Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,18,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(5.49666262034\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{14569}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3642 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-59.8511\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 659.106 | 1.82054 | 0.910271 | − | 0.414014i | \(-0.135873\pi\) | ||||
0.910271 | + | 0.414014i | \(0.135873\pi\) | |||||||
\(3\) | 6561.00 | 0.577350 | ||||||||
\(4\) | 303349. | 2.31437 | ||||||||
\(5\) | −1.08318e6 | −1.24010 | −0.620051 | − | 0.784562i | \(-0.712888\pi\) | ||||
−0.620051 | + | 0.784562i | \(0.712888\pi\) | |||||||
\(6\) | 4.32440e6 | 1.05109 | ||||||||
\(7\) | 1.59855e6 | 0.104808 | 0.0524038 | − | 0.998626i | \(-0.483312\pi\) | ||||
0.0524038 | + | 0.998626i | \(0.483312\pi\) | |||||||
\(8\) | 1.13549e8 | 2.39287 | ||||||||
\(9\) | 4.30467e7 | 0.333333 | ||||||||
\(10\) | −7.13934e8 | −2.25766 | ||||||||
\(11\) | −4.47381e8 | −0.629274 | −0.314637 | − | 0.949212i | \(-0.601883\pi\) | ||||
−0.314637 | + | 0.949212i | \(0.601883\pi\) | |||||||
\(12\) | 1.99027e9 | 1.33620 | ||||||||
\(13\) | −2.48486e9 | −0.844857 | −0.422428 | − | 0.906396i | \(-0.638822\pi\) | ||||
−0.422428 | + | 0.906396i | \(0.638822\pi\) | |||||||
\(14\) | 1.05361e9 | 0.190806 | ||||||||
\(15\) | −7.10677e9 | −0.715973 | ||||||||
\(16\) | 3.50803e10 | 2.04194 | ||||||||
\(17\) | −2.48745e10 | −0.864844 | −0.432422 | − | 0.901671i | \(-0.642341\pi\) | ||||
−0.432422 | + | 0.901671i | \(0.642341\pi\) | |||||||
\(18\) | 2.83724e10 | 0.606847 | ||||||||
\(19\) | 8.23042e10 | 1.11177 | 0.555887 | − | 0.831258i | \(-0.312379\pi\) | ||||
0.555887 | + | 0.831258i | \(0.312379\pi\) | |||||||
\(20\) | −3.28583e11 | −2.87005 | ||||||||
\(21\) | 1.04881e10 | 0.0605106 | ||||||||
\(22\) | −2.94872e11 | −1.14562 | ||||||||
\(23\) | 6.43083e11 | 1.71230 | 0.856151 | − | 0.516726i | \(-0.172850\pi\) | ||||
0.856151 | + | 0.516726i | \(0.172850\pi\) | |||||||
\(24\) | 7.44995e11 | 1.38152 | ||||||||
\(25\) | 4.10349e11 | 0.537852 | ||||||||
\(26\) | −1.63779e12 | −1.53810 | ||||||||
\(27\) | 2.82430e11 | 0.192450 | ||||||||
\(28\) | 4.84918e11 | 0.242563 | ||||||||
\(29\) | −9.82213e11 | −0.364605 | −0.182302 | − | 0.983243i | \(-0.558355\pi\) | ||||
−0.182302 | + | 0.983243i | \(0.558355\pi\) | |||||||
\(30\) | −4.68412e12 | −1.30346 | ||||||||
\(31\) | 3.28632e12 | 0.692046 | 0.346023 | − | 0.938226i | \(-0.387532\pi\) | ||||
0.346023 | + | 0.938226i | \(0.387532\pi\) | |||||||
\(32\) | 8.23853e12 | 1.32457 | ||||||||
\(33\) | −2.93527e12 | −0.363311 | ||||||||
\(34\) | −1.63949e13 | −1.57448 | ||||||||
\(35\) | −1.73152e12 | −0.129972 | ||||||||
\(36\) | 1.30582e13 | 0.771457 | ||||||||
\(37\) | 2.63492e13 | 1.23326 | 0.616628 | − | 0.787254i | \(-0.288498\pi\) | ||||
0.616628 | + | 0.787254i | \(0.288498\pi\) | |||||||
\(38\) | 5.42472e13 | 2.02403 | ||||||||
\(39\) | −1.63032e13 | −0.487778 | ||||||||
\(40\) | −1.22994e14 | −2.96740 | ||||||||
\(41\) | −3.33007e13 | −0.651314 | −0.325657 | − | 0.945488i | \(-0.605585\pi\) | ||||
−0.325657 | + | 0.945488i | \(0.605585\pi\) | |||||||
\(42\) | 6.91276e12 | 0.110162 | ||||||||
\(43\) | 9.83107e13 | 1.28268 | 0.641341 | − | 0.767256i | \(-0.278378\pi\) | ||||
0.641341 | + | 0.767256i | \(0.278378\pi\) | |||||||
\(44\) | −1.35713e14 | −1.45637 | ||||||||
\(45\) | −4.66275e13 | −0.413367 | ||||||||
\(46\) | 4.23860e14 | 3.11732 | ||||||||
\(47\) | −1.62068e14 | −0.992811 | −0.496406 | − | 0.868091i | \(-0.665347\pi\) | ||||
−0.496406 | + | 0.868091i | \(0.665347\pi\) | |||||||
\(48\) | 2.30162e14 | 1.17891 | ||||||||
\(49\) | −2.30075e14 | −0.989015 | ||||||||
\(50\) | 2.70463e14 | 0.979182 | ||||||||
\(51\) | −1.63201e14 | −0.499318 | ||||||||
\(52\) | −7.53780e14 | −1.95531 | ||||||||
\(53\) | −1.40921e14 | −0.310907 | −0.155453 | − | 0.987843i | \(-0.549684\pi\) | ||||
−0.155453 | + | 0.987843i | \(0.549684\pi\) | |||||||
\(54\) | 1.86151e14 | 0.350363 | ||||||||
\(55\) | 4.84596e14 | 0.780363 | ||||||||
\(56\) | 1.81514e14 | 0.250790 | ||||||||
\(57\) | 5.39998e14 | 0.641882 | ||||||||
\(58\) | −6.47383e14 | −0.663778 | ||||||||
\(59\) | −9.80930e13 | −0.0869753 | −0.0434876 | − | 0.999054i | \(-0.513847\pi\) | ||||
−0.0434876 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(60\) | −2.15583e15 | −1.65703 | ||||||||
\(61\) | 1.37376e15 | 0.917503 | 0.458751 | − | 0.888565i | \(-0.348297\pi\) | ||||
0.458751 | + | 0.888565i | \(0.348297\pi\) | |||||||
\(62\) | 2.16603e15 | 1.25990 | ||||||||
\(63\) | 6.88123e13 | 0.0349358 | ||||||||
\(64\) | 8.32030e14 | 0.369495 | ||||||||
\(65\) | 2.69156e15 | 1.04771 | ||||||||
\(66\) | −1.93465e15 | −0.661423 | ||||||||
\(67\) | −1.85816e15 | −0.559046 | −0.279523 | − | 0.960139i | \(-0.590176\pi\) | ||||
−0.279523 | + | 0.960139i | \(0.590176\pi\) | |||||||
\(68\) | −7.54565e15 | −2.00157 | ||||||||
\(69\) | 4.21927e15 | 0.988598 | ||||||||
\(70\) | −1.14126e15 | −0.236619 | ||||||||
\(71\) | −6.17500e15 | −1.13486 | −0.567428 | − | 0.823423i | \(-0.692061\pi\) | ||||
−0.567428 | + | 0.823423i | \(0.692061\pi\) | |||||||
\(72\) | 4.88791e15 | 0.797622 | ||||||||
\(73\) | −1.30214e16 | −1.88979 | −0.944896 | − | 0.327371i | \(-0.893837\pi\) | ||||
−0.944896 | + | 0.327371i | \(0.893837\pi\) | |||||||
\(74\) | 1.73670e16 | 2.24519 | ||||||||
\(75\) | 2.69230e15 | 0.310529 | ||||||||
\(76\) | 2.49669e16 | 2.57305 | ||||||||
\(77\) | −7.15160e14 | −0.0659526 | ||||||||
\(78\) | −1.07455e16 | −0.888021 | ||||||||
\(79\) | 1.27538e16 | 0.945824 | 0.472912 | − | 0.881110i | \(-0.343203\pi\) | ||||
0.472912 | + | 0.881110i | \(0.343203\pi\) | |||||||
\(80\) | −3.79984e16 | −2.53221 | ||||||||
\(81\) | 1.85302e15 | 0.111111 | ||||||||
\(82\) | −2.19487e16 | −1.18574 | ||||||||
\(83\) | −1.42886e16 | −0.696348 | −0.348174 | − | 0.937430i | \(-0.613198\pi\) | ||||
−0.348174 | + | 0.937430i | \(0.613198\pi\) | |||||||
\(84\) | 3.18155e15 | 0.140044 | ||||||||
\(85\) | 2.69436e16 | 1.07250 | ||||||||
\(86\) | 6.47972e16 | 2.33517 | ||||||||
\(87\) | −6.44430e15 | −0.210505 | ||||||||
\(88\) | −5.07996e16 | −1.50577 | ||||||||
\(89\) | −3.77818e16 | −1.01734 | −0.508672 | − | 0.860961i | \(-0.669863\pi\) | ||||
−0.508672 | + | 0.860961i | \(0.669863\pi\) | |||||||
\(90\) | −3.07325e16 | −0.752552 | ||||||||
\(91\) | −3.97217e15 | −0.0885473 | ||||||||
\(92\) | 1.95079e17 | 3.96290 | ||||||||
\(93\) | 2.15615e16 | 0.399553 | ||||||||
\(94\) | −1.06820e17 | −1.80745 | ||||||||
\(95\) | −8.91506e16 | −1.37871 | ||||||||
\(96\) | 5.40530e16 | 0.764741 | ||||||||
\(97\) | 1.09404e17 | 1.41733 | 0.708667 | − | 0.705543i | \(-0.249297\pi\) | ||||
0.708667 | + | 0.705543i | \(0.249297\pi\) | |||||||
\(98\) | −1.51644e17 | −1.80054 | ||||||||
\(99\) | −1.92583e16 | −0.209758 | ||||||||
\(100\) | 1.24479e17 | 1.24479 | ||||||||
\(101\) | 1.19047e17 | 1.09392 | 0.546962 | − | 0.837157i | \(-0.315784\pi\) | ||||
0.546962 | + | 0.837157i | \(0.315784\pi\) | |||||||
\(102\) | −1.07567e17 | −0.909029 | ||||||||
\(103\) | −3.78871e16 | −0.294697 | −0.147348 | − | 0.989085i | \(-0.547074\pi\) | ||||
−0.147348 | + | 0.989085i | \(0.547074\pi\) | |||||||
\(104\) | −2.82153e17 | −2.02163 | ||||||||
\(105\) | −1.13605e16 | −0.0750394 | ||||||||
\(106\) | −9.28817e16 | −0.566018 | ||||||||
\(107\) | −5.58893e16 | −0.314461 | −0.157230 | − | 0.987562i | \(-0.550257\pi\) | ||||
−0.157230 | + | 0.987562i | \(0.550257\pi\) | |||||||
\(108\) | 8.56748e16 | 0.445401 | ||||||||
\(109\) | 3.40417e17 | 1.63639 | 0.818193 | − | 0.574944i | \(-0.194976\pi\) | ||||
0.818193 | + | 0.574944i | \(0.194976\pi\) | |||||||
\(110\) | 3.19400e17 | 1.42068 | ||||||||
\(111\) | 1.72877e17 | 0.712021 | ||||||||
\(112\) | 5.60775e16 | 0.214011 | ||||||||
\(113\) | −1.05411e16 | −0.0373009 | −0.0186505 | − | 0.999826i | \(-0.505937\pi\) | ||||
−0.0186505 | + | 0.999826i | \(0.505937\pi\) | |||||||
\(114\) | 3.55916e17 | 1.16857 | ||||||||
\(115\) | −6.96577e17 | −2.12343 | ||||||||
\(116\) | −2.97953e17 | −0.843831 | ||||||||
\(117\) | −1.06965e17 | −0.281619 | ||||||||
\(118\) | −6.46537e16 | −0.158342 | ||||||||
\(119\) | −3.97630e16 | −0.0906422 | ||||||||
\(120\) | −8.06967e17 | −1.71323 | ||||||||
\(121\) | −3.05297e17 | −0.604015 | ||||||||
\(122\) | 9.05454e17 | 1.67035 | ||||||||
\(123\) | −2.18486e17 | −0.376036 | ||||||||
\(124\) | 9.96902e17 | 1.60165 | ||||||||
\(125\) | 3.81921e17 | 0.573110 | ||||||||
\(126\) | 4.53546e16 | 0.0636021 | ||||||||
\(127\) | −7.32464e17 | −0.960406 | −0.480203 | − | 0.877157i | \(-0.659437\pi\) | ||||
−0.480203 | + | 0.877157i | \(0.659437\pi\) | |||||||
\(128\) | −5.31445e17 | −0.651889 | ||||||||
\(129\) | 6.45016e17 | 0.740557 | ||||||||
\(130\) | 1.77402e18 | 1.90740 | ||||||||
\(131\) | −2.70892e17 | −0.272891 | −0.136446 | − | 0.990648i | \(-0.543568\pi\) | ||||
−0.136446 | + | 0.990648i | \(0.543568\pi\) | |||||||
\(132\) | −8.90410e17 | −0.840837 | ||||||||
\(133\) | 1.31567e17 | 0.116522 | ||||||||
\(134\) | −1.22473e18 | −1.01777 | ||||||||
\(135\) | −3.05923e17 | −0.238658 | ||||||||
\(136\) | −2.82447e18 | −2.06946 | ||||||||
\(137\) | 2.60762e18 | 1.79523 | 0.897614 | − | 0.440782i | \(-0.145299\pi\) | ||||
0.897614 | + | 0.440782i | \(0.145299\pi\) | |||||||
\(138\) | 2.78094e18 | 1.79978 | ||||||||
\(139\) | 1.06238e18 | 0.646628 | 0.323314 | − | 0.946292i | \(-0.395203\pi\) | ||||
0.323314 | + | 0.946292i | \(0.395203\pi\) | |||||||
\(140\) | −5.25256e17 | −0.300803 | ||||||||
\(141\) | −1.06333e18 | −0.573200 | ||||||||
\(142\) | −4.06998e18 | −2.06605 | ||||||||
\(143\) | 1.11168e18 | 0.531646 | ||||||||
\(144\) | 1.51009e18 | 0.680647 | ||||||||
\(145\) | 1.06392e18 | 0.452147 | ||||||||
\(146\) | −8.58250e18 | −3.44044 | ||||||||
\(147\) | −1.50952e18 | −0.571008 | ||||||||
\(148\) | 7.99302e18 | 2.85421 | ||||||||
\(149\) | −1.93103e18 | −0.651186 | −0.325593 | − | 0.945510i | \(-0.605564\pi\) | ||||
−0.325593 | + | 0.945510i | \(0.605564\pi\) | |||||||
\(150\) | 1.77451e18 | 0.565331 | ||||||||
\(151\) | 2.89305e18 | 0.871067 | 0.435533 | − | 0.900173i | \(-0.356560\pi\) | ||||
0.435533 | + | 0.900173i | \(0.356560\pi\) | |||||||
\(152\) | 9.34555e18 | 2.66032 | ||||||||
\(153\) | −1.07076e18 | −0.288281 | ||||||||
\(154\) | −4.71366e17 | −0.120069 | ||||||||
\(155\) | −3.55969e18 | −0.858208 | ||||||||
\(156\) | −4.94555e18 | −1.12890 | ||||||||
\(157\) | −3.49613e18 | −0.755858 | −0.377929 | − | 0.925835i | \(-0.623364\pi\) | ||||
−0.377929 | + | 0.925835i | \(0.623364\pi\) | |||||||
\(158\) | 8.40613e18 | 1.72191 | ||||||||
\(159\) | −9.24581e17 | −0.179502 | ||||||||
\(160\) | −8.92385e18 | −1.64260 | ||||||||
\(161\) | 1.02800e18 | 0.179462 | ||||||||
\(162\) | 1.22134e18 | 0.202282 | ||||||||
\(163\) | −1.15214e18 | −0.181096 | −0.0905481 | − | 0.995892i | \(-0.528862\pi\) | ||||
−0.0905481 | + | 0.995892i | \(0.528862\pi\) | |||||||
\(164\) | −1.01017e19 | −1.50738 | ||||||||
\(165\) | 3.17943e18 | 0.450543 | ||||||||
\(166\) | −9.41771e18 | −1.26773 | ||||||||
\(167\) | 3.89891e18 | 0.498715 | 0.249358 | − | 0.968411i | \(-0.419781\pi\) | ||||
0.249358 | + | 0.968411i | \(0.419781\pi\) | |||||||
\(168\) | 1.19091e18 | 0.144794 | ||||||||
\(169\) | −2.47589e18 | −0.286217 | ||||||||
\(170\) | 1.77587e19 | 1.95252 | ||||||||
\(171\) | 3.54292e18 | 0.370591 | ||||||||
\(172\) | 2.98225e19 | 2.96860 | ||||||||
\(173\) | −6.89759e17 | −0.0653590 | −0.0326795 | − | 0.999466i | \(-0.510404\pi\) | ||||
−0.0326795 | + | 0.999466i | \(0.510404\pi\) | |||||||
\(174\) | −4.24748e18 | −0.383233 | ||||||||
\(175\) | 6.55962e17 | 0.0563710 | ||||||||
\(176\) | −1.56942e19 | −1.28494 | ||||||||
\(177\) | −6.43588e17 | −0.0502152 | ||||||||
\(178\) | −2.49022e19 | −1.85212 | ||||||||
\(179\) | −1.57675e18 | −0.111818 | −0.0559092 | − | 0.998436i | \(-0.517806\pi\) | ||||
−0.0559092 | + | 0.998436i | \(0.517806\pi\) | |||||||
\(180\) | −1.41444e19 | −0.956685 | ||||||||
\(181\) | −8.66463e18 | −0.559091 | −0.279545 | − | 0.960133i | \(-0.590184\pi\) | ||||
−0.279545 | + | 0.960133i | \(0.590184\pi\) | |||||||
\(182\) | −2.61808e18 | −0.161204 | ||||||||
\(183\) | 9.01324e18 | 0.529720 | ||||||||
\(184\) | 7.30214e19 | 4.09731 | ||||||||
\(185\) | −2.85411e19 | −1.52936 | ||||||||
\(186\) | 1.42113e19 | 0.727403 | ||||||||
\(187\) | 1.11284e19 | 0.544224 | ||||||||
\(188\) | −4.91633e19 | −2.29773 | ||||||||
\(189\) | 4.51477e17 | 0.0201702 | ||||||||
\(190\) | −5.87597e19 | −2.51000 | ||||||||
\(191\) | 3.05782e19 | 1.24919 | 0.624595 | − | 0.780949i | \(-0.285264\pi\) | ||||
0.624595 | + | 0.780949i | \(0.285264\pi\) | |||||||
\(192\) | 5.45895e18 | 0.213328 | ||||||||
\(193\) | −8.47673e18 | −0.316950 | −0.158475 | − | 0.987363i | \(-0.550658\pi\) | ||||
−0.158475 | + | 0.987363i | \(0.550658\pi\) | |||||||
\(194\) | 7.21087e19 | 2.58032 | ||||||||
\(195\) | 1.76593e19 | 0.604895 | ||||||||
\(196\) | −6.97931e19 | −2.28895 | ||||||||
\(197\) | −1.02174e18 | −0.0320906 | −0.0160453 | − | 0.999871i | \(-0.505108\pi\) | ||||
−0.0160453 | + | 0.999871i | \(0.505108\pi\) | |||||||
\(198\) | −1.26933e19 | −0.381873 | ||||||||
\(199\) | 1.36420e19 | 0.393213 | 0.196606 | − | 0.980482i | \(-0.437008\pi\) | ||||
0.196606 | + | 0.980482i | \(0.437008\pi\) | |||||||
\(200\) | 4.65947e19 | 1.28701 | ||||||||
\(201\) | −1.21914e19 | −0.322765 | ||||||||
\(202\) | 7.84647e19 | 1.99153 | ||||||||
\(203\) | −1.57011e18 | −0.0382133 | ||||||||
\(204\) | −4.95070e19 | −1.15561 | ||||||||
\(205\) | 3.60708e19 | 0.807696 | ||||||||
\(206\) | −2.49716e19 | −0.536507 | ||||||||
\(207\) | 2.76826e19 | 0.570767 | ||||||||
\(208\) | −8.71695e19 | −1.72515 | ||||||||
\(209\) | −3.68213e19 | −0.699609 | ||||||||
\(210\) | −7.48779e18 | −0.136612 | ||||||||
\(211\) | 3.54105e19 | 0.620485 | 0.310242 | − | 0.950657i | \(-0.399590\pi\) | ||||
0.310242 | + | 0.950657i | \(0.399590\pi\) | |||||||
\(212\) | −4.27482e19 | −0.719553 | ||||||||
\(213\) | −4.05142e19 | −0.655209 | ||||||||
\(214\) | −3.68370e19 | −0.572489 | ||||||||
\(215\) | −1.06489e20 | −1.59066 | ||||||||
\(216\) | 3.20696e19 | 0.460507 | ||||||||
\(217\) | 5.25334e18 | 0.0725317 | ||||||||
\(218\) | 2.24371e20 | 2.97911 | ||||||||
\(219\) | −8.54335e19 | −1.09107 | ||||||||
\(220\) | 1.47002e20 | 1.80605 | ||||||||
\(221\) | 6.18095e19 | 0.730670 | ||||||||
\(222\) | 1.13945e20 | 1.29626 | ||||||||
\(223\) | −1.07563e20 | −1.17780 | −0.588900 | − | 0.808206i | \(-0.700439\pi\) | ||||
−0.588900 | + | 0.808206i | \(0.700439\pi\) | |||||||
\(224\) | 1.31697e19 | 0.138825 | ||||||||
\(225\) | 1.76642e19 | 0.179284 | ||||||||
\(226\) | −6.94771e18 | −0.0679078 | ||||||||
\(227\) | −3.19163e19 | −0.300464 | −0.150232 | − | 0.988651i | \(-0.548002\pi\) | ||||
−0.150232 | + | 0.988651i | \(0.548002\pi\) | |||||||
\(228\) | 1.63808e20 | 1.48555 | ||||||||
\(229\) | −3.62295e19 | −0.316564 | −0.158282 | − | 0.987394i | \(-0.550595\pi\) | ||||
−0.158282 | + | 0.987394i | \(0.550595\pi\) | |||||||
\(230\) | −4.59118e20 | −3.86579 | ||||||||
\(231\) | −4.69216e18 | −0.0380778 | ||||||||
\(232\) | −1.11529e20 | −0.872451 | ||||||||
\(233\) | 1.40197e20 | 1.05734 | 0.528669 | − | 0.848828i | \(-0.322691\pi\) | ||||
0.528669 | + | 0.848828i | \(0.322691\pi\) | |||||||
\(234\) | −7.05013e19 | −0.512699 | ||||||||
\(235\) | 1.75550e20 | 1.23119 | ||||||||
\(236\) | −2.97564e19 | −0.201293 | ||||||||
\(237\) | 8.36779e19 | 0.546072 | ||||||||
\(238\) | −2.62081e19 | −0.165018 | ||||||||
\(239\) | 1.59138e20 | 0.966921 | 0.483461 | − | 0.875366i | \(-0.339380\pi\) | ||||
0.483461 | + | 0.875366i | \(0.339380\pi\) | |||||||
\(240\) | −2.49307e20 | −1.46197 | ||||||||
\(241\) | −7.13132e19 | −0.403669 | −0.201834 | − | 0.979420i | \(-0.564690\pi\) | ||||
−0.201834 | + | 0.979420i | \(0.564690\pi\) | |||||||
\(242\) | −2.01223e20 | −1.09963 | ||||||||
\(243\) | 1.21577e19 | 0.0641500 | ||||||||
\(244\) | 4.16729e20 | 2.12344 | ||||||||
\(245\) | 2.49214e20 | 1.22648 | ||||||||
\(246\) | −1.44005e20 | −0.684590 | ||||||||
\(247\) | −2.04514e20 | −0.939289 | ||||||||
\(248\) | 3.73158e20 | 1.65597 | ||||||||
\(249\) | −9.37476e19 | −0.402037 | ||||||||
\(250\) | 2.51726e20 | 1.04337 | ||||||||
\(251\) | −1.69237e20 | −0.678063 | −0.339031 | − | 0.940775i | \(-0.610099\pi\) | ||||
−0.339031 | + | 0.940775i | \(0.610099\pi\) | |||||||
\(252\) | 2.08741e19 | 0.0808545 | ||||||||
\(253\) | −2.87703e20 | −1.07751 | ||||||||
\(254\) | −4.82772e20 | −1.74846 | ||||||||
\(255\) | 1.76777e20 | 0.619205 | ||||||||
\(256\) | −4.59335e20 | −1.55629 | ||||||||
\(257\) | 4.63024e20 | 1.51765 | 0.758826 | − | 0.651293i | \(-0.225773\pi\) | ||||
0.758826 | + | 0.651293i | \(0.225773\pi\) | |||||||
\(258\) | 4.25134e20 | 1.34821 | ||||||||
\(259\) | 4.21205e19 | 0.129255 | ||||||||
\(260\) | 8.16482e20 | 2.42479 | ||||||||
\(261\) | −4.22810e19 | −0.121535 | ||||||||
\(262\) | −1.78546e20 | −0.496810 | ||||||||
\(263\) | −5.31839e20 | −1.43270 | −0.716351 | − | 0.697740i | \(-0.754189\pi\) | ||||
−0.716351 | + | 0.697740i | \(0.754189\pi\) | |||||||
\(264\) | −3.33296e20 | −0.869355 | ||||||||
\(265\) | 1.52643e20 | 0.385556 | ||||||||
\(266\) | 8.67167e19 | 0.212133 | ||||||||
\(267\) | −2.47886e20 | −0.587363 | ||||||||
\(268\) | −5.63672e20 | −1.29384 | ||||||||
\(269\) | −2.28606e20 | −0.508386 | −0.254193 | − | 0.967154i | \(-0.581810\pi\) | ||||
−0.254193 | + | 0.967154i | \(0.581810\pi\) | |||||||
\(270\) | −2.01636e20 | −0.434486 | ||||||||
\(271\) | −3.88488e20 | −0.811220 | −0.405610 | − | 0.914046i | \(-0.632941\pi\) | ||||
−0.405610 | + | 0.914046i | \(0.632941\pi\) | |||||||
\(272\) | −8.72603e20 | −1.76596 | ||||||||
\(273\) | −2.60614e19 | −0.0511228 | ||||||||
\(274\) | 1.71870e21 | 3.26829 | ||||||||
\(275\) | −1.83582e20 | −0.338456 | ||||||||
\(276\) | 1.27991e21 | 2.28798 | ||||||||
\(277\) | 8.66031e20 | 1.50126 | 0.750629 | − | 0.660724i | \(-0.229751\pi\) | ||||
0.750629 | + | 0.660724i | \(0.229751\pi\) | |||||||
\(278\) | 7.00222e20 | 1.17721 | ||||||||
\(279\) | 1.41465e20 | 0.230682 | ||||||||
\(280\) | −1.96613e20 | −0.311005 | ||||||||
\(281\) | 1.08570e20 | 0.166612 | 0.0833059 | − | 0.996524i | \(-0.473452\pi\) | ||||
0.0833059 | + | 0.996524i | \(0.473452\pi\) | |||||||
\(282\) | −7.00848e20 | −1.04353 | ||||||||
\(283\) | 4.17569e20 | 0.603314 | 0.301657 | − | 0.953416i | \(-0.402460\pi\) | ||||
0.301657 | + | 0.953416i | \(0.402460\pi\) | |||||||
\(284\) | −1.87318e21 | −2.62648 | ||||||||
\(285\) | −5.84917e20 | −0.796000 | ||||||||
\(286\) | 7.32714e20 | 0.967884 | ||||||||
\(287\) | −5.32328e19 | −0.0682626 | ||||||||
\(288\) | 3.54642e20 | 0.441524 | ||||||||
\(289\) | −2.08501e20 | −0.252044 | ||||||||
\(290\) | 7.01235e20 | 0.823153 | ||||||||
\(291\) | 7.17798e20 | 0.818299 | ||||||||
\(292\) | −3.95004e21 | −4.37368 | ||||||||
\(293\) | 2.71816e20 | 0.292348 | 0.146174 | − | 0.989259i | \(-0.453304\pi\) | ||||
0.146174 | + | 0.989259i | \(0.453304\pi\) | |||||||
\(294\) | −9.94936e20 | −1.03954 | ||||||||
\(295\) | 1.06253e20 | 0.107858 | ||||||||
\(296\) | 2.99193e21 | 2.95102 | ||||||||
\(297\) | −1.26354e20 | −0.121104 | ||||||||
\(298\) | −1.27275e21 | −1.18551 | ||||||||
\(299\) | −1.59797e21 | −1.44665 | ||||||||
\(300\) | 8.16706e20 | 0.718680 | ||||||||
\(301\) | 1.57154e20 | 0.134435 | ||||||||
\(302\) | 1.90683e21 | 1.58581 | ||||||||
\(303\) | 7.81068e20 | 0.631577 | ||||||||
\(304\) | 2.88725e21 | 2.27017 | ||||||||
\(305\) | −1.48804e21 | −1.13780 | ||||||||
\(306\) | −7.05748e20 | −0.524828 | ||||||||
\(307\) | 2.41849e21 | 1.74932 | 0.874659 | − | 0.484739i | \(-0.161085\pi\) | ||||
0.874659 | + | 0.484739i | \(0.161085\pi\) | |||||||
\(308\) | −2.16943e20 | −0.152639 | ||||||||
\(309\) | −2.48577e20 | −0.170143 | ||||||||
\(310\) | −2.34621e21 | −1.56240 | ||||||||
\(311\) | 9.44749e20 | 0.612144 | 0.306072 | − | 0.952008i | \(-0.400985\pi\) | ||||
0.306072 | + | 0.952008i | \(0.400985\pi\) | |||||||
\(312\) | −1.85121e21 | −1.16719 | ||||||||
\(313\) | −2.44821e21 | −1.50218 | −0.751089 | − | 0.660201i | \(-0.770471\pi\) | ||||
−0.751089 | + | 0.660201i | \(0.770471\pi\) | |||||||
\(314\) | −2.30432e21 | −1.37607 | ||||||||
\(315\) | −7.45364e19 | −0.0433240 | ||||||||
\(316\) | 3.86886e21 | 2.18899 | ||||||||
\(317\) | 3.49751e21 | 1.92644 | 0.963219 | − | 0.268718i | \(-0.0866001\pi\) | ||||
0.963219 | + | 0.268718i | \(0.0866001\pi\) | |||||||
\(318\) | −6.09397e20 | −0.326791 | ||||||||
\(319\) | 4.39423e20 | 0.229436 | ||||||||
\(320\) | −9.01241e20 | −0.458212 | ||||||||
\(321\) | −3.66690e20 | −0.181554 | ||||||||
\(322\) | 6.77560e20 | 0.326718 | ||||||||
\(323\) | −2.04727e21 | −0.961511 | ||||||||
\(324\) | 5.62112e20 | 0.257152 | ||||||||
\(325\) | −1.01966e21 | −0.454408 | ||||||||
\(326\) | −7.59381e20 | −0.329693 | ||||||||
\(327\) | 2.23347e21 | 0.944768 | ||||||||
\(328\) | −3.78126e21 | −1.55851 | ||||||||
\(329\) | −2.59074e20 | −0.104054 | ||||||||
\(330\) | 2.09558e21 | 0.820232 | ||||||||
\(331\) | −1.98378e20 | −0.0756754 | −0.0378377 | − | 0.999284i | \(-0.512047\pi\) | ||||
−0.0378377 | + | 0.999284i | \(0.512047\pi\) | |||||||
\(332\) | −4.33444e21 | −1.61161 | ||||||||
\(333\) | 1.13425e21 | 0.411086 | ||||||||
\(334\) | 2.56979e21 | 0.907932 | ||||||||
\(335\) | 2.01273e21 | 0.693274 | ||||||||
\(336\) | 3.67924e20 | 0.123559 | ||||||||
\(337\) | −4.38592e21 | −1.43617 | −0.718087 | − | 0.695954i | \(-0.754982\pi\) | ||||
−0.718087 | + | 0.695954i | \(0.754982\pi\) | |||||||
\(338\) | −1.63188e21 | −0.521070 | ||||||||
\(339\) | −6.91602e19 | −0.0215357 | ||||||||
\(340\) | 8.17333e21 | 2.48215 | ||||||||
\(341\) | −1.47024e21 | −0.435487 | ||||||||
\(342\) | 2.33516e21 | 0.674676 | ||||||||
\(343\) | −7.39657e20 | −0.208464 | ||||||||
\(344\) | 1.11631e22 | 3.06928 | ||||||||
\(345\) | −4.57024e21 | −1.22596 | ||||||||
\(346\) | −4.54625e20 | −0.118989 | ||||||||
\(347\) | −1.91053e20 | −0.0487926 | −0.0243963 | − | 0.999702i | \(-0.507766\pi\) | ||||
−0.0243963 | + | 0.999702i | \(0.507766\pi\) | |||||||
\(348\) | −1.95487e21 | −0.487186 | ||||||||
\(349\) | −3.63772e21 | −0.884735 | −0.442368 | − | 0.896834i | \(-0.645861\pi\) | ||||
−0.442368 | + | 0.896834i | \(0.645861\pi\) | |||||||
\(350\) | 4.32349e20 | 0.102626 | ||||||||
\(351\) | −7.01797e20 | −0.162593 | ||||||||
\(352\) | −3.68576e21 | −0.833517 | ||||||||
\(353\) | 3.41663e21 | 0.754245 | 0.377123 | − | 0.926163i | \(-0.376913\pi\) | ||||
0.377123 | + | 0.926163i | \(0.376913\pi\) | |||||||
\(354\) | −4.24193e20 | −0.0914189 | ||||||||
\(355\) | 6.68866e21 | 1.40734 | ||||||||
\(356\) | −1.14611e22 | −2.35451 | ||||||||
\(357\) | −2.60885e20 | −0.0523323 | ||||||||
\(358\) | −1.03925e21 | −0.203570 | ||||||||
\(359\) | −1.00013e22 | −1.91317 | −0.956587 | − | 0.291447i | \(-0.905863\pi\) | ||||
−0.956587 | + | 0.291447i | \(0.905863\pi\) | |||||||
\(360\) | −5.29451e21 | −0.989132 | ||||||||
\(361\) | 1.29359e21 | 0.236039 | ||||||||
\(362\) | −5.71091e21 | −1.01785 | ||||||||
\(363\) | −2.00306e21 | −0.348728 | ||||||||
\(364\) | −1.20495e21 | −0.204931 | ||||||||
\(365\) | 1.41046e22 | 2.34353 | ||||||||
\(366\) | 5.94068e21 | 0.964378 | ||||||||
\(367\) | 1.19598e22 | 1.89698 | 0.948490 | − | 0.316807i | \(-0.102611\pi\) | ||||
0.948490 | + | 0.316807i | \(0.102611\pi\) | |||||||
\(368\) | 2.25595e22 | 3.49642 | ||||||||
\(369\) | −1.43349e21 | −0.217105 | ||||||||
\(370\) | −1.88116e22 | −2.78427 | ||||||||
\(371\) | −2.25269e20 | −0.0325853 | ||||||||
\(372\) | 6.54067e21 | 0.924714 | ||||||||
\(373\) | 6.67362e21 | 0.922224 | 0.461112 | − | 0.887342i | \(-0.347451\pi\) | ||||
0.461112 | + | 0.887342i | \(0.347451\pi\) | |||||||
\(374\) | 7.33477e21 | 0.990782 | ||||||||
\(375\) | 2.50578e21 | 0.330885 | ||||||||
\(376\) | −1.84027e22 | −2.37566 | ||||||||
\(377\) | 2.44066e21 | 0.308039 | ||||||||
\(378\) | 2.97572e20 | 0.0367207 | ||||||||
\(379\) | −1.30692e22 | −1.57694 | −0.788470 | − | 0.615073i | \(-0.789127\pi\) | ||||
−0.788470 | + | 0.615073i | \(0.789127\pi\) | |||||||
\(380\) | −2.70437e22 | −3.19085 | ||||||||
\(381\) | −4.80570e21 | −0.554491 | ||||||||
\(382\) | 2.01543e22 | 2.27420 | ||||||||
\(383\) | 7.55282e19 | 0.00833527 | 0.00416763 | − | 0.999991i | \(-0.498673\pi\) | ||||
0.00416763 | + | 0.999991i | \(0.498673\pi\) | |||||||
\(384\) | −3.48681e21 | −0.376368 | ||||||||
\(385\) | 7.74650e20 | 0.0817879 | ||||||||
\(386\) | −5.58706e21 | −0.577021 | ||||||||
\(387\) | 4.23195e21 | 0.427561 | ||||||||
\(388\) | 3.31875e22 | 3.28024 | ||||||||
\(389\) | 3.90337e21 | 0.377457 | 0.188729 | − | 0.982029i | \(-0.439563\pi\) | ||||
0.188729 | + | 0.982029i | \(0.439563\pi\) | |||||||
\(390\) | 1.16394e22 | 1.10124 | ||||||||
\(391\) | −1.59963e22 | −1.48087 | ||||||||
\(392\) | −2.61248e22 | −2.36658 | ||||||||
\(393\) | −1.77732e21 | −0.157554 | ||||||||
\(394\) | −6.73437e20 | −0.0584224 | ||||||||
\(395\) | −1.38147e22 | −1.17292 | ||||||||
\(396\) | −5.84198e21 | −0.485457 | ||||||||
\(397\) | 6.50366e21 | 0.528979 | 0.264489 | − | 0.964389i | \(-0.414797\pi\) | ||||
0.264489 | + | 0.964389i | \(0.414797\pi\) | |||||||
\(398\) | 8.99155e21 | 0.715860 | ||||||||
\(399\) | 8.63212e20 | 0.0672741 | ||||||||
\(400\) | 1.43951e22 | 1.09826 | ||||||||
\(401\) | 2.12436e21 | 0.158672 | 0.0793361 | − | 0.996848i | \(-0.474720\pi\) | ||||
0.0793361 | + | 0.996848i | \(0.474720\pi\) | |||||||
\(402\) | −8.03543e21 | −0.587608 | ||||||||
\(403\) | −8.16604e21 | −0.584680 | ||||||||
\(404\) | 3.61128e22 | 2.53175 | ||||||||
\(405\) | −2.00716e21 | −0.137789 | ||||||||
\(406\) | −1.03487e21 | −0.0695689 | ||||||||
\(407\) | −1.17881e22 | −0.776056 | ||||||||
\(408\) | −1.85313e22 | −1.19480 | ||||||||
\(409\) | −1.66641e22 | −1.05229 | −0.526143 | − | 0.850396i | \(-0.676362\pi\) | ||||
−0.526143 | + | 0.850396i | \(0.676362\pi\) | |||||||
\(410\) | 2.37745e22 | 1.47044 | ||||||||
\(411\) | 1.71086e22 | 1.03648 | ||||||||
\(412\) | −1.14930e22 | −0.682037 | ||||||||
\(413\) | −1.56806e20 | −0.00911566 | ||||||||
\(414\) | 1.82458e22 | 1.03911 | ||||||||
\(415\) | 1.54772e22 | 0.863542 | ||||||||
\(416\) | −2.04716e22 | −1.11907 | ||||||||
\(417\) | 6.97028e21 | 0.373331 | ||||||||
\(418\) | −2.42692e22 | −1.27367 | ||||||||
\(419\) | 2.00258e22 | 1.02984 | 0.514920 | − | 0.857238i | \(-0.327822\pi\) | ||||
0.514920 | + | 0.857238i | \(0.327822\pi\) | |||||||
\(420\) | −3.44620e21 | −0.173669 | ||||||||
\(421\) | 1.39887e22 | 0.690846 | 0.345423 | − | 0.938447i | \(-0.387736\pi\) | ||||
0.345423 | + | 0.938447i | \(0.387736\pi\) | |||||||
\(422\) | 2.33393e22 | 1.12962 | ||||||||
\(423\) | −6.97651e21 | −0.330937 | ||||||||
\(424\) | −1.60014e22 | −0.743958 | ||||||||
\(425\) | −1.02072e22 | −0.465159 | ||||||||
\(426\) | −2.67031e22 | −1.19284 | ||||||||
\(427\) | 2.19602e21 | 0.0961612 | ||||||||
\(428\) | −1.69540e22 | −0.727779 | ||||||||
\(429\) | 7.29372e21 | 0.306946 | ||||||||
\(430\) | −7.01873e22 | −2.89585 | ||||||||
\(431\) | −3.18029e22 | −1.28650 | −0.643250 | − | 0.765656i | \(-0.722414\pi\) | ||||
−0.643250 | + | 0.765656i | \(0.722414\pi\) | |||||||
\(432\) | 9.90770e21 | 0.392972 | ||||||||
\(433\) | −1.40201e22 | −0.545259 | −0.272630 | − | 0.962119i | \(-0.587893\pi\) | ||||
−0.272630 | + | 0.962119i | \(0.587893\pi\) | |||||||
\(434\) | 3.46251e21 | 0.132047 | ||||||||
\(435\) | 6.98036e21 | 0.261047 | ||||||||
\(436\) | 1.03265e23 | 3.78720 | ||||||||
\(437\) | 5.29284e22 | 1.90369 | ||||||||
\(438\) | −5.63098e22 | −1.98634 | ||||||||
\(439\) | 6.28127e21 | 0.217320 | 0.108660 | − | 0.994079i | \(-0.465344\pi\) | ||||
0.108660 | + | 0.994079i | \(0.465344\pi\) | |||||||
\(440\) | 5.50254e22 | 1.86730 | ||||||||
\(441\) | −9.90398e21 | −0.329672 | ||||||||
\(442\) | 4.07391e22 | 1.33021 | ||||||||
\(443\) | −2.96942e22 | −0.951131 | −0.475566 | − | 0.879680i | \(-0.657757\pi\) | ||||
−0.475566 | + | 0.879680i | \(0.657757\pi\) | |||||||
\(444\) | 5.24422e22 | 1.64788 | ||||||||
\(445\) | 4.09246e22 | 1.26161 | ||||||||
\(446\) | −7.08955e22 | −2.14423 | ||||||||
\(447\) | −1.26695e22 | −0.375962 | ||||||||
\(448\) | 1.33004e21 | 0.0387259 | ||||||||
\(449\) | −6.58706e22 | −1.88190 | −0.940952 | − | 0.338540i | \(-0.890067\pi\) | ||||
−0.940952 | + | 0.338540i | \(0.890067\pi\) | |||||||
\(450\) | 1.16426e22 | 0.326394 | ||||||||
\(451\) | 1.48981e22 | 0.409855 | ||||||||
\(452\) | −3.19764e21 | −0.0863281 | ||||||||
\(453\) | 1.89813e22 | 0.502911 | ||||||||
\(454\) | −2.10362e22 | −0.547007 | ||||||||
\(455\) | 4.30259e21 | 0.109808 | ||||||||
\(456\) | 6.13162e22 | 1.53594 | ||||||||
\(457\) | −4.15015e22 | −1.02041 | −0.510207 | − | 0.860052i | \(-0.670431\pi\) | ||||
−0.510207 | + | 0.860052i | \(0.670431\pi\) | |||||||
\(458\) | −2.38791e22 | −0.576317 | ||||||||
\(459\) | −7.02528e21 | −0.166439 | ||||||||
\(460\) | −2.11306e23 | −4.91440 | ||||||||
\(461\) | 5.89682e22 | 1.34636 | 0.673178 | − | 0.739480i | \(-0.264929\pi\) | ||||
0.673178 | + | 0.739480i | \(0.264929\pi\) | |||||||
\(462\) | −3.09263e21 | −0.0693221 | ||||||||
\(463\) | 5.09403e22 | 1.12104 | 0.560522 | − | 0.828139i | \(-0.310600\pi\) | ||||
0.560522 | + | 0.828139i | \(0.310600\pi\) | |||||||
\(464\) | −3.44563e22 | −0.744501 | ||||||||
\(465\) | −2.33551e22 | −0.495487 | ||||||||
\(466\) | 9.24049e22 | 1.92493 | ||||||||
\(467\) | 3.80032e22 | 0.777369 | 0.388684 | − | 0.921371i | \(-0.372930\pi\) | ||||
0.388684 | + | 0.921371i | \(0.372930\pi\) | |||||||
\(468\) | −3.24477e22 | −0.651771 | ||||||||
\(469\) | −2.97036e21 | −0.0585922 | ||||||||
\(470\) | 1.15706e23 | 2.24143 | ||||||||
\(471\) | −2.29381e22 | −0.436395 | ||||||||
\(472\) | −1.11384e22 | −0.208120 | ||||||||
\(473\) | −4.39823e22 | −0.807158 | ||||||||
\(474\) | 5.51526e22 | 0.994146 | ||||||||
\(475\) | 3.37734e22 | 0.597970 | ||||||||
\(476\) | −1.20621e22 | −0.209780 | ||||||||
\(477\) | −6.06617e21 | −0.103636 | ||||||||
\(478\) | 1.04889e23 | 1.76032 | ||||||||
\(479\) | 2.68315e22 | 0.442378 | 0.221189 | − | 0.975231i | \(-0.429006\pi\) | ||||
0.221189 | + | 0.975231i | \(0.429006\pi\) | |||||||
\(480\) | −5.85494e22 | −0.948357 | ||||||||
\(481\) | −6.54741e22 | −1.04193 | ||||||||
\(482\) | −4.70030e22 | −0.734895 | ||||||||
\(483\) | 6.74470e21 | 0.103612 | ||||||||
\(484\) | −9.26117e22 | −1.39791 | ||||||||
\(485\) | −1.18504e23 | −1.75764 | ||||||||
\(486\) | 8.01319e21 | 0.116788 | ||||||||
\(487\) | −1.42499e22 | −0.204088 | −0.102044 | − | 0.994780i | \(-0.532538\pi\) | ||||
−0.102044 | + | 0.994780i | \(0.532538\pi\) | |||||||
\(488\) | 1.55989e23 | 2.19546 | ||||||||
\(489\) | −7.55917e21 | −0.104556 | ||||||||
\(490\) | 1.64258e23 | 2.23286 | ||||||||
\(491\) | 8.22531e22 | 1.09890 | 0.549452 | − | 0.835525i | \(-0.314837\pi\) | ||||
0.549452 | + | 0.835525i | \(0.314837\pi\) | |||||||
\(492\) | −6.62775e22 | −0.870287 | ||||||||
\(493\) | 2.44320e22 | 0.315327 | ||||||||
\(494\) | −1.34797e23 | −1.71001 | ||||||||
\(495\) | 2.08603e22 | 0.260121 | ||||||||
\(496\) | 1.15285e23 | 1.41312 | ||||||||
\(497\) | −9.87103e21 | −0.118941 | ||||||||
\(498\) | −6.17896e22 | −0.731924 | ||||||||
\(499\) | −1.57611e23 | −1.83541 | −0.917703 | − | 0.397267i | \(-0.869959\pi\) | ||||
−0.917703 | + | 0.397267i | \(0.869959\pi\) | |||||||
\(500\) | 1.15855e23 | 1.32639 | ||||||||
\(501\) | 2.55807e22 | 0.287933 | ||||||||
\(502\) | −1.11545e23 | −1.23444 | ||||||||
\(503\) | 1.64035e23 | 1.78488 | 0.892439 | − | 0.451169i | \(-0.148993\pi\) | ||||
0.892439 | + | 0.451169i | \(0.148993\pi\) | |||||||
\(504\) | 7.81356e21 | 0.0835968 | ||||||||
\(505\) | −1.28950e23 | −1.35658 | ||||||||
\(506\) | −1.89627e23 | −1.96164 | ||||||||
\(507\) | −1.62443e22 | −0.165247 | ||||||||
\(508\) | −2.22192e23 | −2.22274 | ||||||||
\(509\) | 6.26797e22 | 0.616632 | 0.308316 | − | 0.951284i | \(-0.400235\pi\) | ||||
0.308316 | + | 0.951284i | \(0.400235\pi\) | |||||||
\(510\) | 1.16515e23 | 1.12729 | ||||||||
\(511\) | −2.08154e22 | −0.198064 | ||||||||
\(512\) | −2.33093e23 | −2.18139 | ||||||||
\(513\) | 2.32451e22 | 0.213961 | ||||||||
\(514\) | 3.05182e23 | 2.76295 | ||||||||
\(515\) | 4.10387e22 | 0.365454 | ||||||||
\(516\) | 1.95665e23 | 1.71392 | ||||||||
\(517\) | 7.25063e22 | 0.624750 | ||||||||
\(518\) | 2.77619e22 | 0.235313 | ||||||||
\(519\) | −4.52551e21 | −0.0377351 | ||||||||
\(520\) | 3.05624e23 | 2.50703 | ||||||||
\(521\) | 2.67297e21 | 0.0215712 | 0.0107856 | − | 0.999942i | \(-0.496567\pi\) | ||||
0.0107856 | + | 0.999942i | \(0.496567\pi\) | |||||||
\(522\) | −2.78677e22 | −0.221259 | ||||||||
\(523\) | −1.11499e22 | −0.0870975 | −0.0435487 | − | 0.999051i | \(-0.513866\pi\) | ||||
−0.0435487 | + | 0.999051i | \(0.513866\pi\) | |||||||
\(524\) | −8.21748e22 | −0.631572 | ||||||||
\(525\) | 4.30377e21 | 0.0325458 | ||||||||
\(526\) | −3.50538e23 | −2.60829 | ||||||||
\(527\) | −8.17454e22 | −0.598512 | ||||||||
\(528\) | −1.02970e23 | −0.741860 | ||||||||
\(529\) | 2.72505e23 | 1.93198 | ||||||||
\(530\) | 1.00608e23 | 0.701920 | ||||||||
\(531\) | −4.22258e21 | −0.0289918 | ||||||||
\(532\) | 3.99108e22 | 0.269675 | ||||||||
\(533\) | 8.27475e22 | 0.550267 | ||||||||
\(534\) | −1.63383e23 | −1.06932 | ||||||||
\(535\) | 6.05384e22 | 0.389963 | ||||||||
\(536\) | −2.10992e23 | −1.33772 | ||||||||
\(537\) | −1.03451e22 | −0.0645584 | ||||||||
\(538\) | −1.50676e23 | −0.925537 | ||||||||
\(539\) | 1.02931e23 | 0.622361 | ||||||||
\(540\) | −9.28016e22 | −0.552342 | ||||||||
\(541\) | 1.32087e23 | 0.773895 | 0.386948 | − | 0.922102i | \(-0.373529\pi\) | ||||
0.386948 | + | 0.922102i | \(0.373529\pi\) | |||||||
\(542\) | −2.56055e23 | −1.47686 | ||||||||
\(543\) | −5.68486e22 | −0.322791 | ||||||||
\(544\) | −2.04929e23 | −1.14555 | ||||||||
\(545\) | −3.68734e23 | −2.02929 | ||||||||
\(546\) | −1.71772e22 | −0.0930712 | ||||||||
\(547\) | −1.49221e23 | −0.796044 | −0.398022 | − | 0.917376i | \(-0.630303\pi\) | ||||
−0.398022 | + | 0.917376i | \(0.630303\pi\) | |||||||
\(548\) | 7.91020e23 | 4.15482 | ||||||||
\(549\) | 5.91359e22 | 0.305834 | ||||||||
\(550\) | −1.21000e23 | −0.616174 | ||||||||
\(551\) | −8.08402e22 | −0.405358 | ||||||||
\(552\) | 4.79093e23 | 2.36558 | ||||||||
\(553\) | 2.03876e22 | 0.0991295 | ||||||||
\(554\) | 5.70806e23 | 2.73310 | ||||||||
\(555\) | −1.87258e23 | −0.882979 | ||||||||
\(556\) | 3.22272e23 | 1.49654 | ||||||||
\(557\) | −1.16177e23 | −0.531314 | −0.265657 | − | 0.964068i | \(-0.585589\pi\) | ||||
−0.265657 | + | 0.964068i | \(0.585589\pi\) | |||||||
\(558\) | 9.32406e22 | 0.419966 | ||||||||
\(559\) | −2.44288e23 | −1.08368 | ||||||||
\(560\) | −6.07423e22 | −0.265395 | ||||||||
\(561\) | 7.30132e22 | 0.314208 | ||||||||
\(562\) | 7.15591e22 | 0.303324 | ||||||||
\(563\) | −1.98226e23 | −0.827635 | −0.413818 | − | 0.910360i | \(-0.635805\pi\) | ||||
−0.413818 | + | 0.910360i | \(0.635805\pi\) | |||||||
\(564\) | −3.22561e23 | −1.32660 | ||||||||
\(565\) | 1.14180e22 | 0.0462569 | ||||||||
\(566\) | 2.75222e23 | 1.09836 | ||||||||
\(567\) | 2.96214e21 | 0.0116453 | ||||||||
\(568\) | −7.01164e23 | −2.71556 | ||||||||
\(569\) | −1.75181e23 | −0.668393 | −0.334196 | − | 0.942504i | \(-0.608465\pi\) | ||||
−0.334196 | + | 0.942504i | \(0.608465\pi\) | |||||||
\(570\) | −3.85522e23 | −1.44915 | ||||||||
\(571\) | 2.24895e23 | 0.832862 | 0.416431 | − | 0.909167i | \(-0.363281\pi\) | ||||
0.416431 | + | 0.909167i | \(0.363281\pi\) | |||||||
\(572\) | 3.37227e23 | 1.23043 | ||||||||
\(573\) | 2.00624e23 | 0.721220 | ||||||||
\(574\) | −3.50861e22 | −0.124275 | ||||||||
\(575\) | 2.63888e23 | 0.920965 | ||||||||
\(576\) | 3.58161e22 | 0.123165 | ||||||||
\(577\) | 1.19606e23 | 0.405282 | 0.202641 | − | 0.979253i | \(-0.435048\pi\) | ||||
0.202641 | + | 0.979253i | \(0.435048\pi\) | |||||||
\(578\) | −1.37424e23 | −0.458857 | ||||||||
\(579\) | −5.56158e22 | −0.182991 | ||||||||
\(580\) | 3.22738e23 | 1.04644 | ||||||||
\(581\) | −2.28410e22 | −0.0729825 | ||||||||
\(582\) | 4.73105e23 | 1.48975 | ||||||||
\(583\) | 6.30452e22 | 0.195645 | ||||||||
\(584\) | −1.47857e24 | −4.52202 | ||||||||
\(585\) | 1.15863e23 | 0.349236 | ||||||||
\(586\) | 1.79155e23 | 0.532231 | ||||||||
\(587\) | −3.75879e23 | −1.10059 | −0.550294 | − | 0.834971i | \(-0.685484\pi\) | ||||
−0.550294 | + | 0.834971i | \(0.685484\pi\) | |||||||
\(588\) | −4.57913e23 | −1.32152 | ||||||||
\(589\) | 2.70478e23 | 0.769399 | ||||||||
\(590\) | 7.00319e22 | 0.196360 | ||||||||
\(591\) | −6.70365e21 | −0.0185275 | ||||||||
\(592\) | 9.24338e23 | 2.51824 | ||||||||
\(593\) | 5.09614e23 | 1.36860 | 0.684299 | − | 0.729201i | \(-0.260108\pi\) | ||||
0.684299 | + | 0.729201i | \(0.260108\pi\) | |||||||
\(594\) | −8.32804e22 | −0.220474 | ||||||||
\(595\) | 4.30707e22 | 0.112406 | ||||||||
\(596\) | −5.85775e23 | −1.50709 | ||||||||
\(597\) | 8.95053e22 | 0.227022 | ||||||||
\(598\) | −1.05323e24 | −2.63369 | ||||||||
\(599\) | 1.79949e23 | 0.443631 | 0.221816 | − | 0.975089i | \(-0.428802\pi\) | ||||
0.221816 | + | 0.975089i | \(0.428802\pi\) | |||||||
\(600\) | 3.05708e23 | 0.743055 | ||||||||
\(601\) | −2.48454e23 | −0.595406 | −0.297703 | − | 0.954659i | \(-0.596220\pi\) | ||||
−0.297703 | + | 0.954659i | \(0.596220\pi\) | |||||||
\(602\) | 1.03581e23 | 0.244744 | ||||||||
\(603\) | −7.99878e22 | −0.186349 | ||||||||
\(604\) | 8.77603e23 | 2.01597 | ||||||||
\(605\) | 3.30693e23 | 0.749040 | ||||||||
\(606\) | 5.14807e23 | 1.14981 | ||||||||
\(607\) | −6.42239e23 | −1.41447 | −0.707233 | − | 0.706980i | \(-0.750057\pi\) | ||||
−0.707233 | + | 0.706980i | \(0.750057\pi\) | |||||||
\(608\) | 6.78066e23 | 1.47262 | ||||||||
\(609\) | −1.03015e22 | −0.0220625 | ||||||||
\(610\) | −9.80774e23 | −2.07141 | ||||||||
\(611\) | 4.02717e23 | 0.838783 | ||||||||
\(612\) | −3.24815e23 | −0.667190 | ||||||||
\(613\) | −1.05608e23 | −0.213936 | −0.106968 | − | 0.994262i | \(-0.534114\pi\) | ||||
−0.106968 | + | 0.994262i | \(0.534114\pi\) | |||||||
\(614\) | 1.59404e24 | 3.18470 | ||||||||
\(615\) | 2.36660e23 | 0.466323 | ||||||||
\(616\) | −8.12057e22 | −0.157816 | ||||||||
\(617\) | −7.88025e23 | −1.51048 | −0.755242 | − | 0.655446i | \(-0.772481\pi\) | ||||
−0.755242 | + | 0.655446i | \(0.772481\pi\) | |||||||
\(618\) | −1.63839e23 | −0.309753 | ||||||||
\(619\) | 5.08064e23 | 0.947432 | 0.473716 | − | 0.880678i | \(-0.342912\pi\) | ||||
0.473716 | + | 0.880678i | \(0.342912\pi\) | |||||||
\(620\) | −1.07983e24 | −1.98621 | ||||||||
\(621\) | 1.81626e23 | 0.329533 | ||||||||
\(622\) | 6.22690e23 | 1.11443 | ||||||||
\(623\) | −6.03960e22 | −0.106625 | ||||||||
\(624\) | −5.71919e23 | −0.996014 | ||||||||
\(625\) | −7.26762e23 | −1.24857 | ||||||||
\(626\) | −1.61363e24 | −2.73478 | ||||||||
\(627\) | −2.41585e23 | −0.403920 | ||||||||
\(628\) | −1.06055e24 | −1.74934 | ||||||||
\(629\) | −6.55423e23 | −1.06658 | ||||||||
\(630\) | −4.91274e22 | −0.0788731 | ||||||||
\(631\) | −6.58521e23 | −1.04309 | −0.521543 | − | 0.853225i | \(-0.674643\pi\) | ||||
−0.521543 | + | 0.853225i | \(0.674643\pi\) | |||||||
\(632\) | 1.44818e24 | 2.26323 | ||||||||
\(633\) | 2.32328e23 | 0.358237 | ||||||||
\(634\) | 2.30523e24 | 3.50716 | ||||||||
\(635\) | 7.93394e23 | 1.19100 | ||||||||
\(636\) | −2.80471e23 | −0.415434 | ||||||||
\(637\) | 5.71704e23 | 0.835576 | ||||||||
\(638\) | 2.89627e23 | 0.417698 | ||||||||
\(639\) | −2.65813e23 | −0.378285 | ||||||||
\(640\) | 5.75653e23 | 0.808409 | ||||||||
\(641\) | 8.38263e23 | 1.16168 | 0.580841 | − | 0.814017i | \(-0.302724\pi\) | ||||
0.580841 | + | 0.814017i | \(0.302724\pi\) | |||||||
\(642\) | −2.41687e23 | −0.330527 | ||||||||
\(643\) | 4.04743e23 | 0.546243 | 0.273122 | − | 0.961980i | \(-0.411944\pi\) | ||||
0.273122 | + | 0.961980i | \(0.411944\pi\) | |||||||
\(644\) | 3.11843e23 | 0.415342 | ||||||||
\(645\) | −6.98672e23 | −0.918365 | ||||||||
\(646\) | −1.34937e24 | −1.75047 | ||||||||
\(647\) | 1.11703e24 | 1.43014 | 0.715068 | − | 0.699055i | \(-0.246396\pi\) | ||||
0.715068 | + | 0.699055i | \(0.246396\pi\) | |||||||
\(648\) | 2.10409e23 | 0.265874 | ||||||||
\(649\) | 4.38849e22 | 0.0547313 | ||||||||
\(650\) | −6.72063e23 | −0.827269 | ||||||||
\(651\) | 3.44672e22 | 0.0418762 | ||||||||
\(652\) | −3.49500e23 | −0.419124 | ||||||||
\(653\) | −7.44989e23 | −0.881836 | −0.440918 | − | 0.897547i | \(-0.645347\pi\) | ||||
−0.440918 | + | 0.897547i | \(0.645347\pi\) | |||||||
\(654\) | 1.47210e24 | 1.71999 | ||||||||
\(655\) | 2.93426e23 | 0.338413 | ||||||||
\(656\) | −1.16820e24 | −1.32994 | ||||||||
\(657\) | −5.60529e23 | −0.629931 | ||||||||
\(658\) | −1.70757e23 | −0.189435 | ||||||||
\(659\) | −1.19920e24 | −1.31331 | −0.656653 | − | 0.754192i | \(-0.728029\pi\) | ||||
−0.656653 | + | 0.754192i | \(0.728029\pi\) | |||||||
\(660\) | 9.64478e23 | 1.04272 | ||||||||
\(661\) | −8.62286e22 | −0.0920320 | −0.0460160 | − | 0.998941i | \(-0.514653\pi\) | ||||
−0.0460160 | + | 0.998941i | \(0.514653\pi\) | |||||||
\(662\) | −1.30752e23 | −0.137770 | ||||||||
\(663\) | 4.05532e23 | 0.421852 | ||||||||
\(664\) | −1.62246e24 | −1.66627 | ||||||||
\(665\) | −1.42511e23 | −0.144499 | ||||||||
\(666\) | 7.47590e23 | 0.748398 | ||||||||
\(667\) | −6.31644e23 | −0.624313 | ||||||||
\(668\) | 1.18273e24 | 1.15421 | ||||||||
\(669\) | −7.05721e23 | −0.680003 | ||||||||
\(670\) | 1.32660e24 | 1.26213 | ||||||||
\(671\) | −6.14594e23 | −0.577360 | ||||||||
\(672\) | 8.64064e22 | 0.0801506 | ||||||||
\(673\) | 1.93031e24 | 1.76807 | 0.884033 | − | 0.467425i | \(-0.154818\pi\) | ||||
0.884033 | + | 0.467425i | \(0.154818\pi\) | |||||||
\(674\) | −2.89079e24 | −2.61461 | ||||||||
\(675\) | 1.15895e23 | 0.103510 | ||||||||
\(676\) | −7.51061e23 | −0.662412 | ||||||||
\(677\) | −9.44660e22 | −0.0822757 | −0.0411379 | − | 0.999153i | \(-0.513098\pi\) | ||||
−0.0411379 | + | 0.999153i | \(0.513098\pi\) | |||||||
\(678\) | −4.55839e22 | −0.0392066 | ||||||||
\(679\) | 1.74887e23 | 0.148547 | ||||||||
\(680\) | 3.05942e24 | 2.56634 | ||||||||
\(681\) | −2.09403e23 | −0.173473 | ||||||||
\(682\) | −9.69042e23 | −0.792821 | ||||||||
\(683\) | 1.90689e24 | 1.54081 | 0.770404 | − | 0.637556i | \(-0.220055\pi\) | ||||
0.770404 | + | 0.637556i | \(0.220055\pi\) | |||||||
\(684\) | 1.07474e24 | 0.857685 | ||||||||
\(685\) | −2.82453e24 | −2.22627 | ||||||||
\(686\) | −4.87513e23 | −0.379517 | ||||||||
\(687\) | −2.37702e23 | −0.182768 | ||||||||
\(688\) | 3.44876e24 | 2.61916 | ||||||||
\(689\) | 3.50168e23 | 0.262672 | ||||||||
\(690\) | −3.01228e24 | −2.23191 | ||||||||
\(691\) | 1.44684e24 | 1.05890 | 0.529451 | − | 0.848341i | \(-0.322398\pi\) | ||||
0.529451 | + | 0.848341i | \(0.322398\pi\) | |||||||
\(692\) | −2.09238e23 | −0.151265 | ||||||||
\(693\) | −3.07853e22 | −0.0219842 | ||||||||
\(694\) | −1.25924e23 | −0.0888289 | ||||||||
\(695\) | −1.15075e24 | −0.801884 | ||||||||
\(696\) | −7.31743e23 | −0.503710 | ||||||||
\(697\) | 8.28337e23 | 0.563285 | ||||||||
\(698\) | −2.39765e24 | −1.61070 | ||||||||
\(699\) | 9.19834e23 | 0.610455 | ||||||||
\(700\) | 1.98986e23 | 0.130463 | ||||||||
\(701\) | 3.28966e23 | 0.213083 | 0.106541 | − | 0.994308i | \(-0.466022\pi\) | ||||
0.106541 | + | 0.994308i | \(0.466022\pi\) | |||||||
\(702\) | −4.62559e23 | −0.296007 | ||||||||
\(703\) | 2.16865e24 | 1.37110 | ||||||||
\(704\) | −3.72234e23 | −0.232514 | ||||||||
\(705\) | 1.15178e24 | 0.710826 | ||||||||
\(706\) | 2.25192e24 | 1.37313 | ||||||||
\(707\) | 1.90303e23 | 0.114651 | ||||||||
\(708\) | −1.95232e23 | −0.116217 | ||||||||
\(709\) | −3.08015e24 | −1.81167 | −0.905833 | − | 0.423634i | \(-0.860754\pi\) | ||||
−0.905833 | + | 0.423634i | \(0.860754\pi\) | |||||||
\(710\) | 4.40854e24 | 2.56211 | ||||||||
\(711\) | 5.49011e23 | 0.315275 | ||||||||
\(712\) | −4.29008e24 | −2.43437 | ||||||||
\(713\) | 2.11337e24 | 1.18499 | ||||||||
\(714\) | −1.71951e23 | −0.0952731 | ||||||||
\(715\) | −1.20415e24 | −0.659295 | ||||||||
\(716\) | −4.78307e23 | −0.258789 | ||||||||
\(717\) | 1.04410e24 | 0.558252 | ||||||||
\(718\) | −6.59193e24 | −3.48301 | ||||||||
\(719\) | −1.08990e24 | −0.569103 | −0.284551 | − | 0.958661i | \(-0.591845\pi\) | ||||
−0.284551 | + | 0.958661i | \(0.591845\pi\) | |||||||
\(720\) | −1.63571e24 | −0.844071 | ||||||||
\(721\) | −6.05644e22 | −0.0308864 | ||||||||
\(722\) | 8.52611e23 | 0.429719 | ||||||||
\(723\) | −4.67886e23 | −0.233058 | ||||||||
\(724\) | −2.62841e24 | −1.29394 | ||||||||
\(725\) | −4.03050e23 | −0.196104 | ||||||||
\(726\) | −1.32023e24 | −0.634874 | ||||||||
\(727\) | 1.49760e24 | 0.711795 | 0.355897 | − | 0.934525i | \(-0.384175\pi\) | ||||
0.355897 | + | 0.934525i | \(0.384175\pi\) | |||||||
\(728\) | −4.51035e23 | −0.211882 | ||||||||
\(729\) | 7.97664e22 | 0.0370370 | ||||||||
\(730\) | 9.29643e24 | 4.26650 | ||||||||
\(731\) | −2.44543e24 | −1.10932 | ||||||||
\(732\) | 2.73416e24 | 1.22597 | ||||||||
\(733\) | −9.64969e23 | −0.427691 | −0.213845 | − | 0.976868i | \(-0.568599\pi\) | ||||
−0.213845 | + | 0.976868i | \(0.568599\pi\) | |||||||
\(734\) | 7.88279e24 | 3.45353 | ||||||||
\(735\) | 1.63509e24 | 0.708108 | ||||||||
\(736\) | 5.29806e24 | 2.26806 | ||||||||
\(737\) | 8.31306e23 | 0.351793 | ||||||||
\(738\) | −9.44819e23 | −0.395248 | ||||||||
\(739\) | −3.37306e24 | −1.39491 | −0.697456 | − | 0.716627i | \(-0.745685\pi\) | ||||
−0.697456 | + | 0.716627i | \(0.745685\pi\) | |||||||
\(740\) | −8.65791e24 | −3.53951 | ||||||||
\(741\) | −1.34182e24 | −0.542299 | ||||||||
\(742\) | −1.48476e23 | −0.0593230 | ||||||||
\(743\) | −4.24164e24 | −1.67544 | −0.837719 | − | 0.546101i | \(-0.816111\pi\) | ||||
−0.837719 | + | 0.546101i | \(0.816111\pi\) | |||||||
\(744\) | 2.44829e24 | 0.956077 | ||||||||
\(745\) | 2.09166e24 | 0.807537 | ||||||||
\(746\) | 4.39862e24 | 1.67895 | ||||||||
\(747\) | −6.15078e23 | −0.232116 | ||||||||
\(748\) | 3.37578e24 | 1.25954 | ||||||||
\(749\) | −8.93417e22 | −0.0329578 | ||||||||
\(750\) | 1.65158e24 | 0.602390 | ||||||||
\(751\) | −8.44312e23 | −0.304483 | −0.152242 | − | 0.988343i | \(-0.548649\pi\) | ||||
−0.152242 | + | 0.988343i | \(0.548649\pi\) | |||||||
\(752\) | −5.68540e24 | −2.02726 | ||||||||
\(753\) | −1.11037e24 | −0.391480 | ||||||||
\(754\) | 1.60865e24 | 0.560798 | ||||||||
\(755\) | −3.13370e24 | −1.08021 | ||||||||
\(756\) | 1.36955e23 | 0.0466813 | ||||||||
\(757\) | 3.10995e24 | 1.04819 | 0.524093 | − | 0.851661i | \(-0.324404\pi\) | ||||
0.524093 | + | 0.851661i | \(0.324404\pi\) | |||||||
\(758\) | −8.61398e24 | −2.87089 | ||||||||
\(759\) | −1.88762e24 | −0.622098 | ||||||||
\(760\) | −1.01230e25 | −3.29907 | ||||||||
\(761\) | 5.22689e24 | 1.68451 | 0.842256 | − | 0.539078i | \(-0.181227\pi\) | ||||
0.842256 | + | 0.539078i | \(0.181227\pi\) | |||||||
\(762\) | −3.16747e24 | −1.00947 | ||||||||
\(763\) | 5.44173e23 | 0.171506 | ||||||||
\(764\) | 9.27588e24 | 2.89109 | ||||||||
\(765\) | 1.15984e24 | 0.357498 | ||||||||
\(766\) | 4.97811e22 | 0.0151747 | ||||||||
\(767\) | 2.43747e23 | 0.0734817 | ||||||||
\(768\) | −3.01369e24 | −0.898522 | ||||||||
\(769\) | −5.37000e23 | −0.158343 | −0.0791717 | − | 0.996861i | \(-0.525228\pi\) | ||||
−0.0791717 | + | 0.996861i | \(0.525228\pi\) | |||||||
\(770\) | 5.10577e23 | 0.148898 | ||||||||
\(771\) | 3.03790e24 | 0.876217 | ||||||||
\(772\) | −2.57141e24 | −0.733540 | ||||||||
\(773\) | −1.13193e23 | −0.0319370 | −0.0159685 | − | 0.999872i | \(-0.505083\pi\) | ||||
−0.0159685 | + | 0.999872i | \(0.505083\pi\) | |||||||
\(774\) | 2.78931e24 | 0.778392 | ||||||||
\(775\) | 1.34854e24 | 0.372219 | ||||||||
\(776\) | 1.24227e25 | 3.39149 | ||||||||
\(777\) | 2.76353e23 | 0.0746252 | ||||||||
\(778\) | 2.57274e24 | 0.687177 | ||||||||
\(779\) | −2.74079e24 | −0.724113 | ||||||||
\(780\) | 5.35694e24 | 1.39995 | ||||||||
\(781\) | 2.76257e24 | 0.714135 | ||||||||
\(782\) | −1.05433e25 | −2.69599 | ||||||||
\(783\) | −2.77406e23 | −0.0701682 | ||||||||
\(784\) | −8.07110e24 | −2.01951 | ||||||||
\(785\) | 3.78695e24 | 0.937341 | ||||||||
\(786\) | −1.17144e24 | −0.286833 | ||||||||
\(787\) | 4.40987e24 | 1.06817 | 0.534085 | − | 0.845431i | \(-0.320656\pi\) | ||||
0.534085 | + | 0.845431i | \(0.320656\pi\) | |||||||
\(788\) | −3.09945e23 | −0.0742696 | ||||||||
\(789\) | −3.48939e24 | −0.827171 | ||||||||
\(790\) | −9.10539e24 | −2.13535 | ||||||||
\(791\) | −1.68505e22 | −0.00390942 | ||||||||
\(792\) | −2.18676e24 | −0.501922 | ||||||||
\(793\) | −3.41360e24 | −0.775158 | ||||||||
\(794\) | 4.28660e24 | 0.963028 | ||||||||
\(795\) | 1.00149e24 | 0.222601 | ||||||||
\(796\) | 4.13830e24 | 0.910040 | ||||||||
\(797\) | 1.93825e24 | 0.421710 | 0.210855 | − | 0.977517i | \(-0.432375\pi\) | ||||
0.210855 | + | 0.977517i | \(0.432375\pi\) | |||||||
\(798\) | 5.68949e23 | 0.122475 | ||||||||
\(799\) | 4.03137e24 | 0.858627 | ||||||||
\(800\) | 3.38067e24 | 0.712423 | ||||||||
\(801\) | −1.62638e24 | −0.339114 | ||||||||
\(802\) | 1.40018e24 | 0.288869 | ||||||||
\(803\) | 5.82553e24 | 1.18920 | ||||||||
\(804\) | −3.69825e24 | −0.746999 | ||||||||
\(805\) | −1.11351e24 | −0.222551 | ||||||||
\(806\) | −5.38229e24 | −1.06443 | ||||||||
\(807\) | −1.49988e24 | −0.293517 | ||||||||
\(808\) | 1.35177e25 | 2.61761 | ||||||||
\(809\) | −5.28909e24 | −1.01349 | −0.506744 | − | 0.862096i | \(-0.669151\pi\) | ||||
−0.506744 | + | 0.862096i | \(0.669151\pi\) | |||||||
\(810\) | −1.32293e24 | −0.250851 | ||||||||
\(811\) | −9.67847e24 | −1.81606 | −0.908028 | − | 0.418909i | \(-0.862413\pi\) | ||||
−0.908028 | + | 0.418909i | \(0.862413\pi\) | |||||||
\(812\) | −4.76293e23 | −0.0884398 | ||||||||
\(813\) | −2.54887e24 | −0.468358 | ||||||||
\(814\) | −7.76964e24 | −1.41284 | ||||||||
\(815\) | 1.24798e24 | 0.224578 | ||||||||
\(816\) | −5.72515e24 | −1.01958 | ||||||||
\(817\) | 8.09138e24 | 1.42605 | ||||||||
\(818\) | −1.09834e25 | −1.91573 | ||||||||
\(819\) | −1.70989e23 | −0.0295158 | ||||||||
\(820\) | 1.09420e25 | 1.86931 | ||||||||
\(821\) | −1.86577e24 | −0.315458 | −0.157729 | − | 0.987482i | \(-0.550417\pi\) | ||||
−0.157729 | + | 0.987482i | \(0.550417\pi\) | |||||||
\(822\) | 1.12764e25 | 1.88695 | ||||||||
\(823\) | −5.64893e23 | −0.0935552 | −0.0467776 | − | 0.998905i | \(-0.514895\pi\) | ||||
−0.0467776 | + | 0.998905i | \(0.514895\pi\) | |||||||
\(824\) | −4.30204e24 | −0.705169 | ||||||||
\(825\) | −1.20448e24 | −0.195408 | ||||||||
\(826\) | −1.03352e23 | −0.0165954 | ||||||||
\(827\) | −3.63429e24 | −0.577595 | −0.288797 | − | 0.957390i | \(-0.593255\pi\) | ||||
−0.288797 | + | 0.957390i | \(0.593255\pi\) | |||||||
\(828\) | 8.39749e24 | 1.32097 | ||||||||
\(829\) | −1.24734e25 | −1.94210 | −0.971052 | − | 0.238870i | \(-0.923223\pi\) | ||||
−0.971052 | + | 0.238870i | \(0.923223\pi\) | |||||||
\(830\) | 1.02011e25 | 1.57211 | ||||||||
\(831\) | 5.68203e24 | 0.866751 | ||||||||
\(832\) | −2.06748e24 | −0.312171 | ||||||||
\(833\) | 5.72300e24 | 0.855344 | ||||||||
\(834\) | 4.59416e24 | 0.679664 | ||||||||
\(835\) | −4.22323e24 | −0.618458 | ||||||||
\(836\) | −1.11697e25 | −1.61916 | ||||||||
\(837\) | 9.28153e23 | 0.133184 | ||||||||
\(838\) | 1.31991e25 | 1.87487 | ||||||||
\(839\) | −1.32854e24 | −0.186809 | −0.0934045 | − | 0.995628i | \(-0.529775\pi\) | ||||
−0.0934045 | + | 0.995628i | \(0.529775\pi\) | |||||||
\(840\) | −1.28998e24 | −0.179559 | ||||||||
\(841\) | −6.29241e24 | −0.867063 | ||||||||
\(842\) | 9.22007e24 | 1.25771 | ||||||||
\(843\) | 7.12327e23 | 0.0961934 | ||||||||
\(844\) | 1.07417e25 | 1.43603 | ||||||||
\(845\) | 2.68185e24 | 0.354938 | ||||||||
\(846\) | −4.59827e24 | −0.602485 | ||||||||
\(847\) | −4.88033e23 | −0.0633053 | ||||||||
\(848\) | −4.94353e24 | −0.634853 | ||||||||
\(849\) | 2.73967e24 | 0.348324 | ||||||||
\(850\) | −6.72764e24 | −0.846840 | ||||||||
\(851\) | 1.69447e25 | 2.11171 | ||||||||
\(852\) | −1.22899e25 | −1.51640 | ||||||||
\(853\) | −5.83602e23 | −0.0712935 | −0.0356468 | − | 0.999364i | \(-0.511349\pi\) | ||||
−0.0356468 | + | 0.999364i | \(0.511349\pi\) | |||||||
\(854\) | 1.44741e24 | 0.175065 | ||||||||
\(855\) | −3.83764e24 | −0.459571 | ||||||||
\(856\) | −6.34617e24 | −0.752462 | ||||||||
\(857\) | 5.11451e24 | 0.600437 | 0.300218 | − | 0.953871i | \(-0.402940\pi\) | ||||
0.300218 | + | 0.953871i | \(0.402940\pi\) | |||||||
\(858\) | 4.80734e24 | 0.558808 | ||||||||
\(859\) | 2.96778e24 | 0.341578 | 0.170789 | − | 0.985308i | \(-0.445368\pi\) | ||||
0.170789 | + | 0.985308i | \(0.445368\pi\) | |||||||
\(860\) | −3.23032e25 | −3.68137 | ||||||||
\(861\) | −3.49260e23 | −0.0394114 | ||||||||
\(862\) | −2.09615e25 | −2.34213 | ||||||||
\(863\) | −8.25654e24 | −0.913495 | −0.456748 | − | 0.889596i | \(-0.650986\pi\) | ||||
−0.456748 | + | 0.889596i | \(0.650986\pi\) | |||||||
\(864\) | 2.32681e24 | 0.254914 | ||||||||
\(865\) | 7.47136e23 | 0.0810519 | ||||||||
\(866\) | −9.24071e24 | −0.992667 | ||||||||
\(867\) | −1.36798e24 | −0.145518 | ||||||||
\(868\) | 1.59360e24 | 0.167865 | ||||||||
\(869\) | −5.70582e24 | −0.595182 | ||||||||
\(870\) | 4.60080e24 | 0.475247 | ||||||||
\(871\) | 4.61727e24 | 0.472314 | ||||||||
\(872\) | 3.86540e25 | 3.91565 | ||||||||
\(873\) | 4.70947e24 | 0.472445 | ||||||||
\(874\) | 3.48854e25 | 3.46575 | ||||||||
\(875\) | 6.10519e23 | 0.0600662 | ||||||||
\(876\) | −2.59162e25 | −2.52514 | ||||||||
\(877\) | −2.48925e24 | −0.240199 | −0.120100 | − | 0.992762i | \(-0.538321\pi\) | ||||
−0.120100 | + | 0.992762i | \(0.538321\pi\) | |||||||
\(878\) | 4.14002e24 | 0.395639 | ||||||||
\(879\) | 1.78338e24 | 0.168787 | ||||||||
\(880\) | 1.69998e25 | 1.59346 | ||||||||
\(881\) | −1.53069e25 | −1.42099 | −0.710495 | − | 0.703702i | \(-0.751529\pi\) | ||||
−0.710495 | + | 0.703702i | \(0.751529\pi\) | |||||||
\(882\) | −6.52778e24 | −0.600181 | ||||||||
\(883\) | 1.37054e25 | 1.24803 | 0.624014 | − | 0.781413i | \(-0.285501\pi\) | ||||
0.624014 | + | 0.781413i | \(0.285501\pi\) | |||||||
\(884\) | 1.87499e25 | 1.69104 | ||||||||
\(885\) | 6.97125e23 | 0.0622720 | ||||||||
\(886\) | −1.95717e25 | −1.73157 | ||||||||
\(887\) | −1.43271e24 | −0.125548 | −0.0627739 | − | 0.998028i | \(-0.519995\pi\) | ||||
−0.0627739 | + | 0.998028i | \(0.519995\pi\) | |||||||
\(888\) | 1.96300e25 | 1.70377 | ||||||||
\(889\) | −1.17088e24 | −0.100658 | ||||||||
\(890\) | 2.69737e25 | 2.29681 | ||||||||
\(891\) | −8.29006e23 | −0.0699193 | ||||||||
\(892\) | −3.26292e25 | −2.72587 | ||||||||
\(893\) | −1.33389e25 | −1.10378 | ||||||||
\(894\) | −8.35052e24 | −0.684455 | ||||||||
\(895\) | 1.70792e24 | 0.138666 | ||||||||
\(896\) | −8.49541e23 | −0.0683229 | ||||||||
\(897\) | −1.04843e25 | −0.835223 | ||||||||
\(898\) | −4.34157e25 | −3.42608 | ||||||||
\(899\) | −3.22786e24 | −0.252324 | ||||||||
\(900\) | 5.35841e24 | 0.414930 | ||||||||
\(901\) | 3.50533e24 | 0.268886 | ||||||||
\(902\) | 9.81943e24 | 0.746157 | ||||||||
\(903\) | 1.03109e24 | 0.0776159 | ||||||||
\(904\) | −1.19693e24 | −0.0892561 | ||||||||
\(905\) | 9.38539e24 | 0.693329 | ||||||||
\(906\) | 1.25107e25 | 0.915569 | ||||||||
\(907\) | 2.00624e25 | 1.45453 | 0.727263 | − | 0.686359i | \(-0.240792\pi\) | ||||
0.727263 | + | 0.686359i | \(0.240792\pi\) | |||||||
\(908\) | −9.68177e24 | −0.695385 | ||||||||
\(909\) | 5.12459e24 | 0.364641 | ||||||||
\(910\) | 2.83586e24 | 0.199909 | ||||||||
\(911\) | 7.29637e24 | 0.509566 | 0.254783 | − | 0.966998i | \(-0.417996\pi\) | ||||
0.254783 | + | 0.966998i | \(0.417996\pi\) | |||||||
\(912\) | 1.89433e25 | 1.31069 | ||||||||
\(913\) | 6.39245e24 | 0.438193 | ||||||||
\(914\) | −2.73539e25 | −1.85771 | ||||||||
\(915\) | −9.76300e24 | −0.656907 | ||||||||
\(916\) | −1.09902e25 | −0.732645 | ||||||||
\(917\) | −4.33034e23 | −0.0286011 | ||||||||
\(918\) | −4.63041e24 | −0.303010 | ||||||||
\(919\) | 4.06033e24 | 0.263257 | 0.131628 | − | 0.991299i | \(-0.457979\pi\) | ||||
0.131628 | + | 0.991299i | \(0.457979\pi\) | |||||||
\(920\) | −7.90956e25 | −5.08108 | ||||||||
\(921\) | 1.58677e25 | 1.00997 | ||||||||
\(922\) | 3.88663e25 | 2.45110 | ||||||||
\(923\) | 1.53440e25 | 0.958791 | ||||||||
\(924\) | −1.42336e24 | −0.0881260 | ||||||||
\(925\) | 1.08124e25 | 0.663310 | ||||||||
\(926\) | 3.35751e25 | 2.04091 | ||||||||
\(927\) | −1.63092e24 | −0.0982322 | ||||||||
\(928\) | −8.09199e24 | −0.482945 | ||||||||
\(929\) | −2.87442e25 | −1.69987 | −0.849936 | − | 0.526886i | \(-0.823359\pi\) | ||||
−0.849936 | + | 0.526886i | \(0.823359\pi\) | |||||||
\(930\) | −1.53935e25 | −0.902054 | ||||||||
\(931\) | −1.89361e25 | −1.09956 | ||||||||
\(932\) | 4.25287e25 | 2.44707 | ||||||||
\(933\) | 6.19850e24 | 0.353421 | ||||||||
\(934\) | 2.50482e25 | 1.41523 | ||||||||
\(935\) | −1.20541e25 | −0.674893 | ||||||||
\(936\) | −1.21458e25 | −0.673876 | ||||||||
\(937\) | −9.52788e24 | −0.523853 | −0.261927 | − | 0.965088i | \(-0.584358\pi\) | ||||
−0.261927 | + | 0.965088i | \(0.584358\pi\) | |||||||
\(938\) | −1.95778e24 | −0.106670 | ||||||||
\(939\) | −1.60627e25 | −0.867283 | ||||||||
\(940\) | 5.32529e25 | 2.84942 | ||||||||
\(941\) | 4.74128e24 | 0.251411 | 0.125705 | − | 0.992068i | \(-0.459881\pi\) | ||||
0.125705 | + | 0.992068i | \(0.459881\pi\) | |||||||
\(942\) | −1.51186e25 | −0.794475 | ||||||||
\(943\) | −2.14151e25 | −1.11525 | ||||||||
\(944\) | −3.44113e24 | −0.177598 | ||||||||
\(945\) | −4.89033e23 | −0.0250131 | ||||||||
\(946\) | −2.89890e25 | −1.46946 | ||||||||
\(947\) | −1.05058e25 | −0.527780 | −0.263890 | − | 0.964553i | \(-0.585006\pi\) | ||||
−0.263890 | + | 0.964553i | \(0.585006\pi\) | |||||||
\(948\) | 2.53836e25 | 1.26381 | ||||||||
\(949\) | 3.23564e25 | 1.59660 | ||||||||
\(950\) | 2.22603e25 | 1.08863 | ||||||||
\(951\) | 2.29471e25 | 1.11223 | ||||||||
\(952\) | −4.51505e24 | −0.216895 | ||||||||
\(953\) | −2.86764e24 | −0.136532 | −0.0682660 | − | 0.997667i | \(-0.521747\pi\) | ||||
−0.0682660 | + | 0.997667i | \(0.521747\pi\) | |||||||
\(954\) | −3.99825e24 | −0.188673 | ||||||||
\(955\) | −3.31218e25 | −1.54912 | ||||||||
\(956\) | 4.82743e25 | 2.23781 | ||||||||
\(957\) | 2.88305e24 | 0.132465 | ||||||||
\(958\) | 1.76848e25 | 0.805367 | ||||||||
\(959\) | 4.16841e24 | 0.188153 | ||||||||
\(960\) | −5.91304e24 | −0.264549 | ||||||||
\(961\) | −1.17502e25 | −0.521072 | ||||||||
\(962\) | −4.31544e25 | −1.89687 | ||||||||
\(963\) | −2.40585e24 | −0.104820 | ||||||||
\(964\) | −2.16328e25 | −0.934239 | ||||||||
\(965\) | 9.18186e24 | 0.393050 | ||||||||
\(966\) | 4.44547e24 | 0.188631 | ||||||||
\(967\) | −3.11121e25 | −1.30859 | −0.654297 | − | 0.756238i | \(-0.727035\pi\) | ||||
−0.654297 | + | 0.756238i | \(0.727035\pi\) | |||||||
\(968\) | −3.46662e25 | −1.44533 | ||||||||
\(969\) | −1.34322e25 | −0.555128 | ||||||||
\(970\) | −7.81070e25 | −3.19985 | ||||||||
\(971\) | 1.46309e25 | 0.594165 | 0.297083 | − | 0.954852i | \(-0.403986\pi\) | ||||
0.297083 | + | 0.954852i | \(0.403986\pi\) | |||||||
\(972\) | 3.68802e24 | 0.148467 | ||||||||
\(973\) | 1.69827e24 | 0.0677715 | ||||||||
\(974\) | −9.39223e24 | −0.371550 | ||||||||
\(975\) | −6.68998e24 | −0.262353 | ||||||||
\(976\) | 4.81919e25 | 1.87349 | ||||||||
\(977\) | −3.44513e25 | −1.32771 | −0.663853 | − | 0.747863i | \(-0.731080\pi\) | ||||
−0.663853 | + | 0.747863i | \(0.731080\pi\) | |||||||
\(978\) | −4.98230e24 | −0.190348 | ||||||||
\(979\) | 1.69028e25 | 0.640187 | ||||||||
\(980\) | 7.55988e25 | 2.83853 | ||||||||
\(981\) | 1.46538e25 | 0.545462 | ||||||||
\(982\) | 5.42135e25 | 2.00060 | ||||||||
\(983\) | 4.21774e25 | 1.54303 | 0.771515 | − | 0.636211i | \(-0.219499\pi\) | ||||
0.771515 | + | 0.636211i | \(0.219499\pi\) | |||||||
\(984\) | −2.48088e25 | −0.899804 | ||||||||
\(985\) | 1.10674e24 | 0.0397957 | ||||||||
\(986\) | 1.61033e25 | 0.574065 | ||||||||
\(987\) | −1.69979e24 | −0.0600756 | ||||||||
\(988\) | −6.20392e25 | −2.17386 | ||||||||
\(989\) | 6.32219e25 | 2.19634 | ||||||||
\(990\) | 1.37491e25 | 0.473561 | ||||||||
\(991\) | −2.46032e25 | −0.840169 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(992\) | 2.70744e25 | 0.916664 | ||||||||
\(993\) | −1.30156e24 | −0.0436912 | ||||||||
\(994\) | −6.50606e24 | −0.216538 | ||||||||
\(995\) | −1.47768e25 | −0.487624 | ||||||||
\(996\) | −2.84382e25 | −0.930462 | ||||||||
\(997\) | 5.58760e25 | 1.81266 | 0.906330 | − | 0.422571i | \(-0.138872\pi\) | ||||
0.906330 | + | 0.422571i | \(0.138872\pi\) | |||||||
\(998\) | −1.03883e26 | −3.34143 | ||||||||
\(999\) | 7.44180e24 | 0.237340 |
(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 | 3.18.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9.18.a.c.1.1 | 2 | |||
4.3 | odd | 2 | 48.18.a.h.1.1 | 2 | |||
5.2 | odd | 4 | 75.18.b.c.49.4 | 4 | |||
5.3 | odd | 4 | 75.18.b.c.49.1 | 4 | |||
5.4 | even | 2 | 75.18.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.18.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9.18.a.c.1.1 | 2 | 3.2 | odd | 2 | |||
48.18.a.h.1.1 | 2 | 4.3 | odd | 2 | |||
75.18.a.b.1.1 | 2 | 5.4 | even | 2 | |||
75.18.b.c.49.1 | 4 | 5.3 | odd | 4 | |||
75.18.b.c.49.4 | 4 | 5.2 | odd | 4 |