Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(440,1323)]
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, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.o (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 | 440.6 | ||
Character | \(\chi\) | \(=\) | 1323.440 |
Dual form | 1323.2.o.e.881.6 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61855 | − | 0.934468i | −1.14449 | − | 0.660769i | −0.196948 | − | 0.980414i | \(-0.563103\pi\) |
−0.947537 | + | 0.319645i | \(0.896436\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.746462 | + | 1.29291i | 0.373231 | + | 0.646455i | ||||
\(5\) | 1.25287 | + | 2.17003i | 0.560299 | + | 0.970467i | 0.997470 | + | 0.0710881i | \(0.0226472\pi\) |
−0.437171 | + | 0.899378i | \(0.644020\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.947692i | 0.335060i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 4.68306i | − | 1.48091i | ||||||
\(11\) | 4.85803 | + | 2.80479i | 1.46475 | + | 0.845675i | 0.999225 | − | 0.0393590i | \(-0.0125316\pi\) |
0.465527 | + | 0.885034i | \(0.345865\pi\) | |||||||
\(12\) | 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 | ||||||||
\(16\) | 2.37851 | − | 4.11970i | 0.594628 | − | 1.02993i | ||||
\(17\) | 3.07770 | 0.746451 | 0.373226 | − | 0.927741i | \(-0.378252\pi\) | ||||
0.373226 | + | 0.927741i | \(0.378252\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.57419i | 0.590560i | 0.955411 | + | 0.295280i | \(0.0954130\pi\) | ||||
−0.955411 | + | 0.295280i | \(0.904587\pi\) | |||||||
\(20\) | −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 | \(-0.974261\pi\) |
−0.428413 | + | 0.903583i | \(0.640927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.639351 | + | 1.10739i | −0.127870 | + | 0.221478i | ||||
\(26\) | 0.829370 | 0.162653 | ||||||||
\(27\) | 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 | 0.643370 | − | 0.765556i | \(-0.277536\pi\) |
0.984675 | − | 0.174397i | \(-0.0557975\pi\) | |||||||
\(32\) | −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 | ||||||||
\(37\) | −1.41634 | −0.232844 | −0.116422 | − | 0.993200i | \(-0.537143\pi\) | ||||
−0.116422 | + | 0.993200i | \(0.537143\pi\) | |||||||
\(38\) | 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 | \(0.908322\pi\) | |||||||
\(44\) | 8.37467i | 1.26253i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.7498 | 2.17474 | ||||||||
\(47\) | −1.07190 | + | 1.85659i | −0.156353 | + | 0.270811i | −0.933551 | − | 0.358445i | \(-0.883307\pi\) |
0.777198 | + | 0.629256i | \(0.216640\pi\) | |||||||
\(48\) | 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 | ||||
\(53\) | 4.85412i | 0.666764i | 0.942792 | + | 0.333382i | \(0.108190\pi\) | ||||
−0.942792 | + | 0.333382i | \(0.891810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.0561i | 1.89532i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.92461 | + | 5.06558i | 0.384020 | + | 0.665143i | ||||
\(59\) | −3.65496 | − | 6.33057i | −0.475835 | − | 0.824170i | 0.523782 | − | 0.851852i | \(-0.324521\pi\) |
−0.999617 | + | 0.0276824i | \(0.991187\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.40950 | − | 4.27788i | −0.948690 | − | 0.547726i | −0.0560160 | − | 0.998430i | \(-0.517840\pi\) |
−0.892674 | + | 0.450704i | \(0.851173\pi\) | |||||||
\(62\) | −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 | 0.917444 | − | 0.397865i | \(-0.130249\pi\) |
−0.803284 | + | 0.595597i | \(0.796916\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 8.51943i | 0.997124i | 0.866854 | + | 0.498562i | \(0.166138\pi\) | ||||
−0.866854 | + | 0.498562i | \(0.833862\pi\) | |||||||
\(74\) | 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 | ||||||||
\(79\) | 0.287130 | − | 0.497324i | 0.0323047 | − | 0.0559533i | −0.849421 | − | 0.527716i | \(-0.823049\pi\) |
0.881726 | + | 0.471762i | \(0.156382\pi\) | |||||||
\(80\) | 11.9198 | 1.33268 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 6.15497i | − | 0.679702i | ||||||
\(83\) | 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 | ||||
\(89\) | −7.57858 | −0.803328 | −0.401664 | − | 0.915787i | \(-0.631568\pi\) | ||||
−0.401664 | + | 0.915787i | \(0.631568\pi\) | |||||||
\(90\) | 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 | 0.654781 | − | 0.755818i | \(-0.272761\pi\) |
−0.327167 | + | 0.944966i | \(0.606094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.90901 | −0.190901 | ||||||||
\(101\) | −3.76725 | + | 6.52506i | −0.374855 | + | 0.649268i | −0.990305 | − | 0.138908i | \(-0.955641\pi\) |
0.615450 | + | 0.788176i | \(0.288974\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4045 | − | 7.16173i | 1.22225 | − | 0.705666i | 0.256853 | − | 0.966451i | \(-0.417315\pi\) |
0.965397 | + | 0.260784i | \(0.0839812\pi\) | |||||||
\(104\) | −0.210276 | − | 0.364210i | −0.0206193 | − | 0.0357137i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.53602 | − | 7.85662i | 0.440577 | − | 0.763102i | ||||
\(107\) | 13.4866i | 1.30380i | 0.758305 | + | 0.651900i | \(0.226028\pi\) | ||||
−0.758305 | + | 0.651900i | \(0.773972\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.918695 | −0.0879950 | −0.0439975 | − | 0.999032i | \(-0.514009\pi\) | ||||
−0.0439975 | + | 0.999032i | \(0.514009\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −17.1261 | − | 9.88775i | −1.59702 | − | 0.922037i | ||||
\(116\) | − | 4.67242i | − | 0.433823i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.6618i | 1.25767i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2337 | + | 17.7252i | 0.930332 | + | 1.61138i | ||||
\(122\) | 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 | ||||
\(131\) | 3.93150 | + | 6.80955i | 0.343497 | + | 0.594953i | 0.985079 | − | 0.172100i | \(-0.0550553\pi\) |
−0.641583 | + | 0.767054i | \(0.721722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 3.49283i | − | 0.301734i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.91671i | 0.250106i | ||||||||
\(137\) | 10.0198 | + | 5.78491i | 0.856046 | + | 0.494238i | 0.862686 | − | 0.505740i | \(-0.168780\pi\) |
−0.00664016 | + | 0.999978i | \(0.502114\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | 2.75984 | − | 4.78018i | 0.231600 | − | 0.401144i | ||||
\(143\) | −2.48933 | −0.208169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.84221i | − | 0.651260i | ||||||
\(146\) | 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 | \(-0.443630\pi\) |
0.940565 | + | 0.339615i | \(0.110297\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.991353 | − | 1.71707i | 0.0806752 | − | 0.139734i | −0.822865 | − | 0.568237i | \(-0.807626\pi\) |
0.903540 | + | 0.428503i | \(0.140959\pi\) | |||||||
\(152\) | −2.43954 | −0.197873 | ||||||||
\(153\) | 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 | −0.761150 | − | 0.648576i | \(-0.775365\pi\) |
0.181108 | + | 0.983463i | \(0.442031\pi\) | |||||||
\(158\) | −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 | ||||||||
\(163\) | −1.07411 | −0.0841306 | −0.0420653 | − | 0.999115i | \(-0.513394\pi\) | ||||
−0.0420653 | + | 0.999115i | \(0.513394\pi\) | |||||||
\(164\) | −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 | ||||
\(170\) | − | 14.4130i | − | 1.10543i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.2030 | −1.08297 | ||||||||
\(173\) | −0.501744 | + | 0.869046i | −0.0381469 | + | 0.0660723i | −0.884468 | − | 0.466600i | \(-0.845479\pi\) |
0.846322 | + | 0.532672i | \(0.178812\pi\) | |||||||
\(174\) | 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 | ||||
\(179\) | − | 1.47539i | − | 0.110276i | −0.998479 | − | 0.0551379i | \(-0.982440\pi\) | ||
0.998479 | − | 0.0551379i | \(-0.0175599\pi\) | |||||||
\(180\) | 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 | ||||
\(185\) | −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 | \(-0.492123\pi\) |
−0.853388 | + | 0.521276i | \(0.825456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.777855 | + | 1.34728i | 0.0559912 | + | 0.0969796i | 0.892662 | − | 0.450726i | \(-0.148835\pi\) |
−0.836671 | + | 0.547705i | \(0.815501\pi\) | |||||||
\(194\) | −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 | ||||||||
\(199\) | 11.1922i | 0.793394i | 0.917950 | + | 0.396697i | \(0.129844\pi\) | ||||
−0.917950 | + | 0.396697i | \(0.870156\pi\) | |||||||
\(200\) | −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 | ||||||||
\(205\) | −4.12606 | + | 7.14655i | −0.288177 | + | 0.499137i | ||||
\(206\) | −26.7696 | −1.86513 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.11100i | 0.146372i | ||||||||
\(209\) | −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 | ||||
\(215\) | −23.8383 | −1.62576 | ||||||||
\(216\) | 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 | 0.404433 | − | 0.914568i | \(-0.367469\pi\) |
−0.589822 | + | 0.807533i | \(0.700802\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.85695 | 0.589156 | ||||||||
\(227\) | 7.33494 | − | 12.7045i | 0.486837 | − | 0.843227i | −0.513048 | − | 0.858360i | \(-0.671484\pi\) |
0.999885 | + | 0.0151329i | \(0.00481714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.92550 | − | 1.68904i | 0.193322 | − | 0.111615i | −0.400215 | − | 0.916421i | \(-0.631064\pi\) |
0.593537 | + | 0.804807i | \(0.297731\pi\) | |||||||
\(230\) | 18.4796 | + | 32.0076i | 1.21851 | + | 2.11052i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.48300 | − | 2.56863i | 0.0973637 | − | 0.168639i | ||||
\(233\) | 4.88009i | 0.319706i | 0.987141 | + | 0.159853i | \(0.0511020\pi\) | ||||
−0.987141 | + | 0.159853i | \(0.948898\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.37180 | −0.350418 | ||||||||
\(236\) | 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 | ||||||||
\(241\) | −0.666305 | − | 0.384691i | −0.0429205 | − | 0.0247801i | 0.478386 | − | 0.878150i | \(-0.341222\pi\) |
−0.521307 | + | 0.853369i | \(0.674555\pi\) | |||||||
\(242\) | − | 38.2521i | − | 2.45894i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 12.7731i | − | 0.817714i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.571169 | − | 0.989293i | −0.0363426 | − | 0.0629472i | ||||
\(248\) | 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 | \(-0.511509\pi\) | ||||
−0.0361498 | + | 0.999346i | \(0.511509\pi\) | |||||||
\(252\) | 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 | ||||
\(257\) | 14.4917 | + | 25.1004i | 0.903969 | + | 1.56572i | 0.822295 | + | 0.569061i | \(0.192693\pi\) |
0.0816738 | + | 0.996659i | \(0.473973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1.66007i | − | 0.102953i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 14.6954i | − | 0.907887i | ||||||
\(263\) | −11.8643 | − | 6.84988i | −0.731586 | − | 0.422381i | 0.0874160 | − | 0.996172i | \(-0.472139\pi\) |
−0.819002 | + | 0.573790i | \(0.805472\pi\) | |||||||
\(264\) | 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 | ||||
\(269\) | −10.4795 | −0.638944 | −0.319472 | − | 0.947596i | \(-0.603506\pi\) | ||||
−0.319472 | + | 0.947596i | \(0.603506\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.54607i | 0.397646i | 0.980035 | + | 0.198823i | \(0.0637118\pi\) | ||||
−0.980035 | + | 0.198823i | \(0.936288\pi\) | |||||||
\(272\) | 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 | 0.302911 | + | 0.953019i | \(0.402041\pi\) |
−0.976794 | + | 0.214181i | \(0.931292\pi\) | |||||||
\(278\) | −36.6311 | −2.19699 | ||||||||
\(279\) | 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 | 0.0753848 | − | 0.997155i | \(-0.475981\pi\) |
0.901254 | + | 0.433292i | \(0.142648\pi\) | |||||||
\(284\) | −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 | ||||||||
\(289\) | −7.52777 | −0.442810 | ||||||||
\(290\) | −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 | ||||
\(296\) | − | 1.34225i | − | 0.0780167i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −29.4175 | −1.70411 | ||||||||
\(299\) | 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 | ||||||||
\(304\) | 10.6049 | + | 6.12275i | 0.608233 | + | 0.351164i | ||||
\(305\) | − | 21.4385i | − | 1.22756i | ||||||
\(306\) | 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 | ||||
\(311\) | −6.64294 | − | 11.5059i | −0.376687 | − | 0.652441i | 0.613891 | − | 0.789391i | \(-0.289603\pi\) |
−0.990578 | + | 0.136950i | \(0.956270\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.3227 | − | 15.7748i | −1.54437 | − | 0.891643i | −0.998555 | − | 0.0537372i | \(-0.982887\pi\) |
−0.545815 | − | 0.837905i | \(-0.683780\pi\) | |||||||
\(314\) | 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 | \(-0.523935\pi\) |
−0.901140 | + | 0.433528i | \(0.857268\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.77816 | − | 15.2042i | −0.491483 | − | 0.851273i | ||||
\(320\) | 4.45961 | + | 7.72428i | 0.249300 | + | 0.431800i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.92259i | 0.440824i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.567444i | − | 0.0314761i | ||||||
\(326\) | 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 | ||||||||
\(331\) | −0.623957 | + | 1.08073i | −0.0342958 | + | 0.0594020i | −0.882664 | − | 0.470005i | \(-0.844252\pi\) |
0.848368 | + | 0.529407i | \(0.177585\pi\) | |||||||
\(332\) | 12.6457 | 0.694023 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.9414i | 0.817559i | ||||||||
\(335\) | −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 | ||||
\(341\) | 58.7146 | 3.17958 | ||||||||
\(342\) | 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 | \(-0.407799\pi\) |
0.972760 | + | 0.231813i | \(0.0744658\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | −39.2401 | −2.09150 | ||||||||
\(353\) | −1.26256 | + | 2.18682i | −0.0671992 | + | 0.116392i | −0.897667 | − | 0.440674i | \(-0.854740\pi\) |
0.830468 | + | 0.557066i | \(0.188073\pi\) | |||||||
\(354\) | 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 | ||||
\(359\) | 7.26762i | 0.383570i | 0.981437 | + | 0.191785i | \(0.0614277\pi\) | ||||
−0.981437 | + | 0.191785i | \(0.938572\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3735 | 0.651239 | ||||||||
\(362\) | −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 | ||||||||
\(367\) | −11.6714 | − | 6.73848i | −0.609242 | − | 0.351746i | 0.163427 | − | 0.986555i | \(-0.447745\pi\) |
−0.772669 | + | 0.634809i | \(0.781079\pi\) | |||||||
\(368\) | 37.5429i | 1.95706i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.63278i | 0.344822i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.8820 | − | 20.5801i | −0.615224 | − | 1.06560i | −0.990345 | − | 0.138624i | \(-0.955732\pi\) |
0.375121 | − | 0.926976i | \(-0.377601\pi\) | |||||||
\(374\) | −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 | ||||
\(383\) | −6.47930 | − | 11.2225i | −0.331077 | − | 0.573442i | 0.651646 | − | 0.758523i | \(-0.274079\pi\) |
−0.982723 | + | 0.185081i | \(0.940745\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2.90752i | − | 0.147989i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.56231i | 0.282384i | ||||||||
\(389\) | −9.48037 | − | 5.47350i | −0.480674 | − | 0.277517i | 0.240023 | − | 0.970767i | \(-0.422845\pi\) |
−0.720697 | + | 0.693250i | \(0.756178\pi\) | |||||||
\(390\) | 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 | ||||
\(395\) | 1.43894 | 0.0724011 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.8901i | 1.50014i | 0.661358 | + | 0.750071i | \(0.269981\pi\) | ||||
−0.661358 | + | 0.750071i | \(0.730019\pi\) | |||||||
\(398\) | 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 | \(-0.825766\pi\) |
0.0237698 | + | 0.999717i | \(0.492433\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.32242 | + | 4.02254i | −0.115688 | + | 0.200377i | ||||
\(404\) | −11.2484 | −0.559630 | ||||||||
\(405\) | 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 | −0.968041 | − | 0.250790i | \(-0.919309\pi\) |
−0.266830 | + | 0.963744i | \(0.585976\pi\) | |||||||
\(410\) | 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 | ||||||||
\(415\) | 21.2246 | 1.04188 | ||||||||
\(416\) | 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 | \(-0.0459651\pi\) | |||||||
\(422\) | − | 28.7079i | − | 1.39748i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.60021 | −0.223406 | ||||||||
\(425\) | −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 | ||||||||
\(430\) | 38.5834 | + | 22.2762i | 1.86066 | + | 1.07425i | ||||
\(431\) | − | 10.8434i | − | 0.522308i | −0.965297 | − | 0.261154i | \(-0.915897\pi\) | ||
0.965297 | − | 0.261154i | \(-0.0841031\pi\) | |||||||
\(432\) | 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 | ||||
\(437\) | −10.1579 | − | 17.5940i | −0.485918 | − | 0.841634i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.6736 | + | 15.9773i | 1.32079 | + | 0.762557i | 0.983854 | − | 0.178972i | \(-0.0572772\pi\) |
0.336933 | + | 0.941529i | \(0.390611\pi\) | |||||||
\(440\) | −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 | \(-0.533838\pi\) |
−0.914190 | + | 0.405286i | \(0.867172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.49496 | − | 16.4458i | −0.450104 | − | 0.779603i | ||||
\(446\) | 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 | ||||||||
\(451\) | 18.4740i | 0.869906i | ||||||||
\(452\) | −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 | ||||||||
\(457\) | −13.6554 | + | 23.6518i | −0.638771 | + | 1.10638i | 0.346931 | + | 0.937890i | \(0.387224\pi\) |
−0.985703 | + | 0.168494i | \(0.946110\pi\) | |||||||
\(458\) | −6.31340 | −0.295006 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 29.5233i | − | 1.37653i | ||||||
\(461\) | 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 | ||||
\(467\) | −15.9048 | −0.735988 | −0.367994 | − | 0.929828i | \(-0.619955\pi\) | ||||
−0.367994 | + | 0.929828i | \(0.619955\pi\) | |||||||
\(468\) | 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 | ||||||||
\(478\) | 29.4042 | 1.34492 | ||||||||
\(479\) | 6.92685 | − | 11.9976i | 0.316496 | − | 0.548187i | −0.663259 | − | 0.748390i | \(-0.730827\pi\) |
0.979754 | + | 0.200204i | \(0.0641604\pi\) | |||||||
\(480\) | 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 | ||||
\(485\) | 9.33582i | 0.423918i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.7987 | 1.30499 | 0.652496 | − | 0.757792i | \(-0.273722\pi\) | ||||
0.652496 | + | 0.757792i | \(0.273722\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | −8.34181 | − | 4.81615i | −0.375696 | − | 0.216908i | ||||
\(494\) | 2.13496i | 0.0960562i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 49.7911i | − | 2.23569i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.73333 | + | 3.00222i | 0.0775946 | + | 0.134398i | 0.902212 | − | 0.431294i | \(-0.141943\pi\) |
−0.824617 | + | 0.565691i | \(0.808609\pi\) | |||||||
\(500\) | 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 | \(-0.283408\pi\) | ||||
0.629138 | + | 0.777293i | \(0.283408\pi\) | |||||||
\(504\) | 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 | ||||
\(509\) | −17.9062 | − | 31.0144i | −0.793678 | − | 1.37469i | −0.923675 | − | 0.383176i | \(-0.874830\pi\) |
0.129997 | − | 0.991514i | \(-0.458503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.2599i | 1.07215i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 54.1682i | − | 2.38926i | ||||||
\(515\) | 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 | ||||||||
\(520\) | 0.526897 | − | 0.912612i | 0.0231060 | − | 0.0400207i | ||||
\(521\) | 26.9216 | 1.17946 | 0.589729 | − | 0.807601i | \(-0.299234\pi\) | ||||
0.589729 | + | 0.807601i | \(0.299234\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.03185i | 0.394935i | 0.980309 | + | 0.197468i | \(0.0632717\pi\) | ||||
−0.980309 | + | 0.197468i | \(0.936728\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | 22.7321 | 0.987420 | ||||||||
\(531\) | 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 | ||||||||
\(541\) | 11.3358 | 0.487366 | 0.243683 | − | 0.969855i | \(-0.421644\pi\) | ||||
0.243683 | + | 0.969855i | \(0.421644\pi\) | |||||||
\(542\) | 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 | \(-0.145300\pi\) | |||||||
\(548\) | 17.2729i | 0.737861i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.4058 | 0.571627 | ||||||||
\(551\) | 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 | ||||||||
\(556\) | 25.3410 | + | 14.6306i | 1.07470 | + | 0.620478i | ||||
\(557\) | − | 7.26499i | − | 0.307827i | −0.988084 | − | 0.153914i | \(-0.950812\pi\) | ||
0.988084 | − | 0.153914i | \(-0.0491878\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.22177i | − | 0.178562i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.8848 | + | 36.1736i | 0.880973 | + | 1.52589i | ||||
\(563\) | 11.5409 | + | 19.9894i | 0.486390 | + | 0.842453i | 0.999878 | − | 0.0156446i | \(-0.00498004\pi\) |
−0.513487 | + | 0.858097i | \(0.671647\pi\) | |||||||
\(564\) | 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 | \(-0.210521\pi\) |
−0.137336 | + | 0.990525i | \(0.543854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.04234 | + | 12.1977i | 0.294713 | + | 0.510457i | 0.974918 | − | 0.222564i | \(-0.0714427\pi\) |
−0.680205 | + | 0.733022i | \(0.738109\pi\) | |||||||
\(572\) | −1.85819 | − | 3.21849i | −0.0776950 | − | 0.134572i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 10.0916i | − | 0.420851i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 30.0675i | − | 1.25172i | −0.779934 | − | 0.625862i | \(-0.784747\pi\) | ||
0.779934 | − | 0.625862i | \(-0.215253\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −13.6148 | + | 23.5815i | −0.563866 | + | 0.976644i | ||||
\(584\) | −8.07379 | −0.334096 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 16.4891i | − | 0.681158i | ||||||
\(587\) | −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 | ||||
\(593\) | 2.04317 | 0.0839028 | 0.0419514 | − | 0.999120i | \(-0.486643\pi\) | ||||
0.0419514 | + | 0.999120i | \(0.486643\pi\) | |||||||
\(594\) | 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 | \(-0.545195\pi\) |
0.786557 | + | 0.617517i | \(0.211861\pi\) | |||||||
\(600\) | 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 | ||||||||
\(604\) | 2.96003 | 0.120442 | ||||||||
\(605\) | −25.6428 | + | 44.4146i | −1.04253 | + | 1.80571i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.1730 | − | 9.91482i | 0.697030 | − | 0.402430i | −0.109211 | − | 0.994019i | \(-0.534832\pi\) |
0.806240 | + | 0.591588i | \(0.201499\pi\) | |||||||
\(608\) | −9.00349 | − | 15.5945i | −0.365140 | − | 0.632440i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0336 | + | 34.6991i | −0.811135 | + | 1.40493i | ||||
\(611\) | − | 0.951346i | − | 0.0384873i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.6882 | −0.512473 | −0.256237 | − | 0.966614i | \(-0.582483\pi\) | ||||
−0.256237 | + | 0.966614i | \(0.582483\pi\) | |||||||
\(614\) | −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 | ||||||||
\(619\) | 0.231999 | + | 0.133945i | 0.00932485 | + | 0.00538370i | 0.504655 | − | 0.863321i | \(-0.331620\pi\) |
−0.495330 | + | 0.868705i | \(0.664953\pi\) | |||||||
\(620\) | 39.1552i | 1.57251i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.8305i | 0.995611i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8792 | + | 25.7716i | 0.595169 | + | 1.03086i | ||||
\(626\) | 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 | ||||
\(635\) | 9.23671 | + | 15.9984i | 0.366547 | + | 0.634879i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 32.8117i | 1.29903i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.3867i | 0.726799i | ||||||||
\(641\) | −29.7991 | − | 17.2045i | −1.17699 | − | 0.679537i | −0.221676 | − | 0.975120i | \(-0.571153\pi\) |
−0.955317 | + | 0.295583i | \(0.904486\pi\) | |||||||
\(642\) | 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 | ||||||||
\(646\) | 7.40341 | − | 12.8231i | 0.291283 | − | 0.504517i | ||||
\(647\) | 19.6436 | 0.772271 | 0.386136 | − | 0.922442i | \(-0.373810\pi\) | ||||
0.386136 | + | 0.922442i | \(0.373810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 41.0055i | − | 1.60961i | ||||||
\(650\) | −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 | \(-0.686644\pi\) |
0.444699 | + | 0.895680i | \(0.353311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.85129 | + | 17.0629i | −0.384922 | + | 0.666704i | ||||
\(656\) | 15.6663 | 0.611666 | ||||||||
\(657\) | 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 | 0.157143 | − | 0.987576i | \(-0.449772\pi\) |
0.933837 | + | 0.357698i | \(0.116438\pi\) | |||||||
\(662\) | 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 | ||||||||
\(667\) | 24.7000 | 0.956386 | ||||||||
\(668\) | 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 | \(0.296745\pi\) | |||||||
\(674\) | − | 24.6231i | − | 0.948445i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.1140 | −0.735155 | ||||||||
\(677\) | 25.1655 | − | 43.5880i | 0.967190 | − | 1.67522i | 0.263578 | − | 0.964638i | \(-0.415097\pi\) |
0.703612 | − | 0.710585i | \(-0.251569\pi\) | |||||||
\(678\) | 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 | ||||
\(683\) | 13.7445i | 0.525920i | 0.964807 | + | 0.262960i | \(0.0846987\pi\) | ||||
−0.964807 | + | 0.262960i | \(0.915301\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.9909i | 1.10769i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 22.6280 | + | 39.1929i | 0.862685 | + | 1.49421i | ||||
\(689\) | −1.07705 | − | 1.86550i | −0.0410321 | − | 0.0710698i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4328 | + | 14.6837i | 0.967511 | + | 0.558593i | 0.898476 | − | 0.439022i | \(-0.144675\pi\) |
0.0690343 | + | 0.997614i | \(0.478008\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | −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 | ||||||||
\(703\) | − | 3.64592i | − | 0.137508i | ||||||
\(704\) | 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 | ||||||||
\(709\) | 5.66629 | − | 9.81430i | 0.212802 | − | 0.368584i | −0.739788 | − | 0.672840i | \(-0.765074\pi\) |
0.952590 | + | 0.304256i | \(0.0984077\pi\) | |||||||
\(710\) | 13.8308 | 0.519062 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 7.18216i | − | 0.269163i | ||||||
\(713\) | −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 | ||||
\(719\) | 36.1294 | 1.34740 | 0.673700 | − | 0.739005i | \(-0.264704\pi\) | ||||
0.673700 | + | 0.739005i | \(0.264704\pi\) | |||||||
\(720\) | 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 | 0.380492 | − | 0.924784i | \(-0.375755\pi\) |
−0.610640 | + | 0.791908i | \(0.709088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 39.8970 | 1.47665 | ||||||||
\(731\) | −14.6399 | + | 25.3570i | −0.541475 | + | 0.937862i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.4391 | − | 23.9249i | 1.53059 | − | 0.883685i | 0.531253 | − | 0.847213i | \(-0.321721\pi\) |
0.999335 | − | 0.0364726i | \(-0.0116122\pi\) | |||||||
\(734\) | 12.5938 | + | 21.8131i | 0.464846 | + | 0.805136i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.6034 | − | 47.8105i | 1.01747 | − | 1.76232i | ||||
\(737\) | 10.4836i | 0.386170i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.3483 | 0.564597 | 0.282299 | − | 0.959327i | \(-0.408903\pi\) | ||||
0.282299 | + | 0.959327i | \(0.408903\pi\) | |||||||
\(740\) | 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 | ||||||||
\(745\) | 34.1568 | + | 19.7204i | 1.25141 | + | 0.722501i | ||||
\(746\) | 44.4132i | 1.62608i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 25.7747i | 0.942417i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.9449 | − | 29.3494i | −0.618327 | − | 1.07097i | −0.989791 | − | 0.142527i | \(-0.954477\pi\) |
0.371463 | − | 0.928448i | \(-0.378856\pi\) | |||||||
\(752\) | 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 | ||||
\(761\) | −13.2666 | − | 22.9784i | −0.480914 | − | 0.832968i | 0.518846 | − | 0.854868i | \(-0.326362\pi\) |
−0.999760 | + | 0.0218999i | \(0.993028\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 19.7420i | − | 0.714242i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.2188i | 0.875061i | ||||||||
\(767\) | 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 | ||||||||
\(772\) | −1.16128 | + | 2.01139i | −0.0417953 | + | 0.0723916i | ||||
\(773\) | 22.6017 | 0.812927 | 0.406464 | − | 0.913667i | \(-0.366762\pi\) | ||||
0.406464 | + | 0.913667i | \(0.366762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.3840i | 0.480768i | ||||||||
\(776\) | −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 | ||||
\(782\) | 45.3955 | 1.62334 | ||||||||
\(783\) | 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 | −0.0378153 | − | 0.999285i | \(-0.512040\pi\) |
0.846498 | + | 0.532391i | \(0.178707\pi\) | |||||||
\(788\) | −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 | ||||||||
\(793\) | 3.79675 | 0.134827 | ||||||||
\(794\) | 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 | ||||
\(800\) | − | 8.94478i | − | 0.316246i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35.8740 | 1.26676 | ||||||||
\(803\) | −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 | ||||||||
\(808\) | −6.18375 | − | 3.57019i | −0.217543 | − | 0.125599i | ||||
\(809\) | 26.4887i | 0.931292i | 0.884971 | + | 0.465646i | \(0.154178\pi\) | ||||
−0.884971 | + | 0.465646i | \(0.845822\pi\) | |||||||
\(810\) | 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 | ||||
\(815\) | −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 | \(-0.257253\pi\) |
−0.280759 | + | 0.959778i | \(0.590586\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.34857 | − | 12.7281i | −0.256155 | − | 0.443674i | 0.709053 | − | 0.705155i | \(-0.249122\pi\) |
−0.965209 | + | 0.261481i | \(0.915789\pi\) | |||||||
\(824\) | 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 | ||||||||
\(829\) | 20.4600i | 0.710605i | 0.934751 | + | 0.355302i | \(0.115622\pi\) | ||||
−0.934751 | + | 0.355302i | \(0.884378\pi\) | |||||||
\(830\) | −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 | ||||||||
\(835\) | 10.0162 | − | 17.3486i | 0.346625 | − | 0.600372i | ||||
\(836\) | −21.5580 | −0.745599 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.9282i | 0.653865i | ||||||||
\(839\) | 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 | ||||
\(845\) | −32.0811 | −1.10362 | ||||||||
\(846\) | 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 | 0.298396 | − | 0.954442i | \(-0.403548\pi\) |
−0.677373 | + | 0.735640i | \(0.736882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.7812 | −0.436851 | ||||||||
\(857\) | 9.16200 | − | 15.8691i | 0.312968 | − | 0.542077i | −0.666035 | − | 0.745920i | \(-0.732010\pi\) |
0.979003 | + | 0.203844i | \(0.0653434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.4579 | + | 19.3169i | −1.14157 | + | 0.659085i | −0.946819 | − | 0.321768i | \(-0.895723\pi\) |
−0.194750 | + | 0.980853i | \(0.562390\pi\) | |||||||
\(860\) | −17.7944 | − | 30.8208i | −0.606784 | − | 1.05098i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.1328 | + | 17.5505i | −0.345125 | + | 0.597774i | ||||
\(863\) | 16.7000i | 0.568475i | 0.958754 | + | 0.284238i | \(0.0917405\pi\) | ||||
−0.958754 | + | 0.284238i | \(0.908260\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.51447 | −0.0854947 | ||||||||
\(866\) | 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 | ||||||||
\(871\) | −0.718235 | − | 0.414673i | −0.0243365 | − | 0.0140507i | ||||
\(872\) | − | 0.870640i | − | 0.0294836i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 37.9689i | 1.28432i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.7617 | − | 29.0321i | −0.566002 | − | 0.980345i | −0.996956 | − | 0.0779707i | \(-0.975156\pi\) |
0.430953 | − | 0.902374i | \(-0.358177\pi\) | |||||||
\(878\) | −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 | \(-0.660411\pi\) | ||||
−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 | \(0.722277\pi\) | |||||||
\(884\) | −1.76583 | − | 1.01950i | −0.0593912 | − | 0.0342895i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.1719 | + | 40.1350i | 0.778476 | + | 1.34836i | ||||
\(887\) | 17.5914 | + | 30.4692i | 0.590662 | + | 1.02306i | 0.994143 | + | 0.108069i | \(0.0344666\pi\) |
−0.403481 | + | 0.914988i | \(0.632200\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 35.4910i | 1.18966i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 4.77248i | − | 0.159794i | ||||||
\(893\) | −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 | ||||||||
\(898\) | −12.8685 | + | 22.2890i | −0.429429 | + | 0.743792i | ||||
\(899\) | −32.7582 | −1.09255 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.9395i | 0.497707i | ||||||||
\(902\) | 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 | −0.258720 | − | 0.965952i | \(-0.583301\pi\) |
0.965899 | − | 0.258918i | \(-0.0833660\pi\) | |||||||
\(908\) | 21.9010 | 0.726811 | ||||||||
\(909\) | 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 | ||||||||
\(919\) | −58.6972 | −1.93624 | −0.968121 | − | 0.250481i | \(-0.919411\pi\) | ||||
−0.968121 | + | 0.250481i | \(0.919411\pi\) | |||||||
\(920\) | 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 | ||||
\(926\) | 45.7315i | 1.50283i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 21.8929 | 0.718670 | ||||||||
\(929\) | −7.19115 | + | 12.4554i | −0.235934 | + | 0.408650i | −0.959544 | − | 0.281560i | \(-0.909148\pi\) |
0.723610 | + | 0.690209i | \(0.242482\pi\) | |||||||
\(930\) | 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 | ||||
\(935\) | 43.2604i | 1.41477i | ||||||||
\(936\) | 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 | ||||
\(941\) | −7.44400 | − | 12.8934i | −0.242667 | − | 0.420312i | 0.718806 | − | 0.695211i | \(-0.244689\pi\) |
−0.961473 | + | 0.274899i | \(0.911356\pi\) | |||||||
\(942\) | 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 | \(-0.572084\pi\) |
−0.956178 | + | 0.292787i | \(0.905417\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.89031 | − | 3.27412i | −0.0613622 | − | 0.106282i | ||||
\(950\) | 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 | ||||||||
\(955\) | − | 33.1352i | − | 1.07223i | ||||||
\(956\) | −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 | ||||||||
\(961\) | 39.2776 | − | 68.0309i | 1.26702 | − | 2.19454i | ||||
\(962\) | −1.17467 | −0.0378728 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.14863i | − | 0.0369949i | ||||||
\(965\) | −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 | ||||
\(971\) | −43.3737 | −1.39193 | −0.695965 | − | 0.718076i | \(-0.745023\pi\) | ||||
−0.695965 | + | 0.718076i | \(0.745023\pi\) | |||||||
\(972\) | 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 | \(-0.605011\pi\) |
0.657348 | + | 0.753587i | \(0.271678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.8170 | − | 21.2563i | −1.17668 | − | 0.679355i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −72.4304 | −2.31135 | ||||||||
\(983\) | 3.14829 | − | 5.45300i | 0.100415 | − | 0.173924i | −0.811441 | − | 0.584435i | \(-0.801316\pi\) |
0.911856 | + | 0.410511i | \(0.134650\pi\) | |||||||
\(984\) | 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 | ||||
\(989\) | − | 75.0816i | − | 2.38745i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.5627 | 1.06616 | 0.533078 | − | 0.846066i | \(-0.321035\pi\) | ||||
0.533078 | + | 0.846066i | \(0.321035\pi\) | |||||||
\(992\) | −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 | ||||||||
\(997\) | 9.74838 | + | 5.62823i | 0.308734 | + | 0.178248i | 0.646360 | − | 0.763033i | \(-0.276290\pi\) |
−0.337626 | + | 0.941280i | \(0.609624\pi\) | |||||||
\(998\) | − | 6.47898i | − | 0.205088i | ||||||
\(999\) | 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.o.e.440.6 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.146.19 | ✓ | 48 | ||
7.2 | even | 3 | 1323.2.i.d.521.7 | 48 | |||
7.3 | odd | 6 | 1323.2.s.d.656.20 | 48 | |||
7.4 | even | 3 | 1323.2.s.d.656.19 | 48 | |||
7.5 | odd | 6 | 1323.2.i.d.521.22 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.440.5 | 48 | ||
9.4 | even | 3 | 441.2.o.e.293.20 | yes | 48 | ||
9.5 | odd | 6 | inner | 1323.2.o.e.881.5 | 48 | ||
21.2 | odd | 6 | 441.2.i.d.227.6 | 48 | |||
21.5 | even | 6 | 441.2.i.d.227.5 | 48 | |||
21.11 | odd | 6 | 441.2.s.d.362.5 | 48 | |||
21.17 | even | 6 | 441.2.s.d.362.6 | 48 | |||
21.20 | even | 2 | 441.2.o.e.146.20 | yes | 48 | ||
63.4 | even | 3 | 441.2.i.d.68.19 | 48 | |||
63.5 | even | 6 | 1323.2.s.d.962.19 | 48 | |||
63.13 | odd | 6 | 441.2.o.e.293.19 | yes | 48 | ||
63.23 | odd | 6 | 1323.2.s.d.962.20 | 48 | |||
63.31 | odd | 6 | 441.2.i.d.68.20 | 48 | |||
63.32 | odd | 6 | 1323.2.i.d.1097.22 | 48 | |||
63.40 | odd | 6 | 441.2.s.d.374.5 | 48 | |||
63.41 | even | 6 | inner | 1323.2.o.e.881.6 | 48 | ||
63.58 | even | 3 | 441.2.s.d.374.6 | 48 | |||
63.59 | even | 6 | 1323.2.i.d.1097.7 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.19 | 48 | 63.4 | even | 3 | |||
441.2.i.d.68.20 | 48 | 63.31 | odd | 6 | |||
441.2.i.d.227.5 | 48 | 21.5 | even | 6 | |||
441.2.i.d.227.6 | 48 | 21.2 | odd | 6 | |||
441.2.o.e.146.19 | ✓ | 48 | 3.2 | odd | 2 | ||
441.2.o.e.146.20 | yes | 48 | 21.20 | even | 2 | ||
441.2.o.e.293.19 | yes | 48 | 63.13 | odd | 6 | ||
441.2.o.e.293.20 | yes | 48 | 9.4 | even | 3 | ||
441.2.s.d.362.5 | 48 | 21.11 | odd | 6 | |||
441.2.s.d.362.6 | 48 | 21.17 | even | 6 | |||
441.2.s.d.374.5 | 48 | 63.40 | odd | 6 | |||
441.2.s.d.374.6 | 48 | 63.58 | even | 3 | |||
1323.2.i.d.521.7 | 48 | 7.2 | even | 3 | |||
1323.2.i.d.521.22 | 48 | 7.5 | odd | 6 | |||
1323.2.i.d.1097.7 | 48 | 63.59 | even | 6 | |||
1323.2.i.d.1097.22 | 48 | 63.32 | odd | 6 | |||
1323.2.o.e.440.5 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.o.e.440.6 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.o.e.881.5 | 48 | 9.5 | odd | 6 | inner | ||
1323.2.o.e.881.6 | 48 | 63.41 | even | 6 | inner | ||
1323.2.s.d.656.19 | 48 | 7.4 | even | 3 | |||
1323.2.s.d.656.20 | 48 | 7.3 | odd | 6 | |||
1323.2.s.d.962.19 | 48 | 63.5 | even | 6 | |||
1323.2.s.d.962.20 | 48 | 63.23 | odd | 6 |