Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3100,3,Mod(1301,3100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3100.1301");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3100.d (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: | \(84.4688819517\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 620) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.17 | ||
Character | \(\chi\) | \(=\) | 3100.1301 |
Dual form | 3100.3.d.h.1301.18 |
$q$-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 \(\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times\).
\(n\) | \(1551\) | \(1801\) | \(2977\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 0.662053i | − | 0.220684i | −0.993894 | − | 0.110342i | \(-0.964805\pi\) | ||
0.993894 | − | 0.110342i | \(-0.0351946\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.05015 | −1.15002 | −0.575010 | − | 0.818146i | \(-0.695002\pi\) | ||||
−0.575010 | + | 0.818146i | \(0.695002\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.56169 | 0.951298 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.8318i | 1.34834i | 0.738575 | + | 0.674171i | \(0.235499\pi\) | ||||
−0.738575 | + | 0.674171i | \(0.764501\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.12511i | 0.548085i | 0.961718 | + | 0.274043i | \(0.0883610\pi\) | ||||
−0.961718 | + | 0.274043i | \(0.911639\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 26.3657i | − | 1.55092i | −0.631394 | − | 0.775462i | \(-0.717517\pi\) | ||
0.631394 | − | 0.775462i | \(-0.282483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.7364 | 0.565074 | 0.282537 | − | 0.959256i | \(-0.408824\pi\) | ||||
0.282537 | + | 0.959256i | \(0.408824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.32962i | 0.253791i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.66349i | 0.289717i | 0.989452 | + | 0.144858i | \(0.0462727\pi\) | ||||
−0.989452 | + | 0.144858i | \(0.953727\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 11.6268i | − | 0.430621i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.50735i | − | 0.189909i | −0.995482 | − | 0.0949543i | \(-0.969730\pi\) | ||
0.995482 | − | 0.0949543i | \(-0.0302705\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.544361 | + | 30.9952i | 0.0175600 | + | 0.999846i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.81941 | 0.297558 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 30.4173i | − | 0.822089i | −0.911615 | − | 0.411044i | \(-0.865164\pi\) | ||
0.911615 | − | 0.411044i | \(-0.134836\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.71720 | 0.120954 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 27.2630 | 0.664952 | 0.332476 | − | 0.943112i | \(-0.392116\pi\) | ||||
0.332476 | + | 0.943112i | \(0.392116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 34.3776i | − | 0.799479i | −0.916629 | − | 0.399739i | \(-0.869101\pi\) | ||
0.916629 | − | 0.399739i | \(-0.130899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 22.6712 | 0.482367 | 0.241183 | − | 0.970480i | \(-0.422464\pi\) | ||||
0.241183 | + | 0.970480i | \(0.422464\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.8049 | 0.322548 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.4555 | −0.342265 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 42.2112i | 0.796437i | 0.917290 | + | 0.398219i | \(0.130371\pi\) | ||||
−0.917290 | + | 0.398219i | \(0.869629\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.10807i | − | 0.124703i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −55.6539 | −0.943286 | −0.471643 | − | 0.881790i | \(-0.656339\pi\) | ||||
−0.471643 | + | 0.881790i | \(0.656339\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 100.878i | 1.65373i | 0.562401 | + | 0.826865i | \(0.309878\pi\) | ||||
−0.562401 | + | 0.826865i | \(0.690122\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −68.9228 | −1.09401 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 21.3271 | 0.318315 | 0.159158 | − | 0.987253i | \(-0.449122\pi\) | ||||
0.159158 | + | 0.987253i | \(0.449122\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.41158 | 0.0639359 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −78.2254 | −1.10177 | −0.550883 | − | 0.834582i | \(-0.685709\pi\) | ||||
−0.550883 | + | 0.834582i | \(0.685709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.2443i | − | 0.154032i | −0.997030 | − | 0.0770160i | \(-0.975461\pi\) | ||
0.997030 | − | 0.0770160i | \(-0.0245393\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 119.398i | − | 1.55062i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 28.9400i | − | 0.366329i | −0.983082 | − | 0.183164i | \(-0.941366\pi\) | ||
0.983082 | − | 0.183164i | \(-0.0586341\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 69.3577 | 0.856267 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 123.515i | 1.48814i | 0.668104 | + | 0.744068i | \(0.267106\pi\) | ||||
−0.668104 | + | 0.744068i | \(0.732894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.64615 | −0.0419098 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 78.1423i | − | 0.878003i | −0.898486 | − | 0.439001i | \(-0.855332\pi\) | ||
0.898486 | − | 0.439001i | \(-0.144668\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 57.3582i | − | 0.630310i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.5205 | − | 0.360396i | 0.220650 | − | 0.00387522i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 24.3968 | 0.251514 | 0.125757 | − | 0.992061i | \(-0.459864\pi\) | ||||
0.125757 | + | 0.992061i | \(0.459864\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 126.985i | 1.28268i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 27.3184 | 0.270479 | 0.135240 | − | 0.990813i | \(-0.456820\pi\) | ||||
0.135240 | + | 0.990813i | \(0.456820\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.89886 | 0.0766879 | 0.0383440 | − | 0.999265i | \(-0.487792\pi\) | ||||
0.0383440 | + | 0.999265i | \(0.487792\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −132.000 | −1.23364 | −0.616821 | − | 0.787103i | \(-0.711580\pi\) | ||||
−0.616821 | + | 0.787103i | \(0.711580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −157.192 | −1.44213 | −0.721066 | − | 0.692867i | \(-0.756347\pi\) | ||||
−0.721066 | + | 0.692867i | \(0.756347\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.1378 | −0.181422 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.30617 | 0.0381077 | 0.0190538 | − | 0.999818i | \(-0.493935\pi\) | ||||
0.0190538 | + | 0.999818i | \(0.493935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 61.0030i | 0.521393i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 212.248i | 1.78360i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −98.9813 | −0.818027 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 18.0496i | − | 0.146744i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 140.526i | 1.10650i | 0.833014 | + | 0.553251i | \(0.186613\pi\) | ||||
−0.833014 | + | 0.553251i | \(0.813387\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.7598 | −0.176432 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.50981 | 0.0725940 | 0.0362970 | − | 0.999341i | \(-0.488444\pi\) | ||||
0.0362970 | + | 0.999341i | \(0.488444\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −86.4297 | −0.649847 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 185.339i | 1.35284i | 0.736517 | + | 0.676419i | \(0.236469\pi\) | ||||
−0.736517 | + | 0.676419i | \(0.763531\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 123.803i | 0.890671i | 0.895364 | + | 0.445335i | \(0.146916\pi\) | ||||
−0.895364 | + | 0.445335i | \(0.853084\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 15.0095i | − | 0.106451i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −105.678 | −0.739007 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 10.4636i | − | 0.0711813i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 190.006 | 1.27521 | 0.637605 | − | 0.770364i | \(-0.279925\pi\) | ||||
0.637605 | + | 0.770364i | \(0.279925\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 38.6263i | 0.255803i | 0.991787 | + | 0.127902i | \(0.0408242\pi\) | ||||
−0.991787 | + | 0.127902i | \(0.959176\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 225.735i | − | 1.47539i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −184.991 | −1.17829 | −0.589143 | − | 0.808029i | \(-0.700535\pi\) | ||||
−0.589143 | + | 0.808029i | \(0.700535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.9460 | 0.175761 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 53.6420i | − | 0.333180i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 234.011 | 1.43565 | 0.717827 | − | 0.696222i | \(-0.245137\pi\) | ||||
0.717827 | + | 0.696222i | \(0.245137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 192.032i | 1.14989i | 0.818192 | + | 0.574945i | \(0.194977\pi\) | ||||
−0.818192 | + | 0.574945i | \(0.805023\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 118.233 | 0.699602 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91.9218 | 0.537554 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −190.245 | −1.09968 | −0.549842 | − | 0.835269i | \(-0.685312\pi\) | ||||
−0.549842 | + | 0.835269i | \(0.685312\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 36.8458i | 0.208168i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 271.846i | 1.51869i | 0.650688 | + | 0.759345i | \(0.274481\pi\) | ||||
−0.650688 | + | 0.759345i | \(0.725519\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.78601i | 0.0319669i | 0.999872 | + | 0.0159834i | \(0.00508790\pi\) | ||||
−0.999872 | + | 0.0159834i | \(0.994912\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 66.7862 | 0.364952 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 391.050 | 2.09118 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 93.5971i | 0.495223i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 203.298 | 1.06439 | 0.532194 | − | 0.846622i | \(-0.321368\pi\) | ||||
0.532194 | + | 0.846622i | \(0.321368\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 315.180 | 1.63306 | 0.816529 | − | 0.577304i | \(-0.195895\pi\) | ||||
0.816529 | + | 0.577304i | \(0.195895\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.1674i | 0.117601i | 0.998270 | + | 0.0588006i | \(0.0187276\pi\) | ||||
−0.998270 | + | 0.0588006i | \(0.981272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 141.839i | 0.712758i | 0.934341 | + | 0.356379i | \(0.115989\pi\) | ||||
−0.934341 | + | 0.356379i | \(0.884011\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 14.1197i | − | 0.0702472i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 44.3350i | 0.218399i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 57.0507i | 0.275607i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 159.240i | 0.761914i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −286.662 | −1.35859 | −0.679294 | − | 0.733866i | \(-0.737714\pi\) | ||||
−0.679294 | + | 0.733866i | \(0.737714\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 51.7893i | 0.243142i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.38219 | − | 249.516i | −0.0201944 | − | 1.14984i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.44435 | −0.0339924 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 187.859 | 0.850039 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 63.4396i | 0.284482i | 0.989832 | + | 0.142241i | \(0.0454309\pi\) | ||||
−0.989832 | + | 0.142241i | \(0.954569\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.9019 | −0.0524312 | −0.0262156 | − | 0.999656i | \(-0.508346\pi\) | ||||
−0.0262156 | + | 0.999656i | \(0.508346\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 356.022i | 1.55468i | 0.629081 | + | 0.777340i | \(0.283432\pi\) | ||||
−0.629081 | + | 0.777340i | \(0.716568\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −79.0477 | −0.342198 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −201.013 | −0.862718 | −0.431359 | − | 0.902180i | \(-0.641966\pi\) | ||||
−0.431359 | + | 0.902180i | \(0.641966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.1598 | −0.0808430 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 272.587i | 1.14053i | 0.821461 | + | 0.570265i | \(0.193160\pi\) | ||||
−0.821461 | + | 0.570265i | \(0.806840\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 120.703i | 0.500843i | 0.968137 | + | 0.250422i | \(0.0805693\pi\) | ||||
−0.968137 | + | 0.250422i | \(0.919431\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 150.559i | − | 0.619585i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 76.4981i | 0.309709i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 81.7736 | 0.328408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.519867i | 0.00207118i | 0.999999 | + | 0.00103559i | \(0.000329639\pi\) | ||||
−0.999999 | + | 0.00103559i | \(0.999670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −98.8313 | −0.390638 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 255.224 | 0.993091 | 0.496546 | − | 0.868011i | \(-0.334602\pi\) | ||||
0.496546 | + | 0.868011i | \(0.334602\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 244.864i | 0.945419i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 47.1522i | − | 0.180660i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 324.000i | − | 1.23194i | −0.787770 | − | 0.615970i | \(-0.788764\pi\) | ||
0.787770 | − | 0.615970i | \(-0.211236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −51.7343 | −0.193761 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 75.4742i | − | 0.280573i | −0.990111 | − | 0.140287i | \(-0.955198\pi\) | ||
0.990111 | − | 0.140287i | \(-0.0448024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 379.458i | 1.40021i | 0.714038 | + | 0.700107i | \(0.246864\pi\) | ||||
−0.714038 | + | 0.700107i | \(0.753136\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −37.9741 | −0.139099 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 240.276i | − | 0.867423i | −0.901052 | − | 0.433711i | \(-0.857204\pi\) | ||
0.901052 | − | 0.433711i | \(-0.142796\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.66065 | + | 265.371i | 0.0167048 | + | 0.951152i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.47121 | −0.0230292 | −0.0115146 | − | 0.999934i | \(-0.503665\pi\) | ||||
−0.0115146 | + | 0.999934i | \(0.503665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −140.562 | −0.496686 | −0.248343 | − | 0.968672i | \(-0.579886\pi\) | ||||
−0.248343 | + | 0.968672i | \(0.579886\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −219.471 | −0.764708 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −406.151 | −1.40537 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 16.1520i | − | 0.0555051i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 270.986 | 0.924867 | 0.462434 | − | 0.886654i | \(-0.346976\pi\) | ||||
0.462434 | + | 0.886654i | \(0.346976\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 172.445 | 0.580624 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −47.4781 | −0.158790 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 276.745i | 0.919417i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 18.0862i | − | 0.0596905i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −96.0564 | −0.312887 | −0.156444 | − | 0.987687i | \(-0.550003\pi\) | ||||
−0.156444 | + | 0.987687i | \(0.550003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5.22946i | − | 0.0169238i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 160.058 | 0.514656 | 0.257328 | − | 0.966324i | \(-0.417158\pi\) | ||||
0.257328 | + | 0.966324i | \(0.417158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 128.846i | 0.411649i | 0.978589 | + | 0.205824i | \(0.0659876\pi\) | ||||
−0.978589 | + | 0.205824i | \(0.934012\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −596.199 | −1.88075 | −0.940377 | − | 0.340133i | \(-0.889528\pi\) | ||||
−0.940377 | + | 0.340133i | \(0.889528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 81.6837 | 0.256062 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 87.3908i | 0.272245i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 283.073i | − | 0.876388i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 104.070i | 0.318256i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −182.507 | −0.554732 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 129.482i | 0.391185i | 0.980685 | + | 0.195593i | \(0.0626630\pi\) | ||||
−0.980685 | + | 0.195593i | \(0.937337\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 260.423i | − | 0.782052i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 655.496i | − | 1.94509i | −0.232714 | − | 0.972545i | \(-0.574760\pi\) | ||
0.232714 | − | 0.972545i | \(-0.425240\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 2.85091i | − | 0.00840976i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −459.714 | + | 8.07384i | −1.34813 | + | 0.0236769i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 267.226 | 0.779084 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 458.708i | 1.32192i | 0.750419 | + | 0.660962i | \(0.229852\pi\) | ||||
−0.750419 | + | 0.660962i | \(0.770148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.7444 | 0.0451129 | 0.0225564 | − | 0.999746i | \(-0.492819\pi\) | ||||
0.0225564 | + | 0.999746i | \(0.492819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 82.8420 | 0.236017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 620.487i | 1.75775i | 0.477049 | + | 0.878877i | \(0.341706\pi\) | ||||
−0.477049 | + | 0.878877i | \(0.658294\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 140.519 | 0.393611 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −70.8303 | −0.197299 | −0.0986494 | − | 0.995122i | \(-0.531452\pi\) | ||||
−0.0986494 | + | 0.995122i | \(0.531452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −245.730 | −0.680691 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 65.5308i | 0.180526i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 312.134i | − | 0.850502i | −0.905075 | − | 0.425251i | \(-0.860186\pi\) | ||
0.905075 | − | 0.425251i | \(-0.139814\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 233.417 | 0.632568 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 339.806i | − | 0.915920i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −471.910 | −1.26517 | −0.632587 | − | 0.774489i | \(-0.718007\pi\) | ||||
−0.632587 | + | 0.774489i | \(0.718007\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 39.2405 | 0.104086 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −247.630 | −0.653377 | −0.326688 | − | 0.945132i | \(-0.605933\pi\) | ||||
−0.326688 | + | 0.945132i | \(0.605933\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 93.0355 | 0.244188 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 235.094i | 0.613823i | 0.951738 | + | 0.306911i | \(0.0992955\pi\) | ||||
−0.951738 | + | 0.306911i | \(0.900705\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 294.330i | − | 0.760543i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 672.061i | 1.72766i | 0.503780 | + | 0.863832i | \(0.331942\pi\) | ||||
−0.503780 | + | 0.863832i | \(0.668058\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 175.688 | 0.449329 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.29599i | − | 0.0160203i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.8998 | 0.0551632 | 0.0275816 | − | 0.999620i | \(-0.491219\pi\) | ||||
0.0275816 | + | 0.999620i | \(0.491219\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 57.2210i | 0.143411i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 112.124i | 0.279611i | 0.990179 | + | 0.139805i | \(0.0446477\pi\) | ||||
−0.990179 | + | 0.139805i | \(0.955352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −220.844 | + | 3.87863i | −0.548001 | + | 0.00962440i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 451.142 | 1.10846 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 646.615i | − | 1.58097i | −0.612484 | − | 0.790483i | \(-0.709830\pi\) | ||
0.612484 | − | 0.790483i | \(-0.290170\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 122.704 | 0.298550 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 448.022 | 1.08480 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 81.9642 | 0.196557 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −76.6718 | −0.182987 | −0.0914937 | − | 0.995806i | \(-0.529164\pi\) | ||||
−0.0914937 | + | 0.995806i | \(0.529164\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −598.861 | −1.42247 | −0.711236 | − | 0.702953i | \(-0.751864\pi\) | ||||
−0.711236 | + | 0.702953i | \(0.751864\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 194.104 | 0.458875 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 812.079i | − | 1.90182i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 69.9644i | 0.163087i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 433.382 | 1.00553 | 0.502763 | − | 0.864424i | \(-0.332317\pi\) | ||||
0.502763 | + | 0.864424i | \(0.332317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 472.936i | 1.09223i | 0.837710 | + | 0.546115i | \(0.183894\pi\) | ||||
−0.837710 | + | 0.546115i | \(0.816106\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 71.5419i | 0.163712i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 403.672 | 0.919526 | 0.459763 | − | 0.888042i | \(-0.347934\pi\) | ||||
0.459763 | + | 0.888042i | \(0.347934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 135.316 | 0.306840 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 395.134 | 0.891950 | 0.445975 | − | 0.895045i | \(-0.352857\pi\) | ||||
0.445975 | + | 0.895045i | \(0.352857\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 125.794i | − | 0.281419i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 168.750i | − | 0.375836i | −0.982185 | − | 0.187918i | \(-0.939826\pi\) | ||
0.982185 | − | 0.187918i | \(-0.0601740\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 404.359i | 0.896583i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.5726 | 0.0564517 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 183.891i | 0.402386i | 0.979552 | + | 0.201193i | \(0.0644819\pi\) | ||||
−0.979552 | + | 0.201193i | \(0.935518\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −306.548 | −0.667860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 169.485i | − | 0.367646i | −0.982959 | − | 0.183823i | \(-0.941153\pi\) | ||
0.982959 | − | 0.183823i | \(-0.0588473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 665.325i | 1.43699i | 0.695534 | + | 0.718493i | \(0.255168\pi\) | ||||
−0.695534 | + | 0.718493i | \(0.744832\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −454.044 | −0.972257 | −0.486128 | − | 0.873887i | \(-0.661591\pi\) | ||||
−0.486128 | + | 0.873887i | \(0.661591\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −171.687 | −0.366069 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 122.474i | 0.260029i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 509.880 | 1.07797 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 361.399i | 0.757650i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 708.201 | 1.47850 | 0.739250 | − | 0.673432i | \(-0.235180\pi\) | ||||
0.739250 | + | 0.673432i | \(0.235180\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 216.727 | 0.450575 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −35.5139 | −0.0735277 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 757.573i | 1.55559i | 0.628517 | + | 0.777796i | \(0.283662\pi\) | ||||
−0.628517 | + | 0.777796i | \(0.716338\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 154.928i | − | 0.316826i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 725.518i | 1.47763i | 0.673907 | + | 0.738816i | \(0.264615\pi\) | ||||
−0.673907 | + | 0.738816i | \(0.735385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −145.205 | −0.294534 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 629.726 | 1.26705 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 884.066i | − | 1.77168i | −0.463995 | − | 0.885838i | \(-0.653584\pi\) | ||
0.463995 | − | 0.885838i | \(-0.346416\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 127.135 | 0.253763 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −308.976 | −0.614266 | −0.307133 | − | 0.951667i | \(-0.599370\pi\) | ||||
−0.307133 | + | 0.951667i | \(0.599370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 78.2763i | − | 0.154391i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.6472i | 0.0228825i | 0.999935 | + | 0.0114412i | \(0.00364193\pi\) | ||||
−0.999935 | + | 0.0114412i | \(0.996358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 90.5186i | 0.177140i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 124.830i | − | 0.243333i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 336.254i | 0.650395i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 125.952i | 0.242683i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −99.3399 | −0.190672 | −0.0953358 | − | 0.995445i | \(-0.530392\pi\) | ||||
−0.0953358 | + | 0.995445i | \(0.530392\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 793.172i | − | 1.51658i | −0.651916 | − | 0.758291i | \(-0.726035\pi\) | ||
0.651916 | − | 0.758291i | \(-0.273965\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 817.211 | − | 14.3525i | 1.55069 | − | 0.0272343i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 484.598 | 0.916064 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −476.491 | −0.897347 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 194.252i | 0.364450i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 179.976 | 0.335151 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 234.414i | 0.434905i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 704.672 | 1.30254 | 0.651268 | − | 0.758848i | \(-0.274237\pi\) | ||||
0.651268 | + | 0.758848i | \(0.274237\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.83064 | 0.00705459 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 270.733 | 0.494942 | 0.247471 | − | 0.968895i | \(-0.420400\pi\) | ||||
0.247471 | + | 0.968895i | \(0.420400\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 863.682i | 1.57319i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 59.1291i | − | 0.107312i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 232.971i | 0.421286i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1047.43i | 1.88048i | 0.340515 | + | 0.940239i | \(0.389399\pi\) | ||||
−0.340515 | + | 0.940239i | \(0.610601\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 244.944 | 0.438183 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 258.896i | − | 0.461490i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1003.55 | −1.78250 | −0.891251 | − | 0.453510i | \(-0.850172\pi\) | ||||
−0.891251 | + | 0.453510i | \(0.850172\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −558.339 | −0.984725 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 455.807i | 0.801066i | 0.916282 | + | 0.400533i | \(0.131175\pi\) | ||||
−0.916282 | + | 0.400533i | \(0.868825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 706.187i | 1.23675i | 0.785882 | + | 0.618377i | \(0.212210\pi\) | ||||
−0.785882 | + | 0.618377i | \(0.787790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 134.594i | − | 0.234894i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1137.81 | −1.97194 | −0.985969 | − | 0.166927i | \(-0.946616\pi\) | ||||
−0.985969 | + | 0.166927i | \(0.946616\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 208.666i | − | 0.360390i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 994.316i | − | 1.71139i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −626.066 | −1.07387 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 630.730i | − | 1.07450i | −0.843424 | − | 0.537249i | \(-0.819464\pi\) | ||
0.843424 | − | 0.537249i | \(-0.180536\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.84448 | + | 332.777i | 0.00992272 | + | 0.564987i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.3381 | 0.0259527 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 304.441 | 0.513392 | 0.256696 | − | 0.966492i | \(-0.417366\pi\) | ||||
0.256696 | + | 0.966492i | \(0.417366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 93.9048 | 0.157295 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 701.717 | 1.17148 | 0.585740 | − | 0.810499i | \(-0.300804\pi\) | ||||
0.585740 | + | 0.810499i | \(0.300804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 314.899i | 0.523959i | 0.965073 | + | 0.261980i | \(0.0843753\pi\) | ||||
−0.965073 | + | 0.261980i | \(0.915625\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 182.596 | 0.302813 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −973.580 | −1.60392 | −0.801961 | − | 0.597377i | \(-0.796210\pi\) | ||||
−0.801961 | + | 0.597377i | \(0.796210\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.3521 | 0.0481972 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 161.535i | 0.264378i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 585.418i | − | 0.955005i | −0.878630 | − | 0.477503i | \(-0.841542\pi\) | ||
0.878630 | − | 0.477503i | \(-0.158458\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −529.977 | −0.858957 | −0.429479 | − | 0.903077i | \(-0.641303\pi\) | ||||
−0.429479 | + | 0.903077i | \(0.641303\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 117.342i | 0.189568i | 0.995498 | + | 0.0947839i | \(0.0302160\pi\) | ||||
−0.995498 | + | 0.0947839i | \(0.969784\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 77.4748 | 0.124758 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 629.057i | 1.00972i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 105.425 | 0.168142 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −801.974 | −1.27500 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 558.447i | 0.885020i | 0.896764 | + | 0.442510i | \(0.145912\pi\) | ||||
−0.896764 | + | 0.442510i | \(0.854088\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 189.785i | 0.299819i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 112.611i | 0.176784i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −669.742 | −1.04811 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1124.12i | − | 1.75369i | −0.480770 | − | 0.876847i | \(-0.659643\pi\) | ||
0.480770 | − | 0.876847i | \(-0.340357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 138.217i | − | 0.214957i | −0.994207 | − | 0.107478i | \(-0.965722\pi\) | ||
0.994207 | − | 0.107478i | \(-0.0342777\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 309.147i | 0.477817i | 0.971042 | + | 0.238908i | \(0.0767895\pi\) | ||||
−0.971042 | + | 0.238908i | \(0.923210\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 825.446i | − | 1.27187i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −165.193 | + | 2.90124i | −0.253752 | + | 0.00445659i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −568.866 | −0.871158 | −0.435579 | − | 0.900150i | \(-0.643456\pi\) | ||||
−0.435579 | + | 0.900150i | \(0.643456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 96.2705i | − | 0.146530i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1245.80 | −1.89044 | −0.945219 | − | 0.326436i | \(-0.894152\pi\) | ||||
−0.945219 | + | 0.326436i | \(0.894152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −379.992 | −0.574874 | −0.287437 | − | 0.957800i | \(-0.592803\pi\) | ||||
−0.287437 | + | 0.957800i | \(0.592803\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 124.372i | − | 0.187590i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.6981 | 0.0550197 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.0003 | 0.0627808 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1496.19 | −2.22979 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 602.763i | 0.895635i | 0.894125 | + | 0.447818i | \(0.147799\pi\) | ||||
−0.894125 | + | 0.447818i | \(0.852201\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 439.109i | − | 0.648611i | −0.945952 | − | 0.324305i | \(-0.894869\pi\) | ||
0.945952 | − | 0.324305i | \(-0.105131\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −196.398 | −0.289246 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.87967i | 0.0115707i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 795.860 | 1.16524 | 0.582621 | − | 0.812744i | \(-0.302027\pi\) | ||||
0.582621 | + | 0.812744i | \(0.302027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 235.705 | 0.343093 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −300.759 | −0.436516 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1209.16 | 1.74987 | 0.874933 | − | 0.484243i | \(-0.160905\pi\) | ||||
0.874933 | + | 0.484243i | \(0.160905\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1022.25i | − | 1.47510i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 718.809i | − | 1.03129i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 133.081i | 0.190388i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 586.751 | 0.837020 | 0.418510 | − | 0.908212i | \(-0.362552\pi\) | ||||
0.418510 | + | 0.908212i | \(0.362552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 326.572i | − | 0.464541i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −219.917 | −0.311057 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 631.408i | − | 0.890561i | −0.895391 | − | 0.445280i | \(-0.853104\pi\) | ||
0.895391 | − | 0.445280i | \(-0.146896\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 247.775i | − | 0.348488i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −206.536 | + | 3.62734i | −0.289672 | + | 0.00508744i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 180.467 | 0.251697 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 546.760i | − | 0.760446i | −0.924895 | − | 0.380223i | \(-0.875847\pi\) | ||
0.924895 | − | 0.380223i | \(-0.124153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −63.5870 | −0.0881927 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 79.9119 | 0.110528 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 993.901 | 1.36713 | 0.683563 | − | 0.729891i | \(-0.260429\pi\) | ||||
0.683563 | + | 0.729891i | \(0.260429\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 524.541 | 0.719535 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −906.390 | −1.23993 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −569.055 | −0.776336 | −0.388168 | − | 0.921589i | \(-0.626892\pi\) | ||||
−0.388168 | + | 0.921589i | \(0.626892\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 316.319i | 0.429198i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 879.306i | 1.18986i | 0.803778 | + | 0.594930i | \(0.202820\pi\) | ||||
−0.803778 | + | 0.594930i | \(0.797180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50.6458 | 0.0683479 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 943.673i | − | 1.27008i | −0.772477 | − | 0.635042i | \(-0.780983\pi\) | ||
0.772477 | − | 0.635042i | \(-0.219017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1057.50i | 1.41566i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1062.62 | 1.41871 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 245.490 | 0.326884 | 0.163442 | − | 0.986553i | \(-0.447740\pi\) | ||||
0.163442 | + | 0.986553i | \(0.447740\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.344179 | 0.000457077 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 712.011i | 0.940570i | 0.882515 | + | 0.470285i | \(0.155849\pi\) | ||||
−0.882515 | + | 0.470285i | \(0.844151\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 65.4315i | 0.0862075i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1377.65i | − | 1.81032i | −0.425071 | − | 0.905160i | \(-0.639751\pi\) | ||
0.425071 | − | 0.905160i | \(-0.360249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1265.42 | 1.65848 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 396.540i | − | 0.517002i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −421.796 | −0.548499 | −0.274250 | − | 0.961659i | \(-0.588429\pi\) | ||||
−0.274250 | + | 0.961659i | \(0.588429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 168.972i | − | 0.219160i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 567.102i | − | 0.733637i | −0.930292 | − | 0.366819i | \(-0.880447\pi\) | ||
0.930292 | − | 0.366819i | \(-0.119553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 162.113 | 0.208639 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 292.707 | 0.375747 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1160.22i | − | 1.48556i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −64.0326 | −0.0817785 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 715.550i | − | 0.909212i | −0.890693 | − | 0.454606i | \(-0.849780\pi\) | ||
0.890693 | − | 0.454606i | \(-0.150220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −214.505 | −0.271870 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.6653 | −0.0438246 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −718.764 | −0.906385 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 781.911i | 0.981068i | 0.871422 | + | 0.490534i | \(0.163198\pi\) | ||||
−0.871422 | + | 0.490534i | \(0.836802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 597.743i | − | 0.748114i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 669.030i | − | 0.835243i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 166.773 | 0.207688 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −49.9679 | −0.0619181 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1232.69i | − | 1.52372i | −0.647739 | − | 0.761862i | \(-0.724285\pi\) | ||
0.647739 | − | 0.761862i | \(-0.275715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −366.014 | −0.451312 | −0.225656 | − | 0.974207i | \(-0.572453\pi\) | ||||
−0.225656 | + | 0.974207i | \(0.572453\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 251.221 | 0.309005 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 369.092i | − | 0.451765i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 491.083i | − | 0.599613i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 579.420i | − | 0.705750i | −0.935671 | − | 0.352875i | \(-0.885204\pi\) | ||
0.935671 | − | 0.352875i | \(-0.114796\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 213.733i | − | 0.259699i | −0.991534 | − | 0.129850i | \(-0.958551\pi\) | ||
0.991534 | − | 0.129850i | \(-0.0414495\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1360.90i | − | 1.64559i | −0.568340 | − | 0.822794i | \(-0.692414\pi\) | ||
0.568340 | − | 0.822794i | \(-0.307586\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 509.748i | 0.614896i | 0.951565 | + | 0.307448i | \(0.0994749\pi\) | ||||
−0.951565 | + | 0.307448i | \(0.900525\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −159.075 | −0.191427 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 416.707i | − | 0.500248i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 360.374 | − | 6.32916i | 0.430554 | − | 0.00756172i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −904.240 | −1.07776 | −0.538880 | − | 0.842383i | \(-0.681152\pi\) | ||||
−0.538880 | + | 0.842383i | \(0.681152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 810.669 | 0.963935 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.28428i | 0.00508218i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 796.814 | 0.940749 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 93.0596i | 0.109611i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 202.685 | 0.238173 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 905.373 | 1.06140 | 0.530699 | − | 0.847560i | \(-0.321929\pi\) | ||||
0.530699 | + | 0.847560i | \(0.321929\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 690.248 | 0.805424 | 0.402712 | − | 0.915327i | \(-0.368068\pi\) | ||||
0.402712 | + | 0.915327i | \(0.368068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 451.723i | 0.525871i | 0.964813 | + | 0.262936i | \(0.0846907\pi\) | ||||
−0.964813 | + | 0.262936i | \(0.915309\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 145.302i | 0.168759i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 132.226i | − | 0.153217i | −0.997061 | − | 0.0766083i | \(-0.975591\pi\) | ||
0.997061 | − | 0.0766083i | \(-0.0244091\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 268.894i | 0.310142i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 429.231 | 0.493937 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 151.958i | 0.174464i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 208.878 | 0.239265 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 247.457 | 0.282163 | 0.141081 | − | 0.989998i | \(-0.454942\pi\) | ||||
0.141081 | + | 0.989998i | \(0.454942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 179.407i | − | 0.204104i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 989.137i | − | 1.12274i | −0.827564 | − | 0.561372i | \(-0.810274\pi\) | ||
0.827564 | − | 0.561372i | \(-0.189726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1193.22i | 1.35132i | 0.737213 | + | 0.675661i | \(0.236142\pi\) | ||||
−0.737213 | + | 0.675661i | \(0.763858\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1399.51 | −1.57780 | −0.788898 | − | 0.614524i | \(-0.789348\pi\) | ||||
−0.788898 | + | 0.614524i | \(0.789348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1131.25i | − | 1.27250i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1028.70i | 1.15454i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 243.408 | 0.272573 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.4330i | 0.0350424i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 170.701 | − | 2.99799i | 0.189879 | − | 0.00333480i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1112.93 | 1.23521 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 183.220 | 0.202901 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 701.236 | 0.773138 | 0.386569 | − | 0.922260i | \(-0.373660\pi\) | ||||
0.386569 | + | 0.922260i | \(0.373660\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 233.891 | 0.257306 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 306.403i | 0.336337i | 0.985758 | + | 0.168169i | \(0.0537853\pi\) | ||||
−0.985758 | + | 0.168169i | \(0.946215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1831.95 | −2.00652 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −76.5554 | −0.0834846 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1008.81 | 1.09773 | 0.548865 | − | 0.835911i | \(-0.315060\pi\) | ||||
0.548865 | + | 0.835911i | \(0.315060\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 63.5944i | 0.0690493i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 557.365i | − | 0.603862i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 67.6275 | 0.0729531 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1732.51i | − | 1.86492i | −0.361274 | − | 0.932460i | \(-0.617658\pi\) | ||
0.361274 | − | 0.932460i | \(-0.382342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 169.687 | 0.182264 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 105.967i | − | 0.113577i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1275.33 | −1.36108 | −0.680538 | − | 0.732713i | \(-0.738254\pi\) | ||||
−0.680538 | + | 0.732713i | \(0.738254\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 85.3029 | 0.0908444 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1110.88i | − | 1.18053i | −0.807210 | − | 0.590265i | \(-0.799023\pi\) | ||
0.807210 | − | 0.590265i | \(-0.200977\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 181.667i | 0.192648i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1029.36i | − | 1.08697i | −0.839419 | − | 0.543485i | \(-0.817105\pi\) | ||
0.839419 | − | 0.543485i | \(-0.182895\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 80.1172 | 0.0844228 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 394.715i | 0.415053i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 202.156i | − | 0.212126i | −0.994359 | − | 0.106063i | \(-0.966175\pi\) | ||
0.994359 | − | 0.106063i | \(-0.0338245\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 54.0789i | − | 0.0565088i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1492.00i | − | 1.55579i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −960.407 | + | 33.7452i | −0.999383 | + | 0.0351147i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1130.14 | −1.17356 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 274.969i | 0.284353i | 0.989841 | + | 0.142176i | \(0.0454101\pi\) | ||||
−0.989841 | + | 0.142176i | \(0.954590\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −187.409 | −0.193405 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −684.427 | −0.704868 | −0.352434 | − | 0.935837i | \(-0.614646\pi\) | ||||
−0.352434 | + | 0.935837i | \(0.614646\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 996.634i | − | 1.02429i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1777.11 | −1.81894 | −0.909472 | − | 0.415765i | \(-0.863514\pi\) | ||||
−0.909472 | + | 0.415765i | \(0.863514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1158.99 | 1.18385 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1345.83 | −1.37190 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 899.542i | 0.915099i | 0.889184 | + | 0.457549i | \(0.151273\pi\) | ||||
−0.889184 | + | 0.457549i | \(0.848727\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 120.829i | 0.122421i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 229.075 | 0.231622 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 519.695i | 0.524415i | 0.965012 | + | 0.262207i | \(0.0844505\pi\) | ||||
−0.965012 | + | 0.262207i | \(0.915550\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 85.7241 | 0.0863284 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1390.36 | −1.39454 | −0.697269 | − | 0.716809i | \(-0.745602\pi\) | ||||
−0.697269 | + | 0.716809i | \(0.745602\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −353.654 | −0.354008 |
(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 | 3100.3.d.h.1301.17 | 24 | ||
5.2 | odd | 4 | 620.3.f.c.309.11 | ✓ | 24 | ||
5.3 | odd | 4 | 620.3.f.c.309.14 | yes | 24 | ||
5.4 | even | 2 | inner | 3100.3.d.h.1301.8 | 24 | ||
31.30 | odd | 2 | inner | 3100.3.d.h.1301.18 | 24 | ||
155.92 | even | 4 | 620.3.f.c.309.13 | yes | 24 | ||
155.123 | even | 4 | 620.3.f.c.309.12 | yes | 24 | ||
155.154 | odd | 2 | inner | 3100.3.d.h.1301.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
620.3.f.c.309.11 | ✓ | 24 | 5.2 | odd | 4 | ||
620.3.f.c.309.12 | yes | 24 | 155.123 | even | 4 | ||
620.3.f.c.309.13 | yes | 24 | 155.92 | even | 4 | ||
620.3.f.c.309.14 | yes | 24 | 5.3 | odd | 4 | ||
3100.3.d.h.1301.7 | 24 | 155.154 | odd | 2 | inner | ||
3100.3.d.h.1301.8 | 24 | 5.4 | even | 2 | inner | ||
3100.3.d.h.1301.17 | 24 | 1.1 | even | 1 | trivial | ||
3100.3.d.h.1301.18 | 24 | 31.30 | odd | 2 | inner |