Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(1\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(24.0278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.0278 | 1.94700 | 0.973502 | − | 0.228677i | \(-0.0734401\pi\) | ||||
0.973502 | + | 0.228677i | \(0.0734401\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 357.226 | 2.79083 | ||||||||
\(5\) | −492.460 | −1.76188 | −0.880939 | − | 0.473230i | \(-0.843088\pi\) | ||||
−0.880939 | + | 0.473230i | \(0.843088\pi\) | |||||||
\(6\) | 594.752 | 1.12410 | ||||||||
\(7\) | −1209.81 | −1.33314 | −0.666568 | − | 0.745444i | \(-0.732237\pi\) | ||||
−0.666568 | + | 0.745444i | \(0.732237\pi\) | |||||||
\(8\) | 5049.35 | 3.48675 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −10847.8 | −3.43038 | ||||||||
\(11\) | −7759.91 | −1.75785 | −0.878926 | − | 0.476958i | \(-0.841739\pi\) | ||||
−0.878926 | + | 0.476958i | \(0.841739\pi\) | |||||||
\(12\) | 9645.10 | 1.61128 | ||||||||
\(13\) | 1927.14 | 0.243283 | 0.121642 | − | 0.992574i | \(-0.461184\pi\) | ||||
0.121642 | + | 0.992574i | \(0.461184\pi\) | |||||||
\(14\) | −26649.5 | −2.59562 | ||||||||
\(15\) | −13296.4 | −1.01722 | ||||||||
\(16\) | 65501.4 | 3.99789 | ||||||||
\(17\) | −21871.8 | −1.07973 | −0.539864 | − | 0.841752i | \(-0.681524\pi\) | ||||
−0.539864 | + | 0.841752i | \(0.681524\pi\) | |||||||
\(18\) | 16058.3 | 0.649001 | ||||||||
\(19\) | −31682.0 | −1.05968 | −0.529839 | − | 0.848098i | \(-0.677748\pi\) | ||||
−0.529839 | + | 0.848098i | \(0.677748\pi\) | |||||||
\(20\) | −175919. | −4.91710 | ||||||||
\(21\) | −32664.9 | −0.769686 | ||||||||
\(22\) | −170934. | −3.42255 | ||||||||
\(23\) | 76017.8 | 1.30277 | 0.651385 | − | 0.758747i | \(-0.274188\pi\) | ||||
0.651385 | + | 0.758747i | \(0.274188\pi\) | |||||||
\(24\) | 136332. | 2.01307 | ||||||||
\(25\) | 164392. | 2.10421 | ||||||||
\(26\) | 42450.8 | 0.473673 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −432176. | −3.72055 | ||||||||
\(29\) | −107474. | −0.818293 | −0.409146 | − | 0.912469i | \(-0.634173\pi\) | ||||
−0.409146 | + | 0.912469i | \(0.634173\pi\) | |||||||
\(30\) | −292891. | −1.98053 | ||||||||
\(31\) | −56872.6 | −0.342876 | −0.171438 | − | 0.985195i | \(-0.554841\pi\) | ||||
−0.171438 | + | 0.985195i | \(0.554841\pi\) | |||||||
\(32\) | 796537. | 4.29715 | ||||||||
\(33\) | −209518. | −1.01490 | ||||||||
\(34\) | −481789. | −2.10223 | ||||||||
\(35\) | 595783. | 2.34882 | ||||||||
\(36\) | 260418. | 0.930276 | ||||||||
\(37\) | −72532.0 | −0.235409 | −0.117705 | − | 0.993049i | \(-0.537554\pi\) | ||||
−0.117705 | + | 0.993049i | \(0.537554\pi\) | |||||||
\(38\) | −697885. | −2.06320 | ||||||||
\(39\) | 52032.8 | 0.140460 | ||||||||
\(40\) | −2.48660e6 | −6.14322 | ||||||||
\(41\) | −598173. | −1.35545 | −0.677725 | − | 0.735316i | \(-0.737034\pi\) | ||||
−0.677725 | + | 0.735316i | \(0.737034\pi\) | |||||||
\(42\) | −719537. | −1.49858 | ||||||||
\(43\) | −127161. | −0.243902 | −0.121951 | − | 0.992536i | \(-0.538915\pi\) | ||||
−0.121951 | + | 0.992536i | \(0.538915\pi\) | |||||||
\(44\) | −2.77204e6 | −4.90586 | ||||||||
\(45\) | −359003. | −0.587293 | ||||||||
\(46\) | 1.67451e6 | 2.53650 | ||||||||
\(47\) | 20753.9 | 0.0291579 | 0.0145790 | − | 0.999894i | \(-0.495359\pi\) | ||||
0.0145790 | + | 0.999894i | \(0.495359\pi\) | |||||||
\(48\) | 1.76854e6 | 2.30818 | ||||||||
\(49\) | 640100. | 0.777252 | ||||||||
\(50\) | 3.62120e6 | 4.09691 | ||||||||
\(51\) | −590540. | −0.623381 | ||||||||
\(52\) | 688425. | 0.678961 | ||||||||
\(53\) | 1.52906e6 | 1.41078 | 0.705389 | − | 0.708821i | \(-0.250772\pi\) | ||||
0.705389 | + | 0.708821i | \(0.250772\pi\) | |||||||
\(54\) | 433574. | 0.374701 | ||||||||
\(55\) | 3.82145e6 | 3.09712 | ||||||||
\(56\) | −6.10876e6 | −4.64831 | ||||||||
\(57\) | −855413. | −0.611806 | ||||||||
\(58\) | −2.36741e6 | −1.59322 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | −4.74982e6 | −2.83889 | ||||||||
\(61\) | 2.40366e6 | 1.35587 | 0.677935 | − | 0.735122i | \(-0.262875\pi\) | ||||
0.677935 | + | 0.735122i | \(0.262875\pi\) | |||||||
\(62\) | −1.25278e6 | −0.667582 | ||||||||
\(63\) | −881952. | −0.444379 | ||||||||
\(64\) | 9.16182e6 | 4.36869 | ||||||||
\(65\) | −949040. | −0.428635 | ||||||||
\(66\) | −4.61522e6 | −1.97601 | ||||||||
\(67\) | −606916. | −0.246528 | −0.123264 | − | 0.992374i | \(-0.539336\pi\) | ||||
−0.123264 | + | 0.992374i | \(0.539336\pi\) | |||||||
\(68\) | −7.81319e6 | −3.01333 | ||||||||
\(69\) | 2.05248e6 | 0.752155 | ||||||||
\(70\) | 1.31238e7 | 4.57317 | ||||||||
\(71\) | −3.52312e6 | −1.16822 | −0.584108 | − | 0.811676i | \(-0.698556\pi\) | ||||
−0.584108 | + | 0.811676i | \(0.698556\pi\) | |||||||
\(72\) | 3.68098e6 | 1.16225 | ||||||||
\(73\) | 1.27495e6 | 0.383585 | 0.191793 | − | 0.981435i | \(-0.438570\pi\) | ||||
0.191793 | + | 0.981435i | \(0.438570\pi\) | |||||||
\(74\) | −1.59772e6 | −0.458343 | ||||||||
\(75\) | 4.43858e6 | 1.21487 | ||||||||
\(76\) | −1.13176e7 | −2.95738 | ||||||||
\(77\) | 9.38803e6 | 2.34346 | ||||||||
\(78\) | 1.14617e6 | 0.273475 | ||||||||
\(79\) | 3.89830e6 | 0.889571 | 0.444786 | − | 0.895637i | \(-0.353280\pi\) | ||||
0.444786 | + | 0.895637i | \(0.353280\pi\) | |||||||
\(80\) | −3.22568e7 | −7.04379 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −1.31765e7 | −2.63907 | ||||||||
\(83\) | −4.03800e6 | −0.775164 | −0.387582 | − | 0.921835i | \(-0.626690\pi\) | ||||
−0.387582 | + | 0.921835i | \(0.626690\pi\) | |||||||
\(84\) | −1.16687e7 | −2.14806 | ||||||||
\(85\) | 1.07710e7 | 1.90235 | ||||||||
\(86\) | −2.80108e6 | −0.474877 | ||||||||
\(87\) | −2.90179e6 | −0.472442 | ||||||||
\(88\) | −3.91825e7 | −6.12919 | ||||||||
\(89\) | 5.97046e6 | 0.897724 | 0.448862 | − | 0.893601i | \(-0.351830\pi\) | ||||
0.448862 | + | 0.893601i | \(0.351830\pi\) | |||||||
\(90\) | −7.90807e6 | −1.14346 | ||||||||
\(91\) | −2.33148e6 | −0.324330 | ||||||||
\(92\) | 2.71555e7 | 3.63581 | ||||||||
\(93\) | −1.53556e6 | −0.197960 | ||||||||
\(94\) | 457163. | 0.0567706 | ||||||||
\(95\) | 1.56021e7 | 1.86703 | ||||||||
\(96\) | 2.15065e7 | 2.48096 | ||||||||
\(97\) | −1.98127e6 | −0.220415 | −0.110208 | − | 0.993909i | \(-0.535152\pi\) | ||||
−0.110208 | + | 0.993909i | \(0.535152\pi\) | |||||||
\(98\) | 1.41000e7 | 1.51331 | ||||||||
\(99\) | −5.65698e6 | −0.585951 | ||||||||
\(100\) | 5.87250e7 | 5.87250 | ||||||||
\(101\) | −1.54871e7 | −1.49570 | −0.747851 | − | 0.663867i | \(-0.768914\pi\) | ||||
−0.747851 | + | 0.663867i | \(0.768914\pi\) | |||||||
\(102\) | −1.30083e7 | −1.21373 | ||||||||
\(103\) | −1.20275e7 | −1.08454 | −0.542269 | − | 0.840205i | \(-0.682435\pi\) | ||||
−0.542269 | + | 0.840205i | \(0.682435\pi\) | |||||||
\(104\) | 9.73081e6 | 0.848267 | ||||||||
\(105\) | 1.60862e7 | 1.35609 | ||||||||
\(106\) | 3.36819e7 | 2.74679 | ||||||||
\(107\) | −7.69022e6 | −0.606870 | −0.303435 | − | 0.952852i | \(-0.598134\pi\) | ||||
−0.303435 | + | 0.952852i | \(0.598134\pi\) | |||||||
\(108\) | 7.03128e6 | 0.537095 | ||||||||
\(109\) | −2.11383e6 | −0.156342 | −0.0781711 | − | 0.996940i | \(-0.524908\pi\) | ||||
−0.0781711 | + | 0.996940i | \(0.524908\pi\) | |||||||
\(110\) | 8.41782e7 | 6.03011 | ||||||||
\(111\) | −1.95836e6 | −0.135914 | ||||||||
\(112\) | −7.92443e7 | −5.32973 | ||||||||
\(113\) | 2.03050e6 | 0.132382 | 0.0661909 | − | 0.997807i | \(-0.478915\pi\) | ||||
0.0661909 | + | 0.997807i | \(0.478915\pi\) | |||||||
\(114\) | −1.88429e7 | −1.19119 | ||||||||
\(115\) | −3.74357e7 | −2.29532 | ||||||||
\(116\) | −3.83923e7 | −2.28371 | ||||||||
\(117\) | 1.40489e6 | 0.0810944 | ||||||||
\(118\) | −4.52406e6 | −0.253478 | ||||||||
\(119\) | 2.64608e7 | 1.43942 | ||||||||
\(120\) | −6.71383e7 | −3.54679 | ||||||||
\(121\) | 4.07291e7 | 2.09005 | ||||||||
\(122\) | 5.29474e7 | 2.63989 | ||||||||
\(123\) | −1.61507e7 | −0.782569 | ||||||||
\(124\) | −2.03164e7 | −0.956908 | ||||||||
\(125\) | −4.24829e7 | −1.94549 | ||||||||
\(126\) | −1.94275e7 | −0.865207 | ||||||||
\(127\) | 1.37874e7 | 0.597269 | 0.298635 | − | 0.954367i | \(-0.403469\pi\) | ||||
0.298635 | + | 0.954367i | \(0.403469\pi\) | |||||||
\(128\) | 9.98583e7 | 4.20871 | ||||||||
\(129\) | −3.43335e6 | −0.140817 | ||||||||
\(130\) | −2.09053e7 | −0.834555 | ||||||||
\(131\) | −845013. | −0.0328408 | −0.0164204 | − | 0.999865i | \(-0.505227\pi\) | ||||
−0.0164204 | + | 0.999865i | \(0.505227\pi\) | |||||||
\(132\) | −7.48451e7 | −2.83240 | ||||||||
\(133\) | 3.83292e7 | 1.41270 | ||||||||
\(134\) | −1.33690e7 | −0.479992 | ||||||||
\(135\) | −9.69309e6 | −0.339074 | ||||||||
\(136\) | −1.10439e8 | −3.76474 | ||||||||
\(137\) | −4.84595e7 | −1.61012 | −0.805058 | − | 0.593196i | \(-0.797866\pi\) | ||||
−0.805058 | + | 0.593196i | \(0.797866\pi\) | |||||||
\(138\) | 4.52117e7 | 1.46445 | ||||||||
\(139\) | −2.05210e6 | −0.0648106 | −0.0324053 | − | 0.999475i | \(-0.510317\pi\) | ||||
−0.0324053 | + | 0.999475i | \(0.510317\pi\) | |||||||
\(140\) | 2.12829e8 | 6.55516 | ||||||||
\(141\) | 560354. | 0.0168343 | ||||||||
\(142\) | −7.76067e7 | −2.27452 | ||||||||
\(143\) | −1.49545e7 | −0.427656 | ||||||||
\(144\) | 4.77505e7 | 1.33263 | ||||||||
\(145\) | 5.29264e7 | 1.44173 | ||||||||
\(146\) | 2.80843e7 | 0.746842 | ||||||||
\(147\) | 1.72827e7 | 0.448746 | ||||||||
\(148\) | −2.59103e7 | −0.656987 | ||||||||
\(149\) | −2.53433e6 | −0.0627641 | −0.0313821 | − | 0.999507i | \(-0.509991\pi\) | ||||
−0.0313821 | + | 0.999507i | \(0.509991\pi\) | |||||||
\(150\) | 9.77723e7 | 2.36535 | ||||||||
\(151\) | −5.49477e7 | −1.29876 | −0.649382 | − | 0.760462i | \(-0.724972\pi\) | ||||
−0.649382 | + | 0.760462i | \(0.724972\pi\) | |||||||
\(152\) | −1.59973e8 | −3.69483 | ||||||||
\(153\) | −1.59446e7 | −0.359909 | ||||||||
\(154\) | 2.06798e8 | 4.56272 | ||||||||
\(155\) | 2.80075e7 | 0.604106 | ||||||||
\(156\) | 1.85875e7 | 0.391998 | ||||||||
\(157\) | 7.27529e7 | 1.50038 | 0.750191 | − | 0.661221i | \(-0.229962\pi\) | ||||
0.750191 | + | 0.661221i | \(0.229962\pi\) | |||||||
\(158\) | 8.58712e7 | 1.73200 | ||||||||
\(159\) | 4.12846e7 | 0.814513 | ||||||||
\(160\) | −3.92263e8 | −7.57106 | ||||||||
\(161\) | −9.19672e7 | −1.73677 | ||||||||
\(162\) | 1.17065e7 | 0.216334 | ||||||||
\(163\) | 1.99055e6 | 0.0360011 | 0.0180006 | − | 0.999838i | \(-0.494270\pi\) | ||||
0.0180006 | + | 0.999838i | \(0.494270\pi\) | |||||||
\(164\) | −2.13683e8 | −3.78283 | ||||||||
\(165\) | 1.03179e8 | 1.78812 | ||||||||
\(166\) | −8.89485e7 | −1.50925 | ||||||||
\(167\) | −3.49476e7 | −0.580643 | −0.290322 | − | 0.956929i | \(-0.593762\pi\) | ||||
−0.290322 | + | 0.956929i | \(0.593762\pi\) | |||||||
\(168\) | −1.64937e8 | −2.68370 | ||||||||
\(169\) | −5.90346e7 | −0.940813 | ||||||||
\(170\) | 2.37262e8 | 3.70388 | ||||||||
\(171\) | −2.30961e7 | −0.353226 | ||||||||
\(172\) | −4.54252e7 | −0.680687 | ||||||||
\(173\) | −2.91994e7 | −0.428759 | −0.214380 | − | 0.976750i | \(-0.568773\pi\) | ||||
−0.214380 | + | 0.976750i | \(0.568773\pi\) | |||||||
\(174\) | −6.39201e7 | −0.919846 | ||||||||
\(175\) | −1.98883e8 | −2.80520 | ||||||||
\(176\) | −5.08285e8 | −7.02769 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | 1.31516e8 | 1.74787 | ||||||||
\(179\) | 1.31626e8 | 1.71536 | 0.857680 | − | 0.514184i | \(-0.171905\pi\) | ||||
0.857680 | + | 0.514184i | \(0.171905\pi\) | |||||||
\(180\) | −1.28245e8 | −1.63903 | ||||||||
\(181\) | −1.51957e8 | −1.90479 | −0.952393 | − | 0.304872i | \(-0.901386\pi\) | ||||
−0.952393 | + | 0.304872i | \(0.901386\pi\) | |||||||
\(182\) | −5.13574e7 | −0.631471 | ||||||||
\(183\) | 6.48987e7 | 0.782812 | ||||||||
\(184\) | 3.83840e8 | 4.54243 | ||||||||
\(185\) | 3.57191e7 | 0.414763 | ||||||||
\(186\) | −3.38251e7 | −0.385428 | ||||||||
\(187\) | 1.69724e8 | 1.89800 | ||||||||
\(188\) | 7.41382e6 | 0.0813747 | ||||||||
\(189\) | −2.38127e7 | −0.256562 | ||||||||
\(190\) | 3.43680e8 | 3.63511 | ||||||||
\(191\) | −1.21713e8 | −1.26392 | −0.631962 | − | 0.775000i | \(-0.717750\pi\) | ||||
−0.631962 | + | 0.775000i | \(0.717750\pi\) | |||||||
\(192\) | 2.47369e8 | 2.52227 | ||||||||
\(193\) | 1.32612e8 | 1.32780 | 0.663900 | − | 0.747821i | \(-0.268900\pi\) | ||||
0.663900 | + | 0.747821i | \(0.268900\pi\) | |||||||
\(194\) | −4.36430e7 | −0.429149 | ||||||||
\(195\) | −2.56241e7 | −0.247473 | ||||||||
\(196\) | 2.28660e8 | 2.16917 | ||||||||
\(197\) | 1.11991e8 | 1.04364 | 0.521819 | − | 0.853056i | \(-0.325254\pi\) | ||||
0.521819 | + | 0.853056i | \(0.325254\pi\) | |||||||
\(198\) | −1.24611e8 | −1.14085 | ||||||||
\(199\) | −1.81688e8 | −1.63433 | −0.817165 | − | 0.576403i | \(-0.804456\pi\) | ||||
−0.817165 | + | 0.576403i | \(0.804456\pi\) | |||||||
\(200\) | 8.30071e8 | 7.33686 | ||||||||
\(201\) | −1.63867e7 | −0.142333 | ||||||||
\(202\) | −3.41147e8 | −2.91214 | ||||||||
\(203\) | 1.30023e8 | 1.09090 | ||||||||
\(204\) | −2.10956e8 | −1.73975 | ||||||||
\(205\) | 2.94576e8 | 2.38814 | ||||||||
\(206\) | −2.64940e8 | −2.11160 | ||||||||
\(207\) | 5.54170e7 | 0.434257 | ||||||||
\(208\) | 1.26230e8 | 0.972618 | ||||||||
\(209\) | 2.45849e8 | 1.86276 | ||||||||
\(210\) | 3.54343e8 | 2.64032 | ||||||||
\(211\) | −3.34639e6 | −0.0245238 | −0.0122619 | − | 0.999925i | \(-0.503903\pi\) | ||||
−0.0122619 | + | 0.999925i | \(0.503903\pi\) | |||||||
\(212\) | 5.46219e8 | 3.93724 | ||||||||
\(213\) | −9.51243e7 | −0.674470 | ||||||||
\(214\) | −1.69399e8 | −1.18158 | ||||||||
\(215\) | 6.26217e7 | 0.429725 | ||||||||
\(216\) | 9.93863e7 | 0.671025 | ||||||||
\(217\) | 6.88051e7 | 0.457101 | ||||||||
\(218\) | −4.65630e7 | −0.304399 | ||||||||
\(219\) | 3.44236e7 | 0.221463 | ||||||||
\(220\) | 1.36512e9 | 8.64353 | ||||||||
\(221\) | −4.21501e7 | −0.262679 | ||||||||
\(222\) | −4.31385e7 | −0.264624 | ||||||||
\(223\) | 3.23603e7 | 0.195410 | 0.0977048 | − | 0.995215i | \(-0.468850\pi\) | ||||
0.0977048 | + | 0.995215i | \(0.468850\pi\) | |||||||
\(224\) | −9.63659e8 | −5.72869 | ||||||||
\(225\) | 1.19842e8 | 0.701405 | ||||||||
\(226\) | 4.47275e7 | 0.257748 | ||||||||
\(227\) | 1.60575e8 | 0.911145 | 0.455573 | − | 0.890199i | \(-0.349435\pi\) | ||||
0.455573 | + | 0.890199i | \(0.349435\pi\) | |||||||
\(228\) | −3.05575e8 | −1.70744 | ||||||||
\(229\) | 4.34106e7 | 0.238876 | 0.119438 | − | 0.992842i | \(-0.461891\pi\) | ||||
0.119438 | + | 0.992842i | \(0.461891\pi\) | |||||||
\(230\) | −8.24628e8 | −4.46900 | ||||||||
\(231\) | 2.53477e8 | 1.35300 | ||||||||
\(232\) | −5.42672e8 | −2.85318 | ||||||||
\(233\) | −2.86270e7 | −0.148262 | −0.0741310 | − | 0.997249i | \(-0.523618\pi\) | ||||
−0.0741310 | + | 0.997249i | \(0.523618\pi\) | |||||||
\(234\) | 3.09466e7 | 0.157891 | ||||||||
\(235\) | −1.02204e7 | −0.0513727 | ||||||||
\(236\) | −7.33667e7 | −0.363335 | ||||||||
\(237\) | 1.05254e8 | 0.513594 | ||||||||
\(238\) | 5.82874e8 | 2.80256 | ||||||||
\(239\) | −6.06584e7 | −0.287408 | −0.143704 | − | 0.989621i | \(-0.545901\pi\) | ||||
−0.143704 | + | 0.989621i | \(0.545901\pi\) | |||||||
\(240\) | −8.70933e8 | −4.06673 | ||||||||
\(241\) | 5.03046e7 | 0.231498 | 0.115749 | − | 0.993278i | \(-0.463073\pi\) | ||||
0.115749 | + | 0.993278i | \(0.463073\pi\) | |||||||
\(242\) | 8.97173e8 | 4.06933 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 8.58648e8 | 3.78400 | ||||||||
\(245\) | −3.15224e8 | −1.36942 | ||||||||
\(246\) | −3.55765e8 | −1.52367 | ||||||||
\(247\) | −6.10556e7 | −0.257802 | ||||||||
\(248\) | −2.87170e8 | −1.19552 | ||||||||
\(249\) | −1.09026e8 | −0.447541 | ||||||||
\(250\) | −9.35807e8 | −3.78788 | ||||||||
\(251\) | 1.79753e8 | 0.717494 | 0.358747 | − | 0.933435i | \(-0.383204\pi\) | ||||
0.358747 | + | 0.933435i | \(0.383204\pi\) | |||||||
\(252\) | −3.15056e8 | −1.24018 | ||||||||
\(253\) | −5.89891e8 | −2.29008 | ||||||||
\(254\) | 3.03707e8 | 1.16289 | ||||||||
\(255\) | 2.90817e8 | 1.09832 | ||||||||
\(256\) | 1.02695e9 | 3.82569 | ||||||||
\(257\) | 8.52960e7 | 0.313446 | 0.156723 | − | 0.987643i | \(-0.449907\pi\) | ||||
0.156723 | + | 0.987643i | \(0.449907\pi\) | |||||||
\(258\) | −7.56293e7 | −0.274171 | ||||||||
\(259\) | 8.77500e7 | 0.313833 | ||||||||
\(260\) | −3.39022e8 | −1.19625 | ||||||||
\(261\) | −7.83483e7 | −0.272764 | ||||||||
\(262\) | −1.86138e7 | −0.0639412 | ||||||||
\(263\) | 4.14430e8 | 1.40477 | 0.702386 | − | 0.711796i | \(-0.252118\pi\) | ||||
0.702386 | + | 0.711796i | \(0.252118\pi\) | |||||||
\(264\) | −1.05793e9 | −3.53869 | ||||||||
\(265\) | −7.53000e8 | −2.48562 | ||||||||
\(266\) | 8.44309e8 | 2.75053 | ||||||||
\(267\) | 1.61202e8 | 0.518301 | ||||||||
\(268\) | −2.16806e8 | −0.688018 | ||||||||
\(269\) | −3.07821e8 | −0.964196 | −0.482098 | − | 0.876117i | \(-0.660125\pi\) | ||||
−0.482098 | + | 0.876117i | \(0.660125\pi\) | |||||||
\(270\) | −2.13518e8 | −0.660178 | ||||||||
\(271\) | −2.35783e8 | −0.719646 | −0.359823 | − | 0.933021i | \(-0.617163\pi\) | ||||
−0.359823 | + | 0.933021i | \(0.617163\pi\) | |||||||
\(272\) | −1.43264e9 | −4.31663 | ||||||||
\(273\) | −6.29499e7 | −0.187252 | ||||||||
\(274\) | −1.06746e9 | −3.13490 | ||||||||
\(275\) | −1.27567e9 | −3.69890 | ||||||||
\(276\) | 7.33199e8 | 2.09913 | ||||||||
\(277\) | −2.15483e8 | −0.609165 | −0.304582 | − | 0.952486i | \(-0.598517\pi\) | ||||
−0.304582 | + | 0.952486i | \(0.598517\pi\) | |||||||
\(278\) | −4.52032e7 | −0.126186 | ||||||||
\(279\) | −4.14601e7 | −0.114292 | ||||||||
\(280\) | 3.00832e9 | 8.18975 | ||||||||
\(281\) | −2.06356e8 | −0.554810 | −0.277405 | − | 0.960753i | \(-0.589474\pi\) | ||||
−0.277405 | + | 0.960753i | \(0.589474\pi\) | |||||||
\(282\) | 1.23434e7 | 0.0327765 | ||||||||
\(283\) | 6.73678e8 | 1.76685 | 0.883426 | − | 0.468571i | \(-0.155231\pi\) | ||||
0.883426 | + | 0.468571i | \(0.155231\pi\) | |||||||
\(284\) | −1.25855e9 | −3.26029 | ||||||||
\(285\) | 4.21256e8 | 1.07793 | ||||||||
\(286\) | −3.29414e8 | −0.832648 | ||||||||
\(287\) | 7.23677e8 | 1.80700 | ||||||||
\(288\) | 5.80675e8 | 1.43238 | ||||||||
\(289\) | 6.80388e7 | 0.165811 | ||||||||
\(290\) | 1.16586e9 | 2.80706 | ||||||||
\(291\) | −5.34942e7 | −0.127257 | ||||||||
\(292\) | 4.55444e8 | 1.07052 | ||||||||
\(293\) | −2.68265e8 | −0.623056 | −0.311528 | − | 0.950237i | \(-0.600841\pi\) | ||||
−0.311528 | + | 0.950237i | \(0.600841\pi\) | |||||||
\(294\) | 3.80701e8 | 0.873711 | ||||||||
\(295\) | 1.01141e8 | 0.229377 | ||||||||
\(296\) | −3.66239e8 | −0.820813 | ||||||||
\(297\) | −1.52738e8 | −0.338299 | ||||||||
\(298\) | −5.58259e7 | −0.122202 | ||||||||
\(299\) | 1.46497e8 | 0.316942 | ||||||||
\(300\) | 1.58557e9 | 3.39049 | ||||||||
\(301\) | 1.53841e8 | 0.325154 | ||||||||
\(302\) | −1.21038e9 | −2.52870 | ||||||||
\(303\) | −4.18152e8 | −0.863544 | ||||||||
\(304\) | −2.07521e9 | −4.23648 | ||||||||
\(305\) | −1.18370e9 | −2.38888 | ||||||||
\(306\) | −3.51225e8 | −0.700745 | ||||||||
\(307\) | 6.59253e8 | 1.30037 | 0.650186 | − | 0.759775i | \(-0.274691\pi\) | ||||
0.650186 | + | 0.759775i | \(0.274691\pi\) | |||||||
\(308\) | 3.35365e9 | 6.54018 | ||||||||
\(309\) | −3.24742e8 | −0.626158 | ||||||||
\(310\) | 6.16945e8 | 1.17620 | ||||||||
\(311\) | −8.73613e8 | −1.64686 | −0.823432 | − | 0.567415i | \(-0.807944\pi\) | ||||
−0.823432 | + | 0.567415i | \(0.807944\pi\) | |||||||
\(312\) | 2.62732e8 | 0.489747 | ||||||||
\(313\) | 2.84022e8 | 0.523537 | 0.261768 | − | 0.965131i | \(-0.415694\pi\) | ||||
0.261768 | + | 0.965131i | \(0.415694\pi\) | |||||||
\(314\) | 1.60259e9 | 2.92125 | ||||||||
\(315\) | 4.34326e8 | 0.782941 | ||||||||
\(316\) | 1.39257e9 | 2.48264 | ||||||||
\(317\) | −2.16935e8 | −0.382491 | −0.191246 | − | 0.981542i | \(-0.561253\pi\) | ||||
−0.191246 | + | 0.981542i | \(0.561253\pi\) | |||||||
\(318\) | 9.09410e8 | 1.58586 | ||||||||
\(319\) | 8.33986e8 | 1.43844 | ||||||||
\(320\) | −4.51183e9 | −7.69711 | ||||||||
\(321\) | −2.07636e8 | −0.350377 | ||||||||
\(322\) | −2.02584e9 | −3.38150 | ||||||||
\(323\) | 6.92943e8 | 1.14416 | ||||||||
\(324\) | 1.89844e8 | 0.310092 | ||||||||
\(325\) | 3.16806e8 | 0.511920 | ||||||||
\(326\) | 4.38475e7 | 0.0700943 | ||||||||
\(327\) | −5.70733e7 | −0.0902643 | ||||||||
\(328\) | −3.02039e9 | −4.72611 | ||||||||
\(329\) | −2.51083e7 | −0.0388715 | ||||||||
\(330\) | 2.27281e9 | 3.48149 | ||||||||
\(331\) | −9.98498e8 | −1.51338 | −0.756692 | − | 0.653772i | \(-0.773186\pi\) | ||||
−0.756692 | + | 0.653772i | \(0.773186\pi\) | |||||||
\(332\) | −1.44248e9 | −2.16335 | ||||||||
\(333\) | −5.28758e7 | −0.0784698 | ||||||||
\(334\) | −7.69820e8 | −1.13052 | ||||||||
\(335\) | 2.98882e8 | 0.434353 | ||||||||
\(336\) | −2.13960e9 | −3.07712 | ||||||||
\(337\) | −1.17882e9 | −1.67780 | −0.838902 | − | 0.544282i | \(-0.816802\pi\) | ||||
−0.838902 | + | 0.544282i | \(0.816802\pi\) | |||||||
\(338\) | −1.30041e9 | −1.83177 | ||||||||
\(339\) | 5.48234e7 | 0.0764306 | ||||||||
\(340\) | 3.84768e9 | 5.30912 | ||||||||
\(341\) | 4.41327e8 | 0.602726 | ||||||||
\(342\) | −5.08758e8 | −0.687733 | ||||||||
\(343\) | 2.21931e8 | 0.296954 | ||||||||
\(344\) | −6.42081e8 | −0.850423 | ||||||||
\(345\) | −1.01076e9 | −1.32521 | ||||||||
\(346\) | −6.43201e8 | −0.834796 | ||||||||
\(347\) | −8.46545e8 | −1.08767 | −0.543835 | − | 0.839192i | \(-0.683028\pi\) | ||||
−0.543835 | + | 0.839192i | \(0.683028\pi\) | |||||||
\(348\) | −1.03659e9 | −1.31850 | ||||||||
\(349\) | 6.62378e8 | 0.834098 | 0.417049 | − | 0.908884i | \(-0.363064\pi\) | ||||
0.417049 | + | 0.908884i | \(0.363064\pi\) | |||||||
\(350\) | −4.38096e9 | −5.46174 | ||||||||
\(351\) | 3.79319e7 | 0.0468199 | ||||||||
\(352\) | −6.18106e9 | −7.55376 | ||||||||
\(353\) | 8.83004e8 | 1.06844 | 0.534221 | − | 0.845345i | \(-0.320605\pi\) | ||||
0.534221 | + | 0.845345i | \(0.320605\pi\) | |||||||
\(354\) | −1.22150e8 | −0.146346 | ||||||||
\(355\) | 1.73500e9 | 2.05825 | ||||||||
\(356\) | 2.13280e9 | 2.50539 | ||||||||
\(357\) | 7.14442e8 | 0.831052 | ||||||||
\(358\) | 2.89943e9 | 3.33981 | ||||||||
\(359\) | 7.02849e7 | 0.0801736 | 0.0400868 | − | 0.999196i | \(-0.487237\pi\) | ||||
0.0400868 | + | 0.999196i | \(0.487237\pi\) | |||||||
\(360\) | −1.81273e9 | −2.04774 | ||||||||
\(361\) | 1.09874e8 | 0.122919 | ||||||||
\(362\) | −3.34729e9 | −3.70863 | ||||||||
\(363\) | 1.09968e9 | 1.20669 | ||||||||
\(364\) | −8.32864e8 | −0.905147 | ||||||||
\(365\) | −6.27860e8 | −0.675830 | ||||||||
\(366\) | 1.42958e9 | 1.52414 | ||||||||
\(367\) | −1.46843e9 | −1.55068 | −0.775340 | − | 0.631544i | \(-0.782421\pi\) | ||||
−0.775340 | + | 0.631544i | \(0.782421\pi\) | |||||||
\(368\) | 4.97927e9 | 5.20833 | ||||||||
\(369\) | −4.36068e8 | −0.451817 | ||||||||
\(370\) | 7.86815e8 | 0.807544 | ||||||||
\(371\) | −1.84987e9 | −1.88076 | ||||||||
\(372\) | −5.48542e8 | −0.552471 | ||||||||
\(373\) | 1.19545e9 | 1.19275 | 0.596376 | − | 0.802705i | \(-0.296607\pi\) | ||||
0.596376 | + | 0.802705i | \(0.296607\pi\) | |||||||
\(374\) | 3.73864e9 | 3.69542 | ||||||||
\(375\) | −1.14704e9 | −1.12323 | ||||||||
\(376\) | 1.04794e8 | 0.101666 | ||||||||
\(377\) | −2.07117e8 | −0.199077 | ||||||||
\(378\) | −5.24543e8 | −0.499528 | ||||||||
\(379\) | 1.21004e9 | 1.14173 | 0.570863 | − | 0.821045i | \(-0.306609\pi\) | ||||
0.570863 | + | 0.821045i | \(0.306609\pi\) | |||||||
\(380\) | 5.57347e9 | 5.21054 | ||||||||
\(381\) | 3.72261e8 | 0.344834 | ||||||||
\(382\) | −2.68108e9 | −2.46086 | ||||||||
\(383\) | −1.02900e9 | −0.935876 | −0.467938 | − | 0.883761i | \(-0.655003\pi\) | ||||
−0.467938 | + | 0.883761i | \(0.655003\pi\) | |||||||
\(384\) | 2.69617e9 | 2.42990 | ||||||||
\(385\) | −4.62323e9 | −4.12888 | ||||||||
\(386\) | 2.92116e9 | 2.58523 | ||||||||
\(387\) | −9.27004e7 | −0.0813005 | ||||||||
\(388\) | −7.07759e8 | −0.615141 | ||||||||
\(389\) | −2.22572e9 | −1.91711 | −0.958556 | − | 0.284904i | \(-0.908038\pi\) | ||||
−0.958556 | + | 0.284904i | \(0.908038\pi\) | |||||||
\(390\) | −5.64443e8 | −0.481830 | ||||||||
\(391\) | −1.66265e9 | −1.40664 | ||||||||
\(392\) | 3.23209e9 | 2.71008 | ||||||||
\(393\) | −2.28153e7 | −0.0189606 | ||||||||
\(394\) | 2.46691e9 | 2.03197 | ||||||||
\(395\) | −1.91976e9 | −1.56732 | ||||||||
\(396\) | −2.02082e9 | −1.63529 | ||||||||
\(397\) | 9.68593e8 | 0.776917 | 0.388458 | − | 0.921466i | \(-0.373008\pi\) | ||||
0.388458 | + | 0.921466i | \(0.373008\pi\) | |||||||
\(398\) | −4.00219e9 | −3.18205 | ||||||||
\(399\) | 1.03489e9 | 0.815620 | ||||||||
\(400\) | 1.07679e10 | 8.41241 | ||||||||
\(401\) | 9.25332e6 | 0.00716626 | 0.00358313 | − | 0.999994i | \(-0.498859\pi\) | ||||
0.00358313 | + | 0.999994i | \(0.498859\pi\) | |||||||
\(402\) | −3.60964e8 | −0.277123 | ||||||||
\(403\) | −1.09602e8 | −0.0834160 | ||||||||
\(404\) | −5.53239e9 | −4.17425 | ||||||||
\(405\) | −2.61713e8 | −0.195764 | ||||||||
\(406\) | 2.86412e9 | 2.12398 | ||||||||
\(407\) | 5.62842e8 | 0.413815 | ||||||||
\(408\) | −2.98184e9 | −2.17357 | ||||||||
\(409\) | 4.22397e8 | 0.305274 | 0.152637 | − | 0.988282i | \(-0.451224\pi\) | ||||
0.152637 | + | 0.988282i | \(0.451224\pi\) | |||||||
\(410\) | 6.48888e9 | 4.64971 | ||||||||
\(411\) | −1.30841e9 | −0.929601 | ||||||||
\(412\) | −4.29653e9 | −3.02676 | ||||||||
\(413\) | 2.48470e8 | 0.173560 | ||||||||
\(414\) | 1.22072e9 | 0.845500 | ||||||||
\(415\) | 1.98856e9 | 1.36574 | ||||||||
\(416\) | 1.53504e9 | 1.04543 | ||||||||
\(417\) | −5.54066e7 | −0.0374184 | ||||||||
\(418\) | 5.41553e9 | 3.62680 | ||||||||
\(419\) | −1.30988e9 | −0.869925 | −0.434962 | − | 0.900449i | \(-0.643238\pi\) | ||||
−0.434962 | + | 0.900449i | \(0.643238\pi\) | |||||||
\(420\) | 5.74639e9 | 3.78462 | ||||||||
\(421\) | 2.15584e9 | 1.40809 | 0.704043 | − | 0.710158i | \(-0.251376\pi\) | ||||
0.704043 | + | 0.710158i | \(0.251376\pi\) | |||||||
\(422\) | −7.37137e7 | −0.0477479 | ||||||||
\(423\) | 1.51296e7 | 0.00971931 | ||||||||
\(424\) | 7.72075e9 | 4.91902 | ||||||||
\(425\) | −3.59555e9 | −2.27198 | ||||||||
\(426\) | −2.09538e9 | −1.31320 | ||||||||
\(427\) | −2.90797e9 | −1.80756 | ||||||||
\(428\) | −2.74715e9 | −1.69367 | ||||||||
\(429\) | −4.03770e8 | −0.246907 | ||||||||
\(430\) | 1.37942e9 | 0.836676 | ||||||||
\(431\) | 8.50792e8 | 0.511862 | 0.255931 | − | 0.966695i | \(-0.417618\pi\) | ||||
0.255931 | + | 0.966695i | \(0.417618\pi\) | |||||||
\(432\) | 1.28926e9 | 0.769394 | ||||||||
\(433\) | −1.01714e9 | −0.602109 | −0.301054 | − | 0.953607i | \(-0.597339\pi\) | ||||
−0.301054 | + | 0.953607i | \(0.597339\pi\) | |||||||
\(434\) | 1.51563e9 | 0.889977 | ||||||||
\(435\) | 1.42901e9 | 0.832385 | ||||||||
\(436\) | −7.55113e8 | −0.436324 | ||||||||
\(437\) | −2.40839e9 | −1.38052 | ||||||||
\(438\) | 7.58277e8 | 0.431190 | ||||||||
\(439\) | −1.42920e9 | −0.806245 | −0.403123 | − | 0.915146i | \(-0.632075\pi\) | ||||
−0.403123 | + | 0.915146i | \(0.632075\pi\) | |||||||
\(440\) | 1.92958e10 | 10.7989 | ||||||||
\(441\) | 4.66633e8 | 0.259084 | ||||||||
\(442\) | −9.28477e8 | −0.511438 | ||||||||
\(443\) | 2.71763e8 | 0.148517 | 0.0742586 | − | 0.997239i | \(-0.476341\pi\) | ||||
0.0742586 | + | 0.997239i | \(0.476341\pi\) | |||||||
\(444\) | −6.99578e8 | −0.379311 | ||||||||
\(445\) | −2.94021e9 | −1.58168 | ||||||||
\(446\) | 7.12828e8 | 0.380463 | ||||||||
\(447\) | −6.84270e7 | −0.0362369 | ||||||||
\(448\) | −1.10841e10 | −5.82406 | ||||||||
\(449\) | −1.24125e9 | −0.647138 | −0.323569 | − | 0.946205i | \(-0.604883\pi\) | ||||
−0.323569 | + | 0.946205i | \(0.604883\pi\) | |||||||
\(450\) | 2.63985e9 | 1.36564 | ||||||||
\(451\) | 4.64177e9 | 2.38268 | ||||||||
\(452\) | 7.25346e8 | 0.369454 | ||||||||
\(453\) | −1.48359e9 | −0.749842 | ||||||||
\(454\) | 3.53712e9 | 1.77400 | ||||||||
\(455\) | 1.14816e9 | 0.571429 | ||||||||
\(456\) | −4.31928e9 | −2.13321 | ||||||||
\(457\) | −3.37198e9 | −1.65264 | −0.826320 | − | 0.563201i | \(-0.809570\pi\) | ||||
−0.826320 | + | 0.563201i | \(0.809570\pi\) | |||||||
\(458\) | 9.56242e8 | 0.465092 | ||||||||
\(459\) | −4.30503e8 | −0.207794 | ||||||||
\(460\) | −1.33730e10 | −6.40585 | ||||||||
\(461\) | −2.86356e9 | −1.36130 | −0.680650 | − | 0.732609i | \(-0.738302\pi\) | ||||
−0.680650 | + | 0.732609i | \(0.738302\pi\) | |||||||
\(462\) | 5.58355e9 | 2.63429 | ||||||||
\(463\) | 4.00910e8 | 0.187721 | 0.0938607 | − | 0.995585i | \(-0.470079\pi\) | ||||
0.0938607 | + | 0.995585i | \(0.470079\pi\) | |||||||
\(464\) | −7.03967e9 | −3.27144 | ||||||||
\(465\) | 7.56202e8 | 0.348781 | ||||||||
\(466\) | −6.30591e8 | −0.288667 | ||||||||
\(467\) | −8.05487e8 | −0.365973 | −0.182987 | − | 0.983115i | \(-0.558577\pi\) | ||||
−0.182987 | + | 0.983115i | \(0.558577\pi\) | |||||||
\(468\) | 5.01862e8 | 0.226320 | ||||||||
\(469\) | 7.34254e8 | 0.328656 | ||||||||
\(470\) | −2.25134e8 | −0.100023 | ||||||||
\(471\) | 1.96433e9 | 0.866246 | ||||||||
\(472\) | −1.03703e9 | −0.453936 | ||||||||
\(473\) | 9.86759e8 | 0.428743 | ||||||||
\(474\) | 2.31852e9 | 0.999970 | ||||||||
\(475\) | −5.20825e9 | −2.22979 | ||||||||
\(476\) | 9.45248e9 | 4.01718 | ||||||||
\(477\) | 1.11468e9 | 0.470259 | ||||||||
\(478\) | −1.33617e9 | −0.559584 | ||||||||
\(479\) | −1.45641e9 | −0.605495 | −0.302747 | − | 0.953071i | \(-0.597904\pi\) | ||||
−0.302747 | + | 0.953071i | \(0.597904\pi\) | |||||||
\(480\) | −1.05911e10 | −4.37116 | ||||||||
\(481\) | −1.39779e8 | −0.0572711 | ||||||||
\(482\) | 1.10810e9 | 0.450728 | ||||||||
\(483\) | −2.48311e9 | −1.00272 | ||||||||
\(484\) | 1.45495e10 | 5.83295 | ||||||||
\(485\) | 9.75694e8 | 0.388345 | ||||||||
\(486\) | 3.16075e8 | 0.124900 | ||||||||
\(487\) | 1.91160e9 | 0.749973 | 0.374986 | − | 0.927030i | \(-0.377647\pi\) | ||||
0.374986 | + | 0.927030i | \(0.377647\pi\) | |||||||
\(488\) | 1.21369e10 | 4.72758 | ||||||||
\(489\) | 5.37448e7 | 0.0207853 | ||||||||
\(490\) | −6.94370e9 | −2.66627 | ||||||||
\(491\) | 3.11951e8 | 0.118933 | 0.0594663 | − | 0.998230i | \(-0.481060\pi\) | ||||
0.0594663 | + | 0.998230i | \(0.481060\pi\) | |||||||
\(492\) | −5.76944e9 | −2.18402 | ||||||||
\(493\) | 2.35065e9 | 0.883533 | ||||||||
\(494\) | −1.34492e9 | −0.501942 | ||||||||
\(495\) | 2.78583e9 | 1.03237 | ||||||||
\(496\) | −3.72524e9 | −1.37078 | ||||||||
\(497\) | 4.26231e9 | 1.55739 | ||||||||
\(498\) | −2.40161e9 | −0.871364 | ||||||||
\(499\) | −1.10424e9 | −0.397844 | −0.198922 | − | 0.980015i | \(-0.563744\pi\) | ||||
−0.198922 | + | 0.980015i | \(0.563744\pi\) | |||||||
\(500\) | −1.51760e10 | −5.42953 | ||||||||
\(501\) | −9.43585e8 | −0.335235 | ||||||||
\(502\) | 3.95957e9 | 1.39696 | ||||||||
\(503\) | −3.17067e9 | −1.11087 | −0.555434 | − | 0.831560i | \(-0.687448\pi\) | ||||
−0.555434 | + | 0.831560i | \(0.687448\pi\) | |||||||
\(504\) | −4.45329e9 | −1.54944 | ||||||||
\(505\) | 7.62677e9 | 2.63524 | ||||||||
\(506\) | −1.29940e10 | −4.45879 | ||||||||
\(507\) | −1.59394e9 | −0.543179 | ||||||||
\(508\) | 4.92523e9 | 1.66688 | ||||||||
\(509\) | 1.80020e9 | 0.605074 | 0.302537 | − | 0.953138i | \(-0.402166\pi\) | ||||
0.302537 | + | 0.953138i | \(0.402166\pi\) | |||||||
\(510\) | 6.40607e9 | 2.13844 | ||||||||
\(511\) | −1.54244e9 | −0.511371 | ||||||||
\(512\) | 9.83963e9 | 3.23992 | ||||||||
\(513\) | −6.23596e8 | −0.203935 | ||||||||
\(514\) | 1.87889e9 | 0.610281 | ||||||||
\(515\) | 5.92306e9 | 1.91082 | ||||||||
\(516\) | −1.22648e9 | −0.392995 | ||||||||
\(517\) | −1.61048e8 | −0.0512553 | ||||||||
\(518\) | 1.93294e9 | 0.611034 | ||||||||
\(519\) | −7.88385e8 | −0.247544 | ||||||||
\(520\) | −4.79204e9 | −1.49454 | ||||||||
\(521\) | −1.90764e9 | −0.590968 | −0.295484 | − | 0.955348i | \(-0.595481\pi\) | ||||
−0.295484 | + | 0.955348i | \(0.595481\pi\) | |||||||
\(522\) | −1.72584e9 | −0.531073 | ||||||||
\(523\) | 1.01205e9 | 0.309347 | 0.154673 | − | 0.987966i | \(-0.450567\pi\) | ||||
0.154673 | + | 0.987966i | \(0.450567\pi\) | |||||||
\(524\) | −3.01860e8 | −0.0916530 | ||||||||
\(525\) | −5.36984e9 | −1.61959 | ||||||||
\(526\) | 9.12900e9 | 2.73510 | ||||||||
\(527\) | 1.24391e9 | 0.370213 | ||||||||
\(528\) | −1.37237e10 | −4.05744 | ||||||||
\(529\) | 2.37388e9 | 0.697211 | ||||||||
\(530\) | −1.65870e10 | −4.83951 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | 1.36922e10 | 3.94259 | ||||||||
\(533\) | −1.15276e9 | −0.329758 | ||||||||
\(534\) | 3.55094e9 | 1.00913 | ||||||||
\(535\) | 3.78713e9 | 1.06923 | ||||||||
\(536\) | −3.06453e9 | −0.859582 | ||||||||
\(537\) | 3.55389e9 | 0.990363 | ||||||||
\(538\) | −6.78063e9 | −1.87729 | ||||||||
\(539\) | −4.96712e9 | −1.36629 | ||||||||
\(540\) | −3.46262e9 | −0.946296 | ||||||||
\(541\) | −5.50100e9 | −1.49366 | −0.746829 | − | 0.665016i | \(-0.768425\pi\) | ||||
−0.746829 | + | 0.665016i | \(0.768425\pi\) | |||||||
\(542\) | −5.19378e9 | −1.40115 | ||||||||
\(543\) | −4.10285e9 | −1.09973 | ||||||||
\(544\) | −1.74217e10 | −4.63976 | ||||||||
\(545\) | 1.04097e9 | 0.275456 | ||||||||
\(546\) | −1.38665e9 | −0.364580 | ||||||||
\(547\) | 4.40039e9 | 1.14957 | 0.574786 | − | 0.818304i | \(-0.305085\pi\) | ||||
0.574786 | + | 0.818304i | \(0.305085\pi\) | |||||||
\(548\) | −1.73110e10 | −4.49355 | ||||||||
\(549\) | 1.75227e9 | 0.451957 | ||||||||
\(550\) | −2.81002e10 | −7.20177 | ||||||||
\(551\) | 3.40497e9 | 0.867128 | ||||||||
\(552\) | 1.03637e10 | 2.62257 | ||||||||
\(553\) | −4.71621e9 | −1.18592 | ||||||||
\(554\) | −4.74664e9 | −1.18605 | ||||||||
\(555\) | 9.64416e8 | 0.239463 | ||||||||
\(556\) | −7.33062e8 | −0.180875 | ||||||||
\(557\) | 5.20574e9 | 1.27641 | 0.638203 | − | 0.769868i | \(-0.279678\pi\) | ||||
0.638203 | + | 0.769868i | \(0.279678\pi\) | |||||||
\(558\) | −9.13278e8 | −0.222527 | ||||||||
\(559\) | −2.45057e8 | −0.0593371 | ||||||||
\(560\) | 3.90246e10 | 9.39033 | ||||||||
\(561\) | 4.58254e9 | 1.09581 | ||||||||
\(562\) | −4.54557e9 | −1.08022 | ||||||||
\(563\) | 6.20253e9 | 1.46484 | 0.732419 | − | 0.680854i | \(-0.238391\pi\) | ||||
0.732419 | + | 0.680854i | \(0.238391\pi\) | |||||||
\(564\) | 2.00173e8 | 0.0469817 | ||||||||
\(565\) | −9.99939e8 | −0.233240 | ||||||||
\(566\) | 1.48397e10 | 3.44007 | ||||||||
\(567\) | −6.42943e8 | −0.148126 | ||||||||
\(568\) | −1.77895e10 | −4.07328 | ||||||||
\(569\) | 6.72094e9 | 1.52946 | 0.764728 | − | 0.644353i | \(-0.222873\pi\) | ||||
0.764728 | + | 0.644353i | \(0.222873\pi\) | |||||||
\(570\) | 9.27937e9 | 2.09873 | ||||||||
\(571\) | 3.74441e8 | 0.0841700 | 0.0420850 | − | 0.999114i | \(-0.486600\pi\) | ||||
0.0420850 | + | 0.999114i | \(0.486600\pi\) | |||||||
\(572\) | −5.34212e9 | −1.19351 | ||||||||
\(573\) | −3.28626e9 | −0.729727 | ||||||||
\(574\) | 1.59410e10 | 3.51824 | ||||||||
\(575\) | 1.24967e10 | 2.74131 | ||||||||
\(576\) | 6.67896e9 | 1.45623 | ||||||||
\(577\) | 1.91890e9 | 0.415851 | 0.207925 | − | 0.978145i | \(-0.433329\pi\) | ||||
0.207925 | + | 0.978145i | \(0.433329\pi\) | |||||||
\(578\) | 1.49875e9 | 0.322835 | ||||||||
\(579\) | 3.58053e9 | 0.766606 | ||||||||
\(580\) | 1.89067e10 | 4.02362 | ||||||||
\(581\) | 4.88522e9 | 1.03340 | ||||||||
\(582\) | −1.17836e9 | −0.247770 | ||||||||
\(583\) | −1.18654e10 | −2.47994 | ||||||||
\(584\) | 6.43765e9 | 1.33746 | ||||||||
\(585\) | −6.91850e8 | −0.142878 | ||||||||
\(586\) | −5.90929e9 | −1.21309 | ||||||||
\(587\) | −9.08556e9 | −1.85404 | −0.927018 | − | 0.375016i | \(-0.877637\pi\) | ||||
−0.927018 | + | 0.375016i | \(0.877637\pi\) | |||||||
\(588\) | 6.17383e9 | 1.25237 | ||||||||
\(589\) | 1.80184e9 | 0.363339 | ||||||||
\(590\) | 2.22792e9 | 0.446598 | ||||||||
\(591\) | 3.02375e9 | 0.602545 | ||||||||
\(592\) | −4.75095e9 | −0.941140 | ||||||||
\(593\) | −1.90930e9 | −0.375997 | −0.187998 | − | 0.982169i | \(-0.560200\pi\) | ||||
−0.187998 | + | 0.982169i | \(0.560200\pi\) | |||||||
\(594\) | −3.36450e9 | −0.658669 | ||||||||
\(595\) | −1.30309e10 | −2.53609 | ||||||||
\(596\) | −9.05329e8 | −0.175164 | ||||||||
\(597\) | −4.90557e9 | −0.943581 | ||||||||
\(598\) | 3.22701e9 | 0.617088 | ||||||||
\(599\) | −5.47139e9 | −1.04017 | −0.520084 | − | 0.854115i | \(-0.674099\pi\) | ||||
−0.520084 | + | 0.854115i | \(0.674099\pi\) | |||||||
\(600\) | 2.24119e10 | 4.23594 | ||||||||
\(601\) | 3.55169e9 | 0.667381 | 0.333691 | − | 0.942683i | \(-0.391706\pi\) | ||||
0.333691 | + | 0.942683i | \(0.391706\pi\) | |||||||
\(602\) | 3.38878e9 | 0.633076 | ||||||||
\(603\) | −4.42442e8 | −0.0821761 | ||||||||
\(604\) | −1.96287e10 | −3.62463 | ||||||||
\(605\) | −2.00574e10 | −3.68240 | ||||||||
\(606\) | −9.21098e9 | −1.68132 | ||||||||
\(607\) | 5.38370e9 | 0.977057 | 0.488529 | − | 0.872548i | \(-0.337534\pi\) | ||||
0.488529 | + | 0.872548i | \(0.337534\pi\) | |||||||
\(608\) | −2.52358e10 | −4.55360 | ||||||||
\(609\) | 3.51061e9 | 0.629829 | ||||||||
\(610\) | −2.60745e10 | −4.65116 | ||||||||
\(611\) | 3.99956e7 | 0.00709363 | ||||||||
\(612\) | −5.69581e9 | −1.00444 | ||||||||
\(613\) | 5.24608e9 | 0.919863 | 0.459932 | − | 0.887954i | \(-0.347874\pi\) | ||||
0.459932 | + | 0.887954i | \(0.347874\pi\) | |||||||
\(614\) | 1.45219e10 | 2.53183 | ||||||||
\(615\) | 7.95356e9 | 1.37879 | ||||||||
\(616\) | 4.74034e10 | 8.17104 | ||||||||
\(617\) | 6.88172e9 | 1.17950 | 0.589751 | − | 0.807585i | \(-0.299226\pi\) | ||||
0.589751 | + | 0.807585i | \(0.299226\pi\) | |||||||
\(618\) | −7.15337e9 | −1.21913 | ||||||||
\(619\) | 5.67281e9 | 0.961350 | 0.480675 | − | 0.876899i | \(-0.340392\pi\) | ||||
0.480675 | + | 0.876899i | \(0.340392\pi\) | |||||||
\(620\) | 1.00050e10 | 1.68596 | ||||||||
\(621\) | 1.49626e9 | 0.250718 | ||||||||
\(622\) | −1.92438e10 | −3.20645 | ||||||||
\(623\) | −7.22313e9 | −1.19679 | ||||||||
\(624\) | 3.40822e9 | 0.561541 | ||||||||
\(625\) | 8.07802e9 | 1.32350 | ||||||||
\(626\) | 6.25640e9 | 1.01933 | ||||||||
\(627\) | 6.63793e9 | 1.07546 | ||||||||
\(628\) | 2.59892e10 | 4.18730 | ||||||||
\(629\) | 1.58641e9 | 0.254178 | ||||||||
\(630\) | 9.56727e9 | 1.52439 | ||||||||
\(631\) | 1.88338e9 | 0.298425 | 0.149212 | − | 0.988805i | \(-0.452326\pi\) | ||||
0.149212 | + | 0.988805i | \(0.452326\pi\) | |||||||
\(632\) | 1.96839e10 | 3.10171 | ||||||||
\(633\) | −9.03524e7 | −0.0141588 | ||||||||
\(634\) | −4.77860e9 | −0.744713 | ||||||||
\(635\) | −6.78976e9 | −1.05232 | ||||||||
\(636\) | 1.47479e10 | 2.27316 | ||||||||
\(637\) | 1.23356e9 | 0.189092 | ||||||||
\(638\) | 1.83709e10 | 2.80065 | ||||||||
\(639\) | −2.56836e9 | −0.389405 | ||||||||
\(640\) | −4.91762e10 | −7.41524 | ||||||||
\(641\) | 5.23503e9 | 0.785084 | 0.392542 | − | 0.919734i | \(-0.371596\pi\) | ||||
0.392542 | + | 0.919734i | \(0.371596\pi\) | |||||||
\(642\) | −4.57377e9 | −0.682185 | ||||||||
\(643\) | −7.39762e8 | −0.109737 | −0.0548686 | − | 0.998494i | \(-0.517474\pi\) | ||||
−0.0548686 | + | 0.998494i | \(0.517474\pi\) | |||||||
\(644\) | −3.28530e10 | −4.84702 | ||||||||
\(645\) | 1.69079e9 | 0.248102 | ||||||||
\(646\) | 1.52640e10 | 2.22769 | ||||||||
\(647\) | −7.49507e9 | −1.08796 | −0.543978 | − | 0.839100i | \(-0.683082\pi\) | ||||
−0.543978 | + | 0.839100i | \(0.683082\pi\) | |||||||
\(648\) | 2.68343e9 | 0.387416 | ||||||||
\(649\) | 1.59372e9 | 0.228853 | ||||||||
\(650\) | 6.97856e9 | 0.996710 | ||||||||
\(651\) | 1.85774e9 | 0.263907 | ||||||||
\(652\) | 7.11075e8 | 0.100473 | ||||||||
\(653\) | 9.12022e9 | 1.28177 | 0.640884 | − | 0.767638i | \(-0.278568\pi\) | ||||
0.640884 | + | 0.767638i | \(0.278568\pi\) | |||||||
\(654\) | −1.25720e9 | −0.175745 | ||||||||
\(655\) | 4.16135e8 | 0.0578615 | ||||||||
\(656\) | −3.91812e10 | −5.41893 | ||||||||
\(657\) | 9.29436e8 | 0.127862 | ||||||||
\(658\) | −5.53081e8 | −0.0756829 | ||||||||
\(659\) | 8.11531e9 | 1.10460 | 0.552301 | − | 0.833645i | \(-0.313750\pi\) | ||||
0.552301 | + | 0.833645i | \(0.313750\pi\) | |||||||
\(660\) | 3.68582e10 | 4.99034 | ||||||||
\(661\) | 6.72245e9 | 0.905362 | 0.452681 | − | 0.891672i | \(-0.350468\pi\) | ||||
0.452681 | + | 0.891672i | \(0.350468\pi\) | |||||||
\(662\) | −2.19947e10 | −2.94656 | ||||||||
\(663\) | −1.13805e9 | −0.151658 | ||||||||
\(664\) | −2.03893e10 | −2.70280 | ||||||||
\(665\) | −1.88756e10 | −2.48900 | ||||||||
\(666\) | −1.16474e9 | −0.152781 | ||||||||
\(667\) | −8.16991e9 | −1.06605 | ||||||||
\(668\) | −1.24842e10 | −1.62047 | ||||||||
\(669\) | 8.73729e8 | 0.112820 | ||||||||
\(670\) | 6.58372e9 | 0.845687 | ||||||||
\(671\) | −1.86522e10 | −2.38342 | ||||||||
\(672\) | −2.60188e10 | −3.30746 | ||||||||
\(673\) | 1.14461e10 | 1.44745 | 0.723725 | − | 0.690089i | \(-0.242429\pi\) | ||||
0.723725 | + | 0.690089i | \(0.242429\pi\) | |||||||
\(674\) | −2.59668e10 | −3.26669 | ||||||||
\(675\) | 3.23572e9 | 0.404956 | ||||||||
\(676\) | −2.10887e10 | −2.62565 | ||||||||
\(677\) | −4.26750e9 | −0.528583 | −0.264292 | − | 0.964443i | \(-0.585138\pi\) | ||||
−0.264292 | + | 0.964443i | \(0.585138\pi\) | |||||||
\(678\) | 1.20764e9 | 0.148811 | ||||||||
\(679\) | 2.39696e9 | 0.293843 | ||||||||
\(680\) | 5.43866e10 | 6.63301 | ||||||||
\(681\) | 4.33553e9 | 0.526050 | ||||||||
\(682\) | 9.72147e9 | 1.17351 | ||||||||
\(683\) | 6.74829e9 | 0.810441 | 0.405220 | − | 0.914219i | \(-0.367195\pi\) | ||||
0.405220 | + | 0.914219i | \(0.367195\pi\) | |||||||
\(684\) | −8.25054e9 | −0.985793 | ||||||||
\(685\) | 2.38644e10 | 2.83683 | ||||||||
\(686\) | 4.88867e9 | 0.578171 | ||||||||
\(687\) | 1.17209e9 | 0.137915 | ||||||||
\(688\) | −8.32922e9 | −0.975091 | ||||||||
\(689\) | 2.94671e9 | 0.343218 | ||||||||
\(690\) | −2.22650e10 | −2.58018 | ||||||||
\(691\) | −6.41648e9 | −0.739816 | −0.369908 | − | 0.929068i | \(-0.620611\pi\) | ||||
−0.369908 | + | 0.929068i | \(0.620611\pi\) | |||||||
\(692\) | −1.04308e10 | −1.19659 | ||||||||
\(693\) | 6.84387e9 | 0.781152 | ||||||||
\(694\) | −1.86476e10 | −2.11770 | ||||||||
\(695\) | 1.01057e9 | 0.114188 | ||||||||
\(696\) | −1.46521e10 | −1.64728 | ||||||||
\(697\) | 1.30832e10 | 1.46352 | ||||||||
\(698\) | 1.45908e10 | 1.62399 | ||||||||
\(699\) | −7.72929e8 | −0.0855991 | ||||||||
\(700\) | −7.10461e10 | −7.82884 | ||||||||
\(701\) | −1.49165e10 | −1.63552 | −0.817758 | − | 0.575562i | \(-0.804784\pi\) | ||||
−0.817758 | + | 0.575562i | \(0.804784\pi\) | |||||||
\(702\) | 8.35559e8 | 0.0911585 | ||||||||
\(703\) | 2.29796e9 | 0.249458 | ||||||||
\(704\) | −7.10949e10 | −7.67952 | ||||||||
\(705\) | −2.75952e8 | −0.0296600 | ||||||||
\(706\) | 1.94507e10 | 2.08026 | ||||||||
\(707\) | 1.87365e10 | 1.99397 | ||||||||
\(708\) | −1.98090e9 | −0.209771 | ||||||||
\(709\) | 5.36963e9 | 0.565826 | 0.282913 | − | 0.959146i | \(-0.408699\pi\) | ||||
0.282913 | + | 0.959146i | \(0.408699\pi\) | |||||||
\(710\) | 3.82182e10 | 4.00743 | ||||||||
\(711\) | 2.84186e9 | 0.296524 | ||||||||
\(712\) | 3.01469e10 | 3.13014 | ||||||||
\(713\) | −4.32333e9 | −0.446689 | ||||||||
\(714\) | 1.57376e10 | 1.61806 | ||||||||
\(715\) | 7.36447e9 | 0.753477 | ||||||||
\(716\) | 4.70201e10 | 4.78727 | ||||||||
\(717\) | −1.63778e9 | −0.165935 | ||||||||
\(718\) | 1.54822e9 | 0.156098 | ||||||||
\(719\) | −2.42754e9 | −0.243565 | −0.121783 | − | 0.992557i | \(-0.538861\pi\) | ||||
−0.121783 | + | 0.992557i | \(0.538861\pi\) | |||||||
\(720\) | −2.35152e10 | −2.34793 | ||||||||
\(721\) | 1.45510e10 | 1.44584 | ||||||||
\(722\) | 2.42029e9 | 0.239325 | ||||||||
\(723\) | 1.35822e9 | 0.133656 | ||||||||
\(724\) | −5.42830e10 | −5.31593 | ||||||||
\(725\) | −1.76678e10 | −1.72186 | ||||||||
\(726\) | 2.42237e10 | 2.34943 | ||||||||
\(727\) | 1.20971e10 | 1.16764 | 0.583822 | − | 0.811882i | \(-0.301557\pi\) | ||||
0.583822 | + | 0.811882i | \(0.301557\pi\) | |||||||
\(728\) | −1.17724e10 | −1.13086 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.38304e10 | −1.31584 | ||||||||
\(731\) | 2.78125e9 | 0.263347 | ||||||||
\(732\) | 2.31835e10 | 2.18469 | ||||||||
\(733\) | 3.52480e7 | 0.00330575 | 0.00165288 | − | 0.999999i | \(-0.499474\pi\) | ||||
0.00165288 | + | 0.999999i | \(0.499474\pi\) | |||||||
\(734\) | −3.23463e10 | −3.01918 | ||||||||
\(735\) | −8.51104e9 | −0.790636 | ||||||||
\(736\) | 6.05510e10 | 5.59821 | ||||||||
\(737\) | 4.70962e9 | 0.433360 | ||||||||
\(738\) | −9.60564e9 | −0.879689 | ||||||||
\(739\) | 9.27198e9 | 0.845118 | 0.422559 | − | 0.906336i | \(-0.361132\pi\) | ||||
0.422559 | + | 0.906336i | \(0.361132\pi\) | |||||||
\(740\) | 1.27598e10 | 1.15753 | ||||||||
\(741\) | −1.64850e9 | −0.148842 | ||||||||
\(742\) | −4.07487e10 | −3.66184 | ||||||||
\(743\) | −1.63793e10 | −1.46499 | −0.732494 | − | 0.680773i | \(-0.761644\pi\) | ||||
−0.732494 | + | 0.680773i | \(0.761644\pi\) | |||||||
\(744\) | −7.75358e9 | −0.690235 | ||||||||
\(745\) | 1.24806e9 | 0.110583 | ||||||||
\(746\) | 2.63331e10 | 2.32229 | ||||||||
\(747\) | −2.94371e9 | −0.258388 | ||||||||
\(748\) | 6.06296e10 | 5.29699 | ||||||||
\(749\) | 9.30372e9 | 0.809040 | ||||||||
\(750\) | −2.52668e10 | −2.18693 | ||||||||
\(751\) | 2.46248e9 | 0.212145 | 0.106073 | − | 0.994358i | \(-0.466172\pi\) | ||||
0.106073 | + | 0.994358i | \(0.466172\pi\) | |||||||
\(752\) | 1.35941e9 | 0.116570 | ||||||||
\(753\) | 4.85334e9 | 0.414246 | ||||||||
\(754\) | −4.56234e9 | −0.387604 | ||||||||
\(755\) | 2.70596e10 | 2.28826 | ||||||||
\(756\) | −8.50652e9 | −0.716020 | ||||||||
\(757\) | 7.88850e9 | 0.660935 | 0.330468 | − | 0.943817i | \(-0.392794\pi\) | ||||
0.330468 | + | 0.943817i | \(0.392794\pi\) | |||||||
\(758\) | 2.66545e10 | 2.22295 | ||||||||
\(759\) | −1.59271e10 | −1.32218 | ||||||||
\(760\) | 7.87804e10 | 6.50984 | ||||||||
\(761\) | −2.28543e10 | −1.87984 | −0.939922 | − | 0.341390i | \(-0.889102\pi\) | ||||
−0.939922 | + | 0.341390i | \(0.889102\pi\) | |||||||
\(762\) | 8.20010e9 | 0.671393 | ||||||||
\(763\) | 2.55733e9 | 0.208426 | ||||||||
\(764\) | −4.34791e10 | −3.52739 | ||||||||
\(765\) | 7.85206e9 | 0.634116 | ||||||||
\(766\) | −2.26666e10 | −1.82216 | ||||||||
\(767\) | −3.95795e8 | −0.0316728 | ||||||||
\(768\) | 2.77276e10 | 2.20876 | ||||||||
\(769\) | 3.75836e9 | 0.298028 | 0.149014 | − | 0.988835i | \(-0.452390\pi\) | ||||
0.149014 | + | 0.988835i | \(0.452390\pi\) | |||||||
\(770\) | −1.01840e11 | −8.03896 | ||||||||
\(771\) | 2.30299e9 | 0.180968 | ||||||||
\(772\) | 4.73725e10 | 3.70566 | ||||||||
\(773\) | −2.31574e10 | −1.80327 | −0.901637 | − | 0.432494i | \(-0.857634\pi\) | ||||
−0.901637 | + | 0.432494i | \(0.857634\pi\) | |||||||
\(774\) | −2.04199e9 | −0.158292 | ||||||||
\(775\) | −9.34939e9 | −0.721485 | ||||||||
\(776\) | −1.00041e10 | −0.768532 | ||||||||
\(777\) | 2.36925e9 | 0.181191 | ||||||||
\(778\) | −4.90279e10 | −3.73263 | ||||||||
\(779\) | 1.89513e10 | 1.43634 | ||||||||
\(780\) | −9.15358e9 | −0.690653 | ||||||||
\(781\) | 2.73391e10 | 2.05355 | ||||||||
\(782\) | −3.66246e10 | −2.73873 | ||||||||
\(783\) | −2.11540e9 | −0.157481 | ||||||||
\(784\) | 4.19274e10 | 3.10736 | ||||||||
\(785\) | −3.58279e10 | −2.64349 | ||||||||
\(786\) | −5.02573e8 | −0.0369165 | ||||||||
\(787\) | 7.24985e8 | 0.0530173 | 0.0265087 | − | 0.999649i | \(-0.491561\pi\) | ||||
0.0265087 | + | 0.999649i | \(0.491561\pi\) | |||||||
\(788\) | 4.00059e10 | 2.91261 | ||||||||
\(789\) | 1.11896e10 | 0.811046 | ||||||||
\(790\) | −4.22881e10 | −3.05157 | ||||||||
\(791\) | −2.45652e9 | −0.176483 | ||||||||
\(792\) | −2.85640e10 | −2.04306 | ||||||||
\(793\) | 4.63219e9 | 0.329860 | ||||||||
\(794\) | 2.13360e10 | 1.51266 | ||||||||
\(795\) | −2.03310e10 | −1.43507 | ||||||||
\(796\) | −6.49036e10 | −4.56113 | ||||||||
\(797\) | 1.66646e10 | 1.16598 | 0.582989 | − | 0.812480i | \(-0.301883\pi\) | ||||
0.582989 | + | 0.812480i | \(0.301883\pi\) | |||||||
\(798\) | 2.27963e10 | 1.58802 | ||||||||
\(799\) | −4.53925e8 | −0.0314826 | ||||||||
\(800\) | 1.30944e11 | 9.04213 | ||||||||
\(801\) | 4.35247e9 | 0.299241 | ||||||||
\(802\) | 2.03831e8 | 0.0139527 | ||||||||
\(803\) | −9.89347e9 | −0.674286 | ||||||||
\(804\) | −5.85376e9 | −0.397227 | ||||||||
\(805\) | 4.52901e10 | 3.05998 | ||||||||
\(806\) | −2.41429e9 | −0.162411 | ||||||||
\(807\) | −8.31117e9 | −0.556679 | ||||||||
\(808\) | −7.81997e10 | −5.21514 | ||||||||
\(809\) | −1.50299e10 | −0.998010 | −0.499005 | − | 0.866599i | \(-0.666301\pi\) | ||||
−0.499005 | + | 0.866599i | \(0.666301\pi\) | |||||||
\(810\) | −5.76498e9 | −0.381154 | ||||||||
\(811\) | −1.62482e10 | −1.06963 | −0.534813 | − | 0.844971i | \(-0.679618\pi\) | ||||
−0.534813 | + | 0.844971i | \(0.679618\pi\) | |||||||
\(812\) | 4.64475e10 | 3.04450 | ||||||||
\(813\) | −6.36613e9 | −0.415488 | ||||||||
\(814\) | 1.23982e10 | 0.805699 | ||||||||
\(815\) | −9.80265e8 | −0.0634296 | ||||||||
\(816\) | −3.86812e10 | −2.49221 | ||||||||
\(817\) | 4.02871e9 | 0.258457 | ||||||||
\(818\) | 9.30449e9 | 0.594369 | ||||||||
\(819\) | −1.69965e9 | −0.108110 | ||||||||
\(820\) | 1.05230e11 | 6.66488 | ||||||||
\(821\) | −2.31309e10 | −1.45879 | −0.729393 | − | 0.684095i | \(-0.760197\pi\) | ||||
−0.729393 | + | 0.684095i | \(0.760197\pi\) | |||||||
\(822\) | −2.88214e10 | −1.80994 | ||||||||
\(823\) | −2.00237e10 | −1.25211 | −0.626057 | − | 0.779777i | \(-0.715332\pi\) | ||||
−0.626057 | + | 0.779777i | \(0.715332\pi\) | |||||||
\(824\) | −6.07310e10 | −3.78151 | ||||||||
\(825\) | −3.44430e10 | −2.13556 | ||||||||
\(826\) | 5.47325e9 | 0.337921 | ||||||||
\(827\) | −1.75153e10 | −1.07683 | −0.538417 | − | 0.842679i | \(-0.680977\pi\) | ||||
−0.538417 | + | 0.842679i | \(0.680977\pi\) | |||||||
\(828\) | 1.97964e10 | 1.21194 | ||||||||
\(829\) | 1.27473e10 | 0.777099 | 0.388550 | − | 0.921428i | \(-0.372976\pi\) | ||||
0.388550 | + | 0.921428i | \(0.372976\pi\) | |||||||
\(830\) | 4.38036e10 | 2.65911 | ||||||||
\(831\) | −5.81805e9 | −0.351701 | ||||||||
\(832\) | 1.76561e10 | 1.06283 | ||||||||
\(833\) | −1.40002e10 | −0.839220 | ||||||||
\(834\) | −1.22049e9 | −0.0728538 | ||||||||
\(835\) | 1.72103e10 | 1.02302 | ||||||||
\(836\) | 8.78237e10 | 5.19864 | ||||||||
\(837\) | −1.11942e9 | −0.0659866 | ||||||||
\(838\) | −2.88538e10 | −1.69375 | ||||||||
\(839\) | 1.43905e10 | 0.841217 | 0.420609 | − | 0.907242i | \(-0.361817\pi\) | ||||
0.420609 | + | 0.907242i | \(0.361817\pi\) | |||||||
\(840\) | 8.12246e10 | 4.72836 | ||||||||
\(841\) | −5.69930e9 | −0.330397 | ||||||||
\(842\) | 4.74885e10 | 2.74155 | ||||||||
\(843\) | −5.57160e9 | −0.320320 | ||||||||
\(844\) | −1.19542e9 | −0.0684416 | ||||||||
\(845\) | 2.90722e10 | 1.65760 | ||||||||
\(846\) | 3.33272e8 | 0.0189235 | ||||||||
\(847\) | −4.92745e10 | −2.78631 | ||||||||
\(848\) | 1.00155e11 | 5.64013 | ||||||||
\(849\) | 1.81893e10 | 1.02009 | ||||||||
\(850\) | −7.92022e10 | −4.42355 | ||||||||
\(851\) | −5.51372e9 | −0.306684 | ||||||||
\(852\) | −3.39808e10 | −1.88233 | ||||||||
\(853\) | −2.47811e10 | −1.36710 | −0.683549 | − | 0.729905i | \(-0.739564\pi\) | ||||
−0.683549 | + | 0.729905i | \(0.739564\pi\) | |||||||
\(854\) | −6.40563e10 | −3.51933 | ||||||||
\(855\) | 1.13739e10 | 0.622342 | ||||||||
\(856\) | −3.88306e10 | −2.11600 | ||||||||
\(857\) | 1.34333e10 | 0.729036 | 0.364518 | − | 0.931196i | \(-0.381234\pi\) | ||||
0.364518 | + | 0.931196i | \(0.381234\pi\) | |||||||
\(858\) | −8.89419e9 | −0.480729 | ||||||||
\(859\) | 1.54319e10 | 0.830701 | 0.415350 | − | 0.909662i | \(-0.363659\pi\) | ||||
0.415350 | + | 0.909662i | \(0.363659\pi\) | |||||||
\(860\) | 2.23701e10 | 1.19929 | ||||||||
\(861\) | 1.95393e10 | 1.04327 | ||||||||
\(862\) | 1.87411e10 | 0.996598 | ||||||||
\(863\) | −1.32034e10 | −0.699273 | −0.349636 | − | 0.936885i | \(-0.613695\pi\) | ||||
−0.349636 | + | 0.936885i | \(0.613695\pi\) | |||||||
\(864\) | 1.56782e10 | 0.826988 | ||||||||
\(865\) | 1.43796e10 | 0.755421 | ||||||||
\(866\) | −2.24055e10 | −1.17231 | ||||||||
\(867\) | 1.83705e9 | 0.0957312 | ||||||||
\(868\) | 2.45790e10 | 1.27569 | ||||||||
\(869\) | −3.02505e10 | −1.56373 | ||||||||
\(870\) | 3.14781e10 | 1.62066 | ||||||||
\(871\) | −1.16961e9 | −0.0599762 | ||||||||
\(872\) | −1.06734e10 | −0.545126 | ||||||||
\(873\) | −1.44434e9 | −0.0734717 | ||||||||
\(874\) | −5.30517e10 | −2.68788 | ||||||||
\(875\) | 5.13963e10 | 2.59360 | ||||||||
\(876\) | 1.22970e10 | 0.618065 | ||||||||
\(877\) | −1.39419e10 | −0.697949 | −0.348975 | − | 0.937132i | \(-0.613470\pi\) | ||||
−0.348975 | + | 0.937132i | \(0.613470\pi\) | |||||||
\(878\) | −3.14822e10 | −1.56976 | ||||||||
\(879\) | −7.24315e9 | −0.359721 | ||||||||
\(880\) | 2.50310e11 | 12.3819 | ||||||||
\(881\) | 1.37479e10 | 0.677360 | 0.338680 | − | 0.940902i | \(-0.390020\pi\) | ||||
0.338680 | + | 0.940902i | \(0.390020\pi\) | |||||||
\(882\) | 1.02789e10 | 0.504437 | ||||||||
\(883\) | 8.50641e9 | 0.415799 | 0.207900 | − | 0.978150i | \(-0.433337\pi\) | ||||
0.207900 | + | 0.978150i | \(0.433337\pi\) | |||||||
\(884\) | −1.50571e10 | −0.733093 | ||||||||
\(885\) | 2.73080e9 | 0.132431 | ||||||||
\(886\) | 5.98635e9 | 0.289164 | ||||||||
\(887\) | −1.27701e10 | −0.614417 | −0.307208 | − | 0.951642i | \(-0.599395\pi\) | ||||
−0.307208 | + | 0.951642i | \(0.599395\pi\) | |||||||
\(888\) | −9.88846e9 | −0.473896 | ||||||||
\(889\) | −1.66802e10 | −0.796241 | ||||||||
\(890\) | −6.47665e10 | −3.07954 | ||||||||
\(891\) | −4.12394e9 | −0.195317 | ||||||||
\(892\) | 1.15599e10 | 0.545354 | ||||||||
\(893\) | −6.57523e8 | −0.0308980 | ||||||||
\(894\) | −1.50730e9 | −0.0705534 | ||||||||
\(895\) | −6.48204e10 | −3.02225 | ||||||||
\(896\) | −1.20810e11 | −5.61079 | ||||||||
\(897\) | 3.95542e9 | 0.182987 | ||||||||
\(898\) | −2.73420e10 | −1.25998 | ||||||||
\(899\) | 6.11231e9 | 0.280573 | ||||||||
\(900\) | 4.28105e10 | 1.95750 | ||||||||
\(901\) | −3.34433e10 | −1.52326 | ||||||||
\(902\) | 1.02248e11 | 4.63909 | ||||||||
\(903\) | 4.15370e9 | 0.187728 | ||||||||
\(904\) | 1.02527e10 | 0.461582 | ||||||||
\(905\) | 7.48328e10 | 3.35600 | ||||||||
\(906\) | −3.26803e10 | −1.45995 | ||||||||
\(907\) | 3.70884e10 | 1.65049 | 0.825244 | − | 0.564776i | \(-0.191037\pi\) | ||||
0.825244 | + | 0.564776i | \(0.191037\pi\) | |||||||
\(908\) | 5.73616e10 | 2.54285 | ||||||||
\(909\) | −1.12901e10 | −0.498567 | ||||||||
\(910\) | 2.52915e10 | 1.11257 | ||||||||
\(911\) | 1.58470e10 | 0.694436 | 0.347218 | − | 0.937784i | \(-0.387126\pi\) | ||||
0.347218 | + | 0.937784i | \(0.387126\pi\) | |||||||
\(912\) | −5.60307e10 | −2.44593 | ||||||||
\(913\) | 3.13346e10 | 1.36262 | ||||||||
\(914\) | −7.42774e10 | −3.21770 | ||||||||
\(915\) | −3.19600e10 | −1.37922 | ||||||||
\(916\) | 1.55074e10 | 0.666660 | ||||||||
\(917\) | 1.02231e9 | 0.0437813 | ||||||||
\(918\) | −9.48306e9 | −0.404575 | ||||||||
\(919\) | 1.09730e10 | 0.466359 | 0.233180 | − | 0.972434i | \(-0.425087\pi\) | ||||
0.233180 | + | 0.972434i | \(0.425087\pi\) | |||||||
\(920\) | −1.89026e11 | −8.00321 | ||||||||
\(921\) | 1.77998e10 | 0.750770 | ||||||||
\(922\) | −6.30781e10 | −2.65046 | ||||||||
\(923\) | −6.78955e9 | −0.284207 | ||||||||
\(924\) | 9.05484e10 | 3.77597 | ||||||||
\(925\) | −1.19237e10 | −0.495352 | ||||||||
\(926\) | 8.83119e9 | 0.365494 | ||||||||
\(927\) | −8.76804e9 | −0.361513 | ||||||||
\(928\) | −8.56067e10 | −3.51633 | ||||||||
\(929\) | 3.30298e10 | 1.35161 | 0.675804 | − | 0.737081i | \(-0.263797\pi\) | ||||
0.675804 | + | 0.737081i | \(0.263797\pi\) | |||||||
\(930\) | 1.66575e10 | 0.679078 | ||||||||
\(931\) | −2.02796e10 | −0.823637 | ||||||||
\(932\) | −1.02263e10 | −0.413774 | ||||||||
\(933\) | −2.35876e10 | −0.950818 | ||||||||
\(934\) | −1.77431e10 | −0.712552 | ||||||||
\(935\) | −8.35821e10 | −3.34405 | ||||||||
\(936\) | 7.09376e9 | 0.282756 | ||||||||
\(937\) | −1.81069e10 | −0.719045 | −0.359522 | − | 0.933136i | \(-0.617060\pi\) | ||||
−0.359522 | + | 0.933136i | \(0.617060\pi\) | |||||||
\(938\) | 1.61740e10 | 0.639894 | ||||||||
\(939\) | 7.66860e9 | 0.302264 | ||||||||
\(940\) | −3.65101e9 | −0.143372 | ||||||||
\(941\) | 2.38460e10 | 0.932938 | 0.466469 | − | 0.884538i | \(-0.345526\pi\) | ||||
0.466469 | + | 0.884538i | \(0.345526\pi\) | |||||||
\(942\) | 4.32699e10 | 1.68658 | ||||||||
\(943\) | −4.54718e10 | −1.76584 | ||||||||
\(944\) | −1.34526e10 | −0.520480 | ||||||||
\(945\) | 1.17268e10 | 0.452031 | ||||||||
\(946\) | 2.17362e10 | 0.834764 | ||||||||
\(947\) | 2.50480e10 | 0.958404 | 0.479202 | − | 0.877705i | \(-0.340926\pi\) | ||||
0.479202 | + | 0.877705i | \(0.340926\pi\) | |||||||
\(948\) | 3.75995e10 | 1.43335 | ||||||||
\(949\) | 2.45700e9 | 0.0933198 | ||||||||
\(950\) | −1.14727e11 | −4.34141 | ||||||||
\(951\) | −5.85724e9 | −0.220832 | ||||||||
\(952\) | 1.33610e11 | 5.01891 | ||||||||
\(953\) | −2.27700e10 | −0.852194 | −0.426097 | − | 0.904677i | \(-0.640112\pi\) | ||||
−0.426097 | + | 0.904677i | \(0.640112\pi\) | |||||||
\(954\) | 2.45541e10 | 0.915597 | ||||||||
\(955\) | 5.99389e10 | 2.22688 | ||||||||
\(956\) | −2.16688e10 | −0.802105 | ||||||||
\(957\) | 2.25176e10 | 0.830483 | ||||||||
\(958\) | −3.20816e10 | −1.17890 | ||||||||
\(959\) | 5.86269e10 | 2.14650 | ||||||||
\(960\) | −1.21819e11 | −4.44393 | ||||||||
\(961\) | −2.42781e10 | −0.882436 | ||||||||
\(962\) | −3.07904e9 | −0.111507 | ||||||||
\(963\) | −5.60617e9 | −0.202290 | ||||||||
\(964\) | 1.79701e10 | 0.646072 | ||||||||
\(965\) | −6.53062e10 | −2.33942 | ||||||||
\(966\) | −5.46976e10 | −1.95231 | ||||||||
\(967\) | 1.53182e10 | 0.544772 | 0.272386 | − | 0.962188i | \(-0.412187\pi\) | ||||
0.272386 | + | 0.962188i | \(0.412187\pi\) | |||||||
\(968\) | 2.05655e11 | 7.28746 | ||||||||
\(969\) | 1.87095e10 | 0.660584 | ||||||||
\(970\) | 2.14924e10 | 0.756109 | ||||||||
\(971\) | 1.35596e10 | 0.475314 | 0.237657 | − | 0.971349i | \(-0.423621\pi\) | ||||
0.237657 | + | 0.971349i | \(0.423621\pi\) | |||||||
\(972\) | 5.12580e9 | 0.179032 | ||||||||
\(973\) | 2.48265e9 | 0.0864013 | ||||||||
\(974\) | 4.21084e10 | 1.46020 | ||||||||
\(975\) | 8.55377e9 | 0.295557 | ||||||||
\(976\) | 1.57443e11 | 5.42061 | ||||||||
\(977\) | 5.16415e10 | 1.77161 | 0.885804 | − | 0.464060i | \(-0.153608\pi\) | ||||
0.885804 | + | 0.464060i | \(0.153608\pi\) | |||||||
\(978\) | 1.18388e9 | 0.0404690 | ||||||||
\(979\) | −4.63302e10 | −1.57807 | ||||||||
\(980\) | −1.12606e11 | −3.82182 | ||||||||
\(981\) | −1.54098e9 | −0.0521141 | ||||||||
\(982\) | 6.87160e9 | 0.231562 | ||||||||
\(983\) | 2.68451e10 | 0.901421 | 0.450711 | − | 0.892670i | \(-0.351171\pi\) | ||||
0.450711 | + | 0.892670i | \(0.351171\pi\) | |||||||
\(984\) | −8.15504e10 | −2.72862 | ||||||||
\(985\) | −5.51509e10 | −1.83876 | ||||||||
\(986\) | 5.17796e10 | 1.72024 | ||||||||
\(987\) | −6.77923e8 | −0.0224425 | ||||||||
\(988\) | −2.18106e10 | −0.719481 | ||||||||
\(989\) | −9.66650e9 | −0.317748 | ||||||||
\(990\) | 6.13659e10 | 2.01004 | ||||||||
\(991\) | 3.98369e10 | 1.30025 | 0.650126 | − | 0.759826i | \(-0.274716\pi\) | ||||
0.650126 | + | 0.759826i | \(0.274716\pi\) | |||||||
\(992\) | −4.53012e10 | −1.47339 | ||||||||
\(993\) | −2.69594e10 | −0.873753 | ||||||||
\(994\) | 9.38895e10 | 3.03225 | ||||||||
\(995\) | 8.94740e10 | 2.87949 | ||||||||
\(996\) | −3.89469e10 | −1.24901 | ||||||||
\(997\) | −5.65997e9 | −0.180876 | −0.0904380 | − | 0.995902i | \(-0.528827\pi\) | ||||
−0.0904380 | + | 0.995902i | \(0.528827\pi\) | |||||||
\(998\) | −2.43241e10 | −0.774605 | ||||||||
\(999\) | −1.42765e9 | −0.0453045 |
(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 | 177.8.a.b.1.17 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.d.1.1 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.17 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.d.1.1 | 17 | 3.2 | odd | 2 |