Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(17,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.bt (of order \(12\), degree \(4\), 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: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 233.3 | ||
Character | \(\chi\) | \(=\) | 1080.233 |
Dual form | 1080.2.bt.a.737.3 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.06252 | − | 0.863710i | −0.922389 | − | 0.386263i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64986 | + | 0.710029i | 1.00155 | + | 0.268366i | 0.722096 | − | 0.691792i | \(-0.243179\pi\) |
0.279458 | + | 0.960158i | \(0.409845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.765403 | − | 0.441906i | 0.230778 | − | 0.133240i | −0.380153 | − | 0.924924i | \(-0.624129\pi\) |
0.610931 | + | 0.791684i | \(0.290795\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.35352 | − | 0.362674i | 0.375399 | − | 0.100588i | −0.0661862 | − | 0.997807i | \(-0.521083\pi\) |
0.441585 | + | 0.897220i | \(0.354416\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.83033 | − | 3.83033i | −0.928992 | − | 0.928992i | 0.0686484 | − | 0.997641i | \(-0.478131\pi\) |
−0.997641 | + | 0.0686484i | \(0.978131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.46618i | − | 1.02461i | −0.858803 | − | 0.512306i | \(-0.828791\pi\) | ||
0.858803 | − | 0.512306i | \(-0.171209\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.01575 | + | 3.79082i | 0.211798 | + | 0.790440i | 0.987269 | + | 0.159058i | \(0.0508456\pi\) |
−0.775471 | + | 0.631383i | \(0.782488\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.50801 | + | 3.56284i | 0.701602 | + | 0.712569i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.874378 | + | 1.51447i | 0.162368 | + | 0.281229i | 0.935717 | − | 0.352750i | \(-0.114754\pi\) |
−0.773350 | + | 0.633980i | \(0.781420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.74056 | − | 4.74679i | 0.492219 | − | 0.852548i | −0.507741 | − | 0.861510i | \(-0.669519\pi\) |
0.999960 | + | 0.00896169i | \(0.00285263\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.85215 | − | 3.75316i | −0.820163 | − | 0.634400i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.41426 | − | 4.41426i | 0.725699 | − | 0.725699i | −0.244061 | − | 0.969760i | \(-0.578480\pi\) |
0.969760 | + | 0.244061i | \(0.0784796\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.85416 | + | 3.37990i | 0.914266 | + | 0.527852i | 0.881801 | − | 0.471621i | \(-0.156331\pi\) |
0.0324645 | + | 0.999473i | \(0.489664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.28815 | + | 4.80743i | −0.196441 | + | 0.733127i | 0.795449 | + | 0.606021i | \(0.207235\pi\) |
−0.991889 | + | 0.127105i | \(0.959431\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.90134 | − | 10.8280i | 0.423205 | − | 1.57942i | −0.344608 | − | 0.938747i | \(-0.611988\pi\) |
0.767813 | − | 0.640674i | \(-0.221345\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.455456 | + | 0.262958i | 0.0650651 | + | 0.0375654i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.79105 | − | 6.79105i | 0.932823 | − | 0.932823i | −0.0650586 | − | 0.997881i | \(-0.520723\pi\) |
0.997881 | + | 0.0650586i | \(0.0207234\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.96034 | + | 0.250355i | −0.264332 | + | 0.0337579i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.02430 | − | 6.97029i | 0.523919 | − | 0.907455i | −0.475693 | − | 0.879611i | \(-0.657803\pi\) |
0.999612 | − | 0.0278435i | \(-0.00886401\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.25649 | − | 7.37246i | −0.544988 | − | 0.943947i | −0.998608 | − | 0.0527517i | \(-0.983201\pi\) |
0.453620 | − | 0.891195i | \(-0.350133\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.10491 | − | 0.421023i | −0.385117 | − | 0.0522215i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.87853 | − | 14.4749i | −0.473837 | − | 1.76839i | −0.625784 | − | 0.779996i | \(-0.715221\pi\) |
0.151947 | − | 0.988389i | \(-0.451446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.1410i | − | 1.32219i | −0.750302 | − | 0.661095i | \(-0.770092\pi\) | ||
0.750302 | − | 0.661095i | \(-0.229908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.1583 | + | 10.1583i | 1.18894 | + | 1.18894i | 0.977361 | + | 0.211580i | \(0.0678609\pi\) |
0.211580 | + | 0.977361i | \(0.432139\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.34198 | − | 0.627531i | 0.266893 | − | 0.0715138i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.28119 | + | 4.78115i | −0.931707 | + | 0.537921i | −0.887351 | − | 0.461095i | \(-0.847457\pi\) |
−0.0443558 | + | 0.999016i | \(0.514124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.49329 | − | 1.20397i | −0.493203 | − | 0.132153i | 0.00364075 | − | 0.999993i | \(-0.498841\pi\) |
−0.496844 | + | 0.867840i | \(0.665508\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.59186 | + | 11.2085i | 0.498057 | + | 1.21573i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3300 | 1.20097 | 0.600486 | − | 0.799635i | \(-0.294974\pi\) | ||||
0.600486 | + | 0.799635i | \(0.294974\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.84415 | 0.402976 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.85749 | + | 9.21161i | −0.395770 | + | 0.945091i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0528 | + | 2.96160i | 1.12225 | + | 0.300705i | 0.771792 | − | 0.635875i | \(-0.219361\pi\) |
0.350454 | + | 0.936580i | \(0.386027\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.3287 | + | 6.54062i | −1.12725 | + | 0.650816i | −0.943241 | − | 0.332109i | \(-0.892240\pi\) |
−0.184005 | + | 0.982925i | \(0.558906\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.22569 | + | 1.40022i | −0.514902 | + | 0.137968i | −0.506908 | − | 0.862000i | \(-0.669211\pi\) |
−0.00799468 | + | 0.999968i | \(0.502545\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.25184 | + | 5.25184i | 0.507715 | + | 0.507715i | 0.913824 | − | 0.406110i | \(-0.133115\pi\) |
−0.406110 | + | 0.913824i | \(0.633115\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.2761i | − | 0.984270i | −0.870519 | − | 0.492135i | \(-0.836217\pi\) | ||
0.870519 | − | 0.492135i | \(-0.163783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.46206 | + | 16.6526i | 0.419755 | + | 1.56655i | 0.775116 | + | 0.631818i | \(0.217691\pi\) |
−0.355361 | + | 0.934729i | \(0.615642\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.17916 | − | 8.69596i | 0.109958 | − | 0.810903i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.43021 | − | 12.8695i | −0.681127 | − | 1.17975i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.10944 | + | 8.84981i | −0.464494 | + | 0.804528i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.15809 | − | 10.3784i | −0.371911 | − | 0.928268i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6609 | + | 10.6609i | −0.946006 | + | 0.946006i | −0.998615 | − | 0.0526093i | \(-0.983246\pi\) |
0.0526093 | + | 0.998615i | \(0.483246\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.743908 | + | 0.429496i | 0.0649956 | + | 0.0375252i | 0.532146 | − | 0.846653i | \(-0.321386\pi\) |
−0.467150 | + | 0.884178i | \(0.654719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.17112 | − | 11.8348i | 0.274971 | − | 1.02620i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.70813 | + | 13.8389i | −0.316807 | + | 1.18234i | 0.605488 | + | 0.795854i | \(0.292978\pi\) |
−0.922295 | + | 0.386486i | \(0.873689\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.63362 | − | 5.56197i | −0.817113 | − | 0.471760i | 0.0323071 | − | 0.999478i | \(-0.489715\pi\) |
−0.849420 | + | 0.527718i | \(0.823048\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.875720 | − | 0.875720i | 0.0732314 | − | 0.0732314i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.495365 | − | 3.87883i | −0.0411379 | − | 0.322119i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.728908 | + | 1.26251i | −0.0597144 | + | 0.103428i | −0.894337 | − | 0.447394i | \(-0.852352\pi\) |
0.834623 | + | 0.550822i | \(0.185686\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.74576 | + | 9.95194i | 0.467583 | + | 0.809878i | 0.999314 | − | 0.0370357i | \(-0.0117915\pi\) |
−0.531731 | + | 0.846913i | \(0.678458\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.75231 | + | 7.42331i | −0.783325 | + | 0.596255i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.12353 | + | 4.19308i | 0.0896675 | + | 0.334644i | 0.996157 | − | 0.0875844i | \(-0.0279147\pi\) |
−0.906490 | + | 0.422228i | \(0.861248\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7664i | 0.848508i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7949 | + | 10.7949i | 0.845523 | + | 0.845523i | 0.989571 | − | 0.144048i | \(-0.0460120\pi\) |
−0.144048 | + | 0.989571i | \(0.546012\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.3964 | − | 4.66134i | 1.34617 | − | 0.360705i | 0.487451 | − | 0.873150i | \(-0.337927\pi\) |
0.858720 | + | 0.512445i | \(0.171260\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.55785 | + | 5.51823i | −0.735219 | + | 0.424479i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8049 | + | 3.43108i | 0.973542 | + | 0.260860i | 0.710323 | − | 0.703876i | \(-0.248549\pi\) |
0.263219 | + | 0.964736i | \(0.415216\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.76603 | + | 11.9318i | 0.511464 | + | 0.901962i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.78241 | −0.282711 | −0.141355 | − | 0.989959i | \(-0.545146\pi\) | ||||
−0.141355 | + | 0.989959i | \(0.545146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0071 | −1.71010 | −0.855052 | − | 0.518541i | \(-0.826475\pi\) | ||||
−0.855052 | + | 0.518541i | \(0.826475\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.9171 | + | 5.29187i | −0.949688 | + | 0.389066i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.62440 | − | 1.23910i | −0.338169 | − | 0.0906122i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.51688 | + | 5.49457i | −0.688617 | + | 0.397573i | −0.803094 | − | 0.595853i | \(-0.796814\pi\) |
0.114476 | + | 0.993426i | \(0.463481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5657 | − | 2.83107i | 0.760536 | − | 0.203785i | 0.142349 | − | 0.989816i | \(-0.454534\pi\) |
0.618186 | + | 0.786031i | \(0.287868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.49711 | − | 4.49711i | −0.320406 | − | 0.320406i | 0.528517 | − | 0.848923i | \(-0.322748\pi\) |
−0.848923 | + | 0.528517i | \(0.822748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.3650i | − | 1.01831i | −0.860676 | − | 0.509154i | \(-0.829958\pi\) | ||
0.860676 | − | 0.509154i | \(-0.170042\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.24167 | + | 4.63396i | 0.0871479 | + | 0.325240i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.15509 | − | 12.0274i | −0.639419 | − | 0.840031i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.97363 | − | 3.41843i | −0.136519 | − | 0.236458i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.167767 | − | 0.290581i | 0.0115496 | − | 0.0200044i | −0.860193 | − | 0.509969i | \(-0.829657\pi\) |
0.871742 | + | 0.489964i | \(0.162990\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.80906 | − | 8.80286i | 0.464374 | − | 0.600350i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.6325 | − | 10.6325i | 0.721778 | − | 0.721778i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.57359 | − | 3.79527i | −0.442188 | − | 0.255297i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.22007 | − | 8.28540i | 0.148667 | − | 0.554832i | −0.850898 | − | 0.525331i | \(-0.823942\pi\) |
0.999565 | − | 0.0295007i | \(-0.00939174\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.57688 | + | 17.0812i | −0.303778 | + | 1.13372i | 0.630214 | + | 0.776422i | \(0.282967\pi\) |
−0.933992 | + | 0.357294i | \(0.883699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.82045 | + | 2.78309i | 0.318544 | + | 0.183912i | 0.650743 | − | 0.759298i | \(-0.274457\pi\) |
−0.332199 | + | 0.943209i | \(0.607791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.1252 | + | 12.1252i | −0.794347 | + | 0.794347i | −0.982198 | − | 0.187851i | \(-0.939848\pi\) |
0.187851 | + | 0.982198i | \(0.439848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.3363 | + | 19.8270i | −1.00043 | + | 1.29337i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.849620 | − | 1.47159i | 0.0549574 | − | 0.0951889i | −0.837238 | − | 0.546839i | \(-0.815831\pi\) |
0.892195 | + | 0.451650i | \(0.149164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.86365 | − | 6.69204i | −0.248880 | − | 0.431072i | 0.714336 | − | 0.699803i | \(-0.246729\pi\) |
−0.963215 | + | 0.268731i | \(0.913396\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.712270 | − | 0.935738i | −0.0455052 | − | 0.0597821i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.61977 | − | 6.04506i | −0.103063 | − | 0.384638i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.29943i | − | 0.523855i | −0.965088 | − | 0.261928i | \(-0.915642\pi\) | ||
0.965088 | − | 0.261928i | \(-0.0843582\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.45264 | + | 2.45264i | 0.154196 | + | 0.154196i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.35423 | − | 1.97056i | 0.458744 | − | 0.122920i | −0.0220439 | − | 0.999757i | \(-0.507017\pi\) |
0.480788 | + | 0.876837i | \(0.340351\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.8314 | − | 8.56293i | 0.921580 | − | 0.532074i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.77517 | − | 0.743605i | −0.171124 | − | 0.0458527i | 0.172239 | − | 0.985055i | \(-0.444900\pi\) |
−0.343364 | + | 0.939202i | \(0.611566\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.8722 | + | 8.14121i | −1.22074 | + | 0.500111i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.8609 | 1.45483 | 0.727413 | − | 0.686200i | \(-0.240723\pi\) | ||||
0.727413 | + | 0.686200i | \(0.240723\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.4742 | −1.24372 | −0.621859 | − | 0.783129i | \(-0.713622\pi\) | ||||
−0.621859 | + | 0.783129i | \(0.713622\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.25948 | + | 1.17680i | 0.256857 | + | 0.0709638i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.0780948 | − | 0.0209254i | −0.00469226 | − | 0.00125729i | 0.256472 | − | 0.966552i | \(-0.417440\pi\) |
−0.261164 | + | 0.965294i | \(0.584106\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.1783 | + | 9.91792i | −1.02477 | + | 0.591654i | −0.915483 | − | 0.402356i | \(-0.868191\pi\) |
−0.109291 | + | 0.994010i | \(0.534858\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1034 | − | 4.04694i | 0.897803 | − | 0.240565i | 0.219730 | − | 0.975561i | \(-0.429482\pi\) |
0.678072 | + | 0.734995i | \(0.262816\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.1129 | + | 13.1129i | 0.774029 | + | 0.774029i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.3429i | 0.726054i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.44532 | + | 20.3222i | 0.318119 | + | 1.18724i | 0.921051 | + | 0.389443i | \(0.127332\pi\) |
−0.602932 | + | 0.797793i | \(0.706001\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3205 | + | 10.9006i | −0.833773 | + | 0.634656i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.74966 | + | 4.76256i | 0.159017 | + | 0.275426i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.82683 | + | 11.8244i | −0.393492 | + | 0.681548i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.41145 | + | 18.8823i | 0.138079 | + | 1.08119i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.6057 | + | 13.6057i | −0.776518 | + | 0.776518i | −0.979237 | − | 0.202719i | \(-0.935022\pi\) |
0.202719 | + | 0.979237i | \(0.435022\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.94616 | − | 3.43302i | −0.337176 | − | 0.194669i | 0.321847 | − | 0.946792i | \(-0.395696\pi\) |
−0.659022 | + | 0.752123i | \(0.729030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.87818 | + | 10.7415i | −0.162684 | + | 0.607146i | 0.835640 | + | 0.549278i | \(0.185097\pi\) |
−0.998324 | + | 0.0578684i | \(0.981570\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.55850 | − | 17.0126i | 0.256031 | − | 0.955520i | −0.711483 | − | 0.702703i | \(-0.751976\pi\) |
0.967514 | − | 0.252817i | \(-0.0813571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.33850 | + | 0.772785i | 0.0749418 | + | 0.0432676i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.1070 | + | 17.1070i | −0.951857 | + | 0.951857i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.04031 | + | 3.55011i | 0.335056 | + | 0.196925i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.3763 | − | 26.6326i | 0.847725 | − | 1.46830i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0665 | + | 19.1677i | 0.608269 | + | 1.05355i | 0.991526 | + | 0.129910i | \(0.0414689\pi\) |
−0.383257 | + | 0.923642i | \(0.625198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.50252 | + | 33.2047i | −0.245999 | + | 1.81416i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.91267 | − | 18.3343i | −0.267610 | − | 0.998735i | −0.960633 | − | 0.277820i | \(-0.910388\pi\) |
0.693023 | − | 0.720916i | \(-0.256278\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.84427i | − | 0.262332i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.5587 | − | 12.5587i | −0.678104 | − | 0.678104i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.854912 | − | 0.229073i | 0.0458941 | − | 0.0122973i | −0.235799 | − | 0.971802i | \(-0.575771\pi\) |
0.281693 | + | 0.959505i | \(0.409104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.5844 | + | 16.5032i | −1.53009 | + | 0.883395i | −0.530728 | + | 0.847542i | \(0.678082\pi\) |
−0.999357 | + | 0.0358533i | \(0.988585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.2519 | − | 3.55083i | −0.705326 | − | 0.188991i | −0.111711 | − | 0.993741i | \(-0.535633\pi\) |
−0.593615 | + | 0.804749i | \(0.702300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.62257 | + | 22.9785i | −0.510713 | + | 1.21957i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.11438 | −0.217149 | −0.108574 | − | 0.994088i | \(-0.534629\pi\) | ||||
−0.108574 | + | 0.994088i | \(0.534629\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.946788 | −0.0498310 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.1779 | − | 29.7256i | −0.637422 | − | 1.55591i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.89755 | + | 2.38409i | 0.464448 | + | 0.124449i | 0.483452 | − | 0.875371i | \(-0.339383\pi\) |
−0.0190037 | + | 0.999819i | \(0.506049\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.8172 | − | 13.1735i | 1.18461 | − | 0.683935i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.70036 | − | 1.79536i | 0.346931 | − | 0.0929600i | −0.0811456 | − | 0.996702i | \(-0.525858\pi\) |
0.428077 | + | 0.903742i | \(0.359191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.73274 | + | 1.73274i | 0.0892409 | + | 0.0892409i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 28.1201i | − | 1.44443i | −0.691668 | − | 0.722216i | \(-0.743124\pi\) | ||
0.691668 | − | 0.722216i | \(-0.256876\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.95085 | + | 18.4768i | 0.252977 | + | 0.944122i | 0.969205 | + | 0.246256i | \(0.0792003\pi\) |
−0.716228 | + | 0.697866i | \(0.754133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.37239 | − | 0.728491i | −0.273803 | − | 0.0371274i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.75380 | − | 3.03767i | −0.0889211 | − | 0.154016i | 0.818134 | − | 0.575027i | \(-0.195009\pi\) |
−0.907055 | + | 0.421011i | \(0.861675\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.6295 | − | 18.4107i | 0.537554 | − | 0.931072i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.2097 | − | 2.70869i | 1.06717 | − | 0.136289i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.39991 | + | 6.39991i | −0.321202 | + | 0.321202i | −0.849228 | − | 0.528026i | \(-0.822932\pi\) |
0.528026 | + | 0.849228i | \(0.322932\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.59094 | − | 2.07323i | −0.179323 | − | 0.103532i | 0.407652 | − | 0.913138i | \(-0.366348\pi\) |
−0.586975 | + | 0.809605i | \(0.699681\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.98786 | − | 7.41880i | 0.0990224 | − | 0.369557i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.42800 | − | 5.32937i | 0.0707834 | − | 0.264167i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.6500 | + | 15.9637i | 1.36720 | + | 0.789356i | 0.990570 | − | 0.137006i | \(-0.0437479\pi\) |
0.376635 | + | 0.926362i | \(0.377081\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.6130 | − | 15.6130i | 0.768263 | − | 0.768263i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.22764 | + | 6.36413i | 0.403879 | + | 0.312403i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0895 | + | 22.6717i | −0.639466 | + | 1.10759i | 0.346085 | + | 0.938203i | \(0.387511\pi\) |
−0.985550 | + | 0.169384i | \(0.945822\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.259922 | − | 0.450198i | −0.0126678 | − | 0.0219413i | 0.859622 | − | 0.510931i | \(-0.170699\pi\) |
−0.872290 | + | 0.488989i | \(0.837366\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.210029 | − | 27.0837i | 0.0101879 | − | 1.31375i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.04446 | − | 22.5583i | −0.292512 | − | 1.09167i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.8196i | − | 0.954676i | −0.878720 | − | 0.477338i | \(-0.841602\pi\) | ||
0.878720 | − | 0.477338i | \(-0.158398\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.6940 | + | 21.6940i | 1.04254 | + | 1.04254i | 0.999054 | + | 0.0434911i | \(0.0138480\pi\) |
0.0434911 | + | 0.999054i | \(0.486152\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.9305 | − | 4.53651i | 0.809895 | − | 0.217011i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.8104 | − | 6.81876i | 0.563682 | − | 0.325442i | −0.190940 | − | 0.981602i | \(-0.561154\pi\) |
0.754622 | + | 0.656160i | \(0.227820\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.60316 | + | 1.76931i | 0.313726 | + | 0.0840626i | 0.412246 | − | 0.911072i | \(-0.364744\pi\) |
−0.0985205 | + | 0.995135i | \(0.531411\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.3683 | − | 9.78579i | −1.10776 | − | 0.463891i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.2468 | −1.33305 | −0.666525 | − | 0.745482i | \(-0.732219\pi\) | ||||
−0.666525 | + | 0.745482i | \(0.732219\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.97439 | 0.281323 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.92865 | − | 3.32023i | −0.371701 | − | 0.155655i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.7176 | − | 5.81920i | −1.01590 | − | 0.272211i | −0.287810 | − | 0.957687i | \(-0.592927\pi\) |
−0.728095 | + | 0.685477i | \(0.759594\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.2134 | − | 13.4023i | 1.08116 | − | 0.624206i | 0.149948 | − | 0.988694i | \(-0.452089\pi\) |
0.931208 | + | 0.364488i | \(0.118756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7031 | − | 6.88713i | 1.19452 | − | 0.320072i | 0.393852 | − | 0.919174i | \(-0.371142\pi\) |
0.800673 | + | 0.599102i | \(0.204476\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.918499 | − | 0.918499i | −0.0425031 | − | 0.0425031i | 0.685536 | − | 0.728039i | \(-0.259568\pi\) |
−0.728039 | + | 0.685536i | \(0.759568\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 41.1103i | − | 1.89830i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.13848 | + | 4.24886i | 0.0523473 | + | 0.195363i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.9123 | − | 15.6674i | 0.730107 | − | 0.718870i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.07290 | − | 1.85832i | −0.0490222 | − | 0.0849089i | 0.840473 | − | 0.541853i | \(-0.182277\pi\) |
−0.889495 | + | 0.456944i | \(0.848944\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.37384 | − | 7.57572i | 0.199430 | − | 0.345423i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.2388 | − | 15.6548i | −0.918996 | − | 0.710849i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.2421 | − | 17.2421i | 0.781316 | − | 0.781316i | −0.198737 | − | 0.980053i | \(-0.563684\pi\) |
0.980053 | + | 0.198737i | \(0.0636839\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.57448 | − | 4.95048i | −0.386961 | − | 0.223412i | 0.293882 | − | 0.955842i | \(-0.405053\pi\) |
−0.680843 | + | 0.732430i | \(0.738386\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.45175 | − | 9.15007i | 0.110421 | − | 0.412098i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.91041 | − | 29.5221i | 0.354830 | − | 1.32425i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.91417 | + | 4.56925i | 0.354287 | + | 0.204548i | 0.666572 | − | 0.745441i | \(-0.267761\pi\) |
−0.312285 | + | 0.949989i | \(0.601094\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.7908 | + | 10.7908i | −0.481138 | + | 0.481138i | −0.905495 | − | 0.424357i | \(-0.860500\pi\) |
0.424357 | + | 0.905495i | \(0.360500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.0149 | − | 3.70549i | 1.29115 | − | 0.164892i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.74497 | + | 9.95058i | −0.254641 | + | 0.441052i | −0.964798 | − | 0.262992i | \(-0.915291\pi\) |
0.710157 | + | 0.704044i | \(0.248624\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.7054 | + | 34.1308i | 0.871718 | + | 1.50986i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.9875 | + | 1.62549i | 0.528232 | + | 0.0716277i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.56424 | − | 9.56988i | −0.112775 | − | 0.420883i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.40066i | − | 0.411850i | −0.978568 | − | 0.205925i | \(-0.933980\pi\) | ||
0.978568 | − | 0.205925i | \(-0.0660203\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.46556 | + | 1.46556i | 0.0640843 | + | 0.0640843i | 0.738423 | − | 0.674338i | \(-0.235571\pi\) |
−0.674338 | + | 0.738423i | \(0.735571\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.6790 | + | 7.68452i | −1.24928 | + | 0.334743i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.58002 | − | 3.79898i | 0.286088 | − | 0.165173i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.14951 | + | 2.45160i | 0.396309 | + | 0.106191i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.29598 | − | 15.3681i | −0.272199 | − | 0.664422i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.464810 | 0.0200208 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.78309 | −0.334621 | −0.167311 | − | 0.985904i | \(-0.553508\pi\) | ||||
−0.167311 | + | 0.985904i | \(0.553508\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.87555 | + | 21.1947i | −0.380187 | + | 0.907880i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.6694 | + | 9.28964i | 1.48236 | + | 0.397196i | 0.907148 | − | 0.420811i | \(-0.138254\pi\) |
0.575208 | + | 0.818007i | \(0.304921\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.76388 | − | 3.90513i | 0.288151 | − | 0.166364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.3388 | + | 6.78950i | −1.07751 | + | 0.288719i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.17130 | − | 6.17130i | −0.261486 | − | 0.261486i | 0.564171 | − | 0.825658i | \(-0.309196\pi\) |
−0.825658 | + | 0.564171i | \(0.809196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.97413i | 0.294974i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.65058 | − | 36.0164i | −0.406723 | − | 1.51791i | −0.800855 | − | 0.598858i | \(-0.795621\pi\) |
0.394132 | − | 0.919054i | \(-0.371045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.17993 | − | 38.2004i | 0.217921 | − | 1.60710i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.78087 | + | 15.2089i | 0.368113 | + | 0.637591i | 0.989271 | − | 0.146095i | \(-0.0466706\pi\) |
−0.621157 | + | 0.783686i | \(0.713337\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.87707 | + | 6.71529i | −0.162250 | + | 0.281026i | −0.935675 | − | 0.352862i | \(-0.885209\pi\) |
0.773425 | + | 0.633888i | \(0.218542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.94284 | + | 16.9172i | −0.414645 | + | 0.705495i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.1946 | − | 21.1946i | 0.882344 | − | 0.882344i | −0.111428 | − | 0.993772i | \(-0.535542\pi\) |
0.993772 | + | 0.111428i | \(0.0355425\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0518 | − | 6.38073i | −0.458504 | − | 0.264717i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.19689 | − | 8.19890i | 0.0909858 | − | 0.339564i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.98989 | − | 7.42638i | 0.0821317 | − | 0.306520i | −0.912624 | − | 0.408800i | \(-0.865947\pi\) |
0.994756 | + | 0.102281i | \(0.0326139\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.2000 | − | 12.2398i | −0.873532 | − | 0.504334i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.97136 | + | 2.97136i | −0.122019 | + | 0.122019i | −0.765479 | − | 0.643460i | \(-0.777498\pi\) |
0.643460 | + | 0.765479i | \(0.277498\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.20948 | + | 32.9612i | 0.172572 | + | 1.35128i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.40103 | − | 9.35485i | 0.220680 | − | 0.382229i | −0.734335 | − | 0.678788i | \(-0.762506\pi\) |
0.955015 | + | 0.296559i | \(0.0958390\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.2730 | + | 22.9895i | 0.541418 | + | 0.937763i | 0.998823 | + | 0.0485045i | \(0.0154455\pi\) |
−0.457405 | + | 0.889258i | \(0.651221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.1820 | − | 13.8399i | 0.739204 | − | 0.562671i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.19313 | + | 30.5772i | 0.332549 | + | 1.24109i | 0.906502 | + | 0.422201i | \(0.138742\pi\) |
−0.573953 | + | 0.818888i | \(0.694591\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 15.7081i | − | 0.635482i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.6780 | + | 15.6780i | 0.633228 | + | 0.633228i | 0.948876 | − | 0.315648i | \(-0.102222\pi\) |
−0.315648 | + | 0.948876i | \(0.602222\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.01563 | − | 1.61188i | 0.242180 | − | 0.0648920i | −0.135687 | − | 0.990752i | \(-0.543324\pi\) |
0.377867 | + | 0.925860i | \(0.376658\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.1759 | + | 7.02976i | −0.489391 | + | 0.282550i | −0.724322 | − | 0.689462i | \(-0.757847\pi\) |
0.234931 | + | 0.972012i | \(0.424514\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.0228 | + | 8.04459i | 1.20284 | + | 0.322300i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.387717 | + | 24.9970i | −0.0155087 | + | 0.999880i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.8162 | −1.34834 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.2378 | 1.32318 | 0.661589 | − | 0.749867i | \(-0.269882\pi\) | ||||
0.661589 | + | 0.749867i | \(0.269882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.1964 | − | 12.7805i | 1.23799 | − | 0.507178i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.711836 | + | 0.190736i | 0.0282040 | + | 0.00755723i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.3490 | + | 7.12970i | −0.487756 | + | 0.281606i | −0.723643 | − | 0.690174i | \(-0.757534\pi\) |
0.235887 | + | 0.971780i | \(0.424200\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.0630 | + | 9.39510i | −1.38275 | + | 0.370507i | −0.872119 | − | 0.489293i | \(-0.837255\pi\) |
−0.510631 | + | 0.859800i | \(0.670588\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.6172 | + | 11.6172i | 0.456718 | + | 0.456718i | 0.897577 | − | 0.440858i | \(-0.145326\pi\) |
−0.440858 | + | 0.897577i | \(0.645326\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.11345i | − | 0.279227i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.43066 | − | 31.4636i | −0.329917 | − | 1.23127i | −0.909276 | − | 0.416194i | \(-0.863364\pi\) |
0.579359 | − | 0.815073i | \(-0.303303\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.16337 | − | 1.52837i | −0.0454566 | − | 0.0597182i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.2138 | − | 24.6190i | −0.553691 | − | 0.959021i | −0.998004 | − | 0.0631491i | \(-0.979886\pi\) |
0.444313 | − | 0.895871i | \(-0.353448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.00541 | − | 1.74143i | 0.0391060 | − | 0.0677336i | −0.845810 | − | 0.533484i | \(-0.820882\pi\) |
0.884916 | + | 0.465751i | \(0.154216\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.7623 | + | 21.6706i | −0.650015 | + | 0.840349i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.85292 | + | 4.85292i | −0.187906 | + | 0.187906i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.51587 | − | 3.76194i | −0.251542 | − | 0.145228i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.36532 | + | 20.0237i | −0.206818 | + | 0.771855i | 0.782070 | + | 0.623191i | \(0.214164\pi\) |
−0.988888 | + | 0.148664i | \(0.952503\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.55998 | + | 13.2860i | −0.136821 | + | 0.510623i | 0.863163 | + | 0.504926i | \(0.168480\pi\) |
−0.999984 | + | 0.00569716i | \(0.998187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.1857 | + | 15.6957i | 1.04329 | + | 0.602345i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.6518 | + | 17.6518i | −0.675426 | + | 0.675426i | −0.958962 | − | 0.283536i | \(-0.908492\pi\) |
0.283536 | + | 0.958962i | \(0.408492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.6009 | − | 25.3404i | 0.748913 | − | 0.968206i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.72888 | − | 11.6548i | 0.256350 | − | 0.444011i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.36784 | − | 9.29738i | −0.204202 | − | 0.353689i | 0.745676 | − | 0.666309i | \(-0.232127\pi\) |
−0.949878 | + | 0.312620i | \(0.898793\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.0656 | + | 19.7923i | 0.571472 | + | 0.750767i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.47723 | − | 35.3695i | −0.358976 | − | 1.33972i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.4271i | 1.45137i | 0.688026 | + | 0.725686i | \(0.258478\pi\) | ||||
−0.688026 | + | 0.725686i | \(0.741522\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.7149 | − | 19.7149i | −0.743561 | − | 0.743561i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34.6635 | + | 9.28805i | −1.30365 | + | 0.349313i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.01213 | − | 1.73906i | 0.113123 | − | 0.0653116i | −0.442371 | − | 0.896832i | \(-0.645863\pi\) |
0.555494 | + | 0.831521i | \(0.312529\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7779 | + | 5.56743i | 0.778139 | + | 0.208502i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.56256 | + | 1.04983i | −0.0958343 | + | 0.0392612i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.6808 | 0.733970 | 0.366985 | − | 0.930227i | \(-0.380390\pi\) | ||||
0.366985 | + | 0.930227i | \(0.380390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.8416 | −0.552728 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.32848 | + | 8.42804i | −0.0864776 | + | 0.313009i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.1645 | − | 5.40306i | −0.747860 | − | 0.200388i | −0.135291 | − | 0.990806i | \(-0.543197\pi\) |
−0.612569 | + | 0.790417i | \(0.709864\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.3481 | − | 13.4800i | 0.863561 | − | 0.498577i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2977 | − | 3.02722i | 0.417291 | − | 0.111813i | −0.0440635 | − | 0.999029i | \(-0.514030\pi\) |
0.461354 | + | 0.887216i | \(0.347364\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.36516 | − | 9.36516i | −0.344970 | − | 0.344970i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.09434i | 0.113827i | 0.998379 | + | 0.0569136i | \(0.0181259\pi\) | ||||
−0.998379 | + | 0.0569136i | \(0.981874\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.79197 | − | 17.8839i | −0.175800 | − | 0.656096i | −0.996414 | − | 0.0846124i | \(-0.973035\pi\) |
0.820614 | − | 0.571483i | \(-0.193632\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.59383 | − | 1.97438i | 0.0950305 | − | 0.0723358i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.1877 | + | 17.6456i | 0.372251 | + | 0.644757i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.1986 | − | 47.1093i | 0.992490 | − | 1.71904i | 0.390310 | − | 0.920684i | \(-0.372368\pi\) |
0.602181 | − | 0.798360i | \(-0.294299\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.25517 | − | 25.4888i | −0.118468 | − | 0.927632i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.8602 | + | 23.8602i | −0.867215 | + | 0.867215i | −0.992163 | − | 0.124949i | \(-0.960123\pi\) |
0.124949 | + | 0.992163i | \(0.460123\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.20716 | − | 4.73841i | −0.297509 | − | 0.171767i | 0.343814 | − | 0.939038i | \(-0.388281\pi\) |
−0.641323 | + | 0.767271i | \(0.721614\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.29631 | − | 27.2302i | 0.264144 | − | 0.985800i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.91902 | − | 10.8939i | 0.105400 | − | 0.393357i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.0491 | + | 7.53390i | 0.470562 | + | 0.271679i | 0.716475 | − | 0.697613i | \(-0.245754\pi\) |
−0.245913 | + | 0.969292i | \(0.579088\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.1782 | − | 29.1782i | 1.04947 | − | 1.04947i | 0.0507568 | − | 0.998711i | \(-0.483837\pi\) |
0.998711 | − | 0.0507568i | \(-0.0161633\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.5260 | − | 6.88760i | 0.952841 | − | 0.247410i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.0952 | − | 26.1457i | 0.540843 | − | 0.936768i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.92326 | − | 8.52734i | −0.176168 | − | 0.305132i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.30429 | − | 9.61872i | 0.0465521 | − | 0.343307i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.77504 | + | 29.0169i | 0.277150 | + | 1.03434i | 0.954387 | + | 0.298574i | \(0.0965108\pi\) |
−0.677236 | + | 0.735766i | \(0.736823\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 47.2954i | 1.68163i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.43505 | − | 8.43505i | −0.299537 | − | 0.299537i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.09921 | − | 1.90223i | 0.251467 | − | 0.0673804i | −0.130883 | − | 0.991398i | \(-0.541781\pi\) |
0.382350 | + | 0.924017i | \(0.375115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −52.5878 | + | 30.3616i | −1.86042 | + | 1.07412i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.2642 | + | 3.28619i | 0.432795 | + | 0.115967i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.29901 | − | 22.2059i | 0.327747 | − | 0.782654i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.95255 | 0.349913 | 0.174957 | − | 0.984576i | \(-0.444021\pi\) | ||||
0.174957 | + | 0.984576i | \(0.444021\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.0435 | −0.598480 | −0.299240 | − | 0.954178i | \(-0.596733\pi\) | ||||
−0.299240 | + | 0.954178i | \(0.596733\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.9411 | − | 31.5884i | −0.453307 | − | 1.10649i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.4709 | + | 5.75310i | 0.751171 | + | 0.201276i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.0949 | − | 11.6018i | 0.701317 | − | 0.404905i | −0.106521 | − | 0.994310i | \(-0.533971\pi\) |
0.807838 | + | 0.589405i | \(0.200638\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.7186 | + | 9.83871i | −1.27993 | + | 0.342956i | −0.833827 | − | 0.552026i | \(-0.813855\pi\) |
−0.446102 | + | 0.894982i | \(0.647188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.71693 | + | 5.71693i | 0.198797 | + | 0.198797i | 0.799484 | − | 0.600687i | \(-0.205106\pi\) |
−0.600687 | + | 0.799484i | \(0.705106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.6644i | 1.55126i | 0.631189 | + | 0.775629i | \(0.282567\pi\) | ||||
−0.631189 | + | 0.775629i | \(0.717433\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.737333 | − | 2.75176i | −0.0255471 | − | 0.0953430i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.9065 | − | 5.41128i | −1.38102 | − | 0.187265i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.5225 | − | 18.2255i | −0.363277 | − | 0.629215i | 0.625221 | − | 0.780448i | \(-0.285009\pi\) |
−0.988498 | + | 0.151233i | \(0.951676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.9709 | − | 22.4663i | 0.447273 | − | 0.774700i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.4794 | − | 3.12627i | 0.842118 | − | 0.107547i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.8229 | + | 19.8229i | −0.681124 | + | 0.681124i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.2174 | + | 12.2499i | 0.727323 | + | 0.419920i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.07750 | − | 4.02129i | 0.0368929 | − | 0.137686i | −0.945023 | − | 0.327004i | \(-0.893961\pi\) |
0.981916 | + | 0.189318i | \(0.0606276\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.32222 | + | 8.66663i | −0.0793254 | + | 0.296047i | −0.994179 | − | 0.107739i | \(-0.965639\pi\) |
0.914854 | + | 0.403785i | \(0.132306\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.3253 | − | 16.9310i | −1.00057 | − | 0.577677i | −0.0921499 | − | 0.995745i | \(-0.529374\pi\) |
−0.908416 | + | 0.418068i | \(0.862707\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.6082 | + | 23.6082i | −0.803631 | + | 0.803631i | −0.983661 | − | 0.180030i | \(-0.942380\pi\) |
0.180030 | + | 0.983661i | \(0.442380\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.4471 | − | 18.1364i | −0.797224 | − | 0.616657i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.22563 | + | 7.31901i | −0.143345 | + | 0.248280i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.4993 | − | 18.1853i | −0.355756 | − | 0.616187i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.64945 | − | 30.4536i | −0.123374 | − | 1.02952i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.4930 | + | 39.1603i | 0.354322 | + | 1.32235i | 0.881335 | + | 0.472491i | \(0.156645\pi\) |
−0.527013 | + | 0.849857i | \(0.676688\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 55.0463i | 1.85456i | 0.374373 | + | 0.927278i | \(0.377858\pi\) | ||||
−0.374373 | + | 0.927278i | \(0.622142\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.7855 | + | 24.7855i | 0.834098 | + | 0.834098i | 0.988075 | − | 0.153976i | \(-0.0492080\pi\) |
−0.153976 | + | 0.988075i | \(0.549208\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.54754 | + | 1.21851i | −0.152692 | + | 0.0409136i | −0.334355 | − | 0.942447i | \(-0.608518\pi\) |
0.181664 | + | 0.983361i | \(0.441852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.8196 | + | 20.6805i | −1.20135 | + | 0.693601i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.3597 | − | 12.9579i | −1.61829 | − | 0.433621i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.80132 | + | 3.26691i | 0.260769 | + | 0.109201i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.58513 | 0.319682 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.0240 | −1.73317 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 47.4527 | + | 19.8715i | 1.57738 | + | 0.660550i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.0766 | + | 9.93464i | 1.23111 | + | 0.329874i | 0.815011 | − | 0.579446i | \(-0.196731\pi\) |
0.416097 | + | 0.909320i | \(0.363398\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.6058 | + | 11.3194i | −0.649570 | + | 0.375029i | −0.788291 | − | 0.615302i | \(-0.789034\pi\) |
0.138721 | + | 0.990331i | \(0.455701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.97122 | + | 1.06409i | −0.131428 | + | 0.0352161i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.66630 | + | 1.66630i | 0.0550261 | + | 0.0550261i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.4135i | − | 1.13520i | −0.823306 | − | 0.567598i | \(-0.807873\pi\) | ||
0.823306 | − | 0.567598i | \(-0.192127\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.04055 | − | 15.0795i | −0.132996 | − | 0.496348i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.2126 | + | 0.242048i | 1.02626 | + | 0.00795848i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.2552 | + | 50.6715i | 0.959832 | + | 1.66248i | 0.722901 | + | 0.690951i | \(0.242808\pi\) |
0.236931 | + | 0.971527i | \(0.423859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.17442 | − | 2.03415i | 0.0384899 | − | 0.0666665i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.46770 | + | 6.54982i | 0.276923 | + | 0.214202i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.6817 | + | 33.6817i | −1.10033 | + | 1.10033i | −0.105963 | + | 0.994370i | \(0.533793\pi\) |
−0.994370 | + | 0.105963i | \(0.966207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.64011 | − | 2.67897i | −0.151263 | − | 0.0873320i | 0.422458 | − | 0.906383i | \(-0.361167\pi\) |
−0.573721 | + | 0.819051i | \(0.694501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.86624 | + | 25.6252i | −0.223596 | + | 0.834470i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.28954 | + | 30.9370i | −0.269374 | + | 1.00532i | 0.690145 | + | 0.723671i | \(0.257547\pi\) |
−0.959519 | + | 0.281646i | \(0.909120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.4336 | + | 10.0653i | 0.565920 | + | 0.326734i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.7285 | − | 31.7285i | 1.02779 | − | 1.02779i | 0.0281830 | − | 0.999603i | \(-0.491028\pi\) |
0.999603 | − | 0.0281830i | \(-0.00897210\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.3745 | − | 3.11287i | 0.788741 | − | 0.100730i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.6521 | + | 34.0384i | −0.634599 | + | 1.09916i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.478676 | + | 0.829091i | 0.0154412 | + | 0.0267449i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.2372 | − | 3.28655i | −0.780224 | − | 0.105798i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.48992 | − | 24.2207i | −0.208702 | − | 0.778886i | −0.988289 | − | 0.152592i | \(-0.951238\pi\) |
0.779587 | − | 0.626293i | \(-0.215429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.3757i | 0.621794i | 0.950444 | + | 0.310897i | \(0.100629\pi\) | ||||
−0.950444 | + | 0.310897i | \(0.899371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.5786 | − | 21.5786i | −0.691778 | − | 0.691778i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.6816 | + | 12.7763i | −1.52547 | + | 0.408749i | −0.921538 | − | 0.388287i | \(-0.873067\pi\) |
−0.603932 | + | 0.797036i | \(0.706400\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.67198 | − | 5.00677i | 0.277158 | − | 0.160017i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.0191 | − | 2.95256i | −0.351454 | − | 0.0941719i | 0.0787728 | − | 0.996893i | \(-0.474900\pi\) |
−0.430227 | + | 0.902721i | \(0.641567\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.39120 | + | 13.1596i | 0.171778 | + | 0.419300i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.5325 | −0.621099 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4006 | −0.806876 | −0.403438 | − | 0.915007i | \(-0.632185\pi\) | ||||
−0.403438 | + | 0.915007i | \(0.632185\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.4072 | + | 29.6282i | −0.393334 | + | 0.939276i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.6160 | + | 6.59585i | 0.779598 | + | 0.208893i | 0.626607 | − | 0.779335i | \(-0.284443\pi\) |
0.152990 | + | 0.988228i | \(0.451110\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1080.2.bt.a.233.3 | 72 | ||
3.2 | odd | 2 | 360.2.bs.a.113.7 | ✓ | 72 | ||
5.2 | odd | 4 | inner | 1080.2.bt.a.17.4 | 72 | ||
9.2 | odd | 6 | inner | 1080.2.bt.a.953.4 | 72 | ||
9.7 | even | 3 | 360.2.bs.a.353.4 | yes | 72 | ||
12.11 | even | 2 | 720.2.cu.e.113.12 | 72 | |||
15.2 | even | 4 | 360.2.bs.a.257.4 | yes | 72 | ||
36.7 | odd | 6 | 720.2.cu.e.353.15 | 72 | |||
45.2 | even | 12 | inner | 1080.2.bt.a.737.3 | 72 | ||
45.7 | odd | 12 | 360.2.bs.a.137.7 | yes | 72 | ||
60.47 | odd | 4 | 720.2.cu.e.257.15 | 72 | |||
180.7 | even | 12 | 720.2.cu.e.497.12 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bs.a.113.7 | ✓ | 72 | 3.2 | odd | 2 | ||
360.2.bs.a.137.7 | yes | 72 | 45.7 | odd | 12 | ||
360.2.bs.a.257.4 | yes | 72 | 15.2 | even | 4 | ||
360.2.bs.a.353.4 | yes | 72 | 9.7 | even | 3 | ||
720.2.cu.e.113.12 | 72 | 12.11 | even | 2 | |||
720.2.cu.e.257.15 | 72 | 60.47 | odd | 4 | |||
720.2.cu.e.353.15 | 72 | 36.7 | odd | 6 | |||
720.2.cu.e.497.12 | 72 | 180.7 | even | 12 | |||
1080.2.bt.a.17.4 | 72 | 5.2 | odd | 4 | inner | ||
1080.2.bt.a.233.3 | 72 | 1.1 | even | 1 | trivial | ||
1080.2.bt.a.737.3 | 72 | 45.2 | even | 12 | inner | ||
1080.2.bt.a.953.4 | 72 | 9.2 | odd | 6 | inner |