Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(337,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.k (of order \(4\), degree \(2\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 337.7 | ||
Character | \(\chi\) | \(=\) | 1148.337 |
Dual form | 1148.2.k.b.729.7 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.796852 | − | 0.796852i | −0.460063 | − | 0.460063i | 0.438613 | − | 0.898676i | \(-0.355470\pi\) |
−0.898676 | + | 0.438613i | \(0.855470\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.53973i | − | 0.688588i | −0.938862 | − | 0.344294i | \(-0.888118\pi\) | ||
0.938862 | − | 0.344294i | \(-0.111882\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.73005i | − | 0.576684i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.10815 | + | 2.10815i | 0.635630 | + | 0.635630i | 0.949475 | − | 0.313844i | \(-0.101617\pi\) |
−0.313844 | + | 0.949475i | \(0.601617\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.47617 | + | 3.47617i | 0.964117 | + | 0.964117i | 0.999378 | − | 0.0352612i | \(-0.0112263\pi\) |
−0.0352612 | + | 0.999378i | \(0.511226\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.22694 | + | 1.22694i | −0.316794 | + | 0.316794i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.03340 | − | 1.03340i | 0.250635 | − | 0.250635i | −0.570596 | − | 0.821231i | \(-0.693288\pi\) |
0.821231 | + | 0.570596i | \(0.193288\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.78503 | − | 2.78503i | 0.638930 | − | 0.638930i | −0.311361 | − | 0.950292i | \(-0.600785\pi\) |
0.950292 | + | 0.311361i | \(0.100785\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.12692i | − | 0.245914i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.78666 | −0.998087 | −0.499043 | − | 0.866577i | \(-0.666315\pi\) | ||||
−0.499043 | + | 0.866577i | \(0.666315\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.62923 | 0.525846 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.76915 | + | 3.76915i | −0.725374 | + | 0.725374i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.87396 | + | 1.87396i | 0.347985 | + | 0.347985i | 0.859358 | − | 0.511374i | \(-0.170863\pi\) |
−0.511374 | + | 0.859358i | \(0.670863\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.64355 | 0.295190 | 0.147595 | − | 0.989048i | \(-0.452847\pi\) | ||||
0.147595 | + | 0.989048i | \(0.452847\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.35977i | − | 0.584860i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.08875 | − | 1.08875i | 0.184033 | − | 0.184033i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.76973 | 1.27734 | 0.638668 | − | 0.769483i | \(-0.279486\pi\) | ||||
0.638668 | + | 0.769483i | \(0.279486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.53999i | − | 0.887109i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.27426 | − | 3.63073i | −0.823701 | − | 0.567025i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.65515i | − | 1.16740i | −0.811970 | − | 0.583700i | \(-0.801604\pi\) | ||
0.811970 | − | 0.583700i | \(-0.198396\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.66381 | −0.397098 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.34706 | − | 6.34706i | 0.925813 | − | 0.925813i | −0.0716188 | − | 0.997432i | \(-0.522817\pi\) |
0.997432 | + | 0.0716188i | \(0.0228165\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.64693 | −0.230616 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.97278 | − | 3.97278i | −0.545704 | − | 0.545704i | 0.379492 | − | 0.925195i | \(-0.376099\pi\) |
−0.925195 | + | 0.379492i | \(0.876099\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.24598 | − | 3.24598i | 0.437688 | − | 0.437688i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.43852 | −0.587896 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.91766 | −0.640225 | −0.320113 | − | 0.947379i | \(-0.603721\pi\) | ||||
−0.320113 | + | 0.947379i | \(0.603721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 14.5639i | − | 1.86472i | −0.361529 | − | 0.932361i | \(-0.617745\pi\) | ||
0.361529 | − | 0.932361i | \(-0.382255\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.22333 | − | 1.22333i | 0.154125 | − | 0.154125i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.35237 | − | 5.35237i | 0.663879 | − | 0.663879i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3876 | + | 11.3876i | −1.39122 | + | 1.39122i | −0.568621 | + | 0.822600i | \(0.692523\pi\) |
−0.822600 | + | 0.568621i | \(0.807477\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.81426 | + | 3.81426i | 0.459183 | + | 0.459183i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.65860 | + | 6.65860i | 0.790231 | + | 0.790231i | 0.981531 | − | 0.191301i | \(-0.0612706\pi\) |
−0.191301 | + | 0.981531i | \(0.561271\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.2332i | − | 1.43178i | −0.698212 | − | 0.715891i | \(-0.746021\pi\) | ||
0.698212 | − | 0.715891i | \(-0.253979\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.09511 | − | 2.09511i | −0.241922 | − | 0.241922i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.98137i | 0.339759i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.18320 | + | 2.18320i | 0.245629 | + | 0.245629i | 0.819174 | − | 0.573545i | \(-0.194432\pi\) |
−0.573545 | + | 0.819174i | \(0.694432\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.816762 | 0.0907513 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0315 | 1.10110 | 0.550551 | − | 0.834801i | \(-0.314418\pi\) | ||||
0.550551 | + | 0.834801i | \(0.314418\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.59115 | − | 1.59115i | −0.172585 | − | 0.172585i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.98653i | − | 0.320190i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.2796 | + | 11.2796i | 1.19564 | + | 1.19564i | 0.975460 | + | 0.220178i | \(0.0706638\pi\) |
0.220178 | + | 0.975460i | \(0.429336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.91605i | 0.515342i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.30967 | − | 1.30967i | −0.135806 | − | 0.135806i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.28820 | − | 4.28820i | −0.439960 | − | 0.439960i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3703 | − | 12.3703i | 1.25601 | − | 1.25601i | 0.303031 | − | 0.952981i | \(-0.402001\pi\) |
0.952981 | − | 0.303031i | \(-0.0979987\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.64721 | − | 3.64721i | 0.366558 | − | 0.366558i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.57688 | − | 2.57688i | 0.256409 | − | 0.256409i | −0.567183 | − | 0.823592i | \(-0.691967\pi\) |
0.823592 | + | 0.567183i | \(0.191967\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.2949i | 1.60558i | 0.596259 | + | 0.802792i | \(0.296653\pi\) | ||||
−0.596259 | + | 0.802792i | \(0.703347\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.73515 | −0.169333 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2066 | −1.18005 | −0.590027 | − | 0.807383i | \(-0.700883\pi\) | ||||
−0.590027 | + | 0.807383i | \(0.700883\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.78183 | − | 9.78183i | 0.936930 | − | 0.936930i | −0.0611962 | − | 0.998126i | \(-0.519492\pi\) |
0.998126 | + | 0.0611962i | \(0.0194915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.19133 | − | 6.19133i | −0.587655 | − | 0.587655i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.7307 | −1.66796 | −0.833982 | − | 0.551791i | \(-0.813945\pi\) | ||||
−0.833982 | + | 0.551791i | \(0.813945\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.37016i | 0.687271i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.01396 | − | 6.01396i | 0.555991 | − | 0.555991i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.46144 | 0.133970 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.11143i | − | 0.191948i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.30965 | + | 7.09596i | 0.118087 | + | 0.639821i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.7470i | − | 1.05068i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.5312 | −1.20070 | −0.600349 | − | 0.799738i | \(-0.704972\pi\) | ||||
−0.600349 | + | 0.799738i | \(0.704972\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.10003 | + | 6.10003i | −0.537077 | + | 0.537077i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.5159i | − | 0.918783i | −0.888234 | − | 0.459391i | \(-0.848068\pi\) | ||
0.888234 | − | 0.459391i | \(-0.151932\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.93863 | 0.341523 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.80348 | + | 5.80348i | 0.499484 | + | 0.499484i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.2794 | + | 13.2794i | −1.13454 | + | 1.13454i | −0.145126 | + | 0.989413i | \(0.546359\pi\) |
−0.989413 | + | 0.145126i | \(0.953641\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0822 | 1.10962 | 0.554811 | − | 0.831977i | \(-0.312791\pi\) | ||||
0.554811 | + | 0.831977i | \(0.312791\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.1153 | −0.851865 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.6566i | 1.22564i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.88538 | − | 2.88538i | 0.239618 | − | 0.239618i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.796852 | − | 0.796852i | 0.0657233 | − | 0.0657233i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.00680408 | − | 0.00680408i | 0.000557412 | − | 0.000557412i | −0.706828 | − | 0.707385i | \(-0.749875\pi\) |
0.707385 | + | 0.706828i | \(0.249875\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.60095 | + | 5.60095i | 0.455799 | + | 0.455799i | 0.897274 | − | 0.441475i | \(-0.145544\pi\) |
−0.441475 | + | 0.897274i | \(0.645544\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.78783 | − | 1.78783i | −0.144537 | − | 0.144537i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.53062i | − | 0.203265i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.88536 | − | 3.88536i | −0.310085 | − | 0.310085i | 0.534857 | − | 0.844942i | \(-0.320365\pi\) |
−0.844942 | + | 0.534857i | \(0.820365\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.33144i | 0.502116i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.38468 | − | 3.38468i | −0.266750 | − | 0.266750i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.6693 | 0.992338 | 0.496169 | − | 0.868226i | \(-0.334740\pi\) | ||||
0.496169 | + | 0.868226i | \(0.334740\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.17313 | −0.402728 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.0232 | + | 15.0232i | 1.16253 | + | 1.16253i | 0.983920 | + | 0.178611i | \(0.0571603\pi\) |
0.178611 | + | 0.983920i | \(0.442840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1676i | 0.859043i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.81825 | − | 4.81825i | −0.368461 | − | 0.368461i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 11.8997i | − | 0.904715i | −0.891837 | − | 0.452357i | \(-0.850583\pi\) | ||
0.891837 | − | 0.452357i | \(-0.149417\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.85915 | + | 1.85915i | 0.140538 | + | 0.140538i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.91865 | + | 3.91865i | 0.294544 | + | 0.294544i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.37511 | + | 1.37511i | −0.102781 | + | 0.102781i | −0.756627 | − | 0.653846i | \(-0.773154\pi\) |
0.653846 | + | 0.756627i | \(0.273154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.45197 | + | 2.45197i | −0.182254 | + | 0.182254i | −0.792337 | − | 0.610083i | \(-0.791136\pi\) |
0.610083 | + | 0.792337i | \(0.291136\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.6053 | + | 11.6053i | −0.857889 | + | 0.857889i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 11.9633i | − | 0.879558i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.35710 | 0.318623 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.33039 | −0.387729 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.90384 | − | 2.90384i | 0.210114 | − | 0.210114i | −0.594202 | − | 0.804316i | \(-0.702532\pi\) |
0.804316 | + | 0.594202i | \(0.202532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.8483 | + | 15.8483i | 1.14079 | + | 1.14079i | 0.988306 | + | 0.152482i | \(0.0487267\pi\) |
0.152482 | + | 0.988306i | \(0.451273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.53009 | −0.610853 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.1165i | 1.57574i | 0.615842 | + | 0.787869i | \(0.288816\pi\) | ||||
−0.615842 | + | 0.787869i | \(0.711184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.5789 | + | 19.5789i | −1.38791 | + | 1.38791i | −0.558207 | + | 0.829702i | \(0.688510\pi\) |
−0.829702 | + | 0.558207i | \(0.811490\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.1485 | 1.28010 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.65017i | 0.186006i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.59035 | + | 8.12093i | −0.390447 | + | 0.567190i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.28117i | 0.575581i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.7425 | 0.812247 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.45388 | − | 2.45388i | 0.168932 | − | 0.168932i | −0.617578 | − | 0.786510i | \(-0.711886\pi\) |
0.786510 | + | 0.617578i | \(0.211886\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 10.6118i | − | 0.727112i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.7869 | −0.803857 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.16217 | + | 1.16217i | 0.0788930 | + | 0.0788930i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.74802 | + | 9.74802i | −0.658710 | + | 0.658710i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.18453 | 0.483284 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.3444 | −1.42933 | −0.714664 | − | 0.699468i | \(-0.753420\pi\) | ||||
−0.714664 | + | 0.699468i | \(0.753420\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 4.54871i | − | 0.303247i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.4739 | + | 15.4739i | −1.02704 | + | 1.02704i | −0.0274179 | + | 0.999624i | \(0.508728\pi\) |
−0.999624 | + | 0.0274179i | \(0.991272\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.90215 | + | 8.90215i | −0.588271 | + | 0.588271i | −0.937163 | − | 0.348892i | \(-0.886558\pi\) |
0.348892 | + | 0.937163i | \(0.386558\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.37571 | − | 2.37571i | 0.156310 | − | 0.156310i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.4969 | − | 11.4969i | −0.753187 | − | 0.753187i | 0.221886 | − | 0.975073i | \(-0.428779\pi\) |
−0.975073 | + | 0.221886i | \(0.928779\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.77275 | − | 9.77275i | −0.637504 | − | 0.637504i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 3.47937i | − | 0.226010i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4710 | − | 12.4710i | −0.806683 | − | 0.806683i | 0.177447 | − | 0.984130i | \(-0.443216\pi\) |
−0.984130 | + | 0.177447i | \(0.943216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6633i | 1.33104i | 0.746380 | + | 0.665519i | \(0.231790\pi\) | ||||
−0.746380 | + | 0.665519i | \(0.768210\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.6566 | + | 10.6566i | 0.683623 | + | 0.683623i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.53973 | 0.0983697 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.3625 | 1.23201 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.99364 | − | 7.99364i | −0.506576 | − | 0.506576i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.19670i | − | 0.328013i | −0.986459 | − | 0.164006i | \(-0.947558\pi\) | ||
0.986459 | − | 0.164006i | \(-0.0524417\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.0910 | − | 10.0910i | −0.634414 | − | 0.634414i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.53582i | 0.158800i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.69943 | + | 9.69943i | 0.605034 | + | 0.605034i | 0.941644 | − | 0.336610i | \(-0.109280\pi\) |
−0.336610 | + | 0.941644i | \(0.609280\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.49403 | + | 5.49403i | 0.341382 | + | 0.341382i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.24204 | − | 3.24204i | 0.200677 | − | 0.200677i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.8975 | + | 12.8975i | −0.795291 | + | 0.795291i | −0.982349 | − | 0.187058i | \(-0.940105\pi\) |
0.187058 | + | 0.982349i | \(0.440105\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.11701 | + | 6.11701i | −0.375765 | + | 0.375765i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 17.9764i | − | 1.10014i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.5268 | −1.31252 | −0.656258 | − | 0.754537i | \(-0.727862\pi\) | ||||
−0.656258 | + | 0.754537i | \(0.727862\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0928 | 0.613094 | 0.306547 | − | 0.951856i | \(-0.400826\pi\) | ||||
0.306547 | + | 0.951856i | \(0.400826\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.91737 | − | 3.91737i | 0.237090 | − | 0.237090i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.54281 | + | 5.54281i | 0.334244 | + | 0.334244i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.5376 | 1.17390 | 0.586951 | − | 0.809623i | \(-0.300328\pi\) | ||||
0.586951 | + | 0.809623i | \(0.300328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.84343i | − | 0.170232i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.3739 | + | 14.3739i | −0.857473 | + | 0.857473i | −0.991040 | − | 0.133567i | \(-0.957357\pi\) |
0.133567 | + | 0.991040i | \(0.457357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7230 | 0.637415 | 0.318707 | − | 0.947853i | \(-0.396751\pi\) | ||||
0.318707 | + | 0.947853i | \(0.396751\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.83412i | 0.404818i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.16215 | − | 6.29678i | −0.0685994 | − | 0.371687i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.8642i | 0.874364i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.7146 | −1.15569 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.30625 | − | 8.30625i | 0.485256 | − | 0.485256i | −0.421549 | − | 0.906805i | \(-0.638514\pi\) |
0.906805 | + | 0.421549i | \(0.138514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.57187i | 0.440851i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.8919 | −0.922140 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.6392 | − | 16.6392i | −0.962272 | − | 0.962272i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.41301 | − | 5.41301i | 0.312001 | − | 0.312001i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.10678 | −0.235929 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.4245 | −1.28403 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.278293i | − | 0.0158830i | −0.999968 | − | 0.00794151i | \(-0.997472\pi\) | ||
0.999968 | − | 0.00794151i | \(-0.00252789\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9846 | − | 12.9846i | 0.738670 | − | 0.738670i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.3892 | − | 19.3892i | 1.09946 | − | 1.09946i | 0.104989 | − | 0.994473i | \(-0.466519\pi\) |
0.994473 | − | 0.104989i | \(-0.0334807\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.2824 | − | 13.2824i | 0.750767 | − | 0.750767i | −0.223855 | − | 0.974622i | \(-0.571864\pi\) |
0.974622 | + | 0.223855i | \(0.0718644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.88360 | − | 1.88360i | −0.106129 | − | 0.106129i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.98498 | + | 1.98498i | 0.111487 | + | 0.111487i | 0.760650 | − | 0.649162i | \(-0.224880\pi\) |
−0.649162 | + | 0.760650i | \(0.724880\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.90115i | 0.442379i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.72684 | + | 9.72684i | 0.542900 | + | 0.542900i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.75608i | − | 0.320277i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.13967 | + | 9.13967i | 0.506977 | + | 0.506977i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.5894 | −0.862093 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.97609 | 0.494868 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.37823 | − | 6.37823i | −0.350579 | − | 0.350579i | 0.509746 | − | 0.860325i | \(-0.329739\pi\) |
−0.860325 | + | 0.509746i | \(0.829739\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 13.4420i | − | 0.736619i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.5339 | + | 17.5339i | 0.957978 | + | 0.957978i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.4522i | 1.60437i | 0.597079 | + | 0.802183i | \(0.296328\pi\) | ||||
−0.597079 | + | 0.802183i | \(0.703672\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.1288 | + | 14.1288i | 0.767369 | + | 0.767369i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.46485 | + | 3.46485i | 0.187632 | + | 0.187632i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.87293 | − | 5.87293i | 0.316188 | − | 0.316188i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.1930 | + | 11.1930i | −0.600871 | + | 0.600871i | −0.940544 | − | 0.339673i | \(-0.889684\pi\) |
0.339673 | + | 0.940544i | \(0.389684\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.72869i | − | 0.253121i | −0.991959 | − | 0.126560i | \(-0.959606\pi\) | ||
0.991959 | − | 0.126560i | \(-0.0403938\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.2045 | −1.39869 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.62589 | 0.0865376 | 0.0432688 | − | 0.999063i | \(-0.486223\pi\) | ||||
0.0432688 | + | 0.999063i | \(0.486223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.2524 | − | 10.2524i | 0.544143 | − | 0.544143i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.16455 | − | 1.16455i | −0.0616348 | − | 0.0616348i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.1493 | 1.06344 | 0.531720 | − | 0.846920i | \(-0.321546\pi\) | ||||
0.531720 | + | 0.846920i | \(0.321546\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.48718i | 0.183536i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.68250 | + | 1.68250i | −0.0883081 | + | 0.0883081i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.8358 | −0.985908 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5103i | 0.653031i | 0.945192 | + | 0.326515i | \(0.105874\pi\) | ||||
−0.945192 | + | 0.326515i | \(0.894126\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.28136 | + | 9.12474i | −0.326994 | + | 0.475015i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5.61836i | − | 0.291691i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.4653 | 0.800762 | 0.400381 | − | 0.916349i | \(-0.368878\pi\) | ||||
0.400381 | + | 0.916349i | \(0.368878\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.36059 | + | 9.36059i | −0.483379 | + | 0.483379i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.0284i | 0.670996i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.2443 | −0.731683 | −0.365841 | − | 0.930677i | \(-0.619219\pi\) | ||||
−0.365841 | + | 0.930677i | \(0.619219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.7824 | + | 10.7824i | 0.552397 | + | 0.552397i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.84275 | − | 9.84275i | 0.502941 | − | 0.502941i | −0.409409 | − | 0.912351i | \(-0.634265\pi\) |
0.912351 | + | 0.409409i | \(0.134265\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.59051 | 0.233954 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.2438 | −0.673221 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 28.6675i | − | 1.45350i | −0.686903 | − | 0.726749i | \(-0.741030\pi\) | ||
0.686903 | − | 0.726749i | \(-0.258970\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.94651 | + | 4.94651i | −0.250156 | + | 0.250156i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.37966 | + | 8.37966i | −0.422698 | + | 0.422698i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.36153 | − | 3.36153i | 0.169137 | − | 0.169137i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.40102 | + | 9.40102i | 0.471824 | + | 0.471824i | 0.902504 | − | 0.430681i | \(-0.141727\pi\) |
−0.430681 | + | 0.902504i | \(0.641727\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.13851 | − | 3.13851i | −0.157122 | − | 0.157122i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.9770i | 1.04754i | 0.851859 | + | 0.523771i | \(0.175475\pi\) | ||||
−0.851859 | + | 0.523771i | \(0.824525\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.71327 | + | 5.71327i | 0.284598 | + | 0.284598i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.25759i | − | 0.0624903i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.3797 | + | 16.3797i | 0.811913 | + | 0.811913i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.84520 | −0.289027 | −0.144513 | − | 0.989503i | \(-0.546162\pi\) | ||||
−0.144513 | + | 0.989503i | \(0.546162\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.1635 | 1.04392 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.47731 | − | 3.47731i | −0.171107 | − | 0.171107i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.4458i | − | 0.758206i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.4246 | − | 10.4246i | −0.510496 | − | 0.510496i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 9.78788i | − | 0.478169i | −0.970999 | − | 0.239085i | \(-0.923153\pi\) | ||
0.970999 | − | 0.239085i | \(-0.0768474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5522 | − | 12.5522i | −0.611755 | − | 0.611755i | 0.331648 | − | 0.943403i | \(-0.392395\pi\) |
−0.943403 | + | 0.331648i | \(0.892395\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.9807 | − | 10.9807i | −0.533902 | − | 0.533902i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.71704 | − | 2.71704i | 0.131796 | − | 0.131796i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.2983 | − | 10.2983i | 0.498368 | − | 0.498368i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.6791 | − | 11.6791i | 0.563873 | − | 0.563873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.8471i | − | 1.58219i | −0.611693 | − | 0.791095i | \(-0.709511\pi\) | ||
0.611693 | − | 0.791095i | \(-0.290489\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.16476 | 0.0559750 | 0.0279875 | − | 0.999608i | \(-0.491090\pi\) | ||||
0.0279875 | + | 0.999608i | \(0.491090\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.59845 | −0.220479 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.3310 | + | 13.3310i | −0.637708 | + | 0.637708i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.71968 | − | 7.71968i | −0.368440 | − | 0.368440i | 0.498468 | − | 0.866908i | \(-0.333896\pi\) |
−0.866908 | + | 0.498468i | \(0.833896\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.73005 | 0.0823834 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4.62164i | − | 0.219581i | −0.993955 | − | 0.109790i | \(-0.964982\pi\) | ||
0.993955 | − | 0.109790i | \(-0.0350179\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.3676 | − | 17.3676i | 0.823302 | − | 0.823302i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0108437 | −0.000512889 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.7864i | − | 0.745006i | −0.928031 | − | 0.372503i | \(-0.878500\pi\) | ||
0.928031 | − | 0.372503i | \(-0.121500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.46480 | − | 18.7730i | −0.163151 | − | 0.883988i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 8.92627i | − | 0.419393i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.56939 | 0.354858 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.44056 | − | 7.44056i | 0.348055 | − | 0.348055i | −0.511330 | − | 0.859385i | \(-0.670847\pi\) |
0.859385 | + | 0.511330i | \(0.170847\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.79006i | 0.363609i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.885724 | −0.0412523 | −0.0206261 | − | 0.999787i | \(-0.506566\pi\) | ||||
−0.0206261 | + | 0.999787i | \(0.506566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.58178 | + | 1.58178i | 0.0735117 | + | 0.0735117i | 0.742907 | − | 0.669395i | \(-0.233447\pi\) |
−0.669395 | + | 0.742907i | \(0.733447\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.01653 | + | 2.01653i | −0.0935145 | + | 0.0935145i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.75929 | −0.266508 | −0.133254 | − | 0.991082i | \(-0.542543\pi\) | ||||
−0.133254 | + | 0.991082i | \(0.542543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.1045 | −0.743639 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.19211i | 0.285317i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.1382 | − | 16.1382i | 0.742035 | − | 0.742035i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.32250 | − | 7.32250i | 0.335979 | − | 0.335979i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.87312 | + | 6.87312i | −0.314699 | + | 0.314699i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.64839 | − | 4.64839i | −0.212391 | − | 0.212391i | 0.592892 | − | 0.805282i | \(-0.297986\pi\) |
−0.805282 | + | 0.592892i | \(0.797986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.0089 | + | 27.0089i | 1.23150 | + | 1.23150i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.39418i | 0.245444i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.0469 | − | 19.0469i | −0.864875 | − | 0.864875i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.1042i | 1.00164i | 0.865552 | + | 0.500818i | \(0.166968\pi\) | ||||
−0.865552 | + | 0.500818i | \(0.833032\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.0956 | − | 10.0956i | −0.456538 | − | 0.456538i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6325 | −1.29217 | −0.646084 | − | 0.763266i | \(-0.723595\pi\) | ||||
−0.646084 | + | 0.763266i | \(0.723595\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.87308 | 0.174435 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.61571 | − | 5.61571i | −0.252407 | − | 0.252407i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.41669i | 0.422396i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.11218 | − | 3.11218i | −0.139320 | − | 0.139320i | 0.634007 | − | 0.773327i | \(-0.281409\pi\) |
−0.773327 | + | 0.634007i | \(0.781409\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 23.9426i | − | 1.06967i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.93325 | + | 2.93325i | 0.130787 | + | 0.130787i | 0.769470 | − | 0.638683i | \(-0.220520\pi\) |
−0.638683 | + | 0.769470i | \(0.720520\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.96770 | − | 3.96770i | −0.176560 | − | 0.176560i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.89889 | − | 8.89889i | 0.395214 | − | 0.395214i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.8828 | − | 13.8828i | 0.615344 | − | 0.615344i | −0.328989 | − | 0.944334i | \(-0.606708\pi\) |
0.944334 | + | 0.328989i | \(0.106708\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.65015 | − | 8.65015i | 0.382660 | − | 0.382660i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.9944i | 0.926927i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.0897 | 1.10559 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.7611 | 1.17695 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.48228 | + | 9.48228i | −0.416226 | + | 0.416226i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.27330 | + | 2.27330i | 0.0995951 | + | 0.0995951i | 0.755149 | − | 0.655554i | \(-0.227565\pi\) |
−0.655554 | + | 0.755149i | \(0.727565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.07618 | −0.178239 | −0.0891195 | − | 0.996021i | \(-0.528405\pi\) | ||||
−0.0891195 | + | 0.996021i | \(0.528405\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 2.96293i | − | 0.129313i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.69844 | − | 1.69844i | 0.0739852 | − | 0.0739852i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.0879250 | −0.00382283 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.50781i | 0.369208i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.71318 | − | 30.9553i | −0.247465 | − | 1.34082i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.7948i | 0.812572i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.19152 | 0.0945712 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.10815 | + | 2.10815i | −0.0908043 | + | 0.0908043i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 12.8281i | − | 0.551523i | −0.961226 | − | 0.275761i | \(-0.911070\pi\) | ||
0.961226 | − | 0.275761i | \(-0.0889299\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.90772 | 0.167696 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.0614 | − | 15.0614i | −0.645159 | − | 0.645159i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.3801 | + | 30.3801i | −1.29896 | + | 1.29896i | −0.369878 | + | 0.929080i | \(0.620601\pi\) |
−0.929080 | + | 0.369878i | \(0.879399\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.1964 | −1.07536 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.4381 | 0.444676 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.08751i | 0.131294i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.53297 | + | 9.53297i | −0.404652 | + | 0.404652i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.7939 | − | 26.7939i | 1.13530 | − | 1.13530i | 0.146013 | − | 0.989283i | \(-0.453356\pi\) |
0.989283 | − | 0.146013i | \(-0.0466440\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.6106 | − | 26.6106i | 1.12551 | − | 1.12551i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.47197 | − | 3.47197i | −0.146587 | − | 0.146587i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.1972 | − | 14.1972i | −0.598341 | − | 0.598341i | 0.341530 | − | 0.939871i | \(-0.389055\pi\) |
−0.939871 | + | 0.341530i | \(0.889055\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.3005i | 1.14854i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.577538 | + | 0.577538i | 0.0242543 | + | 0.0242543i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.2476i | 0.723059i | 0.932361 | + | 0.361529i | \(0.117745\pi\) | ||||
−0.932361 | + | 0.361529i | \(0.882255\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.2139 | − | 11.2139i | −0.469286 | − | 0.469286i | 0.432397 | − | 0.901683i | \(-0.357668\pi\) |
−0.901683 | + | 0.432397i | \(0.857668\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.62786 | −0.193332 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.5852 | −0.524840 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.19548 | + | 1.19548i | 0.0497686 | + | 0.0497686i | 0.731553 | − | 0.681785i | \(-0.238796\pi\) |
−0.681785 | + | 0.731553i | \(0.738796\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 25.2576i | − | 1.04967i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.09336 | + | 7.09336i | 0.294282 | + | 0.294282i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 16.7504i | − | 0.693732i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.25987 | − | 9.25987i | −0.382849 | − | 0.382849i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.6662 | + | 27.6662i | 1.14191 | + | 1.14191i | 0.988101 | + | 0.153807i | \(0.0491534\pi\) |
0.153807 | + | 0.988101i | \(0.450847\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.57734 | − | 4.57734i | 0.188606 | − | 0.188606i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.6236 | − | 17.6236i | 0.724939 | − | 0.724939i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.1669 | + | 31.1669i | −1.27987 | + | 1.27987i | −0.339135 | + | 0.940738i | \(0.610134\pi\) |
−0.940738 | + | 0.339135i | \(0.889866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2.25023i | − | 0.0922503i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.2029 | 1.27705 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.5895 | −0.800404 | −0.400202 | − | 0.916427i | \(-0.631060\pi\) | ||||
−0.400202 | + | 0.916427i | \(0.631060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.2511 | − | 20.2511i | 0.826060 | − | 0.826060i | −0.160910 | − | 0.986969i | \(-0.551443\pi\) |
0.986969 | + | 0.160910i | \(0.0514427\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.7012 | + | 19.7012i | 0.802295 | + | 0.802295i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.25103 | −0.132173 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.1875i | 0.900564i | 0.892886 | + | 0.450282i | \(0.148677\pi\) | ||||
−0.892886 | + | 0.450282i | \(0.851323\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.11180 | − | 2.11180i | 0.0855743 | − | 0.0855743i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44.1269 | 1.78518 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.4171i | 1.71321i | 0.515972 | + | 0.856605i | \(0.327431\pi\) | ||||
−0.515972 | + | 0.856605i | \(0.672569\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.9259 | − | 2.01650i | 0.440573 | − | 0.0813133i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.3536i | 0.980439i | 0.871599 | + | 0.490219i | \(0.163083\pi\) | ||||
−0.871599 | + | 0.490219i | \(0.836917\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.96324 | 0.400456 | 0.200228 | − | 0.979749i | \(-0.435832\pi\) | ||||
0.200228 | + | 0.979749i | \(0.435832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0416 | − | 18.0416i | 0.723986 | − | 0.723986i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.9518i | 0.639095i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.94098 | −0.197639 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.35706 | − | 9.35706i | −0.373685 | − | 0.373685i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.02921 | − | 8.02921i | 0.320145 | − | 0.320145i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.3991 | 1.88693 | 0.943465 | − | 0.331472i | \(-0.107545\pi\) | ||||
0.943465 | + | 0.331472i | \(0.107545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.91077 | −0.155439 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.8344i | 0.826787i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.47617 | + | 3.47617i | −0.137731 | + | 0.137731i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.5197 | − | 11.5197i | 0.455713 | − | 0.455713i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.8876 | − | 18.8876i | 0.746016 | − | 0.746016i | −0.227713 | − | 0.973728i | \(-0.573125\pi\) |
0.973728 | + | 0.227713i | \(0.0731247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.2009 | − | 15.2009i | −0.599464 | − | 0.599464i | 0.340706 | − | 0.940170i | \(-0.389334\pi\) |
−0.940170 | + | 0.340706i | \(0.889334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.39239 | + | 9.39239i | 0.369825 | + | 0.369825i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 19.2251i | − | 0.755817i | −0.925843 | − | 0.377908i | \(-0.876643\pi\) | ||
0.925843 | − | 0.377908i | \(-0.123357\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.3672 | − | 10.3672i | −0.406947 | − | 0.406947i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.85215i | − | 0.0725915i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.3416 | − | 14.3416i | −0.561231 | − | 0.561231i | 0.368426 | − | 0.929657i | \(-0.379897\pi\) |
−0.929657 | + | 0.368426i | \(0.879897\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.1917 | −0.632663 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.1640 | −0.825686 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.8346 | − | 22.8346i | −0.889509 | − | 0.889509i | 0.104967 | − | 0.994476i | \(-0.466526\pi\) |
−0.994476 | + | 0.104967i | \(0.966526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.9825i | − | 0.427171i | −0.976924 | − | 0.213586i | \(-0.931486\pi\) | ||
0.976924 | − | 0.213586i | \(-0.0685143\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.72501 | − | 5.72501i | −0.222341 | − | 0.222341i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 6.06443i | − | 0.235168i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.96998 | − | 8.96998i | −0.347319 | − | 0.347319i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.0083 | + | 17.0083i | 0.657581 | + | 0.657581i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.7029 | − | 30.7029i | 1.18527 | − | 1.18527i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.7203 | + | 10.7203i | −0.413239 | + | 0.413239i | −0.882865 | − | 0.469626i | \(-0.844389\pi\) |
0.469626 | + | 0.882865i | \(0.344389\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.90998 | + | 9.90998i | −0.381435 | + | 0.381435i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.0998855i | 0.00383891i | 0.999998 | + | 0.00191946i | \(0.000610982\pi\) | ||||
−0.999998 | + | 0.00191946i | \(0.999389\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4942 | 0.671367 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.6609 | 0.945008 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.4954 | + | 18.4954i | −0.707705 | + | 0.707705i | −0.966052 | − | 0.258347i | \(-0.916822\pi\) |
0.258347 | + | 0.966052i | \(0.416822\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.4468 | + | 20.4468i | 0.781230 | + | 0.781230i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.1874 | 0.541283 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 27.6202i | − | 1.05224i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.26188 | − | 4.26188i | 0.162129 | − | 0.162129i | −0.621380 | − | 0.783509i | \(-0.713428\pi\) |
0.783509 | + | 0.621380i | \(0.213428\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.15793 | 0.195933 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 20.1431i | − | 0.764072i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.20238 | + | 1.69841i | −0.348565 | + | 0.0643320i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.3227i | 0.693027i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.5159 | 1.26588 | 0.632939 | − | 0.774202i | \(-0.281848\pi\) | ||||
0.632939 | + | 0.774202i | \(0.281848\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.6389 | − | 21.6389i | 0.816128 | − | 0.816128i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.5749i | 0.586584i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.64426 | 0.137056 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.96607 | − | 1.96607i | −0.0738374 | − | 0.0738374i | 0.669224 | − | 0.743061i | \(-0.266627\pi\) |
−0.743061 | + | 0.669224i | \(0.766627\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.77705 | − | 3.77705i | 0.141650 | − | 0.141650i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.86711 | −0.294626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.5672 | 0.843964 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.8751i | 0.742250i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.4776 | + | 18.4776i | −0.689099 | + | 0.689099i | −0.962033 | − | 0.272934i | \(-0.912006\pi\) |
0.272934 | + | 0.962033i | \(0.412006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5222 | + | 11.5222i | −0.429110 | + | 0.429110i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.4656 | − | 16.4656i | 0.612362 | − | 0.612362i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.92706 | + | 4.92706i | 0.182987 | + | 0.182987i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2309 | − | 18.2309i | −0.676148 | − | 0.676148i | 0.282978 | − | 0.959126i | \(-0.408678\pi\) |
−0.959126 | + | 0.282978i | \(0.908678\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 19.4338i | − | 0.719770i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.91080 | − | 7.91080i | −0.292592 | − | 0.292592i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7998i | 0.472773i | 0.971659 | + | 0.236386i | \(0.0759631\pi\) | ||||
−0.971659 | + | 0.236386i | \(0.924037\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.22694 | − | 1.22694i | −0.0452563 | − | 0.0452563i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.0136 | −1.76860 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.1712 | 1.22022 | 0.610111 | − | 0.792316i | \(-0.291125\pi\) | ||||
0.610111 | + | 0.792316i | \(0.291125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.4291 | − | 15.4291i | −0.566801 | − | 0.566801i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.7424i | 0.760965i | 0.924788 | + | 0.380483i | \(0.124242\pi\) | ||||
−0.924788 | + | 0.380483i | \(0.875758\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0104764 | − | 0.0104764i | −0.000383827 | − | 0.000383827i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 17.3551i | − | 0.634988i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.63136 | − | 8.63136i | −0.315383 | − | 0.315383i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5095 | − | 11.5095i | −0.419988 | − | 0.419988i | 0.465212 | − | 0.885199i | \(-0.345978\pi\) |
−0.885199 | + | 0.465212i | \(0.845978\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.14100 | + | 4.14100i | −0.150906 | + | 0.150906i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.62396 | − | 8.62396i | 0.313858 | − | 0.313858i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.3908 | + | 37.3908i | −1.35899 | + | 1.35899i | −0.483832 | + | 0.875161i | \(0.660755\pi\) |
−0.875161 | + | 0.483832i | \(0.839245\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.0820i | 0.583741i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.5281 | −1.50539 | −0.752696 | − | 0.658368i | \(-0.771247\pi\) | ||||
−0.752696 | + | 0.658368i | \(0.771247\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8336 | 0.500810 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.75277 | + | 2.75277i | −0.0995268 | + | 0.0995268i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.0946 | − | 17.0946i | −0.617252 | − | 0.617252i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.8257 | −1.03948 | −0.519740 | − | 0.854324i | \(-0.673971\pi\) | ||||
−0.519740 | + | 0.854324i | \(0.673971\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 15.4580i | − | 0.556707i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.35719 | + | 9.35719i | −0.336555 | + | 0.336555i | −0.855069 | − | 0.518514i | \(-0.826485\pi\) |
0.518514 | + | 0.855069i | \(0.326485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.32128 | 0.155225 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 8.75586i | − | 0.314115i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.8007 | + | 4.57727i | −0.888577 | + | 0.163998i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.0746i | 1.00459i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.1264 | −0.504838 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.98240 | + | 5.98240i | −0.213521 | + | 0.213521i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.83827i | 0.279404i | 0.990194 | + | 0.139702i | \(0.0446145\pi\) | ||||
−0.990194 | + | 0.139702i | \(0.955385\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.5547 | 0.731768 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.5375 | − | 12.5375i | −0.445782 | − | 0.445782i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.6268 | − | 50.6268i | 1.79781 | − | 1.79781i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.74871 | 0.345751 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.46476 | −0.0873063 | −0.0436531 | − | 0.999047i | \(-0.513900\pi\) | ||||
−0.0436531 | + | 0.999047i | \(0.513900\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 13.1180i | − | 0.464083i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.5143 | − | 19.5143i | 0.689505 | − | 0.689505i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.7893 | − | 25.7893i | 0.910085 | − | 0.910085i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.21149 | + | 5.21149i | −0.183681 | + | 0.183681i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.1537 | + | 17.1537i | 0.603840 | + | 0.603840i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.1927 | + | 37.1927i | 1.30762 | + | 1.30762i | 0.923125 | + | 0.384499i | \(0.125626\pi\) |
0.384499 | + | 0.923125i | \(0.374374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.3121i | 1.59112i | 0.605872 | + | 0.795562i | \(0.292824\pi\) | ||||
−0.605872 | + | 0.795562i | \(0.707176\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.04247 | − | 8.04247i | −0.282062 | − | 0.282062i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 19.5073i | − | 0.683312i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.3198 | − | 21.3198i | −0.745887 | − | 0.745887i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.50503 | 0.297190 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.1172 | 0.632294 | 0.316147 | − | 0.948710i | \(-0.397611\pi\) | ||||
0.316147 | + | 0.948710i | \(0.397611\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.0416319 | − | 0.0416319i | −0.00145120 | − | 0.00145120i | 0.706381 | − | 0.707832i | \(-0.250327\pi\) |
−0.707832 | + | 0.706381i | \(0.750327\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 8.83360i | − | 0.307547i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.5775 | − | 22.5775i | −0.785096 | − | 0.785096i | 0.195590 | − | 0.980686i | \(-0.437338\pi\) |
−0.980686 | + | 0.195590i | \(0.937338\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.15708i | − | 0.144381i | −0.997391 | − | 0.0721907i | \(-0.977001\pi\) | ||
0.997391 | − | 0.0721907i | \(-0.0229990\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.5686 | − | 15.5686i | −0.540069 | − | 0.540069i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.03340 | + | 1.03340i | 0.0358051 | + | 0.0358051i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.1317 | − | 23.1317i | 0.800505 | − | 0.800505i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.19480 | + | 6.19480i | −0.214123 | + | 0.214123i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.1033 | − | 10.1033i | 0.348805 | − | 0.348805i | −0.510860 | − | 0.859664i | \(-0.670673\pi\) |
0.859664 | + | 0.510860i | \(0.170673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 21.9766i | − | 0.757813i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.9077 | 0.788983 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.1950 | 0.591527 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.49300 | − | 1.49300i | 0.0513002 | − | 0.0513002i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.54463 | − | 8.54463i | −0.293251 | − | 0.293251i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.1910 | −1.27489 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.6213i | 0.706059i | 0.935612 | + | 0.353030i | \(0.114849\pi\) | ||||
−0.935612 | + | 0.353030i | \(0.885151\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.41881 | + | 7.41881i | −0.253718 | + | 0.253718i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.8223 | −1.29199 | −0.645993 | − | 0.763343i | \(-0.723557\pi\) | ||||
−0.645993 | + | 0.763343i | \(0.723557\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.95043i | − | 0.203026i | −0.994834 | − | 0.101513i | \(-0.967632\pi\) | ||
0.994834 | − | 0.101513i | \(-0.0323684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.09154 | + | 5.94366i | −0.139439 | + | 0.202560i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.7731i | 1.59218i | 0.605181 | + | 0.796088i | \(0.293101\pi\) | ||||
−0.605181 | + | 0.796088i | \(0.706899\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.3223 | −0.622976 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.8446 | − | 11.8446i | 0.402262 | − | 0.402262i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.20501i | 0.312258i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −79.1707 | −2.68260 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.4012 | − | 21.4012i | −0.724322 | − | 0.724322i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.30635 | − | 8.30635i | 0.280806 | − | 0.280806i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.92942 | −0.200222 | −0.100111 | − | 0.994976i | \(-0.531920\pi\) | ||||
−0.100111 | + | 0.994976i | \(0.531920\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.2377 | −0.446497 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.33561i | 0.314525i | 0.987557 | + | 0.157262i | \(0.0502668\pi\) | ||||
−0.987557 | + | 0.157262i | \(0.949733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.4310 | − | 27.4310i | 0.923126 | − | 0.923126i | −0.0741233 | − | 0.997249i | \(-0.523616\pi\) |
0.997249 | + | 0.0741233i | \(0.0236158\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.03367 | − | 6.03367i | 0.202819 | − | 0.202819i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.0340644 | + | 0.0340644i | −0.00114377 | + | 0.00114377i | −0.707678 | − | 0.706535i | \(-0.750257\pi\) |
0.706535 | + | 0.707678i | \(0.250257\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.56800 | − | 9.56800i | −0.320900 | − | 0.320900i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.72185 | + | 1.72185i | 0.0576843 | + | 0.0576843i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 35.3535i | − | 1.18306i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.11730 | + | 2.11730i | 0.0707736 | + | 0.0707736i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.5180i | 0.885412i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.07994 | + | 3.07994i | 0.102722 | + | 0.102722i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.21092 | −0.273545 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.62674 | −0.287080 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.77537 | + | 3.77537i | 0.125498 | + | 0.125498i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.8248i | 1.25595i | 0.778232 | + | 0.627977i | \(0.216117\pi\) | ||||
−0.778232 | + | 0.627977i | \(0.783883\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.45814 | − | 4.45814i | −0.147867 | − | 0.147867i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0351i | 0.995107i | 0.867433 | + | 0.497554i | \(0.165768\pi\) | ||||
−0.867433 | + | 0.497554i | \(0.834232\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.1479 | + | 21.1479i | 0.699894 | + | 0.699894i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.8690 | + | 17.8690i | 0.590732 | + | 0.590732i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.43590 | − | 7.43590i | 0.245555 | − | 0.245555i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.7481 | + | 10.7481i | −0.354546 | + | 0.354546i | −0.861798 | − | 0.507252i | \(-0.830661\pi\) |
0.507252 | + | 0.861798i | \(0.330661\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.221759 | + | 0.221759i | −0.00730719 | + | 0.00730719i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.2929i | 1.52375i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.4284 | 0.671682 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.1910 | 0.925915 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.6451 | + | 19.6451i | −0.644533 | + | 0.644533i | −0.951667 | − | 0.307133i | \(-0.900630\pi\) |
0.307133 | + | 0.951667i | \(0.400630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.78503 | + | 2.78503i | 0.0912758 | + | 0.0912758i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.9007 | −1.01164 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 6.70876i | − | 0.219400i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.7625 | + | 32.7625i | −1.07030 | + | 1.07030i | −0.0729699 | + | 0.997334i | \(0.523248\pi\) |
−0.997334 | + | 0.0729699i | \(0.976752\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.1683 | −0.690800 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 15.5708i | − | 0.507594i | −0.967257 | − | 0.253797i | \(-0.918320\pi\) | ||
0.967257 | − | 0.253797i | \(-0.0816795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.2461 | + | 17.3791i | 0.822125 | + | 0.565940i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.20736i | 0.266985i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55.7617 | −1.81201 | −0.906006 | − | 0.423264i | \(-0.860884\pi\) | ||||
−0.906006 | + | 0.423264i | \(0.860884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.5246 | − | 42.5246i | 1.38041 | − | 1.38041i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.16347i | − | 0.102582i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.7532 | −0.996195 | −0.498098 | − | 0.867121i | \(-0.665968\pi\) | ||||
−0.498098 | + | 0.867121i | \(0.665968\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.47112 | − | 4.47112i | −0.144682 | − | 0.144682i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.29605 | − | 6.29605i | 0.203522 | − | 0.203522i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.7800 | −0.606437 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2987 | −0.912863 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.1180i | 0.680519i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.4022 | − | 24.4022i | 0.785533 | − | 0.785533i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.5399 | − | 39.5399i | 1.27152 | − | 1.27152i | 0.326224 | − | 0.945293i | \(-0.394224\pi\) |
0.945293 | − | 0.326224i | \(-0.105776\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.58675 | + | 4.58675i | −0.147348 | + | 0.147348i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.829593 | + | 0.829593i | 0.0266229 | + | 0.0266229i | 0.720293 | − | 0.693670i | \(-0.244007\pi\) |
−0.693670 | + | 0.720293i | \(0.744007\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.25054 | + | 9.25054i | 0.296559 | + | 0.296559i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 14.5659i | − | 0.466483i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.0700 | + | 29.0700i | 0.930030 | + | 0.930030i | 0.997707 | − | 0.0676772i | \(-0.0215588\pi\) |
−0.0676772 | + | 0.997707i | \(0.521559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.5582i | 1.51997i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.9231 | − | 16.9231i | −0.540312 | − | 0.540312i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.6150 | 1.10405 | 0.552023 | − | 0.833829i | \(-0.313856\pi\) | ||||
0.552023 | + | 0.833829i | \(0.313856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.0535 | 1.08504 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.15262 | − | 7.15262i | −0.227670 | − | 0.227670i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.6426i | 1.16517i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.6154 | − | 16.6154i | −0.527805 | − | 0.527805i | 0.392112 | − | 0.919917i | \(-0.371744\pi\) |
−0.919917 | + | 0.392112i | \(0.871744\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.1650i | 0.322577i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.1462 | + | 30.1462i | 0.955697 | + | 0.955697i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.91448 | + | 2.91448i | 0.0923024 | + | 0.0923024i | 0.751750 | − | 0.659448i | \(-0.229210\pi\) |
−0.659448 | + | 0.751750i | \(0.729210\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29.2853 | + | 29.2853i | −0.926546 | + | 0.926546i |
(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 | 1148.2.k.b.337.7 | ✓ | 36 | |
41.32 | even | 4 | inner | 1148.2.k.b.729.7 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.k.b.337.7 | ✓ | 36 | 1.1 | even | 1 | trivial | |
1148.2.k.b.729.7 | yes | 36 | 41.32 | even | 4 | inner |