Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(255,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.255");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.2353561680715186176.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 2 x^{14} + 41 x^{12} - 92 x^{11} + 66 x^{10} - 104 x^{9} + 291 x^{8} - 388 x^{7} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 255.4 | ||
Root | \(0.224274 - 0.447866i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.255 |
Dual form | 448.2.p.e.383.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.0913671 | + | 0.158252i | −0.0527508 | + | 0.0913671i | −0.891195 | − | 0.453620i | \(-0.850132\pi\) |
0.838444 | + | 0.544987i | \(0.183466\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.08101 | − | 1.77882i | 1.37787 | − | 0.795514i | 0.385968 | − | 0.922512i | \(-0.373868\pi\) |
0.991903 | + | 0.126998i | \(0.0405342\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64485 | − | 0.0690906i | 0.999659 | − | 0.0261138i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.48330 | + | 2.56916i | 0.494435 | + | 0.856386i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.74455 | − | 2.73927i | −1.43053 | − | 0.825920i | −0.433373 | − | 0.901214i | \(-0.642677\pi\) |
−0.997161 | + | 0.0752949i | \(0.976010\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.70791i | − | 0.751040i | −0.926814 | − | 0.375520i | \(-0.877464\pi\) | ||
0.926814 | − | 0.375520i | \(-0.122536\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.650103i | 0.167856i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.845123 | − | 0.487932i | −0.204972 | − | 0.118341i | 0.394000 | − | 0.919110i | \(-0.371091\pi\) |
−0.598973 | + | 0.800769i | \(0.704424\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.73622 | + | 4.73927i | 0.627731 | + | 1.08726i | 0.988006 | + | 0.154416i | \(0.0493496\pi\) |
−0.360275 | + | 0.932846i | \(0.617317\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.230718 | + | 0.424866i | −0.0503469 | + | 0.0927134i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.90744 | + | 2.25596i | −0.814757 | + | 0.470400i | −0.848605 | − | 0.529027i | \(-0.822557\pi\) |
0.0338478 | + | 0.999427i | \(0.489224\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.82843 | − | 6.63103i | 0.765685 | − | 1.32621i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.09030 | −0.209829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.96661 | 0.550885 | 0.275443 | − | 0.961318i | \(-0.411176\pi\) | ||||
0.275443 | + | 0.961318i | \(0.411176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.27092 | − | 5.66540i | 0.587475 | − | 1.01754i | −0.407087 | − | 0.913389i | \(-0.633455\pi\) |
0.994562 | − | 0.104147i | \(-0.0332112\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.866990 | − | 0.500557i | 0.150924 | − | 0.0871358i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.02591 | − | 4.91759i | 1.35663 | − | 0.831224i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.597709 | − | 1.03526i | −0.0982627 | − | 0.170196i | 0.812703 | − | 0.582678i | \(-0.197995\pi\) |
−0.910966 | + | 0.412482i | \(0.864662\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.428534 | + | 0.247414i | 0.0686204 | + | 0.0396180i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.70791i | 0.422905i | 0.977388 | + | 0.211453i | \(0.0678194\pi\) | ||||
−0.977388 | + | 0.211453i | \(0.932181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.02384i | 0.156135i | 0.996948 | + | 0.0780674i | \(0.0248749\pi\) | ||||
−0.996948 | + | 0.0780674i | \(0.975125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.14016 | + | 5.27707i | 1.36253 | + | 0.786660i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.01878 | + | 3.49662i | 0.294469 | + | 0.510035i | 0.974861 | − | 0.222813i | \(-0.0715239\pi\) |
−0.680392 | + | 0.732848i | \(0.738191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99045 | − | 0.365468i | 0.998636 | − | 0.0522097i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.154433 | − | 0.0891618i | 0.0216249 | − | 0.0124852i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.42614 | + | 5.93424i | −0.470616 | + | 0.815131i | −0.999435 | − | 0.0336037i | \(-0.989302\pi\) |
0.528819 | + | 0.848734i | \(0.322635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.4907 | −2.62812 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.79928 | + | 4.84850i | −0.364435 | + | 0.631221i | −0.988685 | − | 0.150004i | \(-0.952071\pi\) |
0.624250 | + | 0.781225i | \(0.285405\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.53093 | + | 4.34798i | −0.964236 | + | 0.556702i | −0.897474 | − | 0.441067i | \(-0.854600\pi\) |
−0.0667620 | + | 0.997769i | \(0.521267\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.10062 | + | 6.69255i | 0.516630 | + | 0.843182i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.81690 | − | 8.34312i | −0.597463 | − | 1.03484i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.42934 | + | 1.97993i | 0.418960 | + | 0.241887i | 0.694632 | − | 0.719365i | \(-0.255567\pi\) |
−0.275672 | + | 0.961252i | \(0.588900\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 0.824482i | − | 0.0992560i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.3002i | − | 1.57844i | −0.614108 | − | 0.789222i | \(-0.710484\pi\) | ||
0.614108 | − | 0.789222i | \(-0.289516\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.29504 | − | 4.78914i | −0.970860 | − | 0.560527i | −0.0713620 | − | 0.997450i | \(-0.522735\pi\) |
−0.899498 | + | 0.436924i | \(0.856068\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.699584 | + | 1.21172i | 0.0807810 | + | 0.139917i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.7379 | − | 6.91714i | −1.45161 | − | 0.788281i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.35924 | − | 1.93946i | 0.377944 | − | 0.218206i | −0.298980 | − | 0.954260i | \(-0.596646\pi\) |
0.676923 | + | 0.736054i | \(0.263313\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.35029 | + | 7.53493i | −0.483366 | + | 0.837215i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.24331 | −0.246235 | −0.123118 | − | 0.992392i | \(-0.539289\pi\) | ||||
−0.123118 | + | 0.992392i | \(0.539289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.47178 | −0.376567 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.271050 | + | 0.469473i | −0.0290596 | + | 0.0503328i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.3523 | + | 7.13159i | −1.30934 | + | 0.755947i | −0.981986 | − | 0.188956i | \(-0.939490\pi\) |
−0.327353 | + | 0.944902i | \(0.606156\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.187091 | − | 7.16203i | −0.0196125 | − | 0.750784i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.597709 | + | 1.03526i | 0.0619795 | + | 0.107352i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.8606 | + | 9.73449i | 1.72986 | + | 0.998738i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7412i | 1.09061i | 0.838239 | + | 0.545304i | \(0.183586\pi\) | ||||
−0.838239 | + | 0.545304i | \(0.816414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 16.2527i | − | 1.63345i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.39077 | − | 4.26706i | −0.735409 | − | 0.424588i | 0.0849888 | − | 0.996382i | \(-0.472915\pi\) |
−0.820398 | + | 0.571793i | \(0.806248\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.08184 | + | 3.60586i | 0.205130 | + | 0.355296i | 0.950174 | − | 0.311720i | \(-0.100905\pi\) |
−0.745044 | + | 0.667015i | \(0.767572\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0449160 | + | 1.71943i | 0.00438335 | + | 0.167799i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.08264 | + | 4.08916i | −0.684704 | + | 0.395314i | −0.801625 | − | 0.597827i | \(-0.796031\pi\) |
0.116921 | + | 0.993141i | \(0.462698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.74741 | + | 4.75866i | −0.263155 | + | 0.455797i | −0.967078 | − | 0.254478i | \(-0.918096\pi\) |
0.703924 | + | 0.710275i | \(0.251430\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.218444 | 0.0207337 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3574 | −1.06842 | −0.534209 | − | 0.845352i | \(-0.679391\pi\) | ||||
−0.534209 | + | 0.845352i | \(0.679391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.02591 | + | 13.9013i | −0.748420 | + | 1.29630i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.95706 | − | 4.01666i | 0.643181 | − | 0.371340i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.26893 | − | 1.23212i | −0.207993 | − | 0.112948i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.50715 | + | 16.4669i | 0.864286 | + | 1.49699i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.428534 | − | 0.247414i | −0.0386396 | − | 0.0223086i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 9.45215i | − | 0.845426i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.2899i | − | 1.26802i | −0.773325 | − | 0.634010i | \(-0.781408\pi\) | ||
0.773325 | − | 0.634010i | \(-0.218592\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.162026 | − | 0.0935457i | −0.0142656 | − | 0.00823624i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.50272 | + | 11.2630i | 0.568145 | + | 0.984057i | 0.996749 | + | 0.0805641i | \(0.0256722\pi\) |
−0.428604 | + | 0.903492i | \(0.640994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.56432 | + | 12.3456i | 0.655909 | + | 1.07050i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.35924 | + | 1.93946i | −0.289117 | + | 0.166922i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.31690 | − | 12.6732i | 0.625125 | − | 1.08275i | −0.363391 | − | 0.931637i | \(-0.618381\pi\) |
0.988517 | − | 0.151112i | \(-0.0482854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3608 | −0.963613 | −0.481807 | − | 0.876278i | \(-0.660019\pi\) | ||||
−0.481807 | + | 0.876278i | \(0.660019\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.737799 | −0.0621339 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.41770 | + | 12.8478i | −0.620299 | + | 1.07439i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.14016 | − | 5.27707i | 0.759049 | − | 0.438237i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.580861 | + | 1.13965i | −0.0479086 | + | 0.0939965i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.08101 | − | 8.80057i | −0.416253 | − | 0.720971i | 0.579306 | − | 0.815110i | \(-0.303324\pi\) |
−0.995559 | + | 0.0941390i | \(0.969990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.37788 | + | 4.83697i | 0.681783 | + | 0.393627i | 0.800526 | − | 0.599298i | \(-0.204553\pi\) |
−0.118744 | + | 0.992925i | \(0.537887\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.89501i | − | 0.234047i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 23.2736i | − | 1.86938i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.94085 | + | 1.69790i | 0.234706 | + | 0.135507i | 0.612741 | − | 0.790284i | \(-0.290067\pi\) |
−0.378035 | + | 0.925791i | \(0.623400\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.626072 | − | 1.08439i | −0.0496507 | − | 0.0859976i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.1787 | + | 6.23664i | −0.802196 | + | 0.491516i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.8174 | − | 10.2869i | 1.39557 | − | 0.805731i | 0.401643 | − | 0.915796i | \(-0.368439\pi\) |
0.993924 | + | 0.110065i | \(0.0351060\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.78081 | − | 3.08445i | 0.138636 | − | 0.240124i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.01269 | 0.155746 | 0.0778732 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778732 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.66720 | 0.435938 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.11728 | + | 14.0595i | −0.620744 | + | 1.07516i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.00191 | − | 4.61990i | 0.608374 | − | 0.351245i | −0.163955 | − | 0.986468i | \(-0.552425\pi\) |
0.772329 | + | 0.635223i | \(0.219092\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.66747 | − | 17.8026i | 0.730792 | − | 1.34575i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.511524 | − | 0.885986i | −0.0384485 | − | 0.0665948i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.37920 | + | 1.95098i | 0.252573 | + | 0.145823i | 0.620942 | − | 0.783857i | \(-0.286750\pi\) |
−0.368369 | + | 0.929680i | \(0.620084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8227i | 0.953104i | 0.879146 | + | 0.476552i | \(0.158114\pi\) | ||||
−0.879146 | + | 0.476552i | \(0.841886\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.58905i | − | 0.117466i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.68310 | − | 2.12644i | −0.270787 | − | 0.156339i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.67315 | + | 4.63003i | 0.195480 | + | 0.338581i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.88369 | + | 0.0753296i | −0.209757 | + | 0.00547942i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.03941 | + | 4.64156i | −0.581711 | + | 0.335851i | −0.761813 | − | 0.647797i | \(-0.775691\pi\) |
0.180102 | + | 0.983648i | \(0.442357\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.78789 | + | 3.09671i | −0.128695 | + | 0.222906i | −0.923171 | − | 0.384389i | \(-0.874412\pi\) |
0.794476 | + | 0.607295i | \(0.207745\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.76042 | 0.126067 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.41388 | −0.456970 | −0.228485 | − | 0.973547i | \(-0.573377\pi\) | ||||
−0.228485 | + | 0.973547i | \(0.573377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.28322 | + | 12.6149i | −0.516294 | + | 0.894248i | 0.483527 | + | 0.875329i | \(0.339356\pi\) |
−0.999821 | + | 0.0189182i | \(0.993978\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.626657 | + | 0.361801i | −0.0442010 | + | 0.0255194i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.84623 | − | 0.204965i | 0.550697 | − | 0.0143857i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.81690 | + | 8.34312i | 0.336427 | + | 0.582709i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.5918 | − | 6.69255i | −0.805689 | − | 0.465165i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 29.9809i | − | 2.07382i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3376i | 1.12472i | 0.826891 | + | 0.562362i | \(0.190107\pi\) | ||||
−0.826891 | + | 0.562362i | \(0.809893\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.10479 | + | 1.21520i | 0.144218 | + | 0.0832642i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.82124 | + | 3.15448i | 0.124207 | + | 0.215134i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.25967 | − | 15.2101i | 0.560703 | − | 1.03253i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.51579 | − | 0.875139i | 0.102427 | − | 0.0591364i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.32128 | + | 2.28852i | −0.0888788 | + | 0.153943i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.8100 | −1.66140 | −0.830700 | − | 0.556721i | \(-0.812059\pi\) | ||||
−0.830700 | + | 0.556721i | \(0.812059\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 22.7149 | 1.51433 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9166 | − | 18.9080i | 0.724558 | − | 1.25497i | −0.234598 | − | 0.972092i | \(-0.575377\pi\) |
0.959156 | − | 0.282878i | \(-0.0912893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.87605 | + | 2.23784i | −0.256136 | + | 0.147880i | −0.622571 | − | 0.782563i | \(-0.713912\pi\) |
0.366434 | + | 0.930444i | \(0.380578\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.25848 | − | 1.38380i | 0.148597 | − | 0.0910473i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.64016 | − | 13.2331i | −0.500523 | − | 0.866932i | −1.00000 | 0.000604495i | \(-0.999808\pi\) | |
0.499476 | − | 0.866327i | \(-0.333526\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.4398 | + | 7.18210i | 0.811480 | + | 0.468508i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.708810i | 0.0460421i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.13818i | − | 0.526415i | −0.964739 | − | 0.263208i | \(-0.915220\pi\) | ||
0.964739 | − | 0.263208i | \(-0.0847804\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.5143 | + | 14.1533i | 1.57910 | + | 0.911697i | 0.994984 | + | 0.100029i | \(0.0318937\pi\) |
0.584120 | + | 0.811667i | \(0.301440\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.43040 | − | 4.20958i | −0.155910 | − | 0.270045i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.8876 | − | 13.5608i | 1.33446 | − | 0.866367i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.8335 | − | 7.40944i | 0.816578 | − | 0.471451i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.204965 | − | 0.355009i | 0.0129891 | − | 0.0224978i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.19315 | −0.580267 | −0.290133 | − | 0.956986i | \(-0.593700\pi\) | ||||
−0.290133 | + | 0.956986i | \(0.593700\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.7187 | 1.55405 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.317206 | − | 0.549417i | 0.0198642 | − | 0.0344059i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0547 | − | 8.11449i | 0.876708 | − | 0.506168i | 0.00713657 | − | 0.999975i | \(-0.497728\pi\) |
0.869572 | + | 0.493807i | \(0.164395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.65238 | − | 2.69682i | −0.102674 | − | 0.167572i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.40038 | + | 7.62169i | 0.272377 | + | 0.471770i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.9598 | − | 9.79173i | −1.04578 | − | 0.603784i | −0.124318 | − | 0.992242i | \(-0.539674\pi\) |
−0.921466 | + | 0.388459i | \(0.873008\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.3780i | 1.49753i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.60637i | − | 0.159507i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.74939 | − | 1.01001i | −0.106662 | − | 0.0615815i | 0.445720 | − | 0.895172i | \(-0.352948\pi\) |
−0.552382 | + | 0.833591i | \(0.686281\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8231 | + | 22.2102i | 0.778947 | + | 1.34918i | 0.932549 | + | 0.361042i | \(0.117579\pi\) |
−0.153603 | + | 0.988133i | \(0.549088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.15050 | + | 0.624766i | 0.0696315 | + | 0.0378125i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −36.3283 | + | 20.9742i | −2.19068 | + | 1.26479i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.5882 | − | 26.9995i | 0.936602 | − | 1.62224i | 0.164850 | − | 0.986319i | \(-0.447286\pi\) |
0.771752 | − | 0.635923i | \(-0.219381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.4071 | 1.16187 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.97695 | −0.117935 | −0.0589675 | − | 0.998260i | \(-0.518781\pi\) | ||||
−0.0589675 | + | 0.998260i | \(0.518781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8116 | − | 23.9223i | 0.821013 | − | 1.42204i | −0.0839164 | − | 0.996473i | \(-0.526743\pi\) |
0.904929 | − | 0.425563i | \(-0.139924\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.08101 | + | 1.77882i | −0.182503 | + | 0.105368i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.187091 | + | 7.16203i | 0.0110437 | + | 0.422761i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.02384 | − | 13.8977i | −0.471991 | − | 0.817512i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.69983 | − | 0.981395i | −0.0996456 | − | 0.0575304i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.5289i | 0.615105i | 0.951531 | + | 0.307552i | \(0.0995099\pi\) | ||||
−0.951531 | + | 0.307552i | \(0.900490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.9177i | 1.15965i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.17299 | + | 2.98663i | 0.300167 | + | 0.173302i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.10895 | + | 10.5810i | 0.353290 | + | 0.611916i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0707380 | + | 2.70791i | 0.00407727 | + | 0.156082i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.35055 | − | 0.779738i | 0.0775868 | − | 0.0447948i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.4686 | + | 26.7924i | −0.885729 | + | 1.53413i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.0533 | −1.54401 | −0.772007 | − | 0.635615i | \(-0.780747\pi\) | ||||
−0.772007 | + | 0.635615i | \(0.780747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.760847 | −0.0432831 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.6926 | − | 21.9842i | 0.719731 | − | 1.24661i | −0.241376 | − | 0.970432i | \(-0.577599\pi\) |
0.961106 | − | 0.276179i | \(-0.0890681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.98528 | − | 2.30090i | 0.225261 | − | 0.130055i | −0.383123 | − | 0.923697i | \(-0.625151\pi\) |
0.608384 | + | 0.793643i | \(0.291818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.5389 | + | 13.3256i | 1.38261 | + | 0.750810i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.76928 | − | 6.52859i | −0.211704 | − | 0.366682i | 0.740544 | − | 0.672008i | \(-0.234568\pi\) |
−0.952248 | + | 0.305326i | \(0.901235\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.0752 | − | 8.12633i | −0.788061 | − | 0.454987i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1.49446i | − | 0.0834125i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.34035i | − | 0.297145i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.9563 | − | 10.3671i | −0.996034 | − | 0.575061i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.502046 | − | 0.869570i | −0.0277632 | − | 0.0480873i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.58094 | + | 9.10857i | 0.307687 | + | 0.502171i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.40246 | − | 1.38706i | 0.132051 | − | 0.0762398i | −0.432519 | − | 0.901625i | \(-0.642375\pi\) |
0.564570 | + | 0.825385i | \(0.309042\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.77317 | − | 3.07122i | 0.0971690 | − | 0.168302i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.0878 | 0.769697 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.2716 | −1.37663 | −0.688315 | − | 0.725412i | \(-0.741649\pi\) | ||||
−0.688315 | + | 0.725412i | \(0.741649\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.03770 | − | 1.79734i | 0.0563599 | − | 0.0976182i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.0381 | + | 17.9198i | −1.68081 | + | 0.970414i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4634 | − | 1.44958i | 0.996932 | − | 0.0782701i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.46661 | − | 2.54024i | −0.0789595 | − | 0.136762i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.42472 | + | 5.44137i | 0.505946 | + | 0.292108i | 0.731165 | − | 0.682200i | \(-0.238977\pi\) |
−0.225220 | + | 0.974308i | \(0.572310\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.6437i | − | 1.10503i | −0.833503 | − | 0.552516i | \(-0.813668\pi\) | ||
0.833503 | − | 0.552516i | \(-0.186332\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.95245i | 0.157590i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.57831 | + | 0.911236i | 0.0840048 | + | 0.0485002i | 0.541414 | − | 0.840756i | \(-0.317889\pi\) |
−0.457409 | + | 0.889256i | \(0.651223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.6587 | − | 40.9781i | −1.25567 | − | 2.17489i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.402291 | − | 0.246489i | 0.0212915 | − | 0.0130456i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.04403 | + | 1.18012i | −0.107880 | + | 0.0622843i | −0.552969 | − | 0.833202i | \(-0.686505\pi\) |
0.445089 | + | 0.895486i | \(0.353172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.47376 | + | 9.48083i | −0.288092 | + | 0.498991i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.47456 | −0.182367 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.0761 | −1.78363 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.27738 | + | 5.67660i | −0.171078 | + | 0.296316i | −0.938797 | − | 0.344471i | \(-0.888058\pi\) |
0.767719 | + | 0.640787i | \(0.221392\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.95706 | + | 4.01666i | −0.362170 | + | 0.209099i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.65161 | + | 15.9319i | −0.449169 | + | 0.827142i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.426136 | + | 0.738089i | 0.0220645 | + | 0.0382168i | 0.876847 | − | 0.480770i | \(-0.159643\pi\) |
−0.854782 | + | 0.518987i | \(0.826309\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.49583 | + | 0.863615i | 0.0772441 | + | 0.0445969i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.03332i | − | 0.413737i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.3954i | 1.25311i | 0.779377 | + | 0.626555i | \(0.215536\pi\) | ||||
−0.779377 | + | 0.626555i | \(0.784464\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.26140 | + | 1.30562i | 0.115855 | + | 0.0668891i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.411624 | − | 0.712954i | −0.0210330 | − | 0.0364303i | 0.855317 | − | 0.518105i | \(-0.173362\pi\) |
−0.876350 | + | 0.481674i | \(0.840029\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −51.5499 | + | 1.34662i | −2.62723 | + | 0.0686302i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.63042 | + | 1.51867i | −0.133712 | + | 0.0771985i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.0476 | − | 19.1350i | 0.560137 | − | 0.970185i | −0.437347 | − | 0.899293i | \(-0.644082\pi\) |
0.997484 | − | 0.0708924i | \(-0.0225847\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.40302 | 0.222670 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.37654 | −0.119880 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.89990 | − | 11.9510i | 0.347172 | − | 0.601319i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.8196 | − | 12.5976i | 1.09509 | − | 0.632253i | 0.160166 | − | 0.987090i | \(-0.448797\pi\) |
0.934928 | + | 0.354837i | \(0.115464\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.64485 | + | 0.0690906i | −0.132408 | + | 0.00345885i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.8260 | + | 32.6076i | 0.940127 | + | 1.62835i | 0.765226 | + | 0.643762i | \(0.222627\pi\) |
0.174901 | + | 0.984586i | \(0.444039\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.3414 | − | 8.85738i | −0.764211 | − | 0.441217i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30.9536i | 1.53810i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.54913i | 0.324628i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.93641 | − | 4.58209i | −0.392430 | − | 0.226570i | 0.290782 | − | 0.956789i | \(-0.406084\pi\) |
−0.683213 | + | 0.730220i | \(0.739418\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.33705 | + | 2.31583i | 0.0659517 | + | 0.114232i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.06869 | + | 13.0170i | −0.347828 | + | 0.640522i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.91167 | + | 3.99045i | −0.339280 | + | 0.195884i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.03801 | − | 1.79788i | 0.0508314 | − | 0.0880425i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.9867 | 0.536733 | 0.268367 | − | 0.963317i | \(-0.413516\pi\) | ||||
0.268367 | + | 0.963317i | \(0.413516\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.99361 | 0.340848 | 0.170424 | − | 0.985371i | \(-0.445486\pi\) | ||||
0.170424 | + | 0.985371i | \(0.445486\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.98892 | + | 10.3731i | −0.291191 | + | 0.504358i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.47098 | + | 3.73602i | −0.313889 | + | 0.181224i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.6178 | + | 12.0201i | −0.949370 | + | 0.581692i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.35547 | − | 2.34774i | −0.0654425 | − | 0.113350i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.4275 | − | 12.9485i | −1.08029 | − | 0.623708i | −0.149318 | − | 0.988789i | \(-0.547708\pi\) |
−0.930976 | + | 0.365081i | \(0.881041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 33.4629i | − | 1.60812i | −0.594545 | − | 0.804062i | \(-0.702668\pi\) | ||
0.594545 | − | 0.804062i | \(-0.297332\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.92860i | 0.0924694i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.3832 | − | 12.3456i | −1.02290 | − | 0.590570i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.355022 | + | 0.614916i | 0.0169443 | + | 0.0293483i | 0.874373 | − | 0.485254i | \(-0.161273\pi\) |
−0.857429 | + | 0.514602i | \(0.827940\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.3079 | + | 17.4175i | 0.538472 | + | 0.829404i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.5990 | − | 9.00608i | 0.741130 | − | 0.427892i | −0.0813498 | − | 0.996686i | \(-0.525923\pi\) |
0.822480 | + | 0.568794i | \(0.192590\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.3717 | + | 43.9450i | −1.20273 | + | 2.08319i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.85695 | 0.0878307 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.2048 | 1.47264 | 0.736322 | − | 0.676631i | \(-0.236561\pi\) | ||||
0.736322 | + | 0.676631i | \(0.236561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.41770 | − | 12.8478i | 0.349286 | − | 0.604981i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.53093 | + | 0.883880i | −0.0719291 | + | 0.0415283i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.3164 | − | 21.7335i | −0.624283 | − | 1.01888i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.99562 | − | 8.65268i | −0.233685 | − | 0.404755i | 0.725204 | − | 0.688534i | \(-0.241745\pi\) |
−0.958890 | + | 0.283779i | \(0.908412\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.921440 | + | 0.531994i | 0.0430091 | + | 0.0248313i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.5729i | 1.00475i | 0.864650 | + | 0.502375i | \(0.167540\pi\) | ||||
−0.864650 | + | 0.502375i | \(0.832460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6998i | 0.683157i | 0.939853 | + | 0.341579i | \(0.110962\pi\) | ||||
−0.939853 | + | 0.341579i | \(0.889038\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.68310 | + | 2.12644i | 0.170800 | + | 0.0986112i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.5215 | + | 30.3481i | 0.810797 | + | 1.40434i | 0.912307 | + | 0.409507i | \(0.134299\pi\) |
−0.101510 | + | 0.994835i | \(0.532367\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.20687 | + | 4.99968i | 0.425134 | + | 0.230864i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.537394 | + | 0.310265i | −0.0247618 | + | 0.0142962i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.80458 | − | 4.85768i | 0.128955 | − | 0.223356i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41.9016 | 1.92258 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.3280 | −0.930755 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.291956 | + | 0.505682i | −0.0133398 | + | 0.0231052i | −0.872618 | − | 0.488403i | \(-0.837580\pi\) |
0.859278 | + | 0.511508i | \(0.170913\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.80340 | + | 1.61854i | −0.127824 | + | 0.0737993i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0569639 | − | 2.18063i | −0.00259195 | − | 0.0992221i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.1068 | + | 33.0939i | 0.867594 | + | 1.50272i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0977 | + | 13.9128i | 1.09197 | + | 0.630450i | 0.934101 | − | 0.357010i | \(-0.116204\pi\) |
0.157871 | + | 0.987460i | \(0.449537\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.75953i | 0.170012i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.25265i | − | 0.191920i | −0.995385 | − | 0.0959598i | \(-0.969408\pi\) | ||
0.995385 | − | 0.0959598i | \(-0.0305920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.50715 | − | 1.44750i | −0.112916 | − | 0.0651923i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.9106 | − | 50.0746i | −1.29944 | − | 2.25069i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.918919 | − | 35.1770i | −0.0412191 | − | 1.57791i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.8174 | − | 10.2869i | 0.797617 | − | 0.460504i | −0.0450203 | − | 0.998986i | \(-0.514335\pi\) |
0.842637 | + | 0.538482i | \(0.181002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.183893 | + | 0.318513i | −0.00821575 | + | 0.0142301i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.2966 | 1.30627 | 0.653136 | − | 0.757241i | \(-0.273453\pi\) | ||||
0.653136 | + | 0.757241i | \(0.273453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.3614 | −1.35106 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.517795 | + | 0.896847i | −0.0229961 | + | 0.0398304i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.6673 | − | 9.04550i | 0.694439 | − | 0.400935i | −0.110834 | − | 0.993839i | \(-0.535352\pi\) |
0.805273 | + | 0.592904i | \(0.202019\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.2700 | − | 12.0934i | −0.985167 | − | 0.534983i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.98330 | − | 5.16723i | −0.131716 | − | 0.228139i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.8284 | + | 7.40646i | 0.565286 | + | 0.326368i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 22.1199i | − | 0.972831i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.68843i | 0.0741138i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.8279 | − | 13.7570i | −1.04392 | − | 0.602706i | −0.122977 | − | 0.992409i | \(-0.539244\pi\) |
−0.920941 | + | 0.389703i | \(0.872578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.63084 | − | 13.2170i | −0.333673 | − | 0.577939i | 0.649556 | − | 0.760314i | \(-0.274955\pi\) |
−0.983229 | + | 0.182375i | \(0.941622\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.93401 | + | 3.15647i | 0.0844072 | + | 0.137760i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.52866 | + | 3.19197i | −0.240832 | + | 0.139045i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.32128 | + | 2.28852i | −0.0574469 | + | 0.0995009i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.6087 | −0.720758 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.33280 | 0.317619 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.5478 | + | 25.1975i | −0.628956 | + | 1.08938i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.617495 | + | 0.356511i | −0.0266469 | + | 0.0153846i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.1676 | − | 17.4147i | −1.47170 | − | 0.750105i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.8999 | − | 34.4676i | −0.855563 | − | 1.48188i | −0.876122 | − | 0.482090i | \(-0.839878\pi\) |
0.0205583 | − | 0.999789i | \(-0.493456\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.02922 | − | 1.17157i | −0.0870823 | − | 0.0502770i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.5487i | 0.837373i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.19462i | 0.136592i | 0.997665 | + | 0.0682961i | \(0.0217563\pi\) | ||||
−0.997665 | + | 0.0682961i | \(0.978244\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.3413 | − | 12.8988i | −0.953504 | − | 0.550506i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.11728 | + | 14.0595i | 0.345808 | + | 0.598957i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.75068 | − | 5.36166i | 0.372117 | − | 0.228001i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.673027 | − | 0.388573i | 0.0285684 | − | 0.0164940i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.94283 | − | 3.36508i | 0.0823204 | − | 0.142583i | −0.821926 | − | 0.569595i | \(-0.807100\pi\) |
0.904246 | + | 0.427011i | \(0.140434\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.77248 | 0.117264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.976951 | −0.0412469 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.5297 | + | 35.5585i | −0.865223 | + | 1.49861i | 0.00160270 | + | 0.999999i | \(0.499490\pi\) |
−0.866826 | + | 0.498611i | \(0.833843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.9924 | + | 20.2029i | −1.47214 | + | 0.849942i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.9853 | + | 20.2293i | −0.461338 | + | 0.849552i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.75265 | − | 6.49979i | −0.157319 | − | 0.272485i | 0.776582 | − | 0.630017i | \(-0.216952\pi\) |
−0.933901 | + | 0.357531i | \(0.883619\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.60161 | − | 3.23409i | −0.234420 | − | 0.135343i | 0.378189 | − | 0.925728i | \(-0.376547\pi\) |
−0.612610 | + | 0.790386i | \(0.709880\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.69634i | − | 0.0708657i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.5471i | 1.44071i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.9335 | + | 19.0141i | 1.37104 | + | 0.791569i | 0.991059 | − | 0.133426i | \(-0.0425979\pi\) |
0.379979 | + | 0.924995i | \(0.375931\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.326708 | − | 0.565875i | −0.0135775 | − | 0.0235169i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.93322 | + | 0.154992i | −0.246151 | + | 0.00643013i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.5109 | − | 18.7702i | 1.34646 | − | 0.777382i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.2899 | − | 24.7508i | 0.590813 | − | 1.02332i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.0533 | 1.11661 | 0.558305 | − | 0.829636i | \(-0.311452\pi\) | ||||
0.558305 | + | 0.829636i | \(0.311452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.7998 | 1.47510 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.586018 | − | 1.01501i | 0.0241055 | − | 0.0417520i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.3923 | + | 8.88672i | −0.632084 | + | 0.364934i | −0.781559 | − | 0.623832i | \(-0.785575\pi\) |
0.149475 | + | 0.988766i | \(0.452242\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.18233 | + | 0.239867i | −0.376439 | + | 0.00983360i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.33089 | − | 2.30518i | −0.0544698 | − | 0.0943445i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.1418 | − | 7.01006i | −0.496100 | − | 0.286423i | 0.231002 | − | 0.972953i | \(-0.425800\pi\) |
−0.727101 | + | 0.686530i | \(0.759133\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0595i | 1.06299i | 0.847061 | + | 0.531495i | \(0.178370\pi\) | ||||
−0.847061 | + | 0.531495i | \(0.821630\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7473i | 0.478389i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 58.5833 | + | 33.8231i | 2.38175 | + | 1.37510i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0120 | − | 17.3413i | −0.406376 | − | 0.703864i | 0.588105 | − | 0.808785i | \(-0.299874\pi\) |
−0.994481 | + | 0.104921i | \(0.966541\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.684451 | + | 1.26041i | −0.0277353 | + | 0.0510745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.46856 | − | 5.46668i | 0.383057 | − | 0.221158i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.7244 | − | 23.7713i | 0.554322 | − | 0.960114i | −0.443634 | − | 0.896208i | \(-0.646311\pi\) |
0.997956 | − | 0.0639057i | \(-0.0203557\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.76042 | −0.0709872 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.6235 | 0.991303 | 0.495652 | − | 0.868521i | \(-0.334929\pi\) | ||||
0.495652 | + | 0.868521i | \(0.334929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.17095 | + | 12.4205i | −0.288225 | + | 0.499220i | −0.973386 | − | 0.229171i | \(-0.926398\pi\) |
0.685161 | + | 0.728391i | \(0.259732\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.26029 | − | 2.45968i | 0.170960 | − | 0.0987036i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.1772 | + | 19.7154i | −1.28915 | + | 0.789881i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.32843 | + | 4.03295i | 0.0931371 | + | 0.161318i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.74455 | + | 2.73927i | 0.189479 | + | 0.109396i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.16656i | 0.0465140i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.2517i | − | 1.20430i | −0.798383 | − | 0.602150i | \(-0.794311\pi\) | ||
0.798383 | − | 0.602150i | \(-0.205689\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.58546 | − | 1.49271i | −0.102763 | − | 0.0593301i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.4191 | − | 44.0273i | −1.00873 | − | 1.74717i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.989657 | − | 18.9296i | −0.0392116 | − | 0.750016i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34.1703 | − | 19.7283i | 1.35176 | − | 0.780438i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.08612 | + | 5.34531i | −0.121894 | + | 0.211127i | −0.920515 | − | 0.390708i | \(-0.872230\pi\) |
0.798620 | + | 0.601835i | \(0.205564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.7674 | 1.13448 | 0.567238 | − | 0.823554i | \(-0.308012\pi\) | ||||
0.567238 | + | 0.823554i | \(0.308012\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.665605 | −0.0262082 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0534 | − | 41.6618i | 0.945638 | − | 1.63789i | 0.191168 | − | 0.981557i | \(-0.438772\pi\) |
0.754469 | − | 0.656335i | \(-0.227894\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.5626 | − | 15.3360i | 1.04268 | − | 0.601989i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.65238 | + | 2.69682i | 0.0647617 | + | 0.105697i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.04960 | − | 13.9423i | −0.315005 | − | 0.545605i | 0.664433 | − | 0.747347i | \(-0.268673\pi\) |
−0.979439 | + | 0.201743i | \(0.935340\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.0699 | + | 23.1344i | 1.56566 | + | 0.903935i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 28.4150i | − | 1.10858i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.60357i | − | 0.0624663i | −0.999512 | − | 0.0312332i | \(-0.990057\pi\) | ||
0.999512 | − | 0.0312332i | \(-0.00994344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.8217 | + | 22.4137i | 1.50999 | + | 0.871793i | 0.999932 | + | 0.0116530i | \(0.00370936\pi\) |
0.510058 | + | 0.860140i | \(0.329624\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.241443 | − | 0.418191i | −0.00937685 | − | 0.0162412i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 45.2664 | + | 24.5814i | 1.75536 | + | 0.953224i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.5918 | + | 6.69255i | −0.448838 | + | 0.259137i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.26682 | − | 3.92624i | 0.0876401 | − | 0.151797i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47.6411 | 1.83916 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.2430 | 0.587573 | 0.293787 | − | 0.955871i | \(-0.405084\pi\) | ||||
0.293787 | + | 0.955871i | \(0.405084\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.17414 | + | 7.22983i | −0.160663 | + | 0.278276i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.6846 | − | 18.8705i | 1.25617 | − | 0.725250i | 0.283843 | − | 0.958871i | \(-0.408391\pi\) |
0.972328 | + | 0.233620i | \(0.0750573\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.742118 | + | 28.4090i | 0.0284799 | + | 1.09024i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.99483 | + | 3.45514i | 0.0764420 | + | 0.132401i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.72997 | − | 4.46290i | −0.295779 | − | 0.170768i | 0.344766 | − | 0.938689i | \(-0.387958\pi\) |
−0.640545 | + | 0.767920i | \(0.721292\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 52.0619i | − | 1.98918i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 0.817858i | − | 0.0312032i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.0694 | + | 9.27768i | 0.612196 | + | 0.353452i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.4076 | − | 37.0791i | −0.814385 | − | 1.41056i | −0.909769 | − | 0.415116i | \(-0.863741\pi\) |
0.0953835 | − | 0.995441i | \(-0.469592\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.12290 | − | 42.9858i | −0.0426556 | − | 1.63290i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.0029 | + | 20.2089i | −1.32773 | + | 0.766568i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.32128 | − | 2.28852i | 0.0500470 | − | 0.0866839i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.79224 | 0.105612 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3137 | 0.502852 | 0.251426 | − | 0.967877i | \(-0.419101\pi\) | ||||
0.251426 | + | 0.967877i | \(0.419101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.27092 | − | 5.66540i | 0.123365 | − | 0.213675i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.27317 | + | 1.31241i | −0.0856125 | + | 0.0494284i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.8423 | − | 10.7751i | −0.746246 | − | 0.405239i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3689 | + | 28.3518i | 0.614747 | + | 1.06477i | 0.990429 | + | 0.138024i | \(0.0440752\pi\) |
−0.375682 | + | 0.926749i | \(0.622591\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.96554 | + | 5.75361i | 0.373737 | + | 0.215777i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.5163i | 1.10539i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 52.7791i | 1.97383i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.28789 | + | 0.743562i | 0.0480970 | + | 0.0277688i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.7348 | + | 18.5932i | 0.400339 | + | 0.693408i | 0.993767 | − | 0.111480i | \(-0.0355590\pi\) |
−0.593428 | + | 0.804887i | \(0.702226\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.75529 | + | 9.39311i | 0.214338 | + | 0.349818i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.47960 | + | 2.58630i | −0.166598 | + | 0.0961854i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.3574 | − | 19.6717i | 0.421805 | − | 0.730587i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.7591 | −1.17788 | −0.588940 | − | 0.808177i | \(-0.700455\pi\) | ||||
−0.588940 | + | 0.808177i | \(0.700455\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.2135 | −0.933835 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.499567 | − | 0.865275i | 0.0184771 | − | 0.0320033i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.26411 | + | 3.03924i | −0.194434 | + | 0.112257i | −0.594057 | − | 0.804423i | \(-0.702475\pi\) |
0.399622 | + | 0.916680i | \(0.369141\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.237592 | + | 4.54452i | 0.00876372 | + | 0.167627i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.8471 | − | 18.7877i | −0.399558 | − | 0.692055i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.1304 | − | 15.0864i | −0.961221 | − | 0.554961i | −0.0646721 | − | 0.997907i | \(-0.520600\pi\) |
−0.896548 | + | 0.442946i | \(0.853933\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.70791i | 0.0994777i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.49181i | 0.0914155i | 0.998955 | + | 0.0457078i | \(0.0145543\pi\) | ||||
−0.998955 | + | 0.0457078i | \(0.985446\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.3093 | − | 18.0765i | −1.14709 | − | 0.662270i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.32751 | − | 5.76342i | −0.121747 | − | 0.210872i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.4500 | + | 11.3046i | −0.674148 | + | 0.413060i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.3002 | + | 7.67890i | −0.485333 | + | 0.280207i | −0.722636 | − | 0.691228i | \(-0.757070\pi\) |
0.237303 | + | 0.971436i | \(0.423736\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.839951 | − | 1.45484i | 0.0306095 | − | 0.0530173i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.4165 | 1.25254 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.45255 | 0.198176 | 0.0990881 | − | 0.995079i | \(-0.468407\pi\) | ||||
0.0990881 | + | 0.995079i | \(0.468407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.25848 | + | 3.91179i | −0.0819775 | + | 0.141989i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.3439 | − | 9.43616i | 0.592466 | − | 0.342060i | −0.173606 | − | 0.984815i | \(-0.555542\pi\) |
0.766072 | + | 0.642755i | \(0.222209\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.93772 | + | 12.7758i | −0.251162 | + | 0.462514i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.14971 | − | 8.91955i | −0.186188 | − | 0.322487i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.1293 | + | 7.58022i | 0.474072 | + | 0.273706i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.05295i | 0.326458i | 0.986588 | + | 0.163229i | \(0.0521909\pi\) | ||||
−0.986588 | + | 0.163229i | \(0.947809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.96559i | 0.106803i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.9665 | − | 9.21829i | −0.574277 | − | 0.331559i | 0.184579 | − | 0.982818i | \(-0.440908\pi\) |
−0.758856 | + | 0.651259i | \(0.774241\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.0450 | − | 43.3792i | −0.899642 | − | 1.55823i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.577750 | − | 0.0150924i | 0.0207267 | − | 0.000541436i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.8335 | + | 7.40944i | −0.459809 | + | 0.265471i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.4328 | + | 63.1035i | −1.30367 | + | 2.25802i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.23450 | −0.115592 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.0811 | 0.431192 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5424 | − | 30.3843i | 0.625318 | − | 1.08308i | −0.363162 | − | 0.931726i | \(-0.618303\pi\) |
0.988479 | − | 0.151356i | \(-0.0483640\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.09913 | − | 1.78928i | 0.110332 | − | 0.0637002i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.0387 | + | 0.784692i | −1.06805 | + | 0.0279004i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.7740 | + | 20.3931i | 0.418106 | + | 0.724180i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.85787 | − | 2.22734i | −0.136825 | − | 0.0789957i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.81203i | 0.347560i | 0.984785 | + | 0.173780i | \(0.0555981\pi\) | ||||
−0.984785 | + | 0.173780i | \(0.944402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.94010i | − | 0.139391i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36.6444 | − | 21.1566i | −1.29476 | − | 0.747533i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.2375 | + | 45.4446i | 0.925900 | + | 1.60371i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.2669 | + | 37.3213i | −0.714314 | + | 1.31540i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.319673 | − | 0.184564i | 0.0112530 | − | 0.00649695i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.4095 | − | 24.9580i | 0.506611 | − | 0.877477i | −0.493359 | − | 0.869826i | \(-0.664231\pi\) |
0.999971 | − | 0.00765101i | \(-0.00243542\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.4492 | 0.472264 | 0.236132 | − | 0.971721i | \(-0.424120\pi\) | ||||
0.236132 | + | 0.971721i | \(0.424120\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.68643 | −0.164360 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.5971 | − | 63.3881i | 1.28194 | − | 2.22039i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.85227 | + | 2.80146i | −0.169760 | + | 0.0980107i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.1229 | − | 11.1041i | 0.633264 | − | 0.388010i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.356579 | − | 0.617613i | −0.0124447 | − | 0.0215548i | 0.859736 | − | 0.510739i | \(-0.170628\pi\) |
−0.872181 | + | 0.489184i | \(0.837295\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.9518 | − | 21.3341i | −1.28806 | − | 0.743660i | −0.309750 | − | 0.950818i | \(-0.600245\pi\) |
−0.978308 | + | 0.207158i | \(0.933579\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 7.66539i | − | 0.266875i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.85293i | − | 0.342620i | −0.985217 | − | 0.171310i | \(-0.945200\pi\) | ||
0.985217 | − | 0.171310i | \(-0.0548000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0486 | − | 13.3071i | −0.800509 | − | 0.462174i | 0.0431399 | − | 0.999069i | \(-0.486264\pi\) |
−0.843649 | + | 0.536895i | \(0.819597\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.84849 | + | 4.93373i | 0.0988130 | + | 0.171149i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.08612 | − | 3.10200i | −0.210871 | − | 0.107478i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.20112 | − | 3.58022i | 0.214599 | − | 0.123899i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.56629 | + | 6.17700i | −0.123269 | + | 0.213508i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.6975 | −0.714559 | −0.357279 | − | 0.933998i | \(-0.616296\pi\) | ||||
−0.357279 | + | 0.933998i | \(0.616296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1992 | −0.696525 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.180628 | − | 0.312857i | 0.00622117 | − | 0.0107754i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.4607 | − | 10.0809i | 0.600667 | − | 0.346795i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.2827 | + | 42.8955i | 0.903084 | + | 1.47391i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.52384 | + | 4.37143i | 0.0866181 | + | 0.150027i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.67102 | + | 2.69682i | 0.160121 | + | 0.0924457i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.45628i | − | 0.118341i | −0.998248 | − | 0.0591704i | \(-0.981154\pi\) | ||
0.998248 | − | 0.0591704i | \(-0.0188455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 57.7568i | 1.97524i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.2513 | − | 15.1562i | −0.896727 | − | 0.517726i | −0.0205904 | − | 0.999788i | \(-0.506555\pi\) |
−0.876137 | + | 0.482062i | \(0.839888\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.6058 | + | 27.0301i | 0.532463 | + | 0.922254i | 0.999282 | + | 0.0379004i | \(0.0120670\pi\) |
−0.466818 | + | 0.884353i | \(0.654600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.15050 | − | 0.624766i | −0.0392090 | − | 0.0212920i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.77035 | + | 3.90886i | −0.230465 | + | 0.133059i | −0.610787 | − | 0.791795i | \(-0.709147\pi\) |
0.380321 | + | 0.924854i | \(0.375813\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.4360 | − | 28.4680i | 0.558840 | − | 0.967940i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.93246 | 0.0995916 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.2507 | −0.720882 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.36148 | − | 9.28635i | 0.181667 | − | 0.314656i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.5959 | + | 15.9325i | −0.933981 | + | 0.539234i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.653054 | − | 24.9995i | −0.0220773 | − | 0.845138i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.49490 | + | 14.7136i | 0.286852 | + | 0.496843i | 0.973057 | − | 0.230566i | \(-0.0740578\pi\) |
−0.686204 | + | 0.727409i | \(0.740724\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.66622 | − | 0.961994i | −0.0562003 | − | 0.0324473i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.82308i | 0.196185i | 0.995177 | + | 0.0980923i | \(0.0312741\pi\) | ||||
−0.995177 | + | 0.0980923i | \(0.968726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.2143i | 0.915835i | 0.888995 | + | 0.457918i | \(0.151405\pi\) | ||||
−0.888995 | + | 0.457918i | \(0.848595\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.15203 | − | 1.81982i | −0.105954 | − | 0.0611727i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.4991 | − | 44.1658i | −0.856177 | − | 1.48294i | −0.875549 | − | 0.483129i | \(-0.839500\pi\) |
0.0193723 | − | 0.999812i | \(-0.493833\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.987295 | − | 37.7945i | −0.0331128 | − | 1.26759i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41.2804 | − | 23.8332i | 1.38294 | − | 0.798443i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.0476 | + | 19.1350i | −0.369695 | + | 0.640330i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.8818 | 0.464017 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.23263 | −0.0745453 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.70354 | − | 16.8070i | 0.323631 | − | 0.560546i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.79101 | − | 3.34344i | 0.192927 | − | 0.111386i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.434997 | − | 0.236220i | −0.0144758 | − | 0.00786090i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.8093 | + | 39.5069i | 0.758208 | + | 1.31325i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.0523 | − | 23.7016i | −1.36312 | − | 0.786998i | −0.373082 | − | 0.927798i | \(-0.621699\pi\) |
−0.990038 | + | 0.140801i | \(0.955032\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 25.3174i | − | 0.839725i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.4430i | 1.24054i | 0.784388 | + | 0.620271i | \(0.212977\pi\) | ||||
−0.784388 | + | 0.620271i | \(0.787023\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6435 | + | 6.14502i | 0.352248 | + | 0.203371i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.82664 | − | 4.89588i | −0.0934458 | − | 0.161853i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.9769 | + | 29.3398i | 0.593649 | + | 0.968885i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.3207 | + | 7.11334i | −0.406421 | + | 0.234647i | −0.689251 | − | 0.724523i | \(-0.742060\pi\) |
0.282830 | + | 0.959170i | \(0.408727\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.47178 | − | 4.28125i | 0.0814479 | − | 0.141072i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.0158 | −1.18548 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.15314 | −0.300953 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.17601 | + | 10.6972i | −0.202847 | + | 0.351341i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.03283 | + | 1.17366i | −0.0666951 | + | 0.0385065i | −0.532977 | − | 0.846130i | \(-0.678927\pi\) |
0.466282 | + | 0.884636i | \(0.345593\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.8594 | + | 32.1296i | 0.683641 | + | 1.05301i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.31937 | + | 4.01727i | 0.0759327 | + | 0.131519i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.4720 | + | 9.51013i | 0.538693 | + | 0.311014i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.80691i | 0.255041i | 0.991836 | + | 0.127520i | \(0.0407018\pi\) | ||||
−0.991836 | + | 0.127520i | \(0.959298\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.840907i | 0.0274420i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.5730 | + | 24.5795i | 1.38784 | + | 0.801270i | 0.993072 | − | 0.117510i | \(-0.0374912\pi\) |
0.394769 | + | 0.918780i | \(0.370825\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.10895 | − | 10.5810i | −0.198935 | − | 0.344565i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.75068 | + | 5.36166i | −0.284660 | + | 0.174415i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.10205 | − | 4.67772i | 0.263281 | − | 0.152006i | −0.362549 | − | 0.931965i | \(-0.618094\pi\) |
0.625830 | + | 0.779959i | \(0.284760\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9686 | + | 22.4622i | −0.420978 | + | 0.729155i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.37755 | 0.0446702 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.2700 | 0.624216 | 0.312108 | − | 0.950047i | \(-0.398965\pi\) | ||||
0.312108 | + | 0.950047i | \(0.398965\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.5130 | + | 28.6014i | −0.534349 | + | 0.925519i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.57202 | − | 1.48496i | 0.0831416 | − | 0.0480018i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.4765 | − | 34.0244i | 0.596637 | − | 1.09870i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.89785 | − | 10.2154i | −0.190253 | − | 0.329528i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.0114 | − | 12.1309i | −0.677083 | − | 0.390914i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.7213i | 0.409514i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.48146i | 0.111956i | 0.998432 | + | 0.0559782i | \(0.0178277\pi\) | ||||
−0.998432 | + | 0.0559782i | \(0.982172\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.845123 | + | 0.487932i | 0.0271493 | + | 0.0156746i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.35357 | + | 14.4688i | 0.268079 | + | 0.464326i | 0.968366 | − | 0.249536i | \(-0.0802779\pi\) |
−0.700287 | + | 0.713861i | \(0.746945\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.0477 | + | 0.784926i | −0.963285 | + | 0.0251636i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.28122 | − | 1.89441i | 0.105083 | − | 0.0606698i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.1787 | + | 17.6301i | −0.325646 | + | 0.564036i | −0.981643 | − | 0.190728i | \(-0.938915\pi\) |
0.655997 | + | 0.754764i | \(0.272248\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 78.1412 | 2.49740 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.3010 | −0.520451 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.22215 | − | 14.2412i | 0.262246 | − | 0.454223i | −0.704593 | − | 0.709612i | \(-0.748870\pi\) |
0.966838 | + | 0.255389i | \(0.0822036\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.7613 | + | 11.4092i | −0.629646 | + | 0.363526i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.95137 | + | 0.0509749i | −0.0621127 | + | 0.00162255i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.30975 | − | 4.00061i | −0.0734459 | − | 0.127212i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.5177 | − | 18.1967i | −1.00119 | − | 0.578038i | −0.0925907 | − | 0.995704i | \(-0.529515\pi\) |
−0.908601 | + | 0.417666i | \(0.862848\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.506927i | 0.0160868i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 51.8223i | 1.64288i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.4872 | − | 18.1791i | −0.997209 | − | 0.575739i | −0.0897879 | − | 0.995961i | \(-0.528619\pi\) |
−0.907421 | + | 0.420222i | \(0.861952\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.651684 | + | 1.12875i | 0.0206184 | + | 0.0357120i |
(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 | 448.2.p.e.255.4 | 16 | ||
4.3 | odd | 2 | inner | 448.2.p.e.255.5 | 16 | ||
7.3 | odd | 6 | 3136.2.f.j.3135.7 | 16 | |||
7.4 | even | 3 | 3136.2.f.j.3135.10 | 16 | |||
7.5 | odd | 6 | inner | 448.2.p.e.383.5 | 16 | ||
8.3 | odd | 2 | 224.2.p.a.31.4 | ✓ | 16 | ||
8.5 | even | 2 | 224.2.p.a.31.5 | yes | 16 | ||
24.5 | odd | 2 | 2016.2.cs.b.703.8 | 16 | |||
24.11 | even | 2 | 2016.2.cs.b.703.7 | 16 | |||
28.3 | even | 6 | 3136.2.f.j.3135.9 | 16 | |||
28.11 | odd | 6 | 3136.2.f.j.3135.8 | 16 | |||
28.19 | even | 6 | inner | 448.2.p.e.383.4 | 16 | ||
56.3 | even | 6 | 1568.2.f.b.1567.8 | 16 | |||
56.5 | odd | 6 | 224.2.p.a.159.4 | yes | 16 | ||
56.11 | odd | 6 | 1568.2.f.b.1567.9 | 16 | |||
56.13 | odd | 2 | 1568.2.p.b.31.4 | 16 | |||
56.19 | even | 6 | 224.2.p.a.159.5 | yes | 16 | ||
56.27 | even | 2 | 1568.2.p.b.31.5 | 16 | |||
56.37 | even | 6 | 1568.2.p.b.607.5 | 16 | |||
56.45 | odd | 6 | 1568.2.f.b.1567.10 | 16 | |||
56.51 | odd | 6 | 1568.2.p.b.607.4 | 16 | |||
56.53 | even | 6 | 1568.2.f.b.1567.7 | 16 | |||
168.5 | even | 6 | 2016.2.cs.b.1279.7 | 16 | |||
168.131 | odd | 6 | 2016.2.cs.b.1279.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.p.a.31.4 | ✓ | 16 | 8.3 | odd | 2 | ||
224.2.p.a.31.5 | yes | 16 | 8.5 | even | 2 | ||
224.2.p.a.159.4 | yes | 16 | 56.5 | odd | 6 | ||
224.2.p.a.159.5 | yes | 16 | 56.19 | even | 6 | ||
448.2.p.e.255.4 | 16 | 1.1 | even | 1 | trivial | ||
448.2.p.e.255.5 | 16 | 4.3 | odd | 2 | inner | ||
448.2.p.e.383.4 | 16 | 28.19 | even | 6 | inner | ||
448.2.p.e.383.5 | 16 | 7.5 | odd | 6 | inner | ||
1568.2.f.b.1567.7 | 16 | 56.53 | even | 6 | |||
1568.2.f.b.1567.8 | 16 | 56.3 | even | 6 | |||
1568.2.f.b.1567.9 | 16 | 56.11 | odd | 6 | |||
1568.2.f.b.1567.10 | 16 | 56.45 | odd | 6 | |||
1568.2.p.b.31.4 | 16 | 56.13 | odd | 2 | |||
1568.2.p.b.31.5 | 16 | 56.27 | even | 2 | |||
1568.2.p.b.607.4 | 16 | 56.51 | odd | 6 | |||
1568.2.p.b.607.5 | 16 | 56.37 | even | 6 | |||
2016.2.cs.b.703.7 | 16 | 24.11 | even | 2 | |||
2016.2.cs.b.703.8 | 16 | 24.5 | odd | 2 | |||
2016.2.cs.b.1279.7 | 16 | 168.5 | even | 6 | |||
2016.2.cs.b.1279.8 | 16 | 168.131 | odd | 6 | |||
3136.2.f.j.3135.7 | 16 | 7.3 | odd | 6 | |||
3136.2.f.j.3135.8 | 16 | 28.11 | odd | 6 | |||
3136.2.f.j.3135.9 | 16 | 28.3 | even | 6 | |||
3136.2.f.j.3135.10 | 16 | 7.4 | even | 3 |