Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,28,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 28, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 28);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 28 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(41.5670017354\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{30001}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 7500 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3^{2}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-86.1040\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 121.102 | 0.0104531 | 0.00522656 | − | 0.999986i | \(-0.498336\pi\) | ||||
0.00522656 | + | 0.999986i | \(0.498336\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.34203e8 | −0.999891 | ||||||||
\(5\) | 1.07803e9 | 0.394943 | 0.197471 | − | 0.980309i | \(-0.436727\pi\) | ||||
0.197471 | + | 0.980309i | \(0.436727\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.13904e10 | −0.0444340 | −0.0222170 | − | 0.999753i | \(-0.507072\pi\) | ||||
−0.0222170 | + | 0.999753i | \(0.507072\pi\) | |||||||
\(8\) | −3.25063e10 | −0.0209051 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.30551e11 | 0.00412839 | ||||||||
\(11\) | 5.05749e13 | 0.441707 | 0.220853 | − | 0.975307i | \(-0.429116\pi\) | ||||
0.220853 | + | 0.975307i | \(0.429116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.21304e15 | 1.11081 | 0.555405 | − | 0.831580i | \(-0.312563\pi\) | ||||
0.555405 | + | 0.831580i | \(0.312563\pi\) | |||||||
\(14\) | −1.37940e12 | −0.000464474 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.80085e16 | 0.999672 | ||||||||
\(17\) | −7.00452e16 | −1.71521 | −0.857606 | − | 0.514307i | \(-0.828049\pi\) | ||||
−0.857606 | + | 0.514307i | \(0.828049\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.51027e16 | 0.136945 | 0.0684726 | − | 0.997653i | \(-0.478187\pi\) | ||||
0.0684726 | + | 0.997653i | \(0.478187\pi\) | |||||||
\(20\) | −1.44674e17 | −0.394900 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.12472e15 | 0.00461722 | ||||||||
\(23\) | 3.40370e18 | 1.40807 | 0.704037 | − | 0.710164i | \(-0.251379\pi\) | ||||
0.704037 | + | 0.710164i | \(0.251379\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.28844e18 | −0.844020 | ||||||||
\(26\) | 1.46901e17 | 0.0116114 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.52863e18 | 0.0444291 | ||||||||
\(29\) | −5.74556e19 | −1.03982 | −0.519912 | − | 0.854220i | \(-0.674035\pi\) | ||||
−0.519912 | + | 0.854220i | \(0.674035\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.08167e20 | 0.795632 | 0.397816 | − | 0.917465i | \(-0.369768\pi\) | ||||
0.397816 | + | 0.917465i | \(0.369768\pi\) | |||||||
\(32\) | 6.54378e18 | 0.0313548 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.48261e18 | −0.0179293 | ||||||||
\(35\) | −1.22791e19 | −0.0175489 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.90073e21 | −1.28292 | −0.641458 | − | 0.767159i | \(-0.721670\pi\) | ||||
−0.641458 | + | 0.767159i | \(0.721670\pi\) | |||||||
\(38\) | 3.03999e18 | 0.00143151 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.50426e19 | −0.00825632 | ||||||||
\(41\) | −6.66148e21 | −1.12458 | −0.562288 | − | 0.826942i | \(-0.690079\pi\) | ||||
−0.562288 | + | 0.826942i | \(0.690079\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.03265e21 | 0.0916490 | 0.0458245 | − | 0.998950i | \(-0.485408\pi\) | ||||
0.0458245 | + | 0.998950i | \(0.485408\pi\) | |||||||
\(44\) | −6.78731e21 | −0.441659 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.12194e20 | 0.0147188 | ||||||||
\(47\) | −6.43133e22 | −1.71783 | −0.858914 | − | 0.512120i | \(-0.828860\pi\) | ||||
−0.858914 | + | 0.512120i | \(0.828860\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.55826e22 | −0.998026 | ||||||||
\(50\) | −7.61542e20 | −0.00882265 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.62794e23 | −1.11069 | ||||||||
\(53\) | −2.13714e23 | −1.12748 | −0.563740 | − | 0.825953i | \(-0.690638\pi\) | ||||
−0.563740 | + | 0.825953i | \(0.690638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.45211e22 | 0.174449 | ||||||||
\(56\) | 3.70259e20 | 0.000928897 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.95799e21 | −0.0108694 | ||||||||
\(59\) | −1.07026e24 | −1.32736 | −0.663679 | − | 0.748017i | \(-0.731006\pi\) | ||||
−0.663679 | + | 0.748017i | \(0.731006\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.16628e23 | 0.645761 | 0.322880 | − | 0.946440i | \(-0.395349\pi\) | ||||
0.322880 | + | 0.946440i | \(0.395349\pi\) | |||||||
\(62\) | 1.30992e22 | 0.00831684 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.41627e24 | −0.999344 | ||||||||
\(65\) | 1.30769e24 | 0.438706 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.68630e24 | 0.375773 | 0.187886 | − | 0.982191i | \(-0.439836\pi\) | ||||
0.187886 | + | 0.982191i | \(0.439836\pi\) | |||||||
\(68\) | 9.40028e24 | 1.71502 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.48703e21 | −0.000183441 0 | ||||||||
\(71\) | 3.18547e24 | 0.324478 | 0.162239 | − | 0.986751i | \(-0.448128\pi\) | ||||
0.162239 | + | 0.986751i | \(0.448128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.09853e25 | 1.46912 | 0.734559 | − | 0.678545i | \(-0.237389\pi\) | ||||
0.734559 | + | 0.678545i | \(0.237389\pi\) | |||||||
\(74\) | −2.30183e23 | −0.0134105 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.36886e24 | −0.136930 | ||||||||
\(77\) | −5.76068e23 | −0.0196268 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.88148e22 | −0.00214052 | −0.00107026 | − | 0.999999i | \(-0.500341\pi\) | ||||
−0.00107026 | + | 0.999999i | \(0.500341\pi\) | |||||||
\(80\) | 1.94136e25 | 0.394813 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.06718e23 | −0.0117553 | ||||||||
\(83\) | 6.50402e25 | 0.804689 | 0.402344 | − | 0.915488i | \(-0.368195\pi\) | ||||
0.402344 | + | 0.915488i | \(0.368195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.55105e25 | −0.677411 | ||||||||
\(86\) | 1.25056e23 | 0.000958019 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.64400e24 | −0.00923393 | ||||||||
\(89\) | −3.38617e26 | −1.63284 | −0.816420 | − | 0.577459i | \(-0.804044\pi\) | ||||
−0.816420 | + | 0.577459i | \(0.804044\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.38170e25 | −0.0493577 | ||||||||
\(92\) | −4.56787e26 | −1.40792 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.78847e24 | −0.0179567 | ||||||||
\(95\) | 2.70614e25 | 0.0540855 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.16124e26 | −0.627775 | −0.313888 | − | 0.949460i | \(-0.601632\pi\) | ||||
−0.313888 | + | 0.949460i | \(0.601632\pi\) | |||||||
\(98\) | −7.94218e24 | −0.0104325 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.43928e26 | 0.843928 | ||||||||
\(101\) | 9.90798e26 | 0.866256 | 0.433128 | − | 0.901332i | \(-0.357410\pi\) | ||||
0.433128 | + | 0.901332i | \(0.357410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.01221e27 | −1.35012 | −0.675059 | − | 0.737764i | \(-0.735882\pi\) | ||||
−0.675059 | + | 0.737764i | \(0.735882\pi\) | |||||||
\(104\) | −3.94314e25 | −0.0232216 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.58812e25 | −0.0117857 | ||||||||
\(107\) | −2.23219e25 | −0.00895470 | −0.00447735 | − | 0.999990i | \(-0.501425\pi\) | ||||
−0.00447735 | + | 0.999990i | \(0.501425\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.40319e27 | 1.68808 | 0.844039 | − | 0.536281i | \(-0.180171\pi\) | ||||
0.844039 | + | 0.536281i | \(0.180171\pi\) | |||||||
\(110\) | 6.60261e24 | 0.00182354 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.05124e26 | −0.0444194 | ||||||||
\(113\) | 3.71413e27 | 0.713342 | 0.356671 | − | 0.934230i | \(-0.383912\pi\) | ||||
0.356671 | + | 0.934230i | \(0.383912\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.66927e27 | 0.556108 | ||||||||
\(116\) | 7.71072e27 | 1.03971 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.29611e26 | −0.0138750 | ||||||||
\(119\) | 7.97842e26 | 0.0762137 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.05522e28 | −0.804895 | ||||||||
\(122\) | 9.88953e25 | 0.00675022 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.45164e28 | −0.795545 | ||||||||
\(125\) | −1.48110e28 | −0.728282 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.13925e28 | 0.849007 | 0.424503 | − | 0.905426i | \(-0.360449\pi\) | ||||
0.424503 | + | 0.905426i | \(0.360449\pi\) | |||||||
\(128\) | −1.17091e27 | −0.0418011 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.58364e26 | 0.00458585 | ||||||||
\(131\) | −5.14435e28 | −1.34328 | −0.671642 | − | 0.740876i | \(-0.734411\pi\) | ||||
−0.671642 | + | 0.740876i | \(0.734411\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.85930e26 | −0.00608502 | ||||||||
\(134\) | 2.04214e26 | 0.00392800 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.27691e27 | 0.0358567 | ||||||||
\(137\) | −3.71968e28 | −0.530612 | −0.265306 | − | 0.964164i | \(-0.585473\pi\) | ||||
−0.265306 | + | 0.964164i | \(0.585473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.00529e29 | −1.17921 | −0.589605 | − | 0.807692i | \(-0.700717\pi\) | ||||
−0.589605 | + | 0.807692i | \(0.700717\pi\) | |||||||
\(140\) | 1.64790e27 | 0.0175470 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.85766e26 | 0.00339181 | ||||||||
\(143\) | 6.13494e28 | 0.490652 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.19387e28 | −0.410671 | ||||||||
\(146\) | 2.54136e27 | 0.0153569 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.55084e29 | 1.28277 | ||||||||
\(149\) | 2.06193e29 | 0.946801 | 0.473400 | − | 0.880847i | \(-0.343026\pi\) | ||||
0.473400 | + | 0.880847i | \(0.343026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.73857e28 | 0.335160 | 0.167580 | − | 0.985859i | \(-0.446405\pi\) | ||||
0.167580 | + | 0.985859i | \(0.446405\pi\) | |||||||
\(152\) | −8.15995e26 | −0.00286285 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.97630e25 | −0.000205161 0 | ||||||||
\(155\) | 1.16607e29 | 0.314229 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.66647e29 | 0.831004 | 0.415502 | − | 0.909592i | \(-0.363606\pi\) | ||||
0.415502 | + | 0.909592i | \(0.363606\pi\) | |||||||
\(158\) | −1.07556e25 | −2.23751e−5 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.05437e27 | 0.0123834 | ||||||||
\(161\) | −3.87694e28 | −0.0625663 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.33235e29 | −1.27485 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(164\) | 8.93991e29 | 1.12445 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.87650e27 | 0.00841151 | ||||||||
\(167\) | −3.46815e29 | −0.341527 | −0.170764 | − | 0.985312i | \(-0.554623\pi\) | ||||
−0.170764 | + | 0.985312i | \(0.554623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.78930e29 | 0.233897 | ||||||||
\(170\) | −9.14447e27 | −0.00708106 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.38584e29 | −0.0916390 | ||||||||
\(173\) | −2.65803e30 | −1.62532 | −0.812659 | − | 0.582740i | \(-0.801981\pi\) | ||||
−0.812659 | + | 0.582740i | \(0.801981\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.16278e28 | 0.0375032 | ||||||||
\(176\) | 9.10778e29 | 0.441562 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.10072e28 | −0.0170683 | ||||||||
\(179\) | −4.30907e30 | −1.66291 | −0.831454 | − | 0.555594i | \(-0.812491\pi\) | ||||
−0.831454 | + | 0.555594i | \(0.812491\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.56401e29 | −0.184811 | −0.0924053 | − | 0.995721i | \(-0.529456\pi\) | ||||
−0.0924053 | + | 0.995721i | \(0.529456\pi\) | |||||||
\(182\) | −1.67326e27 | −0.000515942 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.10642e29 | −0.0294359 | ||||||||
\(185\) | −2.04904e30 | −0.506678 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.54253e30 | −0.757621 | ||||||||
\(188\) | 8.63104e30 | 1.71764 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.27718e27 | 0.000565363 0 | ||||||||
\(191\) | 4.19469e30 | 0.674139 | 0.337070 | − | 0.941480i | \(-0.390564\pi\) | ||||
0.337070 | + | 0.941480i | \(0.390564\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.85628e28 | 0.00678078 | 0.00339039 | − | 0.999994i | \(-0.498921\pi\) | ||||
0.00339039 | + | 0.999994i | \(0.498921\pi\) | |||||||
\(194\) | −5.03934e28 | −0.00656221 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.80139e30 | 0.997917 | ||||||||
\(197\) | 2.40097e29 | 0.0254151 | 0.0127075 | − | 0.999919i | \(-0.495955\pi\) | ||||
0.0127075 | + | 0.999919i | \(0.495955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.40632e30 | 0.684047 | 0.342024 | − | 0.939691i | \(-0.388888\pi\) | ||||
0.342024 | + | 0.939691i | \(0.388888\pi\) | |||||||
\(200\) | 2.04414e29 | 0.0176443 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.19988e29 | 0.00905509 | ||||||||
\(203\) | 6.54442e29 | 0.0462035 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.18125e30 | −0.444143 | ||||||||
\(206\) | −2.43683e29 | −0.0141129 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.18450e31 | 1.11045 | ||||||||
\(209\) | 1.26957e30 | 0.0604896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.11843e31 | −1.30654 | −0.653271 | − | 0.757124i | \(-0.726604\pi\) | ||||
−0.653271 | + | 0.757124i | \(0.726604\pi\) | |||||||
\(212\) | 2.86811e31 | 1.12736 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.70323e27 | −9.36046e−5 0 | ||||||||
\(215\) | 1.11322e30 | 0.0361961 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.23207e30 | −0.0353531 | ||||||||
\(218\) | 6.54337e29 | 0.0176457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.31690e30 | −0.174430 | ||||||||
\(221\) | −8.49675e31 | −1.90527 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.26940e31 | −0.450605 | −0.225302 | − | 0.974289i | \(-0.572337\pi\) | ||||
−0.225302 | + | 0.974289i | \(0.572337\pi\) | |||||||
\(224\) | −7.45362e28 | −0.00139322 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.49788e29 | 0.00745665 | ||||||||
\(227\) | −8.41908e31 | −1.31497 | −0.657484 | − | 0.753468i | \(-0.728379\pi\) | ||||
−0.657484 | + | 0.753468i | \(0.728379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.09888e31 | 0.568703 | 0.284352 | − | 0.958720i | \(-0.408222\pi\) | ||||
0.284352 | + | 0.958720i | \(0.408222\pi\) | |||||||
\(230\) | 4.44356e29 | 0.00581307 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.86767e30 | 0.0217376 | ||||||||
\(233\) | −6.99046e31 | −0.767717 | −0.383858 | − | 0.923392i | \(-0.625405\pi\) | ||||
−0.383858 | + | 0.923392i | \(0.625405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.93314e31 | −0.678444 | ||||||||
\(236\) | 1.43633e32 | 1.32721 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.66202e28 | 0.000796671 0 | ||||||||
\(239\) | 1.89074e32 | 1.47320 | 0.736598 | − | 0.676330i | \(-0.236431\pi\) | ||||
0.736598 | + | 0.676330i | \(0.236431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.01767e32 | 0.708563 | 0.354281 | − | 0.935139i | \(-0.384725\pi\) | ||||
0.354281 | + | 0.935139i | \(0.384725\pi\) | |||||||
\(242\) | −1.27789e30 | −0.00841367 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.09594e32 | −0.645690 | ||||||||
\(245\) | −7.06998e31 | −0.394163 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.04506e31 | 0.152120 | ||||||||
\(248\) | −3.51611e30 | −0.0166328 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.79364e30 | −0.00761283 | ||||||||
\(251\) | 2.25120e32 | 0.905356 | 0.452678 | − | 0.891674i | \(-0.350469\pi\) | ||||
0.452678 | + | 0.891674i | \(0.350469\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.72142e32 | 0.621955 | ||||||||
\(254\) | 2.59067e30 | 0.00887478 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.24164e32 | 0.998908 | ||||||||
\(257\) | −1.28310e32 | −0.375113 | −0.187557 | − | 0.982254i | \(-0.560057\pi\) | ||||
−0.187557 | + | 0.982254i | \(0.560057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.16501e31 | 0.0570050 | ||||||||
\(260\) | −1.75496e32 | −0.438658 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.22990e30 | −0.0140415 | ||||||||
\(263\) | 6.17345e32 | 1.32168 | 0.660838 | − | 0.750528i | \(-0.270201\pi\) | ||||
0.660838 | + | 0.750528i | \(0.270201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.30389e32 | −0.445290 | ||||||||
\(266\) | −3.46266e28 | −6.36075e−5 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.26307e32 | −0.375732 | ||||||||
\(269\) | 1.70730e31 | 0.0269559 | 0.0134779 | − | 0.999909i | \(-0.495710\pi\) | ||||
0.0134779 | + | 0.999909i | \(0.495710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.06709e33 | −1.52446 | −0.762229 | − | 0.647307i | \(-0.775895\pi\) | ||||
−0.762229 | + | 0.647307i | \(0.775895\pi\) | |||||||
\(272\) | −1.26141e33 | −1.71465 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.50460e30 | −0.00554656 | ||||||||
\(275\) | −3.18037e32 | −0.372809 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.90772e32 | 0.627976 | 0.313988 | − | 0.949427i | \(-0.398335\pi\) | ||||
0.313988 | + | 0.949427i | \(0.398335\pi\) | |||||||
\(278\) | −1.21742e31 | −0.0123264 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.99149e29 | 0.000366861 0 | ||||||||
\(281\) | −3.49531e32 | −0.306161 | −0.153081 | − | 0.988214i | \(-0.548919\pi\) | ||||
−0.153081 | + | 0.988214i | \(0.548919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.04098e32 | −0.0828565 | −0.0414282 | − | 0.999141i | \(-0.513191\pi\) | ||||
−0.0414282 | + | 0.999141i | \(0.513191\pi\) | |||||||
\(284\) | −4.27499e32 | −0.324443 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.42953e30 | 0.00512885 | ||||||||
\(287\) | 7.58768e31 | 0.0499693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.23862e33 | 1.94195 | ||||||||
\(290\) | −7.50089e30 | −0.00429279 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.81629e33 | −1.46896 | ||||||||
\(293\) | 4.57358e32 | 0.227794 | 0.113897 | − | 0.993493i | \(-0.463667\pi\) | ||||
0.113897 | + | 0.993493i | \(0.463667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.15377e33 | −0.524231 | ||||||||
\(296\) | 6.17858e31 | 0.0268195 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.49703e31 | 0.00989703 | ||||||||
\(299\) | 4.12882e33 | 1.56410 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.17623e31 | −0.00407233 | ||||||||
\(302\) | 1.05826e31 | 0.00350346 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.52062e32 | 0.136900 | ||||||||
\(305\) | 8.80347e32 | 0.255039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.50586e33 | 0.664642 | 0.332321 | − | 0.943166i | \(-0.392168\pi\) | ||||
0.332321 | + | 0.943166i | \(0.392168\pi\) | |||||||
\(308\) | 7.73101e31 | 0.0196246 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.41213e31 | 0.00328468 | ||||||||
\(311\) | 4.09104e33 | 0.911104 | 0.455552 | − | 0.890209i | \(-0.349442\pi\) | ||||
0.455552 | + | 0.890209i | \(0.349442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.57324e33 | 1.13831 | 0.569154 | − | 0.822231i | \(-0.307271\pi\) | ||||
0.569154 | + | 0.822231i | \(0.307271\pi\) | |||||||
\(314\) | 4.44017e31 | 0.00868659 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.19192e31 | 0.00214029 | ||||||||
\(317\) | −6.22580e33 | −1.07126 | −0.535631 | − | 0.844452i | \(-0.679926\pi\) | ||||
−0.535631 | + | 0.844452i | \(0.679926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.90581e33 | −0.459297 | ||||||||
\(320\) | −2.60480e33 | −0.394684 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.69505e30 | −0.000654013 0 | ||||||||
\(323\) | −1.75832e33 | −0.234890 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.62812e33 | −0.937545 | ||||||||
\(326\) | −1.13017e32 | −0.0133261 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.16540e32 | 0.0235094 | ||||||||
\(329\) | 7.32553e32 | 0.0763299 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.69049e33 | −0.642363 | −0.321181 | − | 0.947018i | \(-0.604080\pi\) | ||||
−0.321181 | + | 0.947018i | \(0.604080\pi\) | |||||||
\(332\) | −8.72860e33 | −0.804601 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.20000e31 | −0.00357003 | ||||||||
\(335\) | 1.81788e33 | 0.148409 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.45330e33 | −0.636829 | −0.318414 | − | 0.947952i | \(-0.603150\pi\) | ||||
−0.318414 | + | 0.947952i | \(0.603150\pi\) | |||||||
\(338\) | 3.37790e31 | 0.00244496 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.01337e34 | 0.677337 | ||||||||
\(341\) | 5.47054e33 | 0.351436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.49550e33 | 0.0887802 | ||||||||
\(344\) | −3.35675e31 | −0.00191593 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.21893e32 | −0.0169896 | ||||||||
\(347\) | −3.54455e34 | −1.79934 | −0.899671 | − | 0.436568i | \(-0.856194\pi\) | ||||
−0.899671 | + | 0.436568i | \(0.856194\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.62742e34 | 0.764462 | 0.382231 | − | 0.924067i | \(-0.375156\pi\) | ||||
0.382231 | + | 0.924067i | \(0.375156\pi\) | |||||||
\(350\) | 8.67426e30 | 0.000392025 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.30951e32 | 0.0138496 | ||||||||
\(353\) | 6.68547e33 | 0.269261 | 0.134630 | − | 0.990896i | \(-0.457015\pi\) | ||||
0.134630 | + | 0.990896i | \(0.457015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.43402e33 | 0.128150 | ||||||||
\(356\) | 4.54434e34 | 1.63266 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.21837e32 | −0.0173826 | ||||||||
\(359\) | 7.80470e33 | 0.250369 | 0.125185 | − | 0.992133i | \(-0.460048\pi\) | ||||
0.125185 | + | 0.992133i | \(0.460048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.29705e34 | −0.981246 | ||||||||
\(362\) | −6.73812e31 | −0.00193185 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.85428e33 | 0.0493523 | ||||||||
\(365\) | 2.26227e34 | 0.580218 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.61615e34 | 1.57621 | 0.788104 | − | 0.615542i | \(-0.211063\pi\) | ||||
0.788104 | + | 0.615542i | \(0.211063\pi\) | |||||||
\(368\) | 6.12955e34 | 1.40761 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.48143e32 | −0.00529637 | ||||||||
\(371\) | 2.43428e33 | 0.0500984 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.79473e34 | −1.30048 | −0.650239 | − | 0.759729i | \(-0.725331\pi\) | ||||
−0.650239 | + | 0.759729i | \(0.725331\pi\) | |||||||
\(374\) | −4.29007e32 | −0.00791951 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.09059e33 | 0.0359114 | ||||||||
\(377\) | −6.96959e34 | −1.15505 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.98595e34 | 1.23224 | 0.616122 | − | 0.787650i | \(-0.288703\pi\) | ||||
0.616122 | + | 0.787650i | \(0.288703\pi\) | |||||||
\(380\) | −3.63172e33 | −0.0540796 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.07985e32 | 0.00704686 | ||||||||
\(383\) | −1.19033e35 | −1.59399 | −0.796994 | − | 0.603987i | \(-0.793578\pi\) | ||||
−0.796994 | + | 0.603987i | \(0.793578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.21016e32 | −0.00775146 | ||||||||
\(386\) | 5.88105e30 | 7.08804e−5 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.58451e34 | 0.627707 | ||||||||
\(389\) | −1.48935e34 | −0.161688 | −0.0808441 | − | 0.996727i | \(-0.525762\pi\) | ||||
−0.0808441 | + | 0.996727i | \(0.525762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.38413e35 | −2.41514 | ||||||||
\(392\) | 2.13185e33 | 0.0208638 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.90762e31 | 0.000265667 0 | ||||||||
\(395\) | −9.57447e31 | −0.000845384 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.07374e34 | 0.335986 | 0.167993 | − | 0.985788i | \(-0.446271\pi\) | ||||
0.167993 | + | 0.985788i | \(0.446271\pi\) | |||||||
\(398\) | 8.96920e32 | 0.00715043 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.13245e35 | −0.843744 | ||||||||
\(401\) | 1.64933e35 | 1.18812 | 0.594058 | − | 0.804422i | \(-0.297525\pi\) | ||||
0.594058 | + | 0.804422i | \(0.297525\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.31211e35 | 0.883796 | ||||||||
\(404\) | −1.32968e35 | −0.866162 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.92542e31 | 0.000482971 0 | ||||||||
\(407\) | −9.61295e34 | −0.566672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.13655e35 | −1.17882 | −0.589411 | − | 0.807833i | \(-0.700640\pi\) | ||||
−0.589411 | + | 0.807833i | \(0.700640\pi\) | |||||||
\(410\) | −8.69663e32 | −0.00464268 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.70045e35 | 1.34997 | ||||||||
\(413\) | 1.21907e34 | 0.0589798 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.01151e34 | 0.317806 | ||||||||
\(416\) | 7.93786e33 | 0.0348292 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.53747e32 | 0.000632306 0 | ||||||||
\(419\) | −6.25908e34 | −0.249242 | −0.124621 | − | 0.992204i | \(-0.539772\pi\) | ||||
−0.124621 | + | 0.992204i | \(0.539772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.62873e35 | 0.608191 | 0.304096 | − | 0.952641i | \(-0.401646\pi\) | ||||
0.304096 | + | 0.952641i | \(0.401646\pi\) | |||||||
\(422\) | −3.77648e33 | −0.0136574 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.94704e33 | 0.0235701 | ||||||||
\(425\) | 4.40475e35 | 1.44767 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.30171e33 | −0.0286937 | ||||||||
\(428\) | 2.99567e33 | 0.00895372 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.34813e32 | 0.000378363 0 | ||||||||
\(431\) | 6.21025e35 | 1.68914 | 0.844571 | − | 0.535444i | \(-0.179856\pi\) | ||||
0.844571 | + | 0.535444i | \(0.179856\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.04792e35 | 0.267757 | 0.133878 | − | 0.990998i | \(-0.457257\pi\) | ||||
0.133878 | + | 0.990998i | \(0.457257\pi\) | |||||||
\(434\) | −1.49206e32 | −0.000369550 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.25125e35 | −1.68789 | ||||||||
\(437\) | 8.54420e34 | 0.192829 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.93788e35 | 1.47216 | 0.736081 | − | 0.676893i | \(-0.236674\pi\) | ||||
0.736081 | + | 0.676893i | \(0.236674\pi\) | |||||||
\(440\) | −1.77228e33 | −0.00364687 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.02897e34 | −0.0199161 | ||||||||
\(443\) | −5.15844e35 | −0.968430 | −0.484215 | − | 0.874949i | \(-0.660895\pi\) | ||||
−0.484215 | + | 0.874949i | \(0.660895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.65038e35 | −0.644878 | ||||||||
\(446\) | −2.74829e33 | −0.00471023 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.75222e34 | 0.0444048 | ||||||||
\(449\) | −9.16926e35 | −1.43552 | −0.717759 | − | 0.696292i | \(-0.754832\pi\) | ||||
−0.717759 | + | 0.696292i | \(0.754832\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.36904e35 | −0.496732 | ||||||||
\(452\) | −4.98447e35 | −0.713264 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.01957e34 | −0.0137455 | ||||||||
\(455\) | −1.48951e34 | −0.0194934 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.55254e36 | 1.91502 | 0.957510 | − | 0.288400i | \(-0.0931232\pi\) | ||||
0.957510 | + | 0.288400i | \(0.0931232\pi\) | |||||||
\(458\) | 4.96382e33 | 0.00594473 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.92428e35 | −0.556048 | ||||||||
\(461\) | 5.06840e35 | 0.555787 | 0.277893 | − | 0.960612i | \(-0.410364\pi\) | ||||
0.277893 | + | 0.960612i | \(0.410364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.45476e36 | −1.50469 | −0.752347 | − | 0.658767i | \(-0.771078\pi\) | ||||
−0.752347 | + | 0.658767i | \(0.771078\pi\) | |||||||
\(464\) | −1.03469e36 | −1.03948 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.46559e33 | −0.00802504 | ||||||||
\(467\) | 6.89399e35 | 0.634881 | 0.317441 | − | 0.948278i | \(-0.397177\pi\) | ||||
0.317441 | + | 0.948278i | \(0.397177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.92076e34 | −0.0166971 | ||||||||
\(470\) | −8.39617e33 | −0.00709186 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.47903e34 | 0.0277486 | ||||||||
\(473\) | 5.22261e34 | 0.0404820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.57857e35 | −0.115585 | ||||||||
\(476\) | −1.07073e35 | −0.0762053 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.28973e34 | 0.0153995 | ||||||||
\(479\) | 6.34595e35 | 0.414923 | 0.207461 | − | 0.978243i | \(-0.433480\pi\) | ||||
0.207461 | + | 0.978243i | \(0.433480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.30566e36 | −1.42507 | ||||||||
\(482\) | 1.23242e34 | 0.00740670 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.41613e36 | 0.804807 | ||||||||
\(485\) | −4.48592e35 | −0.247935 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.48287e36 | 1.29812 | 0.649058 | − | 0.760739i | \(-0.275163\pi\) | ||||
0.649058 | + | 0.760739i | \(0.275163\pi\) | |||||||
\(488\) | −2.65456e34 | −0.0134997 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.56188e33 | −0.00412024 | ||||||||
\(491\) | 2.37415e36 | 1.11150 | 0.555748 | − | 0.831351i | \(-0.312432\pi\) | ||||
0.555748 | + | 0.831351i | \(0.312432\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.02449e36 | 1.78352 | ||||||||
\(494\) | 3.68762e33 | 0.00159013 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.94793e36 | 0.795371 | ||||||||
\(497\) | −3.62837e34 | −0.0144178 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.00732e36 | −1.88472 | −0.942362 | − | 0.334595i | \(-0.891400\pi\) | ||||
−0.942362 | + | 0.334595i | \(0.891400\pi\) | |||||||
\(500\) | 1.98768e36 | 0.728203 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.72625e34 | 0.00946380 | ||||||||
\(503\) | 1.61560e36 | 0.545966 | 0.272983 | − | 0.962019i | \(-0.411990\pi\) | ||||
0.272983 | + | 0.962019i | \(0.411990\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.06811e36 | 0.342122 | ||||||||
\(506\) | 2.08467e34 | 0.00650138 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.87094e36 | −0.848914 | ||||||||
\(509\) | −1.80638e36 | −0.520139 | −0.260069 | − | 0.965590i | \(-0.583745\pi\) | ||||
−0.260069 | + | 0.965590i | \(0.583745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.39031e35 | −0.0652787 | ||||||||
\(512\) | 1.96413e35 | 0.0522428 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.55386e34 | −0.00392111 | ||||||||
\(515\) | −2.16922e36 | −0.533219 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.25264e36 | −0.758776 | ||||||||
\(518\) | 2.62187e33 | 0.000595880 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.25081e34 | −0.00917120 | ||||||||
\(521\) | −4.59028e36 | −0.965006 | −0.482503 | − | 0.875894i | \(-0.660272\pi\) | ||||
−0.482503 | + | 0.875894i | \(0.660272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.82915e35 | 0.116368 | 0.0581838 | − | 0.998306i | \(-0.481469\pi\) | ||||
0.0581838 | + | 0.998306i | \(0.481469\pi\) | |||||||
\(524\) | 6.90387e36 | 1.34314 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.47617e34 | 0.0138157 | ||||||||
\(527\) | −7.57658e36 | −1.36468 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.74195e36 | 0.982670 | ||||||||
\(530\) | −2.79006e34 | −0.00465467 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.83726e34 | 0.00608435 | ||||||||
\(533\) | −8.08063e36 | −1.24919 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.40636e34 | −0.00353659 | ||||||||
\(536\) | −5.48154e34 | −0.00785558 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.06757e33 | 0.000281773 0 | ||||||||
\(539\) | −3.31684e36 | −0.440835 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.32438e36 | −0.799567 | −0.399783 | − | 0.916610i | \(-0.630915\pi\) | ||||
−0.399783 | + | 0.916610i | \(0.630915\pi\) | |||||||
\(542\) | −1.29227e35 | −0.0159354 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.58360e35 | −0.0537801 | ||||||||
\(545\) | 5.82478e36 | 0.666695 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.05384e36 | −0.986289 | −0.493144 | − | 0.869948i | \(-0.664153\pi\) | ||||
−0.493144 | + | 0.869948i | \(0.664153\pi\) | |||||||
\(548\) | 4.99192e36 | 0.530554 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.85150e34 | −0.00389702 | ||||||||
\(551\) | −1.44229e36 | −0.142399 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.01164e33 | 9.51118e−5 0 | ||||||||
\(554\) | 7.15436e34 | 0.00656431 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.34913e37 | 1.17908 | ||||||||
\(557\) | 1.74285e37 | 1.48668 | 0.743338 | − | 0.668917i | \(-0.233242\pi\) | ||||
0.743338 | + | 0.668917i | \(0.233242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.25264e36 | 0.101805 | ||||||||
\(560\) | −2.21129e35 | −0.0175431 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.23289e34 | −0.00320034 | ||||||||
\(563\) | 7.81650e36 | 0.576964 | 0.288482 | − | 0.957485i | \(-0.406849\pi\) | ||||
0.288482 | + | 0.957485i | \(0.406849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00393e36 | 0.281729 | ||||||||
\(566\) | −1.26065e34 | −0.000866109 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.03548e35 | −0.00678325 | ||||||||
\(569\) | 1.42845e37 | 0.913797 | 0.456899 | − | 0.889519i | \(-0.348960\pi\) | ||||
0.456899 | + | 0.889519i | \(0.348960\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.26975e37 | 1.38481 | 0.692406 | − | 0.721508i | \(-0.256551\pi\) | ||||
0.692406 | + | 0.721508i | \(0.256551\pi\) | |||||||
\(572\) | −8.23327e36 | −0.490598 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.18883e33 | 0.000522336 0 | ||||||||
\(575\) | −2.14040e37 | −1.18844 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.49672e37 | −0.792987 | −0.396494 | − | 0.918038i | \(-0.629773\pi\) | ||||
−0.396494 | + | 0.918038i | \(0.629773\pi\) | |||||||
\(578\) | 3.92203e35 | 0.0202995 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.31236e36 | 0.410626 | ||||||||
\(581\) | −7.40834e35 | −0.0357555 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.08086e37 | −0.498015 | ||||||||
\(584\) | −6.82154e35 | −0.0307121 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.53869e34 | 0.00238116 | ||||||||
\(587\) | 7.65028e36 | 0.321413 | 0.160706 | − | 0.987002i | \(-0.448623\pi\) | ||||
0.160706 | + | 0.987002i | \(0.448623\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.71529e36 | 0.108958 | ||||||||
\(590\) | −1.39724e35 | −0.00547985 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.42293e37 | −1.28249 | ||||||||
\(593\) | 1.64866e37 | 0.603799 | 0.301900 | − | 0.953340i | \(-0.402379\pi\) | ||||
0.301900 | + | 0.953340i | \(0.402379\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.60094e35 | 0.0301000 | ||||||||
\(596\) | −2.76717e37 | −0.946698 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.00008e35 | 0.0163497 | ||||||||
\(599\) | 5.74500e36 | 0.183665 | 0.0918327 | − | 0.995774i | \(-0.470727\pi\) | ||||
0.0918327 | + | 0.995774i | \(0.470727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.09841e36 | −0.155822 | −0.0779112 | − | 0.996960i | \(-0.524825\pi\) | ||||
−0.0779112 | + | 0.996960i | \(0.524825\pi\) | |||||||
\(602\) | −1.42443e33 | −4.25686e−5 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.17274e37 | −0.335123 | ||||||||
\(605\) | −1.13755e37 | −0.317888 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.21769e37 | 0.325453 | 0.162727 | − | 0.986671i | \(-0.447971\pi\) | ||||
0.162727 | + | 0.986671i | \(0.447971\pi\) | |||||||
\(608\) | 1.64267e35 | 0.00429389 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.06612e35 | 0.00266595 | ||||||||
\(611\) | −7.80145e37 | −1.90818 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.55443e37 | 0.597829 | 0.298915 | − | 0.954280i | \(-0.403375\pi\) | ||||
0.298915 | + | 0.954280i | \(0.403375\pi\) | |||||||
\(614\) | 3.03464e35 | 0.00694759 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.87258e34 | 0.000410300 0 | ||||||||
\(617\) | −1.30077e37 | −0.278838 | −0.139419 | − | 0.990234i | \(-0.544523\pi\) | ||||
−0.139419 | + | 0.990234i | \(0.544523\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.04833e37 | −0.420316 | −0.210158 | − | 0.977667i | \(-0.567398\pi\) | ||||
−0.210158 | + | 0.977667i | \(0.567398\pi\) | |||||||
\(620\) | −1.56490e37 | −0.314195 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.95433e35 | 0.00952389 | ||||||||
\(623\) | 3.85698e36 | 0.0725535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.08859e37 | 0.556390 | ||||||||
\(626\) | 6.74931e35 | 0.0118989 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.92052e37 | −0.830913 | ||||||||
\(629\) | 1.33137e38 | 2.20047 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.16988e37 | 1.13531 | 0.567656 | − | 0.823266i | \(-0.307850\pi\) | ||||
0.567656 | + | 0.823266i | \(0.307850\pi\) | |||||||
\(632\) | 2.88704e33 | 4.47478e−5 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.53957e35 | −0.0111980 | ||||||||
\(635\) | 2.30617e37 | 0.335309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.95543e37 | −1.10862 | ||||||||
\(638\) | −3.51900e35 | −0.00480109 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.26227e36 | −0.0165090 | ||||||||
\(641\) | 1.00079e38 | 1.28161 | 0.640807 | − | 0.767702i | \(-0.278600\pi\) | ||||
0.640807 | + | 0.767702i | \(0.278600\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.58172e37 | 0.930936 | 0.465468 | − | 0.885065i | \(-0.345886\pi\) | ||||
0.465468 | + | 0.885065i | \(0.345886\pi\) | |||||||
\(644\) | 5.20298e36 | 0.0625594 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.12936e35 | −0.00245534 | ||||||||
\(647\) | 7.13094e37 | 0.805265 | 0.402632 | − | 0.915362i | \(-0.368095\pi\) | ||||
0.402632 | + | 0.915362i | \(0.368095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.41285e37 | −0.586303 | ||||||||
\(650\) | −9.23781e35 | −0.00980028 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.25243e38 | 1.27471 | ||||||||
\(653\) | −2.47590e37 | −0.246835 | −0.123417 | − | 0.992355i | \(-0.539385\pi\) | ||||
−0.123417 | + | 0.992355i | \(0.539385\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.54574e37 | −0.530520 | ||||||||
\(656\) | −1.19963e38 | −1.12421 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.87136e34 | 0.000797886 0 | ||||||||
\(659\) | −1.51836e38 | −1.33789 | −0.668946 | − | 0.743311i | \(-0.733254\pi\) | ||||
−0.668946 | + | 0.743311i | \(0.733254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.92148e38 | 1.62523 | 0.812617 | − | 0.582798i | \(-0.198042\pi\) | ||||
0.812617 | + | 0.582798i | \(0.198042\pi\) | |||||||
\(662\) | −8.10232e35 | −0.00671470 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.11422e36 | −0.0168221 | ||||||||
\(665\) | −3.08239e35 | −0.00240323 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.95562e38 | −1.46415 | ||||||||
\(668\) | 4.65436e37 | 0.341490 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.20149e35 | 0.00155134 | ||||||||
\(671\) | 4.13009e37 | 0.285237 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.37859e37 | −0.622206 | −0.311103 | − | 0.950376i | \(-0.600698\pi\) | ||||
−0.311103 | + | 0.950376i | \(0.600698\pi\) | |||||||
\(674\) | −1.02371e36 | −0.00665685 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.74333e37 | −0.233872 | ||||||||
\(677\) | 2.93781e37 | 0.179919 | 0.0899595 | − | 0.995945i | \(-0.471326\pi\) | ||||
0.0899595 | + | 0.995945i | \(0.471326\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.73981e36 | 0.0278945 | ||||||||
\(680\) | 2.45457e36 | 0.0141613 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.62494e35 | 0.00367361 | ||||||||
\(683\) | −1.68599e38 | −0.916591 | −0.458295 | − | 0.888800i | \(-0.651540\pi\) | ||||
−0.458295 | + | 0.888800i | \(0.651540\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.00991e37 | −0.209562 | ||||||||
\(686\) | 1.81108e35 | 0.000928031 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.85964e37 | 0.0916190 | ||||||||
\(689\) | −2.59243e38 | −1.25241 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.72820e38 | −1.73199 | −0.865996 | − | 0.500051i | \(-0.833314\pi\) | ||||
−0.865996 | + | 0.500051i | \(0.833314\pi\) | |||||||
\(692\) | 3.56716e38 | 1.62514 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.29252e36 | −0.0188088 | ||||||||
\(695\) | −1.08373e38 | −0.465720 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.66604e38 | 1.92888 | ||||||||
\(698\) | 1.97084e36 | 0.00799102 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.61267e36 | −0.0374991 | ||||||||
\(701\) | −3.38534e38 | −1.29541 | −0.647707 | − | 0.761890i | \(-0.724272\pi\) | ||||
−0.647707 | + | 0.761890i | \(0.724272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.77135e37 | −0.175689 | ||||||||
\(704\) | −1.22203e38 | −0.441417 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.09623e35 | 0.00281462 | ||||||||
\(707\) | −1.12856e37 | −0.0384912 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.34891e38 | 0.771155 | 0.385578 | − | 0.922675i | \(-0.374002\pi\) | ||||
0.385578 | + | 0.922675i | \(0.374002\pi\) | |||||||
\(710\) | 4.15866e35 | 0.00133957 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.10072e37 | 0.0341347 | ||||||||
\(713\) | 3.68168e38 | 1.12031 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.61362e37 | 0.193779 | ||||||||
\(716\) | 5.78291e38 | 1.66273 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.45165e35 | 0.00261714 | ||||||||
\(719\) | 1.57531e38 | 0.428082 | 0.214041 | − | 0.976825i | \(-0.431337\pi\) | ||||
0.214041 | + | 0.976825i | \(0.431337\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.29199e37 | 0.0599911 | ||||||||
\(722\) | −3.99279e36 | −0.0102571 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.46707e37 | 0.184790 | ||||||||
\(725\) | 3.61306e38 | 0.877632 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.38862e38 | −0.559027 | −0.279513 | − | 0.960142i | \(-0.590173\pi\) | ||||
−0.279513 | + | 0.960142i | \(0.590173\pi\) | |||||||
\(728\) | 4.49139e35 | 0.00103183 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.73965e36 | 0.00606509 | ||||||||
\(731\) | −7.23320e37 | −0.157198 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.39015e38 | −0.291177 | −0.145589 | − | 0.989345i | \(-0.546508\pi\) | ||||
−0.145589 | + | 0.989345i | \(0.546508\pi\) | |||||||
\(734\) | 8.01229e36 | 0.0164763 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.22731e37 | 0.0441499 | ||||||||
\(737\) | 8.52846e37 | 0.165981 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.01753e37 | 0.0566176 | 0.0283088 | − | 0.999599i | \(-0.490988\pi\) | ||||
0.0283088 | + | 0.999599i | \(0.490988\pi\) | |||||||
\(740\) | 2.74987e38 | 0.506623 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.94797e35 | 0.000523685 0 | ||||||||
\(743\) | −8.48049e38 | −1.47935 | −0.739677 | − | 0.672962i | \(-0.765022\pi\) | ||||
−0.739677 | + | 0.672962i | \(0.765022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.22281e38 | 0.373932 | ||||||||
\(746\) | −8.22856e36 | −0.0135941 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.75418e38 | 0.757538 | ||||||||
\(749\) | 2.54256e35 | 0.000397893 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00379e39 | −1.51532 | −0.757658 | − | 0.652651i | \(-0.773657\pi\) | ||||
−0.757658 | + | 0.652651i | \(0.773657\pi\) | |||||||
\(752\) | −1.15819e39 | −1.71726 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.44031e36 | −0.0120738 | ||||||||
\(755\) | 9.42041e37 | 0.132369 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.01436e39 | 1.37530 | 0.687652 | − | 0.726040i | \(-0.258641\pi\) | ||||
0.687652 | + | 0.726040i | \(0.258641\pi\) | |||||||
\(758\) | 9.67114e36 | 0.0128808 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.79664e35 | −0.00113066 | ||||||||
\(761\) | 1.18512e39 | 1.49648 | 0.748240 | − | 0.663428i | \(-0.230899\pi\) | ||||
0.748240 | + | 0.663428i | \(0.230899\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.15445e37 | −0.0750080 | ||||||||
\(764\) | −5.62940e38 | −0.674065 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.44152e37 | −0.0166622 | ||||||||
\(767\) | −1.29827e39 | −1.47444 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.38650e39 | −1.52024 | −0.760122 | − | 0.649780i | \(-0.774861\pi\) | ||||
−0.760122 | + | 0.649780i | \(0.774861\pi\) | |||||||
\(770\) | −7.52063e34 | −8.10269e−5 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.51727e36 | −0.00678004 | ||||||||
\(773\) | 3.84501e38 | 0.393074 | 0.196537 | − | 0.980496i | \(-0.437030\pi\) | ||||
0.196537 | + | 0.980496i | \(0.437030\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.80202e38 | −0.671530 | ||||||||
\(776\) | 1.35266e37 | 0.0131237 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.80364e36 | −0.00169015 | ||||||||
\(779\) | −1.67221e38 | −0.154005 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.61105e38 | 0.143324 | ||||||||
\(782\) | −2.88722e37 | −0.0252458 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.18104e39 | −0.997698 | ||||||||
\(785\) | 3.95255e38 | 0.328199 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.31177e38 | 0.666860 | 0.333430 | − | 0.942775i | \(-0.391794\pi\) | ||||
0.333430 | + | 0.942775i | \(0.391794\pi\) | |||||||
\(788\) | −3.22217e37 | −0.0254123 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.15949e34 | −8.83690e−6 0 | ||||||||
\(791\) | −4.23054e37 | −0.0316966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.90602e38 | 0.717317 | ||||||||
\(794\) | 4.93337e36 | 0.00351210 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.93951e38 | −0.683973 | ||||||||
\(797\) | 5.86889e38 | 0.397071 | 0.198536 | − | 0.980094i | \(-0.436381\pi\) | ||||
0.198536 | + | 0.980094i | \(0.436381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.50484e39 | 2.94644 | ||||||||
\(800\) | −4.11502e37 | −0.0264641 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.99737e37 | 0.0124195 | ||||||||
\(803\) | 1.06133e39 | 0.648919 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.17945e37 | −0.0247101 | ||||||||
\(806\) | 1.58899e37 | 0.00923843 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.22072e37 | −0.0181092 | ||||||||
\(809\) | 2.02827e39 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.61063e39 | −0.861421 | −0.430710 | − | 0.902490i | \(-0.641737\pi\) | ||||
−0.430710 | + | 0.902490i | \(0.641737\pi\) | |||||||
\(812\) | −8.78281e37 | −0.0461984 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.16415e37 | −0.00592350 | ||||||||
\(815\) | −1.00605e39 | −0.503492 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.59222e37 | 0.0125509 | ||||||||
\(818\) | −2.58740e37 | −0.0123224 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.63745e38 | 0.444094 | ||||||||
\(821\) | 2.30031e39 | 1.04268 | 0.521342 | − | 0.853348i | \(-0.325431\pi\) | ||||
0.521342 | + | 0.853348i | \(0.325431\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.08776e39 | −0.915764 | −0.457882 | − | 0.889013i | \(-0.651392\pi\) | ||||
−0.457882 | + | 0.889013i | \(0.651392\pi\) | |||||||
\(824\) | 6.54096e37 | 0.0282244 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.47632e36 | 0.000616523 0 | ||||||||
\(827\) | −3.43290e39 | −1.41038 | −0.705192 | − | 0.709017i | \(-0.749139\pi\) | ||||
−0.705192 | + | 0.709017i | \(0.749139\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.03456e38 | 0.319504 | 0.159752 | − | 0.987157i | \(-0.448931\pi\) | ||||
0.159752 | + | 0.987157i | \(0.448931\pi\) | |||||||
\(830\) | 8.49107e36 | 0.00332207 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.93103e39 | −1.11008 | ||||||||
\(833\) | 4.59375e39 | 1.71183 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.73875e38 | −0.134884 | ||||||||
\(836\) | −1.70380e38 | −0.0604830 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.57987e36 | −0.00260536 | ||||||||
\(839\) | −2.54669e39 | −0.861369 | −0.430685 | − | 0.902502i | \(-0.641728\pi\) | ||||
−0.430685 | + | 0.902502i | \(0.641728\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.48015e38 | 0.0812329 | ||||||||
\(842\) | 1.97242e37 | 0.00635750 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.18503e39 | 1.30640 | ||||||||
\(845\) | 3.00694e38 | 0.0923760 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.20193e38 | 0.0357647 | ||||||||
\(848\) | −3.84867e39 | −1.12711 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.33424e37 | 0.0151327 | ||||||||
\(851\) | −6.46952e39 | −1.80644 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.61849e39 | 0.437823 | 0.218912 | − | 0.975745i | \(-0.429749\pi\) | ||||
0.218912 | + | 0.975745i | \(0.429749\pi\) | |||||||
\(854\) | −1.12646e36 | −0.000299939 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.25603e35 | 0.000187199 0 | ||||||||
\(857\) | −1.79678e38 | −0.0456304 | −0.0228152 | − | 0.999740i | \(-0.507263\pi\) | ||||
−0.0228152 | + | 0.999740i | \(0.507263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.83644e39 | −1.68237 | −0.841187 | − | 0.540744i | \(-0.818143\pi\) | ||||
−0.841187 | + | 0.540744i | \(0.818143\pi\) | |||||||
\(860\) | −1.49398e38 | −0.0361922 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.52074e37 | 0.0176568 | ||||||||
\(863\) | 8.93182e37 | 0.0206440 | 0.0103220 | − | 0.999947i | \(-0.496714\pi\) | ||||
0.0103220 | + | 0.999947i | \(0.496714\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.86543e39 | −0.641907 | ||||||||
\(866\) | 1.26905e37 | 0.00279890 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.65347e38 | 0.0353492 | ||||||||
\(869\) | −4.49180e36 | −0.000945483 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.04555e39 | 0.417412 | ||||||||
\(872\) | −1.75638e38 | −0.0352895 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.03472e37 | 0.00201566 | ||||||||
\(875\) | 1.68703e38 | 0.0323605 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.74244e39 | −0.882078 | −0.441039 | − | 0.897488i | \(-0.645390\pi\) | ||||
−0.441039 | + | 0.897488i | \(0.645390\pi\) | |||||||
\(878\) | 8.40191e37 | 0.0153887 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.81843e38 | 0.174392 | ||||||||
\(881\) | 4.04555e39 | 0.707624 | 0.353812 | − | 0.935317i | \(-0.384885\pi\) | ||||
0.353812 | + | 0.935317i | \(0.384885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.15911e39 | 1.21448 | 0.607239 | − | 0.794519i | \(-0.292277\pi\) | ||||
0.607239 | + | 0.794519i | \(0.292277\pi\) | |||||||
\(884\) | 1.14029e40 | 1.90507 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.24697e37 | −0.0101231 | ||||||||
\(887\) | 3.43934e39 | 0.548916 | 0.274458 | − | 0.961599i | \(-0.411502\pi\) | ||||
0.274458 | + | 0.961599i | \(0.411502\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.43669e38 | −0.0377247 | ||||||||
\(890\) | −4.42068e37 | −0.00674099 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.04561e39 | 0.450556 | ||||||||
\(893\) | −1.61444e39 | −0.235248 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.64529e39 | −0.656753 | ||||||||
\(896\) | 1.33371e37 | 0.00185739 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.11041e38 | −0.0150056 | ||||||||
\(899\) | −6.21481e39 | −0.827317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.49696e40 | 1.93387 | ||||||||
\(902\) | −4.07997e37 | −0.00519241 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.20732e38 | −0.0149125 | ||||||||
\(905\) | −5.99814e38 | −0.0729896 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.71200e38 | 0.0320325 | 0.0160163 | − | 0.999872i | \(-0.494902\pi\) | ||||
0.0160163 | + | 0.999872i | \(0.494902\pi\) | |||||||
\(908\) | 1.12987e40 | 1.31482 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.80382e36 | −0.000203767 0 | ||||||||
\(911\) | −1.18591e40 | −1.31994 | −0.659970 | − | 0.751292i | \(-0.729431\pi\) | ||||
−0.659970 | + | 0.751292i | \(0.729431\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.28941e39 | 0.355436 | ||||||||
\(914\) | 1.88015e38 | 0.0200179 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.50082e39 | −0.568641 | ||||||||
\(917\) | 5.85961e38 | 0.0596874 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.70613e40 | −1.68753 | −0.843766 | − | 0.536711i | \(-0.819667\pi\) | ||||
−0.843766 | + | 0.536711i | \(0.819667\pi\) | |||||||
\(920\) | −1.19274e38 | −0.0116255 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.13793e37 | 0.00580971 | ||||||||
\(923\) | 3.86409e39 | 0.360433 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.19526e40 | 1.08281 | ||||||||
\(926\) | −1.76174e38 | −0.0157287 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.75977e38 | −0.0326035 | ||||||||
\(929\) | 8.89239e39 | 0.759987 | 0.379994 | − | 0.924989i | \(-0.375926\pi\) | ||||
0.379994 | + | 0.924989i | \(0.375926\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.64630e39 | −0.136675 | ||||||||
\(932\) | 9.38141e39 | 0.767633 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.34875e37 | 0.00663649 | ||||||||
\(935\) | −3.81894e39 | −0.299217 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.80674e40 | −1.37534 | −0.687670 | − | 0.726023i | \(-0.741367\pi\) | ||||
−0.687670 | + | 0.726023i | \(0.741367\pi\) | |||||||
\(938\) | −2.32608e36 | −0.000174537 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.30449e39 | 0.678370 | ||||||||
\(941\) | −2.62451e40 | −1.88620 | −0.943101 | − | 0.332507i | \(-0.892105\pi\) | ||||
−0.943101 | + | 0.332507i | \(0.892105\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.26737e40 | −1.58348 | ||||||||
\(944\) | −1.92738e40 | −1.32692 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.32468e36 | 0.000423163 0 | ||||||||
\(947\) | 6.71744e39 | 0.443077 | 0.221539 | − | 0.975152i | \(-0.428892\pi\) | ||||
0.221539 | + | 0.975152i | \(0.428892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.54560e40 | 1.63191 | ||||||||
\(950\) | −1.91168e37 | −0.00120822 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.59349e37 | −0.00159325 | ||||||||
\(953\) | −1.95322e39 | −0.118303 | −0.0591516 | − | 0.998249i | \(-0.518840\pi\) | ||||
−0.0591516 | + | 0.998249i | \(0.518840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.52199e39 | 0.266246 | ||||||||
\(956\) | −2.53743e40 | −1.47304 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.68507e37 | 0.00433724 | ||||||||
\(959\) | 4.23686e38 | 0.0235772 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.78259e39 | −0.366969 | ||||||||
\(962\) | −2.79220e38 | −0.0148965 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.36575e40 | −0.708486 | ||||||||
\(965\) | 5.23519e37 | 0.00267802 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.48699e40 | 0.739690 | 0.369845 | − | 0.929093i | \(-0.379411\pi\) | ||||
0.369845 | + | 0.929093i | \(0.379411\pi\) | |||||||
\(968\) | 3.43012e38 | 0.0168264 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.43254e37 | −0.00259170 | ||||||||
\(971\) | 1.17711e40 | 0.553804 | 0.276902 | − | 0.960898i | \(-0.410692\pi\) | ||||
0.276902 | + | 0.960898i | \(0.410692\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.14506e39 | 0.0523970 | ||||||||
\(974\) | 3.00681e38 | 0.0135694 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.47062e40 | 0.645549 | ||||||||
\(977\) | 3.52154e40 | 1.52460 | 0.762300 | − | 0.647224i | \(-0.224070\pi\) | ||||
0.762300 | + | 0.647224i | \(0.224070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.71255e40 | −0.721236 | ||||||||
\(980\) | 9.48813e39 | 0.394120 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.87514e38 | 0.0116186 | ||||||||
\(983\) | 3.23914e40 | 1.29109 | 0.645547 | − | 0.763721i | \(-0.276629\pi\) | ||||
0.645547 | + | 0.763721i | \(0.276629\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.58830e38 | 0.0100375 | ||||||||
\(986\) | 4.87374e38 | 0.0186433 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.08656e39 | −0.152103 | ||||||||
\(989\) | 3.51482e39 | 0.129049 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.97175e38 | 0.0213357 | 0.0106679 | − | 0.999943i | \(-0.496604\pi\) | ||||
0.0106679 | + | 0.999943i | \(0.496604\pi\) | |||||||
\(992\) | 7.07822e38 | 0.0249469 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.39403e36 | −0.000150712 0 | ||||||||
\(995\) | 7.98421e39 | 0.270160 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.51823e40 | −0.499980 | −0.249990 | − | 0.968248i | \(-0.580427\pi\) | ||||
−0.249990 | + | 0.968248i | \(0.580427\pi\) | |||||||
\(998\) | −6.06396e38 | −0.0197013 | ||||||||
\(999\) | 0 | 0 |
(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 | 9.28.a.b.1.2 | 2 | ||
3.2 | odd | 2 | 3.28.a.b.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 48.28.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.28.a.b.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
9.28.a.b.1.2 | 2 | 1.1 | even | 1 | trivial | ||
48.28.a.e.1.1 | 2 | 12.11 | even | 2 |