519i | \(0.595296\pi\) | |||||||
\(660\) | −1.34134e16 | −4.16916 | ||||||||
\(661\) | 1.30744e15 | 0.403007 | 0.201504 | − | 0.979488i | \(-0.435417\pi\) | ||||
0.201504 | + | 0.979488i | \(0.435417\pi\) | |||||||
\(662\) | 9.44940e15 | 2.88858 | ||||||||
\(663\) | −4.11719e15 | −1.24818 | ||||||||
\(664\) | −1.89898e16 | −5.70948 | ||||||||
\(665\) | 7.56265e14 | 0.225504 | ||||||||
\(666\) | 8.62326e15 | 2.55013 | ||||||||
\(667\) | −4.07737e15 | −1.19588 | ||||||||
\(668\) | −1.51034e15 | −0.439344 | ||||||||
\(669\) | 6.99415e15 | 2.01786 | ||||||||
\(670\) | −8.71930e15 | −2.49500 | ||||||||
\(671\) | 1.42745e15 | 0.405123 | ||||||||
\(672\) | 2.91286e16 | 8.19952 | ||||||||
\(673\) | −4.80307e15 | −1.34102 | −0.670512 | − | 0.741899i | \(-0.733925\pi\) | ||||
−0.670512 | + | 0.741899i | \(0.733925\pi\) | |||||||
\(674\) | −9.42059e15 | −2.60885 | ||||||||
\(675\) | 2.29746e16 | 6.31068 | ||||||||
\(676\) | 5.05024e15 | 1.37596 | ||||||||
\(677\) | −6.54600e15 | −1.76904 | −0.884521 | − | 0.466500i | \(-0.845515\pi\) | ||||
−0.884521 | + | 0.466500i | \(0.845515\pi\) | |||||||
\(678\) | −1.41556e16 | −3.79459 | ||||||||
\(679\) | −5.29724e15 | −1.40853 | ||||||||
\(680\) | 1.22686e16 | 3.23591 | ||||||||
\(681\) | −5.68224e15 | −1.48666 | ||||||||
\(682\) | 3.54163e15 | 0.919156 | ||||||||
\(683\) | −3.91112e15 | −1.00690 | −0.503451 | − | 0.864024i | \(-0.667937\pi\) | ||||
−0.503451 | + | 0.864024i | \(0.667937\pi\) | |||||||
\(684\) | −2.76868e15 | −0.707073 | ||||||||
\(685\) | 7.08077e15 | 1.79383 | ||||||||
\(686\) | −5.34259e15 | −1.34267 | ||||||||
\(687\) | −4.17098e15 | −1.03986 | ||||||||
\(688\) | 3.38340e15 | 0.836790 | ||||||||
\(689\) | −9.19397e13 | −0.0225578 | ||||||||
\(690\) | 4.83446e16 | 11.7673 | ||||||||
\(691\) | 6.39806e14 | 0.154497 | 0.0772483 | − | 0.997012i | \(-0.475387\pi\) | ||||
0.0772483 | + | 0.997012i | \(0.475387\pi\) | |||||||
\(692\) | −4.96703e15 | −1.18991 | ||||||||
\(693\) | 5.67594e15 | 1.34898 | ||||||||
\(694\) | 5.34646e15 | 1.26063 | ||||||||
\(695\) | 4.54804e15 | 1.06392 | ||||||||
\(696\) | −1.74949e16 | −4.06033 | ||||||||
\(697\) | 1.20834e15 | 0.278232 | ||||||||
\(698\) | 5.48733e15 | 1.25359 | ||||||||
\(699\) | −7.66781e14 | −0.173799 | ||||||||
\(700\) | −3.24857e16 | −7.30556 | ||||||||
\(701\) | −6.15819e15 | −1.37405 | −0.687027 | − | 0.726631i | \(-0.741085\pi\) | ||||
−0.687027 | + | 0.726631i | \(0.741085\pi\) | |||||||
\(702\) | −2.97080e16 | −6.57687 | ||||||||
\(703\) | 2.54108e14 | 0.0558166 | ||||||||
\(704\) | −7.28803e15 | −1.58840 | ||||||||
\(705\) | 2.23960e16 | 4.84319 | ||||||||
\(706\) | −3.34025e15 | −0.716726 | ||||||||
\(707\) | −7.00280e15 | −1.49096 | ||||||||
\(708\) | 1.04706e16 | 2.21202 | ||||||||
\(709\) | 4.62591e15 | 0.969713 | 0.484857 | − | 0.874594i | \(-0.338872\pi\) | ||||
0.484857 | + | 0.874594i | \(0.338872\pi\) | |||||||
\(710\) | −2.25934e16 | −4.69959 | ||||||||
\(711\) | 1.24715e16 | 2.57417 | ||||||||
\(712\) | 2.65403e16 | 5.43582 | ||||||||
\(713\) | −9.32227e15 | −1.89465 | ||||||||
\(714\) | −1.15379e16 | −2.32695 | ||||||||
\(715\) | −5.05759e15 | −1.01219 | ||||||||
\(716\) | −9.35520e15 | −1.85794 | ||||||||
\(717\) | −1.27215e16 | −2.50717 | ||||||||
\(718\) | −1.54381e16 | −3.01931 | ||||||||
\(719\) | −2.95761e14 | −0.0574027 | −0.0287013 | − | 0.999588i | \(-0.509137\pi\) | ||||
−0.0287013 | + | 0.999588i | \(0.509137\pi\) | |||||||
\(720\) | 8.47072e16 | 16.3152 | ||||||||
\(721\) | −5.82175e15 | −1.11278 | ||||||||
\(722\) | 1.00397e16 | 1.90444 | ||||||||
\(723\) | 2.44063e13 | 0.00459453 | ||||||||
\(724\) | −9.42978e15 | −1.76173 | ||||||||
\(725\) | 8.08808e15 | 1.49964 | ||||||||
\(726\) | 1.54846e16 | 2.84937 | ||||||||
\(727\) | −6.30502e15 | −1.15146 | −0.575728 | − | 0.817642i | \(-0.695281\pi\) | ||||
−0.575728 | + | 0.817642i | \(0.695281\pi\) | |||||||
\(728\) | 2.64949e16 | 4.80219 | ||||||||
\(729\) | 8.56161e15 | 1.54012 | ||||||||
\(730\) | −1.92488e16 | −3.43658 | ||||||||
\(731\) | −7.08783e14 | −0.125594 | ||||||||
\(732\) | −2.55604e16 | −4.49528 | ||||||||
\(733\) | 5.25600e15 | 0.917452 | 0.458726 | − | 0.888578i | \(-0.348306\pi\) | ||||
0.458726 | + | 0.888578i | \(0.348306\pi\) | |||||||
\(734\) | 4.94249e15 | 0.856283 | ||||||||
\(735\) | 8.12174e15 | 1.39659 | ||||||||
\(736\) | 3.91437e16 | 6.68088 | ||||||||
\(737\) | −1.92838e15 | −0.326678 | ||||||||
\(738\) | 1.45745e16 | 2.45067 | ||||||||
\(739\) | −9.12100e15 | −1.52229 | −0.761146 | − | 0.648580i | \(-0.775363\pi\) | ||||
−0.761146 | + | 0.648580i | \(0.775363\pi\) | |||||||
\(740\) | −1.57258e16 | −2.60519 | ||||||||
\(741\) | −1.46337e15 | −0.240632 | ||||||||
\(742\) | −2.57649e14 | −0.0420540 | ||||||||
\(743\) | −2.18359e15 | −0.353780 | −0.176890 | − | 0.984231i | \(-0.556604\pi\) | ||||
−0.176890 | + | 0.984231i | \(0.556604\pi\) | |||||||
\(744\) | −3.99994e16 | −6.43283 | ||||||||
\(745\) | −1.67620e16 | −2.67588 | ||||||||
\(746\) | −9.06956e15 | −1.43722 | ||||||||
\(747\) | 2.74667e16 | 4.32060 | ||||||||
\(748\) | 4.30192e15 | 0.671743 | ||||||||
\(749\) | −4.12461e15 | −0.639341 | ||||||||
\(750\) | −5.36350e16 | −8.25300 | ||||||||
\(751\) | 1.00530e16 | 1.53560 | 0.767798 | − | 0.640692i | \(-0.221353\pi\) | ||||
0.767798 | + | 0.640692i | \(0.221353\pi\) | |||||||
\(752\) | 3.42872e16 | 5.19917 | ||||||||
\(753\) | −7.68837e15 | −1.15734 | ||||||||
\(754\) | −1.04586e16 | −1.56289 | ||||||||
\(755\) | 1.95109e16 | 2.89447 | ||||||||
\(756\) | −6.08009e16 | −8.95447 | ||||||||
\(757\) | 4.05739e15 | 0.593225 | 0.296613 | − | 0.954998i | \(-0.404143\pi\) | ||||
0.296613 | + | 0.954998i | \(0.404143\pi\) | |||||||
\(758\) | 7.93584e14 | 0.115189 | ||||||||
\(759\) | 1.06920e16 | 1.54074 | ||||||||
\(760\) | 4.36062e15 | 0.623840 | ||||||||
\(761\) | −2.25831e15 | −0.320751 | −0.160375 | − | 0.987056i | \(-0.551270\pi\) | ||||
−0.160375 | + | 0.987056i | \(0.551270\pi\) | |||||||
\(762\) | 3.74607e16 | 5.28230 | ||||||||
\(763\) | 2.01580e15 | 0.282204 | ||||||||
\(764\) | 1.53627e16 | 2.13527 | ||||||||
\(765\) | −1.77452e16 | −2.44874 | ||||||||
\(766\) | −4.01633e15 | −0.550264 | ||||||||
\(767\) | 3.94799e15 | 0.537033 | ||||||||
\(768\) | 3.21699e16 | 4.34474 | ||||||||
\(769\) | −3.92462e15 | −0.526263 | −0.263131 | − | 0.964760i | \(-0.584755\pi\) | ||||
−0.263131 | + | 0.964760i | \(0.584755\pi\) | |||||||
\(770\) | −1.41732e16 | −1.88699 | ||||||||
\(771\) | −2.46750e16 | −3.26181 | ||||||||
\(772\) | 1.55406e15 | 0.203974 | ||||||||
\(773\) | −5.34422e15 | −0.696462 | −0.348231 | − | 0.937409i | \(-0.613218\pi\) | ||||
−0.348231 | + | 0.937409i | \(0.613218\pi\) | |||||||
\(774\) | −8.54909e15 | −1.10623 | ||||||||
\(775\) | 1.84921e16 | 2.37590 | ||||||||
\(776\) | −3.05438e16 | −3.89658 | ||||||||
\(777\) | 9.32801e15 | 1.18161 | ||||||||
\(778\) | 1.87244e16 | 2.35516 | ||||||||
\(779\) | 4.29477e14 | 0.0536395 | ||||||||
\(780\) | 9.05629e16 | 11.2313 | ||||||||
\(781\) | −4.99679e15 | −0.615334 | ||||||||
\(782\) | −1.55049e16 | −1.89597 | ||||||||
\(783\) | 1.51378e16 | 1.83812 | ||||||||
\(784\) | 1.24340e16 | 1.49924 | ||||||||
\(785\) | 1.94594e16 | 2.32995 | ||||||||
\(786\) | 2.14486e16 | 2.55021 | ||||||||
\(787\) | 9.57063e15 | 1.13000 | 0.565002 | − | 0.825090i | \(-0.308876\pi\) | ||||
0.565002 | + | 0.825090i | \(0.308876\pi\) | |||||||
\(788\) | −1.64557e15 | −0.192940 | ||||||||
\(789\) | 9.40374e15 | 1.09491 | ||||||||
\(790\) | −3.11423e16 | −3.60083 | ||||||||
\(791\) | −1.09236e16 | −1.25429 | ||||||||
\(792\) | 3.27274e16 | 3.73184 | ||||||||
\(793\) | −9.63764e15 | −1.09136 | ||||||||
\(794\) | 1.21709e16 | 1.36870 | ||||||||
\(795\) | −5.55470e14 | −0.0620356 | ||||||||
\(796\) | 1.42246e16 | 1.57767 | ||||||||
\(797\) | 2.69107e15 | 0.296418 | 0.148209 | − | 0.988956i | \(-0.452649\pi\) | ||||
0.148209 | + | 0.988956i | \(0.452649\pi\) | |||||||
\(798\) | −4.10091e15 | −0.448605 | ||||||||
\(799\) | −7.18279e15 | −0.780343 | ||||||||
\(800\) | −7.76475e16 | −8.37785 | ||||||||
\(801\) | −3.83876e16 | −4.11351 | ||||||||
\(802\) | 3.12031e16 | 3.32077 | ||||||||
\(803\) | −4.25709e15 | −0.449964 | ||||||||
\(804\) | 3.45302e16 | 3.62485 | ||||||||
\(805\) | 3.73068e16 | 3.88965 | ||||||||
\(806\) | −2.39119e16 | −2.47611 | ||||||||
\(807\) | −2.27083e16 | −2.33550 | ||||||||
\(808\) | −4.03781e16 | −4.12461 | ||||||||
\(809\) | −1.22996e16 | −1.24788 | −0.623942 | − | 0.781471i | \(-0.714470\pi\) | ||||
−0.623942 | + | 0.781471i | \(0.714470\pi\) | |||||||
\(810\) | −9.34918e16 | −9.42119 | ||||||||
\(811\) | 1.42153e16 | 1.42279 | 0.711395 | − | 0.702792i | \(-0.248064\pi\) | ||||
0.711395 | + | 0.702792i | \(0.248064\pi\) | |||||||
\(812\) | −2.14047e16 | −2.12789 | ||||||||
\(813\) | −1.37863e16 | −1.36129 | ||||||||
\(814\) | −4.76226e15 | −0.467067 | ||||||||
\(815\) | −3.65543e15 | −0.356100 | ||||||||
\(816\) | −3.80820e16 | −3.68489 | ||||||||
\(817\) | −2.51922e14 | −0.0242128 | ||||||||
\(818\) | −1.32530e16 | −1.26523 | ||||||||
\(819\) | −3.83219e16 | −3.63401 | ||||||||
\(820\) | −2.65789e16 | −2.50357 | ||||||||
\(821\) | 1.42313e16 | 1.33155 | 0.665773 | − | 0.746154i | \(-0.268102\pi\) | ||||
0.665773 | + | 0.746154i | \(0.268102\pi\) | |||||||
\(822\) | −3.83961e16 | −3.56855 | ||||||||
\(823\) | −3.08929e15 | −0.285206 | −0.142603 | − | 0.989780i | \(-0.545547\pi\) | ||||
−0.142603 | + | 0.989780i | \(0.545547\pi\) | |||||||
\(824\) | −3.35682e16 | −3.07842 | ||||||||
\(825\) | −2.12092e16 | −1.93209 | ||||||||
\(826\) | 1.10637e16 | 1.00118 | ||||||||
\(827\) | 1.91274e16 | 1.71940 | 0.859698 | − | 0.510802i | \(-0.170652\pi\) | ||||
0.859698 | + | 0.510802i | \(0.170652\pi\) | |||||||
\(828\) | −1.36580e17 | −12.1961 | ||||||||
\(829\) | 2.34185e15 | 0.207735 | 0.103867 | − | 0.994591i | \(-0.466878\pi\) | ||||
0.103867 | + | 0.994591i | \(0.466878\pi\) | |||||||
\(830\) | −6.85865e16 | −6.04378 | ||||||||
\(831\) | −3.84708e16 | −3.36764 | ||||||||
\(832\) | 4.92062e16 | 4.27899 | ||||||||
\(833\) | −2.60478e15 | −0.225021 | ||||||||
\(834\) | −2.46621e16 | −2.11649 | ||||||||
\(835\) | −3.44061e15 | −0.293332 | ||||||||
\(836\) | 1.52903e15 | 0.129503 | ||||||||
\(837\) | 3.46102e16 | 2.91216 | ||||||||
\(838\) | 2.03522e16 | 1.70125 | ||||||||
\(839\) | 2.07683e16 | 1.72468 | 0.862342 | − | 0.506326i | \(-0.168997\pi\) | ||||
0.862342 | + | 0.506326i | \(0.168997\pi\) | |||||||
\(840\) | 1.60073e17 | 13.2064 | ||||||||
\(841\) | −6.87132e15 | −0.563199 | ||||||||
\(842\) | −6.97590e15 | −0.568047 | ||||||||
\(843\) | −5.45326e15 | −0.441168 | ||||||||
\(844\) | −3.52627e15 | −0.283421 | ||||||||
\(845\) | 1.15046e16 | 0.918672 | ||||||||
\(846\) | −8.66362e16 | −6.87326 | ||||||||
\(847\) | 1.19492e16 | 0.941850 | ||||||||
\(848\) | −8.50397e14 | −0.0665954 | ||||||||
\(849\) | 4.67949e16 | 3.64088 | ||||||||
\(850\) | 3.07564e16 | 2.37756 | ||||||||
\(851\) | 1.25352e16 | 0.962762 | ||||||||
\(852\) | 8.94742e16 | 6.82779 | ||||||||
\(853\) | −1.94025e16 | −1.47108 | −0.735541 | − | 0.677480i | \(-0.763072\pi\) | ||||
−0.735541 | + | 0.677480i | \(0.763072\pi\) | |||||||
\(854\) | −2.70083e16 | −2.03460 | ||||||||
\(855\) | −6.30716e15 | −0.472085 | ||||||||
\(856\) | −2.37825e16 | −1.76869 | ||||||||
\(857\) | 3.13237e15 | 0.231462 | 0.115731 | − | 0.993281i | \(-0.463079\pi\) | ||||
0.115731 | + | 0.993281i | \(0.463079\pi\) | |||||||
\(858\) | 2.74252e16 | 2.01358 | ||||||||
\(859\) | −1.69679e15 | −0.123785 | −0.0618923 | − | 0.998083i | \(-0.519714\pi\) | ||||
−0.0618923 | + | 0.998083i | \(0.519714\pi\) | |||||||
\(860\) | 1.55906e16 | 1.13011 | ||||||||
\(861\) | 1.57656e16 | 1.13552 | ||||||||
\(862\) | −3.05077e16 | −2.18333 | ||||||||
\(863\) | −1.62531e16 | −1.15578 | −0.577891 | − | 0.816114i | \(-0.696124\pi\) | ||||
−0.577891 | + | 0.816114i | \(0.696124\pi\) | |||||||
\(864\) | −1.45326e17 | −10.2688 | ||||||||
\(865\) | −1.13151e16 | −0.794454 | ||||||||
\(866\) | 1.37355e16 | 0.958291 | ||||||||
\(867\) | −1.89657e16 | −1.31481 | ||||||||
\(868\) | −4.89384e16 | −3.37125 | ||||||||
\(869\) | −6.88750e15 | −0.471468 | ||||||||
\(870\) | −6.31872e16 | −4.29807 | ||||||||
\(871\) | 1.30197e16 | 0.880039 | ||||||||
\(872\) | 1.16231e16 | 0.780695 | ||||||||
\(873\) | 4.41783e16 | 2.94870 | ||||||||
\(874\) | −5.51090e15 | −0.365519 | ||||||||
\(875\) | −4.13893e16 | −2.72800 | ||||||||
\(876\) | 7.62289e16 | 4.99283 | ||||||||
\(877\) | 8.57996e15 | 0.558454 | 0.279227 | − | 0.960225i | \(-0.409922\pi\) | ||||
0.279227 | + | 0.960225i | \(0.409922\pi\) | |||||||
\(878\) | 4.35980e16 | 2.81998 | ||||||||
\(879\) | 3.49743e15 | 0.224807 | ||||||||
\(880\) | −4.67802e16 | −2.98818 | ||||||||
\(881\) | 1.89430e16 | 1.20249 | 0.601246 | − | 0.799064i | \(-0.294671\pi\) | ||||
0.601246 | + | 0.799064i | \(0.294671\pi\) | |||||||
\(882\) | −3.14179e16 | −1.98198 | ||||||||
\(883\) | −1.01854e16 | −0.638551 | −0.319275 | − | 0.947662i | \(-0.603440\pi\) | ||||
−0.319275 | + | 0.947662i | \(0.603440\pi\) | |||||||
\(884\) | −2.90450e16 | −1.80961 | ||||||||
\(885\) | 2.38525e16 | 1.47688 | ||||||||
\(886\) | −2.42568e16 | −1.49262 | ||||||||
\(887\) | 3.01644e15 | 0.184465 | 0.0922326 | − | 0.995737i | \(-0.470600\pi\) | ||||
0.0922326 | + | 0.995737i | \(0.470600\pi\) | |||||||
\(888\) | 5.37852e16 | 3.26883 | ||||||||
\(889\) | 2.89078e16 | 1.74605 | ||||||||
\(890\) | 9.58567e16 | 5.75410 | ||||||||
\(891\) | −2.06768e16 | −1.23355 | ||||||||
\(892\) | 4.93407e16 | 2.92549 | ||||||||
\(893\) | −2.55297e15 | −0.150440 | ||||||||
\(894\) | 9.08934e16 | 5.32324 | ||||||||
\(895\) | −2.13115e16 | −1.24047 | ||||||||
\(896\) | 6.20129e16 | 3.58747 | ||||||||
\(897\) | −7.21885e16 | −4.15059 | ||||||||
\(898\) | 4.12963e16 | 2.35989 | ||||||||
\(899\) | 1.21844e16 | 0.692030 | ||||||||
\(900\) | 2.70927e17 | 15.2939 | ||||||||
\(901\) | 1.78148e14 | 0.00999530 | ||||||||
\(902\) | −8.04889e15 | −0.448849 | ||||||||
\(903\) | −9.24778e15 | −0.512572 | ||||||||
\(904\) | −6.29856e16 | −3.46989 | ||||||||
\(905\) | −2.14814e16 | −1.17624 | ||||||||
\(906\) | −1.05799e17 | −5.75809 | ||||||||
\(907\) | −5.94995e15 | −0.321865 | −0.160932 | − | 0.986965i | \(-0.551450\pi\) | ||||
−0.160932 | + | 0.986965i | \(0.551450\pi\) | |||||||
\(908\) | −4.00858e16 | −2.15535 | ||||||||
\(909\) | 5.84025e16 | 3.12126 | ||||||||
\(910\) | 9.56928e16 | 5.08337 | ||||||||
\(911\) | 3.48799e15 | 0.184172 | 0.0920861 | − | 0.995751i | \(-0.470647\pi\) | ||||
0.0920861 | + | 0.995751i | \(0.470647\pi\) | |||||||
\(912\) | −1.35355e16 | −0.710397 | ||||||||
\(913\) | −1.51687e16 | −0.791333 | ||||||||
\(914\) | 3.66802e16 | 1.90208 | ||||||||
\(915\) | −5.82275e16 | −3.00132 | ||||||||
\(916\) | −2.94245e16 | −1.50759 | ||||||||
\(917\) | 1.65516e16 | 0.842961 | ||||||||
\(918\) | 5.75642e16 | 2.91419 | ||||||||
\(919\) | −9.47651e15 | −0.476885 | −0.238442 | − | 0.971157i | \(-0.576637\pi\) | ||||
−0.238442 | + | 0.971157i | \(0.576637\pi\) | |||||||
\(920\) | 2.15110e17 | 10.7604 | ||||||||
\(921\) | 3.42167e16 | 1.70141 | ||||||||
\(922\) | −4.59159e16 | −2.26957 | ||||||||
\(923\) | 3.37366e16 | 1.65765 | ||||||||
\(924\) | 5.61289e16 | 2.74151 | ||||||||
\(925\) | −2.48655e16 | −1.20731 | ||||||||
\(926\) | −3.79818e16 | −1.83322 | ||||||||
\(927\) | 4.85527e16 | 2.32956 | ||||||||
\(928\) | −5.11615e16 | −2.44022 | ||||||||
\(929\) | −1.03025e16 | −0.488492 | −0.244246 | − | 0.969713i | \(-0.578540\pi\) | ||||
−0.244246 | + | 0.969713i | \(0.578540\pi\) | |||||||
\(930\) | −1.44468e17 | −6.80949 | ||||||||
\(931\) | −9.25813e14 | −0.0433811 | ||||||||
\(932\) | −5.40931e15 | −0.251973 | ||||||||
\(933\) | 4.63675e15 | 0.214716 | ||||||||
\(934\) | −3.47385e16 | −1.59920 | ||||||||
\(935\) | 9.79992e15 | 0.448496 | ||||||||
\(936\) | −2.20964e17 | −10.0532 | ||||||||
\(937\) | 2.53627e15 | 0.114717 | 0.0573584 | − | 0.998354i | \(-0.481732\pi\) | ||||
0.0573584 | + | 0.998354i | \(0.481732\pi\) | |||||||
\(938\) | 3.64861e16 | 1.64063 | ||||||||
\(939\) | 2.38286e16 | 1.06521 | ||||||||
\(940\) | 1.57994e17 | 7.02164 | ||||||||
\(941\) | 3.43149e15 | 0.151614 | 0.0758072 | − | 0.997122i | \(-0.475847\pi\) | ||||
0.0758072 | + | 0.997122i | \(0.475847\pi\) | |||||||
\(942\) | −1.05520e17 | −4.63508 | ||||||||
\(943\) | 2.11862e16 | 0.925209 | ||||||||
\(944\) | 3.65169e16 | 1.58544 | ||||||||
\(945\) | −1.38507e17 | −5.97854 | ||||||||
\(946\) | 4.72130e15 | 0.202610 | ||||||||
\(947\) | 1.77905e16 | 0.759038 | 0.379519 | − | 0.925184i | \(-0.376090\pi\) | ||||
0.379519 | + | 0.925184i | \(0.376090\pi\) | |||||||
\(948\) | 1.23330e17 | 5.23145 | ||||||||
\(949\) | 2.87424e16 | 1.21216 | ||||||||
\(950\) | 1.09317e16 | 0.458361 | ||||||||
\(951\) | −6.64829e15 | −0.277151 | ||||||||
\(952\) | −5.13382e16 | −2.12783 | ||||||||
\(953\) | 1.39263e16 | 0.573886 | 0.286943 | − | 0.957948i | \(-0.407361\pi\) | ||||
0.286943 | + | 0.957948i | \(0.407361\pi\) | |||||||
\(954\) | 2.14876e15 | 0.0880385 | ||||||||
\(955\) | 3.49967e16 | 1.42564 | ||||||||
\(956\) | −8.97449e16 | −3.63489 | ||||||||
\(957\) | −1.39746e16 | −0.562761 | ||||||||
\(958\) | −1.00740e16 | −0.403358 | ||||||||
\(959\) | −2.96297e16 | −1.17957 | ||||||||
\(960\) | 2.97288e17 | 11.7675 | ||||||||
\(961\) | 2.44920e15 | 0.0963930 | ||||||||
\(962\) | 3.21531e16 | 1.25823 | ||||||||
\(963\) | 3.43987e16 | 1.33844 | ||||||||
\(964\) | 1.72176e14 | 0.00666115 | ||||||||
\(965\) | 3.54021e15 | 0.136185 | ||||||||
\(966\) | −2.02299e17 | −7.73784 | ||||||||
\(967\) | −4.21314e15 | −0.160236 | −0.0801180 | − | 0.996785i | \(-0.525530\pi\) | ||||
−0.0801180 | + | 0.996785i | \(0.525530\pi\) | |||||||
\(968\) | 6.88993e16 | 2.60555 | ||||||||
\(969\) | 2.83552e15 | 0.106623 | ||||||||
\(970\) | −1.10317e17 | −4.12474 | ||||||||
\(971\) | −1.89268e16 | −0.703674 | −0.351837 | − | 0.936061i | \(-0.614443\pi\) | ||||
−0.351837 | + | 0.936061i | \(0.614443\pi\) | |||||||
\(972\) | 1.66518e17 | 6.15596 | ||||||||
\(973\) | −1.90314e16 | −0.699599 | ||||||||
\(974\) | −3.51458e16 | −1.28469 | ||||||||
\(975\) | 1.43197e17 | 5.20485 | ||||||||
\(976\) | −8.91435e16 | −3.22193 | ||||||||
\(977\) | 1.55524e16 | 0.558956 | 0.279478 | − | 0.960152i | \(-0.409839\pi\) | ||||
0.279478 | + | 0.960152i | \(0.409839\pi\) | |||||||
\(978\) | 1.98219e16 | 0.708405 | ||||||||
\(979\) | 2.11999e16 | 0.753404 | ||||||||
\(980\) | 5.72953e16 | 2.02477 | ||||||||
\(981\) | −1.68115e16 | −0.590783 | ||||||||
\(982\) | −4.04719e16 | −1.41430 | ||||||||
\(983\) | −4.23979e16 | −1.47333 | −0.736665 | − | 0.676258i | \(-0.763600\pi\) | ||||
−0.736665 | + | 0.676258i | \(0.763600\pi\) | |||||||
\(984\) | 9.09046e16 | 3.14132 | ||||||||
\(985\) | −3.74867e15 | −0.128818 | ||||||||
\(986\) | 2.02652e16 | 0.692513 | ||||||||
\(987\) | −9.37168e16 | −3.18473 | ||||||||
\(988\) | −1.03234e16 | −0.348868 | ||||||||
\(989\) | −1.24274e16 | −0.417638 | ||||||||
\(990\) | 1.18203e17 | 3.95035 | ||||||||
\(991\) | −1.03132e16 | −0.342757 | −0.171379 | − | 0.985205i | \(-0.554822\pi\) | ||||
−0.171379 | + | 0.985205i | \(0.554822\pi\) | |||||||
\(992\) | −1.16973e17 | −3.86608 | ||||||||
\(993\) | −8.52475e16 | −2.80195 | ||||||||
\(994\) | 9.45425e16 | 3.09031 | ||||||||
\(995\) | 3.24041e16 | 1.05335 | ||||||||
\(996\) | 2.71616e17 | 8.78070 | ||||||||
\(997\) | 2.96304e16 | 0.952609 | 0.476304 | − | 0.879280i | \(-0.341976\pi\) | ||||
0.476304 | + | 0.879280i | \(0.341976\pi\) | |||||||
\(998\) | −3.25380e16 | −1.04033 | ||||||||
\(999\) | −4.65387e16 | −1.47980 |
(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 | 197.12.a.b.1.2 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.12.a.b.1.2 | ✓ | 92 | 1.1 | even | 1 | trivial |