Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(521,1323)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.i (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 | 521.7 | ||
Character | \(\chi\) | \(=\) | 1323.521 |
Dual form | 1323.2.i.d.1097.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86894i | 1.32154i | 0.750589 | + | 0.660769i | \(0.229770\pi\) | ||||
−0.750589 | + | 0.660769i | \(0.770230\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.49292 | −0.746462 | ||||||||
\(5\) | 1.25287 | − | 2.17003i | 0.560299 | − | 0.970467i | −0.437171 | − | 0.899378i | \(-0.644020\pi\) |
0.997470 | − | 0.0710881i | \(-0.0226472\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.947692i | 0.335060i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.05565 | + | 2.34153i | 1.28251 | + | 0.740457i | ||||
\(11\) | −4.85803 | + | 2.80479i | −1.46475 | + | 0.845675i | −0.999225 | − | 0.0393590i | \(-0.987468\pi\) |
−0.465527 | + | 0.885034i | \(0.654135\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.384312 | + | 0.221883i | −0.106589 | + | 0.0615392i | −0.552347 | − | 0.833614i | \(-0.686268\pi\) |
0.445758 | + | 0.895154i | \(0.352934\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.75703 | −1.18926 | ||||||||
\(17\) | −1.53885 | + | 2.66536i | −0.373226 | + | 0.646446i | −0.990060 | − | 0.140647i | \(-0.955082\pi\) |
0.616834 | + | 0.787093i | \(0.288415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.22932 | − | 1.28710i | 0.511440 | − | 0.295280i | −0.221985 | − | 0.975050i | \(-0.571254\pi\) |
0.733425 | + | 0.679770i | \(0.237920\pi\) | |||||||
\(20\) | −1.87044 | + | 3.23969i | −0.418242 | + | 0.724417i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.24197 | − | 9.07935i | −1.11759 | − | 1.93572i | ||||
\(23\) | 6.83476 | + | 3.94605i | 1.42515 | + | 0.822808i | 0.996732 | − | 0.0807749i | \(-0.0257395\pi\) |
0.428413 | + | 0.903583i | \(0.359073\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.639351 | − | 1.10739i | −0.127870 | − | 0.221478i | ||||
\(26\) | −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 | ||||||||
\(31\) | 10.4669i | 1.87990i | 0.341306 | + | 0.939952i | \(0.389131\pi\) | ||||
−0.341306 | + | 0.939952i | \(0.610869\pi\) | |||||||
\(32\) | − | 6.99520i | − | 1.23659i | ||||||
\(33\) | 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 | 0.918347 | − | 0.395775i | \(-0.129524\pi\) |
−0.801925 | + | 0.597424i | \(0.796191\pi\) | |||||||
\(38\) | 2.40550 | + | 4.16645i | 0.390224 | + | 0.675887i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.05652 | + | 1.18733i | 0.325164 | + | 0.187734i | ||||
\(41\) | 1.64665 | + | 2.85208i | 0.257163 | + | 0.445420i | 0.965481 | − | 0.260474i | \(-0.0838788\pi\) |
−0.708318 | + | 0.705894i | \(0.750545\pi\) | |||||||
\(42\) | 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 | ||||
\(47\) | 2.14380 | 0.312706 | 0.156353 | − | 0.987701i | \(-0.450026\pi\) | ||||
0.156353 | + | 0.987701i | \(0.450026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.06964 | − | 1.19491i | 0.292691 | − | 0.168985i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.573749 | − | 0.331254i | 0.0795647 | − | 0.0459367i | ||||
\(53\) | −4.20379 | − | 2.42706i | −0.577435 | − | 0.333382i | 0.182678 | − | 0.983173i | \(-0.441523\pi\) |
−0.760113 | + | 0.649791i | \(0.774857\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.0561i | 1.89532i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.92461 | − | 5.06558i | 0.384020 | − | 0.665143i | ||||
\(59\) | 7.30991 | 0.951669 | 0.475835 | − | 0.879535i | \(-0.342146\pi\) | ||||
0.475835 | + | 0.879535i | \(0.342146\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.55576i | 1.09545i | 0.836658 | + | 0.547726i | \(0.184506\pi\) | ||||
−0.836658 | + | 0.547726i | \(0.815494\pi\) | |||||||
\(62\) | −19.5619 | −2.48437 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.55953 | 0.444941 | ||||||||
\(65\) | 1.11196i | 0.137921i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.86888 | −0.228321 | −0.114160 | − | 0.993462i | \(-0.536418\pi\) | ||||
−0.114160 | + | 0.993462i | \(0.536418\pi\) | |||||||
\(68\) | 2.29739 | − | 3.97919i | 0.278599 | − | 0.482548i | ||||
\(69\) | 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 | 0.00165984 | − | 0.999999i | \(-0.499472\pi\) |
−0.865194 | + | 0.501437i | \(0.832805\pi\) | |||||||
\(74\) | −2.29241 | + | 1.32352i | −0.266487 | + | 0.153856i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.32820 | + | 1.92154i | −0.381771 | + | 0.220415i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.574261 | −0.0646094 | −0.0323047 | − | 0.999478i | \(-0.510285\pi\) | ||||
−0.0323047 | + | 0.999478i | \(0.510285\pi\) | |||||||
\(80\) | −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 | −0.534321 | − | 0.845281i | \(-0.679433\pi\) |
0.999196 | + | 0.0400951i | \(0.0127661\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.85595 | + | 6.67870i | 0.418236 | + | 0.724406i | ||||
\(86\) | −15.3981 | − | 8.89008i | −1.66042 | − | 0.958642i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.65807 | − | 4.60392i | −0.283352 | − | 0.490779i | ||||
\(89\) | 3.78929 | + | 6.56325i | 0.401664 | + | 0.695703i | 0.993927 | − | 0.110042i | \(-0.0350986\pi\) |
−0.592263 | + | 0.805745i | \(0.701765\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.2038 | − | 5.89115i | −1.06382 | − | 0.614195i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.00663i | 0.413252i | ||||||||
\(95\) | − | 6.45024i | − | 0.661781i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.22662 | + | 1.86289i | 0.327614 | + | 0.189148i | 0.654781 | − | 0.755818i | \(-0.272761\pi\) |
−0.327167 | + | 0.944966i | \(0.606094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.954503 | + | 1.65325i | 0.0954503 | + | 0.165325i | ||||
\(101\) | −3.76725 | − | 6.52506i | −0.374855 | − | 0.649268i | 0.615450 | − | 0.788176i | \(-0.288974\pi\) |
−0.990305 | + | 0.138908i | \(0.955641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4045 | − | 7.16173i | −1.22225 | − | 0.705666i | −0.256853 | − | 0.966451i | \(-0.582685\pi\) |
−0.965397 | + | 0.260784i | \(0.916019\pi\) | |||||||
\(104\) | −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 | \(-0.440639\pi\) |
0.943715 | + | 0.330761i | \(0.107305\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.459348 | − | 0.795613i | 0.0439975 | − | 0.0762059i | −0.843188 | − | 0.537619i | \(-0.819324\pi\) |
0.887186 | + | 0.461413i | \(0.152657\pi\) | |||||||
\(110\) | −26.2700 | −2.50474 | ||||||||
\(111\) | 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 | ||||||||
\(115\) | 17.1261 | − | 9.88775i | 1.59702 | − | 0.922037i | ||||
\(116\) | 4.04643 | + | 2.33621i | 0.375702 | + | 0.216912i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.6618i | 1.25767i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2337 | − | 17.7252i | 0.930332 | − | 1.61138i | ||||
\(122\) | −15.9902 | −1.44768 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 15.6262i | − | 1.40328i | ||||||
\(125\) | 9.32458 | 0.834016 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.37245 | 0.654200 | 0.327100 | − | 0.944990i | \(-0.393929\pi\) | ||||
0.327100 | + | 0.944990i | \(0.393929\pi\) | |||||||
\(128\) | − | 7.33786i | − | 0.648581i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.07818 | −0.182268 | ||||||||
\(131\) | 3.93150 | − | 6.80955i | 0.343497 | − | 0.594953i | −0.641583 | − | 0.767054i | \(-0.721722\pi\) |
0.985079 | + | 0.172100i | \(0.0550553\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 3.49283i | − | 0.301734i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.52594 | − | 1.45835i | −0.216598 | − | 0.125053i | ||||
\(137\) | −10.0198 | + | 5.78491i | −0.856046 | + | 0.494238i | −0.862686 | − | 0.505740i | \(-0.831220\pi\) |
0.00664016 | + | 0.999978i | \(0.497886\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9741 | − | 9.79999i | 1.43972 | − | 0.831224i | 0.441893 | − | 0.897068i | \(-0.354307\pi\) |
0.997830 | + | 0.0658437i | \(0.0209739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.51968 | −0.463201 | ||||||||
\(143\) | 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 | ||||
\(149\) | −13.6315 | − | 7.87012i | −1.11673 | − | 0.644746i | −0.176167 | − | 0.984360i | \(-0.556370\pi\) |
−0.940565 | + | 0.339615i | \(0.889703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.991353 | + | 1.71707i | 0.0806752 | + | 0.139734i | 0.903540 | − | 0.428503i | \(-0.140959\pi\) |
−0.822865 | + | 0.568237i | \(0.807626\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | − | 8.39224i | − | 0.669774i | −0.942258 | − | 0.334887i | \(-0.891302\pi\) | ||
0.942258 | − | 0.334887i | \(-0.108698\pi\) | |||||||
\(158\) | − | 1.07326i | − | 0.0853837i | ||||||
\(159\) | 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 | 0.886291 | − | 0.463128i | \(-0.153273\pi\) |
−0.844226 | + | 0.535987i | \(0.819940\pi\) | |||||||
\(164\) | −2.45832 | − | 4.25794i | −0.191963 | − | 0.332489i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.7098 | + | 7.91534i | 1.06408 | + | 0.614349i | ||||
\(167\) | −3.99731 | − | 6.92354i | −0.309321 | − | 0.535760i | 0.668893 | − | 0.743359i | \(-0.266768\pi\) |
−0.978214 | + | 0.207599i | \(0.933435\pi\) | |||||||
\(168\) | 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 | ||||
\(173\) | 1.00349 | 0.0762938 | 0.0381469 | − | 0.999272i | \(-0.487855\pi\) | ||||
0.0381469 | + | 0.999272i | \(0.487855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.1098 | − | 13.3424i | 1.74197 | − | 1.00572i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.2663 | + | 7.08195i | −0.919398 | + | 0.530814i | ||||
\(179\) | 1.27773 | + | 0.737695i | 0.0955017 | + | 0.0551379i | 0.546990 | − | 0.837139i | \(-0.315773\pi\) |
−0.451489 | + | 0.892277i | \(0.649107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.0440i | − | 1.11821i | −0.829096 | − | 0.559106i | \(-0.811145\pi\) | ||
0.829096 | − | 0.559106i | \(-0.188855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.73964 | + | 6.47724i | −0.275690 | + | 0.477509i | ||||
\(185\) | 3.54896 | 0.260925 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 17.2646i | − | 1.26251i | ||||||
\(188\) | −3.20054 | −0.233423 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0551 | 0.874568 | ||||||||
\(191\) | 13.2237i | 0.956836i | 0.878132 | + | 0.478418i | \(0.158790\pi\) | ||||
−0.878132 | + | 0.478418i | \(0.841210\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.55571 | −0.111982 | −0.0559912 | − | 0.998431i | \(-0.517832\pi\) | ||||
−0.0559912 | + | 0.998431i | \(0.517832\pi\) | |||||||
\(194\) | −3.48163 | + | 6.03035i | −0.249966 | + | 0.432954i | ||||
\(195\) | 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 | 0.115425 | − | 0.993316i | \(-0.463177\pi\) |
−0.802525 | + | 0.596619i | \(0.796510\pi\) | |||||||
\(200\) | 1.04946 | − | 0.605908i | 0.0742083 | − | 0.0428442i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.1949 | − | 7.04074i | 0.858032 | − | 0.495385i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.25213 | 0.576354 | ||||||||
\(206\) | 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 | \(0.656001\pi\) | |||||||
\(212\) | 6.27594 | + | 3.62342i | 0.431033 | + | 0.248857i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.6028 | + | 21.8287i | 0.861511 | + | 1.49218i | ||||
\(215\) | 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 | ||||||||
\(220\) | − | 20.9847i | − | 1.41479i | ||||||
\(221\) | − | 1.36578i | − | 0.0918721i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.76845 | − | 1.59837i | −0.185389 | − | 0.107034i | 0.404433 | − | 0.914568i | \(-0.367469\pi\) |
−0.589822 | + | 0.807533i | \(0.700802\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.42848 | − | 7.67035i | −0.294578 | − | 0.510224i | ||||
\(227\) | 7.33494 | + | 12.7045i | 0.486837 | + | 0.843227i | 0.999885 | − | 0.0151329i | \(-0.00481714\pi\) |
−0.513048 | + | 0.858360i | \(0.671484\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.92550 | − | 1.68904i | −0.193322 | − | 0.111615i | 0.400215 | − | 0.916421i | \(-0.368936\pi\) |
−0.593537 | + | 0.804807i | \(0.702269\pi\) | |||||||
\(230\) | 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 | \(-0.615565\pi\) |
0.632007 | + | 0.774963i | \(0.282231\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.68590 | − | 4.65211i | 0.175209 | − | 0.303470i | ||||
\(236\) | −10.9131 | −0.710385 | ||||||||
\(237\) | 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 | ||||||||
\(241\) | 0.666305 | − | 0.384691i | 0.0429205 | − | 0.0247801i | −0.478386 | − | 0.878150i | \(-0.658778\pi\) |
0.521307 | + | 0.853369i | \(0.325445\pi\) | |||||||
\(242\) | 33.1273 | + | 19.1260i | 2.12950 | + | 1.22947i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 12.7731i | − | 0.817714i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.571169 | + | 0.989293i | −0.0363426 | + | 0.0629472i | ||||
\(248\) | −9.91936 | −0.629880 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.4271i | 1.10218i | ||||||||
\(251\) | −1.14544 | −0.0722996 | −0.0361498 | − | 0.999346i | \(-0.511509\pi\) | ||||
−0.0361498 | + | 0.999346i | \(0.511509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −44.2713 | −2.78331 | ||||||||
\(254\) | 13.7787i | 0.864549i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.8331 | 1.30207 | ||||||||
\(257\) | 14.4917 | − | 25.1004i | 0.903969 | − | 1.56572i | 0.0816738 | − | 0.996659i | \(-0.473973\pi\) |
0.822295 | − | 0.569061i | \(-0.192693\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1.66007i | − | 0.102953i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.7266 | + | 7.34772i | 0.786254 | + | 0.453944i | ||||
\(263\) | 11.8643 | − | 6.84988i | 0.731586 | − | 0.422381i | −0.0874160 | − | 0.996172i | \(-0.527861\pi\) |
0.819002 | + | 0.573790i | \(0.194528\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5336 | + | 6.08156i | −0.647072 | + | 0.373587i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.79010 | 0.170433 | ||||||||
\(269\) | 5.23973 | − | 9.07548i | 0.319472 | − | 0.553342i | −0.660906 | − | 0.750469i | \(-0.729828\pi\) |
0.980378 | + | 0.197127i | \(0.0631611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.66907 | − | 3.27304i | 0.344371 | − | 0.198823i | −0.317832 | − | 0.948147i | \(-0.602955\pi\) |
0.662203 | + | 0.749324i | \(0.269621\pi\) | |||||||
\(272\) | 7.32034 | − | 12.6792i | 0.443861 | − | 0.768790i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.8116 | − | 18.7263i | −0.653155 | − | 1.13130i | ||||
\(275\) | 6.21198 | + | 3.58649i | 0.374596 | + | 0.216273i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2156 | − | 19.4261i | −0.673883 | − | 1.16720i | −0.976794 | − | 0.214181i | \(-0.931292\pi\) |
0.302911 | − | 0.953019i | \(-0.402041\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 18.9713i | 1.12772i | 0.825869 | + | 0.563862i | \(0.190685\pi\) | ||||
−0.825869 | + | 0.563862i | \(0.809315\pi\) | |||||||
\(284\) | − | 4.40917i | − | 0.261636i | ||||||
\(285\) | 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 | ||||
\(290\) | −7.32830 | − | 12.6930i | −0.430333 | − | 0.745358i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.0149 | + | 6.35943i | 0.644596 | + | 0.372158i | ||||
\(293\) | 4.41136 | + | 7.64069i | 0.257714 | + | 0.446374i | 0.965629 | − | 0.259924i | \(-0.0836974\pi\) |
−0.707915 | + | 0.706298i | \(0.750364\pi\) | |||||||
\(294\) | 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 | ||||
\(299\) | −3.50224 | −0.202540 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.20910 | + | 1.85278i | −0.184663 | + | 0.106615i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.6049 | + | 6.12275i | −0.608233 | + | 0.351164i | ||||
\(305\) | 18.5662 | + | 10.7192i | 1.06310 | + | 0.613781i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.7533i | − | 1.64104i | −0.571620 | − | 0.820519i | \(-0.693685\pi\) | ||
0.571620 | − | 0.820519i | \(-0.306315\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.5085 | + | 42.4499i | −1.39199 | + | 2.41099i | ||||
\(311\) | 13.2859 | 0.753373 | 0.376687 | − | 0.926341i | \(-0.377063\pi\) | ||||
0.376687 | + | 0.926341i | \(0.377063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.5495i | 1.78329i | 0.452740 | + | 0.891643i | \(0.350447\pi\) | ||||
−0.452740 | + | 0.891643i | \(0.649553\pi\) | |||||||
\(314\) | 15.6846 | 0.885132 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.857328 | 0.0482285 | ||||||||
\(317\) | 20.0709i | 1.12729i | 0.826016 | + | 0.563646i | \(0.190602\pi\) | ||||
−0.826016 | + | 0.563646i | \(0.809398\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.5563 | 0.982965 | ||||||||
\(320\) | 4.45961 | − | 7.72428i | 0.249300 | − | 0.431800i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.92259i | 0.440824i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.491421 | + | 0.283722i | 0.0272591 | + | 0.0157381i | ||||
\(326\) | −1.73849 | + | 1.00372i | −0.0962862 | + | 0.0555909i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.70289 | + | 1.56052i | −0.149242 | + | 0.0861651i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.24791 | 0.0685915 | 0.0342958 | − | 0.999412i | \(-0.489081\pi\) | ||||
0.0342958 | + | 0.999412i | \(0.489081\pi\) | |||||||
\(332\) | −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 | \(0.716505\pi\) | |||||||
\(338\) | −20.7224 | − | 11.9641i | −1.12715 | − | 0.650759i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.75664 | − | 9.97079i | −0.312198 | − | 0.540742i | ||||
\(341\) | −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 | ||||||||
\(346\) | 1.87545i | 0.100825i | ||||||||
\(347\) | 27.0675i | 1.45306i | 0.687136 | + | 0.726529i | \(0.258868\pi\) | ||||
−0.687136 | + | 0.726529i | \(0.741132\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.3413 | + | 17.5176i | 1.62413 | + | 0.937694i | 0.985798 | + | 0.167936i | \(0.0537101\pi\) |
0.638336 | + | 0.769758i | \(0.279623\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.6200 | + | 33.9829i | 1.04575 | + | 1.81129i | ||||
\(353\) | −1.26256 | − | 2.18682i | −0.0671992 | − | 0.116392i | 0.830468 | − | 0.557066i | \(-0.188073\pi\) |
−0.897667 | + | 0.440674i | \(0.854740\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.40892 | + | 3.70019i | 0.340150 | + | 0.196386i | ||||
\(356\) | −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 | \(-0.605239\pi\) |
0.656809 | + | 0.754057i | \(0.271906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.18677 | + | 10.7158i | −0.325619 | + | 0.563989i | ||||
\(362\) | 28.1163 | 1.47776 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.4874 | + | 10.6737i | −0.967675 | + | 0.558688i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6714 | − | 6.73848i | 0.609242 | − | 0.351746i | −0.163427 | − | 0.986555i | \(-0.552255\pi\) |
0.772669 | + | 0.634809i | \(0.218921\pi\) | |||||||
\(368\) | −32.5131 | − | 18.7715i | −1.69486 | − | 0.978530i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.63278i | 0.344822i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.8820 | + | 20.5801i | −0.615224 | + | 1.06560i | 0.375121 | + | 0.926976i | \(0.377601\pi\) |
−0.990345 | + | 0.138624i | \(0.955732\pi\) | |||||||
\(374\) | 32.2664 | 1.66846 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.03166i | 0.104775i | ||||||||
\(377\) | 1.38886 | 0.0715297 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2283 | 1.09042 | 0.545211 | − | 0.838299i | \(-0.316449\pi\) | ||||
0.545211 | + | 0.838299i | \(0.316449\pi\) | |||||||
\(380\) | 9.62972i | 0.493994i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.7143 | −1.26450 | ||||||||
\(383\) | −6.47930 | + | 11.2225i | −0.331077 | + | 0.573442i | −0.982723 | − | 0.185081i | \(-0.940745\pi\) |
0.651646 | + | 0.758523i | \(0.274079\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2.90752i | − | 0.147989i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.81710 | − | 2.78116i | −0.244551 | − | 0.141192i | ||||
\(389\) | 9.48037 | − | 5.47350i | 0.480674 | − | 0.277517i | −0.240023 | − | 0.970767i | \(-0.577155\pi\) |
0.720697 | + | 0.693250i | \(0.243822\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.0353 | + | 12.1447i | −1.06380 | + | 0.614186i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.27338 | −0.467186 | ||||||||
\(395\) | −0.719472 | + | 1.24616i | −0.0362006 | + | 0.0627012i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.8856 | − | 14.9451i | 1.29916 | − | 0.750071i | 0.318901 | − | 0.947788i | \(-0.396686\pi\) |
0.980259 | + | 0.197717i | \(0.0633528\pi\) | |||||||
\(398\) | 10.4588 | − | 18.1151i | 0.524250 | − | 0.908028i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.04141 | + | 5.26788i | 0.152071 | + | 0.263394i | ||||
\(401\) | 16.6233 | + | 9.59744i | 0.830126 | + | 0.479273i | 0.853896 | − | 0.520444i | \(-0.174234\pi\) |
−0.0237698 | + | 0.999717i | \(0.507567\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.32242 | − | 4.02254i | −0.115688 | − | 0.200377i | ||||
\(404\) | 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 | ||||||||
\(409\) | − | 28.8372i | − | 1.42591i | −0.701212 | − | 0.712953i | \(-0.747357\pi\) | ||
0.701212 | − | 0.712953i | \(-0.252643\pi\) | |||||||
\(410\) | 15.4227i | 0.761673i | ||||||||
\(411\) | 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 | ||||
\(416\) | 1.55211 | + | 2.68834i | 0.0760986 | + | 0.131807i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.3720 | − | 13.4938i | −1.14316 | − | 0.660005i | ||||
\(419\) | −5.06390 | − | 8.77094i | −0.247388 | − | 0.428488i | 0.715412 | − | 0.698702i | \(-0.246239\pi\) |
−0.962800 | + | 0.270214i | \(0.912906\pi\) | |||||||
\(420\) | 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 | ||||
\(425\) | 3.93546 | 0.190898 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −17.4370 | + | 10.0673i | −0.842849 | + | 0.486619i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −38.5834 | + | 22.2762i | −1.86066 | + | 1.07425i | ||||
\(431\) | 9.39066 | + | 5.42170i | 0.452332 | + | 0.261154i | 0.708815 | − | 0.705395i | \(-0.249230\pi\) |
−0.256482 | + | 0.966549i | \(0.582564\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.0519i | 0.627233i | 0.949550 | + | 0.313616i | \(0.101541\pi\) | ||||
−0.949550 | + | 0.313616i | \(0.898459\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.685771 | + | 1.18779i | −0.0328425 | + | 0.0568849i | ||||
\(437\) | 20.3158 | 0.971835 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 31.9547i | − | 1.52511i | −0.646922 | − | 0.762557i | \(-0.723944\pi\) | ||
0.646922 | − | 0.762557i | \(-0.276056\pi\) | |||||||
\(440\) | −13.3208 | −0.635046 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.55255 | 0.121412 | ||||||||
\(443\) | 24.7969i | 1.17814i | 0.808083 | + | 0.589068i | \(0.200505\pi\) | ||||
−0.808083 | + | 0.589068i | \(0.799495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.9899 | 0.900208 | ||||||||
\(446\) | 2.98724 | − | 5.17406i | 0.141450 | − | 0.244999i | ||||
\(447\) | 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 | ||||
\(452\) | 6.12715 | − | 3.53751i | 0.288197 | − | 0.166390i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.7439 | + | 13.7085i | −1.11436 | + | 0.643374i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.3107 | 1.27754 | 0.638771 | − | 0.769397i | \(-0.279443\pi\) | ||||
0.638771 | + | 0.769397i | \(0.279443\pi\) | |||||||
\(458\) | 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 | −0.708430 | − | 0.705781i | \(-0.750596\pi\) |
0.965439 | + | 0.260628i | \(0.0839296\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.2346 | − | 21.1910i | −0.568591 | − | 0.984829i | −0.996706 | − | 0.0811042i | \(-0.974155\pi\) |
0.428115 | − | 0.903724i | \(-0.359178\pi\) | |||||||
\(464\) | 12.8935 | + | 7.44405i | 0.598564 | + | 0.345581i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.56029 | + | 7.89866i | 0.211251 | + | 0.365898i | ||||
\(467\) | 7.95241 | + | 13.7740i | 0.367994 | + | 0.637384i | 0.989252 | − | 0.146222i | \(-0.0467114\pi\) |
−0.621258 | + | 0.783606i | \(0.713378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.69451 | + | 5.01978i | 0.401048 | + | 0.231545i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.92754i | 0.318866i | ||||||||
\(473\) | − | 53.3667i | − | 2.45380i | ||||||
\(474\) | 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 | ||||
\(479\) | 6.92685 | + | 11.9976i | 0.316496 | + | 0.548187i | 0.979754 | − | 0.200204i | \(-0.0641604\pi\) |
−0.663259 | + | 0.748390i | \(0.730827\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.544315 | − | 0.314261i | −0.0248186 | − | 0.0143290i | ||||
\(482\) | 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 | 0.330020 | + | 0.943974i | \(0.392945\pi\) |
−0.982515 | + | 0.186182i | \(0.940389\pi\) | |||||||
\(488\) | −8.10822 | −0.367042 | ||||||||
\(489\) | 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 | ||||||||
\(493\) | 8.34181 | − | 4.81615i | 0.375696 | − | 0.216908i | ||||
\(494\) | −1.84893 | − | 1.06748i | −0.0831872 | − | 0.0480281i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 49.7911i | − | 2.23569i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.73333 | − | 3.00222i | 0.0775946 | − | 0.134398i | −0.824617 | − | 0.565691i | \(-0.808609\pi\) |
0.902212 | + | 0.431294i | \(0.141943\pi\) | |||||||
\(500\) | −13.9209 | −0.622561 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 2.14076i | − | 0.0955467i | ||||||
\(503\) | 28.2202 | 1.25828 | 0.629138 | − | 0.777293i | \(-0.283408\pi\) | ||||
0.629138 | + | 0.777293i | \(0.283408\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.8794 | −0.840124 | ||||||||
\(506\) | − | 82.7403i | − | 3.67825i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.0065 | −0.488335 | ||||||||
\(509\) | −17.9062 | + | 31.0144i | −0.793678 | + | 1.37469i | 0.129997 | + | 0.991514i | \(0.458503\pi\) |
−0.923675 | + | 0.383176i | \(0.874830\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.2599i | 1.07215i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 46.9111 | + | 27.0841i | 2.06916 | + | 1.19463i | ||||
\(515\) | −31.0823 | + | 17.9454i | −1.36965 | + | 0.790768i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.4147 | + | 6.01291i | −0.458036 | + | 0.264447i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.05379 | −0.0462119 | ||||||||
\(521\) | −13.4608 | + | 23.3148i | −0.589729 | + | 1.02144i | 0.404538 | + | 0.914521i | \(0.367432\pi\) |
−0.994268 | + | 0.106920i | \(0.965901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.82181 | − | 4.51593i | 0.342024 | − | 0.197468i | −0.319143 | − | 0.947707i | \(-0.603395\pi\) |
0.661167 | + | 0.750239i | \(0.270062\pi\) | |||||||
\(524\) | −5.86943 | + | 10.1662i | −0.256407 | + | 0.444110i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.8020 | + | 22.1737i | 0.558193 | + | 0.966819i | ||||
\(527\) | −27.8980 | − | 16.1069i | −1.21526 | − | 0.701629i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.6426 | + | 34.0220i | 0.854026 | + | 1.47922i | ||||
\(530\) | −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 | ||||||||
\(535\) | − | 33.7939i | − | 1.46104i | ||||||
\(536\) | − | 1.77113i | − | 0.0765010i | ||||||
\(537\) | 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 | 0.718078 | − | 0.695963i | \(-0.245022\pi\) |
−0.961760 | + | 0.273892i | \(0.911689\pi\) | |||||||
\(542\) | 6.11710 | + | 10.5951i | 0.262752 | + | 0.455100i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.6447 | + | 10.7646i | 0.799387 | + | 0.461526i | ||||
\(545\) | −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 | ||||
\(551\) | −8.05647 | −0.343217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 36.3061 | − | 20.9613i | 1.54250 | − | 0.890562i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.3410 | + | 14.6306i | −1.07470 | + | 0.620478i | ||||
\(557\) | 6.29167 | + | 3.63249i | 0.266586 | + | 0.153914i | 0.627335 | − | 0.778749i | \(-0.284146\pi\) |
−0.360749 | + | 0.932663i | \(0.617479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.22177i | − | 0.178562i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.8848 | − | 36.1736i | 0.880973 | − | 1.52589i | ||||
\(563\) | −23.0818 | −0.972780 | −0.486390 | − | 0.873742i | \(-0.661687\pi\) | ||||
−0.486390 | + | 0.873742i | \(0.661687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.8748i | 0.499575i | ||||||||
\(566\) | −35.4561 | −1.49033 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.79889 | −0.117439 | ||||||||
\(569\) | − | 17.9535i | − | 0.752651i | −0.926487 | − | 0.376326i | \(-0.877187\pi\) | ||
0.926487 | − | 0.376326i | \(-0.122813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0847 | −0.589425 | −0.294713 | − | 0.955586i | \(-0.595224\pi\) | ||||
−0.294713 | + | 0.955586i | \(0.595224\pi\) | |||||||
\(572\) | −1.85819 | + | 3.21849i | −0.0776950 | + | 0.134572i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 10.0916i | − | 0.420851i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0392 | + | 15.0337i | 1.08403 | + | 0.625862i | 0.931979 | − | 0.362511i | \(-0.118081\pi\) |
0.152046 | + | 0.988373i | \(0.451414\pi\) | |||||||
\(578\) | −12.1841 | + | 7.03447i | −0.506790 | + | 0.292595i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.1393 | − | 5.85392i | 0.421011 | − | 0.243071i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.2295 | 1.12773 | ||||||||
\(584\) | 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 | \(0.435164\pi\) |
−0.949264 | + | 0.314481i | \(0.898169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4719 | + | 23.3339i | 0.555098 | + | 0.961459i | ||||
\(590\) | 29.6464 | + | 17.1164i | 1.22052 | + | 0.704670i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.36877 | − | 5.83489i | −0.138456 | − | 0.239812i | ||||
\(593\) | −1.02158 | − | 1.76943i | −0.0419514 | − | 0.0726620i | 0.844287 | − | 0.535891i | \(-0.180024\pi\) |
−0.886239 | + | 0.463229i | \(0.846691\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.3507 | + | 11.7495i | 0.833598 | + | 0.481278i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 6.54547i | − | 0.267664i | ||||||
\(599\) | 18.2296i | 0.744840i | 0.928064 | + | 0.372420i | \(0.121472\pi\) | ||||
−0.928064 | + | 0.372420i | \(0.878528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.1713 | − | 18.5741i | −1.31230 | − | 0.757654i | −0.329820 | − | 0.944044i | \(-0.606988\pi\) |
−0.982476 | + | 0.186390i | \(0.940321\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.48002 | − | 2.56346i | −0.0602210 | − | 0.104306i | ||||
\(605\) | −25.6428 | − | 44.4146i | −1.04253 | − | 1.80571i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.1730 | − | 9.91482i | −0.697030 | − | 0.402430i | 0.109211 | − | 0.994019i | \(-0.465168\pi\) |
−0.806240 | + | 0.591588i | \(0.798501\pi\) | |||||||
\(608\) | −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 | −0.708994 | − | 0.705214i | \(-0.750851\pi\) |
0.965231 | + | 0.261400i | \(0.0841840\pi\) | |||||||
\(614\) | 53.7381 | 2.16869 | ||||||||
\(615\) | 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 | ||||||||
\(619\) | −0.231999 | + | 0.133945i | −0.00932485 | + | 0.00538370i | −0.504655 | − | 0.863321i | \(-0.668380\pi\) |
0.495330 | + | 0.868705i | \(0.335047\pi\) | |||||||
\(620\) | −33.9094 | − | 19.5776i | −1.36183 | − | 0.786255i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.8305i | 0.995611i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8792 | − | 25.7716i | 0.595169 | − | 1.03086i | ||||
\(626\) | −58.9641 | −2.35668 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.5290i | 0.499961i | ||||||||
\(629\) | −4.35905 | −0.173807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.7899 | 1.50439 | 0.752197 | − | 0.658938i | \(-0.228994\pi\) | ||||
0.752197 | + | 0.658938i | \(0.228994\pi\) | |||||||
\(632\) | − | 0.544222i | − | 0.0216480i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −37.5112 | −1.48976 | ||||||||
\(635\) | 9.23671 | − | 15.9984i | 0.366547 | − | 0.634879i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 32.8117i | 1.29903i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.9234 | − | 9.19336i | −0.629426 | − | 0.363400i | ||||
\(641\) | 29.7991 | − | 17.2045i | 1.17699 | − | 0.679537i | 0.221676 | − | 0.975120i | \(-0.428847\pi\) |
0.955317 | + | 0.295583i | \(0.0955140\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.676278 | − | 0.390449i | 0.0266698 | − | 0.0153978i | −0.486606 | − | 0.873622i | \(-0.661765\pi\) |
0.513276 | + | 0.858224i | \(0.328432\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.8068 | −0.582566 | ||||||||
\(647\) | −9.82182 | + | 17.0119i | −0.386136 | + | 0.668807i | −0.991926 | − | 0.126818i | \(-0.959524\pi\) |
0.605790 | + | 0.795624i | \(0.292857\pi\) | |||||||
\(648\) | 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 | ||||
\(653\) | 2.77600 | + | 1.60272i | 0.108633 | + | 0.0627194i | 0.553332 | − | 0.832961i | \(-0.313356\pi\) |
−0.444699 | + | 0.895680i | \(0.646689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.85129 | − | 17.0629i | −0.384922 | − | 0.666704i | ||||
\(656\) | −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 | ||||||||
\(661\) | 32.3882i | 1.25976i | 0.776694 | + | 0.629878i | \(0.216895\pi\) | ||||
−0.776694 | + | 0.629878i | \(0.783105\pi\) | |||||||
\(662\) | 2.33227i | 0.0906463i | ||||||||
\(663\) | 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 | ||||
\(668\) | 5.96768 | + | 10.3363i | 0.230897 | + | 0.399925i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.57953 | − | 4.37605i | −0.292823 | − | 0.169061i | ||||
\(671\) | −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 | ||||
\(677\) | −50.3311 | −1.93438 | −0.967190 | − | 0.254053i | \(-0.918236\pi\) | ||||
−0.967190 | + | 0.254053i | \(0.918236\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.32935 | + | 3.65425i | −0.242719 | + | 0.140134i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 95.0324 | − | 54.8670i | 3.63898 | − | 2.10097i | ||||
\(683\) | −11.9031 | − | 6.87227i | −0.455460 | − | 0.262960i | 0.254673 | − | 0.967027i | \(-0.418032\pi\) |
−0.710133 | + | 0.704067i | \(0.751365\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.9909i | 1.10769i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 22.6280 | − | 39.1929i | 0.862685 | − | 1.49421i | ||||
\(689\) | 2.15409 | 0.0820643 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 29.3673i | − | 1.11719i | −0.829442 | − | 0.558593i | \(-0.811342\pi\) | ||
0.829442 | − | 0.558593i | \(-0.188658\pi\) | |||||||
\(692\) | −1.49813 | −0.0569504 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −50.5874 | −1.92027 | ||||||||
\(695\) | − | 49.1123i | − | 1.86294i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.1358 | −0.383920 | ||||||||
\(698\) | −32.7392 | + | 56.7060i | −1.23920 | + | 2.14635i | ||||
\(699\) | 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 | ||||
\(704\) | −17.2923 | + | 9.98371i | −0.651728 | + | 0.376275i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.08702 | − | 2.35964i | 0.153817 | − | 0.0888063i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.3326 | −0.425604 | −0.212802 | − | 0.977095i | \(-0.568259\pi\) | ||||
−0.212802 | + | 0.977095i | \(0.568259\pi\) | |||||||
\(710\) | −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 | ||||
\(716\) | −1.90755 | − | 1.10132i | −0.0712884 | − | 0.0411584i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.79136 | + | 11.7630i | 0.253451 | + | 0.438991i | ||||
\(719\) | −18.0647 | − | 31.2890i | −0.673700 | − | 1.16688i | −0.976847 | − | 0.213939i | \(-0.931371\pi\) |
0.303147 | − | 0.952944i | \(-0.401963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −20.0271 | − | 11.5627i | −0.745333 | − | 0.430318i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22.4596i | 0.834703i | ||||||||
\(725\) | 4.00197i | 0.148629i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.20547 | − | 3.58273i | −0.230148 | − | 0.132876i | 0.380492 | − | 0.924784i | \(-0.375755\pi\) |
−0.610640 | + | 0.791908i | \(0.709088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.9485 | − | 34.5518i | −0.738327 | − | 1.27882i | ||||
\(731\) | −14.6399 | − | 25.3570i | −0.541475 | − | 0.937862i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.4391 | − | 23.9249i | −1.53059 | − | 0.883685i | −0.999335 | − | 0.0364726i | \(-0.988388\pi\) |
−0.531253 | − | 0.847213i | \(-0.678279\pi\) | |||||||
\(734\) | 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 | −0.971951 | − | 0.235185i | \(-0.924430\pi\) |
0.689652 | + | 0.724141i | \(0.257764\pi\) | |||||||
\(740\) | −5.29833 | −0.194771 | ||||||||
\(741\) | 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 | ||||||||
\(745\) | −34.1568 | + | 19.7204i | −1.25141 | + | 0.722501i | ||||
\(746\) | −38.4630 | − | 22.2066i | −1.40823 | − | 0.813042i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 25.7747i | 0.942417i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.9449 | + | 29.3494i | −0.618327 | + | 1.07097i | 0.371463 | + | 0.928448i | \(0.378856\pi\) |
−0.989791 | + | 0.142527i | \(0.954477\pi\) | |||||||
\(752\) | −10.1981 | −0.371887 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.59568i | 0.0945293i | ||||||||
\(755\) | 4.96814 | 0.180809 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.73237 | −0.208346 | −0.104173 | − | 0.994559i | \(-0.533220\pi\) | ||||
−0.104173 | + | 0.994559i | \(0.533220\pi\) | |||||||
\(758\) | 39.6743i | 1.44103i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.11284 | 0.221736 | ||||||||
\(761\) | −13.2666 | + | 22.9784i | −0.480914 | + | 0.832968i | −0.999760 | − | 0.0218999i | \(-0.993028\pi\) |
0.518846 | + | 0.854868i | \(0.326362\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 19.7420i | − | 0.714242i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.9741 | − | 12.1094i | −0.757825 | − | 0.437531i | ||||
\(767\) | −2.80929 | + | 1.62194i | −0.101438 | + | 0.0585650i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.3944 | − | 13.5068i | 0.843623 | − | 0.487066i | −0.0148711 | − | 0.999889i | \(-0.504734\pi\) |
0.858494 | + | 0.512823i | \(0.171400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.32256 | 0.0835906 | ||||||||
\(773\) | −11.3009 | + | 19.5737i | −0.406464 | + | 0.704016i | −0.994491 | − | 0.104826i | \(-0.966572\pi\) |
0.588027 | + | 0.808841i | \(0.299905\pi\) | |||||||
\(774\) | 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 | ||||
\(779\) | 7.34180 | + | 4.23879i | 0.263047 | + | 0.151870i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.28359 | − | 14.3476i | −0.296410 | − | 0.513398i | ||||
\(782\) | −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 | ||||||||
\(787\) | 26.1960i | 0.933787i | 0.884314 | + | 0.466893i | \(0.154627\pi\) | ||||
−0.884314 | + | 0.466893i | \(0.845373\pi\) | |||||||
\(788\) | − | 7.40767i | − | 0.263887i | ||||||
\(789\) | 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 | ||||
\(794\) | 27.9314 | + | 48.3785i | 0.991247 | + | 1.71689i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.4705 | + | 8.35456i | 0.512894 | + | 0.296120i | ||||
\(797\) | 5.96560 | + | 10.3327i | 0.211312 | + | 0.366004i | 0.952126 | − | 0.305707i | \(-0.0988929\pi\) |
−0.740813 | + | 0.671711i | \(0.765560\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | 47.7904 | 1.68648 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.51788 | − | 4.34045i | 0.264806 | − | 0.152886i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.18375 | − | 3.57019i | 0.217543 | − | 0.125599i | ||||
\(809\) | −22.9399 | − | 13.2443i | −0.806522 | − | 0.465646i | 0.0392244 | − | 0.999230i | \(-0.487511\pi\) |
−0.845747 | + | 0.533585i | \(0.820845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.7419i | − | 0.482544i | −0.970458 | − | 0.241272i | \(-0.922435\pi\) | ||
0.970458 | − | 0.241272i | \(-0.0775646\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.42439 | − | 12.8594i | 0.260225 | − | 0.450722i | ||||
\(815\) | 2.69143 | 0.0942766 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.4896i | 0.856783i | ||||||||
\(818\) | 53.8949 | 1.88439 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.3198 | −0.430226 | ||||||||
\(821\) | − | 13.5669i | − | 0.473489i | −0.971572 | − | 0.236744i | \(-0.923920\pi\) | ||
0.971572 | − | 0.236744i | \(-0.0760804\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6971 | 0.512310 | 0.256155 | − | 0.966636i | \(-0.417544\pi\) | ||||
0.256155 | + | 0.966636i | \(0.417544\pi\) | |||||||
\(824\) | 6.78711 | − | 11.7556i | 0.236440 | − | 0.409527i | ||||
\(825\) | 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 | 0.159675 | − | 0.987170i | \(-0.448955\pi\) |
−0.775077 | + | 0.631867i | \(0.782289\pi\) | |||||||
\(830\) | 34.3530 | − | 19.8337i | 1.19241 | − | 0.688439i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.36797 | + | 0.789798i | −0.0474258 | + | 0.0273813i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.0324 | −0.693249 | ||||||||
\(836\) | 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 | \(-0.440227\pi\) |
0.757462 | − | 0.652880i | \(-0.226439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.60247 | − | 16.6320i | −0.331120 | − | 0.573516i | ||||
\(842\) | 41.1416 | + | 23.7531i | 1.41783 | + | 0.818586i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.4661 | − | 19.8598i | −0.394678 | − | 0.683602i | ||||
\(845\) | 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 | ||||||||
\(850\) | 7.35513i | 0.252279i | ||||||||
\(851\) | 11.1779i | 0.383172i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.0684 | − | 6.39037i | −0.378976 | − | 0.218802i | 0.298396 | − | 0.954442i | \(-0.403548\pi\) |
−0.677373 | + | 0.735640i | \(0.736882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.39058 | + | 11.0688i | 0.218426 | + | 0.378324i | ||||
\(857\) | 9.16200 | + | 15.8691i | 0.312968 | + | 0.542077i | 0.979003 | − | 0.203844i | \(-0.0653434\pi\) |
−0.666035 | + | 0.745920i | \(0.732010\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.4579 | + | 19.3169i | 1.14157 | + | 0.659085i | 0.946819 | − | 0.321768i | \(-0.104277\pi\) |
0.194750 | + | 0.980853i | \(0.437610\pi\) | |||||||
\(860\) | −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 | \(-0.574926\pi\) |
0.725534 | + | 0.688186i | \(0.241593\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.25724 | − | 2.17760i | 0.0427473 | − | 0.0740405i | ||||
\(866\) | −24.3931 | −0.828912 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.78978 | − | 1.61068i | 0.0946367 | − | 0.0546385i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.718235 | − | 0.414673i | 0.0243365 | − | 0.0140507i | ||||
\(872\) | 0.753996 | + | 0.435320i | 0.0255335 | + | 0.0147418i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 37.9689i | 1.28432i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.7617 | + | 29.0321i | −0.566002 | + | 0.980345i | 0.430953 | + | 0.902374i | \(0.358177\pi\) |
−0.996956 | + | 0.0779707i | \(0.975156\pi\) | |||||||
\(878\) | 59.7213 | 2.01549 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 66.8652i | − | 2.25403i | ||||||
\(881\) | −28.6657 | −0.965771 | −0.482885 | − | 0.875684i | \(-0.660411\pi\) | ||||
−0.482885 | + | 0.875684i | \(0.660411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.2091 | −1.28584 | −0.642919 | − | 0.765935i | \(-0.722277\pi\) | ||||
−0.642919 | + | 0.765935i | \(0.722277\pi\) | |||||||
\(884\) | 2.03900i | 0.0685790i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −46.3439 | −1.55695 | ||||||||
\(887\) | 17.5914 | − | 30.4692i | 0.590662 | − | 1.02306i | −0.403481 | − | 0.914988i | \(-0.632200\pi\) |
0.994143 | − | 0.108069i | \(-0.0344666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 35.4910i | 1.18966i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.13309 | + | 2.38624i | 0.138386 | + | 0.0798972i | ||||
\(893\) | 4.77921 | − | 2.75928i | 0.159930 | − | 0.0923358i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.20164 | − | 1.84847i | 0.107019 | − | 0.0617875i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.7371 | 0.858857 | ||||||||
\(899\) | 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 | ||||
\(905\) | −32.6459 | − | 18.8481i | −1.08519 | − | 0.626533i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.2977 | + | 36.8887i | 0.707179 | + | 1.22487i | 0.965899 | + | 0.258918i | \(0.0833660\pi\) |
−0.258720 | + | 0.965952i | \(0.583301\pi\) | |||||||
\(908\) | −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 | ||||||||
\(913\) | 47.5154i | 1.57253i | ||||||||
\(914\) | 51.0420i | 1.68832i | ||||||||
\(915\) | 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 | 0.700984 | + | 0.713177i | \(0.252744\pi\) |
0.267137 | + | 0.963658i | \(0.413922\pi\) | |||||||
\(920\) | 9.37054 | + | 16.2303i | 0.308938 | + | 0.535096i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.8630 | + | 10.3132i | 0.588287 | + | 0.339647i | ||||
\(923\) | −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 | ||||
\(929\) | 14.3823 | 0.471868 | 0.235934 | − | 0.971769i | \(-0.424185\pi\) | ||||
0.235934 | + | 0.971769i | \(0.424185\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.30952 | + | 3.64281i | −0.206675 | + | 0.119324i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −25.7427 | + | 14.8626i | −0.842327 | + | 0.486318i | ||||
\(935\) | −37.4646 | − | 21.6302i | −1.22522 | − | 0.707384i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.2981i | 1.44716i | 0.690243 | + | 0.723578i | \(0.257504\pi\) | ||||
−0.690243 | + | 0.723578i | \(0.742496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.00985 | + | 6.94526i | −0.130787 | + | 0.226529i | ||||
\(941\) | 14.8880 | 0.485335 | 0.242667 | − | 0.970110i | \(-0.421978\pi\) | ||||
0.242667 | + | 0.970110i | \(0.421978\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.9910i | 0.846384i | ||||||||
\(944\) | −34.7734 | −1.13178 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 99.7390 | 3.24280 | ||||||||
\(947\) | 41.9552i | 1.36336i | 0.731650 | + | 0.681681i | \(0.238751\pi\) | ||||
−0.731650 | + | 0.681681i | \(0.761249\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.78063 | 0.122724 | ||||||||
\(950\) | 3.07592 | − | 5.32765i | 0.0997960 | − | 0.172852i | ||||
\(951\) | 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 | ||||
\(956\) | 20.3415 | − | 11.7442i | 0.657892 | − | 0.379834i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.4228 | + | 12.9458i | −0.724449 | + | 0.418261i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −78.5553 | −2.53404 | ||||||||
\(962\) | 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 | \(0.954746\pi\) | |||||||
\(968\) | 16.7980 | + | 9.69835i | 0.539909 | + | 0.311717i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.72403 | + | 15.1105i | 0.280112 | + | 0.485168i | ||||
\(971\) | 21.6869 | + | 37.5628i | 0.695965 | + | 1.20545i | 0.969854 | + | 0.243685i | \(0.0783564\pi\) |
−0.273890 | + | 0.961761i | \(0.588310\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −46.6120 | − | 26.9114i | −1.49354 | − | 0.862298i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 40.7000i | − | 1.30277i | ||||||
\(977\) | 12.0331i | 0.384974i | 0.981300 | + | 0.192487i | \(0.0616553\pi\) | ||||
−0.981300 | + | 0.192487i | \(0.938345\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | 3.14829 | + | 5.45300i | 0.100415 | + | 0.173924i | 0.911856 | − | 0.410511i | \(-0.134650\pi\) |
−0.811441 | + | 0.584435i | \(0.801316\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.7674 | + | 6.21654i | 0.343077 | + | 0.198075i | ||||
\(986\) | 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 | 0.466176 | + | 0.884692i | \(0.345631\pi\) |
−0.999254 | + | 0.0386256i | \(0.987702\pi\) | |||||||
\(992\) | 73.2178 | 2.32467 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.2874 | + | 14.0223i | −0.769963 | + | 0.444538i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.74838 | + | 5.62823i | −0.308734 | + | 0.178248i | −0.646360 | − | 0.763033i | \(-0.723710\pi\) |
0.337626 | + | 0.941280i | \(0.390376\pi\) | |||||||
\(998\) | 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.i.d.521.7 | 48 | ||
3.2 | odd | 2 | 441.2.i.d.227.6 | 48 | |||
7.2 | even | 3 | 1323.2.s.d.656.19 | 48 | |||
7.3 | odd | 6 | 1323.2.o.e.440.5 | 48 | |||
7.4 | even | 3 | 1323.2.o.e.440.6 | 48 | |||
7.5 | odd | 6 | 1323.2.s.d.656.20 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.i.d.521.22 | 48 | ||
9.4 | even | 3 | 441.2.s.d.374.6 | 48 | |||
9.5 | odd | 6 | 1323.2.s.d.962.20 | 48 | |||
21.2 | odd | 6 | 441.2.s.d.362.5 | 48 | |||
21.5 | even | 6 | 441.2.s.d.362.6 | 48 | |||
21.11 | odd | 6 | 441.2.o.e.146.19 | ✓ | 48 | ||
21.17 | even | 6 | 441.2.o.e.146.20 | yes | 48 | ||
21.20 | even | 2 | 441.2.i.d.227.5 | 48 | |||
63.4 | even | 3 | 441.2.o.e.293.20 | yes | 48 | ||
63.5 | even | 6 | inner | 1323.2.i.d.1097.7 | 48 | ||
63.13 | odd | 6 | 441.2.s.d.374.5 | 48 | |||
63.23 | odd | 6 | inner | 1323.2.i.d.1097.22 | 48 | ||
63.31 | odd | 6 | 441.2.o.e.293.19 | yes | 48 | ||
63.32 | odd | 6 | 1323.2.o.e.881.5 | 48 | |||
63.40 | odd | 6 | 441.2.i.d.68.20 | 48 | |||
63.41 | even | 6 | 1323.2.s.d.962.19 | 48 | |||
63.58 | even | 3 | 441.2.i.d.68.19 | 48 | |||
63.59 | even | 6 | 1323.2.o.e.881.6 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.19 | 48 | 63.58 | even | 3 | |||
441.2.i.d.68.20 | 48 | 63.40 | odd | 6 | |||
441.2.i.d.227.5 | 48 | 21.20 | even | 2 | |||
441.2.i.d.227.6 | 48 | 3.2 | odd | 2 | |||
441.2.o.e.146.19 | ✓ | 48 | 21.11 | odd | 6 | ||
441.2.o.e.146.20 | yes | 48 | 21.17 | even | 6 | ||
441.2.o.e.293.19 | yes | 48 | 63.31 | odd | 6 | ||
441.2.o.e.293.20 | yes | 48 | 63.4 | even | 3 | ||
441.2.s.d.362.5 | 48 | 21.2 | odd | 6 | |||
441.2.s.d.362.6 | 48 | 21.5 | even | 6 | |||
441.2.s.d.374.5 | 48 | 63.13 | odd | 6 | |||
441.2.s.d.374.6 | 48 | 9.4 | even | 3 | |||
1323.2.i.d.521.7 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.i.d.521.22 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.i.d.1097.7 | 48 | 63.5 | even | 6 | inner | ||
1323.2.i.d.1097.22 | 48 | 63.23 | odd | 6 | inner | ||
1323.2.o.e.440.5 | 48 | 7.3 | odd | 6 | |||
1323.2.o.e.440.6 | 48 | 7.4 | even | 3 | |||
1323.2.o.e.881.5 | 48 | 63.32 | odd | 6 | |||
1323.2.o.e.881.6 | 48 | 63.59 | even | 6 | |||
1323.2.s.d.656.19 | 48 | 7.2 | even | 3 | |||
1323.2.s.d.656.20 | 48 | 7.5 | odd | 6 | |||
1323.2.s.d.962.19 | 48 | 63.41 | even | 6 | |||
1323.2.s.d.962.20 | 48 | 9.5 | odd | 6 |