Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,24,Mod(17,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.17");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.e (of order \(4\), degree \(2\), not 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: | \(214.530583901\) |
Analytic rank: | \(0\) |
Dimension: | \(90\) |
Relative dimension: | \(45\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.36 | ||
Character | \(\chi\) | \(=\) | 64.17 |
Dual form | 64.24.e.a.49.36 |
$q$-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 \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 270677. | + | 270677.i | 0.882180 | + | 0.882180i | 0.993756 | − | 0.111576i | \(-0.0355897\pi\) |
−0.111576 | + | 0.993756i | \(0.535590\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.51855e8 | + | 1.51855e8i | −1.39083 | + | 1.39083i | −0.567372 | + | 0.823462i | \(0.692040\pi\) |
−0.823462 | + | 0.567372i | \(0.807960\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.83375e9i | 1.87971i | 0.341567 | + | 0.939857i | \(0.389042\pi\) | ||||
−0.341567 | + | 0.939857i | \(0.610958\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.23892e10i | 0.556484i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.93402e11 | + | 1.93402e11i | −0.204383 | + | 0.204383i | −0.801875 | − | 0.597492i | \(-0.796164\pi\) |
0.597492 | + | 0.801875i | \(0.296164\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.48061e12 | − | 3.48061e12i | −0.538651 | − | 0.538651i | 0.384482 | − | 0.923133i | \(-0.374380\pi\) |
−0.923133 | + | 0.384482i | \(0.874380\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.22076e13 | −2.45393 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.03593e13 | −0.285615 | −0.142808 | − | 0.989750i | \(-0.545613\pi\) | ||||
−0.142808 | + | 0.989750i | \(0.545613\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.81860e14 | + | 3.81860e14i | 0.752035 | + | 0.752035i | 0.974859 | − | 0.222823i | \(-0.0715273\pi\) |
−0.222823 | + | 0.974859i | \(0.571527\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.66177e15 | + | 2.66177e15i | −1.65825 | + | 1.65825i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.51116e14i | 0.120607i | 0.998180 | + | 0.0603035i | \(0.0192069\pi\) | ||||
−0.998180 | + | 0.0603035i | \(0.980793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.41992e16i | − | 2.86884i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.13019e16 | − | 1.13019e16i | 0.391261 | − | 0.391261i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.35476e16 | − | 2.35476e16i | −0.358401 | − | 0.358401i | 0.504822 | − | 0.863223i | \(-0.331558\pi\) |
−0.863223 | + | 0.504822i | \(0.831558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.66833e16 | 0.612740 | 0.306370 | − | 0.951913i | \(-0.400886\pi\) | ||||
0.306370 | + | 0.951913i | \(0.400886\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.04699e17 | −0.360606 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.49331e18 | − | 1.49331e18i | −2.61437 | − | 2.61437i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.22561e17 | + | 7.22561e17i | −0.667659 | + | 0.667659i | −0.957174 | − | 0.289515i | \(-0.906506\pi\) |
0.289515 | + | 0.957174i | \(0.406506\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.88425e18i | − | 0.950374i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.41831e17i | − | 0.0970056i | −0.998823 | − | 0.0485028i | \(-0.984555\pi\) | ||
0.998823 | − | 0.0485028i | \(-0.0154450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.79520e18 | − | 4.79520e18i | 0.786900 | − | 0.786900i | −0.194085 | − | 0.980985i | \(-0.562174\pi\) |
0.980985 | + | 0.194085i | \(0.0621738\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.95558e18 | − | 7.95558e18i | −0.773977 | − | 0.773977i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.40438e19 | −0.828627 | −0.414314 | − | 0.910134i | \(-0.635978\pi\) | ||||
−0.414314 | + | 0.910134i | \(0.635978\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.93340e19 | −2.53333 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.09244e19 | − | 1.09244e19i | −0.251964 | − | 0.251964i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.58841e19 | + | 1.58841e19i | −0.235391 | + | 0.235391i | −0.814939 | − | 0.579547i | \(-0.803229\pi\) |
0.579547 | + | 0.814939i | \(0.303229\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.87383e19i | − | 0.568526i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.06722e20i | 1.32686i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.07394e19 | − | 8.07394e19i | 0.348568 | − | 0.348568i | −0.511008 | − | 0.859576i | \(-0.670728\pi\) |
0.859576 | + | 0.511008i | \(0.170728\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.60908e20 | − | 2.60908e20i | −0.767704 | − | 0.767704i | 0.209998 | − | 0.977702i | \(-0.432654\pi\) |
−0.977702 | + | 0.209998i | \(0.932654\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.15183e20 | −1.04603 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.05710e21 | 1.49835 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00472e21 | − | 1.00472e21i | −1.00504 | − | 1.00504i | −0.999987 | − | 0.00505403i | \(-0.998391\pi\) |
−0.00505403 | − | 0.999987i | \(-0.501609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.49175e20 | + | 1.49175e20i | −0.106397 | + | 0.106397i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00814e21i | 0.517668i | 0.965922 | + | 0.258834i | \(0.0833383\pi\) | ||||
−0.965922 | + | 0.258834i | \(0.916662\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.06993e21i | − | 0.399156i | −0.979882 | − | 0.199578i | \(-0.936043\pi\) | ||
0.979882 | − | 0.199578i | \(-0.0639571\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.25694e21 | − | 9.25694e21i | 2.53083 | − | 2.53083i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.90187e21 | − | 1.90187e21i | −0.384182 | − | 0.384182i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.18097e21 | −0.328049 | −0.164025 | − | 0.986456i | \(-0.552448\pi\) | ||||
−0.164025 | + | 0.986456i | \(0.552448\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.10504e22 | 1.24681 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.33029e22 | + | 1.33029e22i | 1.13383 | + | 1.13383i | 0.989535 | + | 0.144292i | \(0.0460903\pi\) |
0.144292 | + | 0.989535i | \(0.453910\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.12878e21 | − | 6.12878e21i | 0.397243 | − | 0.397243i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.27476e22i | − | 0.632349i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.63580e22i | − | 0.624806i | −0.949950 | − | 0.312403i | \(-0.898866\pi\) | ||
0.949950 | − | 0.312403i | \(-0.101134\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.42275e22 | − | 3.42275e22i | 1.01251 | − | 1.01251i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.34632e22 | + | 2.34632e22i | 0.540547 | + | 0.540547i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.15975e23 | −2.09191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.68132e22 | 0.806445 | 0.403222 | − | 0.915102i | \(-0.367890\pi\) | ||||
0.403222 | + | 0.915102i | \(0.367890\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.01322e22 | − | 1.01322e22i | −0.113736 | − | 0.113736i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.48094e22 | + | 5.48094e22i | −0.488831 | + | 0.488831i | −0.907937 | − | 0.419106i | \(-0.862344\pi\) |
0.419106 | + | 0.907937i | \(0.362344\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.88609e22i | − | 0.205439i | −0.994710 | − | 0.102719i | \(-0.967246\pi\) | ||
0.994710 | − | 0.102719i | \(-0.0327543\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 8.08409e23i | − | 4.61269i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.73458e23 | + | 1.73458e23i | −0.796676 | + | 0.796676i | −0.982570 | − | 0.185894i | \(-0.940482\pi\) |
0.185894 | + | 0.982570i | \(0.440482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.73035e23 | + | 1.73035e23i | 0.642288 | + | 0.642288i | 0.951118 | − | 0.308829i | \(-0.0999371\pi\) |
−0.308829 | + | 0.951118i | \(0.599937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.91162e23 | −1.17799 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.37190e23 | −1.07218 | −0.536091 | − | 0.844160i | \(-0.680100\pi\) | ||||
−0.536091 | + | 0.844160i | \(0.680100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.36899e22 | − | 8.36899e22i | −0.167744 | − | 0.167744i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.82347e23 | − | 1.82347e23i | 0.299751 | − | 0.299751i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.96884e23i | − | 0.536875i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.20622e23i | 0.916455i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.25258e22 | − | 9.25258e22i | 0.0855764 | − | 0.0855764i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.38307e24 | + | 3.38307e24i | 2.59924 | + | 2.59924i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.94304e23 | −0.188388 | −0.0941939 | − | 0.995554i | \(-0.530027\pi\) | ||||
−0.0941939 | + | 0.995554i | \(0.530027\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.59590e24 | 1.38837 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.75054e24 | + | 1.75054e24i | 0.784424 | + | 0.784424i | 0.980574 | − | 0.196150i | \(-0.0628439\pi\) |
−0.196150 | + | 0.980574i | \(0.562844\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.75512e24 | + | 3.75512e24i | −1.41361 | + | 1.41361i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.43249e24i | 1.08836i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.08993e23i | 0.0827299i | 0.999144 | + | 0.0413649i | \(0.0131706\pi\) | ||||
−0.999144 | + | 0.0413649i | \(0.986829\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.09547e24 | + | 4.09547e24i | −0.928182 | + | 0.928182i | −0.997588 | − | 0.0694065i | \(-0.977889\pi\) |
0.0694065 | + | 0.997588i | \(0.477889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.80134e24 | − | 3.80134e24i | −0.730999 | − | 0.730999i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.34631e24 | 0.220182 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.15166e24 | 0.996953 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.87671e25 | − | 1.87671e25i | −2.23485 | − | 2.23485i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.10897e25 | − | 1.10897e25i | 1.13052 | − | 1.13052i | 0.140432 | − | 0.990090i | \(-0.455151\pi\) |
0.990090 | − | 0.140432i | \(-0.0448492\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.05535e23i | − | 0.0354645i | −0.999843 | − | 0.0177322i | \(-0.994355\pi\) | ||
0.999843 | − | 0.0177322i | \(-0.00564464\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.11439e24i | − | 0.158940i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.31633e25 | + | 1.31633e25i | −0.852219 | + | 0.852219i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.50527e25 | − | 1.50527e25i | −0.840944 | − | 0.840944i | 0.148037 | − | 0.988982i | \(-0.452704\pi\) |
−0.988982 | + | 0.148037i | \(0.952704\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.59894e24 | −0.415315 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.41954e24 | −0.226707 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.44894e23 | + | 6.44894e23i | 0.0234062 | + | 0.0234062i | 0.718713 | − | 0.695307i | \(-0.244732\pi\) |
−0.695307 | + | 0.718713i | \(0.744732\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.58991e25 | − | 1.58991e25i | 0.501542 | − | 0.501542i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.06935e24i | 0.139224i | 0.997574 | + | 0.0696118i | \(0.0221761\pi\) | ||||
−0.997574 | + | 0.0696118i | \(0.977824\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.75246e25i | − | 0.419711i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00054e25 | + | 2.00054e25i | −0.418496 | + | 0.418496i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.69878e25 | + | 6.69878e25i | 1.22593 | + | 1.22593i | 0.965490 | + | 0.260438i | \(0.0838671\pi\) |
0.260438 | + | 0.965490i | \(0.416133\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.36306e26 | 5.39259 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.37086e25 | 0.614999 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.01063e26 | − | 1.01063e26i | −1.24963 | − | 1.24963i | −0.955884 | − | 0.293746i | \(-0.905098\pi\) |
−0.293746 | − | 0.955884i | \(-0.594902\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.35488e25 | + | 5.35488e25i | −0.582701 | + | 0.582701i | −0.935645 | − | 0.352943i | \(-0.885181\pi\) |
0.352943 | + | 0.935645i | \(0.385181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.41244e26i | − | 1.35451i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.19450e26i | − | 1.85720i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.80558e24 | − | 7.80558e24i | 0.0583750 | − | 0.0583750i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.11140e26 | + | 1.11140e26i | 0.735459 | + | 0.735459i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.09204e26 | −0.640260 | −0.320130 | − | 0.947374i | \(-0.603727\pi\) | ||||
−0.320130 | + | 0.947374i | \(0.603727\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.07215e26 | −1.07774 | −0.538869 | − | 0.842390i | \(-0.681148\pi\) | ||||
−0.538869 | + | 0.842390i | \(0.681148\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.86133e26 | + | 2.86133e26i | 1.32181 | + | 1.32181i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.24730e26 | + | 2.24730e26i | −0.923207 | + | 0.923207i | −0.997255 | − | 0.0740475i | \(-0.976408\pi\) |
0.0740475 | + | 0.997255i | \(0.476408\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.12830e26i | − | 0.778434i | −0.921146 | − | 0.389217i | \(-0.872746\pi\) | ||
0.921146 | − | 0.389217i | \(-0.127254\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 5.43909e26i | − | 1.77326i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.31561e26 | − | 2.31561e26i | 0.673692 | − | 0.673692i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.19088e25 | + | 5.19088e25i | 0.134919 | + | 0.134919i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.88725e25 | −0.0671159 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.47705e26 | −0.307407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.97898e25 | − | 2.97898e25i | −0.0555673 | − | 0.0555673i | 0.678777 | − | 0.734344i | \(-0.262510\pi\) |
−0.734344 | + | 0.678777i | \(0.762510\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.72882e26 | + | 2.72882e26i | −0.456677 | + | 0.456677i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.45635e27i | 2.18889i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.52423e26i | 1.15178i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.89606e26 | − | 2.89606e26i | 0.352127 | − | 0.352127i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.40475e26 | + | 1.40475e26i | 0.153847 | + | 0.153847i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.35645e26 | −0.133937 | −0.0669683 | − | 0.997755i | \(-0.521333\pi\) | ||||
−0.0669683 | + | 0.997755i | \(0.521333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.79167e27 | 1.59646 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.47947e26 | + | 3.47947e26i | 0.280037 | + | 0.280037i | 0.833124 | − | 0.553087i | \(-0.186550\pi\) |
−0.553087 | + | 0.833124i | \(0.686550\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.33106e26 | + | 5.33106e26i | −0.387887 | + | 0.387887i | −0.873933 | − | 0.486046i | \(-0.838439\pi\) |
0.486046 | + | 0.873933i | \(0.338439\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.02958e27i | − | 0.677836i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2.28776e27i | − | 1.36401i | −0.731349 | − | 0.682004i | \(-0.761109\pi\) | ||
0.731349 | − | 0.682004i | \(-0.238891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.13263e27 | − | 2.13263e27i | 1.15248 | − | 1.15248i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.90340e26 | − | 5.90340e26i | −0.289399 | − | 0.289399i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.59509e27 | 1.15499 | 0.577493 | − | 0.816396i | \(-0.304031\pi\) | ||||
0.577493 | + | 0.816396i | \(0.304031\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.19632e27 | 0.888177 | 0.444089 | − | 0.895983i | \(-0.353528\pi\) | ||||
0.444089 | + | 0.895983i | \(0.353528\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.92710e27 | + | 1.92710e27i | 0.708650 | + | 0.708650i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.05287e28 | − | 1.05287e28i | 3.52344 | − | 3.52344i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.65822e27i | − | 0.810169i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.20156e27i | 2.00048i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.68559e27 | + | 2.68559e27i | −0.680444 | + | 0.680444i | −0.960100 | − | 0.279656i | \(-0.909779\pi\) |
0.279656 | + | 0.960100i | \(0.409779\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.06587e26 | − | 1.06587e26i | −0.0246501 | − | 0.0246501i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.31785e27 | 0.700881 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.37554e26 | 0.161727 | 0.0808634 | − | 0.996725i | \(-0.474232\pi\) | ||||
0.0808634 | + | 0.996725i | \(0.474232\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.10549e27 | − | 7.10549e27i | −1.25501 | − | 1.25501i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.23364e27 | − | 1.23364e27i | 0.199445 | − | 0.199445i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.07425e28i | − | 1.59080i | −0.606087 | − | 0.795399i | \(-0.707262\pi\) | ||
0.606087 | − | 0.795399i | \(-0.292738\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.82418e27i | − | 0.654781i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.42774e27 | − | 4.42774e27i | 0.551191 | − | 0.551191i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.28942e27 | + | 7.28942e27i | 0.832802 | + | 0.832802i | 0.987899 | − | 0.155097i | \(-0.0495689\pi\) |
−0.155097 | + | 0.987899i | \(0.549569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.44202e27 | −0.466051 | −0.233026 | − | 0.972471i | \(-0.574863\pi\) | ||||
−0.233026 | + | 0.972471i | \(0.574863\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.85292e28 | 1.78643 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.61419e27 | + | 6.61419e27i | 0.586342 | + | 0.586342i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.43923e27 | − | 5.43923e27i | 0.443629 | − | 0.443629i | −0.449601 | − | 0.893230i | \(-0.648434\pi\) |
0.893230 | + | 0.449601i | \(0.148434\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.54127e27i | 0.340980i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.05886e27i | 0.488216i | 0.969748 | + | 0.244108i | \(0.0784952\pi\) | ||||
−0.969748 | + | 0.244108i | \(0.921505\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.17754e28 | − | 2.17754e28i | 1.38811 | − | 1.38811i | 0.558809 | − | 0.829297i | \(-0.311259\pi\) |
0.829297 | − | 0.558809i | \(-0.188741\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.13918e28 | − | 3.13918e28i | −1.84544 | − | 1.84544i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.36148e27 | 0.182343 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.83387e28 | −0.918424 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.53780e28 | + | 1.53780e28i | 0.711430 | + | 0.711430i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.89148e27 | − | 9.89148e27i | 0.422945 | − | 0.422945i | −0.463271 | − | 0.886216i | \(-0.653325\pi\) |
0.886216 | + | 0.463271i | \(0.153325\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.45214e28i | 0.969599i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.37160e27i | 0.159934i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.91822e27 | − | 1.91822e27i | 0.0649651 | − | 0.0649651i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.71548e28 | + | 4.71548e28i | 1.47915 | + | 1.47915i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.96713e28 | −0.862475 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.92405e28 | 2.13550 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.79524e28 | + | 4.79524e28i | 1.19872 | + | 1.19872i | 0.974549 | + | 0.224176i | \(0.0719690\pi\) |
0.224176 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.81199e27 | − | 7.81199e27i | 0.181234 | − | 0.181234i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.61799e27i | − | 0.0779332i | −0.999241 | − | 0.0389666i | \(-0.987593\pi\) | ||
0.999241 | − | 0.0389666i | \(-0.0124066\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.60366e28i | − | 0.921178i | −0.887614 | − | 0.460589i | \(-0.847638\pi\) | ||
0.887614 | − | 0.460589i | \(-0.152362\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.82332e28 | − | 7.82332e28i | 1.45486 | − | 1.45486i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.10975e28 | + | 4.10975e28i | 0.710614 | + | 0.710614i | 0.966664 | − | 0.256050i | \(-0.0824211\pi\) |
−0.256050 | + | 0.966664i | \(0.582421\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.10831e27 | 0.146502 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.39024e28 | −1.40562 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.54116e28 | − | 1.54116e28i | −0.214793 | − | 0.214793i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.19034e29 | + | 1.19034e29i | −1.54530 | + | 1.54530i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.36735e28i | 1.13323i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.38103e29i | − | 1.55758i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.48582e28 | + | 9.48582e28i | −0.997821 | + | 0.997821i | −0.999998 | − | 0.00217642i | \(-0.999307\pi\) |
0.00217642 | + | 0.999998i | \(0.499307\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.78544e28 | − | 3.78544e28i | −0.371542 | − | 0.371542i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.05144e29 | 2.79569 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.33751e29 | −1.14434 | −0.572168 | − | 0.820136i | \(-0.693898\pi\) | ||||
−0.572168 | + | 0.820136i | \(0.693898\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.18338e29 | − | 1.18338e29i | −0.945858 | − | 0.945858i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.67647e28 | + | 1.67647e28i | −0.125234 | + | 0.125234i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4.12676e29i | − | 2.88222i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 4.53059e28i | − | 0.295962i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.94151e27 | + | 1.94151e27i | −0.0118673 | + | 0.0118673i | −0.713016 | − | 0.701148i | \(-0.752671\pi\) |
0.701148 | + | 0.713016i | \(0.252671\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.03246e28 | + | 2.03246e28i | 0.116286 | + | 0.116286i | 0.762855 | − | 0.646569i | \(-0.223797\pi\) |
−0.646569 | + | 0.762855i | \(0.723797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.86748e28 | −0.421506 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.69206e28 | −0.135106 | −0.0675532 | − | 0.997716i | \(-0.521519\pi\) | ||||
−0.0675532 | + | 0.997716i | \(0.521519\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.53092e29 | − | 1.53092e29i | −0.719990 | − | 0.719990i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.07427e29 | − | 1.07427e29i | 0.473621 | − | 0.473621i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.01350e29i | − | 0.832465i | −0.909258 | − | 0.416233i | \(-0.863350\pi\) | ||
0.909258 | − | 0.416233i | \(-0.136650\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.38052e28i | 0.131115i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.22124e29 | + | 2.22124e29i | −0.808479 | + | 0.808479i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.62475e29 | + | 1.62475e29i | 0.555159 | + | 0.555159i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.32569e28 | 0.202978 | 0.101489 | − | 0.994837i | \(-0.467639\pi\) | ||||
0.101489 | + | 0.994837i | \(0.467639\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.79082e28 | 0.0539821 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.56201e29 | − | 1.56201e29i | −0.442469 | − | 0.442469i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.80897e29 | − | 2.80897e29i | 0.747989 | − | 0.747989i | −0.226112 | − | 0.974101i | \(-0.572602\pi\) |
0.974101 | + | 0.226112i | \(0.0726016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.83144e30i | 4.58599i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.63920e29i | 0.386106i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.80353e29 | + | 2.80353e29i | −0.621377 | + | 0.621377i | −0.945883 | − | 0.324507i | \(-0.894802\pi\) |
0.324507 | + | 0.945883i | \(0.394802\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.96613e28 | − | 7.96613e28i | −0.166192 | − | 0.166192i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.35364e29 | −0.658765 | −0.329383 | − | 0.944197i | \(-0.606841\pi\) | ||||
−0.329383 | + | 0.944197i | \(0.606841\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.77618e29 | 1.06867 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.51217e29 | + | 2.51217e29i | 0.437897 | + | 0.437897i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.08430e29 | + | 3.08430e29i | −0.506682 | + | 0.506682i | −0.913507 | − | 0.406824i | \(-0.866636\pi\) |
0.406824 | + | 0.913507i | \(0.366636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.22427e28i | − | 0.0344472i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.47660e29i | 1.38401i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.31193e29 | − | 3.31193e29i | 0.456262 | − | 0.456262i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.25999e29 | − | 2.25999e29i | −0.293776 | − | 0.293776i | 0.544794 | − | 0.838570i | \(-0.316608\pi\) |
−0.838570 | + | 0.544794i | \(0.816608\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.03285e30 | −2.49412 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.34782e30 | −1.56125 | −0.780624 | − | 0.625000i | \(-0.785099\pi\) | ||||
−0.780624 | + | 0.625000i | \(0.785099\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.01711e29 | − | 3.01711e29i | −0.330053 | − | 0.330053i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.67806e30 | + | 1.67806e30i | −1.73410 | + | 1.73410i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.79489e29i | − | 0.272916i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.63159e30i | − | 1.50589i | −0.658084 | − | 0.752944i | \(-0.728633\pi\) | ||
0.658084 | − | 0.752944i | \(-0.271367\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.36374e28 | + | 8.36374e28i | −0.0729827 | + | 0.0729827i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.93971e29 | + | 7.93971e29i | 0.655208 | + | 0.655208i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.04022e30 | −3.15393 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.21710e30 | −1.63765 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.98958e29 | + | 5.98958e29i | 0.418731 | + | 0.418731i | 0.884766 | − | 0.466035i | \(-0.154318\pi\) |
−0.466035 | + | 0.884766i | \(0.654318\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.98556e29 | − | 5.98556e29i | 0.396151 | − | 0.396151i | −0.480722 | − | 0.876873i | \(-0.659625\pi\) |
0.876873 | + | 0.480722i | \(0.159625\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 7.35743e29i | − | 0.461118i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.38026e30i | 0.819383i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.56570e30 | − | 2.56570e30i | 1.44307 | − | 1.44307i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.64417e29 | + | 3.64417e29i | 0.194240 | + | 0.194240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.71960e29 | −0.288986 | −0.144493 | − | 0.989506i | \(-0.546155\pi\) | ||||
−0.144493 | + | 0.989506i | \(0.546155\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.64080e30 | −1.26510 | −0.632551 | − | 0.774519i | \(-0.717992\pi\) | ||||
−0.632551 | + | 0.774519i | \(0.717992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.93579e30 | + | 1.93579e30i | 0.879493 | + | 0.879493i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.10449e29 | + | 2.10449e29i | −0.0907008 | + | 0.0907008i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.25796e29i | − | 0.0923366i | −0.998934 | − | 0.0461683i | \(-0.985299\pi\) | ||
0.998934 | − | 0.0461683i | \(-0.0147010\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 3.63235e30i | − | 1.40976i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.63800e29 | − | 5.63800e29i | 0.207722 | − | 0.207722i | −0.595577 | − | 0.803299i | \(-0.703076\pi\) |
0.803299 | + | 0.595577i | \(0.203076\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.48405e30 | + | 2.48405e30i | 0.869001 | + | 0.869001i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00348e30 | 1.99465 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.18945e30 | 1.00666 | 0.503330 | − | 0.864094i | \(-0.332108\pi\) | ||||
0.503330 | + | 0.864094i | \(0.332108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.61107e28 | + | 6.61107e28i | 0.0198263 | + | 0.0198263i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.09769e29 | − | 1.09769e29i | 0.0312861 | − | 0.0312861i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.03953e31i | 2.81646i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.87740e28i | 0.0125647i | 0.999980 | + | 0.00628235i | \(0.00199975\pi\) | ||||
−0.999980 | + | 0.00628235i | \(0.998000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.56135e29 | + | 4.56135e29i | −0.111750 | + | 0.111750i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.25019e30 | − | 2.25019e30i | −0.524394 | − | 0.524394i | 0.394501 | − | 0.918896i | \(-0.370917\pi\) |
−0.918896 | + | 0.394501i | \(0.870917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.96033e29 | −0.0434658 | −0.0217329 | − | 0.999764i | \(-0.506918\pi\) | ||||
−0.0217329 | + | 0.999764i | \(0.506918\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.12603e30 | −1.50362 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.11336e30 | − | 2.11336e30i | −0.424452 | − | 0.424452i | 0.462281 | − | 0.886733i | \(-0.347031\pi\) |
−0.886733 | + | 0.462281i | \(0.847031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.88015e30 | − | 9.88015e30i | 1.88919 | − | 1.88919i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 8.14883e30i | − | 1.48373i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.85480e30i | 0.321658i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.30593e31 | − | 1.30593e31i | 2.15747 | − | 2.15747i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.32157e29 | − | 8.32157e29i | −0.130992 | − | 0.130992i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.36090e30 | −1.10426 | −0.552131 | − | 0.833757i | \(-0.686185\pi\) | ||||
−0.552131 | + | 0.833757i | \(0.686185\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.02991e30 | 0.719270 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.46695e30 | − | 1.46695e30i | −0.199996 | − | 0.199996i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.62739e30 | + | 8.62739e30i | −1.12163 | + | 1.12163i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.98979e30i | 0.246731i | 0.992361 | + | 0.123365i | \(0.0393687\pi\) | ||||
−0.992361 | + | 0.123365i | \(0.960631\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.49116e29i | 0.0412970i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.44622e30 | + | 7.44622e30i | −0.840425 | + | 0.840425i | −0.988914 | − | 0.148489i | \(-0.952559\pi\) |
0.148489 | + | 0.988914i | \(0.452559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.50366e29 | + | 9.50366e29i | 0.102365 | + | 0.102365i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.07725e30 | 0.316376 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.91384e30 | −0.973069 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.80043e30 | − | 7.80043e30i | −0.731076 | − | 0.731076i | 0.239757 | − | 0.970833i | \(-0.422932\pi\) |
−0.970833 | + | 0.239757i | \(0.922932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.37216e30 | + | 1.37216e30i | −0.122820 | + | 0.122820i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.33936e31i | 1.14515i | 0.819851 | + | 0.572577i | \(0.194056\pi\) | ||||
−0.819851 | + | 0.572577i | \(0.805944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.66462e31i | − | 1.35977i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.74350e30 | − | 4.74350e30i | 0.370261 | − | 0.370261i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.56104e30 | + | 9.56104e30i | 0.713264 | + | 0.713264i | 0.967217 | − | 0.253952i | \(-0.0817306\pi\) |
−0.253952 | + | 0.967217i | \(0.581731\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.05214e31 | 0.750299 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.63146e30 | 0.588484 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.38269e30 | + | 4.38269e30i | 0.285731 | + | 0.285731i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.71610e30 | − | 2.71610e30i | 0.169357 | − | 0.169357i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.62641e31i | 2.16298i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.57417e31i | − | 1.46894i | −0.678641 | − | 0.734470i | \(-0.737431\pi\) | ||
0.678641 | − | 0.734470i | \(-0.262569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.61915e30 | − | 9.61915e30i | 0.525251 | − | 0.525251i | −0.393901 | − | 0.919153i | \(-0.628875\pi\) |
0.919153 | + | 0.393901i | \(0.128875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.10305e31 | + | 9.10305e31i | 4.75724 | + | 4.75724i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.49848e30 | −0.175008 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.05767e31 | 0.985454 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.22987e30 | + | 4.22987e30i | 0.193972 | + | 0.193972i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.18978e30 | + | 1.18978e30i | −0.0522521 | + | 0.0522521i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5.26811e31i | − | 2.21609i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5.47108e31i | − | 2.20480i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.34093e31 | − | 1.34093e31i | 0.517769 | − | 0.517769i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.95813e31 | − | 1.95813e31i | −0.724557 | − | 0.724557i | 0.244973 | − | 0.969530i | \(-0.421221\pi\) |
−0.969530 | + | 0.244973i | \(0.921221\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.89889e31 | −1.02810 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.25527e31 | −1.78663 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.30856e31 | + | 1.30856e31i | 0.426520 | + | 0.426520i | 0.887441 | − | 0.460921i | \(-0.152481\pi\) |
−0.460921 | + | 0.887441i | \(0.652481\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.36688e31 | − | 1.36688e31i | 0.427215 | − | 0.427215i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.79838e31i | − | 0.539061i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.14472e31i | − | 0.616639i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.94000e31 | − | 5.94000e31i | 1.63839 | − | 1.63839i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.67716e30 | + | 1.67716e30i | 0.0443854 | + | 0.0443854i | 0.728951 | − | 0.684566i | \(-0.240008\pi\) |
−0.684566 | + | 0.728951i | \(0.740008\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.33805e31 | −0.847728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.22559e30 | 0.102994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.89860e30 | + | 7.89860e30i | 0.184801 | + | 0.184801i | 0.793444 | − | 0.608643i | \(-0.208286\pi\) |
−0.608643 | + | 0.793444i | \(0.708286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.63897e31 | − | 6.63897e31i | 1.49123 | − | 1.49123i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.08667e32i | 2.34365i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4.64202e31i | − | 0.961426i | −0.876878 | − | 0.480713i | \(-0.840378\pi\) | ||
0.876878 | − | 0.480713i | \(-0.159622\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.74215e31 | − | 1.74215e31i | 0.346553 | − | 0.346553i | −0.512271 | − | 0.858824i | \(-0.671196\pi\) |
0.858824 | + | 0.512271i | \(0.171196\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.95592e31 | − | 2.95592e31i | −0.564825 | − | 0.564825i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.88477e31 | 0.346002 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.76828e31 | −0.311909 | −0.155955 | − | 0.987764i | \(-0.549845\pi\) | ||||
−0.155955 | + | 0.987764i | \(0.549845\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.60885e31 | − | 5.60885e31i | −0.950759 | − | 0.950759i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.30817e32 | + | 1.30817e32i | −2.13127 | + | 2.13127i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.14404e30i | − | 0.0962201i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.53806e31i | 0.833806i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.35811e31 | − | 5.35811e31i | 0.775664 | − | 0.775664i | −0.203427 | − | 0.979090i | \(-0.565208\pi\) |
0.979090 | + | 0.203427i | \(0.0652078\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.31009e31 | + | 3.31009e31i | 0.460802 | + | 0.460802i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.21659e32 | −1.62887 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.64929e31 | −1.24270 | −0.621350 | − | 0.783533i | \(-0.713416\pi\) | ||||
−0.621350 | + | 0.783533i | \(0.713416\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.02690e31 | + | 6.02690e31i | 0.746704 | + | 0.746704i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.76082e31 | − | 5.76082e31i | 0.686719 | − | 0.686719i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.21951e32i | 1.39886i | 0.714699 | + | 0.699432i | \(0.246564\pi\) | ||||
−0.714699 | + | 0.699432i | \(0.753436\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.50501e32i | 1.66143i | 0.556699 | + | 0.830714i | \(0.312068\pi\) | ||||
−0.556699 | + | 0.830714i | \(0.687932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.26364e31 | − | 5.26364e31i | 0.559290 | − | 0.559290i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.24616e32 | − | 1.24616e32i | −1.27464 | − | 1.27464i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.41878e31 | −0.829047 | −0.414523 | − | 0.910039i | \(-0.636052\pi\) | ||||
−0.414523 | + | 0.910039i | \(0.636052\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.25357e32 | 1.18864 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.88810e31 | + | 4.88810e31i | 0.446341 | + | 0.446341i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.36701e31 | − | 7.36701e31i | 0.647882 | − | 0.647882i | −0.304599 | − | 0.952481i | \(-0.598522\pi\) |
0.952481 | + | 0.304599i | \(0.0985224\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.81011e31i | 0.238045i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.78250e32i | 1.45462i | 0.686310 | + | 0.727309i | \(0.259229\pi\) | ||||
−0.686310 | + | 0.727309i | \(0.740771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.05467e32 | + | 1.05467e32i | −0.829225 | + | 0.829225i | −0.987410 | − | 0.158185i | \(-0.949436\pi\) |
0.158185 | + | 0.987410i | \(0.449436\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.22863e30 | + | 6.22863e30i | 0.0471888 | + | 0.0471888i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.60860e32 | 1.17446 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.19790e32 | −4.36138 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.99804e31 | − | 3.99804e31i | −0.271188 | − | 0.271188i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.91621e31 | − | 2.91621e31i | 0.190694 | − | 0.190694i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.35896e32i | − | 0.856780i | −0.903594 | − | 0.428390i | \(-0.859081\pi\) | ||
0.903594 | − | 0.428390i | \(-0.140919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.61268e31i | − | 0.0980408i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.46916e31 | − | 4.46916e31i | 0.262016 | − | 0.262016i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.41325e32 | + | 2.41325e32i | 1.36458 | + | 1.36458i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.28159e31 | −0.288074 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.63596e32 | 1.38698 | 0.693492 | − | 0.720464i | \(-0.256071\pi\) | ||||
0.693492 | + | 0.720464i | \(0.256071\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.62276e31 | − | 4.62276e31i | −0.234680 | − | 0.234680i | 0.579963 | − | 0.814643i | \(-0.303067\pi\) |
−0.814643 | + | 0.579963i | \(0.803067\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.94202e32 | + | 3.94202e32i | −1.93100 | + | 1.93100i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.71570e32i | 0.811040i | 0.914086 | + | 0.405520i | \(0.132910\pi\) | ||||
−0.914086 | + | 0.405520i | \(0.867090\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.12303e31i | 0.142483i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.30731e32 | + | 2.30731e32i | −1.01607 | + | 1.01607i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.18613e32 | + | 1.18613e32i | 0.504233 | + | 0.504233i | 0.912750 | − | 0.408517i | \(-0.133954\pi\) |
−0.408517 | + | 0.912750i | \(0.633954\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.31656e32 | −2.18201 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.60528e31 | 0.222124 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.26973e31 | + | 3.26973e31i | 0.125121 | + | 0.125121i | 0.766894 | − | 0.641773i | \(-0.221801\pi\) |
−0.641773 | + | 0.766894i | \(0.721801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.06496e32 | + | 1.06496e32i | −0.393566 | + | 0.393566i | −0.875956 | − | 0.482391i | \(-0.839769\pi\) |
0.482391 | + | 0.875956i | \(0.339769\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.60469e31i | 0.271441i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.14047e33i | − | 3.93220i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.29775e31 | − | 1.29775e31i | 0.0432257 | − | 0.0432257i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.67161e31 | − | 3.67161e31i | −0.118156 | − | 0.118156i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.00920e32 | 0.313812 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.76608e32 | −0.831172 | −0.415586 | − | 0.909554i | \(-0.636423\pi\) | ||||
−0.415586 | + | 0.909554i | \(0.636423\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.86514e32 | − | 3.86514e32i | −1.12246 | − | 1.12246i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.32911e32 | − | 3.32911e32i | 0.934455 | − | 0.934455i | −0.0635250 | − | 0.997980i | \(-0.520234\pi\) |
0.997980 | + | 0.0635250i | \(0.0202343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.58687e32i | 1.51589i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.88363e32i | 0.494087i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.04233e32 | + | 3.04233e32i | −0.771558 | + | 0.771558i | −0.978379 | − | 0.206821i | \(-0.933688\pi\) |
0.206821 | + | 0.978379i | \(0.433688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.69223e31 | − | 4.69223e31i | −0.115063 | − | 0.115063i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.88599e32 | −0.684372 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.10573e32 | 0.253588 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.88350e32 | + | 3.88350e32i | 0.861441 | + | 0.861441i | 0.991506 | − | 0.130065i | \(-0.0415184\pi\) |
−0.130065 | + | 0.991506i | \(0.541518\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.96373e31 | − | 9.96373e31i | 0.213791 | − | 0.213791i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.24384e33i | − | 2.58189i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.37961e31i | 0.0277063i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.19244e32 | − | 6.19244e32i | 1.20330 | − | 1.20330i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.88920e32 | − | 2.88920e32i | −0.543275 | − | 0.543275i | 0.381213 | − | 0.924487i | \(-0.375507\pi\) |
−0.924487 | + | 0.381213i | \(0.875507\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.51835e32 | −1.00421 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.15451e33 | 2.03339 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.38982e32 | − | 5.38982e32i | −0.918864 | − | 0.918864i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.50043e32 | + | 2.50043e32i | −0.412651 | + | 0.412651i | −0.882661 | − | 0.470010i | \(-0.844250\pi\) |
0.470010 | + | 0.882661i | \(0.344250\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.14260e32i | − | 0.182554i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.77726e31i | 0.0739008i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.04445e32 | + | 2.04445e32i | −0.306237 | + | 0.306237i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.02432e32 | + | 7.02432e32i | 1.01891 | + | 1.01891i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.60858e32 | 0.928380 | 0.464190 | − | 0.885736i | \(-0.346345\pi\) | ||||
0.464190 | + | 0.885736i | \(0.346345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.83811e32 | 0.386166 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.94494e32 | + | 5.94494e32i | 0.783532 | + | 0.783532i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.05309e32 | + | 8.05309e32i | −1.02819 | + | 1.02819i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.64076e31i | 0.0202955i | 0.999949 | + | 0.0101478i | \(0.00323019\pi\) | ||||
−0.999949 | + | 0.0101478i | \(0.996770\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.92431e30i | 0.00350475i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.93531e32 | + | 1.93531e32i | −0.224751 | + | 0.224751i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.35292e32 | − | 5.35292e32i | −0.602414 | − | 0.602414i | 0.338538 | − | 0.940953i | \(-0.390068\pi\) |
−0.940953 | + | 0.338538i | \(0.890068\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.69978e33 | 6.21661 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.88629e32 | 0.410827 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.31681e32 | − | 5.31681e32i | −0.544804 | − | 0.544804i | 0.380130 | − | 0.924933i | \(-0.375879\pi\) |
−0.924933 | + | 0.380130i | \(0.875879\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.19519e32 | − | 7.19519e32i | 0.714715 | − | 0.714715i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.11766e32i | 0.492834i | 0.969164 | + | 0.246417i | \(0.0792532\pi\) | ||||
−0.969164 | + | 0.246417i | \(0.920747\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.36807e33i | 3.14474i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.96926e32 | + | 6.96926e32i | −0.630957 | + | 0.630957i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.70575e33 | − | 1.70575e33i | −1.49752 | − | 1.49752i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.09027e33 | −0.928267 | −0.464133 | − | 0.885765i | \(-0.653634\pi\) | ||||
−0.464133 | + | 0.885765i | \(0.653634\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.45386e33 | −1.20055 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.15827e31 | + | 6.15827e31i | 0.0493252 | + | 0.0493252i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.46727e33 | − | 1.46727e33i | 1.14001 | − | 1.14001i | 0.151557 | − | 0.988449i | \(-0.451571\pi\) |
0.988449 | − | 0.151557i | \(-0.0484287\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.77013e31i | − | 0.0434916i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.58389e32i | 0.700839i | 0.936593 | + | 0.350419i | \(0.113961\pi\) | ||||
−0.936593 | + | 0.350419i | \(0.886039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.70159e33 | + | 1.70159e33i | −1.20732 | + | 1.20732i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.21082e32 | + | 3.21082e32i | 0.221060 | + | 0.221060i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.62045e32 | −0.375512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.03545e32 | −0.521023 | −0.260512 | − | 0.965471i | \(-0.583891\pi\) | ||||
−0.260512 | + | 0.965471i | \(0.583891\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.26707e32 | + | 2.26707e32i | 0.142672 | + | 0.142672i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.91141e32 | + | 9.91141e32i | −0.605440 | + | 0.605440i | −0.941751 | − | 0.336311i | \(-0.890821\pi\) |
0.336311 | + | 0.941751i | \(0.390821\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.96450e33i | − | 1.75785i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 3.84659e33i | − | 2.21429i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.30532e32 | − | 1.30532e32i | 0.0729516 | − | 0.0729516i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.94977e32 | − | 1.94977e32i | −0.105803 | − | 0.105803i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.32263e32 | −0.280457 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.57165e33 | 2.33923 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.09360e33 | + | 2.09360e33i | 1.04036 | + | 1.04036i | 0.999150 | + | 0.0412119i | \(0.0131219\pi\) |
0.0412119 | + | 0.999150i | \(0.486878\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.90775e33 | − | 2.90775e33i | 1.40337 | − | 1.40337i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.29922e33i | − | 2.01540i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.81624e33i | 0.827049i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.30580e33 | − | 1.30580e33i | 0.577635 | − | 0.577635i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.26822e33 | − | 3.26822e33i | −1.40456 | − | 1.40456i | −0.784756 | − | 0.619805i | \(-0.787212\pi\) |
−0.619805 | − | 0.784756i | \(-0.712788\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.66798e32 | 0.236669 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.56982e32 | 0.347695 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.06927e32 | + | 2.06927e32i | 0.0815807 | + | 0.0815807i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.22986e32 | − | 8.22986e32i | 0.315312 | − | 0.315312i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.94616e33i | 1.46936i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.60492e33i | 0.580824i | 0.956902 | + | 0.290412i | \(0.0937924\pi\) | ||||
−0.956902 | + | 0.290412i | \(0.906208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.22096e33 | − | 2.22096e33i | 0.781270 | − | 0.781270i | −0.198775 | − | 0.980045i | \(-0.563696\pi\) |
0.980045 | + | 0.198775i | \(0.0636964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.20235e33 | − | 1.20235e33i | −0.411141 | − | 0.411141i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.95861e32 | −0.0651083 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.66219e33 | 1.18355 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.79315e33 | + | 1.79315e33i | 0.563446 | + | 0.563446i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.89933e33 | + | 3.89933e33i | −1.19136 | + | 1.19136i | −0.214676 | + | 0.976685i | \(0.568870\pi\) |
−0.976685 | + | 0.214676i | \(0.931130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.16137e33i | − | 0.345042i | −0.985006 | − | 0.172521i | \(-0.944809\pi\) | ||
0.985006 | − | 0.172521i | \(-0.0551913\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.58062e33i | 1.03452i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.77941e33 | − | 1.77941e33i | 0.499992 | − | 0.499992i | −0.411444 | − | 0.911435i | \(-0.634975\pi\) |
0.911435 | + | 0.411444i | \(0.134975\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.65065e32 | + | 3.65065e32i | 0.0997683 | + | 0.0997683i | 0.755229 | − | 0.655461i | \(-0.227526\pi\) |
−0.655461 | + | 0.755229i | \(0.727526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.94455e33 | 0.782721 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.79827e33 | 0.723557 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.69808e32 | − | 7.69808e32i | −0.193637 | − | 0.193637i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.79682e32 | − | 9.79682e32i | 0.239741 | − | 0.239741i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.96177e32i | − | 0.118134i | −0.998254 | − | 0.0590669i | \(-0.981187\pi\) | ||
0.998254 | − | 0.0590669i | \(-0.0188125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 3.20774e33i | − | 0.743097i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.91067e33 | + | 1.91067e33i | −0.430695 | + | 0.430695i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.66120e33 | + | 2.66120e33i | 0.583748 | + | 0.583748i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.06979e33 | −1.72267 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.17882e34 | 2.44912 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.98215e32 | − | 3.98215e32i | −0.0805244 | − | 0.0805244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.43738e33 | − | 1.43738e33i | 0.282917 | − | 0.282917i | −0.551354 | − | 0.834271i | \(-0.685889\pi\) |
0.834271 | + | 0.551354i | \(0.185889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.07584e33i | − | 1.16412i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.00126e33i | 0.746307i | 0.927770 | + | 0.373153i | \(0.121723\pi\) | ||||
−0.927770 | + | 0.373153i | \(0.878277\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.56085e33 | − | 5.56085e33i | 1.00976 | − | 1.00976i | 0.00981133 | − | 0.999952i | \(-0.496877\pi\) |
0.999952 | − | 0.00981133i | \(-0.00312309\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.09876e32 | + | 9.09876e32i | 0.160859 | + | 0.160859i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.88999e33 | −1.18603 | −0.593014 | − | 0.805192i | \(-0.702062\pi\) | ||||
−0.593014 | + | 0.805192i | \(0.702062\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.03449e34 | −3.41013 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.96387e33 | − | 4.96387e33i | −0.810215 | − | 0.810215i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.21805e32 | − | 4.21805e32i | 0.0670477 | − | 0.0670477i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.99407e33i | 1.08273i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.97640e33i | 0.448774i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.32683e34 | + | 3.32683e34i | −4.88583 | + | 4.88583i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.71470e33 | − | 5.71470e33i | −0.817519 | − | 0.817519i | 0.168229 | − | 0.985748i | \(-0.446195\pi\) |
−0.985748 | + | 0.168229i | \(0.946195\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.35480e33 | 0.746227 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.34532e33 | −0.861452 | −0.430726 | − | 0.902483i | \(-0.641742\pi\) | ||||
−0.430726 | + | 0.902483i | \(0.641742\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.69292e33 | − | 8.69292e33i | −1.14979 | − | 1.14979i | −0.986594 | − | 0.163194i | \(-0.947820\pi\) |
−0.163194 | − | 0.986594i | \(-0.552180\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.63739e33 | + | 6.63739e33i | −0.855361 | + | 0.855361i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.18530e34i | − | 1.48836i | −0.667982 | − | 0.744178i | \(-0.732842\pi\) | ||
0.667982 | − | 0.744178i | \(-0.267158\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.89411e33i | − | 0.354115i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.13717e33 | + | 2.13717e33i | −0.254827 | + | 0.254827i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.36277e33 | − | 5.36277e33i | −0.623157 | − | 0.623157i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.06938e34 | 3.47605 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.03844e33 | 0.114622 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.04119e33 | − | 2.04119e33i | −0.219607 | − | 0.219607i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.41073e32 | − | 6.41073e32i | 0.0672314 | − | 0.0672314i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.55275e34i | 2.60975i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.62633e34i | − | 1.62088i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.64414e33 | + | 2.64414e33i | −0.256921 | + | 0.256921i | −0.823801 | − | 0.566879i | \(-0.808151\pi\) |
0.566879 | + | 0.823801i | \(0.308151\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.87142e33 | − | 2.87142e33i | −0.272027 | − | 0.272027i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.75129e33 | −0.715999 | −0.358000 | − | 0.933722i | \(-0.616541\pi\) | ||||
−0.358000 | + | 0.933722i | \(0.616541\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.14560e33 | −0.463470 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.14486e34 | + | 2.14486e34i | 1.88389 | + | 1.88389i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.72143e34 | + | 1.72143e34i | −1.47449 | + | 1.47449i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.55693e34i | − | 1.30059i | −0.759680 | − | 0.650297i | \(-0.774645\pi\) | ||
0.759680 | − | 0.650297i | \(-0.225355\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.59593e34i | 2.11498i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.50896e33 | − | 3.50896e33i | 0.278842 | − | 0.278842i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.47110e34 | + | 2.47110e34i | 1.91540 | + | 1.91540i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.51200e33 | 0.114323 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.86088e34 | 1.37258 | 0.686290 | − | 0.727328i | \(-0.259238\pi\) | ||||
0.686290 | + | 0.727328i | \(0.259238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.64759e34 | − | 2.64759e34i | −1.90515 | − | 1.90515i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.79306e32 | − | 9.79306e32i | 0.0687511 | − | 0.0687511i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.37064e33i | 0.162380i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.57732e33i | 0.239085i | 0.992829 | + | 0.119543i | \(0.0381428\pi\) | ||||
−0.992829 | + | 0.119543i | \(0.961857\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.24611e34 | − | 1.24611e34i | 0.812645 | − | 0.812645i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.01549e33 | − | 7.01549e33i | −0.446455 | − | 0.446455i | 0.447719 | − | 0.894174i | \(-0.352236\pi\) |
−0.894174 | + | 0.447719i | \(0.852236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.88388e32 | 0.0116996 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.37543e34 | −2.04580 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.89121e34 | + | 1.89121e34i | 1.11870 | + | 1.11870i | 0.991932 | + | 0.126773i | \(0.0404619\pi\) |
0.126773 | + | 0.991932i | \(0.459538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.72401e33 | + | 3.72401e33i | −0.215006 | + | 0.215006i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.22483e34i | 1.25378i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.18956e33i | − | 0.395489i | −0.980254 | − | 0.197744i | \(-0.936638\pi\) | ||
0.980254 | − | 0.197744i | \(-0.0633616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.65833e34 | − | 1.65833e34i | 0.890496 | − | 0.890496i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.46541e33 | + | 2.46541e33i | 0.129242 | + | 0.129242i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.03856e33 | −0.155509 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.24993e34 | −0.624550 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.08734e33 | − | 9.08734e33i | −0.443337 | − | 0.443337i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.14668e34 | − | 3.14668e34i | 1.49895 | − | 1.49895i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.64651e33i | − | 0.169618i | −0.996397 | − | 0.0848092i | \(-0.972972\pi\) | ||
0.996397 | − | 0.0848092i | \(-0.0270281\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 8.34316e33i | − | 0.378972i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.24084e34 | − | 2.24084e34i | 0.994008 | − | 0.994008i | −0.00597423 | − | 0.999982i | \(-0.501902\pi\) |
0.999982 | + | 0.00597423i | \(0.00190167\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.02738e34 | − | 4.02738e34i | −1.74472 | − | 1.74472i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.44397e34 | −2.72647 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.46442e34 | 1.43167 | 0.715836 | − | 0.698268i | \(-0.246046\pi\) | ||||
0.715836 | + | 0.698268i | \(0.246046\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.16367e33 | + | 3.16367e33i | 0.127700 | + | 0.127700i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.06518e33 | + | 9.06518e33i | −0.357423 | + | 0.357423i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.88177e34i | − | 1.10993i | −0.831875 | − | 0.554963i | \(-0.812733\pi\) | ||
0.831875 | − | 0.554963i | \(-0.187267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.82529e34i | − | 2.56806i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.73814e34 | − | 3.73814e34i | 1.37407 | − | 1.37407i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.64271e33 | + | 2.64271e33i | 0.0949057 | + | 0.0949057i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.19719e34 | −1.12182 | −0.560908 | − | 0.827878i | \(-0.689548\pi\) | ||||
−0.560908 | + | 0.827878i | \(0.689548\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.13519e34 | −1.76052 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.23193e34 | + | 3.23193e34i | 1.08267 | + | 1.08267i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.97178e34 | + | 1.97178e34i | −0.645453 | + | 0.645453i | −0.951891 | − | 0.306438i | \(-0.900863\pi\) |
0.306438 | + | 0.951891i | \(0.400863\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.63326e34i | 0.522458i |
(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 | 64.24.e.a.17.36 | 90 | ||
4.3 | odd | 2 | 16.24.e.a.13.28 | yes | 90 | ||
16.5 | even | 4 | inner | 64.24.e.a.49.36 | 90 | ||
16.11 | odd | 4 | 16.24.e.a.5.28 | ✓ | 90 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.24.e.a.5.28 | ✓ | 90 | 16.11 | odd | 4 | ||
16.24.e.a.13.28 | yes | 90 | 4.3 | odd | 2 | ||
64.24.e.a.17.36 | 90 | 1.1 | even | 1 | trivial | ||
64.24.e.a.49.36 | 90 | 16.5 | even | 4 | inner |