Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4536,2,Mod(3401,4536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4536, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4536.3401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4536 = 2^{3} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4536.k (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: | \(36.2201423569\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3401.48 | ||
Character | \(\chi\) | \(=\) | 4536.3401 |
Dual form | 4536.2.k.a.3401.47 |
$q$-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 \(\left(\mathbb{Z}/4536\mathbb{Z}\right)^\times\).
\(n\) | \(1135\) | \(2269\) | \(2593\) | \(3809\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.83667 | 1.71581 | 0.857906 | − | 0.513806i | \(-0.171765\pi\) | ||||
0.857906 | + | 0.513806i | \(0.171765\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.13644 | + | 1.56064i | −0.807500 | + | 0.589868i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.676306i | − | 0.203914i | −0.994789 | − | 0.101957i | \(-0.967490\pi\) | ||
0.994789 | − | 0.101957i | \(-0.0325104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.87291i | − | 1.35150i | −0.737130 | − | 0.675751i | \(-0.763820\pi\) | ||
0.737130 | − | 0.675751i | \(-0.236180\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.79523 | 1.40555 | 0.702775 | − | 0.711412i | \(-0.251944\pi\) | ||||
0.702775 | + | 0.711412i | \(0.251944\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.22456i | 0.969181i | 0.874741 | + | 0.484590i | \(0.161031\pi\) | ||||
−0.874741 | + | 0.484590i | \(0.838969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.50300i | 1.14745i | 0.819046 | + | 0.573727i | \(0.194503\pi\) | ||||
−0.819046 | + | 0.573727i | \(0.805497\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.72006 | 1.94401 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.91246i | 1.46931i | 0.678443 | + | 0.734653i | \(0.262655\pi\) | ||||
−0.678443 | + | 0.734653i | \(0.737345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.05833i | 0.369687i | 0.982768 | + | 0.184844i | \(0.0591779\pi\) | ||||
−0.982768 | + | 0.184844i | \(0.940822\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.19684 | + | 5.98768i | −1.38552 | + | 1.01210i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.71513 | −1.43276 | −0.716380 | − | 0.697711i | \(-0.754202\pi\) | ||||
−0.716380 | + | 0.697711i | \(0.754202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.68018 | 1.51179 | 0.755895 | − | 0.654693i | \(-0.227202\pi\) | ||||
0.755895 | + | 0.654693i | \(0.227202\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.15091 | −1.09050 | −0.545251 | − | 0.838273i | \(-0.683566\pi\) | ||||
−0.545251 | + | 0.838273i | \(0.683566\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.33218 | −0.194319 | −0.0971594 | − | 0.995269i | \(-0.530976\pi\) | ||||
−0.0971594 | + | 0.995269i | \(0.530976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.12879 | − | 6.66845i | 0.304113 | − | 0.952636i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.18304i | 0.711945i | 0.934496 | + | 0.355972i | \(0.115850\pi\) | ||||
−0.934496 | + | 0.355972i | \(0.884150\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.59476i | − | 0.349878i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.19238 | 0.545801 | 0.272901 | − | 0.962042i | \(-0.412017\pi\) | ||||
0.272901 | + | 0.962042i | \(0.412017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.75025i | 0.352133i | 0.984378 | + | 0.176066i | \(0.0563374\pi\) | ||||
−0.984378 | + | 0.176066i | \(0.943663\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 18.6957i | − | 2.31892i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.55273 | 0.800543 | 0.400271 | − | 0.916397i | \(-0.368916\pi\) | ||||
0.400271 | + | 0.916397i | \(0.368916\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.1515i | − | 1.32344i | −0.749751 | − | 0.661721i | \(-0.769827\pi\) | ||
0.749751 | − | 0.661721i | \(-0.230173\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.65100i | 0.427318i | 0.976908 | + | 0.213659i | \(0.0685381\pi\) | ||||
−0.976908 | + | 0.213659i | \(0.931462\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.05547 | + | 1.44489i | 0.120282 | + | 0.164660i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.2344 | 1.26397 | 0.631985 | − | 0.774981i | \(-0.282240\pi\) | ||||
0.631985 | + | 0.774981i | \(0.282240\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.22558 | 1.01264 | 0.506320 | − | 0.862346i | \(-0.331006\pi\) | ||||
0.506320 | + | 0.862346i | \(0.331006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.2344 | 2.41166 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.79702 | −0.190484 | −0.0952419 | − | 0.995454i | \(-0.530362\pi\) | ||||
−0.0952419 | + | 0.995454i | \(0.530362\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.60487 | + | 10.4107i | 0.797207 | + | 1.09134i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.2083i | 1.66293i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.00814i | − | 0.305431i | −0.988270 | − | 0.152715i | \(-0.951198\pi\) | ||
0.988270 | − | 0.152715i | \(-0.0488018\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.30988 | −0.826864 | −0.413432 | − | 0.910535i | \(-0.635670\pi\) | ||||
−0.413432 | + | 0.910535i | \(0.635670\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.78968i | 0.767540i | 0.923429 | + | 0.383770i | \(0.125375\pi\) | ||||
−0.923429 | + | 0.383770i | \(0.874625\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.50520i | − | 0.532207i | −0.963944 | − | 0.266104i | \(-0.914264\pi\) | ||
0.963944 | − | 0.266104i | \(-0.0857364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.2890 | 1.36864 | 0.684320 | − | 0.729182i | \(-0.260099\pi\) | ||||
0.684320 | + | 0.729182i | \(0.260099\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.29141i | − | 0.497774i | −0.968533 | − | 0.248887i | \(-0.919935\pi\) | ||
0.968533 | − | 0.248887i | \(-0.0800647\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.1132i | 1.96882i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.3812 | + | 9.04429i | −1.13498 | + | 0.829089i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5426 | 0.958419 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 18.1093 | 1.61975 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.23048 | −0.197923 | −0.0989615 | − | 0.995091i | \(-0.531552\pi\) | ||||
−0.0989615 | + | 0.995091i | \(0.531552\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.949268 | −0.0829380 | −0.0414690 | − | 0.999140i | \(-0.513204\pi\) | ||||
−0.0414690 | + | 0.999140i | \(0.513204\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.59303 | − | 9.02554i | −0.571688 | − | 0.782613i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.0132i | − | 1.02635i | −0.858283 | − | 0.513177i | \(-0.828469\pi\) | ||
0.858283 | − | 0.513177i | \(-0.171531\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.22784i | − | 0.188963i | −0.995527 | − | 0.0944816i | \(-0.969881\pi\) | ||
0.995527 | − | 0.0944816i | \(-0.0301194\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.29557 | −0.275590 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.3575i | 2.52105i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.51342i | 0.533600i | 0.963752 | + | 0.266800i | \(0.0859664\pi\) | ||||
−0.963752 | + | 0.266800i | \(0.914034\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.34212 | 0.190599 | 0.0952997 | − | 0.995449i | \(-0.469619\pi\) | ||||
0.0952997 | + | 0.995449i | \(0.469619\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.89714i | 0.634314i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.35248i | 0.187748i | 0.995584 | + | 0.0938742i | \(0.0299251\pi\) | ||||
−0.995584 | + | 0.0938742i | \(0.970075\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.58822 | − | 11.7569i | −0.676846 | − | 0.926570i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0419 | 1.33482 | 0.667412 | − | 0.744689i | \(-0.267402\pi\) | ||||
0.667412 | + | 0.744689i | \(0.267402\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.79813 | 0.448673 | 0.224336 | − | 0.974512i | \(-0.427979\pi\) | ||||
0.224336 | + | 0.974512i | \(0.427979\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7452 | −0.826555 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.94042 | −0.299585 | −0.149792 | − | 0.988717i | \(-0.547861\pi\) | ||||
−0.149792 | + | 0.988717i | \(0.547861\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.7664 | + | 15.1695i | −1.56979 | + | 1.14671i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.52749i | 0.487888i | 0.969789 | + | 0.243944i | \(0.0784412\pi\) | ||||
−0.969789 | + | 0.243944i | \(0.921559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.39901i | 0.475635i | 0.971310 | + | 0.237817i | \(0.0764320\pi\) | ||||
−0.971310 | + | 0.237817i | \(0.923568\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −33.4371 | −2.45835 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.91935i | − | 0.286611i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.9851i | 1.30135i | 0.759355 | + | 0.650677i | \(0.225515\pi\) | ||||
−0.759355 | + | 0.650677i | \(0.774485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.3454 | −1.10459 | −0.552293 | − | 0.833650i | \(-0.686247\pi\) | ||||
−0.552293 | + | 0.833650i | \(0.686247\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.3420i | − | 0.808086i | −0.914740 | − | 0.404043i | \(-0.867605\pi\) | ||
0.914740 | − | 0.404043i | \(-0.132395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.2568i | − | 0.797971i | −0.916957 | − | 0.398986i | \(-0.869362\pi\) | ||
0.916957 | − | 0.398986i | \(-0.130638\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.3485 | − | 16.9045i | −0.866696 | − | 1.18646i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 37.1397 | 2.59395 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.85709 | 0.197629 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.59545 | 0.522892 | 0.261446 | − | 0.965218i | \(-0.415801\pi\) | ||||
0.261446 | + | 0.965218i | \(0.415801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.4357 | −1.87110 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.21232 | − | 4.39751i | −0.218067 | − | 0.298522i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 28.2396i | − | 1.89960i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.3497i | 1.56361i | 0.623521 | + | 0.781807i | \(0.285702\pi\) | ||||
−0.623521 | + | 0.781807i | \(0.714298\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.6211 | −1.03681 | −0.518405 | − | 0.855135i | \(-0.673474\pi\) | ||||
−0.518405 | + | 0.855135i | \(0.673474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.5730i | 0.698684i | 0.936995 | + | 0.349342i | \(0.113595\pi\) | ||||
−0.936995 | + | 0.349342i | \(0.886405\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.08862i | 0.333367i | 0.986010 | + | 0.166683i | \(0.0533057\pi\) | ||||
−0.986010 | + | 0.166683i | \(0.946694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.11115 | −0.333415 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.77477i | − | 0.502908i | −0.967869 | − | 0.251454i | \(-0.919091\pi\) | ||
0.967869 | − | 0.251454i | \(-0.0809087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9058i | 1.60432i | 0.597108 | + | 0.802161i | \(0.296316\pi\) | ||||
−0.597108 | + | 0.802161i | \(0.703684\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.16746 | − | 25.5847i | 0.521800 | − | 1.63454i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.5859 | 1.30985 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.76999 | 0.616676 | 0.308338 | − | 0.951277i | \(-0.400227\pi\) | ||||
0.308338 | + | 0.951277i | \(0.400227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.72171 | 0.233982 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.9817 | 0.934533 | 0.467267 | − | 0.884117i | \(-0.345239\pi\) | ||||
0.467267 | + | 0.884117i | \(0.345239\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.6194 | − | 13.6012i | 1.15695 | − | 0.845138i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.5518i | − | 1.02063i | −0.859988 | − | 0.510314i | \(-0.829529\pi\) | ||
0.859988 | − | 0.510314i | \(-0.170471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.8856i | 1.22156i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.269785 | −0.0164491 | −0.00822455 | − | 0.999966i | \(-0.502618\pi\) | ||||
−0.00822455 | + | 0.999966i | \(0.502618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.3371i | − | 0.810172i | −0.914279 | − | 0.405086i | \(-0.867242\pi\) | ||
0.914279 | − | 0.405086i | \(-0.132758\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 6.57373i | − | 0.396411i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.06822 | 0.124267 | 0.0621336 | − | 0.998068i | \(-0.480210\pi\) | ||||
0.0621336 | + | 0.998068i | \(0.480210\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.84747i | 0.348831i | 0.984672 | + | 0.174415i | \(0.0558036\pi\) | ||||
−0.984672 | + | 0.174415i | \(0.944196\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.7709i | 1.41303i | 0.707698 | + | 0.706515i | \(0.249734\pi\) | ||||
−0.707698 | + | 0.706515i | \(0.750266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.6812 | + | 15.1073i | −1.22077 | + | 0.891756i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5847 | 0.975572 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.94224 | 0.171887 | 0.0859437 | − | 0.996300i | \(-0.472609\pi\) | ||||
0.0859437 | + | 0.996300i | \(0.472609\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0848 | 0.936492 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.8156 | 1.55079 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.2775 | − | 11.1600i | 0.880581 | − | 0.643252i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.5518i | 0.604194i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.8040i | − | 1.30149i | −0.759296 | − | 0.650745i | \(-0.774457\pi\) | ||
0.759296 | − | 0.650745i | \(-0.225543\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.5029 | −1.72966 | −0.864830 | − | 0.502065i | \(-0.832574\pi\) | ||||
−0.864830 | + | 0.502065i | \(0.832574\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.17785i | 0.462239i | 0.972925 | + | 0.231120i | \(0.0742389\pi\) | ||||
−0.972925 | + | 0.231120i | \(0.925761\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.2541i | 0.800593i | 0.916386 | + | 0.400296i | \(0.131093\pi\) | ||||
−0.916386 | + | 0.400296i | \(0.868907\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.35124 | 0.299612 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.4823i | 1.36223i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 47.3649i | − | 2.62733i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.84613 | − | 2.07906i | 0.156912 | − | 0.114622i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0509 | −1.10210 | −0.551048 | − | 0.834473i | \(-0.685772\pi\) | ||||
−0.551048 | + | 0.834473i | \(0.685772\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.1407 | 1.37358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.3860 | −1.60076 | −0.800378 | − | 0.599496i | \(-0.795368\pi\) | ||||
−0.800378 | + | 0.599496i | \(0.795368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.39206 | 0.0753844 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.85904 | + | 17.5691i | 0.316358 | + | 0.948640i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.82412i | 0.0979238i | 0.998801 | + | 0.0489619i | \(0.0155913\pi\) | ||||
−0.998801 | + | 0.0489619i | \(0.984409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 25.3405i | − | 1.35645i | −0.734855 | − | 0.678224i | \(-0.762750\pi\) | ||
0.734855 | − | 0.678224i | \(-0.237250\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.7341 | −0.730992 | −0.365496 | − | 0.930813i | \(-0.619101\pi\) | ||||
−0.365496 | + | 0.930813i | \(0.619101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 42.7847i | − | 2.27078i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.77932i | 0.305021i | 0.988302 | + | 0.152510i | \(0.0487357\pi\) | ||||
−0.988302 | + | 0.152510i | \(0.951264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.15309 | 0.0606891 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0077i | 0.733197i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 34.5495i | − | 1.80347i | −0.432291 | − | 0.901734i | \(-0.642294\pi\) | ||
0.432291 | − | 0.901734i | \(-0.357706\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.08887 | − | 11.0733i | −0.419953 | − | 0.574895i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.44074 | −0.0745986 | −0.0372993 | − | 0.999304i | \(-0.511875\pi\) | ||||
−0.0372993 | + | 0.999304i | \(0.511875\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 38.5567 | 1.98577 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.53029 | −0.232705 | −0.116353 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116353 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.9831 | 0.765600 | 0.382800 | − | 0.923831i | \(-0.374960\pi\) | ||||
0.382800 | + | 0.923831i | \(0.374960\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.04950 | + | 5.54357i | 0.206382 | + | 0.282526i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.3614i | 1.89430i | 0.320797 | + | 0.947148i | \(0.396049\pi\) | ||||
−0.320797 | + | 0.947148i | \(0.603951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.8912i | 1.61281i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 43.1027 | 2.16873 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.4269i | 0.924820i | 0.886666 | + | 0.462410i | \(0.153015\pi\) | ||||
−0.886666 | + | 0.462410i | \(0.846985\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.9614i | − | 1.59608i | −0.602607 | − | 0.798038i | \(-0.705871\pi\) | ||
0.602607 | − | 0.798038i | \(-0.294129\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0301 | 0.499633 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.89410i | 0.292159i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.93490i | 0.0956745i | 0.998855 | + | 0.0478373i | \(0.0152329\pi\) | ||||
−0.998855 | + | 0.0478373i | \(0.984767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.95678 | + | 6.54281i | −0.440734 | + | 0.321950i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.3955 | 1.73750 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0772 | −1.46937 | −0.734684 | − | 0.678410i | \(-0.762670\pi\) | ||||
−0.734684 | + | 0.678410i | \(0.762670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.35950 | −0.114995 | −0.0574974 | − | 0.998346i | \(-0.518312\pi\) | ||||
−0.0574974 | + | 0.998346i | \(0.518312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 56.3300 | 2.73241 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.29215 | − | 5.87575i | −0.207712 | − | 0.284347i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 33.3518i | − | 1.60650i | −0.595643 | − | 0.803249i | \(-0.703103\pi\) | ||
0.595643 | − | 0.803249i | \(-0.296897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.9121i | 0.572459i | 0.958161 | + | 0.286229i | \(0.0924019\pi\) | ||||
−0.958161 | + | 0.286229i | \(0.907598\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.2478 | −1.11209 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 39.4859i | − | 1.88456i | −0.334830 | − | 0.942279i | \(-0.608679\pi\) | ||
0.334830 | − | 0.942279i | \(-0.391321\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.6785i | 1.41007i | 0.709174 | + | 0.705034i | \(0.249068\pi\) | ||||
−0.709174 | + | 0.705034i | \(0.750932\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.89458 | −0.326834 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.9245i | − | 1.31784i | −0.752213 | − | 0.658920i | \(-0.771014\pi\) | ||
0.752213 | − | 0.658920i | \(-0.228986\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.54676i | − | 0.308275i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 29.1774 | + | 39.9424i | 1.36786 | + | 1.87253i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.0779 | −1.68766 | −0.843828 | − | 0.536614i | \(-0.819703\pi\) | ||||
−0.843828 | + | 0.536614i | \(0.819703\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.69884 | −0.125698 | −0.0628488 | − | 0.998023i | \(-0.520019\pi\) | ||||
−0.0628488 | + | 0.998023i | \(0.520019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.9986 | −1.39415 | −0.697077 | − | 0.716996i | \(-0.745516\pi\) | ||||
−0.697077 | + | 0.716996i | \(0.745516\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.1160 | 0.653211 | 0.326605 | − | 0.945161i | \(-0.394095\pi\) | ||||
0.326605 | + | 0.945161i | \(0.394095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.9995 | + | 10.2265i | −0.646438 | + | 0.472214i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.83620i | 0.222369i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41.0630i | 1.88410i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.7032 | −1.58563 | −0.792815 | − | 0.609463i | \(-0.791385\pi\) | ||||
−0.792815 | + | 0.609463i | \(0.791385\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.4680i | 1.93638i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 11.5413i | − | 0.524062i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.2125 | 1.64094 | 0.820472 | − | 0.571686i | \(-0.193711\pi\) | ||||
0.820472 | + | 0.571686i | \(0.193711\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.8597i | 1.52806i | 0.645178 | + | 0.764032i | \(0.276783\pi\) | ||||
−0.645178 | + | 0.764032i | \(0.723217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.8545i | 2.06518i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.4035 | + | 23.8246i | 0.780655 | + | 1.06868i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.7172 | 1.24079 | 0.620395 | − | 0.784289i | \(-0.286972\pi\) | ||||
0.620395 | + | 0.784289i | \(0.286972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.08643 | 0.405144 | 0.202572 | − | 0.979267i | \(-0.435070\pi\) | ||||
0.202572 | + | 0.979267i | \(0.435070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.8823 | −1.41874 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.5351 | 1.22047 | 0.610236 | − | 0.792220i | \(-0.291075\pi\) | ||||
0.610236 | + | 0.792220i | \(0.291075\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.69791 | − | 7.80017i | −0.252061 | − | 0.345059i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.8865i | 1.31696i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.900963i | 0.0396243i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.47559 | 0.152268 | 0.0761341 | − | 0.997098i | \(-0.475742\pi\) | ||||
0.0761341 | + | 0.997098i | \(0.475742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.315295i | 0.0137869i | 0.999976 | + | 0.00689344i | \(0.00219427\pi\) | ||||
−0.999976 | + | 0.00689344i | \(0.997806\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.9285i | 0.519614i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.28301 | −0.316653 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 47.1706i | − | 2.04319i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 21.1216i | − | 0.913168i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.50991 | − | 1.43971i | −0.194256 | − | 0.0620128i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.0741 | 1.67993 | 0.839964 | − | 0.542643i | \(-0.182576\pi\) | ||||
0.839964 | + | 0.542643i | \(0.182576\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 54.8223 | 2.34833 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.21979 | 0.0521544 | 0.0260772 | − | 0.999660i | \(-0.491698\pi\) | ||||
0.0260772 | + | 0.999660i | \(0.491698\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.4266 | −1.42402 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.0017 | + | 17.5329i | −1.02066 | + | 0.745575i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 0.456650i | − | 0.0193489i | −0.999953 | − | 0.00967444i | \(-0.996920\pi\) | ||
0.999953 | − | 0.00967444i | \(-0.00307952\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.8457i | 1.47382i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.5360 | −1.32908 | −0.664541 | − | 0.747251i | \(-0.731373\pi\) | ||||
−0.664541 | + | 0.747251i | \(0.731373\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 20.3014i | − | 0.854086i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 27.8717i | − | 1.16844i | −0.811594 | − | 0.584221i | \(-0.801400\pi\) | ||
0.811594 | − | 0.584221i | \(-0.198600\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.5176 | 1.10973 | 0.554864 | − | 0.831941i | \(-0.312770\pi\) | ||||
0.554864 | + | 0.831941i | \(0.312770\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 53.4895i | 2.23067i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6.69146i | − | 0.278569i | −0.990252 | − | 0.139285i | \(-0.955520\pi\) | ||
0.990252 | − | 0.139285i | \(-0.0444803\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.7099 | + | 14.3978i | −0.817706 | + | 0.597323i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.50532 | 0.145175 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.98775 | 0.288415 | 0.144208 | − | 0.989547i | \(-0.453937\pi\) | ||||
0.144208 | + | 0.989547i | \(0.453937\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.69554 | −0.358294 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.96766 | 0.368258 | 0.184129 | − | 0.982902i | \(-0.441054\pi\) | ||||
0.184129 | + | 0.982902i | \(0.441054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −47.5026 | + | 34.7000i | −1.94742 | + | 1.42256i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 28.3274i | − | 1.15743i | −0.815531 | − | 0.578714i | \(-0.803555\pi\) | ||
0.815531 | − | 0.578714i | \(-0.196445\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.51462i | 0.388110i | 0.980991 | + | 0.194055i | \(0.0621640\pi\) | ||||
−0.980991 | + | 0.194055i | \(0.937836\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 40.4485 | 1.64447 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.7276i | − | 0.597775i | −0.954288 | − | 0.298888i | \(-0.903384\pi\) | ||
0.954288 | − | 0.298888i | \(-0.0966156\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.49160i | 0.262622i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.63782 | −0.348878 | −0.174439 | − | 0.984668i | \(-0.555811\pi\) | ||||
−0.174439 | + | 0.984668i | \(0.555811\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 17.0907i | − | 0.688044i | −0.938962 | − | 0.344022i | \(-0.888210\pi\) | ||
0.938962 | − | 0.344022i | \(-0.111790\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1653i | 0.448769i | 0.974501 | + | 0.224385i | \(0.0720372\pi\) | ||||
−0.974501 | + | 0.224385i | \(0.927963\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.83923 | − | 2.80451i | 0.153816 | − | 0.112360i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.8792 | 0.835170 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.5062 | −2.01382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.1187 | −1.47767 | −0.738835 | − | 0.673886i | \(-0.764624\pi\) | ||||
−0.738835 | + | 0.673886i | \(0.764624\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.55762 | −0.339599 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.4947 | − | 10.3734i | −1.28749 | − | 0.411008i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 18.6540i | − | 0.736789i | −0.929670 | − | 0.368395i | \(-0.879908\pi\) | ||
0.929670 | − | 0.368395i | \(-0.120092\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 38.2617i | − | 1.50890i | −0.656360 | − | 0.754448i | \(-0.727905\pi\) | ||
0.656360 | − | 0.754448i | \(-0.272095\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.28252 | −0.0897350 | −0.0448675 | − | 0.998993i | \(-0.514287\pi\) | ||||
−0.0448675 | + | 0.998993i | \(0.514287\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.83533i | − | 0.111296i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 40.1471i | − | 1.57108i | −0.618813 | − | 0.785538i | \(-0.712386\pi\) | ||
0.618813 | − | 0.785538i | \(-0.287614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.64203 | −0.142306 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 38.9552i | − | 1.51748i | −0.651394 | − | 0.758740i | \(-0.725815\pi\) | ||
0.651394 | − | 0.758740i | \(-0.274185\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.46618i | 0.329296i | 0.986352 | + | 0.164648i | \(0.0526488\pi\) | ||||
−0.986352 | + | 0.164648i | \(0.947351\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −25.2953 | − | 34.6280i | −0.980910 | − | 1.34282i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.5423 | −1.68596 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.86001 | 0.0718048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4592 | 0.673003 | 0.336501 | − | 0.941683i | \(-0.390756\pi\) | ||||
0.336501 | + | 0.941683i | \(0.390756\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −49.0022 | −1.88331 | −0.941654 | − | 0.336581i | \(-0.890729\pi\) | ||||
−0.941654 | + | 0.336581i | \(0.890729\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.69464 | + | 6.42673i | 0.180164 | + | 0.246635i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.1852i | 0.848893i | 0.905453 | + | 0.424446i | \(0.139531\pi\) | ||||
−0.905453 | + | 0.424446i | \(0.860469\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 46.0905i | − | 1.76103i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.2565 | 0.962194 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 30.9122i | − | 1.17596i | −0.808877 | − | 0.587978i | \(-0.799924\pi\) | ||
0.808877 | − | 0.587978i | \(-0.200076\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.54751i | − | 0.324226i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.0989 | 2.12490 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.4719i | 1.22645i | 0.789910 | + | 0.613223i | \(0.210127\pi\) | ||||
−0.789910 | + | 0.613223i | \(0.789873\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 36.8176i | − | 1.38860i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.7536 | − | 12.9688i | 0.667693 | − | 0.487740i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.3668 | 1.92912 | 0.964560 | − | 0.263863i | \(-0.0849966\pi\) | ||||
0.964560 | + | 0.263863i | \(0.0849966\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.3270 | −0.424199 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.6440 | −0.472860 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.9805 | −1.41643 | −0.708216 | − | 0.705996i | \(-0.750500\pi\) | ||||
−0.708216 | + | 0.705996i | \(0.750500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.1569 | − | 16.6422i | −0.452747 | − | 0.619789i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 76.9095i | 2.85635i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9162i | 0.627385i | 0.949525 | + | 0.313693i | \(0.101566\pi\) | ||||
−0.949525 | + | 0.313693i | \(0.898434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.4412 | −1.53276 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30.5533i | − | 1.12851i | −0.825600 | − | 0.564256i | \(-0.809163\pi\) | ||
0.825600 | − | 0.564256i | \(-0.190837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.43165i | − | 0.163242i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.0562 | −0.848138 | −0.424069 | − | 0.905630i | \(-0.639399\pi\) | ||||
−0.424069 | + | 0.905630i | \(0.639399\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.18162i | − | 0.0800358i | −0.999199 | − | 0.0400179i | \(-0.987259\pi\) | ||
0.999199 | − | 0.0400179i | \(-0.0127415\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.9899i | 0.915558i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.59165 | + | 11.7615i | 0.313932 | + | 0.429758i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9373 | −0.691032 | −0.345516 | − | 0.938413i | \(-0.612296\pi\) | ||||
−0.345516 | + | 0.938413i | \(0.612296\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.98597 | 0.327033 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.6383 | 0.423002 | 0.211501 | − | 0.977378i | \(-0.432165\pi\) | ||||
0.211501 | + | 0.977378i | \(0.432165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.27638 | 0.300019 | 0.150009 | − | 0.988685i | \(-0.452070\pi\) | ||||
0.150009 | + | 0.988685i | \(0.452070\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.5277 | + | 22.3001i | −1.10518 | + | 0.807316i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 20.4291i | − | 0.737651i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 52.9232i | − | 1.90846i | −0.299074 | − | 0.954230i | \(-0.596678\pi\) | ||
0.299074 | − | 0.954230i | \(-0.403322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.1905 | 0.402494 | 0.201247 | − | 0.979540i | \(-0.435501\pi\) | ||||
0.201247 | + | 0.979540i | \(0.435501\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.0071i | 0.718676i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.8945i | 1.46520i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.54183 | −0.269868 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.02570i | 0.322141i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.3849i | − | 1.01181i | −0.862589 | − | 0.505905i | \(-0.831159\pi\) | ||
0.862589 | − | 0.505905i | \(-0.168841\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.25800 | + | 11.3048i | 0.293621 | + | 0.401952i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.4017 | 0.475908 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.702842 | 0.0248960 | 0.0124480 | − | 0.999923i | \(-0.496038\pi\) | ||||
0.0124480 | + | 0.999923i | \(0.496038\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.72031 | −0.273125 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.46919 | 0.0871360 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.9502 | − | 45.1072i | −1.16134 | − | 1.58982i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 40.0190i | − | 1.40699i | −0.710699 | − | 0.703496i | \(-0.751621\pi\) | ||
0.710699 | − | 0.703496i | \(-0.248379\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.5473i | 0.581055i | 0.956867 | + | 0.290528i | \(0.0938309\pi\) | ||||
−0.956867 | + | 0.290528i | \(0.906169\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 65.3841 | 2.29031 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 30.2094i | − | 1.05689i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.4553i | 0.713895i | 0.934124 | + | 0.356948i | \(0.116183\pi\) | ||||
−0.934124 | + | 0.356948i | \(0.883817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.99201 | −0.104295 | −0.0521474 | − | 0.998639i | \(-0.516607\pi\) | ||||
−0.0521474 | + | 0.998639i | \(0.516607\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 37.3399i | − | 1.29843i | −0.760603 | − | 0.649217i | \(-0.775097\pi\) | ||
0.760603 | − | 0.649217i | \(-0.224903\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 12.7334i | − | 0.442250i | −0.975246 | − | 0.221125i | \(-0.929027\pi\) | ||
0.975246 | − | 0.221125i | \(-0.0709728\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.3368 | − | 38.6452i | 0.427446 | − | 1.33898i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.2455 | 0.769838 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.71794 | −0.0938338 | −0.0469169 | − | 0.998899i | \(-0.514940\pi\) | ||||
−0.0469169 | + | 0.998899i | \(0.514940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.6070 | −1.15886 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −41.2259 | −1.41821 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.5237 | + | 16.4532i | −0.773923 | + | 0.565340i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 47.9594i | − | 1.64403i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 50.3927i | − | 1.72541i | −0.505705 | − | 0.862707i | \(-0.668767\pi\) | ||
0.505705 | − | 0.862707i | \(-0.331233\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.9527 | 0.613251 | 0.306626 | − | 0.951830i | \(-0.400800\pi\) | ||||
0.306626 | + | 0.951830i | \(0.400800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.7080i | − | 0.433591i | −0.976217 | − | 0.216796i | \(-0.930439\pi\) | ||
0.976217 | − | 0.216796i | \(-0.0695605\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.05813i | − | 0.0700595i | −0.999386 | − | 0.0350298i | \(-0.988847\pi\) | ||
0.999386 | − | 0.0350298i | \(-0.0111526\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.1181 | −0.514031 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.59789i | − | 0.257741i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 31.9308i | − | 1.08193i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.6896 | + | 28.2622i | −1.30795 | + | 0.955436i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.6154 | −0.932506 | −0.466253 | − | 0.884652i | \(-0.654396\pi\) | ||||
−0.466253 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.2629 | 0.345765 | 0.172882 | − | 0.984942i | \(-0.444692\pi\) | ||||
0.172882 | + | 0.984942i | \(0.444692\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.8978 | 1.67919 | 0.839597 | − | 0.543210i | \(-0.182791\pi\) | ||||
0.839597 | + | 0.543210i | \(0.182791\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.0733 | −0.841880 | −0.420940 | − | 0.907089i | \(-0.638300\pi\) | ||||
−0.420940 | + | 0.907089i | \(0.638300\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.76529 | − | 3.48098i | 0.159823 | − | 0.116748i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.62789i | − | 0.188330i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.0438i | 0.837124i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.2865 | −0.543184 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.0369i | 1.00067i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.5509i | 0.816100i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.6948 | −0.653954 | −0.326977 | − | 0.945032i | \(-0.606030\pi\) | ||||
−0.326977 | + | 0.945032i | \(0.606030\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12.6631i | − | 0.419548i | −0.977750 | − | 0.209774i | \(-0.932727\pi\) | ||
0.977750 | − | 0.209774i | \(-0.0672729\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.23931i | − | 0.206491i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.02806 | − | 1.48147i | 0.0669724 | − | 0.0489224i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.9422 | −1.15264 | −0.576318 | − | 0.817226i | \(-0.695511\pi\) | ||||
−0.576318 | + | 0.817226i | \(0.695511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54.3403 | −1.78863 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −84.7116 | −2.78530 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.8195 | −0.781492 | −0.390746 | − | 0.920499i | \(-0.627783\pi\) | ||||
−0.390746 | + | 0.920499i | \(0.627783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.1713 | + | 8.99319i | 0.923276 | + | 0.294740i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 15.0373i | − | 0.491771i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 30.0910i | − | 0.983029i | −0.870869 | − | 0.491514i | \(-0.836444\pi\) | ||
0.870869 | − | 0.491514i | \(-0.163556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.3345 | −0.728083 | −0.364042 | − | 0.931383i | \(-0.618603\pi\) | ||||
−0.364042 | + | 0.931383i | \(0.618603\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53.2700i | 1.73471i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 36.6828i | − | 1.19203i | −0.802972 | − | 0.596016i | \(-0.796749\pi\) | ||
0.802972 | − | 0.596016i | \(-0.203251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.7910 | 0.577520 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 23.4461i | − | 0.759495i | −0.925090 | − | 0.379747i | \(-0.876011\pi\) | ||
0.925090 | − | 0.379747i | \(-0.123989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 69.0028i | 2.23288i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.7482 | + | 25.6654i | 0.605412 | + | 0.828780i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.7633 | 0.863331 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −58.8753 | −1.89526 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.4743 | −1.36588 | −0.682941 | − | 0.730473i | \(-0.739300\pi\) | ||||
−0.682941 | + | 0.730473i | \(0.739300\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.9007 | −0.414002 | −0.207001 | − | 0.978341i | \(-0.566370\pi\) | ||||
−0.207001 | + | 0.978341i | \(0.566370\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.47687 | + | 4.75966i | 0.111463 | + | 0.152588i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.88179i | 0.156182i | 0.996946 | + | 0.0780911i | \(0.0248825\pi\) | ||||
−0.996946 | + | 0.0780911i | \(0.975118\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.21534i | 0.0388423i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.9662 | −0.604929 | −0.302464 | − | 0.953161i | \(-0.597809\pi\) | ||||
−0.302464 | + | 0.953161i | \(0.597809\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 43.5157i | − | 1.38652i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 39.3514i | − | 1.25130i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.1369 | −1.08439 | −0.542197 | − | 0.840251i | \(-0.682407\pi\) | ||||
−0.542197 | + | 0.840251i | \(0.682407\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 43.1885i | − | 1.36917i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4608i | 0.362967i | 0.983394 | + | 0.181484i | \(0.0580899\pi\) | ||||
−0.983394 | + | 0.181484i | \(0.941910\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4536.2.k.a.3401.48 | 48 | ||
3.2 | odd | 2 | inner | 4536.2.k.a.3401.1 | 48 | ||
7.6 | odd | 2 | inner | 4536.2.k.a.3401.2 | 48 | ||
9.2 | odd | 6 | 504.2.bu.a.41.15 | yes | 48 | ||
9.4 | even | 3 | 504.2.bu.a.209.10 | yes | 48 | ||
9.5 | odd | 6 | 1512.2.bu.a.1385.24 | 48 | |||
9.7 | even | 3 | 1512.2.bu.a.881.1 | 48 | |||
21.20 | even | 2 | inner | 4536.2.k.a.3401.47 | 48 | ||
36.7 | odd | 6 | 3024.2.cc.d.881.1 | 48 | |||
36.11 | even | 6 | 1008.2.cc.d.545.10 | 48 | |||
36.23 | even | 6 | 3024.2.cc.d.2897.24 | 48 | |||
36.31 | odd | 6 | 1008.2.cc.d.209.15 | 48 | |||
63.13 | odd | 6 | 504.2.bu.a.209.15 | yes | 48 | ||
63.20 | even | 6 | 504.2.bu.a.41.10 | ✓ | 48 | ||
63.34 | odd | 6 | 1512.2.bu.a.881.24 | 48 | |||
63.41 | even | 6 | 1512.2.bu.a.1385.1 | 48 | |||
252.83 | odd | 6 | 1008.2.cc.d.545.15 | 48 | |||
252.139 | even | 6 | 1008.2.cc.d.209.10 | 48 | |||
252.167 | odd | 6 | 3024.2.cc.d.2897.1 | 48 | |||
252.223 | even | 6 | 3024.2.cc.d.881.24 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bu.a.41.10 | ✓ | 48 | 63.20 | even | 6 | ||
504.2.bu.a.41.15 | yes | 48 | 9.2 | odd | 6 | ||
504.2.bu.a.209.10 | yes | 48 | 9.4 | even | 3 | ||
504.2.bu.a.209.15 | yes | 48 | 63.13 | odd | 6 | ||
1008.2.cc.d.209.10 | 48 | 252.139 | even | 6 | |||
1008.2.cc.d.209.15 | 48 | 36.31 | odd | 6 | |||
1008.2.cc.d.545.10 | 48 | 36.11 | even | 6 | |||
1008.2.cc.d.545.15 | 48 | 252.83 | odd | 6 | |||
1512.2.bu.a.881.1 | 48 | 9.7 | even | 3 | |||
1512.2.bu.a.881.24 | 48 | 63.34 | odd | 6 | |||
1512.2.bu.a.1385.1 | 48 | 63.41 | even | 6 | |||
1512.2.bu.a.1385.24 | 48 | 9.5 | odd | 6 | |||
3024.2.cc.d.881.1 | 48 | 36.7 | odd | 6 | |||
3024.2.cc.d.881.24 | 48 | 252.223 | even | 6 | |||
3024.2.cc.d.2897.1 | 48 | 252.167 | odd | 6 | |||
3024.2.cc.d.2897.24 | 48 | 36.23 | even | 6 | |||
4536.2.k.a.3401.1 | 48 | 3.2 | odd | 2 | inner | ||
4536.2.k.a.3401.2 | 48 | 7.6 | odd | 2 | inner | ||
4536.2.k.a.3401.47 | 48 | 21.20 | even | 2 | inner | ||
4536.2.k.a.3401.48 | 48 | 1.1 | even | 1 | trivial |