Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,12,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, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(7.68343180560\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1969}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 492 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-21.6867\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 32.0000 | 0.707107 | ||||||||
\(3\) | 745.734 | 1.77181 | 0.885905 | − | 0.463867i | \(-0.153538\pi\) | ||||
0.885905 | + | 0.463867i | \(0.153538\pi\) | |||||||
\(4\) | 1024.00 | 0.500000 | ||||||||
\(5\) | 3125.00 | 0.447214 | ||||||||
\(6\) | 23863.5 | 1.25286 | ||||||||
\(7\) | −71494.9 | −1.60782 | −0.803908 | − | 0.594754i | \(-0.797249\pi\) | ||||
−0.803908 | + | 0.594754i | \(0.797249\pi\) | |||||||
\(8\) | 32768.0 | 0.353553 | ||||||||
\(9\) | 378972. | 2.13931 | ||||||||
\(10\) | 100000. | 0.316228 | ||||||||
\(11\) | −345651. | −0.647109 | −0.323555 | − | 0.946209i | \(-0.604878\pi\) | ||||
−0.323555 | + | 0.946209i | \(0.604878\pi\) | |||||||
\(12\) | 763632. | 0.885905 | ||||||||
\(13\) | 1.50956e6 | 1.12762 | 0.563810 | − | 0.825904i | \(-0.309335\pi\) | ||||
0.563810 | + | 0.825904i | \(0.309335\pi\) | |||||||
\(14\) | −2.28784e6 | −1.13690 | ||||||||
\(15\) | 2.33042e6 | 0.792377 | ||||||||
\(16\) | 1.04858e6 | 0.250000 | ||||||||
\(17\) | −5.39291e6 | −0.921200 | −0.460600 | − | 0.887608i | \(-0.652366\pi\) | ||||
−0.460600 | + | 0.887608i | \(0.652366\pi\) | |||||||
\(18\) | 1.21271e7 | 1.51272 | ||||||||
\(19\) | −1.11633e7 | −1.03430 | −0.517151 | − | 0.855894i | \(-0.673007\pi\) | ||||
−0.517151 | + | 0.855894i | \(0.673007\pi\) | |||||||
\(20\) | 3.20000e6 | 0.223607 | ||||||||
\(21\) | −5.33162e7 | −2.84874 | ||||||||
\(22\) | −1.10608e7 | −0.457575 | ||||||||
\(23\) | −5.27646e6 | −0.170938 | −0.0854692 | − | 0.996341i | \(-0.527239\pi\) | ||||
−0.0854692 | + | 0.996341i | \(0.527239\pi\) | |||||||
\(24\) | 2.44362e7 | 0.626429 | ||||||||
\(25\) | 9.76562e6 | 0.200000 | ||||||||
\(26\) | 4.83060e7 | 0.797348 | ||||||||
\(27\) | 1.50508e8 | 2.01864 | ||||||||
\(28\) | −7.32108e7 | −0.803908 | ||||||||
\(29\) | −1.86291e7 | −0.168657 | −0.0843284 | − | 0.996438i | \(-0.526874\pi\) | ||||
−0.0843284 | + | 0.996438i | \(0.526874\pi\) | |||||||
\(30\) | 7.45734e7 | 0.560295 | ||||||||
\(31\) | 7.10448e7 | 0.445700 | 0.222850 | − | 0.974853i | \(-0.428464\pi\) | ||||
0.222850 | + | 0.974853i | \(0.428464\pi\) | |||||||
\(32\) | 3.35544e7 | 0.176777 | ||||||||
\(33\) | −2.57763e8 | −1.14655 | ||||||||
\(34\) | −1.72573e8 | −0.651387 | ||||||||
\(35\) | −2.23422e8 | −0.719037 | ||||||||
\(36\) | 3.88068e8 | 1.06966 | ||||||||
\(37\) | 3.23164e8 | 0.766150 | 0.383075 | − | 0.923717i | \(-0.374865\pi\) | ||||
0.383075 | + | 0.923717i | \(0.374865\pi\) | |||||||
\(38\) | −3.57225e8 | −0.731362 | ||||||||
\(39\) | 1.12573e9 | 1.99793 | ||||||||
\(40\) | 1.02400e8 | 0.158114 | ||||||||
\(41\) | −9.11277e8 | −1.22840 | −0.614199 | − | 0.789151i | \(-0.710521\pi\) | ||||
−0.614199 | + | 0.789151i | \(0.710521\pi\) | |||||||
\(42\) | −1.70612e9 | −2.01437 | ||||||||
\(43\) | −1.16431e9 | −1.20779 | −0.603897 | − | 0.797063i | \(-0.706386\pi\) | ||||
−0.603897 | + | 0.797063i | \(0.706386\pi\) | |||||||
\(44\) | −3.53946e8 | −0.323555 | ||||||||
\(45\) | 1.18429e9 | 0.956729 | ||||||||
\(46\) | −1.68847e8 | −0.120872 | ||||||||
\(47\) | 2.81949e8 | 0.179321 | 0.0896606 | − | 0.995972i | \(-0.471422\pi\) | ||||
0.0896606 | + | 0.995972i | \(0.471422\pi\) | |||||||
\(48\) | 7.81959e8 | 0.442952 | ||||||||
\(49\) | 3.13420e9 | 1.58507 | ||||||||
\(50\) | 3.12500e8 | 0.141421 | ||||||||
\(51\) | −4.02168e9 | −1.63219 | ||||||||
\(52\) | 1.54579e9 | 0.563810 | ||||||||
\(53\) | 4.05957e9 | 1.33341 | 0.666704 | − | 0.745323i | \(-0.267705\pi\) | ||||
0.666704 | + | 0.745323i | \(0.267705\pi\) | |||||||
\(54\) | 4.81626e9 | 1.42740 | ||||||||
\(55\) | −1.08016e9 | −0.289396 | ||||||||
\(56\) | −2.34275e9 | −0.568449 | ||||||||
\(57\) | −8.32485e9 | −1.83259 | ||||||||
\(58\) | −5.96132e8 | −0.119258 | ||||||||
\(59\) | 4.89828e9 | 0.891986 | 0.445993 | − | 0.895036i | \(-0.352851\pi\) | ||||
0.445993 | + | 0.895036i | \(0.352851\pi\) | |||||||
\(60\) | 2.38635e9 | 0.396189 | ||||||||
\(61\) | 1.07565e10 | 1.63064 | 0.815320 | − | 0.579011i | \(-0.196561\pi\) | ||||
0.815320 | + | 0.579011i | \(0.196561\pi\) | |||||||
\(62\) | 2.27343e9 | 0.315158 | ||||||||
\(63\) | −2.70946e10 | −3.43962 | ||||||||
\(64\) | 1.07374e9 | 0.125000 | ||||||||
\(65\) | 4.71739e9 | 0.504287 | ||||||||
\(66\) | −8.24843e9 | −0.810736 | ||||||||
\(67\) | 3.70812e9 | 0.335539 | 0.167769 | − | 0.985826i | \(-0.446344\pi\) | ||||
0.167769 | + | 0.985826i | \(0.446344\pi\) | |||||||
\(68\) | −5.52234e9 | −0.460600 | ||||||||
\(69\) | −3.93484e9 | −0.302870 | ||||||||
\(70\) | −7.14949e9 | −0.508436 | ||||||||
\(71\) | 3.45274e9 | 0.227113 | 0.113557 | − | 0.993532i | \(-0.463776\pi\) | ||||
0.113557 | + | 0.993532i | \(0.463776\pi\) | |||||||
\(72\) | 1.24182e10 | 0.756360 | ||||||||
\(73\) | −2.21136e10 | −1.24848 | −0.624242 | − | 0.781231i | \(-0.714592\pi\) | ||||
−0.624242 | + | 0.781231i | \(0.714592\pi\) | |||||||
\(74\) | 1.03413e10 | 0.541750 | ||||||||
\(75\) | 7.28256e9 | 0.354362 | ||||||||
\(76\) | −1.14312e10 | −0.517151 | ||||||||
\(77\) | 2.47123e10 | 1.04043 | ||||||||
\(78\) | 3.60235e10 | 1.41275 | ||||||||
\(79\) | 7.02672e9 | 0.256923 | 0.128462 | − | 0.991714i | \(-0.458996\pi\) | ||||
0.128462 | + | 0.991714i | \(0.458996\pi\) | |||||||
\(80\) | 3.27680e9 | 0.111803 | ||||||||
\(81\) | 4.51052e10 | 1.43734 | ||||||||
\(82\) | −2.91609e10 | −0.868609 | ||||||||
\(83\) | 5.55656e10 | 1.54838 | 0.774188 | − | 0.632956i | \(-0.218159\pi\) | ||||
0.774188 | + | 0.632956i | \(0.218159\pi\) | |||||||
\(84\) | −5.45958e10 | −1.42437 | ||||||||
\(85\) | −1.68528e10 | −0.411973 | ||||||||
\(86\) | −3.72580e10 | −0.854039 | ||||||||
\(87\) | −1.38924e10 | −0.298828 | ||||||||
\(88\) | −1.13263e10 | −0.228788 | ||||||||
\(89\) | −9.29706e9 | −0.176482 | −0.0882410 | − | 0.996099i | \(-0.528125\pi\) | ||||
−0.0882410 | + | 0.996099i | \(0.528125\pi\) | |||||||
\(90\) | 3.78972e10 | 0.676509 | ||||||||
\(91\) | −1.07926e11 | −1.81301 | ||||||||
\(92\) | −5.40310e9 | −0.0854692 | ||||||||
\(93\) | 5.29805e10 | 0.789696 | ||||||||
\(94\) | 9.02235e9 | 0.126799 | ||||||||
\(95\) | −3.48853e10 | −0.462554 | ||||||||
\(96\) | 2.50227e10 | 0.313215 | ||||||||
\(97\) | 4.71888e10 | 0.557949 | 0.278975 | − | 0.960298i | \(-0.410005\pi\) | ||||
0.278975 | + | 0.960298i | \(0.410005\pi\) | |||||||
\(98\) | 1.00294e11 | 1.12081 | ||||||||
\(99\) | −1.30992e11 | −1.38437 | ||||||||
\(100\) | 1.00000e10 | 0.100000 | ||||||||
\(101\) | 1.61228e11 | 1.52642 | 0.763209 | − | 0.646151i | \(-0.223622\pi\) | ||||
0.763209 | + | 0.646151i | \(0.223622\pi\) | |||||||
\(102\) | −1.28694e11 | −1.15413 | ||||||||
\(103\) | −1.85579e11 | −1.57733 | −0.788666 | − | 0.614822i | \(-0.789228\pi\) | ||||
−0.788666 | + | 0.614822i | \(0.789228\pi\) | |||||||
\(104\) | 4.94654e10 | 0.398674 | ||||||||
\(105\) | −1.66613e11 | −1.27400 | ||||||||
\(106\) | 1.29906e11 | 0.942861 | ||||||||
\(107\) | −5.45807e10 | −0.376208 | −0.188104 | − | 0.982149i | \(-0.560234\pi\) | ||||
−0.188104 | + | 0.982149i | \(0.560234\pi\) | |||||||
\(108\) | 1.54120e11 | 1.00932 | ||||||||
\(109\) | −3.54035e10 | −0.220394 | −0.110197 | − | 0.993910i | \(-0.535148\pi\) | ||||
−0.110197 | + | 0.993910i | \(0.535148\pi\) | |||||||
\(110\) | −3.45651e10 | −0.204634 | ||||||||
\(111\) | 2.40995e11 | 1.35747 | ||||||||
\(112\) | −7.49679e10 | −0.401954 | ||||||||
\(113\) | 1.20314e11 | 0.614308 | 0.307154 | − | 0.951660i | \(-0.400623\pi\) | ||||
0.307154 | + | 0.951660i | \(0.400623\pi\) | |||||||
\(114\) | −2.66395e11 | −1.29583 | ||||||||
\(115\) | −1.64889e10 | −0.0764460 | ||||||||
\(116\) | −1.90762e10 | −0.0843284 | ||||||||
\(117\) | 5.72083e11 | 2.41233 | ||||||||
\(118\) | 1.56745e11 | 0.630729 | ||||||||
\(119\) | 3.85566e11 | 1.48112 | ||||||||
\(120\) | 7.63632e10 | 0.280148 | ||||||||
\(121\) | −1.65837e11 | −0.581250 | ||||||||
\(122\) | 3.44209e11 | 1.15304 | ||||||||
\(123\) | −6.79571e11 | −2.17649 | ||||||||
\(124\) | 7.27499e10 | 0.222850 | ||||||||
\(125\) | 3.05176e10 | 0.0894427 | ||||||||
\(126\) | −8.67028e11 | −2.43218 | ||||||||
\(127\) | −5.60687e11 | −1.50591 | −0.752957 | − | 0.658070i | \(-0.771373\pi\) | ||||
−0.752957 | + | 0.658070i | \(0.771373\pi\) | |||||||
\(128\) | 3.43597e10 | 0.0883883 | ||||||||
\(129\) | −8.68267e11 | −2.13998 | ||||||||
\(130\) | 1.50956e11 | 0.356585 | ||||||||
\(131\) | 4.11999e11 | 0.933048 | 0.466524 | − | 0.884508i | \(-0.345506\pi\) | ||||
0.466524 | + | 0.884508i | \(0.345506\pi\) | |||||||
\(132\) | −2.63950e11 | −0.573277 | ||||||||
\(133\) | 7.98119e11 | 1.66297 | ||||||||
\(134\) | 1.18660e11 | 0.237262 | ||||||||
\(135\) | 4.70338e11 | 0.902764 | ||||||||
\(136\) | −1.76715e11 | −0.325693 | ||||||||
\(137\) | −7.86259e11 | −1.39188 | −0.695941 | − | 0.718099i | \(-0.745013\pi\) | ||||
−0.695941 | + | 0.718099i | \(0.745013\pi\) | |||||||
\(138\) | −1.25915e11 | −0.214162 | ||||||||
\(139\) | 8.57152e11 | 1.40112 | 0.700562 | − | 0.713592i | \(-0.252933\pi\) | ||||
0.700562 | + | 0.713592i | \(0.252933\pi\) | |||||||
\(140\) | −2.28784e11 | −0.359518 | ||||||||
\(141\) | 2.10259e11 | 0.317723 | ||||||||
\(142\) | 1.10488e11 | 0.160593 | ||||||||
\(143\) | −5.21782e11 | −0.729694 | ||||||||
\(144\) | 3.97381e11 | 0.534828 | ||||||||
\(145\) | −5.82160e10 | −0.0754256 | ||||||||
\(146\) | −7.07634e11 | −0.882812 | ||||||||
\(147\) | 2.33728e12 | 2.80844 | ||||||||
\(148\) | 3.30920e11 | 0.383075 | ||||||||
\(149\) | −2.38606e11 | −0.266168 | −0.133084 | − | 0.991105i | \(-0.542488\pi\) | ||||
−0.133084 | + | 0.991105i | \(0.542488\pi\) | |||||||
\(150\) | 2.33042e11 | 0.250572 | ||||||||
\(151\) | −9.57309e10 | −0.0992382 | −0.0496191 | − | 0.998768i | \(-0.515801\pi\) | ||||
−0.0496191 | + | 0.998768i | \(0.515801\pi\) | |||||||
\(152\) | −3.65799e11 | −0.365681 | ||||||||
\(153\) | −2.04376e12 | −1.97073 | ||||||||
\(154\) | 7.90793e11 | 0.735697 | ||||||||
\(155\) | 2.22015e11 | 0.199323 | ||||||||
\(156\) | 1.15275e12 | 0.998965 | ||||||||
\(157\) | −1.79935e12 | −1.50545 | −0.752727 | − | 0.658333i | \(-0.771262\pi\) | ||||
−0.752727 | + | 0.658333i | \(0.771262\pi\) | |||||||
\(158\) | 2.24855e11 | 0.181672 | ||||||||
\(159\) | 3.02736e12 | 2.36254 | ||||||||
\(160\) | 1.04858e11 | 0.0790569 | ||||||||
\(161\) | 3.77240e11 | 0.274837 | ||||||||
\(162\) | 1.44337e12 | 1.01635 | ||||||||
\(163\) | −2.50619e12 | −1.70601 | −0.853005 | − | 0.521903i | \(-0.825222\pi\) | ||||
−0.853005 | + | 0.521903i | \(0.825222\pi\) | |||||||
\(164\) | −9.33148e11 | −0.614199 | ||||||||
\(165\) | −8.05511e11 | −0.512755 | ||||||||
\(166\) | 1.77810e12 | 1.09487 | ||||||||
\(167\) | −2.69855e12 | −1.60764 | −0.803822 | − | 0.594871i | \(-0.797203\pi\) | ||||
−0.803822 | + | 0.594871i | \(0.797203\pi\) | |||||||
\(168\) | −1.74707e12 | −1.00718 | ||||||||
\(169\) | 4.86623e11 | 0.271529 | ||||||||
\(170\) | −5.39291e11 | −0.291309 | ||||||||
\(171\) | −4.23058e12 | −2.21269 | ||||||||
\(172\) | −1.19225e12 | −0.603897 | ||||||||
\(173\) | 3.07796e12 | 1.51011 | 0.755057 | − | 0.655659i | \(-0.227609\pi\) | ||||
0.755057 | + | 0.655659i | \(0.227609\pi\) | |||||||
\(174\) | −4.44556e11 | −0.211303 | ||||||||
\(175\) | −6.98193e11 | −0.321563 | ||||||||
\(176\) | −3.62441e11 | −0.161777 | ||||||||
\(177\) | 3.65282e12 | 1.58043 | ||||||||
\(178\) | −2.97506e11 | −0.124792 | ||||||||
\(179\) | 3.51154e11 | 0.142826 | 0.0714128 | − | 0.997447i | \(-0.477249\pi\) | ||||
0.0714128 | + | 0.997447i | \(0.477249\pi\) | |||||||
\(180\) | 1.21271e12 | 0.478364 | ||||||||
\(181\) | 6.34106e11 | 0.242622 | 0.121311 | − | 0.992615i | \(-0.461290\pi\) | ||||
0.121311 | + | 0.992615i | \(0.461290\pi\) | |||||||
\(182\) | −3.45364e12 | −1.28199 | ||||||||
\(183\) | 8.02151e12 | 2.88918 | ||||||||
\(184\) | −1.72899e11 | −0.0604359 | ||||||||
\(185\) | 1.00989e12 | 0.342633 | ||||||||
\(186\) | 1.69538e12 | 0.558399 | ||||||||
\(187\) | 1.86406e12 | 0.596117 | ||||||||
\(188\) | 2.88715e11 | 0.0896606 | ||||||||
\(189\) | −1.07606e13 | −3.24560 | ||||||||
\(190\) | −1.11633e12 | −0.327075 | ||||||||
\(191\) | −2.61584e12 | −0.744609 | −0.372304 | − | 0.928111i | \(-0.621432\pi\) | ||||
−0.372304 | + | 0.928111i | \(0.621432\pi\) | |||||||
\(192\) | 8.00726e11 | 0.221476 | ||||||||
\(193\) | 1.59819e12 | 0.429598 | 0.214799 | − | 0.976658i | \(-0.431090\pi\) | ||||
0.214799 | + | 0.976658i | \(0.431090\pi\) | |||||||
\(194\) | 1.51004e12 | 0.394530 | ||||||||
\(195\) | 3.51792e12 | 0.893501 | ||||||||
\(196\) | 3.20942e12 | 0.792535 | ||||||||
\(197\) | −6.16281e10 | −0.0147984 | −0.00739920 | − | 0.999973i | \(-0.502355\pi\) | ||||
−0.00739920 | + | 0.999973i | \(0.502355\pi\) | |||||||
\(198\) | −4.19175e12 | −0.978896 | ||||||||
\(199\) | 2.36544e12 | 0.537303 | 0.268652 | − | 0.963237i | \(-0.413422\pi\) | ||||
0.268652 | + | 0.963237i | \(0.413422\pi\) | |||||||
\(200\) | 3.20000e11 | 0.0707107 | ||||||||
\(201\) | 2.76527e12 | 0.594510 | ||||||||
\(202\) | 5.15931e12 | 1.07934 | ||||||||
\(203\) | 1.33189e12 | 0.271169 | ||||||||
\(204\) | −4.11820e12 | −0.816096 | ||||||||
\(205\) | −2.84774e12 | −0.549357 | ||||||||
\(206\) | −5.93851e12 | −1.11534 | ||||||||
\(207\) | −1.99963e12 | −0.365690 | ||||||||
\(208\) | 1.58289e12 | 0.281905 | ||||||||
\(209\) | 3.85860e12 | 0.669307 | ||||||||
\(210\) | −5.33162e12 | −0.900852 | ||||||||
\(211\) | 5.39734e12 | 0.888436 | 0.444218 | − | 0.895919i | \(-0.353482\pi\) | ||||
0.444218 | + | 0.895919i | \(0.353482\pi\) | |||||||
\(212\) | 4.15700e12 | 0.666704 | ||||||||
\(213\) | 2.57482e12 | 0.402402 | ||||||||
\(214\) | −1.74658e12 | −0.266020 | ||||||||
\(215\) | −3.63847e12 | −0.540142 | ||||||||
\(216\) | 4.93185e12 | 0.713698 | ||||||||
\(217\) | −5.07934e12 | −0.716604 | ||||||||
\(218\) | −1.13291e12 | −0.155842 | ||||||||
\(219\) | −1.64908e13 | −2.21208 | ||||||||
\(220\) | −1.10608e12 | −0.144698 | ||||||||
\(221\) | −8.14094e12 | −1.03876 | ||||||||
\(222\) | 7.71183e12 | 0.959878 | ||||||||
\(223\) | −9.37124e12 | −1.13794 | −0.568971 | − | 0.822357i | \(-0.692658\pi\) | ||||
−0.568971 | + | 0.822357i | \(0.692658\pi\) | |||||||
\(224\) | −2.39897e12 | −0.284224 | ||||||||
\(225\) | 3.70090e12 | 0.427862 | ||||||||
\(226\) | 3.85006e12 | 0.434382 | ||||||||
\(227\) | −6.51561e12 | −0.717485 | −0.358742 | − | 0.933437i | \(-0.616794\pi\) | ||||
−0.358742 | + | 0.933437i | \(0.616794\pi\) | |||||||
\(228\) | −8.52464e12 | −0.916294 | ||||||||
\(229\) | −1.74808e12 | −0.183429 | −0.0917144 | − | 0.995785i | \(-0.529235\pi\) | ||||
−0.0917144 | + | 0.995785i | \(0.529235\pi\) | |||||||
\(230\) | −5.27646e11 | −0.0540555 | ||||||||
\(231\) | 1.84288e13 | 1.84345 | ||||||||
\(232\) | −6.10440e11 | −0.0596292 | ||||||||
\(233\) | 8.64493e12 | 0.824715 | 0.412358 | − | 0.911022i | \(-0.364705\pi\) | ||||
0.412358 | + | 0.911022i | \(0.364705\pi\) | |||||||
\(234\) | 1.83067e13 | 1.70578 | ||||||||
\(235\) | 8.81089e11 | 0.0801949 | ||||||||
\(236\) | 5.01584e12 | 0.445993 | ||||||||
\(237\) | 5.24006e12 | 0.455219 | ||||||||
\(238\) | 1.23381e13 | 1.04731 | ||||||||
\(239\) | 6.71025e12 | 0.556609 | 0.278304 | − | 0.960493i | \(-0.410228\pi\) | ||||
0.278304 | + | 0.960493i | \(0.410228\pi\) | |||||||
\(240\) | 2.44362e12 | 0.198094 | ||||||||
\(241\) | −1.20329e13 | −0.953404 | −0.476702 | − | 0.879065i | \(-0.658168\pi\) | ||||
−0.476702 | + | 0.879065i | \(0.658168\pi\) | |||||||
\(242\) | −5.30679e12 | −0.411006 | ||||||||
\(243\) | 6.97444e12 | 0.528050 | ||||||||
\(244\) | 1.10147e13 | 0.815320 | ||||||||
\(245\) | 9.79438e12 | 0.708865 | ||||||||
\(246\) | −2.17463e13 | −1.53901 | ||||||||
\(247\) | −1.68517e13 | −1.16630 | ||||||||
\(248\) | 2.32800e12 | 0.157579 | ||||||||
\(249\) | 4.14371e13 | 2.74343 | ||||||||
\(250\) | 9.76562e11 | 0.0632456 | ||||||||
\(251\) | −2.23212e13 | −1.41420 | −0.707101 | − | 0.707113i | \(-0.749997\pi\) | ||||
−0.707101 | + | 0.707113i | \(0.749997\pi\) | |||||||
\(252\) | −2.77449e13 | −1.71981 | ||||||||
\(253\) | 1.82381e12 | 0.110616 | ||||||||
\(254\) | −1.79420e13 | −1.06484 | ||||||||
\(255\) | −1.25677e13 | −0.729938 | ||||||||
\(256\) | 1.09951e12 | 0.0625000 | ||||||||
\(257\) | 1.80055e13 | 1.00178 | 0.500890 | − | 0.865511i | \(-0.333006\pi\) | ||||
0.500890 | + | 0.865511i | \(0.333006\pi\) | |||||||
\(258\) | −2.77845e13 | −1.51319 | ||||||||
\(259\) | −2.31046e13 | −1.23183 | ||||||||
\(260\) | 4.83060e12 | 0.252144 | ||||||||
\(261\) | −7.05993e12 | −0.360809 | ||||||||
\(262\) | 1.31840e13 | 0.659765 | ||||||||
\(263\) | 1.38894e13 | 0.680653 | 0.340326 | − | 0.940307i | \(-0.389462\pi\) | ||||
0.340326 | + | 0.940307i | \(0.389462\pi\) | |||||||
\(264\) | −8.44639e12 | −0.405368 | ||||||||
\(265\) | 1.26862e13 | 0.596318 | ||||||||
\(266\) | 2.55398e13 | 1.17590 | ||||||||
\(267\) | −6.93313e12 | −0.312693 | ||||||||
\(268\) | 3.79711e12 | 0.167769 | ||||||||
\(269\) | 2.71611e13 | 1.17574 | 0.587868 | − | 0.808957i | \(-0.299967\pi\) | ||||
0.587868 | + | 0.808957i | \(0.299967\pi\) | |||||||
\(270\) | 1.50508e13 | 0.638351 | ||||||||
\(271\) | −7.24542e12 | −0.301115 | −0.150558 | − | 0.988601i | \(-0.548107\pi\) | ||||
−0.150558 | + | 0.988601i | \(0.548107\pi\) | |||||||
\(272\) | −5.65488e12 | −0.230300 | ||||||||
\(273\) | −8.04842e13 | −3.21230 | ||||||||
\(274\) | −2.51603e13 | −0.984209 | ||||||||
\(275\) | −3.37549e12 | −0.129422 | ||||||||
\(276\) | −4.02928e12 | −0.151435 | ||||||||
\(277\) | 3.97300e13 | 1.46380 | 0.731898 | − | 0.681415i | \(-0.238635\pi\) | ||||
0.731898 | + | 0.681415i | \(0.238635\pi\) | |||||||
\(278\) | 2.74289e13 | 0.990744 | ||||||||
\(279\) | 2.69240e13 | 0.953491 | ||||||||
\(280\) | −7.32108e12 | −0.254218 | ||||||||
\(281\) | 5.95255e12 | 0.202683 | 0.101342 | − | 0.994852i | \(-0.467686\pi\) | ||||
0.101342 | + | 0.994852i | \(0.467686\pi\) | |||||||
\(282\) | 6.72828e12 | 0.224664 | ||||||||
\(283\) | −3.85782e13 | −1.26333 | −0.631665 | − | 0.775241i | \(-0.717628\pi\) | ||||
−0.631665 | + | 0.775241i | \(0.717628\pi\) | |||||||
\(284\) | 3.53560e12 | 0.113557 | ||||||||
\(285\) | −2.60152e13 | −0.819558 | ||||||||
\(286\) | −1.66970e13 | −0.515971 | ||||||||
\(287\) | 6.51517e13 | 1.97504 | ||||||||
\(288\) | 1.27162e13 | 0.378180 | ||||||||
\(289\) | −5.18843e12 | −0.151390 | ||||||||
\(290\) | −1.86291e12 | −0.0533339 | ||||||||
\(291\) | 3.51903e13 | 0.988580 | ||||||||
\(292\) | −2.26443e13 | −0.624242 | ||||||||
\(293\) | −5.32529e13 | −1.44069 | −0.720346 | − | 0.693615i | \(-0.756017\pi\) | ||||
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(294\) | 7.47930e13 | 1.98587 | ||||||||
\(295\) | 1.53071e13 | 0.398908 | ||||||||
\(296\) | 1.05895e13 | 0.270875 | ||||||||
\(297\) | −5.20232e13 | −1.30628 | ||||||||
\(298\) | −7.63539e12 | −0.188210 | ||||||||
\(299\) | −7.96516e12 | −0.192754 | ||||||||
\(300\) | 7.45734e12 | 0.177181 | ||||||||
\(301\) | 8.32424e13 | 1.94191 | ||||||||
\(302\) | −3.06339e12 | −0.0701720 | ||||||||
\(303\) | 1.20233e14 | 2.70452 | ||||||||
\(304\) | −1.17056e13 | −0.258576 | ||||||||
\(305\) | 3.36142e13 | 0.729244 | ||||||||
\(306\) | −6.54004e13 | −1.39352 | ||||||||
\(307\) | −5.74336e13 | −1.20200 | −0.601001 | − | 0.799249i | \(-0.705231\pi\) | ||||
−0.601001 | + | 0.799249i | \(0.705231\pi\) | |||||||
\(308\) | 2.53054e13 | 0.520216 | ||||||||
\(309\) | −1.38392e14 | −2.79473 | ||||||||
\(310\) | 7.10448e12 | 0.140943 | ||||||||
\(311\) | −2.58616e13 | −0.504050 | −0.252025 | − | 0.967721i | \(-0.581097\pi\) | ||||
−0.252025 | + | 0.967721i | \(0.581097\pi\) | |||||||
\(312\) | 3.68880e13 | 0.706375 | ||||||||
\(313\) | −3.57307e13 | −0.672277 | −0.336138 | − | 0.941813i | \(-0.609121\pi\) | ||||
−0.336138 | + | 0.941813i | \(0.609121\pi\) | |||||||
\(314\) | −5.75792e13 | −1.06452 | ||||||||
\(315\) | −8.46707e13 | −1.53824 | ||||||||
\(316\) | 7.19536e12 | 0.128462 | ||||||||
\(317\) | −1.78631e13 | −0.313422 | −0.156711 | − | 0.987644i | \(-0.550089\pi\) | ||||
−0.156711 | + | 0.987644i | \(0.550089\pi\) | |||||||
\(318\) | 9.68755e13 | 1.67057 | ||||||||
\(319\) | 6.43917e12 | 0.109139 | ||||||||
\(320\) | 3.35544e12 | 0.0559017 | ||||||||
\(321\) | −4.07027e13 | −0.666570 | ||||||||
\(322\) | 1.20717e13 | 0.194339 | ||||||||
\(323\) | 6.02026e13 | 0.952800 | ||||||||
\(324\) | 4.61877e13 | 0.718669 | ||||||||
\(325\) | 1.47418e13 | 0.225524 | ||||||||
\(326\) | −8.01980e13 | −1.20633 | ||||||||
\(327\) | −2.64016e13 | −0.390496 | ||||||||
\(328\) | −2.98607e13 | −0.434305 | ||||||||
\(329\) | −2.01579e13 | −0.288315 | ||||||||
\(330\) | −2.57763e13 | −0.362572 | ||||||||
\(331\) | 7.78278e13 | 1.07667 | 0.538333 | − | 0.842732i | \(-0.319054\pi\) | ||||
0.538333 | + | 0.842732i | \(0.319054\pi\) | |||||||
\(332\) | 5.68992e13 | 0.774188 | ||||||||
\(333\) | 1.22470e14 | 1.63903 | ||||||||
\(334\) | −8.63535e13 | −1.13678 | ||||||||
\(335\) | 1.15879e13 | 0.150057 | ||||||||
\(336\) | −5.59061e13 | −0.712186 | ||||||||
\(337\) | 4.95598e12 | 0.0621105 | 0.0310552 | − | 0.999518i | \(-0.490113\pi\) | ||||
0.0310552 | + | 0.999518i | \(0.490113\pi\) | |||||||
\(338\) | 1.55719e13 | 0.192000 | ||||||||
\(339\) | 8.97226e13 | 1.08844 | ||||||||
\(340\) | −1.72573e13 | −0.205987 | ||||||||
\(341\) | −2.45567e13 | −0.288417 | ||||||||
\(342\) | −1.35379e14 | −1.56461 | ||||||||
\(343\) | −8.27106e13 | −0.940684 | ||||||||
\(344\) | −3.81522e13 | −0.427019 | ||||||||
\(345\) | −1.22964e13 | −0.135448 | ||||||||
\(346\) | 9.84948e13 | 1.06781 | ||||||||
\(347\) | −6.55706e13 | −0.699676 | −0.349838 | − | 0.936810i | \(-0.613763\pi\) | ||||
−0.349838 | + | 0.936810i | \(0.613763\pi\) | |||||||
\(348\) | −1.42258e13 | −0.149414 | ||||||||
\(349\) | 1.14750e14 | 1.18635 | 0.593177 | − | 0.805072i | \(-0.297873\pi\) | ||||
0.593177 | + | 0.805072i | \(0.297873\pi\) | |||||||
\(350\) | −2.23422e13 | −0.227379 | ||||||||
\(351\) | 2.27202e14 | 2.27626 | ||||||||
\(352\) | −1.15981e13 | −0.114394 | ||||||||
\(353\) | −5.10272e13 | −0.495497 | −0.247749 | − | 0.968824i | \(-0.579691\pi\) | ||||
−0.247749 | + | 0.968824i | \(0.579691\pi\) | |||||||
\(354\) | 1.16890e14 | 1.11753 | ||||||||
\(355\) | 1.07898e13 | 0.101568 | ||||||||
\(356\) | −9.52019e12 | −0.0882410 | ||||||||
\(357\) | 2.87530e14 | 2.62426 | ||||||||
\(358\) | 1.12369e13 | 0.100993 | ||||||||
\(359\) | −1.16657e14 | −1.03251 | −0.516253 | − | 0.856436i | \(-0.672674\pi\) | ||||
−0.516253 | + | 0.856436i | \(0.672674\pi\) | |||||||
\(360\) | 3.88068e13 | 0.338255 | ||||||||
\(361\) | 8.12884e12 | 0.0697813 | ||||||||
\(362\) | 2.02914e13 | 0.171559 | ||||||||
\(363\) | −1.23671e14 | −1.02986 | ||||||||
\(364\) | −1.10516e14 | −0.906503 | ||||||||
\(365\) | −6.91049e13 | −0.558339 | ||||||||
\(366\) | 2.56688e14 | 2.04296 | ||||||||
\(367\) | 1.44058e14 | 1.12947 | 0.564733 | − | 0.825274i | \(-0.308979\pi\) | ||||
0.564733 | + | 0.825274i | \(0.308979\pi\) | |||||||
\(368\) | −5.53277e12 | −0.0427346 | ||||||||
\(369\) | −3.45349e14 | −2.62793 | ||||||||
\(370\) | 3.23164e13 | 0.242278 | ||||||||
\(371\) | −2.90239e14 | −2.14387 | ||||||||
\(372\) | 5.42521e13 | 0.394848 | ||||||||
\(373\) | 6.90594e13 | 0.495250 | 0.247625 | − | 0.968856i | \(-0.420350\pi\) | ||||
0.247625 | + | 0.968856i | \(0.420350\pi\) | |||||||
\(374\) | 5.96500e13 | 0.421518 | ||||||||
\(375\) | 2.27580e13 | 0.158475 | ||||||||
\(376\) | 9.23889e12 | 0.0633996 | ||||||||
\(377\) | −2.81219e13 | −0.190181 | ||||||||
\(378\) | −3.44338e14 | −2.29499 | ||||||||
\(379\) | 2.28579e14 | 1.50149 | 0.750743 | − | 0.660595i | \(-0.229696\pi\) | ||||
0.750743 | + | 0.660595i | \(0.229696\pi\) | |||||||
\(380\) | −3.57225e13 | −0.231277 | ||||||||
\(381\) | −4.18123e14 | −2.66819 | ||||||||
\(382\) | −8.37070e13 | −0.526518 | ||||||||
\(383\) | −7.16725e13 | −0.444385 | −0.222192 | − | 0.975003i | \(-0.571321\pi\) | ||||
−0.222192 | + | 0.975003i | \(0.571321\pi\) | |||||||
\(384\) | 2.56232e13 | 0.156607 | ||||||||
\(385\) | 7.72259e13 | 0.465295 | ||||||||
\(386\) | 5.11420e13 | 0.303772 | ||||||||
\(387\) | −4.41242e14 | −2.58385 | ||||||||
\(388\) | 4.83214e13 | 0.278975 | ||||||||
\(389\) | 5.31179e13 | 0.302356 | 0.151178 | − | 0.988507i | \(-0.451693\pi\) | ||||
0.151178 | + | 0.988507i | \(0.451693\pi\) | |||||||
\(390\) | 1.12573e14 | 0.631801 | ||||||||
\(391\) | 2.84555e13 | 0.157469 | ||||||||
\(392\) | 1.02701e14 | 0.560407 | ||||||||
\(393\) | 3.07242e14 | 1.65318 | ||||||||
\(394\) | −1.97210e12 | −0.0104641 | ||||||||
\(395\) | 2.19585e13 | 0.114900 | ||||||||
\(396\) | −1.34136e14 | −0.692184 | ||||||||
\(397\) | 9.39721e12 | 0.0478246 | 0.0239123 | − | 0.999714i | \(-0.492388\pi\) | ||||
0.0239123 | + | 0.999714i | \(0.492388\pi\) | |||||||
\(398\) | 7.56940e13 | 0.379931 | ||||||||
\(399\) | 5.95185e14 | 2.94646 | ||||||||
\(400\) | 1.02400e13 | 0.0500000 | ||||||||
\(401\) | 2.20216e14 | 1.06061 | 0.530303 | − | 0.847808i | \(-0.322078\pi\) | ||||
0.530303 | + | 0.847808i | \(0.322078\pi\) | |||||||
\(402\) | 8.84887e13 | 0.420382 | ||||||||
\(403\) | 1.07247e14 | 0.502581 | ||||||||
\(404\) | 1.65098e14 | 0.763209 | ||||||||
\(405\) | 1.40954e14 | 0.642797 | ||||||||
\(406\) | 4.26204e13 | 0.191745 | ||||||||
\(407\) | −1.11702e14 | −0.495783 | ||||||||
\(408\) | −1.31782e14 | −0.577067 | ||||||||
\(409\) | −3.05103e14 | −1.31816 | −0.659080 | − | 0.752072i | \(-0.729054\pi\) | ||||
−0.659080 | + | 0.752072i | \(0.729054\pi\) | |||||||
\(410\) | −9.11277e13 | −0.388454 | ||||||||
\(411\) | −5.86340e14 | −2.46615 | ||||||||
\(412\) | −1.90032e14 | −0.788666 | ||||||||
\(413\) | −3.50203e14 | −1.43415 | ||||||||
\(414\) | −6.39883e13 | −0.258582 | ||||||||
\(415\) | 1.73642e14 | 0.692455 | ||||||||
\(416\) | 5.06526e13 | 0.199337 | ||||||||
\(417\) | 6.39208e14 | 2.48253 | ||||||||
\(418\) | 1.23475e14 | 0.473271 | ||||||||
\(419\) | 4.21440e14 | 1.59426 | 0.797130 | − | 0.603808i | \(-0.206351\pi\) | ||||
0.797130 | + | 0.603808i | \(0.206351\pi\) | |||||||
\(420\) | −1.70612e14 | −0.636998 | ||||||||
\(421\) | 1.11120e12 | 0.00409487 | 0.00204744 | − | 0.999998i | \(-0.499348\pi\) | ||||
0.00204744 | + | 0.999998i | \(0.499348\pi\) | |||||||
\(422\) | 1.72715e14 | 0.628219 | ||||||||
\(423\) | 1.06851e14 | 0.383624 | ||||||||
\(424\) | 1.33024e14 | 0.471431 | ||||||||
\(425\) | −5.26651e13 | −0.184240 | ||||||||
\(426\) | 8.23944e13 | 0.284541 | ||||||||
\(427\) | −7.69037e14 | −2.62177 | ||||||||
\(428\) | −5.58907e13 | −0.188104 | ||||||||
\(429\) | −3.89110e14 | −1.29288 | ||||||||
\(430\) | −1.16431e14 | −0.381938 | ||||||||
\(431\) | 2.29204e14 | 0.742332 | 0.371166 | − | 0.928567i | \(-0.378958\pi\) | ||||
0.371166 | + | 0.928567i | \(0.378958\pi\) | |||||||
\(432\) | 1.57819e14 | 0.504660 | ||||||||
\(433\) | 1.54032e14 | 0.486325 | 0.243162 | − | 0.969986i | \(-0.421815\pi\) | ||||
0.243162 | + | 0.969986i | \(0.421815\pi\) | |||||||
\(434\) | −1.62539e14 | −0.506715 | ||||||||
\(435\) | −4.34137e13 | −0.133640 | ||||||||
\(436\) | −3.62531e13 | −0.110197 | ||||||||
\(437\) | 5.89027e13 | 0.176802 | ||||||||
\(438\) | −5.27707e14 | −1.56417 | ||||||||
\(439\) | −1.25797e14 | −0.368227 | −0.184114 | − | 0.982905i | \(-0.558941\pi\) | ||||
−0.184114 | + | 0.982905i | \(0.558941\pi\) | |||||||
\(440\) | −3.53946e13 | −0.102317 | ||||||||
\(441\) | 1.18778e15 | 3.39096 | ||||||||
\(442\) | −2.60510e14 | −0.734517 | ||||||||
\(443\) | −1.34623e14 | −0.374885 | −0.187443 | − | 0.982276i | \(-0.560020\pi\) | ||||
−0.187443 | + | 0.982276i | \(0.560020\pi\) | |||||||
\(444\) | 2.46779e14 | 0.678736 | ||||||||
\(445\) | −2.90533e13 | −0.0789252 | ||||||||
\(446\) | −2.99880e14 | −0.804647 | ||||||||
\(447\) | −1.77937e14 | −0.471600 | ||||||||
\(448\) | −7.67671e13 | −0.200977 | ||||||||
\(449\) | 4.28972e14 | 1.10937 | 0.554683 | − | 0.832062i | \(-0.312840\pi\) | ||||
0.554683 | + | 0.832062i | \(0.312840\pi\) | |||||||
\(450\) | 1.18429e14 | 0.302544 | ||||||||
\(451\) | 3.14984e14 | 0.794908 | ||||||||
\(452\) | 1.23202e14 | 0.307154 | ||||||||
\(453\) | −7.13898e13 | −0.175831 | ||||||||
\(454\) | −2.08499e14 | −0.507338 | ||||||||
\(455\) | −3.37269e14 | −0.810801 | ||||||||
\(456\) | −2.72789e14 | −0.647917 | ||||||||
\(457\) | −7.89196e14 | −1.85202 | −0.926011 | − | 0.377497i | \(-0.876785\pi\) | ||||
−0.926011 | + | 0.377497i | \(0.876785\pi\) | |||||||
\(458\) | −5.59387e13 | −0.129704 | ||||||||
\(459\) | −8.11677e14 | −1.85957 | ||||||||
\(460\) | −1.68847e13 | −0.0382230 | ||||||||
\(461\) | −6.01739e14 | −1.34602 | −0.673012 | − | 0.739632i | \(-0.735000\pi\) | ||||
−0.673012 | + | 0.739632i | \(0.735000\pi\) | |||||||
\(462\) | 5.89721e14 | 1.30351 | ||||||||
\(463\) | 2.36873e14 | 0.517393 | 0.258696 | − | 0.965959i | \(-0.416707\pi\) | ||||
0.258696 | + | 0.965959i | \(0.416707\pi\) | |||||||
\(464\) | −1.95341e13 | −0.0421642 | ||||||||
\(465\) | 1.65564e14 | 0.353163 | ||||||||
\(466\) | 2.76638e14 | 0.583162 | ||||||||
\(467\) | 8.17060e14 | 1.70220 | 0.851101 | − | 0.525002i | \(-0.175936\pi\) | ||||
0.851101 | + | 0.525002i | \(0.175936\pi\) | |||||||
\(468\) | 5.85813e14 | 1.20617 | ||||||||
\(469\) | −2.65112e14 | −0.539484 | ||||||||
\(470\) | 2.81949e13 | 0.0567063 | ||||||||
\(471\) | −1.34184e15 | −2.66738 | ||||||||
\(472\) | 1.60507e14 | 0.315365 | ||||||||
\(473\) | 4.02445e14 | 0.781574 | ||||||||
\(474\) | 1.67682e14 | 0.321889 | ||||||||
\(475\) | −1.09017e14 | −0.206860 | ||||||||
\(476\) | 3.94819e14 | 0.740560 | ||||||||
\(477\) | 1.53847e15 | 2.85257 | ||||||||
\(478\) | 2.14728e14 | 0.393582 | ||||||||
\(479\) | 2.80917e14 | 0.509018 | 0.254509 | − | 0.967070i | \(-0.418086\pi\) | ||||
0.254509 | + | 0.967070i | \(0.418086\pi\) | |||||||
\(480\) | 7.81959e13 | 0.140074 | ||||||||
\(481\) | 4.87837e14 | 0.863927 | ||||||||
\(482\) | −3.85053e14 | −0.674159 | ||||||||
\(483\) | 2.81321e14 | 0.486960 | ||||||||
\(484\) | −1.69817e14 | −0.290625 | ||||||||
\(485\) | 1.47465e14 | 0.249522 | ||||||||
\(486\) | 2.23182e14 | 0.373387 | ||||||||
\(487\) | −4.06414e14 | −0.672294 | −0.336147 | − | 0.941810i | \(-0.609124\pi\) | ||||
−0.336147 | + | 0.941810i | \(0.609124\pi\) | |||||||
\(488\) | 3.52470e14 | 0.576518 | ||||||||
\(489\) | −1.86895e15 | −3.02273 | ||||||||
\(490\) | 3.13420e14 | 0.501243 | ||||||||
\(491\) | 1.02479e15 | 1.62065 | 0.810324 | − | 0.585982i | \(-0.199291\pi\) | ||||
0.810324 | + | 0.585982i | \(0.199291\pi\) | |||||||
\(492\) | −6.95880e14 | −1.08824 | ||||||||
\(493\) | 1.00465e14 | 0.155367 | ||||||||
\(494\) | −5.39255e14 | −0.824699 | ||||||||
\(495\) | −4.09350e14 | −0.619108 | ||||||||
\(496\) | 7.44959e13 | 0.111425 | ||||||||
\(497\) | −2.46853e14 | −0.365156 | ||||||||
\(498\) | 1.32599e15 | 1.93990 | ||||||||
\(499\) | 1.01593e14 | 0.146997 | 0.0734987 | − | 0.997295i | \(-0.476584\pi\) | ||||
0.0734987 | + | 0.997295i | \(0.476584\pi\) | |||||||
\(500\) | 3.12500e13 | 0.0447214 | ||||||||
\(501\) | −2.01240e15 | −2.84844 | ||||||||
\(502\) | −7.14277e14 | −0.999991 | ||||||||
\(503\) | 9.67924e14 | 1.34035 | 0.670174 | − | 0.742204i | \(-0.266220\pi\) | ||||
0.670174 | + | 0.742204i | \(0.266220\pi\) | |||||||
\(504\) | −8.87836e14 | −1.21609 | ||||||||
\(505\) | 5.03838e14 | 0.682635 | ||||||||
\(506\) | 5.83620e13 | 0.0782172 | ||||||||
\(507\) | 3.62891e14 | 0.481097 | ||||||||
\(508\) | −5.74143e14 | −0.752957 | ||||||||
\(509\) | 9.40088e14 | 1.21961 | 0.609805 | − | 0.792552i | \(-0.291248\pi\) | ||||
0.609805 | + | 0.792552i | \(0.291248\pi\) | |||||||
\(510\) | −4.02168e14 | −0.516144 | ||||||||
\(511\) | 1.58101e15 | 2.00733 | ||||||||
\(512\) | 3.51844e13 | 0.0441942 | ||||||||
\(513\) | −1.68017e15 | −2.08789 | ||||||||
\(514\) | 5.76175e14 | 0.708365 | ||||||||
\(515\) | −5.79933e14 | −0.705404 | ||||||||
\(516\) | −8.89105e14 | −1.06999 | ||||||||
\(517\) | −9.74557e13 | −0.116040 | ||||||||
\(518\) | −7.39348e14 | −0.871034 | ||||||||
\(519\) | 2.29534e15 | 2.67564 | ||||||||
\(520\) | 1.54579e14 | 0.178293 | ||||||||
\(521\) | −1.00574e15 | −1.14783 | −0.573916 | − | 0.818914i | \(-0.694576\pi\) | ||||
−0.573916 | + | 0.818914i | \(0.694576\pi\) | |||||||
\(522\) | −2.25918e14 | −0.255131 | ||||||||
\(523\) | −1.24911e15 | −1.39586 | −0.697931 | − | 0.716165i | \(-0.745896\pi\) | ||||
−0.697931 | + | 0.716165i | \(0.745896\pi\) | |||||||
\(524\) | 4.21887e14 | 0.466524 | ||||||||
\(525\) | −5.20666e14 | −0.569749 | ||||||||
\(526\) | 4.44460e14 | 0.481294 | ||||||||
\(527\) | −3.83138e14 | −0.410579 | ||||||||
\(528\) | −2.70285e14 | −0.286639 | ||||||||
\(529\) | −9.24969e14 | −0.970780 | ||||||||
\(530\) | 4.05957e14 | 0.421660 | ||||||||
\(531\) | 1.85631e15 | 1.90823 | ||||||||
\(532\) | 8.17274e14 | 0.831483 | ||||||||
\(533\) | −1.37563e15 | −1.38517 | ||||||||
\(534\) | −2.21860e14 | −0.221107 | ||||||||
\(535\) | −1.70565e14 | −0.168246 | ||||||||
\(536\) | 1.21508e14 | 0.118631 | ||||||||
\(537\) | 2.61868e14 | 0.253060 | ||||||||
\(538\) | 8.69155e14 | 0.831371 | ||||||||
\(539\) | −1.08334e15 | −1.02571 | ||||||||
\(540\) | 4.81626e14 | 0.451382 | ||||||||
\(541\) | 1.47684e15 | 1.37009 | 0.685046 | − | 0.728500i | \(-0.259782\pi\) | ||||
0.685046 | + | 0.728500i | \(0.259782\pi\) | |||||||
\(542\) | −2.31853e14 | −0.212921 | ||||||||
\(543\) | 4.72874e14 | 0.429880 | ||||||||
\(544\) | −1.80956e14 | −0.162847 | ||||||||
\(545\) | −1.10636e14 | −0.0985632 | ||||||||
\(546\) | −2.57550e15 | −2.27144 | ||||||||
\(547\) | −2.32000e14 | −0.202562 | −0.101281 | − | 0.994858i | \(-0.532294\pi\) | ||||
−0.101281 | + | 0.994858i | \(0.532294\pi\) | |||||||
\(548\) | −8.05129e14 | −0.695941 | ||||||||
\(549\) | 4.07643e15 | 3.48844 | ||||||||
\(550\) | −1.08016e14 | −0.0915151 | ||||||||
\(551\) | 2.07962e14 | 0.174442 | ||||||||
\(552\) | −1.28937e14 | −0.107081 | ||||||||
\(553\) | −5.02375e14 | −0.413085 | ||||||||
\(554\) | 1.27136e15 | 1.03506 | ||||||||
\(555\) | 7.53108e14 | 0.607080 | ||||||||
\(556\) | 8.77724e14 | 0.700562 | ||||||||
\(557\) | 2.34238e15 | 1.85120 | 0.925602 | − | 0.378498i | \(-0.123559\pi\) | ||||
0.925602 | + | 0.378498i | \(0.123559\pi\) | |||||||
\(558\) | 8.61568e14 | 0.674220 | ||||||||
\(559\) | −1.75760e15 | −1.36193 | ||||||||
\(560\) | −2.34275e14 | −0.179759 | ||||||||
\(561\) | 1.39010e15 | 1.05621 | ||||||||
\(562\) | 1.90482e14 | 0.143319 | ||||||||
\(563\) | 2.32309e15 | 1.73089 | 0.865446 | − | 0.501002i | \(-0.167035\pi\) | ||||
0.865446 | + | 0.501002i | \(0.167035\pi\) | |||||||
\(564\) | 2.15305e14 | 0.158862 | ||||||||
\(565\) | 3.75983e14 | 0.274727 | ||||||||
\(566\) | −1.23450e15 | −0.893309 | ||||||||
\(567\) | −3.22479e15 | −2.31098 | ||||||||
\(568\) | 1.13139e14 | 0.0802967 | ||||||||
\(569\) | −2.48598e14 | −0.174735 | −0.0873676 | − | 0.996176i | \(-0.527845\pi\) | ||||
−0.0873676 | + | 0.996176i | \(0.527845\pi\) | |||||||
\(570\) | −8.32485e14 | −0.579515 | ||||||||
\(571\) | −2.44700e15 | −1.68708 | −0.843540 | − | 0.537066i | \(-0.819533\pi\) | ||||
−0.843540 | + | 0.537066i | \(0.819533\pi\) | |||||||
\(572\) | −5.34305e14 | −0.364847 | ||||||||
\(573\) | −1.95072e15 | −1.31931 | ||||||||
\(574\) | 2.08486e15 | 1.39656 | ||||||||
\(575\) | −5.15280e13 | −0.0341877 | ||||||||
\(576\) | 4.06919e14 | 0.267414 | ||||||||
\(577\) | −2.05338e15 | −1.33660 | −0.668302 | − | 0.743890i | \(-0.732979\pi\) | ||||
−0.668302 | + | 0.743890i | \(0.732979\pi\) | |||||||
\(578\) | −1.66030e14 | −0.107049 | ||||||||
\(579\) | 1.19182e15 | 0.761166 | ||||||||
\(580\) | −5.96132e13 | −0.0377128 | ||||||||
\(581\) | −3.97266e15 | −2.48950 | ||||||||
\(582\) | 1.12609e15 | 0.699032 | ||||||||
\(583\) | −1.40319e15 | −0.862860 | ||||||||
\(584\) | −7.24617e14 | −0.441406 | ||||||||
\(585\) | 1.78776e15 | 1.07883 | ||||||||
\(586\) | −1.70409e15 | −1.01872 | ||||||||
\(587\) | 3.00291e14 | 0.177841 | 0.0889207 | − | 0.996039i | \(-0.471658\pi\) | ||||
0.0889207 | + | 0.996039i | \(0.471658\pi\) | |||||||
\(588\) | 2.39338e15 | 1.40422 | ||||||||
\(589\) | −7.93094e14 | −0.460989 | ||||||||
\(590\) | 4.89828e14 | 0.282071 | ||||||||
\(591\) | −4.59582e13 | −0.0262200 | ||||||||
\(592\) | 3.38862e14 | 0.191538 | ||||||||
\(593\) | −2.71460e15 | −1.52022 | −0.760108 | − | 0.649796i | \(-0.774854\pi\) | ||||
−0.760108 | + | 0.649796i | \(0.774854\pi\) | |||||||
\(594\) | −1.66474e15 | −0.923681 | ||||||||
\(595\) | 1.20489e15 | 0.662377 | ||||||||
\(596\) | −2.44332e14 | −0.133084 | ||||||||
\(597\) | 1.76399e15 | 0.951999 | ||||||||
\(598\) | −2.54885e14 | −0.136298 | ||||||||
\(599\) | −2.10006e15 | −1.11272 | −0.556358 | − | 0.830943i | \(-0.687802\pi\) | ||||
−0.556358 | + | 0.830943i | \(0.687802\pi\) | |||||||
\(600\) | 2.38635e14 | 0.125286 | ||||||||
\(601\) | 2.84187e15 | 1.47841 | 0.739204 | − | 0.673481i | \(-0.235202\pi\) | ||||
0.739204 | + | 0.673481i | \(0.235202\pi\) | |||||||
\(602\) | 2.66376e15 | 1.37314 | ||||||||
\(603\) | 1.40528e15 | 0.717821 | ||||||||
\(604\) | −9.80284e13 | −0.0496191 | ||||||||
\(605\) | −5.18242e14 | −0.259943 | ||||||||
\(606\) | 3.84747e15 | 1.91239 | ||||||||
\(607\) | −3.78069e14 | −0.186223 | −0.0931114 | − | 0.995656i | \(-0.529681\pi\) | ||||
−0.0931114 | + | 0.995656i | \(0.529681\pi\) | |||||||
\(608\) | −3.74578e14 | −0.182841 | ||||||||
\(609\) | 9.93235e14 | 0.480460 | ||||||||
\(610\) | 1.07565e15 | 0.515654 | ||||||||
\(611\) | 4.25619e14 | 0.202206 | ||||||||
\(612\) | −2.09281e15 | −0.985367 | ||||||||
\(613\) | 2.97141e15 | 1.38653 | 0.693267 | − | 0.720681i | \(-0.256171\pi\) | ||||
0.693267 | + | 0.720681i | \(0.256171\pi\) | |||||||
\(614\) | −1.83788e15 | −0.849943 | ||||||||
\(615\) | −2.12366e15 | −0.973355 | ||||||||
\(616\) | 8.09772e14 | 0.367848 | ||||||||
\(617\) | −1.19545e15 | −0.538222 | −0.269111 | − | 0.963109i | \(-0.586730\pi\) | ||||
−0.269111 | + | 0.963109i | \(0.586730\pi\) | |||||||
\(618\) | −4.42855e15 | −1.97617 | ||||||||
\(619\) | 3.17735e14 | 0.140529 | 0.0702645 | − | 0.997528i | \(-0.477616\pi\) | ||||
0.0702645 | + | 0.997528i | \(0.477616\pi\) | |||||||
\(620\) | 2.27343e14 | 0.0996616 | ||||||||
\(621\) | −7.94151e14 | −0.345064 | ||||||||
\(622\) | −8.27572e14 | −0.356417 | ||||||||
\(623\) | 6.64693e14 | 0.283750 | ||||||||
\(624\) | 1.18042e15 | 0.499482 | ||||||||
\(625\) | 9.53674e13 | 0.0400000 | ||||||||
\(626\) | −1.14338e15 | −0.475372 | ||||||||
\(627\) | 2.87749e15 | 1.18588 | ||||||||
\(628\) | −1.84253e15 | −0.752727 | ||||||||
\(629\) | −1.74280e15 | −0.705778 | ||||||||
\(630\) | −2.70946e15 | −1.08770 | ||||||||
\(631\) | −7.14141e14 | −0.284199 | −0.142099 | − | 0.989852i | \(-0.545385\pi\) | ||||
−0.142099 | + | 0.989852i | \(0.545385\pi\) | |||||||
\(632\) | 2.30251e14 | 0.0908361 | ||||||||
\(633\) | 4.02498e15 | 1.57414 | ||||||||
\(634\) | −5.71618e14 | −0.221623 | ||||||||
\(635\) | −1.75215e15 | −0.673465 | ||||||||
\(636\) | 3.10002e15 | 1.18127 | ||||||||
\(637\) | 4.73128e15 | 1.78736 | ||||||||
\(638\) | 2.06054e14 | 0.0771732 | ||||||||
\(639\) | 1.30849e15 | 0.485866 | ||||||||
\(640\) | 1.07374e14 | 0.0395285 | ||||||||
\(641\) | 3.74739e15 | 1.36776 | 0.683880 | − | 0.729594i | \(-0.260291\pi\) | ||||
0.683880 | + | 0.729594i | \(0.260291\pi\) | |||||||
\(642\) | −1.30249e15 | −0.471336 | ||||||||
\(643\) | 3.72691e14 | 0.133718 | 0.0668588 | − | 0.997762i | \(-0.478702\pi\) | ||||
0.0668588 | + | 0.997762i | \(0.478702\pi\) | |||||||
\(644\) | 3.86294e14 | 0.137419 | ||||||||
\(645\) | −2.71333e15 | −0.957028 | ||||||||
\(646\) | 1.92648e15 | 0.673731 | ||||||||
\(647\) | 3.55565e15 | 1.23295 | 0.616475 | − | 0.787374i | \(-0.288560\pi\) | ||||
0.616475 | + | 0.787374i | \(0.288560\pi\) | |||||||
\(648\) | 1.47801e15 | 0.508176 | ||||||||
\(649\) | −1.69310e15 | −0.577212 | ||||||||
\(650\) | 4.71739e14 | 0.159470 | ||||||||
\(651\) | −3.78784e15 | −1.26969 | ||||||||
\(652\) | −2.56633e15 | −0.853005 | ||||||||
\(653\) | 5.07282e15 | 1.67196 | 0.835982 | − | 0.548757i | \(-0.184899\pi\) | ||||
0.835982 | + | 0.548757i | \(0.184899\pi\) | |||||||
\(654\) | −8.44850e14 | −0.276123 | ||||||||
\(655\) | 1.28750e15 | 0.417272 | ||||||||
\(656\) | −9.55544e14 | −0.307100 | ||||||||
\(657\) | −8.38043e15 | −2.67090 | ||||||||
\(658\) | −6.45053e14 | −0.203870 | ||||||||
\(659\) | 1.66566e15 | 0.522054 | 0.261027 | − | 0.965331i | \(-0.415939\pi\) | ||||
0.261027 | + | 0.965331i | \(0.415939\pi\) | |||||||
\(660\) | −8.24843e14 | −0.256377 | ||||||||
\(661\) | 3.06978e14 | 0.0946235 | 0.0473118 | − | 0.998880i | \(-0.484935\pi\) | ||||
0.0473118 | + | 0.998880i | \(0.484935\pi\) | |||||||
\(662\) | 2.49049e15 | 0.761318 | ||||||||
\(663\) | −6.07098e15 | −1.84049 | ||||||||
\(664\) | 1.82077e15 | 0.547433 | ||||||||
\(665\) | 2.49412e15 | 0.743701 | ||||||||
\(666\) | 3.91905e15 | 1.15897 | ||||||||
\(667\) | 9.82960e13 | 0.0288299 | ||||||||
\(668\) | −2.76331e15 | −0.803822 | ||||||||
\(669\) | −6.98845e15 | −2.01622 | ||||||||
\(670\) | 3.70812e14 | 0.106107 | ||||||||
\(671\) | −3.71800e15 | −1.05520 | ||||||||
\(672\) | −1.78900e15 | −0.503591 | ||||||||
\(673\) | 3.20107e15 | 0.893742 | 0.446871 | − | 0.894599i | \(-0.352538\pi\) | ||||
0.446871 | + | 0.894599i | \(0.352538\pi\) | |||||||
\(674\) | 1.58591e14 | 0.0439187 | ||||||||
\(675\) | 1.46981e15 | 0.403728 | ||||||||
\(676\) | 4.98302e14 | 0.135764 | ||||||||
\(677\) | −4.88443e15 | −1.32001 | −0.660004 | − | 0.751262i | \(-0.729445\pi\) | ||||
−0.660004 | + | 0.751262i | \(0.729445\pi\) | |||||||
\(678\) | 2.87112e15 | 0.769642 | ||||||||
\(679\) | −3.37376e15 | −0.897079 | ||||||||
\(680\) | −5.52234e14 | −0.145655 | ||||||||
\(681\) | −4.85891e15 | −1.27125 | ||||||||
\(682\) | −7.85814e14 | −0.203941 | ||||||||
\(683\) | 3.43048e15 | 0.883163 | 0.441582 | − | 0.897221i | \(-0.354418\pi\) | ||||
0.441582 | + | 0.897221i | \(0.354418\pi\) | |||||||
\(684\) | −4.33211e15 | −1.10635 | ||||||||
\(685\) | −2.45706e15 | −0.622469 | ||||||||
\(686\) | −2.64674e15 | −0.665164 | ||||||||
\(687\) | −1.30361e15 | −0.325001 | ||||||||
\(688\) | −1.22087e15 | −0.301948 | ||||||||
\(689\) | 6.12818e15 | 1.50358 | ||||||||
\(690\) | −3.93484e14 | −0.0957761 | ||||||||
\(691\) | 1.26067e15 | 0.304420 | 0.152210 | − | 0.988348i | \(-0.451361\pi\) | ||||
0.152210 | + | 0.988348i | \(0.451361\pi\) | |||||||
\(692\) | 3.15183e15 | 0.755057 | ||||||||
\(693\) | 9.36527e15 | 2.22581 | ||||||||
\(694\) | −2.09826e15 | −0.494746 | ||||||||
\(695\) | 2.67860e15 | 0.626602 | ||||||||
\(696\) | −4.55226e14 | −0.105652 | ||||||||
\(697\) | 4.91444e15 | 1.13160 | ||||||||
\(698\) | 3.67201e15 | 0.838879 | ||||||||
\(699\) | 6.44682e15 | 1.46124 | ||||||||
\(700\) | −7.14949e14 | −0.160782 | ||||||||
\(701\) | −1.46416e15 | −0.326693 | −0.163347 | − | 0.986569i | \(-0.552229\pi\) | ||||
−0.163347 | + | 0.986569i | \(0.552229\pi\) | |||||||
\(702\) | 7.27045e15 | 1.60956 | ||||||||
\(703\) | −3.60758e15 | −0.792431 | ||||||||
\(704\) | −3.71140e14 | −0.0808887 | ||||||||
\(705\) | 6.57058e14 | 0.142090 | ||||||||
\(706\) | −1.63287e15 | −0.350369 | ||||||||
\(707\) | −1.15270e16 | −2.45420 | ||||||||
\(708\) | 3.74049e15 | 0.790215 | ||||||||
\(709\) | −2.00407e15 | −0.420105 | −0.210053 | − | 0.977690i | \(-0.567364\pi\) | ||||
−0.210053 | + | 0.977690i | \(0.567364\pi\) | |||||||
\(710\) | 3.45274e14 | 0.0718196 | ||||||||
\(711\) | 2.66293e15 | 0.549639 | ||||||||
\(712\) | −3.04646e14 | −0.0623958 | ||||||||
\(713\) | −3.74865e14 | −0.0761873 | ||||||||
\(714\) | 9.20095e15 | 1.85563 | ||||||||
\(715\) | −1.63057e15 | −0.326329 | ||||||||
\(716\) | 3.59582e14 | 0.0714128 | ||||||||
\(717\) | 5.00406e15 | 0.986205 | ||||||||
\(718\) | −3.73303e15 | −0.730092 | ||||||||
\(719\) | −6.94101e15 | −1.34714 | −0.673571 | − | 0.739122i | \(-0.735241\pi\) | ||||
−0.673571 | + | 0.739122i | \(0.735241\pi\) | |||||||
\(720\) | 1.24182e15 | 0.239182 | ||||||||
\(721\) | 1.32679e16 | 2.53606 | ||||||||
\(722\) | 2.60123e14 | 0.0493428 | ||||||||
\(723\) | −8.97336e15 | −1.68925 | ||||||||
\(724\) | 6.49324e14 | 0.121311 | ||||||||
\(725\) | −1.81925e14 | −0.0337313 | ||||||||
\(726\) | −3.95746e15 | −0.728224 | ||||||||
\(727\) | −8.96895e14 | −0.163796 | −0.0818978 | − | 0.996641i | \(-0.526098\pi\) | ||||
−0.0818978 | + | 0.996641i | \(0.526098\pi\) | |||||||
\(728\) | −3.53653e15 | −0.640994 | ||||||||
\(729\) | −2.78918e15 | −0.501735 | ||||||||
\(730\) | −2.21136e15 | −0.394805 | ||||||||
\(731\) | 6.27903e15 | 1.11262 | ||||||||
\(732\) | 8.21403e15 | 1.44459 | ||||||||
\(733\) | −1.11078e16 | −1.93890 | −0.969451 | − | 0.245286i | \(-0.921118\pi\) | ||||
−0.969451 | + | 0.245286i | \(0.921118\pi\) | |||||||
\(734\) | 4.60985e15 | 0.798653 | ||||||||
\(735\) | 7.30400e15 | 1.25597 | ||||||||
\(736\) | −1.77049e14 | −0.0302179 | ||||||||
\(737\) | −1.28171e15 | −0.217130 | ||||||||
\(738\) | −1.10512e16 | −1.85822 | ||||||||
\(739\) | 5.03625e15 | 0.840548 | 0.420274 | − | 0.907397i | \(-0.361934\pi\) | ||||
0.420274 | + | 0.907397i | \(0.361934\pi\) | |||||||
\(740\) | 1.03413e15 | 0.171316 | ||||||||
\(741\) | −1.25669e16 | −2.06646 | ||||||||
\(742\) | −9.28764e15 | −1.51595 | ||||||||
\(743\) | 1.36645e15 | 0.221389 | 0.110695 | − | 0.993854i | \(-0.464692\pi\) | ||||
0.110695 | + | 0.993854i | \(0.464692\pi\) | |||||||
\(744\) | 1.73607e15 | 0.279200 | ||||||||
\(745\) | −7.45643e14 | −0.119034 | ||||||||
\(746\) | 2.20990e15 | 0.350194 | ||||||||
\(747\) | 2.10578e16 | 3.31246 | ||||||||
\(748\) | 1.90880e15 | 0.298059 | ||||||||
\(749\) | 3.90225e15 | 0.604874 | ||||||||
\(750\) | 7.28256e14 | 0.112059 | ||||||||
\(751\) | −9.78301e15 | −1.49435 | −0.747176 | − | 0.664627i | \(-0.768591\pi\) | ||||
−0.747176 | + | 0.664627i | \(0.768591\pi\) | |||||||
\(752\) | 2.95644e14 | 0.0448303 | ||||||||
\(753\) | −1.66456e16 | −2.50570 | ||||||||
\(754\) | −8.99900e14 | −0.134478 | ||||||||
\(755\) | −2.99159e14 | −0.0443807 | ||||||||
\(756\) | −1.10188e16 | −1.62280 | ||||||||
\(757\) | −1.39502e15 | −0.203964 | −0.101982 | − | 0.994786i | \(-0.532518\pi\) | ||||
−0.101982 | + | 0.994786i | \(0.532518\pi\) | |||||||
\(758\) | 7.31454e15 | 1.06171 | ||||||||
\(759\) | 1.36008e15 | 0.195990 | ||||||||
\(760\) | −1.14312e15 | −0.163538 | ||||||||
\(761\) | 6.09995e15 | 0.866385 | 0.433192 | − | 0.901301i | \(-0.357387\pi\) | ||||
0.433192 | + | 0.901301i | \(0.357387\pi\) | |||||||
\(762\) | −1.33799e16 | −1.88670 | ||||||||
\(763\) | 2.53117e15 | 0.354353 | ||||||||
\(764\) | −2.67862e15 | −0.372304 | ||||||||
\(765\) | −6.38676e15 | −0.881339 | ||||||||
\(766\) | −2.29352e15 | −0.314228 | ||||||||
\(767\) | 7.39427e15 | 1.00582 | ||||||||
\(768\) | 8.19943e14 | 0.110738 | ||||||||
\(769\) | 6.60626e15 | 0.885851 | 0.442925 | − | 0.896558i | \(-0.353941\pi\) | ||||
0.442925 | + | 0.896558i | \(0.353941\pi\) | |||||||
\(770\) | 2.47123e15 | 0.329013 | ||||||||
\(771\) | 1.34273e16 | 1.77496 | ||||||||
\(772\) | 1.63654e15 | 0.214799 | ||||||||
\(773\) | 3.74520e15 | 0.488076 | 0.244038 | − | 0.969766i | \(-0.421528\pi\) | ||||
0.244038 | + | 0.969766i | \(0.421528\pi\) | |||||||
\(774\) | −1.41197e16 | −1.82705 | ||||||||
\(775\) | 6.93797e14 | 0.0891400 | ||||||||
\(776\) | 1.54628e15 | 0.197265 | ||||||||
\(777\) | −1.72299e16 | −2.18257 | ||||||||
\(778\) | 1.69977e15 | 0.213798 | ||||||||
\(779\) | 1.01729e16 | 1.27054 | ||||||||
\(780\) | 3.60235e15 | 0.446751 | ||||||||
\(781\) | −1.19344e15 | −0.146967 | ||||||||
\(782\) | 9.10576e14 | 0.111347 | ||||||||
\(783\) | −2.80384e15 | −0.340458 | ||||||||
\(784\) | 3.28645e15 | 0.396267 | ||||||||
\(785\) | −5.62297e15 | −0.673259 | ||||||||
\(786\) | 9.83174e15 | 1.16898 | ||||||||
\(787\) | −1.01107e16 | −1.19377 | −0.596885 | − | 0.802326i | \(-0.703595\pi\) | ||||
−0.596885 | + | 0.802326i | \(0.703595\pi\) | |||||||
\(788\) | −6.31072e13 | −0.00739920 | ||||||||
\(789\) | 1.03578e16 | 1.20599 | ||||||||
\(790\) | 7.02672e14 | 0.0812463 | ||||||||
\(791\) | −8.60188e15 | −0.987694 | ||||||||
\(792\) | −4.29235e15 | −0.489448 | ||||||||
\(793\) | 1.62377e16 | 1.83874 | ||||||||
\(794\) | 3.00711e14 | 0.0338171 | ||||||||
\(795\) | 9.46050e15 | 1.05656 | ||||||||
\(796\) | 2.42221e15 | 0.268652 | ||||||||
\(797\) | −1.40032e16 | −1.54244 | −0.771219 | − | 0.636570i | \(-0.780353\pi\) | ||||
−0.771219 | + | 0.636570i | \(0.780353\pi\) | |||||||
\(798\) | 1.90459e16 | 2.08346 | ||||||||
\(799\) | −1.52052e15 | −0.165191 | ||||||||
\(800\) | 3.27680e14 | 0.0353553 | ||||||||
\(801\) | −3.52333e15 | −0.377550 | ||||||||
\(802\) | 7.04691e15 | 0.749962 | ||||||||
\(803\) | 7.64357e15 | 0.807906 | ||||||||
\(804\) | 2.83164e15 | 0.297255 | ||||||||
\(805\) | 1.17888e15 | 0.122911 | ||||||||
\(806\) | 3.43189e15 | 0.355378 | ||||||||
\(807\) | 2.02550e16 | 2.08318 | ||||||||
\(808\) | 5.28313e15 | 0.539671 | ||||||||
\(809\) | 2.05016e15 | 0.208004 | 0.104002 | − | 0.994577i | \(-0.466835\pi\) | ||||
0.104002 | + | 0.994577i | \(0.466835\pi\) | |||||||
\(810\) | 4.51052e15 | 0.454526 | ||||||||
\(811\) | −1.45631e16 | −1.45760 | −0.728801 | − | 0.684725i | \(-0.759922\pi\) | ||||
−0.728801 | + | 0.684725i | \(0.759922\pi\) | |||||||
\(812\) | 1.36385e15 | 0.135584 | ||||||||
\(813\) | −5.40316e15 | −0.533519 | ||||||||
\(814\) | −3.57446e15 | −0.350571 | ||||||||
\(815\) | −7.83183e15 | −0.762951 | ||||||||
\(816\) | −4.21703e15 | −0.408048 | ||||||||
\(817\) | 1.29975e16 | 1.24922 | ||||||||
\(818\) | −9.76330e15 | −0.932080 | ||||||||
\(819\) | −4.09011e16 | −3.87858 | ||||||||
\(820\) | −2.91609e15 | −0.274678 | ||||||||
\(821\) | −5.13429e15 | −0.480389 | −0.240195 | − | 0.970725i | \(-0.577211\pi\) | ||||
−0.240195 | + | 0.970725i | \(0.577211\pi\) | |||||||
\(822\) | −1.87629e16 | −1.74383 | ||||||||
\(823\) | −6.16638e15 | −0.569287 | −0.284643 | − | 0.958633i | \(-0.591875\pi\) | ||||
−0.284643 | + | 0.958633i | \(0.591875\pi\) | |||||||
\(824\) | −6.08104e15 | −0.557671 | ||||||||
\(825\) | −2.51722e15 | −0.229311 | ||||||||
\(826\) | −1.12065e16 | −1.01410 | ||||||||
\(827\) | −2.77673e15 | −0.249605 | −0.124803 | − | 0.992182i | \(-0.539830\pi\) | ||||
−0.124803 | + | 0.992182i | \(0.539830\pi\) | |||||||
\(828\) | −2.04763e15 | −0.182845 | ||||||||
\(829\) | 1.33865e16 | 1.18745 | 0.593726 | − | 0.804667i | \(-0.297656\pi\) | ||||
0.593726 | + | 0.804667i | \(0.297656\pi\) | |||||||
\(830\) | 5.55656e15 | 0.489639 | ||||||||
\(831\) | 2.96281e16 | 2.59357 | ||||||||
\(832\) | 1.62088e15 | 0.140953 | ||||||||
\(833\) | −1.69025e16 | −1.46017 | ||||||||
\(834\) | 2.04546e16 | 1.75541 | ||||||||
\(835\) | −8.43296e15 | −0.718960 | ||||||||
\(836\) | 3.95121e15 | 0.334653 | ||||||||
\(837\) | 1.06928e16 | 0.899709 | ||||||||
\(838\) | 1.34861e16 | 1.12731 | ||||||||
\(839\) | 1.47887e16 | 1.22812 | 0.614059 | − | 0.789260i | \(-0.289536\pi\) | ||||
0.614059 | + | 0.789260i | \(0.289536\pi\) | |||||||
\(840\) | −5.45958e15 | −0.450426 | ||||||||
\(841\) | −1.18535e16 | −0.971555 | ||||||||
\(842\) | 3.55584e13 | 0.00289551 | ||||||||
\(843\) | 4.43902e15 | 0.359116 | ||||||||
\(844\) | 5.52687e15 | 0.444218 | ||||||||
\(845\) | 1.52070e15 | 0.121431 | ||||||||
\(846\) | 3.41922e15 | 0.271263 | ||||||||
\(847\) | 1.18565e16 | 0.934542 | ||||||||
\(848\) | 4.25677e15 | 0.333352 | ||||||||
\(849\) | −2.87691e16 | −2.23838 | ||||||||
\(850\) | −1.68528e15 | −0.130277 | ||||||||
\(851\) | −1.70517e15 | −0.130965 | ||||||||
\(852\) | 2.63662e15 | 0.201201 | ||||||||
\(853\) | 1.97554e16 | 1.49784 | 0.748922 | − | 0.662658i | \(-0.230572\pi\) | ||||
0.748922 | + | 0.662658i | \(0.230572\pi\) | |||||||
\(854\) | −2.46092e16 | −1.85387 | ||||||||
\(855\) | −1.32206e16 | −0.989547 | ||||||||
\(856\) | −1.78850e15 | −0.133010 | ||||||||
\(857\) | −2.32233e16 | −1.71605 | −0.858023 | − | 0.513612i | \(-0.828307\pi\) | ||||
−0.858023 | + | 0.513612i | \(0.828307\pi\) | |||||||
\(858\) | −1.24515e16 | −0.914203 | ||||||||
\(859\) | −1.67344e16 | −1.22081 | −0.610405 | − | 0.792089i | \(-0.708993\pi\) | ||||
−0.610405 | + | 0.792089i | \(0.708993\pi\) | |||||||
\(860\) | −3.72580e15 | −0.270071 | ||||||||
\(861\) | 4.85859e16 | 3.49939 | ||||||||
\(862\) | 7.33454e15 | 0.524908 | ||||||||
\(863\) | −2.46024e16 | −1.74951 | −0.874757 | − | 0.484563i | \(-0.838979\pi\) | ||||
−0.874757 | + | 0.484563i | \(0.838979\pi\) | |||||||
\(864\) | 5.05021e15 | 0.356849 | ||||||||
\(865\) | 9.61864e15 | 0.675344 | ||||||||
\(866\) | 4.92901e15 | 0.343883 | ||||||||
\(867\) | −3.86919e15 | −0.268234 | ||||||||
\(868\) | −5.20125e15 | −0.358302 | ||||||||
\(869\) | −2.42879e15 | −0.166257 | ||||||||
\(870\) | −1.38924e15 | −0.0944976 | ||||||||
\(871\) | 5.59764e15 | 0.378360 | ||||||||
\(872\) | −1.16010e15 | −0.0779211 | ||||||||
\(873\) | 1.78833e16 | 1.19363 | ||||||||
\(874\) | 1.88489e15 | 0.125018 | ||||||||
\(875\) | −2.18185e15 | −0.143807 | ||||||||
\(876\) | −1.68866e16 | −1.10604 | ||||||||
\(877\) | −4.55865e15 | −0.296714 | −0.148357 | − | 0.988934i | \(-0.547399\pi\) | ||||
−0.148357 | + | 0.988934i | \(0.547399\pi\) | |||||||
\(878\) | −4.02551e15 | −0.260376 | ||||||||
\(879\) | −3.97125e16 | −2.55263 | ||||||||
\(880\) | −1.13263e15 | −0.0723490 | ||||||||
\(881\) | 1.67834e16 | 1.06540 | 0.532701 | − | 0.846304i | \(-0.321177\pi\) | ||||
0.532701 | + | 0.846304i | \(0.321177\pi\) | |||||||
\(882\) | 3.80088e16 | 2.39777 | ||||||||
\(883\) | −1.13628e16 | −0.712362 | −0.356181 | − | 0.934417i | \(-0.615921\pi\) | ||||
−0.356181 | + | 0.934417i | \(0.615921\pi\) | |||||||
\(884\) | −8.33632e15 | −0.519382 | ||||||||
\(885\) | 1.14151e16 | 0.706789 | ||||||||
\(886\) | −4.30793e15 | −0.265084 | ||||||||
\(887\) | 1.55603e16 | 0.951563 | 0.475782 | − | 0.879563i | \(-0.342165\pi\) | ||||
0.475782 | + | 0.879563i | \(0.342165\pi\) | |||||||
\(888\) | 7.89691e15 | 0.479939 | ||||||||
\(889\) | 4.00863e16 | 2.42123 | ||||||||
\(890\) | −9.29706e14 | −0.0558085 | ||||||||
\(891\) | −1.55906e16 | −0.930115 | ||||||||
\(892\) | −9.59615e15 | −0.568971 | ||||||||
\(893\) | −3.14747e15 | −0.185472 | ||||||||
\(894\) | −5.69397e15 | −0.333471 | ||||||||
\(895\) | 1.09736e15 | 0.0638736 | ||||||||
\(896\) | −2.45655e15 | −0.142112 | ||||||||
\(897\) | −5.93989e15 | −0.341523 | ||||||||
\(898\) | 1.37271e16 | 0.784440 | ||||||||
\(899\) | −1.32350e15 | −0.0751704 | ||||||||
\(900\) | 3.78972e15 | 0.213931 | ||||||||
\(901\) | −2.18929e16 | −1.22834 | ||||||||
\(902\) | 1.00795e16 | 0.562085 | ||||||||
\(903\) | 6.20767e16 | 3.44069 | ||||||||
\(904\) | 3.94246e15 | 0.217191 | ||||||||
\(905\) | 1.98158e15 | 0.108504 | ||||||||
\(906\) | −2.28447e15 | −0.124331 | ||||||||
\(907\) | 3.40764e16 | 1.84338 | 0.921688 | − | 0.387932i | \(-0.126811\pi\) | ||||
0.921688 | + | 0.387932i | \(0.126811\pi\) | |||||||
\(908\) | −6.67198e15 | −0.358742 | ||||||||
\(909\) | 6.11011e16 | 3.26548 | ||||||||
\(910\) | −1.07926e16 | −0.573323 | ||||||||
\(911\) | 1.60732e16 | 0.848697 | 0.424348 | − | 0.905499i | \(-0.360503\pi\) | ||||
0.424348 | + | 0.905499i | \(0.360503\pi\) | |||||||
\(912\) | −8.72924e15 | −0.458147 | ||||||||
\(913\) | −1.92063e16 | −1.00197 | ||||||||
\(914\) | −2.52543e16 | −1.30958 | ||||||||
\(915\) | 2.50672e16 | 1.29208 | ||||||||
\(916\) | −1.79004e15 | −0.0917144 | ||||||||
\(917\) | −2.94559e16 | −1.50017 | ||||||||
\(918\) | −2.59737e16 | −1.31492 | ||||||||
\(919\) | −7.32080e15 | −0.368403 | −0.184201 | − | 0.982889i | \(-0.558970\pi\) | ||||
−0.184201 | + | 0.982889i | \(0.558970\pi\) | |||||||
\(920\) | −5.40310e14 | −0.0270277 | ||||||||
\(921\) | −4.28302e16 | −2.12972 | ||||||||
\(922\) | −1.92556e16 | −0.951783 | ||||||||
\(923\) | 5.21213e15 | 0.256098 | ||||||||
\(924\) | 1.88711e16 | 0.921724 | ||||||||
\(925\) | 3.15590e15 | 0.153230 | ||||||||
\(926\) | 7.57994e15 | 0.365852 | ||||||||
\(927\) | −7.03292e16 | −3.37440 | ||||||||
\(928\) | −6.25090e14 | −0.0298146 | ||||||||
\(929\) | −1.41658e16 | −0.671666 | −0.335833 | − | 0.941922i | \(-0.609018\pi\) | ||||
−0.335833 | + | 0.941922i | \(0.609018\pi\) | |||||||
\(930\) | 5.29805e15 | 0.249724 | ||||||||
\(931\) | −3.49880e16 | −1.63944 | ||||||||
\(932\) | 8.85241e15 | 0.412358 | ||||||||
\(933\) | −1.92859e16 | −0.893081 | ||||||||
\(934\) | 2.61459e16 | 1.20364 | ||||||||
\(935\) | 5.82520e15 | 0.266592 | ||||||||
\(936\) | 1.87460e16 | 0.852888 | ||||||||
\(937\) | 1.51385e16 | 0.684721 | 0.342361 | − | 0.939569i | \(-0.388774\pi\) | ||||
0.342361 | + | 0.939569i | \(0.388774\pi\) | |||||||
\(938\) | −8.48358e15 | −0.381473 | ||||||||
\(939\) | −2.66456e16 | −1.19115 | ||||||||
\(940\) | 9.02235e14 | 0.0400974 | ||||||||
\(941\) | 8.81297e15 | 0.389385 | 0.194693 | − | 0.980864i | \(-0.437629\pi\) | ||||
0.194693 | + | 0.980864i | \(0.437629\pi\) | |||||||
\(942\) | −4.29388e16 | −1.88612 | ||||||||
\(943\) | 4.80832e15 | 0.209981 | ||||||||
\(944\) | 5.13622e15 | 0.222996 | ||||||||
\(945\) | −3.36268e16 | −1.45148 | ||||||||
\(946\) | 1.28782e16 | 0.552656 | ||||||||
\(947\) | 6.85225e15 | 0.292353 | 0.146177 | − | 0.989258i | \(-0.453303\pi\) | ||||
0.146177 | + | 0.989258i | \(0.453303\pi\) | |||||||
\(948\) | 5.36582e15 | 0.227610 | ||||||||
\(949\) | −3.33818e16 | −1.40782 | ||||||||
\(950\) | −3.48853e15 | −0.146272 | ||||||||
\(951\) | −1.33211e16 | −0.555325 | ||||||||
\(952\) | 1.26342e16 | 0.523655 | ||||||||
\(953\) | 3.21185e16 | 1.32356 | 0.661781 | − | 0.749697i | \(-0.269801\pi\) | ||||
0.661781 | + | 0.749697i | \(0.269801\pi\) | |||||||
\(954\) | 4.92309e16 | 2.01707 | ||||||||
\(955\) | −8.17451e15 | −0.332999 | ||||||||
\(956\) | 6.87129e15 | 0.278304 | ||||||||
\(957\) | 4.80191e15 | 0.193374 | ||||||||
\(958\) | 8.98935e15 | 0.359930 | ||||||||
\(959\) | 5.62135e16 | 2.23789 | ||||||||
\(960\) | 2.50227e15 | 0.0990472 | ||||||||
\(961\) | −2.03611e16 | −0.801351 | ||||||||
\(962\) | 1.56108e16 | 0.610889 | ||||||||
\(963\) | −2.06846e16 | −0.804827 | ||||||||
\(964\) | −1.23217e16 | −0.476702 | ||||||||
\(965\) | 4.99433e15 | 0.192122 | ||||||||
\(966\) | 9.00228e15 | 0.344333 | ||||||||
\(967\) | 2.01801e16 | 0.767500 | 0.383750 | − | 0.923437i | \(-0.374633\pi\) | ||||
0.383750 | + | 0.923437i | \(0.374633\pi\) | |||||||
\(968\) | −5.43416e15 | −0.205503 | ||||||||
\(969\) | 4.48952e16 | 1.68818 | ||||||||
\(970\) | 4.71888e15 | 0.176439 | ||||||||
\(971\) | 7.19924e15 | 0.267658 | 0.133829 | − | 0.991004i | \(-0.457273\pi\) | ||||
0.133829 | + | 0.991004i | \(0.457273\pi\) | |||||||
\(972\) | 7.14182e15 | 0.264025 | ||||||||
\(973\) | −6.12821e16 | −2.25275 | ||||||||
\(974\) | −1.30052e16 | −0.475383 | ||||||||
\(975\) | 1.09935e16 | 0.399586 | ||||||||
\(976\) | 1.12790e16 | 0.407660 | ||||||||
\(977\) | 3.14860e16 | 1.13161 | 0.565806 | − | 0.824538i | \(-0.308565\pi\) | ||||
0.565806 | + | 0.824538i | \(0.308565\pi\) | |||||||
\(978\) | −5.98064e16 | −2.13739 | ||||||||
\(979\) | 3.21353e15 | 0.114203 | ||||||||
\(980\) | 1.00294e16 | 0.354432 | ||||||||
\(981\) | −1.34169e16 | −0.471491 | ||||||||
\(982\) | 3.27934e16 | 1.14597 | ||||||||
\(983\) | −1.68059e15 | −0.0584006 | −0.0292003 | − | 0.999574i | \(-0.509296\pi\) | ||||
−0.0292003 | + | 0.999574i | \(0.509296\pi\) | |||||||
\(984\) | −2.22682e16 | −0.769505 | ||||||||
\(985\) | −1.92588e14 | −0.00661805 | ||||||||
\(986\) | 3.21489e15 | 0.109861 | ||||||||
\(987\) | −1.50324e16 | −0.510840 | ||||||||
\(988\) | −1.72561e16 | −0.583150 | ||||||||
\(989\) | 6.14345e15 | 0.206458 | ||||||||
\(990\) | −1.30992e16 | −0.437775 | ||||||||
\(991\) | −2.21678e15 | −0.0736746 | −0.0368373 | − | 0.999321i | \(-0.511728\pi\) | ||||
−0.0368373 | + | 0.999321i | \(0.511728\pi\) | |||||||
\(992\) | 2.38387e15 | 0.0787894 | ||||||||
\(993\) | 5.80389e16 | 1.90765 | ||||||||
\(994\) | −7.89931e15 | −0.258205 | ||||||||
\(995\) | 7.39199e15 | 0.240289 | ||||||||
\(996\) | 4.24316e16 | 1.37171 | ||||||||
\(997\) | 2.59411e14 | 0.00833999 | 0.00416999 | − | 0.999991i | \(-0.498673\pi\) | ||||
0.00416999 | + | 0.999991i | \(0.498673\pi\) | |||||||
\(998\) | 3.25097e15 | 0.103943 | ||||||||
\(999\) | 4.86389e16 | 1.54658 |
(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 | 10.12.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 90.12.a.l.1.1 | 2 | |||
4.3 | odd | 2 | 80.12.a.g.1.1 | 2 | |||
5.2 | odd | 4 | 50.12.b.f.49.3 | 4 | |||
5.3 | odd | 4 | 50.12.b.f.49.2 | 4 | |||
5.4 | even | 2 | 50.12.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.12.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.12.a.f.1.1 | 2 | 5.4 | even | 2 | |||
50.12.b.f.49.2 | 4 | 5.3 | odd | 4 | |||
50.12.b.f.49.3 | 4 | 5.2 | odd | 4 | |||
80.12.a.g.1.1 | 2 | 4.3 | odd | 2 | |||
90.12.a.l.1.1 | 2 | 3.2 | odd | 2 |