Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(656,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.656");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.s (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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 656.20 | ||
Character | \(\chi\) | \(=\) | 1323.656 |
Dual form | 1323.2.s.d.962.20 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61855 | − | 0.934468i | 1.14449 | − | 0.660769i | 0.196948 | − | 0.980414i | \(-0.436897\pi\) |
0.947537 | + | 0.319645i | \(0.103564\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.746462 | − | 1.29291i | 0.373231 | − | 0.646455i | ||||
\(5\) | 2.50573 | 1.12060 | 0.560299 | − | 0.828290i | \(-0.310686\pi\) | ||||
0.560299 | + | 0.828290i | \(0.310686\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.947692i | 0.335060i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.05565 | − | 2.34153i | 1.28251 | − | 0.740457i | ||||
\(11\) | − | 5.60957i | − | 1.69135i | −0.533698 | − | 0.845675i | \(-0.679198\pi\) | ||
0.533698 | − | 0.845675i | \(-0.320802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.384312 | − | 0.221883i | 0.106589 | − | 0.0615392i | −0.445758 | − | 0.895154i | \(-0.647066\pi\) |
0.552347 | + | 0.833614i | \(0.313732\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.37851 | + | 4.11970i | 0.594628 | + | 1.02993i | ||||
\(17\) | 1.53885 | + | 2.66536i | 0.373226 | + | 0.646446i | 0.990060 | − | 0.140647i | \(-0.0449184\pi\) |
−0.616834 | + | 0.787093i | \(0.711585\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.22932 | + | 1.28710i | 0.511440 | + | 0.295280i | 0.733425 | − | 0.679770i | \(-0.237920\pi\) |
−0.221985 | + | 0.975050i | \(0.571254\pi\) | |||||||
\(20\) | 1.87044 | − | 3.23969i | 0.418242 | − | 0.724417i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.24197 | − | 9.07935i | −1.11759 | − | 1.93572i | ||||
\(23\) | − | 7.89210i | − | 1.64562i | −0.568319 | − | 0.822808i | \(-0.692406\pi\) | ||
0.568319 | − | 0.822808i | \(-0.307594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.27870 | 0.255741 | ||||||||
\(26\) | 0.414685 | − | 0.718255i | 0.0813264 | − | 0.140861i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.71041 | − | 1.56485i | −0.503310 | − | 0.290586i | 0.226770 | − | 0.973948i | \(-0.427184\pi\) |
−0.730079 | + | 0.683362i | \(0.760517\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.06457 | + | 5.23343i | 1.62805 | + | 0.939952i | 0.984675 | + | 0.174397i | \(0.0557975\pi\) |
0.643370 | + | 0.765556i | \(0.277536\pi\) | |||||||
\(32\) | 6.05802 | + | 3.49760i | 1.07092 | + | 0.618294i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.98140 | + | 2.87601i | 0.854303 | + | 0.493232i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.708168 | − | 1.22658i | 0.116422 | − | 0.201649i | −0.801925 | − | 0.597424i | \(-0.796191\pi\) |
0.918347 | + | 0.395775i | \(0.129524\pi\) | |||||||
\(38\) | 4.81100 | 0.780448 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.37466i | 0.375467i | ||||||||
\(41\) | −1.64665 | − | 2.85208i | −0.257163 | − | 0.445420i | 0.708318 | − | 0.705894i | \(-0.249455\pi\) |
−0.965481 | + | 0.260474i | \(0.916121\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.75676 | + | 8.23894i | −0.725398 | + | 1.25643i | 0.233411 | + | 0.972378i | \(0.425011\pi\) |
−0.958810 | + | 0.284049i | \(0.908322\pi\) | |||||||
\(44\) | −7.25268 | − | 4.18733i | −1.09338 | − | 0.631264i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.37492 | − | 12.7737i | −1.08737 | − | 1.88338i | ||||
\(47\) | 1.07190 | + | 1.85659i | 0.156353 | + | 0.270811i | 0.933551 | − | 0.358445i | \(-0.116693\pi\) |
−0.777198 | + | 0.629256i | \(0.783360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.06964 | − | 1.19491i | 0.292691 | − | 0.168985i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 0.662509i | − | 0.0918734i | ||||||
\(53\) | 4.20379 | − | 2.42706i | 0.577435 | − | 0.333382i | −0.182678 | − | 0.983173i | \(-0.558477\pi\) |
0.760113 | + | 0.649791i | \(0.225143\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 14.0561i | − | 1.89532i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.84923 | −0.768041 | ||||||||
\(59\) | 3.65496 | − | 6.33057i | 0.475835 | − | 0.824170i | −0.523782 | − | 0.851852i | \(-0.675479\pi\) |
0.999617 | + | 0.0276824i | \(0.00881270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.40950 | + | 4.27788i | −0.948690 | + | 0.547726i | −0.892674 | − | 0.450704i | \(-0.851173\pi\) |
−0.0560160 | + | 0.998430i | \(0.517840\pi\) | |||||||
\(62\) | 19.5619 | 2.48437 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.55953 | 0.444941 | ||||||||
\(65\) | 0.962984 | − | 0.555979i | 0.119443 | − | 0.0689607i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.934442 | − | 1.61850i | 0.114160 | − | 0.197731i | −0.803284 | − | 0.595597i | \(-0.796916\pi\) |
0.917444 | + | 0.397865i | \(0.130249\pi\) | |||||||
\(68\) | 4.59477 | 0.557198 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.95338i | 0.350501i | 0.984524 | + | 0.175251i | \(0.0560736\pi\) | ||||
−0.984524 | + | 0.175251i | \(0.943926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.37804 | + | 4.25971i | −0.863534 | + | 0.498562i | −0.865194 | − | 0.501437i | \(-0.832805\pi\) |
0.00165984 | + | 0.999999i | \(0.499472\pi\) | |||||||
\(74\) | − | 2.64704i | − | 0.307712i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.32820 | − | 1.92154i | 0.381771 | − | 0.220415i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.287130 | + | 0.497324i | 0.0323047 | + | 0.0559533i | 0.881726 | − | 0.471762i | \(-0.156382\pi\) |
−0.849421 | + | 0.527716i | \(0.823049\pi\) | |||||||
\(80\) | 5.95992 | + | 10.3229i | 0.666339 | + | 1.15413i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.33036 | − | 3.07748i | −0.588639 | − | 0.339851i | ||||
\(83\) | −4.23521 | + | 7.33560i | −0.464875 | + | 0.805186i | −0.999196 | − | 0.0400951i | \(-0.987234\pi\) |
0.534321 | + | 0.845281i | \(0.320567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.85595 | + | 6.67870i | 0.418236 | + | 0.724406i | ||||
\(86\) | 17.7802i | 1.91728i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.31615 | 0.566703 | ||||||||
\(89\) | −3.78929 | + | 6.56325i | −0.401664 | + | 0.695703i | −0.993927 | − | 0.110042i | \(-0.964901\pi\) |
0.592263 | + | 0.805745i | \(0.298235\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.2038 | − | 5.89115i | −1.06382 | − | 0.614195i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.46984 | + | 2.00332i | 0.357887 | + | 0.206626i | ||||
\(95\) | 5.58607 | + | 3.22512i | 0.573119 | + | 0.330890i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.22662 | − | 1.86289i | −0.327614 | − | 0.189148i | 0.327167 | − | 0.944966i | \(-0.393906\pi\) |
−0.654781 | + | 0.755818i | \(0.727239\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.954503 | − | 1.65325i | 0.0954503 | − | 0.165325i | ||||
\(101\) | −7.53449 | −0.749710 | −0.374855 | − | 0.927083i | \(-0.622308\pi\) | ||||
−0.374855 | + | 0.927083i | \(0.622308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.3235i | − | 1.41133i | −0.708545 | − | 0.705666i | \(-0.750648\pi\) | ||
0.708545 | − | 0.705666i | \(-0.249352\pi\) | |||||||
\(104\) | 0.210276 | + | 0.364210i | 0.0206193 | + | 0.0357137i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.53602 | − | 7.85662i | 0.440577 | − | 0.763102i | ||||
\(107\) | −11.6798 | − | 6.74331i | −1.12912 | − | 0.651900i | −0.185410 | − | 0.982661i | \(-0.559361\pi\) |
−0.943715 | + | 0.330761i | \(0.892695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.459348 | + | 0.795613i | 0.0439975 | + | 0.0762059i | 0.887186 | − | 0.461413i | \(-0.152657\pi\) |
−0.843188 | + | 0.537619i | \(0.819324\pi\) | |||||||
\(110\) | −13.1350 | − | 22.7504i | −1.25237 | − | 2.16917i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.10412 | + | 2.36952i | −0.386083 | + | 0.222905i | −0.680462 | − | 0.732784i | \(-0.738221\pi\) |
0.294378 | + | 0.955689i | \(0.404887\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 19.7755i | − | 1.84407i | ||||||
\(116\) | −4.04643 | + | 2.33621i | −0.375702 | + | 0.216912i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 13.6618i | − | 1.25767i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20.4673 | −1.86066 | ||||||||
\(122\) | −7.99508 | + | 13.8479i | −0.723841 | + | 1.25373i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.5327 | − | 7.81312i | 1.21527 | − | 0.701639i | ||||
\(125\) | −9.32458 | −0.834016 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.37245 | 0.654200 | 0.327100 | − | 0.944990i | \(-0.393929\pi\) | ||||
0.327100 | + | 0.944990i | \(0.393929\pi\) | |||||||
\(128\) | −6.35477 | + | 3.66893i | −0.561688 | + | 0.324291i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.03909 | − | 1.79976i | 0.0911342 | − | 0.157849i | ||||
\(131\) | 7.86300 | 0.686993 | 0.343497 | − | 0.939154i | \(-0.388389\pi\) | ||||
0.343497 | + | 0.939154i | \(0.388389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 3.49283i | − | 0.301734i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.52594 | + | 1.45835i | −0.216598 | + | 0.125053i | ||||
\(137\) | − | 11.5698i | − | 0.988477i | −0.869326 | − | 0.494238i | \(-0.835447\pi\) | ||
0.869326 | − | 0.494238i | \(-0.164553\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9741 | + | 9.79999i | −1.43972 | + | 0.831224i | −0.997830 | − | 0.0658437i | \(-0.979026\pi\) |
−0.441893 | + | 0.897068i | \(0.645693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.75984 | + | 4.78018i | 0.231600 | + | 0.401144i | ||||
\(143\) | −1.24467 | − | 2.15583i | −0.104084 | − | 0.180279i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.79156 | − | 3.92111i | −0.564008 | − | 0.325630i | ||||
\(146\) | −7.96114 | + | 13.7891i | −0.658868 | + | 1.14119i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.05724 | − | 1.83120i | −0.0869047 | − | 0.150523i | ||||
\(149\) | 15.7402i | 1.28949i | 0.764397 | + | 0.644746i | \(0.223037\pi\) | ||||
−0.764397 | + | 0.644746i | \(0.776963\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.98271 | −0.161350 | −0.0806752 | − | 0.996740i | \(-0.525708\pi\) | ||||
−0.0806752 | + | 0.996740i | \(0.525708\pi\) | |||||||
\(152\) | −1.21977 | + | 2.11270i | −0.0989364 | + | 0.171363i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.7134 | + | 13.1136i | 1.82438 | + | 1.05331i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.26790 | − | 4.19612i | −0.580041 | − | 0.334887i | 0.181108 | − | 0.983463i | \(-0.442031\pi\) |
−0.761150 | + | 0.648576i | \(0.775365\pi\) | |||||||
\(158\) | 0.929468 | + | 0.536628i | 0.0739445 | + | 0.0426919i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.1798 | + | 8.76405i | 1.20007 | + | 0.692859i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.537054 | − | 0.930204i | 0.0420653 | − | 0.0728592i | −0.844226 | − | 0.535987i | \(-0.819940\pi\) |
0.886291 | + | 0.463128i | \(0.153273\pi\) | |||||||
\(164\) | −4.91665 | −0.383926 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.8307i | 1.22870i | ||||||||
\(167\) | 3.99731 | + | 6.92354i | 0.309321 | + | 0.535760i | 0.978214 | − | 0.207599i | \(-0.0665649\pi\) |
−0.668893 | + | 0.743359i | \(0.733232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.40154 | + | 11.0878i | −0.492426 | + | 0.852907i | ||||
\(170\) | 12.4821 | + | 7.20652i | 0.957330 | + | 0.552715i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.10148 | + | 12.3001i | 0.541483 | + | 0.937875i | ||||
\(173\) | 0.501744 | + | 0.869046i | 0.0381469 | + | 0.0660723i | 0.884468 | − | 0.466600i | \(-0.154521\pi\) |
−0.846322 | + | 0.532672i | \(0.821188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.1098 | − | 13.3424i | 1.74197 | − | 1.00572i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.1639i | 1.06163i | ||||||||
\(179\) | −1.27773 | + | 0.737695i | −0.0955017 | + | 0.0551379i | −0.546990 | − | 0.837139i | \(-0.684227\pi\) |
0.451489 | + | 0.892277i | \(0.350893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.0440i | 1.11821i | 0.829096 | + | 0.559106i | \(0.188855\pi\) | ||||
−0.829096 | + | 0.559106i | \(0.811145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.47928 | 0.551380 | ||||||||
\(185\) | 1.77448 | − | 3.07349i | 0.130462 | − | 0.225967i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.9516 | − | 8.63229i | 1.09337 | − | 0.631255i | ||||
\(188\) | 3.20054 | 0.233423 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0551 | 0.874568 | ||||||||
\(191\) | 11.4521 | − | 6.61187i | 0.828644 | − | 0.478418i | −0.0247439 | − | 0.999694i | \(-0.507877\pi\) |
0.853388 | + | 0.521276i | \(0.174544\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.777855 | − | 1.34728i | 0.0559912 | − | 0.0969796i | −0.836671 | − | 0.547705i | \(-0.815501\pi\) |
0.892662 | + | 0.450726i | \(0.148835\pi\) | |||||||
\(194\) | −6.96325 | −0.499932 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.96185i | 0.353517i | 0.984254 | + | 0.176759i | \(0.0565612\pi\) | ||||
−0.984254 | + | 0.176759i | \(0.943439\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.69273 | + | 5.59610i | −0.687100 | + | 0.396697i | −0.802525 | − | 0.596619i | \(-0.796510\pi\) |
0.115425 | + | 0.993316i | \(0.463177\pi\) | |||||||
\(200\) | 1.21182i | 0.0856883i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.1949 | + | 7.04074i | −0.858032 | + | 0.495385i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.12606 | − | 7.14655i | −0.288177 | − | 0.499137i | ||||
\(206\) | −13.3848 | − | 23.1832i | −0.932565 | − | 1.61525i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.82818 | + | 1.05550i | 0.126762 | + | 0.0731859i | ||||
\(209\) | 7.22006 | − | 12.5055i | 0.499422 | − | 0.865024i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.68026 | + | 13.3026i | 0.528731 | + | 0.915789i | 0.999439 | + | 0.0334999i | \(0.0106654\pi\) |
−0.470708 | + | 0.882289i | \(0.656001\pi\) | |||||||
\(212\) | − | 7.24683i | − | 0.497714i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −25.2056 | −1.72302 | ||||||||
\(215\) | −11.9192 | + | 20.6446i | −0.812880 | + | 1.40795i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.48695 | + | 0.858492i | 0.100709 | + | 0.0581444i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18.1733 | − | 10.4923i | −1.22524 | − | 0.707394i | ||||
\(221\) | 1.18280 | + | 0.682888i | 0.0795635 | + | 0.0459360i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.76845 | + | 1.59837i | 0.185389 | + | 0.107034i | 0.589822 | − | 0.807533i | \(-0.299198\pi\) |
−0.404433 | + | 0.914568i | \(0.632531\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.42848 | + | 7.67035i | −0.294578 | + | 0.510224i | ||||
\(227\) | 14.6699 | 0.973675 | 0.486837 | − | 0.873493i | \(-0.338150\pi\) | ||||
0.486837 | + | 0.873493i | \(0.338150\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.37807i | − | 0.223229i | −0.993752 | − | 0.111615i | \(-0.964398\pi\) | ||
0.993752 | − | 0.111615i | \(-0.0356022\pi\) | |||||||
\(230\) | −18.4796 | − | 32.0076i | −1.21851 | − | 2.11052i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.48300 | − | 2.56863i | 0.0973637 | − | 0.168639i | ||||
\(233\) | −4.22628 | − | 2.44005i | −0.276873 | − | 0.159853i | 0.355134 | − | 0.934815i | \(-0.384435\pi\) |
−0.632007 | + | 0.774963i | \(0.717769\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.68590 | + | 4.65211i | 0.175209 | + | 0.303470i | ||||
\(236\) | −5.45657 | − | 9.45106i | −0.355193 | − | 0.615212i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.6253 | + | 7.86657i | −0.881347 | + | 0.508846i | −0.871102 | − | 0.491101i | \(-0.836594\pi\) |
−0.0102448 | + | 0.999948i | \(0.503261\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.769383i | − | 0.0495603i | −0.999693 | − | 0.0247801i | \(-0.992111\pi\) | ||
0.999693 | − | 0.0247801i | \(-0.00788857\pi\) | |||||||
\(242\) | −33.1273 | + | 19.1260i | −2.12950 | + | 1.22947i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.7731i | 0.817714i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.14234 | 0.0726852 | ||||||||
\(248\) | −4.95968 | + | 8.59042i | −0.314940 | + | 0.545492i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.0923 | + | 8.71353i | −0.954519 | + | 0.551092i | ||||
\(251\) | 1.14544 | 0.0722996 | 0.0361498 | − | 0.999346i | \(-0.488491\pi\) | ||||
0.0361498 | + | 0.999346i | \(0.488491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −44.2713 | −2.78331 | ||||||||
\(254\) | 11.9327 | − | 6.88933i | 0.748722 | − | 0.432275i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.4165 | + | 18.0420i | −0.651033 | + | 1.12762i | ||||
\(257\) | 28.9835 | 1.80794 | 0.903969 | − | 0.427598i | \(-0.140640\pi\) | ||||
0.903969 | + | 0.427598i | \(0.140640\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1.66007i | − | 0.102953i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.7266 | − | 7.34772i | 0.786254 | − | 0.453944i | ||||
\(263\) | 13.6998i | 0.844763i | 0.906418 | + | 0.422381i | \(0.138806\pi\) | ||||
−0.906418 | + | 0.422381i | \(0.861194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.5336 | − | 6.08156i | 0.647072 | − | 0.373587i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.39505 | − | 2.41630i | −0.0852163 | − | 0.147599i | ||||
\(269\) | −5.23973 | − | 9.07548i | −0.319472 | − | 0.553342i | 0.660906 | − | 0.750469i | \(-0.270172\pi\) |
−0.980378 | + | 0.197127i | \(0.936839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.66907 | + | 3.27304i | 0.344371 | + | 0.198823i | 0.662203 | − | 0.749324i | \(-0.269621\pi\) |
−0.317832 | + | 0.948147i | \(0.602955\pi\) | |||||||
\(272\) | −7.32034 | + | 12.6792i | −0.443861 | + | 0.768790i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.8116 | − | 18.7263i | −0.653155 | − | 1.13130i | ||||
\(275\) | − | 7.17298i | − | 0.432547i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.4313 | 1.34777 | 0.673883 | − | 0.738838i | \(-0.264625\pi\) | ||||
0.673883 | + | 0.738838i | \(0.264625\pi\) | |||||||
\(278\) | −18.3156 | + | 31.7235i | −1.09849 | + | 1.90265i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.3552 | − | 11.1747i | −1.15463 | − | 0.666627i | −0.204621 | − | 0.978841i | \(-0.565596\pi\) |
−0.950012 | + | 0.312214i | \(0.898929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.4296 | + | 9.48563i | 0.976638 | + | 0.563862i | 0.901254 | − | 0.433292i | \(-0.142648\pi\) |
0.0753848 | + | 0.997155i | \(0.475981\pi\) | |||||||
\(284\) | 3.81845 | + | 2.20459i | 0.226584 | + | 0.130818i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.02910 | − | 2.32620i | −0.238246 | − | 0.137551i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.76389 | − | 6.51924i | 0.221405 | − | 0.383485i | ||||
\(290\) | −14.6566 | −0.860665 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.7189i | 0.744315i | ||||||||
\(293\) | −4.41136 | − | 7.64069i | −0.257714 | − | 0.446374i | 0.707915 | − | 0.706298i | \(-0.249636\pi\) |
−0.965629 | + | 0.259924i | \(0.916303\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.15835 | − | 15.8627i | 0.533220 | − | 0.923563i | ||||
\(296\) | 1.16242 | + | 0.671125i | 0.0675644 | + | 0.0390083i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.7088 | + | 25.4763i | 0.852056 | + | 1.47580i | ||||
\(299\) | −1.75112 | − | 3.03303i | −0.101270 | − | 0.175405i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.20910 | + | 1.85278i | −0.184663 | + | 0.106615i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.2455i | 0.702327i | ||||||||
\(305\) | −18.5662 | + | 10.7192i | −1.06310 | + | 0.613781i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.7533i | 1.64104i | 0.571620 | + | 0.820519i | \(0.306315\pi\) | ||||
−0.571620 | + | 0.820519i | \(0.693685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 49.0169 | 2.78398 | ||||||||
\(311\) | 6.64294 | − | 11.5059i | 0.376687 | − | 0.652441i | −0.613891 | − | 0.789391i | \(-0.710397\pi\) |
0.990578 | + | 0.136950i | \(0.0437300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.3227 | + | 15.7748i | −1.54437 | + | 0.891643i | −0.545815 | + | 0.837905i | \(0.683780\pi\) |
−0.998555 | + | 0.0537372i | \(0.982887\pi\) | |||||||
\(314\) | −15.6846 | −0.885132 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.857328 | 0.0482285 | ||||||||
\(317\) | 17.3819 | − | 10.0354i | 0.976264 | − | 0.563646i | 0.0751236 | − | 0.997174i | \(-0.476065\pi\) |
0.901140 | + | 0.433528i | \(0.142732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.77816 | + | 15.2042i | −0.491483 | + | 0.851273i | ||||
\(320\) | 8.91923 | 0.498600 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.92259i | 0.440824i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.491421 | − | 0.283722i | 0.0272591 | − | 0.0157381i | ||||
\(326\) | − | 2.00744i | − | 0.111182i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.70289 | − | 1.56052i | 0.149242 | − | 0.0861651i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.623957 | − | 1.08073i | −0.0342958 | − | 0.0594020i | 0.848368 | − | 0.529407i | \(-0.177585\pi\) |
−0.882664 | + | 0.470005i | \(0.844252\pi\) | |||||||
\(332\) | 6.32285 | + | 10.9515i | 0.347011 | + | 0.601041i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.9397 | + | 7.47072i | 0.708027 | + | 0.408780i | ||||
\(335\) | 2.34146 | − | 4.05553i | 0.127928 | − | 0.221577i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.58745 | + | 11.4098i | 0.358842 | + | 0.621532i | 0.987768 | − | 0.155933i | \(-0.0498385\pi\) |
−0.628926 | + | 0.777465i | \(0.716505\pi\) | |||||||
\(338\) | 23.9281i | 1.30152i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.5133 | 0.624395 | ||||||||
\(341\) | 29.3573 | − | 50.8484i | 1.58979 | − | 2.75359i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.80798 | − | 4.50794i | −0.420978 | − | 0.243052i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.62419 | + | 0.937727i | 0.0873171 | + | 0.0504125i | ||||
\(347\) | −23.4411 | − | 13.5337i | −1.25838 | − | 0.726529i | −0.285624 | − | 0.958342i | \(-0.592201\pi\) |
−0.972760 | + | 0.231813i | \(0.925534\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.3413 | − | 17.5176i | −1.62413 | − | 0.937694i | −0.985798 | − | 0.167936i | \(-0.946290\pi\) |
−0.638336 | − | 0.769758i | \(-0.720377\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.6200 | − | 33.9829i | 1.04575 | − | 1.81129i | ||||
\(353\) | −2.52512 | −0.134398 | −0.0671992 | − | 0.997740i | \(-0.521406\pi\) | ||||
−0.0671992 | + | 0.997740i | \(0.521406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.40038i | 0.392771i | ||||||||
\(356\) | 5.65713 | + | 9.79843i | 0.299827 | + | 0.519316i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.37871 | + | 2.38799i | −0.0728669 | + | 0.126209i | ||||
\(359\) | −6.29395 | − | 3.63381i | −0.332182 | − | 0.191785i | 0.324628 | − | 0.945842i | \(-0.394761\pi\) |
−0.656809 | + | 0.754057i | \(0.728094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.18677 | − | 10.7158i | −0.325619 | − | 0.563989i | ||||
\(362\) | 14.0581 | + | 24.3494i | 0.738880 | + | 1.27978i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.4874 | + | 10.6737i | −0.967675 | + | 0.558688i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.4770i | − | 0.703492i | −0.936095 | − | 0.351746i | \(-0.885588\pi\) | ||
0.936095 | − | 0.351746i | \(-0.114412\pi\) | |||||||
\(368\) | 32.5131 | − | 18.7715i | 1.69486 | − | 0.978530i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 6.63278i | − | 0.344822i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.7639 | 1.23045 | 0.615224 | − | 0.788352i | \(-0.289065\pi\) | ||||
0.615224 | + | 0.788352i | \(0.289065\pi\) | |||||||
\(374\) | 16.1332 | − | 27.9435i | 0.834228 | − | 1.44492i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.75947 | + | 1.01583i | −0.0907379 | + | 0.0523875i | ||||
\(377\) | −1.38886 | −0.0715297 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2283 | 1.09042 | 0.545211 | − | 0.838299i | \(-0.316449\pi\) | ||||
0.545211 | + | 0.838299i | \(0.316449\pi\) | |||||||
\(380\) | 8.33958 | − | 4.81486i | 0.427812 | − | 0.246997i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.3572 | − | 21.4032i | 0.632248 | − | 1.09509i | ||||
\(383\) | −12.9586 | −0.662154 | −0.331077 | − | 0.943604i | \(-0.607412\pi\) | ||||
−0.331077 | + | 0.943604i | \(0.607412\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2.90752i | − | 0.147989i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.81710 | + | 2.78116i | −0.244551 | + | 0.141192i | ||||
\(389\) | 10.9470i | 0.555035i | 0.960721 | + | 0.277517i | \(0.0895116\pi\) | ||||
−0.960721 | + | 0.277517i | \(0.910488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0353 | − | 12.1447i | 1.06380 | − | 0.614186i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.63669 | + | 8.03098i | 0.233593 | + | 0.404595i | ||||
\(395\) | 0.719472 | + | 1.24616i | 0.0362006 | + | 0.0627012i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.8856 | + | 14.9451i | 1.29916 | + | 0.750071i | 0.980259 | − | 0.197717i | \(-0.0633528\pi\) |
0.318901 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(398\) | −10.4588 | + | 18.1151i | −0.524250 | + | 0.908028i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.04141 | + | 5.26788i | 0.152071 | + | 0.263394i | ||||
\(401\) | − | 19.1949i | − | 0.958547i | −0.877666 | − | 0.479273i | \(-0.840900\pi\) | ||
0.877666 | − | 0.479273i | \(-0.159100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.64483 | 0.231376 | ||||||||
\(404\) | −5.62421 | + | 9.74142i | −0.279815 | + | 0.484654i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.88060 | − | 3.97252i | −0.341059 | − | 0.196910i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.9737 | − | 14.4186i | −1.23487 | − | 0.712953i | −0.266830 | − | 0.963744i | \(-0.585976\pi\) |
−0.968041 | + | 0.250790i | \(0.919309\pi\) | |||||||
\(410\) | −13.3565 | − | 7.71135i | −0.659628 | − | 0.380837i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.5190 | − | 10.6919i | −0.912363 | − | 0.526753i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.6123 | + | 18.3811i | −0.520938 | + | 0.902290i | ||||
\(416\) | 3.10423 | 0.152197 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 26.9877i | − | 1.32001i | ||||||
\(419\) | 5.06390 | + | 8.77094i | 0.247388 | + | 0.428488i | 0.962800 | − | 0.270214i | \(-0.0870945\pi\) |
−0.715412 | + | 0.698702i | \(0.753761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.7094 | − | 22.0134i | 0.619419 | − | 1.07287i | −0.370173 | − | 0.928963i | \(-0.620702\pi\) |
0.989592 | − | 0.143902i | \(-0.0459651\pi\) | |||||||
\(422\) | 24.8617 | + | 14.3539i | 1.21025 | + | 0.698738i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.30010 | + | 3.98390i | 0.111703 | + | 0.193475i | ||||
\(425\) | 1.96773 | + | 3.40821i | 0.0954490 | + | 0.165322i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −17.4370 | + | 10.0673i | −0.842849 | + | 0.486619i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 44.5523i | 2.14850i | ||||||||
\(431\) | −9.39066 | + | 5.42170i | −0.452332 | + | 0.261154i | −0.708815 | − | 0.705395i | \(-0.750770\pi\) |
0.256482 | + | 0.966549i | \(0.417436\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.0519i | − | 0.627233i | −0.949550 | − | 0.313616i | \(-0.898459\pi\) | ||
0.949550 | − | 0.313616i | \(-0.101541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.37154 | 0.0656850 | ||||||||
\(437\) | 10.1579 | − | 17.5940i | 0.485918 | − | 0.841634i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.6736 | − | 15.9773i | 1.32079 | − | 0.762557i | 0.336933 | − | 0.941529i | \(-0.390611\pi\) |
0.983854 | + | 0.178972i | \(0.0572772\pi\) | |||||||
\(440\) | 13.3208 | 0.635046 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.55255 | 0.121412 | ||||||||
\(443\) | 21.4748 | − | 12.3985i | 1.02030 | − | 0.589068i | 0.106107 | − | 0.994355i | \(-0.466162\pi\) |
0.914190 | + | 0.405286i | \(0.132828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.49496 | + | 16.4458i | −0.450104 | + | 0.779603i | ||||
\(446\) | 5.97449 | 0.282900 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13.7710i | − | 0.649892i | −0.945733 | − | 0.324946i | \(-0.894654\pi\) | ||
0.945733 | − | 0.324946i | \(-0.105346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.9989 | + | 9.23700i | −0.753361 | + | 0.434953i | ||||
\(452\) | 7.07502i | 0.332781i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23.7439 | − | 13.7085i | 1.11436 | − | 0.643374i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.6554 | − | 23.6518i | −0.638771 | − | 1.10638i | −0.985703 | − | 0.168494i | \(-0.946110\pi\) |
0.346931 | − | 0.937890i | \(-0.387224\pi\) | |||||||
\(458\) | −3.15670 | − | 5.46757i | −0.147503 | − | 0.255483i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −25.5680 | − | 14.7617i | −1.19211 | − | 0.688266i | ||||
\(461\) | −5.51822 | + | 9.55784i | −0.257009 | + | 0.445153i | −0.965439 | − | 0.260628i | \(-0.916070\pi\) |
0.708430 | + | 0.705781i | \(0.249404\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.2346 | − | 21.1910i | −0.568591 | − | 0.984829i | −0.996706 | − | 0.0811042i | \(-0.974155\pi\) |
0.428115 | − | 0.903724i | \(-0.359178\pi\) | |||||||
\(464\) | − | 14.8881i | − | 0.691163i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.12059 | −0.422503 | ||||||||
\(467\) | −7.95241 | + | 13.7740i | −0.367994 | + | 0.637384i | −0.989252 | − | 0.146222i | \(-0.953289\pi\) |
0.621258 | + | 0.783606i | \(0.286622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.69451 | + | 5.01978i | 0.401048 | + | 0.231545i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.99943 | + | 3.46377i | 0.276146 | + | 0.159433i | ||||
\(473\) | 46.2169 | + | 26.6834i | 2.12506 | + | 1.22690i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.85063 | + | 1.64581i | 0.130796 | + | 0.0755151i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.7021 | + | 25.4648i | −0.672459 | + | 1.16473i | ||||
\(479\) | 13.8537 | 0.632991 | 0.316496 | − | 0.948594i | \(-0.397494\pi\) | ||||
0.316496 | + | 0.948594i | \(0.397494\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 0.628521i | − | 0.0286581i | ||||||
\(482\) | −0.718964 | − | 1.24528i | −0.0327479 | − | 0.0567210i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.2781 | + | 26.4624i | −0.694458 | + | 1.20284i | ||||
\(485\) | −8.08506 | − | 4.66791i | −0.367123 | − | 0.211959i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.3993 | − | 24.9404i | −0.652496 | − | 1.13016i | −0.982515 | − | 0.186182i | \(-0.940389\pi\) |
0.330020 | − | 0.943974i | \(-0.392945\pi\) | |||||||
\(488\) | −4.05411 | − | 7.02193i | −0.183521 | − | 0.317868i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.5627 | − | 19.3774i | 1.51466 | − | 0.874492i | 0.514812 | − | 0.857303i | \(-0.327862\pi\) |
0.999852 | − | 0.0171884i | \(-0.00547151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.63230i | − | 0.433817i | ||||||
\(494\) | 1.84893 | − | 1.06748i | 0.0831872 | − | 0.0480281i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 49.7911i | 2.23569i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.46667 | −0.155189 | −0.0775946 | − | 0.996985i | \(-0.524724\pi\) | ||||
−0.0775946 | + | 0.996985i | \(0.524724\pi\) | |||||||
\(500\) | −6.96045 | + | 12.0558i | −0.311281 | + | 0.539154i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.85395 | − | 1.07038i | 0.0827458 | − | 0.0477733i | ||||
\(503\) | −28.2202 | −1.25828 | −0.629138 | − | 0.777293i | \(-0.716592\pi\) | ||||
−0.629138 | + | 0.777293i | \(0.716592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.8794 | −0.840124 | ||||||||
\(506\) | −71.6552 | + | 41.3701i | −3.18546 | + | 1.83913i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.50326 | − | 9.53193i | 0.244168 | − | 0.422911i | ||||
\(509\) | −35.8124 | −1.58736 | −0.793678 | − | 0.608338i | \(-0.791836\pi\) | ||||
−0.793678 | + | 0.608338i | \(0.791836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.2599i | 1.07215i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 46.9111 | − | 27.0841i | 2.06916 | − | 1.19463i | ||||
\(515\) | − | 35.8908i | − | 1.58154i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4147 | − | 6.01291i | 0.458036 | − | 0.264447i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.526897 | + | 0.912612i | 0.0231060 | + | 0.0400207i | ||||
\(521\) | 13.4608 | + | 23.3148i | 0.589729 | + | 1.02144i | 0.994268 | + | 0.106920i | \(0.0340989\pi\) |
−0.404538 | + | 0.914521i | \(0.632568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.82181 | + | 4.51593i | 0.342024 | + | 0.197468i | 0.661167 | − | 0.750239i | \(-0.270062\pi\) |
−0.319143 | + | 0.947707i | \(0.603395\pi\) | |||||||
\(524\) | 5.86943 | − | 10.1662i | 0.256407 | − | 0.444110i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.8020 | + | 22.1737i | 0.558193 | + | 0.966819i | ||||
\(527\) | 32.2139i | 1.40326i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −39.2852 | −1.70805 | ||||||||
\(530\) | 11.3661 | − | 19.6866i | 0.493710 | − | 0.855131i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.26565 | − | 0.730726i | −0.0548216 | − | 0.0316513i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.2664 | − | 16.8969i | −1.26530 | − | 0.730518i | ||||
\(536\) | 1.53384 | + | 0.885563i | 0.0662518 | + | 0.0382505i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.9615 | − | 9.79273i | −0.731262 | − | 0.422195i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.66792 | + | 9.81713i | −0.243683 | + | 0.422071i | −0.961760 | − | 0.273892i | \(-0.911689\pi\) |
0.718078 | + | 0.695963i | \(0.245022\pi\) | |||||||
\(542\) | 12.2342 | 0.525504 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.5291i | 0.923053i | ||||||||
\(545\) | 1.15100 | + | 1.99360i | 0.0493035 | + | 0.0853962i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4246 | − | 33.6444i | 0.830537 | − | 1.43853i | −0.0670762 | − | 0.997748i | \(-0.521367\pi\) |
0.897613 | − | 0.440784i | \(-0.145300\pi\) | |||||||
\(548\) | −14.9587 | − | 8.63644i | −0.639006 | − | 0.368930i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.70292 | − | 11.6098i | −0.285813 | − | 0.495043i | ||||
\(551\) | −4.02823 | − | 6.97711i | −0.171609 | − | 0.297235i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 36.3061 | − | 20.9613i | 1.54250 | − | 0.890562i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 29.2613i | 1.24096i | ||||||||
\(557\) | −6.29167 | + | 3.63249i | −0.266586 | + | 0.153914i | −0.627335 | − | 0.778749i | \(-0.715854\pi\) |
0.360749 | + | 0.932663i | \(0.382521\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.22177i | 0.178562i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −41.7697 | −1.76195 | ||||||||
\(563\) | −11.5409 | + | 19.9894i | −0.486390 | + | 0.842453i | −0.999878 | − | 0.0156446i | \(-0.995020\pi\) |
0.513487 | + | 0.858097i | \(0.328353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.2838 | + | 5.93738i | −0.432644 | + | 0.249787i | ||||
\(566\) | 35.4561 | 1.49033 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.79889 | −0.117439 | ||||||||
\(569\) | −15.5482 | + | 8.97677i | −0.651815 | + | 0.376326i | −0.789151 | − | 0.614199i | \(-0.789479\pi\) |
0.137336 | + | 0.990525i | \(0.456146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.04234 | − | 12.1977i | 0.294713 | − | 0.510457i | −0.680205 | − | 0.733022i | \(-0.738109\pi\) |
0.974918 | + | 0.222564i | \(0.0714427\pi\) | |||||||
\(572\) | −3.71639 | −0.155390 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 10.0916i | − | 0.420851i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0392 | − | 15.0337i | 1.08403 | − | 0.625862i | 0.152046 | − | 0.988373i | \(-0.451414\pi\) |
0.931979 | + | 0.362511i | \(0.118081\pi\) | |||||||
\(578\) | − | 14.0689i | − | 0.585190i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.1393 | + | 5.85392i | −0.421011 | + | 0.243071i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.6148 | − | 23.5815i | −0.563866 | − | 0.976644i | ||||
\(584\) | −4.03690 | − | 6.99211i | −0.167048 | − | 0.289336i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.2800 | − | 8.24455i | −0.589900 | − | 0.340579i | ||||
\(587\) | 18.0979 | − | 31.3465i | 0.746981 | − | 1.29381i | −0.202283 | − | 0.979327i | \(-0.564836\pi\) |
0.949264 | − | 0.314481i | \(-0.101831\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4719 | + | 23.3339i | 0.555098 | + | 0.961459i | ||||
\(590\) | − | 34.2327i | − | 1.40934i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.73755 | 0.276911 | ||||||||
\(593\) | 1.02158 | − | 1.76943i | 0.0419514 | − | 0.0726620i | −0.844287 | − | 0.535891i | \(-0.819976\pi\) |
0.886239 | + | 0.463229i | \(0.153309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.3507 | + | 11.7495i | 0.833598 | + | 0.481278i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.66854 | − | 3.27273i | −0.231804 | − | 0.133832i | ||||
\(599\) | −15.7873 | − | 9.11478i | −0.645050 | − | 0.372420i | 0.141507 | − | 0.989937i | \(-0.454805\pi\) |
−0.786557 | + | 0.617517i | \(0.788139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.1713 | + | 18.5741i | 1.31230 | + | 0.757654i | 0.982476 | − | 0.186390i | \(-0.0596787\pi\) |
0.329820 | + | 0.944044i | \(0.393012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.48002 | + | 2.56346i | −0.0602210 | + | 0.104306i | ||||
\(605\) | −51.2856 | −2.08506 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 19.8296i | − | 0.804860i | −0.915451 | − | 0.402430i | \(-0.868166\pi\) | ||
0.915451 | − | 0.402430i | \(-0.131834\pi\) | |||||||
\(608\) | 9.00349 | + | 15.5945i | 0.365140 | + | 0.632440i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0336 | + | 34.6991i | −0.811135 | + | 1.40493i | ||||
\(611\) | 0.823890 | + | 0.475673i | 0.0333310 | + | 0.0192437i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.34412 | + | 10.9883i | 0.256237 | + | 0.443815i | 0.965231 | − | 0.261400i | \(-0.0841840\pi\) |
−0.708994 | + | 0.705214i | \(0.750851\pi\) | |||||||
\(614\) | 26.8690 | + | 46.5385i | 1.08435 | + | 1.87814i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.37247 | + | 2.52445i | −0.176029 | + | 0.101630i | −0.585426 | − | 0.810726i | \(-0.699073\pi\) |
0.409397 | + | 0.912357i | \(0.365739\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.267890i | 0.0107674i | 0.999986 | + | 0.00538370i | \(0.00171369\pi\) | ||||
−0.999986 | + | 0.00538370i | \(0.998286\pi\) | |||||||
\(620\) | 33.9094 | − | 19.5776i | 1.36183 | − | 0.786255i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 24.8305i | − | 0.995611i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.7584 | −1.19034 | ||||||||
\(626\) | −29.4820 | + | 51.0644i | −1.17834 | + | 2.04094i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.8504 | + | 6.26449i | −0.432979 | + | 0.249981i | ||||
\(629\) | 4.35905 | 0.173807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.7899 | 1.50439 | 0.752197 | − | 0.658938i | \(-0.228994\pi\) | ||||
0.752197 | + | 0.658938i | \(0.228994\pi\) | |||||||
\(632\) | −0.471310 | + | 0.272111i | −0.0187477 | + | 0.0108240i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.7556 | − | 32.4856i | 0.744880 | − | 1.29017i | ||||
\(635\) | 18.4734 | 0.733095 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 32.8117i | 1.29903i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.9234 | + | 9.19336i | −0.629426 | + | 0.363400i | ||||
\(641\) | 34.4090i | 1.35907i | 0.733641 | + | 0.679537i | \(0.237819\pi\) | ||||
−0.733641 | + | 0.679537i | \(0.762181\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.676278 | + | 0.390449i | −0.0266698 | + | 0.0153978i | −0.513276 | − | 0.858224i | \(-0.671568\pi\) |
0.486606 | + | 0.873622i | \(0.338235\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.40341 | + | 12.8231i | 0.291283 | + | 0.504517i | ||||
\(647\) | 9.82182 | + | 17.0119i | 0.386136 | + | 0.668807i | 0.991926 | − | 0.126818i | \(-0.0404763\pi\) |
−0.605790 | + | 0.795624i | \(0.707143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.5118 | − | 20.5027i | −1.39396 | − | 0.804803i | ||||
\(650\) | 0.530259 | − | 0.918435i | 0.0207985 | − | 0.0360240i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.801781 | − | 1.38872i | −0.0314001 | − | 0.0543867i | ||||
\(653\) | − | 3.20545i | − | 0.125439i | −0.998031 | − | 0.0627194i | \(-0.980023\pi\) | ||
0.998031 | − | 0.0627194i | \(-0.0199773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.7026 | 0.769843 | ||||||||
\(656\) | 7.83315 | − | 13.5674i | 0.305833 | − | 0.529719i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.2959 | + | 14.0273i | 0.946435 | + | 0.546425i | 0.891972 | − | 0.452091i | \(-0.149322\pi\) |
0.0544636 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.0490 | + | 16.1941i | 1.09098 | + | 0.629878i | 0.933837 | − | 0.357698i | \(-0.116438\pi\) |
0.157143 | + | 0.987576i | \(0.449772\pi\) | |||||||
\(662\) | −2.01981 | − | 1.16614i | −0.0785020 | − | 0.0453232i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.95189 | − | 4.01367i | −0.269785 | − | 0.155761i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.3500 | + | 21.3908i | −0.478193 | + | 0.828255i | ||||
\(668\) | 11.9354 | 0.461793 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 8.75209i | − | 0.338123i | ||||||
\(671\) | 23.9971 | + | 41.5641i | 0.926397 | + | 1.60457i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3088 | + | 17.8554i | −0.397375 | + | 0.688273i | −0.993401 | − | 0.114692i | \(-0.963412\pi\) |
0.596026 | + | 0.802965i | \(0.296745\pi\) | |||||||
\(674\) | 21.3242 | + | 12.3115i | 0.821378 | + | 0.474223i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.55701 | + | 16.5532i | 0.367577 | + | 0.636663i | ||||
\(677\) | −25.1655 | − | 43.5880i | −0.967190 | − | 1.67522i | −0.703612 | − | 0.710585i | \(-0.748431\pi\) |
−0.263578 | − | 0.964638i | \(-0.584903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.32935 | + | 3.65425i | −0.242719 | + | 0.140134i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 109.734i | − | 4.20193i | ||||||
\(683\) | 11.9031 | − | 6.87227i | 0.455460 | − | 0.262960i | −0.254673 | − | 0.967027i | \(-0.581968\pi\) |
0.710133 | + | 0.704067i | \(0.248635\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 28.9909i | − | 1.10769i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −45.2560 | −1.72537 | ||||||||
\(689\) | 1.07705 | − | 1.86550i | 0.0410321 | − | 0.0710698i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4328 | − | 14.6837i | 0.967511 | − | 0.558593i | 0.0690343 | − | 0.997614i | \(-0.478008\pi\) |
0.898476 | + | 0.439022i | \(0.144675\pi\) | |||||||
\(692\) | 1.49813 | 0.0569504 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −50.5874 | −1.92027 | ||||||||
\(695\) | −42.5325 | + | 24.5562i | −1.61335 | + | 0.931468i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.06789 | − | 8.77784i | 0.191960 | − | 0.332484i | ||||
\(698\) | −65.4785 | −2.47840 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 44.2011i | − | 1.66945i | −0.550666 | − | 0.834726i | \(-0.685626\pi\) | ||
0.550666 | − | 0.834726i | \(-0.314374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.15746 | − | 1.82296i | 0.119086 | − | 0.0687542i | ||||
\(704\) | − | 19.9674i | − | 0.752551i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.08702 | + | 2.35964i | −0.153817 | + | 0.0888063i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.66629 | + | 9.81430i | 0.212802 | + | 0.368584i | 0.952590 | − | 0.304256i | \(-0.0984077\pi\) |
−0.739788 | + | 0.672840i | \(0.765074\pi\) | |||||||
\(710\) | 6.91542 | + | 11.9779i | 0.259531 | + | 0.449521i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.21994 | − | 3.59108i | −0.233102 | − | 0.134581i | ||||
\(713\) | 41.3028 | − | 71.5385i | 1.54680 | − | 2.67914i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.11881 | − | 5.40193i | −0.116637 | − | 0.202021i | ||||
\(716\) | 2.20265i | 0.0823168i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.5827 | −0.506903 | ||||||||
\(719\) | 18.0647 | − | 31.2890i | 0.673700 | − | 1.16688i | −0.303147 | − | 0.952944i | \(-0.598037\pi\) |
0.976847 | − | 0.213939i | \(-0.0686294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −20.0271 | − | 11.5627i | −0.745333 | − | 0.430318i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.4505 | + | 11.2298i | 0.722874 | + | 0.417351i | ||||
\(725\) | −3.46580 | − | 2.00098i | −0.128717 | − | 0.0743146i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.20547 | + | 3.58273i | 0.230148 | + | 0.132876i | 0.610640 | − | 0.791908i | \(-0.290912\pi\) |
−0.380492 | + | 0.924784i | \(0.624245\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.9485 | + | 34.5518i | −0.738327 | + | 1.27882i | ||||
\(731\) | −29.2797 | −1.08295 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 47.8498i | − | 1.76737i | −0.468081 | − | 0.883685i | \(-0.655055\pi\) | ||
0.468081 | − | 0.883685i | \(-0.344945\pi\) | |||||||
\(734\) | −12.5938 | − | 21.8131i | −0.464846 | − | 0.805136i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.6034 | − | 47.8105i | 1.01747 | − | 1.76232i | ||||
\(737\) | −9.07910 | − | 5.24182i | −0.334433 | − | 0.193085i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.67416 | − | 13.2920i | −0.282299 | − | 0.488956i | 0.689652 | − | 0.724141i | \(-0.257764\pi\) |
−0.971951 | + | 0.235185i | \(0.924430\pi\) | |||||||
\(740\) | −2.64917 | − | 4.58849i | −0.0973853 | − | 0.168676i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.9422 | + | 20.1739i | −1.28191 | + | 0.740109i | −0.977197 | − | 0.212337i | \(-0.931893\pi\) |
−0.304709 | + | 0.952445i | \(0.598559\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.4409i | 1.44500i | ||||||||
\(746\) | 38.4630 | − | 22.2066i | 1.40823 | − | 0.813042i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 25.7747i | − | 0.942417i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.8898 | 1.23665 | 0.618327 | − | 0.785921i | \(-0.287811\pi\) | ||||
0.618327 | + | 0.785921i | \(0.287811\pi\) | |||||||
\(752\) | −5.09906 | + | 8.83183i | −0.185944 | + | 0.322064i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.24793 | + | 1.29784i | −0.0818647 | + | 0.0472646i | ||||
\(755\) | −4.96814 | −0.180809 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.73237 | −0.208346 | −0.104173 | − | 0.994559i | \(-0.533220\pi\) | ||||
−0.104173 | + | 0.994559i | \(0.533220\pi\) | |||||||
\(758\) | 34.3589 | − | 19.8371i | 1.24797 | − | 0.720517i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.05642 | + | 5.29387i | −0.110868 | + | 0.192029i | ||||
\(761\) | −26.5332 | −0.961828 | −0.480914 | − | 0.876768i | \(-0.659695\pi\) | ||||
−0.480914 | + | 0.876768i | \(0.659695\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 19.7420i | − | 0.714242i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.9741 | + | 12.1094i | −0.757825 | + | 0.437531i | ||||
\(767\) | − | 3.24389i | − | 0.117130i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.3944 | + | 13.5068i | −0.843623 | + | 0.487066i | −0.858494 | − | 0.512823i | \(-0.828600\pi\) |
0.0148711 | + | 0.999889i | \(0.495266\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.16128 | − | 2.01139i | −0.0417953 | − | 0.0723916i | ||||
\(773\) | 11.3009 | + | 19.5737i | 0.406464 | + | 0.704016i | 0.994491 | − | 0.104826i | \(-0.0334284\pi\) |
−0.588027 | + | 0.808841i | \(0.700095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.5909 | + | 6.69201i | 0.416357 | + | 0.240384i | ||||
\(776\) | 1.76545 | − | 3.05784i | 0.0633758 | − | 0.109770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2296 | + | 17.7182i | 0.366750 | + | 0.635229i | ||||
\(779\) | − | 8.47758i | − | 0.303741i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.5672 | 0.592821 | ||||||||
\(782\) | 22.6978 | − | 39.3137i | 0.811670 | − | 1.40585i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.2114 | − | 10.5144i | −0.649993 | − | 0.375274i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.6864 | + | 13.0980i | 0.808683 | + | 0.466893i | 0.846498 | − | 0.532391i | \(-0.178707\pi\) |
−0.0378153 | + | 0.999285i | \(0.512040\pi\) | |||||||
\(788\) | 6.41523 | + | 3.70383i | 0.228533 | + | 0.131944i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.32900 | + | 1.34465i | 0.0828620 | + | 0.0478404i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.89838 | + | 3.28808i | −0.0674133 | + | 0.116763i | ||||
\(794\) | 55.8627 | 1.98249 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.7091i | 0.592239i | ||||||||
\(797\) | −5.96560 | − | 10.3327i | −0.211312 | − | 0.366004i | 0.740813 | − | 0.671711i | \(-0.234440\pi\) |
−0.952126 | + | 0.305707i | \(0.901107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.29899 | + | 5.71402i | −0.116710 | + | 0.202147i | ||||
\(800\) | 7.74640 | + | 4.47239i | 0.273877 | + | 0.158123i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.9370 | − | 31.0678i | −0.633378 | − | 1.09704i | ||||
\(803\) | 23.8952 | + | 41.3877i | 0.843242 | + | 1.46054i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.51788 | − | 4.34045i | 0.264806 | − | 0.152886i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 7.14038i | − | 0.251198i | ||||||
\(809\) | 22.9399 | − | 13.2443i | 0.806522 | − | 0.465646i | −0.0392244 | − | 0.999230i | \(-0.512489\pi\) |
0.845747 | + | 0.533585i | \(0.179155\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.7419i | 0.482544i | 0.970458 | + | 0.241272i | \(0.0775646\pi\) | ||||
−0.970458 | + | 0.241272i | \(0.922435\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.8488 | −0.520449 | ||||||||
\(815\) | 1.34571 | − | 2.33084i | 0.0471383 | − | 0.0816459i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.2086 | + | 12.2448i | −0.741996 | + | 0.428391i | ||||
\(818\) | −53.8949 | −1.88439 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.3198 | −0.430226 | ||||||||
\(821\) | −11.7493 | + | 6.78346i | −0.410053 | + | 0.236744i | −0.690813 | − | 0.723034i | \(-0.742747\pi\) |
0.280759 | + | 0.959778i | \(0.409414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.34857 | + | 12.7281i | −0.256155 | + | 0.443674i | −0.965209 | − | 0.261481i | \(-0.915789\pi\) |
0.709053 | + | 0.705155i | \(0.249122\pi\) | |||||||
\(824\) | 13.5742 | 0.472881 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 40.8787i | − | 1.42149i | −0.703449 | − | 0.710746i | \(-0.748358\pi\) | ||
0.703449 | − | 0.710746i | \(-0.251642\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.7189 | + | 10.2300i | −0.615402 | + | 0.355302i | −0.775077 | − | 0.631867i | \(-0.782289\pi\) |
0.159675 | + | 0.987170i | \(0.448955\pi\) | |||||||
\(830\) | 39.6675i | 1.37688i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.36797 | − | 0.789798i | 0.0474258 | − | 0.0273813i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0162 | + | 17.3486i | 0.346625 | + | 0.600372i | ||||
\(836\) | −10.7790 | − | 18.6698i | −0.372800 | − | 0.645708i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.3923 | + | 9.46412i | 0.566264 | + | 0.326932i | ||||
\(839\) | −27.3475 | + | 47.3673i | −0.944141 | + | 1.63530i | −0.186680 | + | 0.982421i | \(0.559773\pi\) |
−0.757462 | + | 0.652880i | \(0.773561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.60247 | − | 16.6320i | −0.331120 | − | 0.573516i | ||||
\(842\) | − | 47.5062i | − | 1.63717i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.9321 | 0.789356 | ||||||||
\(845\) | −16.0405 | + | 27.7830i | −0.551812 | + | 0.955766i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.9975 | + | 11.5456i | 0.686718 | + | 0.396477i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.36973 | + | 3.67756i | 0.218480 | + | 0.126139i | ||||
\(851\) | −9.68031 | − | 5.58893i | −0.331837 | − | 0.191586i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.0684 | + | 6.39037i | 0.378976 | + | 0.218802i | 0.677373 | − | 0.735640i | \(-0.263118\pi\) |
−0.298396 | + | 0.954442i | \(0.596452\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.39058 | − | 11.0688i | 0.218426 | − | 0.378324i | ||||
\(857\) | 18.3240 | 0.625936 | 0.312968 | − | 0.949764i | \(-0.398677\pi\) | ||||
0.312968 | + | 0.949764i | \(0.398677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.6339i | 1.31817i | 0.752068 | + | 0.659085i | \(0.229056\pi\) | ||||
−0.752068 | + | 0.659085i | \(0.770944\pi\) | |||||||
\(860\) | 17.7944 | + | 30.8208i | 0.606784 | + | 1.05098i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.1328 | + | 17.5505i | −0.345125 | + | 0.597774i | ||||
\(863\) | −14.4626 | − | 8.35001i | −0.492314 | − | 0.284238i | 0.233220 | − | 0.972424i | \(-0.425074\pi\) |
−0.725534 | + | 0.688186i | \(0.758407\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.25724 | + | 2.17760i | 0.0427473 | + | 0.0740405i | ||||
\(866\) | −12.1966 | − | 21.1251i | −0.414456 | − | 0.717859i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.78978 | − | 1.61068i | 0.0946367 | − | 0.0546385i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 0.829346i | − | 0.0281013i | ||||||
\(872\) | −0.753996 | + | 0.435320i | −0.0255335 | + | 0.0147418i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 37.9689i | − | 1.28432i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.5234 | 1.13200 | 0.566002 | − | 0.824404i | \(-0.308489\pi\) | ||||
0.566002 | + | 0.824404i | \(0.308489\pi\) | |||||||
\(878\) | 29.8606 | − | 51.7201i | 1.00775 | − | 1.74547i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 57.9070 | − | 33.4326i | 1.95204 | − | 1.12701i | ||||
\(881\) | 28.6657 | 0.965771 | 0.482885 | − | 0.875684i | \(-0.339589\pi\) | ||||
0.482885 | + | 0.875684i | \(0.339589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.2091 | −1.28584 | −0.642919 | − | 0.765935i | \(-0.722277\pi\) | ||||
−0.642919 | + | 0.765935i | \(0.722277\pi\) | |||||||
\(884\) | 1.76583 | − | 1.01950i | 0.0593912 | − | 0.0342895i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.1719 | − | 40.1350i | 0.778476 | − | 1.34836i | ||||
\(887\) | 35.1828 | 1.18132 | 0.590662 | − | 0.806919i | \(-0.298867\pi\) | ||||
0.590662 | + | 0.806919i | \(0.298867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 35.4910i | 1.18966i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.13309 | − | 2.38624i | 0.138386 | − | 0.0798972i | ||||
\(893\) | 5.51856i | 0.184672i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.20164 | + | 1.84847i | −0.107019 | + | 0.0617875i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.8685 | − | 22.2890i | −0.429429 | − | 0.743792i | ||||
\(899\) | −16.3791 | − | 28.3695i | −0.546274 | − | 0.946174i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9380 | + | 7.46975i | 0.431027 | + | 0.248854i | ||||
\(902\) | −17.2634 | + | 29.9010i | −0.574807 | + | 0.995595i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.24557 | − | 3.88944i | −0.0746866 | − | 0.129361i | ||||
\(905\) | 37.6963i | 1.25307i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.5954 | −1.41436 | −0.707179 | − | 0.707034i | \(-0.750033\pi\) | ||||
−0.707179 | + | 0.707034i | \(0.750033\pi\) | |||||||
\(908\) | 10.9505 | − | 18.9669i | 0.363406 | − | 0.629437i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.5221 | + | 25.1275i | 1.44195 | + | 0.832510i | 0.997980 | − | 0.0635313i | \(-0.0202363\pi\) |
0.443970 | + | 0.896042i | \(0.353570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.1496 | + | 23.7577i | 1.36185 | + | 0.786265i | ||||
\(914\) | −44.2037 | − | 25.5210i | −1.46213 | − | 0.844160i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.36754 | − | 2.52160i | −0.144308 | − | 0.0833161i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.3486 | − | 50.8333i | 0.968121 | − | 1.67684i | 0.267137 | − | 0.963658i | \(-0.413922\pi\) |
0.700984 | − | 0.713177i | \(-0.252744\pi\) | |||||||
\(920\) | 18.7411 | 0.617875 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.6264i | 0.679295i | ||||||||
\(923\) | 0.655304 | + | 1.13502i | 0.0215696 | + | 0.0373596i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.905536 | − | 1.56843i | 0.0297738 | − | 0.0515698i | ||||
\(926\) | −39.6046 | − | 22.8657i | −1.30149 | − | 0.751415i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.9465 | − | 18.9598i | −0.359335 | − | 0.622387i | ||||
\(929\) | 7.19115 | + | 12.4554i | 0.235934 | + | 0.408650i | 0.959544 | − | 0.281560i | \(-0.0908518\pi\) |
−0.723610 | + | 0.690209i | \(0.757518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.30952 | + | 3.64281i | −0.206675 | + | 0.119324i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.7251i | 0.972636i | ||||||||
\(935\) | 37.4646 | − | 21.6302i | 1.22522 | − | 0.707384i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 44.2981i | − | 1.44716i | −0.690243 | − | 0.723578i | \(-0.742496\pi\) | ||
0.690243 | − | 0.723578i | \(-0.257504\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.01969 | 0.261573 | ||||||||
\(941\) | 7.44400 | − | 12.8934i | 0.242667 | − | 0.420312i | −0.718806 | − | 0.695211i | \(-0.755311\pi\) |
0.961473 | + | 0.274899i | \(0.0886443\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.5089 | + | 12.9955i | −0.732990 | + | 0.423192i | ||||
\(944\) | 34.7734 | 1.13178 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 99.7390 | 3.24280 | ||||||||
\(947\) | 36.3343 | − | 20.9776i | 1.18071 | − | 0.681681i | 0.224528 | − | 0.974468i | \(-0.427916\pi\) |
0.956178 | + | 0.292787i | \(0.0945827\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.89031 | + | 3.27412i | −0.0613622 | + | 0.106282i | ||||
\(950\) | 6.15184 | 0.199592 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.9821i | 0.452926i | 0.974020 | + | 0.226463i | \(0.0727162\pi\) | ||||
−0.974020 | + | 0.226463i | \(0.927284\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.6959 | − | 16.5676i | 0.928578 | − | 0.536115i | ||||
\(956\) | 23.4884i | 0.759669i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.4228 | − | 12.9458i | 0.724449 | − | 0.418261i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39.2776 | + | 68.0309i | 1.26702 | + | 2.19454i | ||||
\(962\) | −0.587333 | − | 1.01729i | −0.0189364 | − | 0.0327988i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.994743 | − | 0.574315i | −0.0320385 | − | 0.0184974i | ||||
\(965\) | 1.94910 | − | 3.37593i | 0.0627436 | − | 0.108675i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.5757 | − | 20.0497i | −0.372249 | − | 0.644754i | 0.617662 | − | 0.786443i | \(-0.288080\pi\) |
−0.989911 | + | 0.141690i | \(0.954746\pi\) | |||||||
\(968\) | − | 19.3967i | − | 0.623433i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.4481 | −0.560223 | ||||||||
\(971\) | −21.6869 | + | 37.5628i | −0.695965 | + | 1.20545i | 0.273890 | + | 0.961761i | \(0.411690\pi\) |
−0.969854 | + | 0.243685i | \(0.921644\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −46.6120 | − | 26.9114i | −1.49354 | − | 0.862298i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −35.2472 | − | 20.3500i | −1.12824 | − | 0.651387i | ||||
\(977\) | −10.4210 | − | 6.01657i | −0.333397 | − | 0.192487i | 0.323951 | − | 0.946074i | \(-0.394989\pi\) |
−0.657348 | + | 0.753587i | \(0.728322\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.8170 | + | 21.2563i | 1.17668 | + | 0.679355i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.2152 | − | 62.7266i | 1.15567 | − | 2.00169i | ||||
\(983\) | 6.29658 | 0.200830 | 0.100415 | − | 0.994946i | \(-0.467983\pi\) | ||||
0.100415 | + | 0.994946i | \(0.467983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.4331i | 0.396151i | ||||||||
\(986\) | −9.00108 | − | 15.5903i | −0.286653 | − | 0.496497i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.852712 | − | 1.47694i | 0.0271284 | − | 0.0469877i | ||||
\(989\) | 65.0225 | + | 37.5408i | 2.06760 | + | 1.19373i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.7814 | − | 29.0662i | −0.533078 | − | 0.923317i | −0.999254 | − | 0.0386256i | \(-0.987702\pi\) |
0.466176 | − | 0.884692i | \(-0.345631\pi\) | |||||||
\(992\) | 36.6089 | + | 63.4085i | 1.16233 | + | 2.01322i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.2874 | + | 14.0223i | −0.769963 | + | 0.444538i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.2565i | 0.356495i | 0.983986 | + | 0.178248i | \(0.0570428\pi\) | ||||
−0.983986 | + | 0.178248i | \(0.942957\pi\) | |||||||
\(998\) | −5.61096 | + | 3.23949i | −0.177612 | + | 0.102544i | ||||
\(999\) | 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 | 1323.2.s.d.656.20 | 48 | ||
3.2 | odd | 2 | 441.2.s.d.362.6 | 48 | |||
7.2 | even | 3 | 1323.2.o.e.440.5 | 48 | |||
7.3 | odd | 6 | 1323.2.i.d.521.7 | 48 | |||
7.4 | even | 3 | 1323.2.i.d.521.22 | 48 | |||
7.5 | odd | 6 | 1323.2.o.e.440.6 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.s.d.656.19 | 48 | ||
9.4 | even | 3 | 441.2.i.d.68.20 | 48 | |||
9.5 | odd | 6 | 1323.2.i.d.1097.7 | 48 | |||
21.2 | odd | 6 | 441.2.o.e.146.20 | yes | 48 | ||
21.5 | even | 6 | 441.2.o.e.146.19 | ✓ | 48 | ||
21.11 | odd | 6 | 441.2.i.d.227.5 | 48 | |||
21.17 | even | 6 | 441.2.i.d.227.6 | 48 | |||
21.20 | even | 2 | 441.2.s.d.362.5 | 48 | |||
63.4 | even | 3 | 441.2.s.d.374.5 | 48 | |||
63.5 | even | 6 | 1323.2.o.e.881.5 | 48 | |||
63.13 | odd | 6 | 441.2.i.d.68.19 | 48 | |||
63.23 | odd | 6 | 1323.2.o.e.881.6 | 48 | |||
63.31 | odd | 6 | 441.2.s.d.374.6 | 48 | |||
63.32 | odd | 6 | inner | 1323.2.s.d.962.19 | 48 | ||
63.40 | odd | 6 | 441.2.o.e.293.20 | yes | 48 | ||
63.41 | even | 6 | 1323.2.i.d.1097.22 | 48 | |||
63.58 | even | 3 | 441.2.o.e.293.19 | yes | 48 | ||
63.59 | even | 6 | inner | 1323.2.s.d.962.20 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.19 | 48 | 63.13 | odd | 6 | |||
441.2.i.d.68.20 | 48 | 9.4 | even | 3 | |||
441.2.i.d.227.5 | 48 | 21.11 | odd | 6 | |||
441.2.i.d.227.6 | 48 | 21.17 | even | 6 | |||
441.2.o.e.146.19 | ✓ | 48 | 21.5 | even | 6 | ||
441.2.o.e.146.20 | yes | 48 | 21.2 | odd | 6 | ||
441.2.o.e.293.19 | yes | 48 | 63.58 | even | 3 | ||
441.2.o.e.293.20 | yes | 48 | 63.40 | odd | 6 | ||
441.2.s.d.362.5 | 48 | 21.20 | even | 2 | |||
441.2.s.d.362.6 | 48 | 3.2 | odd | 2 | |||
441.2.s.d.374.5 | 48 | 63.4 | even | 3 | |||
441.2.s.d.374.6 | 48 | 63.31 | odd | 6 | |||
1323.2.i.d.521.7 | 48 | 7.3 | odd | 6 | |||
1323.2.i.d.521.22 | 48 | 7.4 | even | 3 | |||
1323.2.i.d.1097.7 | 48 | 9.5 | odd | 6 | |||
1323.2.i.d.1097.22 | 48 | 63.41 | even | 6 | |||
1323.2.o.e.440.5 | 48 | 7.2 | even | 3 | |||
1323.2.o.e.440.6 | 48 | 7.5 | odd | 6 | |||
1323.2.o.e.881.5 | 48 | 63.5 | even | 6 | |||
1323.2.o.e.881.6 | 48 | 63.23 | odd | 6 | |||
1323.2.s.d.656.19 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.s.d.656.20 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.s.d.962.19 | 48 | 63.32 | odd | 6 | inner | ||
1323.2.s.d.962.20 | 48 | 63.59 | even | 6 | inner |