Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,20,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(11.4408348278\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 323561x^{2} - 26738538x + 10870990650 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-267.923\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1360.76 | 1.87930 | 0.939651 | − | 0.342134i | \(-0.111150\pi\) | ||||
0.939651 | + | 0.342134i | \(0.111150\pi\) | |||||||
\(3\) | 10517.7 | 0.308511 | 0.154256 | − | 0.988031i | \(-0.450702\pi\) | ||||
0.154256 | + | 0.988031i | \(0.450702\pi\) | |||||||
\(4\) | 1.32738e6 | 2.53178 | ||||||||
\(5\) | −1.95312e6 | −0.447214 | ||||||||
\(6\) | 1.43121e7 | 0.579786 | ||||||||
\(7\) | 1.23996e8 | 1.16138 | 0.580692 | − | 0.814123i | \(-0.302782\pi\) | ||||
0.580692 | + | 0.814123i | \(0.302782\pi\) | |||||||
\(8\) | 1.09282e9 | 2.87867 | ||||||||
\(9\) | −1.05164e9 | −0.904821 | ||||||||
\(10\) | −2.65773e9 | −0.840450 | ||||||||
\(11\) | 3.15053e9 | 0.402859 | 0.201430 | − | 0.979503i | \(-0.435441\pi\) | ||||
0.201430 | + | 0.979503i | \(0.435441\pi\) | |||||||
\(12\) | 1.39611e10 | 0.781081 | ||||||||
\(13\) | −4.41439e10 | −1.15454 | −0.577270 | − | 0.816553i | \(-0.695882\pi\) | ||||
−0.577270 | + | 0.816553i | \(0.695882\pi\) | |||||||
\(14\) | 1.68729e11 | 2.18259 | ||||||||
\(15\) | −2.05425e10 | −0.137970 | ||||||||
\(16\) | 7.91131e11 | 2.87812 | ||||||||
\(17\) | 6.29241e11 | 1.28692 | 0.643461 | − | 0.765479i | \(-0.277498\pi\) | ||||
0.643461 | + | 0.765479i | \(0.277498\pi\) | |||||||
\(18\) | −1.43103e12 | −1.70043 | ||||||||
\(19\) | −1.75434e12 | −1.24725 | −0.623625 | − | 0.781724i | \(-0.714341\pi\) | ||||
−0.623625 | + | 0.781724i | \(0.714341\pi\) | |||||||
\(20\) | −2.59254e12 | −1.13225 | ||||||||
\(21\) | 1.30416e12 | 0.358300 | ||||||||
\(22\) | 4.28712e12 | 0.757094 | ||||||||
\(23\) | −8.87113e12 | −1.02699 | −0.513493 | − | 0.858094i | \(-0.671649\pi\) | ||||
−0.513493 | + | 0.858094i | \(0.671649\pi\) | |||||||
\(24\) | 1.14940e13 | 0.888102 | ||||||||
\(25\) | 3.81470e12 | 0.200000 | ||||||||
\(26\) | −6.00693e13 | −2.16973 | ||||||||
\(27\) | −2.32852e13 | −0.587659 | ||||||||
\(28\) | 1.64590e14 | 2.94036 | ||||||||
\(29\) | −6.96019e13 | −0.890922 | −0.445461 | − | 0.895301i | \(-0.646960\pi\) | ||||
−0.445461 | + | 0.895301i | \(0.646960\pi\) | |||||||
\(30\) | −2.79534e13 | −0.259288 | ||||||||
\(31\) | −2.01459e14 | −1.36852 | −0.684258 | − | 0.729240i | \(-0.739874\pi\) | ||||
−0.684258 | + | 0.729240i | \(0.739874\pi\) | |||||||
\(32\) | 5.03589e14 | 2.53018 | ||||||||
\(33\) | 3.31365e13 | 0.124287 | ||||||||
\(34\) | 8.56247e14 | 2.41852 | ||||||||
\(35\) | −2.42179e14 | −0.519387 | ||||||||
\(36\) | −1.39592e15 | −2.29080 | ||||||||
\(37\) | 7.44252e14 | 0.941464 | 0.470732 | − | 0.882276i | \(-0.343990\pi\) | ||||
0.470732 | + | 0.882276i | \(0.343990\pi\) | |||||||
\(38\) | −2.38723e15 | −2.34396 | ||||||||
\(39\) | −4.64295e14 | −0.356189 | ||||||||
\(40\) | −2.13441e15 | −1.28738 | ||||||||
\(41\) | 1.02353e15 | 0.488265 | 0.244132 | − | 0.969742i | \(-0.421497\pi\) | ||||
0.244132 | + | 0.969742i | \(0.421497\pi\) | |||||||
\(42\) | 1.77464e15 | 0.673354 | ||||||||
\(43\) | 4.31907e15 | 1.31051 | 0.655255 | − | 0.755408i | \(-0.272561\pi\) | ||||
0.655255 | + | 0.755408i | \(0.272561\pi\) | |||||||
\(44\) | 4.18195e15 | 1.01995 | ||||||||
\(45\) | 2.05398e15 | 0.404648 | ||||||||
\(46\) | −1.20715e16 | −1.93002 | ||||||||
\(47\) | 3.87185e15 | 0.504649 | 0.252324 | − | 0.967643i | \(-0.418805\pi\) | ||||
0.252324 | + | 0.967643i | \(0.418805\pi\) | |||||||
\(48\) | 8.32092e15 | 0.887931 | ||||||||
\(49\) | 3.97607e15 | 0.348812 | ||||||||
\(50\) | 5.19089e15 | 0.375860 | ||||||||
\(51\) | 6.61820e15 | 0.397030 | ||||||||
\(52\) | −5.85958e16 | −2.92304 | ||||||||
\(53\) | 2.20534e16 | 0.918028 | 0.459014 | − | 0.888429i | \(-0.348203\pi\) | ||||
0.459014 | + | 0.888429i | \(0.348203\pi\) | |||||||
\(54\) | −3.16856e16 | −1.10439 | ||||||||
\(55\) | −6.15338e15 | −0.180164 | ||||||||
\(56\) | 1.35505e17 | 3.34324 | ||||||||
\(57\) | −1.84517e16 | −0.384790 | ||||||||
\(58\) | −9.47114e16 | −1.67431 | ||||||||
\(59\) | 2.82151e16 | 0.424020 | 0.212010 | − | 0.977267i | \(-0.431999\pi\) | ||||
0.212010 | + | 0.977267i | \(0.431999\pi\) | |||||||
\(60\) | −2.72677e16 | −0.349310 | ||||||||
\(61\) | 1.90704e16 | 0.208798 | 0.104399 | − | 0.994536i | \(-0.466708\pi\) | ||||
0.104399 | + | 0.994536i | \(0.466708\pi\) | |||||||
\(62\) | −2.74137e17 | −2.57185 | ||||||||
\(63\) | −1.30399e17 | −1.05084 | ||||||||
\(64\) | 2.70484e17 | 1.87686 | ||||||||
\(65\) | 8.62186e16 | 0.516326 | ||||||||
\(66\) | 4.50908e16 | 0.233572 | ||||||||
\(67\) | 2.68524e17 | 1.20579 | 0.602897 | − | 0.797819i | \(-0.294013\pi\) | ||||
0.602897 | + | 0.797819i | \(0.294013\pi\) | |||||||
\(68\) | 8.35243e17 | 3.25820 | ||||||||
\(69\) | −9.33043e16 | −0.316836 | ||||||||
\(70\) | −3.29548e17 | −0.976084 | ||||||||
\(71\) | −1.98938e17 | −0.514949 | −0.257474 | − | 0.966285i | \(-0.582890\pi\) | ||||
−0.257474 | + | 0.966285i | \(0.582890\pi\) | |||||||
\(72\) | −1.14925e18 | −2.60468 | ||||||||
\(73\) | 2.55551e17 | 0.508055 | 0.254028 | − | 0.967197i | \(-0.418245\pi\) | ||||
0.254028 | + | 0.967197i | \(0.418245\pi\) | |||||||
\(74\) | 1.01275e18 | 1.76929 | ||||||||
\(75\) | 4.01220e16 | 0.0617022 | ||||||||
\(76\) | −2.32867e18 | −3.15776 | ||||||||
\(77\) | 3.90653e17 | 0.467874 | ||||||||
\(78\) | −6.31794e17 | −0.669386 | ||||||||
\(79\) | 8.98937e17 | 0.843862 | 0.421931 | − | 0.906628i | \(-0.361352\pi\) | ||||
0.421931 | + | 0.906628i | \(0.361352\pi\) | |||||||
\(80\) | −1.54518e18 | −1.28713 | ||||||||
\(81\) | 9.77370e17 | 0.723522 | ||||||||
\(82\) | 1.39278e18 | 0.917597 | ||||||||
\(83\) | −8.68645e17 | −0.510035 | −0.255018 | − | 0.966936i | \(-0.582081\pi\) | ||||
−0.255018 | + | 0.966936i | \(0.582081\pi\) | |||||||
\(84\) | 1.73111e18 | 0.907135 | ||||||||
\(85\) | −1.22899e18 | −0.575529 | ||||||||
\(86\) | 5.87722e18 | 2.46284 | ||||||||
\(87\) | −7.32055e17 | −0.274860 | ||||||||
\(88\) | 3.44295e18 | 1.15970 | ||||||||
\(89\) | −2.78159e18 | −0.841567 | −0.420783 | − | 0.907161i | \(-0.638245\pi\) | ||||
−0.420783 | + | 0.907161i | \(0.638245\pi\) | |||||||
\(90\) | 2.79498e18 | 0.760456 | ||||||||
\(91\) | −5.47366e18 | −1.34086 | ||||||||
\(92\) | −1.17754e19 | −2.60010 | ||||||||
\(93\) | −2.11889e18 | −0.422202 | ||||||||
\(94\) | 5.26866e18 | 0.948387 | ||||||||
\(95\) | 3.42644e18 | 0.557787 | ||||||||
\(96\) | 5.29663e18 | 0.780589 | ||||||||
\(97\) | −2.57839e18 | −0.344364 | −0.172182 | − | 0.985065i | \(-0.555082\pi\) | ||||
−0.172182 | + | 0.985065i | \(0.555082\pi\) | |||||||
\(98\) | 5.41048e18 | 0.655523 | ||||||||
\(99\) | −3.31322e18 | −0.364515 | ||||||||
\(100\) | 5.06355e18 | 0.506355 | ||||||||
\(101\) | −3.76803e18 | −0.342816 | −0.171408 | − | 0.985200i | \(-0.554832\pi\) | ||||
−0.171408 | + | 0.985200i | \(0.554832\pi\) | |||||||
\(102\) | 9.00579e18 | 0.746140 | ||||||||
\(103\) | −3.38045e18 | −0.255283 | −0.127641 | − | 0.991820i | \(-0.540741\pi\) | ||||
−0.127641 | + | 0.991820i | \(0.540741\pi\) | |||||||
\(104\) | −4.82412e19 | −3.32354 | ||||||||
\(105\) | −2.54718e18 | −0.160237 | ||||||||
\(106\) | 3.00095e19 | 1.72525 | ||||||||
\(107\) | −8.94715e18 | −0.470477 | −0.235239 | − | 0.971938i | \(-0.575587\pi\) | ||||
−0.235239 | + | 0.971938i | \(0.575587\pi\) | |||||||
\(108\) | −3.09084e19 | −1.48782 | ||||||||
\(109\) | 4.27066e19 | 1.88340 | 0.941701 | − | 0.336452i | \(-0.109227\pi\) | ||||
0.941701 | + | 0.336452i | \(0.109227\pi\) | |||||||
\(110\) | −8.37328e18 | −0.338583 | ||||||||
\(111\) | 7.82785e18 | 0.290452 | ||||||||
\(112\) | 9.80969e19 | 3.34260 | ||||||||
\(113\) | −1.68233e19 | −0.526823 | −0.263412 | − | 0.964684i | \(-0.584848\pi\) | ||||
−0.263412 | + | 0.964684i | \(0.584848\pi\) | |||||||
\(114\) | −2.51083e19 | −0.723138 | ||||||||
\(115\) | 1.73264e19 | 0.459282 | ||||||||
\(116\) | −9.23881e19 | −2.25562 | ||||||||
\(117\) | 4.64234e19 | 1.04465 | ||||||||
\(118\) | 3.83939e19 | 0.796862 | ||||||||
\(119\) | 7.80233e19 | 1.49461 | ||||||||
\(120\) | −2.24492e19 | −0.397171 | ||||||||
\(121\) | −5.12332e19 | −0.837704 | ||||||||
\(122\) | 2.59502e19 | 0.392394 | ||||||||
\(123\) | 1.07653e19 | 0.150635 | ||||||||
\(124\) | −2.67412e20 | −3.46478 | ||||||||
\(125\) | −7.45058e18 | −0.0894427 | ||||||||
\(126\) | −1.77441e20 | −1.97485 | ||||||||
\(127\) | −2.55831e19 | −0.264130 | −0.132065 | − | 0.991241i | \(-0.542161\pi\) | ||||
−0.132065 | + | 0.991241i | \(0.542161\pi\) | |||||||
\(128\) | 1.04038e20 | 0.997001 | ||||||||
\(129\) | 4.54269e19 | 0.404307 | ||||||||
\(130\) | 1.17323e20 | 0.970333 | ||||||||
\(131\) | 3.95361e19 | 0.304030 | 0.152015 | − | 0.988378i | \(-0.451424\pi\) | ||||
0.152015 | + | 0.988378i | \(0.451424\pi\) | |||||||
\(132\) | 4.39847e19 | 0.314666 | ||||||||
\(133\) | −2.17530e20 | −1.44854 | ||||||||
\(134\) | 3.65397e20 | 2.26605 | ||||||||
\(135\) | 4.54790e19 | 0.262809 | ||||||||
\(136\) | 6.87645e20 | 3.70463 | ||||||||
\(137\) | −1.82400e20 | −0.916602 | −0.458301 | − | 0.888797i | \(-0.651542\pi\) | ||||
−0.458301 | + | 0.888797i | \(0.651542\pi\) | |||||||
\(138\) | −1.26965e20 | −0.595432 | ||||||||
\(139\) | 9.57423e18 | 0.0419240 | 0.0209620 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209620 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(140\) | −3.21464e20 | −1.31497 | ||||||||
\(141\) | 4.07232e19 | 0.155690 | ||||||||
\(142\) | −2.70707e20 | −0.967744 | ||||||||
\(143\) | −1.39077e20 | −0.465117 | ||||||||
\(144\) | −8.31984e20 | −2.60418 | ||||||||
\(145\) | 1.35941e20 | 0.398433 | ||||||||
\(146\) | 3.47744e20 | 0.954790 | ||||||||
\(147\) | 4.18193e19 | 0.107612 | ||||||||
\(148\) | 9.87905e20 | 2.38358 | ||||||||
\(149\) | 6.85635e20 | 1.55176 | 0.775878 | − | 0.630882i | \(-0.217307\pi\) | ||||
0.775878 | + | 0.630882i | \(0.217307\pi\) | |||||||
\(150\) | 5.45965e19 | 0.115957 | ||||||||
\(151\) | −3.55608e20 | −0.709073 | −0.354537 | − | 0.935042i | \(-0.615361\pi\) | ||||
−0.354537 | + | 0.935042i | \(0.615361\pi\) | |||||||
\(152\) | −1.91717e21 | −3.59042 | ||||||||
\(153\) | −6.61734e20 | −1.16443 | ||||||||
\(154\) | 5.31585e20 | 0.879277 | ||||||||
\(155\) | 3.93474e20 | 0.612019 | ||||||||
\(156\) | −6.16296e20 | −0.901790 | ||||||||
\(157\) | 7.66927e20 | 1.05611 | 0.528053 | − | 0.849212i | \(-0.322922\pi\) | ||||
0.528053 | + | 0.849212i | \(0.322922\pi\) | |||||||
\(158\) | 1.22324e21 | 1.58587 | ||||||||
\(159\) | 2.31953e20 | 0.283222 | ||||||||
\(160\) | −9.83573e20 | −1.13153 | ||||||||
\(161\) | −1.09998e21 | −1.19272 | ||||||||
\(162\) | 1.32997e21 | 1.35972 | ||||||||
\(163\) | −3.87952e20 | −0.374107 | −0.187053 | − | 0.982350i | \(-0.559894\pi\) | ||||
−0.187053 | + | 0.982350i | \(0.559894\pi\) | |||||||
\(164\) | 1.35862e21 | 1.23618 | ||||||||
\(165\) | −6.47197e19 | −0.0555826 | ||||||||
\(166\) | −1.18202e21 | −0.958511 | ||||||||
\(167\) | −2.05376e21 | −1.57306 | −0.786528 | − | 0.617555i | \(-0.788123\pi\) | ||||
−0.786528 | + | 0.617555i | \(0.788123\pi\) | |||||||
\(168\) | 1.42520e21 | 1.03143 | ||||||||
\(169\) | 4.86766e20 | 0.332963 | ||||||||
\(170\) | −1.67236e21 | −1.08159 | ||||||||
\(171\) | 1.84493e21 | 1.12854 | ||||||||
\(172\) | 5.73305e21 | 3.31792 | ||||||||
\(173\) | −2.48811e21 | −1.36280 | −0.681399 | − | 0.731912i | \(-0.738628\pi\) | ||||
−0.681399 | + | 0.731912i | \(0.738628\pi\) | |||||||
\(174\) | −9.96151e20 | −0.516544 | ||||||||
\(175\) | 4.73007e20 | 0.232277 | ||||||||
\(176\) | 2.49248e21 | 1.15948 | ||||||||
\(177\) | 2.96759e20 | 0.130815 | ||||||||
\(178\) | −3.78508e21 | −1.58156 | ||||||||
\(179\) | 3.14092e21 | 1.24438 | 0.622191 | − | 0.782866i | \(-0.286243\pi\) | ||||
0.622191 | + | 0.782866i | \(0.286243\pi\) | |||||||
\(180\) | 2.72641e21 | 1.02448 | ||||||||
\(181\) | −3.35426e21 | −1.19578 | −0.597889 | − | 0.801579i | \(-0.703994\pi\) | ||||
−0.597889 | + | 0.801579i | \(0.703994\pi\) | |||||||
\(182\) | −7.44834e21 | −2.51989 | ||||||||
\(183\) | 2.00577e20 | 0.0644165 | ||||||||
\(184\) | −9.69451e21 | −2.95635 | ||||||||
\(185\) | −1.45362e21 | −0.421035 | ||||||||
\(186\) | −2.88330e21 | −0.793446 | ||||||||
\(187\) | 1.98244e21 | 0.518449 | ||||||||
\(188\) | 5.13942e21 | 1.27766 | ||||||||
\(189\) | −2.88727e21 | −0.682497 | ||||||||
\(190\) | 4.66256e21 | 1.04825 | ||||||||
\(191\) | 6.93292e21 | 1.48286 | 0.741428 | − | 0.671033i | \(-0.234149\pi\) | ||||
0.741428 | + | 0.671033i | \(0.234149\pi\) | |||||||
\(192\) | 2.84488e21 | 0.579032 | ||||||||
\(193\) | 8.38013e21 | 1.62351 | 0.811757 | − | 0.583995i | \(-0.198511\pi\) | ||||
0.811757 | + | 0.583995i | \(0.198511\pi\) | |||||||
\(194\) | −3.50858e21 | −0.647164 | ||||||||
\(195\) | 9.06826e20 | 0.159292 | ||||||||
\(196\) | 5.27776e21 | 0.883114 | ||||||||
\(197\) | 2.41151e21 | 0.384467 | 0.192234 | − | 0.981349i | \(-0.438427\pi\) | ||||
0.192234 | + | 0.981349i | \(0.438427\pi\) | |||||||
\(198\) | −4.50850e21 | −0.685035 | ||||||||
\(199\) | 1.85924e20 | 0.0269296 | 0.0134648 | − | 0.999909i | \(-0.495714\pi\) | ||||
0.0134648 | + | 0.999909i | \(0.495714\pi\) | |||||||
\(200\) | 4.16876e21 | 0.575734 | ||||||||
\(201\) | 2.82427e21 | 0.372001 | ||||||||
\(202\) | −5.12738e21 | −0.644255 | ||||||||
\(203\) | −8.63034e21 | −1.03470 | ||||||||
\(204\) | 8.78487e21 | 1.00519 | ||||||||
\(205\) | −1.99909e21 | −0.218359 | ||||||||
\(206\) | −4.59999e21 | −0.479753 | ||||||||
\(207\) | 9.32922e21 | 0.929238 | ||||||||
\(208\) | −3.49236e22 | −3.32290 | ||||||||
\(209\) | −5.52709e21 | −0.502466 | ||||||||
\(210\) | −3.46610e21 | −0.301133 | ||||||||
\(211\) | 9.50589e21 | 0.789422 | 0.394711 | − | 0.918805i | \(-0.370845\pi\) | ||||
0.394711 | + | 0.918805i | \(0.370845\pi\) | |||||||
\(212\) | 2.92733e22 | 2.32424 | ||||||||
\(213\) | −2.09238e21 | −0.158867 | ||||||||
\(214\) | −1.21749e22 | −0.884169 | ||||||||
\(215\) | −8.43569e21 | −0.586077 | ||||||||
\(216\) | −2.54465e22 | −1.69168 | ||||||||
\(217\) | −2.49800e22 | −1.58937 | ||||||||
\(218\) | 5.81134e22 | 3.53948 | ||||||||
\(219\) | 2.68783e21 | 0.156741 | ||||||||
\(220\) | −8.16788e21 | −0.456135 | ||||||||
\(221\) | −2.77772e22 | −1.48580 | ||||||||
\(222\) | 1.06518e22 | 0.545847 | ||||||||
\(223\) | 2.74715e22 | 1.34892 | 0.674459 | − | 0.738312i | \(-0.264377\pi\) | ||||
0.674459 | + | 0.738312i | \(0.264377\pi\) | |||||||
\(224\) | 6.24430e22 | 2.93851 | ||||||||
\(225\) | −4.01168e21 | −0.180964 | ||||||||
\(226\) | −2.28924e22 | −0.990060 | ||||||||
\(227\) | 1.41286e22 | 0.585942 | 0.292971 | − | 0.956121i | \(-0.405356\pi\) | ||||
0.292971 | + | 0.956121i | \(0.405356\pi\) | |||||||
\(228\) | −2.44924e22 | −0.974204 | ||||||||
\(229\) | −3.83709e22 | −1.46408 | −0.732041 | − | 0.681261i | \(-0.761432\pi\) | ||||
−0.732041 | + | 0.681261i | \(0.761432\pi\) | |||||||
\(230\) | 2.35771e22 | 0.863129 | ||||||||
\(231\) | 4.10879e21 | 0.144344 | ||||||||
\(232\) | −7.60620e22 | −2.56467 | ||||||||
\(233\) | −4.40483e22 | −1.42576 | −0.712882 | − | 0.701284i | \(-0.752611\pi\) | ||||
−0.712882 | + | 0.701284i | \(0.752611\pi\) | |||||||
\(234\) | 6.31712e22 | 1.96322 | ||||||||
\(235\) | −7.56221e21 | −0.225686 | ||||||||
\(236\) | 3.74521e22 | 1.07353 | ||||||||
\(237\) | 9.45479e21 | 0.260341 | ||||||||
\(238\) | 1.06171e23 | 2.80883 | ||||||||
\(239\) | −5.68968e22 | −1.44646 | −0.723232 | − | 0.690605i | \(-0.757344\pi\) | ||||
−0.723232 | + | 0.690605i | \(0.757344\pi\) | |||||||
\(240\) | −1.62518e22 | −0.397095 | ||||||||
\(241\) | 8.31189e22 | 1.95226 | 0.976131 | − | 0.217182i | \(-0.0696866\pi\) | ||||
0.976131 | + | 0.217182i | \(0.0696866\pi\) | |||||||
\(242\) | −6.97162e22 | −1.57430 | ||||||||
\(243\) | 3.73433e22 | 0.810873 | ||||||||
\(244\) | 2.53136e22 | 0.528629 | ||||||||
\(245\) | −7.76576e21 | −0.155993 | ||||||||
\(246\) | 1.46490e22 | 0.283089 | ||||||||
\(247\) | 7.74432e22 | 1.44000 | ||||||||
\(248\) | −2.20157e23 | −3.93951 | ||||||||
\(249\) | −9.13619e21 | −0.157352 | ||||||||
\(250\) | −1.01385e22 | −0.168090 | ||||||||
\(251\) | 5.17728e22 | 0.826421 | 0.413211 | − | 0.910635i | \(-0.364407\pi\) | ||||
0.413211 | + | 0.910635i | \(0.364407\pi\) | |||||||
\(252\) | −1.73089e23 | −2.66050 | ||||||||
\(253\) | −2.79488e22 | −0.413731 | ||||||||
\(254\) | −3.48124e22 | −0.496380 | ||||||||
\(255\) | −1.29262e22 | −0.177557 | ||||||||
\(256\) | −2.41073e20 | −0.00319058 | ||||||||
\(257\) | −3.72920e22 | −0.475610 | −0.237805 | − | 0.971313i | \(-0.576428\pi\) | ||||
−0.237805 | + | 0.971313i | \(0.576428\pi\) | |||||||
\(258\) | 6.18151e22 | 0.759814 | ||||||||
\(259\) | 9.22841e22 | 1.09340 | ||||||||
\(260\) | 1.14445e23 | 1.30722 | ||||||||
\(261\) | 7.31960e22 | 0.806125 | ||||||||
\(262\) | 5.37992e22 | 0.571365 | ||||||||
\(263\) | 3.03845e21 | 0.0311223 | 0.0155612 | − | 0.999879i | \(-0.495047\pi\) | ||||
0.0155612 | + | 0.999879i | \(0.495047\pi\) | |||||||
\(264\) | 3.62121e22 | 0.357780 | ||||||||
\(265\) | −4.30731e22 | −0.410554 | ||||||||
\(266\) | −2.96007e23 | −2.72224 | ||||||||
\(267\) | −2.92561e22 | −0.259633 | ||||||||
\(268\) | 3.56434e23 | 3.05280 | ||||||||
\(269\) | −1.00175e23 | −0.828159 | −0.414079 | − | 0.910241i | \(-0.635896\pi\) | ||||
−0.414079 | + | 0.910241i | \(0.635896\pi\) | |||||||
\(270\) | 6.18860e22 | 0.493897 | ||||||||
\(271\) | 3.74901e22 | 0.288874 | 0.144437 | − | 0.989514i | \(-0.453863\pi\) | ||||
0.144437 | + | 0.989514i | \(0.453863\pi\) | |||||||
\(272\) | 4.97812e23 | 3.70392 | ||||||||
\(273\) | −5.75706e22 | −0.413672 | ||||||||
\(274\) | −2.48203e23 | −1.72257 | ||||||||
\(275\) | 1.20183e22 | 0.0805718 | ||||||||
\(276\) | −1.23850e23 | −0.802159 | ||||||||
\(277\) | 2.51054e22 | 0.157112 | 0.0785559 | − | 0.996910i | \(-0.474969\pi\) | ||||
0.0785559 | + | 0.996910i | \(0.474969\pi\) | |||||||
\(278\) | 1.30282e22 | 0.0787879 | ||||||||
\(279\) | 2.11862e23 | 1.23826 | ||||||||
\(280\) | −2.64657e23 | −1.49514 | ||||||||
\(281\) | −1.50547e23 | −0.822173 | −0.411086 | − | 0.911596i | \(-0.634851\pi\) | ||||
−0.411086 | + | 0.911596i | \(0.634851\pi\) | |||||||
\(282\) | 5.54145e22 | 0.292588 | ||||||||
\(283\) | −2.94312e23 | −1.50258 | −0.751289 | − | 0.659973i | \(-0.770568\pi\) | ||||
−0.751289 | + | 0.659973i | \(0.770568\pi\) | |||||||
\(284\) | −2.64067e23 | −1.30373 | ||||||||
\(285\) | 3.60384e22 | 0.172084 | ||||||||
\(286\) | −1.89250e23 | −0.874096 | ||||||||
\(287\) | 1.26914e23 | 0.567063 | ||||||||
\(288\) | −5.29594e23 | −2.28936 | ||||||||
\(289\) | 1.56872e23 | 0.656171 | ||||||||
\(290\) | 1.84983e23 | 0.748775 | ||||||||
\(291\) | −2.71189e22 | −0.106240 | ||||||||
\(292\) | 3.39214e23 | 1.28628 | ||||||||
\(293\) | −4.17390e23 | −1.53215 | −0.766073 | − | 0.642754i | \(-0.777792\pi\) | ||||
−0.766073 | + | 0.642754i | \(0.777792\pi\) | |||||||
\(294\) | 5.69060e22 | 0.202236 | ||||||||
\(295\) | −5.51075e22 | −0.189628 | ||||||||
\(296\) | 8.13330e23 | 2.71017 | ||||||||
\(297\) | −7.33609e22 | −0.236744 | ||||||||
\(298\) | 9.32985e23 | 2.91622 | ||||||||
\(299\) | 3.91606e23 | 1.18570 | ||||||||
\(300\) | 5.32572e22 | 0.156216 | ||||||||
\(301\) | 5.35547e23 | 1.52200 | ||||||||
\(302\) | −4.83898e23 | −1.33256 | ||||||||
\(303\) | −3.96312e22 | −0.105763 | ||||||||
\(304\) | −1.38791e24 | −3.58973 | ||||||||
\(305\) | −3.72468e22 | −0.0933772 | ||||||||
\(306\) | −9.00462e23 | −2.18832 | ||||||||
\(307\) | −9.44483e22 | −0.222525 | −0.111263 | − | 0.993791i | \(-0.535489\pi\) | ||||
−0.111263 | + | 0.993791i | \(0.535489\pi\) | |||||||
\(308\) | 5.18545e23 | 1.18455 | ||||||||
\(309\) | −3.55548e22 | −0.0787576 | ||||||||
\(310\) | 5.35423e23 | 1.15017 | ||||||||
\(311\) | −2.94596e23 | −0.613766 | −0.306883 | − | 0.951747i | \(-0.599286\pi\) | ||||
−0.306883 | + | 0.951747i | \(0.599286\pi\) | |||||||
\(312\) | −5.07389e23 | −1.02535 | ||||||||
\(313\) | −1.70785e23 | −0.334795 | −0.167398 | − | 0.985889i | \(-0.553536\pi\) | ||||
−0.167398 | + | 0.985889i | \(0.553536\pi\) | |||||||
\(314\) | 1.04360e24 | 1.98474 | ||||||||
\(315\) | 2.54685e23 | 0.469952 | ||||||||
\(316\) | 1.19323e24 | 2.13647 | ||||||||
\(317\) | 9.64787e21 | 0.0167636 | 0.00838182 | − | 0.999965i | \(-0.497332\pi\) | ||||
0.00838182 | + | 0.999965i | \(0.497332\pi\) | |||||||
\(318\) | 3.15632e23 | 0.532259 | ||||||||
\(319\) | −2.19283e23 | −0.358916 | ||||||||
\(320\) | −5.28288e23 | −0.839356 | ||||||||
\(321\) | −9.41039e22 | −0.145148 | ||||||||
\(322\) | −1.49681e24 | −2.24149 | ||||||||
\(323\) | −1.10390e24 | −1.60511 | ||||||||
\(324\) | 1.29734e24 | 1.83180 | ||||||||
\(325\) | −1.68396e23 | −0.230908 | ||||||||
\(326\) | −5.27909e23 | −0.703059 | ||||||||
\(327\) | 4.49177e23 | 0.581050 | ||||||||
\(328\) | 1.11853e24 | 1.40555 | ||||||||
\(329\) | 4.80094e23 | 0.586091 | ||||||||
\(330\) | −8.80680e22 | −0.104457 | ||||||||
\(331\) | 5.66277e23 | 0.652624 | 0.326312 | − | 0.945262i | \(-0.394194\pi\) | ||||
0.326312 | + | 0.945262i | \(0.394194\pi\) | |||||||
\(332\) | −1.15302e24 | −1.29130 | ||||||||
\(333\) | −7.82684e23 | −0.851856 | ||||||||
\(334\) | −2.79468e24 | −2.95625 | ||||||||
\(335\) | −5.24462e23 | −0.539248 | ||||||||
\(336\) | 1.03176e24 | 1.03123 | ||||||||
\(337\) | 1.18640e24 | 1.15278 | 0.576392 | − | 0.817174i | \(-0.304460\pi\) | ||||
0.576392 | + | 0.817174i | \(0.304460\pi\) | |||||||
\(338\) | 6.62372e23 | 0.625739 | ||||||||
\(339\) | −1.76943e23 | −0.162531 | ||||||||
\(340\) | −1.63133e24 | −1.45711 | ||||||||
\(341\) | −6.34702e23 | −0.551319 | ||||||||
\(342\) | 2.51050e24 | 2.12086 | ||||||||
\(343\) | −9.20399e23 | −0.756279 | ||||||||
\(344\) | 4.71995e24 | 3.77253 | ||||||||
\(345\) | 1.82235e23 | 0.141694 | ||||||||
\(346\) | −3.38572e24 | −2.56111 | ||||||||
\(347\) | −1.39897e24 | −1.02962 | −0.514812 | − | 0.857303i | \(-0.672138\pi\) | ||||
−0.514812 | + | 0.857303i | \(0.672138\pi\) | |||||||
\(348\) | −9.71715e23 | −0.695883 | ||||||||
\(349\) | 1.55030e24 | 1.08037 | 0.540186 | − | 0.841546i | \(-0.318354\pi\) | ||||
0.540186 | + | 0.841546i | \(0.318354\pi\) | |||||||
\(350\) | 6.43648e23 | 0.436518 | ||||||||
\(351\) | 1.02790e24 | 0.678475 | ||||||||
\(352\) | 1.58657e24 | 1.01931 | ||||||||
\(353\) | 2.69377e24 | 1.68461 | 0.842307 | − | 0.538997i | \(-0.181197\pi\) | ||||
0.842307 | + | 0.538997i | \(0.181197\pi\) | |||||||
\(354\) | 4.03818e23 | 0.245841 | ||||||||
\(355\) | 3.88551e23 | 0.230292 | ||||||||
\(356\) | −3.69223e24 | −2.13066 | ||||||||
\(357\) | 8.20630e23 | 0.461104 | ||||||||
\(358\) | 4.27404e24 | 2.33857 | ||||||||
\(359\) | −2.68511e23 | −0.143075 | −0.0715376 | − | 0.997438i | \(-0.522791\pi\) | ||||
−0.0715376 | + | 0.997438i | \(0.522791\pi\) | |||||||
\(360\) | 2.24462e24 | 1.16485 | ||||||||
\(361\) | 1.09927e24 | 0.555632 | ||||||||
\(362\) | −4.56435e24 | −2.24723 | ||||||||
\(363\) | −5.38858e23 | −0.258441 | ||||||||
\(364\) | −7.26563e24 | −3.39477 | ||||||||
\(365\) | −4.99124e23 | −0.227209 | ||||||||
\(366\) | 2.72938e23 | 0.121058 | ||||||||
\(367\) | 4.64559e22 | 0.0200777 | 0.0100388 | − | 0.999950i | \(-0.496804\pi\) | ||||
0.0100388 | + | 0.999950i | \(0.496804\pi\) | |||||||
\(368\) | −7.01822e24 | −2.95579 | ||||||||
\(369\) | −1.07639e24 | −0.441792 | ||||||||
\(370\) | −1.97802e24 | −0.791253 | ||||||||
\(371\) | 2.73454e24 | 1.06618 | ||||||||
\(372\) | −2.81257e24 | −1.06892 | ||||||||
\(373\) | 2.90680e24 | 1.07691 | 0.538457 | − | 0.842653i | \(-0.319007\pi\) | ||||
0.538457 | + | 0.842653i | \(0.319007\pi\) | |||||||
\(374\) | 2.69763e24 | 0.974322 | ||||||||
\(375\) | −7.83633e22 | −0.0275941 | ||||||||
\(376\) | 4.23122e24 | 1.45272 | ||||||||
\(377\) | 3.07250e24 | 1.02861 | ||||||||
\(378\) | −3.92889e24 | −1.28262 | ||||||||
\(379\) | −5.17963e24 | −1.64902 | −0.824510 | − | 0.565848i | \(-0.808549\pi\) | ||||
−0.824510 | + | 0.565848i | \(0.808549\pi\) | |||||||
\(380\) | 4.54818e24 | 1.41219 | ||||||||
\(381\) | −2.69077e23 | −0.0814870 | ||||||||
\(382\) | 9.43404e24 | 2.78673 | ||||||||
\(383\) | −1.72726e24 | −0.497703 | −0.248852 | − | 0.968542i | \(-0.580053\pi\) | ||||
−0.248852 | + | 0.968542i | \(0.580053\pi\) | |||||||
\(384\) | 1.09424e24 | 0.307586 | ||||||||
\(385\) | −7.62994e23 | −0.209240 | ||||||||
\(386\) | 1.14033e25 | 3.05107 | ||||||||
\(387\) | −4.54210e24 | −1.18578 | ||||||||
\(388\) | −3.42251e24 | −0.871853 | ||||||||
\(389\) | −1.27175e24 | −0.316141 | −0.158071 | − | 0.987428i | \(-0.550527\pi\) | ||||
−0.158071 | + | 0.987428i | \(0.550527\pi\) | |||||||
\(390\) | 1.23397e24 | 0.299359 | ||||||||
\(391\) | −5.58208e24 | −1.32165 | ||||||||
\(392\) | 4.34511e24 | 1.00411 | ||||||||
\(393\) | 4.15831e23 | 0.0937967 | ||||||||
\(394\) | 3.28148e24 | 0.722530 | ||||||||
\(395\) | −1.75574e24 | −0.377387 | ||||||||
\(396\) | −4.39790e24 | −0.922872 | ||||||||
\(397\) | −5.93194e24 | −1.21531 | −0.607655 | − | 0.794201i | \(-0.707890\pi\) | ||||
−0.607655 | + | 0.794201i | \(0.707890\pi\) | |||||||
\(398\) | 2.52998e23 | 0.0506089 | ||||||||
\(399\) | −2.28793e24 | −0.446889 | ||||||||
\(400\) | 3.01793e24 | 0.575624 | ||||||||
\(401\) | 3.19633e24 | 0.595361 | 0.297680 | − | 0.954666i | \(-0.403787\pi\) | ||||
0.297680 | + | 0.954666i | \(0.403787\pi\) | |||||||
\(402\) | 3.84316e24 | 0.699102 | ||||||||
\(403\) | 8.89317e24 | 1.58001 | ||||||||
\(404\) | −5.00160e24 | −0.867933 | ||||||||
\(405\) | −1.90893e24 | −0.323569 | ||||||||
\(406\) | −1.17438e25 | −1.94452 | ||||||||
\(407\) | 2.34479e24 | 0.379277 | ||||||||
\(408\) | 7.23248e24 | 1.14292 | ||||||||
\(409\) | −1.00284e25 | −1.54831 | −0.774156 | − | 0.632995i | \(-0.781825\pi\) | ||||
−0.774156 | + | 0.632995i | \(0.781825\pi\) | |||||||
\(410\) | −2.72028e24 | −0.410362 | ||||||||
\(411\) | −1.91844e24 | −0.282782 | ||||||||
\(412\) | −4.48715e24 | −0.646319 | ||||||||
\(413\) | 3.49855e24 | 0.492450 | ||||||||
\(414\) | 1.26948e25 | 1.74632 | ||||||||
\(415\) | 1.69657e24 | 0.228095 | ||||||||
\(416\) | −2.22304e25 | −2.92120 | ||||||||
\(417\) | 1.00699e23 | 0.0129340 | ||||||||
\(418\) | −7.52104e24 | −0.944285 | ||||||||
\(419\) | 1.18441e25 | 1.45368 | 0.726840 | − | 0.686807i | \(-0.240988\pi\) | ||||
0.726840 | + | 0.686807i | \(0.240988\pi\) | |||||||
\(420\) | −3.38108e24 | −0.405683 | ||||||||
\(421\) | 1.03966e25 | 1.21958 | 0.609792 | − | 0.792562i | \(-0.291253\pi\) | ||||
0.609792 | + | 0.792562i | \(0.291253\pi\) | |||||||
\(422\) | 1.29352e25 | 1.48356 | ||||||||
\(423\) | −4.07179e24 | −0.456617 | ||||||||
\(424\) | 2.41004e25 | 2.64270 | ||||||||
\(425\) | 2.40037e24 | 0.257385 | ||||||||
\(426\) | −2.84723e24 | −0.298560 | ||||||||
\(427\) | 2.36465e24 | 0.242494 | ||||||||
\(428\) | −1.18763e25 | −1.19114 | ||||||||
\(429\) | −1.46277e24 | −0.143494 | ||||||||
\(430\) | −1.14789e25 | −1.10142 | ||||||||
\(431\) | −2.03143e25 | −1.90663 | −0.953316 | − | 0.301975i | \(-0.902354\pi\) | ||||
−0.953316 | + | 0.301975i | \(0.902354\pi\) | |||||||
\(432\) | −1.84217e25 | −1.69135 | ||||||||
\(433\) | −2.89050e21 | −0.000259620 0 | −0.000129810 | − | 1.00000i | \(-0.500041\pi\) | ||||
−0.000129810 | 1.00000i | \(0.500041\pi\) | ||||||||
\(434\) | −3.39918e25 | −2.98691 | ||||||||
\(435\) | 1.42979e24 | 0.122921 | ||||||||
\(436\) | 5.66878e25 | 4.76835 | ||||||||
\(437\) | 1.55629e25 | 1.28091 | ||||||||
\(438\) | 3.65749e24 | 0.294563 | ||||||||
\(439\) | 1.26912e25 | 1.00020 | 0.500102 | − | 0.865967i | \(-0.333296\pi\) | ||||
0.500102 | + | 0.865967i | \(0.333296\pi\) | |||||||
\(440\) | −6.72451e24 | −0.518633 | ||||||||
\(441\) | −4.18139e24 | −0.315612 | ||||||||
\(442\) | −3.77981e25 | −2.79228 | ||||||||
\(443\) | 8.29689e24 | 0.599901 | 0.299951 | − | 0.953955i | \(-0.403030\pi\) | ||||
0.299951 | + | 0.953955i | \(0.403030\pi\) | |||||||
\(444\) | 1.03905e25 | 0.735360 | ||||||||
\(445\) | 5.43280e24 | 0.376360 | ||||||||
\(446\) | 3.73821e25 | 2.53502 | ||||||||
\(447\) | 7.21134e24 | 0.478734 | ||||||||
\(448\) | 3.35388e25 | 2.17975 | ||||||||
\(449\) | 4.92023e23 | 0.0313073 | 0.0156536 | − | 0.999877i | \(-0.495017\pi\) | ||||
0.0156536 | + | 0.999877i | \(0.495017\pi\) | |||||||
\(450\) | −5.45894e24 | −0.340086 | ||||||||
\(451\) | 3.22467e24 | 0.196702 | ||||||||
\(452\) | −2.23309e25 | −1.33380 | ||||||||
\(453\) | −3.74020e24 | −0.218757 | ||||||||
\(454\) | 1.92257e25 | 1.10116 | ||||||||
\(455\) | 1.06907e25 | 0.599653 | ||||||||
\(456\) | −2.01643e25 | −1.10769 | ||||||||
\(457\) | −2.95954e25 | −1.59228 | −0.796141 | − | 0.605111i | \(-0.793129\pi\) | ||||
−0.796141 | + | 0.605111i | \(0.793129\pi\) | |||||||
\(458\) | −5.22136e25 | −2.75145 | ||||||||
\(459\) | −1.46520e25 | −0.756271 | ||||||||
\(460\) | 2.29987e25 | 1.16280 | ||||||||
\(461\) | −2.39904e25 | −1.18817 | −0.594084 | − | 0.804403i | \(-0.702485\pi\) | ||||
−0.594084 | + | 0.804403i | \(0.702485\pi\) | |||||||
\(462\) | 5.59107e24 | 0.271267 | ||||||||
\(463\) | 1.01589e25 | 0.482869 | 0.241435 | − | 0.970417i | \(-0.422382\pi\) | ||||
0.241435 | + | 0.970417i | \(0.422382\pi\) | |||||||
\(464\) | −5.50642e25 | −2.56418 | ||||||||
\(465\) | 4.13846e24 | 0.188815 | ||||||||
\(466\) | −5.99391e25 | −2.67944 | ||||||||
\(467\) | −2.35296e25 | −1.03063 | −0.515317 | − | 0.857000i | \(-0.672326\pi\) | ||||
−0.515317 | + | 0.857000i | \(0.672326\pi\) | |||||||
\(468\) | 6.16216e25 | 2.64483 | ||||||||
\(469\) | 3.32959e25 | 1.40039 | ||||||||
\(470\) | −1.02904e25 | −0.424132 | ||||||||
\(471\) | 8.06634e24 | 0.325820 | ||||||||
\(472\) | 3.08339e25 | 1.22062 | ||||||||
\(473\) | 1.36074e25 | 0.527951 | ||||||||
\(474\) | 1.28657e25 | 0.489259 | ||||||||
\(475\) | −6.69226e24 | −0.249450 | ||||||||
\(476\) | 1.03567e26 | 3.78402 | ||||||||
\(477\) | −2.31923e25 | −0.830651 | ||||||||
\(478\) | −7.74229e25 | −2.71834 | ||||||||
\(479\) | 3.50521e24 | 0.120650 | 0.0603249 | − | 0.998179i | \(-0.480786\pi\) | ||||
0.0603249 | + | 0.998179i | \(0.480786\pi\) | |||||||
\(480\) | −1.03450e25 | −0.349090 | ||||||||
\(481\) | −3.28542e25 | −1.08696 | ||||||||
\(482\) | 1.13105e26 | 3.66889 | ||||||||
\(483\) | −1.15693e25 | −0.367969 | ||||||||
\(484\) | −6.80060e25 | −2.12088 | ||||||||
\(485\) | 5.03593e24 | 0.154004 | ||||||||
\(486\) | 5.08152e25 | 1.52388 | ||||||||
\(487\) | 5.43728e25 | 1.59903 | 0.799515 | − | 0.600647i | \(-0.205090\pi\) | ||||
0.799515 | + | 0.600647i | \(0.205090\pi\) | |||||||
\(488\) | 2.08404e25 | 0.601060 | ||||||||
\(489\) | −4.08038e24 | −0.115416 | ||||||||
\(490\) | −1.05673e25 | −0.293159 | ||||||||
\(491\) | −5.76237e24 | −0.156793 | −0.0783966 | − | 0.996922i | \(-0.524980\pi\) | ||||
−0.0783966 | + | 0.996922i | \(0.524980\pi\) | |||||||
\(492\) | 1.42896e25 | 0.381375 | ||||||||
\(493\) | −4.37964e25 | −1.14655 | ||||||||
\(494\) | 1.05382e26 | 2.70620 | ||||||||
\(495\) | 6.47113e24 | 0.163016 | ||||||||
\(496\) | −1.59380e26 | −3.93875 | ||||||||
\(497\) | −2.46675e25 | −0.598053 | ||||||||
\(498\) | −1.24322e25 | −0.295711 | ||||||||
\(499\) | 7.67371e25 | 1.79081 | 0.895406 | − | 0.445251i | \(-0.146885\pi\) | ||||
0.895406 | + | 0.445251i | \(0.146885\pi\) | |||||||
\(500\) | −9.88975e24 | −0.226449 | ||||||||
\(501\) | −2.16010e25 | −0.485305 | ||||||||
\(502\) | 7.04504e25 | 1.55310 | ||||||||
\(503\) | 3.38074e24 | 0.0731334 | 0.0365667 | − | 0.999331i | \(-0.488358\pi\) | ||||
0.0365667 | + | 0.999331i | \(0.488358\pi\) | |||||||
\(504\) | −1.42502e26 | −3.02504 | ||||||||
\(505\) | 7.35943e24 | 0.153312 | ||||||||
\(506\) | −3.80316e25 | −0.777525 | ||||||||
\(507\) | 5.11968e24 | 0.102723 | ||||||||
\(508\) | −3.39585e25 | −0.668718 | ||||||||
\(509\) | −5.88807e25 | −1.13803 | −0.569015 | − | 0.822327i | \(-0.692675\pi\) | ||||
−0.569015 | + | 0.822327i | \(0.692675\pi\) | |||||||
\(510\) | −1.75894e25 | −0.333684 | ||||||||
\(511\) | 3.16873e25 | 0.590047 | ||||||||
\(512\) | −5.48737e25 | −1.00300 | ||||||||
\(513\) | 4.08501e25 | 0.732957 | ||||||||
\(514\) | −5.07455e25 | −0.893815 | ||||||||
\(515\) | 6.60245e24 | 0.114166 | ||||||||
\(516\) | 6.02988e25 | 1.02361 | ||||||||
\(517\) | 1.21984e25 | 0.203302 | ||||||||
\(518\) | 1.25577e26 | 2.05483 | ||||||||
\(519\) | −2.61693e25 | −0.420438 | ||||||||
\(520\) | 9.42211e25 | 1.48633 | ||||||||
\(521\) | −1.35023e25 | −0.209145 | −0.104573 | − | 0.994517i | \(-0.533347\pi\) | ||||
−0.104573 | + | 0.994517i | \(0.533347\pi\) | |||||||
\(522\) | 9.96022e25 | 1.51495 | ||||||||
\(523\) | 2.74955e25 | 0.410673 | 0.205336 | − | 0.978691i | \(-0.434171\pi\) | ||||
0.205336 | + | 0.978691i | \(0.434171\pi\) | |||||||
\(524\) | 5.24795e25 | 0.769737 | ||||||||
\(525\) | 4.97496e24 | 0.0716600 | ||||||||
\(526\) | 4.13460e24 | 0.0584883 | ||||||||
\(527\) | −1.26766e26 | −1.76117 | ||||||||
\(528\) | 2.62153e25 | 0.357711 | ||||||||
\(529\) | 4.08140e24 | 0.0546991 | ||||||||
\(530\) | −5.86122e25 | −0.771556 | ||||||||
\(531\) | −2.96720e25 | −0.383662 | ||||||||
\(532\) | −2.88745e26 | −3.66737 | ||||||||
\(533\) | −4.51828e25 | −0.563722 | ||||||||
\(534\) | −3.98105e25 | −0.487928 | ||||||||
\(535\) | 1.74749e25 | 0.210404 | ||||||||
\(536\) | 2.93448e26 | 3.47109 | ||||||||
\(537\) | 3.30354e25 | 0.383906 | ||||||||
\(538\) | −1.36314e26 | −1.55636 | ||||||||
\(539\) | 1.25267e25 | 0.140522 | ||||||||
\(540\) | 6.03679e25 | 0.665373 | ||||||||
\(541\) | 5.00313e25 | 0.541836 | 0.270918 | − | 0.962602i | \(-0.412673\pi\) | ||||
0.270918 | + | 0.962602i | \(0.412673\pi\) | |||||||
\(542\) | 5.10151e25 | 0.542882 | ||||||||
\(543\) | −3.52793e25 | −0.368911 | ||||||||
\(544\) | 3.16879e26 | 3.25615 | ||||||||
\(545\) | −8.34113e25 | −0.842283 | ||||||||
\(546\) | −7.83398e25 | −0.777414 | ||||||||
\(547\) | 7.15124e25 | 0.697431 | 0.348716 | − | 0.937229i | \(-0.386618\pi\) | ||||
0.348716 | + | 0.937229i | \(0.386618\pi\) | |||||||
\(548\) | −2.42115e26 | −2.32063 | ||||||||
\(549\) | −2.00551e25 | −0.188925 | ||||||||
\(550\) | 1.63541e25 | 0.151419 | ||||||||
\(551\) | 1.22105e26 | 1.11120 | ||||||||
\(552\) | −1.01964e26 | −0.912068 | ||||||||
\(553\) | 1.11464e26 | 0.980048 | ||||||||
\(554\) | 3.41624e25 | 0.295261 | ||||||||
\(555\) | −1.52888e25 | −0.129894 | ||||||||
\(556\) | 1.27086e25 | 0.106142 | ||||||||
\(557\) | 5.59071e25 | 0.459031 | 0.229516 | − | 0.973305i | \(-0.426286\pi\) | ||||
0.229516 | + | 0.973305i | \(0.426286\pi\) | |||||||
\(558\) | 2.88293e26 | 2.32707 | ||||||||
\(559\) | −1.90661e26 | −1.51304 | ||||||||
\(560\) | −1.91596e26 | −1.49486 | ||||||||
\(561\) | 2.08509e25 | 0.159947 | ||||||||
\(562\) | −2.04859e26 | −1.54511 | ||||||||
\(563\) | 1.34263e26 | 0.995696 | 0.497848 | − | 0.867264i | \(-0.334124\pi\) | ||||
0.497848 | + | 0.867264i | \(0.334124\pi\) | |||||||
\(564\) | 5.40551e25 | 0.394172 | ||||||||
\(565\) | 3.28579e25 | 0.235602 | ||||||||
\(566\) | −4.00488e26 | −2.82380 | ||||||||
\(567\) | 1.21190e26 | 0.840286 | ||||||||
\(568\) | −2.17403e26 | −1.48237 | ||||||||
\(569\) | −1.78969e26 | −1.20009 | −0.600043 | − | 0.799968i | \(-0.704850\pi\) | ||||
−0.600043 | + | 0.799968i | \(0.704850\pi\) | |||||||
\(570\) | 4.90396e25 | 0.323397 | ||||||||
\(571\) | 9.68510e25 | 0.628147 | 0.314073 | − | 0.949399i | \(-0.398306\pi\) | ||||
0.314073 | + | 0.949399i | \(0.398306\pi\) | |||||||
\(572\) | −1.84608e26 | −1.17757 | ||||||||
\(573\) | 7.29187e25 | 0.457478 | ||||||||
\(574\) | 1.72699e26 | 1.06568 | ||||||||
\(575\) | −3.38407e25 | −0.205397 | ||||||||
\(576\) | −2.84451e26 | −1.69822 | ||||||||
\(577\) | 1.80741e26 | 1.06142 | 0.530708 | − | 0.847555i | \(-0.321926\pi\) | ||||
0.530708 | + | 0.847555i | \(0.321926\pi\) | |||||||
\(578\) | 2.13466e26 | 1.23314 | ||||||||
\(579\) | 8.81401e25 | 0.500872 | ||||||||
\(580\) | 1.80446e26 | 1.00874 | ||||||||
\(581\) | −1.07708e26 | −0.592347 | ||||||||
\(582\) | −3.69023e25 | −0.199657 | ||||||||
\(583\) | 6.94801e25 | 0.369836 | ||||||||
\(584\) | 2.79271e26 | 1.46252 | ||||||||
\(585\) | −9.06708e25 | −0.467183 | ||||||||
\(586\) | −5.67968e26 | −2.87937 | ||||||||
\(587\) | −1.87816e26 | −0.936851 | −0.468425 | − | 0.883503i | \(-0.655179\pi\) | ||||
−0.468425 | + | 0.883503i | \(0.655179\pi\) | |||||||
\(588\) | 5.55101e25 | 0.272450 | ||||||||
\(589\) | 3.53426e26 | 1.70688 | ||||||||
\(590\) | −7.49881e25 | −0.356368 | ||||||||
\(591\) | 2.53636e25 | 0.118612 | ||||||||
\(592\) | 5.88801e26 | 2.70964 | ||||||||
\(593\) | −2.23387e26 | −1.01167 | −0.505835 | − | 0.862630i | \(-0.668815\pi\) | ||||
−0.505835 | + | 0.862630i | \(0.668815\pi\) | |||||||
\(594\) | −9.98266e25 | −0.444913 | ||||||||
\(595\) | −1.52389e26 | −0.668410 | ||||||||
\(596\) | 9.10099e26 | 3.92870 | ||||||||
\(597\) | 1.95550e24 | 0.00830810 | ||||||||
\(598\) | 5.32882e26 | 2.22828 | ||||||||
\(599\) | −4.10335e26 | −1.68882 | −0.844410 | − | 0.535697i | \(-0.820049\pi\) | ||||
−0.844410 | + | 0.535697i | \(0.820049\pi\) | |||||||
\(600\) | 4.38460e25 | 0.177620 | ||||||||
\(601\) | 2.50922e26 | 1.00053 | 0.500267 | − | 0.865871i | \(-0.333235\pi\) | ||||
0.500267 | + | 0.865871i | \(0.333235\pi\) | |||||||
\(602\) | 7.28751e26 | 2.86030 | ||||||||
\(603\) | −2.82391e26 | −1.09103 | ||||||||
\(604\) | −4.72028e26 | −1.79522 | ||||||||
\(605\) | 1.00065e26 | 0.374633 | ||||||||
\(606\) | −5.39285e25 | −0.198760 | ||||||||
\(607\) | −1.61528e26 | −0.586077 | −0.293039 | − | 0.956101i | \(-0.594666\pi\) | ||||
−0.293039 | + | 0.956101i | \(0.594666\pi\) | |||||||
\(608\) | −8.83464e26 | −3.15577 | ||||||||
\(609\) | −9.07718e25 | −0.319217 | ||||||||
\(610\) | −5.06840e25 | −0.175484 | ||||||||
\(611\) | −1.70919e26 | −0.582637 | ||||||||
\(612\) | −8.78373e26 | −2.94809 | ||||||||
\(613\) | −3.72600e26 | −1.23131 | −0.615657 | − | 0.788014i | \(-0.711109\pi\) | ||||
−0.615657 | + | 0.788014i | \(0.711109\pi\) | |||||||
\(614\) | −1.28521e26 | −0.418192 | ||||||||
\(615\) | −2.10259e25 | −0.0673661 | ||||||||
\(616\) | 4.26912e26 | 1.34686 | ||||||||
\(617\) | 1.16664e26 | 0.362432 | 0.181216 | − | 0.983443i | \(-0.441997\pi\) | ||||
0.181216 | + | 0.983443i | \(0.441997\pi\) | |||||||
\(618\) | −4.83815e25 | −0.148009 | ||||||||
\(619\) | −4.75023e25 | −0.143104 | −0.0715522 | − | 0.997437i | \(-0.522795\pi\) | ||||
−0.0715522 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(620\) | 5.22289e26 | 1.54949 | ||||||||
\(621\) | 2.06566e26 | 0.603517 | ||||||||
\(622\) | −4.00874e26 | −1.15345 | ||||||||
\(623\) | −3.44906e26 | −0.977382 | ||||||||
\(624\) | −3.67318e26 | −1.02515 | ||||||||
\(625\) | 1.45519e25 | 0.0400000 | ||||||||
\(626\) | −2.32398e26 | −0.629181 | ||||||||
\(627\) | −5.81325e25 | −0.155016 | ||||||||
\(628\) | 1.01800e27 | 2.67382 | ||||||||
\(629\) | 4.68314e26 | 1.21159 | ||||||||
\(630\) | 3.46565e26 | 0.883181 | ||||||||
\(631\) | −2.59055e26 | −0.650300 | −0.325150 | − | 0.945662i | \(-0.605415\pi\) | ||||
−0.325150 | + | 0.945662i | \(0.605415\pi\) | |||||||
\(632\) | 9.82372e26 | 2.42920 | ||||||||
\(633\) | 9.99805e25 | 0.243546 | ||||||||
\(634\) | 1.31284e25 | 0.0315040 | ||||||||
\(635\) | 4.99670e25 | 0.118122 | ||||||||
\(636\) | 3.07889e26 | 0.717054 | ||||||||
\(637\) | −1.75519e26 | −0.402717 | ||||||||
\(638\) | −2.98391e26 | −0.674512 | ||||||||
\(639\) | 2.09211e26 | 0.465936 | ||||||||
\(640\) | −2.03199e26 | −0.445873 | ||||||||
\(641\) | 6.38588e26 | 1.38061 | 0.690303 | − | 0.723521i | \(-0.257477\pi\) | ||||
0.690303 | + | 0.723521i | \(0.257477\pi\) | |||||||
\(642\) | −1.28053e26 | −0.272776 | ||||||||
\(643\) | 2.77288e26 | 0.582006 | 0.291003 | − | 0.956722i | \(-0.406011\pi\) | ||||
0.291003 | + | 0.956722i | \(0.406011\pi\) | |||||||
\(644\) | −1.46010e27 | −3.01971 | ||||||||
\(645\) | −8.87244e25 | −0.180811 | ||||||||
\(646\) | −1.50214e27 | −3.01649 | ||||||||
\(647\) | 3.56860e26 | 0.706166 | 0.353083 | − | 0.935592i | \(-0.385133\pi\) | ||||
0.353083 | + | 0.935592i | \(0.385133\pi\) | |||||||
\(648\) | 1.06809e27 | 2.08278 | ||||||||
\(649\) | 8.88924e25 | 0.170820 | ||||||||
\(650\) | −2.29146e26 | −0.433946 | ||||||||
\(651\) | −2.62734e26 | −0.490339 | ||||||||
\(652\) | −5.14959e26 | −0.947154 | ||||||||
\(653\) | −1.33562e26 | −0.242106 | −0.121053 | − | 0.992646i | \(-0.538627\pi\) | ||||
−0.121053 | + | 0.992646i | \(0.538627\pi\) | |||||||
\(654\) | 6.11222e26 | 1.09197 | ||||||||
\(655\) | −7.72190e25 | −0.135966 | ||||||||
\(656\) | 8.09749e26 | 1.40528 | ||||||||
\(657\) | −2.68748e26 | −0.459699 | ||||||||
\(658\) | 6.53292e26 | 1.10144 | ||||||||
\(659\) | 1.09829e27 | 1.82518 | 0.912592 | − | 0.408872i | \(-0.134078\pi\) | ||||
0.912592 | + | 0.408872i | \(0.134078\pi\) | |||||||
\(660\) | −8.59077e25 | −0.140723 | ||||||||
\(661\) | −1.98489e25 | −0.0320496 | −0.0160248 | − | 0.999872i | \(-0.505101\pi\) | ||||
−0.0160248 | + | 0.999872i | \(0.505101\pi\) | |||||||
\(662\) | 7.70567e26 | 1.22648 | ||||||||
\(663\) | −2.92153e26 | −0.458387 | ||||||||
\(664\) | −9.49269e26 | −1.46822 | ||||||||
\(665\) | 4.24864e26 | 0.647805 | ||||||||
\(666\) | −1.06505e27 | −1.60089 | ||||||||
\(667\) | 6.17447e26 | 0.914964 | ||||||||
\(668\) | −2.72613e27 | −3.98263 | ||||||||
\(669\) | 2.88938e26 | 0.416156 | ||||||||
\(670\) | −7.13667e26 | −1.01341 | ||||||||
\(671\) | 6.00818e25 | 0.0841161 | ||||||||
\(672\) | 6.56759e26 | 0.906563 | ||||||||
\(673\) | −1.27707e26 | −0.173809 | −0.0869045 | − | 0.996217i | \(-0.527698\pi\) | ||||
−0.0869045 | + | 0.996217i | \(0.527698\pi\) | |||||||
\(674\) | 1.61441e27 | 2.16643 | ||||||||
\(675\) | −8.88262e25 | −0.117532 | ||||||||
\(676\) | 6.46123e26 | 0.842989 | ||||||||
\(677\) | 1.05640e26 | 0.135905 | 0.0679525 | − | 0.997689i | \(-0.478353\pi\) | ||||
0.0679525 | + | 0.997689i | \(0.478353\pi\) | |||||||
\(678\) | −2.40777e26 | −0.305445 | ||||||||
\(679\) | −3.19710e26 | −0.399939 | ||||||||
\(680\) | −1.34306e27 | −1.65676 | ||||||||
\(681\) | 1.48601e26 | 0.180770 | ||||||||
\(682\) | −8.63677e26 | −1.03610 | ||||||||
\(683\) | −5.53869e26 | −0.655256 | −0.327628 | − | 0.944807i | \(-0.606249\pi\) | ||||
−0.327628 | + | 0.944807i | \(0.606249\pi\) | |||||||
\(684\) | 2.44892e27 | 2.85721 | ||||||||
\(685\) | 3.56251e26 | 0.409917 | ||||||||
\(686\) | −1.25244e27 | −1.42128 | ||||||||
\(687\) | −4.03576e26 | −0.451686 | ||||||||
\(688\) | 3.41695e27 | 3.77180 | ||||||||
\(689\) | −9.73526e26 | −1.05990 | ||||||||
\(690\) | 2.47978e26 | 0.266285 | ||||||||
\(691\) | 8.40567e26 | 0.890289 | 0.445144 | − | 0.895459i | \(-0.353152\pi\) | ||||
0.445144 | + | 0.895459i | \(0.353152\pi\) | |||||||
\(692\) | −3.30267e27 | −3.45030 | ||||||||
\(693\) | −4.10825e26 | −0.423342 | ||||||||
\(694\) | −1.90366e27 | −1.93497 | ||||||||
\(695\) | −1.86997e25 | −0.0187490 | ||||||||
\(696\) | −8.00001e26 | −0.791230 | ||||||||
\(697\) | 6.44050e26 | 0.628359 | ||||||||
\(698\) | 2.10958e27 | 2.03035 | ||||||||
\(699\) | −4.63289e26 | −0.439864 | ||||||||
\(700\) | 6.27860e26 | 0.588073 | ||||||||
\(701\) | −2.09875e27 | −1.93927 | −0.969637 | − | 0.244551i | \(-0.921360\pi\) | ||||
−0.969637 | + | 0.244551i | \(0.921360\pi\) | |||||||
\(702\) | 1.39873e27 | 1.27506 | ||||||||
\(703\) | −1.30567e27 | −1.17424 | ||||||||
\(704\) | 8.52167e26 | 0.756109 | ||||||||
\(705\) | −7.95374e25 | −0.0696266 | ||||||||
\(706\) | 3.66557e27 | 3.16590 | ||||||||
\(707\) | −4.67220e26 | −0.398141 | ||||||||
\(708\) | 3.93912e26 | 0.331194 | ||||||||
\(709\) | 5.69598e26 | 0.472530 | 0.236265 | − | 0.971689i | \(-0.424077\pi\) | ||||
0.236265 | + | 0.971689i | \(0.424077\pi\) | |||||||
\(710\) | 5.28725e26 | 0.432788 | ||||||||
\(711\) | −9.45356e26 | −0.763544 | ||||||||
\(712\) | −3.03977e27 | −2.42259 | ||||||||
\(713\) | 1.78716e27 | 1.40545 | ||||||||
\(714\) | 1.11668e27 | 0.866554 | ||||||||
\(715\) | 2.71634e26 | 0.208007 | ||||||||
\(716\) | 4.16920e27 | 3.15050 | ||||||||
\(717\) | −5.98426e26 | −0.446250 | ||||||||
\(718\) | −3.65379e26 | −0.268882 | ||||||||
\(719\) | 2.23197e27 | 1.62093 | 0.810464 | − | 0.585789i | \(-0.199215\pi\) | ||||
0.810464 | + | 0.585789i | \(0.199215\pi\) | |||||||
\(720\) | 1.62497e27 | 1.16463 | ||||||||
\(721\) | −4.19162e26 | −0.296481 | ||||||||
\(722\) | 1.49585e27 | 1.04420 | ||||||||
\(723\) | 8.74224e26 | 0.602295 | ||||||||
\(724\) | −4.45238e27 | −3.02744 | ||||||||
\(725\) | −2.65510e26 | −0.178184 | ||||||||
\(726\) | −7.33257e26 | −0.485689 | ||||||||
\(727\) | −1.57138e27 | −1.02731 | −0.513657 | − | 0.857996i | \(-0.671710\pi\) | ||||
−0.513657 | + | 0.857996i | \(0.671710\pi\) | |||||||
\(728\) | −5.98171e27 | −3.85991 | ||||||||
\(729\) | −7.43193e26 | −0.473358 | ||||||||
\(730\) | −6.79188e26 | −0.426995 | ||||||||
\(731\) | 2.71774e27 | 1.68652 | ||||||||
\(732\) | 2.66243e26 | 0.163088 | ||||||||
\(733\) | −1.63155e27 | −0.986535 | −0.493267 | − | 0.869878i | \(-0.664198\pi\) | ||||
−0.493267 | + | 0.869878i | \(0.664198\pi\) | |||||||
\(734\) | 6.32154e25 | 0.0377320 | ||||||||
\(735\) | −8.16783e25 | −0.0481257 | ||||||||
\(736\) | −4.46740e27 | −2.59846 | ||||||||
\(737\) | 8.45995e26 | 0.485765 | ||||||||
\(738\) | −1.46471e27 | −0.830261 | ||||||||
\(739\) | −2.01351e27 | −1.12676 | −0.563380 | − | 0.826198i | \(-0.690499\pi\) | ||||
−0.563380 | + | 0.826198i | \(0.690499\pi\) | |||||||
\(740\) | −1.92950e27 | −1.06597 | ||||||||
\(741\) | 8.14529e26 | 0.444256 | ||||||||
\(742\) | 3.72105e27 | 2.00368 | ||||||||
\(743\) | 3.00829e27 | 1.59928 | 0.799642 | − | 0.600477i | \(-0.205023\pi\) | ||||
0.799642 | + | 0.600477i | \(0.205023\pi\) | |||||||
\(744\) | −2.31556e27 | −1.21538 | ||||||||
\(745\) | −1.33913e27 | −0.693967 | ||||||||
\(746\) | 3.95545e27 | 2.02385 | ||||||||
\(747\) | 9.13500e26 | 0.461491 | ||||||||
\(748\) | 2.63146e27 | 1.31260 | ||||||||
\(749\) | −1.10941e27 | −0.546405 | ||||||||
\(750\) | −1.06634e26 | −0.0518576 | ||||||||
\(751\) | −1.39340e27 | −0.669108 | −0.334554 | − | 0.942377i | \(-0.608586\pi\) | ||||
−0.334554 | + | 0.942377i | \(0.608586\pi\) | |||||||
\(752\) | 3.06314e27 | 1.45244 | ||||||||
\(753\) | 5.44534e26 | 0.254960 | ||||||||
\(754\) | 4.18093e27 | 1.93306 | ||||||||
\(755\) | 6.94548e26 | 0.317107 | ||||||||
\(756\) | −3.83251e27 | −1.72793 | ||||||||
\(757\) | −1.80766e26 | −0.0804832 | −0.0402416 | − | 0.999190i | \(-0.512813\pi\) | ||||
−0.0402416 | + | 0.999190i | \(0.512813\pi\) | |||||||
\(758\) | −7.04823e27 | −3.09901 | ||||||||
\(759\) | −2.93958e26 | −0.127640 | ||||||||
\(760\) | 3.74446e27 | 1.60569 | ||||||||
\(761\) | −2.60179e27 | −1.10184 | −0.550918 | − | 0.834559i | \(-0.685722\pi\) | ||||
−0.550918 | + | 0.834559i | \(0.685722\pi\) | |||||||
\(762\) | −3.66149e26 | −0.153139 | ||||||||
\(763\) | 5.29544e27 | 2.18735 | ||||||||
\(764\) | 9.20262e27 | 3.75426 | ||||||||
\(765\) | 1.29245e27 | 0.520751 | ||||||||
\(766\) | −2.35039e27 | −0.935335 | ||||||||
\(767\) | −1.24552e27 | −0.489549 | ||||||||
\(768\) | −2.53555e24 | −0.000984330 0 | ||||||||
\(769\) | −3.78836e27 | −1.45262 | −0.726308 | − | 0.687369i | \(-0.758765\pi\) | ||||
−0.726308 | + | 0.687369i | \(0.758765\pi\) | |||||||
\(770\) | −1.03825e27 | −0.393225 | ||||||||
\(771\) | −3.92228e26 | −0.146731 | ||||||||
\(772\) | 1.11236e28 | 4.11038 | ||||||||
\(773\) | 1.74556e27 | 0.637134 | 0.318567 | − | 0.947900i | \(-0.396798\pi\) | ||||
0.318567 | + | 0.947900i | \(0.396798\pi\) | |||||||
\(774\) | −6.18071e27 | −2.22843 | ||||||||
\(775\) | −7.68504e26 | −0.273703 | ||||||||
\(776\) | −2.81771e27 | −0.991311 | ||||||||
\(777\) | 9.70621e26 | 0.337326 | ||||||||
\(778\) | −1.73055e27 | −0.594125 | ||||||||
\(779\) | −1.79562e27 | −0.608988 | ||||||||
\(780\) | 1.20370e27 | 0.403293 | ||||||||
\(781\) | −6.26761e26 | −0.207452 | ||||||||
\(782\) | −7.59587e27 | −2.48378 | ||||||||
\(783\) | 1.62070e27 | 0.523558 | ||||||||
\(784\) | 3.14559e27 | 1.00392 | ||||||||
\(785\) | −1.49790e27 | −0.472305 | ||||||||
\(786\) | 5.65846e26 | 0.176272 | ||||||||
\(787\) | −9.37222e25 | −0.0288458 | −0.0144229 | − | 0.999896i | \(-0.504591\pi\) | ||||
−0.0144229 | + | 0.999896i | \(0.504591\pi\) | |||||||
\(788\) | 3.20099e27 | 0.973385 | ||||||||
\(789\) | 3.19576e25 | 0.00960158 | ||||||||
\(790\) | −2.38913e27 | −0.709224 | ||||||||
\(791\) | −2.08601e27 | −0.611844 | ||||||||
\(792\) | −3.62074e27 | −1.04932 | ||||||||
\(793\) | −8.41841e26 | −0.241065 | ||||||||
\(794\) | −8.07195e27 | −2.28394 | ||||||||
\(795\) | −4.53033e26 | −0.126661 | ||||||||
\(796\) | 2.46791e26 | 0.0681798 | ||||||||
\(797\) | 2.07539e27 | 0.566559 | 0.283280 | − | 0.959037i | \(-0.408578\pi\) | ||||
0.283280 | + | 0.959037i | \(0.408578\pi\) | |||||||
\(798\) | −3.11332e27 | −0.839840 | ||||||||
\(799\) | 2.43633e27 | 0.649444 | ||||||||
\(800\) | 1.92104e27 | 0.506036 | ||||||||
\(801\) | 2.92523e27 | 0.761467 | ||||||||
\(802\) | 4.34944e27 | 1.11886 | ||||||||
\(803\) | 8.05122e26 | 0.204675 | ||||||||
\(804\) | 3.74888e27 | 0.941823 | ||||||||
\(805\) | 2.14840e27 | 0.533402 | ||||||||
\(806\) | 1.21015e28 | 2.96931 | ||||||||
\(807\) | −1.05362e27 | −0.255496 | ||||||||
\(808\) | −4.11776e27 | −0.986855 | ||||||||
\(809\) | 8.60373e26 | 0.203787 | 0.101893 | − | 0.994795i | \(-0.467510\pi\) | ||||
0.101893 | + | 0.994795i | \(0.467510\pi\) | |||||||
\(810\) | −2.59759e27 | −0.608083 | ||||||||
\(811\) | 5.38167e27 | 1.24514 | 0.622572 | − | 0.782563i | \(-0.286088\pi\) | ||||
0.622572 | + | 0.782563i | \(0.286088\pi\) | |||||||
\(812\) | −1.14557e28 | −2.61964 | ||||||||
\(813\) | 3.94312e26 | 0.0891209 | ||||||||
\(814\) | 3.19070e27 | 0.712777 | ||||||||
\(815\) | 7.57718e26 | 0.167306 | ||||||||
\(816\) | 5.23587e27 | 1.14270 | ||||||||
\(817\) | −7.57710e27 | −1.63453 | ||||||||
\(818\) | −1.36462e28 | −2.90974 | ||||||||
\(819\) | 5.75631e27 | 1.21324 | ||||||||
\(820\) | −2.65355e27 | −0.552836 | ||||||||
\(821\) | −2.81042e27 | −0.578778 | −0.289389 | − | 0.957212i | \(-0.593452\pi\) | ||||
−0.289389 | + | 0.957212i | \(0.593452\pi\) | |||||||
\(822\) | −2.61054e27 | −0.531433 | ||||||||
\(823\) | −1.70827e27 | −0.343762 | −0.171881 | − | 0.985118i | \(-0.554984\pi\) | ||||
−0.171881 | + | 0.985118i | \(0.554984\pi\) | |||||||
\(824\) | −3.69421e27 | −0.734875 | ||||||||
\(825\) | 1.26406e26 | 0.0248573 | ||||||||
\(826\) | 4.76069e27 | 0.925463 | ||||||||
\(827\) | 2.86276e27 | 0.550152 | 0.275076 | − | 0.961423i | \(-0.411297\pi\) | ||||
0.275076 | + | 0.961423i | \(0.411297\pi\) | |||||||
\(828\) | 1.23834e28 | 2.35262 | ||||||||
\(829\) | −3.36069e27 | −0.631191 | −0.315595 | − | 0.948894i | \(-0.602204\pi\) | ||||
−0.315595 | + | 0.948894i | \(0.602204\pi\) | |||||||
\(830\) | 2.30863e27 | 0.428659 | ||||||||
\(831\) | 2.64052e26 | 0.0484708 | ||||||||
\(832\) | −1.19402e28 | −2.16691 | ||||||||
\(833\) | 2.50191e27 | 0.448894 | ||||||||
\(834\) | 1.37028e26 | 0.0243070 | ||||||||
\(835\) | 4.01126e27 | 0.703492 | ||||||||
\(836\) | −7.33655e27 | −1.27213 | ||||||||
\(837\) | 4.69101e27 | 0.804220 | ||||||||
\(838\) | 1.61170e28 | 2.73190 | ||||||||
\(839\) | −4.83778e27 | −0.810788 | −0.405394 | − | 0.914142i | \(-0.632866\pi\) | ||||
−0.405394 | + | 0.914142i | \(0.632866\pi\) | |||||||
\(840\) | −2.78360e27 | −0.461268 | ||||||||
\(841\) | −1.25884e27 | −0.206257 | ||||||||
\(842\) | 1.41473e28 | 2.29197 | ||||||||
\(843\) | −1.58342e27 | −0.253649 | ||||||||
\(844\) | 1.26179e28 | 1.99864 | ||||||||
\(845\) | −9.50714e26 | −0.148906 | ||||||||
\(846\) | −5.54073e27 | −0.858121 | ||||||||
\(847\) | −6.35271e27 | −0.972896 | ||||||||
\(848\) | 1.74472e28 | 2.64219 | ||||||||
\(849\) | −3.09550e27 | −0.463562 | ||||||||
\(850\) | 3.26632e27 | 0.483703 | ||||||||
\(851\) | −6.60235e27 | −0.966870 | ||||||||
\(852\) | −2.77739e27 | −0.402217 | ||||||||
\(853\) | −1.95293e27 | −0.279687 | −0.139843 | − | 0.990174i | \(-0.544660\pi\) | ||||
−0.139843 | + | 0.990174i | \(0.544660\pi\) | |||||||
\(854\) | 3.21772e27 | 0.455720 | ||||||||
\(855\) | −3.60337e27 | −0.504697 | ||||||||
\(856\) | −9.77759e27 | −1.35435 | ||||||||
\(857\) | 5.90679e27 | 0.809159 | 0.404579 | − | 0.914503i | \(-0.367418\pi\) | ||||
0.404579 | + | 0.914503i | \(0.367418\pi\) | |||||||
\(858\) | −1.99049e27 | −0.269668 | ||||||||
\(859\) | 1.34994e28 | 1.80876 | 0.904380 | − | 0.426729i | \(-0.140334\pi\) | ||||
0.904380 | + | 0.426729i | \(0.140334\pi\) | |||||||
\(860\) | −1.11974e28 | −1.48382 | ||||||||
\(861\) | 1.33485e27 | 0.174945 | ||||||||
\(862\) | −2.76428e28 | −3.58314 | ||||||||
\(863\) | −1.46014e28 | −1.87194 | −0.935971 | − | 0.352077i | \(-0.885476\pi\) | ||||
−0.935971 | + | 0.352077i | \(0.885476\pi\) | |||||||
\(864\) | −1.17262e28 | −1.48688 | ||||||||
\(865\) | 4.85959e27 | 0.609462 | ||||||||
\(866\) | −3.93328e24 | −0.000487904 0 | ||||||||
\(867\) | 1.64994e27 | 0.202436 | ||||||||
\(868\) | −3.31580e28 | −4.02393 | ||||||||
\(869\) | 2.83213e27 | 0.339958 | ||||||||
\(870\) | 1.94561e27 | 0.231006 | ||||||||
\(871\) | −1.18537e28 | −1.39214 | ||||||||
\(872\) | 4.66704e28 | 5.42169 | ||||||||
\(873\) | 2.71154e27 | 0.311588 | ||||||||
\(874\) | 2.11774e28 | 2.40721 | ||||||||
\(875\) | −9.23841e26 | −0.103877 | ||||||||
\(876\) | 3.56777e27 | 0.396833 | ||||||||
\(877\) | 2.30842e27 | 0.253992 | 0.126996 | − | 0.991903i | \(-0.459467\pi\) | ||||
0.126996 | + | 0.991903i | \(0.459467\pi\) | |||||||
\(878\) | 1.72696e28 | 1.87968 | ||||||||
\(879\) | −4.39001e27 | −0.472684 | ||||||||
\(880\) | −4.86813e27 | −0.518533 | ||||||||
\(881\) | −2.21402e26 | −0.0233298 | −0.0116649 | − | 0.999932i | \(-0.503713\pi\) | ||||
−0.0116649 | + | 0.999932i | \(0.503713\pi\) | |||||||
\(882\) | −5.68987e27 | −0.593131 | ||||||||
\(883\) | −6.85195e27 | −0.706622 | −0.353311 | − | 0.935506i | \(-0.614944\pi\) | ||||
−0.353311 | + | 0.935506i | \(0.614944\pi\) | |||||||
\(884\) | −3.68709e28 | −3.76173 | ||||||||
\(885\) | −5.79607e26 | −0.0585023 | ||||||||
\(886\) | 1.12901e28 | 1.12740 | ||||||||
\(887\) | −1.86889e28 | −1.84633 | −0.923164 | − | 0.384407i | \(-0.874406\pi\) | ||||
−0.923164 | + | 0.384407i | \(0.874406\pi\) | |||||||
\(888\) | 8.55441e27 | 0.836116 | ||||||||
\(889\) | −3.17220e27 | −0.306756 | ||||||||
\(890\) | 7.39274e27 | 0.707294 | ||||||||
\(891\) | 3.07924e27 | 0.291477 | ||||||||
\(892\) | 3.64651e28 | 3.41516 | ||||||||
\(893\) | −6.79253e27 | −0.629423 | ||||||||
\(894\) | 9.81291e27 | 0.899687 | ||||||||
\(895\) | −6.13461e27 | −0.556504 | ||||||||
\(896\) | 1.29002e28 | 1.15790 | ||||||||
\(897\) | 4.11882e27 | 0.365800 | ||||||||
\(898\) | 6.69525e26 | 0.0588358 | ||||||||
\(899\) | 1.40219e28 | 1.21924 | ||||||||
\(900\) | −5.32503e27 | −0.458161 | ||||||||
\(901\) | 1.38769e28 | 1.18143 | ||||||||
\(902\) | 4.38801e27 | 0.369663 | ||||||||
\(903\) | 5.63275e27 | 0.469555 | ||||||||
\(904\) | −1.83847e28 | −1.51655 | ||||||||
\(905\) | 6.55129e27 | 0.534768 | ||||||||
\(906\) | −5.08952e27 | −0.411111 | ||||||||
\(907\) | 2.16205e27 | 0.172821 | 0.0864107 | − | 0.996260i | \(-0.472460\pi\) | ||||
0.0864107 | + | 0.996260i | \(0.472460\pi\) | |||||||
\(908\) | 1.87541e28 | 1.48347 | ||||||||
\(909\) | 3.96260e27 | 0.310187 | ||||||||
\(910\) | 1.45475e28 | 1.12693 | ||||||||
\(911\) | 7.62832e27 | 0.584796 | 0.292398 | − | 0.956297i | \(-0.405547\pi\) | ||||
0.292398 | + | 0.956297i | \(0.405547\pi\) | |||||||
\(912\) | −1.45977e28 | −1.10747 | ||||||||
\(913\) | −2.73669e27 | −0.205472 | ||||||||
\(914\) | −4.02722e28 | −2.99238 | ||||||||
\(915\) | −3.91753e26 | −0.0288079 | ||||||||
\(916\) | −5.09328e28 | −3.70673 | ||||||||
\(917\) | 4.90231e27 | 0.353096 | ||||||||
\(918\) | −1.99379e28 | −1.42126 | ||||||||
\(919\) | 8.34991e27 | 0.589093 | 0.294547 | − | 0.955637i | \(-0.404831\pi\) | ||||
0.294547 | + | 0.955637i | \(0.404831\pi\) | |||||||
\(920\) | 1.89346e28 | 1.32212 | ||||||||
\(921\) | −9.93383e26 | −0.0686516 | ||||||||
\(922\) | −3.26451e28 | −2.23293 | ||||||||
\(923\) | 8.78191e27 | 0.594529 | ||||||||
\(924\) | 5.45392e27 | 0.365448 | ||||||||
\(925\) | 2.83910e27 | 0.188293 | ||||||||
\(926\) | 1.38239e28 | 0.907457 | ||||||||
\(927\) | 3.55501e27 | 0.230985 | ||||||||
\(928\) | −3.50507e28 | −2.25420 | ||||||||
\(929\) | 1.90486e28 | 1.21259 | 0.606295 | − | 0.795240i | \(-0.292655\pi\) | ||||
0.606295 | + | 0.795240i | \(0.292655\pi\) | |||||||
\(930\) | 5.63145e27 | 0.354840 | ||||||||
\(931\) | −6.97536e27 | −0.435055 | ||||||||
\(932\) | −5.84688e28 | −3.60972 | ||||||||
\(933\) | −3.09848e27 | −0.189354 | ||||||||
\(934\) | −3.20182e28 | −1.93687 | ||||||||
\(935\) | −3.87196e27 | −0.231857 | ||||||||
\(936\) | 5.07323e28 | 3.00721 | ||||||||
\(937\) | 1.61387e28 | 0.946986 | 0.473493 | − | 0.880797i | \(-0.342993\pi\) | ||||
0.473493 | + | 0.880797i | \(0.342993\pi\) | |||||||
\(938\) | 4.53077e28 | 2.63176 | ||||||||
\(939\) | −1.79628e27 | −0.103288 | ||||||||
\(940\) | −1.00379e28 | −0.571386 | ||||||||
\(941\) | 1.27180e28 | 0.716670 | 0.358335 | − | 0.933593i | \(-0.383345\pi\) | ||||
0.358335 | + | 0.933593i | \(0.383345\pi\) | |||||||
\(942\) | 1.09764e28 | 0.612315 | ||||||||
\(943\) | −9.07990e27 | −0.501441 | ||||||||
\(944\) | 2.23218e28 | 1.22038 | ||||||||
\(945\) | 5.63921e27 | 0.305222 | ||||||||
\(946\) | 1.85164e28 | 0.992179 | ||||||||
\(947\) | 1.45271e28 | 0.770647 | 0.385323 | − | 0.922782i | \(-0.374090\pi\) | ||||
0.385323 | + | 0.922782i | \(0.374090\pi\) | |||||||
\(948\) | 1.25501e28 | 0.659125 | ||||||||
\(949\) | −1.12810e28 | −0.586570 | ||||||||
\(950\) | −9.10656e27 | −0.468792 | ||||||||
\(951\) | 1.01474e26 | 0.00517177 | ||||||||
\(952\) | 8.52651e28 | 4.30250 | ||||||||
\(953\) | −2.74411e28 | −1.37094 | −0.685471 | − | 0.728100i | \(-0.740403\pi\) | ||||
−0.685471 | + | 0.728100i | \(0.740403\pi\) | |||||||
\(954\) | −3.15591e28 | −1.56104 | ||||||||
\(955\) | −1.35409e28 | −0.663153 | ||||||||
\(956\) | −7.55237e28 | −3.66212 | ||||||||
\(957\) | −2.30636e27 | −0.110730 | ||||||||
\(958\) | 4.76975e27 | 0.226738 | ||||||||
\(959\) | −2.26169e28 | −1.06453 | ||||||||
\(960\) | −5.55641e27 | −0.258951 | ||||||||
\(961\) | 1.89149e28 | 0.872834 | ||||||||
\(962\) | −4.47067e28 | −2.04272 | ||||||||
\(963\) | 9.40917e27 | 0.425698 | ||||||||
\(964\) | 1.10330e29 | 4.94269 | ||||||||
\(965\) | −1.63674e28 | −0.726058 | ||||||||
\(966\) | −1.57431e28 | −0.691524 | ||||||||
\(967\) | −4.38569e28 | −1.90760 | −0.953798 | − | 0.300448i | \(-0.902864\pi\) | ||||
−0.953798 | + | 0.300448i | \(0.902864\pi\) | |||||||
\(968\) | −5.59885e28 | −2.41148 | ||||||||
\(969\) | −1.16105e28 | −0.495196 | ||||||||
\(970\) | 6.85269e27 | 0.289421 | ||||||||
\(971\) | 3.19230e28 | 1.33512 | 0.667561 | − | 0.744555i | \(-0.267338\pi\) | ||||
0.667561 | + | 0.744555i | \(0.267338\pi\) | |||||||
\(972\) | 4.95687e28 | 2.05295 | ||||||||
\(973\) | 1.18716e27 | 0.0486899 | ||||||||
\(974\) | 7.39883e28 | 3.00506 | ||||||||
\(975\) | −1.77114e27 | −0.0712377 | ||||||||
\(976\) | 1.50872e28 | 0.600945 | ||||||||
\(977\) | 2.21216e28 | 0.872605 | 0.436303 | − | 0.899800i | \(-0.356288\pi\) | ||||
0.436303 | + | 0.899800i | \(0.356288\pi\) | |||||||
\(978\) | −5.55242e27 | −0.216902 | ||||||||
\(979\) | −8.76350e27 | −0.339033 | ||||||||
\(980\) | −1.03081e28 | −0.394940 | ||||||||
\(981\) | −4.49119e28 | −1.70414 | ||||||||
\(982\) | −7.84121e27 | −0.294662 | ||||||||
\(983\) | −3.34360e27 | −0.124439 | −0.0622195 | − | 0.998062i | \(-0.519818\pi\) | ||||
−0.0622195 | + | 0.998062i | \(0.519818\pi\) | |||||||
\(984\) | 1.17645e28 | 0.433629 | ||||||||
\(985\) | −4.70997e27 | −0.171939 | ||||||||
\(986\) | −5.95964e28 | −2.15471 | ||||||||
\(987\) | 5.04950e27 | 0.180816 | ||||||||
\(988\) | 1.02797e29 | 3.64576 | ||||||||
\(989\) | −3.83150e28 | −1.34587 | ||||||||
\(990\) | 8.80566e27 | 0.306357 | ||||||||
\(991\) | 1.69711e28 | 0.584803 | 0.292401 | − | 0.956296i | \(-0.405546\pi\) | ||||
0.292401 | + | 0.956296i | \(0.405546\pi\) | |||||||
\(992\) | −1.01452e29 | −3.46259 | ||||||||
\(993\) | 5.95596e27 | 0.201342 | ||||||||
\(994\) | −3.35666e28 | −1.12392 | ||||||||
\(995\) | −3.63132e26 | −0.0120433 | ||||||||
\(996\) | −1.21272e28 | −0.398379 | ||||||||
\(997\) | 4.73263e28 | 1.53992 | 0.769960 | − | 0.638092i | \(-0.220276\pi\) | ||||
0.769960 | + | 0.638092i | \(0.220276\pi\) | |||||||
\(998\) | 1.04421e29 | 3.36548 | ||||||||
\(999\) | −1.73301e28 | −0.553259 |
(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 | 5.20.a.b.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 45.20.a.f.1.1 | 4 | |||
4.3 | odd | 2 | 80.20.a.g.1.2 | 4 | |||
5.2 | odd | 4 | 25.20.b.c.24.7 | 8 | |||
5.3 | odd | 4 | 25.20.b.c.24.2 | 8 | |||
5.4 | even | 2 | 25.20.a.c.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.20.a.b.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
25.20.a.c.1.1 | 4 | 5.4 | even | 2 | |||
25.20.b.c.24.2 | 8 | 5.3 | odd | 4 | |||
25.20.b.c.24.7 | 8 | 5.2 | odd | 4 | |||
45.20.a.f.1.1 | 4 | 3.2 | odd | 2 | |||
80.20.a.g.1.2 | 4 | 4.3 | odd | 2 |