Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,8,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(11.8706309684\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17953}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4488 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-66.4944\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | 61.4944 | 1.31496 | 0.657478 | − | 0.753474i | \(-0.271623\pi\) | ||||
0.657478 | + | 0.753474i | \(0.271623\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −235.483 | −0.842490 | −0.421245 | − | 0.906947i | \(-0.638407\pi\) | ||||
−0.421245 | + | 0.906947i | \(0.638407\pi\) | |||||||
\(6\) | −491.955 | −0.929814 | ||||||||
\(7\) | −1111.92 | −1.22527 | −0.612634 | − | 0.790367i | \(-0.709890\pi\) | ||||
−0.612634 | + | 0.790367i | \(0.709890\pi\) | |||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 1594.56 | 0.729109 | ||||||||
\(10\) | 1883.87 | 0.595731 | ||||||||
\(11\) | 1428.49 | 0.323597 | 0.161798 | − | 0.986824i | \(-0.448271\pi\) | ||||
0.161798 | + | 0.986824i | \(0.448271\pi\) | |||||||
\(12\) | 3935.64 | 0.657478 | ||||||||
\(13\) | −5515.63 | −0.696295 | −0.348148 | − | 0.937440i | \(-0.613189\pi\) | ||||
−0.348148 | + | 0.937440i | \(0.613189\pi\) | |||||||
\(14\) | 8895.37 | 0.866395 | ||||||||
\(15\) | −14480.9 | −1.10784 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −27453.3 | −1.35526 | −0.677632 | − | 0.735402i | \(-0.736994\pi\) | ||||
−0.677632 | + | 0.735402i | \(0.736994\pi\) | |||||||
\(18\) | −12756.5 | −0.515558 | ||||||||
\(19\) | 6859.00 | 0.229416 | ||||||||
\(20\) | −15070.9 | −0.421245 | ||||||||
\(21\) | −68377.0 | −1.61117 | ||||||||
\(22\) | −11428.0 | −0.228817 | ||||||||
\(23\) | −62205.4 | −1.06606 | −0.533029 | − | 0.846097i | \(-0.678946\pi\) | ||||
−0.533029 | + | 0.846097i | \(0.678946\pi\) | |||||||
\(24\) | −31485.1 | −0.464907 | ||||||||
\(25\) | −22672.7 | −0.290210 | ||||||||
\(26\) | 44125.0 | 0.492355 | ||||||||
\(27\) | −36431.6 | −0.356210 | ||||||||
\(28\) | −71163.0 | −0.612634 | ||||||||
\(29\) | 209139. | 1.59236 | 0.796180 | − | 0.605059i | \(-0.206851\pi\) | ||||
0.796180 | + | 0.605059i | \(0.206851\pi\) | |||||||
\(30\) | 115847. | 0.783360 | ||||||||
\(31\) | −130002. | −0.783762 | −0.391881 | − | 0.920016i | \(-0.628175\pi\) | ||||
−0.391881 | + | 0.920016i | \(0.628175\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | 87844.4 | 0.425515 | ||||||||
\(34\) | 219627. | 0.958316 | ||||||||
\(35\) | 261839. | 1.03228 | ||||||||
\(36\) | 102052. | 0.364555 | ||||||||
\(37\) | −35499.1 | −0.115216 | −0.0576078 | − | 0.998339i | \(-0.518347\pi\) | ||||
−0.0576078 | + | 0.998339i | \(0.518347\pi\) | |||||||
\(38\) | −54872.0 | −0.162221 | ||||||||
\(39\) | −339180. | −0.915597 | ||||||||
\(40\) | 120567. | 0.297865 | ||||||||
\(41\) | 563790. | 1.27754 | 0.638769 | − | 0.769399i | \(-0.279444\pi\) | ||||
0.638769 | + | 0.769399i | \(0.279444\pi\) | |||||||
\(42\) | 547016. | 1.13927 | ||||||||
\(43\) | −352181. | −0.675502 | −0.337751 | − | 0.941236i | \(-0.609666\pi\) | ||||
−0.337751 | + | 0.941236i | \(0.609666\pi\) | |||||||
\(44\) | 91423.6 | 0.161798 | ||||||||
\(45\) | −375492. | −0.614267 | ||||||||
\(46\) | 497643. | 0.753816 | ||||||||
\(47\) | −747727. | −1.05051 | −0.525256 | − | 0.850944i | \(-0.676030\pi\) | ||||
−0.525256 | + | 0.850944i | \(0.676030\pi\) | |||||||
\(48\) | 251881. | 0.328739 | ||||||||
\(49\) | 412827. | 0.501281 | ||||||||
\(50\) | 181381. | 0.205209 | ||||||||
\(51\) | −1.68823e6 | −1.78211 | ||||||||
\(52\) | −353000. | −0.348148 | ||||||||
\(53\) | 684889. | 0.631910 | 0.315955 | − | 0.948774i | \(-0.397675\pi\) | ||||
0.315955 | + | 0.948774i | \(0.397675\pi\) | |||||||
\(54\) | 291453. | 0.251878 | ||||||||
\(55\) | −336386. | −0.272627 | ||||||||
\(56\) | 569304. | 0.433198 | ||||||||
\(57\) | 421790. | 0.301672 | ||||||||
\(58\) | −1.67311e6 | −1.12597 | ||||||||
\(59\) | 2.84345e6 | 1.80245 | 0.901225 | − | 0.433352i | \(-0.142669\pi\) | ||||
0.901225 | + | 0.433352i | \(0.142669\pi\) | |||||||
\(60\) | −926778. | −0.553919 | ||||||||
\(61\) | −565615. | −0.319056 | −0.159528 | − | 0.987193i | \(-0.550997\pi\) | ||||
−0.159528 | + | 0.987193i | \(0.550997\pi\) | |||||||
\(62\) | 1.04002e6 | 0.554203 | ||||||||
\(63\) | −1.77303e6 | −0.893354 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 1.29884e6 | 0.586622 | ||||||||
\(66\) | −702755. | −0.300885 | ||||||||
\(67\) | 3.49970e6 | 1.42157 | 0.710787 | − | 0.703407i | \(-0.248339\pi\) | ||||
0.710787 | + | 0.703407i | \(0.248339\pi\) | |||||||
\(68\) | −1.75701e6 | −0.677632 | ||||||||
\(69\) | −3.82528e6 | −1.40182 | ||||||||
\(70\) | −2.09471e6 | −0.729930 | ||||||||
\(71\) | 296273. | 0.0982398 | 0.0491199 | − | 0.998793i | \(-0.484358\pi\) | ||||
0.0491199 | + | 0.998793i | \(0.484358\pi\) | |||||||
\(72\) | −816416. | −0.257779 | ||||||||
\(73\) | −1.60675e6 | −0.483412 | −0.241706 | − | 0.970350i | \(-0.577707\pi\) | ||||
−0.241706 | + | 0.970350i | \(0.577707\pi\) | |||||||
\(74\) | 283993. | 0.0814697 | ||||||||
\(75\) | −1.39424e6 | −0.381613 | ||||||||
\(76\) | 438976. | 0.114708 | ||||||||
\(77\) | −1.58837e6 | −0.396493 | ||||||||
\(78\) | 2.71344e6 | 0.647425 | ||||||||
\(79\) | −2.55303e6 | −0.582586 | −0.291293 | − | 0.956634i | \(-0.594086\pi\) | ||||
−0.291293 | + | 0.956634i | \(0.594086\pi\) | |||||||
\(80\) | −964539. | −0.210623 | ||||||||
\(81\) | −5.72765e6 | −1.19751 | ||||||||
\(82\) | −4.51032e6 | −0.903356 | ||||||||
\(83\) | 352021. | 0.0675764 | 0.0337882 | − | 0.999429i | \(-0.489243\pi\) | ||||
0.0337882 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(84\) | −4.37613e6 | −0.805587 | ||||||||
\(85\) | 6.46480e6 | 1.14180 | ||||||||
\(86\) | 2.81745e6 | 0.477652 | ||||||||
\(87\) | 1.28609e7 | 2.09388 | ||||||||
\(88\) | −731389. | −0.114409 | ||||||||
\(89\) | 5.32675e6 | 0.800935 | 0.400467 | − | 0.916311i | \(-0.368848\pi\) | ||||
0.400467 | + | 0.916311i | \(0.368848\pi\) | |||||||
\(90\) | 3.00394e6 | 0.434353 | ||||||||
\(91\) | 6.13295e6 | 0.853148 | ||||||||
\(92\) | −3.98114e6 | −0.533029 | ||||||||
\(93\) | −7.99439e6 | −1.03061 | ||||||||
\(94\) | 5.98182e6 | 0.742824 | ||||||||
\(95\) | −1.61518e6 | −0.193281 | ||||||||
\(96\) | −2.01505e6 | −0.232454 | ||||||||
\(97\) | 1.35294e7 | 1.50514 | 0.752572 | − | 0.658510i | \(-0.228813\pi\) | ||||
0.752572 | + | 0.658510i | \(0.228813\pi\) | |||||||
\(98\) | −3.30261e6 | −0.354459 | ||||||||
\(99\) | 2.27782e6 | 0.235937 | ||||||||
\(100\) | −1.45105e6 | −0.145105 | ||||||||
\(101\) | −3.78746e6 | −0.365783 | −0.182892 | − | 0.983133i | \(-0.558546\pi\) | ||||
−0.182892 | + | 0.983133i | \(0.558546\pi\) | |||||||
\(102\) | 1.35058e7 | 1.26014 | ||||||||
\(103\) | −1.37733e7 | −1.24196 | −0.620980 | − | 0.783826i | \(-0.713265\pi\) | ||||
−0.620980 | + | 0.783826i | \(0.713265\pi\) | |||||||
\(104\) | 2.82400e6 | 0.246177 | ||||||||
\(105\) | 1.61016e7 | 1.35740 | ||||||||
\(106\) | −5.47912e6 | −0.446827 | ||||||||
\(107\) | 1.75990e7 | 1.38882 | 0.694408 | − | 0.719581i | \(-0.255666\pi\) | ||||
0.694408 | + | 0.719581i | \(0.255666\pi\) | |||||||
\(108\) | −2.33163e6 | −0.178105 | ||||||||
\(109\) | −2.28268e7 | −1.68831 | −0.844155 | − | 0.536099i | \(-0.819897\pi\) | ||||
−0.844155 | + | 0.536099i | \(0.819897\pi\) | |||||||
\(110\) | 2.69109e6 | 0.192776 | ||||||||
\(111\) | −2.18300e6 | −0.151503 | ||||||||
\(112\) | −4.55443e6 | −0.306317 | ||||||||
\(113\) | −1.61795e7 | −1.05485 | −0.527425 | − | 0.849601i | \(-0.676843\pi\) | ||||
−0.527425 | + | 0.849601i | \(0.676843\pi\) | |||||||
\(114\) | −3.37432e6 | −0.213314 | ||||||||
\(115\) | 1.46483e7 | 0.898143 | ||||||||
\(116\) | 1.33849e7 | 0.796180 | ||||||||
\(117\) | −8.79501e6 | −0.507675 | ||||||||
\(118\) | −2.27476e7 | −1.27452 | ||||||||
\(119\) | 3.05259e7 | 1.66056 | ||||||||
\(120\) | 7.41422e6 | 0.391680 | ||||||||
\(121\) | −1.74466e7 | −0.895285 | ||||||||
\(122\) | 4.52492e6 | 0.225607 | ||||||||
\(123\) | 3.46699e7 | 1.67991 | ||||||||
\(124\) | −8.32013e6 | −0.391881 | ||||||||
\(125\) | 2.37362e7 | 1.08699 | ||||||||
\(126\) | 1.41842e7 | 0.631697 | ||||||||
\(127\) | −4.46993e7 | −1.93637 | −0.968183 | − | 0.250245i | \(-0.919489\pi\) | ||||
−0.968183 | + | 0.250245i | \(0.919489\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | −2.16572e7 | −0.888255 | ||||||||
\(130\) | −1.03907e7 | −0.414804 | ||||||||
\(131\) | −1.51806e7 | −0.589984 | −0.294992 | − | 0.955500i | \(-0.595317\pi\) | ||||
−0.294992 | + | 0.955500i | \(0.595317\pi\) | |||||||
\(132\) | 5.62204e6 | 0.212758 | ||||||||
\(133\) | −7.62667e6 | −0.281096 | ||||||||
\(134\) | −2.79976e7 | −1.00520 | ||||||||
\(135\) | 8.57904e6 | 0.300103 | ||||||||
\(136\) | 1.40561e7 | 0.479158 | ||||||||
\(137\) | −2.46831e7 | −0.820120 | −0.410060 | − | 0.912059i | \(-0.634492\pi\) | ||||
−0.410060 | + | 0.912059i | \(0.634492\pi\) | |||||||
\(138\) | 3.06023e7 | 0.991235 | ||||||||
\(139\) | −3.71264e7 | −1.17255 | −0.586275 | − | 0.810112i | \(-0.699406\pi\) | ||||
−0.586275 | + | 0.810112i | \(0.699406\pi\) | |||||||
\(140\) | 1.67577e7 | 0.516138 | ||||||||
\(141\) | −4.59811e7 | −1.38138 | ||||||||
\(142\) | −2.37018e6 | −0.0694660 | ||||||||
\(143\) | −7.87904e6 | −0.225319 | ||||||||
\(144\) | 6.53132e6 | 0.182277 | ||||||||
\(145\) | −4.92487e7 | −1.34155 | ||||||||
\(146\) | 1.28540e7 | 0.341824 | ||||||||
\(147\) | 2.53865e7 | 0.659163 | ||||||||
\(148\) | −2.27194e6 | −0.0576078 | ||||||||
\(149\) | −5.61635e7 | −1.39092 | −0.695460 | − | 0.718565i | \(-0.744799\pi\) | ||||
−0.695460 | + | 0.718565i | \(0.744799\pi\) | |||||||
\(150\) | 1.11539e7 | 0.269841 | ||||||||
\(151\) | −2.90803e7 | −0.687352 | −0.343676 | − | 0.939088i | \(-0.611672\pi\) | ||||
−0.343676 | + | 0.939088i | \(0.611672\pi\) | |||||||
\(152\) | −3.51181e6 | −0.0811107 | ||||||||
\(153\) | −4.37760e7 | −0.988135 | ||||||||
\(154\) | 1.27070e7 | 0.280363 | ||||||||
\(155\) | 3.06133e7 | 0.660312 | ||||||||
\(156\) | −2.17075e7 | −0.457799 | ||||||||
\(157\) | 7.42283e7 | 1.53081 | 0.765404 | − | 0.643550i | \(-0.222539\pi\) | ||||
0.765404 | + | 0.643550i | \(0.222539\pi\) | |||||||
\(158\) | 2.04242e7 | 0.411951 | ||||||||
\(159\) | 4.21169e7 | 0.830933 | ||||||||
\(160\) | 7.71631e6 | 0.148933 | ||||||||
\(161\) | 6.91675e7 | 1.30621 | ||||||||
\(162\) | 4.58212e7 | 0.846767 | ||||||||
\(163\) | 6.25286e7 | 1.13089 | 0.565447 | − | 0.824785i | \(-0.308704\pi\) | ||||
0.565447 | + | 0.824785i | \(0.308704\pi\) | |||||||
\(164\) | 3.60826e7 | 0.638769 | ||||||||
\(165\) | −2.06859e7 | −0.358493 | ||||||||
\(166\) | −2.81616e6 | −0.0477837 | ||||||||
\(167\) | 4.65406e7 | 0.773258 | 0.386629 | − | 0.922235i | \(-0.373639\pi\) | ||||
0.386629 | + | 0.922235i | \(0.373639\pi\) | |||||||
\(168\) | 3.50090e7 | 0.569636 | ||||||||
\(169\) | −3.23264e7 | −0.515173 | ||||||||
\(170\) | −5.17184e7 | −0.807372 | ||||||||
\(171\) | 1.09371e7 | 0.167269 | ||||||||
\(172\) | −2.25396e7 | −0.337751 | ||||||||
\(173\) | −3.78118e7 | −0.555221 | −0.277611 | − | 0.960694i | \(-0.589542\pi\) | ||||
−0.277611 | + | 0.960694i | \(0.589542\pi\) | |||||||
\(174\) | −1.02887e8 | −1.48060 | ||||||||
\(175\) | 2.52102e7 | 0.355585 | ||||||||
\(176\) | 5.85111e6 | 0.0808992 | ||||||||
\(177\) | 1.74856e8 | 2.37014 | ||||||||
\(178\) | −4.26140e7 | −0.566347 | ||||||||
\(179\) | 1.36978e8 | 1.78511 | 0.892554 | − | 0.450941i | \(-0.148912\pi\) | ||||
0.892554 | + | 0.450941i | \(0.148912\pi\) | |||||||
\(180\) | −2.40315e7 | −0.307134 | ||||||||
\(181\) | 3.29158e7 | 0.412600 | 0.206300 | − | 0.978489i | \(-0.433858\pi\) | ||||
0.206300 | + | 0.978489i | \(0.433858\pi\) | |||||||
\(182\) | −4.90636e7 | −0.603267 | ||||||||
\(183\) | −3.47822e7 | −0.419544 | ||||||||
\(184\) | 3.18492e7 | 0.376908 | ||||||||
\(185\) | 8.35944e6 | 0.0970680 | ||||||||
\(186\) | 6.39552e7 | 0.728753 | ||||||||
\(187\) | −3.92169e7 | −0.438559 | ||||||||
\(188\) | −4.78546e7 | −0.525256 | ||||||||
\(189\) | 4.05091e7 | 0.436452 | ||||||||
\(190\) | 1.29214e7 | 0.136670 | ||||||||
\(191\) | −2.19935e7 | −0.228390 | −0.114195 | − | 0.993458i | \(-0.536429\pi\) | ||||
−0.114195 | + | 0.993458i | \(0.536429\pi\) | |||||||
\(192\) | 1.61204e7 | 0.164369 | ||||||||
\(193\) | −1.22938e8 | −1.23094 | −0.615468 | − | 0.788162i | \(-0.711033\pi\) | ||||
−0.615468 | + | 0.788162i | \(0.711033\pi\) | |||||||
\(194\) | −1.08235e8 | −1.06430 | ||||||||
\(195\) | 7.98713e7 | 0.771382 | ||||||||
\(196\) | 2.64209e7 | 0.250641 | ||||||||
\(197\) | −1.51613e8 | −1.41288 | −0.706439 | − | 0.707774i | \(-0.749699\pi\) | ||||
−0.706439 | + | 0.707774i | \(0.749699\pi\) | |||||||
\(198\) | −1.82226e7 | −0.166833 | ||||||||
\(199\) | −6.05312e7 | −0.544495 | −0.272247 | − | 0.962227i | \(-0.587767\pi\) | ||||
−0.272247 | + | 0.962227i | \(0.587767\pi\) | |||||||
\(200\) | 1.16084e7 | 0.102605 | ||||||||
\(201\) | 2.15212e8 | 1.86931 | ||||||||
\(202\) | 3.02997e7 | 0.258648 | ||||||||
\(203\) | −2.32546e8 | −1.95107 | ||||||||
\(204\) | −1.08046e8 | −0.891056 | ||||||||
\(205\) | −1.32763e8 | −1.07631 | ||||||||
\(206\) | 1.10186e8 | 0.878198 | ||||||||
\(207\) | −9.91903e7 | −0.777272 | ||||||||
\(208\) | −2.25920e7 | −0.174074 | ||||||||
\(209\) | 9.79804e6 | 0.0742382 | ||||||||
\(210\) | −1.28813e8 | −0.959825 | ||||||||
\(211\) | 1.35344e7 | 0.0991862 | 0.0495931 | − | 0.998770i | \(-0.484208\pi\) | ||||
0.0495931 | + | 0.998770i | \(0.484208\pi\) | |||||||
\(212\) | 4.38329e7 | 0.315955 | ||||||||
\(213\) | 1.82191e7 | 0.129181 | ||||||||
\(214\) | −1.40792e8 | −0.982042 | ||||||||
\(215\) | 8.29327e7 | 0.569104 | ||||||||
\(216\) | 1.86530e7 | 0.125939 | ||||||||
\(217\) | 1.44552e8 | 0.960318 | ||||||||
\(218\) | 1.82614e8 | 1.19382 | ||||||||
\(219\) | −9.88060e7 | −0.635666 | ||||||||
\(220\) | −2.15287e7 | −0.136314 | ||||||||
\(221\) | 1.51422e8 | 0.943663 | ||||||||
\(222\) | 1.74640e7 | 0.107129 | ||||||||
\(223\) | −4.84849e6 | −0.0292778 | −0.0146389 | − | 0.999893i | \(-0.504660\pi\) | ||||
−0.0146389 | + | 0.999893i | \(0.504660\pi\) | |||||||
\(224\) | 3.64354e7 | 0.216599 | ||||||||
\(225\) | −3.61530e7 | −0.211595 | ||||||||
\(226\) | 1.29436e8 | 0.745892 | ||||||||
\(227\) | 3.45214e8 | 1.95883 | 0.979417 | − | 0.201848i | \(-0.0646948\pi\) | ||||
0.979417 | + | 0.201848i | \(0.0646948\pi\) | |||||||
\(228\) | 2.69946e7 | 0.150836 | ||||||||
\(229\) | 1.36402e8 | 0.750581 | 0.375290 | − | 0.926907i | \(-0.377543\pi\) | ||||
0.375290 | + | 0.926907i | \(0.377543\pi\) | |||||||
\(230\) | −1.17187e8 | −0.635083 | ||||||||
\(231\) | −9.76761e7 | −0.521370 | ||||||||
\(232\) | −1.07079e8 | −0.562984 | ||||||||
\(233\) | −3.27111e8 | −1.69414 | −0.847069 | − | 0.531482i | \(-0.821635\pi\) | ||||
−0.847069 | + | 0.531482i | \(0.821635\pi\) | |||||||
\(234\) | 7.03601e7 | 0.358980 | ||||||||
\(235\) | 1.76077e8 | 0.885046 | ||||||||
\(236\) | 1.81981e8 | 0.901225 | ||||||||
\(237\) | −1.56997e8 | −0.766075 | ||||||||
\(238\) | −2.44207e8 | −1.17419 | ||||||||
\(239\) | −1.78511e8 | −0.845807 | −0.422903 | − | 0.906175i | \(-0.638989\pi\) | ||||
−0.422903 | + | 0.906175i | \(0.638989\pi\) | |||||||
\(240\) | −5.93138e7 | −0.276959 | ||||||||
\(241\) | −2.24108e8 | −1.03133 | −0.515665 | − | 0.856791i | \(-0.672455\pi\) | ||||
−0.515665 | + | 0.856791i | \(0.672455\pi\) | |||||||
\(242\) | 1.39573e8 | 0.633062 | ||||||||
\(243\) | −2.72542e8 | −1.21846 | ||||||||
\(244\) | −3.61994e7 | −0.159528 | ||||||||
\(245\) | −9.72138e7 | −0.422325 | ||||||||
\(246\) | −2.77359e8 | −1.18787 | ||||||||
\(247\) | −3.78317e7 | −0.159741 | ||||||||
\(248\) | 6.65610e7 | 0.277102 | ||||||||
\(249\) | 2.16473e7 | 0.0888599 | ||||||||
\(250\) | −1.89889e8 | −0.768618 | ||||||||
\(251\) | 2.31812e8 | 0.925290 | 0.462645 | − | 0.886544i | \(-0.346901\pi\) | ||||
0.462645 | + | 0.886544i | \(0.346901\pi\) | |||||||
\(252\) | −1.13474e8 | −0.446677 | ||||||||
\(253\) | −8.88601e7 | −0.344973 | ||||||||
\(254\) | 3.57594e8 | 1.36922 | ||||||||
\(255\) | 3.97549e8 | 1.50141 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −3.98240e8 | −1.46345 | −0.731727 | − | 0.681598i | \(-0.761285\pi\) | ||||
−0.731727 | + | 0.681598i | \(0.761285\pi\) | |||||||
\(258\) | 1.73257e8 | 0.628091 | ||||||||
\(259\) | 3.94722e7 | 0.141170 | ||||||||
\(260\) | 8.31256e7 | 0.293311 | ||||||||
\(261\) | 3.33485e8 | 1.16100 | ||||||||
\(262\) | 1.21445e8 | 0.417182 | ||||||||
\(263\) | 3.10207e8 | 1.05149 | 0.525746 | − | 0.850642i | \(-0.323786\pi\) | ||||
0.525746 | + | 0.850642i | \(0.323786\pi\) | |||||||
\(264\) | −4.49763e7 | −0.150442 | ||||||||
\(265\) | −1.61280e8 | −0.532378 | ||||||||
\(266\) | 6.10134e7 | 0.198765 | ||||||||
\(267\) | 3.27565e8 | 1.05319 | ||||||||
\(268\) | 2.23981e8 | 0.710787 | ||||||||
\(269\) | −1.86836e8 | −0.585230 | −0.292615 | − | 0.956230i | \(-0.594525\pi\) | ||||
−0.292615 | + | 0.956230i | \(0.594525\pi\) | |||||||
\(270\) | −6.86323e7 | −0.212205 | ||||||||
\(271\) | −1.10277e8 | −0.336584 | −0.168292 | − | 0.985737i | \(-0.553825\pi\) | ||||
−0.168292 | + | 0.985737i | \(0.553825\pi\) | |||||||
\(272\) | −1.12449e8 | −0.338816 | ||||||||
\(273\) | 3.77142e8 | 1.12185 | ||||||||
\(274\) | 1.97465e8 | 0.579912 | ||||||||
\(275\) | −3.23878e7 | −0.0939110 | ||||||||
\(276\) | −2.44818e8 | −0.700909 | ||||||||
\(277\) | 6.68855e8 | 1.89083 | 0.945415 | − | 0.325868i | \(-0.105656\pi\) | ||||
0.945415 | + | 0.325868i | \(0.105656\pi\) | |||||||
\(278\) | 2.97011e8 | 0.829118 | ||||||||
\(279\) | −2.07296e8 | −0.571448 | ||||||||
\(280\) | −1.34062e8 | −0.364965 | ||||||||
\(281\) | −2.93967e8 | −0.790364 | −0.395182 | − | 0.918603i | \(-0.629318\pi\) | ||||
−0.395182 | + | 0.918603i | \(0.629318\pi\) | |||||||
\(282\) | 3.67848e8 | 0.976781 | ||||||||
\(283\) | −3.03430e8 | −0.795804 | −0.397902 | − | 0.917428i | \(-0.630262\pi\) | ||||
−0.397902 | + | 0.917428i | \(0.630262\pi\) | |||||||
\(284\) | 1.89615e7 | 0.0491199 | ||||||||
\(285\) | −9.93245e7 | −0.254155 | ||||||||
\(286\) | 6.30324e7 | 0.159324 | ||||||||
\(287\) | −6.26890e8 | −1.56533 | ||||||||
\(288\) | −5.22506e7 | −0.128889 | ||||||||
\(289\) | 3.43346e8 | 0.836738 | ||||||||
\(290\) | 3.93989e8 | 0.948618 | ||||||||
\(291\) | 8.31983e8 | 1.97920 | ||||||||
\(292\) | −1.02832e8 | −0.241706 | ||||||||
\(293\) | −4.38613e8 | −1.01870 | −0.509348 | − | 0.860561i | \(-0.670113\pi\) | ||||
−0.509348 | + | 0.860561i | \(0.670113\pi\) | |||||||
\(294\) | −2.03092e8 | −0.466099 | ||||||||
\(295\) | −6.69584e8 | −1.51855 | ||||||||
\(296\) | 1.81755e7 | 0.0407349 | ||||||||
\(297\) | −5.20424e7 | −0.115268 | ||||||||
\(298\) | 4.49308e8 | 0.983529 | ||||||||
\(299\) | 3.43102e8 | 0.742290 | ||||||||
\(300\) | −8.92315e7 | −0.190807 | ||||||||
\(301\) | 3.91598e8 | 0.827671 | ||||||||
\(302\) | 2.32642e8 | 0.486031 | ||||||||
\(303\) | −2.32908e8 | −0.480989 | ||||||||
\(304\) | 2.80945e7 | 0.0573539 | ||||||||
\(305\) | 1.33193e8 | 0.268801 | ||||||||
\(306\) | 3.50208e8 | 0.698717 | ||||||||
\(307\) | −7.09332e8 | −1.39915 | −0.699577 | − | 0.714557i | \(-0.746628\pi\) | ||||
−0.699577 | + | 0.714557i | \(0.746628\pi\) | |||||||
\(308\) | −1.01656e8 | −0.198246 | ||||||||
\(309\) | −8.46980e8 | −1.63312 | ||||||||
\(310\) | −2.44906e8 | −0.466911 | ||||||||
\(311\) | 8.87968e7 | 0.167393 | 0.0836963 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836963 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(312\) | 1.73660e8 | 0.323713 | ||||||||
\(313\) | −3.18179e8 | −0.586498 | −0.293249 | − | 0.956036i | \(-0.594737\pi\) | ||||
−0.293249 | + | 0.956036i | \(0.594737\pi\) | |||||||
\(314\) | −5.93826e8 | −1.08244 | ||||||||
\(315\) | 4.17518e8 | 0.752642 | ||||||||
\(316\) | −1.63394e8 | −0.291293 | ||||||||
\(317\) | −3.59359e8 | −0.633609 | −0.316804 | − | 0.948491i | \(-0.602610\pi\) | ||||
−0.316804 | + | 0.948491i | \(0.602610\pi\) | |||||||
\(318\) | −3.36935e8 | −0.587558 | ||||||||
\(319\) | 2.98753e8 | 0.515283 | ||||||||
\(320\) | −6.17305e7 | −0.105311 | ||||||||
\(321\) | 1.08224e9 | 1.82623 | ||||||||
\(322\) | −5.53340e8 | −0.923627 | ||||||||
\(323\) | −1.88302e8 | −0.310919 | ||||||||
\(324\) | −3.66570e8 | −0.598755 | ||||||||
\(325\) | 1.25054e8 | 0.202072 | ||||||||
\(326\) | −5.00228e8 | −0.799663 | ||||||||
\(327\) | −1.40372e9 | −2.22005 | ||||||||
\(328\) | −2.88660e8 | −0.451678 | ||||||||
\(329\) | 8.31414e8 | 1.28716 | ||||||||
\(330\) | 1.65487e8 | 0.253493 | ||||||||
\(331\) | 3.76118e8 | 0.570068 | 0.285034 | − | 0.958517i | \(-0.407995\pi\) | ||||
0.285034 | + | 0.958517i | \(0.407995\pi\) | |||||||
\(332\) | 2.25293e7 | 0.0337882 | ||||||||
\(333\) | −5.66055e7 | −0.0840047 | ||||||||
\(334\) | −3.72325e8 | −0.546776 | ||||||||
\(335\) | −8.24122e8 | −1.19766 | ||||||||
\(336\) | −2.80072e8 | −0.402793 | ||||||||
\(337\) | −1.77732e8 | −0.252965 | −0.126483 | − | 0.991969i | \(-0.540369\pi\) | ||||
−0.126483 | + | 0.991969i | \(0.540369\pi\) | |||||||
\(338\) | 2.58611e8 | 0.364282 | ||||||||
\(339\) | −9.94950e8 | −1.38708 | ||||||||
\(340\) | 4.13747e8 | 0.570898 | ||||||||
\(341\) | −1.85707e8 | −0.253623 | ||||||||
\(342\) | −8.74968e7 | −0.118277 | ||||||||
\(343\) | 4.56684e8 | 0.611064 | ||||||||
\(344\) | 1.80317e8 | 0.238826 | ||||||||
\(345\) | 9.00790e8 | 1.18102 | ||||||||
\(346\) | 3.02494e8 | 0.392601 | ||||||||
\(347\) | −1.02645e9 | −1.31881 | −0.659406 | − | 0.751787i | \(-0.729192\pi\) | ||||
−0.659406 | + | 0.751787i | \(0.729192\pi\) | |||||||
\(348\) | 8.23095e8 | 1.04694 | ||||||||
\(349\) | 9.58510e8 | 1.20700 | 0.603501 | − | 0.797362i | \(-0.293772\pi\) | ||||
0.603501 | + | 0.797362i | \(0.293772\pi\) | |||||||
\(350\) | −2.01682e8 | −0.251437 | ||||||||
\(351\) | 2.00943e8 | 0.248027 | ||||||||
\(352\) | −4.68089e7 | −0.0572044 | ||||||||
\(353\) | 1.57619e9 | 1.90721 | 0.953603 | − | 0.301065i | \(-0.0973423\pi\) | ||||
0.953603 | + | 0.301065i | \(0.0973423\pi\) | |||||||
\(354\) | −1.39885e9 | −1.67594 | ||||||||
\(355\) | −6.97673e7 | −0.0827661 | ||||||||
\(356\) | 3.40912e8 | 0.400467 | ||||||||
\(357\) | 1.87717e9 | 2.18356 | ||||||||
\(358\) | −1.09582e9 | −1.26226 | ||||||||
\(359\) | 6.66897e8 | 0.760726 | 0.380363 | − | 0.924837i | \(-0.375799\pi\) | ||||
0.380363 | + | 0.924837i | \(0.375799\pi\) | |||||||
\(360\) | 1.92252e8 | 0.217176 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | −2.63326e8 | −0.291752 | ||||||||
\(363\) | −1.07287e9 | −1.17726 | ||||||||
\(364\) | 3.92509e8 | 0.426574 | ||||||||
\(365\) | 3.78362e8 | 0.407270 | ||||||||
\(366\) | 2.78257e8 | 0.296663 | ||||||||
\(367\) | −3.96513e8 | −0.418723 | −0.209361 | − | 0.977838i | \(-0.567138\pi\) | ||||
−0.209361 | + | 0.977838i | \(0.567138\pi\) | |||||||
\(368\) | −2.54793e8 | −0.266514 | ||||||||
\(369\) | 8.98998e8 | 0.931465 | ||||||||
\(370\) | −6.68755e7 | −0.0686375 | ||||||||
\(371\) | −7.61543e8 | −0.774258 | ||||||||
\(372\) | −5.11641e8 | −0.515306 | ||||||||
\(373\) | 7.83723e8 | 0.781955 | 0.390977 | − | 0.920400i | \(-0.372137\pi\) | ||||
0.390977 | + | 0.920400i | \(0.372137\pi\) | |||||||
\(374\) | 3.13735e8 | 0.310108 | ||||||||
\(375\) | 1.45964e9 | 1.42934 | ||||||||
\(376\) | 3.82836e8 | 0.371412 | ||||||||
\(377\) | −1.15353e9 | −1.10875 | ||||||||
\(378\) | −3.24073e8 | −0.308618 | ||||||||
\(379\) | 1.45545e9 | 1.37328 | 0.686641 | − | 0.726997i | \(-0.259085\pi\) | ||||
0.686641 | + | 0.726997i | \(0.259085\pi\) | |||||||
\(380\) | −1.03371e8 | −0.0966403 | ||||||||
\(381\) | −2.74875e9 | −2.54623 | ||||||||
\(382\) | 1.75948e8 | 0.161496 | ||||||||
\(383\) | −2.76212e8 | −0.251215 | −0.125608 | − | 0.992080i | \(-0.540088\pi\) | ||||
−0.125608 | + | 0.992080i | \(0.540088\pi\) | |||||||
\(384\) | −1.28963e8 | −0.116227 | ||||||||
\(385\) | 3.74035e8 | 0.334041 | ||||||||
\(386\) | 9.83504e8 | 0.870403 | ||||||||
\(387\) | −5.61574e8 | −0.492514 | ||||||||
\(388\) | 8.65883e8 | 0.752572 | ||||||||
\(389\) | 1.23552e9 | 1.06421 | 0.532104 | − | 0.846679i | \(-0.321401\pi\) | ||||
0.532104 | + | 0.846679i | \(0.321401\pi\) | |||||||
\(390\) | −6.38970e8 | −0.545449 | ||||||||
\(391\) | 1.70774e9 | 1.44479 | ||||||||
\(392\) | −2.11367e8 | −0.177230 | ||||||||
\(393\) | −9.33523e8 | −0.775803 | ||||||||
\(394\) | 1.21290e9 | 0.999055 | ||||||||
\(395\) | 6.01195e8 | 0.490823 | ||||||||
\(396\) | 1.45781e8 | 0.117969 | ||||||||
\(397\) | −9.34170e8 | −0.749306 | −0.374653 | − | 0.927165i | \(-0.622238\pi\) | ||||
−0.374653 | + | 0.927165i | \(0.622238\pi\) | |||||||
\(398\) | 4.84250e8 | 0.385016 | ||||||||
\(399\) | −4.68998e8 | −0.369628 | ||||||||
\(400\) | −9.28672e7 | −0.0725525 | ||||||||
\(401\) | 3.41301e8 | 0.264321 | 0.132161 | − | 0.991228i | \(-0.457809\pi\) | ||||
0.132161 | + | 0.991228i | \(0.457809\pi\) | |||||||
\(402\) | −1.72170e9 | −1.32180 | ||||||||
\(403\) | 7.17043e8 | 0.545729 | ||||||||
\(404\) | −2.42398e8 | −0.182892 | ||||||||
\(405\) | 1.34877e9 | 1.00889 | ||||||||
\(406\) | 1.86037e9 | 1.37961 | ||||||||
\(407\) | −5.07103e7 | −0.0372834 | ||||||||
\(408\) | 8.64371e8 | 0.630071 | ||||||||
\(409\) | 5.77116e8 | 0.417091 | 0.208546 | − | 0.978013i | \(-0.433127\pi\) | ||||
0.208546 | + | 0.978013i | \(0.433127\pi\) | |||||||
\(410\) | 1.06210e9 | 0.761068 | ||||||||
\(411\) | −1.51787e9 | −1.07842 | ||||||||
\(412\) | −8.81491e8 | −0.620980 | ||||||||
\(413\) | −3.16169e9 | −2.20848 | ||||||||
\(414\) | 7.93523e8 | 0.549614 | ||||||||
\(415\) | −8.28949e7 | −0.0569324 | ||||||||
\(416\) | 1.80736e8 | 0.123089 | ||||||||
\(417\) | −2.28307e9 | −1.54185 | ||||||||
\(418\) | −7.83843e7 | −0.0524943 | ||||||||
\(419\) | −2.35846e9 | −1.56631 | −0.783157 | − | 0.621824i | \(-0.786392\pi\) | ||||
−0.783157 | + | 0.621824i | \(0.786392\pi\) | |||||||
\(420\) | 1.03050e9 | 0.678699 | ||||||||
\(421\) | 1.38293e9 | 0.903258 | 0.451629 | − | 0.892206i | \(-0.350843\pi\) | ||||
0.451629 | + | 0.892206i | \(0.350843\pi\) | |||||||
\(422\) | −1.08275e8 | −0.0701352 | ||||||||
\(423\) | −1.19230e9 | −0.765937 | ||||||||
\(424\) | −3.50663e8 | −0.223414 | ||||||||
\(425\) | 6.22440e8 | 0.393311 | ||||||||
\(426\) | −1.45753e8 | −0.0913448 | ||||||||
\(427\) | 6.28920e8 | 0.390929 | ||||||||
\(428\) | 1.12634e9 | 0.694408 | ||||||||
\(429\) | −4.84517e8 | −0.296284 | ||||||||
\(430\) | −6.63462e8 | −0.402417 | ||||||||
\(431\) | 2.15391e9 | 1.29586 | 0.647929 | − | 0.761701i | \(-0.275636\pi\) | ||||
0.647929 | + | 0.761701i | \(0.275636\pi\) | |||||||
\(432\) | −1.49224e8 | −0.0890524 | ||||||||
\(433\) | 2.51495e9 | 1.48875 | 0.744375 | − | 0.667762i | \(-0.232748\pi\) | ||||
0.744375 | + | 0.667762i | \(0.232748\pi\) | |||||||
\(434\) | −1.15642e9 | −0.679047 | ||||||||
\(435\) | −3.02852e9 | −1.76408 | ||||||||
\(436\) | −1.46091e9 | −0.844155 | ||||||||
\(437\) | −4.26667e8 | −0.244570 | ||||||||
\(438\) | 7.90448e8 | 0.449483 | ||||||||
\(439\) | 2.29307e9 | 1.29357 | 0.646787 | − | 0.762671i | \(-0.276112\pi\) | ||||
0.646787 | + | 0.762671i | \(0.276112\pi\) | |||||||
\(440\) | 1.72230e8 | 0.0963882 | ||||||||
\(441\) | 6.58278e8 | 0.365489 | ||||||||
\(442\) | −1.21138e9 | −0.667270 | ||||||||
\(443\) | −1.06452e9 | −0.581757 | −0.290879 | − | 0.956760i | \(-0.593948\pi\) | ||||
−0.290879 | + | 0.956760i | \(0.593948\pi\) | |||||||
\(444\) | −1.39712e8 | −0.0757517 | ||||||||
\(445\) | −1.25436e9 | −0.674780 | ||||||||
\(446\) | 3.87879e7 | 0.0207026 | ||||||||
\(447\) | −3.45374e9 | −1.82900 | ||||||||
\(448\) | −2.91484e8 | −0.153158 | ||||||||
\(449\) | −1.22692e9 | −0.639665 | −0.319832 | − | 0.947474i | \(-0.603627\pi\) | ||||
−0.319832 | + | 0.947474i | \(0.603627\pi\) | |||||||
\(450\) | 2.89224e8 | 0.149620 | ||||||||
\(451\) | 8.05371e8 | 0.413407 | ||||||||
\(452\) | −1.03549e9 | −0.527425 | ||||||||
\(453\) | −1.78827e9 | −0.903837 | ||||||||
\(454\) | −2.76171e9 | −1.38510 | ||||||||
\(455\) | −1.44421e9 | −0.718769 | ||||||||
\(456\) | −2.15957e8 | −0.106657 | ||||||||
\(457\) | −5.19768e7 | −0.0254743 | −0.0127372 | − | 0.999919i | \(-0.504054\pi\) | ||||
−0.0127372 | + | 0.999919i | \(0.504054\pi\) | |||||||
\(458\) | −1.09122e9 | −0.530741 | ||||||||
\(459\) | 1.00017e9 | 0.482758 | ||||||||
\(460\) | 9.37493e8 | 0.449072 | ||||||||
\(461\) | −1.80708e9 | −0.859060 | −0.429530 | − | 0.903053i | \(-0.641321\pi\) | ||||
−0.429530 | + | 0.903053i | \(0.641321\pi\) | |||||||
\(462\) | 7.81409e8 | 0.368665 | ||||||||
\(463\) | 2.65408e9 | 1.24274 | 0.621372 | − | 0.783516i | \(-0.286576\pi\) | ||||
0.621372 | + | 0.783516i | \(0.286576\pi\) | |||||||
\(464\) | 8.56632e8 | 0.398090 | ||||||||
\(465\) | 1.88255e9 | 0.868281 | ||||||||
\(466\) | 2.61689e9 | 1.19794 | ||||||||
\(467\) | −1.15242e9 | −0.523602 | −0.261801 | − | 0.965122i | \(-0.584316\pi\) | ||||
−0.261801 | + | 0.965122i | \(0.584316\pi\) | |||||||
\(468\) | −5.62881e8 | −0.253838 | ||||||||
\(469\) | −3.89140e9 | −1.74181 | ||||||||
\(470\) | −1.40862e9 | −0.625822 | ||||||||
\(471\) | 4.56462e9 | 2.01294 | ||||||||
\(472\) | −1.45584e9 | −0.637262 | ||||||||
\(473\) | −5.03089e8 | −0.218590 | ||||||||
\(474\) | 1.25597e9 | 0.541697 | ||||||||
\(475\) | −1.55512e8 | −0.0665787 | ||||||||
\(476\) | 1.95366e9 | 0.830280 | ||||||||
\(477\) | 1.09210e9 | 0.460731 | ||||||||
\(478\) | 1.42808e9 | 0.598076 | ||||||||
\(479\) | −1.63103e9 | −0.678089 | −0.339044 | − | 0.940770i | \(-0.610104\pi\) | ||||
−0.339044 | + | 0.940770i | \(0.610104\pi\) | |||||||
\(480\) | 4.74510e8 | 0.195840 | ||||||||
\(481\) | 1.95800e8 | 0.0802240 | ||||||||
\(482\) | 1.79286e9 | 0.729260 | ||||||||
\(483\) | 4.25342e9 | 1.71760 | ||||||||
\(484\) | −1.11658e9 | −0.447643 | ||||||||
\(485\) | −3.18595e9 | −1.26807 | ||||||||
\(486\) | 2.18034e9 | 0.861583 | ||||||||
\(487\) | 4.91566e9 | 1.92855 | 0.964274 | − | 0.264906i | \(-0.0853410\pi\) | ||||
0.964274 | + | 0.264906i | \(0.0853410\pi\) | |||||||
\(488\) | 2.89595e8 | 0.112803 | ||||||||
\(489\) | 3.84516e9 | 1.48708 | ||||||||
\(490\) | 7.77710e8 | 0.298629 | ||||||||
\(491\) | 4.50903e8 | 0.171909 | 0.0859544 | − | 0.996299i | \(-0.472606\pi\) | ||||
0.0859544 | + | 0.996299i | \(0.472606\pi\) | |||||||
\(492\) | 2.21888e9 | 0.839953 | ||||||||
\(493\) | −5.74155e9 | −2.15807 | ||||||||
\(494\) | 3.02654e8 | 0.112954 | ||||||||
\(495\) | −5.36389e8 | −0.198775 | ||||||||
\(496\) | −5.32488e8 | −0.195940 | ||||||||
\(497\) | −3.29432e8 | −0.120370 | ||||||||
\(498\) | −1.73178e8 | −0.0628335 | ||||||||
\(499\) | −4.04813e9 | −1.45849 | −0.729243 | − | 0.684254i | \(-0.760128\pi\) | ||||
−0.729243 | + | 0.684254i | \(0.760128\pi\) | |||||||
\(500\) | 1.51911e9 | 0.543495 | ||||||||
\(501\) | 2.86199e9 | 1.01680 | ||||||||
\(502\) | −1.85449e9 | −0.654278 | ||||||||
\(503\) | 3.61727e9 | 1.26734 | 0.633671 | − | 0.773603i | \(-0.281547\pi\) | ||||
0.633671 | + | 0.773603i | \(0.281547\pi\) | |||||||
\(504\) | 9.07790e8 | 0.315848 | ||||||||
\(505\) | 8.91884e8 | 0.308169 | ||||||||
\(506\) | 7.10880e8 | 0.243933 | ||||||||
\(507\) | −1.98789e9 | −0.677430 | ||||||||
\(508\) | −2.86075e9 | −0.968183 | ||||||||
\(509\) | −2.33518e9 | −0.784889 | −0.392444 | − | 0.919776i | \(-0.628370\pi\) | ||||
−0.392444 | + | 0.919776i | \(0.628370\pi\) | |||||||
\(510\) | −3.18039e9 | −1.06166 | ||||||||
\(511\) | 1.78658e9 | 0.592309 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | −2.49885e8 | −0.0817201 | ||||||||
\(514\) | 3.18592e9 | 1.03482 | ||||||||
\(515\) | 3.24338e9 | 1.04634 | ||||||||
\(516\) | −1.38606e9 | −0.444128 | ||||||||
\(517\) | −1.06812e9 | −0.339942 | ||||||||
\(518\) | −3.15778e8 | −0.0998222 | ||||||||
\(519\) | −2.32521e9 | −0.730091 | ||||||||
\(520\) | −6.65005e8 | −0.207402 | ||||||||
\(521\) | −2.25540e9 | −0.698701 | −0.349350 | − | 0.936992i | \(-0.613598\pi\) | ||||
−0.349350 | + | 0.936992i | \(0.613598\pi\) | |||||||
\(522\) | −2.66788e9 | −0.820954 | ||||||||
\(523\) | 2.97677e8 | 0.0909891 | 0.0454945 | − | 0.998965i | \(-0.485514\pi\) | ||||
0.0454945 | + | 0.998965i | \(0.485514\pi\) | |||||||
\(524\) | −9.71560e8 | −0.294992 | ||||||||
\(525\) | 1.55029e9 | 0.467579 | ||||||||
\(526\) | −2.48165e9 | −0.743517 | ||||||||
\(527\) | 3.56899e9 | 1.06220 | ||||||||
\(528\) | 3.59811e8 | 0.106379 | ||||||||
\(529\) | 4.64685e8 | 0.136478 | ||||||||
\(530\) | 1.29024e9 | 0.376448 | ||||||||
\(531\) | 4.53405e9 | 1.31418 | ||||||||
\(532\) | −4.88107e8 | −0.140548 | ||||||||
\(533\) | −3.10966e9 | −0.889543 | ||||||||
\(534\) | −2.62052e9 | −0.744721 | ||||||||
\(535\) | −4.14427e9 | −1.17006 | ||||||||
\(536\) | −1.79185e9 | −0.502602 | ||||||||
\(537\) | 8.42336e9 | 2.34734 | ||||||||
\(538\) | 1.49468e9 | 0.413820 | ||||||||
\(539\) | 5.89721e8 | 0.162213 | ||||||||
\(540\) | 5.49059e8 | 0.150052 | ||||||||
\(541\) | −3.10860e9 | −0.844061 | −0.422031 | − | 0.906582i | \(-0.638683\pi\) | ||||
−0.422031 | + | 0.906582i | \(0.638683\pi\) | |||||||
\(542\) | 8.82218e8 | 0.238001 | ||||||||
\(543\) | 2.02414e9 | 0.542551 | ||||||||
\(544\) | 8.99590e8 | 0.239579 | ||||||||
\(545\) | 5.37533e9 | 1.42238 | ||||||||
\(546\) | −3.01714e9 | −0.793269 | ||||||||
\(547\) | −4.78922e9 | −1.25115 | −0.625575 | − | 0.780164i | \(-0.715136\pi\) | ||||
−0.625575 | + | 0.780164i | \(0.715136\pi\) | |||||||
\(548\) | −1.57972e9 | −0.410060 | ||||||||
\(549\) | −9.01908e8 | −0.232627 | ||||||||
\(550\) | 2.59102e8 | 0.0664051 | ||||||||
\(551\) | 1.43448e9 | 0.365313 | ||||||||
\(552\) | 1.95855e9 | 0.495618 | ||||||||
\(553\) | 2.83876e9 | 0.713824 | ||||||||
\(554\) | −5.35084e9 | −1.33702 | ||||||||
\(555\) | 5.14059e8 | 0.127640 | ||||||||
\(556\) | −2.37609e9 | −0.586275 | ||||||||
\(557\) | 3.74564e9 | 0.918403 | 0.459201 | − | 0.888332i | \(-0.348136\pi\) | ||||
0.459201 | + | 0.888332i | \(0.348136\pi\) | |||||||
\(558\) | 1.65837e9 | 0.404075 | ||||||||
\(559\) | 1.94250e9 | 0.470349 | ||||||||
\(560\) | 1.07249e9 | 0.258069 | ||||||||
\(561\) | −2.41162e9 | −0.576685 | ||||||||
\(562\) | 2.35174e9 | 0.558872 | ||||||||
\(563\) | −2.35071e8 | −0.0555162 | −0.0277581 | − | 0.999615i | \(-0.508837\pi\) | ||||
−0.0277581 | + | 0.999615i | \(0.508837\pi\) | |||||||
\(564\) | −2.94279e9 | −0.690688 | ||||||||
\(565\) | 3.81000e9 | 0.888701 | ||||||||
\(566\) | 2.42744e9 | 0.562719 | ||||||||
\(567\) | 6.36870e9 | 1.46727 | ||||||||
\(568\) | −1.51692e8 | −0.0347330 | ||||||||
\(569\) | 5.35979e8 | 0.121970 | 0.0609852 | − | 0.998139i | \(-0.480576\pi\) | ||||
0.0609852 | + | 0.998139i | \(0.480576\pi\) | |||||||
\(570\) | 7.94596e8 | 0.179715 | ||||||||
\(571\) | 1.00410e9 | 0.225709 | 0.112854 | − | 0.993612i | \(-0.464001\pi\) | ||||
0.112854 | + | 0.993612i | \(0.464001\pi\) | |||||||
\(572\) | −5.04259e8 | −0.112659 | ||||||||
\(573\) | −1.35248e9 | −0.300323 | ||||||||
\(574\) | 5.01512e9 | 1.10685 | ||||||||
\(575\) | 1.41036e9 | 0.309381 | ||||||||
\(576\) | 4.18005e8 | 0.0911386 | ||||||||
\(577\) | −8.44095e9 | −1.82926 | −0.914631 | − | 0.404290i | \(-0.867519\pi\) | ||||
−0.914631 | + | 0.404290i | \(0.867519\pi\) | |||||||
\(578\) | −2.74677e9 | −0.591663 | ||||||||
\(579\) | −7.56000e9 | −1.61863 | ||||||||
\(580\) | −3.15191e9 | −0.670774 | ||||||||
\(581\) | −3.91419e8 | −0.0827991 | ||||||||
\(582\) | −6.65587e9 | −1.39950 | ||||||||
\(583\) | 9.78361e8 | 0.204484 | ||||||||
\(584\) | 8.22655e8 | 0.170912 | ||||||||
\(585\) | 2.07108e9 | 0.427711 | ||||||||
\(586\) | 3.50890e9 | 0.720327 | ||||||||
\(587\) | 3.06553e9 | 0.625565 | 0.312783 | − | 0.949825i | \(-0.398739\pi\) | ||||
0.312783 | + | 0.949825i | \(0.398739\pi\) | |||||||
\(588\) | 1.62474e9 | 0.329581 | ||||||||
\(589\) | −8.91684e8 | −0.179807 | ||||||||
\(590\) | 5.35667e9 | 1.07377 | ||||||||
\(591\) | −9.32335e9 | −1.85787 | ||||||||
\(592\) | −1.45404e8 | −0.0288039 | ||||||||
\(593\) | 1.66016e9 | 0.326933 | 0.163467 | − | 0.986549i | \(-0.447732\pi\) | ||||
0.163467 | + | 0.986549i | \(0.447732\pi\) | |||||||
\(594\) | 4.16339e8 | 0.0815070 | ||||||||
\(595\) | −7.18835e9 | −1.39901 | ||||||||
\(596\) | −3.59446e9 | −0.695460 | ||||||||
\(597\) | −3.72233e9 | −0.715986 | ||||||||
\(598\) | −2.74481e9 | −0.524879 | ||||||||
\(599\) | −7.40940e9 | −1.40861 | −0.704303 | − | 0.709900i | \(-0.748740\pi\) | ||||
−0.704303 | + | 0.709900i | \(0.748740\pi\) | |||||||
\(600\) | 7.13852e8 | 0.134921 | ||||||||
\(601\) | 1.74087e9 | 0.327118 | 0.163559 | − | 0.986534i | \(-0.447703\pi\) | ||||
0.163559 | + | 0.986534i | \(0.447703\pi\) | |||||||
\(602\) | −3.13278e9 | −0.585251 | ||||||||
\(603\) | 5.58049e9 | 1.03648 | ||||||||
\(604\) | −1.86114e9 | −0.343676 | ||||||||
\(605\) | 4.10838e9 | 0.754269 | ||||||||
\(606\) | 1.86326e9 | 0.340110 | ||||||||
\(607\) | −4.36213e8 | −0.0791658 | −0.0395829 | − | 0.999216i | \(-0.512603\pi\) | ||||
−0.0395829 | + | 0.999216i | \(0.512603\pi\) | |||||||
\(608\) | −2.24756e8 | −0.0405554 | ||||||||
\(609\) | −1.43003e10 | −2.56557 | ||||||||
\(610\) | −1.06554e9 | −0.190071 | ||||||||
\(611\) | 4.12419e9 | 0.731466 | ||||||||
\(612\) | −2.80166e9 | −0.494067 | ||||||||
\(613\) | −6.37962e9 | −1.11862 | −0.559310 | − | 0.828958i | \(-0.688934\pi\) | ||||
−0.559310 | + | 0.828958i | \(0.688934\pi\) | |||||||
\(614\) | 5.67466e9 | 0.989351 | ||||||||
\(615\) | −8.16418e9 | −1.41530 | ||||||||
\(616\) | 8.13247e8 | 0.140181 | ||||||||
\(617\) | 2.32381e9 | 0.398293 | 0.199147 | − | 0.979970i | \(-0.436183\pi\) | ||||
0.199147 | + | 0.979970i | \(0.436183\pi\) | |||||||
\(618\) | 6.77584e9 | 1.15479 | ||||||||
\(619\) | 9.45273e8 | 0.160192 | 0.0800959 | − | 0.996787i | \(-0.474477\pi\) | ||||
0.0800959 | + | 0.996787i | \(0.474477\pi\) | |||||||
\(620\) | 1.95925e9 | 0.330156 | ||||||||
\(621\) | 2.26624e9 | 0.379740 | ||||||||
\(622\) | −7.10375e8 | −0.118364 | ||||||||
\(623\) | −5.92293e9 | −0.981360 | ||||||||
\(624\) | −1.38928e9 | −0.228899 | ||||||||
\(625\) | −3.81816e9 | −0.625568 | ||||||||
\(626\) | 2.54544e9 | 0.414717 | ||||||||
\(627\) | 6.02525e8 | 0.0976199 | ||||||||
\(628\) | 4.75061e9 | 0.765404 | ||||||||
\(629\) | 9.74568e8 | 0.156147 | ||||||||
\(630\) | −3.34015e9 | −0.532198 | ||||||||
\(631\) | −1.09828e10 | −1.74025 | −0.870124 | − | 0.492833i | \(-0.835961\pi\) | ||||
−0.870124 | + | 0.492833i | \(0.835961\pi\) | |||||||
\(632\) | 1.30715e9 | 0.205975 | ||||||||
\(633\) | 8.32291e8 | 0.130425 | ||||||||
\(634\) | 2.87487e9 | 0.448029 | ||||||||
\(635\) | 1.05259e10 | 1.63137 | ||||||||
\(636\) | 2.69548e9 | 0.415467 | ||||||||
\(637\) | −2.27700e9 | −0.349040 | ||||||||
\(638\) | −2.39003e9 | −0.364360 | ||||||||
\(639\) | 4.72425e8 | 0.0716275 | ||||||||
\(640\) | 4.93844e8 | 0.0744663 | ||||||||
\(641\) | −1.79159e9 | −0.268680 | −0.134340 | − | 0.990935i | \(-0.542891\pi\) | ||||
−0.134340 | + | 0.990935i | \(0.542891\pi\) | |||||||
\(642\) | −8.65792e9 | −1.29134 | ||||||||
\(643\) | 1.09669e10 | 1.62684 | 0.813421 | − | 0.581675i | \(-0.197602\pi\) | ||||
0.813421 | + | 0.581675i | \(0.197602\pi\) | |||||||
\(644\) | 4.42672e9 | 0.653103 | ||||||||
\(645\) | 5.09990e9 | 0.748346 | ||||||||
\(646\) | 1.50642e9 | 0.219853 | ||||||||
\(647\) | 6.07249e9 | 0.881458 | 0.440729 | − | 0.897640i | \(-0.354720\pi\) | ||||
0.440729 | + | 0.897640i | \(0.354720\pi\) | |||||||
\(648\) | 2.93256e9 | 0.423383 | ||||||||
\(649\) | 4.06185e9 | 0.583267 | ||||||||
\(650\) | −1.00043e9 | −0.142886 | ||||||||
\(651\) | 8.88914e9 | 1.26278 | ||||||||
\(652\) | 4.00183e9 | 0.565447 | ||||||||
\(653\) | −7.24093e9 | −1.01765 | −0.508825 | − | 0.860870i | \(-0.669920\pi\) | ||||
−0.508825 | + | 0.860870i | \(0.669920\pi\) | |||||||
\(654\) | 1.12298e10 | 1.56981 | ||||||||
\(655\) | 3.57478e9 | 0.497056 | ||||||||
\(656\) | 2.30928e9 | 0.319384 | ||||||||
\(657\) | −2.56206e9 | −0.352460 | ||||||||
\(658\) | −6.65131e9 | −0.910158 | ||||||||
\(659\) | 6.64606e9 | 0.904618 | 0.452309 | − | 0.891861i | \(-0.350600\pi\) | ||||
0.452309 | + | 0.891861i | \(0.350600\pi\) | |||||||
\(660\) | −1.32390e9 | −0.179246 | ||||||||
\(661\) | −4.77702e9 | −0.643357 | −0.321679 | − | 0.946849i | \(-0.604247\pi\) | ||||
−0.321679 | + | 0.946849i | \(0.604247\pi\) | |||||||
\(662\) | −3.00895e9 | −0.403099 | ||||||||
\(663\) | 9.31162e9 | 1.24088 | ||||||||
\(664\) | −1.80235e8 | −0.0238918 | ||||||||
\(665\) | 1.79595e9 | 0.236820 | ||||||||
\(666\) | 4.52844e8 | 0.0594003 | ||||||||
\(667\) | −1.30096e10 | −1.69755 | ||||||||
\(668\) | 2.97860e9 | 0.386629 | ||||||||
\(669\) | −2.98155e8 | −0.0384991 | ||||||||
\(670\) | 6.59297e9 | 0.846875 | ||||||||
\(671\) | −8.07978e8 | −0.103245 | ||||||||
\(672\) | 2.24058e9 | 0.284818 | ||||||||
\(673\) | −1.43274e9 | −0.181182 | −0.0905909 | − | 0.995888i | \(-0.528876\pi\) | ||||
−0.0905909 | + | 0.995888i | \(0.528876\pi\) | |||||||
\(674\) | 1.42186e9 | 0.178873 | ||||||||
\(675\) | 8.26002e8 | 0.103376 | ||||||||
\(676\) | −2.06889e9 | −0.257587 | ||||||||
\(677\) | 1.04906e10 | 1.29939 | 0.649697 | − | 0.760193i | \(-0.274896\pi\) | ||||
0.649697 | + | 0.760193i | \(0.274896\pi\) | |||||||
\(678\) | 7.95960e9 | 0.980815 | ||||||||
\(679\) | −1.50437e10 | −1.84420 | ||||||||
\(680\) | −3.30998e9 | −0.403686 | ||||||||
\(681\) | 2.12287e10 | 2.57578 | ||||||||
\(682\) | 1.48566e9 | 0.179338 | ||||||||
\(683\) | 1.93687e9 | 0.232610 | 0.116305 | − | 0.993214i | \(-0.462895\pi\) | ||||
0.116305 | + | 0.993214i | \(0.462895\pi\) | |||||||
\(684\) | 6.99974e8 | 0.0836345 | ||||||||
\(685\) | 5.81245e9 | 0.690943 | ||||||||
\(686\) | −3.65347e9 | −0.432087 | ||||||||
\(687\) | 8.38797e9 | 0.986980 | ||||||||
\(688\) | −1.44253e9 | −0.168875 | ||||||||
\(689\) | −3.77760e9 | −0.439995 | ||||||||
\(690\) | −7.20632e9 | −0.835106 | ||||||||
\(691\) | 1.36523e10 | 1.57410 | 0.787049 | − | 0.616890i | \(-0.211608\pi\) | ||||
0.787049 | + | 0.616890i | \(0.211608\pi\) | |||||||
\(692\) | −2.41996e9 | −0.277611 | ||||||||
\(693\) | −2.53276e9 | −0.289086 | ||||||||
\(694\) | 8.21157e9 | 0.932542 | ||||||||
\(695\) | 8.74265e9 | 0.987862 | ||||||||
\(696\) | −6.58476e9 | −0.740300 | ||||||||
\(697\) | −1.54779e10 | −1.73140 | ||||||||
\(698\) | −7.66808e9 | −0.853479 | ||||||||
\(699\) | −2.01155e10 | −2.22772 | ||||||||
\(700\) | 1.61345e9 | 0.177793 | ||||||||
\(701\) | −1.23717e10 | −1.35649 | −0.678247 | − | 0.734834i | \(-0.737260\pi\) | ||||
−0.678247 | + | 0.734834i | \(0.737260\pi\) | |||||||
\(702\) | −1.60755e9 | −0.175382 | ||||||||
\(703\) | −2.43488e8 | −0.0264323 | ||||||||
\(704\) | 3.74471e8 | 0.0404496 | ||||||||
\(705\) | 1.08278e10 | 1.16380 | ||||||||
\(706\) | −1.26095e10 | −1.34860 | ||||||||
\(707\) | 4.21136e9 | 0.448182 | ||||||||
\(708\) | 1.11908e10 | 1.18507 | ||||||||
\(709\) | −6.65641e9 | −0.701421 | −0.350710 | − | 0.936484i | \(-0.614060\pi\) | ||||
−0.350710 | + | 0.936484i | \(0.614060\pi\) | |||||||
\(710\) | 5.58138e8 | 0.0585245 | ||||||||
\(711\) | −4.07096e9 | −0.424769 | ||||||||
\(712\) | −2.72730e9 | −0.283173 | ||||||||
\(713\) | 8.08682e9 | 0.835535 | ||||||||
\(714\) | −1.50174e10 | −1.54401 | ||||||||
\(715\) | 1.85538e9 | 0.189829 | ||||||||
\(716\) | 8.76657e9 | 0.892554 | ||||||||
\(717\) | −1.09774e10 | −1.11220 | ||||||||
\(718\) | −5.33517e9 | −0.537914 | ||||||||
\(719\) | −5.16131e9 | −0.517855 | −0.258928 | − | 0.965897i | \(-0.583369\pi\) | ||||
−0.258928 | + | 0.965897i | \(0.583369\pi\) | |||||||
\(720\) | −1.53802e9 | −0.153567 | ||||||||
\(721\) | 1.53148e10 | 1.52173 | ||||||||
\(722\) | −3.76367e8 | −0.0372161 | ||||||||
\(723\) | −1.37814e10 | −1.35615 | ||||||||
\(724\) | 2.10661e9 | 0.206300 | ||||||||
\(725\) | −4.74173e9 | −0.462119 | ||||||||
\(726\) | 8.58293e9 | 0.832449 | ||||||||
\(727\) | −2.85753e9 | −0.275817 | −0.137908 | − | 0.990445i | \(-0.544038\pi\) | ||||
−0.137908 | + | 0.990445i | \(0.544038\pi\) | |||||||
\(728\) | −3.14007e9 | −0.301633 | ||||||||
\(729\) | −4.23346e9 | −0.404715 | ||||||||
\(730\) | −3.02690e9 | −0.287983 | ||||||||
\(731\) | 9.66854e9 | 0.915483 | ||||||||
\(732\) | −2.22606e9 | −0.209772 | ||||||||
\(733\) | −1.01025e10 | −0.947472 | −0.473736 | − | 0.880667i | \(-0.657095\pi\) | ||||
−0.473736 | + | 0.880667i | \(0.657095\pi\) | |||||||
\(734\) | 3.17210e9 | 0.296082 | ||||||||
\(735\) | −5.97810e9 | −0.555338 | ||||||||
\(736\) | 2.03835e9 | 0.188454 | ||||||||
\(737\) | 4.99931e9 | 0.460017 | ||||||||
\(738\) | −7.19198e9 | −0.658645 | ||||||||
\(739\) | −2.37969e9 | −0.216903 | −0.108451 | − | 0.994102i | \(-0.534589\pi\) | ||||
−0.108451 | + | 0.994102i | \(0.534589\pi\) | |||||||
\(740\) | 5.35004e8 | 0.0485340 | ||||||||
\(741\) | −2.32644e9 | −0.210052 | ||||||||
\(742\) | 6.09235e9 | 0.547483 | ||||||||
\(743\) | −1.95551e10 | −1.74904 | −0.874520 | − | 0.484989i | \(-0.838823\pi\) | ||||
−0.874520 | + | 0.484989i | \(0.838823\pi\) | |||||||
\(744\) | 4.09313e9 | 0.364376 | ||||||||
\(745\) | 1.32256e10 | 1.17184 | ||||||||
\(746\) | −6.26978e9 | −0.552925 | ||||||||
\(747\) | 5.61319e8 | 0.0492705 | ||||||||
\(748\) | −2.50988e9 | −0.219279 | ||||||||
\(749\) | −1.95687e10 | −1.70167 | ||||||||
\(750\) | −1.16771e10 | −1.01070 | ||||||||
\(751\) | 7.74452e9 | 0.667198 | 0.333599 | − | 0.942715i | \(-0.391737\pi\) | ||||
0.333599 | + | 0.942715i | \(0.391737\pi\) | |||||||
\(752\) | −3.06269e9 | −0.262628 | ||||||||
\(753\) | 1.42551e10 | 1.21671 | ||||||||
\(754\) | 9.22825e9 | 0.784007 | ||||||||
\(755\) | 6.84791e9 | 0.579087 | ||||||||
\(756\) | 2.59258e9 | 0.218226 | ||||||||
\(757\) | 1.16038e9 | 0.0972219 | 0.0486110 | − | 0.998818i | \(-0.484521\pi\) | ||||
0.0486110 | + | 0.998818i | \(0.484521\pi\) | |||||||
\(758\) | −1.16436e10 | −0.971057 | ||||||||
\(759\) | −5.46440e9 | −0.453624 | ||||||||
\(760\) | 8.26972e8 | 0.0683350 | ||||||||
\(761\) | −1.86077e9 | −0.153054 | −0.0765272 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765272 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(762\) | 2.19900e10 | 1.80046 | ||||||||
\(763\) | 2.53816e10 | 2.06863 | ||||||||
\(764\) | −1.40758e9 | −0.114195 | ||||||||
\(765\) | 1.03085e10 | 0.832494 | ||||||||
\(766\) | 2.20969e9 | 0.177636 | ||||||||
\(767\) | −1.56834e10 | −1.25504 | ||||||||
\(768\) | 1.03170e9 | 0.0821847 | ||||||||
\(769\) | 9.85947e9 | 0.781828 | 0.390914 | − | 0.920427i | \(-0.372159\pi\) | ||||
0.390914 | + | 0.920427i | \(0.372159\pi\) | |||||||
\(770\) | −2.99228e9 | −0.236203 | ||||||||
\(771\) | −2.44895e10 | −1.92438 | ||||||||
\(772\) | −7.86803e9 | −0.615468 | ||||||||
\(773\) | 1.36871e10 | 1.06582 | 0.532910 | − | 0.846172i | \(-0.321098\pi\) | ||||
0.532910 | + | 0.846172i | \(0.321098\pi\) | |||||||
\(774\) | 4.49260e9 | 0.348260 | ||||||||
\(775\) | 2.94749e9 | 0.227456 | ||||||||
\(776\) | −6.92706e9 | −0.532149 | ||||||||
\(777\) | 2.42732e9 | 0.185632 | ||||||||
\(778\) | −9.88417e9 | −0.752509 | ||||||||
\(779\) | 3.86703e9 | 0.293087 | ||||||||
\(780\) | 5.11176e9 | 0.385691 | ||||||||
\(781\) | 4.23224e8 | 0.0317901 | ||||||||
\(782\) | −1.36620e10 | −1.02162 | ||||||||
\(783\) | −7.61927e9 | −0.567214 | ||||||||
\(784\) | 1.69094e9 | 0.125320 | ||||||||
\(785\) | −1.74795e10 | −1.28969 | ||||||||
\(786\) | 7.46819e9 | 0.548575 | ||||||||
\(787\) | −1.99739e10 | −1.46067 | −0.730335 | − | 0.683090i | \(-0.760636\pi\) | ||||
−0.730335 | + | 0.683090i | \(0.760636\pi\) | |||||||
\(788\) | −9.70323e9 | −0.706439 | ||||||||
\(789\) | 1.90760e10 | 1.38267 | ||||||||
\(790\) | −4.80956e9 | −0.347065 | ||||||||
\(791\) | 1.79904e10 | 1.29247 | ||||||||
\(792\) | −1.16625e9 | −0.0834164 | ||||||||
\(793\) | 3.11972e9 | 0.222157 | ||||||||
\(794\) | 7.47336e9 | 0.529839 | ||||||||
\(795\) | −9.91781e9 | −0.700053 | ||||||||
\(796\) | −3.87400e9 | −0.272247 | ||||||||
\(797\) | 8.76673e9 | 0.613386 | 0.306693 | − | 0.951809i | \(-0.400778\pi\) | ||||
0.306693 | + | 0.951809i | \(0.400778\pi\) | |||||||
\(798\) | 3.75198e9 | 0.261367 | ||||||||
\(799\) | 2.05276e10 | 1.42372 | ||||||||
\(800\) | 7.42938e8 | 0.0513024 | ||||||||
\(801\) | 8.49383e9 | 0.583969 | ||||||||
\(802\) | −2.73041e9 | −0.186903 | ||||||||
\(803\) | −2.29523e9 | −0.156431 | ||||||||
\(804\) | 1.37736e10 | 0.934654 | ||||||||
\(805\) | −1.62878e10 | −1.10047 | ||||||||
\(806\) | −5.73634e9 | −0.385889 | ||||||||
\(807\) | −1.14893e10 | −0.769552 | ||||||||
\(808\) | 1.93918e9 | 0.129324 | ||||||||
\(809\) | 2.42316e10 | 1.60902 | 0.804510 | − | 0.593938i | \(-0.202428\pi\) | ||||
0.804510 | + | 0.593938i | \(0.202428\pi\) | |||||||
\(810\) | −1.07901e10 | −0.713393 | ||||||||
\(811\) | −4.37791e8 | −0.0288200 | −0.0144100 | − | 0.999896i | \(-0.504587\pi\) | ||||
−0.0144100 | + | 0.999896i | \(0.504587\pi\) | |||||||
\(812\) | −1.48829e10 | −0.975534 | ||||||||
\(813\) | −6.78144e9 | −0.442593 | ||||||||
\(814\) | 4.05682e8 | 0.0263633 | ||||||||
\(815\) | −1.47244e10 | −0.952767 | ||||||||
\(816\) | −6.91497e9 | −0.445528 | ||||||||
\(817\) | −2.41561e9 | −0.154971 | ||||||||
\(818\) | −4.61693e9 | −0.294928 | ||||||||
\(819\) | 9.77936e9 | 0.622038 | ||||||||
\(820\) | −8.49684e9 | −0.538157 | ||||||||
\(821\) | 1.06296e10 | 0.670371 | 0.335185 | − | 0.942152i | \(-0.391201\pi\) | ||||
0.335185 | + | 0.942152i | \(0.391201\pi\) | |||||||
\(822\) | 1.21430e10 | 0.762559 | ||||||||
\(823\) | −2.11804e10 | −1.32445 | −0.662225 | − | 0.749305i | \(-0.730388\pi\) | ||||
−0.662225 | + | 0.749305i | \(0.730388\pi\) | |||||||
\(824\) | 7.05193e9 | 0.439099 | ||||||||
\(825\) | −1.99167e9 | −0.123489 | ||||||||
\(826\) | 2.52935e10 | 1.56163 | ||||||||
\(827\) | 2.42805e10 | 1.49276 | 0.746378 | − | 0.665522i | \(-0.231791\pi\) | ||||
0.746378 | + | 0.665522i | \(0.231791\pi\) | |||||||
\(828\) | −6.34818e9 | −0.388636 | ||||||||
\(829\) | −4.44427e8 | −0.0270931 | −0.0135466 | − | 0.999908i | \(-0.504312\pi\) | ||||
−0.0135466 | + | 0.999908i | \(0.504312\pi\) | |||||||
\(830\) | 6.63160e8 | 0.0402573 | ||||||||
\(831\) | 4.11308e10 | 2.48636 | ||||||||
\(832\) | −1.44589e9 | −0.0870369 | ||||||||
\(833\) | −1.13335e10 | −0.679368 | ||||||||
\(834\) | 1.82645e10 | 1.09025 | ||||||||
\(835\) | −1.09595e10 | −0.651462 | ||||||||
\(836\) | 6.27075e8 | 0.0371191 | ||||||||
\(837\) | 4.73619e9 | 0.279183 | ||||||||
\(838\) | 1.88677e10 | 1.10755 | ||||||||
\(839\) | 2.28177e10 | 1.33384 | 0.666922 | − | 0.745127i | \(-0.267611\pi\) | ||||
0.666922 | + | 0.745127i | \(0.267611\pi\) | |||||||
\(840\) | −8.24403e9 | −0.479913 | ||||||||
\(841\) | 2.64891e10 | 1.53561 | ||||||||
\(842\) | −1.10634e10 | −0.638700 | ||||||||
\(843\) | −1.80774e10 | −1.03929 | ||||||||
\(844\) | 8.66203e8 | 0.0495931 | ||||||||
\(845\) | 7.61231e9 | 0.434028 | ||||||||
\(846\) | 9.53838e9 | 0.541600 | ||||||||
\(847\) | 1.93992e10 | 1.09696 | ||||||||
\(848\) | 2.80531e9 | 0.157977 | ||||||||
\(849\) | −1.86593e10 | −1.04645 | ||||||||
\(850\) | −4.97952e9 | −0.278113 | ||||||||
\(851\) | 2.20824e9 | 0.122826 | ||||||||
\(852\) | 1.16602e9 | 0.0645905 | ||||||||
\(853\) | 8.62323e9 | 0.475717 | 0.237858 | − | 0.971300i | \(-0.423555\pi\) | ||||
0.237858 | + | 0.971300i | \(0.423555\pi\) | |||||||
\(854\) | −5.03136e9 | −0.276428 | ||||||||
\(855\) | −2.57550e9 | −0.140923 | ||||||||
\(856\) | −9.01069e9 | −0.491021 | ||||||||
\(857\) | 1.18096e10 | 0.640916 | 0.320458 | − | 0.947263i | \(-0.396163\pi\) | ||||
0.320458 | + | 0.947263i | \(0.396163\pi\) | |||||||
\(858\) | 3.87614e9 | 0.209505 | ||||||||
\(859\) | −4.29431e9 | −0.231162 | −0.115581 | − | 0.993298i | \(-0.536873\pi\) | ||||
−0.115581 | + | 0.993298i | \(0.536873\pi\) | |||||||
\(860\) | 5.30770e9 | 0.284552 | ||||||||
\(861\) | −3.85502e10 | −2.05833 | ||||||||
\(862\) | −1.72313e10 | −0.916309 | ||||||||
\(863\) | −1.16286e10 | −0.615869 | −0.307934 | − | 0.951408i | \(-0.599638\pi\) | ||||
−0.307934 | + | 0.951408i | \(0.599638\pi\) | |||||||
\(864\) | 1.19379e9 | 0.0629696 | ||||||||
\(865\) | 8.90405e9 | 0.467769 | ||||||||
\(866\) | −2.01196e10 | −1.05270 | ||||||||
\(867\) | 2.11139e10 | 1.10027 | ||||||||
\(868\) | 9.25133e9 | 0.480159 | ||||||||
\(869\) | −3.64698e9 | −0.188523 | ||||||||
\(870\) | 2.42281e10 | 1.24739 | ||||||||
\(871\) | −1.93031e10 | −0.989835 | ||||||||
\(872\) | 1.16873e10 | 0.596908 | ||||||||
\(873\) | 2.15735e10 | 1.09741 | ||||||||
\(874\) | 3.41333e9 | 0.172937 | ||||||||
\(875\) | −2.63927e10 | −1.33185 | ||||||||
\(876\) | −6.32358e9 | −0.317833 | ||||||||
\(877\) | 2.30911e10 | 1.15597 | 0.577986 | − | 0.816047i | \(-0.303839\pi\) | ||||
0.577986 | + | 0.816047i | \(0.303839\pi\) | |||||||
\(878\) | −1.83446e10 | −0.914695 | ||||||||
\(879\) | −2.69722e10 | −1.33954 | ||||||||
\(880\) | −1.37784e9 | −0.0681568 | ||||||||
\(881\) | −2.75942e10 | −1.35957 | −0.679785 | − | 0.733411i | \(-0.737927\pi\) | ||||
−0.679785 | + | 0.733411i | \(0.737927\pi\) | |||||||
\(882\) | −5.26622e9 | −0.258440 | ||||||||
\(883\) | −2.32713e10 | −1.13752 | −0.568758 | − | 0.822505i | \(-0.692576\pi\) | ||||
−0.568758 | + | 0.822505i | \(0.692576\pi\) | |||||||
\(884\) | 9.69103e9 | 0.471831 | ||||||||
\(885\) | −4.11757e10 | −1.99682 | ||||||||
\(886\) | 8.51618e9 | 0.411364 | ||||||||
\(887\) | −8.19649e9 | −0.394362 | −0.197181 | − | 0.980367i | \(-0.563179\pi\) | ||||
−0.197181 | + | 0.980367i | \(0.563179\pi\) | |||||||
\(888\) | 1.11769e9 | 0.0535646 | ||||||||
\(889\) | 4.97021e10 | 2.37257 | ||||||||
\(890\) | 1.00349e10 | 0.477141 | ||||||||
\(891\) | −8.18191e9 | −0.387510 | ||||||||
\(892\) | −3.10303e8 | −0.0146389 | ||||||||
\(893\) | −5.12866e9 | −0.241004 | ||||||||
\(894\) | 2.76299e10 | 1.29330 | ||||||||
\(895\) | −3.22560e10 | −1.50394 | ||||||||
\(896\) | 2.33187e9 | 0.108299 | ||||||||
\(897\) | 2.10988e10 | 0.976079 | ||||||||
\(898\) | 9.81532e9 | 0.452311 | ||||||||
\(899\) | −2.71884e10 | −1.24803 | ||||||||
\(900\) | −2.31379e9 | −0.105797 | ||||||||
\(901\) | −1.88025e10 | −0.856404 | ||||||||
\(902\) | −6.44297e9 | −0.292323 | ||||||||
\(903\) | 2.40811e10 | 1.08835 | ||||||||
\(904\) | 8.28391e9 | 0.372946 | ||||||||
\(905\) | −7.75112e9 | −0.347612 | ||||||||
\(906\) | 1.43062e10 | 0.639110 | ||||||||
\(907\) | 2.92890e9 | 0.130341 | 0.0651703 | − | 0.997874i | \(-0.479241\pi\) | ||||
0.0651703 | + | 0.997874i | \(0.479241\pi\) | |||||||
\(908\) | 2.20937e10 | 0.979417 | ||||||||
\(909\) | −6.03935e9 | −0.266696 | ||||||||
\(910\) | 1.15536e10 | 0.508246 | ||||||||
\(911\) | −9.42256e9 | −0.412909 | −0.206455 | − | 0.978456i | \(-0.566193\pi\) | ||||
−0.206455 | + | 0.978456i | \(0.566193\pi\) | |||||||
\(912\) | 1.72765e9 | 0.0754179 | ||||||||
\(913\) | 5.02859e8 | 0.0218675 | ||||||||
\(914\) | 4.15814e8 | 0.0180131 | ||||||||
\(915\) | 8.19062e9 | 0.353462 | ||||||||
\(916\) | 8.72974e9 | 0.375290 | ||||||||
\(917\) | 1.68797e10 | 0.722888 | ||||||||
\(918\) | −8.00136e9 | −0.341361 | ||||||||
\(919\) | 8.47572e9 | 0.360224 | 0.180112 | − | 0.983646i | \(-0.442354\pi\) | ||||
0.180112 | + | 0.983646i | \(0.442354\pi\) | |||||||
\(920\) | −7.49994e9 | −0.317542 | ||||||||
\(921\) | −4.36200e10 | −1.83983 | ||||||||
\(922\) | 1.44566e10 | 0.607447 | ||||||||
\(923\) | −1.63413e9 | −0.0684039 | ||||||||
\(924\) | −6.25127e9 | −0.260685 | ||||||||
\(925\) | 8.04859e8 | 0.0334367 | ||||||||
\(926\) | −2.12327e10 | −0.878752 | ||||||||
\(927\) | −2.19624e10 | −0.905524 | ||||||||
\(928\) | −6.85306e9 | −0.281492 | ||||||||
\(929\) | −8.77309e9 | −0.359002 | −0.179501 | − | 0.983758i | \(-0.557448\pi\) | ||||
−0.179501 | + | 0.983758i | \(0.557448\pi\) | |||||||
\(930\) | −1.50604e10 | −0.613967 | ||||||||
\(931\) | 2.83158e9 | 0.115002 | ||||||||
\(932\) | −2.09351e10 | −0.847069 | ||||||||
\(933\) | 5.46051e9 | 0.220114 | ||||||||
\(934\) | 9.21935e9 | 0.370242 | ||||||||
\(935\) | 9.23492e9 | 0.369481 | ||||||||
\(936\) | 4.50304e9 | 0.179490 | ||||||||
\(937\) | 4.37252e10 | 1.73638 | 0.868188 | − | 0.496236i | \(-0.165285\pi\) | ||||
0.868188 | + | 0.496236i | \(0.165285\pi\) | |||||||
\(938\) | 3.11312e10 | 1.23165 | ||||||||
\(939\) | −1.95663e10 | −0.771220 | ||||||||
\(940\) | 1.12689e10 | 0.442523 | ||||||||
\(941\) | −3.76684e10 | −1.47372 | −0.736858 | − | 0.676047i | \(-0.763692\pi\) | ||||
−0.736858 | + | 0.676047i | \(0.763692\pi\) | |||||||
\(942\) | −3.65170e10 | −1.42337 | ||||||||
\(943\) | −3.50708e10 | −1.36193 | ||||||||
\(944\) | 1.16468e10 | 0.450612 | ||||||||
\(945\) | −9.53922e9 | −0.367707 | ||||||||
\(946\) | 4.02471e9 | 0.154567 | ||||||||
\(947\) | 1.23213e10 | 0.471445 | 0.235722 | − | 0.971820i | \(-0.424254\pi\) | ||||
0.235722 | + | 0.971820i | \(0.424254\pi\) | |||||||
\(948\) | −1.00478e10 | −0.383038 | ||||||||
\(949\) | 8.86222e9 | 0.336597 | ||||||||
\(950\) | 1.24409e9 | 0.0470783 | ||||||||
\(951\) | −2.20986e10 | −0.833167 | ||||||||
\(952\) | −1.56293e10 | −0.587097 | ||||||||
\(953\) | −2.03050e10 | −0.759938 | −0.379969 | − | 0.924999i | \(-0.624065\pi\) | ||||
−0.379969 | + | 0.924999i | \(0.624065\pi\) | |||||||
\(954\) | −8.73679e9 | −0.325786 | ||||||||
\(955\) | 5.17910e9 | 0.192416 | ||||||||
\(956\) | −1.14247e10 | −0.422903 | ||||||||
\(957\) | 1.83717e10 | 0.677574 | ||||||||
\(958\) | 1.30482e10 | 0.479481 | ||||||||
\(959\) | 2.74456e10 | 1.00487 | ||||||||
\(960\) | −3.79608e9 | −0.138480 | ||||||||
\(961\) | −1.06121e10 | −0.385718 | ||||||||
\(962\) | −1.56640e9 | −0.0567270 | ||||||||
\(963\) | 2.80627e10 | 1.01260 | ||||||||
\(964\) | −1.43429e10 | −0.515665 | ||||||||
\(965\) | 2.89498e10 | 1.03705 | ||||||||
\(966\) | −3.40273e10 | −1.21453 | ||||||||
\(967\) | −1.00646e10 | −0.357933 | −0.178967 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178967 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(968\) | 8.93265e9 | 0.316531 | ||||||||
\(969\) | −1.15795e10 | −0.408844 | ||||||||
\(970\) | 2.54876e10 | 0.896660 | ||||||||
\(971\) | 2.39617e10 | 0.839942 | 0.419971 | − | 0.907537i | \(-0.362040\pi\) | ||||
0.419971 | + | 0.907537i | \(0.362040\pi\) | |||||||
\(972\) | −1.74427e10 | −0.609231 | ||||||||
\(973\) | 4.12817e10 | 1.43669 | ||||||||
\(974\) | −3.93253e10 | −1.36369 | ||||||||
\(975\) | 7.69012e9 | 0.265716 | ||||||||
\(976\) | −2.31676e9 | −0.0797640 | ||||||||
\(977\) | −2.23861e10 | −0.767977 | −0.383988 | − | 0.923338i | \(-0.625450\pi\) | ||||
−0.383988 | + | 0.923338i | \(0.625450\pi\) | |||||||
\(978\) | −3.07612e10 | −1.05152 | ||||||||
\(979\) | 7.60923e9 | 0.259180 | ||||||||
\(980\) | −6.22168e9 | −0.211162 | ||||||||
\(981\) | −3.63987e10 | −1.23096 | ||||||||
\(982\) | −3.60723e9 | −0.121558 | ||||||||
\(983\) | 3.27462e10 | 1.09957 | 0.549785 | − | 0.835306i | \(-0.314709\pi\) | ||||
0.549785 | + | 0.835306i | \(0.314709\pi\) | |||||||
\(984\) | −1.77510e10 | −0.593936 | ||||||||
\(985\) | 3.57023e10 | 1.19034 | ||||||||
\(986\) | 4.59324e10 | 1.52598 | ||||||||
\(987\) | 5.11273e10 | 1.69256 | ||||||||
\(988\) | −2.42123e9 | −0.0798705 | ||||||||
\(989\) | 2.19076e10 | 0.720124 | ||||||||
\(990\) | 4.29111e9 | 0.140555 | ||||||||
\(991\) | 5.31502e10 | 1.73479 | 0.867396 | − | 0.497619i | \(-0.165792\pi\) | ||||
0.867396 | + | 0.497619i | \(0.165792\pi\) | |||||||
\(992\) | 4.25990e9 | 0.138551 | ||||||||
\(993\) | 2.31292e10 | 0.749614 | ||||||||
\(994\) | 2.63546e9 | 0.0851145 | ||||||||
\(995\) | 1.42541e10 | 0.458731 | ||||||||
\(996\) | 1.38543e9 | 0.0444300 | ||||||||
\(997\) | 3.24019e10 | 1.03547 | 0.517735 | − | 0.855541i | \(-0.326775\pi\) | ||||
0.517735 | + | 0.855541i | \(0.326775\pi\) | |||||||
\(998\) | 3.23850e10 | 1.03131 | ||||||||
\(999\) | 1.29329e9 | 0.0410409 |
(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 | 38.8.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 342.8.a.i.1.2 | 2 | |||
4.3 | odd | 2 | 304.8.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.8.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
304.8.a.b.1.1 | 2 | 4.3 | odd | 2 | |||
342.8.a.i.1.2 | 2 | 3.2 | odd | 2 |