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 | 1.1 | ||
Root | \(60.8511\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −65.1063 | −0.179833 | −0.0899163 | − | 0.995949i | \(-0.528660\pi\) | ||||
−0.0899163 | + | 0.995949i | \(0.528660\pi\) | |||||||
\(3\) | 6561.00 | 0.577350 | ||||||||
\(4\) | −126833. | −0.967660 | ||||||||
\(5\) | 1.46604e6 | 1.67843 | 0.839213 | − | 0.543803i | \(-0.183016\pi\) | ||||
0.839213 | + | 0.543803i | \(0.183016\pi\) | |||||||
\(6\) | −427163. | −0.103826 | ||||||||
\(7\) | 2.28730e7 | 1.49965 | 0.749825 | − | 0.661636i | \(-0.230137\pi\) | ||||
0.749825 | + | 0.661636i | \(0.230137\pi\) | |||||||
\(8\) | 1.67913e7 | 0.353849 | ||||||||
\(9\) | 4.30467e7 | 0.333333 | ||||||||
\(10\) | −9.54488e7 | −0.301836 | ||||||||
\(11\) | −5.40173e8 | −0.759792 | −0.379896 | − | 0.925029i | \(-0.624040\pi\) | ||||
−0.379896 | + | 0.925029i | \(0.624040\pi\) | |||||||
\(12\) | −8.32152e8 | −0.558679 | ||||||||
\(13\) | −3.45398e7 | −0.0117436 | −0.00587181 | − | 0.999983i | \(-0.501869\pi\) | ||||
−0.00587181 | + | 0.999983i | \(0.501869\pi\) | |||||||
\(14\) | −1.48918e9 | −0.269686 | ||||||||
\(15\) | 9.61872e9 | 0.969039 | ||||||||
\(16\) | 1.55311e10 | 0.904027 | ||||||||
\(17\) | −9.43866e9 | −0.328167 | −0.164083 | − | 0.986446i | \(-0.552467\pi\) | ||||
−0.164083 | + | 0.986446i | \(0.552467\pi\) | |||||||
\(18\) | −2.80261e9 | −0.0599442 | ||||||||
\(19\) | −2.25061e9 | −0.0304015 | −0.0152007 | − | 0.999884i | \(-0.504839\pi\) | ||||
−0.0152007 | + | 0.999884i | \(0.504839\pi\) | |||||||
\(20\) | −1.85943e11 | −1.62415 | ||||||||
\(21\) | 1.50070e11 | 0.865824 | ||||||||
\(22\) | 3.51687e10 | 0.136635 | ||||||||
\(23\) | −3.45854e11 | −0.920886 | −0.460443 | − | 0.887689i | \(-0.652310\pi\) | ||||
−0.460443 | + | 0.887689i | \(0.652310\pi\) | |||||||
\(24\) | 1.10167e11 | 0.204295 | ||||||||
\(25\) | 1.38635e12 | 1.81711 | ||||||||
\(26\) | 2.24876e9 | 0.00211188 | ||||||||
\(27\) | 2.82430e11 | 0.192450 | ||||||||
\(28\) | −2.90106e12 | −1.45115 | ||||||||
\(29\) | 5.11838e11 | 0.189998 | 0.0949992 | − | 0.995477i | \(-0.469715\pi\) | ||||
0.0949992 | + | 0.995477i | \(0.469715\pi\) | |||||||
\(30\) | −6.26239e11 | −0.174265 | ||||||||
\(31\) | 1.14436e11 | 0.0240984 | 0.0120492 | − | 0.999927i | \(-0.496165\pi\) | ||||
0.0120492 | + | 0.999927i | \(0.496165\pi\) | |||||||
\(32\) | −3.21203e12 | −0.516423 | ||||||||
\(33\) | −3.54407e12 | −0.438666 | ||||||||
\(34\) | 6.14516e11 | 0.0590150 | ||||||||
\(35\) | 3.35329e13 | 2.51705 | ||||||||
\(36\) | −5.45975e12 | −0.322553 | ||||||||
\(37\) | −1.56972e13 | −0.734697 | −0.367349 | − | 0.930083i | \(-0.619734\pi\) | ||||
−0.367349 | + | 0.930083i | \(0.619734\pi\) | |||||||
\(38\) | 1.46529e11 | 0.00546717 | ||||||||
\(39\) | −2.26616e11 | −0.00678018 | ||||||||
\(40\) | 2.46167e13 | 0.593910 | ||||||||
\(41\) | −8.00761e13 | −1.56617 | −0.783087 | − | 0.621912i | \(-0.786356\pi\) | ||||
−0.783087 | + | 0.621912i | \(0.786356\pi\) | |||||||
\(42\) | −9.77050e12 | −0.155703 | ||||||||
\(43\) | −3.66737e13 | −0.478489 | −0.239245 | − | 0.970959i | \(-0.576900\pi\) | ||||
−0.239245 | + | 0.970959i | \(0.576900\pi\) | |||||||
\(44\) | 6.85118e13 | 0.735221 | ||||||||
\(45\) | 6.31084e13 | 0.559475 | ||||||||
\(46\) | 2.25173e13 | 0.165605 | ||||||||
\(47\) | −1.17577e14 | −0.720263 | −0.360132 | − | 0.932901i | \(-0.617268\pi\) | ||||
−0.360132 | + | 0.932901i | \(0.617268\pi\) | |||||||
\(48\) | 1.01899e14 | 0.521940 | ||||||||
\(49\) | 2.90545e14 | 1.24895 | ||||||||
\(50\) | −9.02599e13 | −0.326776 | ||||||||
\(51\) | −6.19270e13 | −0.189467 | ||||||||
\(52\) | 4.38080e12 | 0.0113638 | ||||||||
\(53\) | −3.90043e14 | −0.860534 | −0.430267 | − | 0.902702i | \(-0.641581\pi\) | ||||
−0.430267 | + | 0.902702i | \(0.641581\pi\) | |||||||
\(54\) | −1.83880e13 | −0.0346088 | ||||||||
\(55\) | −7.91917e14 | −1.27525 | ||||||||
\(56\) | 3.84067e14 | 0.530651 | ||||||||
\(57\) | −1.47663e13 | −0.0175523 | ||||||||
\(58\) | −3.33239e13 | −0.0341679 | ||||||||
\(59\) | 1.82562e15 | 1.61870 | 0.809352 | − | 0.587323i | \(-0.199818\pi\) | ||||
0.809352 | + | 0.587323i | \(0.199818\pi\) | |||||||
\(60\) | −1.21997e15 | −0.937701 | ||||||||
\(61\) | 1.41053e15 | 0.942059 | 0.471029 | − | 0.882118i | \(-0.343883\pi\) | ||||
0.471029 | + | 0.882118i | \(0.343883\pi\) | |||||||
\(62\) | −7.45051e12 | −0.00433368 | ||||||||
\(63\) | 9.84609e14 | 0.499884 | ||||||||
\(64\) | −1.82656e15 | −0.811157 | ||||||||
\(65\) | −5.06369e13 | −0.0197108 | ||||||||
\(66\) | 2.30742e14 | 0.0788865 | ||||||||
\(67\) | −1.47114e15 | −0.442607 | −0.221304 | − | 0.975205i | \(-0.571031\pi\) | ||||
−0.221304 | + | 0.975205i | \(0.571031\pi\) | |||||||
\(68\) | 1.19713e15 | 0.317554 | ||||||||
\(69\) | −2.26915e15 | −0.531674 | ||||||||
\(70\) | −2.18320e15 | −0.452648 | ||||||||
\(71\) | −7.31441e15 | −1.34426 | −0.672130 | − | 0.740433i | \(-0.734620\pi\) | ||||
−0.672130 | + | 0.740433i | \(0.734620\pi\) | |||||||
\(72\) | 7.22809e14 | 0.117950 | ||||||||
\(73\) | 1.34580e16 | 1.95315 | 0.976577 | − | 0.215169i | \(-0.0690302\pi\) | ||||
0.976577 | + | 0.215169i | \(0.0690302\pi\) | |||||||
\(74\) | 1.02199e15 | 0.132122 | ||||||||
\(75\) | 9.09582e15 | 1.04911 | ||||||||
\(76\) | 2.85452e14 | 0.0294183 | ||||||||
\(77\) | −1.23554e16 | −1.13942 | ||||||||
\(78\) | 1.47541e13 | 0.00121930 | ||||||||
\(79\) | −8.37779e15 | −0.621297 | −0.310648 | − | 0.950525i | \(-0.600546\pi\) | ||||
−0.310648 | + | 0.950525i | \(0.600546\pi\) | |||||||
\(80\) | 2.27692e16 | 1.51734 | ||||||||
\(81\) | 1.85302e15 | 0.111111 | ||||||||
\(82\) | 5.21346e15 | 0.281649 | ||||||||
\(83\) | −2.55978e16 | −1.24750 | −0.623748 | − | 0.781625i | \(-0.714391\pi\) | ||||
−0.623748 | + | 0.781625i | \(0.714391\pi\) | |||||||
\(84\) | −1.90338e16 | −0.837823 | ||||||||
\(85\) | −1.38375e16 | −0.550803 | ||||||||
\(86\) | 2.38769e15 | 0.0860480 | ||||||||
\(87\) | 3.35817e15 | 0.109696 | ||||||||
\(88\) | −9.07018e15 | −0.268852 | ||||||||
\(89\) | 4.47540e16 | 1.20508 | 0.602541 | − | 0.798088i | \(-0.294155\pi\) | ||||
0.602541 | + | 0.798088i | \(0.294155\pi\) | |||||||
\(90\) | −4.10876e15 | −0.100612 | ||||||||
\(91\) | −7.90031e14 | −0.0176113 | ||||||||
\(92\) | 4.38657e16 | 0.891105 | ||||||||
\(93\) | 7.50815e14 | 0.0139132 | ||||||||
\(94\) | 7.65502e15 | 0.129527 | ||||||||
\(95\) | −3.29949e15 | −0.0510266 | ||||||||
\(96\) | −2.10742e16 | −0.298157 | ||||||||
\(97\) | 7.41658e16 | 0.960824 | 0.480412 | − | 0.877043i | \(-0.340487\pi\) | ||||
0.480412 | + | 0.877043i | \(0.340487\pi\) | |||||||
\(98\) | −1.89163e16 | −0.224602 | ||||||||
\(99\) | −2.32527e16 | −0.253264 | ||||||||
\(100\) | −1.75835e17 | −1.75835 | ||||||||
\(101\) | −7.87706e16 | −0.723823 | −0.361912 | − | 0.932212i | \(-0.617876\pi\) | ||||
−0.361912 | + | 0.932212i | \(0.617876\pi\) | |||||||
\(102\) | 4.03184e15 | 0.0340723 | ||||||||
\(103\) | 6.67667e16 | 0.519330 | 0.259665 | − | 0.965699i | \(-0.416388\pi\) | ||||
0.259665 | + | 0.965699i | \(0.416388\pi\) | |||||||
\(104\) | −5.79968e14 | −0.00415547 | ||||||||
\(105\) | 2.20009e17 | 1.45322 | ||||||||
\(106\) | 2.53943e16 | 0.154752 | ||||||||
\(107\) | −2.57732e17 | −1.45013 | −0.725064 | − | 0.688681i | \(-0.758190\pi\) | ||||
−0.725064 | + | 0.688681i | \(0.758190\pi\) | |||||||
\(108\) | −3.58214e16 | −0.186226 | ||||||||
\(109\) | 1.67981e17 | 0.807488 | 0.403744 | − | 0.914872i | \(-0.367709\pi\) | ||||
0.403744 | + | 0.914872i | \(0.367709\pi\) | |||||||
\(110\) | 5.15588e16 | 0.229332 | ||||||||
\(111\) | −1.02990e17 | −0.424178 | ||||||||
\(112\) | 3.55242e17 | 1.35572 | ||||||||
\(113\) | 3.01755e17 | 1.06779 | 0.533897 | − | 0.845550i | \(-0.320727\pi\) | ||||
0.533897 | + | 0.845550i | \(0.320727\pi\) | |||||||
\(114\) | 9.61376e14 | 0.00315647 | ||||||||
\(115\) | −5.07037e17 | −1.54564 | ||||||||
\(116\) | −6.49181e16 | −0.183854 | ||||||||
\(117\) | −1.48683e15 | −0.00391454 | ||||||||
\(118\) | −1.18859e17 | −0.291096 | ||||||||
\(119\) | −2.15891e17 | −0.492135 | ||||||||
\(120\) | 1.61510e17 | 0.342894 | ||||||||
\(121\) | −2.13660e17 | −0.422716 | ||||||||
\(122\) | −9.18343e16 | −0.169413 | ||||||||
\(123\) | −5.25379e17 | −0.904231 | ||||||||
\(124\) | −1.45143e16 | −0.0233191 | ||||||||
\(125\) | 9.13942e17 | 1.37146 | ||||||||
\(126\) | −6.41043e16 | −0.0898953 | ||||||||
\(127\) | 1.84942e17 | 0.242496 | 0.121248 | − | 0.992622i | \(-0.461310\pi\) | ||||
0.121248 | + | 0.992622i | \(0.461310\pi\) | |||||||
\(128\) | 5.39929e17 | 0.662295 | ||||||||
\(129\) | −2.40616e17 | −0.276256 | ||||||||
\(130\) | 3.29679e15 | 0.00354464 | ||||||||
\(131\) | 9.78482e16 | 0.0985705 | 0.0492852 | − | 0.998785i | \(-0.484306\pi\) | ||||
0.0492852 | + | 0.998785i | \(0.484306\pi\) | |||||||
\(132\) | 4.49506e17 | 0.424480 | ||||||||
\(133\) | −5.14782e16 | −0.0455916 | ||||||||
\(134\) | 9.57806e16 | 0.0795951 | ||||||||
\(135\) | 4.14054e17 | 0.323013 | ||||||||
\(136\) | −1.58487e17 | −0.116122 | ||||||||
\(137\) | −3.72170e17 | −0.256222 | −0.128111 | − | 0.991760i | \(-0.540891\pi\) | ||||
−0.128111 | + | 0.991760i | \(0.540891\pi\) | |||||||
\(138\) | 1.47736e17 | 0.0956123 | ||||||||
\(139\) | 4.12327e17 | 0.250967 | 0.125483 | − | 0.992096i | \(-0.459952\pi\) | ||||
0.125483 | + | 0.992096i | \(0.459952\pi\) | |||||||
\(140\) | −4.25308e18 | −2.43565 | ||||||||
\(141\) | −7.71424e17 | −0.415844 | ||||||||
\(142\) | 4.76214e17 | 0.241742 | ||||||||
\(143\) | 1.86575e16 | 0.00892271 | ||||||||
\(144\) | 6.68561e17 | 0.301342 | ||||||||
\(145\) | 7.50378e17 | 0.318898 | ||||||||
\(146\) | −8.76202e17 | −0.351241 | ||||||||
\(147\) | 1.90626e18 | 0.721083 | ||||||||
\(148\) | 1.99093e18 | 0.710937 | ||||||||
\(149\) | 4.80416e18 | 1.62007 | 0.810035 | − | 0.586382i | \(-0.199448\pi\) | ||||
0.810035 | + | 0.586382i | \(0.199448\pi\) | |||||||
\(150\) | −5.92195e17 | −0.188664 | ||||||||
\(151\) | −4.91996e18 | −1.48135 | −0.740674 | − | 0.671864i | \(-0.765494\pi\) | ||||
−0.740674 | + | 0.671864i | \(0.765494\pi\) | |||||||
\(152\) | −3.77906e16 | −0.0107575 | ||||||||
\(153\) | −4.06303e17 | −0.109389 | ||||||||
\(154\) | 8.04414e17 | 0.204905 | ||||||||
\(155\) | 1.67768e17 | 0.0404474 | ||||||||
\(156\) | 2.87424e16 | 0.00656091 | ||||||||
\(157\) | 6.42241e18 | 1.38852 | 0.694258 | − | 0.719726i | \(-0.255733\pi\) | ||||
0.694258 | + | 0.719726i | \(0.255733\pi\) | |||||||
\(158\) | 5.45447e17 | 0.111729 | ||||||||
\(159\) | −2.55907e18 | −0.496829 | ||||||||
\(160\) | −4.70898e18 | −0.866777 | ||||||||
\(161\) | −7.91072e18 | −1.38101 | ||||||||
\(162\) | −1.20643e17 | −0.0199814 | ||||||||
\(163\) | −7.83455e18 | −1.23146 | −0.615729 | − | 0.787958i | \(-0.711138\pi\) | ||||
−0.615729 | + | 0.787958i | \(0.711138\pi\) | |||||||
\(164\) | 1.01563e19 | 1.51552 | ||||||||
\(165\) | −5.19577e18 | −0.736269 | ||||||||
\(166\) | 1.66658e18 | 0.224341 | ||||||||
\(167\) | 1.03503e19 | 1.32392 | 0.661962 | − | 0.749537i | \(-0.269724\pi\) | ||||
0.661962 | + | 0.749537i | \(0.269724\pi\) | |||||||
\(168\) | 2.51986e18 | 0.306371 | ||||||||
\(169\) | −8.64922e18 | −0.999862 | ||||||||
\(170\) | 9.00908e17 | 0.0990523 | ||||||||
\(171\) | −9.68814e16 | −0.0101338 | ||||||||
\(172\) | 4.65144e18 | 0.463015 | ||||||||
\(173\) | −8.18965e18 | −0.776021 | −0.388011 | − | 0.921655i | \(-0.626838\pi\) | ||||
−0.388011 | + | 0.921655i | \(0.626838\pi\) | |||||||
\(174\) | −2.18638e17 | −0.0197268 | ||||||||
\(175\) | 3.17099e19 | 2.72503 | ||||||||
\(176\) | −8.38945e18 | −0.686872 | ||||||||
\(177\) | 1.19779e19 | 0.934560 | ||||||||
\(178\) | −2.91377e18 | −0.216713 | ||||||||
\(179\) | −2.91944e18 | −0.207038 | −0.103519 | − | 0.994627i | \(-0.533010\pi\) | ||||
−0.103519 | + | 0.994627i | \(0.533010\pi\) | |||||||
\(180\) | −8.00424e18 | −0.541382 | ||||||||
\(181\) | −2.50385e19 | −1.61562 | −0.807812 | − | 0.589440i | \(-0.799349\pi\) | ||||
−0.807812 | + | 0.589440i | \(0.799349\pi\) | |||||||
\(182\) | 5.14360e16 | 0.00316709 | ||||||||
\(183\) | 9.25447e18 | 0.543898 | ||||||||
\(184\) | −5.80732e18 | −0.325855 | ||||||||
\(185\) | −2.30128e19 | −1.23313 | ||||||||
\(186\) | −4.88828e16 | −0.00250205 | ||||||||
\(187\) | 5.09851e18 | 0.249338 | ||||||||
\(188\) | 1.49127e19 | 0.696970 | ||||||||
\(189\) | 6.46002e18 | 0.288608 | ||||||||
\(190\) | 2.14818e17 | 0.00917624 | ||||||||
\(191\) | −2.01953e19 | −0.825025 | −0.412513 | − | 0.910952i | \(-0.635349\pi\) | ||||
−0.412513 | + | 0.910952i | \(0.635349\pi\) | |||||||
\(192\) | −1.19841e19 | −0.468322 | ||||||||
\(193\) | 4.28113e19 | 1.60074 | 0.800372 | − | 0.599504i | \(-0.204635\pi\) | ||||
0.800372 | + | 0.599504i | \(0.204635\pi\) | |||||||
\(194\) | −4.82866e18 | −0.172788 | ||||||||
\(195\) | −3.32229e17 | −0.0113800 | ||||||||
\(196\) | −3.68507e19 | −1.20856 | ||||||||
\(197\) | 4.01977e19 | 1.26252 | 0.631261 | − | 0.775571i | \(-0.282538\pi\) | ||||
0.631261 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(198\) | 1.51390e18 | 0.0455451 | ||||||||
\(199\) | 4.29123e19 | 1.23689 | 0.618444 | − | 0.785829i | \(-0.287763\pi\) | ||||
0.618444 | + | 0.785829i | \(0.287763\pi\) | |||||||
\(200\) | 2.32785e19 | 0.642984 | ||||||||
\(201\) | −9.65215e18 | −0.255539 | ||||||||
\(202\) | 5.12846e18 | 0.130167 | ||||||||
\(203\) | 1.17073e19 | 0.284931 | ||||||||
\(204\) | 7.85440e18 | 0.183340 | ||||||||
\(205\) | −1.17395e20 | −2.62871 | ||||||||
\(206\) | −4.34694e18 | −0.0933925 | ||||||||
\(207\) | −1.48879e19 | −0.306962 | ||||||||
\(208\) | −5.36440e17 | −0.0106165 | ||||||||
\(209\) | 1.21572e18 | 0.0230988 | ||||||||
\(210\) | −1.43240e19 | −0.261336 | ||||||||
\(211\) | 1.34631e19 | 0.235909 | 0.117955 | − | 0.993019i | \(-0.462366\pi\) | ||||
0.117955 | + | 0.993019i | \(0.462366\pi\) | |||||||
\(212\) | 4.94704e19 | 0.832704 | ||||||||
\(213\) | −4.79898e19 | −0.776109 | ||||||||
\(214\) | 1.67800e19 | 0.260780 | ||||||||
\(215\) | −5.37652e19 | −0.803109 | ||||||||
\(216\) | 4.74235e18 | 0.0680983 | ||||||||
\(217\) | 2.61750e18 | 0.0361392 | ||||||||
\(218\) | −1.09367e19 | −0.145213 | ||||||||
\(219\) | 8.82980e19 | 1.12765 | ||||||||
\(220\) | 1.00441e20 | 1.23401 | ||||||||
\(221\) | 3.26010e17 | 0.00385386 | ||||||||
\(222\) | 6.70527e18 | 0.0762809 | ||||||||
\(223\) | −5.53968e19 | −0.606587 | −0.303293 | − | 0.952897i | \(-0.598086\pi\) | ||||
−0.303293 | + | 0.952897i | \(0.598086\pi\) | |||||||
\(224\) | −7.34689e19 | −0.774454 | ||||||||
\(225\) | 5.96777e19 | 0.605704 | ||||||||
\(226\) | −1.96461e19 | −0.192024 | ||||||||
\(227\) | 1.02921e19 | 0.0968915 | 0.0484457 | − | 0.998826i | \(-0.484573\pi\) | ||||
0.0484457 | + | 0.998826i | \(0.484573\pi\) | |||||||
\(228\) | 1.87285e18 | 0.0169847 | ||||||||
\(229\) | 1.55018e20 | 1.35451 | 0.677254 | − | 0.735750i | \(-0.263170\pi\) | ||||
0.677254 | + | 0.735750i | \(0.263170\pi\) | |||||||
\(230\) | 3.30113e19 | 0.277956 | ||||||||
\(231\) | −8.10637e19 | −0.657846 | ||||||||
\(232\) | 8.59441e18 | 0.0672308 | ||||||||
\(233\) | −1.64581e19 | −0.124124 | −0.0620618 | − | 0.998072i | \(-0.519768\pi\) | ||||
−0.0620618 | + | 0.998072i | \(0.519768\pi\) | |||||||
\(234\) | 9.68019e16 | 0.000703962 0 | ||||||||
\(235\) | −1.72373e20 | −1.20891 | ||||||||
\(236\) | −2.31549e20 | −1.56636 | ||||||||
\(237\) | −5.49667e19 | −0.358706 | ||||||||
\(238\) | 1.40558e19 | 0.0885020 | ||||||||
\(239\) | −7.36122e19 | −0.447268 | −0.223634 | − | 0.974673i | \(-0.571792\pi\) | ||||
−0.223634 | + | 0.974673i | \(0.571792\pi\) | |||||||
\(240\) | 1.49389e20 | 0.876037 | ||||||||
\(241\) | 1.00349e20 | 0.568028 | 0.284014 | − | 0.958820i | \(-0.408334\pi\) | ||||
0.284014 | + | 0.958820i | \(0.408334\pi\) | |||||||
\(242\) | 1.39107e19 | 0.0760181 | ||||||||
\(243\) | 1.21577e19 | 0.0641500 | ||||||||
\(244\) | −1.78902e20 | −0.911593 | ||||||||
\(245\) | 4.25951e20 | 2.09627 | ||||||||
\(246\) | 3.42055e19 | 0.162610 | ||||||||
\(247\) | 7.77357e16 | 0.000357023 0 | ||||||||
\(248\) | 1.92153e18 | 0.00852721 | ||||||||
\(249\) | −1.67947e20 | −0.720243 | ||||||||
\(250\) | −5.95034e19 | −0.246633 | ||||||||
\(251\) | 3.34304e20 | 1.33942 | 0.669708 | − | 0.742624i | \(-0.266419\pi\) | ||||
0.669708 | + | 0.742624i | \(0.266419\pi\) | |||||||
\(252\) | −1.24881e20 | −0.483718 | ||||||||
\(253\) | 1.86821e20 | 0.699682 | ||||||||
\(254\) | −1.20409e19 | −0.0436086 | ||||||||
\(255\) | −9.07878e19 | −0.318006 | ||||||||
\(256\) | 2.04259e20 | 0.692055 | ||||||||
\(257\) | −6.36862e19 | −0.208744 | −0.104372 | − | 0.994538i | \(-0.533283\pi\) | ||||
−0.104372 | + | 0.994538i | \(0.533283\pi\) | |||||||
\(258\) | 1.56656e19 | 0.0496798 | ||||||||
\(259\) | −3.59043e20 | −1.10179 | ||||||||
\(260\) | 6.42244e18 | 0.0190733 | ||||||||
\(261\) | 2.20330e19 | 0.0633328 | ||||||||
\(262\) | −6.37054e18 | −0.0177262 | ||||||||
\(263\) | −3.67784e20 | −0.990761 | −0.495381 | − | 0.868676i | \(-0.664971\pi\) | ||||
−0.495381 | + | 0.868676i | \(0.664971\pi\) | |||||||
\(264\) | −5.95095e19 | −0.155222 | ||||||||
\(265\) | −5.71821e20 | −1.44434 | ||||||||
\(266\) | 3.35156e18 | 0.00819885 | ||||||||
\(267\) | 2.93631e20 | 0.695754 | ||||||||
\(268\) | 1.86589e20 | 0.428293 | ||||||||
\(269\) | 1.44158e20 | 0.320586 | 0.160293 | − | 0.987069i | \(-0.448756\pi\) | ||||
0.160293 | + | 0.987069i | \(0.448756\pi\) | |||||||
\(270\) | −2.69576e19 | −0.0580883 | ||||||||
\(271\) | 6.03451e20 | 1.26009 | 0.630047 | − | 0.776557i | \(-0.283036\pi\) | ||||
0.630047 | + | 0.776557i | \(0.283036\pi\) | |||||||
\(272\) | −1.46592e20 | −0.296671 | ||||||||
\(273\) | −5.18339e18 | −0.0101679 | ||||||||
\(274\) | 2.42306e19 | 0.0460770 | ||||||||
\(275\) | −7.48867e20 | −1.38063 | ||||||||
\(276\) | 2.87803e20 | 0.514480 | ||||||||
\(277\) | 3.10539e20 | 0.538318 | 0.269159 | − | 0.963096i | \(-0.413254\pi\) | ||||
0.269159 | + | 0.963096i | \(0.413254\pi\) | |||||||
\(278\) | −2.68451e19 | −0.0451320 | ||||||||
\(279\) | 4.92610e18 | 0.00803281 | ||||||||
\(280\) | 5.63059e20 | 0.890657 | ||||||||
\(281\) | 6.43730e20 | 0.987871 | 0.493935 | − | 0.869499i | \(-0.335558\pi\) | ||||
0.493935 | + | 0.869499i | \(0.335558\pi\) | |||||||
\(282\) | 5.02246e19 | 0.0747823 | ||||||||
\(283\) | −3.43859e20 | −0.496817 | −0.248408 | − | 0.968655i | \(-0.579907\pi\) | ||||
−0.248408 | + | 0.968655i | \(0.579907\pi\) | |||||||
\(284\) | 9.27709e20 | 1.30079 | ||||||||
\(285\) | −2.16480e19 | −0.0294602 | ||||||||
\(286\) | −1.21472e18 | −0.00160459 | ||||||||
\(287\) | −1.83158e21 | −2.34872 | ||||||||
\(288\) | −1.38268e20 | −0.172141 | ||||||||
\(289\) | −7.38152e20 | −0.892307 | ||||||||
\(290\) | −4.88544e19 | −0.0573483 | ||||||||
\(291\) | 4.86602e20 | 0.554732 | ||||||||
\(292\) | −1.70692e21 | −1.88999 | ||||||||
\(293\) | 4.41631e20 | 0.474990 | 0.237495 | − | 0.971389i | \(-0.423674\pi\) | ||||
0.237495 | + | 0.971389i | \(0.423674\pi\) | |||||||
\(294\) | −1.24110e20 | −0.129674 | ||||||||
\(295\) | 2.67644e21 | 2.71688 | ||||||||
\(296\) | −2.63576e20 | −0.259972 | ||||||||
\(297\) | −1.52561e20 | −0.146222 | ||||||||
\(298\) | −3.12781e20 | −0.291341 | ||||||||
\(299\) | 1.19457e19 | 0.0108145 | ||||||||
\(300\) | −1.15365e21 | −1.01518 | ||||||||
\(301\) | −8.38837e20 | −0.717567 | ||||||||
\(302\) | 3.20320e20 | 0.266395 | ||||||||
\(303\) | −5.16814e20 | −0.417899 | ||||||||
\(304\) | −3.49544e19 | −0.0274837 | ||||||||
\(305\) | 2.06790e21 | 1.58118 | ||||||||
\(306\) | 2.64529e19 | 0.0196717 | ||||||||
\(307\) | −2.55581e20 | −0.184864 | −0.0924319 | − | 0.995719i | \(-0.529464\pi\) | ||||
−0.0924319 | + | 0.995719i | \(0.529464\pi\) | |||||||
\(308\) | 1.56707e21 | 1.10257 | ||||||||
\(309\) | 4.38056e20 | 0.299835 | ||||||||
\(310\) | −1.09228e19 | −0.00727376 | ||||||||
\(311\) | 1.33035e21 | 0.861988 | 0.430994 | − | 0.902355i | \(-0.358163\pi\) | ||||
0.430994 | + | 0.902355i | \(0.358163\pi\) | |||||||
\(312\) | −3.80517e18 | −0.00239916 | ||||||||
\(313\) | −8.09712e20 | −0.496825 | −0.248413 | − | 0.968654i | \(-0.579909\pi\) | ||||
−0.248413 | + | 0.968654i | \(0.579909\pi\) | |||||||
\(314\) | −4.18140e20 | −0.249701 | ||||||||
\(315\) | 1.44348e21 | 0.839017 | ||||||||
\(316\) | 1.06258e21 | 0.601204 | ||||||||
\(317\) | −2.88959e21 | −1.59159 | −0.795797 | − | 0.605564i | \(-0.792948\pi\) | ||||
−0.795797 | + | 0.605564i | \(0.792948\pi\) | |||||||
\(318\) | 1.66612e20 | 0.0893461 | ||||||||
\(319\) | −2.76481e20 | −0.144359 | ||||||||
\(320\) | −2.67782e21 | −1.36147 | ||||||||
\(321\) | −1.69098e21 | −0.837232 | ||||||||
\(322\) | 5.15038e20 | 0.248350 | ||||||||
\(323\) | 2.12427e19 | 0.00997675 | ||||||||
\(324\) | −2.35024e20 | −0.107518 | ||||||||
\(325\) | −4.78842e19 | −0.0213395 | ||||||||
\(326\) | 5.10079e20 | 0.221456 | ||||||||
\(327\) | 1.10213e21 | 0.466203 | ||||||||
\(328\) | −1.34458e21 | −0.554190 | ||||||||
\(329\) | −2.68935e21 | −1.08014 | ||||||||
\(330\) | 3.38277e20 | 0.132405 | ||||||||
\(331\) | 2.93645e21 | 1.12017 | 0.560085 | − | 0.828435i | \(-0.310768\pi\) | ||||
0.560085 | + | 0.828435i | \(0.310768\pi\) | |||||||
\(332\) | 3.24665e21 | 1.20715 | ||||||||
\(333\) | −6.75714e20 | −0.244899 | ||||||||
\(334\) | −6.73871e20 | −0.238085 | ||||||||
\(335\) | −2.15676e21 | −0.742883 | ||||||||
\(336\) | 2.33074e21 | 0.782728 | ||||||||
\(337\) | −3.01200e20 | −0.0986282 | −0.0493141 | − | 0.998783i | \(-0.515704\pi\) | ||||
−0.0493141 | + | 0.998783i | \(0.515704\pi\) | |||||||
\(338\) | 5.63119e20 | 0.179808 | ||||||||
\(339\) | 1.97981e21 | 0.616491 | ||||||||
\(340\) | 1.75505e21 | 0.532990 | ||||||||
\(341\) | −6.18152e19 | −0.0183098 | ||||||||
\(342\) | 6.30759e18 | 0.00182239 | ||||||||
\(343\) | 1.32467e21 | 0.373342 | ||||||||
\(344\) | −6.15797e20 | −0.169313 | ||||||||
\(345\) | −3.32667e21 | −0.892375 | ||||||||
\(346\) | 5.33198e20 | 0.139554 | ||||||||
\(347\) | 1.24669e21 | 0.318390 | 0.159195 | − | 0.987247i | \(-0.449110\pi\) | ||||
0.159195 | + | 0.987247i | \(0.449110\pi\) | |||||||
\(348\) | −4.25928e20 | −0.106148 | ||||||||
\(349\) | −9.93535e18 | −0.00241639 | −0.00120820 | − | 0.999999i | \(-0.500385\pi\) | ||||
−0.00120820 | + | 0.999999i | \(0.500385\pi\) | |||||||
\(350\) | −2.06452e21 | −0.490050 | ||||||||
\(351\) | −9.75507e18 | −0.00226006 | ||||||||
\(352\) | 1.73505e21 | 0.392374 | ||||||||
\(353\) | 6.30999e21 | 1.39298 | 0.696488 | − | 0.717569i | \(-0.254745\pi\) | ||||
0.696488 | + | 0.717569i | \(0.254745\pi\) | |||||||
\(354\) | −7.79836e20 | −0.168064 | ||||||||
\(355\) | −1.07232e22 | −2.25624 | ||||||||
\(356\) | −5.67629e21 | −1.16611 | ||||||||
\(357\) | −1.41646e21 | −0.284134 | ||||||||
\(358\) | 1.90074e20 | 0.0372321 | ||||||||
\(359\) | 1.07474e21 | 0.205589 | 0.102795 | − | 0.994703i | \(-0.467222\pi\) | ||||
0.102795 | + | 0.994703i | \(0.467222\pi\) | |||||||
\(360\) | 1.05967e21 | 0.197970 | ||||||||
\(361\) | −5.47532e21 | −0.999076 | ||||||||
\(362\) | 1.63017e21 | 0.290542 | ||||||||
\(363\) | −1.40183e21 | −0.244055 | ||||||||
\(364\) | 1.00202e20 | 0.0170418 | ||||||||
\(365\) | 1.97300e22 | 3.27822 | ||||||||
\(366\) | −6.02525e20 | −0.0978105 | ||||||||
\(367\) | 4.61598e21 | 0.732153 | 0.366077 | − | 0.930585i | \(-0.380701\pi\) | ||||
0.366077 | + | 0.930585i | \(0.380701\pi\) | |||||||
\(368\) | −5.37148e21 | −0.832506 | ||||||||
\(369\) | −3.44701e21 | −0.522058 | ||||||||
\(370\) | 1.49828e21 | 0.221758 | ||||||||
\(371\) | −8.92147e21 | −1.29050 | ||||||||
\(372\) | −9.52283e19 | −0.0134633 | ||||||||
\(373\) | 6.59694e21 | 0.911628 | 0.455814 | − | 0.890075i | \(-0.349348\pi\) | ||||
0.455814 | + | 0.890075i | \(0.349348\pi\) | |||||||
\(374\) | −3.31945e20 | −0.0448392 | ||||||||
\(375\) | 5.99638e21 | 0.791814 | ||||||||
\(376\) | −1.97427e21 | −0.254865 | ||||||||
\(377\) | −1.76788e19 | −0.00223127 | ||||||||
\(378\) | −4.20588e20 | −0.0519011 | ||||||||
\(379\) | 1.41137e22 | 1.70297 | 0.851485 | − | 0.524379i | \(-0.175702\pi\) | ||||
0.851485 | + | 0.524379i | \(0.175702\pi\) | |||||||
\(380\) | 4.18485e20 | 0.0493764 | ||||||||
\(381\) | 1.21340e21 | 0.140005 | ||||||||
\(382\) | 1.31484e21 | 0.148366 | ||||||||
\(383\) | −1.26426e22 | −1.39523 | −0.697617 | − | 0.716471i | \(-0.745756\pi\) | ||||
−0.697617 | + | 0.716471i | \(0.745756\pi\) | |||||||
\(384\) | 3.54247e21 | 0.382376 | ||||||||
\(385\) | −1.81135e22 | −1.91244 | ||||||||
\(386\) | −2.78729e21 | −0.287866 | ||||||||
\(387\) | −1.57868e21 | −0.159496 | ||||||||
\(388\) | −9.40669e21 | −0.929752 | ||||||||
\(389\) | 5.65745e21 | 0.547078 | 0.273539 | − | 0.961861i | \(-0.411806\pi\) | ||||
0.273539 | + | 0.961861i | \(0.411806\pi\) | |||||||
\(390\) | 2.16302e19 | 0.00204650 | ||||||||
\(391\) | 3.26440e21 | 0.302204 | ||||||||
\(392\) | 4.87861e21 | 0.441941 | ||||||||
\(393\) | 6.41982e20 | 0.0569097 | ||||||||
\(394\) | −2.61713e21 | −0.227042 | ||||||||
\(395\) | −1.22822e22 | −1.04280 | ||||||||
\(396\) | 2.94921e21 | 0.245074 | ||||||||
\(397\) | 5.61679e21 | 0.456845 | 0.228422 | − | 0.973562i | \(-0.426643\pi\) | ||||
0.228422 | + | 0.973562i | \(0.426643\pi\) | |||||||
\(398\) | −2.79386e21 | −0.222433 | ||||||||
\(399\) | −3.37749e20 | −0.0263223 | ||||||||
\(400\) | 2.15314e22 | 1.64272 | ||||||||
\(401\) | −1.90221e22 | −1.42079 | −0.710396 | − | 0.703802i | \(-0.751484\pi\) | ||||
−0.710396 | + | 0.703802i | \(0.751484\pi\) | |||||||
\(402\) | 6.28416e20 | 0.0459543 | ||||||||
\(403\) | −3.95260e18 | −0.000283003 0 | ||||||||
\(404\) | 9.99072e21 | 0.700415 | ||||||||
\(405\) | 2.71661e21 | 0.186492 | ||||||||
\(406\) | −7.62219e20 | −0.0512399 | ||||||||
\(407\) | 8.47922e21 | 0.558217 | ||||||||
\(408\) | −1.03983e21 | −0.0670428 | ||||||||
\(409\) | 1.22737e22 | 0.775045 | 0.387522 | − | 0.921860i | \(-0.373331\pi\) | ||||
0.387522 | + | 0.921860i | \(0.373331\pi\) | |||||||
\(410\) | 7.64317e21 | 0.472727 | ||||||||
\(411\) | −2.44181e21 | −0.147930 | ||||||||
\(412\) | −8.46823e21 | −0.502535 | ||||||||
\(413\) | 4.17574e22 | 2.42749 | ||||||||
\(414\) | 9.69295e20 | 0.0552018 | ||||||||
\(415\) | −3.75276e22 | −2.09383 | ||||||||
\(416\) | 1.10943e20 | 0.00606467 | ||||||||
\(417\) | 2.70528e21 | 0.144896 | ||||||||
\(418\) | −7.91509e19 | −0.00415392 | ||||||||
\(419\) | −2.12528e22 | −1.09294 | −0.546470 | − | 0.837479i | \(-0.684029\pi\) | ||||
−0.546470 | + | 0.837479i | \(0.684029\pi\) | |||||||
\(420\) | −2.79045e22 | −1.40622 | ||||||||
\(421\) | −6.94281e21 | −0.342876 | −0.171438 | − | 0.985195i | \(-0.554841\pi\) | ||||
−0.171438 | + | 0.985195i | \(0.554841\pi\) | |||||||
\(422\) | −8.76535e20 | −0.0424242 | ||||||||
\(423\) | −5.06131e21 | −0.240088 | ||||||||
\(424\) | −6.54932e21 | −0.304499 | ||||||||
\(425\) | −1.30852e22 | −0.596316 | ||||||||
\(426\) | 3.12444e21 | 0.139570 | ||||||||
\(427\) | 3.22630e22 | 1.41276 | ||||||||
\(428\) | 3.26890e22 | 1.40323 | ||||||||
\(429\) | 1.22412e20 | 0.00515153 | ||||||||
\(430\) | 3.50046e21 | 0.144425 | ||||||||
\(431\) | −2.09760e22 | −0.848526 | −0.424263 | − | 0.905539i | \(-0.639467\pi\) | ||||
−0.424263 | + | 0.905539i | \(0.639467\pi\) | |||||||
\(432\) | 4.38643e21 | 0.173980 | ||||||||
\(433\) | −7.77111e21 | −0.302229 | −0.151114 | − | 0.988516i | \(-0.548286\pi\) | ||||
−0.151114 | + | 0.988516i | \(0.548286\pi\) | |||||||
\(434\) | −1.70416e20 | −0.00649901 | ||||||||
\(435\) | 4.92323e21 | 0.184116 | ||||||||
\(436\) | −2.13056e22 | −0.781374 | ||||||||
\(437\) | 7.78382e20 | 0.0279963 | ||||||||
\(438\) | −5.74876e21 | −0.202789 | ||||||||
\(439\) | −3.62044e21 | −0.125260 | −0.0626301 | − | 0.998037i | \(-0.519949\pi\) | ||||
−0.0626301 | + | 0.998037i | \(0.519949\pi\) | |||||||
\(440\) | −1.32973e22 | −0.451248 | ||||||||
\(441\) | 1.25070e22 | 0.416318 | ||||||||
\(442\) | −2.12253e19 | −0.000693050 0 | ||||||||
\(443\) | 4.20160e22 | 1.34581 | 0.672905 | − | 0.739729i | \(-0.265046\pi\) | ||||
0.672905 | + | 0.739729i | \(0.265046\pi\) | |||||||
\(444\) | 1.30625e22 | 0.410460 | ||||||||
\(445\) | 6.56113e22 | 2.02264 | ||||||||
\(446\) | 3.60668e21 | 0.109084 | ||||||||
\(447\) | 3.15201e22 | 0.935348 | ||||||||
\(448\) | −4.17790e22 | −1.21645 | ||||||||
\(449\) | −3.62047e22 | −1.03436 | −0.517180 | − | 0.855877i | \(-0.673018\pi\) | ||||
−0.517180 | + | 0.855877i | \(0.673018\pi\) | |||||||
\(450\) | −3.88539e21 | −0.108925 | ||||||||
\(451\) | 4.32549e22 | 1.18997 | ||||||||
\(452\) | −3.82725e22 | −1.03326 | ||||||||
\(453\) | −3.22798e22 | −0.855257 | ||||||||
\(454\) | −6.70083e20 | −0.0174242 | ||||||||
\(455\) | −1.15822e21 | −0.0295593 | ||||||||
\(456\) | −2.47944e20 | −0.00621087 | ||||||||
\(457\) | −3.85735e22 | −0.948422 | −0.474211 | − | 0.880411i | \(-0.657267\pi\) | ||||
−0.474211 | + | 0.880411i | \(0.657267\pi\) | |||||||
\(458\) | −1.00927e22 | −0.243585 | ||||||||
\(459\) | −2.66576e21 | −0.0631557 | ||||||||
\(460\) | 6.43091e22 | 1.49565 | ||||||||
\(461\) | −3.51617e22 | −0.802809 | −0.401405 | − | 0.915901i | \(-0.631478\pi\) | ||||
−0.401405 | + | 0.915901i | \(0.631478\pi\) | |||||||
\(462\) | 5.27776e21 | 0.118302 | ||||||||
\(463\) | −5.56328e22 | −1.22431 | −0.612157 | − | 0.790737i | \(-0.709698\pi\) | ||||
−0.612157 | + | 0.790737i | \(0.709698\pi\) | |||||||
\(464\) | 7.94939e21 | 0.171764 | ||||||||
\(465\) | 1.10073e21 | 0.0233523 | ||||||||
\(466\) | 1.07153e21 | 0.0223215 | ||||||||
\(467\) | −2.54999e22 | −0.521610 | −0.260805 | − | 0.965392i | \(-0.583988\pi\) | ||||
−0.260805 | + | 0.965392i | \(0.583988\pi\) | |||||||
\(468\) | 1.88579e20 | 0.00378794 | ||||||||
\(469\) | −3.36494e22 | −0.663756 | ||||||||
\(470\) | 1.12226e22 | 0.217401 | ||||||||
\(471\) | 4.21374e22 | 0.801661 | ||||||||
\(472\) | 3.06544e22 | 0.572778 | ||||||||
\(473\) | 1.98101e22 | 0.363553 | ||||||||
\(474\) | 3.57868e21 | 0.0645070 | ||||||||
\(475\) | −3.12012e21 | −0.0552429 | ||||||||
\(476\) | 2.73821e22 | 0.476220 | ||||||||
\(477\) | −1.67901e22 | −0.286845 | ||||||||
\(478\) | 4.79262e21 | 0.0804333 | ||||||||
\(479\) | 7.71958e22 | 1.27275 | 0.636373 | − | 0.771381i | \(-0.280434\pi\) | ||||
0.636373 | + | 0.771381i | \(0.280434\pi\) | |||||||
\(480\) | −3.08957e22 | −0.500434 | ||||||||
\(481\) | 5.42180e20 | 0.00862800 | ||||||||
\(482\) | −6.53338e21 | −0.102150 | ||||||||
\(483\) | −5.19023e22 | −0.797325 | ||||||||
\(484\) | 2.70992e22 | 0.409045 | ||||||||
\(485\) | 1.08730e23 | 1.61267 | ||||||||
\(486\) | −7.91541e20 | −0.0115363 | ||||||||
\(487\) | −3.67556e22 | −0.526413 | −0.263207 | − | 0.964739i | \(-0.584780\pi\) | ||||
−0.263207 | + | 0.964739i | \(0.584780\pi\) | |||||||
\(488\) | 2.36845e22 | 0.333347 | ||||||||
\(489\) | −5.14025e22 | −0.710982 | ||||||||
\(490\) | −2.77321e22 | −0.376978 | ||||||||
\(491\) | 8.85815e21 | 0.118345 | 0.0591726 | − | 0.998248i | \(-0.481154\pi\) | ||||
0.0591726 | + | 0.998248i | \(0.481154\pi\) | |||||||
\(492\) | 6.66355e22 | 0.874989 | ||||||||
\(493\) | −4.83107e21 | −0.0623511 | ||||||||
\(494\) | −5.06109e18 | −6.42044e−5 0 | ||||||||
\(495\) | −3.40894e22 | −0.425085 | ||||||||
\(496\) | 1.77731e21 | 0.0217856 | ||||||||
\(497\) | −1.67303e23 | −2.01592 | ||||||||
\(498\) | 1.09344e22 | 0.129523 | ||||||||
\(499\) | −3.19438e22 | −0.371991 | −0.185995 | − | 0.982551i | \(-0.559551\pi\) | ||||
−0.185995 | + | 0.982551i | \(0.559551\pi\) | |||||||
\(500\) | −1.15918e23 | −1.32711 | ||||||||
\(501\) | 6.79084e22 | 0.764368 | ||||||||
\(502\) | −2.17653e22 | −0.240871 | ||||||||
\(503\) | 1.46736e23 | 1.59664 | 0.798322 | − | 0.602230i | \(-0.205721\pi\) | ||||
0.798322 | + | 0.602230i | \(0.205721\pi\) | |||||||
\(504\) | 1.65328e22 | 0.176884 | ||||||||
\(505\) | −1.15481e23 | −1.21488 | ||||||||
\(506\) | −1.21632e22 | −0.125826 | ||||||||
\(507\) | −5.67476e22 | −0.577271 | ||||||||
\(508\) | −2.34568e22 | −0.234653 | ||||||||
\(509\) | −1.22599e22 | −0.120611 | −0.0603054 | − | 0.998180i | \(-0.519207\pi\) | ||||
−0.0603054 | + | 0.998180i | \(0.519207\pi\) | |||||||
\(510\) | 5.91086e21 | 0.0571879 | ||||||||
\(511\) | 3.07825e23 | 2.92905 | ||||||||
\(512\) | −8.40680e22 | −0.786749 | ||||||||
\(513\) | −6.35639e20 | −0.00585077 | ||||||||
\(514\) | 4.14637e21 | 0.0375389 | ||||||||
\(515\) | 9.78830e22 | 0.871657 | ||||||||
\(516\) | 3.05181e22 | 0.267322 | ||||||||
\(517\) | 6.35120e22 | 0.547250 | ||||||||
\(518\) | 2.33760e22 | 0.198138 | ||||||||
\(519\) | −5.37323e22 | −0.448036 | ||||||||
\(520\) | −8.50258e20 | −0.00697465 | ||||||||
\(521\) | −1.70219e23 | −1.37368 | −0.686842 | − | 0.726807i | \(-0.741004\pi\) | ||||
−0.686842 | + | 0.726807i | \(0.741004\pi\) | |||||||
\(522\) | −1.43449e21 | −0.0113893 | ||||||||
\(523\) | 7.34078e21 | 0.0573427 | 0.0286713 | − | 0.999589i | \(-0.490872\pi\) | ||||
0.0286713 | + | 0.999589i | \(0.490872\pi\) | |||||||
\(524\) | −1.24104e22 | −0.0953828 | ||||||||
\(525\) | 2.08049e23 | 1.57330 | ||||||||
\(526\) | 2.39451e22 | 0.178171 | ||||||||
\(527\) | −1.08012e21 | −0.00790830 | ||||||||
\(528\) | −5.50432e22 | −0.396566 | ||||||||
\(529\) | −2.14351e22 | −0.151968 | ||||||||
\(530\) | 3.72292e22 | 0.259740 | ||||||||
\(531\) | 7.85868e22 | 0.539568 | ||||||||
\(532\) | 6.52915e21 | 0.0441172 | ||||||||
\(533\) | 2.76582e21 | 0.0183926 | ||||||||
\(534\) | −1.91172e22 | −0.125119 | ||||||||
\(535\) | −3.77847e23 | −2.43393 | ||||||||
\(536\) | −2.47023e22 | −0.156616 | ||||||||
\(537\) | −1.91545e22 | −0.119533 | ||||||||
\(538\) | −9.38560e21 | −0.0576518 | ||||||||
\(539\) | −1.56944e23 | −0.948945 | ||||||||
\(540\) | −5.25158e22 | −0.312567 | ||||||||
\(541\) | 2.69319e23 | 1.57794 | 0.788970 | − | 0.614431i | \(-0.210614\pi\) | ||||
0.788970 | + | 0.614431i | \(0.210614\pi\) | |||||||
\(542\) | −3.92885e22 | −0.226606 | ||||||||
\(543\) | −1.64278e23 | −0.932781 | ||||||||
\(544\) | 3.03173e22 | 0.169473 | ||||||||
\(545\) | 2.46268e23 | 1.35531 | ||||||||
\(546\) | 3.37472e20 | 0.00182852 | ||||||||
\(547\) | −5.71353e22 | −0.304798 | −0.152399 | − | 0.988319i | \(-0.548700\pi\) | ||||
−0.152399 | + | 0.988319i | \(0.548700\pi\) | |||||||
\(548\) | 4.72035e22 | 0.247936 | ||||||||
\(549\) | 6.07186e22 | 0.314020 | ||||||||
\(550\) | 4.87560e22 | 0.248282 | ||||||||
\(551\) | −1.15195e21 | −0.00577623 | ||||||||
\(552\) | −3.81018e22 | −0.188133 | ||||||||
\(553\) | −1.91625e23 | −0.931728 | ||||||||
\(554\) | −2.02181e22 | −0.0968070 | ||||||||
\(555\) | −1.50987e23 | −0.711951 | ||||||||
\(556\) | −5.22968e22 | −0.242850 | ||||||||
\(557\) | 8.13046e22 | 0.371831 | 0.185916 | − | 0.982566i | \(-0.440475\pi\) | ||||
0.185916 | + | 0.982566i | \(0.440475\pi\) | |||||||
\(558\) | −3.20720e20 | −0.00144456 | ||||||||
\(559\) | 1.26670e21 | 0.00561920 | ||||||||
\(560\) | 5.20801e23 | 2.27548 | ||||||||
\(561\) | 3.34513e22 | 0.143956 | ||||||||
\(562\) | −4.19109e22 | −0.177651 | ||||||||
\(563\) | 2.45069e23 | 1.02322 | 0.511608 | − | 0.859219i | \(-0.329050\pi\) | ||||
0.511608 | + | 0.859219i | \(0.329050\pi\) | |||||||
\(564\) | 9.78422e22 | 0.402396 | ||||||||
\(565\) | 4.42386e23 | 1.79221 | ||||||||
\(566\) | 2.23874e22 | 0.0893438 | ||||||||
\(567\) | 4.23842e22 | 0.166628 | ||||||||
\(568\) | −1.22818e23 | −0.475665 | ||||||||
\(569\) | −4.48105e23 | −1.70972 | −0.854862 | − | 0.518855i | \(-0.826358\pi\) | ||||
−0.854862 | + | 0.518855i | \(0.826358\pi\) | |||||||
\(570\) | 1.40942e21 | 0.00529791 | ||||||||
\(571\) | −4.10855e23 | −1.52153 | −0.760767 | − | 0.649025i | \(-0.775177\pi\) | ||||
−0.760767 | + | 0.649025i | \(0.775177\pi\) | |||||||
\(572\) | −2.36639e21 | −0.00863415 | ||||||||
\(573\) | −1.32502e23 | −0.476329 | ||||||||
\(574\) | 1.19248e23 | 0.422375 | ||||||||
\(575\) | −4.79473e23 | −1.67335 | ||||||||
\(576\) | −7.86276e22 | −0.270386 | ||||||||
\(577\) | 1.87387e23 | 0.634959 | 0.317480 | − | 0.948265i | \(-0.397163\pi\) | ||||
0.317480 | + | 0.948265i | \(0.397163\pi\) | |||||||
\(578\) | 4.80584e22 | 0.160466 | ||||||||
\(579\) | 2.80885e23 | 0.924190 | ||||||||
\(580\) | −9.51728e22 | −0.308585 | ||||||||
\(581\) | −5.85500e23 | −1.87081 | ||||||||
\(582\) | −3.16809e22 | −0.0997589 | ||||||||
\(583\) | 2.10691e23 | 0.653827 | ||||||||
\(584\) | 2.25977e23 | 0.691122 | ||||||||
\(585\) | −2.17975e21 | −0.00657026 | ||||||||
\(586\) | −2.87530e22 | −0.0854186 | ||||||||
\(587\) | 3.17863e23 | 0.930714 | 0.465357 | − | 0.885123i | \(-0.345926\pi\) | ||||
0.465357 | + | 0.885123i | \(0.345926\pi\) | |||||||
\(588\) | −2.41777e23 | −0.697764 | ||||||||
\(589\) | −2.57551e20 | −0.000732627 0 | ||||||||
\(590\) | −1.74253e23 | −0.488583 | ||||||||
\(591\) | 2.63737e23 | 0.728917 | ||||||||
\(592\) | −2.43795e23 | −0.664186 | ||||||||
\(593\) | 5.64469e23 | 1.51592 | 0.757958 | − | 0.652304i | \(-0.226197\pi\) | ||||
0.757958 | + | 0.652304i | \(0.226197\pi\) | |||||||
\(594\) | 9.93267e21 | 0.0262955 | ||||||||
\(595\) | −3.16505e23 | −0.826013 | ||||||||
\(596\) | −6.09326e23 | −1.56768 | ||||||||
\(597\) | 2.81547e23 | 0.714117 | ||||||||
\(598\) | −7.77743e20 | −0.00194481 | ||||||||
\(599\) | 2.56471e22 | 0.0632282 | 0.0316141 | − | 0.999500i | \(-0.489935\pi\) | ||||
0.0316141 | + | 0.999500i | \(0.489935\pi\) | |||||||
\(600\) | 1.52730e23 | 0.371227 | ||||||||
\(601\) | 5.16554e23 | 1.23789 | 0.618946 | − | 0.785433i | \(-0.287560\pi\) | ||||
0.618946 | + | 0.785433i | \(0.287560\pi\) | |||||||
\(602\) | 5.46136e22 | 0.129042 | ||||||||
\(603\) | −6.33278e22 | −0.147536 | ||||||||
\(604\) | 6.24014e23 | 1.43344 | ||||||||
\(605\) | −3.13236e23 | −0.709497 | ||||||||
\(606\) | 3.36479e22 | 0.0751519 | ||||||||
\(607\) | 6.45213e23 | 1.42102 | 0.710508 | − | 0.703689i | \(-0.248465\pi\) | ||||
0.710508 | + | 0.703689i | \(0.248465\pi\) | |||||||
\(608\) | 7.22904e21 | 0.0157000 | ||||||||
\(609\) | 7.68115e22 | 0.164505 | ||||||||
\(610\) | −1.34633e23 | −0.284347 | ||||||||
\(611\) | 4.06110e21 | 0.00845850 | ||||||||
\(612\) | 5.15327e22 | 0.105851 | ||||||||
\(613\) | −5.11815e23 | −1.03681 | −0.518405 | − | 0.855135i | \(-0.673474\pi\) | ||||
−0.518405 | + | 0.855135i | \(0.673474\pi\) | |||||||
\(614\) | 1.66399e22 | 0.0332445 | ||||||||
\(615\) | −7.70229e23 | −1.51768 | ||||||||
\(616\) | −2.07462e23 | −0.403184 | ||||||||
\(617\) | −3.00782e22 | −0.0576537 | −0.0288269 | − | 0.999584i | \(-0.509177\pi\) | ||||
−0.0288269 | + | 0.999584i | \(0.509177\pi\) | |||||||
\(618\) | −2.85203e22 | −0.0539202 | ||||||||
\(619\) | −6.97971e23 | −1.30157 | −0.650784 | − | 0.759263i | \(-0.725560\pi\) | ||||
−0.650784 | + | 0.759263i | \(0.725560\pi\) | |||||||
\(620\) | −2.12786e22 | −0.0391393 | ||||||||
\(621\) | −9.76794e22 | −0.177225 | ||||||||
\(622\) | −8.66140e22 | −0.155014 | ||||||||
\(623\) | 1.02366e24 | 1.80720 | ||||||||
\(624\) | −3.51959e21 | −0.00612946 | ||||||||
\(625\) | 2.82181e23 | 0.484784 | ||||||||
\(626\) | 5.27174e22 | 0.0893454 | ||||||||
\(627\) | 7.97633e21 | 0.0133361 | ||||||||
\(628\) | −8.14575e23 | −1.34361 | ||||||||
\(629\) | 1.48161e23 | 0.241103 | ||||||||
\(630\) | −9.39797e22 | −0.150883 | ||||||||
\(631\) | −5.56309e23 | −0.881183 | −0.440592 | − | 0.897708i | \(-0.645231\pi\) | ||||
−0.440592 | + | 0.897708i | \(0.645231\pi\) | |||||||
\(632\) | −1.40674e23 | −0.219845 | ||||||||
\(633\) | 8.83316e22 | 0.136202 | ||||||||
\(634\) | 1.88130e23 | 0.286220 | ||||||||
\(635\) | 2.71133e23 | 0.407011 | ||||||||
\(636\) | 3.24576e23 | 0.480762 | ||||||||
\(637\) | −1.00354e22 | −0.0146672 | ||||||||
\(638\) | 1.80007e22 | 0.0259605 | ||||||||
\(639\) | −3.14861e23 | −0.448086 | ||||||||
\(640\) | 7.91559e23 | 1.11161 | ||||||||
\(641\) | −3.15692e23 | −0.437492 | −0.218746 | − | 0.975782i | \(-0.570197\pi\) | ||||
−0.218746 | + | 0.975782i | \(0.570197\pi\) | |||||||
\(642\) | 1.10094e23 | 0.150562 | ||||||||
\(643\) | 1.03616e24 | 1.39841 | 0.699203 | − | 0.714924i | \(-0.253539\pi\) | ||||
0.699203 | + | 0.714924i | \(0.253539\pi\) | |||||||
\(644\) | 1.00334e24 | 1.33635 | ||||||||
\(645\) | −3.52754e23 | −0.463675 | ||||||||
\(646\) | −1.38304e21 | −0.00179414 | ||||||||
\(647\) | −5.82417e23 | −0.745671 | −0.372836 | − | 0.927897i | \(-0.621614\pi\) | ||||
−0.372836 | + | 0.927897i | \(0.621614\pi\) | |||||||
\(648\) | 3.11145e22 | 0.0393166 | ||||||||
\(649\) | −9.86149e23 | −1.22988 | ||||||||
\(650\) | 3.11756e21 | 0.00383753 | ||||||||
\(651\) | 1.71734e22 | 0.0208650 | ||||||||
\(652\) | 9.93680e23 | 1.19163 | ||||||||
\(653\) | 1.52832e23 | 0.180905 | 0.0904526 | − | 0.995901i | \(-0.471169\pi\) | ||||
0.0904526 | + | 0.995901i | \(0.471169\pi\) | |||||||
\(654\) | −7.17554e22 | −0.0838385 | ||||||||
\(655\) | 1.43450e23 | 0.165443 | ||||||||
\(656\) | −1.24367e24 | −1.41586 | ||||||||
\(657\) | 5.79323e23 | 0.651051 | ||||||||
\(658\) | 1.75093e23 | 0.194245 | ||||||||
\(659\) | 6.03187e23 | 0.660581 | 0.330290 | − | 0.943879i | \(-0.392853\pi\) | ||||
0.330290 | + | 0.943879i | \(0.392853\pi\) | |||||||
\(660\) | 6.58996e23 | 0.712458 | ||||||||
\(661\) | −1.09124e24 | −1.16468 | −0.582340 | − | 0.812945i | \(-0.697863\pi\) | ||||
−0.582340 | + | 0.812945i | \(0.697863\pi\) | |||||||
\(662\) | −1.91181e23 | −0.201443 | ||||||||
\(663\) | 2.13895e21 | 0.00222503 | ||||||||
\(664\) | −4.29820e23 | −0.441426 | ||||||||
\(665\) | −7.54694e22 | −0.0765221 | ||||||||
\(666\) | 4.39933e22 | 0.0440408 | ||||||||
\(667\) | −1.77021e23 | −0.174967 | ||||||||
\(668\) | −1.31276e24 | −1.28111 | ||||||||
\(669\) | −3.63458e23 | −0.350213 | ||||||||
\(670\) | 1.40419e23 | 0.133595 | ||||||||
\(671\) | −7.61928e23 | −0.715769 | ||||||||
\(672\) | −4.82030e23 | −0.447131 | ||||||||
\(673\) | −3.64938e23 | −0.334265 | −0.167133 | − | 0.985934i | \(-0.553451\pi\) | ||||
−0.167133 | + | 0.985934i | \(0.553451\pi\) | |||||||
\(674\) | 1.96100e22 | 0.0177366 | ||||||||
\(675\) | 3.91545e23 | 0.349703 | ||||||||
\(676\) | 1.09701e24 | 0.967527 | ||||||||
\(677\) | −3.91131e23 | −0.340658 | −0.170329 | − | 0.985387i | \(-0.554483\pi\) | ||||
−0.170329 | + | 0.985387i | \(0.554483\pi\) | |||||||
\(678\) | −1.28898e23 | −0.110865 | ||||||||
\(679\) | 1.69640e24 | 1.44090 | ||||||||
\(680\) | −2.32349e23 | −0.194901 | ||||||||
\(681\) | 6.75267e22 | 0.0559403 | ||||||||
\(682\) | 4.02456e21 | 0.00329270 | ||||||||
\(683\) | 8.44250e23 | 0.682174 | 0.341087 | − | 0.940032i | \(-0.389205\pi\) | ||||
0.341087 | + | 0.940032i | \(0.389205\pi\) | |||||||
\(684\) | 1.22878e22 | 0.00980610 | ||||||||
\(685\) | −5.45617e23 | −0.430049 | ||||||||
\(686\) | −8.62443e22 | −0.0671391 | ||||||||
\(687\) | 1.01708e24 | 0.782025 | ||||||||
\(688\) | −5.69581e23 | −0.432567 | ||||||||
\(689\) | 1.34720e22 | 0.0101058 | ||||||||
\(690\) | 2.16587e23 | 0.160478 | ||||||||
\(691\) | 1.21416e24 | 0.888610 | 0.444305 | − | 0.895876i | \(-0.353451\pi\) | ||||
0.444305 | + | 0.895876i | \(0.353451\pi\) | |||||||
\(692\) | 1.03872e24 | 0.750925 | ||||||||
\(693\) | −5.31859e23 | −0.379808 | ||||||||
\(694\) | −8.11677e22 | −0.0572569 | ||||||||
\(695\) | 6.04490e23 | 0.421229 | ||||||||
\(696\) | 5.63879e22 | 0.0388157 | ||||||||
\(697\) | 7.55811e23 | 0.513966 | ||||||||
\(698\) | 6.46854e20 | 0.000434546 0 | ||||||||
\(699\) | −1.07982e23 | −0.0716628 | ||||||||
\(700\) | −4.02187e24 | −2.63691 | ||||||||
\(701\) | 2.69078e24 | 1.74291 | 0.871456 | − | 0.490473i | \(-0.163176\pi\) | ||||
0.871456 | + | 0.490473i | \(0.163176\pi\) | |||||||
\(702\) | 6.35117e20 | 0.000406432 0 | ||||||||
\(703\) | 3.53283e22 | 0.0223359 | ||||||||
\(704\) | 9.86660e23 | 0.616311 | ||||||||
\(705\) | −1.13094e24 | −0.697964 | ||||||||
\(706\) | −4.10820e23 | −0.250502 | ||||||||
\(707\) | −1.80172e24 | −1.08548 | ||||||||
\(708\) | −1.51919e24 | −0.904336 | ||||||||
\(709\) | −1.01451e24 | −0.596712 | −0.298356 | − | 0.954455i | \(-0.596438\pi\) | ||||
−0.298356 | + | 0.954455i | \(0.596438\pi\) | |||||||
\(710\) | 6.98151e23 | 0.405745 | ||||||||
\(711\) | −3.60636e23 | −0.207099 | ||||||||
\(712\) | 7.51476e23 | 0.426417 | ||||||||
\(713\) | −3.95782e22 | −0.0221919 | ||||||||
\(714\) | 9.22204e22 | 0.0510966 | ||||||||
\(715\) | 2.73527e22 | 0.0149761 | ||||||||
\(716\) | 3.70282e23 | 0.200342 | ||||||||
\(717\) | −4.82970e23 | −0.258230 | ||||||||
\(718\) | −6.99723e22 | −0.0369716 | ||||||||
\(719\) | −3.62460e24 | −1.89263 | −0.946313 | − | 0.323251i | \(-0.895224\pi\) | ||||
−0.946313 | + | 0.323251i | \(0.895224\pi\) | |||||||
\(720\) | 9.80140e23 | 0.505780 | ||||||||
\(721\) | 1.52716e24 | 0.778814 | ||||||||
\(722\) | 3.56478e23 | 0.179666 | ||||||||
\(723\) | 6.58392e23 | 0.327951 | ||||||||
\(724\) | 3.17571e24 | 1.56338 | ||||||||
\(725\) | 7.09585e23 | 0.345248 | ||||||||
\(726\) | 9.12678e22 | 0.0438891 | ||||||||
\(727\) | −2.60528e24 | −1.23826 | −0.619129 | − | 0.785289i | \(-0.712514\pi\) | ||||
−0.619129 | + | 0.785289i | \(0.712514\pi\) | |||||||
\(728\) | −1.32656e22 | −0.00623176 | ||||||||
\(729\) | 7.97664e22 | 0.0370370 | ||||||||
\(730\) | −1.28455e24 | −0.589531 | ||||||||
\(731\) | 3.46150e23 | 0.157024 | ||||||||
\(732\) | −1.17377e24 | −0.526308 | ||||||||
\(733\) | −2.82031e23 | −0.125001 | −0.0625004 | − | 0.998045i | \(-0.519907\pi\) | ||||
−0.0625004 | + | 0.998045i | \(0.519907\pi\) | |||||||
\(734\) | −3.00529e23 | −0.131665 | ||||||||
\(735\) | 2.79467e24 | 1.21028 | ||||||||
\(736\) | 1.11089e24 | 0.475567 | ||||||||
\(737\) | 7.94670e23 | 0.336289 | ||||||||
\(738\) | 2.24422e23 | 0.0938831 | ||||||||
\(739\) | −2.13421e24 | −0.882592 | −0.441296 | − | 0.897362i | \(-0.645481\pi\) | ||||
−0.441296 | + | 0.897362i | \(0.645481\pi\) | |||||||
\(740\) | 2.91879e24 | 1.19326 | ||||||||
\(741\) | 5.10024e20 | 0.000206127 0 | ||||||||
\(742\) | 5.80844e23 | 0.232074 | ||||||||
\(743\) | 1.65375e24 | 0.653229 | 0.326614 | − | 0.945158i | \(-0.394092\pi\) | ||||
0.326614 | + | 0.945158i | \(0.394092\pi\) | |||||||
\(744\) | 1.26071e22 | 0.00492319 | ||||||||
\(745\) | 7.04311e24 | 2.71917 | ||||||||
\(746\) | −4.29503e23 | −0.163940 | ||||||||
\(747\) | −1.10190e24 | −0.415832 | ||||||||
\(748\) | −6.46660e23 | −0.241275 | ||||||||
\(749\) | −5.89511e24 | −2.17469 | ||||||||
\(750\) | −3.90402e23 | −0.142394 | ||||||||
\(751\) | −1.59968e24 | −0.576890 | −0.288445 | − | 0.957496i | \(-0.593138\pi\) | ||||
−0.288445 | + | 0.957496i | \(0.593138\pi\) | |||||||
\(752\) | −1.82610e24 | −0.651137 | ||||||||
\(753\) | 2.19337e24 | 0.773312 | ||||||||
\(754\) | 1.15100e21 | 0.000401255 0 | ||||||||
\(755\) | −7.21288e24 | −2.48633 | ||||||||
\(756\) | −8.19344e23 | −0.279274 | ||||||||
\(757\) | −3.10841e24 | −1.04767 | −0.523834 | − | 0.851820i | \(-0.675499\pi\) | ||||
−0.523834 | + | 0.851820i | \(0.675499\pi\) | |||||||
\(758\) | −9.18890e23 | −0.306250 | ||||||||
\(759\) | 1.22573e24 | 0.403962 | ||||||||
\(760\) | −5.54027e22 | −0.0180557 | ||||||||
\(761\) | 3.83430e24 | 1.23571 | 0.617856 | − | 0.786292i | \(-0.288002\pi\) | ||||
0.617856 | + | 0.786292i | \(0.288002\pi\) | |||||||
\(762\) | −7.90003e22 | −0.0251774 | ||||||||
\(763\) | 3.84224e24 | 1.21095 | ||||||||
\(764\) | 2.56144e24 | 0.798344 | ||||||||
\(765\) | −5.95659e23 | −0.183601 | ||||||||
\(766\) | 8.23113e23 | 0.250908 | ||||||||
\(767\) | −6.30565e22 | −0.0190094 | ||||||||
\(768\) | 1.34014e24 | 0.399558 | ||||||||
\(769\) | −3.27383e24 | −0.965343 | −0.482672 | − | 0.875801i | \(-0.660334\pi\) | ||||
−0.482672 | + | 0.875801i | \(0.660334\pi\) | |||||||
\(770\) | 1.17931e24 | 0.343918 | ||||||||
\(771\) | −4.17845e23 | −0.120518 | ||||||||
\(772\) | −5.42990e24 | −1.54898 | ||||||||
\(773\) | −7.30757e23 | −0.206180 | −0.103090 | − | 0.994672i | \(-0.532873\pi\) | ||||
−0.103090 | + | 0.994672i | \(0.532873\pi\) | |||||||
\(774\) | 1.02782e23 | 0.0286827 | ||||||||
\(775\) | 1.58648e23 | 0.0437895 | ||||||||
\(776\) | 1.24534e24 | 0.339987 | ||||||||
\(777\) | −2.35568e24 | −0.636118 | ||||||||
\(778\) | −3.68336e23 | −0.0983824 | ||||||||
\(779\) | 1.80220e23 | 0.0476140 | ||||||||
\(780\) | 4.21377e22 | 0.0110120 | ||||||||
\(781\) | 3.95104e24 | 1.02136 | ||||||||
\(782\) | −2.12533e23 | −0.0543461 | ||||||||
\(783\) | 1.44558e23 | 0.0365652 | ||||||||
\(784\) | 4.51246e24 | 1.12909 | ||||||||
\(785\) | 9.41554e24 | 2.33052 | ||||||||
\(786\) | −4.17971e22 | −0.0102342 | ||||||||
\(787\) | 6.01570e23 | 0.145714 | 0.0728570 | − | 0.997342i | \(-0.476788\pi\) | ||||
0.0728570 | + | 0.997342i | \(0.476788\pi\) | |||||||
\(788\) | −5.09841e24 | −1.22169 | ||||||||
\(789\) | −2.41303e24 | −0.572016 | ||||||||
\(790\) | 7.99650e23 | 0.187529 | ||||||||
\(791\) | 6.90204e24 | 1.60132 | ||||||||
\(792\) | −3.90442e23 | −0.0896173 | ||||||||
\(793\) | −4.87194e22 | −0.0110632 | ||||||||
\(794\) | −3.65689e23 | −0.0821556 | ||||||||
\(795\) | −3.75172e24 | −0.833891 | ||||||||
\(796\) | −5.44270e24 | −1.19689 | ||||||||
\(797\) | 5.16820e24 | 1.12446 | 0.562230 | − | 0.826981i | \(-0.309944\pi\) | ||||
0.562230 | + | 0.826981i | \(0.309944\pi\) | |||||||
\(798\) | 2.19896e22 | 0.00473361 | ||||||||
\(799\) | 1.10977e24 | 0.236366 | ||||||||
\(800\) | −4.45299e24 | −0.938398 | ||||||||
\(801\) | 1.92651e24 | 0.401694 | ||||||||
\(802\) | 1.23846e24 | 0.255505 | ||||||||
\(803\) | −7.26965e24 | −1.48399 | ||||||||
\(804\) | 1.22421e24 | 0.247275 | ||||||||
\(805\) | −1.15975e25 | −2.31792 | ||||||||
\(806\) | 2.57340e20 | 5.08931e−5 0 | ||||||||
\(807\) | 9.45821e23 | 0.185090 | ||||||||
\(808\) | −1.32266e24 | −0.256124 | ||||||||
\(809\) | 8.29099e24 | 1.58871 | 0.794354 | − | 0.607455i | \(-0.207810\pi\) | ||||
0.794354 | + | 0.607455i | \(0.207810\pi\) | |||||||
\(810\) | −1.76869e23 | −0.0335373 | ||||||||
\(811\) | −6.74898e23 | −0.126637 | −0.0633185 | − | 0.997993i | \(-0.520168\pi\) | ||||
−0.0633185 | + | 0.997993i | \(0.520168\pi\) | |||||||
\(812\) | −1.48487e24 | −0.275717 | ||||||||
\(813\) | 3.95924e24 | 0.727515 | ||||||||
\(814\) | −5.52051e23 | −0.100386 | ||||||||
\(815\) | −1.14858e25 | −2.06691 | ||||||||
\(816\) | −9.61792e23 | −0.171283 | ||||||||
\(817\) | 8.25381e22 | 0.0145468 | ||||||||
\(818\) | −7.99094e23 | −0.139378 | ||||||||
\(819\) | −3.40082e22 | −0.00587044 | ||||||||
\(820\) | 1.48896e25 | 2.54370 | ||||||||
\(821\) | −3.52716e24 | −0.596361 | −0.298180 | − | 0.954510i | \(-0.596380\pi\) | ||||
−0.298180 | + | 0.954510i | \(0.596380\pi\) | |||||||
\(822\) | 1.58977e23 | 0.0266026 | ||||||||
\(823\) | 2.10509e24 | 0.348636 | 0.174318 | − | 0.984689i | \(-0.444228\pi\) | ||||
0.174318 | + | 0.984689i | \(0.444228\pi\) | |||||||
\(824\) | 1.12110e24 | 0.183765 | ||||||||
\(825\) | −4.91331e24 | −0.797106 | ||||||||
\(826\) | −2.71867e24 | −0.436542 | ||||||||
\(827\) | 7.78739e24 | 1.23764 | 0.618821 | − | 0.785532i | \(-0.287610\pi\) | ||||
0.618821 | + | 0.785532i | \(0.287610\pi\) | |||||||
\(828\) | 1.88828e24 | 0.297035 | ||||||||
\(829\) | −3.67550e24 | −0.572273 | −0.286137 | − | 0.958189i | \(-0.592371\pi\) | ||||
−0.286137 | + | 0.958189i | \(0.592371\pi\) | |||||||
\(830\) | 2.44328e24 | 0.376539 | ||||||||
\(831\) | 2.03745e24 | 0.310798 | ||||||||
\(832\) | 6.30892e22 | 0.00952592 | ||||||||
\(833\) | −2.74235e24 | −0.409865 | ||||||||
\(834\) | −1.76131e23 | −0.0260570 | ||||||||
\(835\) | 1.51740e25 | 2.22211 | ||||||||
\(836\) | −1.54193e23 | −0.0223518 | ||||||||
\(837\) | 3.23201e22 | 0.00463774 | ||||||||
\(838\) | 1.38369e24 | 0.196546 | ||||||||
\(839\) | −7.12132e23 | −0.100135 | −0.0500673 | − | 0.998746i | \(-0.515944\pi\) | ||||
−0.0500673 | + | 0.998746i | \(0.515944\pi\) | |||||||
\(840\) | 3.69423e24 | 0.514221 | ||||||||
\(841\) | −6.99517e24 | −0.963901 | ||||||||
\(842\) | 4.52021e23 | 0.0616603 | ||||||||
\(843\) | 4.22351e24 | 0.570348 | ||||||||
\(844\) | −1.70757e24 | −0.228280 | ||||||||
\(845\) | −1.26801e25 | −1.67819 | ||||||||
\(846\) | 3.29524e23 | 0.0431756 | ||||||||
\(847\) | −4.88706e24 | −0.633926 | ||||||||
\(848\) | −6.05779e24 | −0.777946 | ||||||||
\(849\) | −2.25606e24 | −0.286837 | ||||||||
\(850\) | 8.51933e23 | 0.107237 | ||||||||
\(851\) | 5.42895e24 | 0.676573 | ||||||||
\(852\) | 6.08670e24 | 0.751009 | ||||||||
\(853\) | 9.94213e24 | 1.21454 | 0.607271 | − | 0.794495i | \(-0.292264\pi\) | ||||
0.607271 | + | 0.794495i | \(0.292264\pi\) | |||||||
\(854\) | −2.10053e24 | −0.254060 | ||||||||
\(855\) | −1.42032e23 | −0.0170089 | ||||||||
\(856\) | −4.32765e24 | −0.513127 | ||||||||
\(857\) | −7.12623e23 | −0.0836610 | −0.0418305 | − | 0.999125i | \(-0.513319\pi\) | ||||
−0.0418305 | + | 0.999125i | \(0.513319\pi\) | |||||||
\(858\) | −7.96978e21 | −0.000926413 0 | ||||||||
\(859\) | −6.42042e24 | −0.738961 | −0.369480 | − | 0.929239i | \(-0.620464\pi\) | ||||
−0.369480 | + | 0.929239i | \(0.620464\pi\) | |||||||
\(860\) | 6.81921e24 | 0.777136 | ||||||||
\(861\) | −1.20170e25 | −1.35603 | ||||||||
\(862\) | 1.36567e24 | 0.152593 | ||||||||
\(863\) | −3.45207e24 | −0.381934 | −0.190967 | − | 0.981596i | \(-0.561162\pi\) | ||||
−0.190967 | + | 0.981596i | \(0.561162\pi\) | |||||||
\(864\) | −9.07173e23 | −0.0993856 | ||||||||
\(865\) | −1.20064e25 | −1.30249 | ||||||||
\(866\) | 5.05948e23 | 0.0543506 | ||||||||
\(867\) | −4.84302e24 | −0.515173 | ||||||||
\(868\) | −3.31986e23 | −0.0349705 | ||||||||
\(869\) | 4.52545e24 | 0.472056 | ||||||||
\(870\) | −3.20533e23 | −0.0331100 | ||||||||
\(871\) | 5.08130e22 | 0.00519781 | ||||||||
\(872\) | 2.82062e24 | 0.285729 | ||||||||
\(873\) | 3.19260e24 | 0.320275 | ||||||||
\(874\) | −5.06776e22 | −0.00503465 | ||||||||
\(875\) | 2.09046e25 | 2.05671 | ||||||||
\(876\) | −1.11991e25 | −1.09119 | ||||||||
\(877\) | 1.98750e25 | 1.91783 | 0.958915 | − | 0.283692i | \(-0.0915595\pi\) | ||||
0.958915 | + | 0.283692i | \(0.0915595\pi\) | |||||||
\(878\) | 2.35714e23 | 0.0225259 | ||||||||
\(879\) | 2.89754e24 | 0.274236 | ||||||||
\(880\) | −1.22993e25 | −1.15286 | ||||||||
\(881\) | −1.53861e24 | −0.142835 | −0.0714175 | − | 0.997447i | \(-0.522752\pi\) | ||||
−0.0714175 | + | 0.997447i | \(0.522752\pi\) | |||||||
\(882\) | −8.14284e23 | −0.0748675 | ||||||||
\(883\) | −8.67401e24 | −0.789867 | −0.394934 | − | 0.918710i | \(-0.629232\pi\) | ||||
−0.394934 | + | 0.918710i | \(0.629232\pi\) | |||||||
\(884\) | −4.13489e22 | −0.00372923 | ||||||||
\(885\) | 1.75601e25 | 1.56859 | ||||||||
\(886\) | −2.73551e24 | −0.242020 | ||||||||
\(887\) | 7.74587e24 | 0.678765 | 0.339383 | − | 0.940648i | \(-0.389782\pi\) | ||||
0.339383 | + | 0.940648i | \(0.389782\pi\) | |||||||
\(888\) | −1.72932e24 | −0.150095 | ||||||||
\(889\) | 4.23018e24 | 0.363659 | ||||||||
\(890\) | −4.27171e24 | −0.363737 | ||||||||
\(891\) | −1.00095e24 | −0.0844214 | ||||||||
\(892\) | 7.02615e24 | 0.586970 | ||||||||
\(893\) | 2.64620e23 | 0.0218971 | ||||||||
\(894\) | −2.05216e24 | −0.168206 | ||||||||
\(895\) | −4.28003e24 | −0.347497 | ||||||||
\(896\) | 1.23498e25 | 0.993212 | ||||||||
\(897\) | 7.83760e22 | 0.00624378 | ||||||||
\(898\) | 2.35716e24 | 0.186011 | ||||||||
\(899\) | 5.85728e22 | 0.00457866 | ||||||||
\(900\) | −7.56911e24 | −0.586116 | ||||||||
\(901\) | 3.68149e24 | 0.282399 | ||||||||
\(902\) | −2.81617e24 | −0.213995 | ||||||||
\(903\) | −5.50361e24 | −0.414288 | ||||||||
\(904\) | 5.06684e24 | 0.377838 | ||||||||
\(905\) | −3.67076e25 | −2.71171 | ||||||||
\(906\) | 2.10162e24 | 0.153803 | ||||||||
\(907\) | −9.51449e24 | −0.689801 | −0.344900 | − | 0.938639i | \(-0.612087\pi\) | ||||
−0.344900 | + | 0.938639i | \(0.612087\pi\) | |||||||
\(908\) | −1.30538e24 | −0.0937580 | ||||||||
\(909\) | −3.39082e24 | −0.241274 | ||||||||
\(910\) | 7.54075e22 | 0.00531572 | ||||||||
\(911\) | −5.87611e24 | −0.410378 | −0.205189 | − | 0.978722i | \(-0.565781\pi\) | ||||
−0.205189 | + | 0.978722i | \(0.565781\pi\) | |||||||
\(912\) | −2.29336e23 | −0.0158677 | ||||||||
\(913\) | 1.38272e25 | 0.947838 | ||||||||
\(914\) | 2.51138e24 | 0.170557 | ||||||||
\(915\) | 1.35675e25 | 0.912892 | ||||||||
\(916\) | −1.96615e25 | −1.31070 | ||||||||
\(917\) | 2.23808e24 | 0.147821 | ||||||||
\(918\) | 1.73558e23 | 0.0113574 | ||||||||
\(919\) | 1.95287e25 | 1.26617 | 0.633084 | − | 0.774083i | \(-0.281789\pi\) | ||||
0.633084 | + | 0.774083i | \(0.281789\pi\) | |||||||
\(920\) | −8.51379e24 | −0.546923 | ||||||||
\(921\) | −1.67686e24 | −0.106731 | ||||||||
\(922\) | 2.28925e24 | 0.144371 | ||||||||
\(923\) | 2.52638e23 | 0.0157865 | ||||||||
\(924\) | 1.02816e25 | 0.636572 | ||||||||
\(925\) | −2.17618e25 | −1.33503 | ||||||||
\(926\) | 3.62205e24 | 0.220171 | ||||||||
\(927\) | 2.87409e24 | 0.173110 | ||||||||
\(928\) | −1.64404e24 | −0.0981195 | ||||||||
\(929\) | −4.51245e24 | −0.266857 | −0.133428 | − | 0.991058i | \(-0.542599\pi\) | ||||
−0.133428 | + | 0.991058i | \(0.542599\pi\) | |||||||
\(930\) | −7.16644e22 | −0.00419951 | ||||||||
\(931\) | −6.53902e23 | −0.0379700 | ||||||||
\(932\) | 2.08743e24 | 0.120110 | ||||||||
\(933\) | 8.72840e24 | 0.497669 | ||||||||
\(934\) | 1.66021e24 | 0.0938024 | ||||||||
\(935\) | 7.47463e24 | 0.418496 | ||||||||
\(936\) | −2.49657e22 | −0.00138516 | ||||||||
\(937\) | 9.95126e24 | 0.547131 | 0.273566 | − | 0.961853i | \(-0.411797\pi\) | ||||
0.273566 | + | 0.961853i | \(0.411797\pi\) | |||||||
\(938\) | 2.19079e24 | 0.119365 | ||||||||
\(939\) | −5.31252e24 | −0.286842 | ||||||||
\(940\) | 2.18627e25 | 1.16981 | ||||||||
\(941\) | −1.60734e25 | −0.852309 | −0.426155 | − | 0.904650i | \(-0.640132\pi\) | ||||
−0.426155 | + | 0.904650i | \(0.640132\pi\) | |||||||
\(942\) | −2.74341e24 | −0.144165 | ||||||||
\(943\) | 2.76946e25 | 1.44227 | ||||||||
\(944\) | 2.83538e25 | 1.46335 | ||||||||
\(945\) | 9.47067e24 | 0.484407 | ||||||||
\(946\) | −1.28976e24 | −0.0653786 | ||||||||
\(947\) | −1.75270e25 | −0.880505 | −0.440253 | − | 0.897874i | \(-0.645111\pi\) | ||||
−0.440253 | + | 0.897874i | \(0.645111\pi\) | |||||||
\(948\) | 6.97160e24 | 0.347105 | ||||||||
\(949\) | −4.64838e23 | −0.0229371 | ||||||||
\(950\) | 2.03140e23 | 0.00993447 | ||||||||
\(951\) | −1.89586e25 | −0.918907 | ||||||||
\(952\) | −3.62508e24 | −0.174142 | ||||||||
\(953\) | −2.36935e25 | −1.12808 | −0.564040 | − | 0.825747i | \(-0.690754\pi\) | ||||
−0.564040 | + | 0.825747i | \(0.690754\pi\) | |||||||
\(954\) | 1.09314e24 | 0.0515840 | ||||||||
\(955\) | −2.96072e25 | −1.38474 | ||||||||
\(956\) | 9.33647e24 | 0.432803 | ||||||||
\(957\) | −1.81399e24 | −0.0833459 | ||||||||
\(958\) | −5.02594e24 | −0.228881 | ||||||||
\(959\) | −8.51265e24 | −0.384243 | ||||||||
\(960\) | −1.75692e25 | −0.786043 | ||||||||
\(961\) | −2.25370e25 | −0.999419 | ||||||||
\(962\) | −3.52994e22 | −0.00155160 | ||||||||
\(963\) | −1.10945e25 | −0.483376 | ||||||||
\(964\) | −1.27276e25 | −0.549658 | ||||||||
\(965\) | 6.27633e25 | 2.68673 | ||||||||
\(966\) | 3.37917e24 | 0.143385 | ||||||||
\(967\) | −2.02177e25 | −0.850369 | −0.425185 | − | 0.905107i | \(-0.639791\pi\) | ||||
−0.425185 | + | 0.905107i | \(0.639791\pi\) | |||||||
\(968\) | −3.58763e24 | −0.149578 | ||||||||
\(969\) | 1.39374e23 | 0.00576008 | ||||||||
\(970\) | −7.07904e24 | −0.290011 | ||||||||
\(971\) | 2.75403e25 | 1.11842 | 0.559210 | − | 0.829026i | \(-0.311105\pi\) | ||||
0.559210 | + | 0.829026i | \(0.311105\pi\) | |||||||
\(972\) | −1.54200e24 | −0.0620754 | ||||||||
\(973\) | 9.43117e24 | 0.376362 | ||||||||
\(974\) | 2.39302e24 | 0.0946663 | ||||||||
\(975\) | −3.14168e23 | −0.0123203 | ||||||||
\(976\) | 2.19070e25 | 0.851646 | ||||||||
\(977\) | 3.78814e25 | 1.45990 | 0.729948 | − | 0.683502i | \(-0.239544\pi\) | ||||
0.729948 | + | 0.683502i | \(0.239544\pi\) | |||||||
\(978\) | 3.34663e24 | 0.127858 | ||||||||
\(979\) | −2.41749e25 | −0.915612 | ||||||||
\(980\) | −5.40247e25 | −2.02848 | ||||||||
\(981\) | 7.23105e24 | 0.269163 | ||||||||
\(982\) | −5.76722e23 | −0.0212823 | ||||||||
\(983\) | −5.25889e25 | −1.92393 | −0.961965 | − | 0.273171i | \(-0.911927\pi\) | ||||
−0.961965 | + | 0.273171i | \(0.911927\pi\) | |||||||
\(984\) | −8.82178e24 | −0.319962 | ||||||||
\(985\) | 5.89317e25 | 2.11905 | ||||||||
\(986\) | 3.14533e23 | 0.0112128 | ||||||||
\(987\) | −1.76448e25 | −0.623621 | ||||||||
\(988\) | −9.85947e21 | −0.000345477 0 | ||||||||
\(989\) | 1.26837e25 | 0.440634 | ||||||||
\(990\) | 2.21944e24 | 0.0764441 | ||||||||
\(991\) | 6.05240e24 | 0.206682 | 0.103341 | − | 0.994646i | \(-0.467047\pi\) | ||||
0.103341 | + | 0.994646i | \(0.467047\pi\) | |||||||
\(992\) | −3.67573e23 | −0.0124450 | ||||||||
\(993\) | 1.92660e25 | 0.646731 | ||||||||
\(994\) | 1.08925e25 | 0.362528 | ||||||||
\(995\) | 6.29113e25 | 2.07602 | ||||||||
\(996\) | 2.13013e25 | 0.696950 | ||||||||
\(997\) | −4.03816e24 | −0.131001 | −0.0655005 | − | 0.997853i | \(-0.520864\pi\) | ||||
−0.0655005 | + | 0.997853i | \(0.520864\pi\) | |||||||
\(998\) | 2.07974e24 | 0.0668960 | ||||||||
\(999\) | −4.43336e24 | −0.141393 |
(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.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 9.18.a.c.1.2 | 2 | |||
4.3 | odd | 2 | 48.18.a.h.1.2 | 2 | |||
5.2 | odd | 4 | 75.18.b.c.49.2 | 4 | |||
5.3 | odd | 4 | 75.18.b.c.49.3 | 4 | |||
5.4 | even | 2 | 75.18.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.18.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9.18.a.c.1.2 | 2 | 3.2 | odd | 2 | |||
48.18.a.h.1.2 | 2 | 4.3 | odd | 2 | |||
75.18.a.b.1.2 | 2 | 5.4 | even | 2 | |||
75.18.b.c.49.2 | 4 | 5.2 | odd | 4 | |||
75.18.b.c.49.3 | 4 | 5.3 | odd | 4 |