Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(91.1613430010\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 34.5007 | 1.52473 | 0.762366 | − | 0.647147i | \(-0.224038\pi\) | ||||
0.762366 | + | 0.647147i | \(0.224038\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 678.300 | 1.32481 | ||||||||
\(5\) | −2125.49 | −1.52088 | −0.760439 | − | 0.649409i | \(-0.775016\pi\) | ||||
−0.760439 | + | 0.649409i | \(0.775016\pi\) | |||||||
\(6\) | −2794.56 | −0.880304 | ||||||||
\(7\) | −11083.2 | −1.74471 | −0.872357 | − | 0.488870i | \(-0.837409\pi\) | ||||
−0.872357 | + | 0.488870i | \(0.837409\pi\) | |||||||
\(8\) | 5737.48 | 0.495241 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −73331.0 | −2.31893 | ||||||||
\(11\) | −12849.6 | −0.264620 | −0.132310 | − | 0.991208i | \(-0.542239\pi\) | ||||
−0.132310 | + | 0.991208i | \(0.542239\pi\) | |||||||
\(12\) | −54942.3 | −0.764877 | ||||||||
\(13\) | −98344.5 | −0.955004 | −0.477502 | − | 0.878631i | \(-0.658458\pi\) | ||||
−0.477502 | + | 0.878631i | \(0.658458\pi\) | |||||||
\(14\) | −382379. | −2.66022 | ||||||||
\(15\) | 172165. | 0.878080 | ||||||||
\(16\) | −149342. | −0.569696 | ||||||||
\(17\) | −55245.8 | −0.160428 | −0.0802138 | − | 0.996778i | \(-0.525560\pi\) | ||||
−0.0802138 | + | 0.996778i | \(0.525560\pi\) | |||||||
\(18\) | 226359. | 0.508244 | ||||||||
\(19\) | 134898. | 0.237473 | 0.118736 | − | 0.992926i | \(-0.462116\pi\) | ||||
0.118736 | + | 0.992926i | \(0.462116\pi\) | |||||||
\(20\) | −1.44172e6 | −2.01487 | ||||||||
\(21\) | 897739. | 1.00731 | ||||||||
\(22\) | −443321. | −0.403474 | ||||||||
\(23\) | 1.76768e6 | 1.31713 | 0.658564 | − | 0.752524i | \(-0.271164\pi\) | ||||
0.658564 | + | 0.752524i | \(0.271164\pi\) | |||||||
\(24\) | −464736. | −0.285927 | ||||||||
\(25\) | 2.56459e6 | 1.31307 | ||||||||
\(26\) | −3.39296e6 | −1.45612 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −7.51774e6 | −2.31141 | ||||||||
\(29\) | −1.27561e6 | −0.334909 | −0.167455 | − | 0.985880i | \(-0.553555\pi\) | ||||
−0.167455 | + | 0.985880i | \(0.553555\pi\) | |||||||
\(30\) | 5.93981e6 | 1.33884 | ||||||||
\(31\) | 655974. | 0.127573 | 0.0637866 | − | 0.997964i | \(-0.479682\pi\) | ||||
0.0637866 | + | 0.997964i | \(0.479682\pi\) | |||||||
\(32\) | −8.09001e6 | −1.36387 | ||||||||
\(33\) | 1.04082e6 | 0.152778 | ||||||||
\(34\) | −1.90602e6 | −0.244609 | ||||||||
\(35\) | 2.35573e7 | 2.65350 | ||||||||
\(36\) | 4.45033e6 | 0.441602 | ||||||||
\(37\) | −1.12387e7 | −0.985843 | −0.492922 | − | 0.870074i | \(-0.664071\pi\) | ||||
−0.492922 | + | 0.870074i | \(0.664071\pi\) | |||||||
\(38\) | 4.65407e6 | 0.362082 | ||||||||
\(39\) | 7.96591e6 | 0.551372 | ||||||||
\(40\) | −1.21950e7 | −0.753201 | ||||||||
\(41\) | 9.02546e6 | 0.498818 | 0.249409 | − | 0.968398i | \(-0.419764\pi\) | ||||
0.249409 | + | 0.968398i | \(0.419764\pi\) | |||||||
\(42\) | 3.09727e7 | 1.53588 | ||||||||
\(43\) | −3.12935e7 | −1.39587 | −0.697936 | − | 0.716160i | \(-0.745898\pi\) | ||||
−0.697936 | + | 0.716160i | \(0.745898\pi\) | |||||||
\(44\) | −8.71589e6 | −0.350570 | ||||||||
\(45\) | −1.39454e7 | −0.506960 | ||||||||
\(46\) | 6.09862e7 | 2.00827 | ||||||||
\(47\) | 4.08477e7 | 1.22103 | 0.610517 | − | 0.792003i | \(-0.290962\pi\) | ||||
0.610517 | + | 0.792003i | \(0.290962\pi\) | |||||||
\(48\) | 1.20967e7 | 0.328914 | ||||||||
\(49\) | 8.24838e7 | 2.04403 | ||||||||
\(50\) | 8.84803e7 | 2.00208 | ||||||||
\(51\) | 4.47491e6 | 0.0926229 | ||||||||
\(52\) | −6.67071e7 | −1.26519 | ||||||||
\(53\) | 5.63144e7 | 0.980344 | 0.490172 | − | 0.871626i | \(-0.336934\pi\) | ||||
0.490172 | + | 0.871626i | \(0.336934\pi\) | |||||||
\(54\) | −1.83351e7 | −0.293435 | ||||||||
\(55\) | 2.73117e7 | 0.402455 | ||||||||
\(56\) | −6.35897e7 | −0.864053 | ||||||||
\(57\) | −1.09267e7 | −0.137105 | ||||||||
\(58\) | −4.40095e7 | −0.510647 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | 1.16780e8 | 1.16328 | ||||||||
\(61\) | −5.05723e7 | −0.467658 | −0.233829 | − | 0.972278i | \(-0.575126\pi\) | ||||
−0.233829 | + | 0.972278i | \(0.575126\pi\) | |||||||
\(62\) | 2.26316e7 | 0.194515 | ||||||||
\(63\) | −7.27169e7 | −0.581571 | ||||||||
\(64\) | −2.02648e8 | −1.50985 | ||||||||
\(65\) | 2.09031e8 | 1.45244 | ||||||||
\(66\) | 3.59090e7 | 0.232946 | ||||||||
\(67\) | −2.08793e8 | −1.26584 | −0.632920 | − | 0.774217i | \(-0.718144\pi\) | ||||
−0.632920 | + | 0.774217i | \(0.718144\pi\) | |||||||
\(68\) | −3.74732e7 | −0.212535 | ||||||||
\(69\) | −1.43182e8 | −0.760445 | ||||||||
\(70\) | 8.12743e8 | 4.04587 | ||||||||
\(71\) | −2.83381e8 | −1.32345 | −0.661727 | − | 0.749745i | \(-0.730176\pi\) | ||||
−0.661727 | + | 0.749745i | \(0.730176\pi\) | |||||||
\(72\) | 3.76436e7 | 0.165080 | ||||||||
\(73\) | 3.02362e8 | 1.24616 | 0.623081 | − | 0.782158i | \(-0.285881\pi\) | ||||
0.623081 | + | 0.782158i | \(0.285881\pi\) | |||||||
\(74\) | −3.87743e8 | −1.50315 | ||||||||
\(75\) | −2.07732e8 | −0.758102 | ||||||||
\(76\) | 9.15013e7 | 0.314605 | ||||||||
\(77\) | 1.42415e8 | 0.461686 | ||||||||
\(78\) | 2.74830e8 | 0.840694 | ||||||||
\(79\) | −6.85379e6 | −0.0197974 | −0.00989872 | − | 0.999951i | \(-0.503151\pi\) | ||||
−0.00989872 | + | 0.999951i | \(0.503151\pi\) | |||||||
\(80\) | 3.17426e8 | 0.866439 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 3.11385e8 | 0.760563 | ||||||||
\(83\) | −7.30628e7 | −0.168984 | −0.0844919 | − | 0.996424i | \(-0.526927\pi\) | ||||
−0.0844919 | + | 0.996424i | \(0.526927\pi\) | |||||||
\(84\) | 6.08937e8 | 1.33449 | ||||||||
\(85\) | 1.17425e8 | 0.243991 | ||||||||
\(86\) | −1.07965e9 | −2.12833 | ||||||||
\(87\) | 1.03324e8 | 0.193360 | ||||||||
\(88\) | −7.37244e7 | −0.131051 | ||||||||
\(89\) | −9.42405e8 | −1.59215 | −0.796073 | − | 0.605201i | \(-0.793093\pi\) | ||||
−0.796073 | + | 0.605201i | \(0.793093\pi\) | |||||||
\(90\) | −4.81125e8 | −0.772977 | ||||||||
\(91\) | 1.08997e9 | 1.66621 | ||||||||
\(92\) | 1.19902e9 | 1.74494 | ||||||||
\(93\) | −5.31339e7 | −0.0736544 | ||||||||
\(94\) | 1.40928e9 | 1.86175 | ||||||||
\(95\) | −2.86724e8 | −0.361167 | ||||||||
\(96\) | 6.55291e8 | 0.787433 | ||||||||
\(97\) | 5.45381e8 | 0.625499 | 0.312750 | − | 0.949836i | \(-0.398750\pi\) | ||||
0.312750 | + | 0.949836i | \(0.398750\pi\) | |||||||
\(98\) | 2.84575e9 | 3.11659 | ||||||||
\(99\) | −8.43063e7 | −0.0882067 | ||||||||
\(100\) | 1.73956e9 | 1.73956 | ||||||||
\(101\) | −2.91991e8 | −0.279205 | −0.139603 | − | 0.990208i | \(-0.544583\pi\) | ||||
−0.139603 | + | 0.990208i | \(0.544583\pi\) | |||||||
\(102\) | 1.54388e8 | 0.141225 | ||||||||
\(103\) | 8.14008e8 | 0.712625 | 0.356313 | − | 0.934367i | \(-0.384034\pi\) | ||||
0.356313 | + | 0.934367i | \(0.384034\pi\) | |||||||
\(104\) | −5.64250e8 | −0.472957 | ||||||||
\(105\) | −1.90814e9 | −1.53200 | ||||||||
\(106\) | 1.94289e9 | 1.49476 | ||||||||
\(107\) | −3.35348e8 | −0.247325 | −0.123663 | − | 0.992324i | \(-0.539464\pi\) | ||||
−0.123663 | + | 0.992324i | \(0.539464\pi\) | |||||||
\(108\) | −3.60477e8 | −0.254959 | ||||||||
\(109\) | 1.00621e9 | 0.682761 | 0.341381 | − | 0.939925i | \(-0.389105\pi\) | ||||
0.341381 | + | 0.939925i | \(0.389105\pi\) | |||||||
\(110\) | 9.42275e8 | 0.613636 | ||||||||
\(111\) | 9.10334e8 | 0.569177 | ||||||||
\(112\) | 1.65519e9 | 0.993957 | ||||||||
\(113\) | −3.73099e8 | −0.215264 | −0.107632 | − | 0.994191i | \(-0.534327\pi\) | ||||
−0.107632 | + | 0.994191i | \(0.534327\pi\) | |||||||
\(114\) | −3.76980e8 | −0.209048 | ||||||||
\(115\) | −3.75719e9 | −2.00319 | ||||||||
\(116\) | −8.65247e8 | −0.443690 | ||||||||
\(117\) | −6.45238e8 | −0.318335 | ||||||||
\(118\) | 4.18058e8 | 0.198503 | ||||||||
\(119\) | 6.12300e8 | 0.279900 | ||||||||
\(120\) | 9.87793e8 | 0.434861 | ||||||||
\(121\) | −2.19284e9 | −0.929976 | ||||||||
\(122\) | −1.74478e9 | −0.713053 | ||||||||
\(123\) | −7.31062e8 | −0.287993 | ||||||||
\(124\) | 4.44947e8 | 0.169010 | ||||||||
\(125\) | −1.29967e9 | −0.476144 | ||||||||
\(126\) | −2.50879e9 | −0.886740 | ||||||||
\(127\) | −2.03108e9 | −0.692803 | −0.346401 | − | 0.938086i | \(-0.612596\pi\) | ||||
−0.346401 | + | 0.938086i | \(0.612596\pi\) | |||||||
\(128\) | −2.84942e9 | −0.938234 | ||||||||
\(129\) | 2.53477e9 | 0.805907 | ||||||||
\(130\) | 7.21171e9 | 2.21459 | ||||||||
\(131\) | 3.15608e9 | 0.936326 | 0.468163 | − | 0.883642i | \(-0.344916\pi\) | ||||
0.468163 | + | 0.883642i | \(0.344916\pi\) | |||||||
\(132\) | 7.05987e8 | 0.202402 | ||||||||
\(133\) | −1.49510e9 | −0.414322 | ||||||||
\(134\) | −7.20350e9 | −1.93007 | ||||||||
\(135\) | 1.12957e9 | 0.292693 | ||||||||
\(136\) | −3.16972e8 | −0.0794503 | ||||||||
\(137\) | 5.88365e9 | 1.42693 | 0.713467 | − | 0.700688i | \(-0.247124\pi\) | ||||
0.713467 | + | 0.700688i | \(0.247124\pi\) | |||||||
\(138\) | −4.93988e9 | −1.15947 | ||||||||
\(139\) | −6.07512e9 | −1.38035 | −0.690174 | − | 0.723643i | \(-0.742466\pi\) | ||||
−0.690174 | + | 0.723643i | \(0.742466\pi\) | |||||||
\(140\) | 1.59789e10 | 3.51537 | ||||||||
\(141\) | −3.30867e9 | −0.704964 | ||||||||
\(142\) | −9.77686e9 | −2.01791 | ||||||||
\(143\) | 1.26369e9 | 0.252713 | ||||||||
\(144\) | −9.79836e8 | −0.189899 | ||||||||
\(145\) | 2.71130e9 | 0.509357 | ||||||||
\(146\) | 1.04317e10 | 1.90006 | ||||||||
\(147\) | −6.68119e9 | −1.18012 | ||||||||
\(148\) | −7.62320e9 | −1.30605 | ||||||||
\(149\) | −1.45458e9 | −0.241768 | −0.120884 | − | 0.992667i | \(-0.538573\pi\) | ||||
−0.120884 | + | 0.992667i | \(0.538573\pi\) | |||||||
\(150\) | −7.16691e9 | −1.15590 | ||||||||
\(151\) | 4.99891e9 | 0.782491 | 0.391245 | − | 0.920286i | \(-0.372044\pi\) | ||||
0.391245 | + | 0.920286i | \(0.372044\pi\) | |||||||
\(152\) | 7.73974e8 | 0.117606 | ||||||||
\(153\) | −3.62468e8 | −0.0534759 | ||||||||
\(154\) | 4.91341e9 | 0.703947 | ||||||||
\(155\) | −1.39427e9 | −0.194023 | ||||||||
\(156\) | 5.40328e9 | 0.730460 | ||||||||
\(157\) | −9.43502e8 | −0.123935 | −0.0619675 | − | 0.998078i | \(-0.519738\pi\) | ||||
−0.0619675 | + | 0.998078i | \(0.519738\pi\) | |||||||
\(158\) | −2.36461e8 | −0.0301858 | ||||||||
\(159\) | −4.56147e9 | −0.566002 | ||||||||
\(160\) | 1.71953e10 | 2.07429 | ||||||||
\(161\) | −1.95915e10 | −2.29801 | ||||||||
\(162\) | 1.48514e9 | 0.169415 | ||||||||
\(163\) | −5.47947e9 | −0.607987 | −0.303994 | − | 0.952674i | \(-0.598320\pi\) | ||||
−0.303994 | + | 0.952674i | \(0.598320\pi\) | |||||||
\(164\) | 6.12197e9 | 0.660837 | ||||||||
\(165\) | −2.21225e9 | −0.232357 | ||||||||
\(166\) | −2.52072e9 | −0.257655 | ||||||||
\(167\) | 1.84188e10 | 1.83247 | 0.916236 | − | 0.400639i | \(-0.131212\pi\) | ||||
0.916236 | + | 0.400639i | \(0.131212\pi\) | |||||||
\(168\) | 5.15076e9 | 0.498861 | ||||||||
\(169\) | −9.32855e8 | −0.0879678 | ||||||||
\(170\) | 4.05123e9 | 0.372021 | ||||||||
\(171\) | 8.85065e8 | 0.0791576 | ||||||||
\(172\) | −2.12264e10 | −1.84926 | ||||||||
\(173\) | −4.05329e9 | −0.344033 | −0.172017 | − | 0.985094i | \(-0.555028\pi\) | ||||
−0.172017 | + | 0.985094i | \(0.555028\pi\) | |||||||
\(174\) | 3.56477e9 | 0.294822 | ||||||||
\(175\) | −2.84239e10 | −2.29093 | ||||||||
\(176\) | 1.91899e9 | 0.150753 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | −3.25137e10 | −2.42759 | ||||||||
\(179\) | −1.52337e10 | −1.10909 | −0.554545 | − | 0.832154i | \(-0.687108\pi\) | ||||
−0.554545 | + | 0.832154i | \(0.687108\pi\) | |||||||
\(180\) | −9.45914e9 | −0.671623 | ||||||||
\(181\) | 2.36616e10 | 1.63866 | 0.819332 | − | 0.573320i | \(-0.194345\pi\) | ||||
0.819332 | + | 0.573320i | \(0.194345\pi\) | |||||||
\(182\) | 3.76048e10 | 2.54052 | ||||||||
\(183\) | 4.09636e9 | 0.270003 | ||||||||
\(184\) | 1.01420e10 | 0.652296 | ||||||||
\(185\) | 2.38877e10 | 1.49935 | ||||||||
\(186\) | −1.83316e9 | −0.112303 | ||||||||
\(187\) | 7.09887e8 | 0.0424524 | ||||||||
\(188\) | 2.77070e10 | 1.61763 | ||||||||
\(189\) | 5.89007e9 | 0.335770 | ||||||||
\(190\) | −9.89220e9 | −0.550683 | ||||||||
\(191\) | 1.67134e10 | 0.908686 | 0.454343 | − | 0.890827i | \(-0.349874\pi\) | ||||
0.454343 | + | 0.890827i | \(0.349874\pi\) | |||||||
\(192\) | 1.64145e10 | 0.871710 | ||||||||
\(193\) | 2.66584e10 | 1.38301 | 0.691507 | − | 0.722370i | \(-0.256947\pi\) | ||||
0.691507 | + | 0.722370i | \(0.256947\pi\) | |||||||
\(194\) | 1.88160e10 | 0.953718 | ||||||||
\(195\) | −1.69315e10 | −0.838569 | ||||||||
\(196\) | 5.59488e10 | 2.70794 | ||||||||
\(197\) | 1.97136e9 | 0.0932539 | 0.0466269 | − | 0.998912i | \(-0.485153\pi\) | ||||
0.0466269 | + | 0.998912i | \(0.485153\pi\) | |||||||
\(198\) | −2.90863e9 | −0.134491 | ||||||||
\(199\) | 4.05270e10 | 1.83191 | 0.915957 | − | 0.401276i | \(-0.131433\pi\) | ||||
0.915957 | + | 0.401276i | \(0.131433\pi\) | |||||||
\(200\) | 1.47143e10 | 0.650287 | ||||||||
\(201\) | 1.69122e10 | 0.730833 | ||||||||
\(202\) | −1.00739e10 | −0.425713 | ||||||||
\(203\) | 1.41379e10 | 0.584321 | ||||||||
\(204\) | 3.03533e9 | 0.122707 | ||||||||
\(205\) | −1.91836e10 | −0.758642 | ||||||||
\(206\) | 2.80839e10 | 1.08656 | ||||||||
\(207\) | 1.15977e10 | 0.439043 | ||||||||
\(208\) | 1.46870e10 | 0.544062 | ||||||||
\(209\) | −1.73338e9 | −0.0628401 | ||||||||
\(210\) | −6.58322e10 | −2.33588 | ||||||||
\(211\) | −1.95680e10 | −0.679634 | −0.339817 | − | 0.940492i | \(-0.610365\pi\) | ||||
−0.339817 | + | 0.940492i | \(0.610365\pi\) | |||||||
\(212\) | 3.81981e10 | 1.29876 | ||||||||
\(213\) | 2.29539e10 | 0.764096 | ||||||||
\(214\) | −1.15697e10 | −0.377104 | ||||||||
\(215\) | 6.65140e10 | 2.12295 | ||||||||
\(216\) | −3.04913e9 | −0.0953091 | ||||||||
\(217\) | −7.27030e9 | −0.222579 | ||||||||
\(218\) | 3.47149e10 | 1.04103 | ||||||||
\(219\) | −2.44913e10 | −0.719472 | ||||||||
\(220\) | 1.85256e10 | 0.533174 | ||||||||
\(221\) | 5.43312e9 | 0.153209 | ||||||||
\(222\) | 3.14072e10 | 0.867842 | ||||||||
\(223\) | −4.91878e10 | −1.33194 | −0.665971 | − | 0.745977i | \(-0.731983\pi\) | ||||
−0.665971 | + | 0.745977i | \(0.731983\pi\) | |||||||
\(224\) | 8.96633e10 | 2.37957 | ||||||||
\(225\) | 1.68263e10 | 0.437691 | ||||||||
\(226\) | −1.28722e10 | −0.328219 | ||||||||
\(227\) | −4.48168e10 | −1.12027 | −0.560137 | − | 0.828400i | \(-0.689252\pi\) | ||||
−0.560137 | + | 0.828400i | \(0.689252\pi\) | |||||||
\(228\) | −7.41160e9 | −0.181637 | ||||||||
\(229\) | −4.38357e10 | −1.05334 | −0.526670 | − | 0.850070i | \(-0.676560\pi\) | ||||
−0.526670 | + | 0.850070i | \(0.676560\pi\) | |||||||
\(230\) | −1.29626e11 | −3.05433 | ||||||||
\(231\) | −1.15356e10 | −0.266555 | ||||||||
\(232\) | −7.31880e9 | −0.165861 | ||||||||
\(233\) | −9.01688e9 | −0.200426 | −0.100213 | − | 0.994966i | \(-0.531952\pi\) | ||||
−0.100213 | + | 0.994966i | \(0.531952\pi\) | |||||||
\(234\) | −2.22612e10 | −0.485375 | ||||||||
\(235\) | −8.68215e10 | −1.85704 | ||||||||
\(236\) | 8.21921e9 | 0.172475 | ||||||||
\(237\) | 5.55157e8 | 0.0114301 | ||||||||
\(238\) | 2.11248e10 | 0.426773 | ||||||||
\(239\) | −4.04272e10 | −0.801463 | −0.400731 | − | 0.916196i | \(-0.631244\pi\) | ||||
−0.400731 | + | 0.916196i | \(0.631244\pi\) | |||||||
\(240\) | −2.57115e10 | −0.500239 | ||||||||
\(241\) | −3.52928e9 | −0.0673921 | −0.0336960 | − | 0.999432i | \(-0.510728\pi\) | ||||
−0.0336960 | + | 0.999432i | \(0.510728\pi\) | |||||||
\(242\) | −7.56544e10 | −1.41796 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −3.43032e10 | −0.619556 | ||||||||
\(245\) | −1.75319e11 | −3.10871 | ||||||||
\(246\) | −2.52222e10 | −0.439111 | ||||||||
\(247\) | −1.32665e10 | −0.226787 | ||||||||
\(248\) | 3.76364e9 | 0.0631794 | ||||||||
\(249\) | 5.91809e9 | 0.0975629 | ||||||||
\(250\) | −4.48396e10 | −0.725992 | ||||||||
\(251\) | 1.08446e11 | 1.72458 | 0.862290 | − | 0.506414i | \(-0.169029\pi\) | ||||
0.862290 | + | 0.506414i | \(0.169029\pi\) | |||||||
\(252\) | −4.93239e10 | −0.770469 | ||||||||
\(253\) | −2.27140e10 | −0.348539 | ||||||||
\(254\) | −7.00736e10 | −1.05634 | ||||||||
\(255\) | −9.51139e9 | −0.140868 | ||||||||
\(256\) | 5.44879e9 | 0.0792904 | ||||||||
\(257\) | −1.07464e11 | −1.53661 | −0.768307 | − | 0.640082i | \(-0.778900\pi\) | ||||
−0.768307 | + | 0.640082i | \(0.778900\pi\) | |||||||
\(258\) | 8.74514e10 | 1.22879 | ||||||||
\(259\) | 1.24561e11 | 1.72001 | ||||||||
\(260\) | 1.41785e11 | 1.92421 | ||||||||
\(261\) | −8.36928e9 | −0.111636 | ||||||||
\(262\) | 1.08887e11 | 1.42765 | ||||||||
\(263\) | 2.40331e9 | 0.0309748 | 0.0154874 | − | 0.999880i | \(-0.495070\pi\) | ||||
0.0154874 | + | 0.999880i | \(0.495070\pi\) | |||||||
\(264\) | 5.97168e9 | 0.0756621 | ||||||||
\(265\) | −1.19696e11 | −1.49098 | ||||||||
\(266\) | −5.15821e10 | −0.631730 | ||||||||
\(267\) | 7.63348e10 | 0.919225 | ||||||||
\(268\) | −1.41624e11 | −1.67699 | ||||||||
\(269\) | −1.62916e11 | −1.89705 | −0.948526 | − | 0.316699i | \(-0.897426\pi\) | ||||
−0.948526 | + | 0.316699i | \(0.897426\pi\) | |||||||
\(270\) | 3.89711e10 | 0.446279 | ||||||||
\(271\) | 5.27406e10 | 0.593996 | 0.296998 | − | 0.954878i | \(-0.404015\pi\) | ||||
0.296998 | + | 0.954878i | \(0.404015\pi\) | |||||||
\(272\) | 8.25054e9 | 0.0913950 | ||||||||
\(273\) | −8.82878e10 | −0.961986 | ||||||||
\(274\) | 2.02990e11 | 2.17569 | ||||||||
\(275\) | −3.29540e10 | −0.347465 | ||||||||
\(276\) | −9.71204e10 | −1.00744 | ||||||||
\(277\) | −1.30739e11 | −1.33427 | −0.667137 | − | 0.744935i | \(-0.732480\pi\) | ||||
−0.667137 | + | 0.744935i | \(0.732480\pi\) | |||||||
\(278\) | −2.09596e11 | −2.10466 | ||||||||
\(279\) | 4.30385e9 | 0.0425244 | ||||||||
\(280\) | 1.35159e11 | 1.31412 | ||||||||
\(281\) | −3.34613e10 | −0.320158 | −0.160079 | − | 0.987104i | \(-0.551175\pi\) | ||||
−0.160079 | + | 0.987104i | \(0.551175\pi\) | |||||||
\(282\) | −1.14151e11 | −1.07488 | ||||||||
\(283\) | 1.28327e11 | 1.18926 | 0.594631 | − | 0.803998i | \(-0.297298\pi\) | ||||
0.594631 | + | 0.803998i | \(0.297298\pi\) | |||||||
\(284\) | −1.92218e11 | −1.75332 | ||||||||
\(285\) | 2.32247e10 | 0.208520 | ||||||||
\(286\) | 4.35982e10 | 0.385320 | ||||||||
\(287\) | −1.00031e11 | −0.870294 | ||||||||
\(288\) | −5.30786e10 | −0.454625 | ||||||||
\(289\) | −1.15536e11 | −0.974263 | ||||||||
\(290\) | 9.35419e10 | 0.776632 | ||||||||
\(291\) | −4.41758e10 | −0.361132 | ||||||||
\(292\) | 2.05092e11 | 1.65092 | ||||||||
\(293\) | 1.99282e11 | 1.57966 | 0.789832 | − | 0.613324i | \(-0.210168\pi\) | ||||
0.789832 | + | 0.613324i | \(0.210168\pi\) | |||||||
\(294\) | −2.30506e11 | −1.79936 | ||||||||
\(295\) | −2.57554e10 | −0.198002 | ||||||||
\(296\) | −6.44818e10 | −0.488230 | ||||||||
\(297\) | 6.82881e9 | 0.0509262 | ||||||||
\(298\) | −5.01840e10 | −0.368631 | ||||||||
\(299\) | −1.73842e11 | −1.25786 | ||||||||
\(300\) | −1.40905e11 | −1.00434 | ||||||||
\(301\) | 3.46832e11 | 2.43540 | ||||||||
\(302\) | 1.72466e11 | 1.19309 | ||||||||
\(303\) | 2.36513e10 | 0.161199 | ||||||||
\(304\) | −2.01460e10 | −0.135287 | ||||||||
\(305\) | 1.07491e11 | 0.711251 | ||||||||
\(306\) | −1.25054e10 | −0.0815363 | ||||||||
\(307\) | 1.03383e11 | 0.664244 | 0.332122 | − | 0.943236i | \(-0.392235\pi\) | ||||
0.332122 | + | 0.943236i | \(0.392235\pi\) | |||||||
\(308\) | 9.66000e10 | 0.611644 | ||||||||
\(309\) | −6.59347e10 | −0.411434 | ||||||||
\(310\) | −4.81033e10 | −0.295833 | ||||||||
\(311\) | 2.01487e11 | 1.22131 | 0.610654 | − | 0.791898i | \(-0.290907\pi\) | ||||
0.610654 | + | 0.791898i | \(0.290907\pi\) | |||||||
\(312\) | 4.57042e10 | 0.273062 | ||||||||
\(313\) | −1.69614e11 | −0.998879 | −0.499439 | − | 0.866349i | \(-0.666461\pi\) | ||||
−0.499439 | + | 0.866349i | \(0.666461\pi\) | |||||||
\(314\) | −3.25515e10 | −0.188968 | ||||||||
\(315\) | 1.54559e11 | 0.884499 | ||||||||
\(316\) | −4.64893e9 | −0.0262277 | ||||||||
\(317\) | 1.25759e11 | 0.699474 | 0.349737 | − | 0.936848i | \(-0.386271\pi\) | ||||
0.349737 | + | 0.936848i | \(0.386271\pi\) | |||||||
\(318\) | −1.57374e11 | −0.863001 | ||||||||
\(319\) | 1.63911e10 | 0.0886237 | ||||||||
\(320\) | 4.30727e11 | 2.29629 | ||||||||
\(321\) | 2.71632e10 | 0.142793 | ||||||||
\(322\) | −6.75923e11 | −3.50385 | ||||||||
\(323\) | −7.45254e9 | −0.0380972 | ||||||||
\(324\) | 2.91986e10 | 0.147201 | ||||||||
\(325\) | −2.52214e11 | −1.25399 | ||||||||
\(326\) | −1.89046e11 | −0.927017 | ||||||||
\(327\) | −8.15029e10 | −0.394192 | ||||||||
\(328\) | 5.17834e10 | 0.247035 | ||||||||
\(329\) | −4.52724e11 | −2.13035 | ||||||||
\(330\) | −7.63243e10 | −0.354283 | ||||||||
\(331\) | −4.16265e11 | −1.90609 | −0.953046 | − | 0.302827i | \(-0.902070\pi\) | ||||
−0.953046 | + | 0.302827i | \(0.902070\pi\) | |||||||
\(332\) | −4.95585e10 | −0.223871 | ||||||||
\(333\) | −7.37370e10 | −0.328614 | ||||||||
\(334\) | 6.35462e11 | 2.79403 | ||||||||
\(335\) | 4.43787e11 | 1.92519 | ||||||||
\(336\) | −1.34071e11 | −0.573861 | ||||||||
\(337\) | 3.94584e11 | 1.66650 | 0.833248 | − | 0.552899i | \(-0.186479\pi\) | ||||
0.833248 | + | 0.552899i | \(0.186479\pi\) | |||||||
\(338\) | −3.21842e10 | −0.134127 | ||||||||
\(339\) | 3.02210e10 | 0.124282 | ||||||||
\(340\) | 7.96491e10 | 0.323240 | ||||||||
\(341\) | −8.42901e9 | −0.0337584 | ||||||||
\(342\) | 3.05354e10 | 0.120694 | ||||||||
\(343\) | −4.66937e11 | −1.82152 | ||||||||
\(344\) | −1.79546e11 | −0.691293 | ||||||||
\(345\) | 3.04332e11 | 1.15654 | ||||||||
\(346\) | −1.39842e11 | −0.524558 | ||||||||
\(347\) | −2.58895e11 | −0.958609 | −0.479305 | − | 0.877649i | \(-0.659111\pi\) | ||||
−0.479305 | + | 0.877649i | \(0.659111\pi\) | |||||||
\(348\) | 7.00850e10 | 0.256164 | ||||||||
\(349\) | 3.25345e11 | 1.17390 | 0.586949 | − | 0.809624i | \(-0.300329\pi\) | ||||
0.586949 | + | 0.809624i | \(0.300329\pi\) | |||||||
\(350\) | −9.80646e11 | −3.49306 | ||||||||
\(351\) | 5.22643e10 | 0.183791 | ||||||||
\(352\) | 1.03953e11 | 0.360908 | ||||||||
\(353\) | 5.23092e11 | 1.79305 | 0.896524 | − | 0.442996i | \(-0.146084\pi\) | ||||
0.896524 | + | 0.442996i | \(0.146084\pi\) | |||||||
\(354\) | −3.38627e10 | −0.114606 | ||||||||
\(355\) | 6.02325e11 | 2.01281 | ||||||||
\(356\) | −6.39234e11 | −2.10928 | ||||||||
\(357\) | −4.95963e10 | −0.161600 | ||||||||
\(358\) | −5.25574e11 | −1.69106 | ||||||||
\(359\) | 1.44888e11 | 0.460369 | 0.230184 | − | 0.973147i | \(-0.426067\pi\) | ||||
0.230184 | + | 0.973147i | \(0.426067\pi\) | |||||||
\(360\) | −8.00112e10 | −0.251067 | ||||||||
\(361\) | −3.04490e11 | −0.943607 | ||||||||
\(362\) | 8.16341e11 | 2.49852 | ||||||||
\(363\) | 1.77620e11 | 0.536922 | ||||||||
\(364\) | 7.39329e11 | 2.20740 | ||||||||
\(365\) | −6.42668e11 | −1.89526 | ||||||||
\(366\) | 1.41327e11 | 0.411681 | ||||||||
\(367\) | 5.33904e11 | 1.53626 | 0.768131 | − | 0.640292i | \(-0.221187\pi\) | ||||
0.768131 | + | 0.640292i | \(0.221187\pi\) | |||||||
\(368\) | −2.63990e11 | −0.750363 | ||||||||
\(369\) | 5.92161e10 | 0.166273 | ||||||||
\(370\) | 8.24145e11 | 2.28610 | ||||||||
\(371\) | −6.24144e11 | −1.71042 | ||||||||
\(372\) | −3.60407e10 | −0.0975777 | ||||||||
\(373\) | 4.21409e11 | 1.12724 | 0.563618 | − | 0.826036i | \(-0.309409\pi\) | ||||
0.563618 | + | 0.826036i | \(0.309409\pi\) | |||||||
\(374\) | 2.44916e10 | 0.0647284 | ||||||||
\(375\) | 1.05273e11 | 0.274902 | ||||||||
\(376\) | 2.34363e11 | 0.604705 | ||||||||
\(377\) | 1.25449e11 | 0.319840 | ||||||||
\(378\) | 2.03212e11 | 0.511959 | ||||||||
\(379\) | −2.78603e11 | −0.693600 | −0.346800 | − | 0.937939i | \(-0.612732\pi\) | ||||
−0.346800 | + | 0.937939i | \(0.612732\pi\) | |||||||
\(380\) | −1.94485e11 | −0.478476 | ||||||||
\(381\) | 1.64517e11 | 0.399990 | ||||||||
\(382\) | 5.76624e11 | 1.38550 | ||||||||
\(383\) | −7.13578e11 | −1.69452 | −0.847260 | − | 0.531178i | \(-0.821749\pi\) | ||||
−0.847260 | + | 0.531178i | \(0.821749\pi\) | |||||||
\(384\) | 2.30803e11 | 0.541690 | ||||||||
\(385\) | −3.02702e11 | −0.702169 | ||||||||
\(386\) | 9.19735e11 | 2.10872 | ||||||||
\(387\) | −2.05316e11 | −0.465291 | ||||||||
\(388\) | 3.69932e11 | 0.828665 | ||||||||
\(389\) | −4.13305e10 | −0.0915160 | −0.0457580 | − | 0.998953i | \(-0.514570\pi\) | ||||
−0.0457580 | + | 0.998953i | \(0.514570\pi\) | |||||||
\(390\) | −5.84148e11 | −1.27859 | ||||||||
\(391\) | −9.76569e10 | −0.211304 | ||||||||
\(392\) | 4.73249e11 | 1.01228 | ||||||||
\(393\) | −2.55642e11 | −0.540588 | ||||||||
\(394\) | 6.80132e10 | 0.142187 | ||||||||
\(395\) | 1.45677e10 | 0.0301095 | ||||||||
\(396\) | −5.71850e10 | −0.116857 | ||||||||
\(397\) | −8.80592e10 | −0.177917 | −0.0889585 | − | 0.996035i | \(-0.528354\pi\) | ||||
−0.0889585 | + | 0.996035i | \(0.528354\pi\) | |||||||
\(398\) | 1.39821e12 | 2.79318 | ||||||||
\(399\) | 1.21103e11 | 0.239209 | ||||||||
\(400\) | −3.83003e11 | −0.748052 | ||||||||
\(401\) | 3.55570e11 | 0.686714 | 0.343357 | − | 0.939205i | \(-0.388436\pi\) | ||||
0.343357 | + | 0.939205i | \(0.388436\pi\) | |||||||
\(402\) | 5.83484e11 | 1.11432 | ||||||||
\(403\) | −6.45115e10 | −0.121833 | ||||||||
\(404\) | −1.98058e11 | −0.369893 | ||||||||
\(405\) | −9.14955e10 | −0.168987 | ||||||||
\(406\) | 4.87766e11 | 0.890932 | ||||||||
\(407\) | 1.44413e11 | 0.260874 | ||||||||
\(408\) | 2.56747e10 | 0.0458706 | ||||||||
\(409\) | −6.47031e11 | −1.14333 | −0.571663 | − | 0.820488i | \(-0.693702\pi\) | ||||
−0.571663 | + | 0.820488i | \(0.693702\pi\) | |||||||
\(410\) | −6.61847e11 | −1.15672 | ||||||||
\(411\) | −4.76575e11 | −0.823841 | ||||||||
\(412\) | 5.52142e11 | 0.944090 | ||||||||
\(413\) | −1.34299e11 | −0.227142 | ||||||||
\(414\) | 4.00131e11 | 0.669422 | ||||||||
\(415\) | 1.55295e11 | 0.257004 | ||||||||
\(416\) | 7.95609e11 | 1.30251 | ||||||||
\(417\) | 4.92085e11 | 0.796944 | ||||||||
\(418\) | −5.98030e10 | −0.0958142 | ||||||||
\(419\) | 6.62242e11 | 1.04967 | 0.524836 | − | 0.851203i | \(-0.324127\pi\) | ||||
0.524836 | + | 0.851203i | \(0.324127\pi\) | |||||||
\(420\) | −1.29429e12 | −2.02960 | ||||||||
\(421\) | −7.29715e11 | −1.13210 | −0.566049 | − | 0.824372i | \(-0.691529\pi\) | ||||
−0.566049 | + | 0.824372i | \(0.691529\pi\) | |||||||
\(422\) | −6.75110e11 | −1.03626 | ||||||||
\(423\) | 2.68002e11 | 0.407011 | ||||||||
\(424\) | 3.23103e11 | 0.485506 | ||||||||
\(425\) | −1.41683e11 | −0.210653 | ||||||||
\(426\) | 7.91926e11 | 1.16504 | ||||||||
\(427\) | 5.60503e11 | 0.815929 | ||||||||
\(428\) | −2.27466e11 | −0.327658 | ||||||||
\(429\) | −1.02359e11 | −0.145904 | ||||||||
\(430\) | 2.29478e12 | 3.23693 | ||||||||
\(431\) | 1.04484e10 | 0.0145849 | 0.00729243 | − | 0.999973i | \(-0.497679\pi\) | ||||
0.00729243 | + | 0.999973i | \(0.497679\pi\) | |||||||
\(432\) | 7.93667e10 | 0.109638 | ||||||||
\(433\) | 9.48860e11 | 1.29720 | 0.648599 | − | 0.761130i | \(-0.275355\pi\) | ||||
0.648599 | + | 0.761130i | \(0.275355\pi\) | |||||||
\(434\) | −2.50830e11 | −0.339372 | ||||||||
\(435\) | −2.19615e11 | −0.294077 | ||||||||
\(436\) | 6.82512e11 | 0.904526 | ||||||||
\(437\) | 2.38456e11 | 0.312782 | ||||||||
\(438\) | −8.44968e11 | −1.09700 | ||||||||
\(439\) | 1.41652e12 | 1.82025 | 0.910125 | − | 0.414335i | \(-0.135986\pi\) | ||||
0.910125 | + | 0.414335i | \(0.135986\pi\) | |||||||
\(440\) | 1.56701e11 | 0.199312 | ||||||||
\(441\) | 5.41176e11 | 0.681342 | ||||||||
\(442\) | 1.87447e11 | 0.233602 | ||||||||
\(443\) | 4.09272e11 | 0.504889 | 0.252444 | − | 0.967611i | \(-0.418766\pi\) | ||||
0.252444 | + | 0.967611i | \(0.418766\pi\) | |||||||
\(444\) | 6.17480e11 | 0.754048 | ||||||||
\(445\) | 2.00308e12 | 2.42146 | ||||||||
\(446\) | −1.69702e12 | −2.03085 | ||||||||
\(447\) | 1.17821e11 | 0.139585 | ||||||||
\(448\) | 2.24599e12 | 2.63425 | ||||||||
\(449\) | −3.44730e11 | −0.400287 | −0.200143 | − | 0.979767i | \(-0.564141\pi\) | ||||
−0.200143 | + | 0.979767i | \(0.564141\pi\) | |||||||
\(450\) | 5.80520e11 | 0.667361 | ||||||||
\(451\) | −1.15974e11 | −0.131997 | ||||||||
\(452\) | −2.53073e11 | −0.285182 | ||||||||
\(453\) | −4.04912e11 | −0.451771 | ||||||||
\(454\) | −1.54621e12 | −1.70812 | ||||||||
\(455\) | −2.31673e12 | −2.53410 | ||||||||
\(456\) | −6.26919e10 | −0.0679000 | ||||||||
\(457\) | 9.96315e11 | 1.06850 | 0.534249 | − | 0.845327i | \(-0.320594\pi\) | ||||
0.534249 | + | 0.845327i | \(0.320594\pi\) | |||||||
\(458\) | −1.51236e12 | −1.60606 | ||||||||
\(459\) | 2.93599e10 | 0.0308743 | ||||||||
\(460\) | −2.54850e12 | −2.65384 | ||||||||
\(461\) | −5.63457e11 | −0.581041 | −0.290520 | − | 0.956869i | \(-0.593828\pi\) | ||||
−0.290520 | + | 0.956869i | \(0.593828\pi\) | |||||||
\(462\) | −3.97987e11 | −0.406424 | ||||||||
\(463\) | −1.07447e12 | −1.08663 | −0.543315 | − | 0.839529i | \(-0.682831\pi\) | ||||
−0.543315 | + | 0.839529i | \(0.682831\pi\) | |||||||
\(464\) | 1.90503e11 | 0.190797 | ||||||||
\(465\) | 1.12936e11 | 0.112019 | ||||||||
\(466\) | −3.11089e11 | −0.305596 | ||||||||
\(467\) | −1.72279e11 | −0.167612 | −0.0838062 | − | 0.996482i | \(-0.526708\pi\) | ||||
−0.0838062 | + | 0.996482i | \(0.526708\pi\) | |||||||
\(468\) | −4.37665e11 | −0.421731 | ||||||||
\(469\) | 2.31409e12 | 2.20853 | ||||||||
\(470\) | −2.99541e12 | −2.83149 | ||||||||
\(471\) | 7.64236e10 | 0.0715539 | ||||||||
\(472\) | 6.95231e10 | 0.0644749 | ||||||||
\(473\) | 4.02109e11 | 0.369376 | ||||||||
\(474\) | 1.91533e10 | 0.0174278 | ||||||||
\(475\) | 3.45958e11 | 0.311819 | ||||||||
\(476\) | 4.15324e11 | 0.370813 | ||||||||
\(477\) | 3.69479e11 | 0.326781 | ||||||||
\(478\) | −1.39477e12 | −1.22202 | ||||||||
\(479\) | 1.17803e12 | 1.02246 | 0.511232 | − | 0.859443i | \(-0.329189\pi\) | ||||
0.511232 | + | 0.859443i | \(0.329189\pi\) | |||||||
\(480\) | −1.39282e12 | −1.19759 | ||||||||
\(481\) | 1.10526e12 | 0.941484 | ||||||||
\(482\) | −1.21763e11 | −0.102755 | ||||||||
\(483\) | 1.58692e12 | 1.32676 | ||||||||
\(484\) | −1.48740e12 | −1.23204 | ||||||||
\(485\) | −1.15920e12 | −0.951309 | ||||||||
\(486\) | −1.20297e11 | −0.0978116 | ||||||||
\(487\) | 1.41964e12 | 1.14366 | 0.571830 | − | 0.820372i | \(-0.306234\pi\) | ||||
0.571830 | + | 0.820372i | \(0.306234\pi\) | |||||||
\(488\) | −2.90158e11 | −0.231603 | ||||||||
\(489\) | 4.43837e11 | 0.351022 | ||||||||
\(490\) | −6.04862e12 | −4.73995 | ||||||||
\(491\) | −3.65591e11 | −0.283876 | −0.141938 | − | 0.989876i | \(-0.545333\pi\) | ||||
−0.141938 | + | 0.989876i | \(0.545333\pi\) | |||||||
\(492\) | −4.95880e11 | −0.381534 | ||||||||
\(493\) | 7.04722e10 | 0.0537287 | ||||||||
\(494\) | −4.57703e11 | −0.345790 | ||||||||
\(495\) | 1.79192e11 | 0.134152 | ||||||||
\(496\) | −9.79648e10 | −0.0726779 | ||||||||
\(497\) | 3.14077e12 | 2.30905 | ||||||||
\(498\) | 2.04178e11 | 0.148757 | ||||||||
\(499\) | 2.55102e12 | 1.84188 | 0.920941 | − | 0.389703i | \(-0.127422\pi\) | ||||
0.920941 | + | 0.389703i | \(0.127422\pi\) | |||||||
\(500\) | −8.81568e11 | −0.630799 | ||||||||
\(501\) | −1.49192e12 | −1.05798 | ||||||||
\(502\) | 3.74148e12 | 2.62952 | ||||||||
\(503\) | −1.67849e12 | −1.16913 | −0.584566 | − | 0.811346i | \(-0.698735\pi\) | ||||
−0.584566 | + | 0.811346i | \(0.698735\pi\) | |||||||
\(504\) | −4.17212e11 | −0.288018 | ||||||||
\(505\) | 6.20625e11 | 0.424637 | ||||||||
\(506\) | −7.83649e11 | −0.531428 | ||||||||
\(507\) | 7.55612e10 | 0.0507883 | ||||||||
\(508\) | −1.37768e12 | −0.917829 | ||||||||
\(509\) | −1.57010e12 | −1.03681 | −0.518403 | − | 0.855137i | \(-0.673473\pi\) | ||||
−0.518403 | + | 0.855137i | \(0.673473\pi\) | |||||||
\(510\) | −3.28150e11 | −0.214786 | ||||||||
\(511\) | −3.35114e12 | −2.17419 | ||||||||
\(512\) | 1.64689e12 | 1.05913 | ||||||||
\(513\) | −7.16903e10 | −0.0457017 | ||||||||
\(514\) | −3.70759e12 | −2.34292 | ||||||||
\(515\) | −1.73017e12 | −1.08382 | ||||||||
\(516\) | 1.71934e12 | 1.06767 | ||||||||
\(517\) | −5.24877e11 | −0.323110 | ||||||||
\(518\) | 4.29743e12 | 2.62256 | ||||||||
\(519\) | 3.28317e11 | 0.198628 | ||||||||
\(520\) | 1.19931e12 | 0.719310 | ||||||||
\(521\) | 1.78780e12 | 1.06304 | 0.531519 | − | 0.847046i | \(-0.321621\pi\) | ||||
0.531519 | + | 0.847046i | \(0.321621\pi\) | |||||||
\(522\) | −2.88746e11 | −0.170216 | ||||||||
\(523\) | −1.34218e11 | −0.0784431 | −0.0392215 | − | 0.999231i | \(-0.512488\pi\) | ||||
−0.0392215 | + | 0.999231i | \(0.512488\pi\) | |||||||
\(524\) | 2.14077e12 | 1.24045 | ||||||||
\(525\) | 2.30234e12 | 1.32267 | ||||||||
\(526\) | 8.29160e10 | 0.0472283 | ||||||||
\(527\) | −3.62398e10 | −0.0204662 | ||||||||
\(528\) | −1.55438e11 | −0.0870373 | ||||||||
\(529\) | 1.32354e12 | 0.734828 | ||||||||
\(530\) | −4.12960e12 | −2.27335 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | −1.01413e12 | −0.548896 | ||||||||
\(533\) | −8.87605e11 | −0.476373 | ||||||||
\(534\) | 2.63361e12 | 1.40157 | ||||||||
\(535\) | 7.12779e11 | 0.376152 | ||||||||
\(536\) | −1.19794e12 | −0.626896 | ||||||||
\(537\) | 1.23393e12 | 0.640333 | ||||||||
\(538\) | −5.62073e12 | −2.89249 | ||||||||
\(539\) | −1.05988e12 | −0.540890 | ||||||||
\(540\) | 7.66190e11 | 0.387762 | ||||||||
\(541\) | 1.55224e12 | 0.779060 | 0.389530 | − | 0.921014i | \(-0.372637\pi\) | ||||
0.389530 | + | 0.921014i | \(0.372637\pi\) | |||||||
\(542\) | 1.81959e12 | 0.905684 | ||||||||
\(543\) | −1.91659e12 | −0.946083 | ||||||||
\(544\) | 4.46939e11 | 0.218803 | ||||||||
\(545\) | −2.13869e12 | −1.03840 | ||||||||
\(546\) | −3.04599e12 | −1.46677 | ||||||||
\(547\) | 1.87430e12 | 0.895153 | 0.447576 | − | 0.894246i | \(-0.352287\pi\) | ||||
0.447576 | + | 0.894246i | \(0.352287\pi\) | |||||||
\(548\) | 3.99088e12 | 1.89041 | ||||||||
\(549\) | −3.31805e11 | −0.155886 | ||||||||
\(550\) | −1.13694e12 | −0.529791 | ||||||||
\(551\) | −1.72077e11 | −0.0795319 | ||||||||
\(552\) | −8.21504e11 | −0.376603 | ||||||||
\(553\) | 7.59619e10 | 0.0345408 | ||||||||
\(554\) | −4.51058e12 | −2.03441 | ||||||||
\(555\) | −1.93491e12 | −0.865649 | ||||||||
\(556\) | −4.12076e12 | −1.82869 | ||||||||
\(557\) | 3.54150e12 | 1.55897 | 0.779486 | − | 0.626419i | \(-0.215480\pi\) | ||||
0.779486 | + | 0.626419i | \(0.215480\pi\) | |||||||
\(558\) | 1.48486e11 | 0.0648382 | ||||||||
\(559\) | 3.07754e12 | 1.33306 | ||||||||
\(560\) | −3.51810e12 | −1.51169 | ||||||||
\(561\) | −5.75008e10 | −0.0245099 | ||||||||
\(562\) | −1.15444e12 | −0.488156 | ||||||||
\(563\) | −3.12012e12 | −1.30883 | −0.654416 | − | 0.756135i | \(-0.727085\pi\) | ||||
−0.654416 | + | 0.756135i | \(0.727085\pi\) | |||||||
\(564\) | −2.24427e12 | −0.933940 | ||||||||
\(565\) | 7.93018e11 | 0.327390 | ||||||||
\(566\) | 4.42736e12 | 1.81331 | ||||||||
\(567\) | −4.77096e11 | −0.193857 | ||||||||
\(568\) | −1.62590e12 | −0.655428 | ||||||||
\(569\) | 1.25747e12 | 0.502914 | 0.251457 | − | 0.967868i | \(-0.419090\pi\) | ||||
0.251457 | + | 0.967868i | \(0.419090\pi\) | |||||||
\(570\) | 8.01268e11 | 0.317937 | ||||||||
\(571\) | 3.04709e12 | 1.19956 | 0.599782 | − | 0.800163i | \(-0.295254\pi\) | ||||
0.599782 | + | 0.800163i | \(0.295254\pi\) | |||||||
\(572\) | 8.57160e11 | 0.334796 | ||||||||
\(573\) | −1.35378e12 | −0.524630 | ||||||||
\(574\) | −3.45114e12 | −1.32697 | ||||||||
\(575\) | 4.53338e12 | 1.72948 | ||||||||
\(576\) | −1.32957e12 | −0.503282 | ||||||||
\(577\) | 4.93378e12 | 1.85305 | 0.926527 | − | 0.376227i | \(-0.122779\pi\) | ||||
0.926527 | + | 0.376227i | \(0.122779\pi\) | |||||||
\(578\) | −3.98607e12 | −1.48549 | ||||||||
\(579\) | −2.15933e12 | −0.798483 | ||||||||
\(580\) | 1.83908e12 | 0.674798 | ||||||||
\(581\) | 8.09770e11 | 0.294828 | ||||||||
\(582\) | −1.52410e12 | −0.550630 | ||||||||
\(583\) | −7.23618e11 | −0.259419 | ||||||||
\(584\) | 1.73480e12 | 0.617150 | ||||||||
\(585\) | 1.37145e12 | 0.484148 | ||||||||
\(586\) | 6.87539e12 | 2.40856 | ||||||||
\(587\) | −1.04516e12 | −0.363338 | −0.181669 | − | 0.983360i | \(-0.558150\pi\) | ||||
−0.181669 | + | 0.983360i | \(0.558150\pi\) | |||||||
\(588\) | −4.53185e12 | −1.56343 | ||||||||
\(589\) | 8.84895e10 | 0.0302951 | ||||||||
\(590\) | −8.88579e11 | −0.301899 | ||||||||
\(591\) | −1.59680e11 | −0.0538401 | ||||||||
\(592\) | 1.67841e12 | 0.561631 | ||||||||
\(593\) | 2.78359e12 | 0.924397 | 0.462198 | − | 0.886777i | \(-0.347061\pi\) | ||||
0.462198 | + | 0.886777i | \(0.347061\pi\) | |||||||
\(594\) | 2.35599e11 | 0.0776487 | ||||||||
\(595\) | −1.30144e12 | −0.425694 | ||||||||
\(596\) | −9.86641e11 | −0.320296 | ||||||||
\(597\) | −3.28268e12 | −1.05766 | ||||||||
\(598\) | −5.99766e12 | −1.91790 | ||||||||
\(599\) | −1.00164e12 | −0.317901 | −0.158950 | − | 0.987287i | \(-0.550811\pi\) | ||||
−0.158950 | + | 0.987287i | \(0.550811\pi\) | |||||||
\(600\) | −1.19186e12 | −0.375443 | ||||||||
\(601\) | −5.94601e12 | −1.85905 | −0.929524 | − | 0.368761i | \(-0.879782\pi\) | ||||
−0.929524 | + | 0.368761i | \(0.879782\pi\) | |||||||
\(602\) | 1.19659e13 | 3.71332 | ||||||||
\(603\) | −1.36989e12 | −0.421947 | ||||||||
\(604\) | 3.39076e12 | 1.03665 | ||||||||
\(605\) | 4.66086e12 | 1.41438 | ||||||||
\(606\) | 8.15987e11 | 0.245786 | ||||||||
\(607\) | −1.71818e12 | −0.513713 | −0.256856 | − | 0.966450i | \(-0.582687\pi\) | ||||
−0.256856 | + | 0.966450i | \(0.582687\pi\) | |||||||
\(608\) | −1.09133e12 | −0.323883 | ||||||||
\(609\) | −1.14517e12 | −0.337358 | ||||||||
\(610\) | 3.70852e12 | 1.08447 | ||||||||
\(611\) | −4.01715e12 | −1.16609 | ||||||||
\(612\) | −2.45862e11 | −0.0708451 | ||||||||
\(613\) | 4.34986e12 | 1.24424 | 0.622119 | − | 0.782923i | \(-0.286272\pi\) | ||||
0.622119 | + | 0.782923i | \(0.286272\pi\) | |||||||
\(614\) | 3.56680e12 | 1.01279 | ||||||||
\(615\) | 1.55387e12 | 0.438002 | ||||||||
\(616\) | 8.17102e11 | 0.228646 | ||||||||
\(617\) | 4.75580e12 | 1.32111 | 0.660557 | − | 0.750776i | \(-0.270320\pi\) | ||||
0.660557 | + | 0.750776i | \(0.270320\pi\) | |||||||
\(618\) | −2.27479e12 | −0.627327 | ||||||||
\(619\) | 2.98381e12 | 0.816891 | 0.408445 | − | 0.912783i | \(-0.366071\pi\) | ||||
0.408445 | + | 0.912783i | \(0.366071\pi\) | |||||||
\(620\) | −9.45733e11 | −0.257043 | ||||||||
\(621\) | −9.39417e11 | −0.253482 | ||||||||
\(622\) | 6.95144e12 | 1.86217 | ||||||||
\(623\) | 1.04449e13 | 2.77784 | ||||||||
\(624\) | −1.18965e12 | −0.314114 | ||||||||
\(625\) | −2.24653e12 | −0.588914 | ||||||||
\(626\) | −5.85181e12 | −1.52302 | ||||||||
\(627\) | 1.40404e11 | 0.0362807 | ||||||||
\(628\) | −6.39977e11 | −0.164190 | ||||||||
\(629\) | 6.20890e11 | 0.158156 | ||||||||
\(630\) | 5.33241e12 | 1.34862 | ||||||||
\(631\) | 3.14683e12 | 0.790206 | 0.395103 | − | 0.918637i | \(-0.370709\pi\) | ||||
0.395103 | + | 0.918637i | \(0.370709\pi\) | |||||||
\(632\) | −3.93235e10 | −0.00980450 | ||||||||
\(633\) | 1.58501e12 | 0.392387 | ||||||||
\(634\) | 4.33877e12 | 1.06651 | ||||||||
\(635\) | 4.31704e12 | 1.05367 | ||||||||
\(636\) | −3.09405e12 | −0.749842 | ||||||||
\(637\) | −8.11183e12 | −1.95205 | ||||||||
\(638\) | 5.65505e11 | 0.135127 | ||||||||
\(639\) | −1.85927e12 | −0.441151 | ||||||||
\(640\) | 6.05642e12 | 1.42694 | ||||||||
\(641\) | −6.90121e12 | −1.61460 | −0.807299 | − | 0.590143i | \(-0.799071\pi\) | ||||
−0.807299 | + | 0.590143i | \(0.799071\pi\) | |||||||
\(642\) | 9.37149e11 | 0.217721 | ||||||||
\(643\) | 2.39255e12 | 0.551965 | 0.275983 | − | 0.961163i | \(-0.410997\pi\) | ||||
0.275983 | + | 0.961163i | \(0.410997\pi\) | |||||||
\(644\) | −1.32890e13 | −3.04442 | ||||||||
\(645\) | −5.38764e12 | −1.22569 | ||||||||
\(646\) | −2.57118e11 | −0.0580880 | ||||||||
\(647\) | −5.61890e12 | −1.26061 | −0.630307 | − | 0.776346i | \(-0.717071\pi\) | ||||
−0.630307 | + | 0.776346i | \(0.717071\pi\) | |||||||
\(648\) | 2.46980e11 | 0.0550268 | ||||||||
\(649\) | −1.55703e11 | −0.0344506 | ||||||||
\(650\) | −8.70156e12 | −1.91200 | ||||||||
\(651\) | 5.88894e11 | 0.128506 | ||||||||
\(652\) | −3.71673e12 | −0.805465 | ||||||||
\(653\) | 4.52224e12 | 0.973295 | 0.486647 | − | 0.873599i | \(-0.338220\pi\) | ||||
0.486647 | + | 0.873599i | \(0.338220\pi\) | |||||||
\(654\) | −2.81191e12 | −0.601038 | ||||||||
\(655\) | −6.70822e12 | −1.42404 | ||||||||
\(656\) | −1.34788e12 | −0.284175 | ||||||||
\(657\) | 1.98380e12 | 0.415387 | ||||||||
\(658\) | −1.56193e13 | −3.24822 | ||||||||
\(659\) | 1.98801e12 | 0.410613 | 0.205307 | − | 0.978698i | \(-0.434181\pi\) | ||||
0.205307 | + | 0.978698i | \(0.434181\pi\) | |||||||
\(660\) | −1.50057e12 | −0.307828 | ||||||||
\(661\) | 3.75691e12 | 0.765463 | 0.382731 | − | 0.923860i | \(-0.374983\pi\) | ||||
0.382731 | + | 0.923860i | \(0.374983\pi\) | |||||||
\(662\) | −1.43614e13 | −2.90628 | ||||||||
\(663\) | −4.40083e11 | −0.0884552 | ||||||||
\(664\) | −4.19197e11 | −0.0836877 | ||||||||
\(665\) | 3.17782e12 | 0.630133 | ||||||||
\(666\) | −2.54398e12 | −0.501049 | ||||||||
\(667\) | −2.25487e12 | −0.441119 | ||||||||
\(668\) | 1.24935e13 | 2.42767 | ||||||||
\(669\) | 3.98421e12 | 0.768998 | ||||||||
\(670\) | 1.53110e13 | 2.93540 | ||||||||
\(671\) | 6.49834e11 | 0.123752 | ||||||||
\(672\) | −7.26273e12 | −1.37385 | ||||||||
\(673\) | −4.50273e12 | −0.846074 | −0.423037 | − | 0.906112i | \(-0.639036\pi\) | ||||
−0.423037 | + | 0.906112i | \(0.639036\pi\) | |||||||
\(674\) | 1.36134e13 | 2.54096 | ||||||||
\(675\) | −1.36293e12 | −0.252701 | ||||||||
\(676\) | −6.32756e11 | −0.116540 | ||||||||
\(677\) | −4.77303e12 | −0.873262 | −0.436631 | − | 0.899641i | \(-0.643829\pi\) | ||||
−0.436631 | + | 0.899641i | \(0.643829\pi\) | |||||||
\(678\) | 1.04265e12 | 0.189497 | ||||||||
\(679\) | −6.04456e12 | −1.09132 | ||||||||
\(680\) | 6.73721e11 | 0.120834 | ||||||||
\(681\) | 3.63016e12 | 0.646791 | ||||||||
\(682\) | −2.90807e11 | −0.0514725 | ||||||||
\(683\) | 6.92003e12 | 1.21679 | 0.608394 | − | 0.793635i | \(-0.291814\pi\) | ||||
0.608394 | + | 0.793635i | \(0.291814\pi\) | |||||||
\(684\) | 6.00340e11 | 0.104868 | ||||||||
\(685\) | −1.25056e13 | −2.17019 | ||||||||
\(686\) | −1.61097e13 | −2.77734 | ||||||||
\(687\) | 3.55069e12 | 0.608146 | ||||||||
\(688\) | 4.67344e12 | 0.795223 | ||||||||
\(689\) | −5.53822e12 | −0.936232 | ||||||||
\(690\) | 1.04997e13 | 1.76342 | ||||||||
\(691\) | −3.26738e12 | −0.545190 | −0.272595 | − | 0.962129i | \(-0.587882\pi\) | ||||
−0.272595 | + | 0.962129i | \(0.587882\pi\) | |||||||
\(692\) | −2.74935e12 | −0.455777 | ||||||||
\(693\) | 9.34383e11 | 0.153895 | ||||||||
\(694\) | −8.93208e12 | −1.46162 | ||||||||
\(695\) | 1.29126e13 | 2.09934 | ||||||||
\(696\) | 5.92822e11 | 0.0957598 | ||||||||
\(697\) | −4.98619e11 | −0.0800242 | ||||||||
\(698\) | 1.12247e13 | 1.78988 | ||||||||
\(699\) | 7.30368e11 | 0.115716 | ||||||||
\(700\) | −1.92799e13 | −3.03504 | ||||||||
\(701\) | −8.23416e12 | −1.28792 | −0.643959 | − | 0.765060i | \(-0.722709\pi\) | ||||
−0.643959 | + | 0.765060i | \(0.722709\pi\) | |||||||
\(702\) | 1.80316e12 | 0.280231 | ||||||||
\(703\) | −1.51607e12 | −0.234111 | ||||||||
\(704\) | 2.60395e12 | 0.399535 | ||||||||
\(705\) | 7.03254e12 | 1.07216 | ||||||||
\(706\) | 1.80470e13 | 2.73391 | ||||||||
\(707\) | 3.23620e12 | 0.487133 | ||||||||
\(708\) | −6.65756e11 | −0.0995785 | ||||||||
\(709\) | 7.57359e12 | 1.12563 | 0.562813 | − | 0.826584i | \(-0.309719\pi\) | ||||
0.562813 | + | 0.826584i | \(0.309719\pi\) | |||||||
\(710\) | 2.07807e13 | 3.06900 | ||||||||
\(711\) | −4.49677e10 | −0.00659914 | ||||||||
\(712\) | −5.40703e12 | −0.788495 | ||||||||
\(713\) | 1.15955e12 | 0.168030 | ||||||||
\(714\) | −1.71111e12 | −0.246397 | ||||||||
\(715\) | −2.68596e12 | −0.384346 | ||||||||
\(716\) | −1.03330e13 | −1.46933 | ||||||||
\(717\) | 3.27461e12 | 0.462725 | ||||||||
\(718\) | 4.99872e12 | 0.701939 | ||||||||
\(719\) | 8.97769e12 | 1.25281 | 0.626404 | − | 0.779499i | \(-0.284526\pi\) | ||||
0.626404 | + | 0.779499i | \(0.284526\pi\) | |||||||
\(720\) | 2.08263e12 | 0.288813 | ||||||||
\(721\) | −9.02182e12 | −1.24333 | ||||||||
\(722\) | −1.05051e13 | −1.43875 | ||||||||
\(723\) | 2.85871e11 | 0.0389088 | ||||||||
\(724\) | 1.60496e13 | 2.17091 | ||||||||
\(725\) | −3.27142e12 | −0.439760 | ||||||||
\(726\) | 6.12801e12 | 0.818662 | ||||||||
\(727\) | −9.56364e11 | −0.126975 | −0.0634875 | − | 0.997983i | \(-0.520222\pi\) | ||||
−0.0634875 | + | 0.997983i | \(0.520222\pi\) | |||||||
\(728\) | 6.25370e12 | 0.825174 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −2.21725e13 | −2.88976 | ||||||||
\(731\) | 1.72883e12 | 0.223936 | ||||||||
\(732\) | 2.77856e12 | 0.357701 | ||||||||
\(733\) | 8.77585e12 | 1.12285 | 0.561424 | − | 0.827528i | \(-0.310254\pi\) | ||||
0.561424 | + | 0.827528i | \(0.310254\pi\) | |||||||
\(734\) | 1.84201e13 | 2.34239 | ||||||||
\(735\) | 1.42008e13 | 1.79482 | ||||||||
\(736\) | −1.43006e13 | −1.79640 | ||||||||
\(737\) | 2.68290e12 | 0.334967 | ||||||||
\(738\) | 2.04300e12 | 0.253521 | ||||||||
\(739\) | −9.96504e12 | −1.22908 | −0.614538 | − | 0.788887i | \(-0.710658\pi\) | ||||
−0.614538 | + | 0.788887i | \(0.710658\pi\) | |||||||
\(740\) | 1.62031e13 | 1.98634 | ||||||||
\(741\) | 1.07458e12 | 0.130936 | ||||||||
\(742\) | −2.15334e13 | −2.60793 | ||||||||
\(743\) | −3.30829e12 | −0.398249 | −0.199124 | − | 0.979974i | \(-0.563810\pi\) | ||||
−0.199124 | + | 0.979974i | \(0.563810\pi\) | |||||||
\(744\) | −3.04855e11 | −0.0364766 | ||||||||
\(745\) | 3.09170e12 | 0.367700 | ||||||||
\(746\) | 1.45389e13 | 1.71873 | ||||||||
\(747\) | −4.79365e11 | −0.0563279 | ||||||||
\(748\) | 4.81516e11 | 0.0562411 | ||||||||
\(749\) | 3.71673e12 | 0.431512 | ||||||||
\(750\) | 3.63201e12 | 0.419152 | ||||||||
\(751\) | 6.43513e12 | 0.738206 | 0.369103 | − | 0.929389i | \(-0.379665\pi\) | ||||
0.369103 | + | 0.929389i | \(0.379665\pi\) | |||||||
\(752\) | −6.10030e12 | −0.695618 | ||||||||
\(753\) | −8.78416e12 | −0.995687 | ||||||||
\(754\) | 4.32809e12 | 0.487670 | ||||||||
\(755\) | −1.06251e13 | −1.19007 | ||||||||
\(756\) | 3.99524e12 | 0.444830 | ||||||||
\(757\) | −7.76173e12 | −0.859068 | −0.429534 | − | 0.903051i | \(-0.641322\pi\) | ||||
−0.429534 | + | 0.903051i | \(0.641322\pi\) | |||||||
\(758\) | −9.61200e12 | −1.05755 | ||||||||
\(759\) | 1.83983e12 | 0.201229 | ||||||||
\(760\) | −1.64508e12 | −0.178865 | ||||||||
\(761\) | −9.64688e12 | −1.04269 | −0.521346 | − | 0.853345i | \(-0.674570\pi\) | ||||
−0.521346 | + | 0.853345i | \(0.674570\pi\) | |||||||
\(762\) | 5.67596e12 | 0.609877 | ||||||||
\(763\) | −1.11520e13 | −1.19122 | ||||||||
\(764\) | 1.13367e13 | 1.20383 | ||||||||
\(765\) | 7.70422e11 | 0.0813303 | ||||||||
\(766\) | −2.46190e13 | −2.58369 | ||||||||
\(767\) | −1.19168e12 | −0.124331 | ||||||||
\(768\) | −4.41352e11 | −0.0457783 | ||||||||
\(769\) | −3.19835e12 | −0.329805 | −0.164903 | − | 0.986310i | \(-0.552731\pi\) | ||||
−0.164903 | + | 0.986310i | \(0.552731\pi\) | |||||||
\(770\) | −1.04434e13 | −1.07062 | ||||||||
\(771\) | 8.70460e12 | 0.887164 | ||||||||
\(772\) | 1.80824e13 | 1.83222 | ||||||||
\(773\) | −4.99654e12 | −0.503341 | −0.251670 | − | 0.967813i | \(-0.580980\pi\) | ||||
−0.251670 | + | 0.967813i | \(0.580980\pi\) | |||||||
\(774\) | −7.08356e12 | −0.709443 | ||||||||
\(775\) | 1.68231e12 | 0.167513 | ||||||||
\(776\) | 3.12911e12 | 0.309773 | ||||||||
\(777\) | −1.00894e13 | −0.993050 | ||||||||
\(778\) | −1.42593e12 | −0.139537 | ||||||||
\(779\) | 1.21752e12 | 0.118456 | ||||||||
\(780\) | −1.14846e13 | −1.11094 | ||||||||
\(781\) | 3.64134e12 | 0.350212 | ||||||||
\(782\) | −3.36923e12 | −0.322182 | ||||||||
\(783\) | 6.77912e11 | 0.0644533 | ||||||||
\(784\) | −1.23183e13 | −1.16447 | ||||||||
\(785\) | 2.00541e12 | 0.188490 | ||||||||
\(786\) | −8.81985e12 | −0.824252 | ||||||||
\(787\) | −2.48095e12 | −0.230532 | −0.115266 | − | 0.993335i | \(-0.536772\pi\) | ||||
−0.115266 | + | 0.993335i | \(0.536772\pi\) | |||||||
\(788\) | 1.33717e12 | 0.123543 | ||||||||
\(789\) | −1.94668e11 | −0.0178833 | ||||||||
\(790\) | 5.02596e11 | 0.0459089 | ||||||||
\(791\) | 4.13513e12 | 0.375573 | ||||||||
\(792\) | −4.83706e11 | −0.0436835 | ||||||||
\(793\) | 4.97351e12 | 0.446615 | ||||||||
\(794\) | −3.03811e12 | −0.271275 | ||||||||
\(795\) | 9.69537e12 | 0.860820 | ||||||||
\(796\) | 2.74895e13 | 2.42693 | ||||||||
\(797\) | 4.01929e12 | 0.352847 | 0.176424 | − | 0.984314i | \(-0.443547\pi\) | ||||
0.176424 | + | 0.984314i | \(0.443547\pi\) | |||||||
\(798\) | 4.17815e12 | 0.364729 | ||||||||
\(799\) | −2.25667e12 | −0.195887 | ||||||||
\(800\) | −2.07476e13 | −1.79087 | ||||||||
\(801\) | −6.18312e12 | −0.530715 | ||||||||
\(802\) | 1.22674e13 | 1.04705 | ||||||||
\(803\) | −3.88523e12 | −0.329759 | ||||||||
\(804\) | 1.14716e13 | 0.968212 | ||||||||
\(805\) | 4.16417e13 | 3.49500 | ||||||||
\(806\) | −2.22569e12 | −0.185762 | ||||||||
\(807\) | 1.31962e13 | 1.09526 | ||||||||
\(808\) | −1.67529e12 | −0.138274 | ||||||||
\(809\) | −1.76189e13 | −1.44614 | −0.723068 | − | 0.690776i | \(-0.757269\pi\) | ||||
−0.723068 | + | 0.690776i | \(0.757269\pi\) | |||||||
\(810\) | −3.15666e12 | −0.257659 | ||||||||
\(811\) | 1.43610e13 | 1.16571 | 0.582856 | − | 0.812576i | \(-0.301935\pi\) | ||||
0.582856 | + | 0.812576i | \(0.301935\pi\) | |||||||
\(812\) | 9.58971e12 | 0.774111 | ||||||||
\(813\) | −4.27199e12 | −0.342944 | ||||||||
\(814\) | 4.98234e12 | 0.397762 | ||||||||
\(815\) | 1.16466e13 | 0.924675 | ||||||||
\(816\) | −6.68294e11 | −0.0527669 | ||||||||
\(817\) | −4.22142e12 | −0.331482 | ||||||||
\(818\) | −2.23230e13 | −1.74327 | ||||||||
\(819\) | 7.15131e12 | 0.555403 | ||||||||
\(820\) | −1.30122e13 | −1.00505 | ||||||||
\(821\) | −1.27547e13 | −0.979772 | −0.489886 | − | 0.871787i | \(-0.662962\pi\) | ||||
−0.489886 | + | 0.871787i | \(0.662962\pi\) | |||||||
\(822\) | −1.64422e13 | −1.25614 | ||||||||
\(823\) | −1.55652e13 | −1.18265 | −0.591326 | − | 0.806433i | \(-0.701395\pi\) | ||||
−0.591326 | + | 0.806433i | \(0.701395\pi\) | |||||||
\(824\) | 4.67036e12 | 0.352921 | ||||||||
\(825\) | 2.66928e12 | 0.200609 | ||||||||
\(826\) | −4.63342e12 | −0.346331 | ||||||||
\(827\) | 2.98542e12 | 0.221937 | 0.110969 | − | 0.993824i | \(-0.464605\pi\) | ||||
0.110969 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(828\) | 7.86675e12 | 0.581646 | ||||||||
\(829\) | 1.23183e13 | 0.905848 | 0.452924 | − | 0.891549i | \(-0.350381\pi\) | ||||
0.452924 | + | 0.891549i | \(0.350381\pi\) | |||||||
\(830\) | 5.35777e12 | 0.391862 | ||||||||
\(831\) | 1.05898e13 | 0.770344 | ||||||||
\(832\) | 1.99293e13 | 1.44191 | ||||||||
\(833\) | −4.55688e12 | −0.327918 | ||||||||
\(834\) | 1.69773e13 | 1.21513 | ||||||||
\(835\) | −3.91490e13 | −2.78697 | ||||||||
\(836\) | −1.17576e12 | −0.0832508 | ||||||||
\(837\) | −3.48612e11 | −0.0245515 | ||||||||
\(838\) | 2.28478e13 | 1.60047 | ||||||||
\(839\) | −1.86372e13 | −1.29853 | −0.649264 | − | 0.760563i | \(-0.724923\pi\) | ||||
−0.649264 | + | 0.760563i | \(0.724923\pi\) | |||||||
\(840\) | −1.09479e13 | −0.758708 | ||||||||
\(841\) | −1.28800e13 | −0.887836 | ||||||||
\(842\) | −2.51757e13 | −1.72614 | ||||||||
\(843\) | 2.71037e12 | 0.184844 | ||||||||
\(844\) | −1.32730e13 | −0.900383 | ||||||||
\(845\) | 1.98278e12 | 0.133788 | ||||||||
\(846\) | 9.24626e12 | 0.620583 | ||||||||
\(847\) | 2.43036e13 | 1.62254 | ||||||||
\(848\) | −8.41014e12 | −0.558498 | ||||||||
\(849\) | −1.03945e13 | −0.686621 | ||||||||
\(850\) | −4.88817e12 | −0.321189 | ||||||||
\(851\) | −1.98664e13 | −1.29848 | ||||||||
\(852\) | 1.55696e13 | 1.01228 | ||||||||
\(853\) | 2.02588e13 | 1.31022 | 0.655110 | − | 0.755534i | \(-0.272622\pi\) | ||||
0.655110 | + | 0.755534i | \(0.272622\pi\) | |||||||
\(854\) | 1.93378e13 | 1.24407 | ||||||||
\(855\) | −1.88120e12 | −0.120389 | ||||||||
\(856\) | −1.92405e12 | −0.122486 | ||||||||
\(857\) | −1.79742e13 | −1.13825 | −0.569124 | − | 0.822252i | \(-0.692718\pi\) | ||||
−0.569124 | + | 0.822252i | \(0.692718\pi\) | |||||||
\(858\) | −3.53145e12 | −0.222464 | ||||||||
\(859\) | 8.13333e11 | 0.0509682 | 0.0254841 | − | 0.999675i | \(-0.491887\pi\) | ||||
0.0254841 | + | 0.999675i | \(0.491887\pi\) | |||||||
\(860\) | 4.51165e13 | 2.81250 | ||||||||
\(861\) | 8.10251e12 | 0.502465 | ||||||||
\(862\) | 3.60478e11 | 0.0222380 | ||||||||
\(863\) | 2.73063e13 | 1.67577 | 0.837885 | − | 0.545848i | \(-0.183792\pi\) | ||||
0.837885 | + | 0.545848i | \(0.183792\pi\) | |||||||
\(864\) | 4.29937e12 | 0.262478 | ||||||||
\(865\) | 8.61525e12 | 0.523233 | ||||||||
\(866\) | 3.27363e13 | 1.97788 | ||||||||
\(867\) | 9.35840e12 | 0.562491 | ||||||||
\(868\) | −4.93144e12 | −0.294873 | ||||||||
\(869\) | 8.80685e10 | 0.00523880 | ||||||||
\(870\) | −7.57689e12 | −0.448389 | ||||||||
\(871\) | 2.05336e13 | 1.20888 | ||||||||
\(872\) | 5.77311e12 | 0.338131 | ||||||||
\(873\) | 3.57824e12 | 0.208500 | ||||||||
\(874\) | 8.22691e12 | 0.476909 | ||||||||
\(875\) | 1.44045e13 | 0.830735 | ||||||||
\(876\) | −1.66125e13 | −0.953160 | ||||||||
\(877\) | 2.50307e13 | 1.42881 | 0.714405 | − | 0.699732i | \(-0.246697\pi\) | ||||
0.714405 | + | 0.699732i | \(0.246697\pi\) | |||||||
\(878\) | 4.88708e13 | 2.77539 | ||||||||
\(879\) | −1.61419e13 | −0.912019 | ||||||||
\(880\) | −4.07880e12 | −0.229277 | ||||||||
\(881\) | −3.22785e13 | −1.80518 | −0.902591 | − | 0.430499i | \(-0.858338\pi\) | ||||
−0.902591 | + | 0.430499i | \(0.858338\pi\) | |||||||
\(882\) | 1.86710e13 | 1.03886 | ||||||||
\(883\) | 8.95417e12 | 0.495681 | 0.247840 | − | 0.968801i | \(-0.420279\pi\) | ||||
0.247840 | + | 0.968801i | \(0.420279\pi\) | |||||||
\(884\) | 3.68529e12 | 0.202972 | ||||||||
\(885\) | 2.08618e12 | 0.114316 | ||||||||
\(886\) | 1.41202e13 | 0.769819 | ||||||||
\(887\) | −1.32363e13 | −0.717978 | −0.358989 | − | 0.933342i | \(-0.616879\pi\) | ||||
−0.358989 | + | 0.933342i | \(0.616879\pi\) | |||||||
\(888\) | 5.22302e12 | 0.281880 | ||||||||
\(889\) | 2.25108e13 | 1.20874 | ||||||||
\(890\) | 6.91076e13 | 3.69208 | ||||||||
\(891\) | −5.53133e11 | −0.0294022 | ||||||||
\(892\) | −3.33641e13 | −1.76456 | ||||||||
\(893\) | 5.51027e12 | 0.289962 | ||||||||
\(894\) | 4.06491e12 | 0.212829 | ||||||||
\(895\) | 3.23791e13 | 1.68679 | ||||||||
\(896\) | 3.15807e13 | 1.63695 | ||||||||
\(897\) | 1.40812e13 | 0.726227 | ||||||||
\(898\) | −1.18934e13 | −0.610329 | ||||||||
\(899\) | −8.36768e11 | −0.0427254 | ||||||||
\(900\) | 1.14133e13 | 0.579855 | ||||||||
\(901\) | −3.11114e12 | −0.157274 | ||||||||
\(902\) | −4.00118e12 | −0.201260 | ||||||||
\(903\) | −2.80934e13 | −1.40608 | ||||||||
\(904\) | −2.14065e12 | −0.106607 | ||||||||
\(905\) | −5.02925e13 | −2.49221 | ||||||||
\(906\) | −1.39698e13 | −0.688830 | ||||||||
\(907\) | 3.19713e13 | 1.56866 | 0.784328 | − | 0.620347i | \(-0.213008\pi\) | ||||
0.784328 | + | 0.620347i | \(0.213008\pi\) | |||||||
\(908\) | −3.03992e13 | −1.48415 | ||||||||
\(909\) | −1.91575e12 | −0.0930684 | ||||||||
\(910\) | −7.99288e13 | −3.86382 | ||||||||
\(911\) | 8.00387e12 | 0.385006 | 0.192503 | − | 0.981296i | \(-0.438340\pi\) | ||||
0.192503 | + | 0.981296i | \(0.438340\pi\) | |||||||
\(912\) | 1.63182e12 | 0.0781082 | ||||||||
\(913\) | 9.38829e11 | 0.0447165 | ||||||||
\(914\) | 3.43736e13 | 1.62917 | ||||||||
\(915\) | −8.70677e12 | −0.410641 | ||||||||
\(916\) | −2.97338e13 | −1.39547 | ||||||||
\(917\) | −3.49795e13 | −1.63362 | ||||||||
\(918\) | 1.01294e12 | 0.0470750 | ||||||||
\(919\) | −1.03567e13 | −0.478965 | −0.239482 | − | 0.970901i | \(-0.576978\pi\) | ||||
−0.239482 | + | 0.970901i | \(0.576978\pi\) | |||||||
\(920\) | −2.15568e13 | −0.992063 | ||||||||
\(921\) | −8.37405e12 | −0.383501 | ||||||||
\(922\) | −1.94397e13 | −0.885931 | ||||||||
\(923\) | 2.78690e13 | 1.26390 | ||||||||
\(924\) | −7.82460e12 | −0.353133 | ||||||||
\(925\) | −2.88227e13 | −1.29448 | ||||||||
\(926\) | −3.70701e13 | −1.65682 | ||||||||
\(927\) | 5.34071e12 | 0.237542 | ||||||||
\(928\) | 1.03197e13 | 0.456774 | ||||||||
\(929\) | −3.17313e13 | −1.39771 | −0.698856 | − | 0.715263i | \(-0.746307\pi\) | ||||
−0.698856 | + | 0.715263i | \(0.746307\pi\) | |||||||
\(930\) | 3.89636e12 | 0.170799 | ||||||||
\(931\) | 1.11269e13 | 0.485400 | ||||||||
\(932\) | −6.11616e12 | −0.265526 | ||||||||
\(933\) | −1.63204e13 | −0.705122 | ||||||||
\(934\) | −5.94375e12 | −0.255564 | ||||||||
\(935\) | −1.50886e12 | −0.0645649 | ||||||||
\(936\) | −3.70204e12 | −0.157652 | ||||||||
\(937\) | −1.29178e13 | −0.547469 | −0.273735 | − | 0.961805i | \(-0.588259\pi\) | ||||
−0.273735 | + | 0.961805i | \(0.588259\pi\) | |||||||
\(938\) | 7.98379e13 | 3.36741 | ||||||||
\(939\) | 1.37388e13 | 0.576703 | ||||||||
\(940\) | −5.88911e13 | −2.46022 | ||||||||
\(941\) | −3.12085e13 | −1.29754 | −0.648769 | − | 0.760986i | \(-0.724716\pi\) | ||||
−0.648769 | + | 0.760986i | \(0.724716\pi\) | |||||||
\(942\) | 2.63667e12 | 0.109101 | ||||||||
\(943\) | 1.59541e13 | 0.657008 | ||||||||
\(944\) | −1.80964e12 | −0.0741681 | ||||||||
\(945\) | −1.25193e13 | −0.510666 | ||||||||
\(946\) | 1.38730e13 | 0.563199 | ||||||||
\(947\) | 2.66359e13 | 1.07620 | 0.538099 | − | 0.842882i | \(-0.319143\pi\) | ||||
0.538099 | + | 0.842882i | \(0.319143\pi\) | |||||||
\(948\) | 3.76563e11 | 0.0151426 | ||||||||
\(949\) | −2.97356e13 | −1.19009 | ||||||||
\(950\) | 1.19358e13 | 0.475440 | ||||||||
\(951\) | −1.01865e13 | −0.403842 | ||||||||
\(952\) | 3.51306e12 | 0.138618 | ||||||||
\(953\) | −3.20298e13 | −1.25787 | −0.628936 | − | 0.777457i | \(-0.716509\pi\) | ||||
−0.628936 | + | 0.777457i | \(0.716509\pi\) | |||||||
\(954\) | 1.27473e13 | 0.498254 | ||||||||
\(955\) | −3.55242e13 | −1.38200 | ||||||||
\(956\) | −2.74218e13 | −1.06178 | ||||||||
\(957\) | −1.32768e12 | −0.0511669 | ||||||||
\(958\) | 4.06430e13 | 1.55898 | ||||||||
\(959\) | −6.52097e13 | −2.48959 | ||||||||
\(960\) | −3.48889e13 | −1.32576 | ||||||||
\(961\) | −2.60093e13 | −0.983725 | ||||||||
\(962\) | 3.81324e13 | 1.43551 | ||||||||
\(963\) | −2.20022e12 | −0.0824417 | ||||||||
\(964\) | −2.39391e12 | −0.0892814 | ||||||||
\(965\) | −5.66623e13 | −2.10340 | ||||||||
\(966\) | 5.47497e13 | 2.02295 | ||||||||
\(967\) | 3.00424e12 | 0.110488 | 0.0552440 | − | 0.998473i | \(-0.482406\pi\) | ||||
0.0552440 | + | 0.998473i | \(0.482406\pi\) | |||||||
\(968\) | −1.25814e13 | −0.460562 | ||||||||
\(969\) | 6.03656e11 | 0.0219954 | ||||||||
\(970\) | −3.99933e13 | −1.45049 | ||||||||
\(971\) | −1.27149e13 | −0.459016 | −0.229508 | − | 0.973307i | \(-0.573712\pi\) | ||||
−0.229508 | + | 0.973307i | \(0.573712\pi\) | |||||||
\(972\) | −2.36509e12 | −0.0849863 | ||||||||
\(973\) | 6.73318e13 | 2.40831 | ||||||||
\(974\) | 4.89785e13 | 1.74377 | ||||||||
\(975\) | 2.04293e13 | 0.723991 | ||||||||
\(976\) | 7.55259e12 | 0.266423 | ||||||||
\(977\) | 1.84870e13 | 0.649143 | 0.324571 | − | 0.945861i | \(-0.394780\pi\) | ||||
0.324571 | + | 0.945861i | \(0.394780\pi\) | |||||||
\(978\) | 1.53127e13 | 0.535214 | ||||||||
\(979\) | 1.21095e13 | 0.421314 | ||||||||
\(980\) | −1.18919e14 | −4.11844 | ||||||||
\(981\) | 6.60174e12 | 0.227587 | ||||||||
\(982\) | −1.26131e13 | −0.432834 | ||||||||
\(983\) | 3.61480e13 | 1.23479 | 0.617395 | − | 0.786654i | \(-0.288188\pi\) | ||||
0.617395 | + | 0.786654i | \(0.288188\pi\) | |||||||
\(984\) | −4.19446e12 | −0.142626 | ||||||||
\(985\) | −4.19010e12 | −0.141828 | ||||||||
\(986\) | 2.43134e12 | 0.0819218 | ||||||||
\(987\) | 3.66706e13 | 1.22996 | ||||||||
\(988\) | −8.99865e12 | −0.300449 | ||||||||
\(989\) | −5.53168e13 | −1.83854 | ||||||||
\(990\) | 6.18227e12 | 0.204545 | ||||||||
\(991\) | 3.82897e10 | 0.00126110 | 0.000630552 | − | 1.00000i | \(-0.499799\pi\) | ||||
0.000630552 | 1.00000i | \(0.499799\pi\) | ||||||||
\(992\) | −5.30684e12 | −0.173994 | ||||||||
\(993\) | 3.37174e13 | 1.10048 | ||||||||
\(994\) | 1.08359e14 | 3.52068 | ||||||||
\(995\) | −8.61398e13 | −2.78612 | ||||||||
\(996\) | 4.01424e12 | 0.129252 | ||||||||
\(997\) | −7.31678e12 | −0.234526 | −0.117263 | − | 0.993101i | \(-0.537412\pi\) | ||||
−0.117263 | + | 0.993101i | \(0.537412\pi\) | |||||||
\(998\) | 8.80121e13 | 2.80837 | ||||||||
\(999\) | 5.97270e12 | 0.189726 |
(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 | 177.10.a.c.1.19 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.c.1.19 | ✓ | 22 | 1.1 | even | 1 | trivial |