Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,38,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 38);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 38 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.0142114374\) |
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: | \( x^{4} - x^{3} - 11777633936x^{2} - 35120319927360x + 11967042111800832000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{10}\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(31743.2\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −81067.1 | −0.218670 | −0.109335 | − | 0.994005i | \(-0.534872\pi\) | ||||
−0.109335 | + | 0.994005i | \(0.534872\pi\) | |||||||
\(3\) | 3.87420e8 | 0.577350 | ||||||||
\(4\) | −1.30867e11 | −0.952183 | ||||||||
\(5\) | −7.16603e12 | −0.840105 | −0.420052 | − | 0.907500i | \(-0.637988\pi\) | ||||
−0.420052 | + | 0.907500i | \(0.637988\pi\) | |||||||
\(6\) | −3.14071e13 | −0.126249 | ||||||||
\(7\) | −5.96869e15 | −1.38537 | −0.692684 | − | 0.721241i | \(-0.743572\pi\) | ||||
−0.692684 | + | 0.721241i | \(0.743572\pi\) | |||||||
\(8\) | 2.17508e16 | 0.426885 | ||||||||
\(9\) | 1.50095e17 | 0.333333 | ||||||||
\(10\) | 5.80929e17 | 0.183706 | ||||||||
\(11\) | 2.06526e19 | 1.11998 | 0.559989 | − | 0.828500i | \(-0.310806\pi\) | ||||
0.559989 | + | 0.828500i | \(0.310806\pi\) | |||||||
\(12\) | −5.07006e19 | −0.549743 | ||||||||
\(13\) | −4.02756e20 | −0.993321 | −0.496661 | − | 0.867945i | \(-0.665441\pi\) | ||||
−0.496661 | + | 0.867945i | \(0.665441\pi\) | |||||||
\(14\) | 4.83865e20 | 0.302939 | ||||||||
\(15\) | −2.77627e21 | −0.485035 | ||||||||
\(16\) | 1.62230e22 | 0.858836 | ||||||||
\(17\) | −4.55890e22 | −0.786241 | −0.393120 | − | 0.919487i | \(-0.628604\pi\) | ||||
−0.393120 | + | 0.919487i | \(0.628604\pi\) | |||||||
\(18\) | −1.21677e22 | −0.0728901 | ||||||||
\(19\) | 1.54990e23 | 0.341477 | 0.170738 | − | 0.985316i | \(-0.445385\pi\) | ||||
0.170738 | + | 0.985316i | \(0.445385\pi\) | |||||||
\(20\) | 9.37797e23 | 0.799934 | ||||||||
\(21\) | −2.31239e24 | −0.799843 | ||||||||
\(22\) | −1.67424e24 | −0.244906 | ||||||||
\(23\) | 2.42540e25 | 1.55890 | 0.779450 | − | 0.626464i | \(-0.215499\pi\) | ||||
0.779450 | + | 0.626464i | \(0.215499\pi\) | |||||||
\(24\) | 8.42671e24 | 0.246462 | ||||||||
\(25\) | −2.14076e25 | −0.294224 | ||||||||
\(26\) | 3.26502e25 | 0.217210 | ||||||||
\(27\) | 5.81497e25 | 0.192450 | ||||||||
\(28\) | 7.81105e26 | 1.31912 | ||||||||
\(29\) | 1.52016e27 | 1.34130 | 0.670652 | − | 0.741772i | \(-0.266015\pi\) | ||||
0.670652 | + | 0.741772i | \(0.266015\pi\) | |||||||
\(30\) | 2.25064e26 | 0.106063 | ||||||||
\(31\) | 6.09023e27 | 1.56474 | 0.782370 | − | 0.622814i | \(-0.214011\pi\) | ||||
0.782370 | + | 0.622814i | \(0.214011\pi\) | |||||||
\(32\) | −4.30456e27 | −0.614687 | ||||||||
\(33\) | 8.00122e27 | 0.646619 | ||||||||
\(34\) | 3.69577e27 | 0.171928 | ||||||||
\(35\) | 4.27718e28 | 1.16385 | ||||||||
\(36\) | −1.96424e28 | −0.317394 | ||||||||
\(37\) | −6.28281e28 | −0.611536 | −0.305768 | − | 0.952106i | \(-0.598913\pi\) | ||||
−0.305768 | + | 0.952106i | \(0.598913\pi\) | |||||||
\(38\) | −1.25646e28 | −0.0746709 | ||||||||
\(39\) | −1.56036e29 | −0.573494 | ||||||||
\(40\) | −1.55867e29 | −0.358628 | ||||||||
\(41\) | −8.11303e29 | −1.18217 | −0.591087 | − | 0.806608i | \(-0.701301\pi\) | ||||
−0.591087 | + | 0.806608i | \(0.701301\pi\) | |||||||
\(42\) | 1.87459e29 | 0.174902 | ||||||||
\(43\) | 4.69121e29 | 0.283216 | 0.141608 | − | 0.989923i | \(-0.454773\pi\) | ||||
0.141608 | + | 0.989923i | \(0.454773\pi\) | |||||||
\(44\) | −2.70274e30 | −1.06642 | ||||||||
\(45\) | −1.07558e30 | −0.280035 | ||||||||
\(46\) | −1.96620e30 | −0.340885 | ||||||||
\(47\) | 1.02212e31 | 1.19039 | 0.595196 | − | 0.803581i | \(-0.297074\pi\) | ||||
0.595196 | + | 0.803581i | \(0.297074\pi\) | |||||||
\(48\) | 6.28511e30 | 0.495849 | ||||||||
\(49\) | 1.70631e31 | 0.919245 | ||||||||
\(50\) | 1.73545e30 | 0.0643380 | ||||||||
\(51\) | −1.76621e31 | −0.453936 | ||||||||
\(52\) | 5.27075e31 | 0.945824 | ||||||||
\(53\) | 5.42457e31 | 0.684323 | 0.342162 | − | 0.939641i | \(-0.388841\pi\) | ||||
0.342162 | + | 0.939641i | \(0.388841\pi\) | |||||||
\(54\) | −4.71403e30 | −0.0420831 | ||||||||
\(55\) | −1.47997e32 | −0.940898 | ||||||||
\(56\) | −1.29824e32 | −0.591392 | ||||||||
\(57\) | 6.00462e31 | 0.197152 | ||||||||
\(58\) | −1.23235e32 | −0.293303 | ||||||||
\(59\) | −5.27739e32 | −0.915496 | −0.457748 | − | 0.889082i | \(-0.651344\pi\) | ||||
−0.457748 | + | 0.889082i | \(0.651344\pi\) | |||||||
\(60\) | 3.63322e32 | 0.461842 | ||||||||
\(61\) | −6.19951e31 | −0.0580437 | −0.0290219 | − | 0.999579i | \(-0.509239\pi\) | ||||
−0.0290219 | + | 0.999579i | \(0.509239\pi\) | |||||||
\(62\) | −4.93717e32 | −0.342162 | ||||||||
\(63\) | −8.95868e32 | −0.461789 | ||||||||
\(64\) | −1.88071e33 | −0.724423 | ||||||||
\(65\) | 2.88616e33 | 0.834494 | ||||||||
\(66\) | −6.48636e32 | −0.141396 | ||||||||
\(67\) | 9.30348e33 | 1.53554 | 0.767771 | − | 0.640725i | \(-0.221366\pi\) | ||||
0.767771 | + | 0.640725i | \(0.221366\pi\) | |||||||
\(68\) | 5.96611e33 | 0.748645 | ||||||||
\(69\) | 9.39649e33 | 0.900031 | ||||||||
\(70\) | −3.46739e33 | −0.254500 | ||||||||
\(71\) | −2.75965e34 | −1.55802 | −0.779012 | − | 0.627010i | \(-0.784279\pi\) | ||||
−0.779012 | + | 0.627010i | \(0.784279\pi\) | |||||||
\(72\) | 3.26468e33 | 0.142295 | ||||||||
\(73\) | 2.09192e34 | 0.706436 | 0.353218 | − | 0.935541i | \(-0.385087\pi\) | ||||
0.353218 | + | 0.935541i | \(0.385087\pi\) | |||||||
\(74\) | 5.09329e33 | 0.133725 | ||||||||
\(75\) | −8.29375e33 | −0.169870 | ||||||||
\(76\) | −2.02831e34 | −0.325149 | ||||||||
\(77\) | −1.23269e35 | −1.55158 | ||||||||
\(78\) | 1.26494e34 | 0.125406 | ||||||||
\(79\) | 1.20341e34 | 0.0942567 | 0.0471283 | − | 0.998889i | \(-0.484993\pi\) | ||||
0.0471283 | + | 0.998889i | \(0.484993\pi\) | |||||||
\(80\) | −1.16254e35 | −0.721512 | ||||||||
\(81\) | 2.25284e34 | 0.111111 | ||||||||
\(82\) | 6.57700e34 | 0.258506 | ||||||||
\(83\) | −3.25180e34 | −0.102136 | −0.0510681 | − | 0.998695i | \(-0.516263\pi\) | ||||
−0.0510681 | + | 0.998695i | \(0.516263\pi\) | |||||||
\(84\) | 3.02616e35 | 0.761597 | ||||||||
\(85\) | 3.26692e35 | 0.660525 | ||||||||
\(86\) | −3.80303e34 | −0.0619310 | ||||||||
\(87\) | 5.88942e35 | 0.774402 | ||||||||
\(88\) | 4.49210e35 | 0.478101 | ||||||||
\(89\) | −1.39444e36 | −1.20416 | −0.602081 | − | 0.798435i | \(-0.705662\pi\) | ||||
−0.602081 | + | 0.798435i | \(0.705662\pi\) | |||||||
\(90\) | 8.71944e34 | 0.0612353 | ||||||||
\(91\) | 2.40392e36 | 1.37612 | ||||||||
\(92\) | −3.17405e36 | −1.48436 | ||||||||
\(93\) | 2.35948e36 | 0.903403 | ||||||||
\(94\) | −8.28600e35 | −0.260303 | ||||||||
\(95\) | −1.11066e36 | −0.286876 | ||||||||
\(96\) | −1.66767e36 | −0.354889 | ||||||||
\(97\) | −6.18707e36 | −1.08695 | −0.543473 | − | 0.839427i | \(-0.682891\pi\) | ||||
−0.543473 | + | 0.839427i | \(0.682891\pi\) | |||||||
\(98\) | −1.38326e36 | −0.201012 | ||||||||
\(99\) | 3.09984e36 | 0.373326 | ||||||||
\(100\) | 2.80155e36 | 0.280155 | ||||||||
\(101\) | −1.95203e37 | −1.62384 | −0.811918 | − | 0.583772i | \(-0.801576\pi\) | ||||
−0.811918 | + | 0.583772i | \(0.801576\pi\) | |||||||
\(102\) | 1.43182e36 | 0.0992624 | ||||||||
\(103\) | 3.11250e37 | 1.80144 | 0.900722 | − | 0.434397i | \(-0.143038\pi\) | ||||
0.900722 | + | 0.434397i | \(0.143038\pi\) | |||||||
\(104\) | −8.76026e36 | −0.424033 | ||||||||
\(105\) | 1.65707e37 | 0.671952 | ||||||||
\(106\) | −4.39754e36 | −0.149641 | ||||||||
\(107\) | 2.91526e37 | 0.833831 | 0.416915 | − | 0.908945i | \(-0.363111\pi\) | ||||
0.416915 | + | 0.908945i | \(0.363111\pi\) | |||||||
\(108\) | −7.60989e36 | −0.183248 | ||||||||
\(109\) | 4.34807e37 | 0.882890 | 0.441445 | − | 0.897288i | \(-0.354466\pi\) | ||||
0.441445 | + | 0.897288i | \(0.354466\pi\) | |||||||
\(110\) | 1.19977e37 | 0.205747 | ||||||||
\(111\) | −2.43409e37 | −0.353070 | ||||||||
\(112\) | −9.68298e37 | −1.18980 | ||||||||
\(113\) | 1.30612e38 | 1.36155 | 0.680774 | − | 0.732493i | \(-0.261644\pi\) | ||||
0.680774 | + | 0.732493i | \(0.261644\pi\) | |||||||
\(114\) | −4.86777e36 | −0.0431112 | ||||||||
\(115\) | −1.73805e38 | −1.30964 | ||||||||
\(116\) | −1.98939e38 | −1.27717 | ||||||||
\(117\) | −6.04515e37 | −0.331107 | ||||||||
\(118\) | 4.27822e37 | 0.200192 | ||||||||
\(119\) | 2.72107e38 | 1.08923 | ||||||||
\(120\) | −6.03860e37 | −0.207054 | ||||||||
\(121\) | 8.64886e37 | 0.254349 | ||||||||
\(122\) | 5.02576e36 | 0.0126924 | ||||||||
\(123\) | −3.14315e38 | −0.682529 | ||||||||
\(124\) | −7.97010e38 | −1.48992 | ||||||||
\(125\) | 6.74805e38 | 1.08728 | ||||||||
\(126\) | 7.26255e37 | 0.100980 | ||||||||
\(127\) | 1.12113e39 | 1.34675 | 0.673373 | − | 0.739303i | \(-0.264845\pi\) | ||||
0.673373 | + | 0.739303i | \(0.264845\pi\) | |||||||
\(128\) | 7.44077e38 | 0.773096 | ||||||||
\(129\) | 1.81747e38 | 0.163515 | ||||||||
\(130\) | −2.33973e38 | −0.182479 | ||||||||
\(131\) | 1.51287e39 | 1.02396 | 0.511980 | − | 0.858997i | \(-0.328912\pi\) | ||||
0.511980 | + | 0.858997i | \(0.328912\pi\) | |||||||
\(132\) | −1.04710e39 | −0.615700 | ||||||||
\(133\) | −9.25086e38 | −0.473071 | ||||||||
\(134\) | −7.54206e38 | −0.335777 | ||||||||
\(135\) | −4.16703e38 | −0.161678 | ||||||||
\(136\) | −9.91598e38 | −0.335634 | ||||||||
\(137\) | −5.50009e38 | −0.162570 | −0.0812848 | − | 0.996691i | \(-0.525902\pi\) | ||||
−0.0812848 | + | 0.996691i | \(0.525902\pi\) | |||||||
\(138\) | −7.61747e38 | −0.196810 | ||||||||
\(139\) | 2.01159e39 | 0.454743 | 0.227372 | − | 0.973808i | \(-0.426987\pi\) | ||||
0.227372 | + | 0.973808i | \(0.426987\pi\) | |||||||
\(140\) | −5.59742e39 | −1.10820 | ||||||||
\(141\) | 3.95989e39 | 0.687273 | ||||||||
\(142\) | 2.23717e39 | 0.340693 | ||||||||
\(143\) | −8.31793e39 | −1.11250 | ||||||||
\(144\) | 2.43498e39 | 0.286279 | ||||||||
\(145\) | −1.08935e40 | −1.12684 | ||||||||
\(146\) | −1.69586e39 | −0.154477 | ||||||||
\(147\) | 6.61061e39 | 0.530726 | ||||||||
\(148\) | 8.22213e39 | 0.582294 | ||||||||
\(149\) | 1.36577e40 | 0.853949 | 0.426975 | − | 0.904264i | \(-0.359579\pi\) | ||||
0.426975 | + | 0.904264i | \(0.359579\pi\) | |||||||
\(150\) | 6.72350e38 | 0.0371456 | ||||||||
\(151\) | 3.14967e40 | 1.53883 | 0.769415 | − | 0.638749i | \(-0.220548\pi\) | ||||
0.769415 | + | 0.638749i | \(0.220548\pi\) | |||||||
\(152\) | 3.37115e39 | 0.145771 | ||||||||
\(153\) | −6.84267e39 | −0.262080 | ||||||||
\(154\) | 9.99304e39 | 0.339285 | ||||||||
\(155\) | −4.36428e40 | −1.31455 | ||||||||
\(156\) | 2.04199e40 | 0.546072 | ||||||||
\(157\) | −1.57563e40 | −0.374378 | −0.187189 | − | 0.982324i | \(-0.559938\pi\) | ||||
−0.187189 | + | 0.982324i | \(0.559938\pi\) | |||||||
\(158\) | −9.75569e38 | −0.0206111 | ||||||||
\(159\) | 2.10159e40 | 0.395094 | ||||||||
\(160\) | 3.08466e40 | 0.516401 | ||||||||
\(161\) | −1.44765e41 | −2.15965 | ||||||||
\(162\) | −1.82631e39 | −0.0242967 | ||||||||
\(163\) | −9.57266e40 | −1.13648 | −0.568240 | − | 0.822863i | \(-0.692376\pi\) | ||||
−0.568240 | + | 0.822863i | \(0.692376\pi\) | |||||||
\(164\) | 1.06173e41 | 1.12565 | ||||||||
\(165\) | −5.73370e40 | −0.543228 | ||||||||
\(166\) | 2.63614e39 | 0.0223342 | ||||||||
\(167\) | 1.21079e41 | 0.917942 | 0.458971 | − | 0.888451i | \(-0.348218\pi\) | ||||
0.458971 | + | 0.888451i | \(0.348218\pi\) | |||||||
\(168\) | −5.02964e40 | −0.341441 | ||||||||
\(169\) | −2.18871e39 | −0.0133132 | ||||||||
\(170\) | −2.64840e40 | −0.144437 | ||||||||
\(171\) | 2.32631e40 | 0.113826 | ||||||||
\(172\) | −6.13925e40 | −0.269674 | ||||||||
\(173\) | 2.37365e41 | 0.936621 | 0.468310 | − | 0.883564i | \(-0.344863\pi\) | ||||
0.468310 | + | 0.883564i | \(0.344863\pi\) | |||||||
\(174\) | −4.77438e40 | −0.169339 | ||||||||
\(175\) | 1.27775e41 | 0.407608 | ||||||||
\(176\) | 3.35046e41 | 0.961877 | ||||||||
\(177\) | −2.04457e41 | −0.528562 | ||||||||
\(178\) | 1.13043e41 | 0.263315 | ||||||||
\(179\) | 3.87672e41 | 0.814110 | 0.407055 | − | 0.913404i | \(-0.366556\pi\) | ||||
0.407055 | + | 0.913404i | \(0.366556\pi\) | |||||||
\(180\) | 1.40758e41 | 0.266645 | ||||||||
\(181\) | −9.37245e41 | −1.60250 | −0.801252 | − | 0.598326i | \(-0.795833\pi\) | ||||
−0.801252 | + | 0.598326i | \(0.795833\pi\) | |||||||
\(182\) | −1.94879e41 | −0.300916 | ||||||||
\(183\) | −2.40182e40 | −0.0335115 | ||||||||
\(184\) | 5.27544e41 | 0.665470 | ||||||||
\(185\) | 4.50228e41 | 0.513754 | ||||||||
\(186\) | −1.91276e41 | −0.197547 | ||||||||
\(187\) | −9.41530e41 | −0.880572 | ||||||||
\(188\) | −1.33761e42 | −1.13347 | ||||||||
\(189\) | −3.47078e41 | −0.266614 | ||||||||
\(190\) | 9.00381e40 | 0.0627314 | ||||||||
\(191\) | −7.76327e41 | −0.490826 | −0.245413 | − | 0.969419i | \(-0.578924\pi\) | ||||
−0.245413 | + | 0.969419i | \(0.578924\pi\) | |||||||
\(192\) | −7.28625e41 | −0.418246 | ||||||||
\(193\) | 1.83873e42 | 0.958758 | 0.479379 | − | 0.877608i | \(-0.340862\pi\) | ||||
0.479379 | + | 0.877608i | \(0.340862\pi\) | |||||||
\(194\) | 5.01568e41 | 0.237683 | ||||||||
\(195\) | 1.11816e42 | 0.481795 | ||||||||
\(196\) | −2.23300e42 | −0.875290 | ||||||||
\(197\) | 2.38170e42 | 0.849693 | 0.424847 | − | 0.905265i | \(-0.360328\pi\) | ||||
0.424847 | + | 0.905265i | \(0.360328\pi\) | |||||||
\(198\) | −2.51295e41 | −0.0816353 | ||||||||
\(199\) | 3.72548e42 | 1.10256 | 0.551278 | − | 0.834322i | \(-0.314141\pi\) | ||||
0.551278 | + | 0.834322i | \(0.314141\pi\) | |||||||
\(200\) | −4.65633e41 | −0.125600 | ||||||||
\(201\) | 3.60436e42 | 0.886545 | ||||||||
\(202\) | 1.58246e42 | 0.355085 | ||||||||
\(203\) | −9.07338e42 | −1.85820 | ||||||||
\(204\) | 2.31139e42 | 0.432230 | ||||||||
\(205\) | 5.81382e42 | 0.993150 | ||||||||
\(206\) | −2.52321e42 | −0.393922 | ||||||||
\(207\) | 3.64039e42 | 0.519633 | ||||||||
\(208\) | −6.53389e42 | −0.853100 | ||||||||
\(209\) | 3.20093e42 | 0.382446 | ||||||||
\(210\) | −1.34334e42 | −0.146936 | ||||||||
\(211\) | 5.66343e42 | 0.567354 | 0.283677 | − | 0.958920i | \(-0.408446\pi\) | ||||
0.283677 | + | 0.958920i | \(0.408446\pi\) | |||||||
\(212\) | −7.09897e42 | −0.651601 | ||||||||
\(213\) | −1.06914e43 | −0.899525 | ||||||||
\(214\) | −2.36332e42 | −0.182334 | ||||||||
\(215\) | −3.36173e42 | −0.237932 | ||||||||
\(216\) | 1.26480e42 | 0.0821540 | ||||||||
\(217\) | −3.63507e43 | −2.16774 | ||||||||
\(218\) | −3.52486e42 | −0.193062 | ||||||||
\(219\) | 8.10454e42 | 0.407861 | ||||||||
\(220\) | 1.93679e43 | 0.895907 | ||||||||
\(221\) | 1.83612e43 | 0.780989 | ||||||||
\(222\) | 1.97325e42 | 0.0772060 | ||||||||
\(223\) | 3.12041e43 | 1.12350 | 0.561749 | − | 0.827308i | \(-0.310129\pi\) | ||||
0.561749 | + | 0.827308i | \(0.310129\pi\) | |||||||
\(224\) | 2.56926e43 | 0.851567 | ||||||||
\(225\) | −3.21317e42 | −0.0980746 | ||||||||
\(226\) | −1.05884e43 | −0.297730 | ||||||||
\(227\) | −1.69570e43 | −0.439411 | −0.219705 | − | 0.975566i | \(-0.570510\pi\) | ||||
−0.219705 | + | 0.975566i | \(0.570510\pi\) | |||||||
\(228\) | −7.85807e42 | −0.187725 | ||||||||
\(229\) | −4.70639e42 | −0.103689 | −0.0518444 | − | 0.998655i | \(-0.516510\pi\) | ||||
−0.0518444 | + | 0.998655i | \(0.516510\pi\) | |||||||
\(230\) | 1.40899e43 | 0.286379 | ||||||||
\(231\) | −4.77568e43 | −0.895806 | ||||||||
\(232\) | 3.30648e43 | 0.572582 | ||||||||
\(233\) | 8.91929e43 | 1.42641 | 0.713207 | − | 0.700953i | \(-0.247242\pi\) | ||||
0.713207 | + | 0.700953i | \(0.247242\pi\) | |||||||
\(234\) | 4.90063e42 | 0.0724033 | ||||||||
\(235\) | −7.32451e43 | −1.00005 | ||||||||
\(236\) | 6.90636e43 | 0.871720 | ||||||||
\(237\) | 4.66225e42 | 0.0544191 | ||||||||
\(238\) | −2.20589e43 | −0.238183 | ||||||||
\(239\) | −7.05888e43 | −0.705301 | −0.352651 | − | 0.935755i | \(-0.614720\pi\) | ||||
−0.352651 | + | 0.935755i | \(0.614720\pi\) | |||||||
\(240\) | −4.50393e43 | −0.416565 | ||||||||
\(241\) | −1.03720e44 | −0.888271 | −0.444136 | − | 0.895960i | \(-0.646489\pi\) | ||||
−0.444136 | + | 0.895960i | \(0.646489\pi\) | |||||||
\(242\) | −7.01138e42 | −0.0556185 | ||||||||
\(243\) | 8.72796e42 | 0.0641500 | ||||||||
\(244\) | 8.11311e42 | 0.0552682 | ||||||||
\(245\) | −1.22275e44 | −0.772262 | ||||||||
\(246\) | 2.54806e43 | 0.149249 | ||||||||
\(247\) | −6.24230e43 | −0.339196 | ||||||||
\(248\) | 1.32467e44 | 0.667963 | ||||||||
\(249\) | −1.25982e43 | −0.0589684 | ||||||||
\(250\) | −5.47045e43 | −0.237757 | ||||||||
\(251\) | −1.06389e44 | −0.429470 | −0.214735 | − | 0.976672i | \(-0.568889\pi\) | ||||
−0.214735 | + | 0.976672i | \(0.568889\pi\) | |||||||
\(252\) | 1.17240e44 | 0.439708 | ||||||||
\(253\) | 5.00907e44 | 1.74593 | ||||||||
\(254\) | −9.08865e43 | −0.294494 | ||||||||
\(255\) | 1.26567e44 | 0.381354 | ||||||||
\(256\) | 1.98162e44 | 0.555369 | ||||||||
\(257\) | −2.17429e44 | −0.566962 | −0.283481 | − | 0.958978i | \(-0.591489\pi\) | ||||
−0.283481 | + | 0.958978i | \(0.591489\pi\) | |||||||
\(258\) | −1.47337e43 | −0.0357559 | ||||||||
\(259\) | 3.75001e44 | 0.847202 | ||||||||
\(260\) | −3.77703e44 | −0.794591 | ||||||||
\(261\) | 2.28168e44 | 0.447101 | ||||||||
\(262\) | −1.22644e44 | −0.223910 | ||||||||
\(263\) | 5.98155e44 | 1.01773 | 0.508865 | − | 0.860847i | \(-0.330065\pi\) | ||||
0.508865 | + | 0.860847i | \(0.330065\pi\) | |||||||
\(264\) | 1.74033e44 | 0.276032 | ||||||||
\(265\) | −3.88726e44 | −0.574903 | ||||||||
\(266\) | 7.49940e43 | 0.103447 | ||||||||
\(267\) | −5.40235e44 | −0.695224 | ||||||||
\(268\) | −1.21752e45 | −1.46212 | ||||||||
\(269\) | −1.15434e45 | −1.29394 | −0.646972 | − | 0.762514i | \(-0.723965\pi\) | ||||
−0.646972 | + | 0.762514i | \(0.723965\pi\) | |||||||
\(270\) | 3.37809e43 | 0.0353542 | ||||||||
\(271\) | 1.52915e45 | 1.49457 | 0.747287 | − | 0.664501i | \(-0.231356\pi\) | ||||
0.747287 | + | 0.664501i | \(0.231356\pi\) | |||||||
\(272\) | −7.39589e44 | −0.675252 | ||||||||
\(273\) | 9.31329e44 | 0.794501 | ||||||||
\(274\) | 4.45877e43 | 0.0355492 | ||||||||
\(275\) | −4.42122e44 | −0.329524 | ||||||||
\(276\) | −1.22969e45 | −0.856995 | ||||||||
\(277\) | −5.76088e44 | −0.375503 | −0.187751 | − | 0.982217i | \(-0.560120\pi\) | ||||
−0.187751 | + | 0.982217i | \(0.560120\pi\) | |||||||
\(278\) | −1.63074e44 | −0.0994388 | ||||||||
\(279\) | 9.14111e44 | 0.521580 | ||||||||
\(280\) | 9.30321e44 | 0.496832 | ||||||||
\(281\) | 9.77482e44 | 0.488699 | 0.244350 | − | 0.969687i | \(-0.421426\pi\) | ||||
0.244350 | + | 0.969687i | \(0.421426\pi\) | |||||||
\(282\) | −3.21017e44 | −0.150286 | ||||||||
\(283\) | −2.00519e45 | −0.879237 | −0.439619 | − | 0.898185i | \(-0.644886\pi\) | ||||
−0.439619 | + | 0.898185i | \(0.644886\pi\) | |||||||
\(284\) | 3.61147e45 | 1.48352 | ||||||||
\(285\) | −4.30293e44 | −0.165628 | ||||||||
\(286\) | 6.74311e44 | 0.243270 | ||||||||
\(287\) | 4.84241e45 | 1.63775 | ||||||||
\(288\) | −6.46091e44 | −0.204896 | ||||||||
\(289\) | −1.28373e45 | −0.381826 | ||||||||
\(290\) | 8.83107e44 | 0.246406 | ||||||||
\(291\) | −2.39700e45 | −0.627548 | ||||||||
\(292\) | −2.73764e45 | −0.672656 | ||||||||
\(293\) | 2.43417e45 | 0.561435 | 0.280717 | − | 0.959790i | \(-0.409428\pi\) | ||||
0.280717 | + | 0.959790i | \(0.409428\pi\) | |||||||
\(294\) | −5.35903e44 | −0.116054 | ||||||||
\(295\) | 3.78179e45 | 0.769113 | ||||||||
\(296\) | −1.36656e45 | −0.261055 | ||||||||
\(297\) | 1.20094e45 | 0.215540 | ||||||||
\(298\) | −1.10719e45 | −0.186733 | ||||||||
\(299\) | −9.76843e45 | −1.54849 | ||||||||
\(300\) | 1.08538e45 | 0.161748 | ||||||||
\(301\) | −2.80004e45 | −0.392359 | ||||||||
\(302\) | −2.55334e45 | −0.336497 | ||||||||
\(303\) | −7.56258e45 | −0.937522 | ||||||||
\(304\) | 2.51439e45 | 0.293273 | ||||||||
\(305\) | 4.44258e44 | 0.0487628 | ||||||||
\(306\) | 5.54716e44 | 0.0573092 | ||||||||
\(307\) | −5.23869e45 | −0.509522 | −0.254761 | − | 0.967004i | \(-0.581997\pi\) | ||||
−0.254761 | + | 0.967004i | \(0.581997\pi\) | |||||||
\(308\) | 1.61318e46 | 1.47739 | ||||||||
\(309\) | 1.20585e46 | 1.04006 | ||||||||
\(310\) | 3.53799e45 | 0.287452 | ||||||||
\(311\) | −1.81624e46 | −1.39029 | −0.695146 | − | 0.718869i | \(-0.744660\pi\) | ||||
−0.695146 | + | 0.718869i | \(0.744660\pi\) | |||||||
\(312\) | −3.39390e45 | −0.244816 | ||||||||
\(313\) | −1.26517e45 | −0.0860161 | −0.0430081 | − | 0.999075i | \(-0.513694\pi\) | ||||
−0.0430081 | + | 0.999075i | \(0.513694\pi\) | |||||||
\(314\) | 1.27732e45 | 0.0818655 | ||||||||
\(315\) | 6.41982e45 | 0.387952 | ||||||||
\(316\) | −1.57487e45 | −0.0897496 | ||||||||
\(317\) | −1.12945e46 | −0.607117 | −0.303558 | − | 0.952813i | \(-0.598175\pi\) | ||||
−0.303558 | + | 0.952813i | \(0.598175\pi\) | |||||||
\(318\) | −1.70370e45 | −0.0863954 | ||||||||
\(319\) | 3.13952e46 | 1.50223 | ||||||||
\(320\) | 1.34772e46 | 0.608591 | ||||||||
\(321\) | 1.12943e46 | 0.481412 | ||||||||
\(322\) | 1.17356e46 | 0.472252 | ||||||||
\(323\) | −7.06583e45 | −0.268483 | ||||||||
\(324\) | −2.94823e45 | −0.105798 | ||||||||
\(325\) | 8.62204e45 | 0.292259 | ||||||||
\(326\) | 7.76028e45 | 0.248515 | ||||||||
\(327\) | 1.68453e46 | 0.509737 | ||||||||
\(328\) | −1.76465e46 | −0.504652 | ||||||||
\(329\) | −6.10069e46 | −1.64913 | ||||||||
\(330\) | 4.64815e45 | 0.118788 | ||||||||
\(331\) | −3.60502e46 | −0.871145 | −0.435572 | − | 0.900154i | \(-0.643454\pi\) | ||||
−0.435572 | + | 0.900154i | \(0.643454\pi\) | |||||||
\(332\) | 4.25554e45 | 0.0972524 | ||||||||
\(333\) | −9.43016e45 | −0.203845 | ||||||||
\(334\) | −9.81555e45 | −0.200727 | ||||||||
\(335\) | −6.66690e46 | −1.29002 | ||||||||
\(336\) | −3.75138e46 | −0.686934 | ||||||||
\(337\) | 3.50453e46 | 0.607403 | 0.303701 | − | 0.952767i | \(-0.401777\pi\) | ||||
0.303701 | + | 0.952767i | \(0.401777\pi\) | |||||||
\(338\) | 1.77432e44 | 0.00291121 | ||||||||
\(339\) | 5.06019e46 | 0.786090 | ||||||||
\(340\) | −4.27533e46 | −0.628940 | ||||||||
\(341\) | 1.25779e47 | 1.75247 | ||||||||
\(342\) | −1.88588e45 | −0.0248903 | ||||||||
\(343\) | 8.94695e45 | 0.111875 | ||||||||
\(344\) | 1.02038e46 | 0.120901 | ||||||||
\(345\) | −6.73355e46 | −0.756121 | ||||||||
\(346\) | −1.92425e46 | −0.204811 | ||||||||
\(347\) | 1.32955e47 | 1.34156 | 0.670781 | − | 0.741655i | \(-0.265959\pi\) | ||||
0.670781 | + | 0.741655i | \(0.265959\pi\) | |||||||
\(348\) | −7.70731e46 | −0.737373 | ||||||||
\(349\) | 5.30968e46 | 0.481724 | 0.240862 | − | 0.970559i | \(-0.422570\pi\) | ||||
0.240862 | + | 0.970559i | \(0.422570\pi\) | |||||||
\(350\) | −1.03584e46 | −0.0891319 | ||||||||
\(351\) | −2.34201e46 | −0.191165 | ||||||||
\(352\) | −8.89001e46 | −0.688435 | ||||||||
\(353\) | 9.80590e46 | 0.720535 | 0.360268 | − | 0.932849i | \(-0.382685\pi\) | ||||
0.360268 | + | 0.932849i | \(0.382685\pi\) | |||||||
\(354\) | 1.65747e46 | 0.115581 | ||||||||
\(355\) | 1.97757e47 | 1.30890 | ||||||||
\(356\) | 1.82487e47 | 1.14658 | ||||||||
\(357\) | 1.05420e47 | 0.628869 | ||||||||
\(358\) | −3.14274e46 | −0.178022 | ||||||||
\(359\) | −3.23469e47 | −1.74015 | −0.870073 | − | 0.492924i | \(-0.835928\pi\) | ||||
−0.870073 | + | 0.492924i | \(0.835928\pi\) | |||||||
\(360\) | −2.33948e46 | −0.119543 | ||||||||
\(361\) | −1.81986e47 | −0.883394 | ||||||||
\(362\) | 7.59797e46 | 0.350420 | ||||||||
\(363\) | 3.35075e46 | 0.146848 | ||||||||
\(364\) | −3.14594e47 | −1.31031 | ||||||||
\(365\) | −1.49908e47 | −0.593480 | ||||||||
\(366\) | 1.94708e45 | 0.00732798 | ||||||||
\(367\) | 5.30423e46 | 0.189802 | 0.0949009 | − | 0.995487i | \(-0.469747\pi\) | ||||
0.0949009 | + | 0.995487i | \(0.469747\pi\) | |||||||
\(368\) | 3.93472e47 | 1.33884 | ||||||||
\(369\) | −1.21772e47 | −0.394058 | ||||||||
\(370\) | −3.64987e46 | −0.112343 | ||||||||
\(371\) | −3.23775e47 | −0.948040 | ||||||||
\(372\) | −3.08778e47 | −0.860205 | ||||||||
\(373\) | 1.73609e47 | 0.460212 | 0.230106 | − | 0.973166i | \(-0.426093\pi\) | ||||
0.230106 | + | 0.973166i | \(0.426093\pi\) | |||||||
\(374\) | 7.63272e46 | 0.192555 | ||||||||
\(375\) | 2.61433e47 | 0.627744 | ||||||||
\(376\) | 2.22318e47 | 0.508160 | ||||||||
\(377\) | −6.12254e47 | −1.33235 | ||||||||
\(378\) | 2.81366e46 | 0.0583006 | ||||||||
\(379\) | −7.77135e45 | −0.0153345 | −0.00766727 | − | 0.999971i | \(-0.502441\pi\) | ||||
−0.00766727 | + | 0.999971i | \(0.502441\pi\) | |||||||
\(380\) | 1.45349e47 | 0.273159 | ||||||||
\(381\) | 4.34348e47 | 0.777545 | ||||||||
\(382\) | 6.29346e46 | 0.107329 | ||||||||
\(383\) | −1.37051e47 | −0.222692 | −0.111346 | − | 0.993782i | \(-0.535516\pi\) | ||||
−0.111346 | + | 0.993782i | \(0.535516\pi\) | |||||||
\(384\) | 2.88271e47 | 0.446347 | ||||||||
\(385\) | 8.83347e47 | 1.30349 | ||||||||
\(386\) | −1.49061e47 | −0.209652 | ||||||||
\(387\) | 7.04126e46 | 0.0944055 | ||||||||
\(388\) | 8.09683e47 | 1.03497 | ||||||||
\(389\) | −5.22275e47 | −0.636549 | −0.318274 | − | 0.947999i | \(-0.603103\pi\) | ||||
−0.318274 | + | 0.947999i | \(0.603103\pi\) | |||||||
\(390\) | −9.06458e46 | −0.105354 | ||||||||
\(391\) | −1.10572e48 | −1.22567 | ||||||||
\(392\) | 3.71137e47 | 0.392412 | ||||||||
\(393\) | 5.86118e47 | 0.591184 | ||||||||
\(394\) | −1.93078e47 | −0.185803 | ||||||||
\(395\) | −8.62367e46 | −0.0791855 | ||||||||
\(396\) | −4.05667e47 | −0.355474 | ||||||||
\(397\) | 1.08193e48 | 0.904844 | 0.452422 | − | 0.891804i | \(-0.350560\pi\) | ||||
0.452422 | + | 0.891804i | \(0.350560\pi\) | |||||||
\(398\) | −3.02014e47 | −0.241096 | ||||||||
\(399\) | −3.58397e47 | −0.273128 | ||||||||
\(400\) | −3.47295e47 | −0.252690 | ||||||||
\(401\) | −1.57080e48 | −1.09132 | −0.545659 | − | 0.838007i | \(-0.683721\pi\) | ||||
−0.545659 | + | 0.838007i | \(0.683721\pi\) | |||||||
\(402\) | −2.92195e47 | −0.193861 | ||||||||
\(403\) | −2.45287e48 | −1.55429 | ||||||||
\(404\) | 2.55457e48 | 1.54619 | ||||||||
\(405\) | −1.61439e47 | −0.0933450 | ||||||||
\(406\) | 7.35553e47 | 0.406333 | ||||||||
\(407\) | −1.29756e48 | −0.684906 | ||||||||
\(408\) | −3.84165e47 | −0.193778 | ||||||||
\(409\) | 7.85596e47 | 0.378720 | 0.189360 | − | 0.981908i | \(-0.439359\pi\) | ||||
0.189360 | + | 0.981908i | \(0.439359\pi\) | |||||||
\(410\) | −4.71309e47 | −0.217172 | ||||||||
\(411\) | −2.13085e47 | −0.0938596 | ||||||||
\(412\) | −4.07324e48 | −1.71530 | ||||||||
\(413\) | 3.14991e48 | 1.26830 | ||||||||
\(414\) | −2.95116e47 | −0.113628 | ||||||||
\(415\) | 2.33025e47 | 0.0858051 | ||||||||
\(416\) | 1.73368e48 | 0.610581 | ||||||||
\(417\) | 7.79332e47 | 0.262546 | ||||||||
\(418\) | −2.59491e47 | −0.0836297 | ||||||||
\(419\) | 4.22926e48 | 1.30408 | 0.652040 | − | 0.758184i | \(-0.273913\pi\) | ||||
0.652040 | + | 0.758184i | \(0.273913\pi\) | |||||||
\(420\) | −2.16856e48 | −0.639821 | ||||||||
\(421\) | 4.83549e48 | 1.36528 | 0.682640 | − | 0.730755i | \(-0.260832\pi\) | ||||
0.682640 | + | 0.730755i | \(0.260832\pi\) | |||||||
\(422\) | −4.59118e47 | −0.124063 | ||||||||
\(423\) | 1.53414e48 | 0.396797 | ||||||||
\(424\) | 1.17989e48 | 0.292127 | ||||||||
\(425\) | 9.75953e47 | 0.231331 | ||||||||
\(426\) | 8.66724e47 | 0.196699 | ||||||||
\(427\) | 3.70029e47 | 0.0804119 | ||||||||
\(428\) | −3.81512e48 | −0.793960 | ||||||||
\(429\) | −3.22254e48 | −0.642300 | ||||||||
\(430\) | 2.72526e47 | 0.0520286 | ||||||||
\(431\) | −1.35672e48 | −0.248119 | −0.124060 | − | 0.992275i | \(-0.539591\pi\) | ||||
−0.124060 | + | 0.992275i | \(0.539591\pi\) | |||||||
\(432\) | 9.43361e47 | 0.165283 | ||||||||
\(433\) | −3.36809e48 | −0.565403 | −0.282701 | − | 0.959208i | \(-0.591231\pi\) | ||||
−0.282701 | + | 0.959208i | \(0.591231\pi\) | |||||||
\(434\) | 2.94685e48 | 0.474021 | ||||||||
\(435\) | −4.22038e48 | −0.650579 | ||||||||
\(436\) | −5.69019e48 | −0.840673 | ||||||||
\(437\) | 3.75912e48 | 0.532328 | ||||||||
\(438\) | −6.57012e47 | −0.0891871 | ||||||||
\(439\) | −3.07628e48 | −0.400343 | −0.200172 | − | 0.979761i | \(-0.564150\pi\) | ||||
−0.200172 | + | 0.979761i | \(0.564150\pi\) | |||||||
\(440\) | −3.21905e48 | −0.401655 | ||||||||
\(441\) | 2.56109e48 | 0.306415 | ||||||||
\(442\) | −1.48849e48 | −0.170779 | ||||||||
\(443\) | −1.21772e49 | −1.33992 | −0.669961 | − | 0.742396i | \(-0.733689\pi\) | ||||
−0.669961 | + | 0.742396i | \(0.733689\pi\) | |||||||
\(444\) | 3.18542e48 | 0.336188 | ||||||||
\(445\) | 9.99261e48 | 1.01162 | ||||||||
\(446\) | −2.52963e48 | −0.245675 | ||||||||
\(447\) | 5.29128e48 | 0.493028 | ||||||||
\(448\) | 1.12254e49 | 1.00359 | ||||||||
\(449\) | 6.54698e48 | 0.561674 | 0.280837 | − | 0.959756i | \(-0.409388\pi\) | ||||
0.280837 | + | 0.959756i | \(0.409388\pi\) | |||||||
\(450\) | 2.60482e47 | 0.0214460 | ||||||||
\(451\) | −1.67555e49 | −1.32401 | ||||||||
\(452\) | −1.70929e49 | −1.29644 | ||||||||
\(453\) | 1.22024e49 | 0.888444 | ||||||||
\(454\) | 1.37466e48 | 0.0960861 | ||||||||
\(455\) | −1.72266e49 | −1.15608 | ||||||||
\(456\) | 1.30605e48 | 0.0841611 | ||||||||
\(457\) | 1.51332e49 | 0.936444 | 0.468222 | − | 0.883611i | \(-0.344895\pi\) | ||||
0.468222 | + | 0.883611i | \(0.344895\pi\) | |||||||
\(458\) | 3.81534e47 | 0.0226737 | ||||||||
\(459\) | −2.65099e48 | −0.151312 | ||||||||
\(460\) | 2.27453e49 | 1.24702 | ||||||||
\(461\) | 2.09024e49 | 1.10085 | 0.550426 | − | 0.834884i | \(-0.314465\pi\) | ||||
0.550426 | + | 0.834884i | \(0.314465\pi\) | |||||||
\(462\) | 3.87151e48 | 0.195886 | ||||||||
\(463\) | 1.99414e49 | 0.969412 | 0.484706 | − | 0.874677i | \(-0.338927\pi\) | ||||
0.484706 | + | 0.874677i | \(0.338927\pi\) | |||||||
\(464\) | 2.46615e49 | 1.15196 | ||||||||
\(465\) | −1.69081e49 | −0.758953 | ||||||||
\(466\) | −7.23061e48 | −0.311915 | ||||||||
\(467\) | −1.49903e49 | −0.621508 | −0.310754 | − | 0.950490i | \(-0.600582\pi\) | ||||
−0.310754 | + | 0.950490i | \(0.600582\pi\) | |||||||
\(468\) | 7.91111e48 | 0.315275 | ||||||||
\(469\) | −5.55296e49 | −2.12729 | ||||||||
\(470\) | 5.93777e48 | 0.218682 | ||||||||
\(471\) | −6.10432e48 | −0.216147 | ||||||||
\(472\) | −1.14787e49 | −0.390811 | ||||||||
\(473\) | 9.68855e48 | 0.317196 | ||||||||
\(474\) | −3.77956e47 | −0.0118998 | ||||||||
\(475\) | −3.31796e48 | −0.100471 | ||||||||
\(476\) | −3.56098e49 | −1.03715 | ||||||||
\(477\) | 8.14198e48 | 0.228108 | ||||||||
\(478\) | 5.72243e48 | 0.154229 | ||||||||
\(479\) | −1.97535e49 | −0.512198 | −0.256099 | − | 0.966651i | \(-0.582437\pi\) | ||||
−0.256099 | + | 0.966651i | \(0.582437\pi\) | |||||||
\(480\) | 1.19506e49 | 0.298144 | ||||||||
\(481\) | 2.53044e49 | 0.607451 | ||||||||
\(482\) | 8.40825e48 | 0.194239 | ||||||||
\(483\) | −5.60847e49 | −1.24687 | ||||||||
\(484\) | −1.13185e49 | −0.242187 | ||||||||
\(485\) | 4.43367e49 | 0.913148 | ||||||||
\(486\) | −7.07551e47 | −0.0140277 | ||||||||
\(487\) | −2.15937e49 | −0.412136 | −0.206068 | − | 0.978538i | \(-0.566067\pi\) | ||||
−0.206068 | + | 0.978538i | \(0.566067\pi\) | |||||||
\(488\) | −1.34844e48 | −0.0247780 | ||||||||
\(489\) | −3.70864e49 | −0.656147 | ||||||||
\(490\) | 9.91248e48 | 0.168871 | ||||||||
\(491\) | 4.27399e49 | 0.701174 | 0.350587 | − | 0.936530i | \(-0.385982\pi\) | ||||
0.350587 | + | 0.936530i | \(0.385982\pi\) | |||||||
\(492\) | 4.11335e49 | 0.649892 | ||||||||
\(493\) | −6.93028e49 | −1.05459 | ||||||||
\(494\) | 5.06045e48 | 0.0741722 | ||||||||
\(495\) | −2.22135e49 | −0.313633 | ||||||||
\(496\) | 9.88015e49 | 1.34386 | ||||||||
\(497\) | 1.64715e50 | 2.15844 | ||||||||
\(498\) | 1.02130e48 | 0.0128946 | ||||||||
\(499\) | −6.52314e49 | −0.793591 | −0.396796 | − | 0.917907i | \(-0.629878\pi\) | ||||
−0.396796 | + | 0.917907i | \(0.629878\pi\) | |||||||
\(500\) | −8.83097e49 | −1.03529 | ||||||||
\(501\) | 4.69086e49 | 0.529974 | ||||||||
\(502\) | 8.62466e48 | 0.0939124 | ||||||||
\(503\) | 8.97219e49 | 0.941653 | 0.470826 | − | 0.882226i | \(-0.343956\pi\) | ||||
0.470826 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(504\) | −1.94859e49 | −0.197131 | ||||||||
\(505\) | 1.39883e50 | 1.36419 | ||||||||
\(506\) | −4.06071e49 | −0.381784 | ||||||||
\(507\) | −8.47950e47 | −0.00768640 | ||||||||
\(508\) | −1.46719e50 | −1.28235 | ||||||||
\(509\) | 4.50563e49 | 0.379731 | 0.189866 | − | 0.981810i | \(-0.439195\pi\) | ||||
0.189866 | + | 0.981810i | \(0.439195\pi\) | |||||||
\(510\) | −1.02605e49 | −0.0833908 | ||||||||
\(511\) | −1.24860e50 | −0.978674 | ||||||||
\(512\) | −1.18330e50 | −0.894539 | ||||||||
\(513\) | 9.01261e48 | 0.0657173 | ||||||||
\(514\) | 1.76263e49 | 0.123978 | ||||||||
\(515\) | −2.23043e50 | −1.51340 | ||||||||
\(516\) | −2.37847e49 | −0.155696 | ||||||||
\(517\) | 2.11093e50 | 1.33321 | ||||||||
\(518\) | −3.04003e49 | −0.185258 | ||||||||
\(519\) | 9.19601e49 | 0.540758 | ||||||||
\(520\) | 6.27763e49 | 0.356233 | ||||||||
\(521\) | −5.45339e49 | −0.298654 | −0.149327 | − | 0.988788i | \(-0.547711\pi\) | ||||
−0.149327 | + | 0.988788i | \(0.547711\pi\) | |||||||
\(522\) | −1.84969e49 | −0.0977678 | ||||||||
\(523\) | −1.36223e50 | −0.694975 | −0.347488 | − | 0.937685i | \(-0.612965\pi\) | ||||
−0.347488 | + | 0.937685i | \(0.612965\pi\) | |||||||
\(524\) | −1.97985e50 | −0.974998 | ||||||||
\(525\) | 4.95028e49 | 0.235333 | ||||||||
\(526\) | −4.84907e49 | −0.222547 | ||||||||
\(527\) | −2.77648e50 | −1.23026 | ||||||||
\(528\) | 1.29804e50 | 0.555340 | ||||||||
\(529\) | 3.46192e50 | 1.43017 | ||||||||
\(530\) | 3.15129e49 | 0.125714 | ||||||||
\(531\) | −7.92107e49 | −0.305165 | ||||||||
\(532\) | 1.21063e50 | 0.450451 | ||||||||
\(533\) | 3.26757e50 | 1.17428 | ||||||||
\(534\) | 4.37953e49 | 0.152025 | ||||||||
\(535\) | −2.08909e50 | −0.700505 | ||||||||
\(536\) | 2.02358e50 | 0.655499 | ||||||||
\(537\) | 1.50192e50 | 0.470026 | ||||||||
\(538\) | 9.35787e49 | 0.282947 | ||||||||
\(539\) | 3.52397e50 | 1.02953 | ||||||||
\(540\) | 5.45327e49 | 0.153947 | ||||||||
\(541\) | −1.89994e50 | −0.518310 | −0.259155 | − | 0.965836i | \(-0.583444\pi\) | ||||
−0.259155 | + | 0.965836i | \(0.583444\pi\) | |||||||
\(542\) | −1.23964e50 | −0.326819 | ||||||||
\(543\) | −3.63108e50 | −0.925207 | ||||||||
\(544\) | 1.96241e50 | 0.483292 | ||||||||
\(545\) | −3.11584e50 | −0.741720 | ||||||||
\(546\) | −7.55002e49 | −0.173734 | ||||||||
\(547\) | −1.73538e49 | −0.0386037 | −0.0193019 | − | 0.999814i | \(-0.506144\pi\) | ||||
−0.0193019 | + | 0.999814i | \(0.506144\pi\) | |||||||
\(548\) | 7.19781e49 | 0.154796 | ||||||||
\(549\) | −9.30513e48 | −0.0193479 | ||||||||
\(550\) | 3.58416e49 | 0.0720571 | ||||||||
\(551\) | 2.35610e50 | 0.458024 | ||||||||
\(552\) | 2.04381e50 | 0.384209 | ||||||||
\(553\) | −7.18278e49 | −0.130580 | ||||||||
\(554\) | 4.67018e49 | 0.0821114 | ||||||||
\(555\) | 1.74427e50 | 0.296616 | ||||||||
\(556\) | −2.63251e50 | −0.432999 | ||||||||
\(557\) | −9.83753e50 | −1.56518 | −0.782591 | − | 0.622536i | \(-0.786102\pi\) | ||||
−0.782591 | + | 0.622536i | \(0.786102\pi\) | |||||||
\(558\) | −7.41043e49 | −0.114054 | ||||||||
\(559\) | −1.88941e50 | −0.281325 | ||||||||
\(560\) | 6.93885e50 | 0.999560 | ||||||||
\(561\) | −3.64768e50 | −0.508398 | ||||||||
\(562\) | −7.92416e49 | −0.106864 | ||||||||
\(563\) | 2.99781e50 | 0.391200 | 0.195600 | − | 0.980684i | \(-0.437335\pi\) | ||||
0.195600 | + | 0.980684i | \(0.437335\pi\) | |||||||
\(564\) | −5.18219e50 | −0.654410 | ||||||||
\(565\) | −9.35972e50 | −1.14384 | ||||||||
\(566\) | 1.62555e50 | 0.192263 | ||||||||
\(567\) | −1.34465e50 | −0.153930 | ||||||||
\(568\) | −6.00245e50 | −0.665096 | ||||||||
\(569\) | 1.02631e51 | 1.10078 | 0.550392 | − | 0.834906i | \(-0.314478\pi\) | ||||
0.550392 | + | 0.834906i | \(0.314478\pi\) | |||||||
\(570\) | 3.48826e49 | 0.0362180 | ||||||||
\(571\) | −8.60079e47 | −0.000864511 0 | −0.000432255 | − | 1.00000i | \(-0.500138\pi\) | ||||
−0.000432255 | 1.00000i | \(0.500138\pi\) | ||||||||
\(572\) | 1.08854e51 | 1.05930 | ||||||||
\(573\) | −3.00765e50 | −0.283379 | ||||||||
\(574\) | −3.92560e50 | −0.358127 | ||||||||
\(575\) | −5.19220e50 | −0.458666 | ||||||||
\(576\) | −2.82284e50 | −0.241474 | ||||||||
\(577\) | 1.49637e51 | 1.23961 | 0.619806 | − | 0.784755i | \(-0.287211\pi\) | ||||
0.619806 | + | 0.784755i | \(0.287211\pi\) | |||||||
\(578\) | 1.04069e50 | 0.0834940 | ||||||||
\(579\) | 7.12364e50 | 0.553539 | ||||||||
\(580\) | 1.42560e51 | 1.07295 | ||||||||
\(581\) | 1.94090e50 | 0.141496 | ||||||||
\(582\) | 1.94318e50 | 0.137226 | ||||||||
\(583\) | 1.12031e51 | 0.766427 | ||||||||
\(584\) | 4.55010e50 | 0.301567 | ||||||||
\(585\) | 4.33197e50 | 0.278165 | ||||||||
\(586\) | −1.97331e50 | −0.122769 | ||||||||
\(587\) | −2.21173e51 | −1.33330 | −0.666650 | − | 0.745371i | \(-0.732272\pi\) | ||||
−0.666650 | + | 0.745371i | \(0.732272\pi\) | |||||||
\(588\) | −8.65111e50 | −0.505349 | ||||||||
\(589\) | 9.43923e50 | 0.534323 | ||||||||
\(590\) | −3.06579e50 | −0.168182 | ||||||||
\(591\) | 9.22720e50 | 0.490571 | ||||||||
\(592\) | −1.01926e51 | −0.525209 | ||||||||
\(593\) | −9.58294e50 | −0.478616 | −0.239308 | − | 0.970944i | \(-0.576921\pi\) | ||||
−0.239308 | + | 0.970944i | \(0.576921\pi\) | |||||||
\(594\) | −9.73568e49 | −0.0471321 | ||||||||
\(595\) | −1.94993e51 | −0.915070 | ||||||||
\(596\) | −1.78734e51 | −0.813116 | ||||||||
\(597\) | 1.44333e51 | 0.636560 | ||||||||
\(598\) | 7.91899e50 | 0.338608 | ||||||||
\(599\) | 1.22432e49 | 0.00507572 | 0.00253786 | − | 0.999997i | \(-0.499192\pi\) | ||||
0.00253786 | + | 0.999997i | \(0.499192\pi\) | |||||||
\(600\) | −1.80396e50 | −0.0725150 | ||||||||
\(601\) | −1.08866e51 | −0.424339 | −0.212169 | − | 0.977233i | \(-0.568053\pi\) | ||||
−0.212169 | + | 0.977233i | \(0.568053\pi\) | |||||||
\(602\) | 2.26991e50 | 0.0857973 | ||||||||
\(603\) | 1.39640e51 | 0.511847 | ||||||||
\(604\) | −4.12188e51 | −1.46525 | ||||||||
\(605\) | −6.19780e50 | −0.213680 | ||||||||
\(606\) | 6.13077e50 | 0.205008 | ||||||||
\(607\) | 4.94921e51 | 1.60526 | 0.802629 | − | 0.596479i | \(-0.203434\pi\) | ||||
0.802629 | + | 0.596479i | \(0.203434\pi\) | |||||||
\(608\) | −6.67162e50 | −0.209901 | ||||||||
\(609\) | −3.51521e51 | −1.07283 | ||||||||
\(610\) | −3.60148e49 | −0.0106630 | ||||||||
\(611\) | −4.11663e51 | −1.18244 | ||||||||
\(612\) | 8.95480e50 | 0.249548 | ||||||||
\(613\) | 3.53515e51 | 0.955848 | 0.477924 | − | 0.878401i | \(-0.341390\pi\) | ||||
0.477924 | + | 0.878401i | \(0.341390\pi\) | |||||||
\(614\) | 4.24685e50 | 0.111417 | ||||||||
\(615\) | 2.25239e51 | 0.573396 | ||||||||
\(616\) | −2.68119e51 | −0.662346 | ||||||||
\(617\) | −3.24058e51 | −0.776868 | −0.388434 | − | 0.921477i | \(-0.626984\pi\) | ||||
−0.388434 | + | 0.921477i | \(0.626984\pi\) | |||||||
\(618\) | −9.77545e50 | −0.227431 | ||||||||
\(619\) | 2.49425e51 | 0.563201 | 0.281600 | − | 0.959532i | \(-0.409135\pi\) | ||||
0.281600 | + | 0.959532i | \(0.409135\pi\) | |||||||
\(620\) | 5.71140e51 | 1.25169 | ||||||||
\(621\) | 1.41036e51 | 0.300010 | ||||||||
\(622\) | 1.47237e51 | 0.304016 | ||||||||
\(623\) | 8.32299e51 | 1.66821 | ||||||||
\(624\) | −2.53136e51 | −0.492538 | ||||||||
\(625\) | −3.27806e51 | −0.619208 | ||||||||
\(626\) | 1.02564e50 | 0.0188092 | ||||||||
\(627\) | 1.24011e51 | 0.220805 | ||||||||
\(628\) | 2.06198e51 | 0.356477 | ||||||||
\(629\) | 2.86427e51 | 0.480814 | ||||||||
\(630\) | −5.20436e50 | −0.0848335 | ||||||||
\(631\) | 3.22282e51 | 0.510145 | 0.255072 | − | 0.966922i | \(-0.417901\pi\) | ||||
0.255072 | + | 0.966922i | \(0.417901\pi\) | |||||||
\(632\) | 2.61751e50 | 0.0402367 | ||||||||
\(633\) | 2.19413e51 | 0.327562 | ||||||||
\(634\) | 9.15616e50 | 0.132758 | ||||||||
\(635\) | −8.03403e51 | −1.13141 | ||||||||
\(636\) | −2.75029e51 | −0.376202 | ||||||||
\(637\) | −6.87227e51 | −0.913106 | ||||||||
\(638\) | −2.54512e51 | −0.328493 | ||||||||
\(639\) | −4.14208e51 | −0.519341 | ||||||||
\(640\) | −5.33208e51 | −0.649482 | ||||||||
\(641\) | −8.20930e51 | −0.971477 | −0.485739 | − | 0.874104i | \(-0.661449\pi\) | ||||
−0.485739 | + | 0.874104i | \(0.661449\pi\) | |||||||
\(642\) | −9.15599e50 | −0.105271 | ||||||||
\(643\) | −4.47682e51 | −0.500112 | −0.250056 | − | 0.968231i | \(-0.580449\pi\) | ||||
−0.250056 | + | 0.968231i | \(0.580449\pi\) | |||||||
\(644\) | 1.89449e52 | 2.05638 | ||||||||
\(645\) | −1.30241e51 | −0.137370 | ||||||||
\(646\) | 5.72807e50 | 0.0587093 | ||||||||
\(647\) | 1.90676e52 | 1.89919 | 0.949594 | − | 0.313483i | \(-0.101496\pi\) | ||||
0.949594 | + | 0.313483i | \(0.101496\pi\) | |||||||
\(648\) | 4.90011e50 | 0.0474316 | ||||||||
\(649\) | −1.08991e52 | −1.02533 | ||||||||
\(650\) | −6.98964e50 | −0.0639083 | ||||||||
\(651\) | −1.40830e52 | −1.25155 | ||||||||
\(652\) | 1.25275e52 | 1.08214 | ||||||||
\(653\) | −9.48302e51 | −0.796256 | −0.398128 | − | 0.917330i | \(-0.630340\pi\) | ||||
−0.398128 | + | 0.917330i | \(0.630340\pi\) | |||||||
\(654\) | −1.36560e51 | −0.111464 | ||||||||
\(655\) | −1.08413e52 | −0.860234 | ||||||||
\(656\) | −1.31617e52 | −1.01529 | ||||||||
\(657\) | 3.13986e51 | 0.235479 | ||||||||
\(658\) | 4.94566e51 | 0.360616 | ||||||||
\(659\) | 1.04759e52 | 0.742693 | 0.371347 | − | 0.928494i | \(-0.378896\pi\) | ||||
0.371347 | + | 0.928494i | \(0.378896\pi\) | |||||||
\(660\) | 7.50353e51 | 0.517252 | ||||||||
\(661\) | −8.65976e51 | −0.580469 | −0.290234 | − | 0.956956i | \(-0.593733\pi\) | ||||
−0.290234 | + | 0.956956i | \(0.593733\pi\) | |||||||
\(662\) | 2.92249e51 | 0.190494 | ||||||||
\(663\) | 7.11352e51 | 0.450904 | ||||||||
\(664\) | −7.07293e50 | −0.0436004 | ||||||||
\(665\) | 6.62919e51 | 0.397429 | ||||||||
\(666\) | 7.64476e50 | 0.0445749 | ||||||||
\(667\) | 3.68700e52 | 2.09096 | ||||||||
\(668\) | −1.58453e52 | −0.874049 | ||||||||
\(669\) | 1.20891e52 | 0.648651 | ||||||||
\(670\) | 5.40467e51 | 0.282088 | ||||||||
\(671\) | −1.28036e51 | −0.0650076 | ||||||||
\(672\) | 9.95382e51 | 0.491653 | ||||||||
\(673\) | −2.18723e52 | −1.05103 | −0.525515 | − | 0.850784i | \(-0.676127\pi\) | ||||
−0.525515 | + | 0.850784i | \(0.676127\pi\) | |||||||
\(674\) | −2.84102e51 | −0.132821 | ||||||||
\(675\) | −1.24485e51 | −0.0566234 | ||||||||
\(676\) | 2.86430e50 | 0.0126766 | ||||||||
\(677\) | −1.59031e52 | −0.684845 | −0.342422 | − | 0.939546i | \(-0.611247\pi\) | ||||
−0.342422 | + | 0.939546i | \(0.611247\pi\) | |||||||
\(678\) | −4.10215e51 | −0.171895 | ||||||||
\(679\) | 3.69287e52 | 1.50582 | ||||||||
\(680\) | 7.10582e51 | 0.281968 | ||||||||
\(681\) | −6.56949e51 | −0.253694 | ||||||||
\(682\) | −1.01965e52 | −0.383214 | ||||||||
\(683\) | −3.09230e51 | −0.113109 | −0.0565547 | − | 0.998400i | \(-0.518012\pi\) | ||||
−0.0565547 | + | 0.998400i | \(0.518012\pi\) | |||||||
\(684\) | −3.04438e51 | −0.108383 | ||||||||
\(685\) | 3.94138e51 | 0.136576 | ||||||||
\(686\) | −7.25303e50 | −0.0244638 | ||||||||
\(687\) | −1.82335e51 | −0.0598647 | ||||||||
\(688\) | 7.61053e51 | 0.243237 | ||||||||
\(689\) | −2.18477e52 | −0.679753 | ||||||||
\(690\) | 5.45870e51 | 0.165341 | ||||||||
\(691\) | −4.14754e52 | −1.22306 | −0.611528 | − | 0.791222i | \(-0.709445\pi\) | ||||
−0.611528 | + | 0.791222i | \(0.709445\pi\) | |||||||
\(692\) | −3.10633e52 | −0.891835 | ||||||||
\(693\) | −1.85020e52 | −0.517194 | ||||||||
\(694\) | −1.07783e52 | −0.293360 | ||||||||
\(695\) | −1.44151e52 | −0.382032 | ||||||||
\(696\) | 1.28100e52 | 0.330580 | ||||||||
\(697\) | 3.69865e52 | 0.929473 | ||||||||
\(698\) | −4.30440e51 | −0.105339 | ||||||||
\(699\) | 3.45552e52 | 0.823541 | ||||||||
\(700\) | −1.67216e52 | −0.388118 | ||||||||
\(701\) | −2.82631e52 | −0.638904 | −0.319452 | − | 0.947602i | \(-0.603499\pi\) | ||||
−0.319452 | + | 0.947602i | \(0.603499\pi\) | |||||||
\(702\) | 1.89860e51 | 0.0418021 | ||||||||
\(703\) | −9.73771e51 | −0.208825 | ||||||||
\(704\) | −3.88414e52 | −0.811337 | ||||||||
\(705\) | −2.83767e52 | −0.577381 | ||||||||
\(706\) | −7.94936e51 | −0.157560 | ||||||||
\(707\) | 1.16511e53 | 2.24961 | ||||||||
\(708\) | 2.67567e52 | 0.503288 | ||||||||
\(709\) | 4.89940e52 | 0.897817 | 0.448909 | − | 0.893578i | \(-0.351813\pi\) | ||||
0.448909 | + | 0.893578i | \(0.351813\pi\) | |||||||
\(710\) | −1.60316e52 | −0.286218 | ||||||||
\(711\) | 1.80625e51 | 0.0314189 | ||||||||
\(712\) | −3.03302e52 | −0.514039 | ||||||||
\(713\) | 1.47712e53 | 2.43927 | ||||||||
\(714\) | −8.54608e51 | −0.137515 | ||||||||
\(715\) | 5.96066e52 | 0.934614 | ||||||||
\(716\) | −5.07334e52 | −0.775182 | ||||||||
\(717\) | −2.73476e52 | −0.407206 | ||||||||
\(718\) | 2.62227e52 | 0.380518 | ||||||||
\(719\) | 4.55246e52 | 0.643816 | 0.321908 | − | 0.946771i | \(-0.395676\pi\) | ||||
0.321908 | + | 0.946771i | \(0.395676\pi\) | |||||||
\(720\) | −1.74491e52 | −0.240504 | ||||||||
\(721\) | −1.85775e53 | −2.49566 | ||||||||
\(722\) | 1.47531e52 | 0.193172 | ||||||||
\(723\) | −4.01831e52 | −0.512844 | ||||||||
\(724\) | 1.22654e53 | 1.52588 | ||||||||
\(725\) | −3.25430e52 | −0.394644 | ||||||||
\(726\) | −2.71635e51 | −0.0321114 | ||||||||
\(727\) | −6.55544e52 | −0.755467 | −0.377733 | − | 0.925914i | \(-0.623296\pi\) | ||||
−0.377733 | + | 0.925914i | \(0.623296\pi\) | |||||||
\(728\) | 5.22873e52 | 0.587442 | ||||||||
\(729\) | 3.38139e51 | 0.0370370 | ||||||||
\(730\) | 1.21526e52 | 0.129777 | ||||||||
\(731\) | −2.13868e52 | −0.222676 | ||||||||
\(732\) | 3.14319e51 | 0.0319091 | ||||||||
\(733\) | 5.46489e52 | 0.540951 | 0.270476 | − | 0.962727i | \(-0.412819\pi\) | ||||
0.270476 | + | 0.962727i | \(0.412819\pi\) | |||||||
\(734\) | −4.29999e51 | −0.0415040 | ||||||||
\(735\) | −4.73718e52 | −0.445866 | ||||||||
\(736\) | −1.04403e53 | −0.958235 | ||||||||
\(737\) | 1.92141e53 | 1.71977 | ||||||||
\(738\) | 9.87172e51 | 0.0861688 | ||||||||
\(739\) | −1.98761e53 | −1.69203 | −0.846017 | − | 0.533156i | \(-0.821006\pi\) | ||||
−0.846017 | + | 0.533156i | \(0.821006\pi\) | |||||||
\(740\) | −5.89200e52 | −0.489188 | ||||||||
\(741\) | −2.41839e52 | −0.195835 | ||||||||
\(742\) | 2.62476e52 | 0.207308 | ||||||||
\(743\) | −1.44490e53 | −1.11313 | −0.556564 | − | 0.830805i | \(-0.687880\pi\) | ||||
−0.556564 | + | 0.830805i | \(0.687880\pi\) | |||||||
\(744\) | 5.13206e52 | 0.385649 | ||||||||
\(745\) | −9.78716e52 | −0.717407 | ||||||||
\(746\) | −1.40740e52 | −0.100635 | ||||||||
\(747\) | −4.88078e51 | −0.0340454 | ||||||||
\(748\) | 1.23215e53 | 0.838465 | ||||||||
\(749\) | −1.74003e53 | −1.15516 | ||||||||
\(750\) | −2.11936e52 | −0.137269 | ||||||||
\(751\) | 1.98670e53 | 1.25544 | 0.627718 | − | 0.778441i | \(-0.283989\pi\) | ||||
0.627718 | + | 0.778441i | \(0.283989\pi\) | |||||||
\(752\) | 1.65817e53 | 1.02235 | ||||||||
\(753\) | −4.12173e52 | −0.247955 | ||||||||
\(754\) | 4.96337e52 | 0.291344 | ||||||||
\(755\) | −2.25706e53 | −1.29278 | ||||||||
\(756\) | 4.54210e52 | 0.253866 | ||||||||
\(757\) | 3.23306e53 | 1.76336 | 0.881679 | − | 0.471850i | \(-0.156414\pi\) | ||||
0.881679 | + | 0.471850i | \(0.156414\pi\) | |||||||
\(758\) | 6.30001e50 | 0.00335321 | ||||||||
\(759\) | 1.94062e53 | 1.00801 | ||||||||
\(760\) | −2.41578e52 | −0.122463 | ||||||||
\(761\) | −4.26585e52 | −0.211052 | −0.105526 | − | 0.994417i | \(-0.533653\pi\) | ||||
−0.105526 | + | 0.994417i | \(0.533653\pi\) | |||||||
\(762\) | −3.52113e52 | −0.170026 | ||||||||
\(763\) | −2.59523e53 | −1.22313 | ||||||||
\(764\) | 1.01596e53 | 0.467356 | ||||||||
\(765\) | 4.90348e52 | 0.220175 | ||||||||
\(766\) | 1.11103e52 | 0.0486962 | ||||||||
\(767\) | 2.12550e53 | 0.909382 | ||||||||
\(768\) | 7.67722e52 | 0.320643 | ||||||||
\(769\) | 4.26123e53 | 1.73739 | 0.868695 | − | 0.495347i | \(-0.164959\pi\) | ||||
0.868695 | + | 0.495347i | \(0.164959\pi\) | |||||||
\(770\) | −7.16104e52 | −0.285035 | ||||||||
\(771\) | −8.42364e52 | −0.327336 | ||||||||
\(772\) | −2.40630e53 | −0.912913 | ||||||||
\(773\) | −9.95037e52 | −0.368569 | −0.184284 | − | 0.982873i | \(-0.558997\pi\) | ||||
−0.184284 | + | 0.982873i | \(0.558997\pi\) | |||||||
\(774\) | −5.70814e51 | −0.0206437 | ||||||||
\(775\) | −1.30377e53 | −0.460384 | ||||||||
\(776\) | −1.34574e53 | −0.464000 | ||||||||
\(777\) | 1.45283e53 | 0.489132 | ||||||||
\(778\) | 4.23394e52 | 0.139194 | ||||||||
\(779\) | −1.25744e53 | −0.403685 | ||||||||
\(780\) | −1.46330e53 | −0.458757 | ||||||||
\(781\) | −5.69937e53 | −1.74495 | ||||||||
\(782\) | 8.96373e52 | 0.268018 | ||||||||
\(783\) | 8.83971e52 | 0.258134 | ||||||||
\(784\) | 2.76815e53 | 0.789481 | ||||||||
\(785\) | 1.12910e53 | 0.314517 | ||||||||
\(786\) | −4.75149e52 | −0.129274 | ||||||||
\(787\) | 4.51390e53 | 1.19955 | 0.599777 | − | 0.800167i | \(-0.295256\pi\) | ||||
0.599777 | + | 0.800167i | \(0.295256\pi\) | |||||||
\(788\) | −3.11686e53 | −0.809064 | ||||||||
\(789\) | 2.31737e53 | 0.587586 | ||||||||
\(790\) | 6.99096e51 | 0.0173155 | ||||||||
\(791\) | −7.79585e53 | −1.88625 | ||||||||
\(792\) | 6.74240e52 | 0.159367 | ||||||||
\(793\) | 2.49689e52 | 0.0576560 | ||||||||
\(794\) | −8.77088e52 | −0.197863 | ||||||||
\(795\) | −1.50600e53 | −0.331921 | ||||||||
\(796\) | −4.87543e53 | −1.04983 | ||||||||
\(797\) | 3.86364e53 | 0.812864 | 0.406432 | − | 0.913681i | \(-0.366773\pi\) | ||||
0.406432 | + | 0.913681i | \(0.366773\pi\) | |||||||
\(798\) | 2.90542e52 | 0.0597250 | ||||||||
\(799\) | −4.65973e53 | −0.935934 | ||||||||
\(800\) | 9.21502e52 | 0.180856 | ||||||||
\(801\) | −2.09298e53 | −0.401388 | ||||||||
\(802\) | 1.27341e53 | 0.238639 | ||||||||
\(803\) | 4.32036e53 | 0.791192 | ||||||||
\(804\) | −4.71692e53 | −0.844154 | ||||||||
\(805\) | 1.03739e54 | 1.81433 | ||||||||
\(806\) | 1.98847e53 | 0.339877 | ||||||||
\(807\) | −4.47214e53 | −0.747059 | ||||||||
\(808\) | −4.24583e53 | −0.693190 | ||||||||
\(809\) | 8.90010e53 | 1.42019 | 0.710097 | − | 0.704104i | \(-0.248651\pi\) | ||||
0.710097 | + | 0.704104i | \(0.248651\pi\) | |||||||
\(810\) | 1.30874e52 | 0.0204118 | ||||||||
\(811\) | −3.07699e53 | −0.469072 | −0.234536 | − | 0.972107i | \(-0.575357\pi\) | ||||
−0.234536 | + | 0.972107i | \(0.575357\pi\) | |||||||
\(812\) | 1.18741e54 | 1.76935 | ||||||||
\(813\) | 5.92423e53 | 0.862893 | ||||||||
\(814\) | 1.05189e53 | 0.149769 | ||||||||
\(815\) | 6.85980e53 | 0.954763 | ||||||||
\(816\) | −2.86532e53 | −0.389857 | ||||||||
\(817\) | 7.27090e52 | 0.0967119 | ||||||||
\(818\) | −6.36860e52 | −0.0828148 | ||||||||
\(819\) | 3.60816e53 | 0.458705 | ||||||||
\(820\) | −7.60837e53 | −0.945661 | ||||||||
\(821\) | −1.44038e54 | −1.75037 | −0.875185 | − | 0.483789i | \(-0.839260\pi\) | ||||
−0.875185 | + | 0.483789i | \(0.839260\pi\) | |||||||
\(822\) | 1.72742e52 | 0.0205243 | ||||||||
\(823\) | 7.25265e53 | 0.842558 | 0.421279 | − | 0.906931i | \(-0.361581\pi\) | ||||
0.421279 | + | 0.906931i | \(0.361581\pi\) | |||||||
\(824\) | 6.76993e53 | 0.769008 | ||||||||
\(825\) | −1.71287e53 | −0.190251 | ||||||||
\(826\) | −2.55354e53 | −0.277339 | ||||||||
\(827\) | −4.48759e53 | −0.476608 | −0.238304 | − | 0.971191i | \(-0.576592\pi\) | ||||
−0.238304 | + | 0.971191i | \(0.576592\pi\) | |||||||
\(828\) | −4.76408e53 | −0.494786 | ||||||||
\(829\) | −4.38009e53 | −0.444861 | −0.222430 | − | 0.974949i | \(-0.571399\pi\) | ||||
−0.222430 | + | 0.974949i | \(0.571399\pi\) | |||||||
\(830\) | −1.88907e52 | −0.0187630 | ||||||||
\(831\) | −2.23188e53 | −0.216797 | ||||||||
\(832\) | 7.57466e53 | 0.719584 | ||||||||
\(833\) | −7.77892e53 | −0.722748 | ||||||||
\(834\) | −6.31782e52 | −0.0574110 | ||||||||
\(835\) | −8.67658e53 | −0.771167 | ||||||||
\(836\) | −4.18897e53 | −0.364159 | ||||||||
\(837\) | 3.54145e53 | 0.301134 | ||||||||
\(838\) | −3.42854e53 | −0.285164 | ||||||||
\(839\) | −3.60758e53 | −0.293508 | −0.146754 | − | 0.989173i | \(-0.546883\pi\) | ||||
−0.146754 | + | 0.989173i | \(0.546883\pi\) | |||||||
\(840\) | 3.60425e53 | 0.286846 | ||||||||
\(841\) | 1.02642e54 | 0.799095 | ||||||||
\(842\) | −3.91999e53 | −0.298546 | ||||||||
\(843\) | 3.78696e53 | 0.282151 | ||||||||
\(844\) | −7.41156e53 | −0.540225 | ||||||||
\(845\) | 1.56843e52 | 0.0111845 | ||||||||
\(846\) | −1.24368e53 | −0.0867678 | ||||||||
\(847\) | −5.16224e53 | −0.352367 | ||||||||
\(848\) | 8.80025e53 | 0.587722 | ||||||||
\(849\) | −7.76851e53 | −0.507628 | ||||||||
\(850\) | −7.91177e52 | −0.0505852 | ||||||||
\(851\) | −1.52383e54 | −0.953323 | ||||||||
\(852\) | 1.39916e54 | 0.856513 | ||||||||
\(853\) | −3.15083e53 | −0.188742 | −0.0943708 | − | 0.995537i | \(-0.530084\pi\) | ||||
−0.0943708 | + | 0.995537i | \(0.530084\pi\) | |||||||
\(854\) | −2.99972e52 | −0.0175837 | ||||||||
\(855\) | −1.66704e53 | −0.0956255 | ||||||||
\(856\) | 6.34093e53 | 0.355949 | ||||||||
\(857\) | 9.67011e53 | 0.531234 | 0.265617 | − | 0.964079i | \(-0.414424\pi\) | ||||
0.265617 | + | 0.964079i | \(0.414424\pi\) | |||||||
\(858\) | 2.61242e53 | 0.140452 | ||||||||
\(859\) | 3.56564e54 | 1.87614 | 0.938068 | − | 0.346452i | \(-0.112614\pi\) | ||||
0.938068 | + | 0.346452i | \(0.112614\pi\) | |||||||
\(860\) | 4.39940e53 | 0.226554 | ||||||||
\(861\) | 1.87605e54 | 0.945553 | ||||||||
\(862\) | 1.09985e53 | 0.0542564 | ||||||||
\(863\) | −2.25029e54 | −1.08652 | −0.543262 | − | 0.839564i | \(-0.682811\pi\) | ||||
−0.543262 | + | 0.839564i | \(0.682811\pi\) | |||||||
\(864\) | −2.50309e53 | −0.118296 | ||||||||
\(865\) | −1.70096e54 | −0.786860 | ||||||||
\(866\) | 2.73042e53 | 0.123637 | ||||||||
\(867\) | −4.97345e53 | −0.220447 | ||||||||
\(868\) | 4.75711e54 | 2.06409 | ||||||||
\(869\) | 2.48535e53 | 0.105565 | ||||||||
\(870\) | 3.42134e53 | 0.142262 | ||||||||
\(871\) | −3.74703e54 | −1.52529 | ||||||||
\(872\) | 9.45740e53 | 0.376892 | ||||||||
\(873\) | −9.28645e53 | −0.362315 | ||||||||
\(874\) | −3.04741e53 | −0.116404 | ||||||||
\(875\) | −4.02770e54 | −1.50629 | ||||||||
\(876\) | −1.06062e54 | −0.388358 | ||||||||
\(877\) | 4.14049e54 | 1.48443 | 0.742214 | − | 0.670163i | \(-0.233776\pi\) | ||||
0.742214 | + | 0.670163i | \(0.233776\pi\) | |||||||
\(878\) | 2.49385e53 | 0.0875432 | ||||||||
\(879\) | 9.43046e53 | 0.324145 | ||||||||
\(880\) | −2.40095e54 | −0.808077 | ||||||||
\(881\) | 3.03676e54 | 1.00082 | 0.500410 | − | 0.865789i | \(-0.333183\pi\) | ||||
0.500410 | + | 0.865789i | \(0.333183\pi\) | |||||||
\(882\) | −2.07620e53 | −0.0670039 | ||||||||
\(883\) | 2.77430e54 | 0.876760 | 0.438380 | − | 0.898790i | \(-0.355552\pi\) | ||||
0.438380 | + | 0.898790i | \(0.355552\pi\) | |||||||
\(884\) | −2.40288e54 | −0.743645 | ||||||||
\(885\) | 1.46514e54 | 0.444047 | ||||||||
\(886\) | 9.87173e53 | 0.293001 | ||||||||
\(887\) | −9.39883e53 | −0.273204 | −0.136602 | − | 0.990626i | \(-0.543618\pi\) | ||||
−0.136602 | + | 0.990626i | \(0.543618\pi\) | |||||||
\(888\) | −5.29434e53 | −0.150720 | ||||||||
\(889\) | −6.69166e54 | −1.86574 | ||||||||
\(890\) | −8.10072e53 | −0.221212 | ||||||||
\(891\) | 4.65269e53 | 0.124442 | ||||||||
\(892\) | −4.08359e54 | −1.06978 | ||||||||
\(893\) | 1.58418e54 | 0.406491 | ||||||||
\(894\) | −4.28949e53 | −0.107811 | ||||||||
\(895\) | −2.77807e54 | −0.683937 | ||||||||
\(896\) | −4.44117e54 | −1.07102 | ||||||||
\(897\) | −3.78449e54 | −0.894020 | ||||||||
\(898\) | −5.30745e53 | −0.122821 | ||||||||
\(899\) | 9.25814e54 | 2.09879 | ||||||||
\(900\) | 4.20498e53 | 0.0933850 | ||||||||
\(901\) | −2.47301e54 | −0.538043 | ||||||||
\(902\) | 1.35832e54 | 0.289521 | ||||||||
\(903\) | −1.08479e54 | −0.226529 | ||||||||
\(904\) | 2.84092e54 | 0.581224 | ||||||||
\(905\) | 6.71632e54 | 1.34627 | ||||||||
\(906\) | −9.89218e53 | −0.194276 | ||||||||
\(907\) | 2.17105e54 | 0.417767 | 0.208884 | − | 0.977941i | \(-0.433017\pi\) | ||||
0.208884 | + | 0.977941i | \(0.433017\pi\) | |||||||
\(908\) | 2.21911e54 | 0.418400 | ||||||||
\(909\) | −2.92990e54 | −0.541278 | ||||||||
\(910\) | 1.39651e54 | 0.252801 | ||||||||
\(911\) | 7.42098e54 | 1.31635 | 0.658175 | − | 0.752865i | \(-0.271329\pi\) | ||||
0.658175 | + | 0.752865i | \(0.271329\pi\) | |||||||
\(912\) | 9.74127e53 | 0.169321 | ||||||||
\(913\) | −6.71581e53 | −0.114390 | ||||||||
\(914\) | −1.22681e54 | −0.204772 | ||||||||
\(915\) | 1.72115e53 | 0.0281532 | ||||||||
\(916\) | 6.15912e53 | 0.0987307 | ||||||||
\(917\) | −9.02986e54 | −1.41856 | ||||||||
\(918\) | 2.14908e53 | 0.0330875 | ||||||||
\(919\) | 6.80622e54 | 1.02700 | 0.513498 | − | 0.858091i | \(-0.328349\pi\) | ||||
0.513498 | + | 0.858091i | \(0.328349\pi\) | |||||||
\(920\) | −3.78039e54 | −0.559065 | ||||||||
\(921\) | −2.02958e54 | −0.294172 | ||||||||
\(922\) | −1.69450e54 | −0.240724 | ||||||||
\(923\) | 1.11146e55 | 1.54762 | ||||||||
\(924\) | 6.24979e54 | 0.852971 | ||||||||
\(925\) | 1.34500e54 | 0.179928 | ||||||||
\(926\) | −1.61660e54 | −0.211982 | ||||||||
\(927\) | 4.67169e54 | 0.600481 | ||||||||
\(928\) | −6.54362e54 | −0.824481 | ||||||||
\(929\) | −6.45233e54 | −0.796940 | −0.398470 | − | 0.917181i | \(-0.630459\pi\) | ||||
−0.398470 | + | 0.917181i | \(0.630459\pi\) | |||||||
\(930\) | 1.37069e54 | 0.165961 | ||||||||
\(931\) | 2.64461e54 | 0.313901 | ||||||||
\(932\) | −1.16724e55 | −1.35821 | ||||||||
\(933\) | −7.03648e54 | −0.802685 | ||||||||
\(934\) | 1.21522e54 | 0.135905 | ||||||||
\(935\) | 6.74703e54 | 0.739772 | ||||||||
\(936\) | −1.31487e54 | −0.141344 | ||||||||
\(937\) | 7.02165e53 | 0.0740042 | 0.0370021 | − | 0.999315i | \(-0.488219\pi\) | ||||
0.0370021 | + | 0.999315i | \(0.488219\pi\) | |||||||
\(938\) | 4.50162e54 | 0.465175 | ||||||||
\(939\) | −4.90154e53 | −0.0496614 | ||||||||
\(940\) | 9.58538e54 | 0.952234 | ||||||||
\(941\) | −8.40171e53 | −0.0818388 | −0.0409194 | − | 0.999162i | \(-0.513029\pi\) | ||||
−0.0409194 | + | 0.999162i | \(0.513029\pi\) | |||||||
\(942\) | 4.94859e53 | 0.0472650 | ||||||||
\(943\) | −1.96773e55 | −1.84289 | ||||||||
\(944\) | −8.56148e54 | −0.786261 | ||||||||
\(945\) | 2.48717e54 | 0.223984 | ||||||||
\(946\) | −7.85423e53 | −0.0693613 | ||||||||
\(947\) | −7.39324e54 | −0.640266 | −0.320133 | − | 0.947373i | \(-0.603728\pi\) | ||||
−0.320133 | + | 0.947373i | \(0.603728\pi\) | |||||||
\(948\) | −6.10136e53 | −0.0518170 | ||||||||
\(949\) | −8.42534e54 | −0.701718 | ||||||||
\(950\) | 2.68977e53 | 0.0219700 | ||||||||
\(951\) | −4.37573e54 | −0.350519 | ||||||||
\(952\) | 5.91854e54 | 0.464977 | ||||||||
\(953\) | −2.15051e55 | −1.65700 | −0.828499 | − | 0.559990i | \(-0.810805\pi\) | ||||
−0.828499 | + | 0.559990i | \(0.810805\pi\) | |||||||
\(954\) | −6.60047e53 | −0.0498804 | ||||||||
\(955\) | 5.56319e54 | 0.412345 | ||||||||
\(956\) | 9.23775e54 | 0.671576 | ||||||||
\(957\) | 1.21632e55 | 0.867312 | ||||||||
\(958\) | 1.60136e54 | 0.112002 | ||||||||
\(959\) | 3.28283e54 | 0.225219 | ||||||||
\(960\) | 5.22135e54 | 0.351370 | ||||||||
\(961\) | 2.19419e55 | 1.44841 | ||||||||
\(962\) | −2.05135e54 | −0.132832 | ||||||||
\(963\) | 4.37565e54 | 0.277944 | ||||||||
\(964\) | 1.35735e55 | 0.845797 | ||||||||
\(965\) | −1.31764e55 | −0.805457 | ||||||||
\(966\) | 4.54663e54 | 0.272655 | ||||||||
\(967\) | 1.31747e55 | 0.775085 | 0.387543 | − | 0.921852i | \(-0.373324\pi\) | ||||
0.387543 | + | 0.921852i | \(0.373324\pi\) | |||||||
\(968\) | 1.88120e54 | 0.108578 | ||||||||
\(969\) | −2.73745e54 | −0.155009 | ||||||||
\(970\) | −3.59425e54 | −0.199678 | ||||||||
\(971\) | 8.47915e54 | 0.462164 | 0.231082 | − | 0.972934i | \(-0.425773\pi\) | ||||
0.231082 | + | 0.972934i | \(0.425773\pi\) | |||||||
\(972\) | −1.14220e54 | −0.0610826 | ||||||||
\(973\) | −1.20066e55 | −0.629987 | ||||||||
\(974\) | 1.75054e54 | 0.0901220 | ||||||||
\(975\) | 3.34035e54 | 0.168736 | ||||||||
\(976\) | −1.00574e54 | −0.0498500 | ||||||||
\(977\) | 1.06113e55 | 0.516080 | 0.258040 | − | 0.966134i | \(-0.416923\pi\) | ||||
0.258040 | + | 0.966134i | \(0.416923\pi\) | |||||||
\(978\) | 3.00649e54 | 0.143480 | ||||||||
\(979\) | −2.87988e55 | −1.34863 | ||||||||
\(980\) | 1.60018e55 | 0.735335 | ||||||||
\(981\) | 6.52622e54 | 0.294297 | ||||||||
\(982\) | −3.46480e54 | −0.153326 | ||||||||
\(983\) | 1.52477e54 | 0.0662161 | 0.0331081 | − | 0.999452i | \(-0.489459\pi\) | ||||
0.0331081 | + | 0.999452i | \(0.489459\pi\) | |||||||
\(984\) | −6.83661e54 | −0.291361 | ||||||||
\(985\) | −1.70673e55 | −0.713831 | ||||||||
\(986\) | 5.61818e54 | 0.230607 | ||||||||
\(987\) | −2.36353e55 | −0.952126 | ||||||||
\(988\) | 8.16912e54 | 0.322977 | ||||||||
\(989\) | 1.13781e55 | 0.441506 | ||||||||
\(990\) | 1.80079e54 | 0.0685822 | ||||||||
\(991\) | 2.88078e55 | 1.07683 | 0.538416 | − | 0.842679i | \(-0.319023\pi\) | ||||
0.538416 | + | 0.842679i | \(0.319023\pi\) | |||||||
\(992\) | −2.62157e55 | −0.961825 | ||||||||
\(993\) | −1.39666e55 | −0.502956 | ||||||||
\(994\) | −1.33529e55 | −0.471986 | ||||||||
\(995\) | −2.66969e55 | −0.926262 | ||||||||
\(996\) | 1.64868e54 | 0.0561487 | ||||||||
\(997\) | −2.89753e55 | −0.968651 | −0.484326 | − | 0.874888i | \(-0.660935\pi\) | ||||
−0.484326 | + | 0.874888i | \(0.660935\pi\) | |||||||
\(998\) | 5.28813e54 | 0.173535 | ||||||||
\(999\) | −3.65344e54 | −0.117690 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3.38.a.b.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 9.38.a.c.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.38.a.b.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.38.a.c.1.3 | 4 | 3.2 | odd | 2 |