Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.29 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.c.323.30 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.33436 | − | 0.468477i | 0.943538 | − | 0.331263i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.56106 | − | 1.25024i | 0.780529 | − | 0.625119i | ||||
\(5\) | 3.47003 | 1.55184 | 0.775922 | − | 0.630829i | \(-0.217285\pi\) | ||||
0.775922 | + | 0.630829i | \(0.217285\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 1.49731 | − | 2.39959i | 0.529380 | − | 0.848385i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.63028 | − | 1.62563i | 1.46422 | − | 0.514069i | ||||
\(11\) | 5.11891i | 1.54341i | 0.635981 | + | 0.771705i | \(0.280596\pi\) | ||||
−0.635981 | + | 0.771705i | \(0.719404\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.268602i | 0.0744968i | 0.999306 | + | 0.0372484i | \(0.0118593\pi\) | ||||
−0.999306 | + | 0.0372484i | \(0.988141\pi\) | |||||||
\(14\) | −0.468477 | − | 1.33436i | −0.125206 | − | 0.356624i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.873805 | − | 3.90339i | 0.218451 | − | 0.975848i | ||||
\(17\) | 1.96616i | 0.476864i | 0.971159 | + | 0.238432i | \(0.0766334\pi\) | ||||
−0.971159 | + | 0.238432i | \(0.923367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.909926 | 0.208751 | 0.104376 | − | 0.994538i | \(-0.466716\pi\) | ||||
0.104376 | + | 0.994538i | \(0.466716\pi\) | |||||||
\(20\) | 5.41692 | − | 4.33836i | 1.21126 | − | 0.970088i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.39809 | + | 6.83050i | 0.511275 | + | 1.45627i | ||||
\(23\) | 5.86455 | 1.22284 | 0.611421 | − | 0.791305i | \(-0.290598\pi\) | ||||
0.611421 | + | 0.791305i | \(0.290598\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.04110 | 1.40822 | ||||||||
\(26\) | 0.125834 | + | 0.358413i | 0.0246781 | + | 0.0702906i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.25024 | − | 1.56106i | −0.236273 | − | 0.295012i | ||||
\(29\) | −7.19959 | −1.33693 | −0.668466 | − | 0.743743i | \(-0.733049\pi\) | ||||
−0.668466 | + | 0.743743i | \(0.733049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.57491i | 0.821678i | 0.911708 | + | 0.410839i | \(0.134764\pi\) | ||||
−0.911708 | + | 0.410839i | \(0.865236\pi\) | |||||||
\(32\) | −0.662675 | − | 5.61791i | −0.117145 | − | 0.993115i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.921102 | + | 2.62358i | 0.157968 | + | 0.449940i | ||||
\(35\) | − | 3.47003i | − | 0.586542i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.98312i | − | 1.14802i | −0.818849 | − | 0.574009i | \(-0.805388\pi\) | ||
0.818849 | − | 0.574009i | \(-0.194612\pi\) | |||||||
\(38\) | 1.21417 | − | 0.426280i | 0.196965 | − | 0.0691517i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.19572 | − | 8.32666i | 0.821515 | − | 1.31656i | ||||
\(41\) | − | 8.34605i | − | 1.30343i | −0.758462 | − | 0.651717i | \(-0.774049\pi\) | ||
0.758462 | − | 0.651717i | \(-0.225951\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.25237 | −1.41097 | −0.705487 | − | 0.708723i | \(-0.749272\pi\) | ||||
−0.705487 | + | 0.708723i | \(0.749272\pi\) | |||||||
\(44\) | 6.39986 | + | 7.99092i | 0.964816 | + | 1.20468i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.82544 | − | 2.74741i | 1.15380 | − | 0.405083i | ||||
\(47\) | −6.49316 | −0.947125 | −0.473562 | − | 0.880760i | \(-0.657032\pi\) | ||||
−0.473562 | + | 0.880760i | \(0.657032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 9.39539 | − | 3.29859i | 1.32871 | − | 0.466491i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.335817 | + | 0.419304i | 0.0465694 | + | 0.0581470i | ||||
\(53\) | 4.54325 | 0.624063 | 0.312032 | − | 0.950072i | \(-0.398990\pi\) | ||||
0.312032 | + | 0.950072i | \(0.398990\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.7628i | 2.39513i | ||||||||
\(56\) | −2.39959 | − | 1.49731i | −0.320659 | − | 0.200087i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.60688 | + | 3.37285i | −1.26145 | + | 0.442876i | ||||
\(59\) | 3.50524i | 0.456344i | 0.973621 | + | 0.228172i | \(0.0732748\pi\) | ||||
−0.973621 | + | 0.228172i | \(0.926725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.96254i | − | 0.251278i | −0.992076 | − | 0.125639i | \(-0.959902\pi\) | ||
0.992076 | − | 0.125639i | \(-0.0400980\pi\) | |||||||
\(62\) | 2.14324 | + | 6.10459i | 0.272192 | + | 0.775284i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.51611 | − | 7.18589i | −0.439514 | − | 0.898236i | ||||
\(65\) | 0.932057i | 0.115607i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.0280 | −1.34728 | −0.673641 | − | 0.739059i | \(-0.735271\pi\) | ||||
−0.673641 | + | 0.739059i | \(0.735271\pi\) | |||||||
\(68\) | 2.45817 | + | 3.06929i | 0.298097 | + | 0.372206i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.62563 | − | 4.63028i | −0.194300 | − | 0.553425i | ||||
\(71\) | 1.20092 | 0.142523 | 0.0712616 | − | 0.997458i | \(-0.477297\pi\) | ||||
0.0712616 | + | 0.997458i | \(0.477297\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.01697 | −1.05536 | −0.527679 | − | 0.849444i | \(-0.676937\pi\) | ||||
−0.527679 | + | 0.849444i | \(0.676937\pi\) | |||||||
\(74\) | −3.27143 | − | 9.31802i | −0.380296 | − | 1.08320i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.42045 | − | 1.13762i | 0.162937 | − | 0.130495i | ||||
\(77\) | 5.11891 | 0.583354 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5570i | 1.52528i | 0.646825 | + | 0.762638i | \(0.276096\pi\) | ||||
−0.646825 | + | 0.762638i | \(0.723904\pi\) | |||||||
\(80\) | 3.03213 | − | 13.5449i | 0.339002 | − | 1.51436i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.90994 | − | 11.1367i | −0.431780 | − | 1.22984i | ||||
\(83\) | − | 4.96335i | − | 0.544799i | −0.962184 | − | 0.272399i | \(-0.912183\pi\) | ||
0.962184 | − | 0.272399i | \(-0.0878172\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.82263i | 0.740019i | ||||||||
\(86\) | −12.3460 | + | 4.33452i | −1.33131 | + | 0.467404i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.2833 | + | 7.66461i | 1.30941 | + | 0.817050i | ||||
\(89\) | − | 18.2032i | − | 1.92954i | −0.263100 | − | 0.964769i | \(-0.584745\pi\) | ||
0.263100 | − | 0.964769i | \(-0.415255\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.268602 | 0.0281572 | ||||||||
\(92\) | 9.15490 | − | 7.33208i | 0.954464 | − | 0.764423i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.66424 | + | 3.04190i | −0.893649 | + | 0.313748i | ||||
\(95\) | 3.15747 | 0.323949 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.39139 | 0.344344 | 0.172172 | − | 0.985067i | \(-0.444922\pi\) | ||||
0.172172 | + | 0.985067i | \(0.444922\pi\) | |||||||
\(98\) | −1.33436 | + | 0.468477i | −0.134791 | + | 0.0473233i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.9916 | − | 8.80305i | 1.09916 | − | 0.880305i | ||||
\(101\) | 8.18671 | 0.814608 | 0.407304 | − | 0.913293i | \(-0.366469\pi\) | ||||
0.407304 | + | 0.913293i | \(0.366469\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.5624i | − | 1.63194i | −0.578093 | − | 0.815971i | \(-0.696203\pi\) | ||
0.578093 | − | 0.815971i | \(-0.303797\pi\) | |||||||
\(104\) | 0.644536 | + | 0.402181i | 0.0632020 | + | 0.0394371i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.06235 | − | 2.12841i | 0.588828 | − | 0.206729i | ||||
\(107\) | 15.1480i | 1.46441i | 0.681083 | + | 0.732206i | \(0.261509\pi\) | ||||
−0.681083 | + | 0.732206i | \(0.738491\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.70038i | 0.737562i | 0.929516 | + | 0.368781i | \(0.120225\pi\) | ||||
−0.929516 | + | 0.368781i | \(0.879775\pi\) | |||||||
\(110\) | 8.32145 | + | 23.7020i | 0.793419 | + | 2.25990i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.90339 | − | 0.873805i | −0.368836 | − | 0.0825668i | ||||
\(113\) | − | 14.5822i | − | 1.37178i | −0.727706 | − | 0.685889i | \(-0.759413\pi\) | ||
0.727706 | − | 0.685889i | \(-0.240587\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.3501 | 1.89766 | ||||||||
\(116\) | −11.2390 | + | 9.00121i | −1.04351 | + | 0.835742i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.64213 | + | 4.67727i | 0.151170 | + | 0.430578i | ||||
\(119\) | 1.96616 | 0.180238 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.2033 | −1.38211 | ||||||||
\(122\) | −0.919406 | − | 2.61874i | −0.0832391 | − | 0.237090i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.71973 | + | 7.14170i | 0.513647 | + | 0.641343i | ||||
\(125\) | 7.08266 | 0.633492 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7782i | 1.22262i | 0.791392 | + | 0.611309i | \(0.209357\pi\) | ||||
−0.791392 | + | 0.611309i | \(0.790643\pi\) | |||||||
\(128\) | −8.05820 | − | 7.94138i | −0.712251 | − | 0.701925i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.436648 | + | 1.24370i | 0.0382965 | + | 0.109080i | ||||
\(131\) | − | 11.4226i | − | 0.997997i | −0.866603 | − | 0.498999i | \(-0.833701\pi\) | ||
0.866603 | − | 0.498999i | \(-0.166299\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.909926i | − | 0.0789006i | ||||||
\(134\) | −14.7153 | + | 5.16636i | −1.27121 | + | 0.446305i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.71799 | + | 2.94396i | 0.404564 | + | 0.252442i | ||||
\(137\) | 5.89343i | 0.503510i | 0.967791 | + | 0.251755i | \(0.0810077\pi\) | ||||
−0.967791 | + | 0.251755i | \(0.918992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.67309 | 0.311547 | 0.155774 | − | 0.987793i | \(-0.450213\pi\) | ||||
0.155774 | + | 0.987793i | \(0.450213\pi\) | |||||||
\(140\) | −4.33836 | − | 5.41692i | −0.366659 | − | 0.457813i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.60247 | − | 0.562604i | 0.134476 | − | 0.0472127i | ||||
\(143\) | −1.37495 | −0.114979 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.9828 | −2.07471 | ||||||||
\(146\) | −12.0319 | + | 4.22425i | −0.995770 | + | 0.349601i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.73056 | − | 10.9010i | −0.717648 | − | 0.896061i | ||||
\(149\) | 23.0240 | 1.88620 | 0.943102 | − | 0.332504i | \(-0.107894\pi\) | ||||
0.943102 | + | 0.332504i | \(0.107894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.33860i | 0.108934i | 0.998516 | + | 0.0544669i | \(0.0173459\pi\) | ||||
−0.998516 | + | 0.0544669i | \(0.982654\pi\) | |||||||
\(152\) | 1.36244 | − | 2.18345i | 0.110509 | − | 0.177101i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.83050 | − | 2.39809i | 0.550417 | − | 0.193244i | ||||
\(155\) | 15.8751i | 1.27512i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.7839i | 1.73854i | 0.494333 | + | 0.869272i | \(0.335412\pi\) | ||||
−0.494333 | + | 0.869272i | \(0.664588\pi\) | |||||||
\(158\) | 6.35112 | + | 18.0899i | 0.505268 | + | 1.43916i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.29950 | − | 19.4943i | −0.181792 | − | 1.54116i | ||||
\(161\) | − | 5.86455i | − | 0.462191i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.2710 | −1.58775 | −0.793875 | − | 0.608082i | \(-0.791939\pi\) | ||||
−0.793875 | + | 0.608082i | \(0.791939\pi\) | |||||||
\(164\) | −10.4346 | − | 13.0287i | −0.814802 | − | 1.01737i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.32522 | − | 6.62292i | −0.180472 | − | 0.514039i | ||||
\(167\) | 6.57632 | 0.508891 | 0.254445 | − | 0.967087i | \(-0.418107\pi\) | ||||
0.254445 | + | 0.967087i | \(0.418107\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9279 | 0.994450 | ||||||||
\(170\) | 3.19625 | + | 9.10388i | 0.245141 | + | 0.698236i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.4435 | + | 11.5677i | −1.10131 | + | 0.882027i | ||||
\(173\) | −13.3399 | −1.01421 | −0.507105 | − | 0.861884i | \(-0.669284\pi\) | ||||
−0.507105 | + | 0.861884i | \(0.669284\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.04110i | − | 0.532257i | ||||||
\(176\) | 19.9811 | + | 4.47293i | 1.50613 | + | 0.337160i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.52779 | − | 24.2897i | −0.639185 | − | 1.82059i | ||||
\(179\) | 9.82571i | 0.734408i | 0.930140 | + | 0.367204i | \(0.119685\pi\) | ||||
−0.930140 | + | 0.367204i | \(0.880315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.88753i | 0.363287i | 0.983364 | + | 0.181643i | \(0.0581417\pi\) | ||||
−0.983364 | + | 0.181643i | \(0.941858\pi\) | |||||||
\(182\) | 0.358413 | − | 0.125834i | 0.0265674 | − | 0.00932744i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.78106 | − | 14.0725i | 0.647348 | − | 1.03744i | ||||
\(185\) | − | 24.2316i | − | 1.78154i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0646 | −0.735997 | ||||||||
\(188\) | −10.1362 | + | 8.11800i | −0.739258 | + | 0.592066i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.21322 | − | 1.47920i | 0.305659 | − | 0.107313i | ||||
\(191\) | 11.6129 | 0.840281 | 0.420141 | − | 0.907459i | \(-0.361981\pi\) | ||||
0.420141 | + | 0.907459i | \(0.361981\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.8166 | −0.922562 | −0.461281 | − | 0.887254i | \(-0.652610\pi\) | ||||
−0.461281 | + | 0.887254i | \(0.652610\pi\) | |||||||
\(194\) | 4.52536 | − | 1.58879i | 0.324902 | − | 0.114069i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.56106 | + | 1.25024i | −0.111504 | + | 0.0893028i | ||||
\(197\) | 4.69147 | 0.334253 | 0.167127 | − | 0.985935i | \(-0.446551\pi\) | ||||
0.167127 | + | 0.985935i | \(0.446551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.3555i | 1.08852i | 0.838915 | + | 0.544262i | \(0.183190\pi\) | ||||
−0.838915 | + | 0.544262i | \(0.816810\pi\) | |||||||
\(200\) | 10.5427 | − | 16.8958i | 0.745483 | − | 1.19471i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.9241 | − | 3.83529i | 0.768614 | − | 0.269850i | ||||
\(203\) | 7.19959i | 0.505312i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 28.9610i | − | 2.02273i | ||||||
\(206\) | −7.75911 | − | 22.1003i | −0.540603 | − | 1.53980i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.04846 | + | 0.234706i | 0.0726976 | + | 0.0162739i | ||||
\(209\) | 4.65783i | 0.322189i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.09850 | 0.350995 | 0.175497 | − | 0.984480i | \(-0.443847\pi\) | ||||
0.175497 | + | 0.984480i | \(0.443847\pi\) | |||||||
\(212\) | 7.09228 | − | 5.68015i | 0.487100 | − | 0.390114i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.09649 | + | 20.2130i | 0.485106 | + | 1.38173i | ||||
\(215\) | −32.1060 | −2.18961 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.57491 | 0.310565 | ||||||||
\(218\) | 3.60745 | + | 10.2751i | 0.244327 | + | 0.695918i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 22.2077 | + | 27.7287i | 1.49724 | + | 1.86947i | ||||
\(221\) | −0.528115 | −0.0355249 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 29.5118i | − | 1.97625i | −0.153636 | − | 0.988127i | \(-0.549098\pi\) | ||
0.153636 | − | 0.988127i | \(-0.450902\pi\) | |||||||
\(224\) | −5.61791 | + | 0.662675i | −0.375362 | + | 0.0442768i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.83143 | − | 19.4580i | −0.454420 | − | 1.29433i | ||||
\(227\) | − | 14.4769i | − | 0.960868i | −0.877031 | − | 0.480434i | \(-0.840479\pi\) | ||
0.877031 | − | 0.480434i | \(-0.159521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9120i | 0.787168i | 0.919289 | + | 0.393584i | \(0.128765\pi\) | ||||
−0.919289 | + | 0.393584i | \(0.871235\pi\) | |||||||
\(230\) | 27.1545 | − | 9.53358i | 1.79052 | − | 0.628625i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.7800 | + | 17.2761i | −0.707744 | + | 1.13423i | ||||
\(233\) | 13.2938i | 0.870904i | 0.900212 | + | 0.435452i | \(0.143411\pi\) | ||||
−0.900212 | + | 0.435452i | \(0.856589\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.5315 | −1.46979 | ||||||||
\(236\) | 4.38239 | + | 5.47189i | 0.285269 | + | 0.356190i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.62358 | − | 0.921102i | 0.170061 | − | 0.0597062i | ||||
\(239\) | −11.7744 | −0.761624 | −0.380812 | − | 0.924652i | \(-0.624356\pi\) | ||||
−0.380812 | + | 0.924652i | \(0.624356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.3009 | −1.50094 | −0.750471 | − | 0.660903i | \(-0.770173\pi\) | ||||
−0.750471 | + | 0.660903i | \(0.770173\pi\) | |||||||
\(242\) | −20.2867 | + | 7.12238i | −1.30408 | + | 0.457844i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.45364 | − | 3.06364i | −0.157079 | − | 0.196129i | ||||
\(245\) | −3.47003 | −0.221692 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.244408i | 0.0155513i | ||||||||
\(248\) | 10.9779 | + | 6.85007i | 0.697099 | + | 0.434980i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.45085 | − | 3.31806i | 0.597724 | − | 0.209853i | ||||
\(251\) | 18.5562i | 1.17126i | 0.810579 | + | 0.585629i | \(0.199153\pi\) | ||||
−0.810579 | + | 0.585629i | \(0.800847\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0201i | 1.88735i | ||||||||
\(254\) | 6.45477 | + | 18.3851i | 0.405009 | + | 1.15359i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.4729 | − | 6.82161i | −0.904558 | − | 0.426351i | ||||
\(257\) | − | 12.7179i | − | 0.793318i | −0.917966 | − | 0.396659i | \(-0.870169\pi\) | ||
0.917966 | − | 0.396659i | \(-0.129831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.98312 | −0.433910 | ||||||||
\(260\) | 1.16529 | + | 1.45500i | 0.0722685 | + | 0.0902350i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.35123 | − | 15.2419i | −0.330600 | − | 0.941648i | ||||
\(263\) | −4.04929 | −0.249690 | −0.124845 | − | 0.992176i | \(-0.539843\pi\) | ||||
−0.124845 | + | 0.992176i | \(0.539843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.7652 | 0.968449 | ||||||||
\(266\) | −0.426280 | − | 1.21417i | −0.0261369 | − | 0.0744457i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17.2153 | + | 13.7876i | −1.05159 | + | 0.842212i | ||||
\(269\) | −22.6641 | −1.38185 | −0.690926 | − | 0.722925i | \(-0.742797\pi\) | ||||
−0.690926 | + | 0.722925i | \(0.742797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 0.0619260i | − | 0.00376174i | −0.999998 | − | 0.00188087i | \(-0.999401\pi\) | ||
0.999998 | − | 0.00188087i | \(-0.000598699\pi\) | |||||||
\(272\) | 7.67470 | + | 1.71804i | 0.465347 | + | 0.104172i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.76094 | + | 7.86399i | 0.166794 | + | 0.475081i | ||||
\(275\) | 36.0427i | 2.17346i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9177i | 1.49716i | 0.663045 | + | 0.748580i | \(0.269264\pi\) | ||||
−0.663045 | + | 0.748580i | \(0.730736\pi\) | |||||||
\(278\) | 4.90124 | − | 1.72076i | 0.293957 | − | 0.103204i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.32666 | − | 5.19572i | −0.497613 | − | 0.310503i | ||||
\(281\) | 8.26290i | 0.492923i | 0.969153 | + | 0.246462i | \(0.0792679\pi\) | ||||
−0.969153 | + | 0.246462i | \(0.920732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.4764 | 1.39553 | 0.697763 | − | 0.716329i | \(-0.254179\pi\) | ||||
0.697763 | + | 0.716329i | \(0.254179\pi\) | |||||||
\(284\) | 1.87471 | − | 1.50144i | 0.111243 | − | 0.0890940i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.83469 | + | 0.644133i | −0.108487 | + | 0.0380884i | ||||
\(287\) | −8.34605 | −0.492652 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.1342 | 0.772601 | ||||||||
\(290\) | −33.3362 | + | 11.7039i | −1.95757 | + | 0.687275i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.0760 | + | 11.2734i | −0.823737 | + | 0.659724i | ||||
\(293\) | 6.18958 | 0.361599 | 0.180800 | − | 0.983520i | \(-0.442131\pi\) | ||||
0.180800 | + | 0.983520i | \(0.442131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1633i | 0.708174i | ||||||||
\(296\) | −16.7566 | − | 10.4559i | −0.973960 | − | 0.607737i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 30.7225 | − | 10.7862i | 1.77971 | − | 0.624830i | ||||
\(299\) | 1.57523i | 0.0910979i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.25237i | 0.533298i | ||||||||
\(302\) | 0.627104 | + | 1.78618i | 0.0360858 | + | 0.102783i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.795098 | − | 3.55180i | 0.0456020 | − | 0.203710i | ||||
\(305\) | − | 6.81007i | − | 0.389944i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.4140 | −1.45045 | −0.725226 | − | 0.688511i | \(-0.758265\pi\) | ||||
−0.725226 | + | 0.688511i | \(0.758265\pi\) | |||||||
\(308\) | 7.99092 | − | 6.39986i | 0.455325 | − | 0.364666i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.43710 | + | 21.1831i | 0.422399 | + | 1.20312i | ||||
\(311\) | −7.55273 | −0.428276 | −0.214138 | − | 0.976803i | \(-0.568694\pi\) | ||||
−0.214138 | + | 0.976803i | \(0.568694\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.49790 | 0.141190 | 0.0705948 | − | 0.997505i | \(-0.477510\pi\) | ||||
0.0705948 | + | 0.997505i | \(0.477510\pi\) | |||||||
\(314\) | 10.2053 | + | 29.0677i | 0.575916 | + | 1.64038i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.9494 | + | 21.1632i | 0.953480 | + | 1.19052i | ||||
\(317\) | 10.9643 | 0.615815 | 0.307908 | − | 0.951416i | \(-0.400371\pi\) | ||||
0.307908 | + | 0.951416i | \(0.400371\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36.8541i | − | 2.06343i | ||||||
\(320\) | −12.2010 | − | 24.9352i | −0.682057 | − | 1.39392i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.74741 | − | 7.82544i | −0.153107 | − | 0.436095i | ||||
\(323\) | 1.78906i | 0.0995460i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.89125i | 0.104908i | ||||||||
\(326\) | −27.0489 | + | 9.49651i | −1.49810 | + | 0.525963i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.0271 | − | 12.4967i | −1.10581 | − | 0.690012i | ||||
\(329\) | 6.49316i | 0.357980i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.6043 | 1.95699 | 0.978494 | − | 0.206275i | \(-0.0661341\pi\) | ||||
0.978494 | + | 0.206275i | \(0.0661341\pi\) | |||||||
\(332\) | −6.20538 | − | 7.74808i | −0.340564 | − | 0.425231i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.77521 | − | 3.08086i | 0.480158 | − | 0.168577i | ||||
\(335\) | −38.2674 | −2.09077 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4308 | 1.00399 | 0.501995 | − | 0.864871i | \(-0.332600\pi\) | ||||
0.501995 | + | 0.864871i | \(0.332600\pi\) | |||||||
\(338\) | 17.2505 | − | 6.05640i | 0.938302 | − | 0.329425i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.52992 | + | 10.6505i | 0.462600 | + | 0.577606i | ||||
\(341\) | −23.4185 | −1.26819 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −13.8537 | + | 22.2019i | −0.746941 | + | 1.19705i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.8002 | + | 6.24942i | −0.956946 | + | 0.335971i | ||||
\(347\) | 25.2141i | 1.35356i | 0.736184 | + | 0.676782i | \(0.236626\pi\) | ||||
−0.736184 | + | 0.676782i | \(0.763374\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.82396i | 0.258221i | 0.991630 | + | 0.129110i | \(0.0412121\pi\) | ||||
−0.991630 | + | 0.129110i | \(0.958788\pi\) | |||||||
\(350\) | −3.29859 | − | 9.39539i | −0.176317 | − | 0.502205i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 28.7576 | − | 3.39217i | 1.53278 | − | 0.180804i | ||||
\(353\) | − | 21.2660i | − | 1.13187i | −0.824448 | − | 0.565937i | \(-0.808514\pi\) | ||
0.824448 | − | 0.565937i | \(-0.191486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.16723 | 0.221174 | ||||||||
\(356\) | −22.7584 | − | 28.4163i | −1.20619 | − | 1.50606i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.60312 | + | 13.1111i | 0.243282 | + | 0.692942i | ||||
\(359\) | −24.9785 | −1.31832 | −0.659158 | − | 0.752004i | \(-0.729087\pi\) | ||||
−0.659158 | + | 0.752004i | \(0.729087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1720 | −0.956423 | ||||||||
\(362\) | 2.28969 | + | 6.52174i | 0.120344 | + | 0.342775i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.419304 | − | 0.335817i | 0.0219775 | − | 0.0176016i | ||||
\(365\) | −31.2892 | −1.63775 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.8851i | − | 0.724795i | −0.932024 | − | 0.362397i | \(-0.881958\pi\) | ||
0.932024 | − | 0.362397i | \(-0.118042\pi\) | |||||||
\(368\) | 5.12447 | − | 22.8916i | 0.267132 | − | 1.19331i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.3520 | − | 32.3338i | −0.590160 | − | 1.68095i | ||||
\(371\) | − | 4.54325i | − | 0.235874i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.513970i | 0.0266123i | 0.999911 | + | 0.0133062i | \(0.00423561\pi\) | ||||
−0.999911 | + | 0.0133062i | \(0.995764\pi\) | |||||||
\(374\) | −13.4299 | + | 4.71504i | −0.694441 | + | 0.243809i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.72229 | + | 15.5810i | −0.501389 | + | 0.803526i | ||||
\(377\) | − | 1.93383i | − | 0.0995972i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.97711 | −0.409757 | −0.204878 | − | 0.978787i | \(-0.565680\pi\) | ||||
−0.204878 | + | 0.978787i | \(0.565680\pi\) | |||||||
\(380\) | 4.92899 | − | 3.94759i | 0.252852 | − | 0.202507i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.4959 | − | 5.44039i | 0.792837 | − | 0.278354i | ||||
\(383\) | −8.03401 | −0.410519 | −0.205259 | − | 0.978708i | \(-0.565804\pi\) | ||||
−0.205259 | + | 0.978708i | \(0.565804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.7628 | 0.905275 | ||||||||
\(386\) | −17.1021 | + | 6.00430i | −0.870472 | + | 0.305611i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.29416 | − | 4.24005i | 0.268770 | − | 0.215256i | ||||
\(389\) | −6.60733 | −0.335005 | −0.167503 | − | 0.985872i | \(-0.553570\pi\) | ||||
−0.167503 | + | 0.985872i | \(0.553570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5306i | 0.583130i | ||||||||
\(392\) | −1.49731 | + | 2.39959i | −0.0756257 | + | 0.121198i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.26013 | − | 2.19785i | 0.315381 | − | 0.110726i | ||||
\(395\) | 47.0430i | 2.36699i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 17.4642i | − | 0.876502i | −0.898853 | − | 0.438251i | \(-0.855598\pi\) | ||
0.898853 | − | 0.438251i | \(-0.144402\pi\) | |||||||
\(398\) | 7.19372 | + | 20.4899i | 0.360588 | + | 1.02706i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.15255 | − | 27.4842i | 0.307627 | − | 1.37421i | ||||
\(401\) | 18.6133i | 0.929503i | 0.885441 | + | 0.464751i | \(0.153856\pi\) | ||||
−0.885441 | + | 0.464751i | \(0.846144\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.22883 | −0.0612124 | ||||||||
\(404\) | 12.7799 | − | 10.2353i | 0.635825 | − | 0.509227i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.37285 | + | 9.60688i | 0.167392 | + | 0.476782i | ||||
\(407\) | 35.7460 | 1.77186 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.72844 | 0.184359 | 0.0921797 | − | 0.995742i | \(-0.470617\pi\) | ||||
0.0921797 | + | 0.995742i | \(0.470617\pi\) | |||||||
\(410\) | −13.5676 | − | 38.6446i | −0.670055 | − | 1.90852i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.7070 | − | 25.8549i | −1.02016 | − | 1.27378i | ||||
\(413\) | 3.50524 | 0.172482 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 17.2230i | − | 0.845443i | ||||||
\(416\) | 1.50898 | − | 0.177996i | 0.0739839 | − | 0.00872697i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.18209 | + | 6.21525i | 0.106729 | + | 0.303998i | ||||
\(419\) | 30.1591i | 1.47337i | 0.676237 | + | 0.736684i | \(0.263609\pi\) | ||||
−0.676237 | + | 0.736684i | \(0.736391\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.17416i | − | 0.203436i | −0.994813 | − | 0.101718i | \(-0.967566\pi\) | ||
0.994813 | − | 0.101718i | \(-0.0324340\pi\) | |||||||
\(422\) | 6.80325 | − | 2.38853i | 0.331177 | − | 0.116272i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.80266 | − | 10.9020i | 0.330367 | − | 0.529446i | ||||
\(425\) | 13.8439i | 0.671529i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.96254 | −0.0949740 | ||||||||
\(428\) | 18.9386 | + | 23.6469i | 0.915433 | + | 1.14302i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −42.8411 | + | 15.0409i | −2.06598 | + | 0.725338i | ||||
\(431\) | 20.3147 | 0.978524 | 0.489262 | − | 0.872137i | \(-0.337266\pi\) | ||||
0.489262 | + | 0.872137i | \(0.337266\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.5740 | 1.80569 | 0.902847 | − | 0.429963i | \(-0.141473\pi\) | ||||
0.902847 | + | 0.429963i | \(0.141473\pi\) | |||||||
\(434\) | 6.10459 | − | 2.14324i | 0.293030 | − | 0.102879i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.62731 | + | 12.0207i | 0.461064 | + | 0.575689i | ||||
\(437\) | 5.33630 | 0.255270 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 12.2219i | − | 0.583317i | −0.956522 | − | 0.291659i | \(-0.905793\pi\) | ||
0.956522 | − | 0.291659i | \(-0.0942072\pi\) | |||||||
\(440\) | 42.6234 | + | 26.5964i | 2.03199 | + | 1.26793i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.704698 | + | 0.247410i | −0.0335191 | + | 0.0117681i | ||||
\(443\) | − | 2.13132i | − | 0.101262i | −0.998717 | − | 0.0506311i | \(-0.983877\pi\) | ||
0.998717 | − | 0.0506311i | \(-0.0161233\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 63.1657i | − | 2.99434i | ||||||
\(446\) | −13.8256 | − | 39.3795i | −0.654661 | − | 1.86467i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.18589 | + | 3.51611i | −0.339501 | + | 0.166121i | ||||
\(449\) | − | 24.6873i | − | 1.16506i | −0.812807 | − | 0.582532i | \(-0.802062\pi\) | ||
0.812807 | − | 0.582532i | \(-0.197938\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.7227 | 2.01173 | ||||||||
\(452\) | −18.2312 | − | 22.7637i | −0.857526 | − | 1.07071i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.78211 | − | 19.3175i | −0.318300 | − | 0.906615i | ||||
\(455\) | 0.932057 | 0.0436955 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.2814 | −1.55684 | −0.778419 | − | 0.627745i | \(-0.783978\pi\) | ||||
−0.778419 | + | 0.627745i | \(0.783978\pi\) | |||||||
\(458\) | 5.58051 | + | 15.8950i | 0.260760 | + | 0.742723i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 31.7678 | − | 25.4425i | 1.48118 | − | 1.18626i | ||||
\(461\) | 15.2279 | 0.709233 | 0.354617 | − | 0.935012i | \(-0.384611\pi\) | ||||
0.354617 | + | 0.935012i | \(0.384611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.21883i | − | 0.149592i | −0.997199 | − | 0.0747959i | \(-0.976169\pi\) | ||
0.997199 | − | 0.0747959i | \(-0.0238305\pi\) | |||||||
\(464\) | −6.29104 | + | 28.1028i | −0.292054 | + | 1.30464i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.22783 | + | 17.7387i | 0.288499 | + | 0.821731i | ||||
\(467\) | − | 22.5827i | − | 1.04500i | −0.852638 | − | 0.522502i | \(-0.824999\pi\) | ||
0.852638 | − | 0.522502i | \(-0.175001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0280i | 0.509225i | ||||||||
\(470\) | −30.0652 | + | 10.5555i | −1.38680 | + | 0.486888i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.41117 | + | 5.24845i | 0.387155 | + | 0.241579i | ||||
\(473\) | − | 47.3621i | − | 2.17771i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.40688 | 0.293968 | ||||||||
\(476\) | 3.06929 | − | 2.45817i | 0.140681 | − | 0.112670i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.7114 | + | 5.51605i | −0.718622 | + | 0.252298i | ||||
\(479\) | 28.0140 | 1.27999 | 0.639995 | − | 0.768379i | \(-0.278936\pi\) | ||||
0.639995 | + | 0.768379i | \(0.278936\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.87568 | 0.0855237 | ||||||||
\(482\) | −31.0919 | + | 10.9159i | −1.41620 | + | 0.497207i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −23.7332 | + | 19.0077i | −1.07878 | + | 0.863987i | ||||
\(485\) | 11.7682 | 0.534368 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.55321i | 0.115697i | 0.998325 | + | 0.0578485i | \(0.0184240\pi\) | ||||
−0.998325 | + | 0.0578485i | \(0.981576\pi\) | |||||||
\(488\) | −4.70930 | − | 2.93854i | −0.213180 | − | 0.133021i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.63028 | + | 1.62563i | −0.209175 | + | 0.0734384i | ||||
\(491\) | − | 0.803432i | − | 0.0362584i | −0.999836 | − | 0.0181292i | \(-0.994229\pi\) | ||
0.999836 | − | 0.0181292i | \(-0.00577102\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.1556i | − | 0.637534i | ||||||
\(494\) | 0.114500 | + | 0.326130i | 0.00515158 | + | 0.0146733i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.8577 | + | 3.99758i | 0.801832 | + | 0.179497i | ||||
\(497\) | − | 1.20092i | − | 0.0538687i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.6029 | 1.45950 | 0.729752 | − | 0.683712i | \(-0.239635\pi\) | ||||
0.729752 | + | 0.683712i | \(0.239635\pi\) | |||||||
\(500\) | 11.0564 | − | 8.85502i | 0.494459 | − | 0.396008i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.69317 | + | 24.7608i | 0.387995 | + | 1.10513i | ||||
\(503\) | −11.6962 | −0.521508 | −0.260754 | − | 0.965405i | \(-0.583971\pi\) | ||||
−0.260754 | + | 0.965405i | \(0.583971\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.4081 | 1.26414 | ||||||||
\(506\) | 14.0637 | + | 40.0578i | 0.625209 | + | 1.78078i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.2260 | + | 21.5086i | 0.764282 | + | 0.954289i | ||||
\(509\) | 40.0087 | 1.77335 | 0.886676 | − | 0.462391i | \(-0.153008\pi\) | ||||
0.886676 | + | 0.462391i | \(0.153008\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.01697i | 0.398887i | ||||||||
\(512\) | −22.5079 | − | 2.32228i | −0.994719 | − | 0.102631i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.95803 | − | 16.9703i | −0.262797 | − | 0.748526i | ||||
\(515\) | − | 57.4720i | − | 2.53252i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 33.2379i | − | 1.46180i | ||||||
\(518\) | −9.31802 | + | 3.27143i | −0.409410 | + | 0.143738i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.23656 | + | 1.39558i | 0.0980796 | + | 0.0612003i | ||||
\(521\) | 5.13277i | 0.224871i | 0.993659 | + | 0.112435i | \(0.0358651\pi\) | ||||
−0.993659 | + | 0.112435i | \(0.964135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.3652 | 1.54641 | 0.773207 | − | 0.634154i | \(-0.218652\pi\) | ||||
0.773207 | + | 0.634154i | \(0.218652\pi\) | |||||||
\(524\) | −14.2810 | − | 17.8313i | −0.623867 | − | 0.778966i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.40324 | + | 1.89700i | −0.235592 | + | 0.0827132i | ||||
\(527\) | −8.99500 | −0.391829 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3929 | 0.495344 | ||||||||
\(530\) | 21.0365 | − | 7.38564i | 0.913769 | − | 0.320812i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.13762 | − | 1.42045i | −0.0493223 | − | 0.0615842i | ||||
\(533\) | 2.24177 | 0.0971018 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 52.5640i | 2.27254i | ||||||||
\(536\) | −16.5123 | + | 26.4627i | −0.713224 | + | 1.14301i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.2421 | + | 10.6176i | −1.30383 | + | 0.457757i | ||||
\(539\) | − | 5.11891i | − | 0.220487i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.7038i | 1.32006i | 0.751240 | + | 0.660029i | \(0.229456\pi\) | ||||
−0.751240 | + | 0.660029i | \(0.770544\pi\) | |||||||
\(542\) | −0.0290109 | − | 0.0826319i | −0.00124613 | − | 0.00354934i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 11.0457 | − | 1.30293i | 0.473581 | − | 0.0558625i | ||||
\(545\) | 26.7205i | 1.14458i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.21526 | −0.0947175 | −0.0473588 | − | 0.998878i | \(-0.515080\pi\) | ||||
−0.0473588 | + | 0.998878i | \(0.515080\pi\) | |||||||
\(548\) | 7.36820 | + | 9.19999i | 0.314754 | + | 0.393004i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 16.8852 | + | 48.0942i | 0.719988 | + | 2.05074i | ||||
\(551\) | −6.55110 | −0.279086 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.5570 | 0.576500 | ||||||||
\(554\) | 11.6734 | + | 33.2493i | 0.495954 | + | 1.41263i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.73390 | − | 4.59224i | 0.243172 | − | 0.194754i | ||||
\(557\) | 8.88158 | 0.376325 | 0.188162 | − | 0.982138i | \(-0.439747\pi\) | ||||
0.188162 | + | 0.982138i | \(0.439747\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.48521i | − | 0.105113i | ||||||
\(560\) | −13.5449 | − | 3.03213i | −0.572376 | − | 0.128131i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.87098 | + | 11.0257i | 0.163287 | + | 0.465092i | ||||
\(563\) | − | 28.9398i | − | 1.21967i | −0.792529 | − | 0.609834i | \(-0.791236\pi\) | ||
0.792529 | − | 0.609834i | \(-0.208764\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 50.6007i | − | 2.12879i | ||||||
\(566\) | 31.3260 | − | 10.9981i | 1.31673 | − | 0.462287i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.79815 | − | 2.88173i | 0.0754489 | − | 0.120915i | ||||
\(569\) | 30.8816i | 1.29463i | 0.762224 | + | 0.647313i | \(0.224107\pi\) | ||||
−0.762224 | + | 0.647313i | \(0.775893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.5945 | −1.32219 | −0.661094 | − | 0.750303i | \(-0.729908\pi\) | ||||
−0.661094 | + | 0.750303i | \(0.729908\pi\) | |||||||
\(572\) | −2.14638 | + | 1.71902i | −0.0897446 | + | 0.0718757i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.1367 | + | 3.90994i | −0.464836 | + | 0.163198i | ||||
\(575\) | 41.2928 | 1.72203 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.6007 | −1.56534 | −0.782669 | − | 0.622438i | \(-0.786142\pi\) | ||||
−0.782669 | + | 0.622438i | \(0.786142\pi\) | |||||||
\(578\) | 17.5258 | − | 6.15308i | 0.728978 | − | 0.255934i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −38.9996 | + | 31.2345i | −1.61937 | + | 1.29694i | ||||
\(581\) | −4.96335 | −0.205915 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.2565i | 0.963186i | ||||||||
\(584\) | −13.5012 | + | 21.6371i | −0.558685 | + | 0.895349i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.25916 | − | 2.89968i | 0.341183 | − | 0.119785i | ||||
\(587\) | − | 22.0321i | − | 0.909361i | −0.890655 | − | 0.454680i | \(-0.849754\pi\) | ||
0.890655 | − | 0.454680i | \(-0.150246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.16283i | 0.171526i | ||||||||
\(590\) | 5.69823 | + | 16.2303i | 0.234592 | + | 0.668190i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −27.2578 | − | 6.10188i | −1.12029 | − | 0.250786i | ||||
\(593\) | − | 17.8392i | − | 0.732569i | −0.930503 | − | 0.366284i | \(-0.880630\pi\) | ||
0.930503 | − | 0.366284i | \(-0.119370\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.82263 | 0.279701 | ||||||||
\(596\) | 35.9419 | − | 28.7856i | 1.47224 | − | 1.17910i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.737959 | + | 2.10193i | 0.0301774 | + | 0.0859544i | ||||
\(599\) | −19.5363 | −0.798230 | −0.399115 | − | 0.916901i | \(-0.630683\pi\) | ||||
−0.399115 | + | 0.916901i | \(0.630683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.1240 | −0.820877 | −0.410438 | − | 0.911888i | \(-0.634624\pi\) | ||||
−0.410438 | + | 0.911888i | \(0.634624\pi\) | |||||||
\(602\) | 4.33452 | + | 12.3460i | 0.176662 | + | 0.503187i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.67357 | + | 2.08963i | 0.0680966 | + | 0.0850260i | ||||
\(605\) | −52.7557 | −2.14483 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.3972i | 0.624951i | 0.949926 | + | 0.312476i | \(0.101158\pi\) | ||||
−0.949926 | + | 0.312476i | \(0.898842\pi\) | |||||||
\(608\) | −0.602985 | − | 5.11188i | −0.0244543 | − | 0.207314i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.19036 | − | 9.08712i | −0.129174 | − | 0.367927i | ||||
\(611\) | − | 1.74408i | − | 0.0705578i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 37.9629i | − | 1.53331i | −0.642061 | − | 0.766653i | \(-0.721921\pi\) | ||
0.642061 | − | 0.766653i | \(-0.278079\pi\) | |||||||
\(614\) | −33.9115 | + | 11.9059i | −1.36856 | + | 0.480482i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.66461 | − | 12.2833i | 0.308816 | − | 0.494909i | ||||
\(617\) | − | 43.0532i | − | 1.73326i | −0.498953 | − | 0.866629i | \(-0.666282\pi\) | ||
0.498953 | − | 0.866629i | \(-0.333718\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.75463 | −0.271491 | −0.135746 | − | 0.990744i | \(-0.543343\pi\) | ||||
−0.135746 | + | 0.990744i | \(0.543343\pi\) | |||||||
\(620\) | 19.8476 | + | 24.7819i | 0.797099 | + | 0.995265i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.0781 | + | 3.53828i | −0.404095 | + | 0.141872i | ||||
\(623\) | −18.2032 | −0.729297 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.6285 | −0.425138 | ||||||||
\(626\) | 3.33311 | − | 1.17021i | 0.133218 | − | 0.0467710i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 27.2351 | + | 34.0059i | 1.08680 | + | 1.35698i | ||||
\(629\) | 13.7299 | 0.547448 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.96735i | − | 0.0783189i | −0.999233 | − | 0.0391594i | \(-0.987532\pi\) | ||
0.999233 | − | 0.0391594i | \(-0.0124680\pi\) | |||||||
\(632\) | 32.5312 | + | 20.2990i | 1.29402 | + | 0.807451i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.6303 | − | 5.13652i | 0.581045 | − | 0.203997i | ||||
\(635\) | 47.8108i | 1.89731i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.268602i | − | 0.0106424i | ||||||
\(638\) | −17.2653 | − | 49.1768i | −0.683540 | − | 1.94693i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.9622 | − | 27.5568i | −1.10530 | − | 1.08928i | ||||
\(641\) | − | 30.2998i | − | 1.19677i | −0.801209 | − | 0.598385i | \(-0.795809\pi\) | ||
0.801209 | − | 0.598385i | \(-0.204191\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.85901 | 0.152185 | 0.0760923 | − | 0.997101i | \(-0.475756\pi\) | ||||
0.0760923 | + | 0.997101i | \(0.475756\pi\) | |||||||
\(644\) | −7.33208 | − | 9.15490i | −0.288925 | − | 0.360754i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.838134 | + | 2.38726i | 0.0329760 | + | 0.0939255i | ||||
\(647\) | 33.4004 | 1.31310 | 0.656552 | − | 0.754281i | \(-0.272014\pi\) | ||||
0.656552 | + | 0.754281i | \(0.272014\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.9430 | −0.704326 | ||||||||
\(650\) | 0.886009 | + | 2.52362i | 0.0347521 | + | 0.0989846i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −31.6442 | + | 25.3436i | −1.23928 | + | 0.992533i | ||||
\(653\) | 26.9899 | 1.05620 | 0.528098 | − | 0.849184i | \(-0.322905\pi\) | ||||
0.528098 | + | 0.849184i | \(0.322905\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 39.6367i | − | 1.54874i | ||||||
\(656\) | −32.5779 | − | 7.29283i | −1.27195 | − | 0.284737i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.04190 | + | 8.66424i | 0.118586 | + | 0.337767i | ||||
\(659\) | 13.1888i | 0.513763i | 0.966443 | + | 0.256881i | \(0.0826950\pi\) | ||||
−0.966443 | + | 0.256881i | \(0.917305\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 33.5767i | − | 1.30598i | −0.757366 | − | 0.652990i | \(-0.773514\pi\) | ||
0.757366 | − | 0.652990i | \(-0.226486\pi\) | |||||||
\(662\) | 47.5091 | − | 16.6798i | 1.84649 | − | 0.648279i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.9100 | − | 7.43169i | −0.462199 | − | 0.288406i | ||||
\(665\) | − | 3.15747i | − | 0.122441i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −42.2224 | −1.63486 | ||||||||
\(668\) | 10.2660 | − | 8.22197i | 0.397204 | − | 0.318118i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −51.0627 | + | 17.9274i | −1.97272 | + | 0.692596i | ||||
\(671\) | 10.0461 | 0.387824 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5269 | 0.521424 | 0.260712 | − | 0.965417i | \(-0.416043\pi\) | ||||
0.260712 | + | 0.965417i | \(0.416043\pi\) | |||||||
\(674\) | 24.5934 | − | 8.63441i | 0.947303 | − | 0.332585i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.1811 | − | 16.1629i | 0.776197 | − | 0.621650i | ||||
\(677\) | 25.3388 | 0.973850 | 0.486925 | − | 0.873444i | \(-0.338118\pi\) | ||||
0.486925 | + | 0.873444i | \(0.338118\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.39139i | − | 0.130150i | ||||||
\(680\) | 16.3716 | + | 10.2156i | 0.627821 | + | 0.391751i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −31.2489 | + | 10.9711i | −1.19658 | + | 0.420103i | ||||
\(683\) | 4.74712i | 0.181644i | 0.995867 | + | 0.0908218i | \(0.0289494\pi\) | ||||
−0.995867 | + | 0.0908218i | \(0.971051\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.4504i | 0.781369i | ||||||||
\(686\) | 0.468477 | + | 1.33436i | 0.0178865 | + | 0.0509463i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.08477 | + | 36.1156i | −0.308229 | + | 1.37690i | ||||
\(689\) | 1.22033i | 0.0464908i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.8908 | −1.78381 | −0.891904 | − | 0.452224i | \(-0.850631\pi\) | ||||
−0.891904 | + | 0.452224i | \(0.850631\pi\) | |||||||
\(692\) | −20.8243 | + | 16.6780i | −0.791620 | + | 0.634002i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.8122 | + | 33.6448i | 0.448386 | + | 1.27714i | ||||
\(695\) | 12.7457 | 0.483472 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.4097 | 0.621561 | ||||||||
\(698\) | 2.25991 | + | 6.43692i | 0.0855390 | + | 0.243641i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.80305 | − | 10.9916i | −0.332724 | − | 0.415442i | ||||
\(701\) | 11.8394 | 0.447166 | 0.223583 | − | 0.974685i | \(-0.428225\pi\) | ||||
0.223583 | + | 0.974685i | \(0.428225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.35412i | − | 0.239650i | ||||||
\(704\) | 36.7839 | − | 17.9987i | 1.38635 | − | 0.678350i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.96263 | − | 28.3766i | −0.374949 | − | 1.06797i | ||||
\(707\) | − | 8.18671i | − | 0.307893i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.55487i | − | 0.133506i | −0.997770 | − | 0.0667530i | \(-0.978736\pi\) | ||
0.997770 | − | 0.0667530i | \(-0.0212639\pi\) | |||||||
\(710\) | 5.56061 | − | 1.95225i | 0.208686 | − | 0.0732668i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −43.6803 | − | 27.2559i | −1.63699 | − | 1.02146i | ||||
\(713\) | 26.8298i | 1.00478i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.77112 | −0.178430 | ||||||||
\(716\) | 12.2845 | + | 15.3385i | 0.459093 | + | 0.573227i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.3305 | + | 11.7019i | −1.24388 | + | 0.436710i | ||||
\(719\) | 0.174626 | 0.00651246 | 0.00325623 | − | 0.999995i | \(-0.498964\pi\) | ||||
0.00325623 | + | 0.999995i | \(0.498964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5624 | −0.616816 | ||||||||
\(722\) | −24.2481 | + | 8.51318i | −0.902422 | + | 0.316828i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.11058 | + | 7.62971i | 0.227098 | + | 0.283556i | ||||
\(725\) | −50.6930 | −1.88269 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.37928i | − | 0.310770i | −0.987854 | − | 0.155385i | \(-0.950338\pi\) | ||
0.987854 | − | 0.155385i | \(-0.0496619\pi\) | |||||||
\(728\) | 0.402181 | − | 0.644536i | 0.0149058 | − | 0.0238881i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −41.7511 | + | 14.6583i | −1.54528 | + | 0.542526i | ||||
\(731\) | − | 18.1917i | − | 0.672843i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 15.6312i | − | 0.577351i | −0.957427 | − | 0.288676i | \(-0.906785\pi\) | ||
0.957427 | − | 0.288676i | \(-0.0932149\pi\) | |||||||
\(734\) | −6.50484 | − | 18.5277i | −0.240098 | − | 0.683872i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.88629 | − | 32.9465i | −0.143250 | − | 1.21442i | ||||
\(737\) | − | 56.4512i | − | 2.07941i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.4382 | −0.935760 | −0.467880 | − | 0.883792i | \(-0.654982\pi\) | ||||
−0.467880 | + | 0.883792i | \(0.654982\pi\) | |||||||
\(740\) | −30.2953 | − | 37.8269i | −1.11368 | − | 1.39055i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.12841 | − | 6.06235i | −0.0781364 | − | 0.222556i | ||||
\(743\) | 33.0542 | 1.21264 | 0.606320 | − | 0.795220i | \(-0.292645\pi\) | ||||
0.606320 | + | 0.795220i | \(0.292645\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 79.8941 | 2.92709 | ||||||||
\(746\) | 0.240783 | + | 0.685823i | 0.00881570 | + | 0.0251098i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.7114 | + | 12.5832i | −0.574467 | + | 0.460086i | ||||
\(749\) | 15.1480 | 0.553496 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 40.4075i | − | 1.47449i | −0.675625 | − | 0.737246i | \(-0.736126\pi\) | ||
0.675625 | − | 0.737246i | \(-0.263874\pi\) | |||||||
\(752\) | −5.67376 | + | 25.3453i | −0.206901 | + | 0.924250i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.905954 | − | 2.58043i | −0.0329929 | − | 0.0939737i | ||||
\(755\) | 4.64498i | 0.169048i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0219i | 1.09116i | 0.838057 | + | 0.545582i | \(0.183691\pi\) | ||||
−0.838057 | + | 0.545582i | \(0.816309\pi\) | |||||||
\(758\) | −10.6444 | + | 3.73710i | −0.386621 | + | 0.135737i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.72772 | − | 7.57665i | 0.171492 | − | 0.274834i | ||||
\(761\) | − | 13.9651i | − | 0.506234i | −0.967436 | − | 0.253117i | \(-0.918544\pi\) | ||
0.967436 | − | 0.253117i | \(-0.0814557\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.70038 | 0.278772 | ||||||||
\(764\) | 18.1284 | − | 14.5189i | 0.655864 | − | 0.525276i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.7203 | + | 3.76375i | −0.387340 | + | 0.135990i | ||||
\(767\) | −0.941516 | −0.0339962 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.9999 | 0.649094 | 0.324547 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324547 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 23.7020 | − | 8.32145i | 0.854161 | − | 0.299884i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.0075 | + | 16.0239i | −0.720086 | + | 0.576711i | ||||
\(773\) | 27.2134 | 0.978798 | 0.489399 | − | 0.872060i | \(-0.337216\pi\) | ||||
0.489399 | + | 0.872060i | \(0.337216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.2124i | 1.15710i | ||||||||
\(776\) | 5.07798 | − | 8.13797i | 0.182289 | − | 0.292136i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.81659 | + | 3.09539i | −0.316090 | + | 0.110975i | ||||
\(779\) | − | 7.59429i | − | 0.272094i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.14741i | 0.219972i | ||||||||
\(782\) | 5.40184 | + | 15.3861i | 0.193170 | + | 0.550205i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.873805 | + | 3.90339i | −0.0312073 | + | 0.139407i | ||||
\(785\) | 75.5908i | 2.69795i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.45794 | 0.123262 | 0.0616312 | − | 0.998099i | \(-0.480370\pi\) | ||||
0.0616312 | + | 0.998099i | \(0.480370\pi\) | |||||||
\(788\) | 7.32365 | − | 5.86546i | 0.260894 | − | 0.208948i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22.0386 | + | 62.7725i | 0.784097 | + | 2.23335i | ||||
\(791\) | −14.5822 | −0.518484 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.527143 | 0.0187194 | ||||||||
\(794\) | −8.18157 | − | 23.3036i | −0.290353 | − | 0.827013i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.1981 | + | 23.9709i | 0.680458 | + | 0.849625i | ||||
\(797\) | 44.2671 | 1.56802 | 0.784010 | − | 0.620748i | \(-0.213171\pi\) | ||||
0.784010 | + | 0.620748i | \(0.213171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.7666i | − | 0.451650i | ||||||
\(800\) | −4.66596 | − | 39.5562i | −0.164967 | − | 1.39852i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.71989 | + | 24.8369i | 0.307910 | + | 0.877021i | ||||
\(803\) | − | 46.1571i | − | 1.62885i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 20.3501i | − | 0.717248i | ||||||
\(806\) | −1.63971 | + | 0.575679i | −0.0577562 | + | 0.0202774i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.2581 | − | 19.6448i | 0.431237 | − | 0.691101i | ||||
\(809\) | 14.4191i | 0.506949i | 0.967342 | + | 0.253475i | \(0.0815734\pi\) | ||||
−0.967342 | + | 0.253475i | \(0.918427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3314 | 0.854389 | 0.427195 | − | 0.904160i | \(-0.359502\pi\) | ||||
0.427195 | + | 0.904160i | \(0.359502\pi\) | |||||||
\(812\) | 9.00121 | + | 11.2390i | 0.315881 | + | 0.394411i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 47.6981 | − | 16.7462i | 1.67182 | − | 0.586953i | ||||
\(815\) | −70.3410 | −2.46394 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.41897 | −0.294543 | ||||||||
\(818\) | 4.97510 | − | 1.74669i | 0.173950 | − | 0.0610715i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36.2082 | − | 45.2099i | −1.26445 | − | 1.57880i | ||||
\(821\) | −3.63626 | −0.126906 | −0.0634532 | − | 0.997985i | \(-0.520211\pi\) | ||||
−0.0634532 | + | 0.997985i | \(0.520211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 0.408592i | − | 0.0142426i | −0.999975 | − | 0.00712132i | \(-0.997733\pi\) | ||
0.999975 | − | 0.00712132i | \(-0.00226681\pi\) | |||||||
\(824\) | −39.7431 | − | 24.7991i | −1.38451 | − | 0.863917i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.67727 | − | 1.64213i | 0.162743 | − | 0.0571369i | ||||
\(827\) | 39.3528i | 1.36843i | 0.729280 | + | 0.684215i | \(0.239855\pi\) | ||||
−0.729280 | + | 0.684215i | \(0.760145\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.5641i | − | 1.30465i | −0.757938 | − | 0.652327i | \(-0.773793\pi\) | ||
0.757938 | − | 0.652327i | \(-0.226207\pi\) | |||||||
\(830\) | −8.06857 | − | 22.9817i | −0.280064 | − | 0.797707i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.93014 | − | 0.944435i | 0.0669157 | − | 0.0327424i | ||||
\(833\) | − | 1.96616i | − | 0.0681234i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.8200 | 0.789719 | ||||||||
\(836\) | 5.82340 | + | 7.27115i | 0.201407 | + | 0.251478i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.1288 | + | 40.2432i | 0.488073 | + | 1.39018i | ||||
\(839\) | 35.7770 | 1.23516 | 0.617579 | − | 0.786509i | \(-0.288113\pi\) | ||||
0.617579 | + | 0.786509i | \(0.288113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8342 | 0.787385 | ||||||||
\(842\) | −1.95550 | − | 5.56986i | −0.0673910 | − | 0.191950i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.95905 | − | 6.37434i | 0.273962 | − | 0.219414i | ||||
\(845\) | 44.8600 | 1.54323 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.2033i | 0.522390i | ||||||||
\(848\) | 3.96992 | − | 17.7341i | 0.136327 | − | 0.608991i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.48556 | + | 18.4728i | 0.222453 | + | 0.633613i | ||||
\(851\) | − | 40.9528i | − | 1.40384i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.3988i | 1.79410i | 0.441929 | + | 0.897050i | \(0.354294\pi\) | ||||
−0.441929 | + | 0.897050i | \(0.645706\pi\) | |||||||
\(854\) | −2.61874 | + | 0.919406i | −0.0896116 | + | 0.0314614i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.3491 | + | 22.6813i | 1.24239 | + | 0.775230i | ||||
\(857\) | 19.1325i | 0.653553i | 0.945102 | + | 0.326777i | \(0.105963\pi\) | ||||
−0.945102 | + | 0.326777i | \(0.894037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.1998 | −0.416253 | −0.208127 | − | 0.978102i | \(-0.566737\pi\) | ||||
−0.208127 | + | 0.978102i | \(0.566737\pi\) | |||||||
\(860\) | −50.1193 | + | 40.1402i | −1.70905 | + | 1.36877i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.1072 | − | 9.51696i | 0.923275 | − | 0.324149i | ||||
\(863\) | 31.3575 | 1.06742 | 0.533711 | − | 0.845667i | \(-0.320797\pi\) | ||||
0.533711 | + | 0.845667i | \(0.320797\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.2897 | −1.57390 | ||||||||
\(866\) | 50.1375 | − | 17.6026i | 1.70374 | − | 0.598160i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.14170 | − | 5.71973i | 0.242405 | − | 0.194140i | ||||
\(869\) | −69.3968 | −2.35413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.96214i | − | 0.100368i | ||||||
\(872\) | 18.4778 | + | 11.5299i | 0.625737 | + | 0.390451i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.12057 | − | 2.49994i | 0.240857 | − | 0.0845616i | ||||
\(875\) | − | 7.08266i | − | 0.239438i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.64956i | 0.157004i | 0.996914 | + | 0.0785022i | \(0.0250138\pi\) | ||||
−0.996914 | + | 0.0785022i | \(0.974986\pi\) | |||||||
\(878\) | −5.72566 | − | 16.3084i | −0.193232 | − | 0.550382i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 69.3350 | + | 15.5212i | 2.33728 | + | 0.523220i | ||||
\(881\) | 43.3414i | 1.46021i | 0.683336 | + | 0.730104i | \(0.260528\pi\) | ||||
−0.683336 | + | 0.730104i | \(0.739472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.420653 | 0.0141561 | 0.00707805 | − | 0.999975i | \(-0.497747\pi\) | ||||
0.00707805 | + | 0.999975i | \(0.497747\pi\) | |||||||
\(884\) | −0.824419 | + | 0.660270i | −0.0277282 | + | 0.0222073i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.998477 | − | 2.84396i | −0.0335445 | − | 0.0955448i | ||||
\(887\) | −14.5102 | −0.487204 | −0.243602 | − | 0.969875i | \(-0.578329\pi\) | ||||
−0.243602 | + | 0.969875i | \(0.578329\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.7782 | 0.462106 | ||||||||
\(890\) | −29.5917 | − | 84.2860i | −0.991915 | − | 2.82527i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −36.8968 | − | 46.0696i | −1.23540 | − | 1.54252i | ||||
\(893\) | −5.90830 | −0.197714 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.0955i | 1.13969i | ||||||||
\(896\) | −7.94138 | + | 8.05820i | −0.265303 | + | 0.269206i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.5654 | − | 32.9418i | −0.385943 | − | 1.09928i | ||||
\(899\) | − | 32.9375i | − | 1.09853i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.93276i | 0.297593i | ||||||||
\(902\) | 57.0077 | − | 20.0146i | 1.89815 | − | 0.666414i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.9914 | − | 21.8341i | −1.16380 | − | 0.726192i | ||||
\(905\) | 16.9599i | 0.563765i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.1284 | −1.00040 | −0.500198 | − | 0.865911i | \(-0.666740\pi\) | ||||
−0.500198 | + | 0.865911i | \(0.666740\pi\) | |||||||
\(908\) | −18.0996 | − | 22.5993i | −0.600657 | − | 0.749985i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.24370 | − | 0.436648i | 0.0412284 | − | 0.0144747i | ||||
\(911\) | 15.1934 | 0.503379 | 0.251689 | − | 0.967808i | \(-0.419014\pi\) | ||||
0.251689 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.4070 | 0.840848 | ||||||||
\(914\) | −44.4095 | + | 15.5916i | −1.46894 | + | 0.515724i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.8929 | + | 18.5954i | 0.492074 | + | 0.614408i | ||||
\(917\) | −11.4226 | −0.377207 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 38.7985i | − | 1.27984i | −0.768440 | − | 0.639922i | \(-0.778967\pi\) | ||
0.768440 | − | 0.639922i | \(-0.221033\pi\) | |||||||
\(920\) | 30.4705 | − | 48.8321i | 1.00458 | − | 1.60995i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.3195 | − | 7.13392i | 0.669189 | − | 0.234943i | ||||
\(923\) | 0.322570i | 0.0106175i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 49.1688i | − | 1.61666i | ||||||
\(926\) | −1.50795 | − | 4.29509i | −0.0495543 | − | 0.141146i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.77099 | + | 40.4466i | 0.156615 | + | 1.32773i | ||||
\(929\) | 43.7700i | 1.43605i | 0.696019 | + | 0.718023i | \(0.254953\pi\) | ||||
−0.696019 | + | 0.718023i | \(0.745047\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.909926 | −0.0298216 | ||||||||
\(932\) | 16.6204 | + | 20.7524i | 0.544419 | + | 0.679766i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.5795 | − | 30.1336i | −0.346171 | − | 0.986001i | ||||
\(935\) | −34.9245 | −1.14215 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7605 | 0.580209 | 0.290104 | − | 0.956995i | \(-0.406310\pi\) | ||||
0.290104 | + | 0.956995i | \(0.406310\pi\) | |||||||
\(938\) | 5.16636 | + | 14.7153i | 0.168688 | + | 0.480473i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −35.1729 | + | 28.1697i | −1.14721 | + | 0.918794i | ||||
\(941\) | −32.6364 | −1.06392 | −0.531958 | − | 0.846771i | \(-0.678544\pi\) | ||||
−0.531958 | + | 0.846771i | \(0.678544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 48.9458i | − | 1.59390i | ||||||
\(944\) | 13.6823 | + | 3.06290i | 0.445322 | + | 0.0996889i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.1881 | − | 63.1983i | −0.721396 | − | 2.05475i | ||||
\(947\) | 14.9843i | 0.486925i | 0.969910 | + | 0.243462i | \(0.0782832\pi\) | ||||
−0.969910 | + | 0.243462i | \(0.921717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.42198i | − | 0.0786208i | ||||||
\(950\) | 8.54911 | − | 3.00148i | 0.277370 | − | 0.0973807i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.94396 | − | 4.71799i | 0.0954142 | − | 0.152911i | ||||
\(953\) | 23.1053i | 0.748453i | 0.927337 | + | 0.374226i | \(0.122092\pi\) | ||||
−0.927337 | + | 0.374226i | \(0.877908\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.2971 | 1.30398 | ||||||||
\(956\) | −18.3806 | + | 14.7208i | −0.594470 | + | 0.476106i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.3808 | − | 13.1239i | 1.20772 | − | 0.424014i | ||||
\(959\) | 5.89343 | 0.190309 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.0702 | 0.324846 | ||||||||
\(962\) | 2.50284 | − | 0.878713i | 0.0806948 | − | 0.0283309i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −36.3740 | + | 29.1317i | −1.17153 | + | 0.938268i | ||||
\(965\) | −44.4741 | −1.43167 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 25.1604i | − | 0.809103i | −0.914515 | − | 0.404552i | \(-0.867428\pi\) | ||
0.914515 | − | 0.404552i | \(-0.132572\pi\) | |||||||
\(968\) | −22.7640 | + | 36.4817i | −0.731664 | + | 1.17257i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.7031 | − | 5.51315i | 0.504197 | − | 0.177017i | ||||
\(971\) | − | 24.0973i | − | 0.773318i | −0.922223 | − | 0.386659i | \(-0.873629\pi\) | ||
0.922223 | − | 0.386659i | \(-0.126371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 3.67309i | − | 0.117754i | ||||||
\(974\) | 1.19612 | + | 3.40691i | 0.0383262 | + | 0.109164i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.66056 | − | 1.71488i | −0.245209 | − | 0.0548919i | ||||
\(977\) | 30.9215i | 0.989267i | 0.869102 | + | 0.494634i | \(0.164698\pi\) | ||||
−0.869102 | + | 0.494634i | \(0.835302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 93.1807 | 2.97807 | ||||||||
\(980\) | −5.41692 | + | 4.33836i | −0.173037 | + | 0.138584i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.376390 | − | 1.07207i | −0.0120111 | − | 0.0342112i | ||||
\(983\) | −1.67927 | −0.0535602 | −0.0267801 | − | 0.999641i | \(-0.508525\pi\) | ||||
−0.0267801 | + | 0.999641i | \(0.508525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.2795 | 0.518709 | ||||||||
\(986\) | −6.63156 | − | 18.8887i | −0.211192 | − | 0.601538i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.305569 | + | 0.381535i | 0.00972143 | + | 0.0121383i | ||||
\(989\) | −54.2610 | −1.72540 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 7.63921i | − | 0.242667i | −0.992612 | − | 0.121334i | \(-0.961283\pi\) | ||
0.992612 | − | 0.121334i | \(-0.0387171\pi\) | |||||||
\(992\) | 25.7014 | − | 3.03168i | 0.816020 | − | 0.0962558i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.562604 | − | 1.60247i | −0.0178447 | − | 0.0508272i | ||||
\(995\) | 53.2841i | 1.68922i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.4039i | 1.81800i | 0.416798 | + | 0.908999i | \(0.363152\pi\) | ||||
−0.416798 | + | 0.908999i | \(0.636848\pi\) | |||||||
\(998\) | 43.5041 | − | 15.2737i | 1.37710 | − | 0.483480i | ||||
\(999\) | 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 | 1512.2.j.c.323.29 | yes | 32 | |
3.2 | odd | 2 | inner | 1512.2.j.c.323.4 | yes | 32 | |
4.3 | odd | 2 | 6048.2.j.c.5615.30 | 32 | |||
8.3 | odd | 2 | inner | 1512.2.j.c.323.3 | ✓ | 32 | |
8.5 | even | 2 | 6048.2.j.c.5615.4 | 32 | |||
12.11 | even | 2 | 6048.2.j.c.5615.3 | 32 | |||
24.5 | odd | 2 | 6048.2.j.c.5615.29 | 32 | |||
24.11 | even | 2 | inner | 1512.2.j.c.323.30 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.3 | ✓ | 32 | 8.3 | odd | 2 | inner | |
1512.2.j.c.323.4 | yes | 32 | 3.2 | odd | 2 | inner | |
1512.2.j.c.323.29 | yes | 32 | 1.1 | even | 1 | trivial | |
1512.2.j.c.323.30 | yes | 32 | 24.11 | even | 2 | inner | |
6048.2.j.c.5615.3 | 32 | 12.11 | even | 2 | |||
6048.2.j.c.5615.4 | 32 | 8.5 | even | 2 | |||
6048.2.j.c.5615.29 | 32 | 24.5 | odd | 2 | |||
6048.2.j.c.5615.30 | 32 | 4.3 | odd | 2 |