Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,18,Mod(19,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.19");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.b (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: | \(82.4499393051\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - 1682025200 x^{14} - 16813165927404 x^{13} + \cdots + 36\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{73}\cdot 3^{42}\cdot 5^{34} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.5 | ||
Root | \(-4797.27 + 2068.52i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.19 |
Dual form | 45.18.b.c.19.11 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 406.510i | − | 1.12284i | −0.827532 | − | 0.561418i | \(-0.810256\pi\) | ||
0.827532 | − | 0.561418i | \(-0.189744\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −34178.7 | −0.260762 | ||||||||
\(5\) | −228254. | − | 843113.i | −0.261321 | − | 0.965252i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.76153e7i | 1.81057i | 0.424801 | + | 0.905287i | \(0.360344\pi\) | ||||
−0.424801 | + | 0.905287i | \(0.639656\pi\) | |||||||
\(8\) | − | 3.93881e7i | − | 0.830043i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.42734e8 | + | 9.27876e7i | −1.08382 | + | 0.293420i | ||||
\(11\) | 5.76916e8 | 0.811474 | 0.405737 | − | 0.913990i | \(-0.367015\pi\) | ||||
0.405737 | + | 0.913990i | \(0.367015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.01577e9i | − | 1.02537i | −0.858577 | − | 0.512685i | \(-0.828651\pi\) | ||
0.858577 | − | 0.512685i | \(-0.171349\pi\) | |||||||
\(14\) | 1.12259e10 | 2.03298 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.04916e10 | −1.19277 | ||||||||
\(17\) | 2.06445e10i | 0.717774i | 0.933381 | + | 0.358887i | \(0.116844\pi\) | ||||
−0.933381 | + | 0.358887i | \(0.883156\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.38783e10 | −0.187470 | −0.0937349 | − | 0.995597i | \(-0.529881\pi\) | ||||
−0.0937349 | + | 0.995597i | \(0.529881\pi\) | |||||||
\(20\) | 7.80142e9 | + | 2.88165e10i | 0.0681426 | + | 0.251702i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.34522e11i | − | 0.911153i | ||||||
\(23\) | − | 5.15758e11i | − | 1.37328i | −0.726998 | − | 0.686640i | \(-0.759085\pi\) | ||
0.726998 | − | 0.686640i | \(-0.240915\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.58740e11 | + | 3.84888e11i | −0.863423 | + | 0.504480i | ||||
\(26\) | −1.22594e12 | −1.15132 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 9.43853e11i | − | 0.472130i | ||||||
\(29\) | 5.86433e11 | 0.217689 | 0.108844 | − | 0.994059i | \(-0.465285\pi\) | ||||
0.108844 | + | 0.994059i | \(0.465285\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.42601e12 | −0.510878 | −0.255439 | − | 0.966825i | \(-0.582220\pi\) | ||||
−0.255439 | + | 0.966825i | \(0.582220\pi\) | |||||||
\(32\) | 3.16735e12i | 0.509238i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.39218e12 | 0.805943 | ||||||||
\(35\) | 2.32828e13 | − | 6.30330e12i | 1.74766 | − | 0.473140i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.73827e13i | 0.813586i | 0.913520 | + | 0.406793i | \(0.133353\pi\) | ||||
−0.913520 | + | 0.406793i | \(0.866647\pi\) | |||||||
\(38\) | 5.64168e12i | 0.210498i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.32087e13 | + | 8.99051e12i | −0.801201 | + | 0.216907i | ||||
\(41\) | −8.77960e13 | −1.71716 | −0.858582 | − | 0.512676i | \(-0.828654\pi\) | ||||
−0.858582 | + | 0.512676i | \(0.828654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.31458e14i | − | 1.71516i | −0.514352 | − | 0.857579i | \(-0.671968\pi\) | ||
0.514352 | − | 0.857579i | \(-0.328032\pi\) | |||||||
\(44\) | −1.97182e13 | −0.211602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.09661e14 | −1.54197 | ||||||||
\(47\) | 7.43721e12i | 0.0455594i | 0.999741 | + | 0.0227797i | \(0.00725164\pi\) | ||||
−0.999741 | + | 0.0227797i | \(0.992748\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.29973e14 | −2.27818 | ||||||||
\(50\) | 1.56461e14 | + | 2.67784e14i | 0.566449 | + | 0.969483i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.03075e14i | 0.267378i | ||||||||
\(53\) | − | 3.75793e14i | − | 0.829093i | −0.910028 | − | 0.414546i | \(-0.863940\pi\) | ||
0.910028 | − | 0.414546i | \(-0.136060\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.31683e14 | − | 4.86405e14i | −0.212055 | − | 0.783277i | ||||
\(56\) | 1.08771e15 | 1.50285 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 2.38391e14i | − | 0.244429i | ||||||
\(59\) | −1.43476e15 | −1.27215 | −0.636074 | − | 0.771628i | \(-0.719443\pi\) | ||||
−0.636074 | + | 0.771628i | \(0.719443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.34695e14 | −0.624261 | −0.312131 | − | 0.950039i | \(-0.601043\pi\) | ||||
−0.312131 | + | 0.950039i | \(0.601043\pi\) | |||||||
\(62\) | 9.86197e14i | 0.573633i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.39831e15 | −0.620974 | ||||||||
\(65\) | −2.54264e15 | + | 6.88363e14i | −0.989740 | + | 0.267950i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.23567e15i | 1.87606i | 0.346552 | + | 0.938031i | \(0.387352\pi\) | ||||
−0.346552 | + | 0.938031i | \(0.612648\pi\) | |||||||
\(68\) | − | 7.05600e14i | − | 0.187168i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.56236e15 | − | 9.46470e15i | −0.531259 | − | 1.96234i | ||||
\(71\) | −5.20405e14 | −0.0956414 | −0.0478207 | − | 0.998856i | \(-0.515228\pi\) | ||||
−0.0478207 | + | 0.998856i | \(0.515228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.30547e15i | − | 0.479721i | −0.970807 | − | 0.239861i | \(-0.922898\pi\) | ||
0.970807 | − | 0.239861i | \(-0.0771018\pi\) | |||||||
\(74\) | 7.06626e15 | 0.913524 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.74343e14 | 0.0488851 | ||||||||
\(77\) | 1.59317e16i | 1.46923i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.77897e16 | 1.31928 | 0.659641 | − | 0.751581i | \(-0.270708\pi\) | ||||
0.659641 | + | 0.751581i | \(0.270708\pi\) | |||||||
\(80\) | 4.67728e15 | + | 1.72767e16i | 0.311694 | + | 1.15132i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.56900e16i | 1.92810i | ||||||||
\(83\) | 4.82164e15i | 0.234980i | 0.993074 | + | 0.117490i | \(0.0374848\pi\) | ||||
−0.993074 | + | 0.117490i | \(0.962515\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.74056e16 | − | 4.71218e15i | 0.692833 | − | 0.187569i | ||||
\(86\) | −5.34389e16 | −1.92584 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.27236e16i | − | 0.673558i | ||||||
\(89\) | −5.87120e15 | −0.158093 | −0.0790464 | − | 0.996871i | \(-0.525188\pi\) | ||||
−0.0790464 | + | 0.996871i | \(0.525188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.32815e16 | 1.85651 | ||||||||
\(92\) | 1.76279e16i | 0.358100i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.02330e15 | 0.0511558 | ||||||||
\(95\) | 3.16778e15 | + | 1.17010e16i | 0.0489897 | + | 0.180956i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.56736e16i | 1.10991i | 0.831881 | + | 0.554954i | \(0.187264\pi\) | ||||
−0.831881 | + | 0.554954i | \(0.812736\pi\) | |||||||
\(98\) | 2.15440e17i | 2.55802i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.25148e16 | − | 1.31550e16i | 0.225148 | − | 0.131550i | ||||
\(101\) | 1.19416e17 | 1.09732 | 0.548659 | − | 0.836046i | \(-0.315139\pi\) | ||||
0.548659 | + | 0.836046i | \(0.315139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.36777e16i | − | 0.261954i | −0.991385 | − | 0.130977i | \(-0.958189\pi\) | ||
0.991385 | − | 0.130977i | \(-0.0418115\pi\) | |||||||
\(104\) | −1.18786e17 | −0.851101 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.52764e17 | −0.930936 | ||||||||
\(107\) | 3.12377e17i | 1.75759i | 0.477201 | + | 0.878794i | \(0.341651\pi\) | ||||
−0.477201 | + | 0.878794i | \(0.658349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.72558e17 | −0.829486 | −0.414743 | − | 0.909939i | \(-0.636129\pi\) | ||||
−0.414743 | + | 0.909939i | \(0.636129\pi\) | |||||||
\(110\) | −1.97729e17 | + | 5.35306e16i | −0.879492 | + | 0.238103i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 5.65880e17i | − | 2.15959i | ||||||
\(113\) | 3.26931e17i | 1.15688i | 0.815724 | + | 0.578441i | \(0.196339\pi\) | ||||
−0.815724 | + | 0.578441i | \(0.803661\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.34842e17 | + | 1.17724e17i | −1.32556 | + | 0.358866i | ||||
\(116\) | −2.00435e16 | −0.0567650 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.83245e17i | 1.42841i | ||||||||
\(119\) | −5.70102e17 | −1.29958 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.72615e17 | −0.341510 | ||||||||
\(122\) | 3.79963e17i | 0.700944i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.29177e16 | 0.133218 | ||||||||
\(125\) | 4.74864e17 | + | 4.67540e17i | 0.712581 | + | 0.701590i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.88589e17i | − | 1.29624i | −0.761540 | − | 0.648118i | \(-0.775556\pi\) | ||
0.761540 | − | 0.648118i | \(-0.224444\pi\) | |||||||
\(128\) | 9.83578e17i | 1.20649i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.79827e17 | + | 1.03361e18i | 0.300864 | + | 1.11132i | ||||
\(131\) | −1.16109e18 | −1.16966 | −0.584829 | − | 0.811156i | \(-0.698838\pi\) | ||||
−0.584829 | + | 0.811156i | \(0.698838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.83254e17i | − | 0.339428i | ||||||
\(134\) | 2.53486e18 | 2.10651 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.13147e17 | 0.595783 | ||||||||
\(137\) | − | 5.68166e17i | − | 0.391156i | −0.980688 | − | 0.195578i | \(-0.937342\pi\) | ||
0.980688 | − | 0.195578i | \(-0.0626583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.75129e18 | −1.06594 | −0.532970 | − | 0.846134i | \(-0.678924\pi\) | ||||
−0.532970 | + | 0.846134i | \(0.678924\pi\) | |||||||
\(140\) | −7.95775e17 | + | 2.15438e17i | −0.455724 | + | 0.123377i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.11550e17i | 0.107390i | ||||||||
\(143\) | − | 1.73985e18i | − | 0.832060i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.33856e17 | − | 4.94430e17i | −0.0568865 | − | 0.210124i | ||||
\(146\) | −1.34371e18 | −0.538649 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 5.94118e17i | − | 0.212153i | ||||||
\(149\) | −3.57309e18 | −1.20493 | −0.602463 | − | 0.798147i | \(-0.705814\pi\) | ||||
−0.602463 | + | 0.798147i | \(0.705814\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.80045e18 | 1.14428 | 0.572138 | − | 0.820158i | \(-0.306114\pi\) | ||||
0.572138 | + | 0.820158i | \(0.306114\pi\) | |||||||
\(152\) | 5.46641e17i | 0.155608i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.47639e18 | 1.64971 | ||||||||
\(155\) | 5.53746e17 | + | 2.04540e18i | 0.133503 | + | 0.493127i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.04103e18i | 1.52226i | 0.648599 | + | 0.761130i | \(0.275355\pi\) | ||||
−0.648599 | + | 0.761130i | \(0.724645\pi\) | |||||||
\(158\) | − | 7.23168e18i | − | 1.48134i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.67043e18 | − | 7.22960e17i | 0.491543 | − | 0.133074i | ||||
\(161\) | 1.42428e19 | 2.48642 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.70935e17i | − | 0.121178i | −0.998163 | − | 0.0605889i | \(-0.980702\pi\) | ||
0.998163 | − | 0.0605889i | \(-0.0192979\pi\) | |||||||
\(164\) | 3.00075e18 | 0.447772 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.96005e18 | 0.263844 | ||||||||
\(167\) | − | 1.34073e19i | − | 1.71496i | −0.514521 | − | 0.857478i | \(-0.672030\pi\) | ||
0.514521 | − | 0.857478i | \(-0.327970\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.44482e17 | −0.0513827 | ||||||||
\(170\) | −1.91555e18 | − | 7.07556e18i | −0.210609 | − | 0.777938i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.49305e18i | 0.447249i | ||||||||
\(173\) | 7.18352e17i | 0.0680684i | 0.999421 | + | 0.0340342i | \(0.0108355\pi\) | ||||
−0.999421 | + | 0.0340342i | \(0.989164\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.06288e19 | − | 1.81913e19i | −0.913399 | − | 1.56329i | ||||
\(176\) | −1.18219e19 | −0.967898 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.38671e18i | 0.177512i | ||||||||
\(179\) | −6.38506e18 | −0.452808 | −0.226404 | − | 0.974033i | \(-0.572697\pi\) | ||||
−0.226404 | + | 0.974033i | \(0.572697\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.44646e19 | −1.57860 | −0.789298 | − | 0.614010i | \(-0.789555\pi\) | ||||
−0.789298 | + | 0.614010i | \(0.789555\pi\) | |||||||
\(182\) | − | 3.38548e19i | − | 2.08455i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.03147e19 | −1.13988 | ||||||||
\(185\) | 1.46556e19 | − | 3.96768e18i | 0.785315 | − | 0.212607i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.19101e19i | 0.582455i | ||||||||
\(188\) | − | 2.54194e17i | − | 0.0118802i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.75658e18 | − | 1.28774e18i | 0.203184 | − | 0.0550075i | ||||
\(191\) | −5.68053e18 | −0.232063 | −0.116031 | − | 0.993246i | \(-0.537017\pi\) | ||||
−0.116031 | + | 0.993246i | \(0.537017\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.05325e19i | − | 1.14163i | −0.821078 | − | 0.570815i | \(-0.806627\pi\) | ||
0.821078 | − | 0.570815i | \(-0.193373\pi\) | |||||||
\(194\) | 3.48272e19 | 1.24625 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.81138e19 | 0.594063 | ||||||||
\(197\) | − | 2.61548e19i | − | 0.821462i | −0.911756 | − | 0.410731i | \(-0.865273\pi\) | ||
0.911756 | − | 0.410731i | \(-0.134727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.21379e19 | −0.926331 | −0.463165 | − | 0.886272i | \(-0.653286\pi\) | ||||
−0.463165 | + | 0.886272i | \(0.653286\pi\) | |||||||
\(200\) | 1.51600e19 | + | 2.59465e19i | 0.418740 | + | 0.716678i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 4.85440e19i | − | 1.23211i | ||||||
\(203\) | 1.61945e19i | 0.394141i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00398e19 | + | 7.40219e19i | 0.448730 | + | 1.65750i | ||||
\(206\) | −1.36903e19 | −0.294132 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.17979e19i | 1.22303i | ||||||||
\(209\) | −8.00662e18 | −0.152127 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.63855e19 | −0.812797 | −0.406398 | − | 0.913696i | \(-0.633215\pi\) | ||||
−0.406398 | + | 0.913696i | \(0.633215\pi\) | |||||||
\(212\) | 1.28441e19i | 0.216196i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.26985e20 | 1.97348 | ||||||||
\(215\) | −1.10834e20 | + | 3.00058e19i | −1.65556 | + | 0.448206i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.69948e19i | − | 0.924983i | ||||||
\(218\) | 7.01465e19i | 0.931378i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.50076e18 | + | 1.66247e19i | 0.0552959 | + | 0.204249i | ||||
\(221\) | 6.22590e19 | 0.735983 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.37347e19i | − | 0.369390i | −0.982796 | − | 0.184695i | \(-0.940870\pi\) | ||
0.982796 | − | 0.184695i | \(-0.0591297\pi\) | |||||||
\(224\) | −8.74671e19 | −0.922012 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.32901e20 | 1.29899 | ||||||||
\(227\) | − | 1.21995e20i | − | 1.14848i | −0.818687 | − | 0.574240i | \(-0.805298\pi\) | ||
0.818687 | − | 0.574240i | \(-0.194702\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.07669e18 | −0.00940781 | −0.00470390 | − | 0.999989i | \(-0.501497\pi\) | ||||
−0.00470390 | + | 0.999989i | \(0.501497\pi\) | |||||||
\(230\) | 4.78559e19 | + | 1.76768e20i | 0.402948 | + | 1.48839i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 2.30985e19i | − | 0.180691i | ||||||
\(233\) | 1.45399e20i | 1.09657i | 0.836291 | + | 0.548286i | \(0.184719\pi\) | ||||
−0.836291 | + | 0.548286i | \(0.815281\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.27041e18 | − | 1.69757e18i | 0.0439763 | − | 0.0119056i | ||||
\(236\) | 4.90382e19 | 0.331728 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.31752e20i | 1.45922i | ||||||||
\(239\) | 5.65041e19 | 0.343319 | 0.171660 | − | 0.985156i | \(-0.445087\pi\) | ||||
0.171660 | + | 0.985156i | \(0.445087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.58771e20 | −0.898723 | −0.449362 | − | 0.893350i | \(-0.648349\pi\) | ||||
−0.449362 | + | 0.893350i | \(0.648349\pi\) | |||||||
\(242\) | 7.01700e19i | 0.383460i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.19466e19 | 0.162784 | ||||||||
\(245\) | 1.20969e20 | + | 4.46827e20i | 0.595334 | + | 2.19901i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.18539e19i | 0.192226i | ||||||||
\(248\) | 9.55559e19i | 0.424051i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.90060e20 | − | 1.93037e20i | 0.787771 | − | 0.800112i | ||||
\(251\) | −3.89569e20 | −1.56084 | −0.780419 | − | 0.625257i | \(-0.784994\pi\) | ||||
−0.780419 | + | 0.625257i | \(0.784994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.97549e20i | − | 1.11438i | ||||||
\(254\) | −4.01872e20 | −1.45546 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.16555e20 | 0.733718 | ||||||||
\(257\) | − | 4.60902e20i | − | 1.51070i | −0.655323 | − | 0.755349i | \(-0.727468\pi\) | ||
0.655323 | − | 0.755349i | \(-0.272532\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.80029e20 | −1.47306 | ||||||||
\(260\) | 8.69040e19 | − | 2.35273e19i | 0.258087 | − | 0.0698713i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.71994e20i | 1.31334i | ||||||||
\(263\) | 3.43800e20i | 0.926152i | 0.886319 | + | 0.463076i | \(0.153254\pi\) | ||||
−0.886319 | + | 0.463076i | \(0.846746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.16836e20 | + | 8.57762e19i | −0.800284 | + | 0.216659i | ||||
\(266\) | −1.55797e20 | −0.381122 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 2.13127e20i | − | 0.489206i | ||||||
\(269\) | 8.38824e20 | 1.86542 | 0.932709 | − | 0.360630i | \(-0.117438\pi\) | ||||
0.932709 | + | 0.360630i | \(0.117438\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.68360e20 | −0.978004 | −0.489002 | − | 0.872283i | \(-0.662639\pi\) | ||||
−0.489002 | + | 0.872283i | \(0.662639\pi\) | |||||||
\(272\) | − | 4.23037e20i | − | 0.856136i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.30965e20 | −0.439204 | ||||||||
\(275\) | −3.80037e20 | + | 2.22048e20i | −0.700645 | + | 0.409373i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.95652e20i | 0.512511i | 0.966609 | + | 0.256255i | \(0.0824888\pi\) | ||||
−0.966609 | + | 0.256255i | \(0.917511\pi\) | |||||||
\(278\) | 7.11919e20i | 1.19688i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.48275e20 | − | 9.17066e20i | −0.392727 | − | 1.45063i | ||||
\(281\) | 8.72471e20 | 1.33890 | 0.669449 | − | 0.742858i | \(-0.266530\pi\) | ||||
0.669449 | + | 0.742858i | \(0.266530\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.61943e20i | − | 1.24536i | −0.782478 | − | 0.622679i | \(-0.786044\pi\) | ||
0.782478 | − | 0.622679i | \(-0.213956\pi\) | |||||||
\(284\) | 1.77868e19 | 0.0249397 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.07266e20 | −0.934268 | ||||||||
\(287\) | − | 2.42451e21i | − | 3.10905i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.01047e20 | 0.484801 | ||||||||
\(290\) | −2.00991e20 | + | 5.44138e19i | −0.235935 | + | 0.0638743i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.12977e20i | 0.125093i | ||||||||
\(293\) | − | 9.43270e20i | − | 1.01452i | −0.861793 | − | 0.507261i | \(-0.830658\pi\) | ||
0.861793 | − | 0.507261i | \(-0.169342\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.27490e20 | + | 1.20967e21i | 0.332438 | + | 1.22794i | ||||
\(296\) | 6.84673e20 | 0.675311 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.45250e21i | 1.35294i | ||||||||
\(299\) | −1.55541e21 | −1.40812 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.63024e21 | 3.10542 | ||||||||
\(302\) | − | 1.54492e21i | − | 1.28483i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.84388e20 | 0.223608 | ||||||||
\(305\) | 2.13348e20 | + | 7.88054e20i | 0.163132 | + | 0.602570i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.17966e20i | − | 0.157656i | −0.996888 | − | 0.0788282i | \(-0.974882\pi\) | ||
0.996888 | − | 0.0788282i | \(-0.0251179\pi\) | |||||||
\(308\) | − | 5.44524e20i | − | 0.383121i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.31475e20 | − | 2.25103e20i | 0.553701 | − | 0.149902i | ||||
\(311\) | −9.25823e20 | −0.599881 | −0.299940 | − | 0.953958i | \(-0.596967\pi\) | ||||
−0.299940 | + | 0.953958i | \(0.596967\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.69108e20i | 0.533269i | 0.963798 | + | 0.266635i | \(0.0859117\pi\) | ||||
−0.963798 | + | 0.266635i | \(0.914088\pi\) | |||||||
\(314\) | 2.86225e21 | 1.70925 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.08027e20 | −0.344019 | ||||||||
\(317\) | − | 2.17713e21i | − | 1.19917i | −0.800311 | − | 0.599585i | \(-0.795332\pi\) | ||
0.800311 | − | 0.599585i | \(-0.204668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.38323e20 | 0.176649 | ||||||||
\(320\) | 3.19170e20 | + | 1.17893e21i | 0.162273 | + | 0.599397i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 5.78984e21i | − | 2.79185i | ||||||
\(323\) | − | 2.86510e20i | − | 0.134561i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.16074e21 | + | 1.98661e21i | 0.517279 | + | 0.885328i | ||||
\(326\) | −3.13393e20 | −0.136063 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.45812e21i | 1.42532i | ||||||||
\(329\) | −2.05381e20 | −0.0824887 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.33411e20 | −0.241628 | −0.120814 | − | 0.992675i | \(-0.538550\pi\) | ||||
−0.120814 | + | 0.992675i | \(0.538550\pi\) | |||||||
\(332\) | − | 1.64797e20i | − | 0.0612739i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.45022e21 | −1.92561 | ||||||||
\(335\) | 5.25737e21 | − | 1.42332e21i | 1.81087 | − | 0.490253i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.43586e21i | 0.797624i | 0.917033 | + | 0.398812i | \(0.130577\pi\) | ||||
−0.917033 | + | 0.398812i | \(0.869423\pi\) | |||||||
\(338\) | 1.80686e20i | 0.0576944i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.94900e20 | + | 1.61056e20i | −0.180665 | + | 0.0489110i | ||||
\(341\) | −1.39960e21 | −0.414564 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.21120e21i | − | 2.31423i | ||||||
\(344\) | −5.17787e21 | −1.42366 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.92017e20 | 0.0764296 | ||||||||
\(347\) | 3.46482e20i | 0.0884872i | 0.999021 | + | 0.0442436i | \(0.0140878\pi\) | ||||
−0.999021 | + | 0.0442436i | \(0.985912\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.55028e21 | 0.377045 | 0.188523 | − | 0.982069i | \(-0.439630\pi\) | ||||
0.188523 | + | 0.982069i | \(0.439630\pi\) | |||||||
\(350\) | −7.39494e21 | + | 4.32071e21i | −1.75532 | + | 1.02560i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.82729e21i | 0.413233i | ||||||||
\(353\) | − | 2.37357e21i | − | 0.523983i | −0.965070 | − | 0.261991i | \(-0.915621\pi\) | ||
0.965070 | − | 0.261991i | \(-0.0843792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.18785e20 | + | 4.38760e20i | 0.0249931 | + | 0.0923180i | ||||
\(356\) | 2.00670e20 | 0.0412247 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.59559e21i | 0.508430i | ||||||||
\(359\) | 3.60101e21 | 0.688845 | 0.344422 | − | 0.938815i | \(-0.388075\pi\) | ||||
0.344422 | + | 0.938815i | \(0.388075\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.28778e21 | −0.964855 | ||||||||
\(362\) | 9.94513e21i | 1.77251i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.84645e21 | −0.484107 | ||||||||
\(365\) | −2.78689e21 | + | 7.54487e20i | −0.463052 | + | 0.125361i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.76857e21i | 0.597744i | 0.954293 | + | 0.298872i | \(0.0966103\pi\) | ||||
−0.954293 | + | 0.298872i | \(0.903390\pi\) | |||||||
\(368\) | 1.05687e22i | 1.63800i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.61290e21 | − | 5.95765e21i | −0.238723 | − | 0.881781i | ||||
\(371\) | 1.03776e22 | 1.50113 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.76930e21i | − | 0.244498i | −0.992499 | − | 0.122249i | \(-0.960989\pi\) | ||
0.992499 | − | 0.122249i | \(-0.0390107\pi\) | |||||||
\(374\) | 4.84158e21 | 0.654001 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.92938e20 | 0.0378163 | ||||||||
\(377\) | − | 1.76855e21i | − | 0.223211i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.86999e21 | −1.19092 | −0.595461 | − | 0.803384i | \(-0.703031\pi\) | ||||
−0.595461 | + | 0.803384i | \(0.703031\pi\) | |||||||
\(380\) | −1.08271e20 | − | 3.99924e20i | −0.0127747 | − | 0.0471864i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.30919e21i | 0.260569i | ||||||||
\(383\) | 7.21179e21i | 0.795891i | 0.917409 | + | 0.397945i | \(0.130277\pi\) | ||||
−0.917409 | + | 0.397945i | \(0.869723\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.34322e22 | − | 3.63647e21i | 1.41818 | − | 0.383941i | ||||
\(386\) | −1.24118e22 | −1.28187 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 2.92821e21i | − | 0.289423i | ||||||
\(389\) | −1.09989e22 | −1.06360 | −0.531801 | − | 0.846869i | \(-0.678485\pi\) | ||||
−0.531801 | + | 0.846869i | \(0.678485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.06475e22 | 0.985704 | ||||||||
\(392\) | 2.08747e22i | 1.89098i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.06322e22 | −0.922368 | ||||||||
\(395\) | −4.06056e21 | − | 1.49987e22i | −0.344755 | − | 1.27344i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.36745e22i | 1.11222i | 0.831109 | + | 0.556110i | \(0.187707\pi\) | ||||
−0.831109 | + | 0.556110i | \(0.812293\pi\) | |||||||
\(398\) | 1.30644e22i | 1.04012i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.34986e22 | − | 7.88695e21i | 1.02986 | − | 0.601727i | ||||
\(401\) | −1.56760e22 | −1.17087 | −0.585433 | − | 0.810721i | \(-0.699075\pi\) | ||||
−0.585433 | + | 0.810721i | \(0.699075\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.31629e21i | 0.523839i | ||||||||
\(404\) | −4.08149e21 | −0.286139 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.58324e21 | 0.442556 | ||||||||
\(407\) | 1.00284e22i | 0.660203i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.18697e22 | 0.749533 | 0.374766 | − | 0.927119i | \(-0.377723\pi\) | ||||
0.374766 | + | 0.927119i | \(0.377723\pi\) | |||||||
\(410\) | 3.00907e22 | − | 8.14638e21i | 1.86110 | − | 0.503851i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.15106e21i | 0.0683078i | ||||||||
\(413\) | − | 3.96213e22i | − | 2.30332i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.06518e21 | − | 1.10056e21i | 0.226815 | − | 0.0614051i | ||||
\(416\) | 9.55200e21 | 0.522157 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.25477e21i | 0.170814i | ||||||||
\(419\) | 2.22648e22 | 1.14498 | 0.572491 | − | 0.819911i | \(-0.305977\pi\) | ||||
0.572491 | + | 0.819911i | \(0.305977\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.10465e22 | 1.03940 | 0.519698 | − | 0.854350i | \(-0.326044\pi\) | ||||
0.519698 | + | 0.854350i | \(0.326044\pi\) | |||||||
\(422\) | 1.88562e22i | 0.912638i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.48018e22 | −0.688183 | ||||||||
\(425\) | −7.94580e21 | − | 1.35993e22i | −0.362103 | − | 0.619742i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.58119e22i | − | 1.13027i | ||||||
\(428\) | − | 1.06766e22i | − | 0.458313i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.21977e22 | + | 4.50550e22i | 0.503262 | + | 1.85892i | ||||
\(431\) | 2.49277e22 | 1.00838 | 0.504192 | − | 0.863592i | \(-0.331791\pi\) | ||||
0.504192 | + | 0.863592i | \(0.331791\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.04908e21i | 0.351931i | 0.984396 | + | 0.175966i | \(0.0563047\pi\) | ||||
−0.984396 | + | 0.175966i | \(0.943695\pi\) | |||||||
\(434\) | −2.72341e22 | −1.03860 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.89779e21 | 0.216299 | ||||||||
\(437\) | 7.15785e21i | 0.257449i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.79196e22 | −1.31194 | −0.655971 | − | 0.754786i | \(-0.727741\pi\) | ||||
−0.655971 | + | 0.754786i | \(0.727741\pi\) | |||||||
\(440\) | −1.91586e22 | + | 5.18676e21i | −0.650153 | + | 0.176015i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.53089e22i | − | 0.826389i | ||||||
\(443\) | − | 5.78605e22i | − | 1.85332i | −0.375901 | − | 0.926660i | \(-0.622667\pi\) | ||
0.375901 | − | 0.926660i | \(-0.377333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.34013e21 | + | 4.95009e21i | 0.0413129 | + | 0.152599i | ||||
\(446\) | −1.37135e22 | −0.414765 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3.86147e22i | − | 1.12432i | ||||||
\(449\) | 2.41383e22 | 0.689626 | 0.344813 | − | 0.938671i | \(-0.387942\pi\) | ||||
0.344813 | + | 0.938671i | \(0.387942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.06509e22 | −1.39343 | ||||||||
\(452\) | − | 1.11741e22i | − | 0.301671i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.95924e22 | −1.28956 | ||||||||
\(455\) | −1.90093e22 | − | 7.02157e22i | −0.485143 | − | 1.79200i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.01994e22i | − | 1.48015i | −0.672527 | − | 0.740073i | \(-0.734791\pi\) | ||
0.672527 | − | 0.740073i | \(-0.265209\pi\) | |||||||
\(458\) | 4.37685e20i | 0.0105634i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.48623e22 | − | 4.02364e21i | 0.345657 | − | 0.0935788i | ||||
\(461\) | 4.47482e22 | 1.02169 | 0.510843 | − | 0.859674i | \(-0.329333\pi\) | ||||
0.510843 | + | 0.859674i | \(0.329333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.17509e22i | 1.13888i | 0.822032 | + | 0.569442i | \(0.192841\pi\) | ||||
−0.822032 | + | 0.569442i | \(0.807159\pi\) | |||||||
\(464\) | −1.20169e22 | −0.259651 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.91063e22 | 1.23127 | ||||||||
\(467\) | 1.60093e22i | 0.327476i | 0.986504 | + | 0.163738i | \(0.0523551\pi\) | ||||
−0.986504 | + | 0.163738i | \(0.947645\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.72200e23 | −3.39675 | ||||||||
\(470\) | −6.90081e20 | − | 2.54899e21i | −0.0133681 | − | 0.0493782i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.65126e22i | 1.05594i | ||||||||
\(473\) | − | 7.58400e22i | − | 1.39181i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.14220e21 | − | 5.34160e21i | 0.161866 | − | 0.0945749i | ||||
\(476\) | 1.94853e22 | 0.338882 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 2.29695e22i | − | 0.385491i | ||||||
\(479\) | 5.80933e22 | 0.957799 | 0.478900 | − | 0.877870i | \(-0.341036\pi\) | ||||
0.478900 | + | 0.877870i | \(0.341036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.24224e22 | 0.834226 | ||||||||
\(482\) | 6.45420e22i | 1.00912i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.89976e21 | 0.0890531 | ||||||||
\(485\) | 7.22325e22 | − | 1.95553e22i | 1.07134 | − | 0.290042i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.89874e21i | 0.0701597i | 0.999385 | + | 0.0350799i | \(0.0111686\pi\) | ||||
−0.999385 | + | 0.0350799i | \(0.988831\pi\) | |||||||
\(488\) | 3.68159e22i | 0.518164i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.81640e23 | − | 4.91750e22i | 2.46913 | − | 0.668463i | ||||
\(491\) | −1.07129e23 | −1.43124 | −0.715622 | − | 0.698487i | \(-0.753857\pi\) | ||||
−0.715622 | + | 0.698487i | \(0.753857\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.21066e22i | 0.156251i | ||||||||
\(494\) | 1.70140e22 | 0.215838 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.97126e22 | 0.609358 | ||||||||
\(497\) | − | 1.43711e22i | − | 0.173166i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.77173e22 | 0.322772 | 0.161386 | − | 0.986891i | \(-0.448404\pi\) | ||||
0.161386 | + | 0.986891i | \(0.448404\pi\) | |||||||
\(500\) | −1.62302e22 | − | 1.59799e22i | −0.185814 | − | 0.182948i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.58364e23i | 1.75257i | ||||||||
\(503\) | 1.29566e22i | 0.140981i | 0.997512 | + | 0.0704907i | \(0.0224565\pi\) | ||||
−0.997512 | + | 0.0704907i | \(0.977543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.72573e22 | − | 1.00682e23i | −0.286752 | − | 1.05919i | ||||
\(506\) | −1.20957e23 | −1.25127 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.37886e22i | 0.338010i | ||||||||
\(509\) | −1.02047e23 | −1.00392 | −0.501962 | − | 0.864890i | \(-0.667388\pi\) | ||||
−0.501962 | + | 0.864890i | \(0.667388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.12815e22 | 0.868571 | ||||||||
\(512\) | 4.08876e22i | 0.382645i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.87362e23 | −1.69627 | ||||||||
\(515\) | −2.83941e22 | + | 7.68706e21i | −0.252852 | + | 0.0684540i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.29064e21i | 0.0369703i | ||||||||
\(518\) | 1.95137e23i | 1.65400i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.71133e22 | + | 1.00150e23i | 0.222410 | + | 0.821527i | ||||
\(521\) | 1.08882e23 | 0.878687 | 0.439343 | − | 0.898319i | \(-0.355211\pi\) | ||||
0.439343 | + | 0.898319i | \(0.355211\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.32948e22i | − | 0.650659i | −0.945601 | − | 0.325330i | \(-0.894525\pi\) | ||
0.945601 | − | 0.325330i | \(-0.105475\pi\) | |||||||
\(524\) | 3.96844e22 | 0.305003 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.39758e23 | 1.03992 | ||||||||
\(527\) | − | 5.00836e22i | − | 0.366695i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.24956e23 | −0.885897 | ||||||||
\(530\) | 3.48689e22 | + | 1.28797e23i | 0.243273 | + | 0.898588i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.30991e22i | 0.0885101i | ||||||||
\(533\) | 2.64773e23i | 1.76073i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.63369e23 | − | 7.13014e22i | 1.69652 | − | 0.459294i | ||||
\(536\) | 2.45611e23 | 1.55721 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 3.40990e23i | − | 2.09456i | ||||||
\(539\) | −3.05750e23 | −1.84868 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.32060e23 | −0.773738 | −0.386869 | − | 0.922135i | \(-0.626443\pi\) | ||||
−0.386869 | + | 0.922135i | \(0.626443\pi\) | |||||||
\(542\) | 1.90393e23i | 1.09814i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.53881e22 | −0.365518 | ||||||||
\(545\) | 3.93870e22 | + | 1.45486e23i | 0.216762 | + | 0.800663i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.89705e23i | 1.01201i | 0.862529 | + | 0.506007i | \(0.168879\pi\) | ||||
−0.862529 | + | 0.506007i | \(0.831121\pi\) | |||||||
\(548\) | 1.94191e22i | 0.101999i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.02648e22 | + | 1.54489e23i | 0.459659 | + | 0.786710i | ||||
\(551\) | −8.13871e21 | −0.0408101 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.91267e23i | 2.38866i | ||||||||
\(554\) | 1.20186e23 | 0.575466 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.98569e22 | 0.277957 | ||||||||
\(557\) | − | 4.23248e23i | − | 1.93564i | −0.251634 | − | 0.967822i | \(-0.580968\pi\) | ||
0.251634 | − | 0.967822i | \(-0.419032\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.96447e23 | −1.75867 | ||||||||
\(560\) | −4.77101e23 | + | 1.29164e23i | −2.08455 | + | 0.564345i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 3.54668e23i | − | 1.50336i | ||||||
\(563\) | − | 2.54744e23i | − | 1.06361i | −0.846866 | − | 0.531806i | \(-0.821514\pi\) | ||
0.846866 | − | 0.531806i | \(-0.178486\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.75640e23 | − | 7.46233e22i | 1.11668 | − | 0.302317i | ||||
\(566\) | −3.50389e23 | −1.39833 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.04978e22i | 0.0793865i | ||||||||
\(569\) | 3.72274e23 | 1.42039 | 0.710196 | − | 0.704004i | \(-0.248607\pi\) | ||||
0.710196 | + | 0.704004i | \(0.248607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.97336e23 | 0.730803 | 0.365401 | − | 0.930850i | \(-0.380932\pi\) | ||||
0.365401 | + | 0.930850i | \(0.380932\pi\) | |||||||
\(572\) | 5.94657e22i | 0.216970i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.85589e23 | −3.49096 | ||||||||
\(575\) | 1.98509e23 | + | 3.39750e23i | 0.692793 | + | 1.18572i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4.79665e23i | − | 1.62534i | −0.582725 | − | 0.812669i | \(-0.698014\pi\) | ||
0.582725 | − | 0.812669i | \(-0.301986\pi\) | |||||||
\(578\) | − | 1.63030e23i | − | 0.544352i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.57501e21 | + | 1.68989e22i | 0.0148339 | + | 0.0547926i | ||||
\(581\) | −1.33151e23 | −0.425448 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.16801e23i | − | 0.672787i | ||||||
\(584\) | −1.30196e23 | −0.398189 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.83449e23 | −1.13914 | ||||||||
\(587\) | 2.27706e22i | 0.0666732i | 0.999444 | + | 0.0333366i | \(0.0106133\pi\) | ||||
−0.999444 | + | 0.0333366i | \(0.989387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.36689e22 | 0.0957743 | ||||||||
\(590\) | 4.91742e23 | − | 1.33128e23i | 1.37878 | − | 0.373274i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 3.56199e23i | − | 0.970417i | ||||||
\(593\) | 3.58690e23i | 0.963285i | 0.876368 | + | 0.481642i | \(0.159960\pi\) | ||||
−0.876368 | + | 0.481642i | \(0.840040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.30128e23 | + | 4.80661e23i | 0.339607 | + | 1.25442i | ||||
\(596\) | 1.22123e23 | 0.314200 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.32290e23i | 1.58109i | ||||||||
\(599\) | 2.42668e23 | 0.598252 | 0.299126 | − | 0.954214i | \(-0.403305\pi\) | ||||
0.299126 | + | 0.954214i | \(0.403305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.07797e23 | 0.258328 | 0.129164 | − | 0.991623i | \(-0.458771\pi\) | ||||
0.129164 | + | 0.991623i | \(0.458771\pi\) | |||||||
\(602\) | − | 1.47573e24i | − | 3.48688i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.29894e23 | −0.298384 | ||||||||
\(605\) | 3.94002e22 | + | 1.45534e23i | 0.0892437 | + | 0.329644i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.37475e23i | 0.302775i | 0.988475 | + | 0.151387i | \(0.0483741\pi\) | ||||
−0.988475 | + | 0.151387i | \(0.951626\pi\) | |||||||
\(608\) | − | 4.39574e22i | − | 0.0954667i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.20352e23 | − | 8.67282e22i | 0.676587 | − | 0.183171i | ||||
\(611\) | 2.24289e22 | 0.0467152 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 2.80694e23i | − | 0.568616i | −0.958733 | − | 0.284308i | \(-0.908236\pi\) | ||
0.958733 | − | 0.284308i | \(-0.0917639\pi\) | |||||||
\(614\) | −8.86053e22 | −0.177022 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.27520e23 | 1.21953 | ||||||||
\(617\) | − | 4.17822e23i | − | 0.800880i | −0.916323 | − | 0.400440i | \(-0.868857\pi\) | ||
0.916323 | − | 0.400440i | \(-0.131143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.32143e23 | 0.992335 | 0.496167 | − | 0.868227i | \(-0.334740\pi\) | ||||
0.496167 | + | 0.868227i | \(0.334740\pi\) | |||||||
\(620\) | −1.89263e22 | − | 6.99090e22i | −0.0348126 | − | 0.128589i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.76357e23i | 0.673568i | ||||||||
\(623\) | − | 1.62135e23i | − | 0.286239i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.85799e23 | − | 5.07082e23i | 0.490999 | − | 0.871160i | ||||
\(626\) | 3.53301e23 | 0.598775 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 2.40653e23i | − | 0.396948i | ||||||
\(629\) | −3.58857e23 | −0.583970 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.07303e24 | 1.69965 | 0.849827 | − | 0.527062i | \(-0.176707\pi\) | ||||
0.849827 | + | 0.527062i | \(0.176707\pi\) | |||||||
\(632\) | − | 7.00702e23i | − | 1.09506i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.85027e23 | −1.34647 | ||||||||
\(635\) | −8.33492e23 | + | 2.25649e23i | −1.25119 | + | 0.338733i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.59828e24i | 2.33597i | ||||||||
\(638\) | − | 1.37532e23i | − | 0.198348i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.29267e23 | − | 2.24506e23i | 1.16457 | − | 0.315281i | ||||
\(641\) | −1.05579e22 | −0.0146314 | −0.00731568 | − | 0.999973i | \(-0.502329\pi\) | ||||
−0.00731568 | + | 0.999973i | \(0.502329\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4.81305e23i | − | 0.649572i | −0.945788 | − | 0.324786i | \(-0.894708\pi\) | ||
0.945788 | − | 0.324786i | \(-0.105292\pi\) | |||||||
\(644\) | −4.86799e23 | −0.648366 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.16469e23 | −0.151090 | ||||||||
\(647\) | − | 3.51093e23i | − | 0.449506i | −0.974416 | − | 0.224753i | \(-0.927843\pi\) | ||
0.974416 | − | 0.224753i | \(-0.0721575\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.27736e23 | −1.03231 | ||||||||
\(650\) | 8.07578e23 | − | 4.71851e23i | 0.994079 | − | 0.580820i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.63495e22i | 0.0315986i | ||||||||
\(653\) | − | 2.41714e23i | − | 0.286114i | −0.989714 | − | 0.143057i | \(-0.954307\pi\) | ||
0.989714 | − | 0.143057i | \(-0.0456932\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.65023e23 | + | 9.78928e23i | 0.305656 | + | 1.12902i | ||||
\(656\) | 1.79908e24 | 2.04817 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.34893e22i | 0.0926213i | ||||||||
\(659\) | 6.59216e23 | 0.721941 | 0.360970 | − | 0.932577i | \(-0.382446\pi\) | ||||
0.360970 | + | 0.932577i | \(0.382446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.91029e23 | 0.203886 | 0.101943 | − | 0.994790i | \(-0.467494\pi\) | ||||
0.101943 | + | 0.994790i | \(0.467494\pi\) | |||||||
\(662\) | 2.57488e23i | 0.271309i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.89915e23 | 0.195043 | ||||||||
\(665\) | −3.23126e23 | + | 8.74792e22i | −0.327633 | + | 0.0886995i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.02457e23i | − | 0.298947i | ||||||
\(668\) | 4.58245e23i | 0.447196i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.78593e23 | − | 2.13718e24i | −0.550475 | − | 2.03331i | ||||
\(671\) | −5.39240e23 | −0.506572 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.46782e24i | − | 1.34445i | −0.740346 | − | 0.672226i | \(-0.765338\pi\) | ||
0.740346 | − | 0.672226i | \(-0.234662\pi\) | |||||||
\(674\) | 9.90202e23 | 0.895601 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.51918e22 | 0.0133987 | ||||||||
\(677\) | 1.35936e24i | 1.18394i | 0.805959 | + | 0.591971i | \(0.201650\pi\) | ||||
−0.805959 | + | 0.591971i | \(0.798350\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.36590e24 | −2.00957 | ||||||||
\(680\) | −1.85604e23 | − | 6.85575e23i | −0.155690 | − | 0.575081i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.68952e23i | 0.465488i | ||||||||
\(683\) | 1.20522e24i | 0.973849i | 0.873444 | + | 0.486925i | \(0.161881\pi\) | ||||
−0.873444 | + | 0.486925i | \(0.838119\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.79028e23 | + | 1.29686e23i | −0.377564 | + | 0.102217i | ||||
\(686\) | −3.33794e24 | −2.59850 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.69377e24i | 2.04578i | ||||||||
\(689\) | −1.13331e24 | −0.850127 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.07458e24 | −0.786459 | −0.393230 | − | 0.919440i | \(-0.628642\pi\) | ||||
−0.393230 | + | 0.919440i | \(0.628642\pi\) | |||||||
\(692\) | − | 2.45523e22i | − | 0.0177497i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.40849e23 | 0.0993567 | ||||||||
\(695\) | 3.99740e23 | + | 1.47654e24i | 0.278552 | + | 1.02890i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.81250e24i | − | 1.23254i | ||||||
\(698\) | − | 6.30204e23i | − | 0.423361i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.63278e23 | + | 6.21753e23i | 0.238180 | + | 0.407648i | ||||
\(701\) | −5.52035e23 | −0.357572 | −0.178786 | − | 0.983888i | \(-0.557217\pi\) | ||||
−0.178786 | + | 0.983888i | \(0.557217\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.41243e23i | − | 0.152523i | ||||||
\(704\) | −8.06707e23 | −0.503904 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.64881e23 | −0.588347 | ||||||||
\(707\) | 3.29772e24i | 1.98677i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.00912e24 | 0.593541 | 0.296770 | − | 0.954949i | \(-0.404090\pi\) | ||||
0.296770 | + | 0.954949i | \(0.404090\pi\) | |||||||
\(710\) | 1.78361e23 | − | 4.82872e22i | 0.103658 | − | 0.0280631i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.31256e23i | 0.131224i | ||||||||
\(713\) | 1.25123e24i | 0.701579i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.46689e24 | + | 3.97127e23i | −0.803148 | + | 0.217434i | ||||
\(716\) | 2.18233e23 | 0.118075 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 1.46385e24i | − | 0.773460i | ||||||
\(719\) | 2.57522e24 | 1.34468 | 0.672341 | − | 0.740242i | \(-0.265289\pi\) | ||||
0.672341 | + | 0.740242i | \(0.265289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.30018e23 | 0.474287 | ||||||||
\(722\) | 2.14954e24i | 1.08337i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.36169e23 | 0.411639 | ||||||||
\(725\) | −3.86307e23 | + | 2.25711e23i | −0.187957 | + | 0.109820i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.13745e24i | − | 0.540618i | −0.962774 | − | 0.270309i | \(-0.912874\pi\) | ||
0.962774 | − | 0.270309i | \(-0.0871258\pi\) | |||||||
\(728\) | − | 3.28030e24i | − | 1.54098i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.06707e23 | + | 1.13290e24i | 0.140760 | + | 0.519932i | ||||
\(731\) | 2.71387e24 | 1.23110 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.98752e24i | 1.32412i | 0.749452 | + | 0.662059i | \(0.230317\pi\) | ||||
−0.749452 | + | 0.662059i | \(0.769683\pi\) | |||||||
\(734\) | 1.53196e24 | 0.671168 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.63358e24 | 0.699326 | ||||||||
\(737\) | 3.59745e24i | 1.52237i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.33260e24 | 0.964635 | 0.482318 | − | 0.875996i | \(-0.339795\pi\) | ||||
0.482318 | + | 0.875996i | \(0.339795\pi\) | |||||||
\(740\) | −5.00909e23 | + | 1.35610e23i | −0.204781 | + | 0.0554398i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 4.21861e24i | − | 1.68553i | ||||||
\(743\) | 3.28616e22i | 0.0129803i | 0.999979 | + | 0.00649013i | \(0.00206589\pi\) | ||||
−0.999979 | + | 0.00649013i | \(0.997934\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.15572e23 | + | 3.01252e24i | 0.314872 | + | 1.16306i | ||||
\(746\) | −7.19238e23 | −0.274532 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 4.07071e23i | − | 0.151882i | ||||||
\(749\) | −8.62638e24 | −3.18224 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.79989e24 | −1.37035 | −0.685174 | − | 0.728379i | \(-0.740274\pi\) | ||||
−0.685174 | + | 0.728379i | \(0.740274\pi\) | |||||||
\(752\) | − | 1.52400e23i | − | 0.0543417i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.18934e23 | −0.250630 | ||||||||
\(755\) | −8.67467e23 | − | 3.20421e24i | −0.299023 | − | 1.10451i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.22264e24i | 0.749123i | 0.927202 | + | 0.374562i | \(0.122207\pi\) | ||||
−0.927202 | + | 0.374562i | \(0.877793\pi\) | |||||||
\(758\) | 4.01225e24i | 1.33721i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.60881e23 | − | 1.24773e23i | 0.150201 | − | 0.0406636i | ||||
\(761\) | 2.61895e24 | 0.844028 | 0.422014 | − | 0.906589i | \(-0.361323\pi\) | ||||
0.422014 | + | 0.906589i | \(0.361323\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4.76523e24i | − | 1.50185i | ||||||
\(764\) | 1.94153e23 | 0.0605132 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.93167e24 | 0.893656 | ||||||||
\(767\) | 4.32692e24i | 1.30442i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.71387e23 | 0.286430 | 0.143215 | − | 0.989692i | \(-0.454256\pi\) | ||||
0.143215 | + | 0.989692i | \(0.454256\pi\) | |||||||
\(770\) | −1.47826e24 | − | 5.46033e24i | −0.431103 | − | 1.59238i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.04356e24i | 0.297695i | ||||||||
\(773\) | − | 5.61109e24i | − | 1.58315i | −0.611072 | − | 0.791575i | \(-0.709262\pi\) | ||
0.611072 | − | 0.791575i | \(-0.290738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.59811e24 | − | 9.33741e23i | 0.441104 | − | 0.257728i | ||||
\(776\) | 3.37452e24 | 0.921272 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.47118e24i | 1.19425i | ||||||||
\(779\) | 1.21846e24 | 0.321917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.00230e23 | −0.0776105 | ||||||||
\(782\) | − | 4.32833e24i | − | 1.10678i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.08600e25 | 2.71733 | ||||||||
\(785\) | 5.93638e24 | − | 1.60714e24i | 1.46937 | − | 0.397798i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.78702e23i | 0.188619i | 0.995543 | + | 0.0943097i | \(0.0300644\pi\) | ||||
−0.995543 | + | 0.0943097i | \(0.969936\pi\) | |||||||
\(788\) | 8.93934e23i | 0.214207i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.09713e24 | + | 1.65066e24i | −1.42986 | + | 0.387104i | ||||
\(791\) | −9.02828e24 | −2.09462 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.81883e24i | 0.640099i | ||||||||
\(794\) | 5.55881e24 | 1.24884 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.09843e24 | 0.241552 | ||||||||
\(797\) | 2.98087e24i | 0.648555i | 0.945962 | + | 0.324278i | \(0.105121\pi\) | ||||
−0.945962 | + | 0.324278i | \(0.894879\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.53537e23 | −0.0327014 | ||||||||
\(800\) | −1.21907e24 | − | 2.08646e24i | −0.256900 | − | 0.439688i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.37244e24i | 1.31469i | ||||||||
\(803\) | − | 1.90698e24i | − | 0.389281i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.25097e24 | − | 1.20083e25i | −0.649753 | − | 2.40003i | ||||
\(806\) | 2.97415e24 | 0.588186 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 4.70359e24i | − | 0.910821i | ||||||
\(809\) | 8.38770e24 | 1.60724 | 0.803619 | − | 0.595144i | \(-0.202905\pi\) | ||||
0.803619 | + | 0.595144i | \(0.202905\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.93252e24 | −1.11317 | −0.556585 | − | 0.830790i | \(-0.687889\pi\) | ||||
−0.556585 | + | 0.830790i | \(0.687889\pi\) | |||||||
\(812\) | − | 5.53507e23i | − | 0.102777i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.07663e24 | 0.741301 | ||||||||
\(815\) | −6.49985e23 | + | 1.75969e23i | −0.116967 | + | 0.0316662i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.82441e24i | 0.321540i | ||||||||
\(818\) | − | 4.82514e24i | − | 0.841603i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.84933e23 | − | 2.52997e24i | −0.117012 | − | 0.432213i | ||||
\(821\) | −5.48179e24 | −0.926842 | −0.463421 | − | 0.886138i | \(-0.653378\pi\) | ||||
−0.463421 | + | 0.886138i | \(0.653378\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.56562e22i | 0.00259291i | 0.999999 | + | 0.00129646i | \(0.000412675\pi\) | ||||
−0.999999 | + | 0.00129646i | \(0.999587\pi\) | |||||||
\(824\) | −1.32650e24 | −0.217433 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.61065e25 | −2.58625 | ||||||||
\(827\) | − | 7.60751e24i | − | 1.20905i | −0.796584 | − | 0.604527i | \(-0.793362\pi\) | ||
0.796584 | − | 0.604527i | \(-0.206638\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.32131e24 | 0.205727 | 0.102863 | − | 0.994695i | \(-0.467200\pi\) | ||||
0.102863 | + | 0.994695i | \(0.467200\pi\) | |||||||
\(830\) | −4.47388e23 | − | 1.65254e24i | −0.0689479 | − | 0.254676i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.21699e24i | 0.636728i | ||||||||
\(833\) | − | 1.09410e25i | − | 1.63521i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.13039e25 | + | 3.06028e24i | −1.65536 | + | 0.448153i | ||||
\(836\) | 2.73656e23 | 0.0396690 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 9.05085e24i | − | 1.28563i | ||||||
\(839\) | −5.31605e24 | −0.747502 | −0.373751 | − | 0.927529i | \(-0.621929\pi\) | ||||
−0.373751 | + | 0.927529i | \(0.621929\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.91324e24 | −0.952612 | ||||||||
\(842\) | − | 8.55560e24i | − | 1.16707i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.58540e24 | 0.211947 | ||||||||
\(845\) | 1.01455e23 | + | 3.74748e23i | 0.0134274 | + | 0.0495972i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.76682e24i | − | 0.618330i | ||||||
\(848\) | 7.70057e24i | 0.988913i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.52826e24 | + | 3.23005e24i | −0.695870 | + | 0.406582i | ||||
\(851\) | 8.96527e24 | 1.11728 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.42826e24i | 0.418801i | 0.977830 | + | 0.209400i | \(0.0671512\pi\) | ||||
−0.977830 | + | 0.209400i | \(0.932849\pi\) | |||||||
\(854\) | −1.04928e25 | −1.26911 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.23040e25 | 1.45887 | ||||||||
\(857\) | 1.10696e25i | 1.29956i | 0.760122 | + | 0.649780i | \(0.225139\pi\) | ||||
−0.760122 | + | 0.649780i | \(0.774861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.30612e24 | 0.840901 | 0.420450 | − | 0.907316i | \(-0.361872\pi\) | ||||
0.420450 | + | 0.907316i | \(0.361872\pi\) | |||||||
\(860\) | 3.78815e24 | − | 1.02556e24i | 0.431708 | − | 0.116875i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 1.01334e25i | − | 1.13225i | ||||||
\(863\) | − | 4.59279e24i | − | 0.508141i | −0.967186 | − | 0.254071i | \(-0.918230\pi\) | ||
0.967186 | − | 0.254071i | \(-0.0817696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.05652e23 | − | 1.63967e23i | 0.0657031 | − | 0.0177877i | ||||
\(866\) | 3.67855e24 | 0.395161 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.28979e24i | 0.241201i | ||||||||
\(869\) | 1.02631e25 | 1.07056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.88054e25 | 1.92366 | ||||||||
\(872\) | 6.79673e24i | 0.688509i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.90974e24 | 0.289073 | ||||||||
\(875\) | −1.29112e25 | + | 1.31135e25i | −1.27028 | + | 1.29018i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.95372e24i | 0.574503i | 0.957855 | + | 0.287251i | \(0.0927415\pi\) | ||||
−0.957855 | + | 0.287251i | \(0.907258\pi\) | |||||||
\(878\) | 1.54147e25i | 1.47310i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.69840e24 | + | 9.96720e24i | 0.252932 | + | 0.934265i | ||||
\(881\) | 2.12837e25 | 1.97585 | 0.987923 | − | 0.154949i | \(-0.0495212\pi\) | ||||
0.987923 | + | 0.154949i | \(0.0495212\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.17761e25i | 1.07235i | 0.844106 | + | 0.536176i | \(0.180132\pi\) | ||||
−0.844106 | + | 0.536176i | \(0.819868\pi\) | |||||||
\(884\) | −2.12793e24 | −0.191917 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.35209e25 | −2.08098 | ||||||||
\(887\) | − | 1.58250e25i | − | 1.38673i | −0.720586 | − | 0.693366i | \(-0.756127\pi\) | ||
0.720586 | − | 0.693366i | \(-0.243873\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.73002e25 | 2.34693 | ||||||||
\(890\) | 2.01226e24 | − | 5.44775e23i | 0.171344 | − | 0.0463876i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.15301e24i | 0.0963231i | ||||||||
\(893\) | − | 1.03216e23i | − | 0.00854102i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.45742e24 | + | 5.38333e24i | 0.118328 | + | 0.437074i | ||||
\(896\) | −2.71618e25 | −2.18444 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 9.81249e24i | − | 0.774337i | ||||||
\(899\) | −1.42269e24 | −0.111212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.75803e24 | 0.595101 | ||||||||
\(902\) | 2.05901e25i | 1.56460i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.28772e25 | 0.960262 | ||||||||
\(905\) | 5.58416e24 | + | 2.06265e25i | 0.412520 | + | 1.52374i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.26063e25i | − | 0.913954i | −0.889479 | − | 0.456977i | \(-0.848932\pi\) | ||
0.889479 | − | 0.456977i | \(-0.151068\pi\) | |||||||
\(908\) | 4.16964e24i | 0.299480i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.85434e25 | + | 7.72749e24i | −2.01212 | + | 0.544737i | ||||
\(911\) | −2.37643e25 | −1.65966 | −0.829828 | − | 0.558019i | \(-0.811561\pi\) | ||||
−0.829828 | + | 0.558019i | \(0.811561\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.78168e24i | 0.190680i | ||||||||
\(914\) | −2.44717e25 | −1.66196 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.67998e22 | 0.00245320 | ||||||||
\(917\) | − | 3.20638e25i | − | 2.11775i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.89052e25 | 1.22574 | 0.612870 | − | 0.790183i | \(-0.290015\pi\) | ||||
0.612870 | + | 0.790183i | \(0.290015\pi\) | |||||||
\(920\) | 4.63692e24 | + | 1.71276e25i | 0.297874 | + | 1.10027i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1.81906e25i | − | 1.14719i | ||||||
\(923\) | 1.56943e24i | 0.0980677i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.69040e24 | − | 1.14507e25i | −0.410438 | − | 0.702469i | ||||
\(926\) | 2.10373e25 | 1.27878 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.85744e24i | 0.110855i | ||||||||
\(929\) | 6.68973e24 | 0.395617 | 0.197808 | − | 0.980241i | \(-0.436618\pi\) | ||||
0.197808 | + | 0.980241i | \(0.436618\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.35514e24 | 0.427089 | ||||||||
\(932\) | − | 4.96956e24i | − | 0.285945i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.50795e24 | 0.367702 | ||||||||
\(935\) | 1.00416e25 | − | 2.71853e24i | 0.562215 | − | 0.152207i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.19515e24i | − | 0.395597i | −0.980243 | − | 0.197799i | \(-0.936621\pi\) | ||
0.980243 | − | 0.197799i | \(-0.0633792\pi\) | |||||||
\(938\) | 7.00010e25i | 3.81399i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.14314e23 | + | 5.80208e22i | −0.0114674 | + | 0.00310454i | ||||
\(941\) | −2.21212e25 | −1.17299 | −0.586497 | − | 0.809951i | \(-0.699494\pi\) | ||||
−0.586497 | + | 0.809951i | \(0.699494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.52814e25i | 2.35815i | ||||||||
\(944\) | 2.94005e25 | 1.51737 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.08297e25 | −1.56277 | ||||||||
\(947\) | 1.99520e23i | 0.0100233i | 0.999987 | + | 0.00501166i | \(0.00159527\pi\) | ||||
−0.999987 | + | 0.00501166i | \(0.998405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.96856e24 | −0.491892 | ||||||||
\(950\) | −2.17142e24 | − | 3.71640e24i | −0.106192 | − | 0.181749i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.24553e25i | 1.07871i | ||||||||
\(953\) | − | 1.42481e25i | − | 0.678370i | −0.940720 | − | 0.339185i | \(-0.889849\pi\) | ||
0.940720 | − | 0.339185i | \(-0.110151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.29660e24 | + | 4.78933e24i | 0.0606427 | + | 0.223999i | ||||
\(956\) | −1.93123e24 | −0.0895247 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 2.36155e25i | − | 1.07545i | ||||||
\(959\) | 1.56900e25 | 0.708217 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.66646e25 | −0.739003 | ||||||||
\(962\) | − | 2.13102e25i | − | 0.936699i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.42658e24 | 0.234353 | ||||||||
\(965\) | −2.57424e25 | + | 6.96918e24i | −1.10196 | + | 0.298332i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.07659e25i | − | 0.452822i | −0.974032 | − | 0.226411i | \(-0.927301\pi\) | ||
0.974032 | − | 0.226411i | \(-0.0726992\pi\) | |||||||
\(968\) | 6.79900e24i | 0.283468i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.94945e24 | − | 2.93633e25i | −0.325670 | − | 1.20294i | ||||
\(971\) | 1.66161e25 | 0.674786 | 0.337393 | − | 0.941364i | \(-0.390455\pi\) | ||||
0.337393 | + | 0.941364i | \(0.390455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4.83625e25i | − | 1.92996i | ||||||
\(974\) | 1.99139e24 | 0.0787779 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.91534e25 | 0.744597 | ||||||||
\(977\) | − | 2.38066e25i | − | 0.917475i | −0.888572 | − | 0.458737i | \(-0.848302\pi\) | ||
0.888572 | − | 0.458737i | \(-0.151698\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.38719e24 | −0.128288 | ||||||||
\(980\) | −4.13454e24 | − | 1.52720e25i | −0.155241 | − | 0.573420i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.35490e25i | 1.60705i | ||||||||
\(983\) | − | 1.66009e25i | − | 0.607333i | −0.952778 | − | 0.303667i | \(-0.901789\pi\) | ||
0.952778 | − | 0.303667i | \(-0.0982109\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.20514e25 | + | 5.96993e24i | −0.792918 | + | 0.214665i | ||||
\(986\) | 4.92146e24 | 0.175445 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1.43051e24i | − | 0.0501253i | ||||||
\(989\) | −6.78003e25 | −2.35539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.53873e25 | −1.20843 | −0.604215 | − | 0.796821i | \(-0.706513\pi\) | ||||
−0.604215 | + | 0.796821i | \(0.706513\pi\) | |||||||
\(992\) | − | 7.68400e24i | − | 0.260159i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.84202e24 | −0.194437 | ||||||||
\(995\) | 7.33560e24 | + | 2.70959e25i | 0.242069 | + | 0.894143i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.16783e25i | 1.67648i | 0.545300 | + | 0.838241i | \(0.316416\pi\) | ||||
−0.545300 | + | 0.838241i | \(0.683584\pi\) | |||||||
\(998\) | − | 1.12674e25i | − | 0.362420i | ||||||
\(999\) | 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 | 45.18.b.c.19.5 | ✓ | 16 | |
3.2 | odd | 2 | inner | 45.18.b.c.19.12 | yes | 16 | |
5.4 | even | 2 | inner | 45.18.b.c.19.11 | yes | 16 | |
15.14 | odd | 2 | inner | 45.18.b.c.19.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.18.b.c.19.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
45.18.b.c.19.6 | yes | 16 | 15.14 | odd | 2 | inner | |
45.18.b.c.19.11 | yes | 16 | 5.4 | even | 2 | inner | |
45.18.b.c.19.12 | yes | 16 | 3.2 | odd | 2 | inner |