Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.14336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 8x^{2} + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.60804\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.27411 | 1.01701 | 0.508506 | − | 0.861058i | \(-0.330198\pi\) | ||||
0.508506 | + | 0.861058i | \(0.330198\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.27411 | −0.719136 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.80186 | 0.499747 | 0.249873 | − | 0.968279i | \(-0.419611\pi\) | ||||
0.249873 | + | 0.968279i | \(0.419611\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.27411 | 0.587172 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.10254 | 1.23755 | 0.618773 | − | 0.785570i | \(-0.287630\pi\) | ||||
0.618773 | + | 0.785570i | \(0.287630\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.90440 | −1.58398 | −0.791989 | − | 0.610536i | \(-0.790954\pi\) | ||||
−0.791989 | + | 0.610536i | \(0.790954\pi\) | |||||||
\(20\) | 2.27411 | 0.508506 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 8.59272 | 1.79171 | 0.895853 | − | 0.444350i | \(-0.146565\pi\) | ||||
0.895853 | + | 0.444350i | \(0.146565\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0.171573 | 0.0343146 | ||||||||
\(26\) | −1.80186 | −0.353374 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.82843 | −0.525226 | −0.262613 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262613 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(30\) | −2.27411 | −0.415194 | ||||||||
\(31\) | 3.14010 | 0.563979 | 0.281990 | − | 0.959417i | \(-0.409006\pi\) | ||||
0.281990 | + | 0.959417i | \(0.409006\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −5.10254 | −0.875078 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.44078 | 0.730059 | 0.365030 | − | 0.930996i | \(-0.381059\pi\) | ||||
0.365030 | + | 0.930996i | \(0.381059\pi\) | |||||||
\(38\) | 6.90440 | 1.12004 | ||||||||
\(39\) | 1.80186 | 0.288529 | ||||||||
\(40\) | −2.27411 | −0.359568 | ||||||||
\(41\) | −5.10254 | −0.796882 | −0.398441 | − | 0.917194i | \(-0.630449\pi\) | ||||
−0.398441 | + | 0.917194i | \(0.630449\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.93587 | 1.05771 | 0.528855 | − | 0.848712i | \(-0.322622\pi\) | ||||
0.528855 | + | 0.848712i | \(0.322622\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 2.27411 | 0.339004 | ||||||||
\(46\) | −8.59272 | −1.26693 | ||||||||
\(47\) | −0.0759718 | −0.0110816 | −0.00554082 | − | 0.999985i | \(-0.501764\pi\) | ||||
−0.00554082 | + | 0.999985i | \(0.501764\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.171573 | −0.0242641 | ||||||||
\(51\) | 5.10254 | 0.714498 | ||||||||
\(52\) | 1.80186 | 0.249873 | ||||||||
\(53\) | −6.87293 | −0.944070 | −0.472035 | − | 0.881580i | \(-0.656480\pi\) | ||||
−0.472035 | + | 0.881580i | \(0.656480\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.27411 | −0.306641 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.90440 | −0.914510 | ||||||||
\(58\) | 2.82843 | 0.371391 | ||||||||
\(59\) | 5.17157 | 0.673281 | 0.336641 | − | 0.941633i | \(-0.390709\pi\) | ||||
0.336641 | + | 0.941633i | \(0.390709\pi\) | |||||||
\(60\) | 2.27411 | 0.293586 | ||||||||
\(61\) | 8.63029 | 1.10500 | 0.552498 | − | 0.833514i | \(-0.313675\pi\) | ||||
0.552498 | + | 0.833514i | \(0.313675\pi\) | |||||||
\(62\) | −3.14010 | −0.398794 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.09763 | 0.508249 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 13.4841 | 1.64734 | 0.823672 | − | 0.567067i | \(-0.191922\pi\) | ||||
0.823672 | + | 0.567067i | \(0.191922\pi\) | |||||||
\(68\) | 5.10254 | 0.618773 | ||||||||
\(69\) | 8.59272 | 1.03444 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.26058 | −1.09903 | −0.549514 | − | 0.835484i | \(-0.685187\pi\) | ||||
−0.549514 | + | 0.835484i | \(0.685187\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −3.04941 | −0.356906 | −0.178453 | − | 0.983948i | \(-0.557109\pi\) | ||||
−0.178453 | + | 0.983948i | \(0.557109\pi\) | |||||||
\(74\) | −4.44078 | −0.516230 | ||||||||
\(75\) | 0.171573 | 0.0198115 | ||||||||
\(76\) | −6.90440 | −0.791989 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.80186 | −0.204021 | ||||||||
\(79\) | 9.26921 | 1.04287 | 0.521434 | − | 0.853292i | \(-0.325397\pi\) | ||||
0.521434 | + | 0.853292i | \(0.325397\pi\) | |||||||
\(80\) | 2.27411 | 0.254253 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.10254 | 0.563481 | ||||||||
\(83\) | −1.96853 | −0.216074 | −0.108037 | − | 0.994147i | \(-0.534457\pi\) | ||||
−0.108037 | + | 0.994147i | \(0.534457\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.6037 | 1.25860 | ||||||||
\(86\) | −6.93587 | −0.747914 | ||||||||
\(87\) | −2.82843 | −0.303239 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 15.0624 | 1.59662 | 0.798308 | − | 0.602250i | \(-0.205729\pi\) | ||||
0.798308 | + | 0.602250i | \(0.205729\pi\) | |||||||
\(90\) | −2.27411 | −0.239712 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.59272 | 0.895853 | ||||||||
\(93\) | 3.14010 | 0.325614 | ||||||||
\(94\) | 0.0759718 | 0.00783590 | ||||||||
\(95\) | −15.7014 | −1.61093 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −9.01794 | −0.915633 | −0.457816 | − | 0.889047i | \(-0.651368\pi\) | ||||
−0.457816 | + | 0.889047i | \(0.651368\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0.171573 | 0.0171573 | ||||||||
\(101\) | −11.2230 | −1.11673 | −0.558366 | − | 0.829595i | \(-0.688571\pi\) | ||||
−0.558366 | + | 0.829595i | \(0.688571\pi\) | |||||||
\(102\) | −5.10254 | −0.505226 | ||||||||
\(103\) | 17.0118 | 1.67623 | 0.838113 | − | 0.545496i | \(-0.183659\pi\) | ||||
0.838113 | + | 0.545496i | \(0.183659\pi\) | |||||||
\(104\) | −1.80186 | −0.176687 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.87293 | 0.667558 | ||||||||
\(107\) | 11.6482 | 1.12608 | 0.563038 | − | 0.826431i | \(-0.309632\pi\) | ||||
0.563038 | + | 0.826431i | \(0.309632\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −14.0890 | −1.34948 | −0.674741 | − | 0.738055i | \(-0.735745\pi\) | ||||
−0.674741 | + | 0.738055i | \(0.735745\pi\) | |||||||
\(110\) | 2.27411 | 0.216828 | ||||||||
\(111\) | 4.44078 | 0.421500 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.71979 | −0.538073 | −0.269036 | − | 0.963130i | \(-0.586705\pi\) | ||||
−0.269036 | + | 0.963130i | \(0.586705\pi\) | |||||||
\(114\) | 6.90440 | 0.646656 | ||||||||
\(115\) | 19.5408 | 1.82219 | ||||||||
\(116\) | −2.82843 | −0.262613 | ||||||||
\(117\) | 1.80186 | 0.166582 | ||||||||
\(118\) | −5.17157 | −0.476082 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.27411 | −0.207597 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −8.63029 | −0.781350 | ||||||||
\(123\) | −5.10254 | −0.460080 | ||||||||
\(124\) | 3.14010 | 0.281990 | ||||||||
\(125\) | −10.9804 | −0.982114 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.60492 | 0.586092 | 0.293046 | − | 0.956098i | \(-0.405331\pi\) | ||||
0.293046 | + | 0.956098i | \(0.405331\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.93587 | 0.610669 | ||||||||
\(130\) | −4.09763 | −0.359386 | ||||||||
\(131\) | 5.96853 | 0.521473 | 0.260737 | − | 0.965410i | \(-0.416035\pi\) | ||||
0.260737 | + | 0.965410i | \(0.416035\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.4841 | −1.16485 | ||||||||
\(135\) | 2.27411 | 0.195724 | ||||||||
\(136\) | −5.10254 | −0.437539 | ||||||||
\(137\) | 11.2606 | 0.962056 | 0.481028 | − | 0.876705i | \(-0.340263\pi\) | ||||
0.481028 | + | 0.876705i | \(0.340263\pi\) | |||||||
\(138\) | −8.59272 | −0.731461 | ||||||||
\(139\) | 8.62419 | 0.731494 | 0.365747 | − | 0.930714i | \(-0.380813\pi\) | ||||
0.365747 | + | 0.930714i | \(0.380813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0759718 | −0.00639798 | ||||||||
\(142\) | 9.26058 | 0.777131 | ||||||||
\(143\) | −1.80186 | −0.150679 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.43215 | −0.534161 | ||||||||
\(146\) | 3.04941 | 0.252371 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.44078 | 0.365030 | ||||||||
\(149\) | −12.3211 | −1.00939 | −0.504694 | − | 0.863299i | \(-0.668394\pi\) | ||||
−0.504694 | + | 0.863299i | \(0.668394\pi\) | |||||||
\(150\) | −0.171573 | −0.0140089 | ||||||||
\(151\) | −11.5286 | −0.938183 | −0.469092 | − | 0.883149i | \(-0.655419\pi\) | ||||
−0.469092 | + | 0.883149i | \(0.655419\pi\) | |||||||
\(152\) | 6.90440 | 0.560021 | ||||||||
\(153\) | 5.10254 | 0.412516 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.14094 | 0.573574 | ||||||||
\(156\) | 1.80186 | 0.144264 | ||||||||
\(157\) | 1.49881 | 0.119618 | 0.0598091 | − | 0.998210i | \(-0.480951\pi\) | ||||
0.0598091 | + | 0.998210i | \(0.480951\pi\) | |||||||
\(158\) | −9.26921 | −0.737418 | ||||||||
\(159\) | −6.87293 | −0.545059 | ||||||||
\(160\) | −2.27411 | −0.179784 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 13.6569 | 1.06969 | 0.534844 | − | 0.844951i | \(-0.320370\pi\) | ||||
0.534844 | + | 0.844951i | \(0.320370\pi\) | |||||||
\(164\) | −5.10254 | −0.398441 | ||||||||
\(165\) | −2.27411 | −0.177039 | ||||||||
\(166\) | 1.96853 | 0.152788 | ||||||||
\(167\) | 19.6927 | 1.52387 | 0.761935 | − | 0.647654i | \(-0.224250\pi\) | ||||
0.761935 | + | 0.647654i | \(0.224250\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.75329 | −0.750253 | ||||||||
\(170\) | −11.6037 | −0.889965 | ||||||||
\(171\) | −6.90440 | −0.527993 | ||||||||
\(172\) | 6.93587 | 0.528855 | ||||||||
\(173\) | −14.5107 | −1.10322 | −0.551612 | − | 0.834101i | \(-0.685987\pi\) | ||||
−0.551612 | + | 0.834101i | \(0.685987\pi\) | |||||||
\(174\) | 2.82843 | 0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 5.17157 | 0.388719 | ||||||||
\(178\) | −15.0624 | −1.12898 | ||||||||
\(179\) | −22.3656 | −1.67169 | −0.835843 | − | 0.548968i | \(-0.815021\pi\) | ||||
−0.835843 | + | 0.548968i | \(0.815021\pi\) | |||||||
\(180\) | 2.27411 | 0.169502 | ||||||||
\(181\) | −5.73976 | −0.426633 | −0.213317 | − | 0.976983i | \(-0.568427\pi\) | ||||
−0.213317 | + | 0.976983i | \(0.568427\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.63029 | 0.637969 | ||||||||
\(184\) | −8.59272 | −0.633464 | ||||||||
\(185\) | 10.0988 | 0.742480 | ||||||||
\(186\) | −3.14010 | −0.230244 | ||||||||
\(187\) | −5.10254 | −0.373134 | ||||||||
\(188\) | −0.0759718 | −0.00554082 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.7014 | 1.13910 | ||||||||
\(191\) | −11.7112 | −0.847390 | −0.423695 | − | 0.905805i | \(-0.639267\pi\) | ||||
−0.423695 | + | 0.905805i | \(0.639267\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −12.7533 | −0.918002 | −0.459001 | − | 0.888436i | \(-0.651793\pi\) | ||||
−0.459001 | + | 0.888436i | \(0.651793\pi\) | |||||||
\(194\) | 9.01794 | 0.647450 | ||||||||
\(195\) | 4.09763 | 0.293438 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.2606 | −1.65725 | −0.828624 | − | 0.559806i | \(-0.810876\pi\) | ||||
−0.828624 | + | 0.559806i | \(0.810876\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 1.48325 | 0.105145 | 0.0525724 | − | 0.998617i | \(-0.483258\pi\) | ||||
0.0525724 | + | 0.998617i | \(0.483258\pi\) | |||||||
\(200\) | −0.171573 | −0.0121320 | ||||||||
\(201\) | 13.4841 | 0.951094 | ||||||||
\(202\) | 11.2230 | 0.789648 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.10254 | 0.357249 | ||||||||
\(205\) | −11.6037 | −0.810439 | ||||||||
\(206\) | −17.0118 | −1.18527 | ||||||||
\(207\) | 8.59272 | 0.597235 | ||||||||
\(208\) | 1.80186 | 0.124937 | ||||||||
\(209\) | 6.90440 | 0.477587 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.503715 | 0.0346772 | 0.0173386 | − | 0.999850i | \(-0.494481\pi\) | ||||
0.0173386 | + | 0.999850i | \(0.494481\pi\) | |||||||
\(212\) | −6.87293 | −0.472035 | ||||||||
\(213\) | −9.26058 | −0.634524 | ||||||||
\(214\) | −11.6482 | −0.796257 | ||||||||
\(215\) | 15.7729 | 1.07570 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.0890 | 0.954228 | ||||||||
\(219\) | −3.04941 | −0.206060 | ||||||||
\(220\) | −2.27411 | −0.153320 | ||||||||
\(221\) | 9.19407 | 0.618460 | ||||||||
\(222\) | −4.44078 | −0.298046 | ||||||||
\(223\) | 20.0044 | 1.33959 | 0.669797 | − | 0.742544i | \(-0.266381\pi\) | ||||
0.669797 | + | 0.742544i | \(0.266381\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.171573 | 0.0114382 | ||||||||
\(226\) | 5.71979 | 0.380475 | ||||||||
\(227\) | 13.5601 | 0.900013 | 0.450006 | − | 0.893025i | \(-0.351422\pi\) | ||||
0.450006 | + | 0.893025i | \(0.351422\pi\) | |||||||
\(228\) | −6.90440 | −0.457255 | ||||||||
\(229\) | −5.10254 | −0.337185 | −0.168593 | − | 0.985686i | \(-0.553922\pi\) | ||||
−0.168593 | + | 0.985686i | \(0.553922\pi\) | |||||||
\(230\) | −19.5408 | −1.28848 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.82843 | 0.185695 | ||||||||
\(233\) | −0.343146 | −0.0224802 | −0.0112401 | − | 0.999937i | \(-0.503578\pi\) | ||||
−0.0112401 | + | 0.999937i | \(0.503578\pi\) | |||||||
\(234\) | −1.80186 | −0.117791 | ||||||||
\(235\) | −0.172768 | −0.0112702 | ||||||||
\(236\) | 5.17157 | 0.336641 | ||||||||
\(237\) | 9.26921 | 0.602100 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.4322 | −1.19228 | −0.596138 | − | 0.802882i | \(-0.703299\pi\) | ||||
−0.596138 | + | 0.802882i | \(0.703299\pi\) | |||||||
\(240\) | 2.27411 | 0.146793 | ||||||||
\(241\) | 24.5682 | 1.58258 | 0.791288 | − | 0.611444i | \(-0.209411\pi\) | ||||
0.791288 | + | 0.611444i | \(0.209411\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.63029 | 0.552498 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.10254 | 0.325326 | ||||||||
\(247\) | −12.4408 | −0.791588 | ||||||||
\(248\) | −3.14010 | −0.199397 | ||||||||
\(249\) | −1.96853 | −0.124751 | ||||||||
\(250\) | 10.9804 | 0.694460 | ||||||||
\(251\) | 1.50491 | 0.0949891 | 0.0474946 | − | 0.998871i | \(-0.484876\pi\) | ||||
0.0474946 | + | 0.998871i | \(0.484876\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.59272 | −0.540220 | ||||||||
\(254\) | −6.60492 | −0.414430 | ||||||||
\(255\) | 11.6037 | 0.726653 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.8476 | 0.676652 | 0.338326 | − | 0.941029i | \(-0.390139\pi\) | ||||
0.338326 | + | 0.941029i | \(0.390139\pi\) | |||||||
\(258\) | −6.93587 | −0.431808 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.09763 | 0.254124 | ||||||||
\(261\) | −2.82843 | −0.175075 | ||||||||
\(262\) | −5.96853 | −0.368737 | ||||||||
\(263\) | 6.25938 | 0.385970 | 0.192985 | − | 0.981202i | \(-0.438183\pi\) | ||||
0.192985 | + | 0.981202i | \(0.438183\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | −15.6298 | −0.960131 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.0624 | 0.921806 | ||||||||
\(268\) | 13.4841 | 0.823672 | ||||||||
\(269\) | 14.8345 | 0.904477 | 0.452239 | − | 0.891897i | \(-0.350626\pi\) | ||||
0.452239 | + | 0.891897i | \(0.350626\pi\) | |||||||
\(270\) | −2.27411 | −0.138398 | ||||||||
\(271\) | −2.91743 | −0.177221 | −0.0886107 | − | 0.996066i | \(-0.528243\pi\) | ||||
−0.0886107 | + | 0.996066i | \(0.528243\pi\) | |||||||
\(272\) | 5.10254 | 0.309387 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.2606 | −0.680276 | ||||||||
\(275\) | −0.171573 | −0.0103462 | ||||||||
\(276\) | 8.59272 | 0.517221 | ||||||||
\(277\) | 12.1012 | 0.727091 | 0.363545 | − | 0.931576i | \(-0.381566\pi\) | ||||
0.363545 | + | 0.931576i | \(0.381566\pi\) | |||||||
\(278\) | −8.62419 | −0.517245 | ||||||||
\(279\) | 3.14010 | 0.187993 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.74586 | 0.462079 | 0.231040 | − | 0.972944i | \(-0.425787\pi\) | ||||
0.231040 | + | 0.972944i | \(0.425787\pi\) | |||||||
\(282\) | 0.0759718 | 0.00452406 | ||||||||
\(283\) | 17.5948 | 1.04590 | 0.522950 | − | 0.852364i | \(-0.324832\pi\) | ||||
0.522950 | + | 0.852364i | \(0.324832\pi\) | |||||||
\(284\) | −9.26058 | −0.549514 | ||||||||
\(285\) | −15.7014 | −0.930068 | ||||||||
\(286\) | 1.80186 | 0.106546 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 9.03588 | 0.531522 | ||||||||
\(290\) | 6.43215 | 0.377709 | ||||||||
\(291\) | −9.01794 | −0.528641 | ||||||||
\(292\) | −3.04941 | −0.178453 | ||||||||
\(293\) | −16.1675 | −0.944516 | −0.472258 | − | 0.881460i | \(-0.656561\pi\) | ||||
−0.472258 | + | 0.881460i | \(0.656561\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.7607 | 0.684736 | ||||||||
\(296\) | −4.44078 | −0.258115 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 12.3211 | 0.713744 | ||||||||
\(299\) | 15.4829 | 0.895399 | ||||||||
\(300\) | 0.171573 | 0.00990576 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.5286 | 0.663396 | ||||||||
\(303\) | −11.2230 | −0.644745 | ||||||||
\(304\) | −6.90440 | −0.395994 | ||||||||
\(305\) | 19.6262 | 1.12379 | ||||||||
\(306\) | −5.10254 | −0.291693 | ||||||||
\(307\) | −27.0563 | −1.54419 | −0.772094 | − | 0.635509i | \(-0.780790\pi\) | ||||
−0.772094 | + | 0.635509i | \(0.780790\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.0118 | 0.967770 | ||||||||
\(310\) | −7.14094 | −0.405578 | ||||||||
\(311\) | −24.5751 | −1.39353 | −0.696764 | − | 0.717301i | \(-0.745377\pi\) | ||||
−0.696764 | + | 0.717301i | \(0.745377\pi\) | |||||||
\(312\) | −1.80186 | −0.102010 | ||||||||
\(313\) | 13.0809 | 0.739375 | 0.369687 | − | 0.929156i | \(-0.379465\pi\) | ||||
0.369687 | + | 0.929156i | \(0.379465\pi\) | |||||||
\(314\) | −1.49881 | −0.0845828 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.26921 | 0.521434 | ||||||||
\(317\) | 20.6557 | 1.16014 | 0.580069 | − | 0.814568i | \(-0.303026\pi\) | ||||
0.580069 | + | 0.814568i | \(0.303026\pi\) | |||||||
\(318\) | 6.87293 | 0.385415 | ||||||||
\(319\) | 2.82843 | 0.158362 | ||||||||
\(320\) | 2.27411 | 0.127127 | ||||||||
\(321\) | 11.6482 | 0.650141 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.2299 | −1.96025 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.309151 | 0.0171486 | ||||||||
\(326\) | −13.6569 | −0.756383 | ||||||||
\(327\) | −14.0890 | −0.779124 | ||||||||
\(328\) | 5.10254 | 0.281740 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.27411 | 0.125186 | ||||||||
\(331\) | −19.7014 | −1.08288 | −0.541442 | − | 0.840738i | \(-0.682122\pi\) | ||||
−0.541442 | + | 0.840738i | \(0.682122\pi\) | |||||||
\(332\) | −1.96853 | −0.108037 | ||||||||
\(333\) | 4.44078 | 0.243353 | ||||||||
\(334\) | −19.6927 | −1.07754 | ||||||||
\(335\) | 30.6643 | 1.67537 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.88036 | 0.429271 | 0.214635 | − | 0.976694i | \(-0.431144\pi\) | ||||
0.214635 | + | 0.976694i | \(0.431144\pi\) | |||||||
\(338\) | 9.75329 | 0.530509 | ||||||||
\(339\) | −5.71979 | −0.310656 | ||||||||
\(340\) | 11.6037 | 0.629300 | ||||||||
\(341\) | −3.14010 | −0.170046 | ||||||||
\(342\) | 6.90440 | 0.373347 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.93587 | −0.373957 | ||||||||
\(345\) | 19.5408 | 1.05204 | ||||||||
\(346\) | 14.5107 | 0.780097 | ||||||||
\(347\) | −31.1768 | −1.67366 | −0.836830 | − | 0.547463i | \(-0.815594\pi\) | ||||
−0.836830 | + | 0.547463i | \(0.815594\pi\) | |||||||
\(348\) | −2.82843 | −0.151620 | ||||||||
\(349\) | 2.96124 | 0.158511 | 0.0792557 | − | 0.996854i | \(-0.474746\pi\) | ||||
0.0792557 | + | 0.996854i | \(0.474746\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.80186 | 0.0961763 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −12.9514 | −0.689335 | −0.344667 | − | 0.938725i | \(-0.612008\pi\) | ||||
−0.344667 | + | 0.938725i | \(0.612008\pi\) | |||||||
\(354\) | −5.17157 | −0.274866 | ||||||||
\(355\) | −21.0596 | −1.11773 | ||||||||
\(356\) | 15.0624 | 0.798308 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.3656 | 1.18206 | ||||||||
\(359\) | 25.6621 | 1.35439 | 0.677197 | − | 0.735802i | \(-0.263195\pi\) | ||||
0.677197 | + | 0.735802i | \(0.263195\pi\) | |||||||
\(360\) | −2.27411 | −0.119856 | ||||||||
\(361\) | 28.6707 | 1.50899 | ||||||||
\(362\) | 5.73976 | 0.301675 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.93469 | −0.362978 | ||||||||
\(366\) | −8.63029 | −0.451112 | ||||||||
\(367\) | 28.3885 | 1.48187 | 0.740933 | − | 0.671578i | \(-0.234383\pi\) | ||||
0.740933 | + | 0.671578i | \(0.234383\pi\) | |||||||
\(368\) | 8.59272 | 0.447927 | ||||||||
\(369\) | −5.10254 | −0.265627 | ||||||||
\(370\) | −10.0988 | −0.525012 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.14010 | 0.162807 | ||||||||
\(373\) | 14.5743 | 0.754628 | 0.377314 | − | 0.926085i | \(-0.376848\pi\) | ||||
0.377314 | + | 0.926085i | \(0.376848\pi\) | |||||||
\(374\) | 5.10254 | 0.263846 | ||||||||
\(375\) | −10.9804 | −0.567024 | ||||||||
\(376\) | 0.0759718 | 0.00391795 | ||||||||
\(377\) | −5.09644 | −0.262480 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.64703 | 0.341435 | 0.170718 | − | 0.985320i | \(-0.445391\pi\) | ||||
0.170718 | + | 0.985320i | \(0.445391\pi\) | |||||||
\(380\) | −15.7014 | −0.805463 | ||||||||
\(381\) | 6.60492 | 0.338380 | ||||||||
\(382\) | 11.7112 | 0.599195 | ||||||||
\(383\) | 27.7108 | 1.41596 | 0.707978 | − | 0.706234i | \(-0.249607\pi\) | ||||
0.707978 | + | 0.706234i | \(0.249607\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.7533 | 0.649125 | ||||||||
\(387\) | 6.93587 | 0.352570 | ||||||||
\(388\) | −9.01794 | −0.457816 | ||||||||
\(389\) | −10.6250 | −0.538710 | −0.269355 | − | 0.963041i | \(-0.586811\pi\) | ||||
−0.269355 | + | 0.963041i | \(0.586811\pi\) | |||||||
\(390\) | −4.09763 | −0.207492 | ||||||||
\(391\) | 43.8447 | 2.21732 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.96853 | 0.301073 | ||||||||
\(394\) | 23.2606 | 1.17185 | ||||||||
\(395\) | 21.0792 | 1.06061 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 2.14824 | 0.107817 | 0.0539084 | − | 0.998546i | \(-0.482832\pi\) | ||||
0.0539084 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(398\) | −1.48325 | −0.0743486 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.171573 | 0.00857864 | ||||||||
\(401\) | −34.5743 | −1.72656 | −0.863279 | − | 0.504727i | \(-0.831593\pi\) | ||||
−0.863279 | + | 0.504727i | \(0.831593\pi\) | |||||||
\(402\) | −13.4841 | −0.672525 | ||||||||
\(403\) | 5.65804 | 0.281847 | ||||||||
\(404\) | −11.2230 | −0.558366 | ||||||||
\(405\) | 2.27411 | 0.113001 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.44078 | −0.220121 | ||||||||
\(408\) | −5.10254 | −0.252613 | ||||||||
\(409\) | 38.5323 | 1.90530 | 0.952650 | − | 0.304069i | \(-0.0983453\pi\) | ||||
0.952650 | + | 0.304069i | \(0.0983453\pi\) | |||||||
\(410\) | 11.6037 | 0.573067 | ||||||||
\(411\) | 11.2606 | 0.555443 | ||||||||
\(412\) | 17.0118 | 0.838113 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.59272 | −0.422309 | ||||||||
\(415\) | −4.47666 | −0.219750 | ||||||||
\(416\) | −1.80186 | −0.0883436 | ||||||||
\(417\) | 8.62419 | 0.422328 | ||||||||
\(418\) | −6.90440 | −0.337705 | ||||||||
\(419\) | 11.7729 | 0.575145 | 0.287572 | − | 0.957759i | \(-0.407152\pi\) | ||||
0.287572 | + | 0.957759i | \(0.407152\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.3039 | −0.697129 | −0.348564 | − | 0.937285i | \(-0.613331\pi\) | ||||
−0.348564 | + | 0.937285i | \(0.613331\pi\) | |||||||
\(422\) | −0.503715 | −0.0245205 | ||||||||
\(423\) | −0.0759718 | −0.00369388 | ||||||||
\(424\) | 6.87293 | 0.333779 | ||||||||
\(425\) | 0.875457 | 0.0424659 | ||||||||
\(426\) | 9.26058 | 0.448677 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.6482 | 0.563038 | ||||||||
\(429\) | −1.80186 | −0.0869947 | ||||||||
\(430\) | −15.7729 | −0.760638 | ||||||||
\(431\) | 0.172768 | 0.00832195 | 0.00416098 | − | 0.999991i | \(-0.498676\pi\) | ||||
0.00416098 | + | 0.999991i | \(0.498676\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 19.7712 | 0.950145 | 0.475072 | − | 0.879947i | \(-0.342422\pi\) | ||||
0.475072 | + | 0.879947i | \(0.342422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.43215 | −0.308398 | ||||||||
\(436\) | −14.0890 | −0.674741 | ||||||||
\(437\) | −59.3276 | −2.83802 | ||||||||
\(438\) | 3.04941 | 0.145706 | ||||||||
\(439\) | −1.17157 | −0.0559161 | −0.0279581 | − | 0.999609i | \(-0.508900\pi\) | ||||
−0.0279581 | + | 0.999609i | \(0.508900\pi\) | |||||||
\(440\) | 2.27411 | 0.108414 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.19407 | −0.437317 | ||||||||
\(443\) | −33.6621 | −1.59933 | −0.799667 | − | 0.600443i | \(-0.794991\pi\) | ||||
−0.799667 | + | 0.600443i | \(0.794991\pi\) | |||||||
\(444\) | 4.44078 | 0.210750 | ||||||||
\(445\) | 34.2536 | 1.62378 | ||||||||
\(446\) | −20.0044 | −0.947236 | ||||||||
\(447\) | −12.3211 | −0.582770 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.27039 | 0.343111 | 0.171555 | − | 0.985174i | \(-0.445121\pi\) | ||||
0.171555 | + | 0.985174i | \(0.445121\pi\) | |||||||
\(450\) | −0.171573 | −0.00808802 | ||||||||
\(451\) | 5.10254 | 0.240269 | ||||||||
\(452\) | −5.71979 | −0.269036 | ||||||||
\(453\) | −11.5286 | −0.541660 | ||||||||
\(454\) | −13.5601 | −0.636405 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.90440 | 0.323328 | ||||||||
\(457\) | −31.0596 | −1.45291 | −0.726453 | − | 0.687216i | \(-0.758832\pi\) | ||||
−0.726453 | + | 0.687216i | \(0.758832\pi\) | |||||||
\(458\) | 5.10254 | 0.238426 | ||||||||
\(459\) | 5.10254 | 0.238166 | ||||||||
\(460\) | 19.5408 | 0.911094 | ||||||||
\(461\) | −10.5228 | −0.490098 | −0.245049 | − | 0.969511i | \(-0.578804\pi\) | ||||
−0.245049 | + | 0.969511i | \(0.578804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.30389 | −0.385914 | −0.192957 | − | 0.981207i | \(-0.561808\pi\) | ||||
−0.192957 | + | 0.981207i | \(0.561808\pi\) | |||||||
\(464\) | −2.82843 | −0.131306 | ||||||||
\(465\) | 7.14094 | 0.331153 | ||||||||
\(466\) | 0.343146 | 0.0158959 | ||||||||
\(467\) | 11.5530 | 0.534608 | 0.267304 | − | 0.963612i | \(-0.413867\pi\) | ||||
0.267304 | + | 0.963612i | \(0.413867\pi\) | |||||||
\(468\) | 1.80186 | 0.0832911 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.172768 | 0.00796920 | ||||||||
\(471\) | 1.49881 | 0.0690616 | ||||||||
\(472\) | −5.17157 | −0.238041 | ||||||||
\(473\) | −6.93587 | −0.318912 | ||||||||
\(474\) | −9.26921 | −0.425749 | ||||||||
\(475\) | −1.18461 | −0.0543535 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.87293 | −0.314690 | ||||||||
\(478\) | 18.4322 | 0.843067 | ||||||||
\(479\) | −10.7482 | −0.491100 | −0.245550 | − | 0.969384i | \(-0.578968\pi\) | ||||
−0.245550 | + | 0.969384i | \(0.578968\pi\) | |||||||
\(480\) | −2.27411 | −0.103798 | ||||||||
\(481\) | 8.00167 | 0.364845 | ||||||||
\(482\) | −24.5682 | −1.11905 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −20.5078 | −0.931210 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −38.6164 | −1.74988 | −0.874938 | − | 0.484235i | \(-0.839098\pi\) | ||||
−0.874938 | + | 0.484235i | \(0.839098\pi\) | |||||||
\(488\) | −8.63029 | −0.390675 | ||||||||
\(489\) | 13.6569 | 0.617584 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.68629 | −0.392007 | −0.196003 | − | 0.980603i | \(-0.562796\pi\) | ||||
−0.196003 | + | 0.980603i | \(0.562796\pi\) | |||||||
\(492\) | −5.10254 | −0.230040 | ||||||||
\(493\) | −14.4322 | −0.649991 | ||||||||
\(494\) | 12.4408 | 0.559737 | ||||||||
\(495\) | −2.27411 | −0.102214 | ||||||||
\(496\) | 3.14010 | 0.140995 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.96853 | 0.0882120 | ||||||||
\(499\) | 43.1041 | 1.92960 | 0.964802 | − | 0.262979i | \(-0.0847049\pi\) | ||||
0.964802 | + | 0.262979i | \(0.0847049\pi\) | |||||||
\(500\) | −10.9804 | −0.491057 | ||||||||
\(501\) | 19.6927 | 0.879806 | ||||||||
\(502\) | −1.50491 | −0.0671674 | ||||||||
\(503\) | −24.7174 | −1.10210 | −0.551048 | − | 0.834474i | \(-0.685772\pi\) | ||||
−0.551048 | + | 0.834474i | \(0.685772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.5224 | −1.13573 | ||||||||
\(506\) | 8.59272 | 0.381993 | ||||||||
\(507\) | −9.75329 | −0.433159 | ||||||||
\(508\) | 6.60492 | 0.293046 | ||||||||
\(509\) | 21.4619 | 0.951284 | 0.475642 | − | 0.879639i | \(-0.342216\pi\) | ||||
0.475642 | + | 0.879639i | \(0.342216\pi\) | |||||||
\(510\) | −11.6037 | −0.513822 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.90440 | −0.304837 | ||||||||
\(514\) | −10.8476 | −0.478465 | ||||||||
\(515\) | 38.6868 | 1.70474 | ||||||||
\(516\) | 6.93587 | 0.305335 | ||||||||
\(517\) | 0.0759718 | 0.00334124 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.5107 | −0.636947 | ||||||||
\(520\) | −4.09763 | −0.179693 | ||||||||
\(521\) | −19.2773 | −0.844555 | −0.422277 | − | 0.906467i | \(-0.638769\pi\) | ||||
−0.422277 | + | 0.906467i | \(0.638769\pi\) | |||||||
\(522\) | 2.82843 | 0.123797 | ||||||||
\(523\) | −12.7304 | −0.556664 | −0.278332 | − | 0.960485i | \(-0.589781\pi\) | ||||
−0.278332 | + | 0.960485i | \(0.589781\pi\) | |||||||
\(524\) | 5.96853 | 0.260737 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.25938 | −0.272922 | ||||||||
\(527\) | 16.0225 | 0.697951 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 50.8349 | 2.21021 | ||||||||
\(530\) | 15.6298 | 0.678915 | ||||||||
\(531\) | 5.17157 | 0.224427 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.19407 | −0.398239 | ||||||||
\(534\) | −15.0624 | −0.651816 | ||||||||
\(535\) | 26.4893 | 1.14523 | ||||||||
\(536\) | −13.4841 | −0.582424 | ||||||||
\(537\) | −22.3656 | −0.965149 | ||||||||
\(538\) | −14.8345 | −0.639562 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.27411 | 0.0978621 | ||||||||
\(541\) | −7.36684 | −0.316725 | −0.158363 | − | 0.987381i | \(-0.550621\pi\) | ||||
−0.158363 | + | 0.987381i | \(0.550621\pi\) | |||||||
\(542\) | 2.91743 | 0.125315 | ||||||||
\(543\) | −5.73976 | −0.246317 | ||||||||
\(544\) | −5.10254 | −0.218769 | ||||||||
\(545\) | −32.0399 | −1.37244 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.7320 | 0.587138 | 0.293569 | − | 0.955938i | \(-0.405157\pi\) | ||||
0.293569 | + | 0.955938i | \(0.405157\pi\) | |||||||
\(548\) | 11.2606 | 0.481028 | ||||||||
\(549\) | 8.63029 | 0.368332 | ||||||||
\(550\) | 0.171573 | 0.00731589 | ||||||||
\(551\) | 19.5286 | 0.831946 | ||||||||
\(552\) | −8.59272 | −0.365731 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12.1012 | −0.514131 | ||||||||
\(555\) | 10.0988 | 0.428671 | ||||||||
\(556\) | 8.62419 | 0.365747 | ||||||||
\(557\) | 0.845679 | 0.0358326 | 0.0179163 | − | 0.999839i | \(-0.494297\pi\) | ||||
0.0179163 | + | 0.999839i | \(0.494297\pi\) | |||||||
\(558\) | −3.14010 | −0.132931 | ||||||||
\(559\) | 12.4975 | 0.528587 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.10254 | −0.215429 | ||||||||
\(562\) | −7.74586 | −0.326739 | ||||||||
\(563\) | −18.1009 | −0.762860 | −0.381430 | − | 0.924398i | \(-0.624568\pi\) | ||||
−0.381430 | + | 0.924398i | \(0.624568\pi\) | |||||||
\(564\) | −0.0759718 | −0.00319899 | ||||||||
\(565\) | −13.0074 | −0.547227 | ||||||||
\(566\) | −17.5948 | −0.739563 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.26058 | 0.388565 | ||||||||
\(569\) | −34.4819 | −1.44556 | −0.722778 | − | 0.691080i | \(-0.757135\pi\) | ||||
−0.722778 | + | 0.691080i | \(0.757135\pi\) | |||||||
\(570\) | 15.7014 | 0.657657 | ||||||||
\(571\) | −35.6927 | −1.49369 | −0.746847 | − | 0.664996i | \(-0.768433\pi\) | ||||
−0.746847 | + | 0.664996i | \(0.768433\pi\) | |||||||
\(572\) | −1.80186 | −0.0753397 | ||||||||
\(573\) | −11.7112 | −0.489241 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.47428 | 0.0614816 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −1.64129 | −0.0683279 | −0.0341640 | − | 0.999416i | \(-0.510877\pi\) | ||||
−0.0341640 | + | 0.999416i | \(0.510877\pi\) | |||||||
\(578\) | −9.03588 | −0.375843 | ||||||||
\(579\) | −12.7533 | −0.530009 | ||||||||
\(580\) | −6.43215 | −0.267081 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.01794 | 0.373806 | ||||||||
\(583\) | 6.87293 | 0.284648 | ||||||||
\(584\) | 3.04941 | 0.126185 | ||||||||
\(585\) | 4.09763 | 0.169416 | ||||||||
\(586\) | 16.1675 | 0.667873 | ||||||||
\(587\) | −42.4582 | −1.75244 | −0.876219 | − | 0.481913i | \(-0.839942\pi\) | ||||
−0.876219 | + | 0.481913i | \(0.839942\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.6805 | −0.893331 | ||||||||
\(590\) | −11.7607 | −0.484181 | ||||||||
\(591\) | −23.2606 | −0.956812 | ||||||||
\(592\) | 4.44078 | 0.182515 | ||||||||
\(593\) | −23.4457 | −0.962799 | −0.481399 | − | 0.876501i | \(-0.659871\pi\) | ||||
−0.481399 | + | 0.876501i | \(0.659871\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.3211 | −0.504694 | ||||||||
\(597\) | 1.48325 | 0.0607054 | ||||||||
\(598\) | −15.4829 | −0.633143 | ||||||||
\(599\) | 47.4166 | 1.93739 | 0.968695 | − | 0.248256i | \(-0.0798573\pi\) | ||||
0.968695 | + | 0.248256i | \(0.0798573\pi\) | |||||||
\(600\) | −0.171573 | −0.00700443 | ||||||||
\(601\) | −31.9570 | −1.30355 | −0.651777 | − | 0.758410i | \(-0.725976\pi\) | ||||
−0.651777 | + | 0.758410i | \(0.725976\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.4841 | 0.549114 | ||||||||
\(604\) | −11.5286 | −0.469092 | ||||||||
\(605\) | 2.27411 | 0.0924557 | ||||||||
\(606\) | 11.2230 | 0.455904 | ||||||||
\(607\) | −21.0596 | −0.854782 | −0.427391 | − | 0.904067i | \(-0.640567\pi\) | ||||
−0.427391 | + | 0.904067i | \(0.640567\pi\) | |||||||
\(608\) | 6.90440 | 0.280010 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.6262 | −0.794642 | ||||||||
\(611\) | −0.136891 | −0.00553801 | ||||||||
\(612\) | 5.10254 | 0.206258 | ||||||||
\(613\) | 22.6013 | 0.912860 | 0.456430 | − | 0.889759i | \(-0.349128\pi\) | ||||
0.456430 | + | 0.889759i | \(0.349128\pi\) | |||||||
\(614\) | 27.0563 | 1.09191 | ||||||||
\(615\) | −11.6037 | −0.467907 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.6447 | −1.19345 | −0.596724 | − | 0.802446i | \(-0.703531\pi\) | ||||
−0.596724 | + | 0.802446i | \(0.703531\pi\) | |||||||
\(618\) | −17.0118 | −0.684317 | ||||||||
\(619\) | 1.10864 | 0.0445598 | 0.0222799 | − | 0.999752i | \(-0.492907\pi\) | ||||
0.0222799 | + | 0.999752i | \(0.492907\pi\) | |||||||
\(620\) | 7.14094 | 0.286787 | ||||||||
\(621\) | 8.59272 | 0.344814 | ||||||||
\(622\) | 24.5751 | 0.985373 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.80186 | 0.0721322 | ||||||||
\(625\) | −25.8284 | −1.03314 | ||||||||
\(626\) | −13.0809 | −0.522817 | ||||||||
\(627\) | 6.90440 | 0.275735 | ||||||||
\(628\) | 1.49881 | 0.0598091 | ||||||||
\(629\) | 22.6592 | 0.903483 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.76192 | −0.348806 | −0.174403 | − | 0.984674i | \(-0.555800\pi\) | ||||
−0.174403 | + | 0.984674i | \(0.555800\pi\) | |||||||
\(632\) | −9.26921 | −0.368709 | ||||||||
\(633\) | 0.503715 | 0.0200209 | ||||||||
\(634\) | −20.6557 | −0.820341 | ||||||||
\(635\) | 15.0203 | 0.596063 | ||||||||
\(636\) | −6.87293 | −0.272529 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.82843 | −0.111979 | ||||||||
\(639\) | −9.26058 | −0.366343 | ||||||||
\(640\) | −2.27411 | −0.0898921 | ||||||||
\(641\) | 47.2474 | 1.86616 | 0.933080 | − | 0.359669i | \(-0.117110\pi\) | ||||
0.933080 | + | 0.359669i | \(0.117110\pi\) | |||||||
\(642\) | −11.6482 | −0.459719 | ||||||||
\(643\) | 4.71741 | 0.186037 | 0.0930183 | − | 0.995664i | \(-0.470348\pi\) | ||||
0.0930183 | + | 0.995664i | \(0.470348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.7729 | 0.621058 | ||||||||
\(646\) | 35.2299 | 1.38610 | ||||||||
\(647\) | −28.0391 | −1.10233 | −0.551165 | − | 0.834396i | \(-0.685817\pi\) | ||||
−0.551165 | + | 0.834396i | \(0.685817\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −5.17157 | −0.203002 | ||||||||
\(650\) | −0.309151 | −0.0121259 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.6569 | 0.534844 | ||||||||
\(653\) | 27.0596 | 1.05892 | 0.529461 | − | 0.848334i | \(-0.322394\pi\) | ||||
0.529461 | + | 0.848334i | \(0.322394\pi\) | |||||||
\(654\) | 14.0890 | 0.550924 | ||||||||
\(655\) | 13.5731 | 0.530345 | ||||||||
\(656\) | −5.10254 | −0.199221 | ||||||||
\(657\) | −3.04941 | −0.118969 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.7741 | 0.614472 | 0.307236 | − | 0.951633i | \(-0.400596\pi\) | ||||
0.307236 | + | 0.951633i | \(0.400596\pi\) | |||||||
\(660\) | −2.27411 | −0.0885196 | ||||||||
\(661\) | 20.1597 | 0.784122 | 0.392061 | − | 0.919939i | \(-0.371762\pi\) | ||||
0.392061 | + | 0.919939i | \(0.371762\pi\) | |||||||
\(662\) | 19.7014 | 0.765715 | ||||||||
\(663\) | 9.19407 | 0.357068 | ||||||||
\(664\) | 1.96853 | 0.0763938 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.44078 | −0.172077 | ||||||||
\(667\) | −24.3039 | −0.941050 | ||||||||
\(668\) | 19.6927 | 0.761935 | ||||||||
\(669\) | 20.0044 | 0.773415 | ||||||||
\(670\) | −30.6643 | −1.18466 | ||||||||
\(671\) | −8.63029 | −0.333169 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.77410 | 0.299670 | 0.149835 | − | 0.988711i | \(-0.452126\pi\) | ||||
0.149835 | + | 0.988711i | \(0.452126\pi\) | |||||||
\(674\) | −7.88036 | −0.303540 | ||||||||
\(675\) | 0.171573 | 0.00660384 | ||||||||
\(676\) | −9.75329 | −0.375127 | ||||||||
\(677\) | 49.6568 | 1.90847 | 0.954234 | − | 0.299062i | \(-0.0966738\pi\) | ||||
0.954234 | + | 0.299062i | \(0.0966738\pi\) | |||||||
\(678\) | 5.71979 | 0.219667 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.6037 | −0.444983 | ||||||||
\(681\) | 13.5601 | 0.519623 | ||||||||
\(682\) | 3.14010 | 0.120241 | ||||||||
\(683\) | −22.9261 | −0.877241 | −0.438621 | − | 0.898672i | \(-0.644533\pi\) | ||||
−0.438621 | + | 0.898672i | \(0.644533\pi\) | |||||||
\(684\) | −6.90440 | −0.263996 | ||||||||
\(685\) | 25.6078 | 0.978423 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.10254 | −0.194674 | ||||||||
\(688\) | 6.93587 | 0.264427 | ||||||||
\(689\) | −12.3841 | −0.471796 | ||||||||
\(690\) | −19.5408 | −0.743905 | ||||||||
\(691\) | −34.1299 | −1.29836 | −0.649182 | − | 0.760633i | \(-0.724889\pi\) | ||||
−0.649182 | + | 0.760633i | \(0.724889\pi\) | |||||||
\(692\) | −14.5107 | −0.551612 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.1768 | 1.18346 | ||||||||
\(695\) | 19.6124 | 0.743939 | ||||||||
\(696\) | 2.82843 | 0.107211 | ||||||||
\(697\) | −26.0359 | −0.986179 | ||||||||
\(698\) | −2.96124 | −0.112084 | ||||||||
\(699\) | −0.343146 | −0.0129790 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1929 | 0.460518 | 0.230259 | − | 0.973129i | \(-0.426043\pi\) | ||||
0.230259 | + | 0.973129i | \(0.426043\pi\) | |||||||
\(702\) | −1.80186 | −0.0680069 | ||||||||
\(703\) | −30.6609 | −1.15640 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −0.172768 | −0.00650683 | ||||||||
\(706\) | 12.9514 | 0.487433 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.17157 | 0.194360 | ||||||||
\(709\) | −21.0902 | −0.792059 | −0.396030 | − | 0.918238i | \(-0.629612\pi\) | ||||
−0.396030 | + | 0.918238i | \(0.629612\pi\) | |||||||
\(710\) | 21.0596 | 0.790352 | ||||||||
\(711\) | 9.26921 | 0.347622 | ||||||||
\(712\) | −15.0624 | −0.564489 | ||||||||
\(713\) | 26.9820 | 1.01049 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.09763 | −0.153243 | ||||||||
\(716\) | −22.3656 | −0.835843 | ||||||||
\(717\) | −18.4322 | −0.688361 | ||||||||
\(718\) | −25.6621 | −0.957701 | ||||||||
\(719\) | −22.7403 | −0.848068 | −0.424034 | − | 0.905646i | \(-0.639386\pi\) | ||||
−0.424034 | + | 0.905646i | \(0.639386\pi\) | |||||||
\(720\) | 2.27411 | 0.0847510 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −28.6707 | −1.06701 | ||||||||
\(723\) | 24.5682 | 0.913701 | ||||||||
\(724\) | −5.73976 | −0.213317 | ||||||||
\(725\) | −0.485281 | −0.0180229 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | −1.83046 | −0.0678879 | −0.0339440 | − | 0.999424i | \(-0.510807\pi\) | ||||
−0.0339440 | + | 0.999424i | \(0.510807\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.93469 | 0.256664 | ||||||||
\(731\) | 35.3905 | 1.30897 | ||||||||
\(732\) | 8.63029 | 0.318985 | ||||||||
\(733\) | −36.0191 | −1.33040 | −0.665199 | − | 0.746667i | \(-0.731653\pi\) | ||||
−0.665199 | + | 0.746667i | \(0.731653\pi\) | |||||||
\(734\) | −28.3885 | −1.04784 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.59272 | −0.316732 | ||||||||
\(737\) | −13.4841 | −0.496693 | ||||||||
\(738\) | 5.10254 | 0.187827 | ||||||||
\(739\) | 26.5719 | 0.977463 | 0.488732 | − | 0.872434i | \(-0.337460\pi\) | ||||
0.488732 | + | 0.872434i | \(0.337460\pi\) | |||||||
\(740\) | 10.0988 | 0.371240 | ||||||||
\(741\) | −12.4408 | −0.457023 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5580 | −0.387336 | −0.193668 | − | 0.981067i | \(-0.562039\pi\) | ||||
−0.193668 | + | 0.981067i | \(0.562039\pi\) | |||||||
\(744\) | −3.14010 | −0.115122 | ||||||||
\(745\) | −28.0196 | −1.02656 | ||||||||
\(746\) | −14.5743 | −0.533603 | ||||||||
\(747\) | −1.96853 | −0.0720248 | ||||||||
\(748\) | −5.10254 | −0.186567 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.9804 | 0.400946 | ||||||||
\(751\) | −31.3003 | −1.14217 | −0.571083 | − | 0.820893i | \(-0.693476\pi\) | ||||
−0.571083 | + | 0.820893i | \(0.693476\pi\) | |||||||
\(752\) | −0.0759718 | −0.00277041 | ||||||||
\(753\) | 1.50491 | 0.0548420 | ||||||||
\(754\) | 5.09644 | 0.185601 | ||||||||
\(755\) | −26.2173 | −0.954144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.3223 | −0.774973 | −0.387487 | − | 0.921875i | \(-0.626657\pi\) | ||||
−0.387487 | + | 0.921875i | \(0.626657\pi\) | |||||||
\(758\) | −6.64703 | −0.241431 | ||||||||
\(759\) | −8.59272 | −0.311896 | ||||||||
\(760\) | 15.7014 | 0.569548 | ||||||||
\(761\) | −6.48899 | −0.235226 | −0.117613 | − | 0.993060i | \(-0.537524\pi\) | ||||
−0.117613 | + | 0.993060i | \(0.537524\pi\) | |||||||
\(762\) | −6.60492 | −0.239271 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −11.7112 | −0.423695 | ||||||||
\(765\) | 11.6037 | 0.419534 | ||||||||
\(766\) | −27.7108 | −1.00123 | ||||||||
\(767\) | 9.31846 | 0.336470 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −41.9719 | −1.51355 | −0.756773 | − | 0.653678i | \(-0.773225\pi\) | ||||
−0.756773 | + | 0.653678i | \(0.773225\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8476 | 0.390665 | ||||||||
\(772\) | −12.7533 | −0.459001 | ||||||||
\(773\) | −29.8951 | −1.07525 | −0.537626 | − | 0.843184i | \(-0.680679\pi\) | ||||
−0.537626 | + | 0.843184i | \(0.680679\pi\) | |||||||
\(774\) | −6.93587 | −0.249305 | ||||||||
\(775\) | 0.538757 | 0.0193527 | ||||||||
\(776\) | 9.01794 | 0.323725 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.6250 | 0.380926 | ||||||||
\(779\) | 35.2299 | 1.26224 | ||||||||
\(780\) | 4.09763 | 0.146719 | ||||||||
\(781\) | 9.26058 | 0.331370 | ||||||||
\(782\) | −43.8447 | −1.56788 | ||||||||
\(783\) | −2.82843 | −0.101080 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.40846 | 0.121653 | ||||||||
\(786\) | −5.96853 | −0.212890 | ||||||||
\(787\) | −47.3602 | −1.68821 | −0.844105 | − | 0.536178i | \(-0.819868\pi\) | ||||
−0.844105 | + | 0.536178i | \(0.819868\pi\) | |||||||
\(788\) | −23.2606 | −0.828624 | ||||||||
\(789\) | 6.25938 | 0.222840 | ||||||||
\(790\) | −21.0792 | −0.749964 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 15.5506 | 0.552218 | ||||||||
\(794\) | −2.14824 | −0.0762380 | ||||||||
\(795\) | −15.6298 | −0.554332 | ||||||||
\(796\) | 1.48325 | 0.0525724 | ||||||||
\(797\) | 26.7421 | 0.947255 | 0.473628 | − | 0.880725i | \(-0.342944\pi\) | ||||
0.473628 | + | 0.880725i | \(0.342944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.387649 | −0.0137140 | ||||||||
\(800\) | −0.171573 | −0.00606602 | ||||||||
\(801\) | 15.0624 | 0.532205 | ||||||||
\(802\) | 34.5743 | 1.22086 | ||||||||
\(803\) | 3.04941 | 0.107611 | ||||||||
\(804\) | 13.4841 | 0.475547 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.65804 | −0.199296 | ||||||||
\(807\) | 14.8345 | 0.522200 | ||||||||
\(808\) | 11.2230 | 0.394824 | ||||||||
\(809\) | −9.75924 | −0.343117 | −0.171558 | − | 0.985174i | \(-0.554880\pi\) | ||||
−0.171558 | + | 0.985174i | \(0.554880\pi\) | |||||||
\(810\) | −2.27411 | −0.0799041 | ||||||||
\(811\) | −43.2255 | −1.51785 | −0.758927 | − | 0.651176i | \(-0.774276\pi\) | ||||
−0.758927 | + | 0.651176i | \(0.774276\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.91743 | −0.102319 | ||||||||
\(814\) | 4.44078 | 0.155649 | ||||||||
\(815\) | 31.0572 | 1.08789 | ||||||||
\(816\) | 5.10254 | 0.178625 | ||||||||
\(817\) | −47.8880 | −1.67539 | ||||||||
\(818\) | −38.5323 | −1.34725 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.6037 | −0.405220 | ||||||||
\(821\) | −15.9631 | −0.557117 | −0.278559 | − | 0.960419i | \(-0.589857\pi\) | ||||
−0.278559 | + | 0.960419i | \(0.589857\pi\) | |||||||
\(822\) | −11.2606 | −0.392758 | ||||||||
\(823\) | −51.4980 | −1.79511 | −0.897553 | − | 0.440907i | \(-0.854657\pi\) | ||||
−0.897553 | + | 0.440907i | \(0.854657\pi\) | |||||||
\(824\) | −17.0118 | −0.592636 | ||||||||
\(825\) | −0.171573 | −0.00597340 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.7679 | −0.548302 | −0.274151 | − | 0.961687i | \(-0.588397\pi\) | ||||
−0.274151 | + | 0.961687i | \(0.588397\pi\) | |||||||
\(828\) | 8.59272 | 0.298618 | ||||||||
\(829\) | −47.0437 | −1.63389 | −0.816947 | − | 0.576713i | \(-0.804335\pi\) | ||||
−0.816947 | + | 0.576713i | \(0.804335\pi\) | |||||||
\(830\) | 4.47666 | 0.155387 | ||||||||
\(831\) | 12.1012 | 0.419786 | ||||||||
\(832\) | 1.80186 | 0.0624683 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.62419 | −0.298631 | ||||||||
\(835\) | 44.7834 | 1.54979 | ||||||||
\(836\) | 6.90440 | 0.238794 | ||||||||
\(837\) | 3.14010 | 0.108538 | ||||||||
\(838\) | −11.7729 | −0.406689 | ||||||||
\(839\) | 27.6046 | 0.953015 | 0.476508 | − | 0.879170i | \(-0.341902\pi\) | ||||
0.476508 | + | 0.879170i | \(0.341902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 14.3039 | 0.492945 | ||||||||
\(843\) | 7.74586 | 0.266782 | ||||||||
\(844\) | 0.503715 | 0.0173386 | ||||||||
\(845\) | −22.1800 | −0.763017 | ||||||||
\(846\) | 0.0759718 | 0.00261197 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.87293 | −0.236017 | ||||||||
\(849\) | 17.5948 | 0.603850 | ||||||||
\(850\) | −0.875457 | −0.0300279 | ||||||||
\(851\) | 38.1584 | 1.30805 | ||||||||
\(852\) | −9.26058 | −0.317262 | ||||||||
\(853\) | −47.4171 | −1.62353 | −0.811765 | − | 0.583985i | \(-0.801493\pi\) | ||||
−0.811765 | + | 0.583985i | \(0.801493\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.7014 | −0.536975 | ||||||||
\(856\) | −11.6482 | −0.398128 | ||||||||
\(857\) | −57.6474 | −1.96920 | −0.984598 | − | 0.174831i | \(-0.944062\pi\) | ||||
−0.984598 | + | 0.174831i | \(0.944062\pi\) | |||||||
\(858\) | 1.80186 | 0.0615146 | ||||||||
\(859\) | 33.3865 | 1.13913 | 0.569566 | − | 0.821946i | \(-0.307111\pi\) | ||||
0.569566 | + | 0.821946i | \(0.307111\pi\) | |||||||
\(860\) | 15.7729 | 0.537852 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.172768 | −0.00588451 | ||||||||
\(863\) | −7.13113 | −0.242747 | −0.121373 | − | 0.992607i | \(-0.538730\pi\) | ||||
−0.121373 | + | 0.992607i | \(0.538730\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −32.9988 | −1.12199 | ||||||||
\(866\) | −19.7712 | −0.671854 | ||||||||
\(867\) | 9.03588 | 0.306874 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.26921 | −0.314436 | ||||||||
\(870\) | 6.43215 | 0.218070 | ||||||||
\(871\) | 24.2965 | 0.823254 | ||||||||
\(872\) | 14.0890 | 0.477114 | ||||||||
\(873\) | −9.01794 | −0.305211 | ||||||||
\(874\) | 59.3276 | 2.00679 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.04941 | −0.103030 | ||||||||
\(877\) | −9.46398 | −0.319576 | −0.159788 | − | 0.987151i | \(-0.551081\pi\) | ||||
−0.159788 | + | 0.987151i | \(0.551081\pi\) | |||||||
\(878\) | 1.17157 | 0.0395387 | ||||||||
\(879\) | −16.1675 | −0.545316 | ||||||||
\(880\) | −2.27411 | −0.0766602 | ||||||||
\(881\) | 18.7846 | 0.632870 | 0.316435 | − | 0.948614i | \(-0.397514\pi\) | ||||
0.316435 | + | 0.948614i | \(0.397514\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.2843 | 1.08645 | 0.543226 | − | 0.839586i | \(-0.317203\pi\) | ||||
0.543226 | + | 0.839586i | \(0.317203\pi\) | |||||||
\(884\) | 9.19407 | 0.309230 | ||||||||
\(885\) | 11.7607 | 0.395332 | ||||||||
\(886\) | 33.6621 | 1.13090 | ||||||||
\(887\) | 10.5384 | 0.353845 | 0.176923 | − | 0.984225i | \(-0.443386\pi\) | ||||
0.176923 | + | 0.984225i | \(0.443386\pi\) | |||||||
\(888\) | −4.44078 | −0.149023 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −34.2536 | −1.14818 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 20.0044 | 0.669797 | ||||||||
\(893\) | 0.524540 | 0.0175531 | ||||||||
\(894\) | 12.3211 | 0.412081 | ||||||||
\(895\) | −50.8619 | −1.70013 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.4829 | 0.516959 | ||||||||
\(898\) | −7.27039 | −0.242616 | ||||||||
\(899\) | −8.88156 | −0.296216 | ||||||||
\(900\) | 0.171573 | 0.00571910 | ||||||||
\(901\) | −35.0694 | −1.16833 | ||||||||
\(902\) | −5.10254 | −0.169896 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.71979 | 0.190237 | ||||||||
\(905\) | −13.0528 | −0.433891 | ||||||||
\(906\) | 11.5286 | 0.383012 | ||||||||
\(907\) | −2.49866 | −0.0829667 | −0.0414834 | − | 0.999139i | \(-0.513208\pi\) | ||||
−0.0414834 | + | 0.999139i | \(0.513208\pi\) | |||||||
\(908\) | 13.5601 | 0.450006 | ||||||||
\(909\) | −11.2230 | −0.372244 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.4645 | −0.479229 | −0.239614 | − | 0.970868i | \(-0.577021\pi\) | ||||
−0.239614 | + | 0.970868i | \(0.577021\pi\) | |||||||
\(912\) | −6.90440 | −0.228627 | ||||||||
\(913\) | 1.96853 | 0.0651489 | ||||||||
\(914\) | 31.0596 | 1.02736 | ||||||||
\(915\) | 19.6262 | 0.648823 | ||||||||
\(916\) | −5.10254 | −0.168593 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.10254 | −0.168409 | ||||||||
\(919\) | −3.29646 | −0.108740 | −0.0543700 | − | 0.998521i | \(-0.517315\pi\) | ||||
−0.0543700 | + | 0.998521i | \(0.517315\pi\) | |||||||
\(920\) | −19.5408 | −0.644241 | ||||||||
\(921\) | −27.0563 | −0.891537 | ||||||||
\(922\) | 10.5228 | 0.346552 | ||||||||
\(923\) | −16.6863 | −0.549236 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.761917 | 0.0250517 | ||||||||
\(926\) | 8.30389 | 0.272883 | ||||||||
\(927\) | 17.0118 | 0.558742 | ||||||||
\(928\) | 2.82843 | 0.0928477 | ||||||||
\(929\) | −29.7650 | −0.976558 | −0.488279 | − | 0.872688i | \(-0.662375\pi\) | ||||
−0.488279 | + | 0.872688i | \(0.662375\pi\) | |||||||
\(930\) | −7.14094 | −0.234161 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.343146 | −0.0112401 | ||||||||
\(933\) | −24.5751 | −0.804553 | ||||||||
\(934\) | −11.5530 | −0.378025 | ||||||||
\(935\) | −11.6037 | −0.379482 | ||||||||
\(936\) | −1.80186 | −0.0588957 | ||||||||
\(937\) | 42.4521 | 1.38685 | 0.693425 | − | 0.720529i | \(-0.256101\pi\) | ||||
0.693425 | + | 0.720529i | \(0.256101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.0809 | 0.426878 | ||||||||
\(940\) | −0.172768 | −0.00563508 | ||||||||
\(941\) | 34.4494 | 1.12302 | 0.561509 | − | 0.827471i | \(-0.310221\pi\) | ||||
0.561509 | + | 0.827471i | \(0.310221\pi\) | |||||||
\(942\) | −1.49881 | −0.0488339 | ||||||||
\(943\) | −43.8447 | −1.42778 | ||||||||
\(944\) | 5.17157 | 0.168320 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.93587 | 0.225505 | ||||||||
\(947\) | −51.3611 | −1.66901 | −0.834505 | − | 0.551000i | \(-0.814246\pi\) | ||||
−0.834505 | + | 0.551000i | \(0.814246\pi\) | |||||||
\(948\) | 9.26921 | 0.301050 | ||||||||
\(949\) | −5.49461 | −0.178363 | ||||||||
\(950\) | 1.18461 | 0.0384337 | ||||||||
\(951\) | 20.6557 | 0.669806 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.4015 | 1.63267 | 0.816333 | − | 0.577582i | \(-0.196004\pi\) | ||||
0.816333 | + | 0.577582i | \(0.196004\pi\) | |||||||
\(954\) | 6.87293 | 0.222519 | ||||||||
\(955\) | −26.6325 | −0.861806 | ||||||||
\(956\) | −18.4322 | −0.596138 | ||||||||
\(957\) | 2.82843 | 0.0914301 | ||||||||
\(958\) | 10.7482 | 0.347260 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.27411 | 0.0733966 | ||||||||
\(961\) | −21.1397 | −0.681927 | ||||||||
\(962\) | −8.00167 | −0.257984 | ||||||||
\(963\) | 11.6482 | 0.375359 | ||||||||
\(964\) | 24.5682 | 0.791288 | ||||||||
\(965\) | −29.0024 | −0.933620 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.9141 | 0.994129 | 0.497064 | − | 0.867714i | \(-0.334411\pi\) | ||||
0.497064 | + | 0.867714i | \(0.334411\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −35.2299 | −1.13175 | ||||||||
\(970\) | 20.5078 | 0.658465 | ||||||||
\(971\) | −25.2623 | −0.810704 | −0.405352 | − | 0.914161i | \(-0.632851\pi\) | ||||
−0.405352 | + | 0.914161i | \(0.632851\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 38.6164 | 1.23735 | ||||||||
\(975\) | 0.309151 | 0.00990075 | ||||||||
\(976\) | 8.63029 | 0.276249 | ||||||||
\(977\) | −8.97798 | −0.287231 | −0.143616 | − | 0.989634i | \(-0.545873\pi\) | ||||
−0.143616 | + | 0.989634i | \(0.545873\pi\) | |||||||
\(978\) | −13.6569 | −0.436698 | ||||||||
\(979\) | −15.0624 | −0.481398 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0890 | −0.449827 | ||||||||
\(982\) | 8.68629 | 0.277191 | ||||||||
\(983\) | 19.2638 | 0.614420 | 0.307210 | − | 0.951642i | \(-0.400605\pi\) | ||||
0.307210 | + | 0.951642i | \(0.400605\pi\) | |||||||
\(984\) | 5.10254 | 0.162663 | ||||||||
\(985\) | −52.8971 | −1.68544 | ||||||||
\(986\) | 14.4322 | 0.459613 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.4408 | −0.395794 | ||||||||
\(989\) | 59.5980 | 1.89511 | ||||||||
\(990\) | 2.27411 | 0.0722759 | ||||||||
\(991\) | −46.5858 | −1.47985 | −0.739923 | − | 0.672692i | \(-0.765138\pi\) | ||||
−0.739923 | + | 0.672692i | \(0.765138\pi\) | |||||||
\(992\) | −3.14010 | −0.0996984 | ||||||||
\(993\) | −19.7014 | −0.625204 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.37307 | 0.106934 | ||||||||
\(996\) | −1.96853 | −0.0623753 | ||||||||
\(997\) | 31.0330 | 0.982825 | 0.491412 | − | 0.870927i | \(-0.336481\pi\) | ||||
0.491412 | + | 0.870927i | \(0.336481\pi\) | |||||||
\(998\) | −43.1041 | −1.36444 | ||||||||
\(999\) | 4.44078 | 0.140500 |
(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 | 3234.2.a.bk.1.3 | yes | 4 | |
3.2 | odd | 2 | 9702.2.a.ec.1.2 | 4 | |||
7.6 | odd | 2 | 3234.2.a.bj.1.2 | ✓ | 4 | ||
21.20 | even | 2 | 9702.2.a.eb.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bj.1.2 | ✓ | 4 | 7.6 | odd | 2 | ||
3234.2.a.bk.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
9702.2.a.eb.1.3 | 4 | 21.20 | even | 2 | |||
9702.2.a.ec.1.2 | 4 | 3.2 | odd | 2 |