Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,10,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (of order \(2\), degree \(1\), 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: | \(206.014334466\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{79})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 39x^{2} + 400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-4.44410 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.10.c.l.49.4 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 272.211i | − 1.94026i | −0.242583 | − | 0.970131i | \(-0.577995\pi\) | ||||
0.242583 | − | 0.970131i | \(-0.422005\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10002.6i | 1.57460i | 0.616570 | + | 0.787300i | \(0.288522\pi\) | ||||
−0.616570 | + | 0.787300i | \(0.711478\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −54415.9 | −2.76461 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −47093.7 | −0.969830 | −0.484915 | − | 0.874561i | \(-0.661149\pi\) | ||||
−0.484915 | + | 0.874561i | \(0.661149\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 9362.93i | − 0.0909216i | −0.998966 | − | 0.0454608i | \(-0.985524\pi\) | ||||
0.998966 | − | 0.0454608i | \(-0.0144756\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 108521.i | 0.315131i | 0.987509 | + | 0.157566i | \(0.0503646\pi\) | ||||
−0.987509 | + | 0.157566i | \(0.949635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −665173. | −1.17096 | −0.585482 | − | 0.810685i | \(-0.699095\pi\) | ||||
−0.585482 | + | 0.810685i | \(0.699095\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.72281e6 | 3.05514 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 576426.i | 0.429505i | 0.976669 | + | 0.214752i | \(0.0688945\pi\) | ||||
−0.976669 | + | 0.214752i | \(0.931106\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.45468e6i | 3.42381i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.61067e6 | 0.685427 | 0.342714 | − | 0.939440i | \(-0.388654\pi\) | ||||
0.342714 | + | 0.939440i | \(0.388654\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.87896e6 | −0.754375 | −0.377188 | − | 0.926137i | \(-0.623109\pi\) | ||||
−0.377188 | + | 0.926137i | \(0.623109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.28194e7i | 1.88172i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.41599e7i | 1.24209i | 0.783774 | + | 0.621046i | \(0.213292\pi\) | ||||
−0.783774 | + | 0.621046i | \(0.786708\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.54869e6 | −0.176412 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.62193e6 | 0.255444 | 0.127722 | − | 0.991810i | \(-0.459233\pi\) | ||||
0.127722 | + | 0.991810i | \(0.459233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.31227e6i | 0.370776i | 0.982665 | + | 0.185388i | \(0.0593542\pi\) | ||||
−0.982665 | + | 0.185388i | \(0.940646\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2.51923e7i | − 0.753056i | −0.926405 | − | 0.376528i | \(-0.877118\pi\) | ||||
0.926405 | − | 0.376528i | \(-0.122882\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.96977e7 | −1.47937 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.95405e7 | 0.611437 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.49333e7i | − 0.608133i | −0.952651 | − | 0.304066i | \(-0.901656\pi\) | ||||
0.952651 | − | 0.304066i | \(-0.0983444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.81068e8i | 2.27198i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.71868e6 | 0.0721855 | 0.0360928 | − | 0.999348i | \(-0.488509\pi\) | ||||
0.0360928 | + | 0.999348i | \(0.488509\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.75982e6 | −0.0440156 | −0.0220078 | − | 0.999758i | \(-0.507006\pi\) | ||||
−0.0220078 | + | 0.999758i | \(0.507006\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 5.44299e8i | − 4.35316i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.38772e8i | 0.841330i | 0.907216 | + | 0.420665i | \(0.138203\pi\) | ||||
−0.907216 | + | 0.420665i | \(0.861797\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.56909e8 | 0.833352 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.54359e8 | −1.65494 | −0.827468 | − | 0.561513i | \(-0.810219\pi\) | ||||
−0.827468 | + | 0.561513i | \(0.810219\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 2.41596e8i | − 0.995719i | −0.867258 | − | 0.497859i | \(-0.834120\pi\) | ||||
0.867258 | − | 0.497859i | \(-0.165880\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 4.71058e8i | − 1.52709i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.61173e8 | 0.754409 | 0.377204 | − | 0.926130i | \(-0.376885\pi\) | ||||
0.377204 | + | 0.926130i | \(0.376885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.50260e9 | 3.87847 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 6.55898e8i | − 1.51700i | −0.651674 | − | 0.758499i | \(-0.725933\pi\) | ||||
0.651674 | − | 0.758499i | \(-0.274067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 7.10654e8i | − 1.32991i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00221e9 | 1.69318 | 0.846590 | − | 0.532245i | \(-0.178652\pi\) | ||||
0.846590 | + | 0.532245i | \(0.178652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.36534e7 | 0.143165 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.05590e9i | 1.46368i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.24869e9i | 1.43213i | 0.698034 | + | 0.716065i | \(0.254058\pi\) | ||||
−0.698034 | + | 0.716065i | \(0.745942\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.56264e9 | 2.68120 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.39590e7 | −0.0898446 | −0.0449223 | − | 0.998990i | \(-0.514304\pi\) | ||||
−0.0449223 | + | 0.998990i | \(0.514304\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 3.58300e8i | − 0.313675i | −0.987624 | − | 0.156837i | \(-0.949870\pi\) | ||||
0.987624 | − | 0.156837i | \(-0.0501299\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.02197e9i | 0.753719i | 0.926270 | + | 0.376860i | \(0.122996\pi\) | ||||
−0.926270 | + | 0.376860i | \(0.877004\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.94205e8 | 0.606761 | 0.303380 | − | 0.952869i | \(-0.401885\pi\) | ||||
0.303380 | + | 0.952869i | \(0.401885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.85449e9 | 2.40998 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1.11113e9i | − 0.641077i | −0.947235 | − | 0.320539i | \(-0.896136\pi\) | ||||
0.947235 | − | 0.320539i | \(-0.103864\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.09492e8i | 0.251363i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.08548e9 | −0.496206 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.40134e8 | −0.0594306 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.25814e9i | − 0.495628i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 5.51824e9i | − 1.88228i | −0.338020 | − | 0.941139i | \(-0.609757\pi\) | ||||
0.338020 | − | 0.941139i | \(-0.390243\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.26269e9 | 0.719402 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.66527e9 | −1.38406 | −0.692031 | − | 0.721867i | \(-0.743284\pi\) | ||||
−0.692031 | + | 0.721867i | \(0.743284\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 6.65344e9i | − 1.84380i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 6.97325e9i | − 1.69119i | −0.533825 | − | 0.845595i | \(-0.679246\pi\) | ||||
0.533825 | − | 0.845595i | \(-0.320754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.27736e9 | 1.42630 | 0.713149 | − | 0.701013i | \(-0.247268\pi\) | ||||
0.713149 | + | 0.701013i | \(0.247268\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.85762e9 | −1.46113 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.40935e8i | 0.0881784i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.62504e10i | 2.87036i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.62156e9 | 0.269523 | 0.134761 | − | 0.990878i | \(-0.456973\pi\) | ||||
0.134761 | + | 0.990878i | \(0.456973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.17677e10 | −1.84202 | −0.921011 | − | 0.389537i | \(-0.872635\pi\) | ||||
−0.921011 | + | 0.389537i | \(0.872635\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 5.90524e9i | − 0.871217i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.71288e9i | − 0.224998i | −0.993652 | − | 0.112499i | \(-0.964114\pi\) | ||||
0.993652 | − | 0.112499i | \(-0.0358855\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.50923e9 | −1.17994 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.76574e9 | −0.676298 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.98636e9i | 1.10806i | 0.832497 | + | 0.554030i | \(0.186911\pi\) | ||||
−0.832497 | + | 0.554030i | \(0.813089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.56153e10i | − 1.55355i | −0.629777 | − | 0.776776i | \(-0.716854\pi\) | ||||
0.629777 | − | 0.776776i | \(-0.283146\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.05168e10 | 0.991733 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.61960e10 | 3.23726 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 4.61727e8i | − 0.0391902i | −0.999808 | − | 0.0195951i | \(-0.993762\pi\) | ||||
0.999808 | − | 0.0195951i | \(-0.00623772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1.82890e9i | − 0.140059i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.56860e10 | −1.14202 | −0.571011 | − | 0.820943i | \(-0.693449\pi\) | ||||
−0.571011 | + | 0.820943i | \(0.693449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.26075e8 | 0.0364329 | 0.0182165 | − | 0.999834i | \(-0.494201\pi\) | ||||
0.0182165 | + | 0.999834i | \(0.494201\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.29568e9i | 0.0854017i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.11063e9i | − 0.305624i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.45710e10 | −5.39113 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.60641e10 | 1.41708 | 0.708538 | − | 0.705673i | \(-0.249355\pi\) | ||||
0.708538 | + | 0.705673i | \(0.249355\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 4.83514e9i | − 0.250843i | −0.992104 | − | 0.125421i | \(-0.959972\pi\) | ||||
0.992104 | − | 0.125421i | \(-0.0400283\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.09275e10i | 0.516919i | 0.966022 | + | 0.258460i | \(0.0832149\pi\) | ||||
−0.966022 | + | 0.258460i | \(0.916785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24042e10 | −1.01272 | −0.506361 | − | 0.862322i | \(-0.669010\pi\) | ||||
−0.506361 | + | 0.862322i | \(0.669010\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.77754e10 | 1.63240 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.61134e10i | 1.07927i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 3.13667e10i | − 1.18741i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.13255e10 | 1.13564 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.17129e10 | −1.10145 | −0.550725 | − | 0.834687i | \(-0.685649\pi\) | ||||
−0.550725 | + | 0.834687i | \(0.685649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.64605e10i | 3.21101i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 3.87995e10i | − 1.18784i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.57651e10 | −1.93195 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.01607e9 | 0.0286522 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.52662e10i | 0.413388i | 0.978406 | + | 0.206694i | \(0.0662705\pi\) | ||||
−0.978406 | + | 0.206694i | \(0.933730\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.53481e9i | 0.188346i | 0.995556 | + | 0.0941729i | \(0.0300206\pi\) | ||||
−0.995556 | + | 0.0941729i | \(0.969979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.28244e10 | 0.308160 | 0.154080 | − | 0.988058i | \(-0.450759\pi\) | ||||
0.154080 | + | 0.988058i | \(0.450759\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.28227e11 | −2.96296 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 2.06272e10i | − 0.458500i | −0.973368 | − | 0.229250i | \(-0.926373\pi\) | ||||
0.973368 | − | 0.229250i | \(-0.0736274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 7.10943e10i | − 1.46375i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.96664e10 | 0.786380 | 0.393190 | − | 0.919457i | \(-0.371372\pi\) | ||||
0.393190 | + | 0.919457i | \(0.371372\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.75642e9 | −0.0717294 | −0.0358647 | − | 0.999357i | \(-0.511419\pi\) | ||||
−0.0358647 | + | 0.999357i | \(0.511419\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2.22928e11i | − 4.10144i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.22797e9i | 0.106466i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.78543e11 | −2.94337 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.74656e10 | −1.23191 | −0.615953 | − | 0.787783i | \(-0.711229\pi\) | ||||
−0.615953 | + | 0.787783i | \(0.711229\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.71460e10i | − 0.416546i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.31990e10i | 0.474707i | 0.971423 | + | 0.237354i | \(0.0762800\pi\) | ||||
−0.971423 | + | 0.237354i | \(0.923720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.41636e11 | −1.95580 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.42062e11 | −1.89494 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.00754e11i | 1.29856i | 0.760549 | + | 0.649281i | \(0.224930\pi\) | ||||
−0.760549 | + | 0.649281i | \(0.775070\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.72812e11i | − 3.28521i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.49946e10 | 0.873262 | 0.436631 | − | 0.899641i | \(-0.356172\pi\) | ||||
0.436631 | + | 0.899641i | \(0.356172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.80768e10 | 0.654095 | 0.327048 | − | 0.945008i | \(-0.393946\pi\) | ||||
0.327048 | + | 0.945008i | \(0.393946\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 2.54935e10i | − 0.277778i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.44538e11i | 1.47511i | 0.675289 | + | 0.737554i | \(0.264019\pi\) | ||||
−0.675289 | + | 0.737554i | \(0.735981\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.11077e11 | 2.08556 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.73877e11 | 1.66366 | 0.831828 | − | 0.555034i | \(-0.187295\pi\) | ||||
0.831828 | + | 0.555034i | \(0.187295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.86637e8i | − 0.00358315i | −0.999998 | − | 0.00179157i | \(-0.999430\pi\) | ||||
0.999998 | − | 0.00179157i | \(-0.000570276\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.62311e10i | 0.402222i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.06811e11 | 0.900692 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.39908e11 | 2.77870 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6.25206e10i | − 0.495586i | −0.968813 | − | 0.247793i | \(-0.920295\pi\) | ||||
0.968813 | − | 0.247793i | \(-0.0797053\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 4.45255e11i | − 3.32051i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.39703e9 | 0.0390512 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.31440e10 | −0.583824 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.55767e10i | 0.174322i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.57636e10i | 0.101282i | 0.998717 | + | 0.0506410i | \(0.0161264\pi\) | ||||
−0.998717 | + | 0.0506410i | \(0.983874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.75334e10 | −0.608611 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.01301e10 | 0.122018 | 0.0610091 | − | 0.998137i | \(-0.480568\pi\) | ||||
0.0610091 | + | 0.998137i | \(0.480568\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.03790e10i | 0.355579i | 0.984069 | + | 0.177790i | \(0.0568946\pi\) | ||||
−0.984069 | + | 0.177790i | \(0.943105\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.24292e11i | − 0.691313i | −0.938361 | − | 0.345657i | \(-0.887656\pi\) | ||||
0.938361 | − | 0.345657i | \(-0.112344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.22946e11 | −0.664748 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.78191e11 | 1.46241 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 7.21850e10i | − 0.369008i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 2.43412e11i | − 1.17727i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.51988e11 | 1.18576 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.14638e11 | 0.524930 | 0.262465 | − | 0.964941i | \(-0.415465\pi\) | ||||
0.262465 | + | 0.964941i | \(0.415465\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 7.70526e11i | − 3.43390i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 3.40785e11i | − 1.43928i | −0.694345 | − | 0.719642i | \(-0.744306\pi\) | ||||
0.694345 | − | 0.719642i | \(-0.255694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.02461e11 | −1.24386 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.82674e11 | 0.731615 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.93491e11i | − 0.754809i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.38240e11i | 1.25240i | 0.779664 | + | 0.626198i | \(0.215390\pi\) | ||||
−0.779664 | + | 0.626198i | \(0.784610\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.34359e11 | −0.845603 | −0.422802 | − | 0.906222i | \(-0.638953\pi\) | ||||
−0.422802 | + | 0.906222i | \(0.638953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.85235e10 | 0.311298 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 3.56202e11i | − 1.22098i | −0.792022 | − | 0.610492i | \(-0.790972\pi\) | ||||
0.792022 | − | 0.610492i | \(-0.209028\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.95481e11i | 0.962769i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.37815e11 | 1.07338 | 0.536691 | − | 0.843779i | \(-0.319674\pi\) | ||||
0.536691 | + | 0.843779i | \(0.319674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.19768e11 | 0.371157 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.81461e10i | 0.115311i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.36383e11i | − 0.392431i | −0.980561 | − | 0.196215i | \(-0.937135\pi\) | ||||
0.980561 | − | 0.196215i | \(-0.0628652\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.51506e11 | −0.706204 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.49423e11 | 0.957566 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.08929e11i | − 1.36134i | −0.732589 | − | 0.680672i | \(-0.761688\pi\) | ||||
0.732589 | − | 0.680672i | \(-0.238312\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.44436e10i | − 0.0623201i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.70726e10 | 0.241669 | 0.120834 | − | 0.992673i | \(-0.461443\pi\) | ||||
0.120834 | + | 0.992673i | \(0.461443\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.50213e12 | −3.65211 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 7.13792e11i | − 1.69503i | −0.530772 | − | 0.847514i | \(-0.678098\pi\) | ||||
0.530772 | − | 0.847514i | \(-0.321902\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4.52320e11i | − 1.02505i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.48149e11 | −0.549465 | −0.274732 | − | 0.961521i | \(-0.588589\pi\) | ||||
−0.274732 | + | 0.961521i | \(0.588589\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.25540e10 | −0.135350 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.26994e12i | 2.68544i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.04445e11i | 1.42328i | 0.702545 | + | 0.711640i | \(0.252047\pi\) | ||||
−0.702545 | + | 0.711640i | \(0.747953\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.81114e12 | −3.57745 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.82127e11 | −0.544873 | −0.272437 | − | 0.962174i | \(-0.587830\pi\) | ||||
−0.272437 | + | 0.962174i | \(0.587830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.63184e10i | 0.0685890i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6.66844e11i | − 1.20462i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.15011e11 | −1.61686 | −0.808428 | − | 0.588595i | \(-0.799681\pi\) | ||||
−0.808428 | + | 0.588595i | \(0.799681\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.89820e12 | −3.28135 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.72041e10i | 0.113663i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 1.70877e12i | − 2.76739i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.19010e12 | 1.88635 | 0.943174 | − | 0.332299i | \(-0.107824\pi\) | ||||
0.943174 | + | 0.332299i | \(0.107824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.44534e11 | 1.15509 | 0.577544 | − | 0.816360i | \(-0.304011\pi\) | ||||
0.577544 | + | 0.816360i | \(0.304011\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.37086e12i | 2.08191i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4.76104e10i | − 0.0693069i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.20027e11 | 0.171089 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.47758e11 | 0.485433 | 0.242716 | − | 0.970097i | \(-0.421962\pi\) | ||||
0.242716 | + | 0.970097i | \(0.421962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.13744e11i | 1.11248i | 0.831022 | + | 0.556240i | \(0.187756\pi\) | ||||
−0.831022 | + | 0.556240i | \(0.812244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.83423e11i | − 0.502935i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.09730e12 | −1.41005 | −0.705023 | − | 0.709184i | \(-0.749063\pi\) | ||||
−0.705023 | + | 0.709184i | \(0.749063\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.24851e12 | 4.08987 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.59236e10i | 0.0813251i | 0.999173 | + | 0.0406625i | \(0.0129469\pi\) | ||||
−0.999173 | + | 0.0406625i | \(0.987053\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 4.41407e11i | − 0.522945i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.15220e11 | −0.249905 | −0.124952 | − | 0.992163i | \(-0.539878\pi\) | ||||
−0.124952 | + | 0.992163i | \(0.539878\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.17664e11 | −0.247737 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.20329e12i | 3.57400i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.36259e11i | 0.789601i | 0.918767 | + | 0.394801i | \(0.129186\pi\) | ||||
−0.918767 | + | 0.394801i | \(0.870814\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.02603e12 | −1.07895 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.23730e12 | −1.27591 | −0.637957 | − | 0.770072i | \(-0.720220\pi\) | ||||
−0.637957 | + | 0.770072i | \(0.720220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 7.36969e11i | − 0.745306i | −0.927971 | − | 0.372653i | \(-0.878448\pi\) | ||||
0.927971 | − | 0.372653i | \(-0.121552\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.22439e12i | 1.19123i | 0.803271 | + | 0.595614i | \(0.203091\pi\) | ||||
−0.803271 | + | 0.595614i | \(0.796909\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.38808e12 | −1.32476 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.66265e11 | −0.436555 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3.91455e11i | − 0.359590i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.90093e12i | 1.68125i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.11970e12 | 0.971833 | 0.485916 | − | 0.874005i | \(-0.338486\pi\) | ||||
0.485916 | + | 0.874005i | \(0.338486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.32579e11 | 0.112933 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.56950e12i | 1.31220i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.25337e11i | 0.181532i | 0.995872 | + | 0.0907659i | \(0.0289315\pi\) | ||||
−0.995872 | + | 0.0907659i | \(0.971068\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.71840e12 | 2.14992 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.60716e11 | 0.124794 | 0.0623970 | − | 0.998051i | \(-0.480126\pi\) | ||||
0.0623970 | + | 0.998051i | \(0.480126\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.83312e11i | 0.216000i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 3.54450e12i | − 2.60586i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.05187e11 | 0.581359 | 0.290680 | − | 0.956820i | \(-0.406119\pi\) | ||||
0.290680 | + | 0.956820i | \(0.406119\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.25065e12 | −3.01430 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.68493e12i | − 1.17361i | −0.809727 | − | 0.586807i | \(-0.800385\pi\) | ||||
0.809727 | − | 0.586807i | \(-0.199615\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2.86280e12i | − 1.92422i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.50208e12 | −0.991890 | −0.495945 | − | 0.868354i | \(-0.665178\pi\) | ||||
−0.495945 | + | 0.868354i | \(0.665178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.41658e12 | 1.56786 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 6.28900e12i | − 4.00916i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.18640e12i | 0.730336i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.25687e11 | −0.0760393 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.24724e11 | 0.549848 | 0.274924 | − | 0.961466i | \(-0.411347\pi\) | ||||
0.274924 | + | 0.961466i | \(0.411347\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 3.81782e10i | − 0.0223130i | −0.999938 | − | 0.0111565i | \(-0.996449\pi\) | ||||
0.999938 | − | 0.0111565i | \(-0.00355130\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 4.20947e11i | − 0.237727i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.46889e12 | 0.815526 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.65603e11 | −0.199565 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.32748e10i | − 0.0232254i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.26991e12i | 2.21582i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.81139e12 | 1.43473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.05812e12 | −0.531064 | −0.265532 | − | 0.964102i | \(-0.585548\pi\) | ||||
−0.265532 | + | 0.964102i | \(0.585548\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.43203e11i | − 0.0706894i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.05156e12i | 0.502215i | 0.967959 | + | 0.251108i | \(0.0807948\pi\) | ||||
−0.967959 | + | 0.251108i | \(0.919205\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.59010e11 | 0.121686 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.73655e12 | −0.802611 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.61240e12i | 1.18789i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 3.92684e11i | − 0.172860i | −0.996258 | − | 0.0864301i | \(-0.972454\pi\) | ||||
0.996258 | − | 0.0864301i | \(-0.0275459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.78272e10 | 0.0337115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.39117e12 | −0.592990 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.36287e12i | 0.991180i | 0.868557 | + | 0.495590i | \(0.165048\pi\) | ||||
−0.868557 | + | 0.495590i | \(0.834952\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.50299e13i | 6.10705i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.50603e12 | 1.00226 | 0.501130 | − | 0.865372i | \(-0.332918\pi\) | ||||
0.501130 | + | 0.865372i | \(0.332918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.99195e12 | 1.17785 | 0.588927 | − | 0.808187i | \(-0.299551\pi\) | ||||
0.588927 | + | 0.808187i | \(0.299551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 7.09494e12i | − 2.74950i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 3.06622e11i | − 0.115163i | −0.998341 | − | 0.0575815i | \(-0.981661\pi\) | ||||
0.998341 | − | 0.0575815i | \(-0.0183389\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.31618e12 | −0.486700 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.56067e12 | 2.38867 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.64514e12i | 0.589785i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.80823e12i | 0.976249i | 0.872774 | + | 0.488125i | \(0.162319\pi\) | ||||
−0.872774 | + | 0.488125i | \(0.837681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.58018e12 | 0.883346 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.97459e12 | 1.00296 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.34954e12i | 0.448166i | 0.974570 | + | 0.224083i | \(0.0719387\pi\) | ||||
−0.974570 | + | 0.224083i | \(0.928061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.09867e12i | 1.96494i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.38598e12 | 1.07464 | 0.537321 | − | 0.843378i | \(-0.319436\pi\) | ||||
0.537321 | + | 0.843378i | \(0.319436\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.62837e12 | 1.44708 | 0.723540 | − | 0.690282i | \(-0.242514\pi\) | ||||
0.723540 | + | 0.690282i | \(0.242514\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 7.55142e12i | − 2.32595i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4.78828e12i | − 1.43163i | −0.698291 | − | 0.715814i | \(-0.746056\pi\) | ||||
0.698291 | − | 0.715814i | \(-0.253944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.10837e12 | 2.09407 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.35874e11 | −0.0684690 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.02749e12i | 0.293905i | 0.989144 | + | 0.146953i | \(0.0469465\pi\) | ||||
−0.989144 | + | 0.146953i | \(0.953054\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 4.53079e12i | − 1.25861i | −0.777159 | − | 0.629304i | \(-0.783340\pi\) | ||||
0.777159 | − | 0.629304i | \(-0.216660\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.42902e12 | −0.938777 | −0.469388 | − | 0.882992i | \(-0.655526\pi\) | ||||
−0.469388 | + | 0.882992i | \(0.655526\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.44992e12 | −1.47054 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.00247e13i | 2.66608i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 8.52714e12i | − 2.20343i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.53664e12 | −0.391422 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.52587e12 | 0.885389 | 0.442695 | − | 0.896672i | \(-0.354023\pi\) | ||||
0.442695 | + | 0.896672i | \(0.354023\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.63260e12i | 2.13710i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.58946e11i | 0.134506i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.92828e13 | 4.57526 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.00458e12 | −1.63878 | −0.819390 | − | 0.573236i | \(-0.805688\pi\) | ||||
−0.819390 | + | 0.573236i | \(0.805688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4.31047e12i | − 0.994432i | −0.867627 | − | 0.497216i | \(-0.834356\pi\) | ||||
0.867627 | − | 0.497216i | \(-0.165644\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.84949e12i | 0.639290i | 0.947537 | + | 0.319645i | \(0.103564\pi\) | ||||
−0.947537 | + | 0.319645i | \(0.896436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.16407e11 | −0.0700077 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.05617e13 | −2.30472 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.93213e12i | − 0.415841i | −0.978146 | − | 0.207920i | \(-0.933331\pi\) | ||||
0.978146 | − | 0.207920i | \(-0.0666695\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.31467e13i | 2.75278i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.58675e12 | 1.77355 | 0.886777 | − | 0.462198i | \(-0.152939\pi\) | ||||
0.886777 | + | 0.462198i | \(0.152939\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.11478e12 | 0.227133 | 0.113567 | − | 0.993530i | \(-0.463772\pi\) | ||||
0.113567 | + | 0.993530i | \(0.463772\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.76586e11i | − 0.0555928i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.50486e12i | 0.294394i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.15562e12 | 0.802081 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.24157e11 | 0.0426876 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 7.57716e12i | − 1.42377i | −0.702298 | − | 0.711883i | \(-0.747843\pi\) | ||||
0.702298 | − | 0.711883i | \(-0.252157\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 5.08558e12i | − 0.930447i | −0.885193 | − | 0.465223i | \(-0.845974\pi\) | ||||
0.885193 | − | 0.465223i | \(-0.154026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.24901e13 | −2.25503 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.05106e12 | 0.365440 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.78278e11i | − 0.0313476i | −0.999877 | − | 0.0156738i | \(-0.995011\pi\) | ||||
0.999877 | − | 0.0156738i | \(-0.00498933\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 3.49093e12i | − 0.597911i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.27078e11 | −0.0552924 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.66612e11 | 0.144602 | 0.0723008 | − | 0.997383i | \(-0.476966\pi\) | ||||
0.0723008 | + | 0.997383i | \(0.476966\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.56330e13i | 4.22182i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.01574e11i | 0.0804985i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.61497e12 | −0.889610 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.18099e12 | 0.810367 | 0.405183 | − | 0.914235i | \(-0.367208\pi\) | ||||
0.405183 | + | 0.914235i | \(0.367208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 9.41882e12i | − 1.45445i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 9.39831e11i | − 0.141469i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.22351e13 | 1.81844 | 0.909218 | − | 0.416320i | \(-0.136681\pi\) | ||||
0.909218 | + | 0.416320i | \(0.136681\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.42120e13 | −2.08565 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.23593e12i | − 0.324008i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.07976e13i | − 1.52578i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.11881e13 | −1.56127 | −0.780634 | − | 0.624989i | \(-0.785104\pi\) | ||||
−0.780634 | + | 0.624989i | \(0.785104\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.58392e12 | 0.493913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.02254e12i | 0.139174i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7.94265e12i | − 1.05453i | −0.849699 | − | 0.527267i | \(-0.823217\pi\) | ||||
0.849699 | − | 0.527267i | \(-0.176783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.11078e13 | −4.07940 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.02052e11 | −0.116843 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.09012e13i | − 1.39478i | −0.716690 | − | 0.697392i | \(-0.754344\pi\) | ||||
0.716690 | − | 0.697392i | \(-0.245656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 6.53530e12i | − 0.815947i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.54854e12 | 0.190996 | 0.0954978 | − | 0.995430i | \(-0.469556\pi\) | ||||
0.0954978 | + | 0.995430i | \(0.469556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.69532e12 | 0.206572 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.96254e12i | 0.717764i | 0.933383 | + | 0.358882i | \(0.116842\pi\) | ||||
−0.933383 | + | 0.358882i | \(0.883158\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.56913e13i | 4.19392i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.02223e13 | −1.18681 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.92051e12 | −1.13803 | −0.569016 | − | 0.822326i | \(-0.692676\pi\) | ||||
−0.569016 | + | 0.822326i | \(0.692676\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.10870e13i | 2.39022i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.23733e13i | 1.36947i | 0.728791 | + | 0.684737i | \(0.240083\pi\) | ||||
−0.728791 | + | 0.684737i | \(0.759917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.38944e12 | −0.808209 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.52217e12 | −0.921127 | −0.460563 | − | 0.887627i | \(-0.652353\pi\) | ||||
−0.460563 | + | 0.887627i | \(0.652353\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.94434e12i | 0.955406i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 6.29066e10i | − 0.00656322i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.99595e12 | −0.308934 | −0.154467 | − | 0.987998i | \(-0.549366\pi\) | ||||
−0.154467 | + | 0.987998i | \(0.549366\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.03713e12 | 0.921056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6.44491e11i | − 0.0649245i | −0.999473 | − | 0.0324623i | \(-0.989665\pi\) | ||||
0.999473 | − | 0.0324623i | \(-0.0103349\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.85548e13i | 3.79476i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.07438e12 | −0.299116 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.66881e13 | 1.60501 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.46831e13i | 2.34677i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 8.05096e12i | − 0.748103i | −0.927408 | − | 0.374052i | \(-0.877968\pi\) | ||||
0.927408 | − | 0.374052i | \(-0.122032\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.74264e13 | 2.51955 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.11141e13 | 1.00944 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.45659e10i | 0.00400196i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.11381e13i | − 0.977799i | −0.872340 | − | 0.488899i | \(-0.837399\pi\) | ||||
0.872340 | − | 0.488899i | \(-0.162601\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.73388e12 | 0.237312 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.45361e13 | −4.68099 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.13776e13i | 0.965678i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.04144e13i | − 1.69436i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.69716e13 | −1.39301 | −0.696506 | − | 0.717550i | \(-0.745263\pi\) | ||||
−0.696506 | + | 0.717550i | \(0.745263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.17583e13 | 0.954444 | 0.477222 | − | 0.878783i | \(-0.341644\pi\) | ||||
0.477222 | + | 0.878783i | \(0.341644\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.58092e13i | − 1.26912i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 5.52910e12i | − 0.434165i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.09623e12 | −0.395796 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.99657e13 | 1.53370 | 0.766851 | − | 0.641825i | \(-0.221823\pi\) | ||||
0.766851 | + | 0.641825i | \(0.221823\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.52813e11i | 0.0420029i | 0.999779 | + | 0.0210014i | \(0.00668546\pi\) | ||||
−0.999779 | + | 0.0210014i | \(0.993315\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.57036e13i | 1.16741i | 0.811965 | + | 0.583707i | \(0.198398\pi\) | ||||
−0.811965 | + | 0.583707i | \(0.801602\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.05928e13 | −0.778958 | −0.389479 | − | 0.921035i | \(-0.627345\pi\) | ||||
−0.389479 | + | 0.921035i | \(0.627345\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.93449e13 | 2.86209 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 6.47843e12i | − 0.466195i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3.66743e13i | − 2.58284i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.55506e11 | −0.0456718 | −0.0228359 | − | 0.999739i | \(-0.507270\pi\) | ||||
−0.0228359 | + | 0.999739i | \(0.507270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.69153e12 | −0.530189 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 4.73312e13i | − 3.22793i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.40170e12i | − 0.0935794i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.05247e11 | −0.00695224 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.16215e12 | −0.533484 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.08805e13i | − 1.35043i | −0.737622 | − | 0.675213i | \(-0.764051\pi\) | ||||
0.737622 | − | 0.675213i | \(-0.235949\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 2.19074e13i | − 1.38732i | −0.720303 | − | 0.693660i | \(-0.755997\pi\) | ||||
0.720303 | − | 0.693660i | \(-0.244003\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.47238e13 | 0.922680 | 0.461340 | − | 0.887223i | \(-0.347369\pi\) | ||||
0.461340 | + | 0.887223i | \(0.347369\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.25846e13 | 0.780416 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 2.74805e12i | − 0.168646i | −0.996438 | − | 0.0843230i | \(-0.973127\pi\) | ||||
0.996438 | − | 0.0843230i | \(-0.0268727\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.90752e13i | − 1.74758i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.22996e13 | −0.731648 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.29932e12 | 0.0764950 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 6.79486e13i | − 3.95928i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.68274e12i | 0.381466i | 0.981642 | + | 0.190733i | \(0.0610865\pi\) | ||||
−0.981642 | + | 0.190733i | \(0.938913\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.70188e13 | −0.961567 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.42384e13 | 0.796289 | 0.398144 | − | 0.917323i | \(-0.369654\pi\) | ||||
0.398144 | + | 0.917323i | \(0.369654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.46098e13i | − 1.36234i | −0.732125 | − | 0.681170i | \(-0.761471\pi\) | ||||
0.732125 | − | 0.681170i | \(-0.238529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.12625e12i | 0.495035i | 0.968883 | + | 0.247518i | \(0.0796148\pi\) | ||||
−0.968883 | + | 0.247518i | \(0.920385\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.51966e13 | 2.96384 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.07630e13 | −3.76146 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.67572e13i | 0.881802i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1.46913e12i | − 0.0757696i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.01267e13 | −0.517069 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.79098e12 | 0.191642 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.26327e13i | 1.13277i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.32446e13i | − 1.63113i | −0.578668 | − | 0.815564i | \(-0.696427\pi\) | ||||
0.578668 | − | 0.815564i | \(-0.303573\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.11286e12 | 0.248386 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.42660e13 | 0.686232 | 0.343116 | − | 0.939293i | \(-0.388518\pi\) | ||||
0.343116 | + | 0.939293i | \(0.388518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.08887e13i | 1.47123i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.66647e13i | − 2.17935i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.23171e13 | 1.49456 | 0.747278 | − | 0.664512i | \(-0.231360\pi\) | ||||
0.747278 | + | 0.664512i | \(0.231360\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.29102e12 | 0.196514 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.31784e12i | 0.150469i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.94972e13i | 0.867190i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.49040e12 | 0.153746 | 0.0768732 | − | 0.997041i | \(-0.475506\pi\) | ||||
0.0768732 | + | 0.997041i | \(0.475506\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.97093e13 | 1.73228 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 5.47964e12i | − 0.236747i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1.48063e13i | − 0.627507i | −0.949504 | − | 0.313754i | \(-0.898413\pi\) | ||||
0.949504 | − | 0.313754i | \(-0.101587\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.64358e13 | 0.689916 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.90935e13 | 1.62537 | 0.812684 | − | 0.582705i | \(-0.198006\pi\) | ||||
0.812684 | + | 0.582705i | \(0.198006\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.66420e12i | 0.109714i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.30013e13i | − 0.929346i | −0.885482 | − | 0.464673i | \(-0.846172\pi\) | ||||
0.885482 | − | 0.464673i | \(-0.153828\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.26205e12 | −0.0905323 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.38335e13 | −1.34133 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.32845e13i | 1.30714i | 0.756864 | + | 0.653572i | \(0.226730\pi\) | ||||
−0.756864 | + | 0.653572i | \(0.773270\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.34673e13i | 1.28978i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.97504e13 | 2.66295 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.13933e13 | −0.430918 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 5.56112e13i | − 2.08374i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.77848e12i | 0.212518i | 0.994339 | + | 0.106259i | \(0.0338872\pi\) | ||||
−0.994339 | + | 0.106259i | \(0.966113\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.96495e13 | −0.715971 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.46200e13 | 1.61080 | 0.805402 | − | 0.592728i | \(-0.201949\pi\) | ||||
0.805402 | + | 0.592728i | \(0.201949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.27897e13i | 2.24585i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.90697e13i | 1.37188i | 0.727660 | + | 0.685938i | \(0.240608\pi\) | ||||
−0.727660 | + | 0.685938i | \(0.759392\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.71977e13 | −1.64210 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.86589e13 | −1.67746 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.96137e12i | 0.0669990i | 0.999439 | + | 0.0334995i | \(0.0106652\pi\) | ||||
−0.999439 | + | 0.0334995i | \(0.989335\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 6.85938e13i | − 2.30069i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.79141e12 | −0.159250 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.33785e13 | 1.42871 | 0.714354 | − | 0.699785i | \(-0.246721\pi\) | ||||
0.714354 | + | 0.699785i | \(0.246721\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 3.12057e13i | − 1.01850i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 2.79360e12i | − 0.0895440i | −0.998997 | − | 0.0447720i | \(-0.985744\pi\) | ||||
0.998997 | − | 0.0447720i | \(-0.0142561\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.33878e14 | −4.25269 |
(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 | 400.10.c.l.49.1 | 4 | ||
4.3 | odd | 2 | 100.10.c.c.49.4 | 4 | |||
5.2 | odd | 4 | 400.10.a.l.1.1 | 2 | |||
5.3 | odd | 4 | 80.10.a.j.1.2 | 2 | |||
5.4 | even | 2 | inner | 400.10.c.l.49.4 | 4 | ||
20.3 | even | 4 | 20.10.a.b.1.1 | ✓ | 2 | ||
20.7 | even | 4 | 100.10.a.c.1.2 | 2 | |||
20.19 | odd | 2 | 100.10.c.c.49.1 | 4 | |||
40.3 | even | 4 | 320.10.a.t.1.2 | 2 | |||
40.13 | odd | 4 | 320.10.a.l.1.1 | 2 | |||
60.23 | odd | 4 | 180.10.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.10.a.b.1.1 | ✓ | 2 | 20.3 | even | 4 | ||
80.10.a.j.1.2 | 2 | 5.3 | odd | 4 | |||
100.10.a.c.1.2 | 2 | 20.7 | even | 4 | |||
100.10.c.c.49.1 | 4 | 20.19 | odd | 2 | |||
100.10.c.c.49.4 | 4 | 4.3 | odd | 2 | |||
180.10.a.e.1.1 | 2 | 60.23 | odd | 4 | |||
320.10.a.l.1.1 | 2 | 40.13 | odd | 4 | |||
320.10.a.t.1.2 | 2 | 40.3 | even | 4 | |||
400.10.a.l.1.1 | 2 | 5.2 | odd | 4 | |||
400.10.c.l.49.1 | 4 | 1.1 | even | 1 | trivial | ||
400.10.c.l.49.4 | 4 | 5.4 | even | 2 | inner |