Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,10,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, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(1.54510750849\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −36.0000 | −1.59099 | −0.795495 | − | 0.605960i | \(-0.792789\pi\) | ||||
−0.795495 | + | 0.605960i | \(0.792789\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 784.000 | 1.53125 | ||||||||
\(5\) | −1314.00 | −0.940222 | −0.470111 | − | 0.882607i | \(-0.655786\pi\) | ||||
−0.470111 | + | 0.882607i | \(0.655786\pi\) | |||||||
\(6\) | 2916.00 | 0.918559 | ||||||||
\(7\) | −4480.00 | −0.705240 | −0.352620 | − | 0.935767i | \(-0.614709\pi\) | ||||
−0.352620 | + | 0.935767i | \(0.614709\pi\) | |||||||
\(8\) | −9792.00 | −0.845214 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 47304.0 | 1.49588 | ||||||||
\(11\) | 1476.00 | 0.0303962 | 0.0151981 | − | 0.999885i | \(-0.495162\pi\) | ||||
0.0151981 | + | 0.999885i | \(0.495162\pi\) | |||||||
\(12\) | −63504.0 | −0.884068 | ||||||||
\(13\) | −151522. | −1.47140 | −0.735700 | − | 0.677308i | \(-0.763147\pi\) | ||||
−0.735700 | + | 0.677308i | \(0.763147\pi\) | |||||||
\(14\) | 161280. | 1.12203 | ||||||||
\(15\) | 106434. | 0.542837 | ||||||||
\(16\) | −48896.0 | −0.186523 | ||||||||
\(17\) | 108162. | 0.314090 | 0.157045 | − | 0.987591i | \(-0.449803\pi\) | ||||
0.157045 | + | 0.987591i | \(0.449803\pi\) | |||||||
\(18\) | −236196. | −0.530330 | ||||||||
\(19\) | 593084. | 1.04406 | 0.522029 | − | 0.852927i | \(-0.325175\pi\) | ||||
0.522029 | + | 0.852927i | \(0.325175\pi\) | |||||||
\(20\) | −1.03018e6 | −1.43971 | ||||||||
\(21\) | 362880. | 0.407170 | ||||||||
\(22\) | −53136.0 | −0.0483601 | ||||||||
\(23\) | −969480. | −0.722376 | −0.361188 | − | 0.932493i | \(-0.617629\pi\) | ||||
−0.361188 | + | 0.932493i | \(0.617629\pi\) | |||||||
\(24\) | 793152. | 0.487984 | ||||||||
\(25\) | −226529. | −0.115983 | ||||||||
\(26\) | 5.45479e6 | 2.34098 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −3.51232e6 | −1.07990 | ||||||||
\(29\) | −6.64252e6 | −1.74398 | −0.871991 | − | 0.489522i | \(-0.837171\pi\) | ||||
−0.871991 | + | 0.489522i | \(0.837171\pi\) | |||||||
\(30\) | −3.83162e6 | −0.863649 | ||||||||
\(31\) | 7.07060e6 | 1.37508 | 0.687541 | − | 0.726145i | \(-0.258690\pi\) | ||||
0.687541 | + | 0.726145i | \(0.258690\pi\) | |||||||
\(32\) | 6.77376e6 | 1.14197 | ||||||||
\(33\) | −119556. | −0.0175493 | ||||||||
\(34\) | −3.89383e6 | −0.499715 | ||||||||
\(35\) | 5.88672e6 | 0.663082 | ||||||||
\(36\) | 5.14382e6 | 0.510417 | ||||||||
\(37\) | −7.47241e6 | −0.655470 | −0.327735 | − | 0.944770i | \(-0.606285\pi\) | ||||
−0.327735 | + | 0.944770i | \(0.606285\pi\) | |||||||
\(38\) | −2.13510e7 | −1.66109 | ||||||||
\(39\) | 1.22733e7 | 0.849513 | ||||||||
\(40\) | 1.28667e7 | 0.794688 | ||||||||
\(41\) | −4.35015e6 | −0.240423 | −0.120212 | − | 0.992748i | \(-0.538357\pi\) | ||||
−0.120212 | + | 0.992748i | \(0.538357\pi\) | |||||||
\(42\) | −1.30637e7 | −0.647804 | ||||||||
\(43\) | −4.35872e6 | −0.194424 | −0.0972121 | − | 0.995264i | \(-0.530993\pi\) | ||||
−0.0972121 | + | 0.995264i | \(0.530993\pi\) | |||||||
\(44\) | 1.15718e6 | 0.0465442 | ||||||||
\(45\) | −8.62115e6 | −0.313407 | ||||||||
\(46\) | 3.49013e7 | 1.14929 | ||||||||
\(47\) | 2.83092e7 | 0.846229 | 0.423115 | − | 0.906076i | \(-0.360937\pi\) | ||||
0.423115 | + | 0.906076i | \(0.360937\pi\) | |||||||
\(48\) | 3.96058e6 | 0.107689 | ||||||||
\(49\) | −2.02832e7 | −0.502637 | ||||||||
\(50\) | 8.15504e6 | 0.184528 | ||||||||
\(51\) | −8.76112e6 | −0.181340 | ||||||||
\(52\) | −1.18793e8 | −2.25308 | ||||||||
\(53\) | 1.61117e7 | 0.280479 | 0.140239 | − | 0.990118i | \(-0.455213\pi\) | ||||
0.140239 | + | 0.990118i | \(0.455213\pi\) | |||||||
\(54\) | 1.91319e7 | 0.306186 | ||||||||
\(55\) | −1.93946e6 | −0.0285792 | ||||||||
\(56\) | 4.38682e7 | 0.596078 | ||||||||
\(57\) | −4.80398e7 | −0.602788 | ||||||||
\(58\) | 2.39131e8 | 2.77466 | ||||||||
\(59\) | −8.60760e7 | −0.924800 | −0.462400 | − | 0.886671i | \(-0.653012\pi\) | ||||
−0.462400 | + | 0.886671i | \(0.653012\pi\) | |||||||
\(60\) | 8.34443e7 | 0.831220 | ||||||||
\(61\) | 3.22139e7 | 0.297892 | 0.148946 | − | 0.988845i | \(-0.452412\pi\) | ||||
0.148946 | + | 0.988845i | \(0.452412\pi\) | |||||||
\(62\) | −2.54542e8 | −2.18774 | ||||||||
\(63\) | −2.93933e7 | −0.235080 | ||||||||
\(64\) | −2.18821e8 | −1.63034 | ||||||||
\(65\) | 1.99100e8 | 1.38344 | ||||||||
\(66\) | 4.30402e6 | 0.0279207 | ||||||||
\(67\) | 9.95315e7 | 0.603426 | 0.301713 | − | 0.953399i | \(-0.402442\pi\) | ||||
0.301713 | + | 0.953399i | \(0.402442\pi\) | |||||||
\(68\) | 8.47990e7 | 0.480951 | ||||||||
\(69\) | 7.85279e7 | 0.417064 | ||||||||
\(70\) | −2.11922e8 | −1.05496 | ||||||||
\(71\) | −4.41705e7 | −0.206286 | −0.103143 | − | 0.994667i | \(-0.532890\pi\) | ||||
−0.103143 | + | 0.994667i | \(0.532890\pi\) | |||||||
\(72\) | −6.42453e7 | −0.281738 | ||||||||
\(73\) | −2.35606e7 | −0.0971033 | −0.0485517 | − | 0.998821i | \(-0.515461\pi\) | ||||
−0.0485517 | + | 0.998821i | \(0.515461\pi\) | |||||||
\(74\) | 2.69007e8 | 1.04285 | ||||||||
\(75\) | 1.83488e7 | 0.0669627 | ||||||||
\(76\) | 4.64978e8 | 1.59872 | ||||||||
\(77\) | −6.61248e6 | −0.0214366 | ||||||||
\(78\) | −4.41838e8 | −1.35157 | ||||||||
\(79\) | −4.01755e8 | −1.16048 | −0.580242 | − | 0.814444i | \(-0.697042\pi\) | ||||
−0.580242 | + | 0.814444i | \(0.697042\pi\) | |||||||
\(80\) | 6.42493e7 | 0.175373 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 1.56605e8 | 0.382511 | ||||||||
\(83\) | −7.44529e8 | −1.72199 | −0.860994 | − | 0.508615i | \(-0.830158\pi\) | ||||
−0.860994 | + | 0.508615i | \(0.830158\pi\) | |||||||
\(84\) | 2.84498e8 | 0.623480 | ||||||||
\(85\) | −1.42125e8 | −0.295315 | ||||||||
\(86\) | 1.56914e8 | 0.309327 | ||||||||
\(87\) | 5.38044e8 | 1.00689 | ||||||||
\(88\) | −1.44530e7 | −0.0256913 | ||||||||
\(89\) | 7.69871e8 | 1.30066 | 0.650329 | − | 0.759653i | \(-0.274631\pi\) | ||||
0.650329 | + | 0.759653i | \(0.274631\pi\) | |||||||
\(90\) | 3.10362e8 | 0.498628 | ||||||||
\(91\) | 6.78819e8 | 1.03769 | ||||||||
\(92\) | −7.60072e8 | −1.10614 | ||||||||
\(93\) | −5.72719e8 | −0.793904 | ||||||||
\(94\) | −1.01913e9 | −1.34634 | ||||||||
\(95\) | −7.79312e8 | −0.981647 | ||||||||
\(96\) | −5.48675e8 | −0.659317 | ||||||||
\(97\) | 9.07131e8 | 1.04039 | 0.520196 | − | 0.854047i | \(-0.325859\pi\) | ||||
0.520196 | + | 0.854047i | \(0.325859\pi\) | |||||||
\(98\) | 7.30195e8 | 0.799690 | ||||||||
\(99\) | 9.68404e6 | 0.0101321 | ||||||||
\(100\) | −1.77599e8 | −0.177599 | ||||||||
\(101\) | −4.21902e8 | −0.403427 | −0.201714 | − | 0.979445i | \(-0.564651\pi\) | ||||
−0.201714 | + | 0.979445i | \(0.564651\pi\) | |||||||
\(102\) | 3.15400e8 | 0.288510 | ||||||||
\(103\) | 5.79043e8 | 0.506924 | 0.253462 | − | 0.967345i | \(-0.418431\pi\) | ||||
0.253462 | + | 0.967345i | \(0.418431\pi\) | |||||||
\(104\) | 1.48370e9 | 1.24365 | ||||||||
\(105\) | −4.76824e8 | −0.382831 | ||||||||
\(106\) | −5.80022e8 | −0.446239 | ||||||||
\(107\) | 1.39714e9 | 1.03042 | 0.515208 | − | 0.857065i | \(-0.327715\pi\) | ||||
0.515208 | + | 0.857065i | \(0.327715\pi\) | |||||||
\(108\) | −4.16650e8 | −0.294689 | ||||||||
\(109\) | −2.68530e9 | −1.82211 | −0.911054 | − | 0.412286i | \(-0.864730\pi\) | ||||
−0.911054 | + | 0.412286i | \(0.864730\pi\) | |||||||
\(110\) | 6.98207e7 | 0.0454692 | ||||||||
\(111\) | 6.05265e8 | 0.378436 | ||||||||
\(112\) | 2.19054e8 | 0.131544 | ||||||||
\(113\) | 4.54749e8 | 0.262373 | 0.131186 | − | 0.991358i | \(-0.458121\pi\) | ||||
0.131186 | + | 0.991358i | \(0.458121\pi\) | |||||||
\(114\) | 1.72943e9 | 0.959029 | ||||||||
\(115\) | 1.27390e9 | 0.679194 | ||||||||
\(116\) | −5.20774e9 | −2.67047 | ||||||||
\(117\) | −9.94136e8 | −0.490467 | ||||||||
\(118\) | 3.09873e9 | 1.47135 | ||||||||
\(119\) | −4.84566e8 | −0.221509 | ||||||||
\(120\) | −1.04220e9 | −0.458813 | ||||||||
\(121\) | −2.35577e9 | −0.999076 | ||||||||
\(122\) | −1.15970e9 | −0.473944 | ||||||||
\(123\) | 3.52362e8 | 0.138809 | ||||||||
\(124\) | 5.54335e9 | 2.10559 | ||||||||
\(125\) | 2.86407e9 | 1.04927 | ||||||||
\(126\) | 1.05816e9 | 0.374010 | ||||||||
\(127\) | −8.38650e7 | −0.0286064 | −0.0143032 | − | 0.999898i | \(-0.504553\pi\) | ||||
−0.0143032 | + | 0.999898i | \(0.504553\pi\) | |||||||
\(128\) | 4.40938e9 | 1.45189 | ||||||||
\(129\) | 3.53056e8 | 0.112251 | ||||||||
\(130\) | −7.16760e9 | −2.20104 | ||||||||
\(131\) | −3.73601e9 | −1.10838 | −0.554188 | − | 0.832391i | \(-0.686971\pi\) | ||||
−0.554188 | + | 0.832391i | \(0.686971\pi\) | |||||||
\(132\) | −9.37319e7 | −0.0268723 | ||||||||
\(133\) | −2.65702e9 | −0.736312 | ||||||||
\(134\) | −3.58313e9 | −0.960044 | ||||||||
\(135\) | 6.98313e8 | 0.180946 | ||||||||
\(136\) | −1.05912e9 | −0.265473 | ||||||||
\(137\) | 6.43598e9 | 1.56089 | 0.780444 | − | 0.625225i | \(-0.214993\pi\) | ||||
0.780444 | + | 0.625225i | \(0.214993\pi\) | |||||||
\(138\) | −2.82700e9 | −0.663545 | ||||||||
\(139\) | 1.81833e9 | 0.413148 | 0.206574 | − | 0.978431i | \(-0.433769\pi\) | ||||
0.206574 | + | 0.978431i | \(0.433769\pi\) | |||||||
\(140\) | 4.61519e9 | 1.01534 | ||||||||
\(141\) | −2.29305e9 | −0.488571 | ||||||||
\(142\) | 1.59014e9 | 0.328199 | ||||||||
\(143\) | −2.23646e8 | −0.0447250 | ||||||||
\(144\) | −3.20807e8 | −0.0621745 | ||||||||
\(145\) | 8.72827e9 | 1.63973 | ||||||||
\(146\) | 8.48183e8 | 0.154490 | ||||||||
\(147\) | 1.64294e9 | 0.290197 | ||||||||
\(148\) | −5.85837e9 | −1.00369 | ||||||||
\(149\) | −8.30199e9 | −1.37989 | −0.689944 | − | 0.723863i | \(-0.742365\pi\) | ||||
−0.689944 | + | 0.723863i | \(0.742365\pi\) | |||||||
\(150\) | −6.60559e8 | −0.106537 | ||||||||
\(151\) | 3.84057e9 | 0.601173 | 0.300587 | − | 0.953755i | \(-0.402818\pi\) | ||||
0.300587 | + | 0.953755i | \(0.402818\pi\) | |||||||
\(152\) | −5.80748e9 | −0.882453 | ||||||||
\(153\) | 7.09651e8 | 0.104697 | ||||||||
\(154\) | 2.38049e8 | 0.0341054 | ||||||||
\(155\) | −9.29077e9 | −1.29288 | ||||||||
\(156\) | 9.62225e9 | 1.30082 | ||||||||
\(157\) | −2.17912e9 | −0.286242 | −0.143121 | − | 0.989705i | \(-0.545714\pi\) | ||||
−0.143121 | + | 0.989705i | \(0.545714\pi\) | |||||||
\(158\) | 1.44632e10 | 1.84632 | ||||||||
\(159\) | −1.30505e9 | −0.161935 | ||||||||
\(160\) | −8.90072e9 | −1.07371 | ||||||||
\(161\) | 4.34327e9 | 0.509449 | ||||||||
\(162\) | −1.54968e9 | −0.176777 | ||||||||
\(163\) | −1.54147e10 | −1.71038 | −0.855188 | − | 0.518317i | \(-0.826559\pi\) | ||||
−0.855188 | + | 0.518317i | \(0.826559\pi\) | |||||||
\(164\) | −3.41052e9 | −0.368148 | ||||||||
\(165\) | 1.57097e8 | 0.0165002 | ||||||||
\(166\) | 2.68030e10 | 2.73967 | ||||||||
\(167\) | −5.65506e9 | −0.562617 | −0.281309 | − | 0.959617i | \(-0.590768\pi\) | ||||
−0.281309 | + | 0.959617i | \(0.590768\pi\) | |||||||
\(168\) | −3.55332e9 | −0.344146 | ||||||||
\(169\) | 1.23544e10 | 1.16502 | ||||||||
\(170\) | 5.11650e9 | 0.469843 | ||||||||
\(171\) | 3.89122e9 | 0.348020 | ||||||||
\(172\) | −3.41723e9 | −0.297712 | ||||||||
\(173\) | 7.69892e7 | 0.00653465 | 0.00326733 | − | 0.999995i | \(-0.498960\pi\) | ||||
0.00326733 | + | 0.999995i | \(0.498960\pi\) | |||||||
\(174\) | −1.93696e10 | −1.60195 | ||||||||
\(175\) | 1.01485e9 | 0.0817957 | ||||||||
\(176\) | −7.21705e7 | −0.00566960 | ||||||||
\(177\) | 6.97215e9 | 0.533934 | ||||||||
\(178\) | −2.77154e10 | −2.06933 | ||||||||
\(179\) | 2.32247e10 | 1.69087 | 0.845436 | − | 0.534077i | \(-0.179341\pi\) | ||||
0.845436 | + | 0.534077i | \(0.179341\pi\) | |||||||
\(180\) | −6.75898e9 | −0.479905 | ||||||||
\(181\) | −1.23532e10 | −0.855513 | −0.427756 | − | 0.903894i | \(-0.640696\pi\) | ||||
−0.427756 | + | 0.903894i | \(0.640696\pi\) | |||||||
\(182\) | −2.44375e10 | −1.65095 | ||||||||
\(183\) | −2.60933e9 | −0.171988 | ||||||||
\(184\) | 9.49315e9 | 0.610562 | ||||||||
\(185\) | 9.81875e9 | 0.616287 | ||||||||
\(186\) | 2.06179e10 | 1.26309 | ||||||||
\(187\) | 1.59647e8 | 0.00954715 | ||||||||
\(188\) | 2.21945e10 | 1.29579 | ||||||||
\(189\) | 2.38086e9 | 0.135723 | ||||||||
\(190\) | 2.80552e10 | 1.56179 | ||||||||
\(191\) | −4.20433e9 | −0.228584 | −0.114292 | − | 0.993447i | \(-0.536460\pi\) | ||||
−0.114292 | + | 0.993447i | \(0.536460\pi\) | |||||||
\(192\) | 1.77245e10 | 0.941278 | ||||||||
\(193\) | −4.38611e9 | −0.227547 | −0.113774 | − | 0.993507i | \(-0.536294\pi\) | ||||
−0.113774 | + | 0.993507i | \(0.536294\pi\) | |||||||
\(194\) | −3.26567e10 | −1.65525 | ||||||||
\(195\) | −1.61271e10 | −0.798731 | ||||||||
\(196\) | −1.59020e10 | −0.769663 | ||||||||
\(197\) | −3.36694e10 | −1.59271 | −0.796356 | − | 0.604828i | \(-0.793242\pi\) | ||||
−0.796356 | + | 0.604828i | \(0.793242\pi\) | |||||||
\(198\) | −3.48625e8 | −0.0161200 | ||||||||
\(199\) | 1.02732e10 | 0.464374 | 0.232187 | − | 0.972671i | \(-0.425412\pi\) | ||||
0.232187 | + | 0.972671i | \(0.425412\pi\) | |||||||
\(200\) | 2.21817e9 | 0.0980303 | ||||||||
\(201\) | −8.06205e9 | −0.348388 | ||||||||
\(202\) | 1.51885e10 | 0.641849 | ||||||||
\(203\) | 2.97585e10 | 1.22993 | ||||||||
\(204\) | −6.86872e9 | −0.277677 | ||||||||
\(205\) | 5.71610e9 | 0.226051 | ||||||||
\(206\) | −2.08455e10 | −0.806512 | ||||||||
\(207\) | −6.36076e9 | −0.240792 | ||||||||
\(208\) | 7.40882e9 | 0.274450 | ||||||||
\(209\) | 8.75392e8 | 0.0317354 | ||||||||
\(210\) | 1.71657e10 | 0.609080 | ||||||||
\(211\) | 7.96696e9 | 0.276708 | 0.138354 | − | 0.990383i | \(-0.455819\pi\) | ||||
0.138354 | + | 0.990383i | \(0.455819\pi\) | |||||||
\(212\) | 1.26316e10 | 0.429483 | ||||||||
\(213\) | 3.57781e9 | 0.119099 | ||||||||
\(214\) | −5.02970e10 | −1.63938 | ||||||||
\(215\) | 5.72735e9 | 0.182802 | ||||||||
\(216\) | 5.20387e9 | 0.162661 | ||||||||
\(217\) | −3.16763e10 | −0.969763 | ||||||||
\(218\) | 9.66710e10 | 2.89896 | ||||||||
\(219\) | 1.90841e9 | 0.0560626 | ||||||||
\(220\) | −1.52054e9 | −0.0437619 | ||||||||
\(221\) | −1.63889e10 | −0.462152 | ||||||||
\(222\) | −2.17895e10 | −0.602088 | ||||||||
\(223\) | 6.96581e9 | 0.188625 | 0.0943126 | − | 0.995543i | \(-0.469935\pi\) | ||||
0.0943126 | + | 0.995543i | \(0.469935\pi\) | |||||||
\(224\) | −3.03464e10 | −0.805363 | ||||||||
\(225\) | −1.48626e9 | −0.0386609 | ||||||||
\(226\) | −1.63709e10 | −0.417432 | ||||||||
\(227\) | 3.35697e10 | 0.839133 | 0.419567 | − | 0.907725i | \(-0.362182\pi\) | ||||
0.419567 | + | 0.907725i | \(0.362182\pi\) | |||||||
\(228\) | −3.76632e10 | −0.923019 | ||||||||
\(229\) | 2.93198e10 | 0.704534 | 0.352267 | − | 0.935900i | \(-0.385411\pi\) | ||||
0.352267 | + | 0.935900i | \(0.385411\pi\) | |||||||
\(230\) | −4.58603e10 | −1.08059 | ||||||||
\(231\) | 5.35611e8 | 0.0123764 | ||||||||
\(232\) | 6.50436e10 | 1.47404 | ||||||||
\(233\) | −8.20079e10 | −1.82286 | −0.911431 | − | 0.411453i | \(-0.865022\pi\) | ||||
−0.911431 | + | 0.411453i | \(0.865022\pi\) | |||||||
\(234\) | 3.57889e10 | 0.780327 | ||||||||
\(235\) | −3.71984e10 | −0.795643 | ||||||||
\(236\) | −6.74836e10 | −1.41610 | ||||||||
\(237\) | 3.25421e10 | 0.670006 | ||||||||
\(238\) | 1.74444e10 | 0.352419 | ||||||||
\(239\) | 6.26609e10 | 1.24224 | 0.621121 | − | 0.783715i | \(-0.286677\pi\) | ||||
0.621121 | + | 0.783715i | \(0.286677\pi\) | |||||||
\(240\) | −5.20420e9 | −0.101252 | ||||||||
\(241\) | 7.75548e10 | 1.48092 | 0.740460 | − | 0.672100i | \(-0.234608\pi\) | ||||
0.740460 | + | 0.672100i | \(0.234608\pi\) | |||||||
\(242\) | 8.48077e10 | 1.58952 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 2.52557e10 | 0.456148 | ||||||||
\(245\) | 2.66521e10 | 0.472590 | ||||||||
\(246\) | −1.26850e10 | −0.220843 | ||||||||
\(247\) | −8.98653e10 | −1.53623 | ||||||||
\(248\) | −6.92353e10 | −1.16224 | ||||||||
\(249\) | 6.03068e10 | 0.994190 | ||||||||
\(250\) | −1.03106e11 | −1.66938 | ||||||||
\(251\) | −5.81901e10 | −0.925374 | −0.462687 | − | 0.886522i | \(-0.653115\pi\) | ||||
−0.462687 | + | 0.886522i | \(0.653115\pi\) | |||||||
\(252\) | −2.30443e10 | −0.359966 | ||||||||
\(253\) | −1.43095e9 | −0.0219575 | ||||||||
\(254\) | 3.01914e9 | 0.0455126 | ||||||||
\(255\) | 1.15121e10 | 0.170500 | ||||||||
\(256\) | −4.67014e10 | −0.679595 | ||||||||
\(257\) | −7.41485e9 | −0.106024 | −0.0530119 | − | 0.998594i | \(-0.516882\pi\) | ||||
−0.0530119 | + | 0.998594i | \(0.516882\pi\) | |||||||
\(258\) | −1.27100e10 | −0.178590 | ||||||||
\(259\) | 3.34764e10 | 0.462264 | ||||||||
\(260\) | 1.56094e11 | 2.11840 | ||||||||
\(261\) | −4.35816e10 | −0.581327 | ||||||||
\(262\) | 1.34496e11 | 1.76342 | ||||||||
\(263\) | −1.05271e11 | −1.35677 | −0.678387 | − | 0.734705i | \(-0.737321\pi\) | ||||
−0.678387 | + | 0.734705i | \(0.737321\pi\) | |||||||
\(264\) | 1.17069e9 | 0.0148329 | ||||||||
\(265\) | −2.11708e10 | −0.263712 | ||||||||
\(266\) | 9.56526e10 | 1.17147 | ||||||||
\(267\) | −6.23596e10 | −0.750935 | ||||||||
\(268\) | 7.80327e10 | 0.923995 | ||||||||
\(269\) | 4.67239e10 | 0.544069 | 0.272034 | − | 0.962288i | \(-0.412304\pi\) | ||||
0.272034 | + | 0.962288i | \(0.412304\pi\) | |||||||
\(270\) | −2.51393e10 | −0.287883 | ||||||||
\(271\) | 2.86868e10 | 0.323087 | 0.161544 | − | 0.986866i | \(-0.448353\pi\) | ||||
0.161544 | + | 0.986866i | \(0.448353\pi\) | |||||||
\(272\) | −5.28869e9 | −0.0585852 | ||||||||
\(273\) | −5.49843e10 | −0.599110 | ||||||||
\(274\) | −2.31695e11 | −2.48336 | ||||||||
\(275\) | −3.34357e8 | −0.00352544 | ||||||||
\(276\) | 6.15659e10 | 0.638630 | ||||||||
\(277\) | 8.50676e10 | 0.868171 | 0.434085 | − | 0.900872i | \(-0.357072\pi\) | ||||
0.434085 | + | 0.900872i | \(0.357072\pi\) | |||||||
\(278\) | −6.54598e10 | −0.657314 | ||||||||
\(279\) | 4.63902e10 | 0.458361 | ||||||||
\(280\) | −5.76428e10 | −0.560446 | ||||||||
\(281\) | −7.87257e8 | −0.00753248 | −0.00376624 | − | 0.999993i | \(-0.501199\pi\) | ||||
−0.00376624 | + | 0.999993i | \(0.501199\pi\) | |||||||
\(282\) | 8.25498e10 | 0.777311 | ||||||||
\(283\) | 2.48961e10 | 0.230724 | 0.115362 | − | 0.993324i | \(-0.463197\pi\) | ||||
0.115362 | + | 0.993324i | \(0.463197\pi\) | |||||||
\(284\) | −3.46297e10 | −0.315875 | ||||||||
\(285\) | 6.31243e10 | 0.566754 | ||||||||
\(286\) | 8.05127e9 | 0.0711570 | ||||||||
\(287\) | 1.94887e10 | 0.169556 | ||||||||
\(288\) | 4.44426e10 | 0.380657 | ||||||||
\(289\) | −1.06889e11 | −0.901347 | ||||||||
\(290\) | −3.14218e11 | −2.60879 | ||||||||
\(291\) | −7.34776e10 | −0.600671 | ||||||||
\(292\) | −1.84715e10 | −0.148689 | ||||||||
\(293\) | 1.57074e11 | 1.24509 | 0.622543 | − | 0.782586i | \(-0.286100\pi\) | ||||
0.622543 | + | 0.782586i | \(0.286100\pi\) | |||||||
\(294\) | −5.91458e10 | −0.461701 | ||||||||
\(295\) | 1.13104e11 | 0.869517 | ||||||||
\(296\) | 7.31698e10 | 0.554012 | ||||||||
\(297\) | −7.84407e8 | −0.00584975 | ||||||||
\(298\) | 2.98871e11 | 2.19539 | ||||||||
\(299\) | 1.46898e11 | 1.06290 | ||||||||
\(300\) | 1.43855e10 | 0.102537 | ||||||||
\(301\) | 1.95270e10 | 0.137116 | ||||||||
\(302\) | −1.38261e11 | −0.956461 | ||||||||
\(303\) | 3.41741e10 | 0.232919 | ||||||||
\(304\) | −2.89994e10 | −0.194741 | ||||||||
\(305\) | −4.23291e10 | −0.280085 | ||||||||
\(306\) | −2.55474e10 | −0.166572 | ||||||||
\(307\) | −2.45737e11 | −1.57887 | −0.789437 | − | 0.613831i | \(-0.789628\pi\) | ||||
−0.789437 | + | 0.613831i | \(0.789628\pi\) | |||||||
\(308\) | −5.18418e9 | −0.0328248 | ||||||||
\(309\) | −4.69025e10 | −0.292673 | ||||||||
\(310\) | 3.34468e11 | 2.05696 | ||||||||
\(311\) | −1.61050e11 | −0.976201 | −0.488101 | − | 0.872787i | \(-0.662310\pi\) | ||||
−0.488101 | + | 0.872787i | \(0.662310\pi\) | |||||||
\(312\) | −1.20180e11 | −0.718020 | ||||||||
\(313\) | −2.44646e11 | −1.44075 | −0.720374 | − | 0.693586i | \(-0.756030\pi\) | ||||
−0.720374 | + | 0.693586i | \(0.756030\pi\) | |||||||
\(314\) | 7.84484e10 | 0.455408 | ||||||||
\(315\) | 3.86228e10 | 0.221027 | ||||||||
\(316\) | −3.14976e11 | −1.77699 | ||||||||
\(317\) | 1.12832e11 | 0.627575 | 0.313787 | − | 0.949493i | \(-0.398402\pi\) | ||||
0.313787 | + | 0.949493i | \(0.398402\pi\) | |||||||
\(318\) | 4.69817e10 | 0.257636 | ||||||||
\(319\) | −9.80436e9 | −0.0530104 | ||||||||
\(320\) | 2.87530e11 | 1.53288 | ||||||||
\(321\) | −1.13168e11 | −0.594911 | ||||||||
\(322\) | −1.56358e11 | −0.810528 | ||||||||
\(323\) | 6.41492e10 | 0.327929 | ||||||||
\(324\) | 3.37486e10 | 0.170139 | ||||||||
\(325\) | 3.43241e10 | 0.170657 | ||||||||
\(326\) | 5.54930e11 | 2.72119 | ||||||||
\(327\) | 2.17510e11 | 1.05200 | ||||||||
\(328\) | 4.25967e10 | 0.203209 | ||||||||
\(329\) | −1.26825e11 | −0.596794 | ||||||||
\(330\) | −5.65548e9 | −0.0262516 | ||||||||
\(331\) | 2.87348e11 | 1.31578 | 0.657889 | − | 0.753115i | \(-0.271450\pi\) | ||||
0.657889 | + | 0.753115i | \(0.271450\pi\) | |||||||
\(332\) | −5.83711e11 | −2.63679 | ||||||||
\(333\) | −4.90265e10 | −0.218490 | ||||||||
\(334\) | 2.03582e11 | 0.895119 | ||||||||
\(335\) | −1.30784e11 | −0.567354 | ||||||||
\(336\) | −1.77434e10 | −0.0759468 | ||||||||
\(337\) | −2.52635e10 | −0.106699 | −0.0533494 | − | 0.998576i | \(-0.516990\pi\) | ||||
−0.0533494 | + | 0.998576i | \(0.516990\pi\) | |||||||
\(338\) | −4.44759e11 | −1.85353 | ||||||||
\(339\) | −3.68346e10 | −0.151481 | ||||||||
\(340\) | −1.11426e11 | −0.452200 | ||||||||
\(341\) | 1.04362e10 | 0.0417973 | ||||||||
\(342\) | −1.40084e11 | −0.553696 | ||||||||
\(343\) | 2.71653e11 | 1.05972 | ||||||||
\(344\) | 4.26805e10 | 0.164330 | ||||||||
\(345\) | −1.03186e11 | −0.392133 | ||||||||
\(346\) | −2.77161e9 | −0.0103966 | ||||||||
\(347\) | 9.04803e10 | 0.335020 | 0.167510 | − | 0.985870i | \(-0.446427\pi\) | ||||
0.167510 | + | 0.985870i | \(0.446427\pi\) | |||||||
\(348\) | 4.21827e11 | 1.54180 | ||||||||
\(349\) | −1.53822e10 | −0.0555016 | −0.0277508 | − | 0.999615i | \(-0.508834\pi\) | ||||
−0.0277508 | + | 0.999615i | \(0.508834\pi\) | |||||||
\(350\) | −3.65346e10 | −0.130136 | ||||||||
\(351\) | 8.05250e10 | 0.283171 | ||||||||
\(352\) | 9.99807e9 | 0.0347116 | ||||||||
\(353\) | −1.46875e11 | −0.503457 | −0.251728 | − | 0.967798i | \(-0.580999\pi\) | ||||
−0.251728 | + | 0.967798i | \(0.580999\pi\) | |||||||
\(354\) | −2.50998e11 | −0.849483 | ||||||||
\(355\) | 5.80400e10 | 0.193955 | ||||||||
\(356\) | 6.03579e11 | 1.99163 | ||||||||
\(357\) | 3.92498e10 | 0.127888 | ||||||||
\(358\) | −8.36088e11 | −2.69016 | ||||||||
\(359\) | −4.42246e11 | −1.40520 | −0.702602 | − | 0.711583i | \(-0.747979\pi\) | ||||
−0.702602 | + | 0.711583i | \(0.747979\pi\) | |||||||
\(360\) | 8.44183e10 | 0.264896 | ||||||||
\(361\) | 2.90609e10 | 0.0900590 | ||||||||
\(362\) | 4.44716e11 | 1.36111 | ||||||||
\(363\) | 1.90817e11 | 0.576817 | ||||||||
\(364\) | 5.32194e11 | 1.58896 | ||||||||
\(365\) | 3.09587e10 | 0.0912987 | ||||||||
\(366\) | 9.39358e10 | 0.273632 | ||||||||
\(367\) | 1.48110e11 | 0.426175 | 0.213088 | − | 0.977033i | \(-0.431648\pi\) | ||||
0.213088 | + | 0.977033i | \(0.431648\pi\) | |||||||
\(368\) | 4.74037e10 | 0.134740 | ||||||||
\(369\) | −2.85413e10 | −0.0801412 | ||||||||
\(370\) | −3.53475e11 | −0.980507 | ||||||||
\(371\) | −7.21805e10 | −0.197805 | ||||||||
\(372\) | −4.49011e11 | −1.21567 | ||||||||
\(373\) | 7.63489e10 | 0.204227 | 0.102114 | − | 0.994773i | \(-0.467440\pi\) | ||||
0.102114 | + | 0.994773i | \(0.467440\pi\) | |||||||
\(374\) | −5.74730e9 | −0.0151894 | ||||||||
\(375\) | −2.31989e11 | −0.605797 | ||||||||
\(376\) | −2.77204e11 | −0.715244 | ||||||||
\(377\) | 1.00649e12 | 2.56609 | ||||||||
\(378\) | −8.57108e10 | −0.215935 | ||||||||
\(379\) | −2.70192e11 | −0.672660 | −0.336330 | − | 0.941744i | \(-0.609186\pi\) | ||||
−0.336330 | + | 0.941744i | \(0.609186\pi\) | |||||||
\(380\) | −6.10981e11 | −1.50315 | ||||||||
\(381\) | 6.79306e9 | 0.0165159 | ||||||||
\(382\) | 1.51356e11 | 0.363676 | ||||||||
\(383\) | −6.61033e11 | −1.56974 | −0.784872 | − | 0.619658i | \(-0.787271\pi\) | ||||
−0.784872 | + | 0.619658i | \(0.787271\pi\) | |||||||
\(384\) | −3.57160e11 | −0.838246 | ||||||||
\(385\) | 8.68880e9 | 0.0201552 | ||||||||
\(386\) | 1.57900e11 | 0.362026 | ||||||||
\(387\) | −2.85975e10 | −0.0648081 | ||||||||
\(388\) | 7.11191e11 | 1.59310 | ||||||||
\(389\) | −3.09861e11 | −0.686109 | −0.343054 | − | 0.939316i | \(-0.611462\pi\) | ||||
−0.343054 | + | 0.939316i | \(0.611462\pi\) | |||||||
\(390\) | 5.80575e11 | 1.27077 | ||||||||
\(391\) | −1.04861e11 | −0.226891 | ||||||||
\(392\) | 1.98613e11 | 0.424835 | ||||||||
\(393\) | 3.02617e11 | 0.639921 | ||||||||
\(394\) | 1.21210e12 | 2.53399 | ||||||||
\(395\) | 5.27906e11 | 1.09111 | ||||||||
\(396\) | 7.59228e9 | 0.0155147 | ||||||||
\(397\) | −6.50589e11 | −1.31447 | −0.657233 | − | 0.753688i | \(-0.728273\pi\) | ||||
−0.657233 | + | 0.753688i | \(0.728273\pi\) | |||||||
\(398\) | −3.69836e11 | −0.738814 | ||||||||
\(399\) | 2.15218e11 | 0.425110 | ||||||||
\(400\) | 1.10764e10 | 0.0216335 | ||||||||
\(401\) | 2.76701e10 | 0.0534393 | 0.0267196 | − | 0.999643i | \(-0.491494\pi\) | ||||
0.0267196 | + | 0.999643i | \(0.491494\pi\) | |||||||
\(402\) | 2.90234e11 | 0.554282 | ||||||||
\(403\) | −1.07135e12 | −2.02330 | ||||||||
\(404\) | −3.30771e11 | −0.617748 | ||||||||
\(405\) | −5.65634e10 | −0.104469 | ||||||||
\(406\) | −1.07131e12 | −1.95680 | ||||||||
\(407\) | −1.10293e10 | −0.0199238 | ||||||||
\(408\) | 8.57889e10 | 0.153271 | ||||||||
\(409\) | 2.08505e11 | 0.368436 | 0.184218 | − | 0.982885i | \(-0.441025\pi\) | ||||
0.184218 | + | 0.982885i | \(0.441025\pi\) | |||||||
\(410\) | −2.05779e11 | −0.359646 | ||||||||
\(411\) | −5.21314e11 | −0.901180 | ||||||||
\(412\) | 4.53969e11 | 0.776228 | ||||||||
\(413\) | 3.85620e11 | 0.652206 | ||||||||
\(414\) | 2.28987e11 | 0.383098 | ||||||||
\(415\) | 9.78311e11 | 1.61905 | ||||||||
\(416\) | −1.02637e12 | −1.68029 | ||||||||
\(417\) | −1.47285e11 | −0.238531 | ||||||||
\(418\) | −3.15141e10 | −0.0504907 | ||||||||
\(419\) | 4.50465e11 | 0.714000 | 0.357000 | − | 0.934104i | \(-0.383800\pi\) | ||||
0.357000 | + | 0.934104i | \(0.383800\pi\) | |||||||
\(420\) | −3.73830e11 | −0.586209 | ||||||||
\(421\) | 8.60883e11 | 1.33559 | 0.667797 | − | 0.744343i | \(-0.267237\pi\) | ||||
0.667797 | + | 0.744343i | \(0.267237\pi\) | |||||||
\(422\) | −2.86810e11 | −0.440239 | ||||||||
\(423\) | 1.85737e11 | 0.282076 | ||||||||
\(424\) | −1.57766e11 | −0.237065 | ||||||||
\(425\) | −2.45018e10 | −0.0364291 | ||||||||
\(426\) | −1.28801e11 | −0.189486 | ||||||||
\(427\) | −1.44318e11 | −0.210086 | ||||||||
\(428\) | 1.09536e12 | 1.57782 | ||||||||
\(429\) | 1.81154e10 | 0.0258220 | ||||||||
\(430\) | −2.06185e11 | −0.290836 | ||||||||
\(431\) | −3.02405e10 | −0.0422125 | −0.0211063 | − | 0.999777i | \(-0.506719\pi\) | ||||
−0.0211063 | + | 0.999777i | \(0.506719\pi\) | |||||||
\(432\) | 2.59853e10 | 0.0358965 | ||||||||
\(433\) | 1.03636e12 | 1.41682 | 0.708410 | − | 0.705802i | \(-0.249413\pi\) | ||||
0.708410 | + | 0.705802i | \(0.249413\pi\) | |||||||
\(434\) | 1.14035e12 | 1.54288 | ||||||||
\(435\) | −7.06990e11 | −0.946699 | ||||||||
\(436\) | −2.10528e12 | −2.79010 | ||||||||
\(437\) | −5.74983e11 | −0.754204 | ||||||||
\(438\) | −6.87028e10 | −0.0891951 | ||||||||
\(439\) | −5.90670e11 | −0.759022 | −0.379511 | − | 0.925187i | \(-0.623908\pi\) | ||||
−0.379511 | + | 0.925187i | \(0.623908\pi\) | |||||||
\(440\) | 1.89912e10 | 0.0241555 | ||||||||
\(441\) | −1.33078e11 | −0.167546 | ||||||||
\(442\) | 5.90001e11 | 0.735280 | ||||||||
\(443\) | 1.27097e12 | 1.56790 | 0.783948 | − | 0.620827i | \(-0.213203\pi\) | ||||
0.783948 | + | 0.620827i | \(0.213203\pi\) | |||||||
\(444\) | 4.74528e11 | 0.579480 | ||||||||
\(445\) | −1.01161e12 | −1.22291 | ||||||||
\(446\) | −2.50769e11 | −0.300101 | ||||||||
\(447\) | 6.72461e11 | 0.796679 | ||||||||
\(448\) | 9.80316e11 | 1.14978 | ||||||||
\(449\) | −9.34644e11 | −1.08527 | −0.542635 | − | 0.839969i | \(-0.682573\pi\) | ||||
−0.542635 | + | 0.839969i | \(0.682573\pi\) | |||||||
\(450\) | 5.35052e10 | 0.0615092 | ||||||||
\(451\) | −6.42082e9 | −0.00730796 | ||||||||
\(452\) | 3.56523e11 | 0.401758 | ||||||||
\(453\) | −3.11086e11 | −0.347087 | ||||||||
\(454\) | −1.20851e12 | −1.33505 | ||||||||
\(455\) | −8.91968e11 | −0.975658 | ||||||||
\(456\) | 4.70406e11 | 0.509484 | ||||||||
\(457\) | −4.52481e11 | −0.485263 | −0.242632 | − | 0.970119i | \(-0.578011\pi\) | ||||
−0.242632 | + | 0.970119i | \(0.578011\pi\) | |||||||
\(458\) | −1.05551e12 | −1.12091 | ||||||||
\(459\) | −5.74817e10 | −0.0604467 | ||||||||
\(460\) | 9.98735e11 | 1.04002 | ||||||||
\(461\) | −8.56467e11 | −0.883195 | −0.441597 | − | 0.897213i | \(-0.645588\pi\) | ||||
−0.441597 | + | 0.897213i | \(0.645588\pi\) | |||||||
\(462\) | −1.92820e10 | −0.0196908 | ||||||||
\(463\) | 9.21380e11 | 0.931803 | 0.465902 | − | 0.884836i | \(-0.345730\pi\) | ||||
0.465902 | + | 0.884836i | \(0.345730\pi\) | |||||||
\(464\) | 3.24793e11 | 0.325294 | ||||||||
\(465\) | 7.52552e11 | 0.746446 | ||||||||
\(466\) | 2.95228e12 | 2.90016 | ||||||||
\(467\) | 8.65382e10 | 0.0841941 | 0.0420971 | − | 0.999114i | \(-0.486596\pi\) | ||||
0.0420971 | + | 0.999114i | \(0.486596\pi\) | |||||||
\(468\) | −7.79403e11 | −0.751027 | ||||||||
\(469\) | −4.45901e11 | −0.425560 | ||||||||
\(470\) | 1.33914e12 | 1.26586 | ||||||||
\(471\) | 1.76509e11 | 0.165262 | ||||||||
\(472\) | 8.42856e11 | 0.781654 | ||||||||
\(473\) | −6.43346e9 | −0.00590976 | ||||||||
\(474\) | −1.17152e12 | −1.06597 | ||||||||
\(475\) | −1.34351e11 | −0.121093 | ||||||||
\(476\) | −3.79900e11 | −0.339186 | ||||||||
\(477\) | 1.05709e11 | 0.0934930 | ||||||||
\(478\) | −2.25579e12 | −1.97640 | ||||||||
\(479\) | 7.63707e11 | 0.662852 | 0.331426 | − | 0.943481i | \(-0.392470\pi\) | ||||
0.331426 | + | 0.943481i | \(0.392470\pi\) | |||||||
\(480\) | 7.20958e11 | 0.619904 | ||||||||
\(481\) | 1.13223e12 | 0.964458 | ||||||||
\(482\) | −2.79197e12 | −2.35613 | ||||||||
\(483\) | −3.51805e11 | −0.294130 | ||||||||
\(484\) | −1.84692e12 | −1.52984 | ||||||||
\(485\) | −1.19197e12 | −0.978200 | ||||||||
\(486\) | 1.25524e11 | 0.102062 | ||||||||
\(487\) | −5.25531e11 | −0.423368 | −0.211684 | − | 0.977338i | \(-0.567895\pi\) | ||||
−0.211684 | + | 0.977338i | \(0.567895\pi\) | |||||||
\(488\) | −3.15439e11 | −0.251783 | ||||||||
\(489\) | 1.24859e12 | 0.987487 | ||||||||
\(490\) | −9.59477e11 | −0.751886 | ||||||||
\(491\) | 2.37265e12 | 1.84233 | 0.921163 | − | 0.389177i | \(-0.127241\pi\) | ||||
0.921163 | + | 0.389177i | \(0.127241\pi\) | |||||||
\(492\) | 2.76252e11 | 0.212551 | ||||||||
\(493\) | −7.18468e11 | −0.547768 | ||||||||
\(494\) | 3.23515e12 | 2.44412 | ||||||||
\(495\) | −1.27248e10 | −0.00952639 | ||||||||
\(496\) | −3.45724e11 | −0.256485 | ||||||||
\(497\) | 1.97884e11 | 0.145481 | ||||||||
\(498\) | −2.17105e12 | −1.58175 | ||||||||
\(499\) | −1.33387e11 | −0.0963080 | −0.0481540 | − | 0.998840i | \(-0.515334\pi\) | ||||
−0.0481540 | + | 0.998840i | \(0.515334\pi\) | |||||||
\(500\) | 2.24543e12 | 1.60670 | ||||||||
\(501\) | 4.58060e11 | 0.324827 | ||||||||
\(502\) | 2.09484e12 | 1.47226 | ||||||||
\(503\) | −6.58632e11 | −0.458762 | −0.229381 | − | 0.973337i | \(-0.573670\pi\) | ||||
−0.229381 | + | 0.973337i | \(0.573670\pi\) | |||||||
\(504\) | 2.87819e11 | 0.198693 | ||||||||
\(505\) | 5.54379e11 | 0.379311 | ||||||||
\(506\) | 5.15143e10 | 0.0349342 | ||||||||
\(507\) | −1.00071e12 | −0.672623 | ||||||||
\(508\) | −6.57501e10 | −0.0438036 | ||||||||
\(509\) | −1.01965e12 | −0.673322 | −0.336661 | − | 0.941626i | \(-0.609298\pi\) | ||||
−0.336661 | + | 0.941626i | \(0.609298\pi\) | |||||||
\(510\) | −4.14436e11 | −0.271264 | ||||||||
\(511\) | 1.05552e11 | 0.0684811 | ||||||||
\(512\) | −5.76350e11 | −0.370656 | ||||||||
\(513\) | −3.15189e11 | −0.200929 | ||||||||
\(514\) | 2.66935e11 | 0.168683 | ||||||||
\(515\) | −7.60862e11 | −0.476621 | ||||||||
\(516\) | 2.76796e11 | 0.171884 | ||||||||
\(517\) | 4.17845e10 | 0.0257221 | ||||||||
\(518\) | −1.20515e12 | −0.735457 | ||||||||
\(519\) | −6.23613e9 | −0.00377278 | ||||||||
\(520\) | −1.94959e12 | −1.16930 | ||||||||
\(521\) | −5.57535e11 | −0.331514 | −0.165757 | − | 0.986167i | \(-0.553007\pi\) | ||||
−0.165757 | + | 0.986167i | \(0.553007\pi\) | |||||||
\(522\) | 1.56894e12 | 0.924886 | ||||||||
\(523\) | 2.12050e12 | 1.23931 | 0.619657 | − | 0.784873i | \(-0.287272\pi\) | ||||
0.619657 | + | 0.784873i | \(0.287272\pi\) | |||||||
\(524\) | −2.92903e12 | −1.69720 | ||||||||
\(525\) | −8.22028e10 | −0.0472248 | ||||||||
\(526\) | 3.78975e12 | 2.15861 | ||||||||
\(527\) | 7.64770e11 | 0.431900 | ||||||||
\(528\) | 5.84581e9 | 0.00327335 | ||||||||
\(529\) | −8.61261e11 | −0.478172 | ||||||||
\(530\) | 7.62148e11 | 0.419564 | ||||||||
\(531\) | −5.64744e11 | −0.308267 | ||||||||
\(532\) | −2.08310e12 | −1.12748 | ||||||||
\(533\) | 6.59143e11 | 0.353759 | ||||||||
\(534\) | 2.24494e12 | 1.19473 | ||||||||
\(535\) | −1.83584e12 | −0.968820 | ||||||||
\(536\) | −9.74612e11 | −0.510024 | ||||||||
\(537\) | −1.88120e12 | −0.976225 | ||||||||
\(538\) | −1.68206e12 | −0.865608 | ||||||||
\(539\) | −2.99380e10 | −0.0152782 | ||||||||
\(540\) | 5.47478e11 | 0.277073 | ||||||||
\(541\) | 1.92746e12 | 0.967379 | 0.483690 | − | 0.875240i | \(-0.339296\pi\) | ||||
0.483690 | + | 0.875240i | \(0.339296\pi\) | |||||||
\(542\) | −1.03272e12 | −0.514029 | ||||||||
\(543\) | 1.00061e12 | 0.493931 | ||||||||
\(544\) | 7.32663e11 | 0.358682 | ||||||||
\(545\) | 3.52849e12 | 1.71319 | ||||||||
\(546\) | 1.97943e12 | 0.953179 | ||||||||
\(547\) | −2.32751e12 | −1.11160 | −0.555799 | − | 0.831317i | \(-0.687588\pi\) | ||||
−0.555799 | + | 0.831317i | \(0.687588\pi\) | |||||||
\(548\) | 5.04581e12 | 2.39011 | ||||||||
\(549\) | 2.11356e11 | 0.0992974 | ||||||||
\(550\) | 1.20368e10 | 0.00560894 | ||||||||
\(551\) | −3.93957e12 | −1.82082 | ||||||||
\(552\) | −7.68945e11 | −0.352508 | ||||||||
\(553\) | 1.79986e12 | 0.818419 | ||||||||
\(554\) | −3.06243e12 | −1.38125 | ||||||||
\(555\) | −7.95318e11 | −0.355814 | ||||||||
\(556\) | 1.42557e12 | 0.632633 | ||||||||
\(557\) | 4.94739e11 | 0.217785 | 0.108892 | − | 0.994054i | \(-0.465270\pi\) | ||||
0.108892 | + | 0.994054i | \(0.465270\pi\) | |||||||
\(558\) | −1.67005e12 | −0.729247 | ||||||||
\(559\) | 6.60441e11 | 0.286076 | ||||||||
\(560\) | −2.87837e11 | −0.123680 | ||||||||
\(561\) | −1.29314e10 | −0.00551205 | ||||||||
\(562\) | 2.83413e10 | 0.0119841 | ||||||||
\(563\) | 1.14083e12 | 0.478557 | 0.239279 | − | 0.970951i | \(-0.423089\pi\) | ||||
0.239279 | + | 0.970951i | \(0.423089\pi\) | |||||||
\(564\) | −1.79775e12 | −0.748124 | ||||||||
\(565\) | −5.97540e11 | −0.246688 | ||||||||
\(566\) | −8.96260e11 | −0.367079 | ||||||||
\(567\) | −1.92849e11 | −0.0783600 | ||||||||
\(568\) | 4.32517e11 | 0.174356 | ||||||||
\(569\) | −1.64398e10 | −0.00657495 | −0.00328747 | − | 0.999995i | \(-0.501046\pi\) | ||||
−0.00328747 | + | 0.999995i | \(0.501046\pi\) | |||||||
\(570\) | −2.27247e12 | −0.901700 | ||||||||
\(571\) | −3.67652e12 | −1.44735 | −0.723676 | − | 0.690139i | \(-0.757549\pi\) | ||||
−0.723676 | + | 0.690139i | \(0.757549\pi\) | |||||||
\(572\) | −1.75339e11 | −0.0684851 | ||||||||
\(573\) | 3.40551e11 | 0.131973 | ||||||||
\(574\) | −7.01592e11 | −0.269762 | ||||||||
\(575\) | 2.19615e11 | 0.0837833 | ||||||||
\(576\) | −1.43568e12 | −0.543447 | ||||||||
\(577\) | −2.29045e12 | −0.860260 | −0.430130 | − | 0.902767i | \(-0.641532\pi\) | ||||
−0.430130 | + | 0.902767i | \(0.641532\pi\) | |||||||
\(578\) | 3.84800e12 | 1.43403 | ||||||||
\(579\) | 3.55275e11 | 0.131375 | ||||||||
\(580\) | 6.84297e12 | 2.51084 | ||||||||
\(581\) | 3.33549e12 | 1.21441 | ||||||||
\(582\) | 2.64519e12 | 0.955661 | ||||||||
\(583\) | 2.37809e10 | 0.00852549 | ||||||||
\(584\) | 2.30706e11 | 0.0820730 | ||||||||
\(585\) | 1.30629e12 | 0.461147 | ||||||||
\(586\) | −5.65465e12 | −1.98092 | ||||||||
\(587\) | 4.68750e12 | 1.62956 | 0.814780 | − | 0.579771i | \(-0.196858\pi\) | ||||
0.814780 | + | 0.579771i | \(0.196858\pi\) | |||||||
\(588\) | 1.28806e12 | 0.444365 | ||||||||
\(589\) | 4.19346e12 | 1.43567 | ||||||||
\(590\) | −4.07174e12 | −1.38339 | ||||||||
\(591\) | 2.72722e12 | 0.919553 | ||||||||
\(592\) | 3.65371e11 | 0.122261 | ||||||||
\(593\) | −2.33770e12 | −0.776323 | −0.388162 | − | 0.921591i | \(-0.626890\pi\) | ||||
−0.388162 | + | 0.921591i | \(0.626890\pi\) | |||||||
\(594\) | 2.82386e10 | 0.00930690 | ||||||||
\(595\) | 6.36719e11 | 0.208268 | ||||||||
\(596\) | −6.50876e12 | −2.11295 | ||||||||
\(597\) | −8.32131e11 | −0.268106 | ||||||||
\(598\) | −5.28831e12 | −1.69107 | ||||||||
\(599\) | −4.66995e12 | −1.48215 | −0.741075 | − | 0.671423i | \(-0.765684\pi\) | ||||
−0.741075 | + | 0.671423i | \(0.765684\pi\) | |||||||
\(600\) | −1.79672e11 | −0.0565978 | ||||||||
\(601\) | −3.96517e12 | −1.23973 | −0.619864 | − | 0.784709i | \(-0.712812\pi\) | ||||
−0.619864 | + | 0.784709i | \(0.712812\pi\) | |||||||
\(602\) | −7.02974e11 | −0.218150 | ||||||||
\(603\) | 6.53026e11 | 0.201142 | ||||||||
\(604\) | 3.01101e12 | 0.920546 | ||||||||
\(605\) | 3.09548e12 | 0.939353 | ||||||||
\(606\) | −1.23027e12 | −0.370572 | ||||||||
\(607\) | 6.24743e12 | 1.86790 | 0.933948 | − | 0.357409i | \(-0.116340\pi\) | ||||
0.933948 | + | 0.357409i | \(0.116340\pi\) | |||||||
\(608\) | 4.01741e12 | 1.19228 | ||||||||
\(609\) | −2.41044e12 | −0.710098 | ||||||||
\(610\) | 1.52385e12 | 0.445612 | ||||||||
\(611\) | −4.28947e12 | −1.24514 | ||||||||
\(612\) | 5.56366e11 | 0.160317 | ||||||||
\(613\) | −3.73193e12 | −1.06748 | −0.533742 | − | 0.845647i | \(-0.679215\pi\) | ||||
−0.533742 | + | 0.845647i | \(0.679215\pi\) | |||||||
\(614\) | 8.84653e12 | 2.51197 | ||||||||
\(615\) | −4.63004e11 | −0.130511 | ||||||||
\(616\) | 6.47494e10 | 0.0181185 | ||||||||
\(617\) | −6.05181e12 | −1.68113 | −0.840567 | − | 0.541708i | \(-0.817778\pi\) | ||||
−0.840567 | + | 0.541708i | \(0.817778\pi\) | |||||||
\(618\) | 1.68849e12 | 0.465640 | ||||||||
\(619\) | 4.69849e12 | 1.28632 | 0.643162 | − | 0.765730i | \(-0.277622\pi\) | ||||
0.643162 | + | 0.765730i | \(0.277622\pi\) | |||||||
\(620\) | −7.28396e12 | −1.97973 | ||||||||
\(621\) | 5.15221e11 | 0.139021 | ||||||||
\(622\) | 5.79780e12 | 1.55313 | ||||||||
\(623\) | −3.44902e12 | −0.917275 | ||||||||
\(624\) | −6.00114e11 | −0.158454 | ||||||||
\(625\) | −3.32094e12 | −0.870565 | ||||||||
\(626\) | 8.80724e12 | 2.29222 | ||||||||
\(627\) | −7.09068e10 | −0.0183225 | ||||||||
\(628\) | −1.70843e12 | −0.438308 | ||||||||
\(629\) | −8.08231e11 | −0.205877 | ||||||||
\(630\) | −1.39042e12 | −0.351652 | ||||||||
\(631\) | 2.16875e12 | 0.544600 | 0.272300 | − | 0.962212i | \(-0.412216\pi\) | ||||
0.272300 | + | 0.962212i | \(0.412216\pi\) | |||||||
\(632\) | 3.93398e12 | 0.980857 | ||||||||
\(633\) | −6.45323e11 | −0.159757 | ||||||||
\(634\) | −4.06195e12 | −0.998466 | ||||||||
\(635\) | 1.10199e11 | 0.0268964 | ||||||||
\(636\) | −1.02316e12 | −0.247962 | ||||||||
\(637\) | 3.07335e12 | 0.739580 | ||||||||
\(638\) | 3.52957e11 | 0.0843391 | ||||||||
\(639\) | −2.89803e11 | −0.0687620 | ||||||||
\(640\) | −5.79392e12 | −1.36509 | ||||||||
\(641\) | 3.56446e12 | 0.833936 | 0.416968 | − | 0.908921i | \(-0.363093\pi\) | ||||
0.416968 | + | 0.908921i | \(0.363093\pi\) | |||||||
\(642\) | 4.07406e12 | 0.946497 | ||||||||
\(643\) | −5.37917e12 | −1.24098 | −0.620491 | − | 0.784213i | \(-0.713067\pi\) | ||||
−0.620491 | + | 0.784213i | \(0.713067\pi\) | |||||||
\(644\) | 3.40512e12 | 0.780093 | ||||||||
\(645\) | −4.63916e11 | −0.105541 | ||||||||
\(646\) | −2.30937e12 | −0.521732 | ||||||||
\(647\) | 6.01827e12 | 1.35021 | 0.675107 | − | 0.737720i | \(-0.264097\pi\) | ||||
0.675107 | + | 0.737720i | \(0.264097\pi\) | |||||||
\(648\) | −4.21513e11 | −0.0939126 | ||||||||
\(649\) | −1.27048e11 | −0.0281104 | ||||||||
\(650\) | −1.23567e12 | −0.271514 | ||||||||
\(651\) | 2.56578e12 | 0.559893 | ||||||||
\(652\) | −1.20852e13 | −2.61901 | ||||||||
\(653\) | −3.68383e11 | −0.0792849 | −0.0396424 | − | 0.999214i | \(-0.512622\pi\) | ||||
−0.0396424 | + | 0.999214i | \(0.512622\pi\) | |||||||
\(654\) | −7.83035e12 | −1.67371 | ||||||||
\(655\) | 4.90912e12 | 1.04212 | ||||||||
\(656\) | 2.12705e11 | 0.0448446 | ||||||||
\(657\) | −1.54581e11 | −0.0323678 | ||||||||
\(658\) | 4.56572e12 | 0.949494 | ||||||||
\(659\) | −5.24810e12 | −1.08397 | −0.541985 | − | 0.840388i | \(-0.682327\pi\) | ||||
−0.541985 | + | 0.840388i | \(0.682327\pi\) | |||||||
\(660\) | 1.23164e11 | 0.0252659 | ||||||||
\(661\) | 1.55039e11 | 0.0315888 | 0.0157944 | − | 0.999875i | \(-0.494972\pi\) | ||||
0.0157944 | + | 0.999875i | \(0.494972\pi\) | |||||||
\(662\) | −1.03445e13 | −2.09339 | ||||||||
\(663\) | 1.32750e12 | 0.266824 | ||||||||
\(664\) | 7.29043e12 | 1.45545 | ||||||||
\(665\) | 3.49132e12 | 0.692297 | ||||||||
\(666\) | 1.76495e12 | 0.347616 | ||||||||
\(667\) | 6.43979e12 | 1.25981 | ||||||||
\(668\) | −4.43357e12 | −0.861508 | ||||||||
\(669\) | −5.64230e11 | −0.108903 | ||||||||
\(670\) | 4.70824e12 | 0.902655 | ||||||||
\(671\) | 4.75477e10 | 0.00905479 | ||||||||
\(672\) | 2.45806e12 | 0.464977 | ||||||||
\(673\) | 5.89588e11 | 0.110785 | 0.0553925 | − | 0.998465i | \(-0.482359\pi\) | ||||
0.0553925 | + | 0.998465i | \(0.482359\pi\) | |||||||
\(674\) | 9.09487e11 | 0.169757 | ||||||||
\(675\) | 1.20387e11 | 0.0223209 | ||||||||
\(676\) | 9.68586e12 | 1.78393 | ||||||||
\(677\) | 3.32980e12 | 0.609214 | 0.304607 | − | 0.952478i | \(-0.401475\pi\) | ||||
0.304607 | + | 0.952478i | \(0.401475\pi\) | |||||||
\(678\) | 1.32605e12 | 0.241005 | ||||||||
\(679\) | −4.06395e12 | −0.733726 | ||||||||
\(680\) | 1.39169e12 | 0.249604 | ||||||||
\(681\) | −2.71914e12 | −0.484474 | ||||||||
\(682\) | −3.75703e11 | −0.0664991 | ||||||||
\(683\) | 2.28928e12 | 0.402536 | 0.201268 | − | 0.979536i | \(-0.435494\pi\) | ||||
0.201268 | + | 0.979536i | \(0.435494\pi\) | |||||||
\(684\) | 3.05072e12 | 0.532905 | ||||||||
\(685\) | −8.45687e12 | −1.46758 | ||||||||
\(686\) | −9.77951e12 | −1.68600 | ||||||||
\(687\) | −2.37491e12 | −0.406763 | ||||||||
\(688\) | 2.13124e11 | 0.0362647 | ||||||||
\(689\) | −2.44128e12 | −0.412697 | ||||||||
\(690\) | 3.71468e12 | 0.623880 | ||||||||
\(691\) | −9.46129e12 | −1.57870 | −0.789349 | − | 0.613945i | \(-0.789582\pi\) | ||||
−0.789349 | + | 0.613945i | \(0.789582\pi\) | |||||||
\(692\) | 6.03596e10 | 0.0100062 | ||||||||
\(693\) | −4.33845e10 | −0.00714554 | ||||||||
\(694\) | −3.25729e12 | −0.533014 | ||||||||
\(695\) | −2.38928e12 | −0.388451 | ||||||||
\(696\) | −5.26853e12 | −0.851036 | ||||||||
\(697\) | −4.70521e11 | −0.0755147 | ||||||||
\(698\) | 5.53761e11 | 0.0883024 | ||||||||
\(699\) | 6.64264e12 | 1.05243 | ||||||||
\(700\) | 7.95642e11 | 0.125250 | ||||||||
\(701\) | 8.22209e12 | 1.28603 | 0.643015 | − | 0.765854i | \(-0.277683\pi\) | ||||
0.643015 | + | 0.765854i | \(0.277683\pi\) | |||||||
\(702\) | −2.89890e12 | −0.450522 | ||||||||
\(703\) | −4.43177e12 | −0.684349 | ||||||||
\(704\) | −3.22979e11 | −0.0495562 | ||||||||
\(705\) | 3.01307e12 | 0.459365 | ||||||||
\(706\) | 5.28751e12 | 0.800995 | ||||||||
\(707\) | 1.89012e12 | 0.284513 | ||||||||
\(708\) | 5.46617e12 | 0.817586 | ||||||||
\(709\) | 7.61957e12 | 1.13246 | 0.566230 | − | 0.824247i | \(-0.308401\pi\) | ||||
0.566230 | + | 0.824247i | \(0.308401\pi\) | |||||||
\(710\) | −2.08944e12 | −0.308580 | ||||||||
\(711\) | −2.63591e12 | −0.386828 | ||||||||
\(712\) | −7.53858e12 | −1.09933 | ||||||||
\(713\) | −6.85481e12 | −0.993327 | ||||||||
\(714\) | −1.41299e12 | −0.203469 | ||||||||
\(715\) | 2.93871e11 | 0.0420514 | ||||||||
\(716\) | 1.82081e13 | 2.58915 | ||||||||
\(717\) | −5.07554e12 | −0.717209 | ||||||||
\(718\) | 1.59209e13 | 2.23567 | ||||||||
\(719\) | 7.94823e12 | 1.10915 | 0.554575 | − | 0.832134i | \(-0.312881\pi\) | ||||
0.554575 | + | 0.832134i | \(0.312881\pi\) | |||||||
\(720\) | 4.21540e11 | 0.0584578 | ||||||||
\(721\) | −2.59411e12 | −0.357503 | ||||||||
\(722\) | −1.04619e12 | −0.143283 | ||||||||
\(723\) | −6.28194e12 | −0.855010 | ||||||||
\(724\) | −9.68492e12 | −1.31000 | ||||||||
\(725\) | 1.50472e12 | 0.202272 | ||||||||
\(726\) | −6.86942e12 | −0.917710 | ||||||||
\(727\) | −5.75787e12 | −0.764464 | −0.382232 | − | 0.924066i | \(-0.624844\pi\) | ||||
−0.382232 | + | 0.924066i | \(0.624844\pi\) | |||||||
\(728\) | −6.64699e12 | −0.877069 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −1.11451e12 | −0.145255 | ||||||||
\(731\) | −4.71447e11 | −0.0610668 | ||||||||
\(732\) | −2.04571e12 | −0.263357 | ||||||||
\(733\) | 1.07808e13 | 1.37938 | 0.689690 | − | 0.724105i | \(-0.257747\pi\) | ||||
0.689690 | + | 0.724105i | \(0.257747\pi\) | |||||||
\(734\) | −5.33198e12 | −0.678041 | ||||||||
\(735\) | −2.15882e12 | −0.272850 | ||||||||
\(736\) | −6.56702e12 | −0.824933 | ||||||||
\(737\) | 1.46908e11 | 0.0183418 | ||||||||
\(738\) | 1.02749e12 | 0.127504 | ||||||||
\(739\) | 7.37756e12 | 0.909940 | 0.454970 | − | 0.890507i | \(-0.349650\pi\) | ||||
0.454970 | + | 0.890507i | \(0.349650\pi\) | |||||||
\(740\) | 7.69790e12 | 0.943690 | ||||||||
\(741\) | 7.27909e12 | 0.886942 | ||||||||
\(742\) | 2.59850e12 | 0.314706 | ||||||||
\(743\) | −1.02899e13 | −1.23869 | −0.619346 | − | 0.785118i | \(-0.712602\pi\) | ||||
−0.619346 | + | 0.785118i | \(0.712602\pi\) | |||||||
\(744\) | 5.60806e12 | 0.671018 | ||||||||
\(745\) | 1.09088e13 | 1.29740 | ||||||||
\(746\) | −2.74856e12 | −0.324923 | ||||||||
\(747\) | −4.88485e12 | −0.573996 | ||||||||
\(748\) | 1.25163e11 | 0.0146191 | ||||||||
\(749\) | −6.25918e12 | −0.726690 | ||||||||
\(750\) | 8.35161e12 | 0.963817 | ||||||||
\(751\) | −7.56555e12 | −0.867882 | −0.433941 | − | 0.900941i | \(-0.642877\pi\) | ||||
−0.433941 | + | 0.900941i | \(0.642877\pi\) | |||||||
\(752\) | −1.38421e12 | −0.157842 | ||||||||
\(753\) | 4.71340e12 | 0.534265 | ||||||||
\(754\) | −3.62336e13 | −4.08263 | ||||||||
\(755\) | −5.04651e12 | −0.565236 | ||||||||
\(756\) | 1.86659e12 | 0.207827 | ||||||||
\(757\) | −6.88713e12 | −0.762267 | −0.381133 | − | 0.924520i | \(-0.624466\pi\) | ||||
−0.381133 | + | 0.924520i | \(0.624466\pi\) | |||||||
\(758\) | 9.72690e12 | 1.07020 | ||||||||
\(759\) | 1.15907e11 | 0.0126772 | ||||||||
\(760\) | 7.63103e12 | 0.829701 | ||||||||
\(761\) | 4.30641e12 | 0.465462 | 0.232731 | − | 0.972541i | \(-0.425234\pi\) | ||||
0.232731 | + | 0.972541i | \(0.425234\pi\) | |||||||
\(762\) | −2.44550e11 | −0.0262767 | ||||||||
\(763\) | 1.20302e13 | 1.28502 | ||||||||
\(764\) | −3.29619e12 | −0.350020 | ||||||||
\(765\) | −9.32481e11 | −0.0984382 | ||||||||
\(766\) | 2.37972e13 | 2.49745 | ||||||||
\(767\) | 1.30424e13 | 1.36075 | ||||||||
\(768\) | 3.78281e12 | 0.392364 | ||||||||
\(769\) | 2.16296e12 | 0.223039 | 0.111519 | − | 0.993762i | \(-0.464428\pi\) | ||||
0.111519 | + | 0.993762i | \(0.464428\pi\) | |||||||
\(770\) | −3.12797e11 | −0.0320667 | ||||||||
\(771\) | 6.00603e11 | 0.0612129 | ||||||||
\(772\) | −3.43871e12 | −0.348432 | ||||||||
\(773\) | −8.15447e12 | −0.821463 | −0.410731 | − | 0.911756i | \(-0.634727\pi\) | ||||
−0.410731 | + | 0.911756i | \(0.634727\pi\) | |||||||
\(774\) | 1.02951e12 | 0.103109 | ||||||||
\(775\) | −1.60170e12 | −0.159486 | ||||||||
\(776\) | −8.88263e12 | −0.879354 | ||||||||
\(777\) | −2.71159e12 | −0.266888 | ||||||||
\(778\) | 1.11550e13 | 1.09159 | ||||||||
\(779\) | −2.58000e12 | −0.251016 | ||||||||
\(780\) | −1.26436e13 | −1.22306 | ||||||||
\(781\) | −6.51956e10 | −0.00627031 | ||||||||
\(782\) | 3.77499e12 | 0.360982 | ||||||||
\(783\) | 3.53011e12 | 0.335630 | ||||||||
\(784\) | 9.91768e11 | 0.0937535 | ||||||||
\(785\) | 2.86337e12 | 0.269131 | ||||||||
\(786\) | −1.08942e13 | −1.01811 | ||||||||
\(787\) | −2.25199e12 | −0.209257 | −0.104629 | − | 0.994511i | \(-0.533365\pi\) | ||||
−0.104629 | + | 0.994511i | \(0.533365\pi\) | |||||||
\(788\) | −2.63968e13 | −2.43884 | ||||||||
\(789\) | 8.52694e12 | 0.783334 | ||||||||
\(790\) | −1.90046e13 | −1.73595 | ||||||||
\(791\) | −2.03727e12 | −0.185036 | ||||||||
\(792\) | −9.48261e10 | −0.00856376 | ||||||||
\(793\) | −4.88112e12 | −0.438319 | ||||||||
\(794\) | 2.34212e13 | 2.09130 | ||||||||
\(795\) | 1.71483e12 | 0.152254 | ||||||||
\(796\) | 8.05420e12 | 0.711072 | ||||||||
\(797\) | −1.16128e13 | −1.01947 | −0.509737 | − | 0.860331i | \(-0.670257\pi\) | ||||
−0.509737 | + | 0.860331i | \(0.670257\pi\) | |||||||
\(798\) | −7.74786e12 | −0.676346 | ||||||||
\(799\) | 3.06198e12 | 0.265792 | ||||||||
\(800\) | −1.53445e12 | −0.132449 | ||||||||
\(801\) | 5.05112e12 | 0.433553 | ||||||||
\(802\) | −9.96122e11 | −0.0850214 | ||||||||
\(803\) | −3.47755e10 | −0.00295157 | ||||||||
\(804\) | −6.32065e12 | −0.533469 | ||||||||
\(805\) | −5.70706e12 | −0.478995 | ||||||||
\(806\) | 3.85687e13 | 3.21904 | ||||||||
\(807\) | −3.78464e12 | −0.314118 | ||||||||
\(808\) | 4.13126e12 | 0.340982 | ||||||||
\(809\) | 2.31768e12 | 0.190233 | 0.0951165 | − | 0.995466i | \(-0.469678\pi\) | ||||
0.0951165 | + | 0.995466i | \(0.469678\pi\) | |||||||
\(810\) | 2.03628e12 | 0.166209 | ||||||||
\(811\) | −9.18815e12 | −0.745821 | −0.372910 | − | 0.927867i | \(-0.621640\pi\) | ||||
−0.372910 | + | 0.927867i | \(0.621640\pi\) | |||||||
\(812\) | 2.33307e13 | 1.88332 | ||||||||
\(813\) | −2.32363e12 | −0.186535 | ||||||||
\(814\) | 3.97054e11 | 0.0316986 | ||||||||
\(815\) | 2.02550e13 | 1.60813 | ||||||||
\(816\) | 4.28384e11 | 0.0338242 | ||||||||
\(817\) | −2.58508e12 | −0.202990 | ||||||||
\(818\) | −7.50620e12 | −0.586179 | ||||||||
\(819\) | 4.45373e12 | 0.345897 | ||||||||
\(820\) | 4.48142e12 | 0.346141 | ||||||||
\(821\) | −1.92679e13 | −1.48010 | −0.740048 | − | 0.672554i | \(-0.765197\pi\) | ||||
−0.740048 | + | 0.672554i | \(0.765197\pi\) | |||||||
\(822\) | 1.87673e13 | 1.43377 | ||||||||
\(823\) | −1.04990e13 | −0.797713 | −0.398857 | − | 0.917013i | \(-0.630593\pi\) | ||||
−0.398857 | + | 0.917013i | \(0.630593\pi\) | |||||||
\(824\) | −5.66999e12 | −0.428459 | ||||||||
\(825\) | 2.70829e10 | 0.00203541 | ||||||||
\(826\) | −1.38823e13 | −1.03765 | ||||||||
\(827\) | −8.10053e12 | −0.602197 | −0.301098 | − | 0.953593i | \(-0.597353\pi\) | ||||
−0.301098 | + | 0.953593i | \(0.597353\pi\) | |||||||
\(828\) | −4.98683e12 | −0.368713 | ||||||||
\(829\) | −1.52452e13 | −1.12108 | −0.560542 | − | 0.828126i | \(-0.689407\pi\) | ||||
−0.560542 | + | 0.828126i | \(0.689407\pi\) | |||||||
\(830\) | −3.52192e13 | −2.57589 | ||||||||
\(831\) | −6.89048e12 | −0.501239 | ||||||||
\(832\) | 3.31561e13 | 2.39888 | ||||||||
\(833\) | −2.19387e12 | −0.157873 | ||||||||
\(834\) | 5.30224e12 | 0.379501 | ||||||||
\(835\) | 7.43075e12 | 0.528985 | ||||||||
\(836\) | 6.86307e11 | 0.0485949 | ||||||||
\(837\) | −3.75761e12 | −0.264635 | ||||||||
\(838\) | −1.62168e13 | −1.13597 | ||||||||
\(839\) | 2.72258e13 | 1.89694 | 0.948468 | − | 0.316874i | \(-0.102633\pi\) | ||||
0.948468 | + | 0.316874i | \(0.102633\pi\) | |||||||
\(840\) | 4.66906e12 | 0.323574 | ||||||||
\(841\) | 2.96160e13 | 2.04147 | ||||||||
\(842\) | −3.09918e13 | −2.12492 | ||||||||
\(843\) | 6.37678e10 | 0.00434888 | ||||||||
\(844\) | 6.24609e12 | 0.423709 | ||||||||
\(845\) | −1.62337e13 | −1.09537 | ||||||||
\(846\) | −6.68653e12 | −0.448781 | ||||||||
\(847\) | 1.05538e13 | 0.704588 | ||||||||
\(848\) | −7.87798e11 | −0.0523159 | ||||||||
\(849\) | −2.01658e12 | −0.133208 | ||||||||
\(850\) | 8.82066e11 | 0.0579583 | ||||||||
\(851\) | 7.24435e12 | 0.473496 | ||||||||
\(852\) | 2.80500e12 | 0.182371 | ||||||||
\(853\) | 5.38234e12 | 0.348097 | 0.174048 | − | 0.984737i | \(-0.444315\pi\) | ||||
0.174048 | + | 0.984737i | \(0.444315\pi\) | |||||||
\(854\) | 5.19546e12 | 0.334244 | ||||||||
\(855\) | −5.11307e12 | −0.327216 | ||||||||
\(856\) | −1.36808e13 | −0.870922 | ||||||||
\(857\) | 2.13114e12 | 0.134958 | 0.0674791 | − | 0.997721i | \(-0.478504\pi\) | ||||
0.0674791 | + | 0.997721i | \(0.478504\pi\) | |||||||
\(858\) | −6.52153e11 | −0.0410825 | ||||||||
\(859\) | 1.07650e13 | 0.674598 | 0.337299 | − | 0.941398i | \(-0.390487\pi\) | ||||
0.337299 | + | 0.941398i | \(0.390487\pi\) | |||||||
\(860\) | 4.49024e12 | 0.279916 | ||||||||
\(861\) | −1.57858e12 | −0.0978933 | ||||||||
\(862\) | 1.08866e12 | 0.0671597 | ||||||||
\(863\) | 2.36698e13 | 1.45260 | 0.726299 | − | 0.687379i | \(-0.241239\pi\) | ||||
0.726299 | + | 0.687379i | \(0.241239\pi\) | |||||||
\(864\) | −3.59985e12 | −0.219772 | ||||||||
\(865\) | −1.01164e11 | −0.00614402 | ||||||||
\(866\) | −3.73089e13 | −2.25415 | ||||||||
\(867\) | 8.65800e12 | 0.520393 | ||||||||
\(868\) | −2.48342e13 | −1.48495 | ||||||||
\(869\) | −5.92990e11 | −0.0352743 | ||||||||
\(870\) | 2.54516e13 | 1.50619 | ||||||||
\(871\) | −1.50812e13 | −0.887880 | ||||||||
\(872\) | 2.62945e13 | 1.54007 | ||||||||
\(873\) | 5.95169e12 | 0.346797 | ||||||||
\(874\) | 2.06994e13 | 1.19993 | ||||||||
\(875\) | −1.28310e13 | −0.739988 | ||||||||
\(876\) | 1.49619e12 | 0.0858459 | ||||||||
\(877\) | −9.91806e12 | −0.566146 | −0.283073 | − | 0.959098i | \(-0.591354\pi\) | ||||
−0.283073 | + | 0.959098i | \(0.591354\pi\) | |||||||
\(878\) | 2.12641e13 | 1.20760 | ||||||||
\(879\) | −1.27230e13 | −0.718851 | ||||||||
\(880\) | 9.48320e10 | 0.00533069 | ||||||||
\(881\) | 1.28992e13 | 0.721391 | 0.360696 | − | 0.932684i | \(-0.382539\pi\) | ||||
0.360696 | + | 0.932684i | \(0.382539\pi\) | |||||||
\(882\) | 4.79081e12 | 0.266563 | ||||||||
\(883\) | 1.00956e13 | 0.558866 | 0.279433 | − | 0.960165i | \(-0.409854\pi\) | ||||
0.279433 | + | 0.960165i | \(0.409854\pi\) | |||||||
\(884\) | −1.28489e13 | −0.707671 | ||||||||
\(885\) | −9.16141e12 | −0.502016 | ||||||||
\(886\) | −4.57548e13 | −2.49451 | ||||||||
\(887\) | −2.22403e12 | −0.120638 | −0.0603190 | − | 0.998179i | \(-0.519212\pi\) | ||||
−0.0603190 | + | 0.998179i | \(0.519212\pi\) | |||||||
\(888\) | −5.92676e12 | −0.319859 | ||||||||
\(889\) | 3.75715e11 | 0.0201744 | ||||||||
\(890\) | 3.64180e13 | 1.94563 | ||||||||
\(891\) | 6.35370e10 | 0.00337736 | ||||||||
\(892\) | 5.46119e12 | 0.288832 | ||||||||
\(893\) | 1.67898e13 | 0.883513 | ||||||||
\(894\) | −2.42086e13 | −1.26751 | ||||||||
\(895\) | −3.05172e13 | −1.58979 | ||||||||
\(896\) | −1.97540e13 | −1.02393 | ||||||||
\(897\) | −1.18987e13 | −0.613668 | ||||||||
\(898\) | 3.36472e13 | 1.72665 | ||||||||
\(899\) | −4.69666e13 | −2.39812 | ||||||||
\(900\) | −1.16523e12 | −0.0591996 | ||||||||
\(901\) | 1.74267e12 | 0.0880957 | ||||||||
\(902\) | 2.31150e11 | 0.0116269 | ||||||||
\(903\) | −1.58169e12 | −0.0791638 | ||||||||
\(904\) | −4.45290e12 | −0.221761 | ||||||||
\(905\) | 1.62321e13 | 0.804372 | ||||||||
\(906\) | 1.11991e13 | 0.552213 | ||||||||
\(907\) | −6.35542e12 | −0.311825 | −0.155913 | − | 0.987771i | \(-0.549832\pi\) | ||||
−0.155913 | + | 0.987771i | \(0.549832\pi\) | |||||||
\(908\) | 2.63186e13 | 1.28492 | ||||||||
\(909\) | −2.76810e12 | −0.134476 | ||||||||
\(910\) | 3.21108e13 | 1.55226 | ||||||||
\(911\) | −1.91432e13 | −0.920837 | −0.460418 | − | 0.887702i | \(-0.652301\pi\) | ||||
−0.460418 | + | 0.887702i | \(0.652301\pi\) | |||||||
\(912\) | 2.34895e12 | 0.112434 | ||||||||
\(913\) | −1.09892e12 | −0.0523419 | ||||||||
\(914\) | 1.62893e13 | 0.772049 | ||||||||
\(915\) | 3.42866e12 | 0.161707 | ||||||||
\(916\) | 2.29867e13 | 1.07882 | ||||||||
\(917\) | 1.67373e13 | 0.781671 | ||||||||
\(918\) | 2.06934e12 | 0.0961701 | ||||||||
\(919\) | 2.86053e13 | 1.32290 | 0.661449 | − | 0.749991i | \(-0.269942\pi\) | ||||
0.661449 | + | 0.749991i | \(0.269942\pi\) | |||||||
\(920\) | −1.24740e13 | −0.574064 | ||||||||
\(921\) | 1.99047e13 | 0.911564 | ||||||||
\(922\) | 3.08328e13 | 1.40515 | ||||||||
\(923\) | 6.69280e12 | 0.303529 | ||||||||
\(924\) | 4.19919e11 | 0.0189514 | ||||||||
\(925\) | 1.69272e12 | 0.0760233 | ||||||||
\(926\) | −3.31697e13 | −1.48249 | ||||||||
\(927\) | 3.79910e12 | 0.168975 | ||||||||
\(928\) | −4.49948e13 | −1.99158 | ||||||||
\(929\) | −1.18899e13 | −0.523728 | −0.261864 | − | 0.965105i | \(-0.584337\pi\) | ||||
−0.261864 | + | 0.965105i | \(0.584337\pi\) | |||||||
\(930\) | −2.70919e13 | −1.18759 | ||||||||
\(931\) | −1.20296e13 | −0.524782 | ||||||||
\(932\) | −6.42942e13 | −2.79126 | ||||||||
\(933\) | 1.30451e13 | 0.563610 | ||||||||
\(934\) | −3.11537e12 | −0.133952 | ||||||||
\(935\) | −2.09776e11 | −0.00897644 | ||||||||
\(936\) | 9.73458e12 | 0.414549 | ||||||||
\(937\) | −3.45871e13 | −1.46584 | −0.732920 | − | 0.680315i | \(-0.761843\pi\) | ||||
−0.732920 | + | 0.680315i | \(0.761843\pi\) | |||||||
\(938\) | 1.60524e13 | 0.677061 | ||||||||
\(939\) | 1.98163e13 | 0.831816 | ||||||||
\(940\) | −2.91635e13 | −1.21833 | ||||||||
\(941\) | 2.59742e13 | 1.07991 | 0.539956 | − | 0.841693i | \(-0.318441\pi\) | ||||
0.539956 | + | 0.841693i | \(0.318441\pi\) | |||||||
\(942\) | −6.35432e12 | −0.262930 | ||||||||
\(943\) | 4.21738e12 | 0.173676 | ||||||||
\(944\) | 4.20877e12 | 0.172497 | ||||||||
\(945\) | −3.12844e12 | −0.127610 | ||||||||
\(946\) | 2.31605e11 | 0.00940237 | ||||||||
\(947\) | 2.43739e13 | 0.984804 | 0.492402 | − | 0.870368i | \(-0.336119\pi\) | ||||
0.492402 | + | 0.870368i | \(0.336119\pi\) | |||||||
\(948\) | 2.55130e13 | 1.02595 | ||||||||
\(949\) | 3.56995e12 | 0.142878 | ||||||||
\(950\) | 4.83663e12 | 0.192658 | ||||||||
\(951\) | −9.13939e12 | −0.362331 | ||||||||
\(952\) | 4.74487e12 | 0.187222 | ||||||||
\(953\) | −2.34891e13 | −0.922461 | −0.461230 | − | 0.887280i | \(-0.652592\pi\) | ||||
−0.461230 | + | 0.887280i | \(0.652592\pi\) | |||||||
\(954\) | −3.80552e12 | −0.148746 | ||||||||
\(955\) | 5.52449e12 | 0.214920 | ||||||||
\(956\) | 4.91262e13 | 1.90218 | ||||||||
\(957\) | 7.94153e11 | 0.0306056 | ||||||||
\(958\) | −2.74934e13 | −1.05459 | ||||||||
\(959\) | −2.88332e13 | −1.10080 | ||||||||
\(960\) | −2.32900e13 | −0.885010 | ||||||||
\(961\) | 2.35538e13 | 0.890851 | ||||||||
\(962\) | −4.07604e13 | −1.53444 | ||||||||
\(963\) | 9.16663e12 | 0.343472 | ||||||||
\(964\) | 6.08029e13 | 2.26766 | ||||||||
\(965\) | 5.76335e12 | 0.213945 | ||||||||
\(966\) | 1.26650e13 | 0.467958 | ||||||||
\(967\) | 4.68639e12 | 0.172353 | 0.0861766 | − | 0.996280i | \(-0.472535\pi\) | ||||
0.0861766 | + | 0.996280i | \(0.472535\pi\) | |||||||
\(968\) | 2.30677e13 | 0.844433 | ||||||||
\(969\) | −5.19608e12 | −0.189330 | ||||||||
\(970\) | 4.29109e13 | 1.55631 | ||||||||
\(971\) | −4.63936e13 | −1.67483 | −0.837416 | − | 0.546566i | \(-0.815935\pi\) | ||||
−0.837416 | + | 0.546566i | \(0.815935\pi\) | |||||||
\(972\) | −2.73364e12 | −0.0982297 | ||||||||
\(973\) | −8.14611e12 | −0.291368 | ||||||||
\(974\) | 1.89191e13 | 0.673574 | ||||||||
\(975\) | −2.78025e12 | −0.0985289 | ||||||||
\(976\) | −1.57513e12 | −0.0555639 | ||||||||
\(977\) | 2.53890e13 | 0.891496 | 0.445748 | − | 0.895159i | \(-0.352938\pi\) | ||||
0.445748 | + | 0.895159i | \(0.352938\pi\) | |||||||
\(978\) | −4.49494e13 | −1.57108 | ||||||||
\(979\) | 1.13633e12 | 0.0395350 | ||||||||
\(980\) | 2.08953e13 | 0.723654 | ||||||||
\(981\) | −1.76183e13 | −0.607370 | ||||||||
\(982\) | −8.54153e13 | −2.93112 | ||||||||
\(983\) | −8.90780e12 | −0.304284 | −0.152142 | − | 0.988359i | \(-0.548617\pi\) | ||||
−0.152142 | + | 0.988359i | \(0.548617\pi\) | |||||||
\(984\) | −3.45033e12 | −0.117323 | ||||||||
\(985\) | 4.42416e13 | 1.49750 | ||||||||
\(986\) | 2.58649e13 | 0.871493 | ||||||||
\(987\) | 1.02729e13 | 0.344559 | ||||||||
\(988\) | −7.04544e13 | −2.35235 | ||||||||
\(989\) | 4.22569e12 | 0.140448 | ||||||||
\(990\) | 4.58094e11 | 0.0151564 | ||||||||
\(991\) | 3.90840e13 | 1.28727 | 0.643633 | − | 0.765335i | \(-0.277427\pi\) | ||||
0.643633 | + | 0.765335i | \(0.277427\pi\) | |||||||
\(992\) | 4.78945e13 | 1.57030 | ||||||||
\(993\) | −2.32752e13 | −0.759665 | ||||||||
\(994\) | −7.12382e12 | −0.231459 | ||||||||
\(995\) | −1.34990e13 | −0.436614 | ||||||||
\(996\) | 4.72806e13 | 1.52235 | ||||||||
\(997\) | −1.94045e12 | −0.0621975 | −0.0310988 | − | 0.999516i | \(-0.509901\pi\) | ||||
−0.0310988 | + | 0.999516i | \(0.509901\pi\) | |||||||
\(998\) | 4.80195e12 | 0.153225 | ||||||||
\(999\) | 3.97115e12 | 0.126145 |
(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 | 3.10.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.10.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 48.10.a.e.1.1 | 1 | |||
5.2 | odd | 4 | 75.10.b.a.49.1 | 2 | |||
5.3 | odd | 4 | 75.10.b.a.49.2 | 2 | |||
5.4 | even | 2 | 75.10.a.d.1.1 | 1 | |||
7.6 | odd | 2 | 147.10.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 192.10.a.f.1.1 | 1 | |||
8.5 | even | 2 | 192.10.a.m.1.1 | 1 | |||
9.2 | odd | 6 | 81.10.c.a.28.1 | 2 | |||
9.4 | even | 3 | 81.10.c.e.55.1 | 2 | |||
9.5 | odd | 6 | 81.10.c.a.55.1 | 2 | |||
9.7 | even | 3 | 81.10.c.e.28.1 | 2 | |||
11.10 | odd | 2 | 363.10.a.b.1.1 | 1 | |||
12.11 | even | 2 | 144.10.a.l.1.1 | 1 | |||
15.2 | even | 4 | 225.10.b.a.199.2 | 2 | |||
15.8 | even | 4 | 225.10.b.a.199.1 | 2 | |||
15.14 | odd | 2 | 225.10.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.10.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.10.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
48.10.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
75.10.a.d.1.1 | 1 | 5.4 | even | 2 | |||
75.10.b.a.49.1 | 2 | 5.2 | odd | 4 | |||
75.10.b.a.49.2 | 2 | 5.3 | odd | 4 | |||
81.10.c.a.28.1 | 2 | 9.2 | odd | 6 | |||
81.10.c.a.55.1 | 2 | 9.5 | odd | 6 | |||
81.10.c.e.28.1 | 2 | 9.7 | even | 3 | |||
81.10.c.e.55.1 | 2 | 9.4 | even | 3 | |||
144.10.a.l.1.1 | 1 | 12.11 | even | 2 | |||
147.10.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
192.10.a.f.1.1 | 1 | 8.3 | odd | 2 | |||
192.10.a.m.1.1 | 1 | 8.5 | even | 2 | |||
225.10.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
225.10.b.a.199.1 | 2 | 15.8 | even | 4 | |||
225.10.b.a.199.2 | 2 | 15.2 | even | 4 | |||
363.10.a.b.1.1 | 1 | 11.10 | odd | 2 |