Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,2,Mod(647,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.c (of order \(2\), degree \(1\), 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: | \(5.46176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 647.20 | ||
Character | \(\chi\) | \(=\) | 684.647 |
Dual form | 684.2.c.b.647.19 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.647279 | + | 1.25739i | 0.457695 | + | 0.889109i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.16206 | + | 1.62776i | −0.581030 | + | 0.813882i | ||||
\(5\) | − | 1.07823i | − | 0.482198i | −0.970501 | − | 0.241099i | \(-0.922492\pi\) | ||
0.970501 | − | 0.241099i | \(-0.0775079\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.32412i | − | 1.25640i | −0.778052 | − | 0.628200i | \(-0.783792\pi\) | ||
0.778052 | − | 0.628200i | \(-0.216208\pi\) | |||||||
\(8\) | −2.79891 | − | 0.407546i | −0.989565 | − | 0.144089i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.35575 | − | 0.697914i | 0.428727 | − | 0.220700i | ||||
\(11\) | 1.96175 | 0.591489 | 0.295744 | − | 0.955267i | \(-0.404432\pi\) | ||||
0.295744 | + | 0.955267i | \(0.404432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.47134 | 1.51748 | 0.758738 | − | 0.651396i | \(-0.225816\pi\) | ||||
0.758738 | + | 0.651396i | \(0.225816\pi\) | |||||||
\(14\) | 4.17972 | − | 2.15163i | 1.11708 | − | 0.575048i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.29923 | − | 3.78312i | −0.324808 | − | 0.945780i | ||||
\(17\) | − | 3.80151i | − | 0.922001i | −0.887400 | − | 0.461001i | \(-0.847491\pi\) | ||
0.887400 | − | 0.461001i | \(-0.152509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 1.75510 | + | 1.25297i | 0.392452 | + | 0.280172i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.26980 | + | 2.46668i | 0.270722 | + | 0.525898i | ||||
\(23\) | 0.563522 | 0.117502 | 0.0587512 | − | 0.998273i | \(-0.481288\pi\) | ||||
0.0587512 | + | 0.998273i | \(0.481288\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.83743 | 0.767485 | ||||||||
\(26\) | 3.54148 | + | 6.87961i | 0.694542 | + | 1.34920i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.41088 | + | 3.86283i | 1.02256 | + | 0.730006i | ||||
\(29\) | 10.2866i | 1.91017i | 0.296332 | + | 0.955085i | \(0.404237\pi\) | ||||
−0.296332 | + | 0.955085i | \(0.595763\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.19699i | − | 1.29262i | −0.763076 | − | 0.646309i | \(-0.776312\pi\) | ||
0.763076 | − | 0.646309i | \(-0.223688\pi\) | |||||||
\(32\) | 3.91589 | − | 4.08238i | 0.692238 | − | 0.721669i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.77998 | − | 2.46064i | 0.819760 | − | 0.421996i | ||||
\(35\) | −3.58416 | −0.605833 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.71282 | 0.774783 | 0.387391 | − | 0.921915i | \(-0.373376\pi\) | ||||
0.387391 | + | 0.921915i | \(0.373376\pi\) | |||||||
\(38\) | −1.25739 | + | 0.647279i | −0.203976 | + | 0.105002i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.439427 | + | 3.01786i | −0.0694795 | + | 0.477166i | ||||
\(41\) | 2.44045i | 0.381134i | 0.981674 | + | 0.190567i | \(0.0610326\pi\) | ||||
−0.981674 | + | 0.190567i | \(0.938967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.9618i | − | 1.82416i | −0.410009 | − | 0.912082i | \(-0.634474\pi\) | ||
0.410009 | − | 0.912082i | \(-0.365526\pi\) | |||||||
\(44\) | −2.27967 | + | 3.19326i | −0.343673 | + | 0.481402i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.364756 | + | 0.708567i | 0.0537803 | + | 0.104473i | ||||
\(47\) | −4.38837 | −0.640110 | −0.320055 | − | 0.947399i | \(-0.603701\pi\) | ||||
−0.320055 | + | 0.947399i | \(0.603701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.04978 | −0.578539 | ||||||||
\(50\) | 2.48388 | + | 4.82514i | 0.351274 | + | 0.682378i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.35802 | + | 8.90605i | −0.881699 | + | 1.23505i | ||||
\(53\) | 3.92349i | 0.538933i | 0.963010 | + | 0.269467i | \(0.0868474\pi\) | ||||
−0.963010 | + | 0.269467i | \(0.913153\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.11521i | − | 0.285215i | ||||||
\(56\) | −1.35473 | + | 9.30392i | −0.181034 | + | 1.24329i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.9342 | + | 6.65829i | −1.69835 | + | 0.874276i | ||||
\(59\) | −12.4430 | −1.61995 | −0.809973 | − | 0.586468i | \(-0.800518\pi\) | ||||
−0.809973 | + | 0.586468i | \(0.800518\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.74286 | −0.863335 | −0.431668 | − | 0.902033i | \(-0.642075\pi\) | ||||
−0.431668 | + | 0.902033i | \(0.642075\pi\) | |||||||
\(62\) | 9.04943 | − | 4.65846i | 1.14928 | − | 0.591625i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.66781 | + | 2.28137i | 0.958477 | + | 0.285171i | ||||
\(65\) | − | 5.89935i | − | 0.731724i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.40676i | 0.416202i | 0.978107 | + | 0.208101i | \(0.0667283\pi\) | ||||
−0.978107 | + | 0.208101i | \(0.933272\pi\) | |||||||
\(68\) | 6.18796 | + | 4.41758i | 0.750400 | + | 0.535710i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.31995 | − | 4.50669i | −0.277287 | − | 0.538652i | ||||
\(71\) | 0.390266 | 0.0463161 | 0.0231580 | − | 0.999732i | \(-0.492628\pi\) | ||||
0.0231580 | + | 0.999732i | \(0.492628\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.10952 | 0.715065 | 0.357533 | − | 0.933901i | \(-0.383618\pi\) | ||||
0.357533 | + | 0.933901i | \(0.383618\pi\) | |||||||
\(74\) | 3.05051 | + | 5.92585i | 0.354614 | + | 0.688866i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.62776 | − | 1.16206i | −0.186717 | − | 0.133297i | ||||
\(77\) | − | 6.52108i | − | 0.743146i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.10895i | 0.912328i | 0.889896 | + | 0.456164i | \(0.150777\pi\) | ||||
−0.889896 | + | 0.456164i | \(0.849223\pi\) | |||||||
\(80\) | −4.07906 | + | 1.40087i | −0.456053 | + | 0.156622i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.06859 | + | 1.57965i | −0.338869 | + | 0.174443i | ||||
\(83\) | 11.1298 | 1.22166 | 0.610830 | − | 0.791762i | \(-0.290836\pi\) | ||||
0.610830 | + | 0.791762i | \(0.290836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.09889 | −0.444587 | ||||||||
\(86\) | 15.0407 | − | 7.74264i | 1.62188 | − | 0.834911i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.49075 | − | 0.799501i | −0.585316 | − | 0.0852271i | ||||
\(89\) | − | 11.2732i | − | 1.19495i | −0.801887 | − | 0.597476i | \(-0.796170\pi\) | ||
0.801887 | − | 0.597476i | \(-0.203830\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 18.1874i | − | 1.90656i | ||||||
\(92\) | −0.654846 | + | 0.917281i | −0.0682725 | + | 0.0956331i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.84050 | − | 5.51790i | −0.292975 | − | 0.569128i | ||||
\(95\) | 1.07823 | 0.110624 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.56020 | −0.970691 | −0.485345 | − | 0.874323i | \(-0.661306\pi\) | ||||
−0.485345 | + | 0.874323i | \(0.661306\pi\) | |||||||
\(98\) | −2.62133 | − | 5.09215i | −0.264795 | − | 0.514385i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.45932 | + | 6.24642i | −0.445932 | + | 0.624642i | ||||
\(101\) | 0.547862i | 0.0545143i | 0.999628 | + | 0.0272571i | \(0.00867729\pi\) | ||||
−0.999628 | + | 0.0272571i | \(0.991323\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7223i | 1.25357i | 0.779194 | + | 0.626783i | \(0.215629\pi\) | ||||
−0.779194 | + | 0.626783i | \(0.784371\pi\) | |||||||
\(104\) | −15.3138 | − | 2.22982i | −1.50164 | − | 0.218652i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.93336 | + | 2.53959i | −0.479170 | + | 0.246667i | ||||
\(107\) | 5.79148 | 0.559883 | 0.279942 | − | 0.960017i | \(-0.409685\pi\) | ||||
0.279942 | + | 0.960017i | \(0.409685\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7901 | 1.32085 | 0.660424 | − | 0.750893i | \(-0.270377\pi\) | ||||
0.660424 | + | 0.750893i | \(0.270377\pi\) | |||||||
\(110\) | 2.65964 | − | 1.36913i | 0.253587 | − | 0.130541i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.5755 | + | 4.31880i | −1.18828 | + | 0.408089i | ||||
\(113\) | 5.13667i | 0.483218i | 0.970374 | + | 0.241609i | \(0.0776751\pi\) | ||||
−0.970374 | + | 0.241609i | \(0.922325\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.607605i | − | 0.0566595i | ||||||
\(116\) | −16.7441 | − | 11.9536i | −1.55465 | − | 1.10987i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.05411 | − | 15.6458i | −0.741441 | − | 1.44031i | ||||
\(119\) | −12.6367 | −1.15840 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.15155 | −0.650141 | ||||||||
\(122\) | −4.36451 | − | 8.47841i | −0.395144 | − | 0.767599i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.7150 | + | 8.36334i | 1.05204 | + | 0.751050i | ||||
\(125\) | − | 9.52876i | − | 0.852278i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.00490i | − | 0.355377i | −0.984087 | − | 0.177689i | \(-0.943138\pi\) | ||
0.984087 | − | 0.177689i | \(-0.0568620\pi\) | |||||||
\(128\) | 2.09464 | + | 11.1181i | 0.185142 | + | 0.982712i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.41778 | − | 3.81852i | 0.650583 | − | 0.334907i | ||||
\(131\) | −18.9380 | −1.65462 | −0.827308 | − | 0.561748i | \(-0.810129\pi\) | ||||
−0.827308 | + | 0.561748i | \(0.810129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.32412 | 0.288238 | ||||||||
\(134\) | −4.28363 | + | 2.20512i | −0.370049 | + | 0.190494i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.54929 | + | 10.6401i | −0.132850 | + | 0.912380i | ||||
\(137\) | − | 1.57895i | − | 0.134899i | −0.997723 | − | 0.0674496i | \(-0.978514\pi\) | ||
0.997723 | − | 0.0674496i | \(-0.0214862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.09687i | − | 0.0930353i | −0.998917 | − | 0.0465177i | \(-0.985188\pi\) | ||
0.998917 | − | 0.0465177i | \(-0.0148124\pi\) | |||||||
\(140\) | 4.16501 | − | 5.83416i | 0.352007 | − | 0.493077i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.252611 | + | 0.490717i | 0.0211987 | + | 0.0411800i | ||||
\(143\) | 10.7334 | 0.897570 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.0913 | 0.921080 | ||||||||
\(146\) | 3.95456 | + | 7.68205i | 0.327282 | + | 0.635771i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.47658 | + | 7.67136i | −0.450172 | + | 0.630582i | ||||
\(149\) | 3.63911i | 0.298127i | 0.988828 | + | 0.149064i | \(0.0476259\pi\) | ||||
−0.988828 | + | 0.149064i | \(0.952374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.9298i | 1.13359i | 0.823857 | + | 0.566797i | \(0.191818\pi\) | ||||
−0.823857 | + | 0.566797i | \(0.808182\pi\) | |||||||
\(152\) | 0.407546 | − | 2.79891i | 0.0330563 | − | 0.227022i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.19954 | − | 4.22096i | 0.660738 | − | 0.340134i | ||||
\(155\) | −7.76000 | −0.623298 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.52169 | −0.520487 | −0.260244 | − | 0.965543i | \(-0.583803\pi\) | ||||
−0.260244 | + | 0.965543i | \(0.583803\pi\) | |||||||
\(158\) | −10.1961 | + | 5.24875i | −0.811159 | + | 0.417568i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.40173 | − | 4.22222i | −0.347987 | − | 0.333796i | ||||
\(161\) | − | 1.87321i | − | 0.147630i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.21662i | − | 0.330271i | −0.986271 | − | 0.165136i | \(-0.947194\pi\) | ||
0.986271 | − | 0.165136i | \(-0.0528062\pi\) | |||||||
\(164\) | −3.97247 | − | 2.83594i | −0.310198 | − | 0.221450i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.20411 | + | 13.9946i | 0.559148 | + | 1.08619i | ||||
\(167\) | −17.8978 | −1.38497 | −0.692486 | − | 0.721431i | \(-0.743485\pi\) | ||||
−0.692486 | + | 0.721431i | \(0.743485\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.9355 | 1.30273 | ||||||||
\(170\) | −2.65313 | − | 5.15391i | −0.203485 | − | 0.395286i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 19.4711 | + | 13.9004i | 1.48465 | + | 1.05989i | ||||
\(173\) | − | 11.5422i | − | 0.877535i | −0.898601 | − | 0.438767i | \(-0.855415\pi\) | ||
0.898601 | − | 0.438767i | \(-0.144585\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 12.7561i | − | 0.964268i | ||||||
\(176\) | −2.54876 | − | 7.42152i | −0.192120 | − | 0.559418i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.1748 | − | 7.29687i | 1.06244 | − | 0.546924i | ||||
\(179\) | 23.9339 | 1.78890 | 0.894451 | − | 0.447167i | \(-0.147567\pi\) | ||||
0.894451 | + | 0.447167i | \(0.147567\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2682 | −0.911886 | −0.455943 | − | 0.890009i | \(-0.650698\pi\) | ||||
−0.455943 | + | 0.890009i | \(0.650698\pi\) | |||||||
\(182\) | 22.8686 | − | 11.7723i | 1.69514 | − | 0.872622i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.57725 | − | 0.229661i | −0.116276 | − | 0.0169308i | ||||
\(185\) | − | 5.08149i | − | 0.373599i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.45759i | − | 0.545353i | ||||||
\(188\) | 5.09955 | − | 7.14324i | 0.371923 | − | 0.520974i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.697914 | + | 1.35575i | 0.0506320 | + | 0.0983566i | ||||
\(191\) | −20.5274 | −1.48531 | −0.742657 | − | 0.669672i | \(-0.766435\pi\) | ||||
−0.742657 | + | 0.669672i | \(0.766435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.6621 | −1.34333 | −0.671663 | − | 0.740857i | \(-0.734420\pi\) | ||||
−0.671663 | + | 0.740857i | \(0.734420\pi\) | |||||||
\(194\) | −6.18811 | − | 12.0209i | −0.444281 | − | 0.863050i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.70608 | − | 6.59208i | 0.336149 | − | 0.470863i | ||||
\(197\) | 14.8835i | 1.06041i | 0.847871 | + | 0.530203i | \(0.177884\pi\) | ||||
−0.847871 | + | 0.530203i | \(0.822116\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.4995i | 1.66584i | 0.553397 | + | 0.832918i | \(0.313331\pi\) | ||||
−0.553397 | + | 0.832918i | \(0.686669\pi\) | |||||||
\(200\) | −10.7406 | − | 1.56393i | −0.759476 | − | 0.110586i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.688876 | + | 0.354619i | −0.0484692 | + | 0.0249509i | ||||
\(203\) | 34.1938 | 2.39994 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.63136 | 0.183782 | ||||||||
\(206\) | −15.9969 | + | 8.23488i | −1.11456 | + | 0.573751i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.10854 | − | 20.6987i | −0.492889 | − | 1.43520i | ||||
\(209\) | 1.96175i | 0.135697i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.83240i | 0.608047i | 0.952664 | + | 0.304024i | \(0.0983302\pi\) | ||||
−0.952664 | + | 0.304024i | \(0.901670\pi\) | |||||||
\(212\) | −6.38652 | − | 4.55933i | −0.438628 | − | 0.313136i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.74870 | + | 7.28215i | 0.256256 | + | 0.497798i | ||||
\(215\) | −12.8976 | −0.879608 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.9237 | −1.62404 | ||||||||
\(218\) | 8.92601 | + | 17.3395i | 0.604546 | + | 1.17438i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.44306 | + | 2.45800i | 0.232131 | + | 0.165718i | ||||
\(221\) | − | 20.7993i | − | 1.39911i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.5423i | 1.77741i | 0.458484 | + | 0.888703i | \(0.348393\pi\) | ||||
−0.458484 | + | 0.888703i | \(0.651607\pi\) | |||||||
\(224\) | −13.5703 | − | 13.0169i | −0.906704 | − | 0.869728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.45880 | + | 3.32486i | −0.429633 | + | 0.221166i | ||||
\(227\) | 11.7947 | 0.782840 | 0.391420 | − | 0.920212i | \(-0.371984\pi\) | ||||
0.391420 | + | 0.920212i | \(0.371984\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.84691 | 0.452457 | 0.226228 | − | 0.974074i | \(-0.427360\pi\) | ||||
0.226228 | + | 0.974074i | \(0.427360\pi\) | |||||||
\(230\) | 0.763996 | − | 0.393290i | 0.0503764 | − | 0.0259328i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.19225 | − | 28.7912i | 0.275235 | − | 1.89024i | ||||
\(233\) | 17.5158i | 1.14750i | 0.819031 | + | 0.573749i | \(0.194511\pi\) | ||||
−0.819031 | + | 0.573749i | \(0.805489\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.73166i | 0.308660i | ||||||||
\(236\) | 14.4596 | − | 20.2543i | 0.941237 | − | 1.31844i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.17945 | − | 15.8892i | −0.530195 | − | 1.02995i | ||||
\(239\) | 12.9244 | 0.836012 | 0.418006 | − | 0.908444i | \(-0.362729\pi\) | ||||
0.418006 | + | 0.908444i | \(0.362729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7444 | −0.756520 | −0.378260 | − | 0.925699i | \(-0.623478\pi\) | ||||
−0.378260 | + | 0.925699i | \(0.623478\pi\) | |||||||
\(242\) | −4.62905 | − | 8.99229i | −0.297567 | − | 0.578046i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.83561 | − | 10.9758i | 0.501624 | − | 0.702653i | ||||
\(245\) | 4.36658i | 0.278971i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.47134i | 0.348133i | ||||||||
\(248\) | −2.93310 | + | 20.1438i | −0.186252 | + | 1.27913i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.9814 | − | 6.16776i | 0.757768 | − | 0.390084i | ||||
\(251\) | 17.3203 | 1.09325 | 0.546623 | − | 0.837379i | \(-0.315913\pi\) | ||||
0.546623 | + | 0.837379i | \(0.315913\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.10549 | 0.0695014 | ||||||||
\(254\) | 5.03572 | − | 2.59229i | 0.315969 | − | 0.162655i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.6240 | + | 9.83030i | −0.788999 | + | 0.614394i | ||||
\(257\) | − | 19.5964i | − | 1.22239i | −0.791479 | − | 0.611196i | \(-0.790689\pi\) | ||
0.791479 | − | 0.611196i | \(-0.209311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 15.6660i | − | 0.973436i | ||||||
\(260\) | 9.60275 | + | 6.85540i | 0.595537 | + | 0.425154i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.2581 | − | 23.8124i | −0.757310 | − | 1.47113i | ||||
\(263\) | −20.1348 | −1.24156 | −0.620781 | − | 0.783984i | \(-0.713185\pi\) | ||||
−0.620781 | + | 0.783984i | \(0.713185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.23042 | 0.259872 | ||||||||
\(266\) | 2.15163 | + | 4.17972i | 0.131925 | + | 0.256275i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.54540 | − | 3.95886i | −0.338739 | − | 0.241826i | ||||
\(269\) | 11.7206i | 0.714620i | 0.933986 | + | 0.357310i | \(0.116306\pi\) | ||||
−0.933986 | + | 0.357310i | \(0.883694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.1065i | − | 0.856907i | −0.903564 | − | 0.428454i | \(-0.859059\pi\) | ||
0.903564 | − | 0.428454i | \(-0.140941\pi\) | |||||||
\(272\) | −14.3816 | + | 4.93904i | −0.872010 | + | 0.299473i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.98536 | − | 1.02202i | 0.119940 | − | 0.0617427i | ||||
\(275\) | 7.52805 | 0.453959 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.1942 | 0.852845 | 0.426423 | − | 0.904524i | \(-0.359774\pi\) | ||||
0.426423 | + | 0.904524i | \(0.359774\pi\) | |||||||
\(278\) | 1.37919 | − | 0.709981i | 0.0827185 | − | 0.0425818i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.0317 | + | 1.46071i | 0.599511 | + | 0.0872940i | ||||
\(281\) | 23.8492i | 1.42272i | 0.702826 | + | 0.711362i | \(0.251921\pi\) | ||||
−0.702826 | + | 0.711362i | \(0.748079\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.2442i | 0.846729i | 0.905959 | + | 0.423364i | \(0.139151\pi\) | ||||
−0.905959 | + | 0.423364i | \(0.860849\pi\) | |||||||
\(284\) | −0.453513 | + | 0.635261i | −0.0269110 | + | 0.0376958i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.94749 | + | 13.4960i | 0.410814 | + | 0.798038i | ||||
\(287\) | 8.11233 | 0.478856 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.54854 | 0.149914 | ||||||||
\(290\) | 7.17915 | + | 13.9461i | 0.421574 | + | 0.818941i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.09963 | + | 9.94486i | −0.415475 | + | 0.581979i | ||||
\(293\) | 12.9038i | 0.753850i | 0.926244 | + | 0.376925i | \(0.123019\pi\) | ||||
−0.926244 | + | 0.376925i | \(0.876981\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.4164i | 0.781134i | ||||||||
\(296\) | −13.1908 | − | 1.92069i | −0.766698 | − | 0.111638i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.57578 | + | 2.35552i | −0.265068 | + | 0.136451i | ||||
\(299\) | 3.08322 | 0.178307 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −39.7626 | −2.29188 | ||||||||
\(302\) | −17.5152 | + | 9.01649i | −1.00789 | + | 0.518841i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.78312 | − | 1.29923i | 0.216977 | − | 0.0745161i | ||||
\(305\) | 7.27034i | 0.416298i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.9638i | 0.682813i | 0.939916 | + | 0.341406i | \(0.110903\pi\) | ||||
−0.939916 | + | 0.341406i | \(0.889097\pi\) | |||||||
\(308\) | 10.6148 | + | 7.57789i | 0.604833 | + | 0.431790i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.02288 | − | 9.75735i | −0.285281 | − | 0.554180i | ||||
\(311\) | −6.69344 | −0.379550 | −0.189775 | − | 0.981828i | \(-0.560776\pi\) | ||||
−0.189775 | + | 0.981828i | \(0.560776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.9071 | 1.57740 | 0.788701 | − | 0.614777i | \(-0.210754\pi\) | ||||
0.788701 | + | 0.614777i | \(0.210754\pi\) | |||||||
\(314\) | −4.22135 | − | 8.20031i | −0.238225 | − | 0.462770i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.1995 | − | 9.42309i | −0.742527 | − | 0.530090i | ||||
\(317\) | − | 14.6011i | − | 0.820079i | −0.912068 | − | 0.410039i | \(-0.865515\pi\) | ||
0.912068 | − | 0.410039i | \(-0.134485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.1797i | 1.12984i | ||||||||
\(320\) | 2.45983 | − | 8.26765i | 0.137509 | − | 0.462176i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.35536 | − | 1.21249i | 0.131259 | − | 0.0675696i | ||||
\(323\) | 3.80151 | 0.211522 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.9959 | 1.16464 | ||||||||
\(326\) | 5.30194 | − | 2.72933i | 0.293647 | − | 0.151164i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.994593 | − | 6.83059i | 0.0549172 | − | 0.377156i | ||||
\(329\) | 14.5875i | 0.804234i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.60254i | 0.362909i | 0.983399 | + | 0.181454i | \(0.0580805\pi\) | ||||
−0.983399 | + | 0.181454i | \(0.941920\pi\) | |||||||
\(332\) | −12.9335 | + | 18.1168i | −0.709821 | + | 0.994286i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.5849 | − | 22.5045i | −0.633895 | − | 1.23139i | ||||
\(335\) | 3.67326 | 0.200692 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0810 | 0.712568 | 0.356284 | − | 0.934378i | \(-0.384044\pi\) | ||||
0.356284 | + | 0.934378i | \(0.384044\pi\) | |||||||
\(338\) | 10.9620 | + | 21.2946i | 0.596255 | + | 1.15827i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.76316 | − | 6.67203i | 0.258318 | − | 0.361842i | ||||
\(341\) | − | 14.1187i | − | 0.764569i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.80690i | − | 0.529523i | ||||||
\(344\) | −4.87500 | + | 33.4801i | −0.262842 | + | 1.80513i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.5130 | − | 7.47100i | 0.780224 | − | 0.401644i | ||||
\(347\) | 9.56551 | 0.513504 | 0.256752 | − | 0.966477i | \(-0.417348\pi\) | ||||
0.256752 | + | 0.966477i | \(0.417348\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.4091 | −0.771304 | −0.385652 | − | 0.922644i | \(-0.626023\pi\) | ||||
−0.385652 | + | 0.922644i | \(0.626023\pi\) | |||||||
\(350\) | 16.0393 | − | 8.25673i | 0.857339 | − | 0.441341i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.68199 | − | 8.00858i | 0.409451 | − | 0.426859i | ||||
\(353\) | 10.3693i | 0.551901i | 0.961172 | + | 0.275950i | \(0.0889925\pi\) | ||||
−0.961172 | + | 0.275950i | \(0.911007\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 0.420796i | − | 0.0223335i | ||||||
\(356\) | 18.3500 | + | 13.1001i | 0.972550 | + | 0.694303i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.4919 | + | 30.0942i | 0.818772 | + | 1.59053i | ||||
\(359\) | 24.5107 | 1.29363 | 0.646813 | − | 0.762649i | \(-0.276102\pi\) | ||||
0.646813 | + | 0.762649i | \(0.276102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −7.94093 | − | 15.4259i | −0.417366 | − | 0.810767i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 29.6048 | + | 21.1348i | 1.55171 | + | 1.10777i | ||||
\(365\) | − | 6.58745i | − | 0.344803i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 0.293849i | − | 0.0153388i | −0.999971 | − | 0.00766940i | \(-0.997559\pi\) | ||
0.999971 | − | 0.00766940i | \(-0.00244127\pi\) | |||||||
\(368\) | −0.732146 | − | 2.13187i | −0.0381658 | − | 0.111131i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.38942 | − | 3.28914i | 0.332170 | − | 0.170994i | ||||
\(371\) | 13.0422 | 0.677115 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.5282 | −1.73602 | −0.868012 | − | 0.496544i | \(-0.834602\pi\) | ||||
−0.868012 | + | 0.496544i | \(0.834602\pi\) | |||||||
\(374\) | 9.37711 | − | 4.82714i | 0.484879 | − | 0.249606i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.2827 | + | 1.78846i | 0.633430 | + | 0.0922329i | ||||
\(377\) | 56.2814i | 2.89864i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.30352i | 0.0669572i | 0.999439 | + | 0.0334786i | \(0.0106586\pi\) | ||||
−0.999439 | + | 0.0334786i | \(0.989341\pi\) | |||||||
\(380\) | −1.25297 | + | 1.75510i | −0.0642758 | + | 0.0900347i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.2870 | − | 25.8110i | −0.679821 | − | 1.32061i | ||||
\(383\) | 12.3689 | 0.632020 | 0.316010 | − | 0.948756i | \(-0.397657\pi\) | ||||
0.316010 | + | 0.948756i | \(0.397657\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.03121 | −0.358344 | ||||||||
\(386\) | −12.0796 | − | 23.4655i | −0.614834 | − | 1.19436i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.1095 | − | 15.5617i | 0.564001 | − | 0.790028i | ||||
\(389\) | 9.18330i | 0.465612i | 0.972523 | + | 0.232806i | \(0.0747907\pi\) | ||||
−0.972523 | + | 0.232806i | \(0.925209\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.14223i | − | 0.108337i | ||||||
\(392\) | 11.3350 | + | 1.65047i | 0.572502 | + | 0.0833612i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.7144 | + | 9.63377i | −0.942816 | + | 0.485342i | ||||
\(395\) | 8.74329 | 0.439923 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.4486 | −1.02629 | −0.513143 | − | 0.858303i | \(-0.671519\pi\) | ||||
−0.513143 | + | 0.858303i | \(0.671519\pi\) | |||||||
\(398\) | −29.5480 | + | 15.2107i | −1.48111 | + | 0.762445i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.98571 | − | 14.5174i | −0.249285 | − | 0.725872i | ||||
\(401\) | 20.3860i | 1.01803i | 0.860758 | + | 0.509014i | \(0.169990\pi\) | ||||
−0.860758 | + | 0.509014i | \(0.830010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 39.3772i | − | 1.96152i | ||||||
\(404\) | −0.891790 | − | 0.636648i | −0.0443682 | − | 0.0316744i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.1329 | + | 42.9950i | 1.09844 | + | 2.13381i | ||||
\(407\) | 9.24535 | 0.458275 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.0275 | 0.891403 | 0.445701 | − | 0.895182i | \(-0.352954\pi\) | ||||
0.445701 | + | 0.895182i | \(0.352954\pi\) | |||||||
\(410\) | 1.70322 | + | 3.30864i | 0.0841161 | + | 0.163402i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.7089 | − | 14.7841i | −1.02025 | − | 0.728359i | ||||
\(413\) | 41.3622i | 2.03530i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 12.0005i | − | 0.589082i | ||||||
\(416\) | 21.4252 | − | 22.3361i | 1.05046 | − | 1.09512i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.46668 | + | 1.26980i | −0.120649 | + | 0.0621078i | ||||
\(419\) | 10.0028 | 0.488669 | 0.244334 | − | 0.969691i | \(-0.421431\pi\) | ||||
0.244334 | + | 0.969691i | \(0.421431\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7949 | 0.672322 | 0.336161 | − | 0.941805i | \(-0.390871\pi\) | ||||
0.336161 | + | 0.941805i | \(0.390871\pi\) | |||||||
\(422\) | −11.1058 | + | 5.71702i | −0.540620 | + | 0.278300i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.59900 | − | 10.9815i | 0.0776544 | − | 0.533309i | ||||
\(425\) | − | 14.5880i | − | 0.707622i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.4141i | 1.08469i | ||||||||
\(428\) | −6.73005 | + | 9.42716i | −0.325309 | + | 0.455679i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.34833 | − | 16.2173i | −0.402592 | − | 0.782067i | ||||
\(431\) | 9.29350 | 0.447652 | 0.223826 | − | 0.974629i | \(-0.428145\pi\) | ||||
0.223826 | + | 0.974629i | \(0.428145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.48297 | 0.359608 | 0.179804 | − | 0.983702i | \(-0.442454\pi\) | ||||
0.179804 | + | 0.983702i | \(0.442454\pi\) | |||||||
\(434\) | −15.4853 | − | 30.0814i | −0.743318 | − | 1.44395i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.0249 | + | 22.4470i | −0.767452 | + | 1.07501i | ||||
\(437\) | 0.563522i | 0.0269569i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.3437i | − | 0.780044i | −0.920806 | − | 0.390022i | \(-0.872467\pi\) | ||
0.920806 | − | 0.390022i | \(-0.127533\pi\) | |||||||
\(440\) | −0.862044 | + | 5.92028i | −0.0410963 | + | 0.282238i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.1529 | − | 13.4630i | 1.24397 | − | 0.640368i | ||||
\(443\) | −33.7560 | −1.60379 | −0.801897 | − | 0.597462i | \(-0.796176\pi\) | ||||
−0.801897 | + | 0.597462i | \(0.796176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.1550 | −0.576203 | ||||||||
\(446\) | −33.3741 | + | 17.1803i | −1.58031 | + | 0.813510i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.58354 | − | 25.4887i | 0.358289 | − | 1.20423i | ||||
\(449\) | − | 31.3987i | − | 1.48180i | −0.671616 | − | 0.740899i | \(-0.734400\pi\) | ||
0.671616 | − | 0.740899i | \(-0.265600\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.78753i | 0.225436i | ||||||||
\(452\) | −8.36130 | − | 5.96912i | −0.393282 | − | 0.280764i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.63444 | + | 14.8305i | 0.358302 | + | 0.696030i | ||||
\(455\) | −19.6101 | −0.919338 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.1757 | −1.27123 | −0.635613 | − | 0.772007i | \(-0.719253\pi\) | ||||
−0.635613 | + | 0.772007i | \(0.719253\pi\) | |||||||
\(458\) | 4.43186 | + | 8.60924i | 0.207087 | + | 0.402283i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.989038 | + | 0.706073i | 0.0461141 | + | 0.0329208i | ||||
\(461\) | − | 20.7663i | − | 0.967182i | −0.875294 | − | 0.483591i | \(-0.839332\pi\) | ||
0.875294 | − | 0.483591i | \(-0.160668\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1728i | 1.21635i | 0.793802 | + | 0.608177i | \(0.208099\pi\) | ||||
−0.793802 | + | 0.608177i | \(0.791901\pi\) | |||||||
\(464\) | 38.9154 | − | 13.3647i | 1.80660 | − | 0.620439i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.0242 | + | 11.3376i | −1.02025 | + | 0.525204i | ||||
\(467\) | 31.1792 | 1.44280 | 0.721401 | − | 0.692518i | \(-0.243499\pi\) | ||||
0.721401 | + | 0.692518i | \(0.243499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3245 | 0.522916 | ||||||||
\(470\) | −5.94955 | + | 3.06271i | −0.274432 | + | 0.141272i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 34.8270 | + | 5.07111i | 1.60304 | + | 0.233417i | ||||
\(473\) | − | 23.4661i | − | 1.07897i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.83743i | 0.176073i | ||||||||
\(476\) | 14.6846 | − | 20.5695i | 0.673066 | − | 0.942802i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.36571 | + | 16.2510i | 0.382639 | + | 0.743306i | ||||
\(479\) | −23.1488 | −1.05770 | −0.528848 | − | 0.848716i | \(-0.677376\pi\) | ||||
−0.528848 | + | 0.848716i | \(0.677376\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.7854 | 1.17571 | ||||||||
\(482\) | −7.60187 | − | 14.7672i | −0.346256 | − | 0.672629i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.31053 | − | 11.6410i | 0.377752 | − | 0.529138i | ||||
\(485\) | 10.3081i | 0.468065i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.6821i | 1.11845i | 0.829015 | + | 0.559227i | \(0.188902\pi\) | ||||
−0.829015 | + | 0.559227i | \(0.811098\pi\) | |||||||
\(488\) | 18.8727 | + | 2.74802i | 0.854326 | + | 0.124397i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.49049 | + | 2.82639i | −0.248035 | + | 0.127684i | ||||
\(491\) | −39.6452 | −1.78916 | −0.894581 | − | 0.446905i | \(-0.852526\pi\) | ||||
−0.894581 | + | 0.446905i | \(0.852526\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.1045 | 1.76118 | ||||||||
\(494\) | −6.87961 | + | 3.54148i | −0.309528 | + | 0.159339i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −27.2271 | + | 9.35057i | −1.22253 | + | 0.419853i | ||||
\(497\) | − | 1.29729i | − | 0.0581915i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.8060i | − | 0.752340i | −0.926551 | − | 0.376170i | \(-0.877241\pi\) | ||
0.926551 | − | 0.376170i | \(-0.122759\pi\) | |||||||
\(500\) | 15.5106 | + | 11.0730i | 0.693654 | + | 0.495199i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.2111 | + | 21.7784i | 0.500374 | + | 0.972015i | ||||
\(503\) | −9.42278 | −0.420141 | −0.210070 | − | 0.977686i | \(-0.567369\pi\) | ||||
−0.210070 | + | 0.977686i | \(0.567369\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.590720 | 0.0262867 | ||||||||
\(506\) | 0.715558 | + | 1.39003i | 0.0318105 | + | 0.0617943i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.51903 | + | 4.65394i | 0.289235 | + | 0.206485i | ||||
\(509\) | − | 33.7698i | − | 1.49682i | −0.663236 | − | 0.748410i | \(-0.730817\pi\) | ||
0.663236 | − | 0.748410i | \(-0.269183\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 20.3088i | − | 0.898408i | ||||||
\(512\) | −20.5318 | − | 9.51033i | −0.907385 | − | 0.420301i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.6404 | − | 12.6844i | 1.08684 | − | 0.559483i | ||||
\(515\) | 13.7175 | 0.604467 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.60887 | −0.378618 | ||||||||
\(518\) | 19.6982 | − | 10.1403i | 0.865491 | − | 0.445537i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.40425 | + | 16.5118i | −0.105434 | + | 0.724088i | ||||
\(521\) | − | 6.21098i | − | 0.272108i | −0.990701 | − | 0.136054i | \(-0.956558\pi\) | ||
0.990701 | − | 0.136054i | \(-0.0434420\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.62567i | − | 0.202267i | −0.994873 | − | 0.101133i | \(-0.967753\pi\) | ||
0.994873 | − | 0.101133i | \(-0.0322468\pi\) | |||||||
\(524\) | 22.0070 | − | 30.8265i | 0.961382 | − | 1.34666i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.0328 | − | 25.3173i | −0.568257 | − | 1.10388i | ||||
\(527\) | −27.3594 | −1.19180 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6824 | −0.986193 | ||||||||
\(530\) | 2.73826 | + | 5.31929i | 0.118942 | + | 0.231055i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.86283 | + | 5.41088i | −0.167475 | + | 0.234592i | ||||
\(533\) | 13.3525i | 0.578361i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.24453i | − | 0.269975i | ||||||
\(536\) | 1.38841 | − | 9.53522i | 0.0599702 | − | 0.411859i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.7374 | + | 7.58652i | −0.635375 | + | 0.327078i | ||||
\(539\) | −7.94463 | −0.342200 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.8653 | 1.97191 | 0.985953 | − | 0.167025i | \(-0.0534161\pi\) | ||||
0.985953 | + | 0.167025i | \(0.0534161\pi\) | |||||||
\(542\) | 17.7373 | − | 9.13082i | 0.761884 | − | 0.392202i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.5192 | − | 14.8863i | −0.665380 | − | 0.638245i | ||||
\(545\) | − | 14.8688i | − | 0.636910i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.755289i | − | 0.0322938i | −0.999870 | − | 0.0161469i | \(-0.994860\pi\) | ||
0.999870 | − | 0.0161469i | \(-0.00513995\pi\) | |||||||
\(548\) | 2.57016 | + | 1.83484i | 0.109792 | + | 0.0783804i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.87275 | + | 9.46570i | 0.207775 | + | 0.403619i | ||||
\(551\) | −10.2866 | −0.438223 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.9551 | 1.14625 | ||||||||
\(554\) | 9.18759 | + | 17.8476i | 0.390343 | + | 0.758272i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.78545 | + | 1.27463i | 0.0757198 | + | 0.0540563i | ||||
\(557\) | − | 12.3000i | − | 0.521169i | −0.965451 | − | 0.260585i | \(-0.916085\pi\) | ||
0.965451 | − | 0.260585i | \(-0.0839153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 65.4473i | − | 2.76812i | ||||||
\(560\) | 4.65665 | + | 13.5593i | 0.196780 | + | 0.572985i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.9877 | + | 15.4371i | −1.26496 | + | 0.651174i | ||||
\(563\) | 36.3248 | 1.53091 | 0.765455 | − | 0.643490i | \(-0.222514\pi\) | ||||
0.765455 | + | 0.643490i | \(0.222514\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.53850 | 0.233007 | ||||||||
\(566\) | −17.9105 | + | 9.21996i | −0.752834 | + | 0.387544i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.09232 | − | 0.159051i | −0.0458328 | − | 0.00667364i | ||||
\(569\) | − | 42.8218i | − | 1.79518i | −0.440829 | − | 0.897591i | \(-0.645315\pi\) | ||
0.440829 | − | 0.897591i | \(-0.354685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.91400i | 0.289342i | 0.989480 | + | 0.144671i | \(0.0462124\pi\) | ||||
−0.989480 | + | 0.144671i | \(0.953788\pi\) | |||||||
\(572\) | −12.4728 | + | 17.4714i | −0.521515 | + | 0.730516i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.25094 | + | 10.2004i | 0.219170 | + | 0.425755i | ||||
\(575\) | 2.16247 | 0.0901814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.8663 | −1.36824 | −0.684121 | − | 0.729369i | \(-0.739814\pi\) | ||||
−0.684121 | + | 0.729369i | \(0.739814\pi\) | |||||||
\(578\) | 1.64961 | + | 3.20450i | 0.0686149 | + | 0.133290i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.8887 | + | 18.0540i | −0.535175 | + | 0.749651i | ||||
\(581\) | − | 36.9969i | − | 1.53489i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.69690i | 0.318773i | ||||||||
\(584\) | −17.1000 | − | 2.48991i | −0.707604 | − | 0.103033i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.2252 | + | 8.35238i | −0.670255 | + | 0.345034i | ||||
\(587\) | 36.3279 | 1.49941 | 0.749707 | − | 0.661770i | \(-0.230194\pi\) | ||||
0.749707 | + | 0.661770i | \(0.230194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.19699 | 0.296547 | ||||||||
\(590\) | −16.8697 | + | 8.68417i | −0.694514 | + | 0.357522i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.12305 | − | 17.8292i | −0.251656 | − | 0.732774i | ||||
\(593\) | 7.98112i | 0.327745i | 0.986481 | + | 0.163873i | \(0.0523986\pi\) | ||||
−0.986481 | + | 0.163873i | \(0.947601\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.6252i | 0.558579i | ||||||||
\(596\) | −5.92361 | − | 4.22886i | −0.242640 | − | 0.173221i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.99570 | + | 3.87681i | 0.0816104 | + | 0.158535i | ||||
\(599\) | −44.9807 | −1.83786 | −0.918932 | − | 0.394417i | \(-0.870947\pi\) | ||||
−0.918932 | + | 0.394417i | \(0.870947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.6878 | 0.843874 | 0.421937 | − | 0.906625i | \(-0.361350\pi\) | ||||
0.421937 | + | 0.906625i | \(0.361350\pi\) | |||||||
\(602\) | −25.7375 | − | 49.9971i | −1.04898 | − | 2.03773i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −22.6745 | − | 16.1873i | −0.922612 | − | 0.658652i | ||||
\(605\) | 7.71100i | 0.313497i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.7915i | 0.843900i | 0.906619 | + | 0.421950i | \(0.138654\pi\) | ||||
−0.906619 | + | 0.421950i | \(0.861346\pi\) | |||||||
\(608\) | 4.08238 | + | 3.91589i | 0.165562 | + | 0.158810i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.14165 | + | 4.70594i | −0.370135 | + | 0.190538i | ||||
\(611\) | −24.0103 | −0.971352 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.5535 | −0.789760 | −0.394880 | − | 0.918733i | \(-0.629214\pi\) | ||||
−0.394880 | + | 0.918733i | \(0.629214\pi\) | |||||||
\(614\) | −15.0432 | + | 7.74395i | −0.607095 | + | 0.312520i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.65764 | + | 18.2519i | −0.107079 | + | 0.735391i | ||||
\(617\) | − | 11.2359i | − | 0.452341i | −0.974088 | − | 0.226171i | \(-0.927379\pi\) | ||
0.974088 | − | 0.226171i | \(-0.0726207\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.49897i | − | 0.261216i | −0.991434 | − | 0.130608i | \(-0.958307\pi\) | ||
0.991434 | − | 0.130608i | \(-0.0416929\pi\) | |||||||
\(620\) | 9.01758 | − | 12.6314i | 0.362155 | − | 0.507291i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.33252 | − | 8.41627i | −0.173718 | − | 0.337462i | ||||
\(623\) | −37.4733 | −1.50134 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.91296 | 0.356518 | ||||||||
\(626\) | 18.0637 | + | 35.0901i | 0.721969 | + | 1.40248i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.57859 | − | 10.6158i | 0.302419 | − | 0.423615i | ||||
\(629\) | − | 17.9158i | − | 0.714351i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.9091i | 0.951805i | 0.879498 | + | 0.475902i | \(0.157878\pi\) | ||||
−0.879498 | + | 0.475902i | \(0.842122\pi\) | |||||||
\(632\) | 3.30477 | − | 22.6962i | 0.131457 | − | 0.902808i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.3593 | − | 9.45097i | 0.729139 | − | 0.375346i | ||||
\(635\) | −4.31819 | −0.171362 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.1577 | −0.877920 | ||||||||
\(638\) | −25.3737 | + | 13.0619i | −1.00455 | + | 0.517124i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.9879 | − | 2.25850i | 0.473862 | − | 0.0892751i | ||||
\(641\) | − | 38.3200i | − | 1.51355i | −0.653675 | − | 0.756775i | \(-0.726774\pi\) | ||
0.653675 | − | 0.756775i | \(-0.273226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 42.5273i | − | 1.67711i | −0.544814 | − | 0.838557i | \(-0.683400\pi\) | ||
0.544814 | − | 0.838557i | \(-0.316600\pi\) | |||||||
\(644\) | 3.04915 | + | 2.17679i | 0.120153 | + | 0.0857775i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.46064 | + | 4.77998i | 0.0968124 | + | 0.188066i | ||||
\(647\) | 5.85813 | 0.230307 | 0.115153 | − | 0.993348i | \(-0.463264\pi\) | ||||
0.115153 | + | 0.993348i | \(0.463264\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.4101 | −0.958179 | ||||||||
\(650\) | 13.5902 | + | 26.4000i | 0.533050 | + | 1.03549i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.86366 | + | 4.89997i | 0.268802 | + | 0.191897i | ||||
\(653\) | 47.2139i | 1.84762i | 0.382847 | + | 0.923812i | \(0.374944\pi\) | ||||
−0.382847 | + | 0.923812i | \(0.625056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.4194i | 0.797853i | ||||||||
\(656\) | 9.23250 | − | 3.17071i | 0.360468 | − | 0.123795i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.3422 | + | 9.44217i | −0.715052 | + | 0.368094i | ||||
\(659\) | 10.3713 | 0.404009 | 0.202004 | − | 0.979385i | \(-0.435254\pi\) | ||||
0.202004 | + | 0.979385i | \(0.435254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.14135 | −0.238871 | −0.119435 | − | 0.992842i | \(-0.538108\pi\) | ||||
−0.119435 | + | 0.992842i | \(0.538108\pi\) | |||||||
\(662\) | −8.30197 | + | 4.27369i | −0.322665 | + | 0.166102i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31.1515 | − | 4.53592i | −1.20891 | − | 0.176028i | ||||
\(665\) | − | 3.58416i | − | 0.138988i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.79671i | 0.224450i | ||||||||
\(668\) | 20.7983 | − | 29.1334i | 0.804710 | − | 1.12720i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.37763 | + | 4.61872i | 0.0918557 | + | 0.178437i | ||||
\(671\) | −13.2278 | −0.510653 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.2087 | −0.778986 | −0.389493 | − | 0.921029i | \(-0.627350\pi\) | ||||
−0.389493 | + | 0.921029i | \(0.627350\pi\) | |||||||
\(674\) | 8.46706 | + | 16.4479i | 0.326139 | + | 0.633551i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.6801 | + | 27.5671i | −0.756928 | + | 1.06027i | ||||
\(677\) | − | 12.3735i | − | 0.475551i | −0.971320 | − | 0.237776i | \(-0.923582\pi\) | ||
0.971320 | − | 0.237776i | \(-0.0764183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.7792i | 1.21958i | ||||||||
\(680\) | 11.4724 | + | 1.67049i | 0.439948 | + | 0.0640602i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.7527 | − | 9.13872i | 0.679785 | − | 0.349940i | ||||
\(683\) | −9.84657 | −0.376769 | −0.188384 | − | 0.982095i | \(-0.560325\pi\) | ||||
−0.188384 | + | 0.982095i | \(0.560325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.70247 | −0.0650481 | ||||||||
\(686\) | 12.3311 | − | 6.34780i | 0.470804 | − | 0.242360i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −45.2531 | + | 15.5412i | −1.72526 | + | 0.592503i | ||||
\(689\) | 21.4668i | 0.817818i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 43.1590i | − | 1.64185i | −0.571040 | − | 0.820923i | \(-0.693460\pi\) | ||
0.571040 | − | 0.820923i | \(-0.306540\pi\) | |||||||
\(692\) | 18.7879 | + | 13.4127i | 0.714210 | + | 0.509874i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.19155 | + | 12.0276i | 0.235028 | + | 0.456561i | ||||
\(695\) | −1.18268 | −0.0448614 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.27737 | 0.351406 | ||||||||
\(698\) | −9.32673 | − | 18.1179i | −0.353022 | − | 0.685773i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20.7639 | + | 14.8233i | 0.784800 | + | 0.560269i | ||||
\(701\) | 30.9785i | 1.17004i | 0.811019 | + | 0.585020i | \(0.198913\pi\) | ||||
−0.811019 | + | 0.585020i | \(0.801087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.71282i | 0.177747i | ||||||||
\(704\) | 15.0423 | + | 4.47547i | 0.566928 | + | 0.168675i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.0382 | + | 6.71181i | −0.490700 | + | 0.252602i | ||||
\(707\) | 1.82116 | 0.0684917 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.6140 | −0.886841 | −0.443420 | − | 0.896314i | \(-0.646235\pi\) | ||||
−0.443420 | + | 0.896314i | \(0.646235\pi\) | |||||||
\(710\) | 0.529105 | − | 0.272372i | 0.0198569 | − | 0.0102219i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.59432 | + | 31.5526i | −0.172180 | + | 1.18248i | ||||
\(713\) | − | 4.05566i | − | 0.151886i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 11.5730i | − | 0.432807i | ||||||
\(716\) | −27.8126 | + | 38.9587i | −1.03941 | + | 1.45595i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.8653 | + | 30.8195i | 0.592086 | + | 1.15017i | ||||
\(719\) | −26.8975 | −1.00311 | −0.501554 | − | 0.865126i | \(-0.667238\pi\) | ||||
−0.501554 | + | 0.865126i | \(0.667238\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.2905 | 1.57498 | ||||||||
\(722\) | −0.647279 | − | 1.25739i | −0.0240892 | − | 0.0467952i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.2564 | − | 19.9697i | 0.529833 | − | 0.742168i | ||||
\(725\) | 39.4740i | 1.46603i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.8029i | 1.29077i | 0.763859 | + | 0.645383i | \(0.223302\pi\) | ||||
−0.763859 | + | 0.645383i | \(0.776698\pi\) | |||||||
\(728\) | −7.41219 | + | 50.9049i | −0.274714 | + | 1.88666i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.28300 | − | 4.26392i | 0.306568 | − | 0.157815i | ||||
\(731\) | −45.4730 | −1.68188 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.7355 | −0.655075 | −0.327537 | − | 0.944838i | \(-0.606219\pi\) | ||||
−0.327537 | + | 0.944838i | \(0.606219\pi\) | |||||||
\(734\) | 0.369483 | − | 0.190202i | 0.0136379 | − | 0.00702050i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.20669 | − | 2.30051i | 0.0813397 | − | 0.0847979i | ||||
\(737\) | 6.68320i | 0.246179i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.4077i | 0.750710i | 0.926881 | + | 0.375355i | \(0.122479\pi\) | ||||
−0.926881 | + | 0.375355i | \(0.877521\pi\) | |||||||
\(740\) | 8.27147 | + | 5.90500i | 0.304065 | + | 0.217072i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.44191 | + | 16.3991i | 0.309912 | + | 0.602029i | ||||
\(743\) | 16.0882 | 0.590219 | 0.295110 | − | 0.955463i | \(-0.404644\pi\) | ||||
0.295110 | + | 0.955463i | \(0.404644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.92379 | 0.143756 | ||||||||
\(746\) | −21.7021 | − | 42.1580i | −0.794570 | − | 1.54351i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.1392 | + | 8.66617i | 0.443853 | + | 0.316867i | ||||
\(749\) | − | 19.2516i | − | 0.703437i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 51.9976i | − | 1.89742i | −0.316148 | − | 0.948710i | \(-0.602389\pi\) | ||
0.316148 | − | 0.948710i | \(-0.397611\pi\) | |||||||
\(752\) | 5.70152 | + | 16.6017i | 0.207913 | + | 0.605403i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −70.7676 | + | 36.4297i | −2.57721 | + | 1.32669i | ||||
\(755\) | 15.0195 | 0.546617 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.09089 | 0.257723 | 0.128861 | − | 0.991663i | \(-0.458868\pi\) | ||||
0.128861 | + | 0.991663i | \(0.458868\pi\) | |||||||
\(758\) | −1.63903 | + | 0.843740i | −0.0595323 | + | 0.0306460i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.01786 | − | 0.439427i | −0.109469 | − | 0.0159397i | ||||
\(761\) | 37.6919i | 1.36633i | 0.730264 | + | 0.683165i | \(0.239397\pi\) | ||||
−0.730264 | + | 0.683165i | \(0.760603\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 45.8398i | − | 1.65951i | ||||||
\(764\) | 23.8541 | − | 33.4138i | 0.863012 | − | 1.20887i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.00611 | + | 15.5525i | 0.289273 | + | 0.561935i | ||||
\(767\) | −68.0801 | −2.45823 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.3608 | 0.373619 | 0.186810 | − | 0.982396i | \(-0.440185\pi\) | ||||
0.186810 | + | 0.982396i | \(0.440185\pi\) | |||||||
\(770\) | −4.55115 | − | 8.84097i | −0.164012 | − | 0.318607i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.6865 | − | 30.3775i | 0.780513 | − | 1.09331i | ||||
\(773\) | − | 30.3425i | − | 1.09134i | −0.837999 | − | 0.545672i | \(-0.816275\pi\) | ||
0.837999 | − | 0.545672i | \(-0.183725\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 27.6179i | − | 0.992065i | ||||||
\(776\) | 26.7581 | + | 3.89622i | 0.960561 | + | 0.139866i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.5470 | + | 5.94416i | −0.413980 | + | 0.213108i | ||||
\(779\) | −2.44045 | −0.0874380 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.765603 | 0.0273954 | ||||||||
\(782\) | 2.69362 | − | 1.38662i | 0.0963238 | − | 0.0495855i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.26160 | + | 15.3208i | 0.187914 | + | 0.547171i | ||||
\(785\) | 7.03186i | 0.250978i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 47.3060i | − | 1.68628i | −0.537698 | − | 0.843138i | \(-0.680706\pi\) | ||
0.537698 | − | 0.843138i | \(-0.319294\pi\) | |||||||
\(788\) | −24.2268 | − | 17.2955i | −0.863045 | − | 0.616127i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.65935 | + | 10.9937i | 0.201351 | + | 0.391139i | ||||
\(791\) | 17.0749 | 0.607114 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.8925 | −1.31009 | ||||||||
\(794\) | −13.2359 | − | 25.7119i | −0.469726 | − | 0.912480i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −38.2517 | − | 27.3078i | −1.35579 | − | 0.967901i | ||||
\(797\) | 20.8231i | 0.737591i | 0.929511 | + | 0.368795i | \(0.120230\pi\) | ||||
−0.929511 | + | 0.368795i | \(0.879770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.6824i | 0.590182i | ||||||||
\(800\) | 15.0269 | − | 15.6658i | 0.531283 | − | 0.553870i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −25.6332 | + | 13.1954i | −0.905138 | + | 0.465947i | ||||
\(803\) | 11.9853 | 0.422953 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.01975 | −0.0711869 | ||||||||
\(806\) | 49.5125 | − | 25.4880i | 1.74400 | − | 0.897777i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.223279 | − | 1.53342i | 0.00785492 | − | 0.0539454i | ||||
\(809\) | − | 31.9587i | − | 1.12361i | −0.827270 | − | 0.561804i | \(-0.810107\pi\) | ||
0.827270 | − | 0.561804i | \(-0.189893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.1734i | − | 1.34045i | −0.742159 | − | 0.670224i | \(-0.766198\pi\) | ||
0.742159 | − | 0.670224i | \(-0.233802\pi\) | |||||||
\(812\) | −39.7353 | + | 55.6595i | −1.39444 | + | 1.95327i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.98432 | + | 11.6250i | 0.209750 | + | 0.407457i | ||||
\(815\) | −4.54648 | −0.159256 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.9618 | 0.418492 | ||||||||
\(818\) | 11.6688 | + | 22.6676i | 0.407991 | + | 0.792554i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.05779 | + | 4.28323i | −0.106783 | + | 0.149577i | ||||
\(821\) | − | 52.2726i | − | 1.82433i | −0.409827 | − | 0.912163i | \(-0.634411\pi\) | ||
0.409827 | − | 0.912163i | \(-0.365589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 11.6243i | − | 0.405198i | −0.979262 | − | 0.202599i | \(-0.935061\pi\) | ||
0.979262 | − | 0.202599i | \(-0.0649387\pi\) | |||||||
\(824\) | 5.18492 | − | 35.6086i | 0.180625 | − | 1.24048i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −52.0084 | + | 26.7728i | −1.80960 | + | 0.931546i | ||||
\(827\) | 25.0618 | 0.871485 | 0.435742 | − | 0.900071i | \(-0.356486\pi\) | ||||
0.435742 | + | 0.900071i | \(0.356486\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.6763 | 1.34328 | 0.671642 | − | 0.740875i | \(-0.265589\pi\) | ||||
0.671642 | + | 0.740875i | \(0.265589\pi\) | |||||||
\(830\) | 15.0893 | − | 7.76767i | 0.523758 | − | 0.269620i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.9532 | + | 12.4821i | 1.45447 | + | 0.432740i | ||||
\(833\) | 15.3953i | 0.533414i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.2979i | 0.667831i | ||||||||
\(836\) | −3.19326 | − | 2.27967i | −0.110441 | − | 0.0788439i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.47460 | + | 12.5774i | 0.223661 | + | 0.434480i | ||||
\(839\) | −10.7634 | −0.371592 | −0.185796 | − | 0.982588i | \(-0.559486\pi\) | ||||
−0.185796 | + | 0.982588i | \(0.559486\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −76.8138 | −2.64875 | ||||||||
\(842\) | 8.92914 | + | 17.3456i | 0.307719 | + | 0.597767i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.3771 | − | 10.2638i | −0.494879 | − | 0.353294i | ||||
\(845\) | − | 18.2604i | − | 0.628176i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.7726i | 0.816837i | ||||||||
\(848\) | 14.8430 | − | 5.09753i | 0.509712 | − | 0.175050i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.3428 | − | 9.44251i | 0.629153 | − | 0.323875i | ||||
\(851\) | 2.65578 | 0.0910389 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.6869 | 1.53005 | 0.765025 | − | 0.644000i | \(-0.222726\pi\) | ||||
0.765025 | + | 0.644000i | \(0.222726\pi\) | |||||||
\(854\) | −28.1833 | + | 14.5082i | −0.964411 | + | 0.496459i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.2098 | − | 2.36029i | −0.554041 | − | 0.0806731i | ||||
\(857\) | − | 33.1559i | − | 1.13258i | −0.824205 | − | 0.566292i | \(-0.808378\pi\) | ||
0.824205 | − | 0.566292i | \(-0.191622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.48402i | − | 0.0506342i | −0.999679 | − | 0.0253171i | \(-0.991940\pi\) | ||
0.999679 | − | 0.0253171i | \(-0.00805955\pi\) | |||||||
\(860\) | 14.9878 | − | 20.9942i | 0.511079 | − | 0.715897i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.01549 | + | 11.6856i | 0.204888 | + | 0.398012i | ||||
\(863\) | 52.7184 | 1.79456 | 0.897278 | − | 0.441466i | \(-0.145542\pi\) | ||||
0.897278 | + | 0.441466i | \(0.145542\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.4451 | −0.423146 | ||||||||
\(866\) | 4.84357 | + | 9.40901i | 0.164591 | + | 0.319731i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 27.8007 | − | 38.9421i | 0.943619 | − | 1.32178i | ||||
\(869\) | 15.9077i | 0.539632i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.6395i | 0.631577i | ||||||||
\(872\) | −38.5971 | − | 5.62008i | −1.30706 | − | 0.190320i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.708567 | + | 0.364756i | −0.0239676 | + | 0.0123381i | ||||
\(875\) | −31.6747 | −1.07080 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.3112 | −0.415718 | −0.207859 | − | 0.978159i | \(-0.566650\pi\) | ||||
−0.207859 | + | 0.978159i | \(0.566650\pi\) | |||||||
\(878\) | 20.5504 | − | 10.5790i | 0.693544 | − | 0.357022i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.00209 | + | 2.74815i | −0.269750 | + | 0.0926400i | ||||
\(881\) | − | 9.90718i | − | 0.333781i | −0.985975 | − | 0.166891i | \(-0.946627\pi\) | ||
0.985975 | − | 0.166891i | \(-0.0533727\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 18.0076i | − | 0.606006i | −0.952990 | − | 0.303003i | \(-0.902011\pi\) | ||
0.952990 | − | 0.303003i | \(-0.0979891\pi\) | |||||||
\(884\) | 33.8564 | + | 24.1701i | 1.13871 | + | 0.812928i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.8495 | − | 42.4444i | −0.734049 | − | 1.42595i | ||||
\(887\) | −17.2920 | −0.580608 | −0.290304 | − | 0.956935i | \(-0.593756\pi\) | ||||
−0.290304 | + | 0.956935i | \(0.593756\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.3128 | −0.446496 | ||||||||
\(890\) | −7.86769 | − | 15.2836i | −0.263726 | − | 0.512308i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −43.2046 | − | 30.8438i | −1.44660 | − | 1.03273i | ||||
\(893\) | − | 4.38837i | − | 0.146851i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 25.8062i | − | 0.862605i | ||||||
\(896\) | 36.9580 | − | 6.96284i | 1.23468 | − | 0.232612i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.4805 | − | 20.3237i | 1.31748 | − | 0.678212i | ||||
\(899\) | 74.0325 | 2.46912 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.9152 | 0.496897 | ||||||||
\(902\) | −6.01980 | + | 3.09887i | −0.200437 | + | 0.103181i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.09343 | − | 14.3771i | 0.0696264 | − | 0.478175i | ||||
\(905\) | 13.2279i | 0.439710i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.6923i | 0.487851i | 0.969794 | + | 0.243925i | \(0.0784352\pi\) | ||||
−0.969794 | + | 0.243925i | \(0.921565\pi\) | |||||||
\(908\) | −13.7061 | + | 19.1990i | −0.454854 | + | 0.637140i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.6932 | − | 24.6576i | −0.420777 | − | 0.817392i | ||||
\(911\) | 37.4076 | 1.23937 | 0.619684 | − | 0.784851i | \(-0.287261\pi\) | ||||
0.619684 | + | 0.784851i | \(0.287261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.8339 | 0.722598 | ||||||||
\(914\) | −17.5903 | − | 34.1705i | −0.581835 | − | 1.13026i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.95652 | + | 11.1452i | −0.262891 | + | 0.368246i | ||||
\(917\) | 62.9520i | 2.07886i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.25183i | − | 0.272203i | −0.990695 | − | 0.136101i | \(-0.956543\pi\) | ||
0.990695 | − | 0.136101i | \(-0.0434573\pi\) | |||||||
\(920\) | −0.247627 | + | 1.70063i | −0.00816401 | + | 0.0560682i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.1113 | − | 13.4416i | 0.859930 | − | 0.442675i | ||||
\(923\) | 2.13528 | 0.0702836 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.0851 | 0.594634 | ||||||||
\(926\) | −32.9094 | + | 16.9411i | −1.08147 | + | 0.556719i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 41.9937 | + | 40.2811i | 1.37851 | + | 1.32229i | ||||
\(929\) | − | 5.56369i | − | 0.182539i | −0.995826 | − | 0.0912694i | \(-0.970908\pi\) | ||
0.995826 | − | 0.0912694i | \(-0.0290924\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.04978i | − | 0.132726i | ||||||
\(932\) | −28.5116 | − | 20.3544i | −0.933928 | − | 0.666731i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.1816 | + | 39.2044i | 0.660363 | + | 1.28281i | ||||
\(935\) | −8.04098 | −0.262968 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.9005 | 1.27082 | 0.635411 | − | 0.772174i | \(-0.280831\pi\) | ||||
0.635411 | + | 0.772174i | \(0.280831\pi\) | |||||||
\(938\) | 7.33010 | + | 14.2393i | 0.239336 | + | 0.464929i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.70203 | − | 5.49848i | −0.251213 | − | 0.179341i | ||||
\(941\) | − | 2.70718i | − | 0.0882516i | −0.999026 | − | 0.0441258i | \(-0.985950\pi\) | ||
0.999026 | − | 0.0441258i | \(-0.0140502\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.37524i | 0.0447841i | ||||||||
\(944\) | 16.1664 | + | 47.0735i | 0.526171 | + | 1.53211i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.5060 | − | 15.1891i | 0.959324 | − | 0.493840i | ||||
\(947\) | 21.7767 | 0.707648 | 0.353824 | − | 0.935312i | \(-0.384881\pi\) | ||||
0.353824 | + | 0.935312i | \(0.384881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.4273 | 1.08509 | ||||||||
\(950\) | −4.82514 | + | 2.48388i | −0.156548 | + | 0.0805878i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 35.3689 | + | 5.15002i | 1.14631 | + | 0.166913i | ||||
\(953\) | 33.7212i | 1.09234i | 0.837676 | + | 0.546168i | \(0.183914\pi\) | ||||
−0.837676 | + | 0.546168i | \(0.816086\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.1333i | 0.716215i | ||||||||
\(956\) | −15.0190 | + | 21.0379i | −0.485748 | + | 0.680415i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.9837 | − | 29.1071i | −0.484103 | − | 0.940408i | ||||
\(959\) | −5.24863 | −0.169487 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7967 | −0.670862 | ||||||||
\(962\) | 16.6904 | + | 32.4223i | 0.538119 | + | 1.04534i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.6476 | − | 19.1170i | 0.439561 | − | 0.615718i | ||||
\(965\) | 20.1220i | 0.647749i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3424i | 1.04006i | 0.854147 | + | 0.520031i | \(0.174080\pi\) | ||||
−0.854147 | + | 0.520031i | \(0.825920\pi\) | |||||||
\(968\) | 20.0166 | + | 2.91458i | 0.643357 | + | 0.0936783i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.9613 | + | 6.67219i | −0.416161 | + | 0.214231i | ||||
\(971\) | −36.3523 | −1.16660 | −0.583301 | − | 0.812256i | \(-0.698239\pi\) | ||||
−0.583301 | + | 0.812256i | \(0.698239\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.64613 | −0.116889 | ||||||||
\(974\) | −31.0351 | + | 15.9762i | −0.994428 | + | 0.511911i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.76055 | + | 25.5091i | 0.280418 | + | 0.816525i | ||||
\(977\) | − | 31.0762i | − | 0.994215i | −0.867689 | − | 0.497107i | \(-0.834396\pi\) | ||
0.867689 | − | 0.497107i | \(-0.165604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 22.1151i | − | 0.706800i | ||||||
\(980\) | −7.10776 | − | 5.07423i | −0.227049 | − | 0.162090i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.6615 | − | 49.8495i | −0.818891 | − | 1.59076i | ||||
\(983\) | −1.99707 | −0.0636967 | −0.0318483 | − | 0.999493i | \(-0.510139\pi\) | ||||
−0.0318483 | + | 0.999493i | \(0.510139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0478 | 0.511325 | ||||||||
\(986\) | 25.3115 | + | 49.1696i | 0.806083 | + | 1.56588i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.90605 | − | 6.35802i | −0.283339 | − | 0.202276i | ||||
\(989\) | − | 6.74076i | − | 0.214344i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 27.4432i | − | 0.871762i | −0.900004 | − | 0.435881i | \(-0.856437\pi\) | ||
0.900004 | − | 0.435881i | \(-0.143563\pi\) | |||||||
\(992\) | −29.3808 | − | 28.1827i | −0.932842 | − | 0.894800i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.63120 | − | 0.839710i | 0.0517386 | − | 0.0266340i | ||||
\(995\) | 25.3378 | 0.803263 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.3996 | 0.709401 | 0.354701 | − | 0.934980i | \(-0.384583\pi\) | ||||
0.354701 | + | 0.934980i | \(0.384583\pi\) | |||||||
\(998\) | 21.1317 | − | 10.8782i | 0.668912 | − | 0.344342i | ||||
\(999\) | 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 | 684.2.c.b.647.20 | yes | 32 | |
3.2 | odd | 2 | inner | 684.2.c.b.647.13 | ✓ | 32 | |
4.3 | odd | 2 | inner | 684.2.c.b.647.14 | yes | 32 | |
12.11 | even | 2 | inner | 684.2.c.b.647.19 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.2.c.b.647.13 | ✓ | 32 | 3.2 | odd | 2 | inner | |
684.2.c.b.647.14 | yes | 32 | 4.3 | odd | 2 | inner | |
684.2.c.b.647.19 | yes | 32 | 12.11 | even | 2 | inner | |
684.2.c.b.647.20 | yes | 32 | 1.1 | even | 1 | trivial |