Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,22,Mod(35,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.35");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.f (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(201.223687887\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 35.32 | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.22.f.a.35.31 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −621.545 | + | 1307.99i | −0.429198 | + | 0.903210i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.32452e6 | − | 1.62595e6i | −0.631578 | − | 0.775312i | ||||
\(5\) | −9.14091e6 | −0.418605 | −0.209303 | − | 0.977851i | \(-0.567119\pi\) | ||||
−0.209303 | + | 0.977851i | \(0.567119\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 8.56630e8i | − | 1.14621i | −0.819482 | − | 0.573105i | \(-0.805739\pi\) | ||
0.819482 | − | 0.573105i | \(-0.194261\pi\) | |||||||
\(8\) | 2.94997e9 | − | 7.21852e8i | 0.971342 | − | 0.237686i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.68149e9 | − | 1.19562e10i | 0.179664 | − | 0.378089i | ||||
\(11\) | 7.02798e10i | 0.816972i | 0.912765 | + | 0.408486i | \(0.133943\pi\) | ||||
−0.912765 | + | 0.408486i | \(0.866057\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.08698e11i | 1.22461i | 0.790623 | + | 0.612303i | \(0.209757\pi\) | ||||
−0.790623 | + | 0.612303i | \(0.790243\pi\) | |||||||
\(14\) | 1.12046e12 | + | 5.32434e11i | 1.03527 | + | 0.491951i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.89362e11 | + | 4.30719e12i | −0.202218 | + | 0.979341i | ||||
\(17\) | 1.35143e13i | 1.62585i | 0.582367 | + | 0.812926i | \(0.302127\pi\) | ||||
−0.582367 | + | 0.812926i | \(0.697873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.66607e13 | 0.997605 | 0.498802 | − | 0.866716i | \(-0.333773\pi\) | ||||
0.498802 | + | 0.866716i | \(0.333773\pi\) | |||||||
\(20\) | 1.21073e13 | + | 1.48626e13i | 0.264382 | + | 0.324550i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.19251e13 | − | 4.36820e13i | −0.737897 | − | 0.350643i | ||||
\(23\) | 6.73238e13 | 0.338865 | 0.169432 | − | 0.985542i | \(-0.445807\pi\) | ||||
0.169432 | + | 0.985542i | \(0.445807\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.93281e14 | −0.824770 | ||||||||
\(26\) | −7.96170e14 | − | 3.78333e14i | −1.10608 | − | 0.525599i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.39284e15 | + | 1.13462e15i | −0.888670 | + | 0.723921i | ||||
\(29\) | 3.07544e15 | 1.35746 | 0.678732 | − | 0.734386i | \(-0.262530\pi\) | ||||
0.678732 | + | 0.734386i | \(0.262530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.73440e15i | − | 0.818320i | −0.912463 | − | 0.409160i | \(-0.865822\pi\) | ||
0.912463 | − | 0.409160i | \(-0.134178\pi\) | |||||||
\(32\) | −5.08097e15 | − | 3.84038e15i | −0.797759 | − | 0.602976i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.76766e16 | − | 8.39977e15i | −1.46849 | − | 0.697812i | ||||
\(35\) | 7.83038e15i | 0.479809i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.88634e15i | − | 0.338001i | −0.985616 | − | 0.169000i | \(-0.945946\pi\) | ||
0.985616 | − | 0.169000i | \(-0.0540539\pi\) | |||||||
\(38\) | −1.65708e16 | + | 3.48719e16i | −0.428170 | + | 0.901047i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.69654e16 | + | 6.59839e15i | −0.406609 | + | 0.0994965i | ||||
\(41\) | − | 1.48280e17i | − | 1.72525i | −0.505840 | − | 0.862627i | \(-0.668817\pi\) | ||
0.505840 | − | 0.862627i | \(-0.331183\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.92658e16 | 0.559329 | 0.279664 | − | 0.960098i | \(-0.409777\pi\) | ||||
0.279664 | + | 0.960098i | \(0.409777\pi\) | |||||||
\(44\) | 1.14271e17 | − | 9.30866e16i | 0.633408 | − | 0.515982i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.18448e16 | + | 8.80588e16i | −0.145440 | + | 0.306066i | ||||
\(47\) | 3.94989e17 | 1.09536 | 0.547680 | − | 0.836688i | \(-0.315511\pi\) | ||||
0.547680 | + | 0.836688i | \(0.315511\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.75270e17 | −0.313796 | ||||||||
\(50\) | 2.44442e17 | − | 5.14407e17i | 0.353989 | − | 0.744941i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.89711e17 | − | 8.06230e17i | 0.949452 | − | 0.773435i | ||||
\(53\) | −4.73280e17 | −0.371725 | −0.185862 | − | 0.982576i | \(-0.559508\pi\) | ||||
−0.185862 | + | 0.982576i | \(0.559508\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.42421e17i | − | 0.341989i | ||||||
\(56\) | −6.18361e17 | − | 2.52703e18i | −0.272438 | − | 1.11336i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.91152e18 | + | 4.02264e18i | −0.582621 | + | 1.22608i | ||||
\(59\) | 5.97069e18i | 1.52082i | 0.649442 | + | 0.760411i | \(0.275003\pi\) | ||||
−0.649442 | + | 0.760411i | \(0.724997\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.79657e18i | − | 1.75837i | −0.476479 | − | 0.879186i | \(-0.658087\pi\) | ||
0.476479 | − | 0.879186i | \(-0.341913\pi\) | |||||||
\(62\) | 4.88456e18 | + | 2.32110e18i | 0.739115 | + | 0.351221i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.18123e18 | − | 4.25888e18i | 0.887011 | − | 0.461749i | ||||
\(65\) | − | 5.56405e18i | − | 0.512627i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.69202e19 | −1.13402 | −0.567008 | − | 0.823712i | \(-0.691899\pi\) | ||||
−0.567008 | + | 0.823712i | \(0.691899\pi\) | |||||||
\(68\) | 2.19736e19 | − | 1.79000e19i | 1.26054 | − | 1.02685i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.02421e19 | − | 4.86693e18i | −0.433369 | − | 0.205933i | ||||
\(71\) | −2.88571e19 | −1.05206 | −0.526030 | − | 0.850466i | \(-0.676320\pi\) | ||||
−0.526030 | + | 0.850466i | \(0.676320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.35107e19 | −1.45731 | −0.728653 | − | 0.684883i | \(-0.759853\pi\) | ||||
−0.728653 | + | 0.684883i | \(0.759853\pi\) | |||||||
\(74\) | 1.29312e19 | + | 6.14480e18i | 0.305286 | + | 0.145069i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.53125e19 | − | 4.33489e19i | −0.630066 | − | 0.773455i | ||||
\(77\) | 6.02038e19 | 0.936421 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.29094e19i | 0.509880i | 0.966957 | + | 0.254940i | \(0.0820557\pi\) | ||||
−0.966957 | + | 0.254940i | \(0.917944\pi\) | |||||||
\(80\) | 8.12958e18 | − | 3.93716e19i | 0.0846493 | − | 0.409957i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.93949e20 | + | 9.21629e19i | 1.55827 | + | 0.740476i | ||||
\(83\) | − | 9.50389e19i | − | 0.672328i | −0.941803 | − | 0.336164i | \(-0.890870\pi\) | ||
0.941803 | − | 0.336164i | \(-0.109130\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.23533e20i | − | 0.680590i | ||||||
\(86\) | −4.92673e19 | + | 1.03679e20i | −0.240063 | + | 0.505192i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.07316e19 | + | 2.07323e20i | 0.194183 | + | 0.793559i | ||||
\(89\) | 4.33090e20i | 1.47226i | 0.676843 | + | 0.736128i | \(0.263348\pi\) | ||||
−0.676843 | + | 0.736128i | \(0.736652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.21429e20 | 1.40366 | ||||||||
\(92\) | −8.91715e19 | − | 1.09465e20i | −0.214020 | − | 0.262726i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.45503e20 | + | 5.16641e20i | −0.470126 | + | 0.989341i | ||||
\(95\) | −2.43703e20 | −0.417602 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.63333e20 | −0.637955 | −0.318977 | − | 0.947762i | \(-0.603339\pi\) | ||||
−0.318977 | + | 0.947762i | \(0.603339\pi\) | |||||||
\(98\) | 1.08938e20 | − | 2.29251e20i | 0.134681 | − | 0.283424i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.20907e20 | + | 6.39454e20i | 0.520907 | + | 0.639454i | ||||
\(101\) | 1.48594e21 | 1.33853 | 0.669265 | − | 0.743024i | \(-0.266609\pi\) | ||||
0.669265 | + | 0.743024i | \(0.266609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.18041e20i | 0.599769i | 0.953975 | + | 0.299885i | \(0.0969482\pi\) | ||||
−0.953975 | + | 0.299885i | \(0.903052\pi\) | |||||||
\(104\) | 4.39390e20 | + | 1.79564e21i | 0.291072 | + | 1.18951i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.94165e20 | − | 6.19045e20i | 0.159544 | − | 0.335746i | ||||
\(107\) | − | 1.83283e21i | − | 0.900725i | −0.892846 | − | 0.450362i | \(-0.851295\pi\) | ||
0.892846 | − | 0.450362i | \(-0.148705\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.66660e21i | 1.07889i | 0.842019 | + | 0.539447i | \(0.181367\pi\) | ||||
−0.842019 | + | 0.539447i | \(0.818633\pi\) | |||||||
\(110\) | 8.40279e20 | + | 3.99294e20i | 0.308888 | + | 0.146781i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.68967e21 | + | 7.61854e20i | 1.12253 | + | 0.231784i | ||||
\(113\) | − | 6.00368e21i | − | 1.66377i | −0.554946 | − | 0.831887i | \(-0.687261\pi\) | ||
0.554946 | − | 0.831887i | \(-0.312739\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.15401e20 | −0.141851 | ||||||||
\(116\) | −4.07347e21 | − | 5.00051e21i | −0.857345 | − | 1.05246i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.80960e21 | − | 3.71105e21i | −1.37362 | − | 0.652734i | ||||
\(119\) | 1.15768e22 | 1.86357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.46101e21 | 0.332557 | ||||||||
\(122\) | 1.28138e22 | + | 6.08901e21i | 1.58818 | + | 0.754689i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.07194e21 | + | 4.94627e21i | −0.634454 | + | 0.516833i | ||||
\(125\) | 7.95367e21 | 0.763858 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.28059e22i | 1.04105i | 0.853846 | + | 0.520526i | \(0.174264\pi\) | ||||
−0.853846 | + | 0.520526i | \(0.825736\pi\) | |||||||
\(128\) | 4.85564e20 | + | 1.33480e22i | 0.0363531 | + | 0.999339i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.27772e21 | + | 3.45831e21i | 0.463010 | + | 0.220018i | ||||
\(131\) | 1.19685e22i | 0.702573i | 0.936268 | + | 0.351286i | \(0.114256\pi\) | ||||
−0.936268 | + | 0.351286i | \(0.885744\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.28384e22i | − | 1.14346i | ||||||
\(134\) | 1.05166e22 | − | 2.21314e22i | 0.486717 | − | 1.02425i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.75536e21 | + | 3.98668e22i | 0.386442 | + | 1.57926i | ||||
\(137\) | 7.62483e21i | 0.279682i | 0.990174 | + | 0.139841i | \(0.0446591\pi\) | ||||
−0.990174 | + | 0.139841i | \(0.955341\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.47248e21 | −0.109392 | −0.0546958 | − | 0.998503i | \(-0.517419\pi\) | ||||
−0.0546958 | + | 0.998503i | \(0.517419\pi\) | |||||||
\(140\) | 1.27318e22 | − | 1.03715e22i | 0.372002 | − | 0.303037i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.79360e22 | − | 3.77448e22i | 0.451542 | − | 0.950231i | ||||
\(143\) | −4.27791e22 | −1.00047 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.81123e22 | −0.568242 | ||||||||
\(146\) | 3.32593e22 | − | 6.99914e22i | 0.625473 | − | 1.31625i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.60747e22 | + | 1.30946e22i | −0.262056 | + | 0.213474i | ||||
\(149\) | 5.75779e22 | 0.874580 | 0.437290 | − | 0.899320i | \(-0.355938\pi\) | ||||
0.437290 | + | 0.899320i | \(0.355938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.42237e23i | 1.87826i | 0.343561 | + | 0.939130i | \(0.388367\pi\) | ||||
−0.343561 | + | 0.939130i | \(0.611633\pi\) | |||||||
\(152\) | 7.86481e22 | − | 1.92451e22i | 0.969016 | − | 0.237117i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.74193e22 | + | 7.87458e22i | −0.401910 | + | 0.845785i | ||||
\(155\) | 3.41358e22i | 0.342553i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.31724e22i | − | 0.290958i | −0.989361 | − | 0.145479i | \(-0.953528\pi\) | ||
0.989361 | − | 0.145479i | \(-0.0464724\pi\) | |||||||
\(158\) | −5.61250e22 | − | 2.66701e22i | −0.460529 | − | 0.218839i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.64447e22 | + | 3.51046e22i | 0.333946 | + | 0.252409i | ||||
\(161\) | − | 5.76716e22i | − | 0.388410i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.86744e23 | 1.69638 | 0.848192 | − | 0.529689i | \(-0.177691\pi\) | ||||
0.848192 | + | 0.529689i | \(0.177691\pi\) | |||||||
\(164\) | −2.41096e23 | + | 1.96400e23i | −1.33761 | + | 1.08963i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.24310e23 | + | 5.90710e22i | 0.607254 | + | 0.288562i | ||||
\(167\) | −1.28937e23 | −0.591363 | −0.295681 | − | 0.955287i | \(-0.595547\pi\) | ||||
−0.295681 | + | 0.955287i | \(0.595547\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.23449e23 | −0.499662 | ||||||||
\(170\) | 1.61580e23 | + | 7.67815e22i | 0.614716 | + | 0.292108i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.04989e23 | − | 1.28882e23i | −0.353260 | − | 0.433654i | ||||
\(173\) | −2.63925e23 | −0.835595 | −0.417798 | − | 0.908540i | \(-0.637198\pi\) | ||||
−0.417798 | + | 0.908540i | \(0.637198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.36896e23i | 0.945359i | ||||||||
\(176\) | −3.02708e23 | − | 6.25041e22i | −0.800094 | − | 0.165206i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.66477e23 | − | 2.69185e23i | −1.32976 | − | 0.631889i | ||||
\(179\) | − | 2.69566e22i | − | 0.0596634i | −0.999555 | − | 0.0298317i | \(-0.990503\pi\) | ||
0.999555 | − | 0.0298317i | \(-0.00949714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.59898e23i | − | 0.314932i | −0.987524 | − | 0.157466i | \(-0.949667\pi\) | ||
0.987524 | − | 0.157466i | \(-0.0503325\pi\) | |||||||
\(182\) | −3.24092e23 | + | 6.82023e23i | −0.602446 | + | 1.26780i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.98603e23 | − | 4.85979e22i | 0.329154 | − | 0.0805434i | ||||
\(185\) | 9.03701e22i | 0.141489i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.49784e23 | −1.32828 | ||||||||
\(188\) | −5.23169e23 | − | 6.42231e23i | −0.691806 | − | 0.849246i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.51472e23 | − | 3.18761e23i | 0.179234 | − | 0.377183i | ||||
\(191\) | 2.03348e23 | 0.227714 | 0.113857 | − | 0.993497i | \(-0.463679\pi\) | ||||
0.113857 | + | 0.993497i | \(0.463679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.73611e23 | 0.274651 | 0.137326 | − | 0.990526i | \(-0.456149\pi\) | ||||
0.137326 | + | 0.990526i | \(0.456149\pi\) | |||||||
\(194\) | 2.87982e23 | − | 6.06034e23i | 0.273809 | − | 0.576208i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.32147e23 | + | 2.84979e23i | 0.198187 | + | 0.243290i | ||||
\(197\) | −1.23248e24 | −0.997432 | −0.498716 | − | 0.866765i | \(-0.666195\pi\) | ||||
−0.498716 | + | 0.866765i | \(0.666195\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.06155e24i | − | 1.50050i | −0.661152 | − | 0.750252i | \(-0.729932\pi\) | ||
0.661152 | − | 0.750252i | \(-0.270068\pi\) | |||||||
\(200\) | −1.16017e24 | + | 2.83891e23i | −0.801134 | + | 0.196036i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.23581e23 | + | 1.94360e24i | −0.574494 | + | 1.20897i | ||||
\(203\) | − | 2.63452e24i | − | 1.55594i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.35542e24i | 0.722200i | ||||||||
\(206\) | −1.06999e24 | − | 5.08449e23i | −0.541718 | − | 0.257420i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.62178e24 | − | 5.41353e23i | −1.19931 | − | 0.247637i | ||||
\(209\) | 1.87371e24i | 0.815015i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.34998e23 | 0.131849 | 0.0659244 | − | 0.997825i | \(-0.479000\pi\) | ||||
0.0659244 | + | 0.997825i | \(0.479000\pi\) | |||||||
\(212\) | 6.26867e23 | + | 7.69529e23i | 0.234773 | + | 0.288203i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.39732e24 | + | 1.13918e24i | 0.813544 | + | 0.386589i | ||||
\(215\) | −7.24562e23 | −0.234138 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.19900e24 | −0.937966 | ||||||||
\(218\) | −3.48788e24 | − | 1.65741e24i | −0.974469 | − | 0.463059i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.04454e24 | + | 8.50897e23i | −0.265148 | + | 0.215993i | ||||
\(221\) | −8.22615e24 | −1.99103 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.19991e24i | 1.36516i | 0.730810 | + | 0.682581i | \(0.239143\pi\) | ||||
−0.730810 | + | 0.682581i | \(0.760857\pi\) | |||||||
\(224\) | −3.28979e24 | + | 4.35251e24i | −0.691137 | + | 0.914399i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.85275e24 | + | 3.73156e24i | 1.50274 | + | 0.714088i | ||||
\(227\) | 6.02396e24i | 1.10055i | 0.834983 | + | 0.550276i | \(0.185477\pi\) | ||||
−0.834983 | + | 0.550276i | \(0.814523\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.82574e24i | 1.47055i | 0.677771 | + | 0.735273i | \(0.262946\pi\) | ||||
−0.677771 | + | 0.735273i | \(0.737054\pi\) | |||||||
\(230\) | 3.82500e23 | − | 8.04938e23i | 0.0608820 | − | 0.128121i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.07245e24 | − | 2.22001e24i | 1.31856 | − | 0.322650i | ||||
\(233\) | − | 3.03738e24i | − | 0.421951i | −0.977491 | − | 0.210976i | \(-0.932336\pi\) | ||
0.977491 | − | 0.210976i | \(-0.0676641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.61056e24 | −0.458524 | ||||||||
\(236\) | 9.70803e24 | − | 7.90828e24i | 1.17911 | − | 0.960519i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.19549e24 | + | 1.51423e25i | −0.799839 | + | 1.68319i | ||||
\(239\) | −1.90994e24 | −0.203162 | −0.101581 | − | 0.994827i | \(-0.532390\pi\) | ||||
−0.101581 | + | 0.994827i | \(0.532390\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.14356e24 | 0.696203 | 0.348101 | − | 0.937457i | \(-0.386827\pi\) | ||||
0.348101 | + | 0.937457i | \(0.386827\pi\) | |||||||
\(242\) | −1.52963e24 | + | 3.21897e24i | −0.142733 | + | 0.300369i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.59287e25 | + | 1.29757e25i | −1.36329 | + | 1.11055i | ||||
\(245\) | 1.60212e24 | 0.131357 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.62283e25i | 1.22167i | ||||||||
\(248\) | −2.69569e24 | − | 1.10164e25i | −0.194503 | − | 0.794869i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.94356e24 | + | 1.04033e25i | −0.327846 | + | 0.689924i | ||||
\(251\) | − | 8.23698e24i | − | 0.523834i | −0.965090 | − | 0.261917i | \(-0.915645\pi\) | ||
0.965090 | − | 0.261917i | \(-0.0843547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.73150e24i | 0.276843i | ||||||||
\(254\) | −1.67500e25 | − | 7.95947e24i | −0.940289 | − | 0.446817i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.77609e25 | − | 7.66129e24i | −0.918216 | − | 0.396080i | ||||
\(257\) | − | 9.16966e24i | − | 0.455046i | −0.973773 | − | 0.227523i | \(-0.926937\pi\) | ||
0.973773 | − | 0.227523i | \(-0.0730627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.46894e24 | −0.387419 | ||||||||
\(260\) | −9.04686e24 | + | 7.36968e24i | −0.397446 | + | 0.323764i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.56547e25 | − | 7.43896e24i | −0.634571 | − | 0.301543i | ||||
\(263\) | 1.93641e25 | 0.754157 | 0.377079 | − | 0.926181i | \(-0.376929\pi\) | ||||
0.377079 | + | 0.926181i | \(0.376929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.32621e24 | 0.155606 | ||||||||
\(266\) | 2.98723e25 | + | 1.41951e25i | 1.03279 | + | 0.490772i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.24110e25 | + | 2.75113e25i | 0.716220 | + | 0.879216i | ||||
\(269\) | 1.39331e25 | 0.428202 | 0.214101 | − | 0.976811i | \(-0.431318\pi\) | ||||
0.214101 | + | 0.976811i | \(0.431318\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.15914e25i | 1.46690i | 0.679744 | + | 0.733449i | \(0.262091\pi\) | ||||
−0.679744 | + | 0.733449i | \(0.737909\pi\) | |||||||
\(272\) | −5.82088e25 | − | 1.20191e25i | −1.59226 | − | 0.328776i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.97319e24 | − | 4.73917e24i | −0.252611 | − | 0.120039i | ||||
\(275\) | − | 2.76397e25i | − | 0.673814i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.31335e25i | 1.87819i | 0.343664 | + | 0.939093i | \(0.388332\pi\) | ||||
−0.343664 | + | 0.939093i | \(0.611668\pi\) | |||||||
\(278\) | 2.15830e24 | − | 4.54196e24i | 0.0469507 | − | 0.0988037i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.65238e24 | + | 2.30994e25i | 0.114044 | + | 0.466059i | ||||
\(281\) | 1.09118e24i | 0.0212071i | 0.999944 | + | 0.0106036i | \(0.00337528\pi\) | ||||
−0.999944 | + | 0.0106036i | \(0.996625\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.42534e25 | 0.978745 | 0.489373 | − | 0.872075i | \(-0.337226\pi\) | ||||
0.489373 | + | 0.872075i | \(0.337226\pi\) | |||||||
\(284\) | 3.82217e25 | + | 4.69201e25i | 0.664458 | + | 0.815674i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.65892e25 | − | 5.59546e25i | 0.429399 | − | 0.903634i | ||||
\(287\) | −1.27021e26 | −1.97750 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.13545e26 | −1.64340 | ||||||||
\(290\) | 1.74731e25 | − | 3.67706e25i | 0.243888 | − | 0.513242i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.08758e25 | + | 8.70056e25i | 0.920403 | + | 1.12987i | ||||
\(293\) | −1.47231e25 | −0.184454 | −0.0922271 | − | 0.995738i | \(-0.529399\pi\) | ||||
−0.0922271 | + | 0.995738i | \(0.529399\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.45776e25i | − | 0.636624i | ||||||
\(296\) | −7.13648e24 | − | 2.91644e25i | −0.0803380 | − | 0.328314i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.57872e25 | + | 7.53112e25i | −0.375368 | + | 0.789930i | ||||
\(299\) | 4.09799e25i | 0.414976i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6.79015e25i | − | 0.641108i | ||||||
\(302\) | −1.86045e26 | − | 8.84069e25i | −1.69646 | − | 0.806145i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.37110e25 | + | 1.14833e26i | −0.201733 | + | 0.976995i | ||||
\(305\) | 8.95496e25i | 0.736063i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.27760e26 | −0.980487 | −0.490243 | − | 0.871586i | \(-0.663092\pi\) | ||||
−0.490243 | + | 0.871586i | \(0.663092\pi\) | |||||||
\(308\) | −7.97408e25 | − | 9.78881e25i | −0.591423 | − | 0.726018i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.46493e25 | − | 2.12170e25i | −0.309397 | − | 0.147023i | ||||
\(311\) | −1.10157e26 | −0.737953 | −0.368977 | − | 0.929439i | \(-0.620292\pi\) | ||||
−0.368977 | + | 0.929439i | \(0.620292\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.02008e25 | 0.377040 | 0.188520 | − | 0.982069i | \(-0.439631\pi\) | ||||
0.188520 | + | 0.982069i | \(0.439631\pi\) | |||||||
\(314\) | 4.33892e25 | + | 2.06182e25i | 0.262797 | + | 0.124879i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.97684e25 | − | 5.68342e25i | 0.395316 | − | 0.322029i | ||||
\(317\) | −3.88386e25 | −0.212883 | −0.106442 | − | 0.994319i | \(-0.533946\pi\) | ||||
−0.106442 | + | 0.994319i | \(0.533946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.16141e26i | 1.10901i | ||||||||
\(320\) | −7.47839e25 | + | 3.89301e25i | −0.371307 | + | 0.193290i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.54338e25 | + | 3.58455e25i | 0.350816 | + | 0.166705i | ||||
\(323\) | 3.60302e26i | 1.62196i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.39389e26i | − | 1.01002i | ||||||
\(326\) | −1.78224e26 | + | 3.75058e26i | −0.728084 | + | 1.53219i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.07037e26 | − | 4.37422e26i | −0.410069 | − | 1.67581i | ||||
\(329\) | − | 3.38359e26i | − | 1.25551i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.22368e26 | −0.426064 | −0.213032 | − | 0.977045i | \(-0.568334\pi\) | ||||
−0.213032 | + | 0.977045i | \(0.568334\pi\) | |||||||
\(332\) | −1.54528e26 | + | 1.25881e26i | −0.521264 | + | 0.424628i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.01400e25 | − | 1.68648e26i | 0.253812 | − | 0.534125i | ||||
\(335\) | 1.54666e26 | 0.474705 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.54747e26 | 0.446178 | 0.223089 | − | 0.974798i | \(-0.428386\pi\) | ||||
0.223089 | + | 0.974798i | \(0.428386\pi\) | |||||||
\(338\) | 7.67289e25 | − | 1.61469e26i | 0.214454 | − | 0.451300i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.00859e26 | + | 1.63622e26i | −0.527670 | + | 0.429846i | ||||
\(341\) | 2.62453e26 | 0.668545 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.28326e26i | − | 0.786533i | ||||||
\(344\) | 2.33832e26 | − | 5.72182e25i | 0.543300 | − | 0.132945i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.64041e26 | − | 3.45210e26i | 0.358636 | − | 0.754718i | ||||
\(347\) | − | 5.05152e26i | − | 1.07143i | −0.844400 | − | 0.535713i | \(-0.820043\pi\) | ||
0.844400 | − | 0.535713i | \(-0.179957\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.20691e26i | 0.840033i | 0.907516 | + | 0.420017i | \(0.137976\pi\) | ||||
−0.907516 | + | 0.420017i | \(0.862024\pi\) | |||||||
\(350\) | −4.40657e26 | − | 2.09396e26i | −0.853858 | − | 0.405746i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.69901e26 | − | 3.57089e26i | 0.492614 | − | 0.651747i | ||||
\(353\) | 2.50714e26i | 0.444165i | 0.975028 | + | 0.222082i | \(0.0712854\pi\) | ||||
−0.975028 | + | 0.222082i | \(0.928715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.63780e26 | 0.440397 | ||||||||
\(356\) | 7.04182e26 | − | 5.73635e26i | 1.14146 | − | 0.929845i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.52589e25 | + | 1.67547e25i | 0.0538887 | + | 0.0256074i | ||||
\(359\) | 8.98020e26 | 1.33289 | 0.666445 | − | 0.745554i | \(-0.267815\pi\) | ||||
0.666445 | + | 0.745554i | \(0.267815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.41722e24 | −0.00478462 | ||||||||
\(362\) | 2.09144e26 | + | 9.93836e25i | 0.284450 | + | 0.135168i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.90641e26 | − | 8.47816e26i | −0.886519 | − | 1.08827i | ||||
\(365\) | 4.89137e26 | 0.610036 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.17224e27i | − | 1.38046i | −0.723592 | − | 0.690228i | \(-0.757510\pi\) | ||
0.723592 | − | 0.690228i | \(-0.242490\pi\) | |||||||
\(368\) | −5.98753e25 | + | 2.89976e26i | −0.0685244 | + | 0.331864i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.18203e26 | − | 5.61691e25i | −0.127794 | − | 0.0607267i | ||||
\(371\) | 4.05426e26i | 0.426075i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.52010e26i | 0.945581i | 0.881175 | + | 0.472791i | \(0.156753\pi\) | ||||
−0.881175 | + | 0.472791i | \(0.843247\pi\) | |||||||
\(374\) | 5.90334e26 | − | 1.24231e27i | 0.570093 | − | 1.19971i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.16520e27 | − | 2.85124e26i | 1.06397 | − | 0.260352i | ||||
\(377\) | 1.87201e27i | 1.66236i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.96225e26 | −0.584841 | −0.292421 | − | 0.956290i | \(-0.594461\pi\) | ||||
−0.292421 | + | 0.956290i | \(0.594461\pi\) | |||||||
\(380\) | 3.22789e26 | + | 3.96248e26i | 0.263749 | + | 0.323772i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.26390e26 | + | 2.65977e26i | −0.0977342 | + | 0.205673i | ||||
\(383\) | 2.33002e27 | 1.75296 | 0.876481 | − | 0.481436i | \(-0.159885\pi\) | ||||
0.876481 | + | 0.481436i | \(0.159885\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.50317e26 | −0.391991 | ||||||||
\(386\) | −1.70062e26 | + | 3.57880e26i | −0.117880 | + | 0.248068i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.13692e26 | + | 7.53355e26i | 0.402919 | + | 0.494614i | ||||
\(389\) | 1.26866e26 | 0.0810727 | 0.0405364 | − | 0.999178i | \(-0.487093\pi\) | ||||
0.0405364 | + | 0.999178i | \(0.487093\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.09837e26i | 0.550944i | ||||||||
\(392\) | −5.17039e26 | + | 1.26519e26i | −0.304804 | + | 0.0745850i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.66040e26 | − | 1.61207e27i | 0.428096 | − | 0.900891i | ||||
\(395\) | − | 3.92231e26i | − | 0.213438i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.05838e26i | − | 0.467466i | −0.972301 | − | 0.233733i | \(-0.924906\pi\) | ||
0.972301 | − | 0.233733i | \(-0.0750942\pi\) | |||||||
\(398\) | 2.69649e27 | + | 1.28135e27i | 1.35527 | + | 0.644013i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.49769e26 | − | 1.69393e27i | 0.166783 | − | 0.807731i | ||||
\(401\) | 1.88202e27i | 0.874195i | 0.899414 | + | 0.437097i | \(0.143993\pi\) | ||||
−0.899414 | + | 0.437097i | \(0.856007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.27312e27 | 1.00212 | ||||||||
\(404\) | −1.96816e27 | − | 2.41607e27i | −0.845387 | − | 1.03778i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.44592e27 | + | 1.63747e27i | 1.40534 | + | 0.667806i | ||||
\(407\) | 6.94809e26 | 0.276137 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.99576e27 | 0.753378 | 0.376689 | − | 0.926340i | \(-0.377063\pi\) | ||||
0.376689 | + | 0.926340i | \(0.377063\pi\) | |||||||
\(410\) | −1.77287e27 | − | 8.42453e26i | −0.652299 | − | 0.309967i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.33009e27 | − | 1.08351e27i | 0.465008 | − | 0.378801i | ||||
\(413\) | 5.11468e27 | 1.74318 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.68742e26i | 0.281440i | ||||||||
\(416\) | 2.33763e27 | − | 3.09278e27i | 0.738408 | − | 0.976942i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.45079e27 | − | 1.16459e27i | −0.736130 | − | 0.349803i | ||||
\(419\) | 6.25017e27i | 1.83082i | 0.402528 | + | 0.915408i | \(0.368132\pi\) | ||||
−0.402528 | + | 0.915408i | \(0.631868\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.95405e27i | − | 1.10174i | −0.834590 | − | 0.550872i | \(-0.814295\pi\) | ||
0.834590 | − | 0.550872i | \(-0.185705\pi\) | |||||||
\(422\) | −2.08216e26 | + | 4.38174e26i | −0.0565893 | + | 0.119087i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.39616e27 | + | 3.41638e26i | −0.361072 | + | 0.0883538i | ||||
\(425\) | − | 5.31493e27i | − | 1.34095i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.39204e27 | −2.01546 | ||||||||
\(428\) | −2.98008e27 | + | 2.42761e27i | −0.698343 | + | 0.568878i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.50348e26 | − | 9.47719e26i | 0.100491 | − | 0.211476i | ||||
\(431\) | 4.37336e27 | 0.952365 | 0.476183 | − | 0.879346i | \(-0.342020\pi\) | ||||
0.476183 | + | 0.879346i | \(0.342020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.34089e27 | −1.93761 | −0.968803 | − | 0.247832i | \(-0.920282\pi\) | ||||
−0.968803 | + | 0.247832i | \(0.920282\pi\) | |||||||
\(434\) | 1.98832e27 | − | 4.18426e27i | 0.402573 | − | 0.847181i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.33575e27 | − | 3.53195e27i | 0.836480 | − | 0.681407i | ||||
\(437\) | 1.79490e27 | 0.338053 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.55087e27i | 0.996514i | 0.867029 | + | 0.498257i | \(0.166026\pi\) | ||||
−0.867029 | + | 0.498257i | \(0.833974\pi\) | |||||||
\(440\) | −4.63733e26 | − | 1.89512e27i | −0.0812859 | − | 0.332188i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.11292e27 | − | 1.07597e28i | 0.854546 | − | 1.79832i | ||||
\(443\) | − | 3.65113e27i | − | 0.595921i | −0.954578 | − | 0.297960i | \(-0.903694\pi\) | ||
0.954578 | − | 0.297960i | \(-0.0963063\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 3.95884e27i | − | 0.616294i | ||||||
\(446\) | −8.10941e27 | − | 3.85352e27i | −1.23303 | − | 0.585925i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.64829e27 | − | 7.00829e27i | −0.529261 | − | 1.01670i | ||||
\(449\) | 8.18341e27i | 1.15970i | 0.814722 | + | 0.579852i | \(0.196890\pi\) | ||||
−0.814722 | + | 0.579852i | \(0.803110\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04211e28 | 1.40948 | ||||||||
\(452\) | −9.76167e27 | + | 7.95197e27i | −1.28994 | + | 1.05080i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.87927e27 | − | 3.74416e27i | −0.994030 | − | 0.472355i | ||||
\(455\) | −4.76634e27 | −0.587577 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.24771e27 | −0.146890 | −0.0734451 | − | 0.997299i | \(-0.523399\pi\) | ||||
−0.0734451 | + | 0.997299i | \(0.523399\pi\) | |||||||
\(458\) | −1.15440e28 | − | 5.48559e27i | −1.32821 | − | 0.631155i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.15109e26 | + | 1.00061e27i | 0.0895898 | + | 0.109978i | ||||
\(461\) | 3.85761e27 | 0.414437 | 0.207219 | − | 0.978295i | \(-0.433559\pi\) | ||||
0.207219 | + | 0.978295i | \(0.433559\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.26959e27i | 0.746293i | 0.927772 | + | 0.373147i | \(0.121721\pi\) | ||||
−0.927772 | + | 0.373147i | \(0.878279\pi\) | |||||||
\(464\) | −2.73518e27 | + | 1.32465e28i | −0.274503 | + | 1.32942i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.97286e27 | + | 1.88787e27i | 0.381111 | + | 0.181101i | ||||
\(467\) | 8.03132e27i | 0.753286i | 0.926359 | + | 0.376643i | \(0.122922\pi\) | ||||
−0.926359 | + | 0.376643i | \(0.877078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.44943e28i | 1.29982i | ||||||||
\(470\) | 2.24412e27 | − | 4.72257e27i | 0.196797 | − | 0.414143i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.30996e27 | + | 1.76133e28i | 0.361478 | + | 1.47724i | ||||
\(473\) | 5.57078e27i | 0.456956i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.04851e28 | −0.822794 | ||||||||
\(476\) | −1.53336e28 | − | 1.88232e28i | −1.17699 | − | 1.44485i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.18712e27 | − | 2.49818e27i | 0.0871967 | − | 0.183498i | ||||
\(479\) | 1.10351e28 | 0.792961 | 0.396481 | − | 0.918043i | \(-0.370231\pi\) | ||||
0.396481 | + | 0.918043i | \(0.370231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.01779e27 | 0.413918 | ||||||||
\(482\) | −4.44004e27 | + | 9.34369e27i | −0.298809 | + | 0.628817i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.25964e27 | − | 4.00147e27i | −0.210036 | − | 0.257836i | ||||
\(485\) | 4.23529e27 | 0.267051 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.03058e27i | − | 0.303783i | −0.988397 | − | 0.151892i | \(-0.951464\pi\) | ||
0.988397 | − | 0.151892i | \(-0.0485365\pi\) | |||||||
\(488\) | −7.07167e27 | − | 2.88995e28i | −0.417940 | − | 1.70798i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.95792e26 | + | 2.09556e27i | −0.0563780 | + | 0.118643i | ||||
\(491\) | 2.28402e28i | 1.26574i | 0.774258 | + | 0.632871i | \(0.218123\pi\) | ||||
−0.774258 | + | 0.632871i | \(0.781877\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.15625e28i | 2.20704i | ||||||||
\(494\) | −2.12264e28 | − | 1.00866e28i | −1.10343 | − | 0.524340i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.60848e28 | + | 3.32124e27i | 0.801414 | + | 0.165479i | ||||
\(497\) | 2.47199e28i | 1.20588i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.77677e28 | −1.29863 | −0.649313 | − | 0.760521i | \(-0.724943\pi\) | ||||
−0.649313 | + | 0.760521i | \(0.724943\pi\) | |||||||
\(500\) | −1.05348e28 | − | 1.29323e28i | −0.482436 | − | 0.592228i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.07739e28 | + | 5.11965e27i | 0.473132 | + | 0.224828i | ||||
\(503\) | −1.44043e28 | −0.619480 | −0.309740 | − | 0.950821i | \(-0.600242\pi\) | ||||
−0.309740 | + | 0.950821i | \(0.600242\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.35829e28 | −0.560315 | ||||||||
\(506\) | −6.18875e27 | − | 2.94084e27i | −0.250048 | − | 0.118820i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.08218e28 | − | 1.69617e28i | 0.807140 | − | 0.657506i | ||||
\(509\) | −2.02542e28 | −0.769094 | −0.384547 | − | 0.923105i | \(-0.625642\pi\) | ||||
−0.384547 | + | 0.923105i | \(0.625642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.58389e28i | 1.67038i | ||||||||
\(512\) | 2.10601e28 | − | 1.84692e28i | 0.751840 | − | 0.659346i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.19938e28 | + | 5.69935e27i | 0.411002 | + | 0.195305i | ||||
\(515\) | − | 7.47764e27i | − | 0.251067i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.77597e28i | 0.894879i | ||||||||
\(518\) | 5.26382e27 | − | 1.10773e28i | 0.166280 | − | 0.349921i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.01643e27 | − | 1.64138e28i | −0.121844 | − | 0.497936i | ||||
\(521\) | 9.41777e27i | 0.279996i | 0.990152 | + | 0.139998i | \(0.0447096\pi\) | ||||
−0.990152 | + | 0.139998i | \(0.955290\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.74316e28 | −1.35457 | −0.677283 | − | 0.735723i | \(-0.736843\pi\) | ||||
−0.677283 | + | 0.735723i | \(0.736843\pi\) | |||||||
\(524\) | 1.94602e28 | − | 1.58525e28i | 0.544713 | − | 0.443730i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.20357e28 | + | 2.53280e28i | −0.323683 | + | 0.681163i | ||||
\(527\) | 5.04680e28 | 1.33047 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.49391e28 | −0.885171 | ||||||||
\(530\) | −2.68894e27 | + | 5.65864e27i | −0.0667858 | + | 0.140545i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.71340e28 | + | 3.02498e28i | −0.886542 | + | 0.722187i | ||||
\(533\) | 9.02580e28 | 2.11276 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.67537e28i | 0.377048i | ||||||||
\(536\) | −4.99139e28 | + | 1.22139e28i | −1.10152 | + | 0.269540i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.66005e27 | + | 1.82243e28i | −0.183784 | + | 0.386757i | ||||
\(539\) | − | 1.23179e28i | − | 0.256363i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.11838e28i | 0.824433i | 0.911086 | + | 0.412217i | \(0.135245\pi\) | ||||
−0.911086 | + | 0.412217i | \(0.864755\pi\) | |||||||
\(542\) | −6.74810e28 | − | 3.20664e28i | −1.32492 | − | 0.629590i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.19002e28 | − | 6.86660e28i | 0.980350 | − | 1.29704i | ||||
\(545\) | − | 2.43751e28i | − | 0.451631i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.40507e28 | 1.67685 | 0.838426 | − | 0.545015i | \(-0.183476\pi\) | ||||
0.838426 | + | 0.545015i | \(0.183476\pi\) | |||||||
\(548\) | 1.23976e28 | − | 1.00992e28i | 0.216841 | − | 0.176641i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.61524e28 | + | 1.71793e28i | 0.608596 | + | 0.289199i | ||||
\(551\) | 8.19934e28 | 1.35421 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.67575e28 | 0.584429 | ||||||||
\(554\) | −1.08738e29 | − | 5.16712e28i | −1.69640 | − | 0.806113i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.59935e27 | + | 5.64607e27i | 0.0690894 | + | 0.0848127i | ||||
\(557\) | 8.21528e28 | 1.21100 | 0.605498 | − | 0.795847i | \(-0.292974\pi\) | ||||
0.605498 | + | 0.795847i | \(0.292974\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.82489e28i | 0.684958i | ||||||||
\(560\) | −3.37269e28 | − | 6.96404e27i | −0.469897 | − | 0.0970258i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.42726e27 | − | 6.78220e26i | −0.0191545 | − | 0.00910205i | ||||
\(563\) | 8.17084e28i | 1.07629i | 0.842853 | + | 0.538144i | \(0.180874\pi\) | ||||
−0.842853 | + | 0.538144i | \(0.819126\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.48792e28i | 0.696464i | ||||||||
\(566\) | −3.37209e28 | + | 7.09629e28i | −0.420075 | + | 0.884013i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.51275e28 | + | 2.08306e28i | −1.02191 | + | 0.250060i | ||||
\(569\) | 9.39824e28i | 1.10756i | 0.832663 | + | 0.553781i | \(0.186815\pi\) | ||||
−0.832663 | + | 0.553781i | \(0.813185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.51570e29 | −1.72160 | −0.860801 | − | 0.508942i | \(-0.830037\pi\) | ||||
−0.860801 | + | 0.508942i | \(0.830037\pi\) | |||||||
\(572\) | 5.66617e28 | + | 6.95566e28i | 0.631875 | + | 0.775676i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.89496e28 | − | 1.66143e29i | 0.848740 | − | 1.78610i | ||||
\(575\) | −2.64772e28 | −0.279486 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.58548e28 | −0.975591 | −0.487796 | − | 0.872958i | \(-0.662199\pi\) | ||||
−0.487796 | + | 0.872958i | \(0.662199\pi\) | |||||||
\(578\) | 7.05735e28 | − | 1.48516e29i | 0.705342 | − | 1.48433i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.72352e28 | + | 4.57092e28i | 0.358889 | + | 0.440565i | ||||
\(581\) | −8.14132e28 | −0.770629 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.32620e28i | − | 0.303689i | ||||||
\(584\) | −1.57855e29 | + | 3.86268e28i | −1.41554 | + | 0.346381i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.15106e27 | − | 1.92576e28i | 0.0791674 | − | 0.166601i | ||||
\(587\) | − | 3.41368e28i | − | 0.290083i | −0.989426 | − | 0.145042i | \(-0.953668\pi\) | ||
0.989426 | − | 0.145042i | \(-0.0463316\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.95617e28i | − | 0.816360i | ||||||
\(590\) | 7.13868e28 | + | 3.39224e28i | 0.575005 | + | 0.273238i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.25823e28 | + | 8.79253e27i | 0.331018 | + | 0.0683496i | ||||
\(593\) | − | 2.84826e28i | − | 0.217523i | −0.994068 | − | 0.108761i | \(-0.965312\pi\) | ||
0.994068 | − | 0.108761i | \(-0.0346885\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.05822e29 | −0.780099 | ||||||||
\(596\) | −7.62628e28 | − | 9.36186e28i | −0.552366 | − | 0.678073i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.36012e28 | − | 2.54708e28i | −0.374811 | − | 0.178107i | ||||
\(599\) | −7.13826e28 | −0.490468 | −0.245234 | − | 0.969464i | \(-0.578865\pi\) | ||||
−0.245234 | + | 0.969464i | \(0.578865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.80749e28 | 0.584346 | 0.292173 | − | 0.956365i | \(-0.405622\pi\) | ||||
0.292173 | + | 0.956365i | \(0.405622\pi\) | |||||||
\(602\) | 8.88144e28 | + | 4.22038e28i | 0.579056 | + | 0.275162i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.31271e29 | − | 1.88396e29i | 1.45624 | − | 1.18627i | ||||
\(605\) | −2.24958e28 | −0.139210 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.54245e29i | 1.51975i | 0.650072 | + | 0.759873i | \(0.274739\pi\) | ||||
−0.650072 | + | 0.759873i | \(0.725261\pi\) | |||||||
\(608\) | −1.35462e29 | − | 1.02387e29i | −0.795849 | − | 0.601532i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.17130e29 | − | 5.56591e28i | −0.664820 | − | 0.315917i | ||||
\(611\) | 2.40429e29i | 1.34139i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 2.82720e29i | − | 1.52413i | −0.647502 | − | 0.762063i | \(-0.724186\pi\) | ||
0.647502 | − | 0.762063i | \(-0.275814\pi\) | |||||||
\(614\) | 7.94085e28 | − | 1.67109e29i | 0.420823 | − | 0.885586i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.77599e29 | − | 4.34582e28i | 0.909585 | − | 0.222574i | ||||
\(617\) | 2.83868e29i | 1.42930i | 0.699484 | + | 0.714648i | \(0.253413\pi\) | ||||
−0.699484 | + | 0.714648i | \(0.746587\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.13868e29 | 1.04087 | 0.520433 | − | 0.853903i | \(-0.325771\pi\) | ||||
0.520433 | + | 0.853903i | \(0.325771\pi\) | |||||||
\(620\) | 5.55031e28 | − | 4.52135e28i | 0.265585 | − | 0.216349i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.84676e28 | − | 1.44084e29i | 0.316728 | − | 0.666527i | ||||
\(623\) | 3.70998e29 | 1.68751 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.14827e29 | 0.505015 | ||||||||
\(626\) | −3.74175e28 | + | 7.87420e28i | −0.161825 | + | 0.340546i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.39366e28 | + | 4.39374e28i | −0.225584 | + | 0.183763i | ||||
\(629\) | 1.33607e29 | 0.549539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.45573e29i | − | 1.77260i | −0.463113 | − | 0.886299i | \(-0.653268\pi\) | ||
0.463113 | − | 0.886299i | \(-0.346732\pi\) | |||||||
\(632\) | 3.09742e28 | + | 1.26581e29i | 0.121191 | + | 0.495268i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.41400e28 | − | 5.08005e28i | 0.0913691 | − | 0.192279i | ||||
\(635\) | − | 1.17058e29i | − | 0.435790i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.06686e29i | − | 0.384277i | ||||||
\(638\) | −2.82710e29 | − | 1.34341e29i | −1.00167 | − | 0.475985i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.43850e27 | − | 1.22013e29i | −0.0152176 | − | 0.418328i | ||||
\(641\) | − | 8.98916e28i | − | 0.303186i | −0.988443 | − | 0.151593i | \(-0.951560\pi\) | ||
0.988443 | − | 0.151593i | \(-0.0484404\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.88791e28 | 0.0616262 | 0.0308131 | − | 0.999525i | \(-0.490190\pi\) | ||||
0.0308131 | + | 0.999525i | \(0.490190\pi\) | |||||||
\(644\) | −9.37710e28 | + | 7.63870e28i | −0.301139 | + | 0.245311i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.71270e29 | − | 2.23944e29i | −1.46497 | − | 0.696141i | ||||
\(647\) | −5.73966e29 | −1.75546 | −0.877731 | − | 0.479155i | \(-0.840943\pi\) | ||||
−0.877731 | + | 0.479155i | \(0.840943\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.19619e29 | −1.24247 | ||||||||
\(650\) | 3.13118e29 | + | 1.48791e29i | 0.912259 | + | 0.433498i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.79797e29 | − | 4.66230e29i | −1.07140 | − | 1.31523i | ||||
\(653\) | 4.98246e29 | 1.38311 | 0.691553 | − | 0.722326i | \(-0.256927\pi\) | ||||
0.691553 | + | 0.722326i | \(0.256927\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.09403e29i | − | 0.294101i | ||||||
\(656\) | 6.38671e29 | + | 1.31875e29i | 1.68961 | + | 0.348877i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.42570e29 | + | 2.10305e29i | 1.13399 | + | 0.538863i | ||||
\(659\) | − | 4.47292e29i | − | 1.12796i | −0.825788 | − | 0.563981i | \(-0.809269\pi\) | ||
0.825788 | − | 0.563981i | \(-0.190731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.76146e29i | − | 0.430286i | −0.976583 | − | 0.215143i | \(-0.930978\pi\) | ||
0.976583 | − | 0.215143i | \(-0.0690218\pi\) | |||||||
\(662\) | 7.60573e28 | − | 1.60056e29i | 0.182866 | − | 0.384825i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.86041e28 | − | 2.80362e29i | −0.159803 | − | 0.653061i | ||||
\(665\) | 2.08763e29i | 0.478660i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.07051e29 | 0.459997 | ||||||||
\(668\) | 1.70779e29 | + | 2.09644e29i | 0.373492 | + | 0.458491i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.61317e28 | + | 2.02301e29i | −0.203742 | + | 0.428758i | ||||
\(671\) | 6.88500e29 | 1.43654 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.19960e29 | 0.242594 | 0.121297 | − | 0.992616i | \(-0.461295\pi\) | ||||
0.121297 | + | 0.992616i | \(0.461295\pi\) | |||||||
\(674\) | −9.61821e28 | + | 2.02407e29i | −0.191499 | + | 0.402992i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.63510e29 | + | 2.00721e29i | 0.315575 | + | 0.387394i | ||||
\(677\) | −1.71924e29 | −0.326706 | −0.163353 | − | 0.986568i | \(-0.552231\pi\) | ||||
−0.163353 | + | 0.986568i | \(0.552231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.96905e29i | 0.731230i | ||||||||
\(680\) | −8.91728e28 | − | 3.64419e29i | −0.161767 | − | 0.661086i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.63126e29 | + | 3.43285e29i | −0.286938 | + | 0.603836i | ||||
\(683\) | 1.02511e29i | 0.177563i | 0.996051 | + | 0.0887814i | \(0.0282973\pi\) | ||||
−0.996051 | + | 0.0887814i | \(0.971703\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.96979e28i | − | 0.117076i | ||||||
\(686\) | 4.29447e29 | + | 2.04069e29i | 0.710405 | + | 0.337578i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.04960e28 | + | 3.41413e29i | −0.113106 | + | 0.547774i | ||||
\(689\) | − | 2.88085e29i | − | 0.455217i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.64568e29 | −1.47847 | −0.739236 | − | 0.673446i | \(-0.764813\pi\) | ||||
−0.739236 | + | 0.673446i | \(0.764813\pi\) | |||||||
\(692\) | 3.49572e29 | + | 4.29128e29i | 0.527744 | + | 0.647847i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.60733e29 | + | 3.13975e29i | 0.967724 | + | 0.459854i | ||||
\(695\) | 3.17416e28 | 0.0457919 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.00391e30 | 2.80501 | ||||||||
\(698\) | −5.50259e29 | − | 2.61479e29i | −0.758727 | − | 0.360541i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.47776e29 | − | 4.46225e29i | 0.732948 | − | 0.597068i | ||||
\(701\) | −1.27758e29 | −0.168403 | −0.0842015 | − | 0.996449i | \(-0.526834\pi\) | ||||
−0.0842015 | + | 0.996449i | \(0.526834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.63577e29i | − | 0.337191i | ||||||
\(704\) | 2.99313e29 | + | 5.74975e29i | 0.377236 | + | 0.724663i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.27931e29 | − | 1.55830e29i | −0.401174 | − | 0.190635i | ||||
\(707\) | − | 1.27290e30i | − | 1.53424i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.70376e29i | 0.901399i | 0.892676 | + | 0.450700i | \(0.148825\pi\) | ||||
−0.892676 | + | 0.450700i | \(0.851175\pi\) | |||||||
\(710\) | −1.63951e29 | + | 3.45022e29i | −0.189018 | + | 0.397772i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.12627e29 | + | 1.27760e30i | 0.349934 | + | 1.43006i | ||||
\(713\) | − | 2.51414e29i | − | 0.277300i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.91040e29 | 0.418801 | ||||||||
\(716\) | −4.38300e28 | + | 3.57044e28i | −0.0462578 | + | 0.0376821i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.58160e29 | + | 1.17460e30i | −0.572074 | + | 1.20388i | ||||
\(719\) | −2.43997e29 | −0.246451 | −0.123225 | − | 0.992379i | \(-0.539324\pi\) | ||||
−0.123225 | + | 0.992379i | \(0.539324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.00759e29 | 0.687461 | ||||||||
\(722\) | 2.12396e27 | − | 4.46969e27i | 0.00205355 | − | 0.00432152i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.59985e29 | + | 2.11787e29i | −0.244171 | + | 0.198904i | ||||
\(725\) | −1.20951e30 | −1.11960 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.46599e29i | − | 0.671392i | −0.941970 | − | 0.335696i | \(-0.891029\pi\) | ||
0.941970 | − | 0.335696i | \(-0.108971\pi\) | |||||||
\(728\) | 1.53820e30 | − | 3.76395e29i | 1.36343 | − | 0.333629i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.04020e29 | + | 6.39785e29i | −0.261826 | + | 0.550991i | ||||
\(731\) | 1.07123e30i | 0.909386i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.15780e29i | 0.590456i | 0.955427 | + | 0.295228i | \(0.0953957\pi\) | ||||
−0.955427 | + | 0.295228i | \(0.904604\pi\) | |||||||
\(734\) | 1.53328e30 | + | 7.28599e29i | 1.24684 | + | 0.592489i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.42070e29 | − | 2.58549e29i | −0.270333 | − | 0.204327i | ||||
\(737\) | − | 1.18914e30i | − | 0.926459i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.47378e30 | −1.87324 | −0.936622 | − | 0.350342i | \(-0.886065\pi\) | ||||
−0.936622 | + | 0.350342i | \(0.886065\pi\) | |||||||
\(740\) | 1.46937e29 | − | 1.19697e29i | 0.109698 | − | 0.0893612i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.30293e29 | − | 2.51991e29i | −0.384835 | − | 0.182870i | ||||
\(743\) | −2.04663e30 | −1.46439 | −0.732194 | − | 0.681096i | \(-0.761504\pi\) | ||||
−0.732194 | + | 0.681096i | \(0.761504\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.26314e29 | −0.366104 | ||||||||
\(746\) | −1.24522e30 | − | 5.91717e29i | −0.854059 | − | 0.405842i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.25800e30 | + | 1.54430e30i | 0.838910 | + | 1.02983i | ||||
\(749\) | −1.57006e30 | −1.03242 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6.93466e29i | − | 0.443410i | −0.975114 | − | 0.221705i | \(-0.928838\pi\) | ||
0.975114 | − | 0.221705i | \(-0.0711623\pi\) | |||||||
\(752\) | −3.51288e29 | + | 1.70129e30i | −0.221501 | + | 1.07273i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.44857e30 | − | 1.16354e30i | −1.50146 | − | 0.713481i | ||||
\(755\) | − | 1.30018e30i | − | 0.786249i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.65899e30i | − | 1.56390i | −0.623339 | − | 0.781952i | \(-0.714224\pi\) | ||
0.623339 | − | 0.781952i | \(-0.285776\pi\) | |||||||
\(758\) | 4.32735e29 | − | 9.10655e29i | 0.251013 | − | 0.528235i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.18916e29 | + | 1.75918e29i | −0.405635 | + | 0.0992582i | ||||
\(761\) | 1.97349e30i | 1.09824i | 0.835745 | + | 0.549118i | \(0.185036\pi\) | ||||
−0.835745 | + | 0.549118i | \(0.814964\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.28429e30 | 1.23664 | ||||||||
\(764\) | −2.69337e29 | − | 3.30633e29i | −0.143819 | − | 0.176549i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.44821e30 | + | 3.04764e30i | −0.752368 | + | 1.58329i | ||||
\(767\) | −3.63435e30 | −1.86241 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.82104e30 | −0.908014 | −0.454007 | − | 0.890998i | \(-0.650006\pi\) | ||||
−0.454007 | + | 0.890998i | \(0.650006\pi\) | |||||||
\(770\) | 3.42047e29 | − | 7.19809e29i | 0.168241 | − | 0.354050i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.62402e29 | − | 4.44877e29i | −0.173464 | − | 0.212941i | ||||
\(773\) | 6.47814e29 | 0.305890 | 0.152945 | − | 0.988235i | \(-0.451124\pi\) | ||||
0.152945 | + | 0.988235i | \(0.451124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.46867e30i | 0.674926i | ||||||||
\(776\) | −1.36682e30 | + | 3.34458e29i | −0.619672 | + | 0.151633i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.88530e28 | + | 1.65939e29i | −0.0347962 | + | 0.0732257i | ||||
\(779\) | − | 3.95326e30i | − | 1.72112i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.02807e30i | − | 0.859503i | ||||||
\(782\) | −1.19006e30 | − | 5.65505e29i | −0.497619 | − | 0.236464i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.55878e29 | − | 7.54919e29i | 0.0634551 | − | 0.307313i | ||||
\(785\) | 3.03226e29i | 0.121797i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.62777e30 | 0.636587 | 0.318293 | − | 0.947992i | \(-0.396890\pi\) | ||||
0.318293 | + | 0.947992i | \(0.396890\pi\) | |||||||
\(788\) | 1.63244e30 | + | 2.00394e30i | 0.629957 | + | 0.773321i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.13034e29 | + | 2.43789e29i | 0.192780 | + | 0.0916073i | ||||
\(791\) | −5.14294e30 | −1.90703 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.96315e30 | 2.15331 | ||||||||
\(794\) | 1.18483e30 | + | 5.63019e29i | 0.422221 | + | 0.200636i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.35197e30 | + | 2.73056e30i | −1.16336 | + | 0.947686i | ||||
\(797\) | −2.71983e28 | −0.00931600 | −0.00465800 | − | 0.999989i | \(-0.501483\pi\) | ||||
−0.00465800 | + | 0.999989i | \(0.501483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.33801e30i | 1.78089i | ||||||||
\(800\) | 1.99825e30 | + | 1.51035e30i | 0.657968 | + | 0.497316i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.46166e30 | − | 1.16976e30i | −0.789582 | − | 0.375203i | ||||
\(803\) | − | 3.76072e30i | − | 1.19058i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.27171e29i | 0.162590i | ||||||||
\(806\) | −1.41285e30 | + | 2.97322e30i | −0.430108 | + | 0.905126i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.38349e30 | − | 1.07263e30i | 1.30017 | − | 0.318150i | ||||
\(809\) | − | 2.33462e30i | − | 0.683530i | −0.939786 | − | 0.341765i | \(-0.888975\pi\) | ||
0.939786 | − | 0.341765i | \(-0.111025\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.29570e30 | −1.22550 | −0.612752 | − | 0.790275i | \(-0.709938\pi\) | ||||
−0.612752 | + | 0.790275i | \(0.709938\pi\) | |||||||
\(812\) | −4.28358e30 | + | 3.48946e30i | −1.20634 | + | 0.982697i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.31855e29 | + | 9.08803e29i | −0.118517 | + | 0.249410i | ||||
\(815\) | −2.62110e30 | −0.710115 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.11328e30 | 0.557989 | ||||||||
\(818\) | −1.24045e30 | + | 2.61043e30i | −0.323348 | + | 0.680459i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.20384e30 | − | 1.79527e30i | 0.559931 | − | 0.456126i | ||||
\(821\) | −4.13604e30 | −1.03748 | −0.518742 | − | 0.854931i | \(-0.673600\pi\) | ||||
−0.518742 | + | 0.854931i | \(0.673600\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.55343e30i | 0.379835i | 0.981800 | + | 0.189917i | \(0.0608220\pi\) | ||||
−0.981800 | + | 0.189917i | \(0.939178\pi\) | |||||||
\(824\) | 5.90505e29 | + | 2.41319e30i | 0.142557 | + | 0.582581i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.17900e30 | + | 6.68994e30i | −0.748170 | + | 1.57446i | ||||
\(827\) | 1.45005e30i | 0.336958i | 0.985705 | + | 0.168479i | \(0.0538856\pi\) | ||||
−0.985705 | + | 0.168479i | \(0.946114\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.05819e30i | − | 0.919412i | −0.888071 | − | 0.459706i | \(-0.847955\pi\) | ||
0.888071 | − | 0.459706i | \(-0.152045\pi\) | |||||||
\(830\) | −1.13631e30 | − | 5.39962e29i | −0.254200 | − | 0.120794i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.59237e30 | + | 4.97990e30i | 0.565461 | + | 1.08624i | ||||
\(833\) | − | 2.36865e30i | − | 0.510186i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.17860e30 | 0.247547 | ||||||||
\(836\) | 3.04655e30 | − | 2.48175e30i | 0.631891 | − | 0.514746i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.17515e30 | − | 3.88476e30i | −1.65361 | − | 0.785782i | ||||
\(839\) | 4.25565e30 | 0.850091 | 0.425046 | − | 0.905172i | \(-0.360258\pi\) | ||||
0.425046 | + | 0.905172i | \(0.360258\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.32550e30 | 0.842710 | ||||||||
\(842\) | 5.17185e30 | + | 2.45762e30i | 0.995106 | + | 0.472866i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.43710e29 | − | 5.44689e29i | −0.0832729 | − | 0.102224i | ||||
\(845\) | 1.12843e30 | 0.209161 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.10817e30i | − | 0.381180i | ||||||
\(848\) | 4.20917e29 | − | 2.03851e30i | 0.0751693 | − | 0.364045i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.95187e30 | + | 3.30347e30i | 1.21116 | + | 0.575534i | ||||
\(851\) | − | 6.65586e29i | − | 0.114537i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.82384e30i | − | 0.977788i | −0.872343 | − | 0.488894i | \(-0.837400\pi\) | ||
0.872343 | − | 0.488894i | \(-0.162600\pi\) | |||||||
\(854\) | 5.21603e30 | − | 1.09767e31i | 0.865032 | − | 1.82039i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.32303e30 | − | 5.40678e30i | −0.214090 | − | 0.874912i | ||||
\(857\) | 4.29932e30i | 0.687229i | 0.939111 | + | 0.343615i | \(0.111651\pi\) | ||||
−0.939111 | + | 0.343615i | \(0.888349\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.79229e30 | −1.52741 | −0.763705 | − | 0.645565i | \(-0.776622\pi\) | ||||
−0.763705 | + | 0.645565i | \(0.776622\pi\) | |||||||
\(860\) | 9.59694e29 | + | 1.17810e30i | 0.147876 | + | 0.181530i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.71824e30 | + | 5.72030e30i | −0.408753 | + | 0.860186i | ||||
\(863\) | 2.46176e30 | 0.365706 | 0.182853 | − | 0.983140i | \(-0.441467\pi\) | ||||
0.182853 | + | 0.983140i | \(0.441467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.41251e30 | 0.349784 | ||||||||
\(866\) | 5.80578e30 | − | 1.22178e31i | 0.831616 | − | 1.75007i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.23713e30 | + | 5.20141e30i | 0.592399 | + | 0.727217i | ||||
\(869\) | −3.01566e30 | −0.416558 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.02993e31i | − | 1.38872i | ||||||
\(872\) | 1.92489e30 | + | 7.86637e30i | 0.256438 | + | 1.04798i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.11561e30 | + | 2.34771e30i | −0.145092 | + | 0.305333i | ||||
\(875\) | − | 6.81336e30i | − | 0.875541i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.61432e30i | 0.453451i | 0.973959 | + | 0.226726i | \(0.0728021\pi\) | ||||
−0.973959 | + | 0.226726i | \(0.927198\pi\) | |||||||
\(878\) | −7.26047e30 | − | 3.45011e30i | −0.900062 | − | 0.427702i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.76703e30 | + | 5.71345e29i | 0.334923 | + | 0.0691561i | ||||
\(881\) | 1.37063e31i | 1.63936i | 0.572824 | + | 0.819679i | \(0.305848\pi\) | ||||
−0.572824 | + | 0.819679i | \(0.694152\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.28213e30 | −0.733701 | −0.366851 | − | 0.930280i | \(-0.619564\pi\) | ||||
−0.366851 | + | 0.930280i | \(0.619564\pi\) | |||||||
\(884\) | 1.08957e31 | + | 1.33753e31i | 1.25749 | + | 1.54367i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.77564e30 | + | 2.26934e30i | 0.538242 | + | 0.255768i | ||||
\(887\) | 1.57890e31 | 1.75856 | 0.879280 | − | 0.476305i | \(-0.158024\pi\) | ||||
0.879280 | + | 0.476305i | \(0.158024\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.09700e31 | 1.19326 | ||||||||
\(890\) | 5.17812e30 | + | 2.46060e30i | 0.556643 | + | 0.264512i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.00807e31 | − | 8.21188e30i | 1.05843 | − | 0.862207i | ||||
\(893\) | 1.05307e31 | 1.09274 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.46408e29i | 0.0249754i | ||||||||
\(896\) | 1.14343e31 | − | 4.15949e29i | 1.14545 | − | 0.0416683i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.07038e31 | − | 5.08635e30i | −1.04746 | − | 0.497743i | ||||
\(899\) | − | 1.14849e31i | − | 1.11084i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.39607e30i | − | 0.604370i | ||||||
\(902\) | −6.47719e30 | + | 1.36307e31i | −0.604948 | + | 1.27306i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.33377e30 | − | 1.77107e31i | −0.395456 | − | 1.61609i | ||||
\(905\) | 1.46161e30i | 0.131832i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.40300e30 | −0.828686 | −0.414343 | − | 0.910121i | \(-0.635989\pi\) | ||||
−0.414343 | + | 0.910121i | \(0.635989\pi\) | |||||||
\(908\) | 9.79464e30 | − | 7.97883e30i | 0.853271 | − | 0.695085i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.96249e30 | − | 6.23432e30i | 0.252187 | − | 0.530706i | ||||
\(911\) | −1.96936e31 | −1.65723 | −0.828616 | − | 0.559818i | \(-0.810871\pi\) | ||||
−0.828616 | + | 0.559818i | \(0.810871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.67931e30 | 0.549273 | ||||||||
\(914\) | 7.75506e29 | − | 1.63199e30i | 0.0630449 | − | 0.132673i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.43502e31 | − | 1.16898e31i | 1.14013 | − | 0.928765i | ||||
\(917\) | 1.02526e31 | 0.805296 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.40760e31i | 1.08060i | 0.841472 | + | 0.540301i | \(0.181689\pi\) | ||||
−0.841472 | + | 0.540301i | \(0.818311\pi\) | |||||||
\(920\) | −1.81541e30 | + | 4.44229e29i | −0.137785 | + | 0.0337159i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.39768e30 | + | 5.04571e30i | −0.177876 | + | 0.374324i | ||||
\(923\) | − | 1.75653e31i | − | 1.28836i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.88811e30i | 0.278773i | ||||||||
\(926\) | −9.50854e30 | − | 4.51838e30i | −0.674060 | − | 0.320307i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.56262e31 | − | 1.18109e31i | −1.08293 | − | 0.818518i | ||||
\(929\) | 1.68648e31i | 1.15562i | 0.816171 | + | 0.577811i | \(0.196093\pi\) | ||||
−0.816171 | + | 0.577811i | \(0.803907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.67281e30 | −0.313045 | ||||||||
\(932\) | −4.93863e30 | + | 4.02306e30i | −0.327144 | + | 0.266495i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.05049e31 | − | 4.99183e30i | −0.680376 | − | 0.323309i | ||||
\(935\) | 8.68189e30 | 0.556023 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.90911e31 | 1.19554 | 0.597771 | − | 0.801667i | \(-0.296053\pi\) | ||||
0.597771 | + | 0.801667i | \(0.296053\pi\) | |||||||
\(938\) | −1.89584e31 | − | 9.00887e30i | −1.17401 | − | 0.557880i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.78224e30 | + | 5.87058e30i | 0.289594 | + | 0.355499i | ||||
\(941\) | 2.69612e31 | 1.61454 | 0.807268 | − | 0.590185i | \(-0.200945\pi\) | ||||
0.807268 | + | 0.590185i | \(0.200945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 9.98281e30i | − | 0.584628i | ||||||
\(944\) | −2.57169e31 | − | 5.31011e30i | −1.48940 | − | 0.307537i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.28652e30 | − | 3.46249e30i | −0.412727 | − | 0.196124i | ||||
\(947\) | 2.07970e31i | 1.16500i | 0.812831 | + | 0.582499i | \(0.197925\pi\) | ||||
−0.812831 | + | 0.582499i | \(0.802075\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.25719e31i | − | 1.78463i | ||||||
\(950\) | 6.51698e30 | − | 1.37144e31i | 0.353142 | − | 0.743156i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.41511e31 | − | 8.35673e30i | 1.81016 | − | 0.442944i | ||||
\(953\) | 1.56863e31i | 0.822328i | 0.911561 | + | 0.411164i | \(0.134878\pi\) | ||||
−0.911561 | + | 0.411164i | \(0.865122\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.85878e30 | −0.0953221 | ||||||||
\(956\) | 2.52975e30 | + | 3.10547e30i | 0.128313 | + | 0.157514i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.85879e30 | + | 1.44337e31i | −0.340337 | + | 0.716211i | ||||
\(959\) | 6.53166e30 | 0.320574 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.87975e30 | 0.330352 | ||||||||
\(962\) | −3.74033e30 | + | 7.87120e30i | −0.177653 | + | 0.373855i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.46176e30 | − | 1.16150e31i | −0.439706 | − | 0.539774i | ||||
\(965\) | −2.50105e30 | −0.114970 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.13834e31i | 1.86144i | 0.365737 | + | 0.930718i | \(0.380817\pi\) | ||||
−0.365737 | + | 0.930718i | \(0.619183\pi\) | |||||||
\(968\) | 7.25989e30 | − | 1.77648e30i | 0.323027 | − | 0.0790442i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.63242e30 | + | 5.53971e30i | −0.114618 | + | 0.241203i | ||||
\(971\) | 1.59891e30i | 0.0688689i | 0.999407 | + | 0.0344345i | \(0.0109630\pi\) | ||||
−0.999407 | + | 0.0344345i | \(0.989037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.97463e30i | 0.125386i | ||||||||
\(974\) | 6.57994e30 | + | 3.12673e30i | 0.274380 | + | 0.130383i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.21956e31 | + | 8.71269e30i | 1.72204 | + | 0.355573i | ||||
\(977\) | − | 3.05439e29i | − | 0.0123319i | −0.999981 | − | 0.00616597i | \(-0.998037\pi\) | ||
0.999981 | − | 0.00616597i | \(-0.00196270\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.04375e31 | −1.20279 | ||||||||
\(980\) | −2.12204e30 | − | 2.60497e30i | −0.0829621 | − | 0.101842i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.98748e31 | − | 1.41962e31i | −1.14323 | − | 0.543253i | ||||
\(983\) | −3.73513e31 | −1.41414 | −0.707072 | − | 0.707142i | \(-0.749984\pi\) | ||||
−0.707072 | + | 0.707142i | \(0.749984\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.12660e31 | 0.417530 | ||||||||
\(986\) | −5.43633e31 | − | 2.58330e31i | −1.99342 | − | 0.947255i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.63864e31 | − | 2.14946e31i | 0.947178 | − | 0.771583i | ||||
\(989\) | 5.33648e30 | 0.189537 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 7.12374e30i | − | 0.247705i | −0.992301 | − | 0.123853i | \(-0.960475\pi\) | ||
0.992301 | − | 0.123853i | \(-0.0395250\pi\) | |||||||
\(992\) | −1.43415e31 | + | 1.89744e31i | −0.493427 | + | 0.652823i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.23333e31 | − | 1.53645e31i | −1.08916 | − | 0.517561i | ||||
\(995\) | 1.88445e31i | 0.628118i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 7.44835e30i | − | 0.243086i | −0.992586 | − | 0.121543i | \(-0.961216\pi\) | ||
0.992586 | − | 0.121543i | \(-0.0387843\pi\) | |||||||
\(998\) | 1.72589e31 | − | 3.63198e31i | 0.557367 | − | 1.17293i | ||||
\(999\) | 0 | 0 |
(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 | 72.22.f.a.35.32 | yes | 84 | |
3.2 | odd | 2 | inner | 72.22.f.a.35.53 | yes | 84 | |
8.3 | odd | 2 | inner | 72.22.f.a.35.54 | yes | 84 | |
24.11 | even | 2 | inner | 72.22.f.a.35.31 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.22.f.a.35.31 | ✓ | 84 | 24.11 | even | 2 | inner | |
72.22.f.a.35.32 | yes | 84 | 1.1 | even | 1 | trivial | |
72.22.f.a.35.53 | yes | 84 | 3.2 | odd | 2 | inner | |
72.22.f.a.35.54 | yes | 84 | 8.3 | odd | 2 | inner |