Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,16,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(14.2693505100\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 128.000 | 0.707107 | ||||||||
\(3\) | −1302.00 | −0.343717 | −0.171859 | − | 0.985122i | \(-0.554977\pi\) | ||||
−0.171859 | + | 0.985122i | \(0.554977\pi\) | |||||||
\(4\) | 16384.0 | 0.500000 | ||||||||
\(5\) | −78125.0 | −0.447214 | ||||||||
\(6\) | −166656. | −0.243045 | ||||||||
\(7\) | −90706.0 | −0.0416295 | −0.0208147 | − | 0.999783i | \(-0.506626\pi\) | ||||
−0.0208147 | + | 0.999783i | \(0.506626\pi\) | |||||||
\(8\) | 2.09715e6 | 0.353553 | ||||||||
\(9\) | −1.26537e7 | −0.881858 | ||||||||
\(10\) | −1.00000e7 | −0.316228 | ||||||||
\(11\) | −6.94116e7 | −1.07396 | −0.536979 | − | 0.843596i | \(-0.680435\pi\) | ||||
−0.536979 | + | 0.843596i | \(0.680435\pi\) | |||||||
\(12\) | −2.13320e7 | −0.171859 | ||||||||
\(13\) | −3.70575e7 | −0.163795 | −0.0818975 | − | 0.996641i | \(-0.526098\pi\) | ||||
−0.0818975 | + | 0.996641i | \(0.526098\pi\) | |||||||
\(14\) | −1.16104e7 | −0.0294365 | ||||||||
\(15\) | 1.01719e8 | 0.153715 | ||||||||
\(16\) | 2.68435e8 | 0.250000 | ||||||||
\(17\) | −1.37203e9 | −0.810954 | −0.405477 | − | 0.914105i | \(-0.632894\pi\) | ||||
−0.405477 | + | 0.914105i | \(0.632894\pi\) | |||||||
\(18\) | −1.61967e9 | −0.623568 | ||||||||
\(19\) | −5.06876e9 | −1.30092 | −0.650459 | − | 0.759542i | \(-0.725423\pi\) | ||||
−0.650459 | + | 0.759542i | \(0.725423\pi\) | |||||||
\(20\) | −1.28000e9 | −0.223607 | ||||||||
\(21\) | 1.18099e8 | 0.0143088 | ||||||||
\(22\) | −8.88469e9 | −0.759403 | ||||||||
\(23\) | −1.23426e10 | −0.755873 | −0.377937 | − | 0.925831i | \(-0.623366\pi\) | ||||
−0.377937 | + | 0.925831i | \(0.623366\pi\) | |||||||
\(24\) | −2.73049e9 | −0.121522 | ||||||||
\(25\) | 6.10352e9 | 0.200000 | ||||||||
\(26\) | −4.74336e9 | −0.115821 | ||||||||
\(27\) | 3.51574e10 | 0.646828 | ||||||||
\(28\) | −1.48613e9 | −0.0208147 | ||||||||
\(29\) | 5.78257e10 | 0.622495 | 0.311248 | − | 0.950329i | \(-0.399253\pi\) | ||||
0.311248 | + | 0.950329i | \(0.399253\pi\) | |||||||
\(30\) | 1.30200e10 | 0.108693 | ||||||||
\(31\) | 2.33728e11 | 1.52580 | 0.762901 | − | 0.646516i | \(-0.223775\pi\) | ||||
0.762901 | + | 0.646516i | \(0.223775\pi\) | |||||||
\(32\) | 3.43597e10 | 0.176777 | ||||||||
\(33\) | 9.03740e10 | 0.369138 | ||||||||
\(34\) | −1.75620e11 | −0.573431 | ||||||||
\(35\) | 7.08641e9 | 0.0186173 | ||||||||
\(36\) | −2.07318e11 | −0.440929 | ||||||||
\(37\) | 7.42248e11 | 1.28539 | 0.642696 | − | 0.766121i | \(-0.277816\pi\) | ||||
0.642696 | + | 0.766121i | \(0.277816\pi\) | |||||||
\(38\) | −6.48801e11 | −0.919888 | ||||||||
\(39\) | 4.82488e10 | 0.0562992 | ||||||||
\(40\) | −1.63840e11 | −0.158114 | ||||||||
\(41\) | −7.72700e11 | −0.619629 | −0.309815 | − | 0.950797i | \(-0.600267\pi\) | ||||
−0.309815 | + | 0.950797i | \(0.600267\pi\) | |||||||
\(42\) | 1.51167e10 | 0.0101178 | ||||||||
\(43\) | −4.05994e11 | −0.227775 | −0.113888 | − | 0.993494i | \(-0.536330\pi\) | ||||
−0.113888 | + | 0.993494i | \(0.536330\pi\) | |||||||
\(44\) | −1.13724e12 | −0.536979 | ||||||||
\(45\) | 9.88571e11 | 0.394379 | ||||||||
\(46\) | −1.57986e12 | −0.534483 | ||||||||
\(47\) | 1.62301e12 | 0.467291 | 0.233646 | − | 0.972322i | \(-0.424934\pi\) | ||||
0.233646 | + | 0.972322i | \(0.424934\pi\) | |||||||
\(48\) | −3.49503e11 | −0.0859294 | ||||||||
\(49\) | −4.73933e12 | −0.998267 | ||||||||
\(50\) | 7.81250e11 | 0.141421 | ||||||||
\(51\) | 1.78638e12 | 0.278739 | ||||||||
\(52\) | −6.07149e11 | −0.0818975 | ||||||||
\(53\) | −5.36560e12 | −0.627407 | −0.313703 | − | 0.949521i | \(-0.601570\pi\) | ||||
−0.313703 | + | 0.949521i | \(0.601570\pi\) | |||||||
\(54\) | 4.50015e12 | 0.457376 | ||||||||
\(55\) | 5.42278e12 | 0.480289 | ||||||||
\(56\) | −1.90224e11 | −0.0147182 | ||||||||
\(57\) | 6.59953e12 | 0.447148 | ||||||||
\(58\) | 7.40169e12 | 0.440171 | ||||||||
\(59\) | 9.24016e12 | 0.483381 | 0.241690 | − | 0.970353i | \(-0.422298\pi\) | ||||
0.241690 | + | 0.970353i | \(0.422298\pi\) | |||||||
\(60\) | 1.66656e12 | 0.0768576 | ||||||||
\(61\) | 9.44308e11 | 0.0384716 | 0.0192358 | − | 0.999815i | \(-0.493877\pi\) | ||||
0.0192358 | + | 0.999815i | \(0.493877\pi\) | |||||||
\(62\) | 2.99172e13 | 1.07890 | ||||||||
\(63\) | 1.14777e12 | 0.0367113 | ||||||||
\(64\) | 4.39805e12 | 0.125000 | ||||||||
\(65\) | 2.89511e12 | 0.0732513 | ||||||||
\(66\) | 1.15679e13 | 0.261020 | ||||||||
\(67\) | −7.05676e13 | −1.42247 | −0.711237 | − | 0.702953i | \(-0.751865\pi\) | ||||
−0.711237 | + | 0.702953i | \(0.751865\pi\) | |||||||
\(68\) | −2.24793e13 | −0.405477 | ||||||||
\(69\) | 1.60701e13 | 0.259807 | ||||||||
\(70\) | 9.07060e11 | 0.0131644 | ||||||||
\(71\) | −8.25347e13 | −1.07696 | −0.538479 | − | 0.842639i | \(-0.681001\pi\) | ||||
−0.538479 | + | 0.842639i | \(0.681001\pi\) | |||||||
\(72\) | −2.65367e13 | −0.311784 | ||||||||
\(73\) | −1.78432e14 | −1.89039 | −0.945197 | − | 0.326502i | \(-0.894130\pi\) | ||||
−0.945197 | + | 0.326502i | \(0.894130\pi\) | |||||||
\(74\) | 9.50077e13 | 0.908910 | ||||||||
\(75\) | −7.94678e12 | −0.0687435 | ||||||||
\(76\) | −8.30466e13 | −0.650459 | ||||||||
\(77\) | 6.29605e12 | 0.0447083 | ||||||||
\(78\) | 6.17585e12 | 0.0398095 | ||||||||
\(79\) | 3.07261e14 | 1.80013 | 0.900067 | − | 0.435752i | \(-0.143518\pi\) | ||||
0.900067 | + | 0.435752i | \(0.143518\pi\) | |||||||
\(80\) | −2.09715e13 | −0.111803 | ||||||||
\(81\) | 1.35792e14 | 0.659532 | ||||||||
\(82\) | −9.89056e13 | −0.438144 | ||||||||
\(83\) | 4.31597e13 | 0.174579 | 0.0872897 | − | 0.996183i | \(-0.472179\pi\) | ||||
0.0872897 | + | 0.996183i | \(0.472179\pi\) | |||||||
\(84\) | 1.93494e12 | 0.00715438 | ||||||||
\(85\) | 1.07190e14 | 0.362669 | ||||||||
\(86\) | −5.19673e13 | −0.161061 | ||||||||
\(87\) | −7.52891e13 | −0.213962 | ||||||||
\(88\) | −1.45567e14 | −0.379701 | ||||||||
\(89\) | 6.81678e14 | 1.63363 | 0.816816 | − | 0.576899i | \(-0.195737\pi\) | ||||
0.816816 | + | 0.576899i | \(0.195737\pi\) | |||||||
\(90\) | 1.26537e14 | 0.278868 | ||||||||
\(91\) | 3.36133e12 | 0.00681869 | ||||||||
\(92\) | −2.02222e14 | −0.377937 | ||||||||
\(93\) | −3.04314e14 | −0.524445 | ||||||||
\(94\) | 2.07745e14 | 0.330425 | ||||||||
\(95\) | 3.95997e14 | 0.581788 | ||||||||
\(96\) | −4.47364e13 | −0.0607612 | ||||||||
\(97\) | −2.36520e14 | −0.297222 | −0.148611 | − | 0.988896i | \(-0.547480\pi\) | ||||
−0.148611 | + | 0.988896i | \(0.547480\pi\) | |||||||
\(98\) | −6.06635e14 | −0.705881 | ||||||||
\(99\) | 8.78314e14 | 0.947079 | ||||||||
\(100\) | 1.00000e14 | 0.100000 | ||||||||
\(101\) | −1.39643e15 | −1.29601 | −0.648005 | − | 0.761636i | \(-0.724397\pi\) | ||||
−0.648005 | + | 0.761636i | \(0.724397\pi\) | |||||||
\(102\) | 2.28657e14 | 0.197098 | ||||||||
\(103\) | −1.46886e15 | −1.17680 | −0.588398 | − | 0.808572i | \(-0.700241\pi\) | ||||
−0.588398 | + | 0.808572i | \(0.700241\pi\) | |||||||
\(104\) | −7.77151e13 | −0.0579103 | ||||||||
\(105\) | −9.22650e12 | −0.00639908 | ||||||||
\(106\) | −6.86797e14 | −0.443644 | ||||||||
\(107\) | 1.19960e15 | 0.722203 | 0.361102 | − | 0.932526i | \(-0.382401\pi\) | ||||
0.361102 | + | 0.932526i | \(0.382401\pi\) | |||||||
\(108\) | 5.76019e14 | 0.323414 | ||||||||
\(109\) | 2.63914e14 | 0.138281 | 0.0691407 | − | 0.997607i | \(-0.477974\pi\) | ||||
0.0691407 | + | 0.997607i | \(0.477974\pi\) | |||||||
\(110\) | 6.94116e14 | 0.339615 | ||||||||
\(111\) | −9.66406e14 | −0.441812 | ||||||||
\(112\) | −2.43487e13 | −0.0104074 | ||||||||
\(113\) | −4.67332e15 | −1.86869 | −0.934346 | − | 0.356368i | \(-0.884015\pi\) | ||||
−0.934346 | + | 0.356368i | \(0.884015\pi\) | |||||||
\(114\) | 8.44739e14 | 0.316181 | ||||||||
\(115\) | 9.64268e14 | 0.338037 | ||||||||
\(116\) | 9.47417e14 | 0.311248 | ||||||||
\(117\) | 4.68914e14 | 0.144444 | ||||||||
\(118\) | 1.18274e15 | 0.341802 | ||||||||
\(119\) | 1.24451e14 | 0.0337596 | ||||||||
\(120\) | 2.13320e14 | 0.0543465 | ||||||||
\(121\) | 6.40729e14 | 0.153385 | ||||||||
\(122\) | 1.20871e14 | 0.0272035 | ||||||||
\(123\) | 1.00606e15 | 0.212977 | ||||||||
\(124\) | 3.82940e15 | 0.762901 | ||||||||
\(125\) | −4.76837e14 | −0.0894427 | ||||||||
\(126\) | 1.46914e14 | 0.0259588 | ||||||||
\(127\) | 5.53712e15 | 0.922053 | 0.461027 | − | 0.887386i | \(-0.347481\pi\) | ||||
0.461027 | + | 0.887386i | \(0.347481\pi\) | |||||||
\(128\) | 5.62950e14 | 0.0883883 | ||||||||
\(129\) | 5.28605e14 | 0.0782903 | ||||||||
\(130\) | 3.70575e14 | 0.0517965 | ||||||||
\(131\) | 7.83095e15 | 1.03343 | 0.516714 | − | 0.856158i | \(-0.327155\pi\) | ||||
0.516714 | + | 0.856158i | \(0.327155\pi\) | |||||||
\(132\) | 1.48069e15 | 0.184569 | ||||||||
\(133\) | 4.59767e14 | 0.0541565 | ||||||||
\(134\) | −9.03265e15 | −1.00584 | ||||||||
\(135\) | −2.74667e15 | −0.289270 | ||||||||
\(136\) | −2.87735e15 | −0.286715 | ||||||||
\(137\) | −1.88872e16 | −1.78140 | −0.890702 | − | 0.454587i | \(-0.849787\pi\) | ||||
−0.890702 | + | 0.454587i | \(0.849787\pi\) | |||||||
\(138\) | 2.05697e15 | 0.183711 | ||||||||
\(139\) | 6.08888e15 | 0.515142 | 0.257571 | − | 0.966259i | \(-0.417078\pi\) | ||||
0.257571 | + | 0.966259i | \(0.417078\pi\) | |||||||
\(140\) | 1.16104e14 | 0.00930863 | ||||||||
\(141\) | −2.11316e15 | −0.160616 | ||||||||
\(142\) | −1.05644e16 | −0.761525 | ||||||||
\(143\) | 2.57222e15 | 0.175909 | ||||||||
\(144\) | −3.39670e15 | −0.220465 | ||||||||
\(145\) | −4.51763e15 | −0.278388 | ||||||||
\(146\) | −2.28393e16 | −1.33671 | ||||||||
\(147\) | 6.17061e15 | 0.343122 | ||||||||
\(148\) | 1.21610e16 | 0.642696 | ||||||||
\(149\) | −2.97847e16 | −1.49657 | −0.748285 | − | 0.663378i | \(-0.769122\pi\) | ||||
−0.748285 | + | 0.663378i | \(0.769122\pi\) | |||||||
\(150\) | −1.01719e15 | −0.0486090 | ||||||||
\(151\) | 3.43750e16 | 1.56284 | 0.781421 | − | 0.624004i | \(-0.214495\pi\) | ||||
0.781421 | + | 0.624004i | \(0.214495\pi\) | |||||||
\(152\) | −1.06300e16 | −0.459944 | ||||||||
\(153\) | 1.73612e16 | 0.715146 | ||||||||
\(154\) | 8.05895e14 | 0.0316135 | ||||||||
\(155\) | −1.82600e16 | −0.682359 | ||||||||
\(156\) | 7.90509e14 | 0.0281496 | ||||||||
\(157\) | 3.24674e16 | 1.10205 | 0.551024 | − | 0.834490i | \(-0.314237\pi\) | ||||
0.551024 | + | 0.834490i | \(0.314237\pi\) | |||||||
\(158\) | 3.93294e16 | 1.27289 | ||||||||
\(159\) | 6.98601e15 | 0.215651 | ||||||||
\(160\) | −2.68435e15 | −0.0790569 | ||||||||
\(161\) | 1.11955e15 | 0.0314666 | ||||||||
\(162\) | 1.73814e16 | 0.466360 | ||||||||
\(163\) | 2.42386e16 | 0.621013 | 0.310506 | − | 0.950571i | \(-0.399501\pi\) | ||||
0.310506 | + | 0.950571i | \(0.399501\pi\) | |||||||
\(164\) | −1.26599e16 | −0.309815 | ||||||||
\(165\) | −7.06047e15 | −0.165084 | ||||||||
\(166\) | 5.52445e15 | 0.123446 | ||||||||
\(167\) | 3.26384e15 | 0.0697196 | 0.0348598 | − | 0.999392i | \(-0.488902\pi\) | ||||
0.0348598 | + | 0.999392i | \(0.488902\pi\) | |||||||
\(168\) | 2.47672e14 | 0.00505891 | ||||||||
\(169\) | −4.98126e16 | −0.973171 | ||||||||
\(170\) | 1.37203e16 | 0.256446 | ||||||||
\(171\) | 6.41386e16 | 1.14722 | ||||||||
\(172\) | −6.65181e15 | −0.113888 | ||||||||
\(173\) | −9.54205e16 | −1.56421 | −0.782106 | − | 0.623145i | \(-0.785855\pi\) | ||||
−0.782106 | + | 0.623145i | \(0.785855\pi\) | |||||||
\(174\) | −9.63700e15 | −0.151294 | ||||||||
\(175\) | −5.53625e14 | −0.00832589 | ||||||||
\(176\) | −1.86325e16 | −0.268489 | ||||||||
\(177\) | −1.20307e16 | −0.166146 | ||||||||
\(178\) | 8.72548e16 | 1.15515 | ||||||||
\(179\) | −1.08211e17 | −1.37365 | −0.686823 | − | 0.726824i | \(-0.740995\pi\) | ||||
−0.686823 | + | 0.726824i | \(0.740995\pi\) | |||||||
\(180\) | 1.61967e16 | 0.197190 | ||||||||
\(181\) | 2.21984e16 | 0.259258 | 0.129629 | − | 0.991563i | \(-0.458621\pi\) | ||||
0.129629 | + | 0.991563i | \(0.458621\pi\) | |||||||
\(182\) | 4.30251e14 | 0.00482155 | ||||||||
\(183\) | −1.22949e15 | −0.0132234 | ||||||||
\(184\) | −2.58844e16 | −0.267242 | ||||||||
\(185\) | −5.79881e16 | −0.574845 | ||||||||
\(186\) | −3.89522e16 | −0.370838 | ||||||||
\(187\) | 9.52347e16 | 0.870930 | ||||||||
\(188\) | 2.65914e16 | 0.233646 | ||||||||
\(189\) | −3.18899e15 | −0.0269271 | ||||||||
\(190\) | 5.06876e16 | 0.411386 | ||||||||
\(191\) | −3.42389e16 | −0.267159 | −0.133580 | − | 0.991038i | \(-0.542647\pi\) | ||||
−0.133580 | + | 0.991038i | \(0.542647\pi\) | |||||||
\(192\) | −5.72626e15 | −0.0429647 | ||||||||
\(193\) | −2.27131e17 | −1.63907 | −0.819533 | − | 0.573031i | \(-0.805767\pi\) | ||||
−0.819533 | + | 0.573031i | \(0.805767\pi\) | |||||||
\(194\) | −3.02746e16 | −0.210167 | ||||||||
\(195\) | −3.76944e15 | −0.0251778 | ||||||||
\(196\) | −7.76492e16 | −0.499133 | ||||||||
\(197\) | 2.63870e16 | 0.163265 | 0.0816325 | − | 0.996662i | \(-0.473987\pi\) | ||||
0.0816325 | + | 0.996662i | \(0.473987\pi\) | |||||||
\(198\) | 1.12424e17 | 0.669686 | ||||||||
\(199\) | 1.99493e17 | 1.14427 | 0.572137 | − | 0.820158i | \(-0.306115\pi\) | ||||
0.572137 | + | 0.820158i | \(0.306115\pi\) | |||||||
\(200\) | 1.28000e16 | 0.0707107 | ||||||||
\(201\) | 9.18790e16 | 0.488929 | ||||||||
\(202\) | −1.78743e17 | −0.916418 | ||||||||
\(203\) | −5.24514e15 | −0.0259141 | ||||||||
\(204\) | 2.92681e16 | 0.139369 | ||||||||
\(205\) | 6.03672e16 | 0.277107 | ||||||||
\(206\) | −1.88014e17 | −0.832120 | ||||||||
\(207\) | 1.56180e17 | 0.666573 | ||||||||
\(208\) | −9.94754e15 | −0.0409487 | ||||||||
\(209\) | 3.51831e17 | 1.39713 | ||||||||
\(210\) | −1.18099e15 | −0.00452483 | ||||||||
\(211\) | 6.45604e16 | 0.238697 | 0.119349 | − | 0.992852i | \(-0.461919\pi\) | ||||
0.119349 | + | 0.992852i | \(0.461919\pi\) | |||||||
\(212\) | −8.79100e16 | −0.313703 | ||||||||
\(213\) | 1.07460e17 | 0.370170 | ||||||||
\(214\) | 1.53549e17 | 0.510675 | ||||||||
\(215\) | 3.17183e16 | 0.101864 | ||||||||
\(216\) | 7.37304e16 | 0.228688 | ||||||||
\(217\) | −2.12005e16 | −0.0635183 | ||||||||
\(218\) | 3.37810e16 | 0.0977797 | ||||||||
\(219\) | 2.32319e17 | 0.649761 | ||||||||
\(220\) | 8.88469e16 | 0.240144 | ||||||||
\(221\) | 5.08439e16 | 0.132830 | ||||||||
\(222\) | −1.23700e17 | −0.312408 | ||||||||
\(223\) | −6.71970e17 | −1.64083 | −0.820415 | − | 0.571769i | \(-0.806257\pi\) | ||||
−0.820415 | + | 0.571769i | \(0.806257\pi\) | |||||||
\(224\) | −3.11663e15 | −0.00735912 | ||||||||
\(225\) | −7.72321e16 | −0.176372 | ||||||||
\(226\) | −5.98185e17 | −1.32136 | ||||||||
\(227\) | −5.40955e17 | −1.15602 | −0.578012 | − | 0.816028i | \(-0.696171\pi\) | ||||
−0.578012 | + | 0.816028i | \(0.696171\pi\) | |||||||
\(228\) | 1.08127e17 | 0.223574 | ||||||||
\(229\) | 7.52317e17 | 1.50534 | 0.752671 | − | 0.658397i | \(-0.228765\pi\) | ||||
0.752671 | + | 0.658397i | \(0.228765\pi\) | |||||||
\(230\) | 1.23426e17 | 0.239028 | ||||||||
\(231\) | −8.19746e15 | −0.0153670 | ||||||||
\(232\) | 1.21269e17 | 0.220085 | ||||||||
\(233\) | −7.64780e17 | −1.34390 | −0.671951 | − | 0.740596i | \(-0.734543\pi\) | ||||
−0.671951 | + | 0.740596i | \(0.734543\pi\) | |||||||
\(234\) | 6.00210e16 | 0.102137 | ||||||||
\(235\) | −1.26798e17 | −0.208979 | ||||||||
\(236\) | 1.51391e17 | 0.241690 | ||||||||
\(237\) | −4.00054e17 | −0.618737 | ||||||||
\(238\) | 1.59297e16 | 0.0238716 | ||||||||
\(239\) | −6.74103e17 | −0.978908 | −0.489454 | − | 0.872029i | \(-0.662804\pi\) | ||||
−0.489454 | + | 0.872029i | \(0.662804\pi\) | |||||||
\(240\) | 2.73049e16 | 0.0384288 | ||||||||
\(241\) | 3.16938e17 | 0.432361 | 0.216180 | − | 0.976353i | \(-0.430640\pi\) | ||||
0.216180 | + | 0.976353i | \(0.430640\pi\) | |||||||
\(242\) | 8.20133e16 | 0.108460 | ||||||||
\(243\) | −6.81271e17 | −0.873520 | ||||||||
\(244\) | 1.54715e16 | 0.0192358 | ||||||||
\(245\) | 3.70260e17 | 0.446439 | ||||||||
\(246\) | 1.28775e17 | 0.150598 | ||||||||
\(247\) | 1.87835e17 | 0.213084 | ||||||||
\(248\) | 4.90163e17 | 0.539452 | ||||||||
\(249\) | −5.61940e16 | −0.0600060 | ||||||||
\(250\) | −6.10352e16 | −0.0632456 | ||||||||
\(251\) | −1.54964e17 | −0.155840 | −0.0779200 | − | 0.996960i | \(-0.524828\pi\) | ||||
−0.0779200 | + | 0.996960i | \(0.524828\pi\) | |||||||
\(252\) | 1.88050e16 | 0.0183556 | ||||||||
\(253\) | 8.56722e17 | 0.811776 | ||||||||
\(254\) | 7.08751e17 | 0.651990 | ||||||||
\(255\) | −1.39561e17 | −0.124656 | ||||||||
\(256\) | 7.20576e16 | 0.0625000 | ||||||||
\(257\) | 2.25253e18 | 1.89746 | 0.948731 | − | 0.316086i | \(-0.102369\pi\) | ||||
0.948731 | + | 0.316086i | \(0.102369\pi\) | |||||||
\(258\) | 6.76614e16 | 0.0553596 | ||||||||
\(259\) | −6.73263e16 | −0.0535102 | ||||||||
\(260\) | 4.74336e16 | 0.0366257 | ||||||||
\(261\) | −7.31710e17 | −0.548953 | ||||||||
\(262\) | 1.00236e18 | 0.730744 | ||||||||
\(263\) | 1.00925e18 | 0.715044 | 0.357522 | − | 0.933905i | \(-0.383622\pi\) | ||||
0.357522 | + | 0.933905i | \(0.383622\pi\) | |||||||
\(264\) | 1.89528e17 | 0.130510 | ||||||||
\(265\) | 4.19187e17 | 0.280585 | ||||||||
\(266\) | 5.88502e16 | 0.0382944 | ||||||||
\(267\) | −8.87544e17 | −0.561508 | ||||||||
\(268\) | −1.15618e18 | −0.711237 | ||||||||
\(269\) | −9.29818e17 | −0.556232 | −0.278116 | − | 0.960548i | \(-0.589710\pi\) | ||||
−0.278116 | + | 0.960548i | \(0.589710\pi\) | |||||||
\(270\) | −3.51574e17 | −0.204545 | ||||||||
\(271\) | −6.51376e16 | −0.0368606 | −0.0184303 | − | 0.999830i | \(-0.505867\pi\) | ||||
−0.0184303 | + | 0.999830i | \(0.505867\pi\) | |||||||
\(272\) | −3.68301e17 | −0.202738 | ||||||||
\(273\) | −4.37646e15 | −0.00234370 | ||||||||
\(274\) | −2.41756e18 | −1.25964 | ||||||||
\(275\) | −4.23655e17 | −0.214792 | ||||||||
\(276\) | 2.63293e17 | 0.129903 | ||||||||
\(277\) | −8.74228e16 | −0.0419784 | −0.0209892 | − | 0.999780i | \(-0.506682\pi\) | ||||
−0.0209892 | + | 0.999780i | \(0.506682\pi\) | |||||||
\(278\) | 7.79377e17 | 0.364260 | ||||||||
\(279\) | −2.95752e18 | −1.34554 | ||||||||
\(280\) | 1.48613e16 | 0.00658219 | ||||||||
\(281\) | 1.10585e18 | 0.476867 | 0.238433 | − | 0.971159i | \(-0.423366\pi\) | ||||
0.238433 | + | 0.971159i | \(0.423366\pi\) | |||||||
\(282\) | −2.70484e17 | −0.113573 | ||||||||
\(283\) | 2.15159e18 | 0.879756 | 0.439878 | − | 0.898058i | \(-0.355022\pi\) | ||||
0.439878 | + | 0.898058i | \(0.355022\pi\) | |||||||
\(284\) | −1.35225e18 | −0.538479 | ||||||||
\(285\) | −5.15588e17 | −0.199971 | ||||||||
\(286\) | 3.29244e17 | 0.124386 | ||||||||
\(287\) | 7.00885e16 | 0.0257948 | ||||||||
\(288\) | −4.34778e17 | −0.155892 | ||||||||
\(289\) | −9.79963e17 | −0.342354 | ||||||||
\(290\) | −5.78257e17 | −0.196850 | ||||||||
\(291\) | 3.07949e17 | 0.102160 | ||||||||
\(292\) | −2.92344e18 | −0.945197 | ||||||||
\(293\) | 5.52332e18 | 1.74058 | 0.870288 | − | 0.492543i | \(-0.163933\pi\) | ||||
0.870288 | + | 0.492543i | \(0.163933\pi\) | |||||||
\(294\) | 7.89838e17 | 0.242624 | ||||||||
\(295\) | −7.21887e17 | −0.216174 | ||||||||
\(296\) | 1.55661e18 | 0.454455 | ||||||||
\(297\) | −2.44033e18 | −0.694665 | ||||||||
\(298\) | −3.81245e18 | −1.05823 | ||||||||
\(299\) | 4.57387e17 | 0.123808 | ||||||||
\(300\) | −1.30200e17 | −0.0343717 | ||||||||
\(301\) | 3.68261e16 | 0.00948216 | ||||||||
\(302\) | 4.40000e18 | 1.10510 | ||||||||
\(303\) | 1.81815e18 | 0.445461 | ||||||||
\(304\) | −1.36064e18 | −0.325229 | ||||||||
\(305\) | −7.37741e16 | −0.0172050 | ||||||||
\(306\) | 2.22224e18 | 0.505685 | ||||||||
\(307\) | 9.87586e17 | 0.219299 | 0.109650 | − | 0.993970i | \(-0.465027\pi\) | ||||
0.109650 | + | 0.993970i | \(0.465027\pi\) | |||||||
\(308\) | 1.03155e17 | 0.0223541 | ||||||||
\(309\) | 1.91245e18 | 0.404485 | ||||||||
\(310\) | −2.33728e18 | −0.482501 | ||||||||
\(311\) | −3.09644e18 | −0.623965 | −0.311982 | − | 0.950088i | \(-0.600993\pi\) | ||||
−0.311982 | + | 0.950088i | \(0.600993\pi\) | |||||||
\(312\) | 1.01185e17 | 0.0199048 | ||||||||
\(313\) | 1.19355e18 | 0.229224 | 0.114612 | − | 0.993410i | \(-0.463438\pi\) | ||||
0.114612 | + | 0.993410i | \(0.463438\pi\) | |||||||
\(314\) | 4.15583e18 | 0.779265 | ||||||||
\(315\) | −8.96693e16 | −0.0164178 | ||||||||
\(316\) | 5.03417e18 | 0.900067 | ||||||||
\(317\) | −2.70108e18 | −0.471621 | −0.235811 | − | 0.971799i | \(-0.575774\pi\) | ||||
−0.235811 | + | 0.971799i | \(0.575774\pi\) | |||||||
\(318\) | 8.94209e17 | 0.152488 | ||||||||
\(319\) | −4.01378e18 | −0.668534 | ||||||||
\(320\) | −3.43597e17 | −0.0559017 | ||||||||
\(321\) | −1.56188e18 | −0.248234 | ||||||||
\(322\) | 1.43302e17 | 0.0222502 | ||||||||
\(323\) | 6.95448e18 | 1.05498 | ||||||||
\(324\) | 2.22481e18 | 0.329766 | ||||||||
\(325\) | −2.26181e17 | −0.0327590 | ||||||||
\(326\) | 3.10254e18 | 0.439122 | ||||||||
\(327\) | −3.43616e17 | −0.0475297 | ||||||||
\(328\) | −1.62047e18 | −0.219072 | ||||||||
\(329\) | −1.47217e17 | −0.0194531 | ||||||||
\(330\) | −9.03740e17 | −0.116732 | ||||||||
\(331\) | −9.04958e17 | −0.114266 | −0.0571332 | − | 0.998367i | \(-0.518196\pi\) | ||||
−0.0571332 | + | 0.998367i | \(0.518196\pi\) | |||||||
\(332\) | 7.07129e17 | 0.0872897 | ||||||||
\(333\) | −9.39218e18 | −1.13353 | ||||||||
\(334\) | 4.17771e17 | 0.0492992 | ||||||||
\(335\) | 5.51309e18 | 0.636150 | ||||||||
\(336\) | 3.17020e16 | 0.00357719 | ||||||||
\(337\) | −6.84140e17 | −0.0754955 | −0.0377477 | − | 0.999287i | \(-0.512018\pi\) | ||||
−0.0377477 | + | 0.999287i | \(0.512018\pi\) | |||||||
\(338\) | −6.37602e18 | −0.688136 | ||||||||
\(339\) | 6.08467e18 | 0.642302 | ||||||||
\(340\) | 1.75620e18 | 0.181335 | ||||||||
\(341\) | −1.62234e19 | −1.63865 | ||||||||
\(342\) | 8.20974e18 | 0.811211 | ||||||||
\(343\) | 8.60518e17 | 0.0831868 | ||||||||
\(344\) | −8.51432e17 | −0.0805307 | ||||||||
\(345\) | −1.25548e18 | −0.116189 | ||||||||
\(346\) | −1.22138e19 | −1.10607 | ||||||||
\(347\) | −1.18426e19 | −1.04948 | −0.524742 | − | 0.851261i | \(-0.675838\pi\) | ||||
−0.524742 | + | 0.851261i | \(0.675838\pi\) | |||||||
\(348\) | −1.23354e18 | −0.106981 | ||||||||
\(349\) | −4.67865e18 | −0.397127 | −0.198564 | − | 0.980088i | \(-0.563628\pi\) | ||||
−0.198564 | + | 0.980088i | \(0.563628\pi\) | |||||||
\(350\) | −7.08641e16 | −0.00588729 | ||||||||
\(351\) | −1.30284e18 | −0.105947 | ||||||||
\(352\) | −2.38497e18 | −0.189851 | ||||||||
\(353\) | −6.21571e18 | −0.484374 | −0.242187 | − | 0.970230i | \(-0.577865\pi\) | ||||
−0.242187 | + | 0.970230i | \(0.577865\pi\) | |||||||
\(354\) | −1.53993e18 | −0.117483 | ||||||||
\(355\) | 6.44803e18 | 0.481631 | ||||||||
\(356\) | 1.11686e19 | 0.816816 | ||||||||
\(357\) | −1.62035e17 | −0.0116037 | ||||||||
\(358\) | −1.38511e19 | −0.971315 | ||||||||
\(359\) | 8.67422e18 | 0.595693 | 0.297846 | − | 0.954614i | \(-0.403732\pi\) | ||||
0.297846 | + | 0.954614i | \(0.403732\pi\) | |||||||
\(360\) | 2.07318e18 | 0.139434 | ||||||||
\(361\) | 1.05112e19 | 0.692386 | ||||||||
\(362\) | 2.84139e18 | 0.183323 | ||||||||
\(363\) | −8.34229e17 | −0.0527212 | ||||||||
\(364\) | 5.50721e16 | 0.00340935 | ||||||||
\(365\) | 1.39400e19 | 0.845410 | ||||||||
\(366\) | −1.57375e17 | −0.00935032 | ||||||||
\(367\) | 2.60076e19 | 1.51393 | 0.756964 | − | 0.653457i | \(-0.226682\pi\) | ||||
0.756964 | + | 0.653457i | \(0.226682\pi\) | |||||||
\(368\) | −3.31320e18 | −0.188968 | ||||||||
\(369\) | 9.77751e18 | 0.546425 | ||||||||
\(370\) | −7.42248e18 | −0.406477 | ||||||||
\(371\) | 4.86692e17 | 0.0261186 | ||||||||
\(372\) | −4.98588e18 | −0.262222 | ||||||||
\(373\) | 3.24522e18 | 0.167274 | 0.0836369 | − | 0.996496i | \(-0.473346\pi\) | ||||
0.0836369 | + | 0.996496i | \(0.473346\pi\) | |||||||
\(374\) | 1.21900e19 | 0.615840 | ||||||||
\(375\) | 6.20842e17 | 0.0307430 | ||||||||
\(376\) | 3.40370e18 | 0.165212 | ||||||||
\(377\) | −2.14287e18 | −0.101962 | ||||||||
\(378\) | −4.08190e17 | −0.0190403 | ||||||||
\(379\) | 3.97275e19 | 1.81676 | 0.908379 | − | 0.418148i | \(-0.137321\pi\) | ||||
0.908379 | + | 0.418148i | \(0.137321\pi\) | |||||||
\(380\) | 6.48801e18 | 0.290894 | ||||||||
\(381\) | −7.20933e18 | −0.316926 | ||||||||
\(382\) | −4.38258e18 | −0.188910 | ||||||||
\(383\) | −1.39053e19 | −0.587747 | −0.293874 | − | 0.955844i | \(-0.594944\pi\) | ||||
−0.293874 | + | 0.955844i | \(0.594944\pi\) | |||||||
\(384\) | −7.32961e17 | −0.0303806 | ||||||||
\(385\) | −4.91879e17 | −0.0199941 | ||||||||
\(386\) | −2.90728e19 | −1.15900 | ||||||||
\(387\) | 5.13733e18 | 0.200866 | ||||||||
\(388\) | −3.87515e18 | −0.148611 | ||||||||
\(389\) | −2.40519e19 | −0.904749 | −0.452374 | − | 0.891828i | \(-0.649423\pi\) | ||||
−0.452374 | + | 0.891828i | \(0.649423\pi\) | |||||||
\(390\) | −4.82488e17 | −0.0178034 | ||||||||
\(391\) | 1.69344e19 | 0.612978 | ||||||||
\(392\) | −9.93910e18 | −0.352941 | ||||||||
\(393\) | −1.01959e19 | −0.355207 | ||||||||
\(394\) | 3.37754e18 | 0.115446 | ||||||||
\(395\) | −2.40048e19 | −0.805044 | ||||||||
\(396\) | 1.43903e19 | 0.473539 | ||||||||
\(397\) | 4.68747e17 | 0.0151359 | 0.00756797 | − | 0.999971i | \(-0.497591\pi\) | ||||
0.00756797 | + | 0.999971i | \(0.497591\pi\) | |||||||
\(398\) | 2.55351e19 | 0.809124 | ||||||||
\(399\) | −5.98617e17 | −0.0186145 | ||||||||
\(400\) | 1.63840e18 | 0.0500000 | ||||||||
\(401\) | −4.59281e19 | −1.37561 | −0.687806 | − | 0.725894i | \(-0.741426\pi\) | ||||
−0.687806 | + | 0.725894i | \(0.741426\pi\) | |||||||
\(402\) | 1.17605e19 | 0.345725 | ||||||||
\(403\) | −8.66137e18 | −0.249919 | ||||||||
\(404\) | −2.28791e19 | −0.648005 | ||||||||
\(405\) | −1.06087e19 | −0.294952 | ||||||||
\(406\) | −6.71378e17 | −0.0183241 | ||||||||
\(407\) | −5.15206e19 | −1.38046 | ||||||||
\(408\) | 3.74631e18 | 0.0985491 | ||||||||
\(409\) | −2.87071e18 | −0.0741421 | −0.0370710 | − | 0.999313i | \(-0.511803\pi\) | ||||
−0.0370710 | + | 0.999313i | \(0.511803\pi\) | |||||||
\(410\) | 7.72700e18 | 0.195944 | ||||||||
\(411\) | 2.45911e19 | 0.612300 | ||||||||
\(412\) | −2.40658e19 | −0.588398 | ||||||||
\(413\) | −8.38138e17 | −0.0201229 | ||||||||
\(414\) | 1.99910e19 | 0.471338 | ||||||||
\(415\) | −3.37185e18 | −0.0780743 | ||||||||
\(416\) | −1.27328e18 | −0.0289551 | ||||||||
\(417\) | −7.92773e18 | −0.177063 | ||||||||
\(418\) | 4.50344e19 | 0.987920 | ||||||||
\(419\) | −1.95181e19 | −0.420563 | −0.210282 | − | 0.977641i | \(-0.567438\pi\) | ||||
−0.210282 | + | 0.977641i | \(0.567438\pi\) | |||||||
\(420\) | −1.51167e17 | −0.00319954 | ||||||||
\(421\) | 7.84258e19 | 1.63058 | 0.815292 | − | 0.579049i | \(-0.196576\pi\) | ||||
0.815292 | + | 0.579049i | \(0.196576\pi\) | |||||||
\(422\) | 8.26373e18 | 0.168785 | ||||||||
\(423\) | −2.05371e19 | −0.412084 | ||||||||
\(424\) | −1.12525e19 | −0.221822 | ||||||||
\(425\) | −8.37419e18 | −0.162191 | ||||||||
\(426\) | 1.37549e19 | 0.261749 | ||||||||
\(427\) | −8.56544e16 | −0.00160155 | ||||||||
\(428\) | 1.96543e19 | 0.361102 | ||||||||
\(429\) | −3.34903e18 | −0.0604629 | ||||||||
\(430\) | 4.05994e18 | 0.0720289 | ||||||||
\(431\) | −5.24106e19 | −0.913776 | −0.456888 | − | 0.889524i | \(-0.651036\pi\) | ||||
−0.456888 | + | 0.889524i | \(0.651036\pi\) | |||||||
\(432\) | 9.43749e18 | 0.161707 | ||||||||
\(433\) | 6.72089e19 | 1.13179 | 0.565897 | − | 0.824476i | \(-0.308530\pi\) | ||||
0.565897 | + | 0.824476i | \(0.308530\pi\) | |||||||
\(434\) | −2.71367e18 | −0.0449142 | ||||||||
\(435\) | 5.88196e18 | 0.0956869 | ||||||||
\(436\) | 4.32397e18 | 0.0691407 | ||||||||
\(437\) | 6.25618e19 | 0.983329 | ||||||||
\(438\) | 2.97368e19 | 0.459450 | ||||||||
\(439\) | −6.41938e19 | −0.975010 | −0.487505 | − | 0.873120i | \(-0.662093\pi\) | ||||
−0.487505 | + | 0.873120i | \(0.662093\pi\) | |||||||
\(440\) | 1.13724e19 | 0.169808 | ||||||||
\(441\) | 5.99701e19 | 0.880330 | ||||||||
\(442\) | 6.50801e18 | 0.0939251 | ||||||||
\(443\) | 8.09420e19 | 1.14854 | 0.574270 | − | 0.818666i | \(-0.305286\pi\) | ||||
0.574270 | + | 0.818666i | \(0.305286\pi\) | |||||||
\(444\) | −1.58336e19 | −0.220906 | ||||||||
\(445\) | −5.32561e19 | −0.730582 | ||||||||
\(446\) | −8.60122e19 | −1.16024 | ||||||||
\(447\) | 3.87797e19 | 0.514397 | ||||||||
\(448\) | −3.98929e17 | −0.00520368 | ||||||||
\(449\) | −5.63441e19 | −0.722771 | −0.361386 | − | 0.932416i | \(-0.617696\pi\) | ||||
−0.361386 | + | 0.932416i | \(0.617696\pi\) | |||||||
\(450\) | −9.88571e18 | −0.124714 | ||||||||
\(451\) | 5.36344e19 | 0.665456 | ||||||||
\(452\) | −7.65677e19 | −0.934346 | ||||||||
\(453\) | −4.47562e19 | −0.537176 | ||||||||
\(454\) | −6.92422e19 | −0.817433 | ||||||||
\(455\) | −2.62604e17 | −0.00304941 | ||||||||
\(456\) | 1.38402e19 | 0.158091 | ||||||||
\(457\) | 8.12666e19 | 0.913147 | 0.456573 | − | 0.889686i | \(-0.349077\pi\) | ||||
0.456573 | + | 0.889686i | \(0.349077\pi\) | |||||||
\(458\) | 9.62966e19 | 1.06444 | ||||||||
\(459\) | −4.82369e19 | −0.524547 | ||||||||
\(460\) | 1.57986e19 | 0.169018 | ||||||||
\(461\) | 1.12727e20 | 1.18651 | 0.593255 | − | 0.805015i | \(-0.297843\pi\) | ||||
0.593255 | + | 0.805015i | \(0.297843\pi\) | |||||||
\(462\) | −1.04927e18 | −0.0108661 | ||||||||
\(463\) | −1.79852e20 | −1.83256 | −0.916278 | − | 0.400542i | \(-0.868822\pi\) | ||||
−0.916278 | + | 0.400542i | \(0.868822\pi\) | |||||||
\(464\) | 1.55225e19 | 0.155624 | ||||||||
\(465\) | 2.37745e19 | 0.234539 | ||||||||
\(466\) | −9.78919e19 | −0.950282 | ||||||||
\(467\) | 3.50796e19 | 0.335103 | 0.167552 | − | 0.985863i | \(-0.446414\pi\) | ||||
0.167552 | + | 0.985863i | \(0.446414\pi\) | |||||||
\(468\) | 7.68269e18 | 0.0722220 | ||||||||
\(469\) | 6.40090e18 | 0.0592168 | ||||||||
\(470\) | −1.62301e19 | −0.147770 | ||||||||
\(471\) | −4.22726e19 | −0.378793 | ||||||||
\(472\) | 1.93780e19 | 0.170901 | ||||||||
\(473\) | 2.81807e19 | 0.244621 | ||||||||
\(474\) | −5.12069e19 | −0.437513 | ||||||||
\(475\) | −3.09373e19 | −0.260184 | ||||||||
\(476\) | 2.03901e18 | 0.0168798 | ||||||||
\(477\) | 6.78947e19 | 0.553284 | ||||||||
\(478\) | −8.62852e19 | −0.692192 | ||||||||
\(479\) | 1.32716e19 | 0.104811 | 0.0524053 | − | 0.998626i | \(-0.483311\pi\) | ||||
0.0524053 | + | 0.998626i | \(0.483311\pi\) | |||||||
\(480\) | 3.49503e18 | 0.0271732 | ||||||||
\(481\) | −2.75058e19 | −0.210541 | ||||||||
\(482\) | 4.05681e19 | 0.305725 | ||||||||
\(483\) | −1.45766e18 | −0.0108156 | ||||||||
\(484\) | 1.04977e19 | 0.0766927 | ||||||||
\(485\) | 1.84781e19 | 0.132922 | ||||||||
\(486\) | −8.72027e19 | −0.617672 | ||||||||
\(487\) | −2.27726e20 | −1.58835 | −0.794173 | − | 0.607692i | \(-0.792096\pi\) | ||||
−0.794173 | + | 0.607692i | \(0.792096\pi\) | |||||||
\(488\) | 1.98036e18 | 0.0136018 | ||||||||
\(489\) | −3.15587e19 | −0.213453 | ||||||||
\(490\) | 4.73933e19 | 0.315680 | ||||||||
\(491\) | 2.06518e19 | 0.135471 | 0.0677356 | − | 0.997703i | \(-0.478423\pi\) | ||||
0.0677356 | + | 0.997703i | \(0.478423\pi\) | |||||||
\(492\) | 1.64832e19 | 0.106489 | ||||||||
\(493\) | −7.93385e19 | −0.504815 | ||||||||
\(494\) | 2.40429e19 | 0.150673 | ||||||||
\(495\) | −6.86183e19 | −0.423546 | ||||||||
\(496\) | 6.27409e19 | 0.381450 | ||||||||
\(497\) | 7.48639e18 | 0.0448332 | ||||||||
\(498\) | −7.19283e18 | −0.0424306 | ||||||||
\(499\) | 2.08538e20 | 1.21180 | 0.605901 | − | 0.795540i | \(-0.292813\pi\) | ||||
0.605901 | + | 0.795540i | \(0.292813\pi\) | |||||||
\(500\) | −7.81250e18 | −0.0447214 | ||||||||
\(501\) | −4.24952e18 | −0.0239638 | ||||||||
\(502\) | −1.98354e19 | −0.110196 | ||||||||
\(503\) | 1.61975e20 | 0.886516 | 0.443258 | − | 0.896394i | \(-0.353822\pi\) | ||||
0.443258 | + | 0.896394i | \(0.353822\pi\) | |||||||
\(504\) | 2.40704e18 | 0.0129794 | ||||||||
\(505\) | 1.09096e20 | 0.579594 | ||||||||
\(506\) | 1.09660e20 | 0.574012 | ||||||||
\(507\) | 6.48561e19 | 0.334496 | ||||||||
\(508\) | 9.07202e19 | 0.461027 | ||||||||
\(509\) | 1.84945e20 | 0.926102 | 0.463051 | − | 0.886332i | \(-0.346755\pi\) | ||||
0.463051 | + | 0.886332i | \(0.346755\pi\) | |||||||
\(510\) | −1.78638e19 | −0.0881450 | ||||||||
\(511\) | 1.61849e19 | 0.0786960 | ||||||||
\(512\) | 9.22337e18 | 0.0441942 | ||||||||
\(513\) | −1.78204e20 | −0.841469 | ||||||||
\(514\) | 2.88324e20 | 1.34171 | ||||||||
\(515\) | 1.14755e20 | 0.526279 | ||||||||
\(516\) | 8.66066e18 | 0.0391452 | ||||||||
\(517\) | −1.12656e20 | −0.501851 | ||||||||
\(518\) | −8.61777e18 | −0.0378374 | ||||||||
\(519\) | 1.24237e20 | 0.537647 | ||||||||
\(520\) | 6.07149e18 | 0.0258983 | ||||||||
\(521\) | −1.19106e20 | −0.500785 | −0.250392 | − | 0.968144i | \(-0.580560\pi\) | ||||
−0.250392 | + | 0.968144i | \(0.580560\pi\) | |||||||
\(522\) | −9.36588e19 | −0.388168 | ||||||||
\(523\) | −2.07240e20 | −0.846663 | −0.423331 | − | 0.905975i | \(-0.639139\pi\) | ||||
−0.423331 | + | 0.905975i | \(0.639139\pi\) | |||||||
\(524\) | 1.28302e20 | 0.516714 | ||||||||
\(525\) | 7.20820e17 | 0.00286175 | ||||||||
\(526\) | 1.29185e20 | 0.505612 | ||||||||
\(527\) | −3.20681e20 | −1.23735 | ||||||||
\(528\) | 2.42596e19 | 0.0922845 | ||||||||
\(529\) | −1.14295e20 | −0.428656 | ||||||||
\(530\) | 5.36560e19 | 0.198403 | ||||||||
\(531\) | −1.16922e20 | −0.426273 | ||||||||
\(532\) | 7.53282e18 | 0.0270782 | ||||||||
\(533\) | 2.86343e19 | 0.101492 | ||||||||
\(534\) | −1.13606e20 | −0.397046 | ||||||||
\(535\) | −9.37190e19 | −0.322979 | ||||||||
\(536\) | −1.47991e20 | −0.502920 | ||||||||
\(537\) | 1.40891e20 | 0.472146 | ||||||||
\(538\) | −1.19017e20 | −0.393315 | ||||||||
\(539\) | 3.28965e20 | 1.07210 | ||||||||
\(540\) | −4.50015e19 | −0.144635 | ||||||||
\(541\) | −4.26438e20 | −1.35169 | −0.675844 | − | 0.737045i | \(-0.736221\pi\) | ||||
−0.675844 | + | 0.737045i | \(0.736221\pi\) | |||||||
\(542\) | −8.33761e18 | −0.0260644 | ||||||||
\(543\) | −2.89023e19 | −0.0891114 | ||||||||
\(544\) | −4.71425e19 | −0.143358 | ||||||||
\(545\) | −2.06183e19 | −0.0618413 | ||||||||
\(546\) | −5.60187e17 | −0.00165725 | ||||||||
\(547\) | −1.46134e20 | −0.426427 | −0.213214 | − | 0.977006i | \(-0.568393\pi\) | ||||
−0.213214 | + | 0.977006i | \(0.568393\pi\) | |||||||
\(548\) | −3.09447e20 | −0.890702 | ||||||||
\(549\) | −1.19490e19 | −0.0339265 | ||||||||
\(550\) | −5.42278e19 | −0.151881 | ||||||||
\(551\) | −2.93105e20 | −0.809815 | ||||||||
\(552\) | 3.37015e19 | 0.0918556 | ||||||||
\(553\) | −2.78704e19 | −0.0749386 | ||||||||
\(554\) | −1.11901e19 | −0.0296832 | ||||||||
\(555\) | 7.55005e19 | 0.197584 | ||||||||
\(556\) | 9.97603e19 | 0.257571 | ||||||||
\(557\) | 3.01056e20 | 0.766891 | 0.383445 | − | 0.923564i | \(-0.374737\pi\) | ||||
0.383445 | + | 0.923564i | \(0.374737\pi\) | |||||||
\(558\) | −3.78563e20 | −0.951441 | ||||||||
\(559\) | 1.50451e19 | 0.0373084 | ||||||||
\(560\) | 1.90224e18 | 0.00465431 | ||||||||
\(561\) | −1.23996e20 | −0.299354 | ||||||||
\(562\) | 1.41548e20 | 0.337196 | ||||||||
\(563\) | 5.43653e20 | 1.27793 | 0.638967 | − | 0.769234i | \(-0.279362\pi\) | ||||
0.638967 | + | 0.769234i | \(0.279362\pi\) | |||||||
\(564\) | −3.46220e19 | −0.0803080 | ||||||||
\(565\) | 3.65103e20 | 0.835704 | ||||||||
\(566\) | 2.75404e20 | 0.622081 | ||||||||
\(567\) | −1.23171e19 | −0.0274560 | ||||||||
\(568\) | −1.73088e20 | −0.380762 | ||||||||
\(569\) | 2.77606e19 | 0.0602681 | 0.0301340 | − | 0.999546i | \(-0.490407\pi\) | ||||
0.0301340 | + | 0.999546i | \(0.490407\pi\) | |||||||
\(570\) | −6.59953e19 | −0.141401 | ||||||||
\(571\) | 7.86073e20 | 1.66223 | 0.831116 | − | 0.556098i | \(-0.187702\pi\) | ||||
0.831116 | + | 0.556098i | \(0.187702\pi\) | |||||||
\(572\) | 4.21432e19 | 0.0879544 | ||||||||
\(573\) | 4.45791e19 | 0.0918272 | ||||||||
\(574\) | 8.97133e18 | 0.0182397 | ||||||||
\(575\) | −7.53334e19 | −0.151175 | ||||||||
\(576\) | −5.56516e19 | −0.110232 | ||||||||
\(577\) | −9.30552e19 | −0.181937 | −0.0909687 | − | 0.995854i | \(-0.528996\pi\) | ||||
−0.0909687 | + | 0.995854i | \(0.528996\pi\) | |||||||
\(578\) | −1.25435e20 | −0.242081 | ||||||||
\(579\) | 2.95725e20 | 0.563376 | ||||||||
\(580\) | −7.40169e19 | −0.139194 | ||||||||
\(581\) | −3.91485e18 | −0.00726765 | ||||||||
\(582\) | 3.94175e19 | 0.0722382 | ||||||||
\(583\) | 3.72435e20 | 0.673808 | ||||||||
\(584\) | −3.74200e20 | −0.668355 | ||||||||
\(585\) | −3.66339e19 | −0.0645973 | ||||||||
\(586\) | 7.06985e20 | 1.23077 | ||||||||
\(587\) | 9.75604e20 | 1.67682 | 0.838412 | − | 0.545036i | \(-0.183484\pi\) | ||||
0.838412 | + | 0.545036i | \(0.183484\pi\) | |||||||
\(588\) | 1.01099e20 | 0.171561 | ||||||||
\(589\) | −1.18471e21 | −1.98494 | ||||||||
\(590\) | −9.24016e19 | −0.152858 | ||||||||
\(591\) | −3.43559e19 | −0.0561171 | ||||||||
\(592\) | 1.99246e20 | 0.321348 | ||||||||
\(593\) | 1.11954e20 | 0.178292 | 0.0891459 | − | 0.996019i | \(-0.471586\pi\) | ||||
0.0891459 | + | 0.996019i | \(0.471586\pi\) | |||||||
\(594\) | −3.12363e20 | −0.491203 | ||||||||
\(595\) | −9.72275e18 | −0.0150977 | ||||||||
\(596\) | −4.87993e20 | −0.748285 | ||||||||
\(597\) | −2.59740e20 | −0.393307 | ||||||||
\(598\) | 5.85455e19 | 0.0875456 | ||||||||
\(599\) | −7.49099e20 | −1.10621 | −0.553106 | − | 0.833111i | \(-0.686558\pi\) | ||||
−0.553106 | + | 0.833111i | \(0.686558\pi\) | |||||||
\(600\) | −1.66656e19 | −0.0243045 | ||||||||
\(601\) | −1.59205e20 | −0.229297 | −0.114649 | − | 0.993406i | \(-0.536574\pi\) | ||||
−0.114649 | + | 0.993406i | \(0.536574\pi\) | |||||||
\(602\) | 4.71374e18 | 0.00670490 | ||||||||
\(603\) | 8.92941e20 | 1.25442 | ||||||||
\(604\) | 5.63199e20 | 0.781421 | ||||||||
\(605\) | −5.00569e19 | −0.0685960 | ||||||||
\(606\) | 2.32723e20 | 0.314989 | ||||||||
\(607\) | −8.11583e20 | −1.08497 | −0.542485 | − | 0.840065i | \(-0.682517\pi\) | ||||
−0.542485 | + | 0.840065i | \(0.682517\pi\) | |||||||
\(608\) | −1.74161e20 | −0.229972 | ||||||||
\(609\) | 6.82917e18 | 0.00890714 | ||||||||
\(610\) | −9.44308e18 | −0.0121658 | ||||||||
\(611\) | −6.01447e19 | −0.0765399 | ||||||||
\(612\) | 2.84446e20 | 0.357573 | ||||||||
\(613\) | 5.55939e19 | 0.0690357 | 0.0345179 | − | 0.999404i | \(-0.489010\pi\) | ||||
0.0345179 | + | 0.999404i | \(0.489010\pi\) | |||||||
\(614\) | 1.26411e20 | 0.155068 | ||||||||
\(615\) | −7.85981e19 | −0.0952464 | ||||||||
\(616\) | 1.32038e19 | 0.0158068 | ||||||||
\(617\) | −6.97947e19 | −0.0825437 | −0.0412718 | − | 0.999148i | \(-0.513141\pi\) | ||||
−0.0412718 | + | 0.999148i | \(0.513141\pi\) | |||||||
\(618\) | 2.44794e20 | 0.286014 | ||||||||
\(619\) | −6.03520e20 | −0.696646 | −0.348323 | − | 0.937375i | \(-0.613249\pi\) | ||||
−0.348323 | + | 0.937375i | \(0.613249\pi\) | |||||||
\(620\) | −2.99172e20 | −0.341180 | ||||||||
\(621\) | −4.33935e20 | −0.488920 | ||||||||
\(622\) | −3.96344e20 | −0.441210 | ||||||||
\(623\) | −6.18323e19 | −0.0680072 | ||||||||
\(624\) | 1.29517e19 | 0.0140748 | ||||||||
\(625\) | 3.72529e19 | 0.0400000 | ||||||||
\(626\) | 1.52775e20 | 0.162086 | ||||||||
\(627\) | −4.58084e20 | −0.480218 | ||||||||
\(628\) | 5.31946e20 | 0.551024 | ||||||||
\(629\) | −1.01838e21 | −1.04239 | ||||||||
\(630\) | −1.14777e19 | −0.0116091 | ||||||||
\(631\) | −3.64878e20 | −0.364693 | −0.182346 | − | 0.983234i | \(-0.558369\pi\) | ||||
−0.182346 | + | 0.983234i | \(0.558369\pi\) | |||||||
\(632\) | 6.44374e20 | 0.636443 | ||||||||
\(633\) | −8.40576e19 | −0.0820445 | ||||||||
\(634\) | −3.45739e20 | −0.333487 | ||||||||
\(635\) | −4.32587e20 | −0.412355 | ||||||||
\(636\) | 1.14459e20 | 0.107825 | ||||||||
\(637\) | 1.75628e20 | 0.163511 | ||||||||
\(638\) | −5.13764e20 | −0.472725 | ||||||||
\(639\) | 1.04437e21 | 0.949725 | ||||||||
\(640\) | −4.39805e19 | −0.0395285 | ||||||||
\(641\) | 2.06269e20 | 0.183231 | 0.0916156 | − | 0.995794i | \(-0.470797\pi\) | ||||
0.0916156 | + | 0.995794i | \(0.470797\pi\) | |||||||
\(642\) | −1.99921e20 | −0.175528 | ||||||||
\(643\) | 2.11836e21 | 1.83830 | 0.919152 | − | 0.393903i | \(-0.128875\pi\) | ||||
0.919152 | + | 0.393903i | \(0.128875\pi\) | |||||||
\(644\) | 1.83427e19 | 0.0157333 | ||||||||
\(645\) | −4.12972e19 | −0.0350125 | ||||||||
\(646\) | 8.90173e20 | 0.745986 | ||||||||
\(647\) | −2.29485e21 | −1.90096 | −0.950480 | − | 0.310787i | \(-0.899407\pi\) | ||||
−0.950480 | + | 0.310787i | \(0.899407\pi\) | |||||||
\(648\) | 2.84776e20 | 0.233180 | ||||||||
\(649\) | −6.41375e20 | −0.519130 | ||||||||
\(650\) | −2.89511e19 | −0.0231641 | ||||||||
\(651\) | 2.76031e19 | 0.0218323 | ||||||||
\(652\) | 3.97125e20 | 0.310506 | ||||||||
\(653\) | −5.84612e20 | −0.451876 | −0.225938 | − | 0.974142i | \(-0.572545\pi\) | ||||
−0.225938 | + | 0.974142i | \(0.572545\pi\) | |||||||
\(654\) | −4.39829e19 | −0.0336086 | ||||||||
\(655\) | −6.11793e20 | −0.462163 | ||||||||
\(656\) | −2.07420e20 | −0.154907 | ||||||||
\(657\) | 2.25783e21 | 1.66706 | ||||||||
\(658\) | −1.88438e19 | −0.0137554 | ||||||||
\(659\) | 1.79922e21 | 1.29850 | 0.649252 | − | 0.760573i | \(-0.275082\pi\) | ||||
0.649252 | + | 0.760573i | \(0.275082\pi\) | |||||||
\(660\) | −1.15679e20 | −0.0825418 | ||||||||
\(661\) | 1.48620e21 | 1.04849 | 0.524247 | − | 0.851566i | \(-0.324347\pi\) | ||||
0.524247 | + | 0.851566i | \(0.324347\pi\) | |||||||
\(662\) | −1.15835e20 | −0.0807985 | ||||||||
\(663\) | −6.61987e19 | −0.0456560 | ||||||||
\(664\) | 9.05125e19 | 0.0617231 | ||||||||
\(665\) | −3.59193e19 | −0.0242195 | ||||||||
\(666\) | −1.20220e21 | −0.801530 | ||||||||
\(667\) | −7.13722e20 | −0.470528 | ||||||||
\(668\) | 5.34747e19 | 0.0348598 | ||||||||
\(669\) | 8.74905e20 | 0.563982 | ||||||||
\(670\) | 7.05676e20 | 0.449826 | ||||||||
\(671\) | −6.55460e19 | −0.0413168 | ||||||||
\(672\) | 4.05786e18 | 0.00252946 | ||||||||
\(673\) | −1.01586e21 | −0.626214 | −0.313107 | − | 0.949718i | \(-0.601370\pi\) | ||||
−0.313107 | + | 0.949718i | \(0.601370\pi\) | |||||||
\(674\) | −8.75700e19 | −0.0533834 | ||||||||
\(675\) | 2.14584e20 | 0.129366 | ||||||||
\(676\) | −8.16130e20 | −0.486586 | ||||||||
\(677\) | 2.64661e21 | 1.56054 | 0.780269 | − | 0.625445i | \(-0.215082\pi\) | ||||
0.780269 | + | 0.625445i | \(0.215082\pi\) | |||||||
\(678\) | 7.78837e20 | 0.454176 | ||||||||
\(679\) | 2.14538e19 | 0.0123732 | ||||||||
\(680\) | 2.24793e20 | 0.128223 | ||||||||
\(681\) | 7.04323e20 | 0.397346 | ||||||||
\(682\) | −2.07660e21 | −1.15870 | ||||||||
\(683\) | −1.97807e21 | −1.09166 | −0.545830 | − | 0.837896i | \(-0.683786\pi\) | ||||
−0.545830 | + | 0.837896i | \(0.683786\pi\) | |||||||
\(684\) | 1.05085e21 | 0.573612 | ||||||||
\(685\) | 1.47556e21 | 0.796668 | ||||||||
\(686\) | 1.10146e20 | 0.0588219 | ||||||||
\(687\) | −9.79517e20 | −0.517412 | ||||||||
\(688\) | −1.08983e20 | −0.0569438 | ||||||||
\(689\) | 1.98835e20 | 0.102766 | ||||||||
\(690\) | −1.60701e20 | −0.0821581 | ||||||||
\(691\) | 2.52634e21 | 1.27763 | 0.638817 | − | 0.769359i | \(-0.279424\pi\) | ||||
0.638817 | + | 0.769359i | \(0.279424\pi\) | |||||||
\(692\) | −1.56337e21 | −0.782106 | ||||||||
\(693\) | −7.96684e19 | −0.0394264 | ||||||||
\(694\) | −1.51585e21 | −0.742097 | ||||||||
\(695\) | −4.75694e20 | −0.230378 | ||||||||
\(696\) | −1.57893e20 | −0.0756472 | ||||||||
\(697\) | 1.06017e21 | 0.502491 | ||||||||
\(698\) | −5.98867e20 | −0.280811 | ||||||||
\(699\) | 9.95744e20 | 0.461922 | ||||||||
\(700\) | −9.07060e18 | −0.00416295 | ||||||||
\(701\) | −2.18514e21 | −0.992190 | −0.496095 | − | 0.868268i | \(-0.665233\pi\) | ||||
−0.496095 | + | 0.868268i | \(0.665233\pi\) | |||||||
\(702\) | −1.66764e20 | −0.0749159 | ||||||||
\(703\) | −3.76228e21 | −1.67219 | ||||||||
\(704\) | −3.05276e20 | −0.134245 | ||||||||
\(705\) | 1.65091e20 | 0.0718297 | ||||||||
\(706\) | −7.95611e20 | −0.342504 | ||||||||
\(707\) | 1.26664e20 | 0.0539522 | ||||||||
\(708\) | −1.97111e20 | −0.0830732 | ||||||||
\(709\) | −2.66228e19 | −0.0111021 | −0.00555107 | − | 0.999985i | \(-0.501767\pi\) | ||||
−0.00555107 | + | 0.999985i | \(0.501767\pi\) | |||||||
\(710\) | 8.25347e20 | 0.340564 | ||||||||
\(711\) | −3.88799e21 | −1.58746 | ||||||||
\(712\) | 1.42958e21 | 0.577576 | ||||||||
\(713\) | −2.88482e21 | −1.15331 | ||||||||
\(714\) | −2.07405e19 | −0.00820509 | ||||||||
\(715\) | −2.00955e20 | −0.0786688 | ||||||||
\(716\) | −1.77293e21 | −0.686823 | ||||||||
\(717\) | 8.77682e20 | 0.336468 | ||||||||
\(718\) | 1.11030e21 | 0.421218 | ||||||||
\(719\) | 9.86146e20 | 0.370233 | 0.185116 | − | 0.982717i | \(-0.440734\pi\) | ||||
0.185116 | + | 0.982717i | \(0.440734\pi\) | |||||||
\(720\) | 2.65367e20 | 0.0985948 | ||||||||
\(721\) | 1.33234e20 | 0.0489894 | ||||||||
\(722\) | 1.34543e21 | 0.489591 | ||||||||
\(723\) | −4.12653e20 | −0.148610 | ||||||||
\(724\) | 3.63698e20 | 0.129629 | ||||||||
\(725\) | 3.52940e20 | 0.124499 | ||||||||
\(726\) | −1.06781e20 | −0.0372795 | ||||||||
\(727\) | −2.40230e21 | −0.830078 | −0.415039 | − | 0.909804i | \(-0.636232\pi\) | ||||
−0.415039 | + | 0.909804i | \(0.636232\pi\) | |||||||
\(728\) | 7.04923e18 | 0.00241077 | ||||||||
\(729\) | −1.06145e21 | −0.359288 | ||||||||
\(730\) | 1.78432e21 | 0.597795 | ||||||||
\(731\) | 5.57036e20 | 0.184715 | ||||||||
\(732\) | −2.01440e19 | −0.00661168 | ||||||||
\(733\) | 1.87874e21 | 0.610361 | 0.305181 | − | 0.952295i | \(-0.401283\pi\) | ||||
0.305181 | + | 0.952295i | \(0.401283\pi\) | |||||||
\(734\) | 3.32898e21 | 1.07051 | ||||||||
\(735\) | −4.82079e20 | −0.153449 | ||||||||
\(736\) | −4.24090e20 | −0.133621 | ||||||||
\(737\) | 4.89821e21 | 1.52768 | ||||||||
\(738\) | 1.25152e21 | 0.386381 | ||||||||
\(739\) | 5.37988e21 | 1.64414 | 0.822072 | − | 0.569384i | \(-0.192818\pi\) | ||||
0.822072 | + | 0.569384i | \(0.192818\pi\) | |||||||
\(740\) | −9.50077e20 | −0.287423 | ||||||||
\(741\) | −2.44562e20 | −0.0732406 | ||||||||
\(742\) | 6.22966e19 | 0.0184686 | ||||||||
\(743\) | −2.67434e21 | −0.784876 | −0.392438 | − | 0.919778i | \(-0.628368\pi\) | ||||
−0.392438 | + | 0.919778i | \(0.628368\pi\) | |||||||
\(744\) | −6.38192e20 | −0.185419 | ||||||||
\(745\) | 2.32693e21 | 0.669286 | ||||||||
\(746\) | 4.15388e20 | 0.118280 | ||||||||
\(747\) | −5.46130e20 | −0.153954 | ||||||||
\(748\) | 1.56033e21 | 0.435465 | ||||||||
\(749\) | −1.08811e20 | −0.0300649 | ||||||||
\(750\) | 7.94678e19 | 0.0217386 | ||||||||
\(751\) | 4.11797e21 | 1.11528 | 0.557640 | − | 0.830083i | \(-0.311707\pi\) | ||||
0.557640 | + | 0.830083i | \(0.311707\pi\) | |||||||
\(752\) | 4.35674e20 | 0.116823 | ||||||||
\(753\) | 2.01764e20 | 0.0535649 | ||||||||
\(754\) | −2.74288e20 | −0.0720977 | ||||||||
\(755\) | −2.68554e21 | −0.698924 | ||||||||
\(756\) | −5.22484e19 | −0.0134635 | ||||||||
\(757\) | −3.83231e21 | −0.977781 | −0.488890 | − | 0.872345i | \(-0.662598\pi\) | ||||
−0.488890 | + | 0.872345i | \(0.662598\pi\) | |||||||
\(758\) | 5.08512e21 | 1.28464 | ||||||||
\(759\) | −1.11545e21 | −0.279022 | ||||||||
\(760\) | 8.30466e20 | 0.205693 | ||||||||
\(761\) | 3.19772e21 | 0.784253 | 0.392126 | − | 0.919911i | \(-0.371740\pi\) | ||||
0.392126 | + | 0.919911i | \(0.371740\pi\) | |||||||
\(762\) | −9.22794e20 | −0.224100 | ||||||||
\(763\) | −2.39386e19 | −0.00575658 | ||||||||
\(764\) | −5.60971e20 | −0.133580 | ||||||||
\(765\) | −1.35635e21 | −0.319823 | ||||||||
\(766\) | −1.77988e21 | −0.415600 | ||||||||
\(767\) | −3.42417e20 | −0.0791753 | ||||||||
\(768\) | −9.38190e19 | −0.0214823 | ||||||||
\(769\) | −5.42196e21 | −1.22944 | −0.614722 | − | 0.788744i | \(-0.710732\pi\) | ||||
−0.614722 | + | 0.788744i | \(0.710732\pi\) | |||||||
\(770\) | −6.29605e19 | −0.0141380 | ||||||||
\(771\) | −2.93280e21 | −0.652191 | ||||||||
\(772\) | −3.72132e21 | −0.819533 | ||||||||
\(773\) | −4.69088e21 | −1.02308 | −0.511538 | − | 0.859261i | \(-0.670924\pi\) | ||||
−0.511538 | + | 0.859261i | \(0.670924\pi\) | |||||||
\(774\) | 6.57579e20 | 0.142033 | ||||||||
\(775\) | 1.42656e21 | 0.305160 | ||||||||
\(776\) | −4.96019e20 | −0.105084 | ||||||||
\(777\) | 8.76589e19 | 0.0183924 | ||||||||
\(778\) | −3.07865e21 | −0.639754 | ||||||||
\(779\) | 3.91663e21 | 0.806087 | ||||||||
\(780\) | −6.17585e19 | −0.0125889 | ||||||||
\(781\) | 5.72887e21 | 1.15661 | ||||||||
\(782\) | 2.16761e21 | 0.433441 | ||||||||
\(783\) | 2.03300e21 | 0.402647 | ||||||||
\(784\) | −1.27221e21 | −0.249567 | ||||||||
\(785\) | −2.53652e21 | −0.492851 | ||||||||
\(786\) | −1.30508e21 | −0.251169 | ||||||||
\(787\) | −9.27131e21 | −1.76738 | −0.883691 | − | 0.468070i | \(-0.844949\pi\) | ||||
−0.883691 | + | 0.468070i | \(0.844949\pi\) | |||||||
\(788\) | 4.32325e20 | 0.0816325 | ||||||||
\(789\) | −1.31405e21 | −0.245773 | ||||||||
\(790\) | −3.07261e21 | −0.569252 | ||||||||
\(791\) | 4.23899e20 | 0.0777926 | ||||||||
\(792\) | 1.84196e21 | 0.334843 | ||||||||
\(793\) | −3.49937e19 | −0.00630145 | ||||||||
\(794\) | 5.99996e19 | 0.0107027 | ||||||||
\(795\) | −5.45782e20 | −0.0964419 | ||||||||
\(796\) | 3.26850e21 | 0.572137 | ||||||||
\(797\) | 8.35314e21 | 1.44848 | 0.724240 | − | 0.689548i | \(-0.242191\pi\) | ||||
0.724240 | + | 0.689548i | \(0.242191\pi\) | |||||||
\(798\) | −7.66229e19 | −0.0131625 | ||||||||
\(799\) | −2.22682e21 | −0.378951 | ||||||||
\(800\) | 2.09715e20 | 0.0353553 | ||||||||
\(801\) | −8.62575e21 | −1.44063 | ||||||||
\(802\) | −5.87880e21 | −0.972705 | ||||||||
\(803\) | 1.23853e22 | 2.03020 | ||||||||
\(804\) | 1.50535e21 | 0.244464 | ||||||||
\(805\) | −8.74649e19 | −0.0140723 | ||||||||
\(806\) | −1.10865e21 | −0.176719 | ||||||||
\(807\) | 1.21062e21 | 0.191187 | ||||||||
\(808\) | −2.92852e21 | −0.458209 | ||||||||
\(809\) | −5.86882e21 | −0.909781 | −0.454890 | − | 0.890547i | \(-0.650322\pi\) | ||||
−0.454890 | + | 0.890547i | \(0.650322\pi\) | |||||||
\(810\) | −1.35792e21 | −0.208562 | ||||||||
\(811\) | 9.20718e21 | 1.40110 | 0.700552 | − | 0.713602i | \(-0.252937\pi\) | ||||
0.700552 | + | 0.713602i | \(0.252937\pi\) | |||||||
\(812\) | −8.59364e19 | −0.0129571 | ||||||||
\(813\) | 8.48091e19 | 0.0126696 | ||||||||
\(814\) | −6.59464e21 | −0.976131 | ||||||||
\(815\) | −1.89364e21 | −0.277725 | ||||||||
\(816\) | 4.79528e20 | 0.0696847 | ||||||||
\(817\) | 2.05789e21 | 0.296317 | ||||||||
\(818\) | −3.67451e20 | −0.0524264 | ||||||||
\(819\) | −4.25333e19 | −0.00601312 | ||||||||
\(820\) | 9.89056e20 | 0.138553 | ||||||||
\(821\) | 2.78078e21 | 0.386005 | 0.193003 | − | 0.981198i | \(-0.438177\pi\) | ||||
0.193003 | + | 0.981198i | \(0.438177\pi\) | |||||||
\(822\) | 3.14766e21 | 0.432961 | ||||||||
\(823\) | 1.08620e22 | 1.48051 | 0.740257 | − | 0.672324i | \(-0.234704\pi\) | ||||
0.740257 | + | 0.672324i | \(0.234704\pi\) | |||||||
\(824\) | −3.08042e21 | −0.416060 | ||||||||
\(825\) | 5.51599e20 | 0.0738276 | ||||||||
\(826\) | −1.07282e20 | −0.0142290 | ||||||||
\(827\) | −4.48033e21 | −0.588869 | −0.294435 | − | 0.955672i | \(-0.595131\pi\) | ||||
−0.294435 | + | 0.955672i | \(0.595131\pi\) | |||||||
\(828\) | 2.55885e21 | 0.333287 | ||||||||
\(829\) | −1.15562e22 | −1.49161 | −0.745807 | − | 0.666163i | \(-0.767936\pi\) | ||||
−0.745807 | + | 0.666163i | \(0.767936\pi\) | |||||||
\(830\) | −4.31597e20 | −0.0552069 | ||||||||
\(831\) | 1.13824e20 | 0.0144287 | ||||||||
\(832\) | −1.62980e20 | −0.0204744 | ||||||||
\(833\) | 6.50250e21 | 0.809548 | ||||||||
\(834\) | −1.01475e21 | −0.125203 | ||||||||
\(835\) | −2.54987e20 | −0.0311796 | ||||||||
\(836\) | 5.76440e21 | 0.698565 | ||||||||
\(837\) | 8.21727e21 | 0.986930 | ||||||||
\(838\) | −2.49831e21 | −0.297383 | ||||||||
\(839\) | 1.16410e22 | 1.37333 | 0.686666 | − | 0.726973i | \(-0.259074\pi\) | ||||
0.686666 | + | 0.726973i | \(0.259074\pi\) | |||||||
\(840\) | −1.93494e19 | −0.00226242 | ||||||||
\(841\) | −5.28537e21 | −0.612500 | ||||||||
\(842\) | 1.00385e22 | 1.15300 | ||||||||
\(843\) | −1.43981e21 | −0.163907 | ||||||||
\(844\) | 1.05776e21 | 0.119349 | ||||||||
\(845\) | 3.89161e21 | 0.435215 | ||||||||
\(846\) | −2.62875e21 | −0.291388 | ||||||||
\(847\) | −5.81179e19 | −0.00638535 | ||||||||
\(848\) | −1.44032e21 | −0.156852 | ||||||||
\(849\) | −2.80138e21 | −0.302387 | ||||||||
\(850\) | −1.07190e21 | −0.114686 | ||||||||
\(851\) | −9.16129e21 | −0.971594 | ||||||||
\(852\) | 1.76063e21 | 0.185085 | ||||||||
\(853\) | −8.05337e21 | −0.839189 | −0.419595 | − | 0.907712i | \(-0.637828\pi\) | ||||
−0.419595 | + | 0.907712i | \(0.637828\pi\) | |||||||
\(854\) | −1.09638e19 | −0.00113247 | ||||||||
\(855\) | −5.01083e21 | −0.513055 | ||||||||
\(856\) | 2.51575e21 | 0.255337 | ||||||||
\(857\) | 3.51278e21 | 0.353423 | 0.176712 | − | 0.984263i | \(-0.443454\pi\) | ||||
0.176712 | + | 0.984263i | \(0.443454\pi\) | |||||||
\(858\) | −4.28676e20 | −0.0427538 | ||||||||
\(859\) | 4.79620e21 | 0.474186 | 0.237093 | − | 0.971487i | \(-0.423805\pi\) | ||||
0.237093 | + | 0.971487i | \(0.423805\pi\) | |||||||
\(860\) | 5.19673e20 | 0.0509321 | ||||||||
\(861\) | −9.12552e19 | −0.00886613 | ||||||||
\(862\) | −6.70856e21 | −0.646137 | ||||||||
\(863\) | 6.27772e21 | 0.599406 | 0.299703 | − | 0.954033i | \(-0.403112\pi\) | ||||
0.299703 | + | 0.954033i | \(0.403112\pi\) | |||||||
\(864\) | 1.20800e21 | 0.114344 | ||||||||
\(865\) | 7.45472e21 | 0.699537 | ||||||||
\(866\) | 8.60274e21 | 0.800300 | ||||||||
\(867\) | 1.27591e21 | 0.117673 | ||||||||
\(868\) | −3.47349e20 | −0.0317591 | ||||||||
\(869\) | −2.13275e22 | −1.93327 | ||||||||
\(870\) | 7.52891e20 | 0.0676609 | ||||||||
\(871\) | 2.61506e21 | 0.232994 | ||||||||
\(872\) | 5.53468e20 | 0.0488899 | ||||||||
\(873\) | 2.99286e21 | 0.262107 | ||||||||
\(874\) | 8.00792e21 | 0.695319 | ||||||||
\(875\) | 4.32520e19 | 0.00372345 | ||||||||
\(876\) | 3.80631e21 | 0.324881 | ||||||||
\(877\) | −4.69963e21 | −0.397711 | −0.198855 | − | 0.980029i | \(-0.563722\pi\) | ||||
−0.198855 | + | 0.980029i | \(0.563722\pi\) | |||||||
\(878\) | −8.21680e21 | −0.689436 | ||||||||
\(879\) | −7.19136e21 | −0.598266 | ||||||||
\(880\) | 1.45567e21 | 0.120072 | ||||||||
\(881\) | −1.89876e22 | −1.55293 | −0.776465 | − | 0.630161i | \(-0.782989\pi\) | ||||
−0.776465 | + | 0.630161i | \(0.782989\pi\) | |||||||
\(882\) | 7.67618e21 | 0.622487 | ||||||||
\(883\) | −5.43744e21 | −0.437209 | −0.218605 | − | 0.975814i | \(-0.570151\pi\) | ||||
−0.218605 | + | 0.975814i | \(0.570151\pi\) | |||||||
\(884\) | 8.33026e20 | 0.0664150 | ||||||||
\(885\) | 9.39897e20 | 0.0743029 | ||||||||
\(886\) | 1.03606e22 | 0.812140 | ||||||||
\(887\) | −1.43529e22 | −1.11561 | −0.557807 | − | 0.829971i | \(-0.688357\pi\) | ||||
−0.557807 | + | 0.829971i | \(0.688357\pi\) | |||||||
\(888\) | −2.02670e21 | −0.156204 | ||||||||
\(889\) | −5.02250e20 | −0.0383846 | ||||||||
\(890\) | −6.81678e21 | −0.516600 | ||||||||
\(891\) | −9.42554e21 | −0.708310 | ||||||||
\(892\) | −1.10096e22 | −0.820415 | ||||||||
\(893\) | −8.22665e21 | −0.607907 | ||||||||
\(894\) | 4.96381e21 | 0.363734 | ||||||||
\(895\) | 8.45401e21 | 0.614314 | ||||||||
\(896\) | −5.10629e19 | −0.00367956 | ||||||||
\(897\) | −5.95517e20 | −0.0425551 | ||||||||
\(898\) | −7.21204e21 | −0.511076 | ||||||||
\(899\) | 1.35155e22 | 0.949804 | ||||||||
\(900\) | −1.26537e21 | −0.0881858 | ||||||||
\(901\) | 7.36175e21 | 0.508798 | ||||||||
\(902\) | 6.86520e21 | 0.470548 | ||||||||
\(903\) | −4.79476e19 | −0.00325918 | ||||||||
\(904\) | −9.80067e21 | −0.660682 | ||||||||
\(905\) | −1.73425e21 | −0.115944 | ||||||||
\(906\) | −5.72879e21 | −0.379841 | ||||||||
\(907\) | −1.44404e22 | −0.949564 | −0.474782 | − | 0.880103i | \(-0.657473\pi\) | ||||
−0.474782 | + | 0.880103i | \(0.657473\pi\) | |||||||
\(908\) | −8.86301e21 | −0.578012 | ||||||||
\(909\) | 1.76700e22 | 1.14290 | ||||||||
\(910\) | −3.36133e19 | −0.00215626 | ||||||||
\(911\) | −6.00661e21 | −0.382157 | −0.191078 | − | 0.981575i | \(-0.561198\pi\) | ||||
−0.191078 | + | 0.981575i | \(0.561198\pi\) | |||||||
\(912\) | 1.77155e21 | 0.111787 | ||||||||
\(913\) | −2.99579e21 | −0.187491 | ||||||||
\(914\) | 1.04021e22 | 0.645692 | ||||||||
\(915\) | 9.60538e19 | 0.00591366 | ||||||||
\(916\) | 1.23260e22 | 0.752671 | ||||||||
\(917\) | −7.10315e20 | −0.0430210 | ||||||||
\(918\) | −6.17433e21 | −0.370911 | ||||||||
\(919\) | 2.25875e22 | 1.34586 | 0.672932 | − | 0.739704i | \(-0.265034\pi\) | ||||
0.672932 | + | 0.739704i | \(0.265034\pi\) | |||||||
\(920\) | 2.02222e21 | 0.119514 | ||||||||
\(921\) | −1.28584e21 | −0.0753770 | ||||||||
\(922\) | 1.44291e22 | 0.838989 | ||||||||
\(923\) | 3.05853e21 | 0.176400 | ||||||||
\(924\) | −1.34307e20 | −0.00768351 | ||||||||
\(925\) | 4.53032e21 | 0.257079 | ||||||||
\(926\) | −2.30210e22 | −1.29581 | ||||||||
\(927\) | 1.85865e22 | 1.03777 | ||||||||
\(928\) | 1.98688e21 | 0.110043 | ||||||||
\(929\) | 3.26962e22 | 1.79630 | 0.898151 | − | 0.439686i | \(-0.144910\pi\) | ||||
0.898151 | + | 0.439686i | \(0.144910\pi\) | |||||||
\(930\) | 3.04314e21 | 0.165844 | ||||||||
\(931\) | 2.40225e22 | 1.29866 | ||||||||
\(932\) | −1.25302e22 | −0.671951 | ||||||||
\(933\) | 4.03157e21 | 0.214468 | ||||||||
\(934\) | 4.49019e21 | 0.236954 | ||||||||
\(935\) | −7.44021e21 | −0.389492 | ||||||||
\(936\) | 9.83384e20 | 0.0510686 | ||||||||
\(937\) | 2.67083e21 | 0.137594 | 0.0687970 | − | 0.997631i | \(-0.478084\pi\) | ||||
0.0687970 | + | 0.997631i | \(0.478084\pi\) | |||||||
\(938\) | 8.19316e20 | 0.0418726 | ||||||||
\(939\) | −1.55401e21 | −0.0787881 | ||||||||
\(940\) | −2.07745e21 | −0.104489 | ||||||||
\(941\) | −2.61162e22 | −1.30313 | −0.651565 | − | 0.758593i | \(-0.725887\pi\) | ||||
−0.651565 | + | 0.758593i | \(0.725887\pi\) | |||||||
\(942\) | −5.41089e21 | −0.267847 | ||||||||
\(943\) | 9.53715e21 | 0.468361 | ||||||||
\(944\) | 2.48039e21 | 0.120845 | ||||||||
\(945\) | 2.49140e20 | 0.0120422 | ||||||||
\(946\) | 3.60713e21 | 0.172973 | ||||||||
\(947\) | −1.03859e22 | −0.494105 | −0.247053 | − | 0.969002i | \(-0.579462\pi\) | ||||
−0.247053 | + | 0.969002i | \(0.579462\pi\) | |||||||
\(948\) | −6.55449e21 | −0.309369 | ||||||||
\(949\) | 6.61225e21 | 0.309637 | ||||||||
\(950\) | −3.95997e21 | −0.183978 | ||||||||
\(951\) | 3.51681e21 | 0.162104 | ||||||||
\(952\) | 2.60993e20 | 0.0119358 | ||||||||
\(953\) | 1.16131e20 | 0.00526929 | 0.00263464 | − | 0.999997i | \(-0.499161\pi\) | ||||
0.00263464 | + | 0.999997i | \(0.499161\pi\) | |||||||
\(954\) | 8.69052e21 | 0.391231 | ||||||||
\(955\) | 2.67492e21 | 0.119477 | ||||||||
\(956\) | −1.10445e22 | −0.489454 | ||||||||
\(957\) | 5.22594e21 | 0.229787 | ||||||||
\(958\) | 1.69876e21 | 0.0741123 | ||||||||
\(959\) | 1.71318e21 | 0.0741589 | ||||||||
\(960\) | 4.47364e20 | 0.0192144 | ||||||||
\(961\) | 3.11635e22 | 1.32807 | ||||||||
\(962\) | −3.52074e21 | −0.148875 | ||||||||
\(963\) | −1.51794e22 | −0.636881 | ||||||||
\(964\) | 5.19271e21 | 0.216180 | ||||||||
\(965\) | 1.77446e22 | 0.733013 | ||||||||
\(966\) | −1.86580e20 | −0.00764780 | ||||||||
\(967\) | −3.55619e22 | −1.44639 | −0.723197 | − | 0.690642i | \(-0.757328\pi\) | ||||
−0.723197 | + | 0.690642i | \(0.757328\pi\) | |||||||
\(968\) | 1.34371e21 | 0.0542299 | ||||||||
\(969\) | −9.05473e21 | −0.362616 | ||||||||
\(970\) | 2.36520e21 | 0.0939897 | ||||||||
\(971\) | −4.08883e22 | −1.61233 | −0.806166 | − | 0.591690i | \(-0.798461\pi\) | ||||
−0.806166 | + | 0.591690i | \(0.798461\pi\) | |||||||
\(972\) | −1.11619e22 | −0.436760 | ||||||||
\(973\) | −5.52298e20 | −0.0214451 | ||||||||
\(974\) | −2.91489e22 | −1.12313 | ||||||||
\(975\) | 2.94487e20 | 0.0112598 | ||||||||
\(976\) | 2.53486e20 | 0.00961789 | ||||||||
\(977\) | 1.47056e22 | 0.553700 | 0.276850 | − | 0.960913i | \(-0.410709\pi\) | ||||
0.276850 | + | 0.960913i | \(0.410709\pi\) | |||||||
\(978\) | −4.03951e21 | −0.150934 | ||||||||
\(979\) | −4.73164e22 | −1.75445 | ||||||||
\(980\) | 6.06635e21 | 0.223219 | ||||||||
\(981\) | −3.33949e21 | −0.121945 | ||||||||
\(982\) | 2.64343e21 | 0.0957926 | ||||||||
\(983\) | −2.02443e22 | −0.728034 | −0.364017 | − | 0.931392i | \(-0.618595\pi\) | ||||
−0.364017 | + | 0.931392i | \(0.618595\pi\) | |||||||
\(984\) | 2.10985e21 | 0.0752989 | ||||||||
\(985\) | −2.06148e21 | −0.0730144 | ||||||||
\(986\) | −1.01553e22 | −0.356958 | ||||||||
\(987\) | 1.91676e20 | 0.00668636 | ||||||||
\(988\) | 3.07750e21 | 0.106542 | ||||||||
\(989\) | 5.01104e21 | 0.172169 | ||||||||
\(990\) | −8.78314e21 | −0.299493 | ||||||||
\(991\) | 1.99356e22 | 0.674649 | 0.337324 | − | 0.941389i | \(-0.390478\pi\) | ||||
0.337324 | + | 0.941389i | \(0.390478\pi\) | |||||||
\(992\) | 8.03083e21 | 0.269726 | ||||||||
\(993\) | 1.17825e21 | 0.0392753 | ||||||||
\(994\) | 9.58259e20 | 0.0317019 | ||||||||
\(995\) | −1.55854e22 | −0.511735 | ||||||||
\(996\) | −9.20682e20 | −0.0300030 | ||||||||
\(997\) | −4.00115e21 | −0.129411 | −0.0647056 | − | 0.997904i | \(-0.520611\pi\) | ||||
−0.0647056 | + | 0.997904i | \(0.520611\pi\) | |||||||
\(998\) | 2.66929e22 | 0.856874 | ||||||||
\(999\) | 2.60955e22 | 0.831427 |
(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 | 10.16.a.c.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 90.16.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 80.16.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 50.16.b.b.49.2 | 2 | |||
5.3 | odd | 4 | 50.16.b.b.49.1 | 2 | |||
5.4 | even | 2 | 50.16.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.16.a.c.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
50.16.a.a.1.1 | 1 | 5.4 | even | 2 | |||
50.16.b.b.49.1 | 2 | 5.3 | odd | 4 | |||
50.16.b.b.49.2 | 2 | 5.2 | odd | 4 | |||
80.16.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
90.16.a.d.1.1 | 1 | 3.2 | odd | 2 |